Finite Group Databasebeta

← #17243121

Subgroups — #17243121

Order 4352.

2142 conjugacy classes of subgroups.

The subgroup lattice has 1628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14537075C211yesmaximal, characteristic, complemented
2#14537065C211yesmaximal, characteristic, complemented
3#14536726C211yesmaximal, characteristic, complemented
4#14536527C211yesmaximal, characteristic, complemented
5#14536485C211yesmaximal, characteristic, complemented
6#14536429C211yesmaximal, characteristic, complemented
7#14536403C211yesmaximal, characteristic, complemented
8#14536040C211yesmaximal, characteristic, complemented
9#14536017C211yesmaximal, characteristic, complemented
10#14535950C211yesmaximal, characteristic, complemented
11#14535582C211yesmaximal, characteristic, complemented
12#14535533C211yesmaximal, characteristic, complemented
13#14535501C211yesmaximal, characteristic, complemented
14#14535495C211yesmaximal, characteristic, complemented
15#14535312C211yesmaximal, characteristic, complemented
16#14535183C211yesmaximal, characteristic, complemented
17#14535147C211yesmaximal, characteristic, complemented
18#14534736C211yesmaximal, characteristic, complemented
19#14534711C211yesmaximal, characteristic, complemented
20#14533040C211yesmaximal, characteristic, complemented
21#14532911C211yesmaximal, characteristic, complemented
22#14532526C211yesmaximal, characteristic, complemented
23#14532465C211yesmaximal, characteristic, complemented
24#14532389C211yesmaximal, characteristic, complemented
25#14532327C211yesmaximal, characteristic, complemented
26#14532168C211yesmaximal, characteristic, complemented
27#14532098C211yesmaximal, characteristic, complemented
28#14531457C211yesmaximal, characteristic, complemented
29#14531374C211yesmaximal, characteristic, complemented
30D17×#385C211yesmaximal, characteristic, complemented
31C17×#2797C211yesmaximal, characteristic, complemented
32C22×#63254C2211yescharacteristic
33C23×C4×D17C2211yescharacteristic
34C2×#10587565C2211yescharacteristic, complemented
35C2×#10587571C2211yescharacteristic
36C2×#10587580C2211yescharacteristic
37C2×#10587569C2211yescharacteristic
38C2×#10587569C2211yescharacteristic
39C2×#10587569C2211yescharacteristic, complemented
40C2×#10587583C2211yescharacteristic
41C2×#10587570C2211yescharacteristic
42C2×#10587570C2211yescharacteristic
43C2×#10587570C2211yescharacteristic
44C2×#10587570C2211yescharacteristic
45C2×#10587625C2211yescharacteristic
46C2×#10587568C2211yescharacteristic
47C2×#10587623C2211yescharacteristic
48C2×#10587623C2211yescharacteristic
49C2×C4×D68C2211yescharacteristic
50C2×#10587558C2211yescharacteristic
51C2×C4⋊C4×D17C2211yescharacteristic
52C2×C4⋊C4×D17C2211yescharacteristic
53C2×C22⋊C4×D17C2211yescharacteristic
54C2×C22⋊C4×D17C2211yescharacteristic
55C17⋊#401C2211yescharacteristic, complemented
56#11762751C2211yescharacteristic, complemented
57#11762751C2211yescharacteristic, complemented
58#11762751C2211yescharacteristic, complemented
59#11762750C2211yescharacteristic, complemented
60#11762750C2211yescharacteristic, complemented
61#11762749C2211yescharacteristic, complemented
62#11762748C2211yescharacteristic, complemented
63#11762747C2211yescharacteristic, complemented
64#11762745C2211yescharacteristic, complemented
65#11762743C2211yescharacteristic, complemented
66#11762742C2211yescharacteristic, complemented
67#11762741C2211yescharacteristic, complemented
68#11762738C2211yescharacteristic, complemented
69#11762737C2211yescharacteristic, complemented
70#11762736C2211yescharacteristic
71#11762735C2211yescharacteristic, complemented
72#11762734C2211yescharacteristic, complemented
73#11762733C2211yescharacteristic
74#11762732C2211yescharacteristic
75#11762732C2211yescharacteristic
76#11762732C2211yescharacteristic, complemented
77#11762732C2211yescharacteristic, complemented
78#11762729C2211yescharacteristic, complemented
79#11762729C2211yescharacteristic, complemented
80#11762727C2211yescharacteristic
81#11762726C2211yescharacteristic
82#11762725C2211yescharacteristic
83#11762725C2211yescharacteristic
84#11762725C2211yescharacteristic, complemented
85#11762725C2211yescharacteristic, complemented
86#11762725C2211yescharacteristic, complemented
87#11762724C2211yescharacteristic
88#11762722C2211yescharacteristic
89#11762722C2211yescharacteristic, complemented
90#11762722C2211yescharacteristic, complemented
91#11762721C2211yescharacteristic
92#11762721C2211yescharacteristic
93#11762721C2211yescharacteristic, complemented
94#11762717C2211yescharacteristic
95#11762717C2211yescharacteristic
96#11762717C2211yescharacteristic, complemented
97#11762715C2211yescharacteristic, complemented
98#11762714C2211yescharacteristic, complemented
99#11762713C2211yescharacteristic, complemented
100#11762712C2211yescharacteristic
101#11762712C2211yescharacteristic, complemented
102#11762711C2211yescharacteristic
103#11762709C2211yescharacteristic
104#11762708C2211yescharacteristic, complemented
105#11762707C2211yescharacteristic, complemented
106#11762706C2211yescharacteristic, complemented
107#11762702C2211yescharacteristic
108#11762701C2211yescharacteristic, complemented
109#11762700C2211yescharacteristic
110#11762699C2211yescharacteristic
111#11762699C2211yescharacteristic
112#11762698C2211yescharacteristic, complemented
113#11762697C2211yescharacteristic, complemented
114#11762696C2211yescharacteristic, complemented
115#11762693C2211yescharacteristic, complemented
116#11762693C2211yescharacteristic, complemented
117#11762692C2211yescharacteristic, complemented
118#11762692C2211yescharacteristic, complemented
119#11762689C2211yescharacteristic
120#11762689C2211yescharacteristic
121#11762689C2211yescharacteristic
122#11762688C2211yescharacteristic
123#11762687C2211yescharacteristic
124#11762687C2211yescharacteristic
125#11762687C2211yescharacteristic
126#11762686C2211yescharacteristic
127#11762686C2211yescharacteristic
128#11762686C2211yescharacteristic, complemented
129#11762686C2211yescharacteristic, complemented
130#11762685C2211yescharacteristic
131#11762685C2211yescharacteristic
132#11762685C2211yescharacteristic
133#11762685C2211yescharacteristic
134#11762685C2211yescharacteristic
135#11762685C2211yescharacteristic
136#11762685C2211yescharacteristic
137#11762685C2211yescharacteristic
138#11762685C2211yescharacteristic
139#11762685C2211yescharacteristic
140#11762684C2211yescharacteristic
141#11762684C2211yescharacteristic
142#11762683C2211yescharacteristic
143#11762683C2211yescharacteristic
144#11762683C2211yescharacteristic
145#11762683C2211yescharacteristic
146#11762683C2211yescharacteristic
147#11762683C2211yescharacteristic, complemented
148#11762682C2211yescharacteristic
149#11762682C2211yescharacteristic
150#11762681C2211yescharacteristic
151#11762681C2211yescharacteristic, complemented
152#11762681C2211yescharacteristic, complemented
153#11762680C2211yescharacteristic
154#11762680C2211yescharacteristic
155#11762680C2211yescharacteristic
156#11762680C2211yescharacteristic, complemented
157#11762680C2211yescharacteristic, complemented
158#11762671C2211yescharacteristic
159#11762671C2211yescharacteristic
160#11762671C2211yescharacteristic
161#11762668C2211yescharacteristic
162#11762668C2211yescharacteristic
163#11762667C2211yescharacteristic
164#11762667C2211yescharacteristic, complemented
165#11762667C2211yescharacteristic, complemented
166#11762667C2211yescharacteristic, complemented
167#11762667C2211yescharacteristic, complemented
168#11762664C2211yescharacteristic
169#11762656C2211yescharacteristic
170#95×D17C2211yescharacteristic
171#95×D17C2211yescharacteristic
172C17×#397C2211yescharacteristic, complemented
173C17×#397C2211yescharacteristic, complemented
174C17×#397C2211yescharacteristic, complemented
175C17×#394C2211yescharacteristic
176C17×#394C2211yescharacteristic, complemented
177C17×#392C2211yescharacteristic
178C17×#390C2211yescharacteristic
179C17×#390C2211yescharacteristic, complemented
180C17×#388C2211yescharacteristic
181C17×#388C2211yescharacteristic, complemented
182C17×#387C2211yescharacteristic, complemented
183C17×#387C2211yescharacteristic, complemented
184C17×#386C2211yescharacteristic
185C17×#386C2211yescharacteristic
186C17×#385C2211yescharacteristic
187C24×D17C2311yescharacteristic
188C22×D4×C17C2311yescharacteristic
189C22×D4×C17C2311yescharacteristic
190C22×D4×C17C2311yescharacteristic
191C23×C4×C17C2311yescharacteristic
192C22×C22⋊D17C2311yescharacteristic
193C22×C22⋊D17C2311yescharacteristic
194C22×C22⋊D17C2311yescharacteristic
195C22×C22⋊D17C2311yescharacteristic
196C22×C22⋊D17C2311yescharacteristic
197C22×C22⋊D17C2311yescharacteristic
198C22×C22⋊D17C2311yescharacteristic
199C23×Dic17C2311yescharacteristic
200C23×Dic17C2311yescharacteristic
201C23×Dic17C2311yescharacteristic
202C2×#63254—24no—
203C2×#63254—42no—
204C2×#63254—42no—
205C22×D68C2311yescharacteristic
206C22×D68C2311yescharacteristic
207C22×C4×D17—42no—
208C22×C4×D17—42no—
209C22×C4×D17—42no—
210C22×C4×D17C2311yescharacteristic
211C22×C4×D17C2311yescharacteristic
212C22×C4×D17C2311yescharacteristic
213C22×C4×D17C2311yescharacteristic
214C22×C4×D17C2311yescharacteristic
215C22×C4×D17C2311yescharacteristic
216C22×C4×D17C2311yescharacteristic
217C22×C4×D17C2311yescharacteristic
218C22×C4×D17C2311yescharacteristic
219C22×Dic34C2311yescharacteristic
220C22×Dic34C2311yescharacteristic
221C2×C4⋊C4×C17C2311yescharacteristic
222C2×C4⋊C4×C17C2311yescharacteristic
223C2×C4⋊C4×C17C2311yescharacteristic
224C2×C4⋊C4×C17C2311yescharacteristic
225C2×C4⋊C4×C17C2311yescharacteristic
226C2×C22⋊C4×C17C2311yescharacteristic
227C2×C22⋊C4×C17C2311yescharacteristic
228C2×C22⋊C4×C17C2311yescharacteristic
229C2×C22⋊C4×C17C2311yescharacteristic
230C2×C22⋊C4×C17C2311yescharacteristic
231C2×C22⋊C4×C17C2311yescharacteristic
232C2×C22⋊C4×C17C2311yescharacteristic
233C2×C22⋊C4×C17C2311yescharacteristic
234C2×C22⋊C4×C17C2311yescharacteristic
235C2×C22⋊C4×C17C2311yescharacteristic
236C2×C22⋊C4×C17C2311yescharacteristic
237C2×C22⋊C4×C17C2311yescharacteristic
238C2×C22⋊C4×C17C2311yescharacteristic
239C2×C22⋊C4×C17C2311yescharacteristic
240C2×C42×C17C2311yescharacteristic
241C2×C42×C17C2311yescharacteristic
242C2×C22⋊Dic17C2311yescharacteristic
243C2×C22⋊Dic17C2311yescharacteristic
244C2×C22⋊Dic17C2311yescharacteristic
245C2×C22⋊Dic17C2311yescharacteristic
246C2×C22⋊Dic17C2311yescharacteristic
247C2×C22⋊Dic17C2311yescharacteristic
248C2×C22⋊Dic17C2311yescharacteristic
249C2×C22⋊Dic17C2311yescharacteristic
250C2×C22⋊Dic17C2311yescharacteristic
251C2×C22⋊Dic17C2311yescharacteristic
252C2×C22⋊Dic17C2311yescharacteristic
253C2×C22⋊Dic17C2311yescharacteristic
254C2×C22⋊Dic17C2311yescharacteristic
255#10587625—42no—
256#10587623—42no—
257#10587623—42no—
258C2×#63227C2311yescharacteristic
259C2×#63227C2311yescharacteristic
260C2×#63227C2311yescharacteristic
261C2×#63227C2311yescharacteristic
262C2×#63227C2311yescharacteristic
263C2×#63227C2311yescharacteristic
264C2×#63227C2311yescharacteristic
265C2×#63227C2311yescharacteristic
266C2×#63227C2311yescharacteristic
267C2×#63227C2311yescharacteristic
268C2×#63227C2311yescharacteristic
269C2×#63227C2311yescharacteristic
270C2×#63227C2311yescharacteristic
271C2×#63227C2311yescharacteristic
272C2×#63227C2311yescharacteristic
273C2×#63227C2311yescharacteristic
274C2×#63227C2311yescharacteristic
275C2×#63227C2311yescharacteristic
276C2×#63227C2311yescharacteristic
277C2×#63227C2311yescharacteristic
278C2×#63227C2311yescharacteristic
279C2×#63227C2311yescharacteristic
280C2×#63227C2311yescharacteristic
281C2×C4⋊Dic17C2311yescharacteristic
282C2×C4⋊Dic17C2311yescharacteristic
283C2×C4⋊Dic17C2311yescharacteristic
284C2×C4⋊Dic17C2311yescharacteristic
285C2×C4⋊Dic17C2311yescharacteristic
286C2×C4⋊Dic17C2311yescharacteristic
287C2×C4⋊Dic17C2311yescharacteristic
288C2×C4⋊Dic17C2311yescharacteristic
289C2×#63225C2311yescharacteristic
290C2×#63225C2311yescharacteristic
291C2×#63225C2311yescharacteristic
292C2×#63225C2311yescharacteristic
293C2×#63225C2311yescharacteristic
294C2×#63225C2311yescharacteristic
295C2×#63225C2311yescharacteristic
296C2×#63225C2311yescharacteristic
297C2×#63225C2311yescharacteristic
298C2×#63225C2311yescharacteristic
299C2×#63225C2311yescharacteristic
300C2×#63225C2311yescharacteristic
301C2×#63225C2311yescharacteristic
302C2×#63225C2311yescharacteristic
303C2×#63225C2311yescharacteristic
304C2×C4×Dic17C2311yescharacteristic
305C2×C4×Dic17C2311yescharacteristic
306C2×C4×Dic17C2311yescharacteristic
307#10587583—42no—
308#10587580—24no—
309C4⋊C4×D17—42no—
310C4⋊C4×D17—42no—
311#10587571—42no—
312#10587570—42no—
313#10587570—42no—
314#10587570—42no—
315#10587570—42no—
316#10587569—42no—
317#10587569—42no—
318#10587569—42no—
319#10587568—42no—
320C22⋊C4×D17—24no—
321C22⋊C4×D17—42no—
322#10587565—42no—
323C4×D68—42no—
324#10587558—42no—
325C17×#95C2311yescharacteristic
326C17×#95C2311yescharacteristic
327C17×#95C2311yescharacteristic
328C17×#95C2311yescharacteristic
329C17×#95C2311yescharacteristic
330C17×#95C2311yescharacteristic
331C17×#95C2311yescharacteristic
332C17×#95C2311yescharacteristic
333C17×#95C2311yescharacteristic
334C17×#95C2311yescharacteristic
335#10587502C2311yescharacteristic
336#10587502C2311yescharacteristic
337#10587502C2311yescharacteristic
338#10587502C2311yescharacteristic
339#10587502C2311yescharacteristic
340#10587502C2311yescharacteristic
341#10587502C2311yescharacteristic
342#10587502C2311yescharacteristic
343#10587502C2311yescharacteristic
344#10587502C2311yescharacteristic
345#10587502C2311yescharacteristic
346#10587502C2311yescharacteristic
347#10587502C2311yescharacteristic
348#10587502C2311yescharacteristic
349#10587502C2311yescharacteristic
350#10587502C2311yescharacteristic
351#10587502C2311yescharacteristic
352#10587502C2311yescharacteristic
353#10587502C2311yescharacteristic
354#10587502C2311yescharacteristic
355#10587502C2311yescharacteristic
356#10587502C2311yescharacteristic
357#10587502C2311yescharacteristic
358#10587502C2311yescharacteristic
359#10587502C2311yescharacteristic
360#10587502C2311yescharacteristic
361#10587502C2311yescharacteristic
362#10587502C2311yescharacteristic
363#10587502C2311yescharacteristic
364#10587502C2311yescharacteristic
365#10587502C2311yescharacteristic
366#10587502C2311yescharacteristic
367#10587502C2311yescharacteristic
368#10587502C2311yescharacteristic
369C24×C17C2411yescharacteristic
370C24×C17C2411yescharacteristic
371C24×C17C2411yescharacteristic
372C23×D17—22no—
373C23×D17—22no—
374C23×D17—22no—
375C23×D17—22no—
376C23×D17—22no—
377C23×D17—41no—
378C23×D17—41no—
379C23×D17C2411yescharacteristic
380C23×D17C2411yescharacteristic
381C23×D17C2411yescharacteristic
382C2×D4×C17—22no—
383C2×D4×C17—22no—
384C2×D4×C17—22no—
385C2×D4×C17—41no—
386C2×D4×C17—41no—
387C2×D4×C17—41no—
388C2×D4×C17—41no—
389C2×D4×C17—41no—
390C2×D4×C17—41no—
391C22×C4×C17—41no—
392C22×C4×C17—41no—
393C22×C4×C17—41no—
394C22×C4×C17C2411yescharacteristic
395C22×C4×C17C2411yescharacteristic
396C22×C4×C17C2411yescharacteristic
397C22×C4×C17C2411yescharacteristic
398C22×C4×C17C2411yescharacteristic
399C22×C4×C17C2411yescharacteristic
400C22×C4×C17C2411yescharacteristic
401C22×C4×C17C2411yescharacteristic
402C22×C4×C17C2411yescharacteristic
403C22×C4×C17C2411yescharacteristic
404C22×C4×C17C2411yescharacteristic
405C22×C4×C17C2411yescharacteristic
406C2×C22⋊D17—22no—
407C2×C22⋊D17—22no—
408C2×C22⋊D17—22no—
409C2×C22⋊D17—22no—
410C2×C22⋊D17—22no—
411C2×C22⋊D17—22no—
412C2×C22⋊D17—22no—
413C2×C22⋊D17—22no—
414C2×C22⋊D17—22no—
415C2×C22⋊D17—22no—
416C2×C22⋊D17—41no—
417C2×C22⋊D17—41no—
418C2×C22⋊D17—41no—
419C2×C22⋊D17—41no—
420C2×C22⋊D17—41no—
421C2×C22⋊D17—41no—
422C2×C22⋊D17—41no—
423C2×C22⋊D17—41no—
424C2×C22⋊D17—41no—
425C2×C22⋊D17—41no—
426C2×C22⋊D17—41no—
427C22×Dic17—22no—
428C22×Dic17—22no—
429C22×Dic17—22no—
430C22×Dic17—41no—
431C22×Dic17—41no—
432C22×Dic17—41no—
433C22×Dic17—41no—
434C22×Dic17—41no—
435C22×Dic17—41no—
436C22×Dic17C2411yescharacteristic
437C22×Dic17C2411yescharacteristic
438C22×Dic17C2411yescharacteristic
439C22×Dic17C2411yescharacteristic
440C22×Dic17C2411yescharacteristic
441C22×Dic17C2411yescharacteristic
442C22×Dic17C2411yescharacteristic
443C22×Dic17C2411yescharacteristic
444C22×Dic17C2411yescharacteristic
445C22×Dic17C2411yescharacteristic
446C22×Dic17C2411yescharacteristic
447C22×Dic17C2411yescharacteristic
448C22×Dic17C2411yescharacteristic
449#63254—416no—
450C2×D68—22no—
451C2×D68—22no—
452C2×D68—22no—
453C2×D68—22no—
454C2×D68—41no—
455C2×D68—41no—
456C2×C4×D17—22no—
457C2×C4×D17—22no—
458C2×C4×D17—22no—
459C2×C4×D17—22no—
460C2×C4×D17—22no—
461C2×C4×D17—22no—
462C2×C4×D17—22no—
463C2×C4×D17—22no—
464C2×C4×D17—22no—
465C2×C4×D17—22no—
466C2×C4×D17—22no—
467C2×C4×D17—41no—
468C2×C4×D17—41no—
469C2×C4×D17—41no—
470C2×C4×D17—41no—
471C2×C4×D17—41no—
472C2×C4×D17—41no—
473C2×C4×D17—41no—
474C2×C4×D17—41no—
475C2×C4×D17—416no—
476C2×C4×D17—41no—
477C2×C4×D17—41no—
478C2×C4×D17—41no—
479C2×C4×D17—41no—
480C2×C4×D17—41no—
481C2×C4×D17—41no—
482C2×C4×D17—41no—
483C2×C4×D17#4114yes—
484C2×Dic34—22no—
485C2×Dic34—41no—
486C2×Dic34—41no—
487C2×Dic34—41no—
488C2×Dic34—41no—
489C2×Dic34—41no—
490C4⋊C4×C17—22no—
491C4⋊C4×C17—41no—
492C4⋊C4×C17—41no—
493C4⋊C4×C17—41no—
494C4⋊C4×C17—41no—
495C22⋊C4×C17—22no—
496C22⋊C4×C17—22no—
497C22⋊C4×C17—41no—
498C22⋊C4×C17—41no—
499C22⋊C4×C17—41no—
500C22⋊C4×C17—41no—
501C22⋊C4×C17—41no—
502C22⋊C4×C17—41no—
503C22⋊C4×C17—41no—
504C22⋊C4×C17—41no—
505C22⋊C4×C17—41no—
506C22⋊C4×C17—41no—
507C22⋊C4×C17—41no—
508C22⋊C4×C17—41no—
509C42×C17—41no—
510C42×C17—41no—
511C22⋊Dic17—22no—
512C22⋊Dic17—22no—
513C22⋊Dic17—41no—
514C22⋊Dic17—41no—
515C22⋊Dic17—41no—
516C22⋊Dic17—41no—
517C22⋊Dic17—41no—
518C22⋊Dic17—41no—
519C22⋊Dic17—41no—
520C22⋊Dic17—41no—
521C22⋊Dic17—41no—
522C22⋊Dic17—41no—
523C22⋊Dic17—41no—
524#63227—22no—
525#63227—22no—
526#63227—22no—
527#63227—22no—
528#63227—22no—
529#63227—22no—
530#63227—22no—
531#63227—22no—
532#63227—22no—
533#63227—22no—
534#63227—22no—
535#63227—22no—
536#63227—41no—
537#63227—41no—
538#63227—41no—
539#63227—41no—
540#63227—41no—
541#63227—41no—
542#63227—41no—
543#63227—41no—
544#63227—41no—
545#63227—41no—
546#63227—41no—
547C4⋊Dic17—22no—
548C4⋊Dic17—22no—
549C4⋊Dic17—41no—
550C4⋊Dic17—41no—
551C4⋊Dic17—41no—
552C4⋊Dic17—41no—
553C4⋊Dic17—41no—
554C4⋊Dic17—41no—
555#63225—22no—
556#63225—22no—
557#63225—22no—
558#63225—41no—
559#63225—41no—
560#63225—41no—
561#63225—41no—
562#63225—41no—
563#63225—41no—
564#63225—41no—
565#63225—41no—
566#63225—41no—
567#63225—41no—
568#63225—41no—
569#63225—41no—
570C4×Dic17—41no—
571C4×Dic17—41no—
572C4×Dic17—41no—
573#36791—171nomaximal, Sylow
574C23×C17—21no—
575C23×C17—21no—
576C23×C17—21no—
577C23×C17—21no—
578C23×C17—21no—
579C23×C17—21no—
580C23×C17—21no—
581C23×C17—21no—
582C23×C17—21no—
583C23×C17—21no—
584C23×C17—21no—
585C23×C17—21no—
586C23×C17—21no—
587C23×C17—21no—
588C23×C17—21no—
589C23×C17—21no—
590C23×C17—21no—
591C23×C17—21no—
592C23×C17—21no—
593C23×C17—21no—
594C23×C172−1+412yes—
595C23×C17C2511yescharacteristic
596C22×D17—21no—
597C22×D17—21no—
598C22×D17—21no—
599C22×D17—21no—
600C22×D17—28no—
601C22×D17—21no—
602C22×D17—21no—
603C22×D17—21no—
604C22×D17—21no—
605C22×D17—21no—
606C22×D17—21no—
607C22×D17—21no—
608C22×D17—21no—
609C22×D17—21no—
610C22×D17—21no—
611C22×D17—21no—
612C22×D17—21no—
613C22×D17—21no—
614C22×D17—44no—
615C22×D17—44no—
616C22×D17—44no—
617C22×D17—44no—
618C22×D17—44no—
619C22×D17—44no—
620C22×D17C2×#4112yes—
621C22×D17H(5,𝔽2)12yes—
622C22×D17H(5,𝔽2)12yes—
623C22×D17H(5,𝔽2)12yes—
624D4×C17—44no—
625D4×C17—82no—
626D4×C17—82no—
627C2×C4×C17—21no—
628C2×C4×C17—21no—
629C2×C4×C17—21no—
630C2×C4×C17—21no—
631C2×C4×C17—21no—
632C2×C4×C17—21no—
633C2×C4×C17—21no—
634C2×C4×C17—21no—
635C2×C4×C17—21no—
636C2×C4×C17—21no—
637C2×C4×C17—21no—
638C2×C4×C17—21no—
639C2×C4×C17—21no—
640C2×C4×C17—21no—
641C2×C4×C17—21no—
642C2×C4×C17—21no—
643C2×C4×C17—21no—
644C2×C4×C17—21no—
645C2×C4×C17—21no—
646C2×C4×C17—21no—
647C2×C4×C17—21no—
648C2×C4×C17—21no—
649C2×C4×C17—21no—
650C2×C4×C17—21no—
651C2×C4×C17—21no—
652C2×C4×C17—21no—
653C2×C4×C17—21no—
654C2×C4×C17—21no—
655C2×C4×C17—21no—
656C2×C4×C17—21no—
657C2×C4×C17—21no—
658C2×C4×C17—21no—
659C2×C4×C17—21no—
660C2×C4×C17—21no—
661C2×C4×C17—21no—
662C2×C4×C17—44no—
663C2×C4×C17C2×#4112yes—
664C22⋊D17—44no—
665C22⋊D17—44no—
666C22⋊D17—82no—
667C22⋊D17—82no—
668C22⋊D17—82no—
669C22⋊D17—82no—
670C22⋊D17—82no—
671C2×Dic17—21no—
672C2×Dic17—21no—
673C2×Dic17—21no—
674C2×Dic17—21no—
675C2×Dic17—21no—
676C2×Dic17—21no—
677C2×Dic17—21no—
678C2×Dic17—21no—
679C2×Dic17—21no—
680C2×Dic17—21no—
681C2×Dic17—21no—
682C2×Dic17—21no—
683C2×Dic17—21no—
684C2×Dic17—21no—
685C2×Dic17—21no—
686C2×Dic17—21no—
687C2×Dic17—21no—
688C2×Dic17—21no—
689C2×Dic17—21no—
690C2×Dic17—21no—
691C2×Dic17—21no—
692C2×Dic17—21no—
693C2×Dic17—21no—
694C2×Dic17—21no—
695C2×Dic17—21no—
696C2×Dic17—21no—
697C2×Dic17—21no—
698C2×Dic17—21no—
699C2×Dic17—21no—
700C2×Dic17—21no—
701C2×Dic17—21no—
702C2×Dic17—21no—
703C2×Dic17—21no—
704C2×Dic17—21no—
705C2×Dic17—21no—
706C2×Dic17—21no—
707C2×Dic17—21no—
708C2×Dic17—44no—
709C2×Dic17—44no—
710C2×Dic17—44no—
711C2×Dic17C2×#4112yes—
712C2×Dic17H(5,𝔽2)12yes—
713D68—44no—
714D68—82no—
715C4×D17—28no—
716C4×D17—44no—
717C4×D17—44no—
718C4×D17—44no—
719C4×D17—44no—
720C4×D17—44no—
721C4×D17—82no—
722C4×D17—82no—
723C4×D17—82no—
724Dic34—44no—
725Dic34—82no—
726#2849—171no—
727#2847—171no—
728#2804—171no—
729#2797D1711yescharacteristic, complemented
730#2788—171no—
731#2784—171no—
732#2780—171no—
733#2778—171no—
734#2751—171no—
735#2750—171no—
736#2745—171no—
737#2714—171no—
738#2710—171no—
739#2708—171no—
740#2708—171no—
741#2695—171no—
742#2686—171no—
743#2682—171no—
744#2643—171no—
745#2639—171no—
746#2481—171no—
747#2472—171no—
748#2443—171no—
749#2438—171no—
750#2430—171no—
751#2424—171no—
752#2411—171no—
753#2404—171no—
754#2322—171no—
755#2311—171no—
756C2×#385—171no—
757C22×C17—22no—
758C22×C17—22no—
759C22×C17—22no—
760C22×C17—41no—
761C22×C17—41no—
762C22×C17—41no—
763C22×C17—41no—
764C22×C17—41no—
765C22×C17—41no—
766C22×C17—41no—
767C22×C17—41no—
768C22×C17—41no—
769C22×C17—41no—
770C22×C17—41no—
771C22×C17—41no—
772C22×C17—41no—
773C22×C17—41no—
774C22×C17—41no—
775C22×C17—41no—
776C22×C17—41no—
777C22×C17—41no—
778C22×C17C22×#4111yescharacteristic
779C22×C17C2×H(5,𝔽2)11yescharacteristic
780C22×C17C2×H(5,𝔽2)11yescharacteristic
781C22×C17C2×H(5,𝔽2)11yescharacteristic
782C22×C17C2×H(5,𝔽2)11yescharacteristic
783C22×C17C2×2−1+411yescharacteristic
784C22×C17#58511yescharacteristic
785C2×D17—22no—
786C2×D17—22no—
787C2×D17—22no—
788C2×D17—22no—
789C2×D17—22no—
790C2×D17—22no—
791C2×D17—22no—
792C2×D17—22no—
793C2×D17—22no—
794C2×D17—416no—
795C2×D17—41no—
796C2×D17—41no—
797C2×D17—41no—
798C2×D17—41no—
799C2×D17—41no—
800C2×D17—41no—
801C2×D17—41no—
802C2×D17—41no—
803C2×D17—41no—
804C2×D17—41no—
805C2×D17—41no—
806C2×D17#53814yes—
807C4×C17—22no—
808C4×C17—41no—
809C4×C17—41no—
810C4×C17—41no—
811C4×C17—41no—
812C4×C17—41no—
813C4×C17—41no—
814C4×C17—41no—
815C4×C17—41no—
816C4×C17—41no—
817C4×C17—41no—
818C4×C17—41no—
819Dic17—22no—
820Dic17—22no—
821Dic17—41no—
822Dic17—41no—
823Dic17—41no—
824Dic17—41no—
825Dic17—41no—
826Dic17—41no—
827Dic17—41no—
828Dic17—41no—
829Dic17—41no—
830Dic17—41no—
831Dic17—41no—
832C22×#41—171no—
833C24×C4—171no—
834C2×#126—171no—
835C2×#124—171no—
836C2×#123—171no—
837C2×#123—171no—
838C2×#123—171no—
839C2×#123—171no—
840C2×C22⋊Q8—171no—
841C2×#121—171no—
842C2×#121—171no—
843C2×#121—171no—
844C2×#121—171no—
845C2×#121—171no—
846C2×#120—171no—
847C2×#120—171no—
848C2×#120—171no—
849C2×C4×D4—171no—
850C2×#117—171no—
851C22×C4⋊C4—171no—
852C22×C4⋊C4—171no—
853C22×C22⋊C4—171no—
854C22×C22⋊C4—171no—
855#401—171no—
856#400—171no—
857#400—171no—
858#400—171no—
859#400—171no—
860#400—171no—
861#400—171no—
862#400—171no—
863#400—171no—
864#399—171no—
865#398—171no—
866#398—171no—
867#398—171no—
868#397—171no—
869#397—171no—
870#397—171no—
871#397—171no—
872#397—171no—
873#397C2×D1711yescharacteristic, complemented
874#397C2×D1711yescharacteristic, complemented
875#397C2×D1711yescharacteristic, complemented
876#396—171no—
877#396—171no—
878#396—171no—
879#396—171no—
880#396—171no—
881#395—171no—
882#395—171no—
883#394—171no—
884#394—171no—
885#394—171no—
886#394—171no—
887#394—171no—
888#394—171no—
889#394—171no—
890#394—171no—
891#394C2×D1711yescharacteristic
892#394C2×D1711yescharacteristic, complemented
893#393—171no—
894#393—171no—
895#393—171no—
896#393—171no—
897#393—171no—
898#393—171no—
899#392—171no—
900#392—171no—
901#392—171no—
902#392C2×D1711yescharacteristic
903#391—171no—
904#391—171no—
905#391—171no—
906#390—171no—
907#390—171no—
908#390—171no—
909#390—171no—
910#390C2×D1711yescharacteristic
911#390C2×D1711yescharacteristic, complemented
912#389—171no—
913#389—171no—
914#389—171no—
915#388—171no—
916#388—171no—
917#388—171no—
918#388—171no—
919#388—171no—
920#388—171no—
921#388—171no—
922#388C2×D1711yescharacteristic
923#388C2×D1711yescharacteristic, complemented
924#387—171no—
925#387—171no—
926#387—171no—
927#387—171no—
928#387—171no—
929#387C2×D1711yescharacteristic, complemented
930#387C2×D1711yescharacteristic, complemented
931#386—171no—
932#386—171no—
933#386—171no—
934#386—171no—
935#386—171no—
936#386—171no—
937#386—171no—
938#386—171no—
939#386—171no—
940#386—171no—
941#386—171no—
942#386—171no—
943#386—171no—
944#386—171no—
945#386—171no—
946#386—171no—
947#386—171no—
948#386—171no—
949#386—171no—
950#386—171no—
951#386—171no—
952#386C2×D1711yescharacteristic
953#386C2×D1711yescharacteristic
954#385—171no—
955#385—171no—
956#385—171no—
957#385—171no—
958#385—171no—
959#385—171no—
960#385—171no—
961#385—171no—
962#385—171no—
963#385—171no—
964#385—171no—
965#385—171no—
966#385—171no—
967#385—171no—
968#385—171no—
969#385—171no—
970#385—171no—
971#385—171no—
972#385C2×D1711yescharacteristic
973#381—171no—
974#381—171no—
975#381—171no—
976#380—171no—
977#380—171no—
978#380—171no—
979#380—171no—
980#380—171no—
981#380—171no—
982#380—171no—
983#379—171no—
984C4×C22⋊C4—171no—
985C2×#95—171no—
986C2×#95—171no—
987C2×C17—42no—
988C2×C17—81no—
989C2×C17—81no—
990C2×C17C2×#53811yescharacteristic
991C2×C17#349211yescharacteristic
992C2×C17#350611yescharacteristic
993C2×C17#353211yescharacteristic
994C2×C17#353411yescharacteristic
995C2×C17#353511yescharacteristic
996C2×C17#353611yescharacteristic
997D17—24no—
998D17—42no—
999D17—81no—
1000C25—171no—
1001C2×#41—344no—
1002C2×#41—682no—
1003C2×#41—682no—
1004C22×Q8—171no—
1005C22×Q8—171no—
1006C22×D4—171no—
1007C22×D4—171no—
1008C22×D4—171no—
1009C22×D4—171no—
1010C22×D4—171no—
1011C22×D4—171no—
1012C22×D4—171no—
1013C22×D4—171no—
1014C22×D4—171no—
1015C22×D4C22×D1711yescharacteristic
1016C22×D4C22×D1711yescharacteristic
1017C22×D4C22×D1711yescharacteristic
1018C23×C4—171no—
1019C23×C4—171no—
1020C23×C4—171no—
1021C23×C4—171no—
1022C23×C4—171no—
1023C23×C4—171no—
1024C23×C4—171no—
1025C23×C4—171no—
1026C23×C4—171no—
1027C23×C4—171no—
1028C23×C4—171no—
1029C23×C4—171no—
1030C23×C4—682no—
1031C23×C4—682no—
1032C23×C4—682no—
1033C23×C4C22×D1711yescharacteristic
1034#126—682no—
1035#124—682no—
1036#123—344no—
1037#123—682no—
1038#123—682no—
1039#123—682no—
1040C22⋊Q8—682no—
1041#121—682no—
1042#121—682no—
1043#121—682no—
1044#121—682no—
1045#121—682no—
1046#120—682no—
1047#120—682no—
1048#120—682no—
1049C4×D4—682no—
1050#117—682no—
1051C2×C4⋊C4—171no—
1052C2×C4⋊C4—171no—
1053C2×C4⋊C4—171no—
1054C2×C4⋊C4—171no—
1055C2×C4⋊C4—171no—
1056C2×C4⋊C4—171no—
1057C2×C4⋊C4—171no—
1058C2×C4⋊C4—171no—
1059C2×C4⋊C4—171no—
1060C2×C4⋊C4—171no—
1061C2×C4⋊C4—171no—
1062C2×C4⋊C4—171no—
1063C2×C4⋊C4—171no—
1064C2×C4⋊C4—171no—
1065C2×C4⋊C4—171no—
1066C2×C4⋊C4—171no—
1067C2×C4⋊C4—171no—
1068C2×C4⋊C4—171no—
1069C2×C4⋊C4—171no—
1070C2×C4⋊C4—171no—
1071C2×C4⋊C4—171no—
1072C2×C4⋊C4—171no—
1073C2×C4⋊C4—171no—
1074C2×C4⋊C4—682no—
1075C2×C4⋊C4—682no—
1076C2×C4⋊C4C22×D1711yescharacteristic
1077C2×C4⋊C4C22×D1711yescharacteristic
1078C2×C4⋊C4C22×D1711yescharacteristic
1079C2×C4⋊C4C22×D1711yescharacteristic
1080C2×C4⋊C4C22×D1711yescharacteristic
1081C2×C22⋊C4—171no—
1082C2×C22⋊C4—171no—
1083C2×C22⋊C4—171no—
1084C2×C22⋊C4—171no—
1085C2×C22⋊C4—171no—
1086C2×C22⋊C4—171no—
1087C2×C22⋊C4—171no—
1088C2×C22⋊C4—171no—
1089C2×C22⋊C4—171no—
1090C2×C22⋊C4—171no—
1091C2×C22⋊C4—171no—
1092C2×C22⋊C4—171no—
1093C2×C22⋊C4—171no—
1094C2×C22⋊C4—171no—
1095C2×C22⋊C4—171no—
1096C2×C22⋊C4—171no—
1097C2×C22⋊C4—171no—
1098C2×C22⋊C4—171no—
1099C2×C22⋊C4—171no—
1100C2×C22⋊C4—171no—
1101C2×C22⋊C4—171no—
1102C2×C22⋊C4—171no—
1103C2×C22⋊C4—171no—
1104C2×C22⋊C4—171no—
1105C2×C22⋊C4—171no—
1106C2×C22⋊C4—171no—
1107C2×C22⋊C4—171no—
1108C2×C22⋊C4—171no—
1109C2×C22⋊C4—171no—
1110C2×C22⋊C4—171no—
1111C2×C22⋊C4—171no—
1112C2×C22⋊C4—171no—
1113C2×C22⋊C4—171no—
1114C2×C22⋊C4—171no—
1115C2×C22⋊C4—171no—
1116C2×C22⋊C4—171no—
1117C2×C22⋊C4—344no—
1118C2×C22⋊C4—682no—
1119C2×C22⋊C4C22×D1711yescharacteristic
1120C2×C22⋊C4C22×D1711yescharacteristic
1121C2×C22⋊C4C22×D1711yescharacteristic
1122C2×C22⋊C4C22×D1711yescharacteristic
1123C2×C22⋊C4C22×D1711yescharacteristic
1124C2×C22⋊C4C22×D1711yescharacteristic
1125C2×C22⋊C4C22×D1711yescharacteristic
1126C2×C22⋊C4C22×D1711yescharacteristic
1127C2×C22⋊C4C22×D1711yescharacteristic
1128C2×C22⋊C4C22×D1711yescharacteristic
1129C2×C22⋊C4C22×D1711yescharacteristic
1130C2×C22⋊C4C22×D1711yescharacteristic
1131C2×C22⋊C4C22×D1711yescharacteristic
1132C2×C22⋊C4C22×D1711yescharacteristic
1133C2×C42—171no—
1134C2×C42—171no—
1135C2×C42—171no—
1136C2×C42C22×D1711yescharacteristic
1137C2×C42C22×D1711yescharacteristic
1138#95—171no—
1139#95—171no—
1140#95—171no—
1141#95—171no—
1142#95—171no—
1143#95—171no—
1144#95—171no—
1145#95—171no—
1146#95—171no—
1147#95—171no—
1148#95—171no—
1149#95—171no—
1150#95—171no—
1151#95—171no—
1152#95—171no—
1153#95—171no—
1154#95—171no—
1155#95—171no—
1156#95—171no—
1157#95—171no—
1158#95—171no—
1159#95—171no—
1160#95—171no—
1161#95—171no—
1162#95—171no—
1163#95—171no—
1164#95—171no—
1165#95—171no—
1166#95—171no—
1167#95—171no—
1168#95—171no—
1169#95—171no—
1170#95—171no—
1171#95—171no—
1172#95C22×D1711yescharacteristic
1173#95C22×D1711yescharacteristic
1174#95C22×D1711yescharacteristic
1175#95C22×D1711yescharacteristic
1176#95C22×D1711yescharacteristic
1177#95C22×D1711yescharacteristic
1178#95C22×D1711yescharacteristic
1179#95C22×D1711yescharacteristic
1180#95C22×D1711yescharacteristic
1181#95C22×D1711yescharacteristic
1182C17#3679111yescharacteristic, complemented, Sylow
1183C24—171no—
1184C24—171no—
1185C24—171no—
1186C24—342no—
1187C24—342no—
1188C24—342no—
1189C24—342no—
1190C24—342no—
1191C24—681no—
1192C24—681no—
1193C24C23×D1711yescharacteristic
1194C24C23×D1711yescharacteristic
1195C24C23×D1711yescharacteristic
1196#41—6816no—
1197C2×Q8—342no—
1198C2×Q8—681no—
1199C2×Q8—681no—
1200C2×Q8—681no—
1201C2×Q8—681no—
1202C2×Q8—681no—
1203C2×D4—22no—
1204C2×D4—22no—
1205C2×D4—22no—
1206C2×D4—41no—
1207C2×D4—41no—
1208C2×D4—41no—
1209C2×D4—41no—
1210C2×D4—41no—
1211C2×D4—41no—
1212C2×D4—342no—
1213C2×D4—342no—
1214C2×D4—342no—
1215C2×D4—342no—
1216C2×D4—342no—
1217C2×D4—342no—
1218C2×D4—342no—
1219C2×D4—342no—
1220C2×D4—342no—
1221C2×D4—342no—
1222C2×D4—342no—
1223C2×D4—342no—
1224C2×D4—342no—
1225C2×D4—342no—
1226C2×D4—681no—
1227C2×D4—681no—
1228C2×D4—681no—
1229C2×D4—681no—
1230C2×D4—681no—
1231C2×D4—681no—
1232C2×D4—681no—
1233C2×D4—681no—
1234C2×D4—681no—
1235C2×D4—681no—
1236C2×D4—681no—
1237C2×D4—681no—
1238C2×D4—681no—
1239C22×C4—41no—
1240C22×C4—41no—
1241C22×C4—41no—
1242C22×C4—171no—
1243C22×C4—171no—
1244C22×C4—174no—
1245C22×C4—171no—
1246C22×C4—171no—
1247C22×C4—171no—
1248C22×C4—171no—
1249C22×C4—171no—
1250C22×C4—171no—
1251C22×C4—171no—
1252C22×C4—171no—
1253C22×C4—171no—
1254C22×C4—171no—
1255C22×C4—171no—
1256C22×C4—342no—
1257C22×C4—342no—
1258C22×C4—342no—
1259C22×C4—342no—
1260C22×C4—342no—
1261C22×C4—342no—
1262C22×C4—342no—
1263C22×C4—342no—
1264C22×C4—342no—
1265C22×C4—342no—
1266C22×C4—342no—
1267C22×C4—342no—
1268C22×C4—342no—
1269C22×C4—342no—
1270C22×C4—681no—
1271C22×C4—681no—
1272C22×C4—681no—
1273C22×C4—681no—
1274C22×C4—681no—
1275C22×C4—681no—
1276C22×C4—681no—
1277C22×C4—681no—
1278C22×C4—681no—
1279C22×C4—681no—
1280C22×C4—681no—
1281C22×C4—681no—
1282C22×C4—681no—
1283C22×C4—681no—
1284C22×C4—681no—
1285C22×C4—6816no—
1286C22×C4—681no—
1287C22×C4—681no—
1288C22×C4—681no—
1289C22×C4—681no—
1290C22×C4—681no—
1291C22×C4—681no—
1292C22×C4C23×D1711yescharacteristic
1293C22×C4C23×D1711yescharacteristic
1294C22×C4C23×D1711yescharacteristic
1295C22×C4C23×D1711yescharacteristic
1296C22×C4C23×D1711yescharacteristic
1297C22×C4C23×D1711yescharacteristic
1298C22×C4C23×D1711yescharacteristic
1299C22×C4C23×D1711yescharacteristic
1300C22×C4C23×D1711yescharacteristic
1301C22×C4C23×D1711yescharacteristic
1302C22×C4C23×D1711yescharacteristic
1303C22×C4C23×D1711yescharacteristic
1304C4⋊C4—22no—
1305C4⋊C4—41no—
1306C4⋊C4—41no—
1307C4⋊C4—41no—
1308C4⋊C4—41no—
1309C4⋊C4—342no—
1310C4⋊C4—342no—
1311C4⋊C4—342no—
1312C4⋊C4—342no—
1313C4⋊C4—342no—
1314C4⋊C4—681no—
1315C4⋊C4—681no—
1316C4⋊C4—681no—
1317C4⋊C4—681no—
1318C4⋊C4—681no—
1319C4⋊C4—681no—
1320C4⋊C4—681no—
1321C4⋊C4—681no—
1322C4⋊C4—681no—
1323C4⋊C4—681no—
1324C4⋊C4—681no—
1325C4⋊C4—681no—
1326C4⋊C4—681no—
1327C4⋊C4—681no—
1328C4⋊C4—681no—
1329C4⋊C4—681no—
1330C4⋊C4—681no—
1331C4⋊C4—681no—
1332C22⋊C4—22no—
1333C22⋊C4—22no—
1334C22⋊C4—41no—
1335C22⋊C4—41no—
1336C22⋊C4—41no—
1337C22⋊C4—41no—
1338C22⋊C4—41no—
1339C22⋊C4—41no—
1340C22⋊C4—41no—
1341C22⋊C4—41no—
1342C22⋊C4—41no—
1343C22⋊C4—41no—
1344C22⋊C4—41no—
1345C22⋊C4—41no—
1346C22⋊C4—342no—
1347C22⋊C4—342no—
1348C22⋊C4—342no—
1349C22⋊C4—342no—
1350C22⋊C4—342no—
1351C22⋊C4—342no—
1352C22⋊C4—342no—
1353C22⋊C4—342no—
1354C22⋊C4—342no—
1355C22⋊C4—342no—
1356C22⋊C4—342no—
1357C22⋊C4—342no—
1358C22⋊C4—342no—
1359C22⋊C4—342no—
1360C22⋊C4—681no—
1361C22⋊C4—681no—
1362C22⋊C4—681no—
1363C22⋊C4—681no—
1364C22⋊C4—681no—
1365C22⋊C4—681no—
1366C22⋊C4—681no—
1367C22⋊C4—681no—
1368C22⋊C4—681no—
1369C22⋊C4—681no—
1370C22⋊C4—681no—
1371C22⋊C4—681no—
1372C22⋊C4—681no—
1373C22⋊C4—681no—
1374C22⋊C4—681no—
1375C22⋊C4—681no—
1376C22⋊C4—681no—
1377C22⋊C4—681no—
1378C22⋊C4—681no—
1379C22⋊C4—681no—
1380C22⋊C4—681no—
1381C22⋊C4—681no—
1382C42—41no—
1383C42—41no—
1384C42—681no—
1385C42—681no—
1386C42—681no—
1387C23—21no—
1388C23—21no—
1389C23—21no—
1390C23—21no—
1391C23—21no—
1392C23—21no—
1393C23—21no—
1394C23—21no—
1395C23—21no—
1396C23—21no—
1397C23—21no—
1398C23—21no—
1399C23—21no—
1400C23—21no—
1401C23—21no—
1402C23—21no—
1403C23—21no—
1404C23—21no—
1405C23—21no—
1406C23—21no—
1407C23—172no—
1408C23—172no—
1409C23—172no—
1410C23—172no—
1411C23—348no—
1412C23—341no—
1413C23—341no—
1414C23—341no—
1415C23—341no—
1416C23—341no—
1417C23—341no—
1418C23—341no—
1419C23—341no—
1420C23—341no—
1421C23—341no—
1422C23—341no—
1423C23—341no—
1424C23—341no—
1425C23—341no—
1426C23—341no—
1427C23—341no—
1428C23—341no—
1429C23—684no—
1430C23—684no—
1431C23—684no—
1432C23—684no—
1433C23—684no—
1434C23—684no—
1435C23#1058769712yes—
1436C23C24×D1711yescharacteristic
1437Q8—684no—
1438Q8—1362no—
1439D4—44no—
1440D4—82no—
1441D4—82no—
1442D4—684no—
1443D4—684no—
1444D4—684no—
1445D4—1362no—
1446D4—1362no—
1447D4—1362no—
1448D4—1362no—
1449D4—1362no—
1450D4—1362no—
1451C2×C4—21no—
1452C2×C4—21no—
1453C2×C4—21no—
1454C2×C4—21no—
1455C2×C4—21no—
1456C2×C4—21no—
1457C2×C4—21no—
1458C2×C4—21no—
1459C2×C4—21no—
1460C2×C4—21no—
1461C2×C4—21no—
1462C2×C4—21no—
1463C2×C4—21no—
1464C2×C4—21no—
1465C2×C4—21no—
1466C2×C4—21no—
1467C2×C4—21no—
1468C2×C4—21no—
1469C2×C4—21no—
1470C2×C4—21no—
1471C2×C4—21no—
1472C2×C4—21no—
1473C2×C4—21no—
1474C2×C4—21no—
1475C2×C4—21no—
1476C2×C4—21no—
1477C2×C4—21no—
1478C2×C4—21no—
1479C2×C4—21no—
1480C2×C4—21no—
1481C2×C4—21no—
1482C2×C4—21no—
1483C2×C4—21no—
1484C2×C4—21no—
1485C2×C4—21no—
1486C2×C4—44no—
1487C2×C4—172no—
1488C2×C4—172no—
1489C2×C4—348no—
1490C2×C4—341no—
1491C2×C4—341no—
1492C2×C4—341no—
1493C2×C4—341no—
1494C2×C4—341no—
1495C2×C4—341no—
1496C2×C4—341no—
1497C2×C4—341no—
1498C2×C4—341no—
1499C2×C4—341no—
1500C2×C4—341no—
1501C2×C4—341no—
1502C2×C4—341no—
1503C2×C4—341no—
1504C2×C4—341no—
1505C2×C4—341no—
1506C2×C4—341no—
1507C2×C4—341no—
1508C2×C4—341no—
1509C2×C4—341no—
1510C2×C4—341no—
1511C2×C4—341no—
1512C2×C4—341no—
1513C2×C4—341no—
1514C2×C4—341no—
1515C2×C4—341no—
1516C2×C4—341no—
1517C2×C4—341no—
1518C2×C4—341no—
1519C2×C4—341no—
1520C2×C4—341no—
1521C2×C4—341no—
1522C2×C4—341no—
1523C2×C4—341no—
1524C2×C4—341no—
1525C2×C4—341no—
1526C2×C4—341no—
1527C2×C4—684no—
1528C2×C4—684no—
1529C2×C4—684no—
1530C2×C4—684no—
1531C2×C4—684no—
1532C2×C4—684no—
1533C2×C4—684no—
1534C2×C4—684no—
1535C2×C4—1362no—
1536C2×C4—1362no—
1537C2×C4—1362no—
1538C2×C4#41×D1712yes—
1539C22—22no—
1540C22—22no—
1541C22—22no—
1542C22—41no—
1543C22—41no—
1544C22—41no—
1545C22—41no—
1546C22—41no—
1547C22—41no—
1548C22—41no—
1549C22—41no—
1550C22—41no—
1551C22—41no—
1552C22—41no—
1553C22—41no—
1554C22—41no—
1555C22—41no—
1556C22—41no—
1557C22—41no—
1558C22—41no—
1559C22—41no—
1560C22—174no—
1561C22—342no—
1562C22—342no—
1563C22—342no—
1564C22—342no—
1565C22—342no—
1566C22—342no—
1567C22—342no—
1568C22—342no—
1569C22—342no—
1570C22—6816no—
1571C22—681no—
1572C22—681no—
1573C22—681no—
1574C22—681no—
1575C22—681no—
1576C22—681no—
1577C22—681no—
1578C22—681no—
1579C22—681no—
1580C22—681no—
1581C22—681no—
1582C22C2×#41×D1711yescharacteristic
1583C22H(5,𝔽2)×D1711yescharacteristic
1584C22H(5,𝔽2)×D1711yescharacteristic
1585C22H(5,𝔽2)×D1711yescharacteristic
1586C22H(5,𝔽2)×D1711yescharacteristic
1587C22C2×#1058769711yescharacteristic
1588C22#1176364511yescharacteristic
1589C4—22no—
1590C4—41no—
1591C4—41no—
1592C4—41no—
1593C4—41no—
1594C4—41no—
1595C4—41no—
1596C4—41no—
1597C4—41no—
1598C4—41no—
1599C4—41no—
1600C4—41no—
1601C4—342no—
1602C4—342no—
1603C4—681no—
1604C4—681no—
1605C4—681no—
1606C4—681no—
1607C4—681no—
1608C4—681no—
1609C4—681no—
1610C4—681no—
1611C4—681no—
1612C4—681no—
1613C4—681no—
1614C2—42no—
1615C2—81no—
1616C2—81no—
1617C2—344no—
1618C2—682no—
1619C2—1361no—
1620C2D17×#53811yescharacteristic
1621C2#1454248811yescharacteristic
1622C2#1454263211yescharacteristic
1623C2#1454293711yescharacteristic
1624C2#1454296711yescharacteristic
1625C2#1454298011yescharacteristic
1626C2#1454300511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2797C2
hypercenter#2797D17
hypocenterC17#36791
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2797

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #14537075C2semidirect
2. #14537065C2semidirect
3. #14536726C2semidirect
4. #14536527C2semidirect
5. #14536485C2semidirect
6. #14536429C2semidirect
7. #14536403C2semidirect
8. #14536040C2semidirect
9. #14536017C2semidirect
10. #14535950C2semidirect
11. #14535582C2semidirect
12. #14535533C2semidirect
13. #14535501C2semidirect
14. #14535495C2semidirect
15. #14535312C2semidirect
16. #14535183C2semidirect
17. #14535147C2semidirect
18. #14534736C2semidirect
19. #14534711C2semidirect
20. #14533040C2semidirect
21. #14532911C2semidirect
22. #14532526C2semidirect
23. #14532465C2semidirect
24. #14532389C2semidirect
25. #14532327C2semidirect
26. #14532168C2semidirect
27. #14532098C2semidirect
28. #14531457C2semidirect
29. #14531374C2semidirect
30. D17×#385C2semidirect
31. C17×#2797C2semidirect
34. C2×#10587565C22semidirect
39. C2×#10587569C22semidirect
55. C17⋊#401C22semidirect
56. #11762751C22semidirect
57. #11762751C22semidirect
58. #11762751C22semidirect
59. #11762750C22semidirect
60. #11762750C22semidirect
61. #11762749C22semidirect
62. #11762748C22semidirect
63. #11762747C22semidirect
64. #11762745C22semidirect
65. #11762743C22semidirect
66. #11762742C22semidirect
67. #11762741C22semidirect
68. #11762738C22semidirect
69. #11762737C22semidirect
71. #11762735C22semidirect
72. #11762734C22semidirect
76. #11762732C22semidirect
77. #11762732C22semidirect
78. #11762729C22semidirect
79. #11762729C22semidirect
84. #11762725C22semidirect
85. #11762725C22semidirect
86. #11762725C22semidirect
89. #11762722C22semidirect
90. #11762722C22semidirect
93. #11762721C22semidirect
96. #11762717C22semidirect
97. #11762715C22semidirect
98. #11762714C22semidirect
99. #11762713C22semidirect
101. #11762712C22semidirect
104. #11762708C22semidirect
105. #11762707C22semidirect
106. #11762706C22semidirect
108. #11762701C22semidirect
112. #11762698C22semidirect
113. #11762697C22semidirect
114. #11762696C22semidirect
115. #11762693C22semidirect
116. #11762693C22semidirect
117. #11762692C22semidirect
118. #11762692C22semidirect
128. #11762686C22semidirect
129. #11762686C22semidirect
147. #11762683C22semidirect
151. #11762681C22semidirect
152. #11762681C22semidirect
156. #11762680C22semidirect
157. #11762680C22semidirect
164. #11762667C22semidirect
165. #11762667C22semidirect
166. #11762667C22semidirect
167. #11762667C22semidirect
172. C17×#397C22semidirect
173. C17×#397C22semidirect
174. C17×#397C22semidirect
176. C17×#394C22semidirect
179. C17×#390C22semidirect
181. C17×#388C22semidirect
182. C17×#387C22semidirect
183. C17×#387C22semidirect
729. #2797D17semidirect
873. #397C2×D17semidirect
874. #397C2×D17semidirect
875. #397C2×D17semidirect
892. #394C2×D17semidirect
911. #390C2×D17semidirect
923. #388C2×D17semidirect
929. #387C2×D17semidirect
930. #387C2×D17semidirect
1182. C17#36791semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#145370752
#145370652
#145367262
#145365272
#145364852
#145364292
#145364032
#145360402
#145360172
#145359502
#145355822
#145355332
#145355012
#145354952
#145353122
#145351832
#145351472
#145347362
#145347112
#145330402
#145329112
#145325262
#145324652
#145323892
#145323272
#145321682
#145320982
#145314572
#145313742
D17×#3852
C17×#27972
#3679117