Finite Group Databasebeta

← #17197456

Subgroups — #17197456

Order 4352.

2458 conjugacy classes of subgroups.

The subgroup lattice has 1574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763315C211yesmaximal, characteristic
2#14531925C211yesmaximal, characteristic, complemented
3#14531923C211yesmaximal, characteristic, complemented
4#14531923C211yesmaximal, characteristic, complemented
5#14531825C211yesmaximal, characteristic, complemented
6#14531819C211yesmaximal, characteristic, complemented
7#14531814C211yesmaximal, characteristic, complemented
8#14531808C211yesmaximal, characteristic, complemented
9#14531756C211yesmaximal, characteristic, complemented
10#14531754C211yesmaximal, characteristic, complemented
11#14531722C211yesmaximal, characteristic, complemented
12#14531719C211yesmaximal, characteristic, complemented
13#14531674C211yesmaximal, characteristic, complemented
14#14531666C211yesmaximal, characteristic, complemented
15#14531623C211yesmaximal, characteristic, complemented
16#14531610C211yesmaximal, characteristic, complemented
17#14531579C211yesmaximal, characteristic, complemented
18#14531575C211yesmaximal, characteristic, complemented
19#14531571C211yesmaximal, characteristic, complemented
20#14531567C211yesmaximal, characteristic, complemented
21#14531474C211yesmaximal, characteristic, complemented
22#14531470C211yesmaximal, characteristic, complemented
23#14531463C211yesmaximal, characteristic, complemented
24#14531459C211yesmaximal, characteristic, complemented
25#14531425C211yesmaximal, characteristic, complemented
26#14531421C211yesmaximal, characteristic, complemented
27#14531414C211yesmaximal, characteristic, complemented
28#14531410C211yesmaximal, characteristic, complemented
29#14531162C211yesmaximal, characteristic, complemented
30#14531162C211yesmaximal, characteristic, complemented
31C17×#2375C211yesmaximal, characteristic, complemented
32C22×#63254C2211yescharacteristic
33C24×Dic17C2211yescharacteristic
34#11763315C4116yescomplemented
35C2×#10587572C2211yescharacteristic
36C2×#10587621C2211yescharacteristic
37C2×#10587564C2211yescharacteristic
38C2×#10587564C2211yescharacteristic
39C2×#10587625C2211yescharacteristic
40C2×#10587625C2211yescharacteristic
41C2×#10587639C2211yescharacteristic
42C2×C4×Dic34C2211yescharacteristic, complemented
43C2×#10587573C2211yescharacteristic, complemented
44C2×D4×Dic17C2211yescharacteristic
45C2×D4×Dic17C2211yescharacteristic
46C2×C4×C22⋊D17C2211yescharacteristic, complemented
47C2×#10587567C2211yescharacteristic
48C2×#10587567C2211yescharacteristic
49C2×#10587567C2211yescharacteristic, complemented
50C2×#10587563C2211yescharacteristic
51C2×#10587563C2211yescharacteristic
52C2×#10587563C2211yescharacteristic
53C2×#10587563C2211yescharacteristic
54C2×#10587563C2211yescharacteristic
55#11762713C2211yescharacteristic, complemented
56#11762713C2211yescharacteristic, complemented
57#11762712C2211yescharacteristic
58#11762712C2211yescharacteristic
59#11762712C2211yescharacteristic
60#11762709C2211yescharacteristic
61#11762709C2211yescharacteristic
62#11762709C2211yescharacteristic
63#11762709C2211yescharacteristic
64#11762709C2211yescharacteristic
65#11762709C2211yescharacteristic
66#11762709C2211yescharacteristic, complemented
67#11762709C2211yescharacteristic, complemented
68#11762707C2211yescharacteristic, complemented
69#11762706C2211yescharacteristic, complemented
70#11762706C2211yescharacteristic, complemented
71#11762706C2211yescharacteristic, complemented
72#11762705C2211yescharacteristic, complemented
73#11762704C2211yescharacteristic, complemented
74#11762704C2211yescharacteristic, complemented
75#11762704C2211yescharacteristic, complemented
76#11762703C2211yescharacteristic
77#11762703C2211yescharacteristic
78#11762703C2211yescharacteristic
79#11762703C2211yescharacteristic
80#11762703C2211yescharacteristic
81#11762703C2211yescharacteristic
82#11762703C2211yescharacteristic, complemented
83#11762703C2211yescharacteristic, complemented
84#11762702C2211yescharacteristic
85#11762702C2211yescharacteristic
86#11762702C2211yescharacteristic
87#11762702C2211yescharacteristic
88#11762702C2211yescharacteristic
89#11762702C2211yescharacteristic
90#11762701C2211yescharacteristic, complemented
91#11762700C2211yescharacteristic, complemented
92#11762699C2211yescharacteristic, complemented
93#11762698C2211yescharacteristic, complemented
94#11762697C2211yescharacteristic
95#11762697C2211yescharacteristic
96#11762697C2211yescharacteristic
97#11762697C2211yescharacteristic
98#11762697C2211yescharacteristic
99#11762697C2211yescharacteristic
100#11762697C2211yescharacteristic, complemented
101#11762697C2211yescharacteristic, complemented
102#11762696C2211yescharacteristic, complemented
103#11762694C2211yescharacteristic, complemented
104#11762694C2211yescharacteristic, complemented
105#11762693C2211yescharacteristic, complemented
106#11762692C2211yescharacteristic, complemented
107#11762692C2211yescharacteristic, complemented
108#11762691C2211yescharacteristic, complemented
109#11762690C2211yescharacteristic, complemented
110#11762689C2211yescharacteristic
111#11762689C2211yescharacteristic
112#11762689C2211yescharacteristic
113#11762685C2211yescharacteristic
114#11762685C2211yescharacteristic
115#11762685C2211yescharacteristic
116#11762685C2211yescharacteristic
117#11762685C2211yescharacteristic
118#11762685C2211yescharacteristic
119#11762683C2211yescharacteristic, complemented
120#11762682C2211yescharacteristic, complemented
121#11762681C2211yescharacteristic, complemented
122#11762680C2211yescharacteristic, complemented
123#11762676C2211yescharacteristic, complemented
124#11762676C2211yescharacteristic, complemented
125#11762674C2211yescharacteristic, complemented
126#11762673C2211yescharacteristic, complemented
127#11762671C2211yescharacteristic, complemented
128#11762670C2211yescharacteristic
129#11762670C2211yescharacteristic
130#11762670C2211yescharacteristic
131#11762670C2211yescharacteristic
132#11762670C2211yescharacteristic, complemented
133#11762667C2211yescharacteristic
134#11762667C2211yescharacteristic
135#11762667C2211yescharacteristic
136#11762667C2211yescharacteristic
137#11762667C2211yescharacteristic
138#11762667C2211yescharacteristic
139#11762667C2211yescharacteristic
140#11762667C2211yescharacteristic
141#11762667C2211yescharacteristic, complemented
142#11762666C2211yescharacteristic, complemented
143#11762665C2211yescharacteristic
144#11762665C2211yescharacteristic
145C4⋊C4×Dic17C2211yescharacteristic, complemented
146C4⋊C4×Dic17C2211yescharacteristic, complemented
147C4×#63225C2211yescharacteristic, complemented
148C4×#63225C2211yescharacteristic, complemented
149C4×#63225C2211yescharacteristic, complemented
150C4×#63225C2211yescharacteristic, complemented
151C4×C4⋊Dic17C2211yescharacteristic, complemented
152#11762660C2211yescharacteristic, complemented
153#11762660C2211yescharacteristic, complemented
154#11762660C2211yescharacteristic, complemented
155C22⋊C4×Dic17C2211yescharacteristic
156C22⋊C4×Dic17C2211yescharacteristic
157C22⋊C4×Dic17C2211yescharacteristic
158C22⋊C4×Dic17C2211yescharacteristic
159C22⋊C4×Dic17C2211yescharacteristic
160C22⋊C4×Dic17C2211yescharacteristic
161C22⋊C4×Dic17C2211yescharacteristic
162C22⋊C4×Dic17C2211yescharacteristic
163C22⋊C4×Dic17C2211yescharacteristic, complemented
164C22⋊C4×Dic17C2211yescharacteristic, complemented
165C4×#63227C2211yescharacteristic, complemented
166C4×#63227C2211yescharacteristic, complemented
167C4×C22⋊Dic17C2211yescharacteristic, complemented
168#11762656C2211yescharacteristic, complemented
169#11762655C2211yescharacteristic, complemented
170#11762654C2211yescharacteristic, complemented
171C2×#10587502C2211yescharacteristic, complemented
172#95×D17C2211yescharacteristic, complemented
173C2×C17×#120C2211yescharacteristic
174C17×#390C2211yescharacteristic
175C17×#390C2211yescharacteristic
176C17×#390C2211yescharacteristic
177C17×#388C2211yescharacteristic
178C17×#388C2211yescharacteristic
179C17×#388C2211yescharacteristic
180C17×#388C2211yescharacteristic
181C17×#388C2211yescharacteristic
182C17×#388C2211yescharacteristic
183C17×#386C2211yescharacteristic
184C17×#386C2211yescharacteristic
185C17×#386C2211yescharacteristic
186C17×#379C2211yescharacteristic
187C17×#379C2211yescharacteristic
188C25×C17C2311yescharacteristic
189C22×D4×C17C2311yescharacteristic
190C22×D4×C17C2311yescharacteristic
191C22×D4×C17C2311yescharacteristic
192C23×C4×C17C2311yescharacteristic
193C22×C22⋊D17C2311yescharacteristic
194C22×C22⋊D17C2311yescharacteristic
195C22×C22⋊D17C2311yescharacteristic
196C22×C22⋊D17C2311yescharacteristic
197C23×Dic17—42no—
198C23×Dic17—42no—
199C23×Dic17C2×C418yescomplemented
200C23×Dic17C2311yescharacteristic
201C23×Dic17C2311yescharacteristic
202C23×Dic17C2311yescharacteristic
203C23×Dic17C2311yescharacteristic
204C23×Dic17C2311yescharacteristic
205C23×Dic17C2311yescharacteristic
206C23×Dic17C2311yescharacteristic
207C23×Dic17C2311yescharacteristic
208C2×#63254—42no—
209C2×#63254—42no—
210C2×#63254C2×C418yes—
211C22×C4×D17C2311yescharacteristic
212C22×C4×D17C2311yescharacteristic
213C22×C4×D17C2311yescharacteristic
214C22×Dic34C2311yescharacteristic
215C17×#120C2×C418yescomplemented
216C2×C4⋊C4×C17C2311yescharacteristic
217C2×C4⋊C4×C17C2311yescharacteristic
218C2×C4⋊C4×C17C2311yescharacteristic
219C2×C22⋊C4×C17C2311yescharacteristic
220C2×C22⋊C4×C17C2311yescharacteristic
221C2×C22⋊C4×C17C2311yescharacteristic
222C2×C22⋊C4×C17C2311yescharacteristic
223C2×C22⋊C4×C17C2311yescharacteristic
224C2×C22⋊C4×C17C2311yescharacteristic
225C2×C22⋊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×C42×C17C2311yescharacteristic
238C2×C42×C17C2311yescharacteristic
239C2×C42×C17C2311yescharacteristic
240#10587639C2×C418yescomplemented
241C2×C22⋊Dic17C2311yescharacteristic
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
255C2×C22⋊Dic17C2311yescharacteristic
256C2×C22⋊Dic17C2311yescharacteristic
257C2×C22⋊Dic17C2311yescharacteristic
258C2×C22⋊Dic17C2311yescharacteristic
259C2×C22⋊Dic17C2311yescharacteristic
260C2×C22⋊Dic17C2311yescharacteristic
261#10587625C2×C418yes—
262#10587625C2×C418yes—
263#10587621C2×C418yescomplemented
264D4×Dic17C2×C418yescomplemented
265D4×Dic17C2×C418yescomplemented
266C4×C22⋊D17—42no—
267C2×#63227C2311yescharacteristic
268C2×#63227C2311yescharacteristic
269C2×#63227C2311yescharacteristic
270C2×#63227C2311yescharacteristic
271C2×#63227C2311yescharacteristic
272C2×#63227C2311yescharacteristic
273C2×#63227C2311yescharacteristic
274C2×#63227C2311yescharacteristic
275C2×C4⋊Dic17C2311yescharacteristic
276C2×C4⋊Dic17C2311yescharacteristic
277C2×C4⋊Dic17C2311yescharacteristic
278C2×C4⋊Dic17C2311yescharacteristic
279C2×C4⋊Dic17C2311yescharacteristic
280C2×#63225C2311yescharacteristic
281C2×#63225C2311yescharacteristic
282C2×#63225C2311yescharacteristic
283C2×#63225C2311yescharacteristic
284C2×#63225C2311yescharacteristic
285C2×#63225C2311yescharacteristic
286C2×#63225C2311yescharacteristic
287C2×#63225C2311yescharacteristic
288C2×#63225C2311yescharacteristic
289C2×#63225C2311yescharacteristic
290C2×#63225C2311yescharacteristic
291C2×#63225C2311yescharacteristic
292C2×#63225C2311yescharacteristic
293C2×#63225C2311yescharacteristic
294C2×#63225C2311yescharacteristic
295C2×#63225C2311yescharacteristic
296C2×#63225C2311yescharacteristic
297C2×#63225C2311yescharacteristic
298C2×C4×Dic17C2311yescharacteristic
299C2×C4×Dic17C2311yescharacteristic
300C2×C4×Dic17C2311yescharacteristic
301C2×C4×Dic17C2311yescharacteristic
302C2×C4×Dic17C2311yescharacteristic
303C2×C4×Dic17C2311yescharacteristic
304C2×C4×Dic17C2311yescharacteristic
305C2×C4×Dic17C2311yescharacteristic
306C2×C4×Dic17C2311yescharacteristic
307C2×C4×Dic17C2311yescharacteristic
308C2×C4×Dic17C2311yescharacteristic
309C2×C4×Dic17C2311yescharacteristic
310C2×C4×Dic17C2311yescharacteristic
311C2×C4×Dic17C2311yescharacteristic
312C2×C4×Dic17C2311yescharacteristic
313C2×C4×Dic17C2311yescharacteristic
314C2×C4×Dic17C2311yescharacteristic
315C2×C4×Dic17C2311yescharacteristic
316C2×C4×Dic17C2311yescharacteristic
317#10587573—42no—
318#10587572C2×C418yescomplemented
319#10587567—42no—
320#10587567C2×C418yescomplemented
321#10587567C2×C418yescomplemented
322#10587564C2×C418yescomplemented
323#10587564C2×C418yescomplemented
324#10587563—42no—
325#10587563—42no—
326#10587563—42no—
327#10587563—42no—
328#10587563C2×C418yescomplemented
329C4×Dic34—42no—
330C17×#95C2311yescharacteristic
331C17×#95C2311yescharacteristic
332C17×#95C2311yescharacteristic
333C17×#95C2311yescharacteristic
334C17×#95C2311yescharacteristic
335C17×#95C2311yescharacteristic
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
369#10587502C2311yescharacteristic
370C24×C17—41no—
371C24×C17—41no—
372C24×C17—41no—
373C24×C17—41no—
374C24×C17—41no—
375C24×C17—41no—
376C24×C17C22×C414yes—
377C24×C17C2411yescharacteristic
378C24×C17C2411yescharacteristic
379C24×C17C2411yescharacteristic
380C24×C17C2411yescharacteristic
381C23×D17C2411yescharacteristic
382C2×D4×C17—41no—
383C2×D4×C17—41no—
384C2×D4×C17—41no—
385C2×D4×C17—41no—
386C2×D4×C17—41no—
387C2×D4×C17—41no—
388C2×D4×C17C22×C414yes—
389C2×D4×C17C22×C414yes—
390C2×D4×C17C22×C414yes—
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
405C2×C22⋊D17—22no—
406C2×C22⋊D17—22no—
407C2×C22⋊D17—41no—
408C2×C22⋊D17—41no—
409C2×C22⋊D17—41no—
410C2×C22⋊D17—41no—
411C2×C22⋊D17—41no—
412C2×C22⋊D17—41no—
413C2×C22⋊D17C22×C414yes—
414C2×C22⋊D17C22×C414yes—
415C2×C22⋊D17C22×C414yes—
416C2×C22⋊D17C22×C414yes—
417C22×Dic17—22no—
418C22×Dic17—22no—
419C22×Dic17—22no—
420C22×Dic17—22no—
421C22×Dic17—22no—
422C22×Dic17—22no—
423C22×Dic17—416no—
424C22×Dic17—41no—
425C22×Dic17—41no—
426C22×Dic17—41no—
427C22×Dic17—41no—
428C22×Dic17—41no—
429C22×Dic17—41no—
430C22×Dic17—41no—
431C22×Dic17—41no—
432C22×Dic17—41no—
433C22×Dic17—41no—
434C22×Dic17—41no—
435C22×Dic17C22×C414yes—
436C22×Dic17C22×C414yes—
437C22×Dic17C22×C414yes—
438C22×Dic17C22×C414yes—
439C22×Dic17C22×C414yes—
440C22×Dic17C22×C414yes—
441C22×Dic17C22×C414yes—
442C22×Dic17C2411yescharacteristic
443C22×Dic17C2411yescharacteristic
444C22×Dic17C2411yescharacteristic
445C22×Dic17C2411yescharacteristic
446C22×Dic17C2411yescharacteristic
447C22×Dic17C2411yescharacteristic
448C22×Dic17C2411yescharacteristic
449C22×Dic17C2411yescharacteristic
450C22×Dic17C2411yescharacteristic
451C22×Dic17C2411yescharacteristic
452C22×Dic17C2411yescharacteristic
453C22×Dic17C2411yescharacteristic
454C22×Dic17C2411yescharacteristic
455C22×Dic17C2411yescharacteristic
456C22×Dic17C2411yescharacteristic
457#63254—416no—
458C2×C4×D17—41no—
459C2×C4×D17—41no—
460C2×C4×D17—41no—
461C2×C4×D17—41no—
462C2×C4×D17—41no—
463C2×C4×D17—41no—
464C2×C4×D17—41no—
465C2×C4×D17—41no—
466C2×C4×D17C22×C414yes—
467C2×Dic34—22no—
468C2×Dic34—22no—
469C2×Dic34C22×C414yes—
470C4⋊C4×C17—41no—
471C4⋊C4×C17—41no—
472C4⋊C4×C17—41no—
473C22⋊C4×C17—41no—
474C22⋊C4×C17—41no—
475C22⋊C4×C17—41no—
476C22⋊C4×C17—41no—
477C22⋊C4×C17—41no—
478C22⋊C4×C17—41no—
479C22⋊C4×C17—41no—
480C22⋊C4×C17—41no—
481C22⋊C4×C17—41no—
482C22⋊C4×C17—41no—
483C22⋊C4×C17—41no—
484C22⋊C4×C17—41no—
485C22⋊C4×C17—41no—
486C22⋊C4×C17—41no—
487C22⋊C4×C17—41no—
488C22⋊C4×C17C22×C414yes—
489C22⋊C4×C17C22×C414yes—
490C22⋊C4×C17C22×C414yes—
491C42×C17—41no—
492C42×C17—41no—
493C42×C17—41no—
494C22⋊Dic17—41no—
495C22⋊Dic17—41no—
496C22⋊Dic17—41no—
497C22⋊Dic17—41no—
498C22⋊Dic17—41no—
499C22⋊Dic17—41no—
500C22⋊Dic17—41no—
501C22⋊Dic17—41no—
502C22⋊Dic17—41no—
503C22⋊Dic17—41no—
504C22⋊Dic17—41no—
505C22⋊Dic17—41no—
506C22⋊Dic17—41no—
507C22⋊Dic17—41no—
508C22⋊Dic17—41no—
509C22⋊Dic17C22×C414yes—
510C22⋊Dic17C22×C414yes—
511C22⋊Dic17C22×C414yes—
512C22⋊Dic17C22×C414yes—
513C22⋊Dic17C22×C414yes—
514#63227—41no—
515#63227—41no—
516#63227—41no—
517#63227—41no—
518#63227—41no—
519#63227—41no—
520#63227C22×C414yes—
521#63227C22×C414yes—
522C4⋊Dic17—41no—
523C4⋊Dic17—41no—
524C4⋊Dic17—41no—
525C4⋊Dic17C22×C414yes—
526C4⋊Dic17C22×C414yes—
527#63225—22no—
528#63225—22no—
529#63225—22no—
530#63225—22no—
531#63225—41no—
532#63225—41no—
533#63225—41no—
534#63225—41no—
535#63225—41no—
536#63225—41no—
537#63225—41no—
538#63225—41no—
539#63225—41no—
540#63225—41no—
541#63225C22×C414yes—
542#63225C22×C414yes—
543#63225C22×C414yes—
544#63225C22×C414yes—
545C4×Dic17—22no—
546C4×Dic17—22no—
547C4×Dic17—22no—
548C4×Dic17—22no—
549C4×Dic17—41no—
550C4×Dic17—41no—
551C4×Dic17—41no—
552C4×Dic17—41no—
553C4×Dic17—41no—
554C4×Dic17—41no—
555C4×Dic17—41no—
556C4×Dic17—41no—
557C4×Dic17—41no—
558C4×Dic17—41no—
559C4×Dic17—41no—
560C4×Dic17—41no—
561C4×Dic17—41no—
562C4×Dic17C22×C414yes—
563C4×Dic17C22×C414yes—
564#34391—171nomaximal, Sylow
565C23×C17—21no—
566C23×C17—21no—
567C23×C17—21no—
568C23×C17—21no—
569C23×C17—21no—
570C23×C17—21no—
571C23×C17—21no—
572C23×C17—21no—
573C23×C17—21no—
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—44no—
590C23×C17—44no—
591C23×C17—44no—
592C23×C17—44no—
593C23×C17—44no—
594C23×C17—44no—
595C23×C17—44no—
596C23×C17C23×C412yes—
597C23×C17C23×C412yes—
598C23×C17C23×C412yes—
599C23×C17C23×C412yes—
600C23×C17C2511yescharacteristic
601C22×D17—21no—
602C22×D17—21no—
603C22×D17—21no—
604C22×D17—21no—
605C22×D17—21no—
606C22×D17—21no—
607C22×D17C23×C412yes—
608D4×C17—44no—
609D4×C17—44no—
610D4×C17—44no—
611C2×C4×C17—21no—
612C2×C4×C17—21no—
613C2×C4×C17—21no—
614C2×C4×C17—21no—
615C2×C4×C17—21no—
616C2×C4×C17—21no—
617C2×C4×C17—21no—
618C2×C4×C17—21no—
619C2×C4×C17—21no—
620C2×C4×C17—21no—
621C2×C4×C17—21no—
622C2×C4×C17—21no—
623C2×C4×C17—21no—
624C2×C4×C17—21no—
625C2×C4×C17—21no—
626C2×C4×C17—21no—
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—82no—
642C2×C4×C17C23×C412yes—
643C2×C4×C17C23×C412yes—
644C2×C4×C17C23×C412yes—
645C22⋊D17—28no—
646C22⋊D17—44no—
647C22⋊D17—44no—
648C22⋊D17—44no—
649C2×Dic17—21no—
650C2×Dic17—21no—
651C2×Dic17—21no—
652C2×Dic17—21no—
653C2×Dic17—21no—
654C2×Dic17—21no—
655C2×Dic17—21no—
656C2×Dic17—21no—
657C2×Dic17—21no—
658C2×Dic17—21no—
659C2×Dic17—21no—
660C2×Dic17—21no—
661C2×Dic17—28no—
662C2×Dic17—28no—
663C2×Dic17—28no—
664C2×Dic17—21no—
665C2×Dic17—21no—
666C2×Dic17—21no—
667C2×Dic17—21no—
668C2×Dic17—21no—
669C2×Dic17—21no—
670C2×Dic17—21no—
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—44no—
689C2×Dic17—44no—
690C2×Dic17—44no—
691C2×Dic17—44no—
692C2×Dic17—82no—
693C2×Dic17C23×C412yes—
694C2×Dic17C23×C412yes—
695C2×Dic17C23×C412yes—
696C2×Dic17C23×C412yes—
697C2×Dic17C23×C412yes—
698C2×Dic17C23×C412yes—
699C2×Dic17C23×C412yes—
700C2×Dic17H(5,𝔽2)12yes—
701C2×Dic17H(5,𝔽2)12yes—
702C4×D17—44no—
703C4×D17—82no—
704C4×D17—82no—
705Dic34—28no—
706C2×#525—171no—
707#2375—171no—
708#2375—171no—
709#2375—171no—
710#2375D1711yescharacteristic, complemented
711#2363—171no—
712#2363—171no—
713#2362—171no—
714#2362—171no—
715#2357—171no—
716#2357—171no—
717#2353—171no—
718#2353—171no—
719#2347—171no—
720#2346—171no—
721#2341—171no—
722#2339—171no—
723#2335—171no—
724#2335—171no—
725#2335—171no—
726#2335—171no—
727#2324—171no—
728#2324—171no—
729#2323—171no—
730#2323—171no—
731#2319—171no—
732#2319—171no—
733#2318—171no—
734#2318—171no—
735#2280—171no—
736#2280—171no—
737C22×C17—22no—
738C22×C17—22no—
739C22×C17—22no—
740C22×C17—22no—
741C22×C17—22no—
742C22×C17—22no—
743C22×C17—22no—
744C22×C17—22no—
745C22×C17—22no—
746C22×C17—22no—
747C22×C17—22no—
748C22×C17—22no—
749C22×C17—416no—
750C22×C17—41no—
751C22×C17—41no—
752C22×C17—41no—
753C22×C17—41no—
754C22×C17—41no—
755C22×C17—41no—
756C22×C17—41no—
757C22×C17—41no—
758C22×C17—41no—
759C22×C17—41no—
760C22×C17—41no—
761C22×C17—41no—
762C22×C17—41no—
763C22×C17—41no—
764C22×C17—41no—
765C22×C17—41no—
766C22×C17C24×C411yescharacteristic
767C22×C17C2×H(5,𝔽2)11yescharacteristic
768C22×C17C2×H(5,𝔽2)11yescharacteristic
769C22×C17#58511yescharacteristic
770C22×C17#58511yescharacteristic
771C22×C17#58511yescharacteristic
772C22×C17#58511yescharacteristic
773C2×D17—22no—
774C2×D17—22no—
775C2×D17—22no—
776C2×D17—41no—
777C2×D17—41no—
778C2×D17—41no—
779C2×D17—41no—
780C4×C17—22no—
781C4×C17—22no—
782C4×C17—22no—
783C4×C17—41no—
784C4×C17—41no—
785C4×C17—41no—
786C4×C17—41no—
787C4×C17—41no—
788C4×C17—41no—
789C4×C17—41no—
790C4×C17—41no—
791Dic17—22no—
792Dic17—22no—
793Dic17—22no—
794Dic17—22no—
795Dic17—22no—
796Dic17—22no—
797Dic17—41no—
798Dic17—41no—
799Dic17—41no—
800Dic17—41no—
801Dic17—41no—
802Dic17—41no—
803Dic17—41no—
804Dic17—41no—
805Dic17#51814yes—
806C22×#41—171no—
807C24×C4—171no—
808#525—1716no—
809C2×#123—171no—
810C2×#123—171no—
811C2×C22⋊Q8—171no—
812C2×C22⋊Q8—171no—
813C2×#121—171no—
814C2×#121—171no—
815C2×#120—171no—
816C2×#120C2×D1711yescharacteristic
817C2×C4×Q8—171no—
818C2×C4×Q8—171no—
819C2×C4×D4—171no—
820C2×C4×D4—171no—
821C2×C4×D4—171no—
822C2×C4×D4—171no—
823C2×C4×D4—171no—
824C2×C4×D4—171no—
825C2×#117—171no—
826C2×#117—171no—
827C2×#117—171no—
828C2×#117—171no—
829C2×#117—171no—
830#391—171no—
831#391—171no—
832#390—171no—
833#390—171no—
834#390—171no—
835#390—171no—
836#390—171no—
837#390—171no—
838#390—171no—
839#390—171no—
840#390—171no—
841#390—171no—
842#390—171no—
843#390C2×D1711yescharacteristic
844#390C2×D1711yescharacteristic
845#390C2×D1711yescharacteristic
846#389—171no—
847#389—171no—
848#389—171no—
849#389—171no—
850#389—171no—
851#389—171no—
852#389—171no—
853#389—171no—
854#388—171no—
855#388—171no—
856#388—171no—
857#388—171no—
858#388—171no—
859#388—171no—
860#388—171no—
861#388—171no—
862#388—171no—
863#388—171no—
864#388—171no—
865#388—171no—
866#388—171no—
867#388—171no—
868#388—171no—
869#388—171no—
870#388—171no—
871#388—171no—
872#388—171no—
873#388—171no—
874#388—171no—
875#388—171no—
876#388—171no—
877#388—171no—
878#388—171no—
879#388—171no—
880#388C2×D1711yescharacteristic
881#388C2×D1711yescharacteristic
882#388C2×D1711yescharacteristic
883#388C2×D1711yescharacteristic
884#388C2×D1711yescharacteristic
885#388C2×D1711yescharacteristic
886#387—171no—
887#387—171no—
888#387—171no—
889#387—171no—
890#387—171no—
891#387—171no—
892#387—171no—
893#387—171no—
894#386—171no—
895#386—171no—
896#386—171no—
897#386—171no—
898#386—171no—
899#386—171no—
900#386—171no—
901#386—171no—
902#386—171no—
903#386C2×D1711yescharacteristic
904#386C2×D1711yescharacteristic
905#386C2×D1711yescharacteristic
906#385—171no—
907#385—171no—
908#385—171no—
909#385—171no—
910#383—171no—
911#383—171no—
912#382—171no—
913#382—171no—
914#381—171no—
915#381—171no—
916#381—171no—
917#381—171no—
918#381—171no—
919#381—171no—
920#380—171no—
921#380—171no—
922#380—171no—
923#380—171no—
924#380—171no—
925#380—171no—
926#380—171no—
927#380—171no—
928#380—171no—
929#380—171no—
930#379—171no—
931#379—171no—
932#379C2×D1711yescharacteristic
933#379C2×D1711yescharacteristic
934C4×C4⋊C4—171no—
935C4×C4⋊C4—171no—
936C4×C4⋊C4—171no—
937C4×C4⋊C4—171no—
938C4×C4⋊C4—171no—
939C4×C4⋊C4—171no—
940C4×C4⋊C4—171no—
941C4×C4⋊C4—171no—
942C4×C4⋊C4—171no—
943C4×C4⋊C4—171no—
944C4×C22⋊C4—171no—
945C4×C22⋊C4—171no—
946C4×C22⋊C4—171no—
947C4×C22⋊C4—171no—
948C4×C22⋊C4—171no—
949C4×C22⋊C4—171no—
950C4×C22⋊C4—171no—
951C4×C22⋊C4—171no—
952C4×C22⋊C4—171no—
953C4×C22⋊C4—171no—
954C4×C22⋊C4—171no—
955C4×C22⋊C4—171no—
956C4×C22⋊C4—171no—
957C4×C22⋊C4—171no—
958#376—171no—
959#376—171no—
960C2×#95—171no—
961C2×#95—171no—
962C2×C17—42no—
963C2×C17—42no—
964C2×C17—42no—
965C2×C17—42no—
966C2×C17C2×#51811yescharacteristic
967C2×C17#342811yescharacteristic
968C2×C17#342811yescharacteristic
969C2×C17#353911yescharacteristic
970C2×C17#353911yescharacteristic
971C2×C17#354011yescharacteristic
972C2×C17#354011yescharacteristic
973D17—42no—
974C25C22×D1711yescharacteristic
975C2×#41—178no—
976C2×#41—682no—
977C2×#41—682no—
978C22×Q8—171no—
979C22×D4—171no—
980C22×D4—171no—
981C22×D4—171no—
982C22×D4—171no—
983C22×D4C22×D1711yescharacteristic
984C22×D4C22×D1711yescharacteristic
985C22×D4C22×D1711yescharacteristic
986C23×C4—171no—
987C23×C4—171no—
988C23×C4—171no—
989C23×C4—178no—
990C23×C4—171no—
991C23×C4—171no—
992C23×C4—171no—
993C23×C4—171no—
994C23×C4—171no—
995C23×C4—171no—
996C23×C4—171no—
997C23×C4—171no—
998C23×C4—682no—
999C23×C4—682no—
1000C23×C4C22×D1711yescharacteristic
1001#123—178no—
1002#123—178no—
1003C22⋊Q8—178no—
1004C22⋊Q8—178no—
1005#121—178no—
1006#121—178no—
1007#120—178no—
1008#120C4×D1718yescomplemented
1009C4×Q8—682no—
1010C4×Q8—682no—
1011C4×D4—178no—
1012C4×D4—178no—
1013C4×D4—178no—
1014C4×D4—178no—
1015C4×D4—682no—
1016C4×D4—682no—
1017#117—178no—
1018#117—682no—
1019#117—682no—
1020#117—682no—
1021#117—682no—
1022C2×C4⋊C4—171no—
1023C2×C4⋊C4—171no—
1024C2×C4⋊C4—171no—
1025C2×C4⋊C4—171no—
1026C2×C4⋊C4—171no—
1027C2×C4⋊C4—171no—
1028C2×C4⋊C4—171no—
1029C2×C4⋊C4—171no—
1030C2×C4⋊C4—171no—
1031C2×C4⋊C4—171no—
1032C2×C4⋊C4—171no—
1033C2×C4⋊C4—171no—
1034C2×C4⋊C4—171no—
1035C2×C4⋊C4—171no—
1036C2×C4⋊C4—171no—
1037C2×C4⋊C4—171no—
1038C2×C4⋊C4—171no—
1039C2×C4⋊C4—171no—
1040C2×C4⋊C4—171no—
1041C2×C4⋊C4—171no—
1042C2×C4⋊C4—171no—
1043C2×C4⋊C4—171no—
1044C2×C4⋊C4—171no—
1045C2×C4⋊C4C22×D1711yescharacteristic
1046C2×C4⋊C4C22×D1711yescharacteristic
1047C2×C4⋊C4C22×D1711yescharacteristic
1048C2×C22⋊C4—171no—
1049C2×C22⋊C4—171no—
1050C2×C22⋊C4—171no—
1051C2×C22⋊C4—171no—
1052C2×C22⋊C4—171no—
1053C2×C22⋊C4—171no—
1054C2×C22⋊C4—171no—
1055C2×C22⋊C4—171no—
1056C2×C22⋊C4—171no—
1057C2×C22⋊C4—171no—
1058C2×C22⋊C4—171no—
1059C2×C22⋊C4—171no—
1060C2×C22⋊C4—171no—
1061C2×C22⋊C4—171no—
1062C2×C22⋊C4—171no—
1063C2×C22⋊C4—171no—
1064C2×C22⋊C4—171no—
1065C2×C22⋊C4—171no—
1066C2×C22⋊C4—171no—
1067C2×C22⋊C4—171no—
1068C2×C22⋊C4—171no—
1069C2×C22⋊C4—171no—
1070C2×C22⋊C4—171no—
1071C2×C22⋊C4—171no—
1072C2×C22⋊C4—171no—
1073C2×C22⋊C4—171no—
1074C2×C22⋊C4—171no—
1075C2×C22⋊C4—171no—
1076C2×C22⋊C4C22×D1711yescharacteristic
1077C2×C22⋊C4C22×D1711yescharacteristic
1078C2×C22⋊C4C22×D1711yescharacteristic
1079C2×C22⋊C4C22×D1711yescharacteristic
1080C2×C22⋊C4C22×D1711yescharacteristic
1081C2×C22⋊C4C22×D1711yescharacteristic
1082C2×C22⋊C4C22×D1711yescharacteristic
1083C2×C22⋊C4C22×D1711yescharacteristic
1084C2×C22⋊C4C22×D1711yescharacteristic
1085C2×C22⋊C4C22×D1711yescharacteristic
1086C2×C22⋊C4C22×D1711yescharacteristic
1087C2×C22⋊C4C22×D1711yescharacteristic
1088C2×C22⋊C4C22×D1711yescharacteristic
1089C2×C22⋊C4C22×D1711yescharacteristic
1090C2×C22⋊C4C22×D1711yescharacteristic
1091C2×C22⋊C4C22×D1711yescharacteristic
1092C2×C22⋊C4C22×D1711yescharacteristic
1093C2×C22⋊C4C22×D1711yescharacteristic
1094C2×C42—171no—
1095C2×C42—171no—
1096C2×C42—171no—
1097C2×C42—171no—
1098C2×C42—171no—
1099C2×C42—171no—
1100C2×C42—171no—
1101C2×C42—171no—
1102C2×C42—171no—
1103C2×C42—171no—
1104C2×C42—171no—
1105C2×C42—171no—
1106C2×C42—171no—
1107C2×C42—171no—
1108C2×C42—171no—
1109C2×C42—171no—
1110C2×C42—171no—
1111C2×C42—171no—
1112C2×C42—171no—
1113C2×C42C22×D1711yescharacteristic
1114C2×C42C22×D1711yescharacteristic
1115C2×C42C22×D1711yescharacteristic
1116#95—171no—
1117#95—171no—
1118#95—171no—
1119#95—171no—
1120#95—171no—
1121#95—171no—
1122#95—171no—
1123#95—171no—
1124#95—171no—
1125#95—171no—
1126#95—171no—
1127#95—171no—
1128#95—171no—
1129#95—171no—
1130#95—171no—
1131#95—171no—
1132#95—171no—
1133#95—171no—
1134#95—171no—
1135#95—171no—
1136#95—171no—
1137#95—171no—
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#95C22×D1711yescharacteristic
1151#95C22×D1711yescharacteristic
1152#95C22×D1711yescharacteristic
1153#95C22×D1711yescharacteristic
1154#95C22×D1711yescharacteristic
1155#95C22×D1711yescharacteristic
1156C17#3439111yescharacteristic, complemented, Sylow
1157C24—41no—
1158C24—41no—
1159C24—41no—
1160C24—41no—
1161C24—41no—
1162C24—41no—
1163C24—171no—
1164C24C2×C4×D1714yes—
1165C24C23×D1711yescharacteristic
1166C24C23×D1711yescharacteristic
1167C24C23×D1711yescharacteristic
1168C24C23×D1711yescharacteristic
1169#41—6816no—
1170C2×Q8—174no—
1171C2×Q8—342no—
1172C2×Q8—342no—
1173C2×D4—41no—
1174C2×D4—41no—
1175C2×D4—41no—
1176C2×D4—41no—
1177C2×D4—41no—
1178C2×D4—41no—
1179C2×D4—174no—
1180C2×D4—174no—
1181C2×D4—174no—
1182C2×D4—174no—
1183C2×D4—342no—
1184C2×D4—342no—
1185C2×D4—681no—
1186C2×D4—681no—
1187C2×D4—681no—
1188C2×D4—681no—
1189C2×D4—681no—
1190C2×D4—681no—
1191C2×D4C2×C4×D1714yes—
1192C2×D4C2×C4×D1714yes—
1193C2×D4C2×C4×D1714yes—
1194C22×C4—41no—
1195C22×C4—41no—
1196C22×C4—41no—
1197C22×C4—171no—
1198C22×C4—174no—
1199C22×C4—174no—
1200C22×C4—174no—
1201C22×C4—171no—
1202C22×C4—171no—
1203C22×C4—171no—
1204C22×C4—171no—
1205C22×C4—171no—
1206C22×C4—171no—
1207C22×C4—174no—
1208C22×C4—174no—
1209C22×C4—174no—
1210C22×C4—174no—
1211C22×C4—174no—
1212C22×C4—171no—
1213C22×C4—171no—
1214C22×C4—171no—
1215C22×C4—171no—
1216C22×C4—171no—
1217C22×C4—171no—
1218C22×C4—171no—
1219C22×C4—171no—
1220C22×C4—342no—
1221C22×C4—342no—
1222C22×C4—342no—
1223C22×C4—342no—
1224C22×C4—342no—
1225C22×C4—342no—
1226C22×C4—681no—
1227C22×C4—681no—
1228C22×C4—681no—
1229C22×C4—681no—
1230C22×C4—681no—
1231C22×C4—681no—
1232C22×C4—681no—
1233C22×C4—681no—
1234C22×C4—6816no—
1235C22×C4—681no—
1236C22×C4—681no—
1237C22×C4—681no—
1238C22×C4—681no—
1239C22×C4—681no—
1240C22×C4—681no—
1241C22×C4—681no—
1242C22×C4—681no—
1243C22×C4—681no—
1244C22×C4—681no—
1245C22×C4—681no—
1246C22×C4C23×D1711yescharacteristic
1247C22×C4C23×D1711yescharacteristic
1248C22×C4C23×D1711yescharacteristic
1249C22×C4C23×D1711yescharacteristic
1250C22×C4C23×D1711yescharacteristic
1251C22×C4C23×D1711yescharacteristic
1252C22×C4C23×D1711yescharacteristic
1253C22×C4C23×D1711yescharacteristic
1254C22×C4C23×D1711yescharacteristic
1255C22×C4C23×D1711yescharacteristic
1256C22×C4C23×D1711yescharacteristic
1257C4⋊C4—41no—
1258C4⋊C4—41no—
1259C4⋊C4—41no—
1260C4⋊C4—174no—
1261C4⋊C4—174no—
1262C4⋊C4—174no—
1263C4⋊C4—174no—
1264C4⋊C4—174no—
1265C4⋊C4—174no—
1266C4⋊C4—342no—
1267C4⋊C4—342no—
1268C4⋊C4—342no—
1269C4⋊C4—342no—
1270C4⋊C4—681no—
1271C4⋊C4—681no—
1272C4⋊C4—681no—
1273C4⋊C4—681no—
1274C4⋊C4—681no—
1275C4⋊C4—681no—
1276C4⋊C4—681no—
1277C4⋊C4—681no—
1278C4⋊C4—681no—
1279C4⋊C4—681no—
1280C4⋊C4—681no—
1281C4⋊C4—681no—
1282C4⋊C4—681no—
1283C22⋊C4—41no—
1284C22⋊C4—41no—
1285C22⋊C4—41no—
1286C22⋊C4—41no—
1287C22⋊C4—41no—
1288C22⋊C4—41no—
1289C22⋊C4—41no—
1290C22⋊C4—41no—
1291C22⋊C4—41no—
1292C22⋊C4—41no—
1293C22⋊C4—41no—
1294C22⋊C4—41no—
1295C22⋊C4—41no—
1296C22⋊C4—41no—
1297C22⋊C4—41no—
1298C22⋊C4—174no—
1299C22⋊C4—174no—
1300C22⋊C4—174no—
1301C22⋊C4—174no—
1302C22⋊C4—174no—
1303C22⋊C4—174no—
1304C22⋊C4—174no—
1305C22⋊C4—681no—
1306C22⋊C4—681no—
1307C22⋊C4—681no—
1308C22⋊C4—681no—
1309C22⋊C4—681no—
1310C22⋊C4—681no—
1311C22⋊C4—681no—
1312C22⋊C4—681no—
1313C22⋊C4—681no—
1314C22⋊C4—681no—
1315C22⋊C4—681no—
1316C22⋊C4—681no—
1317C22⋊C4—681no—
1318C22⋊C4—681no—
1319C22⋊C4—681no—
1320C22⋊C4—681no—
1321C22⋊C4—681no—
1322C22⋊C4—681no—
1323C22⋊C4—681no—
1324C22⋊C4—681no—
1325C22⋊C4—681no—
1326C22⋊C4C2×C4×D1714yes—
1327C22⋊C4C2×C4×D1714yes—
1328C22⋊C4C2×C4×D1714yes—
1329C42—41no—
1330C42—41no—
1331C42—41no—
1332C42—174no—
1333C42—174no—
1334C42—342no—
1335C42—342no—
1336C42—342no—
1337C42—342no—
1338C42—681no—
1339C42—681no—
1340C42—681no—
1341C42—681no—
1342C42—681no—
1343C42—681no—
1344C42—681no—
1345C42—681no—
1346C42—681no—
1347C42—681no—
1348C42—681no—
1349C42—681no—
1350C42—681no—
1351C23—21no—
1352C23—21no—
1353C23—21no—
1354C23—21no—
1355C23—21no—
1356C23—21no—
1357C23—21no—
1358C23—21no—
1359C23—21no—
1360C23—21no—
1361C23—21no—
1362C23—21no—
1363C23—21no—
1364C23—21no—
1365C23—21no—
1366C23—21no—
1367C23—21no—
1368C23—21no—
1369C23—21no—
1370C23—21no—
1371C23—21no—
1372C23—21no—
1373C23—21no—
1374C23—21no—
1375C23—44no—
1376C23—44no—
1377C23—44no—
1378C23—44no—
1379C23—44no—
1380C23—44no—
1381C23—44no—
1382C23—172no—
1383C23—341no—
1384C23—341no—
1385C23—341no—
1386C23—341no—
1387C23—341no—
1388C23—341no—
1389C23C22×C4×D1712yes—
1390C23C22×C4×D1712yes—
1391C23C22×C4×D1712yes—
1392C23C22×C4×D1712yes—
1393C23C24×D1711yescharacteristic
1394Q8—348no—
1395D4—44no—
1396D4—44no—
1397D4—44no—
1398D4—348no—
1399D4—684no—
1400D4—684no—
1401D4—684no—
1402C2×C4—21no—
1403C2×C4—21no—
1404C2×C4—21no—
1405C2×C4—21no—
1406C2×C4—21no—
1407C2×C4—21no—
1408C2×C4—21no—
1409C2×C4—21no—
1410C2×C4—21no—
1411C2×C4—21no—
1412C2×C4—21no—
1413C2×C4—21no—
1414C2×C4—21no—
1415C2×C4—21no—
1416C2×C4—21no—
1417C2×C4—21no—
1418C2×C4—21no—
1419C2×C4—21no—
1420C2×C4—21no—
1421C2×C4—21no—
1422C2×C4—21no—
1423C2×C4—21no—
1424C2×C4—21no—
1425C2×C4—21no—
1426C2×C4—21no—
1427C2×C4—21no—
1428C2×C4—21no—
1429C2×C4—21no—
1430C2×C4—21no—
1431C2×C4—21no—
1432C2×C4—82no—
1433C2×C4—172no—
1434C2×C4—172no—
1435C2×C4—172no—
1436C2×C4—172no—
1437C2×C4—172no—
1438C2×C4—172no—
1439C2×C4—172no—
1440C2×C4—172no—
1441C2×C4—172no—
1442C2×C4—348no—
1443C2×C4—348no—
1444C2×C4—348no—
1445C2×C4—341no—
1446C2×C4—341no—
1447C2×C4—341no—
1448C2×C4—341no—
1449C2×C4—341no—
1450C2×C4—341no—
1451C2×C4—341no—
1452C2×C4—341no—
1453C2×C4—341no—
1454C2×C4—341no—
1455C2×C4—341no—
1456C2×C4—341no—
1457C2×C4—341no—
1458C2×C4—341no—
1459C2×C4—341no—
1460C2×C4—341no—
1461C2×C4—341no—
1462C2×C4—341no—
1463C2×C4—341no—
1464C2×C4—341no—
1465C2×C4—341no—
1466C2×C4—341no—
1467C2×C4—341no—
1468C2×C4—341no—
1469C2×C4—341no—
1470C2×C4—341no—
1471C2×C4—341no—
1472C2×C4—341no—
1473C2×C4—341no—
1474C2×C4—341no—
1475C2×C4—341no—
1476C2×C4—341no—
1477C2×C4—341no—
1478C2×C4—341no—
1479C2×C4—341no—
1480C2×C4—341no—
1481C2×C4—684no—
1482C2×C4—684no—
1483C2×C4—684no—
1484C2×C4—684no—
1485C2×C4—684no—
1486C2×C4—1362no—
1487C2×C4—1362no—
1488C2×C4—1362no—
1489C2×C4C22×C4×D1712yes—
1490C2×C4C22×C4×D1712yes—
1491C2×C4C22×C4×D1712yes—
1492C22—22no—
1493C22—22no—
1494C22—22no—
1495C22—22no—
1496C22—22no—
1497C22—22no—
1498C22—22no—
1499C22—22no—
1500C22—22no—
1501C22—22no—
1502C22—22no—
1503C22—22no—
1504C22—416no—
1505C22—41no—
1506C22—41no—
1507C22—41no—
1508C22—41no—
1509C22—41no—
1510C22—41no—
1511C22—41no—
1512C22—41no—
1513C22—41no—
1514C22—41no—
1515C22—41no—
1516C22—41no—
1517C22—41no—
1518C22—41no—
1519C22—41no—
1520C22—41no—
1521C22—342no—
1522C22—342no—
1523C22—342no—
1524C22—681no—
1525C22—681no—
1526C22—681no—
1527C22—681no—
1528C22C23×C4×D1711yescharacteristic
1529C22H(5,𝔽2)×D1711yescharacteristic
1530C22H(5,𝔽2)×D1711yescharacteristic
1531C22#1176364411yescharacteristic
1532C22#1176364411yescharacteristic
1533C22#1176364411yescharacteristic
1534C22#1176364411yescharacteristic
1535C4—22no—
1536C4—22no—
1537C4—22no—
1538C4—41no—
1539C4—41no—
1540C4—41no—
1541C4—41no—
1542C4—41no—
1543C4—41no—
1544C4—41no—
1545C4—41no—
1546C4—174no—
1547C4—342no—
1548C4—342no—
1549C4—342no—
1550C4—342no—
1551C4—342no—
1552C4—342no—
1553C4—681no—
1554C4—681no—
1555C4—681no—
1556C4—681no—
1557C4—681no—
1558C4—681no—
1559C4—681no—
1560C4—681no—
1561C2—42no—
1562C2—42no—
1563C2—42no—
1564C2—42no—
1565C2—682no—
1566C2D17×#51811yescharacteristic
1567C2#1454198211yescharacteristic
1568C2#1454198211yescharacteristic
1569C2#1454303811yescharacteristic
1570C2#1454303811yescharacteristic
1571C2#1454305111yescharacteristic
1572C2#1454305711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC17×#2375C2
socle, cosocleC23×C17C25
prime radicalC2×#11763315C2
hypercenter#2375D17
hypocenterC17#34391
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2375

Complements

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

NH ≅ G/Ntype
2. #14531925C2semidirect
3. #14531923C2semidirect
4. #14531923C2semidirect
5. #14531825C2semidirect
6. #14531819C2semidirect
7. #14531814C2semidirect
8. #14531808C2semidirect
9. #14531756C2semidirect
10. #14531754C2semidirect
11. #14531722C2semidirect
12. #14531719C2semidirect
13. #14531674C2semidirect
14. #14531666C2semidirect
15. #14531623C2semidirect
16. #14531610C2semidirect
17. #14531579C2semidirect
18. #14531575C2semidirect
19. #14531571C2semidirect
20. #14531567C2semidirect
21. #14531474C2semidirect
22. #14531470C2semidirect
23. #14531463C2semidirect
24. #14531459C2semidirect
25. #14531425C2semidirect
26. #14531421C2semidirect
27. #14531414C2semidirect
28. #14531410C2semidirect
29. #14531162C2semidirect
30. #14531162C2semidirect
31. C17×#2375C2semidirect
34. #11763315C4semidirect
42. C2×C4×Dic34C22semidirect
43. C2×#10587573C22semidirect
46. C2×C4×C22⋊D17C22semidirect
49. C2×#10587567C22semidirect
55. #11762713C22semidirect
56. #11762713C22semidirect
66. #11762709C22semidirect
67. #11762709C22semidirect
68. #11762707C22semidirect
69. #11762706C22semidirect
70. #11762706C22semidirect
71. #11762706C22semidirect
72. #11762705C22semidirect
73. #11762704C22semidirect
74. #11762704C22semidirect
75. #11762704C22semidirect
82. #11762703C22semidirect
83. #11762703C22semidirect
90. #11762701C22semidirect
91. #11762700C22semidirect
92. #11762699C22semidirect
93. #11762698C22semidirect
100. #11762697C22semidirect
101. #11762697C22semidirect
102. #11762696C22semidirect
103. #11762694C22semidirect
104. #11762694C22semidirect
105. #11762693C22semidirect
106. #11762692C22semidirect
107. #11762692C22semidirect
108. #11762691C22semidirect
109. #11762690C22semidirect
119. #11762683C22semidirect
120. #11762682C22semidirect
121. #11762681C22semidirect
122. #11762680C22semidirect
123. #11762676C22semidirect
124. #11762676C22semidirect
125. #11762674C22semidirect
126. #11762673C22semidirect
127. #11762671C22semidirect
132. #11762670C22semidirect
141. #11762667C22semidirect
142. #11762666C22semidirect
145. C4⋊C4×Dic17C22semidirect
146. C4⋊C4×Dic17C22semidirect
147. C4×#63225C22semidirect
148. C4×#63225C22semidirect
149. C4×#63225C22semidirect
150. C4×#63225C22semidirect
151. C4×C4⋊Dic17C22semidirect
152. #11762660C22semidirect
153. #11762660C22semidirect
154. #11762660C22semidirect
163. C22⋊C4×Dic17C22semidirect
164. C22⋊C4×Dic17C22semidirect
165. C4×#63227C22semidirect
166. C4×#63227C22semidirect
167. C4×C22⋊Dic17C22semidirect
168. #11762656C22semidirect
169. #11762655C22semidirect
170. #11762654C22semidirect
171. C2×#10587502C22semidirect
172. #95×D17C22semidirect
199. C23×Dic17C2×C4semidirect
215. C17×#120C2×C4semidirect
240. #10587639C2×C4semidirect
263. #10587621C2×C4semidirect
264. D4×Dic17C2×C4semidirect
265. D4×Dic17C2×C4semidirect
318. #10587572C2×C4semidirect
320. #10587567C2×C4semidirect
321. #10587567C2×C4semidirect
322. #10587564C2×C4semidirect
323. #10587564C2×C4semidirect
328. #10587563C2×C4semidirect
710. #2375D17semidirect
1008. #120C4×D17semidirect
1156. C17#34391semidirect

Maximal subgroups

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

subgroupindex
C2×#117633152
#145319252
#145319232
#145318252
#145318192
#145318142
#145318082
#145317562
#145317542
#145317222
#145317192
#145316742
#145316662
#145316232
#145316102
#145315792
#145315752
#145315712
#145315672
#145314742
#145314702
#145314632
#145314592
#145314252
#145314212
#145314142
#145314102
#145311622
C17×#23752
#3439117