Finite Group Databasebeta

← #17243099

Subgroups — #17243099

Order 4352.

1548 conjugacy classes of subgroups.

The subgroup lattice has 1368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14537125C211yesmaximal, characteristic, complemented
2#14537102C211yesmaximal, characteristic, complemented
3#14536396C211yesmaximal, characteristic
4#14536286C211yesmaximal, characteristic, complemented
5#14536286C211yesmaximal, characteristic, complemented
6#14536270C211yesmaximal, characteristic, complemented
7#14536203C211yesmaximal, characteristic, complemented
8#14536192C211yesmaximal, characteristic, complemented
9#14536138C211yesmaximal, characteristic, complemented
10#14536023C211yesmaximal, characteristic, complemented
11#14536008C211yesmaximal, characteristic
12#14535982C211yesmaximal, characteristic, complemented
13#14535922C211yesmaximal, characteristic, complemented
14#14535895C211yesmaximal, characteristic, complemented
15#14535751C211yesmaximal, characteristic, complemented
16#14535408C211yesmaximal, characteristic, complemented
17#14535287C211yesmaximal, characteristic, complemented
18#14535242C211yesmaximal, characteristic, complemented
19#14534883C211yesmaximal, characteristic, complemented
20#14534868C211yesmaximal, characteristic, complemented
21#14534371C211yesmaximal, characteristic
22#14534312C211yesmaximal, characteristic, complemented
23#14534212C211yesmaximal, characteristic, complemented
24#14533964C211yesmaximal, characteristic, complemented
25#14533668C211yesmaximal, characteristic, complemented
26#14533653C211yesmaximal, characteristic, complemented
27#14532207C211yesmaximal, characteristic, complemented
28#14531537C211yesmaximal, characteristic, complemented
29#14531418C211yesmaximal, characteristic, complemented
30#14531221C211yesmaximal, characteristic, complemented
31C17×#2438C211yesmaximal, characteristic, complemented
32C2×#10587584C2211yescharacteristic
33C2×#10587583C2211yescharacteristic
34C2×#10587610C2211yescharacteristic
35C2×#10587632C2211yescharacteristic
36C2×C4×C22⋊D17C2211yescharacteristic
37C2×C4×C22⋊D17C2211yescharacteristic
38C2×C42×D17C2211yescharacteristic
39C17⋊#401C2211yescharacteristic
40#11762751C2211yescharacteristic
41#11762751C2211yescharacteristic
42#11762751C2211yescharacteristic
43#11762751C2211yescharacteristic
44#11762751C2211yescharacteristic
45#11762749C2211yescharacteristic
46#11762748C2211yescharacteristic
47#11762748C2211yescharacteristic
48#11762748C2211yescharacteristic
49#11762748C2211yescharacteristic
50#11762748C2211yescharacteristic
51#11762747C2211yescharacteristic
52#11762747C2211yescharacteristic
53#11762747C2211yescharacteristic
54#11762746C2211yescharacteristic
55#11762744C2211yescharacteristic
56#11762742C2211yescharacteristic
57#11762742C2211yescharacteristic
58#11762742C2211yescharacteristic
59#11762742C2211yescharacteristic
60#11762742C2211yescharacteristic
61#11762742C2211yescharacteristic
62#11762741C2211yescharacteristic
63#11762738C2211yescharacteristic
64#11762736C2211yescharacteristic
65#11762735C2211yescharacteristic
66#11762735C2211yescharacteristic
67#11762735C2211yescharacteristic
68#11762734C2211yescharacteristic
69#11762734C2211yescharacteristic
70#11762734C2211yescharacteristic
71#11762731C2211yescharacteristic
72#11762731C2211yescharacteristic
73#11762731C2211yescharacteristic
74#11762730C2211yescharacteristic
75#11762727C2211yescharacteristic
76#11762725C2211yescharacteristic
77#11762725C2211yescharacteristic
78#11762725C2211yescharacteristic
79#11762725C2211yescharacteristic
80#11762722C2211yescharacteristic
81#11762720C2211yescharacteristic
82#11762718C2211yescharacteristic
83#11762716C2211yescharacteristic
84#11762716C2211yescharacteristic
85#11762714C2211yescharacteristic
86#11762713C2211yescharacteristic
87#11762713C2211yescharacteristic
88#11762710C2211yescharacteristic
89#11762708C2211yescharacteristic
90#11762708C2211yescharacteristic
91#11762708C2211yescharacteristic
92#11762708C2211yescharacteristic
93#11762707C2211yescharacteristic
94#11762707C2211yescharacteristic
95#11762703C2211yescharacteristic
96#11762703C2211yescharacteristic
97#11762701C2211yescharacteristic
98#11762701C2211yescharacteristic
99#11762701C2211yescharacteristic
100#11762700C2211yescharacteristic
101#11762700C2211yescharacteristic
102#11762699C2211yescharacteristic
103#11762699C2211yescharacteristic
104#11762699C2211yescharacteristic
105#11762699C2211yescharacteristic
106#11762699C2211yescharacteristic
107#11762698C2211yescharacteristic
108#11762698C2211yescharacteristic
109#11762698C2211yescharacteristic
110#11762697C2211yescharacteristic
111#11762697C2211yescharacteristic
112#11762697C2211yescharacteristic
113#11762697C2211yescharacteristic
114#11762696C2211yescharacteristic
115#11762696C2211yescharacteristic
116#11762695C2211yescharacteristic
117#11762694C2211yescharacteristic
118#11762694C2211yescharacteristic
119#11762694C2211yescharacteristic
120#11762694C2211yescharacteristic
121#11762692C2211yescharacteristic
122#11762692C2211yescharacteristic
123#11762692C2211yescharacteristic
124#11762692C2211yescharacteristic
125#11762692C2211yescharacteristic
126#11762691C2211yescharacteristic
127#11762691C2211yescharacteristic
128#11762691C2211yescharacteristic
129#11762691C2211yescharacteristic
130#11762690C2211yescharacteristic
131#11762690C2211yescharacteristic
132#11762690C2211yescharacteristic
133#11762688C2211yescharacteristic
134#11762688C2211yescharacteristic
135#11762688C2211yescharacteristic
136#11762688C2211yescharacteristic
137#11762687C2211yescharacteristic
138#11762687C2211yescharacteristic
139#11762687C2211yescharacteristic
140#11762687C2211yescharacteristic
141#11762685C2211yescharacteristic
142#11762685C2211yescharacteristic
143#11762683C2211yescharacteristic
144#11762683C2211yescharacteristic
145#11762683C2211yescharacteristic
146#11762683C2211yescharacteristic
147#11762682C2211yescharacteristic
148#11762682C2211yescharacteristic
149#11762680C2211yescharacteristic
150#11762680C2211yescharacteristic
151#11762680C2211yescharacteristic
152#11762680C2211yescharacteristic
153#11762676C2211yescharacteristic
154#11762676C2211yescharacteristic
155#11762676C2211yescharacteristic
156#11762676C2211yescharacteristic
157#11762673C2211yescharacteristic
158#11762671C2211yescharacteristic
159#11762671C2211yescharacteristic
160#11762671C2211yescharacteristic
161#11762669C2211yescharacteristic
162#11762669C2211yescharacteristic
163#11762668C2211yescharacteristic
164#11762666C2211yescharacteristic
165#11762666C2211yescharacteristic
166C4×#63225C2211yescharacteristic
167#11762660C2211yescharacteristic
168#11762660C2211yescharacteristic
169C4×#63227C2211yescharacteristic
170C4×C22⋊Dic17C2211yescharacteristic
171#11762655C2211yescharacteristic
172C2×C17×C22⋊Q8C2211yescharacteristic
173C2×C17×#117C2211yescharacteristic
174C17×#400C2211yescharacteristic
175C17×#398C2211yescharacteristic
176C17×#398C2211yescharacteristic
177C17×#395C2211yescharacteristic
178C17×#391C2211yescharacteristic
179C17×#389C2211yescharacteristic
180C17×#387C2211yescharacteristic
181C17×#387C2211yescharacteristic
182C17×#385C2211yescharacteristic
183C17×#385C2211yescharacteristic
184C17×#381C2211yescharacteristic
185C17×#380C2211yescharacteristic
186C2×C17×#95C2211yescharacteristic
187C22×Q8×C17C2311yescharacteristic
188C23×C4×C17C2311yescharacteristic
189C23×C4×C17C2311yescharacteristic
190C23×C4×C17C2311yescharacteristic
191C22×C22⋊D17C2311yescharacteristic
192C22×C22⋊D17C2311yescharacteristic
193C22×D68C2311yescharacteristic
194C22×C4×D17C2311yescharacteristic
195C22×C4×D17C2311yescharacteristic
196C22×C4×D17C2311yescharacteristic
197C22×C4×D17C2311yescharacteristic
198C22×Dic34C2311yescharacteristic
199C17×C22⋊Q8—42no—
200C17×#117—42no—
201C2×C4⋊C4×C17C2311yescharacteristic
202C2×C4⋊C4×C17C2311yescharacteristic
203C2×C4⋊C4×C17C2311yescharacteristic
204C2×C4⋊C4×C17C2311yescharacteristic
205C2×C4⋊C4×C17C2311yescharacteristic
206C2×C4⋊C4×C17C2311yescharacteristic
207C2×C4⋊C4×C17C2311yescharacteristic
208C2×C4⋊C4×C17C2311yescharacteristic
209C2×C4⋊C4×C17C2311yescharacteristic
210C2×C4⋊C4×C17C2311yescharacteristic
211C2×C4⋊C4×C17C2311yescharacteristic
212C2×C22⋊C4×C17C2311yescharacteristic
213C2×C22⋊C4×C17C2311yescharacteristic
214C2×C22⋊C4×C17C2311yescharacteristic
215C2×C22⋊C4×C17C2311yescharacteristic
216C2×C42×C17C2311yescharacteristic
217C2×C42×C17C2311yescharacteristic
218C2×C22⋊Dic17C2311yescharacteristic
219C2×C22⋊Dic17C2311yescharacteristic
220C2×C22⋊Dic17C2311yescharacteristic
221C2×C22⋊Dic17C2311yescharacteristic
222C2×C22⋊Dic17C2311yescharacteristic
223C2×C22⋊Dic17C2311yescharacteristic
224#10587632—42no—
225C4×C22⋊D17—24no—
226C4×C22⋊D17—24no—
227C2×#63227C2311yescharacteristic
228C2×#63227C2311yescharacteristic
229C2×#63227C2311yescharacteristic
230C2×#63227C2311yescharacteristic
231C2×#63227C2311yescharacteristic
232C2×#63227C2311yescharacteristic
233C2×#63227C2311yescharacteristic
234C2×#63227C2311yescharacteristic
235C2×#63227C2311yescharacteristic
236C2×#63227C2311yescharacteristic
237C2×#63227C2311yescharacteristic
238C2×#63227C2311yescharacteristic
239C2×#63227C2311yescharacteristic
240C2×#63227C2311yescharacteristic
241C2×#63227C2311yescharacteristic
242C2×#63227C2311yescharacteristic
243C2×#63227C2311yescharacteristic
244C2×#63227C2311yescharacteristic
245C2×#63227C2311yescharacteristic
246C2×#63227C2311yescharacteristic
247C2×#63227C2311yescharacteristic
248C2×#63227C2311yescharacteristic
249C2×C4⋊Dic17C2311yescharacteristic
250C2×C4⋊Dic17C2311yescharacteristic
251C2×C4⋊Dic17C2311yescharacteristic
252C2×C4⋊Dic17C2311yescharacteristic
253C2×C4⋊Dic17C2311yescharacteristic
254C2×C4⋊Dic17C2311yescharacteristic
255C2×C4⋊Dic17C2311yescharacteristic
256C2×C4⋊Dic17C2311yescharacteristic
257C2×C4⋊Dic17C2311yescharacteristic
258C2×C4⋊Dic17C2311yescharacteristic
259C2×C4⋊Dic17C2311yescharacteristic
260C2×C4⋊Dic17C2311yescharacteristic
261#10587610—24no—
262C2×#63225C2311yescharacteristic
263C2×#63225C2311yescharacteristic
264C2×#63225C2311yescharacteristic
265C2×#63225C2311yescharacteristic
266C2×#63225C2311yescharacteristic
267C2×#63225C2311yescharacteristic
268C2×#63225C2311yescharacteristic
269C2×#63225C2311yescharacteristic
270C2×#63225C2311yescharacteristic
271C2×#63225C2311yescharacteristic
272C2×#63225C2311yescharacteristic
273C2×#63225C2311yescharacteristic
274C2×#63225C2311yescharacteristic
275C2×#63225C2311yescharacteristic
276C2×C4×Dic17C2311yescharacteristic
277C2×C4×Dic17C2311yescharacteristic
278C2×C4×Dic17C2311yescharacteristic
279C2×C4×Dic17C2311yescharacteristic
280C2×C4×Dic17C2311yescharacteristic
281C2×C4×Dic17C2311yescharacteristic
282C2×C4×Dic17C2311yescharacteristic
283C2×C4×Dic17C2311yescharacteristic
284C2×C4×Dic17C2311yescharacteristic
285C2×C4×Dic17C2311yescharacteristic
286#10587584—42no—
287#10587583—42no—
288C42×D17—42no—
289C17×#95C2311yescharacteristic
290C17×#95C2311yescharacteristic
291C17×#95C2311yescharacteristic
292C17×#95C2311yescharacteristic
293C17×#95C2311yescharacteristic
294C17×#95C2311yescharacteristic
295C17×#95C2311yescharacteristic
296C17×#95C2311yescharacteristic
297C17×#95C2311yescharacteristic
298C17×#95C2311yescharacteristic
299C17×#95C2311yescharacteristic
300C17×#95C2311yescharacteristic
301C17×#95C2311yescharacteristic
302C17×#95C2311yescharacteristic
303#10587502C2311yescharacteristic
304#10587502C2311yescharacteristic
305#10587502C2311yescharacteristic
306#10587502C2311yescharacteristic
307#10587502C2311yescharacteristic
308#10587502C2311yescharacteristic
309#10587502C2311yescharacteristic
310#10587502C2311yescharacteristic
311#10587502C2311yescharacteristic
312#10587502C2311yescharacteristic
313#10587502C2311yescharacteristic
314#10587502C2311yescharacteristic
315#10587502C2311yescharacteristic
316#10587502C2311yescharacteristic
317#10587502C2311yescharacteristic
318#10587502C2311yescharacteristic
319#10587502C2311yescharacteristic
320#10587502C2311yescharacteristic
321#10587502C2311yescharacteristic
322#10587502C2311yescharacteristic
323#10587502C2311yescharacteristic
324#10587502C2311yescharacteristic
325#10587502C2311yescharacteristic
326#10587502C2311yescharacteristic
327#10587502C2311yescharacteristic
328#10587502C2311yescharacteristic
329#10587502C2311yescharacteristic
330#10587502C2311yescharacteristic
331#10587502C2311yescharacteristic
332#10587502C2311yescharacteristic
333#10587502C2311yescharacteristic
334#10587502C2311yescharacteristic
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
351C24×C17C2411yescharacteristic
352C23×D17C2411yescharacteristic
353C23×D17C2411yescharacteristic
354C2×Q8×C17—22no—
355C2×Q8×C17—41no—
356C2×Q8×C17—41no—
357C22×C4×C17—41no—
358C22×C4×C17—41no—
359C22×C4×C17—41no—
360C22×C4×C17—41no—
361C22×C4×C17—41no—
362C22×C4×C17—41no—
363C22×C4×C17—41no—
364C22×C4×C17—41no—
365C22×C4×C17#4114yes—
366C22×C4×C17C2411yescharacteristic
367C22×C4×C17C2411yescharacteristic
368C22×C4×C17C2411yescharacteristic
369C22×C4×C17C2411yescharacteristic
370C22×C4×C17C2411yescharacteristic
371C22×C4×C17C2411yescharacteristic
372C22×C4×C17C2411yescharacteristic
373C22×C4×C17C2411yescharacteristic
374C22×C4×C17C2411yescharacteristic
375C22×C4×C17C2411yescharacteristic
376C22×C4×C17C2411yescharacteristic
377C22×C4×C17C2411yescharacteristic
378C22×C4×C17C2411yescharacteristic
379C22×C4×C17C2411yescharacteristic
380C2×C22⋊D17—22no—
381C2×C22⋊D17—22no—
382C2×C22⋊D17—22no—
383C2×C22⋊D17—41no—
384C2×C22⋊D17—41no—
385C2×C22⋊D17—41no—
386C22×Dic17C2411yescharacteristic
387C22×Dic17C2411yescharacteristic
388C22×Dic17C2411yescharacteristic
389C22×Dic17C2411yescharacteristic
390C22×Dic17C2411yescharacteristic
391C22×Dic17C2411yescharacteristic
392C22×Dic17C2411yescharacteristic
393C22×Dic17C2411yescharacteristic
394C22×Dic17C2411yescharacteristic
395C22×Dic17C2411yescharacteristic
396C22×Dic17C2411yescharacteristic
397C22×Dic17C2411yescharacteristic
398C22×Dic17C2411yescharacteristic
399C22×Dic17C2411yescharacteristic
400C2×D68—22no—
401C2×D68—41no—
402C2×D68—41no—
403C2×C4×D17—22no—
404C2×C4×D17—22no—
405C2×C4×D17—22no—
406C2×C4×D17—22no—
407C2×C4×D17—41no—
408C2×C4×D17—41no—
409C2×C4×D17—41no—
410C2×C4×D17—41no—
411C2×C4×D17—41no—
412C2×C4×D17—41no—
413C2×C4×D17—41no—
414C2×C4×D17—41no—
415C2×Dic34—22no—
416C2×Dic34—41no—
417C2×Dic34—41no—
418C4⋊C4×C17—22no—
419C4⋊C4×C17—22no—
420C4⋊C4×C17—41no—
421C4⋊C4×C17—41no—
422C4⋊C4×C17—41no—
423C4⋊C4×C17—41no—
424C4⋊C4×C17—41no—
425C4⋊C4×C17—41no—
426C4⋊C4×C17—41no—
427C4⋊C4×C17—41no—
428C4⋊C4×C17—41no—
429C22⋊C4×C17—22no—
430C22⋊C4×C17—41no—
431C22⋊C4×C17—41no—
432C22⋊C4×C17—41no—
433C42×C17—22no—
434C42×C17—41no—
435C22⋊Dic17—22no—
436C22⋊Dic17—22no—
437C22⋊Dic17—22no—
438C22⋊Dic17—22no—
439C22⋊Dic17—41no—
440C22⋊Dic17—41no—
441#63227—22no—
442#63227—22no—
443#63227—22no—
444#63227—22no—
445#63227—22no—
446#63227—41no—
447#63227—41no—
448#63227—41no—
449#63227—41no—
450#63227—41no—
451#63227—41no—
452#63227—41no—
453#63227—41no—
454#63227—41no—
455#63227—41no—
456#63227—41no—
457#63227—41no—
458#63227—41no—
459#63227—41no—
460#63227—41no—
461#63227—41no—
462#63227—41no—
463C4⋊Dic17—22no—
464C4⋊Dic17—22no—
465C4⋊Dic17—41no—
466C4⋊Dic17—41no—
467C4⋊Dic17—41no—
468C4⋊Dic17—41no—
469C4⋊Dic17—41no—
470C4⋊Dic17—41no—
471C4⋊Dic17—41no—
472C4⋊Dic17—41no—
473C4⋊Dic17—41no—
474C4⋊Dic17—41no—
475#63225—22no—
476#63225—22no—
477#63225—22no—
478#63225—22no—
479#63225—41no—
480#63225—41no—
481#63225—41no—
482#63225—41no—
483#63225—41no—
484#63225—41no—
485#63225—41no—
486#63225—41no—
487#63225—41no—
488#63225—41no—
489C4×Dic17—22no—
490C4×Dic17—22no—
491C4×Dic17—22no—
492C4×Dic17—41no—
493C4×Dic17—41no—
494C4×Dic17—41no—
495C4×Dic17—41no—
496C4×Dic17—41no—
497C4×Dic17—41no—
498C4×Dic17—41no—
499#36790—171nomaximal, Sylow
500C23×C17—21no—
501C23×C17—21no—
502C23×C17—21no—
503C23×C17—21no—
504C23×C17—21no—
505C23×C17—21no—
506C23×C17C2×#4112yes—
507C23×C17C2511yescharacteristic
508C22×D17—21no—
509C22×D17—21no—
510C22×D17—21no—
511C22×D17—21no—
512C22×D17—21no—
513C22×D17—21no—
514C22×D17—21no—
515C22×D17—21no—
516C22×D17—21no—
517C22×D17—21no—
518C22×D17—21no—
519C22×D17—21no—
520C22×D17—21no—
521C22×D172−1+412yes—
522Q8×C17—82no—
523C2×C4×C17—21no—
524C2×C4×C17—21no—
525C2×C4×C17—21no—
526C2×C4×C17—21no—
527C2×C4×C17—21no—
528C2×C4×C17—21no—
529C2×C4×C17—21no—
530C2×C4×C17—21no—
531C2×C4×C17—21no—
532C2×C4×C17—21no—
533C2×C4×C17—21no—
534C2×C4×C17—21no—
535C2×C4×C17—21no—
536C2×C4×C17—21no—
537C2×C4×C17—21no—
538C2×C4×C17—21no—
539C2×C4×C17—21no—
540C2×C4×C17—21no—
541C2×C4×C17—21no—
542C2×C4×C17—21no—
543C2×C4×C17—21no—
544C2×C4×C17—21no—
545C2×C4×C17—21no—
546C2×C4×C17—21no—
547C2×C4×C17—21no—
548C2×C4×C17—21no—
549C2×C4×C17—21no—
550C2×C4×C17—21no—
551C2×C4×C17—21no—
552C2×C4×C17—21no—
553C2×C4×C17—21no—
554C2×C4×C17—21no—
555C2×C4×C17—21no—
556C2×C4×C17—21no—
557C2×C4×C17—21no—
558C2×C4×C17—21no—
559C2×C4×C17—21no—
560C2×C4×C17—21no—
561C2×C4×C17—21no—
562C2×C4×C17—44no—
563C2×C4×C17—82no—
564C2×C4×C17—82no—
565C2×C4×C17C2×#4112yes—
566C2×C4×C17C2×#4112yes—
567C2×C4×C17H(5,𝔽2)12yes—
568C22⋊D17—44no—
569C22⋊D17—44no—
570C2×Dic17—21no—
571C2×Dic17—21no—
572C2×Dic17—21no—
573C2×Dic17—21no—
574C2×Dic17—21no—
575C2×Dic17—21no—
576C2×Dic17—21no—
577C2×Dic17—21no—
578C2×Dic17—21no—
579C2×Dic17—21no—
580C2×Dic17—21no—
581C2×Dic17—21no—
582C2×Dic17—21no—
583C2×Dic17—21no—
584C2×Dic17—21no—
585C2×Dic17—21no—
586C2×Dic17—21no—
587C2×Dic17—21no—
588C2×Dic17—21no—
589C2×Dic17—21no—
590C2×Dic17—21no—
591C2×Dic17—21no—
592C2×Dic17—21no—
593C2×Dic17—21no—
594C2×Dic17—21no—
595C2×Dic17—21no—
596C2×Dic17—21no—
597C2×Dic17—21no—
598C2×Dic17—21no—
599C2×Dic17—21no—
600C2×Dic17—21no—
601C2×Dic17—21no—
602C2×Dic17—21no—
603C2×Dic17—21no—
604C2×Dic17—21no—
605C2×Dic17—21no—
606C2×Dic17—21no—
607C2×Dic17—21no—
608C2×Dic17—21no—
609C2×Dic17—21no—
610C2×Dic17—21no—
611C2×Dic17—21no—
612D68—82no—
613C4×D17—44no—
614C4×D17—44no—
615C4×D17—44no—
616C4×D17—82no—
617Dic34—82no—
618#2855—171no—
619#2852—171no—
620#2778—171no—
621#2770—171no—
622#2770—171no—
623#2768—171no—
624#2764—171no—
625#2762—171no—
626#2758—171no—
627#2750—171no—
628#2749—171no—
629#2747—171no—
630#2743—171no—
631#2741—171no—
632#2728—171no—
633#2702—171no—
634#2692—171no—
635#2689—171no—
636#2655—171no—
637#2654—171no—
638#2600—171no—
639#2595—171no—
640#2587—171no—
641#2564—171no—
642#2533—171no—
643#2532—171no—
644#2438D1711yescharacteristic, complemented
645#2415—171no—
646#2332—171no—
647#2318—171no—
648#2290—171no—
649C22×C17—22no—
650C22×C17—22no—
651C22×C17—22no—
652C22×C17—41no—
653C22×C17—41no—
654C22×C17—41no—
655C22×C17—41no—
656C22×C17C22×#4111yescharacteristic
657C22×C17C2×H(5,𝔽2)11yescharacteristic
658C22×C17C2×2−1+411yescharacteristic
659C22×C17#58511yescharacteristic
660C22×C17#58511yescharacteristic
661C22×C17#58511yescharacteristic
662C22×C17#58511yescharacteristic
663C2×D17—22no—
664C2×D17—22no—
665C2×D17—22no—
666C2×D17—41no—
667C2×D17—41no—
668C2×D17—41no—
669C2×D17—41no—
670C2×D17—41no—
671C2×D17—41no—
672C2×D17—41no—
673C2×D17—41no—
674C2×D17—41no—
675C2×D17—41no—
676C2×D17—41no—
677C4×C17—22no—
678C4×C17—22no—
679C4×C17—22no—
680C4×C17—41no—
681C4×C17—41no—
682C4×C17—41no—
683C4×C17—41no—
684C4×C17—41no—
685C4×C17—41no—
686C4×C17—41no—
687C4×C17—41no—
688C4×C17—41no—
689C4×C17—41no—
690C4×C17—41no—
691Dic17—41no—
692Dic17—41no—
693Dic17—41no—
694Dic17—41no—
695Dic17—41no—
696Dic17—41no—
697Dic17—41no—
698Dic17—41no—
699Dic17—41no—
700Dic17—41no—
701Dic17—41no—
702Dic17—41no—
703Dic17—41no—
704Dic17—41no—
705C2×#126—171no—
706C2×C22⋊Q8—171no—
707C2×C22⋊Q8—171no—
708C2×C22⋊Q8—171no—
709C2×C22⋊Q8C2×D1711yescharacteristic
710C2×C4×D4—171no—
711C2×C4×D4—171no—
712C2×#117C2×D1711yescharacteristic
713C22×C42—171no—
714#401—171no—
715#400—171no—
716#400—171no—
717#400—171no—
718#400—171no—
719#400—171no—
720#400—171no—
721#400—171no—
722#400—171no—
723#400—171no—
724#400—171no—
725#400—171no—
726#400—171no—
727#400—171no—
728#400—171no—
729#400C2×D1711yescharacteristic
730#399—171no—
731#399—171no—
732#398—171no—
733#398—171no—
734#398—171no—
735#398—171no—
736#398—171no—
737#398—171no—
738#398—171no—
739#398C2×D1711yescharacteristic
740#398C2×D1711yescharacteristic
741#397—171no—
742#397—171no—
743#397—171no—
744#397—171no—
745#397—171no—
746#397—171no—
747#397—171no—
748#397—171no—
749#396—171no—
750#396—171no—
751#396—171no—
752#395—171no—
753#395C2×D1711yescharacteristic
754#394—171no—
755#394—171no—
756#394—171no—
757#394—171no—
758#394—171no—
759#393—171no—
760#393—171no—
761#392—171no—
762#391—171no—
763#391—171no—
764#391—171no—
765#391—171no—
766#391—171no—
767#391C2×D1711yescharacteristic
768#390—171no—
769#389—171no—
770#389—171no—
771#389—171no—
772#389—171no—
773#389—171no—
774#389—171no—
775#389C2×D1711yescharacteristic
776#388—171no—
777#388—171no—
778#388—171no—
779#388—171no—
780#388—171no—
781#388—171no—
782#388—171no—
783#388—171no—
784#388—171no—
785#388—171no—
786#388—171no—
787#388—171no—
788#388—171no—
789#388—171no—
790#388—171no—
791#388—171no—
792#388—171no—
793#388—171no—
794#388—171no—
795#387—171no—
796#387—171no—
797#387—171no—
798#387—171no—
799#387—171no—
800#387—171no—
801#387—171no—
802#387—171no—
803#387—171no—
804#387—171no—
805#387—171no—
806#387—171no—
807#387—171no—
808#387—171no—
809#387—171no—
810#387—171no—
811#387—171no—
812#387—171no—
813#387—171no—
814#387C2×D1711yescharacteristic
815#387C2×D1711yescharacteristic
816#386—171no—
817#386—171no—
818#386—171no—
819#386—171no—
820#386—171no—
821#386—171no—
822#386—171no—
823#386—171no—
824#386—171no—
825#386—171no—
826#385—171no—
827#385—171no—
828#385—171no—
829#385—171no—
830#385—171no—
831#385—171no—
832#385—171no—
833#385—171no—
834#385—171no—
835#385—171no—
836#385C2×D1711yescharacteristic
837#385C2×D1711yescharacteristic
838#383—171no—
839#383—171no—
840#383—171no—
841#383—171no—
842#382—171no—
843#381—171no—
844#381—171no—
845#381—171no—
846#381C2×D1711yescharacteristic
847#380—171no—
848#380—171no—
849#380—171no—
850#380—171no—
851#380—171no—
852#380C2×D1711yescharacteristic
853C4×C4⋊C4—171no—
854C4×C4⋊C4—171no—
855C4×C4⋊C4—171no—
856C4×C22⋊C4—171no—
857C4×C22⋊C4—171no—
858#376—171no—
859C2×#95C2×D1711yescharacteristic
860C2×C17—42no—
861C2×C17#345511yescharacteristic
862C2×C17#349511yescharacteristic
863C2×C17#350511yescharacteristic
864C2×C17#353311yescharacteristic
865C2×C17#354111yescharacteristic
866C2×C17#356411yescharacteristic
867C2×C17#356611yescharacteristic
868D17—42no—
869D17—81no—
870C22×Q8—171no—
871C22×Q8C22×D1711yescharacteristic
872C22×D4—171no—
873C22×D4—171no—
874C22×D4—171no—
875C23×C4—171no—
876C23×C4—171no—
877C23×C4—171no—
878C23×C4—171no—
879C23×C4C22×D1711yescharacteristic
880C23×C4C22×D1711yescharacteristic
881C23×C4C22×D1711yescharacteristic
882#126—682no—
883C22⋊Q8—42no—
884C22⋊Q8—344no—
885C22⋊Q8—682no—
886C22⋊Q8—682no—
887C4×D4—344no—
888C4×D4—344no—
889#117—42no—
890C2×C4⋊C4—171no—
891C2×C4⋊C4—171no—
892C2×C4⋊C4—171no—
893C2×C4⋊C4—171no—
894C2×C4⋊C4—171no—
895C2×C4⋊C4—171no—
896C2×C4⋊C4—171no—
897C2×C4⋊C4—171no—
898C2×C4⋊C4—171no—
899C2×C4⋊C4—171no—
900C2×C4⋊C4—171no—
901C2×C4⋊C4—171no—
902C2×C4⋊C4—171no—
903C2×C4⋊C4—171no—
904C2×C4⋊C4—171no—
905C2×C4⋊C4—171no—
906C2×C4⋊C4—171no—
907C2×C4⋊C4—171no—
908C2×C4⋊C4—171no—
909C2×C4⋊C4—171no—
910C2×C4⋊C4—171no—
911C2×C4⋊C4—171no—
912C2×C4⋊C4—171no—
913C2×C4⋊C4—171no—
914C2×C4⋊C4—171no—
915C2×C4⋊C4—171no—
916C2×C4⋊C4C22×D1711yescharacteristic
917C2×C4⋊C4C22×D1711yescharacteristic
918C2×C4⋊C4C22×D1711yescharacteristic
919C2×C4⋊C4C22×D1711yescharacteristic
920C2×C4⋊C4C22×D1711yescharacteristic
921C2×C4⋊C4C22×D1711yescharacteristic
922C2×C4⋊C4C22×D1711yescharacteristic
923C2×C4⋊C4C22×D1711yescharacteristic
924C2×C4⋊C4C22×D1711yescharacteristic
925C2×C4⋊C4C22×D1711yescharacteristic
926C2×C4⋊C4C22×D1711yescharacteristic
927C2×C22⋊C4—171no—
928C2×C22⋊C4—171no—
929C2×C22⋊C4—171no—
930C2×C22⋊C4—171no—
931C2×C22⋊C4—171no—
932C2×C22⋊C4—171no—
933C2×C22⋊C4—171no—
934C2×C22⋊C4—171no—
935C2×C22⋊C4—171no—
936C2×C22⋊C4—171no—
937C2×C22⋊C4—171no—
938C2×C22⋊C4—171no—
939C2×C22⋊C4—171no—
940C2×C22⋊C4—171no—
941C2×C22⋊C4—171no—
942C2×C22⋊C4—171no—
943C2×C22⋊C4—171no—
944C2×C22⋊C4—171no—
945C2×C22⋊C4—171no—
946C2×C22⋊C4—171no—
947C2×C22⋊C4—171no—
948C2×C22⋊C4—171no—
949C2×C22⋊C4—171no—
950C2×C22⋊C4—171no—
951C2×C22⋊C4—171no—
952C2×C22⋊C4—171no—
953C2×C22⋊C4—171no—
954C2×C22⋊C4—171no—
955C2×C22⋊C4C22×D1711yescharacteristic
956C2×C22⋊C4C22×D1711yescharacteristic
957C2×C22⋊C4C22×D1711yescharacteristic
958C2×C22⋊C4C22×D1711yescharacteristic
959C2×C42—171no—
960C2×C42—171no—
961C2×C42—171no—
962C2×C42—171no—
963C2×C42—171no—
964C2×C42—171no—
965C2×C42—171no—
966C2×C42—171no—
967C2×C42—171no—
968C2×C42—171no—
969C2×C42—682no—
970C2×C42C22×D1711yescharacteristic
971C2×C42C22×D1711yescharacteristic
972#95—171no—
973#95—171no—
974#95—171no—
975#95—171no—
976#95—171no—
977#95—171no—
978#95—171no—
979#95—171no—
980#95—171no—
981#95—171no—
982#95—171no—
983#95—171no—
984#95—171no—
985#95—171no—
986#95—171no—
987#95—171no—
988#95—171no—
989#95—171no—
990#95—171no—
991#95—171no—
992#95—171no—
993#95—171no—
994#95—171no—
995#95—171no—
996#95—171no—
997#95—171no—
998#95—171no—
999#95—171no—
1000#95—171no—
1001#95—171no—
1002#95—171no—
1003#95—171no—
1004#95—171no—
1005#95—171no—
1006#95—171no—
1007#95—171no—
1008#95—171no—
1009#95—171no—
1010#95—171no—
1011#95—171no—
1012#95—171no—
1013#95—171no—
1014#95—171no—
1015#95—171no—
1016#95—171no—
1017#95—171no—
1018#95—171no—
1019#95—171no—
1020#95C22×D1711yescharacteristic
1021#95C22×D1711yescharacteristic
1022#95C22×D1711yescharacteristic
1023#95C22×D1711yescharacteristic
1024#95C22×D1711yescharacteristic
1025#95C22×D1711yescharacteristic
1026#95C22×D1711yescharacteristic
1027#95C22×D1711yescharacteristic
1028#95C22×D1711yescharacteristic
1029#95C22×D1711yescharacteristic
1030#95C22×D1711yescharacteristic
1031#95C22×D1711yescharacteristic
1032#95C22×D1711yescharacteristic
1033#95C22×D1711yescharacteristic
1034C17#3679011yescharacteristic, complemented, Sylow
1035C24—171no—
1036C24—171no—
1037C24C23×D1711yescharacteristic
1038C2×Q8—22no—
1039C2×Q8—41no—
1040C2×Q8—41no—
1041C2×Q8—342no—
1042C2×Q8—681no—
1043C2×Q8—681no—
1044C2×D4—342no—
1045C2×D4—342no—
1046C2×D4—342no—
1047C2×D4—342no—
1048C2×D4—681no—
1049C2×D4—681no—
1050C2×D4—681no—
1051C2×D4—681no—
1052C2×D4—681no—
1053C22×C4—41no—
1054C22×C4—41no—
1055C22×C4—41no—
1056C22×C4—41no—
1057C22×C4—41no—
1058C22×C4—41no—
1059C22×C4—41no—
1060C22×C4—41no—
1061C22×C4—171no—
1062C22×C4—171no—
1063C22×C4—171no—
1064C22×C4—171no—
1065C22×C4—171no—
1066C22×C4—171no—
1067C22×C4—171no—
1068C22×C4—171no—
1069C22×C4—171no—
1070C22×C4—171no—
1071C22×C4—171no—
1072C22×C4—171no—
1073C22×C4—171no—
1074C22×C4—171no—
1075C22×C4—342no—
1076C22×C4—342no—
1077C22×C4—342no—
1078C22×C4—342no—
1079C22×C4—681no—
1080C22×C4—681no—
1081C22×C4—681no—
1082C22×C4—681no—
1083C22×C4—681no—
1084C22×C4—681no—
1085C22×C4—681no—
1086C22×C4—681no—
1087C22×C4#6325614yes—
1088C22×C4C23×D1711yescharacteristic
1089C22×C4C23×D1711yescharacteristic
1090C22×C4C23×D1711yescharacteristic
1091C22×C4C23×D1711yescharacteristic
1092C22×C4C23×D1711yescharacteristic
1093C22×C4C23×D1711yescharacteristic
1094C22×C4C23×D1711yescharacteristic
1095C22×C4C23×D1711yescharacteristic
1096C22×C4C23×D1711yescharacteristic
1097C22×C4C23×D1711yescharacteristic
1098C22×C4C23×D1711yescharacteristic
1099C22×C4C23×D1711yescharacteristic
1100C22×C4C23×D1711yescharacteristic
1101C22×C4C23×D1711yescharacteristic
1102C4⋊C4—22no—
1103C4⋊C4—22no—
1104C4⋊C4—41no—
1105C4⋊C4—41no—
1106C4⋊C4—41no—
1107C4⋊C4—41no—
1108C4⋊C4—41no—
1109C4⋊C4—41no—
1110C4⋊C4—41no—
1111C4⋊C4—41no—
1112C4⋊C4—41no—
1113C4⋊C4—342no—
1114C4⋊C4—342no—
1115C4⋊C4—342no—
1116C4⋊C4—342no—
1117C4⋊C4—342no—
1118C4⋊C4—342no—
1119C4⋊C4—681no—
1120C4⋊C4—681no—
1121C4⋊C4—681no—
1122C4⋊C4—681no—
1123C4⋊C4—681no—
1124C4⋊C4—681no—
1125C4⋊C4—681no—
1126C4⋊C4—681no—
1127C4⋊C4—681no—
1128C4⋊C4—681no—
1129C4⋊C4—681no—
1130C4⋊C4—681no—
1131C4⋊C4—681no—
1132C4⋊C4—681no—
1133C4⋊C4—681no—
1134C4⋊C4—681no—
1135C4⋊C4—681no—
1136C4⋊C4—681no—
1137C4⋊C4—681no—
1138C4⋊C4—681no—
1139C22⋊C4—22no—
1140C22⋊C4—41no—
1141C22⋊C4—41no—
1142C22⋊C4—41no—
1143C22⋊C4—342no—
1144C22⋊C4—342no—
1145C22⋊C4—342no—
1146C22⋊C4—342no—
1147C22⋊C4—342no—
1148C22⋊C4—342no—
1149C22⋊C4—342no—
1150C22⋊C4—342no—
1151C22⋊C4—342no—
1152C22⋊C4—681no—
1153C22⋊C4—681no—
1154C22⋊C4—681no—
1155C22⋊C4—681no—
1156C22⋊C4—681no—
1157C22⋊C4—681no—
1158C22⋊C4—681no—
1159C22⋊C4—681no—
1160C22⋊C4—681no—
1161C22⋊C4—681no—
1162C22⋊C4—681no—
1163C22⋊C4—681no—
1164C22⋊C4—681no—
1165C22⋊C4—681no—
1166C22⋊C4—681no—
1167C22⋊C4—681no—
1168C22⋊C4—681no—
1169C22⋊C4—681no—
1170C22⋊C4—681no—
1171C42—22no—
1172C42—41no—
1173C42—342no—
1174C42—342no—
1175C42—342no—
1176C42—681no—
1177C42—681no—
1178C42—681no—
1179C42—681no—
1180C42—681no—
1181C42—681no—
1182C42—681no—
1183C23—21no—
1184C23—21no—
1185C23—21no—
1186C23—21no—
1187C23—21no—
1188C23—21no—
1189C23—172no—
1190C23—341no—
1191C23—341no—
1192C23—341no—
1193C23—341no—
1194C23—341no—
1195C23—341no—
1196C23—341no—
1197C23—341no—
1198C23—341no—
1199C23—341no—
1200C23—341no—
1201C23—341no—
1202C23—341no—
1203C23C2×#6325612yes—
1204C23C24×D1711yescharacteristic
1205Q8—82no—
1206Q8—1362no—
1207D4—684no—
1208D4—684no—
1209D4—1362no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—44no—
1250C2×C4—82no—
1251C2×C4—82no—
1252C2×C4—341no—
1253C2×C4—341no—
1254C2×C4—341no—
1255C2×C4—341no—
1256C2×C4—341no—
1257C2×C4—341no—
1258C2×C4—341no—
1259C2×C4—341no—
1260C2×C4—341no—
1261C2×C4—341no—
1262C2×C4—341no—
1263C2×C4—341no—
1264C2×C4—341no—
1265C2×C4—341no—
1266C2×C4—341no—
1267C2×C4—341no—
1268C2×C4—341no—
1269C2×C4—341no—
1270C2×C4—341no—
1271C2×C4—341no—
1272C2×C4—341no—
1273C2×C4—341no—
1274C2×C4—341no—
1275C2×C4—341no—
1276C2×C4—341no—
1277C2×C4—341no—
1278C2×C4—341no—
1279C2×C4—341no—
1280C2×C4—341no—
1281C2×C4—341no—
1282C2×C4—341no—
1283C2×C4—341no—
1284C2×C4—341no—
1285C2×C4—341no—
1286C2×C4—341no—
1287C2×C4—341no—
1288C2×C4—341no—
1289C2×C4—341no—
1290C2×C4—341no—
1291C2×C4—341no—
1292C2×C4—341no—
1293C2×C4—341no—
1294C2×C4—684no—
1295C2×C4—684no—
1296C2×C4—684no—
1297C2×C4—1362no—
1298C2×C4#1058769112yes—
1299C2×C4C2×#6325612yes—
1300C2×C4C2×#6325612yes—
1301C22—22no—
1302C22—22no—
1303C22—22no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—342no—
1309C22—342no—
1310C22—342no—
1311C22—681no—
1312C22—681no—
1313C22—681no—
1314C22—681no—
1315C22—681no—
1316C22—681no—
1317C22—681no—
1318C22—681no—
1319C22—681no—
1320C22—681no—
1321C22—681no—
1322C22C22×#6325611yescharacteristic
1323C22C2×#1058769111yescharacteristic
1324C222−1+4×D1711yescharacteristic
1325C22#1176364411yescharacteristic
1326C22#1176364511yescharacteristic
1327C22#1176364511yescharacteristic
1328C22#1176364511yescharacteristic
1329C4—22no—
1330C4—22no—
1331C4—22no—
1332C4—41no—
1333C4—41no—
1334C4—41no—
1335C4—41no—
1336C4—41no—
1337C4—41no—
1338C4—41no—
1339C4—41no—
1340C4—41no—
1341C4—41no—
1342C4—41no—
1343C4—681no—
1344C4—681no—
1345C4—681no—
1346C4—681no—
1347C4—681no—
1348C4—681no—
1349C4—681no—
1350C4—681no—
1351C4—681no—
1352C4—681no—
1353C4—681no—
1354C4—681no—
1355C4—681no—
1356C4—681no—
1357C2—42no—
1358C2—682no—
1359C2—1361no—
1360C2#1454217611yescharacteristic
1361C2#1454253911yescharacteristic
1362C2#1454262511yescharacteristic
1363C2#1454294311yescharacteristic
1364C2#1454306711yescharacteristic
1365C2#1454339511yescharacteristic
1366C2#1454344611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2438C2
prime radical#11762718C22
hypercenter#2438D17
hypocenterC17#36790
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2438

Complements

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

NH ≅ G/Ntype
1. #14537125C2semidirect
2. #14537102C2semidirect
4. #14536286C2semidirect
5. #14536286C2semidirect
6. #14536270C2semidirect
7. #14536203C2semidirect
8. #14536192C2semidirect
9. #14536138C2semidirect
10. #14536023C2semidirect
12. #14535982C2semidirect
13. #14535922C2semidirect
14. #14535895C2semidirect
15. #14535751C2semidirect
16. #14535408C2semidirect
17. #14535287C2semidirect
18. #14535242C2semidirect
19. #14534883C2semidirect
20. #14534868C2semidirect
22. #14534312C2semidirect
23. #14534212C2semidirect
24. #14533964C2semidirect
25. #14533668C2semidirect
26. #14533653C2semidirect
27. #14532207C2semidirect
28. #14531537C2semidirect
29. #14531418C2semidirect
30. #14531221C2semidirect
31. C17×#2438C2semidirect
644. #2438D17semidirect
1034. C17#36790semidirect

Maximal subgroups

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

subgroupindex
#145371252
#145371022
#145363962
#145362862
#145362702
#145362032
#145361922
#145361382
#145360232
#145360082
#145359822
#145359222
#145358952
#145357512
#145354082
#145352872
#145352422
#145348832
#145348682
#145343712
#145343122
#145342122
#145339642
#145336682
#145336532
#145322072
#145315372
#145314182
#145312212
C17×#24382
#3679017