Finite Group Databasebeta

← #11861710

Subgroups — #11861710

Order 1152.

808 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593973C211yesmaximal, characteristic
2#10592389C211yesmaximal, characteristic, complemented
3C3×#4690C211yesmaximal, characteristic, complemented
4C3×C4×D3×C8C211yesmaximal, characteristic, complemented
5#10590785C211yesmaximal, characteristic, complemented
6#10590730C211yesmaximal, characteristic, complemented
7#10590727C211yesmaximal, characteristic, complemented
8#10590723C211yesmaximal, characteristic, complemented
9#10590721C211yesmaximal, characteristic, complemented
10#10590720C211yesmaximal, characteristic, complemented
11#10590717C211yesmaximal, characteristic, complemented
12#10590644C211yesmaximal, characteristic, complemented
13#10590321C211yesmaximal, characteristic, complemented
14#10590318C211yesmaximal, characteristic, complemented
15#10590262C211yesmaximal, characteristic, complemented
16#79366—31nomaximal
17#78448—31nomaximal
18#64081C2211yescharacteristic
19C2×C3×D3×C8C2211yescharacteristic
20C2×C3×D3×C8C2211yescharacteristic
21C3×#872C2211yescharacteristic
22C3×C42×D3C2211yescharacteristic
23C4×#627C2211yescharacteristic
24#63906C411yescharacteristic
25#63905C411yescharacteristic
26C4×#626C2211yescharacteristic
27C4×#626C2211yescharacteristic
28C4×#625C2211yescharacteristic
29#63868C411yescharacteristic
30#63867C411yescharacteristic
31#63859C411yescharacteristic
32#63852C411yescharacteristic
33#63851C411yescharacteristic
34#63850C411yescharacteristic
35C2×#3712C2211yescharacteristic
36C2×#3711C2211yescharacteristic
37C2×#3710C2211yescharacteristic
38C2×D3×C3⋊C8C2211yescharacteristic
39C32×C4×C8C2211yescharacteristic
40#63647C2211yescharacteristic
41#63647C2211yescharacteristic
42#63641C2211yescharacteristic
43#63641C2211yescharacteristic
44#63630C2211yescharacteristic
45C3×(C2×D3)⋊C8C2211yescharacteristic
46C3×(C2×D3)⋊C8C2211yescharacteristic
47C3×Dic3⋊C8C2211yescharacteristic
48C3×Dic3⋊C8C2211yescharacteristic
49C3×C8×Dic3C2211yescharacteristic
50C3×C8×Dic3C2211yescharacteristic
51C3×#803C2211yescharacteristic
52C3×C4×C3⋊C8C2211yescharacteristic
53Dic3⋊(C3⋊C8)C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
56(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
57#63555C2211yescharacteristic
58#63554C2211yescharacteristic
59#63553C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5528—31no—
62#5479—31no—
63C3×#433—31no—
64C2×C3×C4×C8—31no—
65#5111—31no—
66#5111—31no—
67C8×#67—31no—
68C8×#67—31no—
69#4997—31no—
70#4926—31no—
71#4836—31no—
72#4834—31no—
73#4830—31no—
74#4828—31no—
75#4729—31no—
76#4728—31no—
77#67⋊C8—31no—
78#67⋊C8—31no—
79#4708—31no—
80#4705—31no—
81#4690—31no—
82#4690—31no—
83#4690—61no—
84#4690D311yescharacteristic, complemented
85#4689—31no—
86#4689—31no—
87#4688—31no—
88C8×D12—31no—
89C4×D3×C8D311yescharacteristic, complemented
90#4679—31no—
91C8×Dic6—31no—
92C2×C4×C3⋊D3C2311yescharacteristic
93C2×C3×C4×D3C2×C411yescharacteristic
94C2×C3×C4×D3C2×C411yescharacteristic
95C2×C3×C4×D3C2311yescharacteristic
96C2×C3×C4×D3C2311yescharacteristic
97C2×#627C2×C411yescharacteristic
98C2×#626C2×C411yescharacteristic
99C2×#626C2×C411yescharacteristic
100C2×#625C2×C411yescharacteristic
101C2×C32×C8C2311yescharacteristic
102C2×C32×C8C2311yescharacteristic
103C32×C42C2311yescharacteristic
104#3752C2×C411yescharacteristic
105#3752C2×C411yescharacteristic
106#3750C2×C411yescharacteristic
107#3750C2×C411yescharacteristic
108C4×C3⋊Dic3C2311yescharacteristic
109C2×C3⋊(C3⋊C8)C2311yescharacteristic
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111C3×(C2×D3)⋊C4C2×C411yescharacteristic
112C3×(C2×D3)⋊C4C2×C411yescharacteristic
113C3×Dic3⋊C4C2×C411yescharacteristic
114C3×Dic3⋊C4C2×C411yescharacteristic
115C3×C4×Dic3C2×C411yescharacteristic
116C3×C4×Dic3C2×C411yescharacteristic
117C3×C4×Dic3C2311yescharacteristic
118C3×C4×Dic3C2311yescharacteristic
119C2×C3×C3⋊C8C2311yescharacteristic
120C2×C3×C3⋊C8C2311yescharacteristic
121C2×C3×C3⋊C8C2311yescharacteristic
122C2×C3×C3⋊C8C2311yescharacteristic
123C3×D3×C8—22no—
124C3×D3×C8—22no—
125#3724C2×C411yescharacteristic
126#3724C2×C411yescharacteristic
127Dic3⋊Dic3C2×C411yescharacteristic
128Dic3⋊Dic3C2×C411yescharacteristic
129Dic3⋊Dic3C2×C411yescharacteristic
130Dic3⋊Dic3C2×C411yescharacteristic
131#3722C2×C411yescharacteristic
132#3722C2×C411yescharacteristic
133(C2×D3)⋊Dic3C2×C411yescharacteristic
134(C2×D3)⋊Dic3C2×C411yescharacteristic
135(C2×D3)⋊Dic3C2×C411yescharacteristic
136(C2×D3)⋊Dic3C2×C411yescharacteristic
137#3712—22no—
138#3711—22no—
139#3710—22no—
140D3×C3⋊C8—22no—
141#2966—91noSylow
142C22×C3×C8—31no—
143C22×C3×C8—31no—
144C3×#117—31no—
145C2×C3×C42—31no—
146#930—31no—
147#929—31no—
148#929—31no—
149C4×#67—31no—
150C4×#67—31no—
151C4×#67—31no—
152C4×#67—31no—
153#924—31no—
154C2×#208—31no—
155C22×C3⋊C8—31no—
156C2×ΓL(1,𝔽25)—31no—
157C2×ΓL(1,𝔽25)—31no—
158C2×ΓL(1,𝔽25)—31no—
159C2×D3×C8—31no—
160C2×D3×C8—31no—
161C2×D3×C8—31no—
162C2×D3×C8C2×D311yescharacteristic
163C2×D3×C8C2×D311yescharacteristic
164#898—31no—
165#896—31no—
166#894—31no—
167#889—31no—
168#885—31no—
169#884—31no—
170#883—31no—
171#879—31no—
172#876—31no—
173#876—31no—
174#875—31no—
175C4×D12—31no—
176C4×D12—31no—
177#872—31no—
178#872—31no—
179#872—61no—
180#872C2×D311yescharacteristic
181C42×D3C2×D311yescharacteristic
182#870—31no—
183C4×Dic6—31no—
184C4×Dic6—31no—
185C3×C4⋊C8—31no—
186C3×C4⋊C8—31no—
187C3×C22⋊C8—31no—
188C3×C22⋊C8—31no—
189C3×#97—31no—
190C3×C4×C8—21no—
191C3×C4×C8—31no—
192C3×C4×C8—31no—
193C3×C4×C8—31no—
194C3×C4×C8C2×D311yescharacteristic
195C3×C4×C8C2×D311yescharacteristic
196#830—31no—
197#830—31no—
198(C2×D3)⋊C8—31no—
199(C2×D3)⋊C8—31no—
200(C2×D3)⋊C8—31no—
201(C2×D3)⋊C8—31no—
202(C2×D3)⋊C8—31no—
203(C2×D3)⋊C8—31no—
204(C2×D3)⋊C8—61no—
205(C2×D3)⋊C8—61no—
206(C2×D3)⋊C8C2×D311yescharacteristic
207(C2×D3)⋊C8C2×D311yescharacteristic
208#815—31no—
209#815—31no—
210#815—31no—
211Dic3⋊C8—31no—
212Dic3⋊C8—31no—
213Dic3⋊C8—31no—
214Dic3⋊C8—31no—
215Dic3⋊C8—31no—
216Dic3⋊C8—31no—
217Dic3⋊C8—61no—
218Dic3⋊C8—61no—
219Dic3⋊C8C2×D311yescharacteristic
220Dic3⋊C8C2×D311yescharacteristic
221C8×Dic3—31no—
222C8×Dic3—31no—
223C8×Dic3—31no—
224C8×Dic3C2×D311yescharacteristic
225C8×Dic3C2×D311yescharacteristic
226C4⋊(C3⋊C8)—31no—
227C4⋊(C3⋊C8)—31no—
228#803—31no—
229#803—31no—
230#803—31no—
231#803—61no—
232#803C2×D311yescharacteristic
233C4×C3⋊C8—31no—
234C4×C3⋊C8C2×D311yescharacteristic
235C22×C3⋊D3C22×C411yescharacteristic
236C22×C3×D3C22×C411yescharacteristic
237C22×C3×D3C22×C411yescharacteristic
238C2×C32×C4C22×C411yescharacteristic
239C2×C32×C4C22×C411yescharacteristic
240C2×C32×C4C2411yescharacteristic
241C2×C3⋊Dic3C22×C411yescharacteristic
242C2×C3⋊Dic3C22×C411yescharacteristic
243C2×C3⋊Dic3C22×C411yescharacteristic
244C4×C3⋊D3—21no—
245C4×C3⋊D3—21no—
246C2×C3×Dic3C22×C411yescharacteristic
247C2×C3×Dic3C22×C411yescharacteristic
248C2×C3×Dic3C22×C411yescharacteristic
249C2×C3×Dic3C22×C411yescharacteristic
250C2×C3×Dic3C22×C411yescharacteristic
251C2×C3×Dic3C22×C411yescharacteristic
252C3×C4×D3—22no—
253C3×C4×D3—21no—
254C3×C4×D3—21no—
255C3×C4×D3—21no—
256C3×C4×D3—21no—
257C3×C4×D3—22no—
258#627—22no—
259#626—22no—
260#626—22no—
261#625—22no—
262C32×C8—21no—
263C32×C8—21no—
264C3⋊(C3⋊C8)—21no—
265C3⋊(C3⋊C8)—21no—
266C3×C3⋊C8—21no—
267C3×C3⋊C8—21no—
268C3×C3⋊C8#4112yes—
269C3×C3⋊C8#4112yes—
270#529—91no—
271#446—91no—
272C8×Q8—91no—
273#436—91no—
274#435—91no—
275#435—91no—
276C8×D4—91no—
277C8×D4—91no—
278C8×D4—91no—
279#433—31no—
280#433—91no—
281#432—91no—
282#405—91no—
283#405—91no—
284C2×C4×C8—31no—
285C22×C3×C4—31no—
286C22×C3×C4—31no—
287C22×C3×C4—31no—
288C22×C3×C4—31no—
289C2×#67—31no—
290C2×#67—31no—
291C2×#67—31no—
292C2×#67—31no—
293C2×D12—31no—
294C2×D12—31no—
295C2×C4×D3—31no—
296C2×C4×D3—31no—
297C2×C4×D3—61no—
298C2×C4×D3C4×D311yescharacteristic
299C2×C4×D3C4×D311yescharacteristic
300C2×C4×D3C22×D311yescharacteristic
301C2×C4×D3C22×D311yescharacteristic
302C2×Dic6—31no—
303C2×Dic6—31no—
304C2×C3×C8—21no—
305C2×C3×C8—21no—
306C2×C3×C8—31no—
307C2×C3×C8—31no—
308C2×C3×C8—31no—
309C2×C3×C8—31no—
310C2×C3×C8—62no—
311C2×C3×C8—62no—
312C2×C3×C8C22×D311yescharacteristic
313C2×C3×C8C22×D311yescharacteristic
314C2×C3×C8C22×D311yescharacteristic
315C2×C3×C8C22×D311yescharacteristic
316C3×C4⋊C4—31no—
317C3×C4⋊C4—31no—
318C3×C22⋊C4—31no—
319C3×C22⋊C4—31no—
320C3×C42—21no—
321C3×C42—31no—
322C3×C42—31no—
323C3×C42—31no—
324C3×C42—31no—
325C3×C42C22×D311yescharacteristic
326C3×C42C22×D311yescharacteristic
327#217—31no—
328#217—31no—
329#217—31no—
330#217—31no—
331(C2×D3)⋊C4—31no—
332(C2×D3)⋊C4—31no—
333(C2×D3)⋊C4—31no—
334(C2×D3)⋊C4—31no—
335(C2×D3)⋊C4—31no—
336(C2×D3)⋊C4—31no—
337(C2×D3)⋊C4—31no—
338(C2×D3)⋊C4—31no—
339(C2×D3)⋊C4—31no—
340(C2×D3)⋊C4—31no—
341(C2×D3)⋊C4—31no—
342(C2×D3)⋊C4—31no—
343(C2×D3)⋊C4—61no—
344(C2×D3)⋊C4—61no—
345(C2×D3)⋊C4C4×D311yescharacteristic
346(C2×D3)⋊C4C4×D311yescharacteristic
347C4⋊Dic3—31no—
348C4⋊Dic3—31no—
349C4⋊Dic3—31no—
350C4⋊Dic3—31no—
351Dic3⋊C4—31no—
352Dic3⋊C4—31no—
353Dic3⋊C4—31no—
354Dic3⋊C4—31no—
355Dic3⋊C4—31no—
356Dic3⋊C4—31no—
357Dic3⋊C4—31no—
358Dic3⋊C4—31no—
359Dic3⋊C4—31no—
360Dic3⋊C4—31no—
361Dic3⋊C4—31no—
362Dic3⋊C4—31no—
363Dic3⋊C4—61no—
364Dic3⋊C4—61no—
365Dic3⋊C4C4×D311yescharacteristic
366Dic3⋊C4C4×D311yescharacteristic
367C4×Dic3—31no—
368C4×Dic3—31no—
369C4×Dic3—61no—
370C4×Dic3C4×D311yescharacteristic
371C4×Dic3C4×D311yescharacteristic
372C4×Dic3C22×D311yescharacteristic
373C4×Dic3C22×D311yescharacteristic
374#208—62no—
375C2×C3⋊C8—31no—
376C2×C3⋊C8—31no—
377C2×C3⋊C8—31no—
378C2×C3⋊C8—31no—
379C2×C3⋊C8—61no—
380C2×C3⋊C8—61no—
381C2×C3⋊C8—62no—
382C2×C3⋊C8C22×D311yescharacteristic
383C2×C3⋊C8C22×D311yescharacteristic
384C2×C3⋊C8C22×D311yescharacteristic
385C2×C3⋊C8C22×D311yescharacteristic
386ΓL(1,𝔽25)—62no—
387ΓL(1,𝔽25)—62no—
388ΓL(1,𝔽25)—62no—
389D3×C8—22no—
390D3×C8—22no—
391D3×C8—62no—
392D3×C8—62no—
393D3×C8—62no—
394C22×C32C23×C411yescharacteristic
395C2×C3⋊D3—21no—
396C2×C3⋊D3—21no—
397C2×C3⋊D3—21no—
398C2×C3×D3—21no—
399C2×C3×D3—21no—
400C2×C3×D3—21no—
401C2×C3×D3—21no—
402C2×C3×D3—21no—
403C2×C3×D3#13112yes—
404C32×C4—21no—
405C32×C4—21no—
406C32×C4C2×#4111yescharacteristic
407C32×C4C2×#4111yescharacteristic
408C3⋊Dic3—21no—
409C3⋊Dic3—21no—
410C3⋊Dic3—21no—
411C3×Dic3—21no—
412C3×Dic3—21no—
413C3×Dic3—21no—
414C3×Dic3—21no—
415C3×Dic3—21no—
416C3×Dic3#13112yes—
417C2×M16—91no—
418C2×M16—91no—
419C22×C8—31no—
420C22×C8—31no—
421C22×C8—91no—
422C22×C8—91no—
423#126—91no—
424#126—91no—
425#125—91no—
426#124—91no—
427#123—91no—
428#123—91no—
429C22⋊Q8—91no—
430#121—91no—
431C4×Q8—91no—
432C4×D4—91no—
433C4×D4—91no—
434C4×D4—91no—
435#117—31no—
436#117—91no—
437C2×C42—31no—
438C4⋊C8—31no—
439C4⋊C8—31no—
440C4⋊C8—91no—
441C4⋊C8—91no—
442C4⋊C8—91no—
443C4⋊C8—91no—
444C22⋊C8—31no—
445C22⋊C8—31no—
446C22⋊C8—91no—
447C22⋊C8—91no—
448C22⋊C8—91no—
449C22⋊C8—91no—
450#97—31no—
451#97—91no—
452#97—91no—
453#97—91no—
454C4×C8—31no—
455C4×C8—31no—
456C4×C8—31no—
457C4×C8—91no—
458C4×C8—91no—
459C4×C8D3211yescharacteristic
460C23×C3—31no—
461C23×C3—31no—
462C22×D3—31no—
463C22×D3—31no—
464C22×D3—61no—
465C22×D3C2×C4×D311yescharacteristic
466C22×D3C2×C4×D311yescharacteristic
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—31no—
471C2×C3×C4—31no—
472C2×C3×C4—31no—
473C2×C3×C4—31no—
474C2×C3×C4—31no—
475C2×C3×C4—31no—
476C2×C3×C4—62no—
477C2×C3×C4—62no—
478C2×C3×C4—61no—
479C2×C3×C4—61no—
480C2×C3×C4—61no—
481C2×C3×C4—61no—
482C2×C3×C4C2×C4×D311yescharacteristic
483C2×C3×C4C2×C4×D311yescharacteristic
484C2×C3×C4C2×C4×D311yescharacteristic
485C2×C3×C4C2×C4×D311yescharacteristic
486C2×C3×C4C23×D311yescharacteristic
487C2×C3×C4C23×D311yescharacteristic
488#67—62no—
489#67—62no—
490#67—62no—
491#67—62no—
492C2×Dic3—31no—
493C2×Dic3—31no—
494C2×Dic3—31no—
495C2×Dic3—31no—
496C2×Dic3—31no—
497C2×Dic3—31no—
498C2×Dic3—61no—
499C2×Dic3—61no—
500C2×Dic3—61no—
501C2×Dic3C2×C4×D311yescharacteristic
502C2×Dic3C2×C4×D311yescharacteristic
503C2×Dic3C2×C4×D311yescharacteristic
504C2×Dic3C2×C4×D311yescharacteristic
505C2×Dic3C2×C4×D311yescharacteristic
506C2×Dic3C2×C4×D311yescharacteristic
507D12—62no—
508D12—62no—
509C4×D3—22no—
510C4×D3—21no—
511C4×D3—21no—
512C4×D3—21no—
513C4×D3—21no—
514C4×D3—22no—
515C4×D3—61no—
516C4×D3—61no—
517C4×D3—61no—
518C4×D3—61no—
519C4×D3—121no—
520C4×D3—121no—
521Dic6—62no—
522Dic6—62no—
523C3×C8—21no—
524C3×C8—21no—
525C3×C8—21no—
526C3×C8—21no—
527C3×C8—32no—
528C3×C8—32no—
529C3×C8—41no—
530C3×C8—41no—
531C3×C8—61no—
532C3×C8—61no—
533C3⋊C8—21no—
534C3⋊C8—21no—
535C3⋊C8—61no—
536C3⋊C8—61no—
537C3⋊C8—61no—
538C3⋊C8—61no—
539C3⋊C8—121no—
540C3⋊C8—121no—
541C3⋊C8#23512yes—
542C3⋊C8#23512yes—
543C2×C32C4×#4111yescharacteristic
544C2×C32C2×#13111yescharacteristic
545C2×C32C2×#13111yescharacteristic
546C3⋊D3—41no—
547C3×D3—22no—
548C3×D3—41no—
549C2×Q8—91no—
550C2×D4—91no—
551C2×D4—91no—
552C2×D4—91no—
553C22×C4—31no—
554C22×C4—31no—
555C22×C4—31no—
556C22×C4—31no—
557C22×C4—91no—
558M16—182no—
559M16—182no—
560C2×C8—31no—
561C2×C8—31no—
562C2×C8—31no—
563C2×C8—31no—
564C2×C8—62no—
565C2×C8—62no—
566C2×C8—91no—
567C2×C8—91no—
568C2×C8—182no—
569C2×C8—182no—
570C2×C8C2×D3211yescharacteristic
571C2×C8C2×D3211yescharacteristic
572C4⋊C4—31no—
573C4⋊C4—31no—
574C4⋊C4—91no—
575C4⋊C4—91no—
576C4⋊C4—91no—
577C4⋊C4—91no—
578C4⋊C4—91no—
579C4⋊C4—91no—
580C4⋊C4—91no—
581C4⋊C4—91no—
582C22⋊C4—31no—
583C22⋊C4—31no—
584C22⋊C4—91no—
585C22⋊C4—91no—
586C22⋊C4—91no—
587C22⋊C4—91no—
588C22⋊C4—91no—
589C22⋊C4—91no—
590C22⋊C4—91no—
591C22⋊C4—91no—
592C42—31no—
593C42—31no—
594C42—31no—
595C42—31no—
596C42—91no—
597C42C2×D3211yescharacteristic
598C22×C3—21no—
599C22×C3—32no—
600C22×C3—61no—
601C22×C3—61no—
602C22×C3—61no—
603C22×C3—61no—
604C22×C3—61no—
605C22×C3C22×C4×D311yescharacteristic
606C22×C3C22×C4×D311yescharacteristic
607C2×D3—21no—
608C2×D3—21no—
609C2×D3—21no—
610C2×D3—21no—
611C2×D3—21no—
612C2×D3—61no—
613C2×D3—61no—
614C2×D3—61no—
615C2×D3—61no—
616C2×D3—61no—
617C2×D3—61no—
618C2×D3—121no—
619C2×D3—121no—
620C2×D3—121no—
621C2×D3#90112yes—
622C3×C4—21no—
623C3×C4—21no—
624C3×C4—21no—
625C3×C4—21no—
626C3×C4—21no—
627C3×C4—21no—
628C3×C4—32no—
629C3×C4—41no—
630C3×C4—41no—
631C3×C4—61no—
632C3×C4—61no—
633C3×C4—61no—
634C3×C4—61no—
635C3×C4—61no—
636C3×C4C2×#23511yescharacteristic
637C3×C4C2×#23511yescharacteristic
638C3×C4D3×#4111yescharacteristic
639C3×C4D3×#4111yescharacteristic
640Dic3—21no—
641Dic3—21no—
642Dic3—21no—
643Dic3—21no—
644Dic3—21no—
645Dic3—61no—
646Dic3—61no—
647Dic3—61no—
648Dic3—61no—
649Dic3—61no—
650Dic3—61no—
651Dic3—121no—
652Dic3—121no—
653Dic3—121no—
654Dic3#90112yes—
655C32#296611yescharacteristic, complemented, Sylow
656C23—31no—
657C23—31no—
658C23—91no—
659Q8—182no—
660D4—182no—
661D4—182no—
662D4—182no—
663C2×C4—31no—
664C2×C4—31no—
665C2×C4—31no—
666C2×C4—31no—
667C2×C4—31no—
668C2×C4—31no—
669C2×C4—62no—
670C2×C4—62no—
671C2×C4—61no—
672C2×C4—61no—
673C2×C4—61no—
674C2×C4—61no—
675C2×C4—91no—
676C2×C4—91no—
677C2×C4—91no—
678C2×C4—181no—
679C2×C4—181no—
680C2×C4C4×D3211yescharacteristic
681C2×C4C4×D3211yescharacteristic
682C2×C4C22×D3211yescharacteristic
683C8—21no—
684C8—21no—
685C8—32no—
686C8—32no—
687C8—61no—
688C8—61no—
689C8—181no—
690C8—181no—
691C2×C3—21no—
692C2×C3—21no—
693C2×C3—21no—
694C2×C3—62no—
695C2×C3—121no—
696C2×C3C4×#23511yescharacteristic
697C2×C3#552211yescharacteristic
698C2×C3C2×#90111yescharacteristic
699C2×C3C2×#90111yescharacteristic
700C2×C3D3×#13111yescharacteristic
701C2×C3D3×#13111yescharacteristic
702D3—22no—
703D3—41no—
704D3—121no—
705D3—121no—
706D3—241no—
707C22—32no—
708C22—61no—
709C22—61no—
710C22—61no—
711C22—61no—
712C22—61no—
713C22—181no—
714C22—181no—
715C22—181no—
716C22C2×C4×D3211yescharacteristic
717C4—21no—
718C4—21no—
719C4—32no—
720C4—61no—
721C4—61no—
722C4—61no—
723C4—61no—
724C4—61no—
725C4—181no—
726C4—181no—
727C4—181no—
728C4D3×#23511yescharacteristic
729C4D3×#23511yescharacteristic
730C3—21no—
731C3#7844811yescharacteristic, complemented
732C3#7936611yescharacteristic, complemented
733C2—62no—
734C2—121no—
735C2—361no—
736C2#1059396511yescharacteristic
737C2D3×#90111yescharacteristic
738C2D3×#90111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×C4×C8C22
prime radical#63906C4
cosocleC2×C32×C4C24
hypercenterC4×C8D32
hypocenterC32#2966
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. #10592389C2semidirect
3. C3×#4690C2semidirect
4. C3×C4×D3×C8C2semidirect
5. #10590785C2semidirect
6. #10590730C2semidirect
7. #10590727C2semidirect
8. #10590723C2semidirect
9. #10590721C2semidirect
10. #10590720C2semidirect
11. #10590717C2semidirect
12. #10590644C2semidirect
13. #10590321C2semidirect
14. #10590318C2semidirect
15. #10590262C2semidirect
84. #4690D3semidirect
89. C4×D3×C8D3semidirect
655. C32#2966semidirect
731. C3#78448semidirect
732. C3#79366semidirect

Maximal subgroups

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

subgroupindex
#105939732
#105923892
C3×#46902
C3×C4×D3×C82
#105907852
#105907302
#105907272
#105907232
#105907212
#105907202
#105907172
#105906442
#105903212
#105903182
#105902622
#793663
#784483