Finite Group Databasebeta

← #11859112

Subgroups — #11859112

Order 1152.

839 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593966C211yesmaximal, characteristic
2#10592404C211yesmaximal, characteristic, complemented
3C3×#4709C211yesmaximal, characteristic, complemented
4C3×#4708C211yesmaximal, characteristic, complemented
5#10590955C211yesmaximal, characteristic
6#10590953C211yesmaximal, characteristic
7#10590663C211yesmaximal, characteristic, complemented
8#10590660C211yesmaximal, characteristic, complemented
9#10590655C211yesmaximal, characteristic, complemented
10D3×Dic3⋊C8C211yesmaximal, characteristic, complemented
11#10590648C211yesmaximal, characteristic, complemented
12#10590647C211yesmaximal, characteristic, complemented
13#10590318C211yesmaximal, characteristic, complemented
14#10590297C211yesmaximal, characteristic, complemented
15#10590264C211yesmaximal, characteristic, complemented
16#79375—31nomaximal
17#78552—31nomaximal
18C2×#3798C2211yescharacteristic
19C42×C3⋊D3C2211yescharacteristic
20C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
21C2×C3×D3×C8C2211yescharacteristic
22C3×#872C2211yescharacteristic
23C3×#872C2211yescharacteristic
24#63902C411yescharacteristic
25#63902C411yescharacteristic
26#63881C411yescharacteristic
27#63881C411yescharacteristic
28#63881C411yescharacteristic
29#63881C411yescharacteristic
30C4×D3×Dic3C2211yescharacteristic
31C4×D3×Dic3C2211yescharacteristic
32#63874C2211yescharacteristic
33#63838C411yescharacteristic
34#63838C411yescharacteristic
35C2×#3711C2211yescharacteristic
36C2×D3×C3⋊C8C2211yescharacteristic
37C32×#97C2211yescharacteristic
38#63647C2211yescharacteristic
39#63647C2211yescharacteristic
40#63641C2211yescharacteristic
41#63641C2211yescharacteristic
42#63630C2211yescharacteristic
43C3×(C2×D3)⋊C8C2211yescharacteristic
44C3×(C2×D3)⋊C8C2211yescharacteristic
45C3×#815C2211yescharacteristic
46C3×Dic3⋊C8C2211yescharacteristic
47C3×Dic3⋊C8C2211yescharacteristic
48C3×C8×Dic3C2211yescharacteristic
49C3×C4×C3⋊C8C2211yescharacteristic
50C3×C4×C3⋊C8C2211yescharacteristic
51#63572C2211yescharacteristic
52#63572C2211yescharacteristic
53Dic3⋊(C3⋊C8)C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63557C2211yescharacteristic
56#63557C2211yescharacteristic
57(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
58(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5522—31no—
62#5522—31no—
63C3×#433—31no—
64C3×#405—31no—
65#5129—31no—
66#5118—31no—
67#5110—31no—
68C2×Dic3⋊C8—31no—
69#5000—31no—
70#4997—31no—
71#4840—31no—
72#4840—31no—
73#4837—31no—
74D3×C4⋊C8—31no—
75#4727—31no—
76#4727—31no—
77#4719—31no—
78#4718—31no—
79#4709—31no—
80#4709D311yescharacteristic, complemented
81#4708D311yescharacteristic, complemented
82#4705—31no—
83#4705—31no—
84#4705—31no—
85#4705—61no—
86#4690—31no—
87#4690—31no—
88#4689—31no—
89#4685—31no—
90#4685—31no—
91#4685—31no—
92C2×C4×C3⋊D3C2×C411yescharacteristic
93C2×C4×C3⋊D3C2×C411yescharacteristic
94C2×C4×C3⋊D3C2311yescharacteristic
95C2×C3×C4×D3C2311yescharacteristic
96C2×C3×C4×D3C2311yescharacteristic
97C2×#627C2×C411yescharacteristic
98C2×#626C2×C411yescharacteristic
99C2×#626C2×C411yescharacteristic
100C2×#625C2×C411yescharacteristic
101C2×D3×Dic3C2×C411yescharacteristic
102C2×D3×Dic3C2×C411yescharacteristic
103C2×D3×Dic3C2×C411yescharacteristic
104C2×D3×Dic3C2×C411yescharacteristic
105#3798—22no—
106#3798—22no—
107C2×C32×C8C2311yescharacteristic
108C2×C32×C8C2311yescharacteristic
109C32×C42C2311yescharacteristic
110C4×C3⋊Dic3C2×C411yescharacteristic
111C4×C3⋊Dic3C2×C411yescharacteristic
112C4×C3⋊Dic3C2311yescharacteristic
113C2×C3⋊(C3⋊C8)C2311yescharacteristic
114C2×C3⋊(C3⋊C8)C2311yescharacteristic
115C3×(C2×D3)⋊C4C2×C411yescharacteristic
116C3×(C2×D3)⋊C4C2×C411yescharacteristic
117C3×(C2×D3)⋊C4C2×C411yescharacteristic
118C3×(C2×D3)⋊C4C2×C411yescharacteristic
119C3×Dic3⋊C4C2×C411yescharacteristic
120C3×Dic3⋊C4C2×C411yescharacteristic
121C3×Dic3⋊C4C2×C411yescharacteristic
122C3×Dic3⋊C4C2×C411yescharacteristic
123C3×C4×Dic3C2311yescharacteristic
124C3×C4×Dic3C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C3×ΓL(1,𝔽25)—22no—
130C3×D3×C8—22no—
131#3724C2×C411yescharacteristic
132#3724C2×C411yescharacteristic
133#3722C2×C411yescharacteristic
134#3722C2×C411yescharacteristic
135Dic32C2×C411yescharacteristic
136Dic32C2×C411yescharacteristic
137Dic32C2×C411yescharacteristic
138Dic32C2×C411yescharacteristic
139#3711—22no—
140D3×C3⋊C8—22no—
141#2925—91noSylow
142C2×#235—31no—
143C2×#235—31no—
144C2×C3×M16—31no—
145C22×C3×C8—31no—
146C3×#117—31no—
147C3×#117—31no—
148C2×C4×Dic3—31no—
149C2×C4×Dic3—31no—
150C2×#208—31no—
151C22×C3⋊C8—31no—
152C2×ΓL(1,𝔽25)—31no—
153C2×ΓL(1,𝔽25)C2×D311yescharacteristic
154C2×D3×C8—31no—
155C2×D3×C8C2×D311yescharacteristic
156#893—31no—
157#893—31no—
158#893—31no—
159#893—31no—
160#887—31no—
161#887—31no—
162#887—31no—
163#887—31no—
164#67⋊C4—31no—
165#67⋊C4—31no—
166#67⋊C4—31no—
167#67⋊C4—31no—
168#67⋊C4—31no—
169#67⋊C4—31no—
170#67⋊C4—31no—
171#67⋊C4—31no—
172#872—31no—
173#872—31no—
174#872C2×D311yescharacteristic
175#872C2×D311yescharacteristic
176C42×D3—31no—
177C42×D3—31no—
178C42×D3—31no—
179C42×D3—31no—
180C42×D3—61no—
181C3×C4⋊C8—31no—
182C3×C4⋊C8—31no—
183C3×C22⋊C8—31no—
184C3×C22⋊C8—31no—
185C3×#97—21no—
186C3×#97—31no—
187C3×#97C2×D311yescharacteristic
188C3×#97C2×D311yescharacteristic
189C3×C4×C8—31no—
190C3×C4×C8—31no—
191C3×C4×C8—31no—
192#830—31no—
193#830—31no—
194(C2×D3)⋊C8—31no—
195(C2×D3)⋊C8—31no—
196(C2×D3)⋊C8—31no—
197(C2×D3)⋊C8—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#815C2×D311yescharacteristic
210Dic3⋊C8—31no—
211Dic3⋊C8—31no—
212Dic3⋊C8—31no—
213Dic3⋊C8—31no—
214Dic3⋊C8—31no—
215Dic3⋊C8—31no—
216Dic3⋊C8—31no—
217Dic3⋊C8—31no—
218Dic3⋊C8—31no—
219Dic3⋊C8—31no—
220Dic3⋊C8—61no—
221Dic3⋊C8—61no—
222Dic3⋊C8C2×D311yescharacteristic
223Dic3⋊C8C2×D311yescharacteristic
224C8×Dic3—31no—
225C8×Dic3C2×D311yescharacteristic
226C4⋊(C3⋊C8)—31no—
227C4⋊(C3⋊C8)—31no—
228#803—31no—
229#803—31no—
230#803—31no—
231#803—61no—
232C4×C3⋊C8—31no—
233C4×C3⋊C8C2×D311yescharacteristic
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—
246C4×C3⋊D3—22no—
247C4×C3⋊D3—41no—
248C2×C3×Dic3C22×C411yescharacteristic
249C2×C3×Dic3C22×C411yescharacteristic
250C2×C3×Dic3C22×C411yescharacteristic
251C2×C3×Dic3C22×C411yescharacteristic
252C2×C3×Dic3C22×C411yescharacteristic
253C2×C3×Dic3C22×C411yescharacteristic
254C3×C4×D3—21no—
255C3×C4×D3—21no—
256C3×C4×D3#4112yes—
257C3×C4×D3#4112yes—
258#627—22no—
259#626—22no—
260#626—22no—
261#625—22no—
262D3×Dic3—22no—
263D3×Dic3—22no—
264D3×Dic3—41no—
265D3×Dic3—41no—
266C32×C8—21no—
267C32×C8—21no—
268C3⋊(C3⋊C8)—21no—
269C3⋊(C3⋊C8)—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272C3×C3⋊C8—21no—
273C3×C3⋊C8—21no—
274C4×#41—91no—
275#433—31no—
276#433—91no—
277#433—91no—
278#433—91no—
279#432—91no—
280#432—91no—
281#431—91no—
282#431—91no—
283#423—91no—
284C2×C4⋊C8—91no—
285#408—91no—
286#408—91no—
287#405—31no—
288#405—91no—
289C22×C3×C4—31no—
290C22×C3×C4—31no—
291C2×#67—31no—
292C2×#67—31no—
293C2×#67—31no—
294C2×#67—31no—
295C22×Dic3—31no—
296C22×Dic3—31no—
297C22×Dic3—31no—
298C22×Dic3—31no—
299#235—62no—
300#235—62no—
301#235—62no—
302#235—62no—
303C2×D12—31no—
304C2×D12—31no—
305C2×C4×D3—31no—
306C2×C4×D3—31no—
307C2×C4×D3—31no—
308C2×C4×D3—31no—
309C2×C4×D3—31no—
310C2×C4×D3—31no—
311C2×C4×D3—31no—
312C2×C4×D3—31no—
313C2×C4×D3—31no—
314C2×C4×D3—31no—
315C2×C4×D3—61no—
316C2×C4×D3—61no—
317C2×C4×D3—61no—
318C2×C4×D3C22×D311yescharacteristic
319C2×C4×D3C22×D311yescharacteristic
320C2×Dic6—31no—
321C2×Dic6—31no—
322C3×M16—62no—
323C2×C3×C8—21no—
324C2×C3×C8—21no—
325C2×C3×C8—31no—
326C2×C3×C8—31no—
327C2×C3×C8—31no—
328C2×C3×C8—31no—
329C2×C3×C8—62no—
330C2×C3×C8C22×D311yescharacteristic
331C2×C3×C8C22×D311yescharacteristic
332C2×C3×C8C22×D311yescharacteristic
333C2×C3×C8C22×D311yescharacteristic
334C3×C4⋊C4—31no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C22⋊C4—31no—
339C3×C22⋊C4—31no—
340C3×C22⋊C4—31no—
341C3×C22⋊C4—31no—
342C3×C42—21no—
343C3×C42—31no—
344C3×C42—31no—
345C3×C42C22×D311yescharacteristic
346C3×C42C22×D311yescharacteristic
347(C2×D3)⋊C4—31no—
348(C2×D3)⋊C4—31no—
349(C2×D3)⋊C4—31no—
350(C2×D3)⋊C4—31no—
351(C2×D3)⋊C4C4×D311yescharacteristic
352(C2×D3)⋊C4C4×D311yescharacteristic
353(C2×D3)⋊C4C4×D311yescharacteristic
354(C2×D3)⋊C4C4×D311yescharacteristic
355Dic3⋊C4—31no—
356Dic3⋊C4—31no—
357Dic3⋊C4—31no—
358Dic3⋊C4—31no—
359Dic3⋊C4C4×D311yescharacteristic
360Dic3⋊C4C4×D311yescharacteristic
361Dic3⋊C4C4×D311yescharacteristic
362Dic3⋊C4C4×D311yescharacteristic
363C4×Dic3—31no—
364C4×Dic3—31no—
365C4×Dic3—31no—
366C4×Dic3—31no—
367C4×Dic3—31no—
368C4×Dic3—31no—
369C4×Dic3—31no—
370C4×Dic3—31no—
371C4×Dic3—31no—
372C4×Dic3—31no—
373C4×Dic3—31no—
374C4×Dic3—31no—
375C4×Dic3—31no—
376C4×Dic3—31no—
377C4×Dic3—61no—
378C4×Dic3—61no—
379C4×Dic3—61no—
380C4×Dic3C22×D311yescharacteristic
381C4×Dic3C22×D311yescharacteristic
382#208—62no—
383C2×C3⋊C8—31no—
384C2×C3⋊C8—31no—
385C2×C3⋊C8—31no—
386C2×C3⋊C8—31no—
387C2×C3⋊C8—61no—
388C2×C3⋊C8—61no—
389C2×C3⋊C8—62no—
390C2×C3⋊C8C22×D311yescharacteristic
391C2×C3⋊C8C22×D311yescharacteristic
392C2×C3⋊C8C22×D311yescharacteristic
393C2×C3⋊C8C22×D311yescharacteristic
394ΓL(1,𝔽25)—22no—
395ΓL(1,𝔽25)—62no—
396D3×C8—22no—
397D3×C8—62no—
398C22×C32C23×C411yescharacteristic
399C2×C3⋊D3—21no—
400C2×C3⋊D3—21no—
401C2×C3⋊D3—21no—
402C2×C3×D3—21no—
403C2×C3×D3—21no—
404C2×C3×D3—21no—
405C2×C3×D3—21no—
406C2×C3×D3—21no—
407C2×C3×D3#11712yes—
408C32×C4—21no—
409C32×C4—21no—
410C32×C4C2×#4111yescharacteristic
411C32×C4C2×#4111yescharacteristic
412C3⋊Dic3—21no—
413C3⋊Dic3—21no—
414C3⋊Dic3#13112yes—
415C3×Dic3—21no—
416C3×Dic3—21no—
417C3×Dic3—21no—
418C3×Dic3—21no—
419C3×Dic3—21no—
420C3×Dic3#11712yes—
421C2×#41—91no—
422C2×M16—31no—
423C2×M16—91no—
424C22×C8—31no—
425C22×C8—91no—
426C4×Q8—91no—
427C4×Q8—91no—
428C4×D4—91no—
429C4×D4—91no—
430C4×D4—91no—
431C4×D4—91no—
432C4×D4—91no—
433C4×D4—91no—
434#117—31no—
435#117—31no—
436#117—91no—
437C2×C42—91no—
438C2×C42—91no—
439C2×C42—91no—
440C4⋊C8—31no—
441C4⋊C8—31no—
442C4⋊C8—91no—
443C4⋊C8—91no—
444C4⋊C8—91no—
445C4⋊C8—91no—
446C4⋊C8—91no—
447C4⋊C8—91no—
448C22⋊C8—31no—
449C22⋊C8—31no—
450C22⋊C8—91no—
451C22⋊C8—91no—
452C22⋊C8—91no—
453C22⋊C8—91no—
454C22⋊C8—91no—
455C22⋊C8—91no—
456#97—31no—
457#97—91no—
458#97—91no—
459#97D3211yescharacteristic
460C4×C8—31no—
461C4×C8—31no—
462C4×C8—31no—
463C4×C8—91no—
464C23×C3—31no—
465C23×C3—31no—
466C22×D3—31no—
467C22×D3—31no—
468C22×D3—61no—
469C22×D3C2×C4×D311yescharacteristic
470C22×D3C2×C4×D311yescharacteristic
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—31no—
475C2×C3×C4—32no—
476C2×C3×C4—32no—
477C2×C3×C4—31no—
478C2×C3×C4—31no—
479C2×C3×C4—31no—
480C2×C3×C4—31no—
481C2×C3×C4—31no—
482C2×C3×C4—61no—
483C2×C3×C4—61no—
484C2×C3×C4C2×C4×D311yescharacteristic
485C2×C3×C4C2×C4×D311yescharacteristic
486C2×C3×C4C2×C4×D311yescharacteristic
487C2×C3×C4C2×C4×D311yescharacteristic
488C2×C3×C4C23×D311yescharacteristic
489C2×C3×C4C23×D311yescharacteristic
490#67—62no—
491#67—62no—
492#67—62no—
493#67—62no—
494C2×Dic3—31no—
495C2×Dic3—31no—
496C2×Dic3—31no—
497C2×Dic3—31no—
498C2×Dic3—31no—
499C2×Dic3—31no—
500C2×Dic3—61no—
501C2×Dic3—61no—
502C2×Dic3—61no—
503C2×Dic3—62no—
504C2×Dic3—62no—
505C2×Dic3—121no—
506C2×Dic3—121no—
507C2×Dic3C2×C4×D311yescharacteristic
508C2×Dic3C2×C4×D311yescharacteristic
509C2×Dic3C2×C4×D311yescharacteristic
510C2×Dic3C2×C4×D311yescharacteristic
511C2×Dic3C2×C4×D311yescharacteristic
512C2×Dic3C2×C4×D311yescharacteristic
513D12—62no—
514D12—62no—
515C4×D3—21no—
516C4×D3—21no—
517C4×D3—62no—
518C4×D3—62no—
519C4×D3—62no—
520C4×D3—62no—
521C4×D3—61no—
522C4×D3—61no—
523C4×D3—61no—
524C4×D3—61no—
525C4×D3—122no—
526C4×D3—121no—
527C4×D3—121no—
528C4×D3—121no—
529C4×D3—121no—
530C4×D3—121no—
531C4×D3—121no—
532C4×D3—122no—
533C4×D3#23512yes—
534C4×D3#23512yes—
535Dic6—62no—
536Dic6—62no—
537C3×C8—21no—
538C3×C8—21no—
539C3×C8—21no—
540C3×C8—21no—
541C3×C8—41no—
542C3×C8—41no—
543C3×C8—61no—
544C3×C8—61no—
545C3×C8—61no—
546C3×C8—61no—
547C3⋊C8—21no—
548C3⋊C8—21no—
549C3⋊C8—21no—
550C3⋊C8—21no—
551C3⋊C8—61no—
552C3⋊C8—61no—
553C3⋊C8—61no—
554C3⋊C8—61no—
555C3⋊C8—121no—
556C3⋊C8—121no—
557C2×C32C2×#11711yescharacteristic
558C2×C32C2×#13111yescharacteristic
559C2×C32#56811yescharacteristic
560C3⋊D3—41no—
561C3×D3—22no—
562C3×D3—41no—
563#41—182no—
564#41—182no—
565C2×Q8—91no—
566C2×D4—91no—
567C2×D4—91no—
568C2×D4—91no—
569C22×C4—31no—
570C22×C4—31no—
571C22×C4—91no—
572C22×C4—91no—
573C22×C4—91no—
574C22×C4—91no—
575C22×C4—91no—
576C22×C4—91no—
577C22×C4—91no—
578M16—62no—
579M16—182no—
580C2×C8—31no—
581C2×C8—31no—
582C2×C8—31no—
583C2×C8—31no—
584C2×C8—62no—
585C2×C8—91no—
586C2×C8—91no—
587C2×C8—182no—
588C2×C8C2×D3211yescharacteristic
589C2×C8C2×D3211yescharacteristic
590C4⋊C4—31no—
591C4⋊C4—31no—
592C4⋊C4—31no—
593C4⋊C4—31no—
594C4⋊C4—91no—
595C4⋊C4—91no—
596C22⋊C4—31no—
597C22⋊C4—31no—
598C22⋊C4—31no—
599C22⋊C4—31no—
600C22⋊C4—91no—
601C22⋊C4—91no—
602C42—31no—
603C42—31no—
604C42—91no—
605C42—91no—
606C42—91no—
607C42—91no—
608C42—91no—
609C42—91no—
610C42—91no—
611C42C2×D3211yescharacteristic
612C22×C3—21no—
613C22×C3—32no—
614C22×C3—61no—
615C22×C3—61no—
616C22×C3—61no—
617C22×C3—61no—
618C22×C3—61no—
619C22×C3C22×C4×D311yescharacteristic
620C22×C3C22×C4×D311yescharacteristic
621C2×D3—21no—
622C2×D3—21no—
623C2×D3—21no—
624C2×D3—21no—
625C2×D3—21no—
626C2×D3—62no—
627C2×D3—61no—
628C2×D3—61no—
629C2×D3—61no—
630C2×D3—61no—
631C2×D3—61no—
632C2×D3—61no—
633C2×D3—121no—
634C2×D3—121no—
635C2×D3#87212yes—
636C3×C4—21no—
637C3×C4—21no—
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—32no—
643C3×C4—41no—
644C3×C4—41no—
645C3×C4—61no—
646C3×C4—61no—
647C3×C4—61no—
648C3×C4—61no—
649C3×C4—61no—
650C3×C4C2×#23511yescharacteristic
651C3×C4C2×#23511yescharacteristic
652C3×C4D3×#4111yescharacteristic
653C3×C4D3×#4111yescharacteristic
654Dic3—21no—
655Dic3—21no—
656Dic3—21no—
657Dic3—21no—
658Dic3—21no—
659Dic3—32no—
660Dic3—32no—
661Dic3—62no—
662Dic3—61no—
663Dic3—61no—
664Dic3—61no—
665Dic3—61no—
666Dic3—121no—
667Dic3—121no—
668Dic3#87212yes—
669C32#292511yescharacteristic, complemented, Sylow
670C23—31no—
671C23—31no—
672C23—91no—
673Q8—182no—
674D4—182no—
675D4—182no—
676D4—182no—
677C2×C4—31no—
678C2×C4—32no—
679C2×C4—32no—
680C2×C4—31no—
681C2×C4—31no—
682C2×C4—31no—
683C2×C4—31no—
684C2×C4—31no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—91no—
688C2×C4—91no—
689C2×C4—91no—
690C2×C4—182no—
691C2×C4—182no—
692C2×C4—182no—
693C2×C4—181no—
694C2×C4—181no—
695C2×C4—361no—
696C2×C4—361no—
697C2×C4—361no—
698C2×C4C4×D3211yescharacteristic
699C2×C4C4×D3211yescharacteristic
700C2×C4C22×D3211yescharacteristic
701C8—21no—
702C8—21no—
703C8—61no—
704C8—61no—
705C8—61no—
706C8—61no—
707C8—181no—
708C8—181no—
709C2×C3—21no—
710C2×C3—21no—
711C2×C3—21no—
712C2×C3—62no—
713C2×C3—121no—
714C2×C3C2×#87211yescharacteristic
715C2×C3D3×#11711yescharacteristic
716C2×C3D3×#13111yescharacteristic
717C2×C3D3×#13111yescharacteristic
718C2×C3#575011yescharacteristic
719C2×C3#575011yescharacteristic
720D3—22no—
721D3—41no—
722D3—122no—
723D3—121no—
724D3—121no—
725C22—32no—
726C22—61no—
727C22—61no—
728C22—61no—
729C22—61no—
730C22—61no—
731C22—181no—
732C22—181no—
733C22—181no—
734C22C2×C4×D3211yescharacteristic
735C4—21no—
736C4—21no—
737C4—32no—
738C4—61no—
739C4—61no—
740C4—61no—
741C4—61no—
742C4—61no—
743C4—92no—
744C4—181no—
745C4—181no—
746C4D3×#23511yescharacteristic
747C4D3×#23511yescharacteristic
748C3—21no—
749C3#7855211yescharacteristic, complemented
750C3#7937511yescharacteristic, complemented
751C2—62no—
752C2—121no—
753C2—361no—
754C2D3×#87211yescharacteristic
755C2#1059470711yescharacteristic
756C2#1059470811yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×#97C22
prime radicalC2×#3798C22
cosocleC2×C32×C4C24
hypercenter#97D32
hypocenterC32#2925
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ #97

Complements

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

NH ≅ G/Ntype
2. #10592404C2semidirect
3. C3×#4709C2semidirect
4. C3×#4708C2semidirect
7. #10590663C2semidirect
8. #10590660C2semidirect
9. #10590655C2semidirect
10. D3×Dic3⋊C8C2semidirect
11. #10590648C2semidirect
12. #10590647C2semidirect
13. #10590318C2semidirect
14. #10590297C2semidirect
15. #10590264C2semidirect
80. #4709D3semidirect
81. #4708D3semidirect
669. C32#2925semidirect
749. C3#78552semidirect
750. C3#79375semidirect

Maximal subgroups

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

subgroupindex
#105939662
#105924042
C3×#47092
C3×#47082
#105909552
#105909532
#105906632
#105906602
#105906552
D3×Dic3⋊C82
#105906482
#105906472
#105903182
#105902972
#105902642
#793753
#785523