Finite Group Databasebeta

← #11889707

Subgroups — #11889707

Order 1152.

921 conjugacy classes of subgroups.

The subgroup lattice has 817 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5511C211yesmaximal, characteristic, complemented
2#10595018C211yesmaximal, characteristic
3C2×#63636C211yesmaximal, characteristic, complemented
4C3×#4970C211yesmaximal, characteristic, complemented
5#10591188C211yesmaximal, characteristic, complemented
6#10591183C211yesmaximal, characteristic, complemented
7#10591158C211yesmaximal, characteristic, complemented
8#10590616C211yesmaximal, characteristic, complemented
9#10590609C211yesmaximal, characteristic, complemented
10#10590585C211yesmaximal, characteristic, complemented
11#10590536C211yesmaximal, characteristic, complemented
12#10590535C211yesmaximal, characteristic, complemented
13#10590464C211yesmaximal, characteristic, complemented
14#10590457C211yesmaximal, characteristic, complemented
15#10590422C211yesmaximal, characteristic, complemented
16#83635—31nomaximal
17#81486—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C22×C3⋊(C3⋊C8)C2211yescharacteristic
22C3×C4×#67—21no—
23C3×C4×#67C2211yescharacteristic
24C3×#924—21no—
25C3×#924C2211yescharacteristic
26C3×#924C2211yescharacteristic
27C3×#897C2211yescharacteristic, complemented
28C3×#896—21no—
29C3×D3×C4⋊C4C2211yescharacteristic, complemented
30C3×#889—21no—
31C3×#888C2211yescharacteristic, complemented
32C3×#887C2211yescharacteristic, complemented
33#63981—21no—
34#63974—21no—
35#63910—21no—
36#63909C2211yescharacteristic
37#63897—21no—
38#63894C2211yescharacteristic
39#63864C2211yescharacteristic
40C2×#3718C2211yescharacteristic, complemented
41C2×#3717C2211yescharacteristic
42C2×#3717C2211yescharacteristic
43C2×#3711C2211yescharacteristic, complemented
44#63636C2211yescharacteristic
45#63636C2211yescharacteristic
46#63636C2211yescharacteristic
47#63636C2211yescharacteristic
48C3×#830C2211yescharacteristic
49C3×#810C2211yescharacteristic, complemented
50C3×#810C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52C3×#807C2211yescharacteristic, complemented
53#63576C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63565C2211yescharacteristic, complemented
56#63565C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60#63554C2211yescharacteristic, complemented
61C3×#554—31no—
62#5630—31no—
63#5550—31no—
64#5511D311yescharacteristic, complemented
65C3×#484—31no—
66#5089—31no—
67#5087—31no—
68#5051—31no—
69#5051—31no—
70#5049—31no—
71#5047—31no—
72#5046—31no—
73#5028—31no—
74#5026—31no—
75#5011—31no—
76#4970D311yescharacteristic, complemented
77#4967—31no—
78#4966—31no—
79C2×#809—31no—
80C2×#809—31no—
81C2×#809—61no—
82#4890—31no—
83#4889—31no—
84#4886—31no—
85#4882—31no—
86#4808—31no—
87#4803—31no—
88#4798—31no—
89#4794—31no—
90#4731—31no—
91#4730—31no—
92C23×C3⋊D3—21no—
93C22×C32×C4—21no—
94C22×C32×C4C2311yescharacteristic
95C2×C4⋊(C3⋊D3)—22no—
96C2×C4⋊(C3⋊D3)—21no—
97C2×C4⋊(C3⋊D3)—41no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C3×#67D411yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6—21no—
104C2×C3×Dic6C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×#626—21no—
107C2×#626—21no—
108C2×#624—21no—
109C2×#624—21no—
110#3799—22no—
111#3799—41no—
112C32×C4⋊C4—21no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115C2×C3⋊(C3⋊C8)—41no—
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×#217—21no—
119C3×#217—21no—
120C3×#217D411yescharacteristic
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4D411yescharacteristic
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4D411yescharacteristic
132C3×C4×Dic3—21no—
133C3×C4×Dic3C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136#3722—21no—
137#3722—21no—
138#3722—21no—
139#3722—21no—
140#3718—41no—
141#3717—22no—
142#3717—41no—
143#3711—41no—
144#3314—91noSylow
145C2×#239—31no—
146C2×#235—31no—
147C22×D12—31no—
148C22×D12—31no—
149C22×D12—61no—
150C3×C4⋊Q8—31no—
151C3×#125—61no—
152C3×C22⋊Q8—31no—
153C3×C22⋊Q8—31no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8—61no—
156C3×C22⋊Q8—61no—
157C3×C4×Q8—31no—
158C3×C4×D4—31no—
159C3×C4×D4—61no—
160C2×C3×C4⋊C4—21no—
161C2×C3×C4⋊C4—31no—
162C2×C3×C4⋊C4C2×D311yescharacteristic
163C2×C3×C4⋊C4C2×D311yescharacteristic
164#947—31no—
165C2×#216—31no—
166C2×#216—31no—
167C2×#215—31no—
168C2×#215—31no—
169#937—61no—
170#930—31no—
171C4×#67—21no—
172C4×#67C2×D311yescharacteristic
173#924—21no—
174#924C2×D311yescharacteristic
175#924C2×D311yescharacteristic
176C2×#208—31no—
177C22×C3⋊C8—31no—
178C22×C3⋊C8—31no—
179C22×C3⋊C8—61no—
180C2×#204—31no—
181C2×#204—31no—
182C2×ΓL(1,𝔽25)—31no—
183#897C2×D311yescharacteristic, complemented
184#896—21no—
185#895—31no—
186#895—61no—
187#894—61no—
188#894—61no—
189#893—31no—
190D3×C4⋊C4C2×D311yescharacteristic, complemented
191#889—21no—
192#888C2×D311yescharacteristic, complemented
193#887C2×D311yescharacteristic, complemented
194#884—61no—
195#882—61no—
196D3×C22⋊C4—61no—
197D3×C22⋊C4—61no—
198#875—31no—
199C4×D12—31no—
200C3×#107—31no—
201C3×#107—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×C22⋊C8—31no—
205#835—31no—
206#835—31no—
207#830—31no—
208#830C2×D311yescharacteristic
209#821—31no—
210#821—31no—
211(C2×D3)⋊C8—31no—
212#815—31no—
213Dic3⋊C8—31no—
214#810—31no—
215#810—31no—
216#810C2×D311yescharacteristic, complemented
217#810C2×D311yescharacteristic, complemented
218#809—31no—
219#809—31no—
220#809—31no—
221#809—31no—
222#809—31no—
223#809—31no—
224#809—31no—
225#809—31no—
226#809—31no—
227#809—31no—
228#809—61no—
229#809—61no—
230#809—61no—
231#809—61no—
232#807—31no—
233#807—31no—
234#807C2×D311yescharacteristic, complemented
235#807C2×D311yescharacteristic, complemented
236C4⋊(C3⋊C8)—31no—
237#803—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3⋊D3—21no—
240C22×C3⋊D3—21no—
241C22×C3⋊D3—42no—
242C22×C3⋊D3—42no—
243C22×C3⋊D3—81no—
244C22×C3×D3C2×D411yescharacteristic
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—81no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252C4⋊(C3⋊D3)—21no—
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)—21no—
255C4⋊(C3⋊D3)—42no—
256C4⋊(C3⋊D3)#4112yes—
257C3×#67—22no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—81no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272C3×Dic6—81no—
273#626—42no—
274#626—81no—
275#624—42no—
276#624—81no—
277C3⋊(C3⋊C8)—21no—
278C3⋊(C3⋊C8)—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281#554—31no—
282#546—91no—
283#489—91no—
284#484—31no—
285#480—91no—
286#474—91no—
287#468—91no—
288#467—91no—
289#464—91no—
290#452—91no—
291#450—91no—
292#440—91no—
293#435—91no—
294#417—91no—
295C2×#102—91no—
296C23×D3—61no—
297C23×D3—61no—
298C23×D3—121no—
299C2×C3×Q8—31no—
300C2×C3×Q8—31no—
301C2×C3×Q8—61no—
302C2×C3×D4—31no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—31no—
307C22×C3×C4—41no—
308C22×C3×C4—61no—
309C22×C3×C4C22×D311yescharacteristic
310C22×C3×C4C22×D311yescharacteristic
311C2×#67—61no—
312C2×#67—61no—
313C2×#67#6711yescharacteristic
314#239—62no—
315#239—121no—
316#235—62no—
317#235—121no—
318C2×D12—31no—
319C2×D12—31no—
320C2×D12—31no—
321C2×D12—31no—
322C2×D12—61no—
323C2×D12—61no—
324C2×D12—62no—
325C2×D12—62no—
326C2×D12—64no—
327C2×D12—61no—
328C2×D12—61no—
329C2×D12—61no—
330C2×D12—61no—
331C2×D12—121no—
332C2×D12—121no—
333C2×D12—121no—
334C2×D12—122no—
335C2×C4×D3—21no—
336C2×C4×D3—61no—
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3—61no—
340C2×C4×D3C22×D311yescharacteristic
341C2×Dic6—21no—
342C2×Dic6C22×D311yescharacteristic
343C2×Dic6C22×D311yescharacteristic
344C2×C3×C8—31no—
345C2×C3×C8—31no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—21no—
349C3×C4⋊C4—21no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—41no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4—61no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4C22×D311yescharacteristic
361C3×C4⋊C4C22×D311yescharacteristic
362C3×C4⋊C4C22×D311yescharacteristic
363C3×C4⋊C4C22×D311yescharacteristic
364C3×C22⋊C4—31no—
365C3×C22⋊C4—31no—
366C3×C22⋊C4—61no—
367C3×C22⋊C4—61no—
368C3×C22⋊C4—61no—
369C3×C42—31no—
370C3×C42—61no—
371#217—21no—
372#217—21no—
373#217#6711yescharacteristic
374#216—121no—
375#216—121no—
376#215—62no—
377#215—121no—
378(C2×D3)⋊C4—21no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4#6711yescharacteristic
388C4⋊Dic3—21no—
389C4⋊Dic3C22×D311yescharacteristic
390C4⋊Dic3C22×D311yescharacteristic
391Dic3⋊C4—21no—
392Dic3⋊C4—21no—
393Dic3⋊C4—21no—
394Dic3⋊C4—21no—
395Dic3⋊C4—21no—
396Dic3⋊C4#6711yescharacteristic
397C4×Dic3—21no—
398C4×Dic3C22×D311yescharacteristic
399#208—121no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—61no—
405C2×C3⋊C8—61no—
406C2×C3⋊C8—121no—
407C2×C3⋊C8—121no—
408C2×C3⋊C8—122no—
409C2×C3⋊C8C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411#204—62no—
412#204—121no—
413ΓL(1,𝔽25)—121no—
414C22×C32—21no—
415C22×C32—21no—
416C22×C32#13712yes—
417C22×C32C22×D411yescharacteristic
418C2×C3⋊D3—22no—
419C2×C3⋊D3—41no—
420C2×C3⋊D3—41no—
421C2×C3⋊D3—41no—
422C2×C3⋊D3—41no—
423C2×C3⋊D3—41no—
424C2×C3⋊D3—84no—
425C2×C3×D3—21no—
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C32×C4—21no—
429C32×C4—41no—
430C32×C4—41no—
431C32×C4C2×#4111yescharacteristic
432C32×C4H(5,𝔽2)11yescharacteristic
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—21no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C2×#41—91no—
441C22×D4—91no—
442C2×Q16—91no—
443C2×SD16—91no—
444C2×SD16—91no—
445C2×M16—91no—
446C22×C8—91no—
447C4⋊Q8—31no—
448#125—61no—
449#124—91no—
450#123—181no—
451C22⋊Q8—31no—
452C22⋊Q8—31no—
453C22⋊Q8—31no—
454C22⋊Q8—61no—
455C22⋊Q8—61no—
456#121—91no—
457#121—181no—
458#120—181no—
459C4×Q8—31no—
460C4×D4—31no—
461C4×D4—61no—
462C4×D4—91no—
463C2×C4⋊C4—31no—
464C2×C4⋊C4D3211yescharacteristic
465C2×C22⋊C4—181no—
466#107—31no—
467#107—31no—
468#107—91no—
469C4⋊C8—91no—
470#103—31no—
471#103—31no—
472#103—91no—
473#103—91no—
474#102—91no—
475#102—91no—
476#102—91no—
477#102—91no—
478#102—91no—
479#102—91no—
480C22⋊C8—31no—
481C22⋊C8—91no—
482#97—91no—
483C23×C3—21no—
484C23×C3—31no—
485C23×C3D3×D411yescharacteristic
486C23×C3C2×#6711yescharacteristic
487C22×D3—61no—
488C22×D3—61no—
489C22×D3—61no—
490C22×D3—61no—
491C22×D3—121no—
492C22×D3—121no—
493C22×D3—122no—
494C22×D3—122no—
495C22×D3—124no—
496C22×D3—122no—
497C22×D3—122no—
498C22×D3—242no—
499C22×D3—241no—
500C22×D3—241no—
501C22×D3—242no—
502C22×D3C2×#6711yescharacteristic
503C3×Q8—61no—
504C3×Q8—61no—
505C3×Q8—61no—
506C3×Q8—61no—
507C3×Q8—241no—
508C3×D4—62no—
509C2×C3×C4—22no—
510C2×C3×C4—22no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—31no—
522C2×C3×C4—31no—
523C2×C3×C4—31no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—81no—
533C2×C3×C4—81no—
534C2×C3×C4—82no—
535C2×C3×C4—241no—
536C2×C3×C4D3×D411yescharacteristic
537C2×C3×C4C2×#6711yescharacteristic
538C2×C3×C4C23×D311yescharacteristic
539C2×C3×C4C23×D311yescharacteristic
540#67—22no—
541#67—122no—
542#67—241no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3C2×#6711yescharacteristic
548C2×Dic3C2×#6711yescharacteristic
549C2×Dic3C2×#6711yescharacteristic
550D12—32no—
551D12—32no—
552D12—62no—
553D12—62no—
554D12—61no—
555D12—61no—
556D12—61no—
557D12—61no—
558D12—61no—
559D12—61no—
560D12—121no—
561D12—121no—
562D12—122no—
563D12—122no—
564D12—124no—
565D12—122no—
566D12—241no—
567C4×D3—21no—
568C4×D3—21no—
569C4×D3—81no—
570C4×D3—122no—
571C4×D3—122no—
572C4×D3—241no—
573C4×D3—241no—
574Dic6—21no—
575Dic6—21no—
576Dic6—21no—
577Dic6—21no—
578Dic6—81no—
579C3×C8—61no—
580C3×C8—61no—
581C3⋊C8—21no—
582C3⋊C8—21no—
583C3⋊C8—61no—
584C3⋊C8—61no—
585C3⋊C8—61no—
586C3⋊C8—61no—
587C3⋊C8—121no—
588C3⋊C8—121no—
589C2×C32—22no—
590C2×C32#54611yescharacteristic
591C2×C32C2×#13711yescharacteristic
592C2×C32#57611yescharacteristic
593C3⋊D3—42no—
594C3⋊D3—81no—
595C3×D3—41no—
596C24—181no—
597#41—182no—
598#41—361no—
599C2×Q8—31no—
600C2×Q8—31no—
601C2×Q8—61no—
602C2×D4—31no—
603C2×D4—91no—
604C2×D4—91no—
605C2×D4—182no—
606C2×D4—181no—
607C2×D4—181no—
608C2×D4—181no—
609C2×D4—361no—
610C22×C4—21no—
611C22×C4—31no—
612C22×C4—61no—
613C22×C4—181no—
614C22×C4—181no—
615C22×C4C2×D3211yescharacteristic
616Q16—361no—
617SD16—182no—
618SD16—361no—
619M16—361no—
620C2×C8—31no—
621C2×C8—31no—
622C2×C8—91no—
623C2×C8—91no—
624C2×C8—361no—
625C4⋊C4—21no—
626C4⋊C4—31no—
627C4⋊C4—31no—
628C4⋊C4—31no—
629C4⋊C4—61no—
630C4⋊C4—61no—
631C4⋊C4—61no—
632C4⋊C4—61no—
633C4⋊C4—61no—
634C4⋊C4—61no—
635C4⋊C4C2×D3211yescharacteristic
636C4⋊C4C2×D3211yescharacteristic
637C22⋊C4—31no—
638C22⋊C4—31no—
639C22⋊C4—61no—
640C22⋊C4—61no—
641C22⋊C4—61no—
642C22⋊C4—181no—
643C22⋊C4—181no—
644C22⋊C4—181no—
645C22⋊C4—181no—
646C42—31no—
647C42—61no—
648C22×C3—22no—
649C22×C3—22no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—22no—
656C22×C3—61no—
657C22×C3—61no—
658C22×C3—61no—
659C22×C3#91812yes—
660C22×C3#94212yes—
661C22×C3C2×D3×D411yescharacteristic
662C22×C3C22×#6711yescharacteristic
663C2×D3—21no—
664C2×D3—21no—
665C2×D3—21no—
666C2×D3—62no—
667C2×D3—62no—
668C2×D3—122no—
669C2×D3—121no—
670C2×D3—121no—
671C2×D3—121no—
672C2×D3—121no—
673C2×D3—122no—
674C2×D3—121no—
675C2×D3—121no—
676C2×D3—121no—
677C2×D3—121no—
678C2×D3—121no—
679C2×D3—121no—
680C2×D3—241no—
681C2×D3—241no—
682C2×D3—241no—
683C2×D3—241no—
684C2×D3—244no—
685C2×D3—244no—
686C2×D3—248no—
687C3×C4—22no—
688C3×C4—21no—
689C3×C4—21no—
690C3×C4—21no—
691C3×C4—21no—
692C3×C4—41no—
693C3×C4—41no—
694C3×C4—41no—
695C3×C4—41no—
696C3×C4—61no—
697C3×C4—61no—
698C3×C4—61no—
699C3×C4—81no—
700C3×C4—81no—
701C3×C4—121no—
702C3×C4—121no—
703C3×C4—121no—
704C3×C4—121no—
705C3×C4D3×#4111yescharacteristic
706C3×C4D3×#4111yescharacteristic
707C3×C4#100911yescharacteristic
708C3×C4#100911yescharacteristic
709Dic3—21no—
710Dic3—21no—
711Dic3—21no—
712Dic3—41no—
713Dic3—41no—
714Dic3—41no—
715Dic3—41no—
716C32#331411yescharacteristic, complemented, Sylow
717C23—31no—
718C23—181no—
719C23—181no—
720C23—362no—
721C23—362no—
722C23—721no—
723C23D3×#6711yescharacteristic
724Q8—61no—
725Q8—61no—
726Q8—61no—
727Q8—61no—
728Q8—241no—
729D4—62no—
730D4—92no—
731D4—181no—
732D4—181no—
733D4—181no—
734D4—362no—
735D4—362no—
736D4—721no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—31no—
742C2×C4—31no—
743C2×C4—31no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—81no—
751C2×C4—241no—
752C2×C4—362no—
753C2×C4—721no—
754C2×C4D3×#6711yescharacteristic
755C2×C4C22×D3211yescharacteristic
756C8—61no—
757C8—61no—
758C8—181no—
759C8—181no—
760C2×C3—24no—
761C2×C3—22no—
762C2×C3—22no—
763C2×C3—21no—
764C2×C3—21no—
765C2×C3—21no—
766C2×C3—121no—
767C2×C3#565411yescharacteristic
768C2×C3C2×#91811yescharacteristic
769C2×C3#577411yescharacteristic
770C2×C3C2×#94211yescharacteristic
771C2×C3#582911yescharacteristic
772C2×C3#583511yescharacteristic
773D3—41no—
774D3—122no—
775D3—122no—
776D3—242no—
777D3—242no—
778D3—241no—
779D3—241no—
780C22—21no—
781C22—21no—
782C22—61no—
783C22—61no—
784C22—61no—
785C22—182no—
786C22—361no—
787C22—361no—
788C22—361no—
789C22—361no—
790C22—361no—
791C22—724no—
792C22#6394812yes—
793C22C2×D3×#6711yescharacteristic
794C4—21no—
795C4—41no—
796C4—41no—
797C4—61no—
798C4—61no—
799C4—61no—
800C4—121no—
801C4—121no—
802C4—121no—
803C4—121no—
804C4#6430611yescharacteristic
805C4#6430811yescharacteristic
806C3—21no—
807C3#8148611yescharacteristic, complemented
808C3#8363511yescharacteristic, complemented
809C2—22no—
810C2—121no—
811C2—362no—
812C2—721no—
813C2#1059506811yescharacteristic
814C2#1059509711yescharacteristic
815C2C2×#6394811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radical#10595018C2
hypercenterC2×C4⋊C4D32
hypocenterC32#3314
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#5511C2semidirect
3. C2×#63636C2semidirect
4. C3×#4970C2semidirect
5. #10591188C2semidirect
6. #10591183C2semidirect
7. #10591158C2semidirect
8. #10590616C2semidirect
9. #10590609C2semidirect
10. #10590585C2semidirect
11. #10590536C2semidirect
12. #10590535C2semidirect
13. #10590464C2semidirect
14. #10590457C2semidirect
15. #10590422C2semidirect
27. C3×#897C22semidirect
29. C3×D3×C4⋊C4C22semidirect
31. C3×#888C22semidirect
32. C3×#887C22semidirect
40. C2×#3718C22semidirect
43. C2×#3711C22semidirect
49. C3×#810C22semidirect
50. C3×#810C22semidirect
51. C3×#807C22semidirect
52. C3×#807C22semidirect
53. #63576C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63565C22semidirect
56. #63565C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. #63554C22semidirect
64. #5511D3semidirect
76. #4970D3semidirect
183. #897C2×D3semidirect
190. D3×C4⋊C4C2×D3semidirect
192. #888C2×D3semidirect
193. #887C2×D3semidirect
216. #810C2×D3semidirect
217. #810C2×D3semidirect
234. #807C2×D3semidirect
235. #807C2×D3semidirect
716. C32#3314semidirect
807. C3#81486semidirect
808. C3#83635semidirect

Maximal subgroups

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

subgroupindex
C3×#55112
#105950182
C2×#636362
C3×#49702
#105911882
#105911832
#105911582
#105906162
#105906092
#105905852
#105905362
#105905352
#105904642
#105904572
#105904222
#836353
#814863