Finite Group Databasebeta

← #11888600

Subgroups — #11888600

Order 1152.

848 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5618C211yesmaximal, characteristic, complemented
2#10594887C211yesmaximal, characteristic, complemented
3#10592741C211yesmaximal, characteristic, complemented
4C3×#5037C211yesmaximal, characteristic, complemented
5#10591519C211yesmaximal, characteristic, complemented
6#10591499C211yesmaximal, characteristic, complemented
7#10591489C211yesmaximal, characteristic, complemented
8#10591430C211yesmaximal, characteristic, complemented
9#10591151C211yesmaximal, characteristic, complemented
10#10591124C211yesmaximal, characteristic, complemented
11#10591087C211yesmaximal, characteristic, complemented
12#10590608C211yesmaximal, characteristic, complemented
13#10590562C211yesmaximal, characteristic, complemented
14#10590521C211yesmaximal, characteristic, complemented
15#10590467C211yesmaximal, characteristic, complemented
16#83615—31nomaximal
17#80108—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20C32×#121C2211yescharacteristic
21C2×#3754C2211yescharacteristic
22#64133C2211yescharacteristic
23C2×#3748C2211yescharacteristic
24C3×#939—21no—
25C3×#938C2211yescharacteristic
26C3×D4×Dic3—21no—
27C3×D4×Dic3C2211yescharacteristic
28C2×C3×#214C2211yescharacteristic
29C2×C3×#213C2211yescharacteristic
30C3×C4×#67C2211yescharacteristic
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C3×#892C2211yescharacteristic
33C3×#890C2211yescharacteristic
34C3×#886—21no—
35C3×#879—21no—
36#63970—21no—
37#63969—21no—
38#63905—21no—
39Dic3×D12C2211yescharacteristic
40D3×Dic3⋊C4—21no—
41#63866C2211yescharacteristic
42#63856C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44#63659C2211yescharacteristic
45#63637C2211yescharacteristic
46#63634C2211yescharacteristic
47C3×#830C2211yescharacteristic
48C3×#810C2211yescharacteristic
49C3×#809C2211yescharacteristic
50#63573C2211yescharacteristic
51#63573C2211yescharacteristic
52Dic3⋊(C3⋊C8)C2211yescharacteristic
53#63567C2211yescharacteristic
54#63567C2211yescharacteristic
55#63565C2211yescharacteristic
56#63565C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63554C2211yescharacteristic
61C3×#553—31no—
62#5824—31no—
63#5618D311yescharacteristic, complemented
64#5551—31no—
65C3×#449—31no—
66#5232—31no—
67#5171—31no—
68#5162—31no—
69#5158—31no—
70#5152—31no—
71#5069—31no—
72#5066—31no—
73#5042—31no—
74#5042—31no—
75#5042—61no—
76#5041—31no—
77#5037—31no—
78#5037D311yescharacteristic, complemented
79#5019—31no—
80#5014—31no—
81#5011—31no—
82#5002—31no—
83#4996—31no—
84#4971—31no—
85#4966—31no—
86#4815—31no—
87#4797—31no—
88#4772—31no—
89#4763—31no—
90#4728—31no—
91#4721—31no—
92C2×C32×D4—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C2×#634C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C2×C3×#67D411yescharacteristic
99C22×C3×Dic3—21no—
100C22×C3×Dic3—21no—
101C3×#235—22no—
102C3×#235—41no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×#625—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110#3795—22no—
111#3795—41no—
112C32×C4⋊C4C2311yescharacteristic
113C32×C22⋊C4—21no—
114#3757—21no—
115#3754—41no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118#3748—41no—
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C3×#217—21no—
122C3×#217—21no—
123C3×#217D411yescharacteristic
124C3×#214—41no—
125C3×#213—22no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4D411yescharacteristic
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3—21no—
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4D411yescharacteristic
134C3×C4×Dic3—21no—
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138#3724—21no—
139Dic3⋊Dic3—21no—
140Dic3⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143D3×C3⋊C8—41no—
144#3307—91noSylow
145C2×C3×#41—31no—
146C2×#237—31no—
147C2×#235—31no—
148C2×#235C2×D311yescharacteristic
149C2×C3×SD16—31no—
150C2×C3×D8—31no—
151C3×#126—61no—
152C3×#125—31no—
153C3×#123—61no—
154C3×#121—21no—
155C3×#121—31no—
156C3×#121—61no—
157C3×#121C2×D311yescharacteristic
158C3×#121C2×D311yescharacteristic
159C3×C4×D4—31no—
160C3×C4×D4—31no—
161C3×C4×D4—61no—
162C3×#117—31no—
163C2×C3×C4⋊C4—31no—
164#946—31no—
165#944—31no—
166#939—21no—
167#939—61no—
168#938—61no—
169#938C2×D311yescharacteristic
170#935—61no—
171D4×Dic3—21no—
172D4×Dic3—31no—
173D4×Dic3C2×D311yescharacteristic
174C2×#214—31no—
175C2×#214—31no—
176C2×#214—61no—
177C2×#214C2×D311yescharacteristic
178C2×#213C2×D311yescharacteristic
179#929—61no—
180C4×#67C2×D311yescharacteristic
181C2×C4⋊Dic3C2×D311yescharacteristic
182#924—31no—
183#924—31no—
184#924—31no—
185#924—61no—
186C2×Dic3⋊C4—61no—
187C2×#208—31no—
188C2×#208—31no—
189C2×#208—61no—
190C22×C3⋊C8—31no—
191C2×D3×C8—31no—
192#892C2×D311yescharacteristic
193D3×C4⋊C4—61no—
194#890C2×D311yescharacteristic
195#886—21no—
196#883—61no—
197#883—61no—
198#879—21no—
199C4×D12—31no—
200#869—31no—
201C3×#103—31no—
202C3×#102—31no—
203C3×C22⋊C8—31no—
204#835—31no—
205#835—31no—
206#832—31no—
207#832—31no—
208#832—31no—
209#832—31no—
210#832—61no—
211#830—31no—
212#830C2×D311yescharacteristic
213(C2×D3)⋊C8—31no—
214#817—31no—
215#817—31no—
216#816—31no—
217#816—31no—
218#815—31no—
219Dic3⋊C8—31no—
220#810—31no—
221#810—31no—
222#810—31no—
223#810—31no—
224#810—31no—
225#810—31no—
226#810—61no—
227#810C2×D311yescharacteristic
228#809—31no—
229#809—31no—
230#809C2×D311yescharacteristic
231#808—31no—
232#808—31no—
233#807—31no—
234#807—31no—
235#807—61no—
236C4⋊(C3⋊C8)—31no—
237#803—31no—
238C23×C32—21no—
239C23×C32C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C32×D4—21no—
243C32×D4—21no—
244C32×D4—42no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2411yescharacteristic
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252#634—21no—
253#634—21no—
254C3×#67—41no—
255C3×#67—42no—
256C3×#67—81no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—81no—
261C2×C3×Dic3—81no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—21no—
266C3×D12#4112yes—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—42no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272#625—42no—
273D3×Dic3—42no—
274D3×Dic3—42no—
275C3⋊(C3⋊C8)—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#553—31no—
280#547—91no—
281#491—91no—
282#485—91no—
283#483—91no—
284#478—91no—
285#468—91no—
286#465—91no—
287#461—91no—
288#449—31no—
289#449—91no—
290#442—91no—
291#435—91no—
292#417—91no—
293#416—91no—
294C3×#41—62no—
295C3×#41—121no—
296C2×C3×Q8—31no—
297C2×C3×D4—21no—
298C2×C3×D4—21no—
299C2×C3×D4—21no—
300C2×C3×D4—31no—
301C2×C3×D4—31no—
302C2×C3×D4—41no—
303C2×C3×D4—61no—
304C2×C3×D4—61no—
305C2×C3×D4C22×D311yescharacteristic
306C2×C3×D4C22×D311yescharacteristic
307C22×C3×C4—21no—
308C22×C3×C4—31no—
309C22×C3×C4—61no—
310C22×C3×C4—61no—
311C22×C3×C4—61no—
312C22×C3×C4C22×D311yescharacteristic
313C22×C3×C4C22×D311yescharacteristic
314C2×#67—21no—
315C2×#67—21no—
316C2×#67—61no—
317C2×#67—61no—
318C2×#67#6711yescharacteristic
319C22×Dic3—21no—
320C22×Dic3—21no—
321C22×Dic3—61no—
322C22×Dic3—61no—
323#237—62no—
324#237—121no—
325#235—22no—
326#235—41no—
327#235—62no—
328#235—121no—
329C2×D12C22×D311yescharacteristic
330C2×C4×D3—21no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3C22×D311yescharacteristic
334C2×Dic6—31no—
335C2×Dic6—31no—
336C2×Dic6—61no—
337C2×Dic6C22×D311yescharacteristic
338C3×SD16—121no—
339C3×D8—62no—
340C2×C3×C8—31no—
341C2×C3×C8—31no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C4⋊C4C22×D311yescharacteristic
351C3×C22⋊C4—21no—
352C3×C22⋊C4—21no—
353C3×C22⋊C4—31no—
354C3×C22⋊C4—31no—
355C3×C22⋊C4—41no—
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C22⋊C4—61no—
359C3×C42—31no—
360C3×C42—61no—
361#217—21no—
362#217—21no—
363#217—61no—
364#217—61no—
365#217—61no—
366#217—61no—
367#217—121no—
368#217#6711yescharacteristic
369#214—41no—
370#214—121no—
371#214—121no—
372#214—122no—
373#213—22no—
374(C2×D3)⋊C4—21no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4#6711yescharacteristic
378C4⋊Dic3—21no—
379C4⋊Dic3—21no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3C22×D311yescharacteristic
386C4⋊Dic3C22×D311yescharacteristic
387Dic3⋊C4—21no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—121no—
395Dic3⋊C4#6711yescharacteristic
396C4×Dic3—21no—
397C4×Dic3C22×D311yescharacteristic
398#208—121no—
399#208—121no—
400#208—122no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—61no—
406C2×C3⋊C8—61no—
407C2×C3⋊C8—121no—
408C2×C3⋊C8C22×D311yescharacteristic
409C2×C3⋊C8C22×D311yescharacteristic
410D3×C8—121no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32—41no—
415C22×C32—41no—
416C22×C32—41no—
417C22×C32C22×D411yescharacteristic
418C2×C3×D3—22no—
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C32×C4—21no—
425C32×C4—41no—
426C32×C4C2×#4111yescharacteristic
427C32×C4H(5,𝔽2)11yescharacteristic
428C3⋊Dic3—41no—
429C3⋊Dic3—41no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C2×#41—31no—
437C2×#41—91no—
438C2×SD16—31no—
439C2×SD16—91no—
440C2×D8—31no—
441C2×M16—91no—
442C22×C8—91no—
443C4⋊Q8—91no—
444#126—61no—
445#125—31no—
446#123—61no—
447#123—181no—
448#123—181no—
449C22⋊Q8—91no—
450C22⋊Q8—91no—
451#121—31no—
452#121—61no—
453#121—181no—
454#121D3211yescharacteristic
455C4×D4—31no—
456C4×D4—31no—
457C4×D4—61no—
458C4×D4—91no—
459#117—31no—
460C2×C4⋊C4—31no—
461C2×C4⋊C4—181no—
462#107—91no—
463#106—91no—
464#106—91no—
465C4⋊C8—91no—
466#103—31no—
467#103—91no—
468#103—91no—
469#103—91no—
470#103—91no—
471#103—91no—
472#102—31no—
473#102—91no—
474#102—91no—
475#102—91no—
476C22⋊C8—31no—
477C22⋊C8—91no—
478#97—91no—
479C23×C3—21no—
480C23×C3—21no—
481C23×C3—21no—
482C23×C3—31no—
483C23×C3—41no—
484C23×C3—61no—
485C23×C3D3×D411yescharacteristic
486C23×C3C2×#6711yescharacteristic
487C22×D3—21no—
488C22×D3C2×#6711yescharacteristic
489C3×Q8—61no—
490C3×Q8—61no—
491C3×D4—21no—
492C3×D4—21no—
493C3×D4—21no—
494C3×D4—21no—
495C3×D4—32no—
496C3×D4—41no—
497C3×D4—41no—
498C3×D4—42no—
499C3×D4—42no—
500C3×D4—61no—
501C3×D4—82no—
502C3×D4—121no—
503C3×D4—122no—
504C3×D4—241no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—31no—
514C2×C3×C4—31no—
515C2×C3×C4—31no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—122no—
525C2×C3×C4—241no—
526C2×C3×C4—241no—
527C2×C3×C4D3×D411yescharacteristic
528C2×C3×C4C2×#6711yescharacteristic
529C2×C3×C4C23×D311yescharacteristic
530C2×C3×C4C23×D311yescharacteristic
531#67—41no—
532#67—42no—
533#67—81no—
534#67—122no—
535#67—122no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—81no—
544C2×Dic3—81no—
545C2×Dic3—121no—
546C2×Dic3—121no—
547C2×Dic3—122no—
548C2×Dic3—122no—
549C2×Dic3C2×#6711yescharacteristic
550C2×Dic3C2×#6711yescharacteristic
551C2×Dic3C2×#6711yescharacteristic
552D12—21no—
553D12#23712yes—
554C4×D3—21no—
555C4×D3—21no—
556C4×D3—42no—
557C4×D3—122no—
558C4×D3—122no—
559Dic6—21no—
560Dic6—21no—
561Dic6—61no—
562Dic6—61no—
563Dic6—61no—
564Dic6—61no—
565Dic6—121no—
566Dic6—121no—
567C3×C8—61no—
568C3×C8—61no—
569C3⋊C8—21no—
570C3⋊C8—21no—
571C3⋊C8—62no—
572C3⋊C8—61no—
573C3⋊C8—61no—
574C3⋊C8—61no—
575C3⋊C8—61no—
576C3⋊C8—121no—
577C2×C32—41no—
578C2×C32—81no—
579C2×C32#54611yescharacteristic
580C2×C32#57511yescharacteristic
581C2×C32#57711yescharacteristic
582C3×D3—41no—
583C3×D3—42no—
584#41—62no—
585#41—121no—
586#41—182no—
587#41—361no—
588C2×Q8—31no—
589C2×Q8—91no—
590C2×D4—21no—
591C2×D4—31no—
592C2×D4—31no—
593C2×D4—61no—
594C2×D4—61no—
595C2×D4—181no—
596C2×D4C2×D3211yescharacteristic
597C22×C4—31no—
598C22×C4—61no—
599C22×C4—61no—
600C22×C4—61no—
601C22×C4—181no—
602C22×C4—181no—
603C22×C4C2×D3211yescharacteristic
604SD16—121no—
605SD16—361no—
606D8—62no—
607M16—361no—
608C2×C8—31no—
609C2×C8—31no—
610C2×C8—91no—
611C2×C8—91no—
612C2×C8—361no—
613C4⋊C4—31no—
614C4⋊C4—31no—
615C4⋊C4—31no—
616C4⋊C4—61no—
617C4⋊C4—61no—
618C4⋊C4—61no—
619C4⋊C4—91no—
620C4⋊C4—181no—
621C4⋊C4—181no—
622C4⋊C4—181no—
623C4⋊C4—181no—
624C4⋊C4C2×D3211yescharacteristic
625C22⋊C4—21no—
626C22⋊C4—31no—
627C22⋊C4—31no—
628C22⋊C4—61no—
629C22⋊C4—61no—
630C22⋊C4—61no—
631C22⋊C4—181no—
632C22⋊C4—181no—
633C22⋊C4—181no—
634C42—31no—
635C42—61no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—61no—
653C22×C3—61no—
654C22×C3—62no—
655C22×C3—61no—
656C22×C3—81no—
657C22×C3—81no—
658C22×C3—81no—
659C22×C3—121no—
660C22×C3—121no—
661C22×C3C2×D3×D411yescharacteristic
662C22×C3C22×#6711yescharacteristic
663C2×D3—21no—
664C2×D3—21no—
665C2×D3—21no—
666C2×D3—22no—
667C2×D3—41no—
668C2×D3—41no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—21no—
672C3×C4—21no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—41no—
676C3×C4—61no—
677C3×C4—61no—
678C3×C4—61no—
679C3×C4—81no—
680C3×C4—121no—
681C3×C4—121no—
682C3×C4—121no—
683C3×C4C2×#23711yescharacteristic
684C3×C4#100411yescharacteristic
685C3×C4D3×#4111yescharacteristic
686C3×C4#100911yescharacteristic
687Dic3—21no—
688Dic3—21no—
689Dic3—21no—
690Dic3—41no—
691Dic3—41no—
692Dic3—41no—
693Dic3—121no—
694Dic3—121no—
695Dic3—121no—
696Dic3—121no—
697Dic3—241no—
698Dic3—241no—
699C32#330711yescharacteristic, complemented, Sylow
700C23—21no—
701C23—31no—
702C23—61no—
703C23D3×#6711yescharacteristic
704Q8—61no—
705Q8—61no—
706Q8—181no—
707Q8—181no—
708D4—21no—
709D4—21no—
710D4—32no—
711D4—42no—
712D4—61no—
713D4—121no—
714D4—122no—
715D4—241no—
716D4—362no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—31no—
721C2×C4—31no—
722C2×C4—31no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—122no—
729C2×C4—181no—
730C2×C4—181no—
731C2×C4—241no—
732C2×C4—241no—
733C2×C4—362no—
734C2×C4—362no—
735C2×C4D3×#6711yescharacteristic
736C2×C4C22×D3211yescharacteristic
737C8—61no—
738C8—61no—
739C8—181no—
740C8—181no—
741C2×C3—21no—
742C2×C3—21no—
743C2×C3—21no—
744C2×C3—41no—
745C2×C3—41no—
746C2×C3—81no—
747C2×C3—81no—
748C2×C3—81no—
749C2×C3—122no—
750C2×C3—121no—
751C2×C3—161no—
752C2×C3#559111yescharacteristic
753C2×C3#577011yescharacteristic
754C2×C3#577311yescharacteristic
755C2×C3#582211yescharacteristic
756C2×C3#582911yescharacteristic
757C2×C3#583611yescharacteristic
758D3—41no—
759D3—42no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—61no—
767C22—61no—
768C22—61no—
769C22—62no—
770C22—121no—
771C22—121no—
772C22C2×D3×#6711yescharacteristic
773C4—21no—
774C4—41no—
775C4—61no—
776C4—61no—
777C4—61no—
778C4—121no—
779C4—121no—
780C4—121no—
781C4—361no—
782C4—361no—
783C4D3×#23711yescharacteristic
784C4#6431411yescharacteristic
785C3—21no—
786C3#8010811yescharacteristic, complemented
787C3#8361511yescharacteristic, complemented
788C2—41no—
789C2—81no—
790C2—121no—
791C2—122no—
792C2#1059509511yescharacteristic
793C2#1059530411yescharacteristic
794C2#1059546611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
hypercenter#121D32
hypocenterC32#3307
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C3×#5618C2semidirect
2. #10594887C2semidirect
3. #10592741C2semidirect
4. C3×#5037C2semidirect
5. #10591519C2semidirect
6. #10591499C2semidirect
7. #10591489C2semidirect
8. #10591430C2semidirect
9. #10591151C2semidirect
10. #10591124C2semidirect
11. #10591087C2semidirect
12. #10590608C2semidirect
13. #10590562C2semidirect
14. #10590521C2semidirect
15. #10590467C2semidirect
63. #5618D3semidirect
78. #5037D3semidirect
699. C32#3307semidirect
786. C3#80108semidirect
787. C3#83615semidirect

Maximal subgroups

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

subgroupindex
C3×#56182
#105948872
#105927412
C3×#50372
#105915192
#105914992
#105914892
#105914302
#105911512
#105911242
#105910872
#105906082
#105905622
#105905212
#105904672
#836153
#801083