Finite Group Databasebeta

← #11888613

Subgroups — #11888613

Order 1152.

869 conjugacy classes of subgroups.

The subgroup lattice has 805 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5824C211yesmaximal, characteristic, complemented
2#10594843C211yesmaximal, characteristic, complemented
3#10592937C211yesmaximal, characteristic, complemented
4C3×#5232C211yesmaximal, characteristic, complemented
5#10591613C211yesmaximal, characteristic, complemented
6#10591585C211yesmaximal, characteristic, complemented
7#10591565C211yesmaximal, characteristic, complemented
8#10591558C211yesmaximal, characteristic, complemented
9#10591452C211yesmaximal, characteristic, complemented
10#10591420C211yesmaximal, characteristic, complemented
11#10591411C211yesmaximal, characteristic, complemented
12#10591404C211yesmaximal, characteristic, complemented
13#10591178C211yesmaximal, characteristic, complemented
14#10591147C211yesmaximal, characteristic, complemented
15#10591101C211yesmaximal, characteristic, complemented
16#83512—31nomaximal
17#78895—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×#3755C2211yescharacteristic
21C2×#3753C2211yescharacteristic
22#64139C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C3×#944C2211yescharacteristic
25C3×#939—21no—
26C3×#935—21no—
27C3×D4×Dic3C2211yescharacteristic
28C3×#929—21no—
29C3×C4×#67C2211yescharacteristic
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C3×#924C2211yescharacteristic
32C2×C3×Dic3⋊C4—21no—
33C2×C3×#208C2211yescharacteristic
34#63978—21no—
35#63952—21no—
36#63909C2211yescharacteristic
37#63894C2211yescharacteristic
38#63869C2211yescharacteristic
39#63854—21no—
40#63848—21no—
41#63841C2211yescharacteristic
42C2×#3717C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44#63662C2211yescharacteristic
45#63659C2211yescharacteristic
46#63657C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#832C2211yescharacteristic
51#63575C2211yescharacteristic
52#63574C2211yescharacteristic
53#63574C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63566C2211yescharacteristic
56#63565C2211yescharacteristic
57#63565C2211yescharacteristic
58#63564C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63554C2211yescharacteristic
61C3×#547—31no—
62#5824D311yescharacteristic, complemented
63#5565—31no—
64#5514—31no—
65C3×#417—31no—
66#5238—31no—
67#5238—31no—
68#5238—31no—
69#5238—61no—
70#5233—31no—
71#5232D311yescharacteristic, complemented
72#5134—31no—
73#5127—31no—
74#5083—31no—
75#5082—31no—
76#5049—31no—
77#5048—31no—
78#5045—31no—
79#5043—31no—
80#5014—31no—
81#5011—31no—
82#5009—31no—
83#4971—31no—
84#4818—31no—
85#4814—31no—
86#4807—31no—
87#4797—31no—
88#4785—31no—
89#4781—31no—
90#4772—31no—
91#4766—31no—
92C32×#41—22no—
93C32×#41—41no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×D4—21no—
96C2×C32×D4C2311yescharacteristic
97C22×C32×C4—21no—
98C22×C32×C4C2311yescharacteristic
99C2×#638—21no—
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×#67D411yescharacteristic
103C22×C3×Dic3—21no—
104C22×C3×Dic3—21no—
105C22×C3×Dic3—21no—
106C3×#237—22no—
107C3×#237—41no—
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C2×#626—21no—
111C2×#624—21no—
112#3755—41no—
113#3753—22no—
114#3752—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
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×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4D411yescharacteristic
132C3×C4×Dic3C2311yescharacteristic
133C3×#208—41no—
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136#3724—21no—
137Dic3⋊Dic3—21no—
138#3722—21no—
139#3722—21no—
140(C2×D3)⋊Dic3—21no—
141Dic32—21no—
142#3717—41no—
143D3×C3⋊C8—41no—
144#3307—91noSylow
145C2×C3×#41—21no—
146C2×C3×#41—31no—
147C2×C3×#41C2×D311yescharacteristic
148C2×C3×#41C2×D311yescharacteristic
149C2×#237C2×D311yescharacteristic
150C2×C3×M16—31no—
151C3×C4⋊Q8—31no—
152C3×#123—61no—
153C3×#123—61no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8—31no—
156C3×#121—61no—
157C3×C4×D4—31no—
158C3×C4×D4—31no—
159C2×C3×C4⋊C4—31no—
160C2×C3×C4⋊C4—61no—
161#946C2×D311yescharacteristic
162#944C2×D311yescharacteristic
163C2×#215—31no—
164C2×#215—31no—
165C2×#215—31no—
166C2×#215—61no—
167#939—21no—
168#939—61no—
169#935—21no—
170D4×Dic3C2×D311yescharacteristic
171C2×#213—31no—
172C2×#213—31no—
173C2×#213—61no—
174#930—31no—
175#930—31no—
176#930—31no—
177#930—61no—
178#930—61no—
179#929—21no—
180C4×#67—61no—
181C4×#67C2×D311yescharacteristic
182#926—31no—
183C2×C4⋊Dic3C2×D311yescharacteristic
184#924C2×D311yescharacteristic
185C2×Dic3⋊C4—21no—
186C2×#208C2×D311yescharacteristic
187C22×C3⋊C8—31no—
188C2×#204—31no—
189C2×D3×C8—31no—
190#898—61no—
191#898—61no—
192#895—31no—
193#894—61no—
194#893—31no—
195#892—31no—
196#890—31no—
197#883—61no—
198#67⋊C4—61no—
199C4×D12—31no—
200#870—31no—
201C3×#103—31no—
202C3×#103—31no—
203C3×#102—31no—
204C3×#102—31no—
205#835—31no—
206#835—31no—
207#835—31no—
208#835—31no—
209#835—31no—
210#835—61no—
211#835C2×D311yescharacteristic
212#835C2×D311yescharacteristic
213#832—31no—
214#832—31no—
215#832—61no—
216#832C2×D311yescharacteristic
217#832C2×D311yescharacteristic
218#830—31no—
219#830—31no—
220#830—31no—
221#830—61no—
222#821—31no—
223(C2×D3)⋊C8—31no—
224#818—31no—
225#816—31no—
226#815—31no—
227Dic3⋊C8—31no—
228#810—31no—
229#810—31no—
230#809—31no—
231#808—31no—
232#808—31no—
233#808—31no—
234#808—31no—
235#807—31no—
236C4⋊(C3⋊C8)—31no—
237#803—31no—
238C23×C32—21no—
239C23×C32C2×D411yescharacteristic
240C22×C3⋊D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C32×Q8—21no—
243C32×Q8—21no—
244C32×D4—21no—
245C32×D4—42no—
246C32×D4#4112yes—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—42no—
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2411yescharacteristic
253#638—42no—
254C2×C3⋊Dic3—21no—
255C4⋊(C3⋊D3)—21no—
256C4⋊(C3⋊D3)—21no—
257C3×#67—41no—
258C3×#67—42no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—42no—
264C2×C3×Dic3—42no—
265C2×C3×Dic3—81no—
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C2×C3×Dic3C2×D411yescharacteristic
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271C3×Dic6—21no—
272C3×Dic6—21no—
273#626—81no—
274#624—81no—
275C3⋊(C3⋊C8)—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#553—91no—
280#547—31no—
281#491—91no—
282#485—91no—
283#483—91no—
284#478—91no—
285#468—91no—
286#465—91no—
287#461—91no—
288#449—91no—
289#449—91no—
290#442—91no—
291#435—91no—
292#417—31no—
293#416—91no—
294C3×#41—22no—
295C3×#41—22no—
296C3×#41—42no—
297C3×#41—41no—
298C3×#41—41no—
299C3×#41—42no—
300C3×#41—62no—
301C3×#41—121no—
302C2×C3×Q8—21no—
303C2×C3×Q8—31no—
304C2×C3×Q8C22×D311yescharacteristic
305C2×C3×Q8C22×D311yescharacteristic
306C2×C3×D4—21no—
307C2×C3×D4—21no—
308C2×C3×D4—21no—
309C2×C3×D4—31no—
310C2×C3×D4—41no—
311C2×C3×D4—61no—
312C2×C3×D4C22×D311yescharacteristic
313C2×C3×D4C22×D311yescharacteristic
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4—21no—
317C22×C3×C4—31no—
318C22×C3×C4—41no—
319C22×C3×C4—61no—
320C22×C3×C4—61no—
321C22×C3×C4—61no—
322C22×C3×C4C22×D311yescharacteristic
323C22×C3×C4C22×D311yescharacteristic
324C2×#67—21no—
325C2×#67—61no—
326C2×#67—61no—
327C2×#67—61no—
328C2×#67—121no—
329C2×#67#6711yescharacteristic
330C22×Dic3—21no—
331C22×Dic3—21no—
332C22×Dic3—21no—
333#237—22no—
334#237—41no—
335C2×D12—31no—
336C2×D12—31no—
337C2×D12—61no—
338C2×D12—61no—
339C2×C4×D3—61no—
340C2×C4×D3—61no—
341C2×C4×D3C22×D311yescharacteristic
342C2×Dic6C22×D311yescharacteristic
343C3×M16—121no—
344C2×C3×C8—31no—
345C2×C3×C8—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—61no—
355C3×C22⋊C4—31no—
356C3×C22⋊C4—31no—
357C3×C22⋊C4—61no—
358C3×C22⋊C4—61no—
359C3×C22⋊C4—61no—
360C3×C42—31no—
361#217—21no—
362#217—21no—
363#217—61no—
364#217#6711yescharacteristic
365#215—121no—
366#215—121no—
367#215—121no—
368#215—122no—
369#213—62no—
370#213—62no—
371#213—122no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—121no—
381(C2×D3)⋊C4#6711yescharacteristic
382C4⋊Dic3—21no—
383C4⋊Dic3—31no—
384C4⋊Dic3—31no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3C22×D311yescharacteristic
388C4⋊Dic3C22×D311yescharacteristic
389C4⋊Dic3C22×D311yescharacteristic
390Dic3⋊C4—21no—
391Dic3⋊C4—21no—
392Dic3⋊C4—21no—
393Dic3⋊C4—21no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4#6711yescharacteristic
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3C22×D311yescharacteristic
401#208—41no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—61no—
407C2×C3⋊C8—61no—
408C2×C3⋊C8—121no—
409C2×C3⋊C8C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411#204—121no—
412D3×C8—121no—
413C22×C32—22no—
414C22×C32—21no—
415C22×C32—21no—
416C22×C32—21no—
417C22×C32—41no—
418C22×C32—41no—
419C22×C32C22×D411yescharacteristic
420C2×C3⋊D3—41no—
421C2×C3⋊D3—41no—
422C2×C3⋊D3—41no—
423C2×C3×D3—21no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C32×C4—21no—
427C32×C4—41no—
428C32×C4C2×#4111yescharacteristic
429C32×C4H(5,𝔽2)11yescharacteristic
430C3⋊Dic3—41no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C2×#41—31no—
439C2×#41D3211yescharacteristic
440C2×SD16—91no—
441C2×SD16—91no—
442C2×D8—91no—
443C2×M16—31no—
444C22×C8—91no—
445C4⋊Q8—31no—
446#126—181no—
447#125—91no—
448#123—61no—
449#123—61no—
450#123—181no—
451C22⋊Q8—31no—
452C22⋊Q8—31no—
453#121—61no—
454#121—91no—
455#121—91no—
456#121—181no—
457C4×D4—31no—
458C4×D4—31no—
459C4×D4—91no—
460C4×D4—181no—
461#117—91no—
462C2×C4⋊C4—31no—
463C2×C4⋊C4—61no—
464#107—91no—
465#106—91no—
466#106—91no—
467C4⋊C8—91no—
468#103—31no—
469#103—31no—
470#103—91no—
471#103—91no—
472#103—91no—
473#103—91no—
474#102—31no—
475#102—31no—
476#102—91no—
477#102—91no—
478C22⋊C8—91no—
479C22⋊C8—91no—
480#97—91no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—31no—
485C23×C3—41no—
486C23×C3D3×D411yescharacteristic
487C23×C3C2×#6711yescharacteristic
488C22×D3—61no—
489C22×D3—61no—
490C22×D3—121no—
491C22×D3C2×#6711yescharacteristic
492C3×Q8—22no—
493C3×Q8—21no—
494C3×Q8—21no—
495C3×Q8—21no—
496C3×Q8—21no—
497C3×Q8—41no—
498C3×Q8—61no—
499C3×Q8—61no—
500C3×D4—21no—
501C3×D4—21no—
502C3×D4—22no—
503C3×D4—41no—
504C3×D4—42no—
505C3×D4—42no—
506C3×D4—44no—
507C3×D4—121no—
508C3×D4—122no—
509C3×D4#23512yes—
510C3×D4#23712yes—
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—31no—
520C2×C3×C4—31no—
521C2×C3×C4—31no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—42no—
526C2×C3×C4—42no—
527C2×C3×C4—44no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—122no—
535C2×C3×C4—122no—
536C2×C3×C4—241no—
537C2×C3×C4D3×D411yescharacteristic
538C2×C3×C4C2×#6711yescharacteristic
539C2×C3×C4C23×D311yescharacteristic
540C2×C3×C4C23×D311yescharacteristic
541#67—41no—
542#67—42no—
543#67—122no—
544#67—122no—
545#67—242no—
546#67—241no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—42no—
552C2×Dic3—42no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555C2×Dic3—81no—
556C2×Dic3—121no—
557C2×Dic3C2×#6711yescharacteristic
558C2×Dic3C2×#6711yescharacteristic
559C2×Dic3C2×#6711yescharacteristic
560D12—61no—
561D12—61no—
562D12—61no—
563D12—61no—
564D12—121no—
565D12—121no—
566D12—241no—
567C4×D3—21no—
568C4×D3—21no—
569C4×D3—241no—
570C4×D3—241no—
571Dic6—21no—
572Dic6—21no—
573C3×C8—61no—
574C3×C8—61no—
575C3⋊C8—21no—
576C3⋊C8—21no—
577C3⋊C8—61no—
578C3⋊C8—61no—
579C3⋊C8—61no—
580C3⋊C8—61no—
581C3⋊C8—121no—
582C3⋊C8—121no—
583C2×C32—41no—
584C2×C32—42no—
585C2×C32#54611yescharacteristic
586C2×C32#57511yescharacteristic
587C2×C32#57711yescharacteristic
588C3⋊D3—81no—
589C3×D3—41no—
590#41—22no—
591#41—41no—
592#41—62no—
593#41—121no—
594C2×Q8—31no—
595C2×Q8C2×D3211yescharacteristic
596C2×D4—21no—
597C2×D4—31no—
598C2×D4—61no—
599C2×D4—91no—
600C2×D4—181no—
601C2×D4—181no—
602C2×D4C2×D3211yescharacteristic
603C22×C4—21no—
604C22×C4—31no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—61no—
608C22×C4—181no—
609C22×C4C2×D3211yescharacteristic
610SD16—361no—
611SD16—361no—
612D8—182no—
613M16—121no—
614C2×C8—31no—
615C2×C8—31no—
616C2×C8—91no—
617C2×C8—91no—
618C2×C8—361no—
619C4⋊C4—31no—
620C4⋊C4—31no—
621C4⋊C4—31no—
622C4⋊C4—31no—
623C4⋊C4—61no—
624C4⋊C4—61no—
625C4⋊C4—61no—
626C4⋊C4—61no—
627C4⋊C4—61no—
628C4⋊C4—91no—
629C4⋊C4—181no—
630C4⋊C4—181no—
631C22⋊C4—31no—
632C22⋊C4—31no—
633C22⋊C4—61no—
634C22⋊C4—61no—
635C22⋊C4—61no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C42—31no—
641C42—181no—
642C22×C3—21no—
643C22×C3—22no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—22no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—41no—
652C22×C3—42no—
653C22×C3—41no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—41no—
659C22×C3—61no—
660C22×C3—61no—
661C22×C3—61no—
662C22×C3—81no—
663C22×C3—81no—
664C22×C3C2×D3×D411yescharacteristic
665C22×C3C22×#6711yescharacteristic
666C2×D3—21no—
667C2×D3—21no—
668C2×D3—21no—
669C2×D3—121no—
670C2×D3—121no—
671C2×D3—121no—
672C2×D3—121no—
673C2×D3—121no—
674C2×D3—121no—
675C2×D3—241no—
676C2×D3—241no—
677C2×D3—241no—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—21no—
681C3×C4—21no—
682C3×C4—41no—
683C3×C4—42no—
684C3×C4—41no—
685C3×C4—41no—
686C3×C4—61no—
687C3×C4—61no—
688C3×C4—61no—
689C3×C4—121no—
690C3×C4—121no—
691C3×C4—121no—
692C3×C4—121no—
693C3×C4C2×#23511yescharacteristic
694C3×C4C2×#23711yescharacteristic
695C3×C4#100411yescharacteristic
696C3×C4#100411yescharacteristic
697Dic3—21no—
698Dic3—21no—
699Dic3—21no—
700Dic3—41no—
701Dic3—41no—
702Dic3—41no—
703Dic3—41no—
704Dic3—121no—
705Dic3—121no—
706Dic3—241no—
707C32#330711yescharacteristic, complemented, Sylow
708C23—21no—
709C23—31no—
710C23—181no—
711C23D3×#6711yescharacteristic
712Q8—21no—
713Q8—21no—
714Q8—61no—
715Q8—61no—
716D4—21no—
717D4—42no—
718D4—121no—
719D4—122no—
720D4—181no—
721D4—181no—
722D4—362no—
723D4—721no—
724D4#380412yes—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—31no—
729C2×C4—31no—
730C2×C4—31no—
731C2×C4—42no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—122no—
739C2×C4—122no—
740C2×C4—181no—
741C2×C4—241no—
742C2×C4—721no—
743C2×C4D3×#6711yescharacteristic
744C2×C4C22×D3211yescharacteristic
745C8—61no—
746C8—61no—
747C8—181no—
748C8—181no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—41no—
753C2×C3—42no—
754C2×C3—41no—
755C2×C3—42no—
756C2×C3—81no—
757C2×C3—82no—
758C2×C3—121no—
759C2×C3#549011yescharacteristic
760C2×C3#577511yescharacteristic
761C2×C3#577711yescharacteristic
762C2×C3#580611yescharacteristic
763C2×C3#582211yescharacteristic
764C2×C3#583711yescharacteristic
765D3—41no—
766D3—241no—
767D3—241no—
768D3—481no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—22no—
773C22—41no—
774C22—41no—
775C22—61no—
776C22—61no—
777C22—61no—
778C22—361no—
779C22—361no—
780C22—361no—
781C22C2×D3×#6711yescharacteristic
782C4—21no—
783C4—41no—
784C4—61no—
785C4—61no—
786C4—61no—
787C4—121no—
788C4—121no—
789C4—121no—
790C4—121no—
791C4—361no—
792C4C2×#380411yescharacteristic
793C4#6433011yescharacteristic
794C3—21no—
795C3#7889511yescharacteristic, complemented
796C3#8351211yescharacteristic, complemented
797C2—41no—
798C2—42no—
799C2—121no—
800C2—721no—
801C2#1059545511yescharacteristic
802C2#1059547011yescharacteristic
803C2#1059549311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3307
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C3×#5824C2semidirect
2. #10594843C2semidirect
3. #10592937C2semidirect
4. C3×#5232C2semidirect
5. #10591613C2semidirect
6. #10591585C2semidirect
7. #10591565C2semidirect
8. #10591558C2semidirect
9. #10591452C2semidirect
10. #10591420C2semidirect
11. #10591411C2semidirect
12. #10591404C2semidirect
13. #10591178C2semidirect
14. #10591147C2semidirect
15. #10591101C2semidirect
62. #5824D3semidirect
71. #5232D3semidirect
707. C32#3307semidirect
795. C3#78895semidirect
796. C3#83512semidirect

Maximal subgroups

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

subgroupindex
C3×#58242
#105948432
#105929372
C3×#52322
#105916132
#105915852
#105915652
#105915582
#105914522
#105914202
#105914112
#105914042
#105911782
#105911472
#105911012
#835123
#788953