Finite Group Databasebeta

← #11888615

Subgroups — #11888615

Order 1152.

869 conjugacy classes of subgroups.

The subgroup lattice has 799 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5824C211yesmaximal, characteristic, complemented
2#10594995C211yesmaximal, characteristic, complemented
3#10592931C211yesmaximal, characteristic, complemented
4C3×#5238C211yesmaximal, characteristic, complemented
5#10591634C211yesmaximal, characteristic, complemented
6#10591613C211yesmaximal, characteristic, complemented
7#10591564C211yesmaximal, characteristic, complemented
8#10591559C211yesmaximal, characteristic, complemented
9#10591450C211yesmaximal, characteristic, complemented
10#10591430C211yesmaximal, characteristic, complemented
11#10591420C211yesmaximal, characteristic, complemented
12#10591409C211yesmaximal, characteristic, complemented
13#10591180C211yesmaximal, characteristic, complemented
14#10591151C211yesmaximal, characteristic, complemented
15#10591126C211yesmaximal, characteristic, complemented
16#83512—31nomaximal
17#80108—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C2×#3748C2211yescharacteristic
22C3×#946C2211yescharacteristic
23C3×#944C2211yescharacteristic
24C2×C3×#215C2211yescharacteristic
25C3×#939—21no—
26C3×#935—21no—
27C3×D4×Dic3C2211yescharacteristic
28C2×C3×#213C2211yescharacteristic
29C3×#930C2211yescharacteristic
30C3×#929—21no—
31C3×C4×#67C2211yescharacteristic
32C3×#924C2211yescharacteristic
33C2×C3×Dic3⋊C4—21no—
34#63980—21no—
35#67⋊Dic3—21no—
36#63908C2211yescharacteristic
37Dic3×D12C2211yescharacteristic
38#63891—21no—
39#63869C2211yescharacteristic
40#63861—21no—
41#63841C2211yescharacteristic
42C2×#3715C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44#63662C2211yescharacteristic
45#63662C2211yescharacteristic
46#63659C2211yescharacteristic
47#63659C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#830C2211yescharacteristic
51#63576C2211yescharacteristic
52#63573C2211yescharacteristic
53#63573C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63566C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63554C2211yescharacteristic
61C3×#547—31no—
62#5824D311yescharacteristic, complemented
63#5618—31no—
64#5565—31no—
65C3×#449—31no—
66#5238—31no—
67#5238D311yescharacteristic, complemented
68#5233—31no—
69#5232—31no—
70#5232—31no—
71#5232—61no—
72#5171—31no—
73#5162—31no—
74#5158—31no—
75#5152—31no—
76#5083—31no—
77#5082—31no—
78#5049—31no—
79#5048—31no—
80#5045—31no—
81#5043—31no—
82#5042—31no—
83#5014—31no—
84#5011—31no—
85#5009—31no—
86#4815—31no—
87#4797—31no—
88#4772—31no—
89#4763—31no—
90#4728—31no—
91#4721—31no—
92C32×#41—22no—
93C32×#41—41no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×D4—21no—
96C2×C32×D4C2311yescharacteristic
97C22×C32×C4—21no—
98C22×C32×C4C2311yescharacteristic
99C22×C3⋊Dic3—21no—
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67D411yescharacteristic
103C22×C3×Dic3—21no—
104C22×C3×Dic3—21no—
105C3×#237—22no—
106C3×#237—41no—
107C2×C3×D12C2311yescharacteristic
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C2×#625—21no—
111C2×D3×Dic3—21no—
112C4⋊(C3⋊Dic3)—21no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3748—41no—
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×#217—21no—
119C3×#217—21no—
120C3×#217D411yescharacteristic
121C3×#215—41no—
122C3×#213—22no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4D411yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4D411yescharacteristic
133C3×C4×Dic3C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136#3724—21no—
137Dic3⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141Dic32—21no—
142#3715—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×SD16—31no—
151C2×C3×D8—31no—
152C3×C4⋊Q8—31no—
153C3×#123—61no—
154C3×#123—61no—
155C3×C22⋊Q8—31no—
156C3×C22⋊Q8—31no—
157C3×#121—31no—
158C3×#121—61no—
159C3×C4×D4—31no—
160C3×C4×D4—31no—
161C2×C3×C4⋊C4—61no—
162#946C2×D311yescharacteristic
163#944C2×D311yescharacteristic
164C2×#215—31no—
165C2×#215C2×D311yescharacteristic
166#939—21no—
167#939—61no—
168#939—61no—
169#938—31no—
170#935—21no—
171D4×Dic3—31no—
172D4×Dic3—61no—
173D4×Dic3C2×D311yescharacteristic
174C2×#214—31no—
175C2×#213C2×D311yescharacteristic
176#930—31no—
177#930C2×D311yescharacteristic
178#929—21no—
179C4×#67C2×D311yescharacteristic
180#926—31no—
181C2×C4⋊Dic3—31no—
182C2×C4⋊Dic3—31no—
183C2×C4⋊Dic3—61no—
184#924C2×D311yescharacteristic
185C2×Dic3⋊C4—21no—
186C2×#208—31no—
187C2×#208—31no—
188C2×#208—61no—
189C22×C3⋊C8—31no—
190C2×D3×C8—31no—
191#898—61no—
192#892—31no—
193#890—31no—
194#886—61no—
195#883—61no—
196#67⋊C4—61no—
197#879—61no—
198C4×D12—31no—
199#870—31no—
200C3×#103—31no—
201C3×#102—31no—
202C3×C22⋊C8—31no—
203#835—31no—
204#835—31no—
205#835—31no—
206#835—31no—
207#835—31no—
208#835—31no—
209#835—31no—
210#835—61no—
211#835—61no—
212#835C2×D311yescharacteristic
213#832—31no—
214#832—31no—
215#832—31no—
216#832—31no—
217#832—31no—
218#832—61no—
219#832—61no—
220#832C2×D311yescharacteristic
221#830—31no—
222#830C2×D311yescharacteristic
223(C2×D3)⋊C8—31no—
224#817—31no—
225#817—31no—
226#816—31no—
227#816—31no—
228#815—31no—
229Dic3⋊C8—31no—
230#810—31no—
231#809—31no—
232#808—31no—
233#808—31no—
234#807—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
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—81no—
256C3×#67—41no—
257C3×#67—42no—
258C3×#67—42no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—42no—
263C2×C3×Dic3—42no—
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C3×D12—21no—
268C3×D12—21no—
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271C3×Dic6—21no—
272C3×Dic6—21no—
273#625—81no—
274D3×Dic3—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—31no—
289#449—91no—
290#442—91no—
291#435—91no—
292#417—91no—
293#416—91no—
294C3×#41—24no—
295C3×#41—22no—
296C3×#41—22no—
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—31no—
311C2×C3×D4—41no—
312C2×C3×D4—61no—
313C2×C3×D4—61no—
314C2×C3×D4C22×D311yescharacteristic
315C2×C3×D4C22×D311yescharacteristic
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—31no—
320C22×C3×C4—41no—
321C22×C3×C4—61no—
322C22×C3×C4—61no—
323C22×C3×C4C22×D311yescharacteristic
324C22×C3×C4C22×D311yescharacteristic
325C2×#67—21no—
326C2×#67—21no—
327C2×#67—61no—
328C2×#67—61no—
329C2×#67#6711yescharacteristic
330C22×Dic3—21no—
331C22×Dic3—21no—
332C22×Dic3—61no—
333C22×Dic3—61no—
334C22×Dic3—61no—
335C22×Dic3—121no—
336#237—22no—
337#237—41no—
338C2×D12C22×D311yescharacteristic
339C2×C4×D3—61no—
340C2×C4×D3C22×D311yescharacteristic
341C2×Dic6C22×D311yescharacteristic
342C3×SD16—121no—
343C3×D8—62no—
344C2×C3×C8—31no—
345C2×C3×C8—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C22⋊C4—31no—
354C3×C22⋊C4—31no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C22⋊C4—61no—
359C3×C42—31no—
360#217—21no—
361#217—21no—
362#217—61no—
363#217—61no—
364#217—61no—
365#217#6711yescharacteristic
366#215—41no—
367#215—121no—
368#214—121no—
369#213—22no—
370(C2×D3)⋊C4—21no—
371(C2×D3)⋊C4—21no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4#6711yescharacteristic
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—121no—
386C4⋊Dic3C22×D311yescharacteristic
387C4⋊Dic3C22×D311yescharacteristic
388Dic3⋊C4—21no—
389Dic3⋊C4—21no—
390Dic3⋊C4—21no—
391Dic3⋊C4—21no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4#6711yescharacteristic
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3C22×D311yescharacteristic
399#208—121no—
400#208—121no—
401#208—122no—
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
411D3×C8—121no—
412C22×C32—21no—
413C22×C32—22no—
414C22×C32—21no—
415C22×C32—21no—
416C22×C32—41no—
417C22×C32—41no—
418C22×C32C22×D411yescharacteristic
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C32×C4—21no—
426C32×C4—41no—
427C32×C4C2×#4111yescharacteristic
428C32×C4H(5,𝔽2)11yescharacteristic
429C3⋊Dic3—41no—
430C3⋊Dic3—41no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C2×#41—31no—
438C2×#41D3211yescharacteristic
439C2×SD16—31no—
440C2×SD16—91no—
441C2×D8—31no—
442C2×M16—91no—
443C22×C8—91no—
444C4⋊Q8—31no—
445#126—181no—
446#125—91no—
447#123—61no—
448#123—61no—
449#123—181no—
450C22⋊Q8—31no—
451C22⋊Q8—31no—
452#121—31no—
453#121—61no—
454#121—91no—
455#121—181no—
456C4×D4—31no—
457C4×D4—31no—
458C4×D4—91no—
459C4×D4—181no—
460#117—91no—
461C2×C4⋊C4—61no—
462C2×C4⋊C4—91no—
463#107—91no—
464#106—91no—
465#106—91no—
466C4⋊C8—91no—
467#103—31no—
468#103—91no—
469#103—91no—
470#103—91no—
471#103—91no—
472#103—91no—
473#102—31no—
474#102—91no—
475#102—91no—
476#102—91no—
477C22⋊C8—31no—
478C22⋊C8—91no—
479#97—91no—
480C23×C3—21no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—31no—
484C23×C3—41no—
485C23×C3—61no—
486C23×C3D3×D411yescharacteristic
487C23×C3C2×#6711yescharacteristic
488C22×D3—21no—
489C22×D3C2×#6711yescharacteristic
490C3×Q8—22no—
491C3×Q8—21no—
492C3×Q8—21no—
493C3×Q8—21no—
494C3×Q8—21no—
495C3×Q8—41no—
496C3×Q8—61no—
497C3×Q8—61no—
498C3×D4—21no—
499C3×D4—21no—
500C3×D4—22no—
501C3×D4—41no—
502C3×D4—42no—
503C3×D4—42no—
504C3×D4—44no—
505C3×D4—61no—
506C3×D4—61no—
507C3×D4—121no—
508C3×D4—122no—
509C3×D4—122no—
510C3×D4#23712yes—
511C3×D4#23712yes—
512C2×C3×C4—22no—
513C2×C3×C4—22no—
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—21no—
522C2×C3×C4—31no—
523C2×C3×C4—31no—
524C2×C3×C4—31no—
525C2×C3×C4—41no—
526C2×C3×C4—42no—
527C2×C3×C4—42no—
528C2×C3×C4—44no—
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×C4D3×D411yescharacteristic
537C2×C3×C4C2×#6711yescharacteristic
538C2×C3×C4C23×D311yescharacteristic
539C2×C3×C4C23×D311yescharacteristic
540#67—41no—
541#67—42no—
542#67—42no—
543#67—241no—
544#67—241no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—42no—
549C2×Dic3—42no—
550C2×Dic3—61no—
551C2×Dic3—61no—
552C2×Dic3—61no—
553C2×Dic3—61no—
554C2×Dic3—121no—
555C2×Dic3—121no—
556C2×Dic3—241no—
557C2×Dic3—241no—
558C2×Dic3—241no—
559C2×Dic3—242no—
560C2×Dic3C2×#6711yescharacteristic
561C2×Dic3C2×#6711yescharacteristic
562C2×Dic3C2×#6711yescharacteristic
563D12—21no—
564D12—21no—
565C4×D3—21no—
566C4×D3—21no—
567C4×D3—241no—
568Dic6—21no—
569Dic6—21no—
570C3×C8—61no—
571C3×C8—61no—
572C3⋊C8—21no—
573C3⋊C8—21no—
574C3⋊C8—61no—
575C3⋊C8—61no—
576C3⋊C8—61no—
577C3⋊C8—61no—
578C3⋊C8—121no—
579C3⋊C8—121no—
580C2×C32—41no—
581C2×C32—42no—
582C2×C32#54611yescharacteristic
583C2×C32#57511yescharacteristic
584C2×C32#57711yescharacteristic
585C3×D3—41no—
586C3×D3—81no—
587#41—22no—
588#41—41no—
589#41—62no—
590#41—121no—
591C2×Q8—31no—
592C2×Q8C2×D3211yescharacteristic
593C2×D4—21no—
594C2×D4—31no—
595C2×D4—31no—
596C2×D4—61no—
597C2×D4—61no—
598C2×D4—181no—
599C2×D4C2×D3211yescharacteristic
600C22×C4—21no—
601C22×C4—31no—
602C22×C4—61no—
603C22×C4—61no—
604C22×C4—181no—
605C22×C4—181no—
606C22×C4C2×D3211yescharacteristic
607SD16—121no—
608SD16—361no—
609D8—62no—
610M16—361no—
611C2×C8—31no—
612C2×C8—31no—
613C2×C8—91no—
614C2×C8—91no—
615C2×C8—361no—
616C4⋊C4—31no—
617C4⋊C4—31no—
618C4⋊C4—31no—
619C4⋊C4—61no—
620C4⋊C4—61no—
621C4⋊C4—61no—
622C4⋊C4—61no—
623C4⋊C4—91no—
624C4⋊C4—91no—
625C4⋊C4—181no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C22⋊C4—31no—
629C22⋊C4—31no—
630C22⋊C4—61no—
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—61no—
634C22⋊C4—181no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C42—31no—
638C42—181no—
639C22×C3—22no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—22no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—22no—
648C22×C3—21no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—42no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3—61no—
657C22×C3—61no—
658C22×C3—61no—
659C22×C3—81no—
660C22×C3—81no—
661C22×C3—121no—
662C22×C3—121no—
663C22×C3—121no—
664C22×C3C2×D3×D411yescharacteristic
665C22×C3C22×#6711yescharacteristic
666C2×D3—21no—
667C2×D3—21no—
668C2×D3—21no—
669C2×D3—41no—
670C2×D3—41no—
671C2×D3—41no—
672C3×C4—22no—
673C3×C4—21no—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—42no—
678C3×C4—41no—
679C3×C4—41no—
680C3×C4—61no—
681C3×C4—61no—
682C3×C4—61no—
683C3×C4—121no—
684C3×C4—121no—
685C3×C4—121no—
686C3×C4C2×#23711yescharacteristic
687C3×C4C2×#23711yescharacteristic
688C3×C4#100411yescharacteristic
689C3×C4#100411yescharacteristic
690Dic3—21no—
691Dic3—21no—
692Dic3—21no—
693Dic3—41no—
694Dic3—41no—
695Dic3—41no—
696Dic3—121no—
697Dic3—121no—
698Dic3—121no—
699Dic3—121no—
700Dic3—241no—
701Dic3—241no—
702C32#330711yescharacteristic, complemented, Sylow
703C23—21no—
704C23—31no—
705C23—61no—
706C23D3×#6711yescharacteristic
707Q8—21no—
708Q8—21no—
709Q8—61no—
710Q8—61no—
711D4—21no—
712D4—42no—
713D4—61no—
714D4—61no—
715D4—121no—
716D4—122no—
717D4—122no—
718D4—721no—
719D4#380512yes—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—31no—
724C2×C4—31no—
725C2×C4—31no—
726C2×C4—42no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—122no—
733C2×C4—122no—
734C2×C4—181no—
735C2×C4—181no—
736C2×C4—721no—
737C2×C4—721no—
738C2×C4D3×#6711yescharacteristic
739C2×C4C22×D3211yescharacteristic
740C8—61no—
741C8—61no—
742C8—181no—
743C8—181no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—42no—
748C2×C3—41no—
749C2×C3—42no—
750C2×C3—41no—
751C2×C3—42no—
752C2×C3—82no—
753C2×C3—121no—
754C2×C3—241no—
755C2×C3#559111yescharacteristic
756C2×C3#577011yescharacteristic
757C2×C3#577311yescharacteristic
758C2×C3#580611yescharacteristic
759C2×C3#582211yescharacteristic
760C2×C3#583711yescharacteristic
761D3—41no—
762D3—81no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—22no—
767C22—41no—
768C22—41no—
769C22—61no—
770C22—61no—
771C22—61no—
772C22—121no—
773C22—121no—
774C22—121no—
775C22C2×D3×#6711yescharacteristic
776C4—21no—
777C4—41no—
778C4—61no—
779C4—61no—
780C4—61no—
781C4—121no—
782C4—121no—
783C4—121no—
784C4—361no—
785C4—361no—
786C4C2×#380511yescharacteristic
787C4#6433011yescharacteristic
788C3—21no—
789C3#8010811yescharacteristic, complemented
790C3#8351211yescharacteristic, complemented
791C2—41no—
792C2—42no—
793C2—121no—
794C2—241no—
795C2#1059545711yescharacteristic
796C2#1059546911yescharacteristic
797C2#1059549411yescharacteristic
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. #10594995C2semidirect
3. #10592931C2semidirect
4. C3×#5238C2semidirect
5. #10591634C2semidirect
6. #10591613C2semidirect
7. #10591564C2semidirect
8. #10591559C2semidirect
9. #10591450C2semidirect
10. #10591430C2semidirect
11. #10591420C2semidirect
12. #10591409C2semidirect
13. #10591180C2semidirect
14. #10591151C2semidirect
15. #10591126C2semidirect
62. #5824D3semidirect
67. #5238D3semidirect
702. C32#3307semidirect
789. C3#80108semidirect
790. C3#83512semidirect

Maximal subgroups

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

subgroupindex
C3×#58242
#105949952
#105929312
C3×#52382
#105916342
#105916132
#105915642
#105915592
#105914502
#105914302
#105914202
#105914092
#105911802
#105911512
#105911262
#835123
#801083