Finite Group Databasebeta

← #11870392

Subgroups — #11870392

Order 1152.

849 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5523C211yesmaximal, characteristic, complemented
2#10594894C211yesmaximal, characteristic
3#10592702C211yesmaximal, characteristic, complemented
4C3×#4996C211yesmaximal, characteristic, complemented
5#10591145C211yesmaximal, characteristic, complemented
6#10591125C211yesmaximal, characteristic, complemented
7#10591101C211yesmaximal, characteristic, complemented
8#10590610C211yesmaximal, characteristic, complemented
9#10590609C211yesmaximal, characteristic, complemented
10D3×#808C211yesmaximal, characteristic, complemented
11#10590521C211yesmaximal, characteristic, complemented
12#10590516C211yesmaximal, characteristic, complemented
13#10590436C211yesmaximal, characteristic, complemented
14#10590424C211yesmaximal, characteristic, complemented
15#10590423C211yesmaximal, characteristic, complemented
16#82574—31nomaximal
17#81521—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C32×#117C2211yescharacteristic
21#64139C2211yescharacteristic
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C3×#924C2211yescharacteristic
24C3×#892C2211yescharacteristic
25C3×#892C2211yescharacteristic
26C3×D3×C4⋊C4C2211yescharacteristic
27C3×D3×C4⋊C4C2211yescharacteristic
28C3×#67⋊C4—21no—
29C3×#67⋊C4—21no—
30C3×C4×D12—21no—
31C3×C4×Dic6—21no—
32#63971—21no—
33#63958—21no—
34#63909C2211yescharacteristic
35D3×C4⋊Dic3C2211yescharacteristic
36#63888—21no—
37#63886—21no—
38#63856C2211yescharacteristic
39C2×#3711C2211yescharacteristic
40C2×D3×C3⋊C8C2211yescharacteristic
41#63657C2211yescharacteristic
42#63636C2211yescharacteristic
43#63636C2211yescharacteristic
44#63635C2211yescharacteristic
45#63634C2211yescharacteristic
46C3×#830C2211yescharacteristic
47C3×#810C2211yescharacteristic
48C3×#810C2211yescharacteristic
49C3×#808C2211yescharacteristic
50C3×#807C2211yescharacteristic
51#63574C2211yescharacteristic
52#63574C2211yescharacteristic
53#63573C2211yescharacteristic
54#63573C2211yescharacteristic
55#63565C2211yescharacteristic
56#63565C2211yescharacteristic
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C3×#520—31no—
62#5833—31no—
63#5629—31no—
64#5523D311yescharacteristic, complemented
65C3×#485—31no—
66#5234—31no—
67#5043—31no—
68#5003—31no—
69#5003—31no—
70#5003—31no—
71#5003—61no—
72#5002—31no—
73#4996—31no—
74#4996D311yescharacteristic, complemented
75#4995—31no—
76#4971—31no—
77#4971—31no—
78#4968—31no—
79#4968—31no—
80#4966—31no—
81C2×#808—31no—
82#4885—31no—
83#4881—31no—
84#4863—31no—
85D3×#106—31no—
86#4815—31no—
87#4805—31no—
88#4804—31no—
89#4803—31no—
90#4735—31no—
91#4727—31no—
92C22×C32×C4C2311yescharacteristic
93C2×#638—21no—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C3×#67D411yescharacteristic
96C2×C3×#67D411yescharacteristic
97C22×C3×Dic3—21no—
98C3×#235—22no—
99C3×#235—22no—
100C2×C3×D12D411yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6D411yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×#626—21no—
108C2×#626—21no—
109C2×#624—21no—
110C2×D3×Dic3—21no—
111#3799—22no—
112#3799—22no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115C32×C22⋊C4—21no—
116C32×C42—21no—
117#3752—21no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C3×#217—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×C4×Dic3—21no—
132C3×C4×Dic3—21no—
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135#3724—21no—
136Dic3⋊Dic3—21no—
137#3722—21no—
138(C2×D3)⋊Dic3—21no—
139#3711—22no—
140D3×C3⋊C8—22no—
141#3099—91noSylow
142C2×C3×#41—31no—
143C2×#239—31no—
144C2×#235—31no—
145C2×#235C2×D311yescharacteristic
146C3×C22⋊Q8—31no—
147C3×C4×Q8—61no—
148C3×C4×D4—61no—
149C3×C4×D4—61no—
150C3×C4×D4—61no—
151C3×#117—21no—
152C3×#117—31no—
153C3×#117—31no—
154C3×#117C2×D311yescharacteristic
155C3×#117C2×D311yescharacteristic
156C2×C3×C4⋊C4—31no—
157C2×C3×C4⋊C4—31no—
158C2×C3×C4⋊C4—31no—
159#946—31no—
160#946—61no—
161#939—61no—
162#939—61no—
163#938—61no—
164#930—31no—
165#930—31no—
166#930—31no—
167#930—61no—
168C2×C4⋊Dic3—31no—
169C2×C4⋊Dic3C2×D311yescharacteristic
170#924—31no—
171#924C2×D311yescharacteristic
172C2×#208—31no—
173C22×C3⋊C8—31no—
174C2×ΓL(1,𝔽25)—31no—
175C2×D3×C8—31no—
176#896—61no—
177#895—31no—
178#895—61no—
179#892C2×D311yescharacteristic
180#892C2×D311yescharacteristic
181D3×C4⋊C4—31no—
182D3×C4⋊C4C2×D311yescharacteristic
183D3×C4⋊C4C2×D311yescharacteristic
184#884—61no—
185#884—61no—
186#67⋊C4—21no—
187#67⋊C4—21no—
188C4×D12—21no—
189C4×Dic6—21no—
190C3×#107—31no—
191C3×#106—31no—
192C3×#103—31no—
193C3×#103—31no—
194C3×C22⋊C8—31no—
195#835—31no—
196#835—31no—
197#830—31no—
198#830—31no—
199#830—31no—
200#830—31no—
201#830—61no—
202#830C2×D311yescharacteristic
203#821—31no—
204#821—31no—
205(C2×D3)⋊C8—31no—
206(C2×D3)⋊C8—31no—
207#817—31no—
208#817—31no—
209#810—31no—
210#810—31no—
211#810C2×D311yescharacteristic
212#810C2×D311yescharacteristic
213#809—31no—
214#809—31no—
215#809—31no—
216#809—31no—
217#809—31no—
218#809—31no—
219#809—61no—
220#809—61no—
221#808—31no—
222#808—31no—
223#808—31no—
224#808—31no—
225#808—31no—
226#808—31no—
227#808—31no—
228#808—31no—
229#808—61no—
230#808C2×D311yescharacteristic
231#807—31no—
232#807—31no—
233#807—61no—
234#807C2×D311yescharacteristic
235C23×C32C2×D411yescharacteristic
236C22×C3⋊D3—21no—
237C22×C3×D3C2×D411yescharacteristic
238C22×C3×D3C2×D411yescharacteristic
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4C2×D411yescharacteristic
244C2×C32×C4C2411yescharacteristic
245#638—81no—
246C2×C3⋊Dic3—21no—
247C4⋊(C3⋊D3)—21no—
248C4⋊(C3⋊D3)—21no—
249C3×#67—22no—
250C3×#67—22no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—81no—
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C3×D12—22no—
259C3×C4×D3—21no—
260C3×C4×D3—21no—
261C3×C4×D3—81no—
262C3×C4×D3—81no—
263C3×C4×D3#4112yes—
264C3×C4×D3#4112yes—
265C3×Dic6—22no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268#626—42no—
269#626—81no—
270#624—42no—
271D3×Dic3—81no—
272C3⋊(C3⋊C8)—21no—
273C3⋊(C3⋊C8)—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#537—91no—
277#520—31no—
278#485—31no—
279#485—91no—
280#483—91no—
281#483—91no—
282#482—91no—
283#482—91no—
284#481—91no—
285#481—91no—
286#428—91no—
287C2×#106—91no—
288#417—91no—
289#416—91no—
290#408—91no—
291C3×#41—62no—
292C3×#41—62no—
293C2×C3×Q8—31no—
294C2×C3×Q8—31no—
295C2×C3×D4—31no—
296C2×C3×D4—31no—
297C2×C3×D4—31no—
298C22×C3×C4—21no—
299C22×C3×C4—31no—
300C22×C3×C4—31no—
301C22×C3×C4—61no—
302C22×C3×C4—61no—
303C22×C3×C4—61no—
304C22×C3×C4C22×D311yescharacteristic
305C22×C3×C4C22×D311yescharacteristic
306C2×#67—61no—
307C2×#67—61no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—121no—
311C2×#67#6711yescharacteristic
312C2×#67#6711yescharacteristic
313C22×Dic3—21no—
314C22×Dic3—61no—
315#239—62no—
316#239—62no—
317#235—22no—
318#235—22no—
319#235—62no—
320#235—62no—
321C2×D12—31no—
322C2×D12—31no—
323C2×D12—61no—
324C2×D12—61no—
325C2×D12—61no—
326C2×D12#6711yescharacteristic
327C2×C4×D3—21no—
328C2×C4×D3—21no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3C22×D311yescharacteristic
333C2×C4×D3C22×D311yescharacteristic
334C2×Dic6#6711yescharacteristic
335C2×Dic6C22×D311yescharacteristic
336C2×C3×C8—31no—
337C2×C3×C8—31no—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—21no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C4⋊C4C22×D311yescharacteristic
351C3×C22⋊C4—21no—
352C3×C22⋊C4—21no—
353C3×C22⋊C4—41no—
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C42—21no—
358C3×C42—21no—
359C3×C42—41no—
360C3×C42—61no—
361C3×C42—61no—
362#217—21no—
363#217—61no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—121no—
372C4⋊Dic3—21no—
373C4⋊Dic3—31no—
374C4⋊Dic3—31no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3C22×D311yescharacteristic
378C4⋊Dic3C22×D311yescharacteristic
379C4⋊Dic3C22×D311yescharacteristic
380Dic3⋊C4—21no—
381Dic3⋊C4—21no—
382Dic3⋊C4—21no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386C4×Dic3—21no—
387C4×Dic3—21no—
388#208—62no—
389C2×C3⋊C8—31no—
390C2×C3⋊C8—31no—
391C2×C3⋊C8—31no—
392C2×C3⋊C8—31no—
393C2×C3⋊C8—61no—
394C2×C3⋊C8—61no—
395C2×C3⋊C8—62no—
396C2×C3⋊C8C22×D311yescharacteristic
397C2×C3⋊C8C22×D311yescharacteristic
398ΓL(1,𝔽25)—62no—
399D3×C8—62no—
400C22×C32—21no—
401C22×C32—21no—
402C22×C32—21no—
403C22×C32C22×D411yescharacteristic
404C2×C3⋊D3—41no—
405C2×C3⋊D3—41no—
406C2×C3⋊D3—41no—
407C2×C3×D3—21no—
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3#12312yes—
413C32×C4—21no—
414C32×C4—41no—
415C32×C4—41no—
416C32×C4C2×#4111yescharacteristic
417C32×C4C2×#4111yescharacteristic
418C3⋊Dic3—41no—
419C3×Dic3—21no—
420C3×Dic3—41no—
421C3×Dic3—41no—
422C3×Dic3—41no—
423C3×Dic3—41no—
424C3×Dic3#12312yes—
425C2×#41—31no—
426C2×#41—91no—
427C2×M16—91no—
428C22×C8—91no—
429C22⋊Q8—31no—
430C22⋊Q8—91no—
431C22⋊Q8—181no—
432#121—91no—
433#121—91no—
434#121—181no—
435#121—181no—
436#121—181no—
437C4×Q8—61no—
438C4×D4—61no—
439C4×D4—61no—
440C4×D4—61no—
441#117—31no—
442#117—31no—
443#117D3211yescharacteristic
444C2×C4⋊C4—31no—
445C2×C4⋊C4—31no—
446C2×C4⋊C4—31no—
447C2×C4⋊C4—91no—
448#107—31no—
449#107—91no—
450#106—31no—
451#106—91no—
452#106—91no—
453#106—91no—
454#106—91no—
455#106—91no—
456#103—31no—
457#103—31no—
458#103—91no—
459#103—91no—
460#102—91no—
461#102—91no—
462#102—91no—
463#102—91no—
464C22⋊C8—31no—
465C22⋊C8—91no—
466C22⋊C8—91no—
467C22⋊C8—91no—
468C23×C3—21no—
469C23×C3—31no—
470C23×C3—31no—
471C23×C3D3×D411yescharacteristic
472C23×C3C2×#6711yescharacteristic
473C22×D3—61no—
474C22×D3—61no—
475C22×D3—121no—
476C22×D3C2×#6711yescharacteristic
477C22×D3C2×#6711yescharacteristic
478C3×Q8—62no—
479C3×Q8—61no—
480C3×Q8—61no—
481C3×D4—62no—
482C3×D4—62no—
483C3×D4—62no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—31no—
495C2×C3×C4—32no—
496C2×C3×C4—32no—
497C2×C3×C4—31no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—241no—
509C2×C3×C4—241no—
510C2×C3×C4—241no—
511C2×C3×C4D3×D411yescharacteristic
512C2×C3×C4C2×#6711yescharacteristic
513C2×C3×C4C23×D311yescharacteristic
514C2×C3×C4C23×D311yescharacteristic
515#67—22no—
516#67—22no—
517#67—122no—
518#67—241no—
519#67—241no—
520#67—241no—
521#67—242no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—81no—
529C2×Dic3—121no—
530C2×Dic3—241no—
531C2×Dic3C2×#6711yescharacteristic
532C2×Dic3C2×#6711yescharacteristic
533D12—22no—
534D12—61no—
535D12—61no—
536D12—61no—
537D12—61no—
538D12—121no—
539D12—121no—
540D12—122no—
541D12—241no—
542C4×D3—21no—
543C4×D3—21no—
544C4×D3—81no—
545C4×D3—81no—
546C4×D3—122no—
547C4×D3—122no—
548C4×D3—241no—
549C4×D3#23512yes—
550C4×D3#23512yes—
551Dic6—22no—
552Dic6—21no—
553Dic6—21no—
554C3×C8—61no—
555C3×C8—61no—
556C3⋊C8—21no—
557C3⋊C8—21no—
558C3⋊C8—61no—
559C3⋊C8—61no—
560C3⋊C8—61no—
561C3⋊C8—61no—
562C3⋊C8—121no—
563C3⋊C8—121no—
564C2×C32—41no—
565C2×C32C2×#12311yescharacteristic
566C2×C32#57711yescharacteristic
567C2×C32#57711yescharacteristic
568C3⋊D3—81no—
569C3×D3—22no—
570C3×D3—41no—
571#41—62no—
572#41—62no—
573#41—182no—
574#41—182no—
575C2×Q8—31no—
576C2×Q8—31no—
577C2×D4—31no—
578C2×D4—31no—
579C2×D4—31no—
580C2×D4—91no—
581C2×D4—181no—
582C2×D4—181no—
583C2×D4—181no—
584C22×C4—31no—
585C22×C4—31no—
586C22×C4—61no—
587C22×C4—61no—
588C22×C4—61no—
589C22×C4—181no—
590C22×C4—181no—
591C22×C4C2×D3211yescharacteristic
592M16—182no—
593C2×C8—31no—
594C2×C8—31no—
595C2×C8—91no—
596C2×C8—91no—
597C2×C8—182no—
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—31no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4—61no—
605C4⋊C4—91no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4C2×D3211yescharacteristic
609C4⋊C4C2×D3211yescharacteristic
610C22⋊C4—21no—
611C22⋊C4—61no—
612C22⋊C4—61no—
613C22⋊C4—61no—
614C22⋊C4—181no—
615C22⋊C4—181no—
616C22⋊C4—181no—
617C42—21no—
618C42—61no—
619C42—61no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—32no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—61no—
632C22×C3—61no—
633C22×C3—61no—
634C22×C3—61no—
635C22×C3—61no—
636C22×C3C2×D3×D411yescharacteristic
637C22×C3C22×#6711yescharacteristic
638C2×D3—21no—
639C2×D3—21no—
640C2×D3—21no—
641C2×D3—21no—
642C2×D3—21no—
643C2×D3—121no—
644C2×D3—121no—
645C2×D3—121no—
646C2×D3—121no—
647C2×D3—121no—
648C2×D3—121no—
649C2×D3—241no—
650C2×D3—241no—
651C2×D3—241no—
652C2×D3#92912yes—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—32no—
658C3×C4—41no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—41no—
662C3×C4—41no—
663C3×C4—61no—
664C3×C4—81no—
665C3×C4—81no—
666C3×C4—121no—
667C3×C4—121no—
668C3×C4—121no—
669C3×C4—121no—
670C3×C4C2×#23511yescharacteristic
671C3×C4C2×#23511yescharacteristic
672C3×C4D3×#4111yescharacteristic
673C3×C4D3×#4111yescharacteristic
674Dic3—21no—
675Dic3—41no—
676Dic3—41no—
677Dic3—41no—
678Dic3—41no—
679Dic3—121no—
680Dic3—121no—
681Dic3—241no—
682Dic3#92912yes—
683C32#309911yescharacteristic, complemented, Sylow
684C23—31no—
685C23—31no—
686C23—181no—
687C23D3×#6711yescharacteristic
688Q8—62no—
689Q8—61no—
690Q8—61no—
691D4—62no—
692D4—62no—
693D4—62no—
694D4—181no—
695D4—181no—
696D4—362no—
697D4—721no—
698D4—721no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—31no—
704C2×C4—32no—
705C2×C4—32no—
706C2×C4—31no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—181no—
714C2×C4—241no—
715C2×C4—241no—
716C2×C4—241no—
717C2×C4—362no—
718C2×C4—721no—
719C2×C4D3×#6711yescharacteristic
720C2×C4C22×D3211yescharacteristic
721C8—61no—
722C8—61no—
723C8—181no—
724C8—181no—
725C2×C3—21no—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—41no—
729C2×C3—41no—
730C2×C3—62no—
731C2×C3—81no—
732C2×C3—121no—
733C2×C3D3×#12311yescharacteristic
734C2×C3#577011yescharacteristic
735C2×C3#577811yescharacteristic
736C2×C3C2×#92911yescharacteristic
737C2×C3#583611yescharacteristic
738C2×C3#583711yescharacteristic
739D3—22no—
740D3—41no—
741D3—241no—
742D3—241no—
743D3—481no—
744C22—21no—
745C22—21no—
746C22—21no—
747C22—32no—
748C22—61no—
749C22—61no—
750C22—61no—
751C22—61no—
752C22—61no—
753C22—361no—
754C22—361no—
755C22—361no—
756C22C2×D3×#6711yescharacteristic
757C4—21no—
758C4—32no—
759C4—41no—
760C4—41no—
761C4—61no—
762C4—121no—
763C4—121no—
764C4—121no—
765C4—121no—
766C4—361no—
767C4D3×#23511yescharacteristic
768C4D3×#23511yescharacteristic
769C3—21no—
770C3#8152111yescharacteristic, complemented
771C3#8257411yescharacteristic, complemented
772C2—41no—
773C2—62no—
774C2—121no—
775C2—721no—
776C2D3×#92911yescharacteristic
777C2#1059545711yescharacteristic
778C2#1059546411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radical#10594894C2
hypercenter#117D32
hypocenterC32#3099
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C3×#5523C2semidirect
3. #10592702C2semidirect
4. C3×#4996C2semidirect
5. #10591145C2semidirect
6. #10591125C2semidirect
7. #10591101C2semidirect
8. #10590610C2semidirect
9. #10590609C2semidirect
10. D3×#808C2semidirect
11. #10590521C2semidirect
12. #10590516C2semidirect
13. #10590436C2semidirect
14. #10590424C2semidirect
15. #10590423C2semidirect
64. #5523D3semidirect
74. #4996D3semidirect
683. C32#3099semidirect
770. C3#81521semidirect
771. C3#82574semidirect

Maximal subgroups

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

subgroupindex
C3×#55232
#105948942
#105927022
C3×#49962
#105911452
#105911252
#105911012
#105906102
#105906092
D3×#8082
#105905212
#105905162
#105904362
#105904242
#105904232
#825743
#815213