Finite Group Databasebeta

← #11870390

Subgroups — #11870390

Order 1152.

844 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5523C211yesmaximal, characteristic, complemented
2#10595004C211yesmaximal, characteristic
3#10592695C211yesmaximal, characteristic, complemented
4C3×#5003C211yesmaximal, characteristic, complemented
5#10591145C211yesmaximal, characteristic, complemented
6#10591124C211yesmaximal, characteristic, complemented
7#10591091C211yesmaximal, characteristic, complemented
8#10590608C211yesmaximal, characteristic, complemented
9#10590607C211yesmaximal, characteristic, complemented
10D3×#808C211yesmaximal, characteristic, complemented
11#10590502C211yesmaximal, characteristic, complemented
12#10590500C211yesmaximal, characteristic, complemented
13#10590436C211yesmaximal, characteristic, complemented
14#10590429C211yesmaximal, characteristic, complemented
15#10590426C211yesmaximal, characteristic, complemented
16#82574—31nomaximal
17#81377—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20C32×#117C2211yescharacteristic
21#64133C2211yescharacteristic
22C3×#930C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
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#63970—21no—
33#63970—21no—
34#63908C2211yescharacteristic
35D3×C4⋊Dic3C2211yescharacteristic
36#63887—21no—
37#63885—21no—
38#63857C2211yescharacteristic
39C2×#3711C2211yescharacteristic
40C2×D3×C3⋊C8C2211yescharacteristic
41#63657C2211yescharacteristic
42#63637C2211yescharacteristic
43#63637C2211yescharacteristic
44#63635C2211yescharacteristic
45#63634C2211yescharacteristic
46C3×#830C2211yescharacteristic
47C3×#809C2211yescharacteristic
48C3×#809C2211yescharacteristic
49C3×#808C2211yescharacteristic
50C3×#807C2211yescharacteristic
51#63574C2211yescharacteristic
52#63574C2211yescharacteristic
53#63573C2211yescharacteristic
54#63573C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C3×#520—31no—
62#5833—31no—
63#5608—31no—
64#5523D311yescharacteristic, complemented
65C3×#482—31no—
66#5234—31no—
67#5034—31no—
68#5003—31no—
69#5003D311yescharacteristic, complemented
70#5002—31no—
71#4996—31no—
72#4996—31no—
73#4996—31no—
74#4996—61no—
75#4995—31no—
76#4971—31no—
77#4971—31no—
78#4968—31no—
79#4968—31no—
80#4966—31no—
81C2×#808—31no—
82#4888—31no—
83#4881—31no—
84#4862—31no—
85D3×#106—31no—
86#4779—31no—
87#4777—31no—
88#4772—31no—
89#4771—31no—
90#4727—31no—
91#4721—31no—
92C22×C32×C4C2311yescharacteristic
93C2×#634C2311yescharacteristic
94C2×C3×#67—21no—
95C2×C3×#67D411yescharacteristic
96C2×C3×#67D411yescharacteristic
97C22×C3×Dic3—21no—
98C3×#235—22no—
99C3×#235—22no—
100C2×C3×D12D411yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6D411yescharacteristic
107C2×#625—21no—
108C2×#625—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111#3795—22no—
112#3795—22no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115C32×C22⋊C4—21no—
116C32×C42—21no—
117#3757—21no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119#3750—21no—
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×C4×Dic3—21no—
132C3×C4×Dic3—21no—
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139#3711—22no—
140D3×C3⋊C8—22no—
141#3099—91noSylow
142C2×C3×#41—31no—
143C2×#237—31no—
144C2×#235—31no—
145C2×#235C2×D311yescharacteristic
146C3×#121—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—61no—
160#939—61no—
161#939—61no—
162#939—61no—
163#938—31no—
164#938—61no—
165#938—61no—
166#930—31no—
167#930C2×D311yescharacteristic
168C2×C4⋊Dic3—31no—
169C2×C4⋊Dic3C2×D311yescharacteristic
170#924—31no—
171#924—31no—
172#924—31no—
173#924—61no—
174C2×#208—31no—
175C22×C3⋊C8—31no—
176C2×ΓL(1,𝔽25)—31no—
177C2×D3×C8—31no—
178#897—31no—
179#892C2×D311yescharacteristic
180#892C2×D311yescharacteristic
181D3×C4⋊C4—31no—
182D3×C4⋊C4C2×D311yescharacteristic
183D3×C4⋊C4C2×D311yescharacteristic
184#884—61no—
185#67⋊C4—21no—
186#67⋊C4—21no—
187#878—61no—
188C4×D12—21no—
189C4×Dic6—21no—
190C3×#107—31no—
191C3×#106—31no—
192C3×#102—31no—
193C3×#102—31no—
194C3×C22⋊C8—31no—
195#832—31no—
196#832—31no—
197#830—31no—
198#830—31no—
199#830—31no—
200#830—31no—
201#830—61no—
202#830C2×D311yescharacteristic
203(C2×D3)⋊C8—31no—
204(C2×D3)⋊C8—31no—
205#817—31no—
206#817—31no—
207#816—31no—
208#816—31no—
209#810—31no—
210#810—31no—
211#810—31no—
212#810—31no—
213#810—31no—
214#810—31no—
215#810—61no—
216#810—61no—
217#809—31no—
218#809—31no—
219#809C2×D311yescharacteristic
220#809C2×D311yescharacteristic
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
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—21no—
247#634—21no—
248#634—21no—
249C3×#67—22no—
250C3×#67—22no—
251C3×#67—81no—
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×D12—21no—
260C3×D12—21no—
261C3×C4×D3—21no—
262C3×C4×D3—21no—
263C3×C4×D3—81no—
264C3×C4×D3—81no—
265C3×C4×D3#4112yes—
266C3×C4×D3#4112yes—
267C3×Dic6—22no—
268#625—42no—
269#625—81no—
270D3×Dic3—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—91no—
279#485—91no—
280#483—91no—
281#483—91no—
282#482—31no—
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×D4—31no—
295C2×C3×D4—31no—
296C2×C3×D4—31no—
297C2×C3×D4—31no—
298C2×C3×D4—61no—
299C22×C3×C4—21no—
300C22×C3×C4—31no—
301C22×C3×C4—31no—
302C22×C3×C4—61no—
303C22×C3×C4—61no—
304C22×C3×C4—61no—
305C22×C3×C4C22×D311yescharacteristic
306C22×C3×C4C22×D311yescharacteristic
307C2×#67—21no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67#6711yescharacteristic
313C2×#67#6711yescharacteristic
314C22×Dic3—21no—
315C22×Dic3—61no—
316C22×Dic3—61no—
317#237—62no—
318#237—62no—
319#235—22no—
320#235—22no—
321#235—62no—
322#235—62no—
323C2×D12#6711yescharacteristic
324C2×D12C22×D311yescharacteristic
325C2×C4×D3—21no—
326C2×C4×D3—21no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3C22×D311yescharacteristic
330C2×C4×D3C22×D311yescharacteristic
331C2×Dic6—31no—
332C2×Dic6—31no—
333C2×Dic6—61no—
334C2×Dic6#6711yescharacteristic
335C2×C3×C8—31no—
336C2×C3×C8—31no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C22⋊C4—21no—
350C3×C22⋊C4—21no—
351C3×C22⋊C4—41no—
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C42—21no—
356C3×C42—21no—
357C3×C42—41no—
358C3×C42—61no—
359C3×C42—61no—
360#217—61no—
361#217—61no—
362#217—61no—
363#217—61no—
364#217—121no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—21no—
367(C2×D3)⋊C4—21no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370C4⋊Dic3—21no—
371C4⋊Dic3—31no—
372C4⋊Dic3—31no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3C22×D311yescharacteristic
377C4⋊Dic3C22×D311yescharacteristic
378C4⋊Dic3C22×D311yescharacteristic
379Dic3⋊C4—21no—
380Dic3⋊C4—21no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—121no—
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—21no—
405C2×C3×D3—21no—
406C2×C3×D3—21no—
407C2×C3×D3—21no—
408C2×C3×D3—21no—
409C2×C3×D3—41no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3#12312yes—
413C32×C4—21no—
414C32×C4—41no—
415C32×C4—41no—
416C32×C4C2×#4111yescharacteristic
417C32×C4C2×#4111yescharacteristic
418C3⋊Dic3—41no—
419C3⋊Dic3—41no—
420C3×Dic3—21no—
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—91no—
430C22⋊Q8—91no—
431C22⋊Q8—181no—
432#121—31no—
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—91no—
457#103—91no—
458#103—91no—
459#103—91no—
460#102—31no—
461#102—31no—
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×C3—61no—
472C23×C3D3×D411yescharacteristic
473C23×C3C2×#6711yescharacteristic
474C22×D3—21no—
475C22×D3C2×#6711yescharacteristic
476C22×D3C2×#6711yescharacteristic
477C3×Q8—62no—
478C3×D4—62no—
479C3×D4—62no—
480C3×D4—62no—
481C3×D4—61no—
482C3×D4—61no—
483C3×D4—241no—
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—241no—
508C2×C3×C4—241no—
509C2×C3×C4—241no—
510C2×C3×C4D3×D411yescharacteristic
511C2×C3×C4C2×#6711yescharacteristic
512C2×C3×C4C23×D311yescharacteristic
513C2×C3×C4C23×D311yescharacteristic
514#67—22no—
515#67—22no—
516#67—81no—
517#67—122no—
518#67—122no—
519#67—241no—
520#67—241no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—81no—
529C2×Dic3—121no—
530C2×Dic3—121no—
531C2×Dic3—122no—
532C2×Dic3—241no—
533C2×Dic3C2×#6711yescharacteristic
534C2×Dic3C2×#6711yescharacteristic
535D12—22no—
536D12—21no—
537D12—21no—
538C4×D3—21no—
539C4×D3—21no—
540C4×D3—81no—
541C4×D3—81no—
542C4×D3—122no—
543C4×D3—241no—
544C4×D3#23512yes—
545C4×D3#23512yes—
546Dic6—22no—
547Dic6—61no—
548Dic6—61no—
549Dic6—61no—
550Dic6—61no—
551Dic6—121no—
552Dic6—121no—
553C3×C8—61no—
554C3×C8—61no—
555C3⋊C8—21no—
556C3⋊C8—21no—
557C3⋊C8—61no—
558C3⋊C8—61no—
559C3⋊C8—61no—
560C3⋊C8—61no—
561C3⋊C8—121no—
562C3⋊C8—121no—
563C2×C32—41no—
564C2×C32C2×#12311yescharacteristic
565C2×C32#57711yescharacteristic
566C2×C32#57711yescharacteristic
567C3×D3—22no—
568C3×D3—41no—
569C3×D3—81no—
570#41—62no—
571#41—62no—
572#41—182no—
573#41—182no—
574C2×Q8—31no—
575C2×Q8—91no—
576C2×D4—31no—
577C2×D4—31no—
578C2×D4—31no—
579C2×D4—31no—
580C2×D4—61no—
581C2×D4—181no—
582C2×D4—181no—
583C22×C4—31no—
584C22×C4—31no—
585C22×C4—61no—
586C22×C4—61no—
587C22×C4—61no—
588C22×C4—181no—
589C22×C4—181no—
590C22×C4C2×D3211yescharacteristic
591M16—182no—
592C2×C8—31no—
593C2×C8—31no—
594C2×C8—91no—
595C2×C8—91no—
596C2×C8—182no—
597C4⋊C4—31no—
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—91no—
604C4⋊C4—181no—
605C4⋊C4—181no—
606C4⋊C4—181no—
607C4⋊C4C2×D3211yescharacteristic
608C4⋊C4C2×D3211yescharacteristic
609C22⋊C4—21no—
610C22⋊C4—61no—
611C22⋊C4—61no—
612C22⋊C4—61no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C22⋊C4—181no—
616C42—21no—
617C42—61no—
618C42—61no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—32no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—61no—
631C22×C3—61no—
632C22×C3—61no—
633C22×C3—61no—
634C22×C3—61no—
635C22×C3—121no—
636C22×C3—121no—
637C22×C3—121no—
638C22×C3C2×D3×D411yescharacteristic
639C22×C3C22×#6711yescharacteristic
640C2×D3—21no—
641C2×D3—21no—
642C2×D3—21no—
643C2×D3—21no—
644C2×D3—21no—
645C2×D3—41no—
646C2×D3—41no—
647C2×D3—41no—
648C2×D3#92912yes—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—32no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4—41no—
657C3×C4—41no—
658C3×C4—41no—
659C3×C4—61no—
660C3×C4—81no—
661C3×C4—81no—
662C3×C4—121no—
663C3×C4—121no—
664C3×C4—121no—
665C3×C4C2×#23511yescharacteristic
666C3×C4C2×#23511yescharacteristic
667C3×C4D3×#4111yescharacteristic
668C3×C4D3×#4111yescharacteristic
669Dic3—21no—
670Dic3—41no—
671Dic3—41no—
672Dic3—41no—
673Dic3—121no—
674Dic3—121no—
675Dic3—121no—
676Dic3—121no—
677Dic3—241no—
678Dic3—241no—
679Dic3#92912yes—
680C32#309911yescharacteristic, complemented, Sylow
681C23—31no—
682C23—31no—
683C23—61no—
684C23D3×#6711yescharacteristic
685Q8—62no—
686Q8—181no—
687Q8—181no—
688D4—62no—
689D4—62no—
690D4—62no—
691D4—61no—
692D4—61no—
693D4—241no—
694D4—362no—
695D4—721no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—31no—
701C2×C4—32no—
702C2×C4—32no—
703C2×C4—31no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—181no—
710C2×C4—181no—
711C2×C4—241no—
712C2×C4—241no—
713C2×C4—241no—
714C2×C4—362no—
715C2×C4—721no—
716C2×C4D3×#6711yescharacteristic
717C2×C4C22×D3211yescharacteristic
718C8—61no—
719C8—61no—
720C8—181no—
721C8—181no—
722C2×C3—21no—
723C2×C3—21no—
724C2×C3—21no—
725C2×C3—41no—
726C2×C3—41no—
727C2×C3—62no—
728C2×C3—81no—
729C2×C3—121no—
730C2×C3—241no—
731C2×C3D3×#12311yescharacteristic
732C2×C3#577011yescharacteristic
733C2×C3#577511yescharacteristic
734C2×C3C2×#92911yescharacteristic
735C2×C3#583611yescharacteristic
736C2×C3#583711yescharacteristic
737D3—22no—
738D3—41no—
739D3—81no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—32no—
744C22—61no—
745C22—61no—
746C22—61no—
747C22—61no—
748C22—61no—
749C22—121no—
750C22—121no—
751C22—121no—
752C22C2×D3×#6711yescharacteristic
753C4—21no—
754C4—32no—
755C4—41no—
756C4—41no—
757C4—61no—
758C4—121no—
759C4—121no—
760C4—121no—
761C4—361no—
762C4—361no—
763C4D3×#23511yescharacteristic
764C4D3×#23511yescharacteristic
765C3—21no—
766C3#8137711yescharacteristic, complemented
767C3#8257411yescharacteristic, complemented
768C2—41no—
769C2—62no—
770C2—121no—
771C2—241no—
772C2D3×#92911yescharacteristic
773C2#1059545511yescharacteristic
774C2#1059546611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radical#10595004C2
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. #10592695C2semidirect
4. C3×#5003C2semidirect
5. #10591145C2semidirect
6. #10591124C2semidirect
7. #10591091C2semidirect
8. #10590608C2semidirect
9. #10590607C2semidirect
10. D3×#808C2semidirect
11. #10590502C2semidirect
12. #10590500C2semidirect
13. #10590436C2semidirect
14. #10590429C2semidirect
15. #10590426C2semidirect
64. #5523D3semidirect
69. #5003D3semidirect
680. C32#3099semidirect
766. C3#81377semidirect
767. C3#82574semidirect

Maximal subgroups

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

subgroupindex
C3×#55232
#105950042
#105926952
C3×#50032
#105911452
#105911242
#105910912
#105906082
#105906072
D3×#8082
#105905022
#105905002
#105904362
#105904292
#105904262
#825743
#813773