Finite Group Databasebeta

← #11870377

Subgroups — #11870377

Order 1152.

877 conjugacy classes of subgroups.

The subgroup lattice has 787 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595404C211yesmaximal, characteristic
2#10594510C211yesmaximal, characteristic, complemented
3#10592502C211yesmaximal, characteristic, complemented
4C3×#4814C211yesmaximal, characteristic, complemented
5C3×#4805C211yesmaximal, characteristic, complemented
6#10591560C211yesmaximal, characteristic, complemented
7#10591559C211yesmaximal, characteristic, complemented
8#10591549C211yesmaximal, characteristic, complemented
9#10590959C211yesmaximal, characteristic, complemented
10#10590705C211yesmaximal, characteristic, complemented
11#10590688C211yesmaximal, characteristic, complemented
12#10590677C211yesmaximal, characteristic, complemented
13#10590575C211yesmaximal, characteristic, complemented
14#10590425C211yesmaximal, characteristic, complemented
15#10590423C211yesmaximal, characteristic, complemented
16#81521—31nomaximal
17#81430—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×#3798C2211yescharacteristic
20C2×#3743C2211yescharacteristic
21C4⋊C4×C3⋊D3C2211yescharacteristic
22C3×#946C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C3×#892C2211yescharacteristic
25C3×D3×C4⋊C4C2211yescharacteristic
26#63912—21no—
27#63910—21no—
28#63910—21no—
29#63909C2211yescharacteristic
30#63909C2211yescharacteristic
31C4×#626—21no—
32#63900C2211yescharacteristic
33D3×C4⋊Dic3C2211yescharacteristic
34#63881—21no—
35#63879—21no—
36#63865—21no—
37#63849C2211yescharacteristic
38#63841C2211yescharacteristic
39#63837—21no—
40C2×#3710C2211yescharacteristic
41C32×#103C2211yescharacteristic
42#63662C2211yescharacteristic
43#63648C2211yescharacteristic
44#63636C2211yescharacteristic
45C3×#835C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×(C2×D3)⋊C8C2211yescharacteristic
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×#818C2211yescharacteristic
50C3×#817C2211yescharacteristic
51C3×#808C2211yescharacteristic
52C3×#808C2211yescharacteristic
53#63576C2211yescharacteristic
54#63574C2211yescharacteristic
55#63573C2211yescharacteristic
56#63573C2211yescharacteristic
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61#5629—31no—
62#5629—31no—
63#5523—31no—
64#5504—31no—
65C3×#485—31no—
66C3×#483—31no—
67#5045—31no—
68#5043—31no—
69#5003—31no—
70#4968—31no—
71#4885—31no—
72#4881—31no—
73#4866—31no—
74#4863—31no—
75#4863—31no—
76#4861—31no—
77D3×#106—31no—
78D3×#106—31no—
79#4815—31no—
80#4814D311yescharacteristic, complemented
81#4805—31no—
82#4805D311yescharacteristic, complemented
83#4804—31no—
84#4804—31no—
85#4803—31no—
86#4803—31no—
87#4803—61no—
88#4737—31no—
89#4735—31no—
90#4727—31no—
91#4727—31no—
92C2×C32×Q8C2311yescharacteristic
93#3832—22no—
94#3832—22no—
95C2×C4⋊(C3⋊D3)—21no—
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4×C3⋊D3—21no—
98C2×C4×C3⋊D3—21no—
99C2×C4×C3⋊D3C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×C4×D3C2311yescharacteristic
103C2×#627D411yescharacteristic
104C2×#626—21no—
105C2×#626—21no—
106C2×#626D411yescharacteristic
107C2×#626D411yescharacteristic
108C2×#625D411yescharacteristic
109C2×#624—21no—
110C2×D3×Dic3—21no—
111#3798—22no—
112#3798—22no—
113C2×C32×C8C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116#3750—21no—
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118#3743—22no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×C4×Dic3—21no—
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132#3724—21no—
133Dic3⋊Dic3—21no—
134#3722—21no—
135#3722—21no—
136#3722—21no—
137(C2×D3)⋊Dic3—21no—
138Dic32—21no—
139Dic32—21no—
140#3710—22no—
141#3099—91noSylow
142C2×#239—31no—
143C2×#239—31no—
144C2×#239—61no—
145C2×#235—31no—
146C2×#235—31no—
147C3×C22⋊Q8—31no—
148C3×C22⋊Q8—31no—
149C3×#117—31no—
150C2×C3×C4⋊C4—31no—
151#946C2×D311yescharacteristic
152#946C2×D311yescharacteristic
153#930—31no—
154#930—31no—
155C4×#67—61no—
156C4×#67—61no—
157#926—31no—
158C2×C4⋊Dic3—31no—
159C2×ΓL(1,𝔽25)—31no—
160C2×ΓL(1,𝔽25)—31no—
161C2×ΓL(1,𝔽25)—61no—
162C2×D3×C8—31no—
163C2×D3×C8—31no—
164#896—61no—
165#896—61no—
166#895—31no—
167#895—31no—
168#895—61no—
169#895—61no—
170#893—61no—
171#892—31no—
172#892—31no—
173#892—31no—
174#892C2×D311yescharacteristic
175D3×C4⋊C4—31no—
176D3×C4⋊C4—31no—
177D3×C4⋊C4—31no—
178D3×C4⋊C4—31no—
179D3×C4⋊C4—31no—
180D3×C4⋊C4—61no—
181D3×C4⋊C4C2×D311yescharacteristic
182#887—61no—
183#884—61no—
184#884—61no—
185#884—61no—
186#884—61no—
187#67⋊C4—61no—
188#67⋊C4—61no—
189C4×D12—61no—
190C4×Dic6—61no—
191C3×#107—31no—
192C3×#106—31no—
193C3×#106—31no—
194C3×#106—31no—
195C3×#103—21no—
196C3×#103—31no—
197C3×#103—31no—
198C3×#103C2×D311yescharacteristic
199C3×#103C2×D311yescharacteristic
200C3×C22⋊C8—31no—
201C3×C22⋊C8—31no—
202#835—31no—
203#835—31no—
204#835—61no—
205#835C2×D311yescharacteristic
206#835C2×D311yescharacteristic
207#830—31no—
208#830—31no—
209#821—31no—
210#821—31no—
211#821—31no—
212#821—31no—
213#821—61no—
214(C2×D3)⋊C8—31no—
215(C2×D3)⋊C8—31no—
216(C2×D3)⋊C8C2×D311yescharacteristic
217(C2×D3)⋊C8C2×D311yescharacteristic
218#818C2×D311yescharacteristic
219#817—31no—
220#817—31no—
221#817C2×D311yescharacteristic
222#809—31no—
223#809—31no—
224#809—31no—
225#809—31no—
226#809—61no—
227#808—31no—
228#808—31no—
229#808—31no—
230#808—31no—
231#808C2×D311yescharacteristic
232#808C2×D311yescharacteristic
233#807—31no—
234#807—31no—
235C22×C3⋊D3—21no—
236C22×C3⋊D3C2×D411yescharacteristic
237C22×C3×D3C2×D411yescharacteristic
238C22×C3×D3C2×D411yescharacteristic
239C32×Q8—21no—
240C32×Q8—21no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4C2411yescharacteristic
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3C2×D411yescharacteristic
246C4⋊(C3⋊D3)—21no—
247C4⋊(C3⋊D3)—21no—
248C4⋊(C3⋊D3)—42no—
249C4×C3⋊D3—42no—
250C4×C3⋊D3—81no—
251C4×C3⋊D3#4112yes—
252C4×C3⋊D3#4112yes—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×C4×D3—21no—
260C3×C4×D3—21no—
261C3×C4×D3—21no—
262C3×C4×D3—21no—
263C3×C4×D3—81no—
264#627—22no—
265#626—22no—
266#626—22no—
267#626—81no—
268#626—81no—
269#625—22no—
270#624—81no—
271D3×Dic3—81no—
272C32×C8—21no—
273C3⋊(C3⋊C8)—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#537—91no—
277#520—91no—
278#485—31no—
279#485—91no—
280#483—31no—
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—
291C2×C3×Q8—21no—
292C2×C3×Q8C22×D311yescharacteristic
293C2×C3×Q8C22×D311yescharacteristic
294C22×C3×C4—31no—
295C22×C3×C4—31no—
296C22×C3×C4—61no—
297C2×#67—31no—
298C2×#67—31no—
299C2×#67—31no—
300C2×#67—31no—
301C2×#67—61no—
302C2×#67—61no—
303C22×Dic3—61no—
304#239—62no—
305#239—62no—
306#239—62no—
307#239—62no—
308#239—64no—
309#239—122no—
310#235—62no—
311#235—62no—
312#235—62no—
313#235—62no—
314C2×D12—31no—
315C2×D12—31no—
316C2×D12—31no—
317C2×D12—31no—
318C2×D12—61no—
319C2×D12—61no—
320C2×D12—61no—
321C2×D12—61no—
322C2×D12—61no—
323C2×D12—121no—
324C2×C4×D3—21no—
325C2×C4×D3—31no—
326C2×C4×D3—31no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3—121no—
336C2×C4×D3—121no—
337C2×C4×D3C22×D311yescharacteristic
338C2×C4×D3C22×D311yescharacteristic
339C2×Dic6—31no—
340C2×Dic6—31no—
341C2×C3×C8—21no—
342C2×C3×C8—31no—
343C2×C3×C8—31no—
344C2×C3×C8C22×D311yescharacteristic
345C2×C3×C8C22×D311yescharacteristic
346C3×C4⋊C4—21no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4C22×D311yescharacteristic
355C3×C4⋊C4C22×D311yescharacteristic
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C22⋊C4—61no—
359C3×C42—61no—
360#217—61no—
361(C2×D3)⋊C4—21no—
362(C2×D3)⋊C4—21no—
363(C2×D3)⋊C4—21no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
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—
371C4⋊Dic3—31no—
372C4⋊Dic3—31no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3C22×D311yescharacteristic
376C4⋊Dic3C22×D311yescharacteristic
377C4⋊Dic3C22×D311yescharacteristic
378C4⋊Dic3C22×D311yescharacteristic
379Dic3⋊C4—21no—
380Dic3⋊C4—21no—
381Dic3⋊C4—21no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—121no—
388C4×Dic3—21no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C2×C3⋊C8—31no—
394C2×C3⋊C8—31no—
395C2×C3⋊C8—61no—
396C2×C3⋊C8C22×D311yescharacteristic
397C2×C3⋊C8C22×D311yescharacteristic
398ΓL(1,𝔽25)—62no—
399ΓL(1,𝔽25)—62no—
400ΓL(1,𝔽25)—122no—
401D3×C8—62no—
402D3×C8—62no—
403C22×C32C22×D411yescharacteristic
404C2×C3⋊D3—21no—
405C2×C3⋊D3—21no—
406C2×C3⋊D3—41no—
407C2×C3⋊D3—41no—
408C2×C3⋊D3—41no—
409C2×C3⋊D3#12312yes—
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3—21no—
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C32×C4—41no—
417C32×C4—41no—
418C32×C4C2×#4111yescharacteristic
419C32×C4C2×#4111yescharacteristic
420C3⋊Dic3—41no—
421C3⋊Dic3#12312yes—
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C2×#41—91no—
429C2×#41—91no—
430C2×M16—91no—
431C22×C8—91no—
432C22⋊Q8—31no—
433C22⋊Q8—31no—
434C22⋊Q8—181no—
435#121—91no—
436#121—91no—
437#121—181no—
438#121—181no—
439#121—181no—
440C4×Q8—181no—
441C4×D4—181no—
442C4×D4—181no—
443C4×D4—181no—
444#117—31no—
445#117—91no—
446#117—91no—
447C2×C4⋊C4—31no—
448C2×C4⋊C4—91no—
449C2×C4⋊C4—91no—
450C2×C4⋊C4—91no—
451#107—31no—
452#107—91no—
453#106—31no—
454#106—31no—
455#106—31no—
456#106—91no—
457#106—91no—
458#106—91no—
459#103—31no—
460#103—31no—
461#103—91no—
462#103D3211yescharacteristic
463#102—91no—
464#102—91no—
465#102—91no—
466#102—91no—
467C22⋊C8—31no—
468C22⋊C8—31no—
469C22⋊C8—91no—
470C22⋊C8—91no—
471C23×C3—31no—
472C23×C3—31no—
473C22×D3—31no—
474C22×D3—31no—
475C22×D3—61no—
476C22×D3—61no—
477C22×D3—61no—
478C22×D3—121no—
479C22×D3D3×D411yescharacteristic
480C22×D3D3×D411yescharacteristic
481C3×Q8—22no—
482C3×Q8—21no—
483C3×Q8—21no—
484C3×Q8—21no—
485C3×Q8—21no—
486C3×Q8—41no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—31no—
493C2×C3×C4—31no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—241no—
505C2×C3×C4C23×D311yescharacteristic
506C2×C3×C4C23×D311yescharacteristic
507#67—62no—
508#67—62no—
509#67—62no—
510#67—62no—
511#67—241no—
512#67—241no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—31no—
518C2×Dic3—31no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—121no—
523C2×Dic3—241no—
524C2×Dic3D3×D411yescharacteristic
525C2×Dic3D3×D411yescharacteristic
526D12—62no—
527D12—62no—
528D12—62no—
529D12—61no—
530D12—61no—
531D12—61no—
532D12—61no—
533D12—121no—
534D12—122no—
535D12—122no—
536D12—124no—
537D12—241no—
538D12—241no—
539C4×D3—21no—
540C4×D3—21no—
541C4×D3—21no—
542C4×D3—21no—
543C4×D3—32no—
544C4×D3—32no—
545C4×D3—32no—
546C4×D3—32no—
547C4×D3—62no—
548C4×D3—62no—
549C4×D3—81no—
550C4×D3—122no—
551C4×D3—122no—
552C4×D3—124no—
553C4×D3—241no—
554C4×D3—241no—
555C4×D3—241no—
556C4×D3—241no—
557C4×D3—241no—
558C4×D3—242no—
559Dic6—62no—
560Dic6—62no—
561C3×C8—21no—
562C3×C8—21no—
563C3×C8—41no—
564C3×C8—61no—
565C3×C8—61no—
566C3⋊C8—21no—
567C3⋊C8—21no—
568C3⋊C8—61no—
569C3⋊C8—61no—
570C3⋊C8—121no—
571C2×C32C2×#12311yescharacteristic
572C2×C32#57711yescharacteristic
573C2×C32#57711yescharacteristic
574C3⋊D3—22no—
575C3⋊D3—81no—
576C3×D3—41no—
577C3×D3—41no—
578#41—182no—
579#41—182no—
580#41—182no—
581#41—182no—
582C2×Q8—91no—
583C2×Q8C2×D3211yescharacteristic
584C2×D4—91no—
585C2×D4—91no—
586C2×D4—91no—
587C2×D4—91no—
588C2×D4—181no—
589C2×D4—181no—
590C2×D4—181no—
591C22×C4—31no—
592C22×C4—31no—
593C22×C4—61no—
594C22×C4—91no—
595C22×C4—181no—
596C22×C4—181no—
597C22×C4—181no—
598C22×C4—181no—
599M16—182no—
600C2×C8—31no—
601C2×C8—31no—
602C2×C8—91no—
603C2×C8—182no—
604C2×C8C2×D3211yescharacteristic
605C4⋊C4—31no—
606C4⋊C4—31no—
607C4⋊C4—31no—
608C4⋊C4—31no—
609C4⋊C4—61no—
610C4⋊C4—61no—
611C4⋊C4—61no—
612C4⋊C4—91no—
613C4⋊C4—181no—
614C4⋊C4—181no—
615C4⋊C4—181no—
616C4⋊C4C2×D3211yescharacteristic
617C22⋊C4—61no—
618C22⋊C4—61no—
619C22⋊C4—61no—
620C22⋊C4—181no—
621C22⋊C4—181no—
622C22⋊C4—181no—
623C22⋊C4—181no—
624C42—61no—
625C42—181no—
626C42—181no—
627C22×C3—21no—
628C22×C3—61no—
629C22×C3—61no—
630C22×C3—61no—
631C22×C3—61no—
632C22×C3—61no—
633C22×C3—61no—
634C22×C3C2×D3×D411yescharacteristic
635C22×C3C2×D3×D411yescharacteristic
636C2×D3—21no—
637C2×D3—21no—
638C2×D3—21no—
639C2×D3—21no—
640C2×D3—21no—
641C2×D3—21no—
642C2×D3—32no—
643C2×D3—32no—
644C2×D3—62no—
645C2×D3—61no—
646C2×D3—61no—
647C2×D3—61no—
648C2×D3—61no—
649C2×D3—121no—
650C2×D3—121no—
651C2×D3—122no—
652C2×D3—121no—
653C2×D3—121no—
654C2×D3—121no—
655C2×D3—121no—
656C2×D3—121no—
657C2×D3—121no—
658C2×D3—241no—
659C2×D3—241no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—42no—
663C3×C4—41no—
664C3×C4—41no—
665C3×C4—41no—
666C3×C4—41no—
667C3×C4—61no—
668C3×C4—61no—
669C3×C4—81no—
670C3×C4—121no—
671C3×C4—121no—
672C3×C4—121no—
673C3×C4—121no—
674C3×C4D3×#4111yescharacteristic
675C3×C4D3×#4111yescharacteristic
676C3×C4D3×#4111yescharacteristic
677C3×C4D3×#4111yescharacteristic
678Dic3—21no—
679Dic3—21no—
680Dic3—32no—
681Dic3—32no—
682Dic3—41no—
683Dic3—41no—
684Dic3—41no—
685Dic3—41no—
686Dic3—62no—
687Dic3—121no—
688Dic3—121no—
689Dic3—241no—
690C32#309911yescharacteristic, complemented, Sylow
691C23—31no—
692C23—31no—
693C23—91no—
694C23—181no—
695Q8—21no—
696Q8—21no—
697Q8—182no—
698D4—182no—
699D4—182no—
700D4—182no—
701D4—181no—
702D4—181no—
703D4—362no—
704D4—721no—
705D4—721no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—31no—
709C2×C4—31no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—91no—
719C2×C4—92no—
720C2×C4—92no—
721C2×C4—181no—
722C2×C4—241no—
723C2×C4—362no—
724C2×C4—721no—
725C2×C4—721no—
726C2×C4—721no—
727C2×C4C22×D3211yescharacteristic
728C8—21no—
729C8—61no—
730C8—61no—
731C8—181no—
732C2×C3—21no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—121no—
736C2×C3—121no—
737C2×C3D3×#12311yescharacteristic
738C2×C3D3×#12311yescharacteristic
739C2×C3#576211yescharacteristic
740C2×C3#577011yescharacteristic
741C2×C3#577811yescharacteristic
742C2×C3#577811yescharacteristic
743D3—41no—
744D3—41no—
745D3—62no—
746D3—62no—
747D3—122no—
748D3—242no—
749D3—241no—
750D3—241no—
751C22—61no—
752C22—61no—
753C22—61no—
754C22—61no—
755C22—61no—
756C22—61no—
757C22—92no—
758C22—181no—
759C22—181no—
760C22—361no—
761C22—361no—
762C22—361no—
763C22D32×D411yescharacteristic
764C4—41no—
765C4—41no—
766C4—61no—
767C4—61no—
768C4—92no—
769C4—121no—
770C4—121no—
771C4—121no—
772C4—121no—
773C4—361no—
774C4#6430611yescharacteristic
775C4#6431211yescharacteristic
776C3—21no—
777C3#8143011yescharacteristic, complemented
778C3#8152111yescharacteristic, complemented
779C2—121no—
780C2—121no—
781C2—182no—
782C2—721no—
783C2#1059426011yescharacteristic
784C2#1059475111yescharacteristic
785C2#1059477011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radical#10595404C2
hypercenter#103D32
hypocenterC32#3099
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
2. #10594510C2semidirect
3. #10592502C2semidirect
4. C3×#4814C2semidirect
5. C3×#4805C2semidirect
6. #10591560C2semidirect
7. #10591559C2semidirect
8. #10591549C2semidirect
9. #10590959C2semidirect
10. #10590705C2semidirect
11. #10590688C2semidirect
12. #10590677C2semidirect
13. #10590575C2semidirect
14. #10590425C2semidirect
15. #10590423C2semidirect
80. #4814D3semidirect
82. #4805D3semidirect
690. C32#3099semidirect
777. C3#81430semidirect
778. C3#81521semidirect

Maximal subgroups

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

subgroupindex
#105954042
#105945102
#105925022
C3×#48142
C3×#48052
#105915602
#105915592
#105915492
#105909592
#105907052
#105906882
#105906772
#105905752
#105904252
#105904232
#815213
#814303