Finite Group Databasebeta

← #11872133

Subgroups — #11872133

Order 1152.

906 conjugacy classes of subgroups.

The subgroup lattice has 795 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594996C211yesmaximal, characteristic, complemented
2#10594983C211yesmaximal, characteristic, complemented
3#10592430C211yesmaximal, characteristic, complemented
4C3×#4737C211yesmaximal, characteristic, complemented
5C3×#4720C211yesmaximal, characteristic, complemented
6#10591168C211yesmaximal, characteristic
7#10591134C211yesmaximal, characteristic, complemented
8#10590860C211yesmaximal, characteristic, complemented
9#10590860C211yesmaximal, characteristic, complemented
10#10590773C211yesmaximal, characteristic, complemented
11#10590764C211yesmaximal, characteristic, complemented
12#10590759C211yesmaximal, characteristic, complemented
13#10590758C211yesmaximal, characteristic, complemented
14#10590746C211yesmaximal, characteristic, complemented
15#10590745C211yesmaximal, characteristic, complemented
16#81352—31nomaximal
17#79383—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19#64133C2211yescharacteristic
20C2×#3744C2211yescharacteristic
21C2×#3744C2211yescharacteristic
22C3×#930C2211yescharacteristic
23C3×#926C2211yescharacteristic
24C3×#926C2211yescharacteristic
25#63974—21no—
26#63974—21no—
27#63969—21no—
28#63959—21no—
29#63918C2211yescharacteristic, complemented
30#63899—21no—
31#63894—21no—
32#63894—21no—
33#63894C2211yescharacteristic
34#63894C2211yescharacteristic
35#63894C2211yescharacteristic
36#63894C2211yescharacteristic
37Dic3×D12C2211yescharacteristic, complemented
38#63860C2211yescharacteristic, complemented
39#63858—21no—
40#63844C2211yescharacteristic, complemented
41C2×#3714C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C32×C22⋊C8C2211yescharacteristic
44#63648C2211yescharacteristic
45#63648C2211yescharacteristic
46C3×#830C2211yescharacteristic
47C3×#821C2211yescharacteristic, complemented
48C3×#821C2211yescharacteristic, complemented
49C3×#818C2211yescharacteristic, complemented
50C3×#817C2211yescharacteristic, complemented
51C3×#815C2211yescharacteristic, complemented
52C3×Dic3⋊C8C2211yescharacteristic, complemented
53C3×Dic3⋊C8C2211yescharacteristic, complemented
54C3×C8×Dic3C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56#63573C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63567C2211yescharacteristic, complemented
59#63564C2211yescharacteristic
60#63564C2211yescharacteristic
61#5603—31no—
62#5534—31no—
63#5521—31no—
64#5521—31no—
65C3×#482—31no—
66C3×#433—31no—
67#5036—31no—
68#4996—31no—
69#4890—31no—
70#4889—31no—
71#4870—31no—
72#4852—31no—
73#4846—31no—
74#4844—31no—
75#4844—31no—
76#4842—31no—
77#4787—31no—
78#4787—31no—
79#4785—31no—
80#4756—31no—
81#4737D311yescharacteristic, complemented
82#4732—31no—
83#4731—31no—
84#4731—31no—
85#4731—61no—
86#4723—31no—
87#4720D311yescharacteristic, complemented
88#4711—31no—
89#4710—31no—
90C4×D24—31no—
91C4×#204—31no—
92C23×C3⋊D3—21no—
93C22×C32×C4C2311yescharacteristic
94C2×C4⋊(C3⋊D3)—21no—
95C2×C4⋊(C3⋊D3)—22no—
96C2×C4⋊(C3⋊D3)—22no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×D12C2311yescharacteristic
102C2×#627—21no—
103C2×#624—21no—
104C2×#624—21no—
105C2×#624—21no—
106C2×#624—21no—
107C2×D3×Dic3—21no—
108C2×C32×C8C2311yescharacteristic
109C2×C32×C8C2311yescharacteristic
110#3757—21no—
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112#3750—21no—
113#3744—22no—
114#3744—22no—
115C3×#217—21no—
116C3×#217D411yescharacteristic
117C3×#217D411yescharacteristic
118C3×(C2×D3)⋊C4—21no—
119C3×C4⋊Dic3D411yescharacteristic
120C3×C4⋊Dic3D411yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4×Dic3—21no—
125C3×C4×Dic3C2311yescharacteristic
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129#3724—21no—
130Dic3⋊Dic3—21no—
131#3722—21no—
132#3722—21no—
133#3722—21no—
134#3722—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138Dic32—21no—
139#3714—22no—
140#3714—22no—
141#3118—91noSylow
142C22×D12—31no—
143C22×D12—31no—
144C22×D12—61no—
145C3×#121—31no—
146C3×#117—31no—
147C3×#117—31no—
148#936—31no—
149#936—61no—
150#935—61no—
151D4×Dic3—31no—
152C2×#213—31no—
153C2×#213—31no—
154#930C2×D311yescharacteristic
155#926C2×D311yescharacteristic
156#926C2×D311yescharacteristic
157#924—31no—
158#924—31no—
159#924—61no—
160C2×D24—31no—
161C2×D24—31no—
162C2×#204—31no—
163C2×#204—31no—
164C2×#204—31no—
165C2×#204—31no—
166C2×#204—61no—
167C2×#204—61no—
168#898—61no—
169#896—61no—
170#893—31no—
171#893—31no—
172#893—31no—
173#893—31no—
174#893—61no—
175#893—61no—
176#888—31no—
177#887—31no—
178#885—61no—
179#883—61no—
180D3×C22⋊C4—61no—
181D3×C22⋊C4—61no—
182D3×C22⋊C4—61no—
183D3×C22⋊C4—61no—
184#879—61no—
185#878—61no—
186#875—31no—
187C4×D12—31no—
188C4×D12—31no—
189C4×D12—31no—
190C4×D12—31no—
191C4×D12—31no—
192C4×D12—61no—
193C4×D12—61no—
194#869—31no—
195C4×Dic6—31no—
196C3×#107—31no—
197C3×#106—31no—
198C3×C4⋊C8—31no—
199C3×C4⋊C8—31no—
200C3×#102—31no—
201C3×#102—31no—
202C3×C22⋊C8—21no—
203C3×C22⋊C8—31no—
204C3×C22⋊C8C2×D311yescharacteristic
205C3×C22⋊C8C2×D311yescharacteristic
206C3×#97—31no—
207C3×C4×C8—31no—
208#830C2×D311yescharacteristic
209#821—31no—
210#821—31no—
211#821—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215#821—61no—
216#821—61no—
217#821C2×D311yescharacteristic, complemented
218#821C2×D311yescharacteristic, complemented
219#818—31no—
220#818C2×D311yescharacteristic, complemented
221#817—31no—
222#817C2×D311yescharacteristic, complemented
223#816—31no—
224#816—31no—
225#815C2×D311yescharacteristic, complemented
226Dic3⋊C8C2×D311yescharacteristic, complemented
227Dic3⋊C8C2×D311yescharacteristic, complemented
228C8×Dic3C2×D311yescharacteristic, complemented
229#810—31no—
230#810—31no—
231#809—31no—
232#809—31no—
233#808—31no—
234#807—31no—
235C23×C32C2×D411yescharacteristic
236C22×C3⋊D3—21no—
237C22×C3⋊D3—21no—
238C22×C3⋊D3—24no—
239C22×C3⋊D3—81no—
240C22×C3⋊D3—81no—
241C22×C3×D3—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2411yescharacteristic
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—21no—
248C4⋊(C3⋊D3)—24no—
249C4⋊(C3⋊D3)—21no—
250C4⋊(C3⋊D3)—21no—
251C4⋊(C3⋊D3)#4112yes—
252C4⋊(C3⋊D3)#4112yes—
253#634—21no—
254#634—21no—
255C3×#67—81no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C3×D12—21no—
264C3×D12—21no—
265#627—81no—
266#624—81no—
267#624—81no—
268#624—81no—
269#624—81no—
270D3×Dic3—81no—
271C32×C8—21no—
272C32×C8—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#542—91no—
276#518—91no—
277#485—91no—
278#482—31no—
279#476—91no—
280#474—91no—
281#463—91no—
282#463—91no—
283#450—91no—
284#447—91no—
285#442—91no—
286#440—91no—
287C4×SD16—91no—
288C4×D8—91no—
289#433—31no—
290C23×D3—61no—
291C23×D3—61no—
292C23×D3—121no—
293C2×C3×D4—31no—
294C2×C3×D4—61no—
295C22×C3×C4—21no—
296C22×C3×C4C22×D311yescharacteristic
297C22×C3×C4C22×D311yescharacteristic
298C2×#67—21no—
299C22×Dic3—61no—
300C2×D12—31no—
301C2×D12—31no—
302C2×D12—31no—
303C2×D12—31no—
304C2×D12—61no—
305C2×D12—61no—
306C2×D12—62no—
307C2×D12—62no—
308C2×D12—62no—
309C2×D12—62no—
310C2×D12—61no—
311C2×D12—61no—
312C2×D12—122no—
313C2×D12—122no—
314C2×D12—121no—
315C2×D12C22×D311yescharacteristic
316C2×C4×D3—61no—
317C2×C4×D3—61no—
318C2×C4×D3—61no—
319C2×C4×D3—61no—
320C2×C4×D3—61no—
321C2×C4×D3—61no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×Dic6—31no—
326C2×Dic6—31no—
327C2×Dic6—61no—
328C2×Dic6—61no—
329C2×Dic6—61no—
330C2×C3×C8—21no—
331C2×C3×C8—21no—
332C2×C3×C8—31no—
333C2×C3×C8—31no—
334C2×C3×C8C22×D311yescharacteristic
335C2×C3×C8C22×D311yescharacteristic
336C2×C3×C8C22×D311yescharacteristic
337C2×C3×C8C22×D311yescharacteristic
338C3×C4⋊C4—31no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C22⋊C4—31no—
344C3×C22⋊C4—31no—
345C3×C22⋊C4—61no—
346C3×C22⋊C4—61no—
347C3×C42—31no—
348C3×C42—31no—
349C3×C42—61no—
350#217—21no—
351#217—61no—
352#217—61no—
353#217—61no—
354#217—61no—
355#217—61no—
356#217—121no—
357#217D1211yescharacteristic
358#217D1211yescharacteristic
359#213—62no—
360#213—62no—
361(C2×D3)⋊C4—21no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
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—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373C4⋊Dic3—31no—
374C4⋊Dic3—31no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3D1211yescharacteristic
378C4⋊Dic3D1211yescharacteristic
379C4⋊Dic3C22×D311yescharacteristic
380C4⋊Dic3C22×D311yescharacteristic
381C4⋊Dic3C22×D311yescharacteristic
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×Dic3C22×D311yescharacteristic
392C4×Dic3C22×D311yescharacteristic
393C2×C3⋊C8C22×D311yescharacteristic
394C2×C3⋊C8C22×D311yescharacteristic
395D24—62no—
396D24—62no—
397#204—62no—
398#204—62no—
399#204—62no—
400#204—62no—
401#204—122no—
402#204—122no—
403C22×C32—21no—
404C22×C32—21no—
405C22×C32—21no—
406C22×C32C22×D411yescharacteristic
407C2×C3⋊D3—22no—
408C2×C3⋊D3—22no—
409C2×C3⋊D3—41no—
410C2×C3⋊D3—41no—
411C2×C3⋊D3—41no—
412C2×C3⋊D3—41no—
413C2×C3⋊D3—84no—
414C2×C3×D3—41no—
415C2×C3×D3—41no—
416C2×C3×D3—41no—
417C32×C4—21no—
418C32×C4C2×#4111yescharacteristic
419C32×C4C2×#4111yescharacteristic
420C3⋊Dic3—41no—
421C3⋊Dic3—41no—
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3—21no—
425C3×Dic3—21no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C22×D4—91no—
430C2×SD16—91no—
431C2×SD16—91no—
432C2×D8—91no—
433C2×D8—91no—
434C4⋊Q8—91no—
435#126—181no—
436#124—91no—
437#124—181no—
438#123—181no—
439C22⋊Q8—91no—
440C22⋊Q8—181no—
441#121—31no—
442C4×Q8—91no—
443C4×D4—91no—
444C4×D4—91no—
445C4×D4—91no—
446C4×D4—91no—
447C4×D4—91no—
448C4×D4—181no—
449C4×D4—181no—
450#117—31no—
451#117—31no—
452C2×C22⋊C4—181no—
453C2×C22⋊C4—181no—
454#107—31no—
455#107—91no—
456#106—31no—
457#106—91no—
458C4⋊C8—31no—
459C4⋊C8—31no—
460#103—91no—
461#103—91no—
462#102—31no—
463#102—31no—
464#102—91no—
465#102—91no—
466#102—91no—
467#102—91no—
468C22⋊C8—31no—
469C22⋊C8D3211yescharacteristic
470#97—31no—
471C4×C8—31no—
472C23×C3—21no—
473C23×C3—61no—
474C23×C3C2×D1211yescharacteristic
475C23×C3D3×D411yescharacteristic
476C22×D3—21no—
477C22×D3—61no—
478C22×D3—61no—
479C22×D3—61no—
480C22×D3—61no—
481C22×D3—64no—
482C22×D3—64no—
483C22×D3—121no—
484C22×D3—121no—
485C22×D3—124no—
486C22×D3—241no—
487C22×D3—241no—
488C22×D3—241no—
489C22×D3—241no—
490C22×D3—242no—
491C22×D3—242no—
492C3×D4—61no—
493C3×D4—61no—
494C3×D4—241no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—31no—
502C2×C3×C4—31no—
503C2×C3×C4—31no—
504C2×C3×C4—31no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4C2×D1211yescharacteristic
511C2×C3×C4D3×D411yescharacteristic
512C2×C3×C4C23×D311yescharacteristic
513C2×C3×C4C23×D311yescharacteristic
514#67—81no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—61no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—121no—
523C2×Dic3—121no—
524C2×Dic3—241no—
525C2×Dic3C2×D1211yescharacteristic
526C2×Dic3C2×D1211yescharacteristic
527C2×Dic3C2×D1211yescharacteristic
528C2×Dic3C2×D1211yescharacteristic
529D12—21no—
530D12—21no—
531D12—32no—
532D12—32no—
533D12—32no—
534D12—32no—
535D12—62no—
536D12—62no—
537D12—64no—
538D12—64no—
539D12—61no—
540D12—61no—
541D12—61no—
542D12—61no—
543D12—121no—
544D12—121no—
545D12—124no—
546C4×D3—241no—
547C4×D3—241no—
548C4×D3—241no—
549C4×D3—241no—
550C4×D3—241no—
551C4×D3—241no—
552C4×D3—241no—
553C4×D3—241no—
554C4×D3—241no—
555Dic6—61no—
556Dic6—61no—
557Dic6—61no—
558Dic6—61no—
559Dic6—121no—
560Dic6—121no—
561Dic6—241no—
562Dic6—241no—
563C3×C8—21no—
564C3×C8—21no—
565C3×C8—21no—
566C3×C8—21no—
567C3×C8—41no—
568C3×C8—41no—
569C3×C8—61no—
570C3×C8—61no—
571C3⋊C8—21no—
572C3⋊C8—21no—
573C2×C32—41no—
574C2×C32#52511yescharacteristic
575C2×C32#57611yescharacteristic
576C2×C32#57711yescharacteristic
577C3⋊D3—42no—
578C3⋊D3—42no—
579C3×D3—81no—
580C24—181no—
581C2×Q8—91no—
582C2×Q8—181no—
583C2×D4—31no—
584C2×D4—61no—
585C2×D4—91no—
586C2×D4—91no—
587C2×D4—182no—
588C2×D4—182no—
589C2×D4—181no—
590C22×C4—181no—
591C22×C4—181no—
592C22×C4—181no—
593C22×C4—181no—
594C22×C4—181no—
595C22×C4C2×D3211yescharacteristic
596SD16—182no—
597SD16—182no—
598D8—182no—
599D8—182no—
600C2×C8—31no—
601C2×C8—31no—
602C2×C8C2×D3211yescharacteristic
603C2×C8C2×D3211yescharacteristic
604C4⋊C4—31no—
605C4⋊C4—31no—
606C4⋊C4—31no—
607C4⋊C4—31no—
608C4⋊C4—31no—
609C4⋊C4—91no—
610C4⋊C4—181no—
611C4⋊C4—181no—
612C4⋊C4—181no—
613C22⋊C4—31no—
614C22⋊C4—31no—
615C22⋊C4—61no—
616C22⋊C4—61no—
617C22⋊C4—181no—
618C22⋊C4—181no—
619C22⋊C4—181no—
620C22⋊C4—181no—
621C22⋊C4—181no—
622C22⋊C4—181no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C42—31no—
626C42—31no—
627C42—61no—
628C42—181no—
629C22×C3—22no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—121no—
640C22×C3—121no—
641C22×C3—121no—
642C22×C3C22×D1211yescharacteristic
643C22×C3C2×D3×D411yescharacteristic
644C2×D3—41no—
645C2×D3—41no—
646C2×D3—41no—
647C2×D3—62no—
648C2×D3—62no—
649C2×D3—62no—
650C2×D3—62no—
651C2×D3—122no—
652C2×D3—122no—
653C2×D3—121no—
654C2×D3—121no—
655C2×D3—121no—
656C2×D3—121no—
657C2×D3—121no—
658C2×D3—121no—
659C2×D3—121no—
660C2×D3—121no—
661C2×D3—241no—
662C2×D3—241no—
663C2×D3—241no—
664C2×D3—241no—
665C2×D3—244no—
666C2×D3—244no—
667C2×D3—248no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—21no—
672C3×C4—41no—
673C3×C4—61no—
674C3×C4—61no—
675C3×C4—61no—
676C3×C4—61no—
677C3×C4—121no—
678C3×C4—121no—
679C3×C4—121no—
680C3×C4D3×#4111yescharacteristic
681C3×C4D3×#4111yescharacteristic
682C3×C4D3×#4111yescharacteristic
683C3×C4D3×#4111yescharacteristic
684Dic3—21no—
685Dic3—21no—
686Dic3—21no—
687Dic3—21no—
688Dic3—41no—
689Dic3—41no—
690Dic3—41no—
691Dic3—121no—
692Dic3—121no—
693Dic3—121no—
694Dic3—121no—
695Dic3—241no—
696Dic3—241no—
697C32#311811yescharacteristic, complemented, Sylow
698C23—61no—
699C23—184no—
700C23—181no—
701C23—181no—
702C23—721no—
703C23—721no—
704C23D3×D1211yescharacteristic
705Q8—181no—
706Q8—181no—
707Q8—721no—
708D4—61no—
709D4—61no—
710D4—92no—
711D4—92no—
712D4—184no—
713D4—181no—
714D4—181no—
715D4—241no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—31no—
719C2×C4—31no—
720C2×C4—31no—
721C2×C4—31no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—181no—
726C2×C4—181no—
727C2×C4—721no—
728C2×C4—721no—
729C2×C4—721no—
730C2×C4—721no—
731C2×C4—721no—
732C2×C4D3×D1211yescharacteristic
733C2×C4C22×D3211yescharacteristic
734C8—21no—
735C8—21no—
736C8—61no—
737C8—61no—
738C2×C3—21no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—42no—
742C2×C3—41no—
743C2×C3—41no—
744C2×C3—241no—
745C2×C3#552411yescharacteristic
746C2×C3#565611yescharacteristic
747C2×C3#575111yescharacteristic
748C2×C3#575211yescharacteristic
749C2×C3#577011yescharacteristic
750C2×C3#577411yescharacteristic
751D3—81no—
752D3—122no—
753D3—122no—
754D3—122no—
755D3—122no—
756D3—242no—
757D3—242no—
758C22—21no—
759C22—21no—
760C22—21no—
761C22—121no—
762C22—121no—
763C22—121no—
764C22—182no—
765C22—182no—
766C22—361no—
767C22—361no—
768C22—361no—
769C22—361no—
770C22—724no—
771C22C2×D3×D1211yescharacteristic
772C4—21no—
773C4—61no—
774C4—61no—
775C4—61no—
776C4—61no—
777C4—121no—
778C4—121no—
779C4—121no—
780C4—361no—
781C4—361no—
782C4#6431211yescharacteristic
783C4#6431211yescharacteristic
784C3—21no—
785C3#7938311yescharacteristic, complemented
786C3#8135211yescharacteristic, complemented
787C2—41no—
788C2—241no—
789C2—362no—
790C2—362no—
791C2#1059407911yescharacteristic
792C2#1059467911yescharacteristic
793C2#1059471411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radical#10591168C2
hypercenterC22⋊C8D32
hypocenterC32#3118
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #10594996C2semidirect
2. #10594983C2semidirect
3. #10592430C2semidirect
4. C3×#4737C2semidirect
5. C3×#4720C2semidirect
7. #10591134C2semidirect
8. #10590860C2semidirect
9. #10590860C2semidirect
10. #10590773C2semidirect
11. #10590764C2semidirect
12. #10590759C2semidirect
13. #10590758C2semidirect
14. #10590746C2semidirect
15. #10590745C2semidirect
29. #63918C22semidirect
37. Dic3×D12C22semidirect
38. #63860C22semidirect
40. #63844C22semidirect
47. C3×#821C22semidirect
48. C3×#821C22semidirect
49. C3×#818C22semidirect
50. C3×#817C22semidirect
51. C3×#815C22semidirect
52. C3×Dic3⋊C8C22semidirect
53. C3×Dic3⋊C8C22semidirect
54. C3×C8×Dic3C22semidirect
55. #63575C22semidirect
56. #63573C22semidirect
57. #63567C22semidirect
58. #63567C22semidirect
81. #4737D3semidirect
87. #4720D3semidirect
217. #821C2×D3semidirect
218. #821C2×D3semidirect
220. #818C2×D3semidirect
222. #817C2×D3semidirect
225. #815C2×D3semidirect
226. Dic3⋊C8C2×D3semidirect
227. Dic3⋊C8C2×D3semidirect
228. C8×Dic3C2×D3semidirect
697. C32#3118semidirect
785. C3#79383semidirect
786. C3#81352semidirect

Maximal subgroups

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

subgroupindex
#105949962
#105949832
#105924302
C3×#47372
C3×#47202
#105911682
#105911342
#105908602
#105907732
#105907642
#105907592
#105907582
#105907462
#105907452
#813523
#793833