Finite Group Databasebeta

← #11860597

Subgroups — #11860597

Order 1152.

1021 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595339C211yesmaximal, characteristic, complemented
2C2×#63951C211yesmaximal, characteristic
3#10594361C211yesmaximal, characteristic
4C3⋊D3×#103C211yesmaximal, characteristic, complemented
5C3×#4817C211yesmaximal, characteristic, complemented
6C3×#4789C211yesmaximal, characteristic, complemented
7Dic3×#216C211yesmaximal, characteristic, complemented
8Dic3×#215C211yesmaximal, characteristic, complemented
9#10590956C211yesmaximal, characteristic
10#10590794C211yesmaximal, characteristic, complemented
11#10590747C211yesmaximal, characteristic, complemented
12#10590703C211yesmaximal, characteristic, complemented
13#10590583C211yesmaximal, characteristic, complemented
14#10590481C211yesmaximal, characteristic, complemented
15#10590479C211yesmaximal, characteristic, complemented
16#79830—31nomaximal
17#79776—31nomaximal
18C2×Q8×C3⋊D3C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20C2×C8×C3⋊D3C2211yescharacteristic
21C4⋊C4×C3⋊D3C2211yescharacteristic
22C3×Q8×Dic3C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic
25C2×C3×#215C2211yescharacteristic
26C3×#893C2211yescharacteristic
27C3×#887C2211yescharacteristic
28#63951C418yescomplemented
29C4×#626—21no—
30Dic3×D12C2211yescharacteristic
31#63881—21no—
32#63877—21no—
33D3×Dic3⋊C4—21no—
34#63874—21no—
35#63874C2211yescharacteristic
36#63849—21no—
37#63849C2211yescharacteristic
38#63844—21no—
39#63844—21no—
40#63844C2211yescharacteristic
41#63844C2211yescharacteristic
42Dic3×Dic6C2211yescharacteristic
43C2×#3719C2211yescharacteristic
44C2×#3716C2211yescharacteristic
45C2×#3712C2211yescharacteristic
46C32×#103C2211yescharacteristic
47#63662C2211yescharacteristic
48#63643C2211yescharacteristic
49#63637C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#815C2211yescharacteristic
53C3×#815C2211yescharacteristic
54C3×#808C2211yescharacteristic
55C3×#807C2211yescharacteristic
56#63575C2211yescharacteristic
57#63573C2211yescharacteristic
58#63565C2211yescharacteristic
59#63562C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61Dic3×C3⋊C8C2211yescharacteristic
62C2×#918—31no—
63C2×#915—31no—
64#5574—31no—
65#5572—31no—
66#5572—31no—
67#5546—31no—
68C3×#441—31no—
69C3×#440—31no—
70Dic3×Q16—31no—
71Dic3×SD16—31no—
72C4×#216—31no—
73C4×#216—31no—
74C4×#215—31no—
75C4×#214—31no—
76#4881—31no—
77#4873—31no—
78#4861—31no—
79#4852—31no—
80#4817D311yescharacteristic, complemented
81#4804—31no—
82D3×#103—31no—
83D3×#103—31no—
84D3×#103—61no—
85#4789—31no—
86#4789D311yescharacteristic, complemented
87#4772—31no—
88#4757—31no—
89#4716—31no—
90#4710—31no—
91#4708—31no—
92#4708—31no—
93C2×C32×Q8C2311yescharacteristic
94Q8×C3⋊D3—22no—
95Q8×C3⋊D3C2×C414yescomplemented
96C2×C4×C3⋊D3—21no—
97C2×C4×C3⋊D3—21no—
98C2×C4×C3⋊D3C2311yescharacteristic
99C2×#634—21no—
100C2×#634C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×Dic6C2311yescharacteristic
104C2×#626—21no—
105C2×D3×Dic3—21no—
106C2×D3×Dic3—21no—
107#3796—22no—
108#3796C2×C414yes—
109C2×C32×C8C2311yescharacteristic
110C32×C4⋊C4C2311yescharacteristic
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112#3750—21no—
113C2×C3⋊(C3⋊C8)C2311yescharacteristic
114C8×C3⋊D3—22no—
115C3×#216C2×C414yescomplemented
116C3×#215C2×C414yescomplemented
117C3×(C2×D3)⋊C4—21no—
118C3×C4⋊Dic3—21no—
119C3×C4⋊Dic3—21no—
120C3×C4⋊Dic3C2311yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×Dic3⋊C4—21no—
123C3×C4×Dic3—21no—
124C3×C4×Dic3—21no—
125C3×C4×Dic3—21no—
126C3×C4×Dic3C2311yescharacteristic
127C3×C4×Dic3C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130#3724—21no—
131#3724—21no—
132#3724D411yescharacteristic
133#3724D411yescharacteristic
134Dic3⋊Dic3—21no—
135#3722—21no—
136#3722D411yescharacteristic
137#3722D411yescharacteristic
138(C2×D3)⋊Dic3—21no—
139Dic32—21no—
140Dic32—21no—
141Dic32—21no—
142Dic32—21no—
143#3719C2×C414yescomplemented
144#3716C2×C414yescomplemented
145#3712C2×C414yescomplemented
146#2947—91noSylow
147C2×#239—31no—
148C2×D3×Q8—31no—
149C2×D3×Q8—31no—
150C2×D3×Q8—61no—
151C2×#237—31no—
152C2×C3×Q16—31no—
153C2×C3×SD16—31no—
154C3×C4×Q8—31no—
155C3×C4×Q8—31no—
156C3×C4×Q8—31no—
157C3×C4×D4—31no—
158Q8×Dic3—31no—
159Q8×Dic3C2×D311yescharacteristic
160Q8×Dic3C2×D311yescharacteristic
161C2×#216—31no—
162C2×#216C2×D311yescharacteristic
163C2×#215C2×D311yescharacteristic
164D4×Dic3—31no—
165C2×#214—31no—
166C4×#67—61no—
167C2×Dic3⋊C4—61no—
168#918—38no—
169#915—38no—
170C2×Dic12—31no—
171C2×#204—31no—
172C2×ΓL(1,𝔽25)—31no—
173C2×ΓL(1,𝔽25)—31no—
174C2×D3×C8—31no—
175C2×D3×C8—31no—
176C2×D3×C8—61no—
177#893—61no—
178#893C2×D311yescharacteristic
179#892—31no—
180#892—31no—
181#892—61no—
182#892—61no—
183D3×C4⋊C4—31no—
184D3×C4⋊C4—31no—
185D3×C4⋊C4—61no—
186D3×C4⋊C4—61no—
187#887—31no—
188#887—31no—
189#887—61no—
190#887—61no—
191#887C2×D311yescharacteristic
192#67⋊C4—61no—
193#877—61no—
194C4×D12—31no—
195C4×D12—61no—
196#872—31no—
197#872—31no—
198#872—61no—
199#872—61no—
200#872—61no—
201C4×Dic6—31no—
202C4×Dic6—31no—
203C4×Dic6—31no—
204C4×Dic6—61no—
205C4×Dic6—61no—
206C3×#107—31no—
207C3×#106—31no—
208C3×#103—21no—
209C3×#103—31no—
210C3×#103C2×D311yescharacteristic
211C3×#103C2×D311yescharacteristic
212C3×#102—31no—
213C3×#97—31no—
214C3×#97—31no—
215#835—31no—
216#835—31no—
217#835—31no—
218#835—61no—
219#832—31no—
220#821C2×D311yescharacteristic
221#818—31no—
222#817—31no—
223#816—31no—
224#816—31no—
225#816—61no—
226#816C2×D311yescharacteristic
227#815C2×D311yescharacteristic
228#815C2×D311yescharacteristic
229C8×Dic3—31no—
230C8×Dic3—31no—
231#810—31no—
232#810—31no—
233#810—31no—
234#810—61no—
235#809—31no—
236#808—31no—
237#808C2×D311yescharacteristic
238#807—31no—
239#807C2×D311yescharacteristic
240C4×C3⋊C8—31no—
241C4×C3⋊C8—31no—
242C22×C3⋊D3C2×D411yescharacteristic
243C22×C3×D3—21no—
244C32×Q8—21no—
245C32×Q8C22×C412yes—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2411yescharacteristic
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3C2×D411yescharacteristic
252C4×C3⋊D3—24no—
253C4×C3⋊D3—81no—
254C4×C3⋊D3C22×C412yes—
255C4×C3⋊D3#4112yes—
256#634—21no—
257#634—24no—
258#634C22×C412yes—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C3×D12—21no—
267C3×D12C22×C412yes—
268C3×C4×D3—81no—
269C3×Dic6—21no—
270C3×Dic6C22×C412yes—
271#626—24no—
272D3×Dic3—24no—
273D3×Dic3—81no—
274C32×C8—21no—
275C3⋊(C3⋊C8)—21no—
276C3×C3⋊C8C22×C412yes—
277C3×C3⋊C8C22×C412yes—
278C2×#137—91no—
279#520—91no—
280#519—91no—
281#441—31no—
282#441—91no—
283#440—31no—
284#440—91no—
285C4×Q16—91no—
286C4×Q16—91no—
287C4×SD16—91no—
288C4×SD16—91no—
289#428—91no—
290#416—91no—
291C2×#103—91no—
292#405—91no—
293C2×C3×Q8—21no—
294C2×C3×Q8—31no—
295C2×C3×Q8C22×D311yescharacteristic
296C2×C3×Q8C22×D311yescharacteristic
297C2×C3×D4—31no—
298C22×C3×C4—61no—
299C2×#67—61no—
300C22×Dic3—61no—
301C22×Dic3—61no—
302#239—34no—
303#239—62no—
304D3×Q8—34no—
305D3×Q8—34no—
306D3×Q8—64no—
307D3×Q8—62no—
308D3×Q8—62no—
309D3×Q8—122no—
310#237—34no—
311#237—62no—
312C2×D12—61no—
313C2×D12C22×D311yescharacteristic
314C2×C4×D3—21no—
315C2×C4×D3—31no—
316C2×C4×D3—31no—
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—121no—
325C2×C4×D3—121no—
326C2×Dic6—31no—
327C2×Dic6—31no—
328C2×Dic6—61no—
329C2×Dic6—61no—
330C2×Dic6—61no—
331C2×Dic6—121no—
332C2×Dic6C22×D311yescharacteristic
333C3×Q16—34no—
334C3×SD16—34no—
335C2×C3×C8—21no—
336C2×C3×C8—31no—
337C2×C3×C8—31no—
338C2×C3×C8C22×D311yescharacteristic
339C2×C3×C8C22×D311yescharacteristic
340C3×C4⋊C4—21no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C22⋊C4—61no—
349C3×C42—31no—
350C3×C42—31no—
351C3×C42—61no—
352C3×C42—61no—
353C3×C42—61no—
354#217—61no—
355#216—34no—
356#216C4×D314yescomplemented
357#215C4×D314yescomplemented
358#214—34no—
359(C2×D3)⋊C4—21no—
360(C2×D3)⋊C4—31no—
361(C2×D3)⋊C4—31no—
362(C2×D3)⋊C4—31no—
363(C2×D3)⋊C4—31no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367C4⋊Dic3—21no—
368C4⋊Dic3—21no—
369C4⋊Dic3—31no—
370C4⋊Dic3—31no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3C22×D311yescharacteristic
374C4⋊Dic3C22×D311yescharacteristic
375Dic3⋊C4—21no—
376Dic3⋊C4—31no—
377Dic3⋊C4—31no—
378Dic3⋊C4—31no—
379Dic3⋊C4—31no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—121no—
388C4×Dic3—21no—
389C4×Dic3—21no—
390C4×Dic3—21no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3C22×D311yescharacteristic
400C4×Dic3C22×D311yescharacteristic
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—61no—
404C2×C3⋊C8C22×D311yescharacteristic
405C2×C3⋊C8C22×D311yescharacteristic
406Dic12—34no—
407#204—34no—
408ΓL(1,𝔽25)—34no—
409ΓL(1,𝔽25)—34no—
410D3×C8—62no—
411D3×C8—62no—
412D3×C8—122no—
413C22×C32C22×D411yescharacteristic
414C2×C3⋊D3—21no—
415C2×C3⋊D3—21no—
416C2×C3⋊D3C4×D412yes—
417C2×C3×D3—22no—
418C2×C3×D3—41no—
419C2×C3×D3—41no—
420C32×C4—22no—
421C32×C4—41no—
422C32×C4C23×C411yescharacteristic
423C32×C4C2×#4111yescharacteristic
424C3⋊Dic3—22no—
425C3⋊Dic3—41no—
426C3⋊Dic3C4×D412yes—
427C3×Dic3—22no—
428C3×Dic3—21no—
429C3×Dic3—21no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—41no—
433C3×Dic3—41no—
434C2×#41—91no—
435C22×Q8—91no—
436#137—98no—
437C2×Q16—31no—
438C2×Q16—91no—
439C2×SD16—31no—
440C2×SD16—91no—
441C2×M16—91no—
442C22×C8—91no—
443C4×Q8—31no—
444C4×Q8—31no—
445C4×Q8—31no—
446C4×Q8—91no—
447C4×Q8—91no—
448C4×Q8—91no—
449C4×Q8—181no—
450C4×Q8—181no—
451C4×D4—31no—
452C4×D4—91no—
453C4×D4—181no—
454C4×D4—181no—
455#117—91no—
456#117—91no—
457#117—181no—
458#117—181no—
459#117—181no—
460C2×C4⋊C4—91no—
461C2×C4⋊C4—181no—
462#107—31no—
463#107—91no—
464#106—31no—
465#106—91no—
466#103—31no—
467#103—91no—
468#103—91no—
469#103—91no—
470#103—91no—
471#103D3211yescharacteristic
472#102—31no—
473#102—91no—
474#97—31no—
475#97—31no—
476C4×C8—91no—
477C4×C8—91no—
478C23×C3—61no—
479C22×D3—21no—
480C22×D3—31no—
481C22×D3—31no—
482C22×D3—61no—
483C3×Q8—21no—
484C3×Q8—21no—
485C3×Q8—22no—
486C3×Q8—32no—
487C3×Q8—41no—
488C3×Q8—61no—
489C3×Q8C2×C4×D312yes—
490C3×Q8C2×C4×D312yes—
491C3×D4—32no—
492C3×D4—61no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—31no—
499C2×C3×C4—31no—
500C2×C3×C4—31no—
501C2×C3×C4—31no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—241no—
508C2×C3×C4C23×D311yescharacteristic
509C2×C3×C4C23×D311yescharacteristic
510#67—64no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—31no—
515C2×Dic3—31no—
516C2×Dic3—61no—
517C2×Dic3—64no—
518C2×Dic3—61no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—121no—
523C2×Dic3—121no—
524C2×Dic3—241no—
525C2×Dic3D3×D411yescharacteristic
526C2×Dic3D3×D411yescharacteristic
527C2×Dic3D3×D411yescharacteristic
528C2×Dic3D3×D411yescharacteristic
529D12—21no—
530D12—64no—
531D12C2×C4×D312yes—
532C4×D3—32no—
533C4×D3—32no—
534C4×D3—32no—
535C4×D3—32no—
536C4×D3—62no—
537C4×D3—62no—
538C4×D3—64no—
539C4×D3—64no—
540C4×D3—64no—
541C4×D3—81no—
542C4×D3—124no—
543C4×D3—241no—
544C4×D3—241no—
545C4×D3—241no—
546C4×D3—242no—
547Dic6—21no—
548Dic6—32no—
549Dic6—32no—
550Dic6—62no—
551Dic6—64no—
552Dic6—64no—
553Dic6—61no—
554Dic6—61no—
555Dic6—124no—
556Dic6—121no—
557Dic6C2×C4×D312yes—
558C3×C8—21no—
559C3×C8—21no—
560C3×C8—32no—
561C3×C8—32no—
562C3×C8—41no—
563C3⋊C8—61no—
564C3⋊C8—61no—
565C3⋊C8—121no—
566C3⋊C8C2×C4×D312yes—
567C3⋊C8C2×C4×D312yes—
568C2×C32C2×C4×D411yescharacteristic
569C2×C32#57711yescharacteristic
570C2×C32#57811yescharacteristic
571C3⋊D3—22no—
572C3×D3—42no—
573#41—94no—
574#41—182no—
575C2×Q8—31no—
576C2×Q8—94no—
577C2×Q8—91no—
578C2×Q8—181no—
579C2×Q8—182no—
580C2×Q8C2×D3211yescharacteristic
581C2×D4—31no—
582C2×D4—181no—
583C22×C4—61no—
584C22×C4—91no—
585C22×C4—181no—
586C22×C4—181no—
587C22×C4—181no—
588C22×C4—181no—
589Q16—34no—
590Q16—94no—
591SD16—34no—
592SD16—94no—
593M16—94no—
594C2×C8—31no—
595C2×C8—31no—
596C2×C8—91no—
597C2×C8—182no—
598C2×C8C2×D3211yescharacteristic
599C4⋊C4—31no—
600C4⋊C4—31no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4—91no—
605C4⋊C4—91no—
606C4⋊C4—91no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C4⋊C4—181no—
611C4⋊C4C2×D3211yescharacteristic
612C22⋊C4—61no—
613C22⋊C4—91no—
614C22⋊C4—91no—
615C22⋊C4—181no—
616C22⋊C4—181no—
617C42—31no—
618C42—31no—
619C42—61no—
620C42—61no—
621C42—61no—
622C42—181no—
623C42—181no—
624C42—181no—
625C42—181no—
626C22×C3—21no—
627C22×C3—62no—
628C22×C3—121no—
629C22×C3—121no—
630C22×C3C2×D3×D411yescharacteristic
631C22×C3C2×D3×D411yescharacteristic
632C2×D3—22no—
633C2×D3—32no—
634C2×D3—32no—
635C2×D3—41no—
636C2×D3—41no—
637C2×D3—62no—
638C2×D3—62no—
639C2×D3—62no—
640C2×D3—61no—
641C2×D3—61no—
642C2×D3—61no—
643C2×D3—61no—
644C3×C4—22no—
645C3×C4—22no—
646C3×C4—21no—
647C3×C4—21no—
648C3×C4—42no—
649C3×C4—41no—
650C3×C4—41no—
651C3×C4—61no—
652C3×C4—61no—
653C3×C4—61no—
654C3×C4—61no—
655C3×C4—62no—
656C3×C4—81no—
657C3×C4—121no—
658C3×C4—121no—
659C3×C4C22×C4×D311yescharacteristic
660C3×C4C22×C4×D311yescharacteristic
661C3×C4D3×#4111yescharacteristic
662C3×C4D3×#4111yescharacteristic
663Dic3—21no—
664Dic3—21no—
665Dic3—21no—
666Dic3—21no—
667Dic3—22no—
668Dic3—32no—
669Dic3—32no—
670Dic3—41no—
671Dic3—41no—
672Dic3—62no—
673Dic3—62no—
674Dic3—62no—
675Dic3—122no—
676Dic3—121no—
677Dic3—121no—
678Dic3—241no—
679C32#294711yescharacteristic, complemented, Sylow
680C23—61no—
681C23—91no—
682Q8—21no—
683Q8—32no—
684Q8—61no—
685Q8—92no—
686Q8—184no—
687Q8—181no—
688Q8C4×D3212yes—
689D4—32no—
690D4—61no—
691D4—184no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—31no—
695C2×C4—31no—
696C2×C4—31no—
697C2×C4—31no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—91no—
702C2×C4—92no—
703C2×C4—92no—
704C2×C4—184no—
705C2×C4—184no—
706C2×C4—181no—
707C2×C4—181no—
708C2×C4—241no—
709C2×C4—721no—
710C2×C4—721no—
711C2×C4C22×D3211yescharacteristic
712C8—21no—
713C8—32no—
714C8—32no—
715C8—181no—
716C2×C3—21no—
717C2×C3—21no—
718C2×C3—21no—
719C2×C3—122no—
720C2×C3C4×D3×D411yescharacteristic
721C2×C3C4×D3×D411yescharacteristic
722C2×C3#577511yescharacteristic
723C2×C3#577811yescharacteristic
724C2×C3#577911yescharacteristic
725C2×C3#577911yescharacteristic
726D3—42no—
727D3—64no—
728D3—62no—
729D3—62no—
730C22—62no—
731C22—92no—
732C22—121no—
733C22—121no—
734C22—181no—
735C22—181no—
736C22D32×D411yescharacteristic
737C4—22no—
738C4—41no—
739C4—61no—
740C4—61no—
741C4—62no—
742C4—61no—
743C4—61no—
744C4—92no—
745C4—121no—
746C4—121no—
747C4—182no—
748C4—361no—
749C4C2×C4×D3211yescharacteristic
750C4#6431211yescharacteristic
751C3—21no—
752C3#7977611yescharacteristic, complemented
753C3#7983011yescharacteristic, complemented
754C2—122no—
755C2—182no—
756C2#1059425511yescharacteristic
757C2#1059475411yescharacteristic
758C2#1059476911yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×#3796C22
cosocleC2×C32×C4C24
hypercenter#103D32
hypocenterC32#2947
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. #10595339C2semidirect
4. C3⋊D3×#103C2semidirect
5. C3×#4817C2semidirect
6. C3×#4789C2semidirect
7. Dic3×#216C2semidirect
8. Dic3×#215C2semidirect
10. #10590794C2semidirect
11. #10590747C2semidirect
12. #10590703C2semidirect
13. #10590583C2semidirect
14. #10590481C2semidirect
15. #10590479C2semidirect
28. #63951C4semidirect
80. #4817D3semidirect
86. #4789D3semidirect
95. Q8×C3⋊D3C2×C4semidirect
115. C3×#216C2×C4semidirect
116. C3×#215C2×C4semidirect
143. #3719C2×C4semidirect
144. #3716C2×C4semidirect
145. #3712C2×C4semidirect
356. #216C4×D3semidirect
357. #215C4×D3semidirect
679. C32#2947semidirect
752. C3#79776semidirect
753. C3#79830semidirect

Maximal subgroups

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

subgroupindex
#105953392
C2×#639512
#105943612
C3⋊D3×#1032
C3×#48172
C3×#47892
Dic3×#2162
Dic3×#2152
#105909562
#105907942
#105907472
#105907032
#105905832
#105904812
#105904792
#798303
#797763