Finite Group Databasebeta

← #11860642

Subgroups — #11860642

Order 1152.

999 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63811C211yesmaximal, characteristic
2#10594361C211yesmaximal, characteristic
3#10594347C211yesmaximal, characteristic, complemented
4#10592560C211yesmaximal, characteristic, complemented
5C3×#4853C211yesmaximal, characteristic, complemented
6C3×#4852C211yesmaximal, characteristic, complemented
7#10590910C211yesmaximal, characteristic, complemented
8Dic3×Dic12C211yesmaximal, characteristic, complemented
9#10590766C211yesmaximal, characteristic, complemented
10#10590611C211yesmaximal, characteristic
11#10590601C211yesmaximal, characteristic, complemented
12#10590478C211yesmaximal, characteristic, complemented
13#10590477C211yesmaximal, characteristic, complemented
14#10590476C211yesmaximal, characteristic, complemented
15#10590453C211yesmaximal, characteristic, complemented
16#79830—31nomaximal
17#79648—31nomaximal
18C2×#3797C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20C2×#3743C2211yescharacteristic
21#64101C2211yescharacteristic
22C4⋊C4×C3⋊D3C2211yescharacteristic
23C2×C3×Dic12C2211yescharacteristic
24C2×C3×#204C2211yescharacteristic
25C3×#893C2211yescharacteristic
26C3×#887C2211yescharacteristic
27C3×#887C2211yescharacteristic
28C3×#887C2211yescharacteristic
29C4×#627—21no—
30C4×#626—21no—
31Dic3×D12C2211yescharacteristic
32#63881—21no—
33#63877—21no—
34D3×Dic3⋊C4—21no—
35#63874C2211yescharacteristic
36Dic3×Dic6C2211yescharacteristic
37Dic3×Dic6C2211yescharacteristic
38Dic3×Dic6C2211yescharacteristic
39#63838—21no—
40#63836—21no—
41#63836—21no—
42C2×#3718C2211yescharacteristic
43C2×#3715C2211yescharacteristic
44C2×#3710C2211yescharacteristic
45#63811C418yescomplemented
46C32×#106C2211yescharacteristic
47#63645C2211yescharacteristic
48#63635C2211yescharacteristic
49#63634C2211yescharacteristic
50C3×#815C2211yescharacteristic
51C3×C8×Dic3C2211yescharacteristic
52C3×#810C2211yescharacteristic
53C3×#810C2211yescharacteristic
54C3×#810C2211yescharacteristic
55C3×#809C2211yescharacteristic
56#63566C2211yescharacteristic
57#63566C2211yescharacteristic
58#63566C2211yescharacteristic
59#63563C2211yescharacteristic
60#63554C2211yescharacteristic
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×C4×SD16—31no—
70Dic3×Q16—31no—
71#5164—31no—
72#5030—31no—
73C4×#216—31no—
74C4×#215—31no—
75#5018—31no—
76#4861—31no—
77#4861—31no—
78#4861—61no—
79#4853D311yescharacteristic, complemented
80#4852D311yescharacteristic, complemented
81#4817—31no—
82#4804—31no—
83D3×#103—31no—
84D3×#103—31no—
85#4790—31no—
86#4789—31no—
87#4772—31no—
88#4758—31no—
89#4710—31no—
90#4708—31no—
91C4×Dic12—31no—
92#4689—31no—
93C2×C4×C3⋊D3—21no—
94C2×C4×C3⋊D3C2311yescharacteristic
95C2×C3×D12C2311yescharacteristic
96C2×C3×C4×D3—21no—
97C2×C3×Dic6C2311yescharacteristic
98C2×C3×Dic6C2311yescharacteristic
99C2×C3×Dic6C2311yescharacteristic
100C2×#627—21no—
101C2×#626—21no—
102C2×#624—21no—
103C2×D3×Dic3—21no—
104C2×D3×Dic3—21no—
105#3797—22no—
106#3797C2×C414yescomplemented
107#3796—22no—
108#3796C2×C414yes—
109C2×C32×C8C2311yescharacteristic
110C32×C4⋊C4C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112#3752—21no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750—21no—
116C4×C3⋊Dic3—21no—
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118#3743C2×C414yescomplemented
119C3×(C2×D3)⋊C4—21no—
120C3×Dic3⋊C4—21no—
121C3×Dic3⋊C4—21no—
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
130C3×Dic12C2×C414yescomplemented
131C3×#204C2×C414yescomplemented
132#3724D411yescharacteristic
133#3724D411yescharacteristic
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137#3722D411yescharacteristic
138#3722D411yescharacteristic
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141Dic32—21no—
142Dic32—21no—
143#3718C2×C414yescomplemented
144#3715C2×C414yescomplemented
145#3710—22no—
146#2947—91noSylow
147C2×#239—31no—
148C2×D3×Q8—31no—
149C2×D3×Q8—31no—
150C2×#237—31no—
151C2×C3×Q16—31no—
152C2×C3×SD16—31no—
153C3×C4×Q8—31no—
154C3×C4×Q8—31no—
155C3×C4×Q8—31no—
156C3×C4×D4—31no—
157Q8×Dic3—31no—
158Q8×Dic3—31no—
159Q8×Dic3—31no—
160C2×#216—31no—
161C2×#216—31no—
162C2×#215—31no—
163D4×Dic3—31no—
164C2×#214—31no—
165C4×#67—61no—
166C2×Dic3⋊C4—61no—
167#918—38no—
168#915—38no—
169C2×Dic12C2×D311yescharacteristic
170C2×#204C2×D311yescharacteristic
171C2×ΓL(1,𝔽25)—31no—
172C2×ΓL(1,𝔽25)—31no—
173C2×ΓL(1,𝔽25)—61no—
174C2×D3×C8—31no—
175C2×D3×C8—31no—
176#893—61no—
177#893C2×D311yescharacteristic
178#892—31no—
179#892—31no—
180#892—61no—
181#892—61no—
182#892—61no—
183D3×C4⋊C4—31no—
184D3×C4⋊C4—31no—
185D3×C4⋊C4—61no—
186D3×C4⋊C4—61no—
187#887—61no—
188#887—61no—
189#887C2×D311yescharacteristic
190#887C2×D311yescharacteristic
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×#106—21no—
207C3×#106C2×D311yescharacteristic
208C3×#106C2×D311yescharacteristic
209C3×#103—31no—
210C3×#103—31no—
211C3×#103—31no—
212C3×#102—31no—
213C3×#97—31no—
214C3×C4×C8—31no—
215#835—31no—
216#835—31no—
217#835—31no—
218#832—31no—
219#821—31no—
220#818—31no—
221#818—31no—
222#818—61no—
223#816—31no—
224#816—31no—
225#816—31no—
226#815—31no—
227#815C2×D311yescharacteristic
228C8×Dic3—31no—
229C8×Dic3C2×D311yescharacteristic
230#810C2×D311yescharacteristic
231#810C2×D311yescharacteristic
232#810C2×D311yescharacteristic
233#809C2×D311yescharacteristic
234#808—31no—
235#808—31no—
236#808—61no—
237#807—31no—
238#807—31no—
239#807—61no—
240#803—31no—
241C4×C3⋊C8—31no—
242C22×C3⋊D3C2×D411yescharacteristic
243C22×C3×D3—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4C2411yescharacteristic
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3C2×D411yescharacteristic
250C4×C3⋊D3—81no—
251C4×C3⋊D3C22×C412yes—
252C4×C3⋊D3#4112yes—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C3×D12—21no—
261C3×D12C22×C412yes—
262C3×C4×D3—81no—
263C3×Dic6—21no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266C3×Dic6C22×C412yes—
267C3×Dic6C22×C412yes—
268C3×Dic6C22×C412yes—
269#627—24no—
270#626—24no—
271#624—24no—
272D3×Dic3—24no—
273D3×Dic3—81no—
274C32×C8C22×C412yes—
275C3⋊(C3⋊C8)C22×C412yes—
276C3×C3⋊C8—21no—
277C3×C3⋊C8—21no—
278C2×#137—91no—
279#520—91no—
280#519—91no—
281#441—31no—
282#441—91no—
283#440—91no—
284#440—91no—
285C4×Q16—91no—
286C4×Q16—91no—
287C4×SD16—31no—
288C4×SD16—91no—
289#428—91no—
290#416—91no—
291C2×#103—91no—
292#405—91no—
293C2×C3×Q8—31no—
294C2×C3×Q8—31no—
295C2×C3×Q8—31no—
296C2×C3×D4—31no—
297C22×C3×C4—61no—
298C2×#67—61no—
299C22×Dic3—61no—
300C22×Dic3—61no—
301#239—34no—
302#239—62no—
303D3×Q8—34no—
304D3×Q8—34no—
305D3×Q8—62no—
306D3×Q8—62no—
307#237—34no—
308#237—62no—
309C2×D12—61no—
310C2×D12C22×D311yescharacteristic
311C2×C4×D3—21no—
312C2×C4×D3—31no—
313C2×C4×D3—31no—
314C2×C4×D3—61no—
315C2×C4×D3—61no—
316C2×C4×D3—61no—
317C2×C4×D3—61no—
318C2×C4×D3—61no—
319C2×C4×D3—61no—
320C2×C4×D3—61no—
321C2×C4×D3—121no—
322C2×Dic6—61no—
323C2×Dic6—61no—
324C2×Dic6C22×D311yescharacteristic
325C2×Dic6C22×D311yescharacteristic
326C2×Dic6C22×D311yescharacteristic
327C3×Q16—34no—
328C3×SD16—34no—
329C2×C3×C8—21no—
330C2×C3×C8—31no—
331C2×C3×C8—31no—
332C2×C3×C8C22×D311yescharacteristic
333C2×C3×C8C22×D311yescharacteristic
334C3×C4⋊C4—21no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—61no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4C22×D311yescharacteristic
340C3×C4⋊C4C22×D311yescharacteristic
341C3×C4⋊C4C22×D311yescharacteristic
342C3×C4⋊C4C22×D311yescharacteristic
343C3×C22⋊C4—61no—
344C3×C42—31no—
345C3×C42—31no—
346C3×C42—61no—
347C3×C42—61no—
348C3×C42—61no—
349#217—61no—
350#216—34no—
351#216—34no—
352#215—34no—
353#214—34no—
354(C2×D3)⋊C4—21no—
355(C2×D3)⋊C4—31no—
356(C2×D3)⋊C4—31no—
357(C2×D3)⋊C4—31no—
358(C2×D3)⋊C4—31no—
359(C2×D3)⋊C4—61no—
360(C2×D3)⋊C4—61no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—121no—
363C4⋊Dic3—31no—
364C4⋊Dic3—31no—
365C4⋊Dic3—31no—
366C4⋊Dic3—31no—
367C4⋊Dic3—61no—
368C4⋊Dic3—61no—
369C4⋊Dic3—61no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372Dic3⋊C4—21no—
373Dic3⋊C4—21no—
374Dic3⋊C4—21no—
375Dic3⋊C4—31no—
376Dic3⋊C4—31no—
377Dic3⋊C4—31no—
378Dic3⋊C4—31no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—121no—
385C4×Dic3—21no—
386C4×Dic3—21no—
387C4×Dic3—21no—
388C4×Dic3—61no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—121no—
397C4×Dic3C22×D311yescharacteristic
398C4×Dic3C22×D311yescharacteristic
399C2×C3⋊C8—31no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—61no—
402C2×C3⋊C8C22×D311yescharacteristic
403C2×C3⋊C8C22×D311yescharacteristic
404Dic12C4×D314yescomplemented
405#204C4×D314yescomplemented
406ΓL(1,𝔽25)—34no—
407ΓL(1,𝔽25)—34no—
408ΓL(1,𝔽25)—64no—
409D3×C8—62no—
410D3×C8—62no—
411C22×C32C22×D411yescharacteristic
412C2×C3⋊D3—21no—
413C2×C3⋊D3—21no—
414C2×C3⋊D3C4×D412yes—
415C2×C3×D3—22no—
416C2×C3×D3—41no—
417C2×C3×D3—41no—
418C32×C4—41no—
419C32×C4—41no—
420C32×C4C23×C411yescharacteristic
421C32×C4C2×#4111yescharacteristic
422C3⋊Dic3—41no—
423C3⋊Dic3—41no—
424C3⋊Dic3C4×D412yes—
425C3×Dic3—22no—
426C3×Dic3—22no—
427C3×Dic3—22no—
428C3×Dic3—21no—
429C3×Dic3—21no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C2×#41—91no—
433C22×Q8—91no—
434#137—98no—
435C2×Q16—31no—
436C2×Q16—91no—
437C2×SD16—31no—
438C2×SD16—91no—
439C2×M16—91no—
440C22×C8—91no—
441C4×Q8—31no—
442C4×Q8—31no—
443C4×Q8—31no—
444C4×Q8—91no—
445C4×Q8—91no—
446C4×Q8—91no—
447C4×Q8—181no—
448C4×Q8—181no—
449C4×D4—31no—
450C4×D4—91no—
451C4×D4—181no—
452C4×D4—181no—
453#117—91no—
454#117—91no—
455#117—181no—
456#117—181no—
457#117—181no—
458C2×C4⋊C4—91no—
459C2×C4⋊C4—181no—
460#107—91no—
461#107—91no—
462#106—91no—
463#106D3211yescharacteristic
464#103—31no—
465#103—31no—
466#103—31no—
467#103—91no—
468#103—91no—
469#103—91no—
470#102—31no—
471#102—91no—
472#97—31no—
473#97—91no—
474C4×C8—31no—
475C4×C8—91no—
476C23×C3—61no—
477C22×D3—21no—
478C22×D3—31no—
479C22×D3—31no—
480C22×D3—61no—
481C3×Q8—32no—
482C3×Q8—32no—
483C3×Q8—32no—
484C3×Q8—61no—
485C3×Q8—61no—
486C3×Q8—61no—
487C3×D4—32no—
488C3×D4—61no—
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—31no—
496C2×C3×C4—31no—
497C2×C3×C4—31no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—241no—
504C2×C3×C4C23×D311yescharacteristic
505C2×C3×C4C23×D311yescharacteristic
506#67—64no—
507C2×Dic3—21no—
508C2×Dic3—21no—
509C2×Dic3—21no—
510C2×Dic3—31no—
511C2×Dic3—31no—
512C2×Dic3—61no—
513C2×Dic3—64no—
514C2×Dic3—61no—
515C2×Dic3—61no—
516C2×Dic3—61no—
517C2×Dic3—61no—
518C2×Dic3—121no—
519C2×Dic3—121no—
520C2×Dic3—241no—
521C2×Dic3D3×D411yescharacteristic
522C2×Dic3D3×D411yescharacteristic
523C2×Dic3D3×D411yescharacteristic
524C2×Dic3D3×D411yescharacteristic
525D12—21no—
526D12—64no—
527D12C2×C4×D312yes—
528C4×D3—32no—
529C4×D3—32no—
530C4×D3—32no—
531C4×D3—32no—
532C4×D3—62no—
533C4×D3—62no—
534C4×D3—64no—
535C4×D3—64no—
536C4×D3—64no—
537C4×D3—81no—
538C4×D3—241no—
539C4×D3—241no—
540C4×D3—241no—
541C4×D3—242no—
542Dic6—21no—
543Dic6—21no—
544Dic6—21no—
545Dic6—64no—
546Dic6—64no—
547Dic6C2×C4×D312yes—
548Dic6C2×C4×D312yes—
549Dic6C2×C4×D312yes—
550C3×C8—22no—
551C3×C8—61no—
552C3×C8—61no—
553C3×C8C2×C4×D312yes—
554C3×C8C2×C4×D312yes—
555C3⋊C8—21no—
556C3⋊C8—21no—
557C3⋊C8—32no—
558C3⋊C8—32no—
559C3⋊C8—62no—
560C2×C32C2×C4×D411yescharacteristic
561C2×C32#57711yescharacteristic
562C2×C32#57811yescharacteristic
563C3⋊D3—22no—
564C3×D3—42no—
565#41—94no—
566#41—182no—
567C2×Q8—31no—
568C2×Q8—31no—
569C2×Q8—31no—
570C2×Q8—94no—
571C2×Q8—181no—
572C2×Q8—182no—
573C2×D4—31no—
574C2×D4—181no—
575C22×C4—61no—
576C22×C4—91no—
577C22×C4—181no—
578C22×C4—181no—
579C22×C4—181no—
580C22×C4—181no—
581Q16—34no—
582Q16—94no—
583SD16—34no—
584SD16—94no—
585M16—94no—
586C2×C8—31no—
587C2×C8—31no—
588C2×C8—91no—
589C2×C8—182no—
590C2×C8C2×D3211yescharacteristic
591C4⋊C4—61no—
592C4⋊C4—61no—
593C4⋊C4—61no—
594C4⋊C4—91no—
595C4⋊C4—91no—
596C4⋊C4—91no—
597C4⋊C4—91no—
598C4⋊C4—181no—
599C4⋊C4—181no—
600C4⋊C4—181no—
601C4⋊C4—181no—
602C4⋊C4C2×D3211yescharacteristic
603C4⋊C4C2×D3211yescharacteristic
604C22⋊C4—61no—
605C22⋊C4—91no—
606C22⋊C4—91no—
607C22⋊C4—181no—
608C22⋊C4—181no—
609C42—31no—
610C42—31no—
611C42—61no—
612C42—61no—
613C42—61no—
614C42—181no—
615C42—181no—
616C42—181no—
617C42—181no—
618C22×C3—21no—
619C22×C3—62no—
620C22×C3—121no—
621C22×C3—121no—
622C22×C3C2×D3×D411yescharacteristic
623C22×C3C2×D3×D411yescharacteristic
624C2×D3—22no—
625C2×D3—32no—
626C2×D3—32no—
627C2×D3—41no—
628C2×D3—41no—
629C2×D3—62no—
630C2×D3—61no—
631C2×D3—61no—
632C2×D3—61no—
633C2×D3—61no—
634C2×D3—121no—
635C2×D3—121no—
636C3×C4—21no—
637C3×C4—21no—
638C3×C4—41no—
639C3×C4—41no—
640C3×C4—41no—
641C3×C4—41no—
642C3×C4—61no—
643C3×C4—61no—
644C3×C4—61no—
645C3×C4—61no—
646C3×C4—62no—
647C3×C4—62no—
648C3×C4—62no—
649C3×C4—81no—
650C3×C4—81no—
651C3×C4C22×C4×D311yescharacteristic
652C3×C4C22×C4×D311yescharacteristic
653C3×C4D3×#4111yescharacteristic
654C3×C4D3×#4111yescharacteristic
655Dic3—21no—
656Dic3—21no—
657Dic3—21no—
658Dic3—21no—
659Dic3—22no—
660Dic3—22no—
661Dic3—22no—
662Dic3—32no—
663Dic3—32no—
664Dic3—62no—
665Dic3—121no—
666Dic3—121no—
667Dic3—121no—
668Dic3—121no—
669Dic3—241no—
670Dic3—241no—
671C32#294711yescharacteristic, complemented, Sylow
672C23—61no—
673C23—91no—
674Q8—32no—
675Q8—32no—
676Q8—32no—
677Q8—61no—
678Q8—61no—
679Q8—61no—
680Q8—184no—
681D4—32no—
682D4—61no—
683D4—184no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—31no—
687C2×C4—31no—
688C2×C4—31no—
689C2×C4—31no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—91no—
694C2×C4—92no—
695C2×C4—92no—
696C2×C4—184no—
697C2×C4—184no—
698C2×C4—181no—
699C2×C4—181no—
700C2×C4—241no—
701C2×C4—721no—
702C2×C4—721no—
703C2×C4C22×D3211yescharacteristic
704C8—61no—
705C8—61no—
706C8—92no—
707C8C4×D3212yes—
708C2×C3—21no—
709C2×C3—21no—
710C2×C3—21no—
711C2×C3—122no—
712C2×C3C4×D3×D411yescharacteristic
713C2×C3C4×D3×D411yescharacteristic
714C2×C3#576211yescharacteristic
715C2×C3#577111yescharacteristic
716C2×C3#577811yescharacteristic
717C2×C3#577911yescharacteristic
718D3—42no—
719D3—62no—
720D3—62no—
721D3—122no—
722C22—62no—
723C22—92no—
724C22—121no—
725C22—121no—
726C22—181no—
727C22—181no—
728C22D32×D411yescharacteristic
729C4—41no—
730C4—41no—
731C4—62no—
732C4—62no—
733C4—62no—
734C4—61no—
735C4—61no—
736C4—61no—
737C4—61no—
738C4—92no—
739C4—361no—
740C4—361no—
741C4C2×C4×D3211yescharacteristic
742C4#6431911yescharacteristic
743C3—21no—
744C3#7964811yescharacteristic, complemented
745C3#7983011yescharacteristic, complemented
746C2—122no—
747C2—182no—
748C2#1059460511yescharacteristic
749C2#1059475111yescharacteristic
750C2#1059475611yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC2×#3796C22
cosocleC2×C32×C4C24
hypercenter#106D32
hypocenterC32#2947
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
3. #10594347C2semidirect
4. #10592560C2semidirect
5. C3×#4853C2semidirect
6. C3×#4852C2semidirect
7. #10590910C2semidirect
8. Dic3×Dic12C2semidirect
9. #10590766C2semidirect
11. #10590601C2semidirect
12. #10590478C2semidirect
13. #10590477C2semidirect
14. #10590476C2semidirect
15. #10590453C2semidirect
45. #63811C4semidirect
79. #4853D3semidirect
80. #4852D3semidirect
106. #3797C2×C4semidirect
118. #3743C2×C4semidirect
130. C3×Dic12C2×C4semidirect
131. C3×#204C2×C4semidirect
143. #3718C2×C4semidirect
144. #3715C2×C4semidirect
404. Dic12C4×D3semidirect
405. #204C4×D3semidirect
671. C32#2947semidirect
744. C3#79648semidirect
745. C3#79830semidirect

Maximal subgroups

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

subgroupindex
C2×#638112
#105943612
#105943472
#105925602
C3×#48532
C3×#48522
#105909102
Dic3×Dic122
#105907662
#105906112
#105906012
#105904782
#105904772
#105904762
#105904532
#798303
#796483