Finite Group Databasebeta

← #11887652

Subgroups — #11887652

Order 1152.

825 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595400C211yesmaximal, characteristic
2#10594532C211yesmaximal, characteristic
3#10592491C211yesmaximal, characteristic, complemented
4C3×#4811C211yesmaximal, characteristic, complemented
5C3×#4809C211yesmaximal, characteristic, complemented
6#10591635C211yesmaximal, characteristic, complemented
7#10591580C211yesmaximal, characteristic, complemented
8D3×#835C211yesmaximal, characteristic, complemented
9#10590949C211yesmaximal, characteristic, complemented
10#10590818C211yesmaximal, characteristic, complemented
11#10590718C211yesmaximal, characteristic
12#10590684C211yesmaximal, characteristic, complemented
13D3×#810C211yesmaximal, characteristic, complemented
14#10590579C211yesmaximal, characteristic, complemented
15#10590496C211yesmaximal, characteristic, complemented
16#81490—31nomaximal
17#80193—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×D3×Dic6C2211yescharacteristic
20#64153C2211yescharacteristic
21#64097C2211yescharacteristic
22C3×#946C2211yescharacteristic
23C2×C3×#216C2211yescharacteristic
24C2×C3×Dic12C2211yescharacteristic
25C3×#897C2211yescharacteristic
26C3×D3×C4⋊C4C2211yescharacteristic
27C4×#625C2211yescharacteristic
28#63896—21no—
29D3×C4⋊Dic3C2211yescharacteristic
30#63887—21no—
31#63879—21no—
32#63879—21no—
33#63857—21no—
34#63857C2211yescharacteristic
35#63856C2211yescharacteristic
36#63851—21no—
37#63847—21no—
38#63843C2211yescharacteristic
39#63843C2211yescharacteristic
40#63839—21no—
41C2×#3719C2211yescharacteristic
42C2×D3×C3⋊C8C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44C32×#103C2211yescharacteristic
45#63662C2211yescharacteristic
46#63643C2211yescharacteristic
47C8×C3⋊Dic3C2211yescharacteristic
48#63637C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×#818C2211yescharacteristic
53C3×#810C2211yescharacteristic
54C3×#807C2211yescharacteristic
55#63575C2211yescharacteristic
56#63572C2211yescharacteristic
57#63567C2211yescharacteristic
58#63566C2211yescharacteristic
59#63565C2211yescharacteristic
60#63565C2211yescharacteristic
61Q8×#67—31no—
62#5635—31no—
63#5632—31no—
64#5511—31no—
65C3×#484—31no—
66C3×#451—31no—
67C2×#835—31no—
68#5188—31no—
69#5186—31no—
70#5182—31no—
71Dic3×Q16—31no—
72#5051—31no—
73#5051—31no—
74C2×#810—31no—
75#4887—31no—
76#4884—31no—
77#4875—31no—
78#4873—31no—
79#4811D311yescharacteristic, complemented
80#4809D311yescharacteristic, complemented
81D3×#103—31no—
82D3×#103—31no—
83#4795—31no—
84#4793—31no—
85#4792—31no—
86#4792—31no—
87#4792—61no—
88#4739—31no—
89#67⋊C8—31no—
90#67⋊C8—31no—
91#4722—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×#634—21no—
94C2×#634C2311yescharacteristic
95C3×D3×Q8—22no—
96C3×D3×Q8—41no—
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×Dic6—21no—
102C2×C3×Dic6C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×#627—21no—
105C2×#625D411yescharacteristic
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108D3×Dic6—22no—
109D3×Dic6—41no—
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113#3750—21no—
114#3750—21no—
115#3750—21no—
116C4×C3⋊Dic3C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×#216—41no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C2×C3×C3⋊C8C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C3×Dic12—22no—
129#3724—21no—
130#3724D411yescharacteristic
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3D411yescharacteristic
138(C2×D3)⋊Dic3D411yescharacteristic
139Dic32—21no—
140Dic32—21no—
141#3719—41no—
142D3×C3⋊C8—41no—
143D3×C3⋊C8—41no—
144#3299—91noSylow
145C22×C3×Q8—31no—
146C2×D3×Q8—31no—
147C2×D3×Q8C2×D311yescharacteristic
148C22×Dic6—31no—
149C2×C3×Q16—31no—
150C2×C3×Q16—31no—
151C3×C22⋊Q8—31no—
152C3×C22⋊Q8—31no—
153C2×C3×C4⋊C4—31no—
154#946—31no—
155#946—61no—
156#946C2×D311yescharacteristic
157Q8×Dic3—31no—
158Q8×Dic3—31no—
159#944—31no—
160#944—31no—
161#944—61no—
162#944—61no—
163C2×#216—31no—
164C2×#216C2×D311yescharacteristic
165C4×#67—31no—
166C4×#67—31no—
167C4×#67—61no—
168C4×#67—61no—
169C2×C4⋊Dic3—31no—
170#924—31no—
171#924—31no—
172#924—61no—
173#924—61no—
174C22×C3⋊C8—31no—
175C22×C3⋊C8—31no—
176C2×Dic12—31no—
177C2×Dic12C2×D311yescharacteristic
178C2×D3×C8—31no—
179C2×D3×C8—31no—
180#897—31no—
181#897—61no—
182#897C2×D311yescharacteristic
183#896—61no—
184#896—61no—
185D3×C4⋊C4—31no—
186D3×C4⋊C4C2×D311yescharacteristic
187#889—61no—
188#889—61no—
189#888—31no—
190#888—31no—
191#888—61no—
192#888—61no—
193#887—31no—
194#887—31no—
195#67⋊C4—61no—
196#67⋊C4—61no—
197#878—61no—
198#878—61no—
199C3×#107—31no—
200C3×#107—31no—
201C3×#103—21no—
202C3×#103—31no—
203C3×#103—31no—
204C3×#103C2×D311yescharacteristic
205C3×#103C2×D311yescharacteristic
206C3×C22⋊C8—31no—
207C3×C22⋊C8—31no—
208#835—31no—
209#835—31no—
210#835—31no—
211#835—31no—
212#835—31no—
213#835—61no—
214#835C2×D311yescharacteristic
215(C2×D3)⋊C8C2×D311yescharacteristic
216(C2×D3)⋊C8C2×D311yescharacteristic
217#818—31no—
218#818C2×D311yescharacteristic
219#816—31no—
220#816—31no—
221#816—31no—
222#816—31no—
223#816—61no—
224Dic3⋊C8—31no—
225Dic3⋊C8—31no—
226C8×Dic3—31no—
227C8×Dic3—31no—
228C8×Dic3—61no—
229#810—31no—
230#810—31no—
231#810—31no—
232#810—31no—
233#810—31no—
234#810—61no—
235#810C2×D311yescharacteristic
236#807—31no—
237#807C2×D311yescharacteristic
238C22×C3×D3C2×D411yescharacteristic
239C22×C3×D3C2×D411yescharacteristic
240C32×Q8—21no—
241C32×Q8—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C2411yescharacteristic
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3C2×D411yescharacteristic
248C2×C3⋊Dic3C2×D411yescharacteristic
249#634—21no—
250#634—21no—
251#634—81no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C3×C4×D3—21no—
259C3×C4×D3—21no—
260C3×C4×D3—21no—
261C3×C4×D3—21no—
262C3×C4×D3—42no—
263C3×C4×D3—81no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6—42no—
268C3×Dic6#4112yes—
269#627—42no—
270#625Q1614yescomplemented
271D3×Dic3—42no—
272D3×Dic3—81no—
273C32×C8—21no—
274C3⋊(C3⋊C8)—21no—
275C3×C3⋊C8—21no—
276C3×C3⋊C8—21no—
277#554—91no—
278D4×Q8—91no—
279#487—91no—
280#484—31no—
281#484—91no—
282#477—91no—
283#467—91no—
284#467—91no—
285#462—91no—
286#451—31no—
287#451—91no—
288C4×Q16—91no—
289C8×D4—91no—
290C2×#103—91no—
291C2×#103—91no—
292C2×C3×Q8—21no—
293C2×C3×Q8—31no—
294C2×C3×Q8—31no—
295C2×C3×Q8—61no—
296C2×C3×Q8—62no—
297C2×C3×Q8—121no—
298C2×C3×Q8C22×D311yescharacteristic
299C2×C3×Q8C22×D311yescharacteristic
300C22×C3×C4—31no—
301C22×C3×C4—31no—
302C22×C3×C4—61no—
303C22×C3×C4—61no—
304C2×#67—31no—
305C2×#67—31no—
306C22×Dic3—61no—
307C22×Dic3—61no—
308D3×Q8—22no—
309D3×Q8—41no—
310D3×Q8—62no—
311D3×Q8—121no—
312C2×C4×D3—21no—
313C2×C4×D3—21no—
314C2×C4×D3—61no—
315C2×C4×D3—61no—
316C2×C4×D3C22×D311yescharacteristic
317C2×C4×D3C22×D311yescharacteristic
318C2×Dic6—21no—
319C2×Dic6—31no—
320C2×Dic6—31no—
321C2×Dic6—61no—
322C2×Dic6—62no—
323C2×Dic6—61no—
324C2×Dic6—61no—
325C2×Dic6—61no—
326C2×Dic6—61no—
327C2×Dic6—121no—
328C2×Dic6—121no—
329C2×Dic6C22×D311yescharacteristic
330C2×Dic6C22×D311yescharacteristic
331C3×Q16—62no—
332C3×Q16—121no—
333C2×C3×C8—21no—
334C2×C3×C8—31no—
335C2×C3×C8—31no—
336C2×C3×C8C22×D311yescharacteristic
337C2×C3×C8C22×D311yescharacteristic
338C3×C4⋊C4—21no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348#217—31no—
349#217—31no—
350#217—61no—
351#217—61no—
352#216—41no—
353#216—121no—
354(C2×D3)⋊C4—21no—
355(C2×D3)⋊C4—21no—
356(C2×D3)⋊C4—31no—
357(C2×D3)⋊C4—31no—
358(C2×D3)⋊C4—61no—
359(C2×D3)⋊C4—61no—
360C4⋊Dic3—21no—
361C4⋊Dic3—31no—
362C4⋊Dic3—31no—
363C4⋊Dic3—61no—
364C4⋊Dic3—61no—
365C4⋊Dic3—61no—
366C4⋊Dic3—61no—
367C4⋊Dic3—61no—
368C4⋊Dic3C22×D311yescharacteristic
369C4⋊Dic3C22×D311yescharacteristic
370Dic3⋊C4—21no—
371Dic3⋊C4—21no—
372Dic3⋊C4—31no—
373Dic3⋊C4—31no—
374Dic3⋊C4—61no—
375Dic3⋊C4—61no—
376Dic3⋊C4—61no—
377Dic3⋊C4—61no—
378Dic3⋊C4—61no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—121no—
387Dic3⋊C4—121no—
388Dic3⋊C4—121no—
389C4×Dic3—31no—
390C4×Dic3—31no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C2×C3⋊C8—31no—
397C2×C3⋊C8—31no—
398C2×C3⋊C8—61no—
399C2×C3⋊C8—121no—
400C2×C3⋊C8—121no—
401C2×C3⋊C8C22×D311yescharacteristic
402C2×C3⋊C8C22×D311yescharacteristic
403Dic12—22no—
404Dic12—121no—
405D3×C8—121no—
406D3×C8—121no—
407C22×C32C22×D411yescharacteristic
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3C2×Q1612yes—
413C2×C3×D3C2×Q1612yes—
414C32×C4—41no—
415C32×C4—41no—
416C32×C4C2×#4111yescharacteristic
417C32×C4H(5,𝔽2)11yescharacteristic
418C3⋊Dic3—21no—
419C3⋊Dic3—41no—
420C3⋊Dic3—41no—
421C3⋊Dic3C2×Q1612yes—
422C3×Dic3—22no—
423C3×Dic3—21no—
424C3×Dic3—21no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C22×Q8—31no—
429C22×Q8—91no—
430C2×Q16—31no—
431C2×Q16—31no—
432C2×Q16—91no—
433C22×C8—91no—
434C22×C8—91no—
435C4⋊Q8—91no—
436C4⋊Q8—91no—
437C4⋊Q8—181no—
438#125—181no—
439C22⋊Q8—31no—
440C22⋊Q8—31no—
441C22⋊Q8—91no—
442C22⋊Q8—91no—
443C22⋊Q8—181no—
444C22⋊Q8—181no—
445C22⋊Q8—181no—
446C22⋊Q8—181no—
447C4×Q8—91no—
448C4×Q8—91no—
449C4×D4—91no—
450C4×D4—181no—
451C4×D4—181no—
452C2×C4⋊C4—31no—
453C2×C4⋊C4—91no—
454#107—31no—
455#107—31no—
456#107—91no—
457C4⋊C8—91no—
458#103—31no—
459#103—31no—
460#103—91no—
461#103—91no—
462#103—91no—
463#103—91no—
464#103—91no—
465#103—91no—
466#103—91no—
467#103D3211yescharacteristic
468C22⋊C8—31no—
469C22⋊C8—31no—
470C4×C8—91no—
471C23×C3—31no—
472C23×C3—31no—
473C22×D3D3×D411yescharacteristic
474C22×D3D3×D411yescharacteristic
475C3×Q8—21no—
476C3×Q8—21no—
477C3×Q8—21no—
478C3×Q8—21no—
479C3×Q8—32no—
480C3×Q8—41no—
481C3×Q8—41no—
482C3×Q8—61no—
483C3×Q8—61no—
484C3×Q8—61no—
485C3×Q8—122no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—31no—
492C2×C3×C4—31no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—61no—
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—122no—
504C2×C3×C4—241no—
505C2×C3×C4C23×D311yescharacteristic
506C2×C3×C4C23×D311yescharacteristic
507#67—34no—
508#67—34no—
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—31no—
514C2×Dic3—31no—
515C2×Dic3—31no—
516C2×Dic3—31no—
517C2×Dic3—61no—
518C2×Dic3—61no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—121no—
524C2×Dic3—121no—
525C2×Dic3—122no—
526C2×Dic3—241no—
527C2×Dic3D3×D411yescharacteristic
528C2×Dic3D3×D411yescharacteristic
529C4×D3—21no—
530C4×D3—21no—
531C4×D3—21no—
532C4×D3—21no—
533C4×D3—42no—
534C4×D3—81no—
535C4×D3—122no—
536C4×D3—241no—
537Dic6—21no—
538Dic6—21no—
539Dic6—21no—
540Dic6—42no—
541Dic6—61no—
542Dic6—61no—
543Dic6—61no—
544Dic6—61no—
545Dic6—121no—
546Dic6—121no—
547Dic6—122no—
548Dic6—122no—
549Dic6—241no—
550Dic6—241no—
551Dic6—242no—
552Dic6#23712yes—
553C3×C8—21no—
554C3×C8—21no—
555C3×C8—41no—
556C3×C8—61no—
557C3×C8—61no—
558C3⋊C8—21no—
559C3⋊C8—21no—
560C3⋊C8—61no—
561C3⋊C8—61no—
562C3⋊C8—121no—
563C2×C32#54611yescharacteristic
564C2×C32C22×Q1611yescharacteristic
565C2×C32#57711yescharacteristic
566C3×D3—22no—
567C3×D3—22no—
568C2×Q8—31no—
569C2×Q8—31no—
570C2×Q8—61no—
571C2×Q8—62no—
572C2×Q8—91no—
573C2×Q8—121no—
574C2×Q8—181no—
575C2×Q8—181no—
576C2×Q8—182no—
577C2×Q8—361no—
578C2×Q8C2×D3211yescharacteristic
579C2×D4—91no—
580C22×C4—31no—
581C22×C4—31no—
582C22×C4—61no—
583C22×C4—61no—
584C22×C4—181no—
585C22×C4—181no—
586Q16—62no—
587Q16—121no—
588Q16—361no—
589C2×C8—31no—
590C2×C8—31no—
591C2×C8—91no—
592C2×C8—361no—
593C2×C8—361no—
594C2×C8C2×D3211yescharacteristic
595C4⋊C4—31no—
596C4⋊C4—31no—
597C4⋊C4—61no—
598C4⋊C4—61no—
599C4⋊C4—61no—
600C4⋊C4—91no—
601C4⋊C4—91no—
602C4⋊C4—181no—
603C4⋊C4—181no—
604C4⋊C4—181no—
605C4⋊C4—181no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C4⋊C4C2×D3211yescharacteristic
611C22⋊C4—61no—
612C22⋊C4—61no—
613C22⋊C4—91no—
614C22⋊C4—91no—
615C22⋊C4—181no—
616C22⋊C4—181no—
617C42—91no—
618C42—181no—
619C42—181no—
620C22×C3—21no—
621C22×C3—32no—
622C22×C3—32no—
623C22×C3—61no—
624C22×C3—61no—
625C22×C3—61no—
626C22×C3—61no—
627C22×C3C2×D3×D411yescharacteristic
628C22×C3C2×D3×D411yescharacteristic
629C2×D3—21no—
630C2×D3—21no—
631C2×D3—21no—
632C2×D3—21no—
633C2×D3D3×Q1612yes—
634C2×D3D3×Q1612yes—
635C3×C4—21no—
636C3×C4—21no—
637C3×C4—41no—
638C3×C4—41no—
639C3×C4—41no—
640C3×C4—41no—
641C3×C4—62no—
642C3×C4—61no—
643C3×C4—61no—
644C3×C4—81no—
645C3×C4—81no—
646C3×C4—121no—
647C3×C4—121no—
648C3×C4—121no—
649C3×C4C2×#23711yescharacteristic
650C3×C4#100411yescharacteristic
651C3×C4D3×#4111yescharacteristic
652C3×C4#100911yescharacteristic
653Dic3—21no—
654Dic3—22no—
655Dic3—21no—
656Dic3—32no—
657Dic3—32no—
658Dic3—41no—
659Dic3—41no—
660Dic3—41no—
661Dic3—62no—
662Dic3—62no—
663Dic3—61no—
664Dic3—61no—
665Dic3—121no—
666Dic3—121no—
667Dic3—121no—
668Dic3—121no—
669Dic3—241no—
670Dic3—241no—
671C32#329911yescharacteristic, complemented, Sylow
672C23—31no—
673C23—31no—
674Q8—21no—
675Q8—21no—
676Q8—32no—
677Q8—61no—
678Q8—61no—
679Q8—61no—
680Q8—122no—
681Q8—181no—
682Q8—181no—
683Q8—362no—
684Q8—721no—
685D4—94no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—31no—
689C2×C4—31no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—91no—
699C2×C4—91no—
700C2×C4—122no—
701C2×C4—181no—
702C2×C4—181no—
703C2×C4—241no—
704C2×C4—362no—
705C2×C4—721no—
706C2×C4C22×D3211yescharacteristic
707C8—21no—
708C8—61no—
709C8—61no—
710C8—181no—
711C2×C3—21no—
712C2×C3—21no—
713C2×C3—21no—
714C2×C3—62no—
715C2×C3—62no—
716C2×C3#559111yescharacteristic
717C2×C3#565411yescharacteristic
718C2×C3C2×D3×Q1611yescharacteristic
719C2×C3C2×D3×Q1611yescharacteristic
720C2×C3#577511yescharacteristic
721C2×C3#577811yescharacteristic
722D3—22no—
723D3—22no—
724C22—32no—
725C22—32no—
726C22—61no—
727C22—61no—
728C22—61no—
729C22—61no—
730C22D32×D411yescharacteristic
731C4—41no—
732C4—41no—
733C4—61no—
734C4—61no—
735C4—62no—
736C4—92no—
737C4—121no—
738C4—121no—
739C4—121no—
740C4—181no—
741C4—361no—
742C4—361no—
743C4#6430711yescharacteristic
744C4D3×#23711yescharacteristic
745C3—21no—
746C3#8019311yescharacteristic, complemented
747C3#8149011yescharacteristic, complemented
748C2—62no—
749C2—62no—
750C2#1059427411yescharacteristic
751C2#1059475411yescharacteristic
752C2D32×Q1611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×#625D4
hypercenter#103D32
hypocenterC32#3299
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
3. #10592491C2semidirect
4. C3×#4811C2semidirect
5. C3×#4809C2semidirect
6. #10591635C2semidirect
7. #10591580C2semidirect
8. D3×#835C2semidirect
9. #10590949C2semidirect
10. #10590818C2semidirect
12. #10590684C2semidirect
13. D3×#810C2semidirect
14. #10590579C2semidirect
15. #10590496C2semidirect
79. #4811D3semidirect
80. #4809D3semidirect
270. #625Q16semidirect
671. C32#3299semidirect
746. C3#80193semidirect
747. C3#81490semidirect

Maximal subgroups

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

subgroupindex
#105954002
#105945322
#105924912
C3×#48112
C3×#48092
#105916352
#105915802
D3×#8352
#105909492
#105908182
#105907182
#105906842
D3×#8102
#105905792
#105904962
#814903
#801933