Finite Group Databasebeta

← #11887679

Subgroups — #11887679

Order 1152.

833 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#10594537C211yesmaximal, characteristic
2#10594383C211yesmaximal, characteristic
3#10592586C211yesmaximal, characteristic, complemented
4C3×#4884C211yesmaximal, characteristic, complemented
5C3×#4875C211yesmaximal, characteristic, complemented
6#10590952C211yesmaximal, characteristic, complemented
7#10590906C211yesmaximal, characteristic
8#10590808C211yesmaximal, characteristic, complemented
9#10590672C211yesmaximal, characteristic, complemented
10#10590605C211yesmaximal, characteristic, complemented
11D3×#810C211yesmaximal, characteristic, complemented
12#10590579C211yesmaximal, characteristic, complemented
13#10590560C211yesmaximal, characteristic, complemented
14#10590481C211yesmaximal, characteristic, complemented
15#10590444C211yesmaximal, characteristic, complemented
16#81490—31nomaximal
17#81119—31nomaximal
18C2×#3797C2211yescharacteristic
19C2×D3×Dic6C2211yescharacteristic
20C2×#3746C2211yescharacteristic
21C2×C8×C3⋊D3C2211yescharacteristic
22#64106C2211yescharacteristic
23#64106C2211yescharacteristic
24C3×#897C2211yescharacteristic
25C3×D3×C4⋊C4C2211yescharacteristic
26C3×#888C2211yescharacteristic
27C3×#887C2211yescharacteristic
28#63918—21no—
29#63904—21no—
30C4×#626C2211yescharacteristic
31#63900C2211yescharacteristic
32#63895—21no—
33#63893—21no—
34#63888—21no—
35#63880—21no—
36#63866C2211yescharacteristic
37#63857C2211yescharacteristic
38#63856—21no—
39#63845—21no—
40#63844C2211yescharacteristic
41C2×#3719C2211yescharacteristic
42C2×#3719C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44C32×#107C2211yescharacteristic
45#63637C2211yescharacteristic
46#63637C2211yescharacteristic
47C3×(C2×D3)⋊C8C2211yescharacteristic
48C3×#816C2211yescharacteristic
49C3×#816C2211yescharacteristic
50C3×Dic3⋊C8C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#810C2211yescharacteristic
53C3×#807C2211yescharacteristic
54C3×#807C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59#63557C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5730—31no—
62#5632—31no—
63Q8×D12—31no—
64#5511—31no—
65C3×#484—31no—
66C3×#477—31no—
67#5093—31no—
68#5051—31no—
69C4×#216—31no—
70C2×#810—31no—
71#4887—31no—
72#4887—31no—
73#4887—31no—
74#4887—61no—
75#4884—31no—
76#4884—31no—
77#4884D311yescharacteristic, complemented
78#4875D311yescharacteristic, complemented
79#4873—31no—
80#4849—31no—
81#4834—31no—
82#4809—31no—
83#4809—31no—
84#4809—31no—
85D3×#103—31no—
86D3×#103—31no—
87D3×#103—31no—
88#4795—31no—
89#4792—31no—
90#4739—31no—
91#67⋊C8—31no—
92C2×C4×C3⋊D3C2311yescharacteristic
93C2×#634C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×C3×C4×D3—21no—
96C2×C3×C4×D3C2311yescharacteristic
97C2×C3×Dic6—21no—
98C2×C3×Dic6C2311yescharacteristic
99C2×C3×Dic6C2311yescharacteristic
100C2×#627—21no—
101C2×#627—21no—
102C2×#626D411yescharacteristic
103C2×#624—21no—
104C2×#624—21no—
105C2×D3×Dic3—21no—
106#3797—22no—
107#3797—41no—
108D3×Dic6—22no—
109D3×Dic6—41no—
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113#3752—21no—
114#3752—21no—
115C4⋊(C3⋊Dic3)—21no—
116C4⋊(C3⋊Dic3)—21no—
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118#3746—41no—
119C8×C3⋊D3—41no—
120C3×(C2×D3)⋊C4—21no—
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×C4×Dic3—21no—
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131#3724—21no—
132#3724—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3D411yescharacteristic
137#3722D411yescharacteristic
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3D411yescharacteristic
140Dic32—21no—
141#3719—22no—
142#3719—41no—
143D3×C3⋊C8—41no—
144#3299—91noSylow
145C2×D3×Q8—31no—
146C2×D3×Q8—31no—
147C2×D3×Q8—31no—
148C22×Dic6—31no—
149C3×C4⋊Q8—31no—
150C3×C22⋊Q8—31no—
151C3×C4×Q8—31no—
152C2×C3×C4⋊C4—31no—
153#946—61no—
154#946—61no—
155#944—31no—
156C2×#216—31no—
157C2×#216—31no—
158C4×#67—31no—
159C4×#67—61no—
160#924—31no—
161#924—61no—
162C22×C3⋊C8—31no—
163C2×Dic12—31no—
164C2×Dic12—31no—
165C2×Dic12—31no—
166C2×Dic12—31no—
167C2×Dic12—61no—
168C2×D3×C8—31no—
169C2×D3×C8—31no—
170C2×D3×C8—31no—
171C2×D3×C8—61no—
172#897—31no—
173#897—31no—
174#897—31no—
175#897—31no—
176#897—31no—
177#897—61no—
178#897—61no—
179#897—61no—
180#897—61no—
181#897C2×D311yescharacteristic
182#896—61no—
183#896—61no—
184#893—61no—
185D3×C4⋊C4—31no—
186D3×C4⋊C4—31no—
187D3×C4⋊C4C2×D311yescharacteristic
188#890—61no—
189#889—61no—
190#888—61no—
191#888C2×D311yescharacteristic
192#887—31no—
193#887C2×D311yescharacteristic
194#67⋊C4—61no—
195#878—61no—
196C4×D12—31no—
197C4×D12—61no—
198#869—31no—
199#869—61no—
200C4×Dic6—31no—
201C3×#107—21no—
202C3×#107—31no—
203C3×#107—31no—
204C3×#107C2×D311yescharacteristic
205C3×#107C2×D311yescharacteristic
206C3×C4⋊C8—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#103—31no—
211C3×C22⋊C8—31no—
212#835—31no—
213#835—31no—
214(C2×D3)⋊C8—31no—
215(C2×D3)⋊C8—31no—
216(C2×D3)⋊C8C2×D311yescharacteristic
217#816—31no—
218#816—31no—
219#816C2×D311yescharacteristic
220#816C2×D311yescharacteristic
221Dic3⋊C8C2×D311yescharacteristic
222C8×Dic3—31no—
223#810—31no—
224#810—31no—
225#810—31no—
226#810—31no—
227#810—31no—
228#810—31no—
229#810—31no—
230#810—31no—
231#810—61no—
232#810—61no—
233#810C2×D311yescharacteristic
234#810C2×D311yescharacteristic
235#807C2×D311yescharacteristic
236#807C2×D311yescharacteristic
237C4×C3⋊C8—31no—
238C22×C3⋊D3C2×D411yescharacteristic
239C22×C3×D3C2×D411yescharacteristic
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4C2411yescharacteristic
243C2×C3⋊Dic3—21no—
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3C2×D411yescharacteristic
246C4×C3⋊D3—21no—
247C4×C3⋊D3—21no—
248#634—21no—
249#634—21no—
250#634—21no—
251#634—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×C4×D3—21no—
260C3×C4×D3—21no—
261C3×C4×D3—81no—
262C3×Dic6—21no—
263C3×Dic6—21no—
264C3×Dic6—21no—
265C3×Dic6—81no—
266C3×Dic6#4112yes—
267#627—42no—
268#627—42no—
269#626Q1614yescomplemented
270#624—42no—
271#624—81no—
272D3×Dic3—42no—
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—31no—
283#467—91no—
284#467—91no—
285#462—91no—
286#451—91no—
287#451—91no—
288C4×Q16—91no—
289C8×D4—91no—
290C2×#103—91no—
291C2×#103—91no—
292C2×C3×Q8—31no—
293C2×C3×Q8—31no—
294C2×C3×Q8—61no—
295C22×C3×C4—31no—
296C22×C3×C4—61no—
297C2×#67—31no—
298C22×Dic3—61no—
299D3×Q8—62no—
300D3×Q8—62no—
301D3×Q8—62no—
302D3×Q8—121no—
303D3×Q8—121no—
304D3×Q8—121no—
305C2×D12—31no—
306C2×C4×D3—21no—
307C2×C4×D3—31no—
308C2×C4×D3—31no—
309C2×C4×D3—61no—
310C2×C4×D3—61no—
311C2×C4×D3—61no—
312C2×C4×D3—61no—
313C2×C4×D3—61no—
314C2×C4×D3—61no—
315C2×C4×D3C22×D311yescharacteristic
316C2×Dic6—21no—
317C2×Dic6—31no—
318C2×Dic6—31no—
319C2×Dic6—31no—
320C2×Dic6—31no—
321C2×Dic6—61no—
322C2×Dic6—61no—
323C2×Dic6—62no—
324C2×Dic6—61no—
325C2×Dic6—61no—
326C2×Dic6—61no—
327C2×Dic6—61no—
328C2×Dic6—121no—
329C2×Dic6C22×D311yescharacteristic
330C2×Dic6C22×D311yescharacteristic
331C2×C3×C8—21no—
332C2×C3×C8—31no—
333C2×C3×C8—31no—
334C2×C3×C8C22×D311yescharacteristic
335C2×C3×C8C22×D311yescharacteristic
336C3×C4⋊C4—21no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C22⋊C4—61no—
349C3×C42—31no—
350C3×C42—61no—
351#217—31no—
352#217—61no—
353#216—62no—
354#216—121no—
355(C2×D3)⋊C4—21no—
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—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—121no—
365(C2×D3)⋊C4—121no—
366C4⋊Dic3—21no—
367C4⋊Dic3—31no—
368C4⋊Dic3—61no—
369C4⋊Dic3—61no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—121no—
376C4⋊Dic3—121no—
377C4⋊Dic3C22×D311yescharacteristic
378C4⋊Dic3C22×D311yescharacteristic
379Dic3⋊C4—21no—
380Dic3⋊C4—21no—
381Dic3⋊C4—21no—
382Dic3⋊C4—31no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390C4×Dic3—21no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3C22×D311yescharacteristic
394C2×C3⋊C8—31no—
395C2×C3⋊C8—31no—
396C2×C3⋊C8—61no—
397C2×C3⋊C8—121no—
398C2×C3⋊C8C22×D311yescharacteristic
399C2×C3⋊C8C22×D311yescharacteristic
400Dic12—62no—
401Dic12—121no—
402Dic12—121no—
403Dic12—122no—
404Dic12—121no—
405D3×C8—121no—
406D3×C8—121no—
407D3×C8—121no—
408D3×C8—122no—
409C22×C32C22×D411yescharacteristic
410C2×C3⋊D3—21no—
411C2×C3⋊D3—21no—
412C2×C3⋊D3C2×Q1612yes—
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3C2×Q1612yes—
416C32×C4—41no—
417C32×C4—41no—
418C32×C4C2×#4111yescharacteristic
419C32×C4H(5,𝔽2)11yescharacteristic
420C3⋊Dic3—21no—
421C3⋊Dic3—41no—
422C3⋊Dic3—41no—
423C3×Dic3—22no—
424C3×Dic3—21no—
425C3×Dic3—21no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C3×Dic3C2×Q1612yes—
430C22×Q8—91no—
431C22×Q8—91no—
432C2×Q16—91no—
433C2×Q16—91no—
434C2×Q16—91no—
435C22×C8—91no—
436C22×C8—91no—
437C4⋊Q8—31no—
438C4⋊Q8—91no—
439C4⋊Q8—181no—
440#125—181no—
441C22⋊Q8—31no—
442C22⋊Q8—91no—
443C22⋊Q8—91no—
444C22⋊Q8—91no—
445C22⋊Q8—181no—
446C22⋊Q8—181no—
447C22⋊Q8—181no—
448C22⋊Q8—181no—
449C4×Q8—31no—
450C4×Q8—91no—
451C4×D4—91no—
452C4×D4—181no—
453C4×D4—181no—
454C2×C4⋊C4—31no—
455C2×C4⋊C4—91no—
456#107—31no—
457#107—31no—
458#107D3211yescharacteristic
459C4⋊C8—31no—
460#103—31no—
461#103—31no—
462#103—31no—
463#103—31no—
464#103—91no—
465#103—91no—
466#103—91no—
467#103—91no—
468#103—91no—
469#103—91no—
470C22⋊C8—31no—
471C22⋊C8—91no—
472C4×C8—91no—
473C23×C3—31no—
474C22×D3—31no—
475C22×D3—31no—
476C22×D3—61no—
477C22×D3D3×D411yescharacteristic
478C3×Q8—32no—
479C3×Q8—61no—
480C3×Q8—61no—
481C3×Q8—61no—
482C3×Q8—241no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—31no—
489C2×C3×C4—31no—
490C2×C3×C4—31no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
493C2×C3×C4—61no—
494C2×C3×C4—61no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—241no—
500C2×C3×C4C23×D311yescharacteristic
501C2×C3×C4C23×D311yescharacteristic
502#67—34no—
503C2×Dic3—21no—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—21no—
507C2×Dic3—31no—
508C2×Dic3—31no—
509C2×Dic3—61no—
510C2×Dic3—61no—
511C2×Dic3—61no—
512C2×Dic3—61no—
513C2×Dic3—61no—
514C2×Dic3—121no—
515C2×Dic3—121no—
516C2×Dic3—122no—
517C2×Dic3D3×D411yescharacteristic
518C2×Dic3D3×D411yescharacteristic
519C2×Dic3D3×D411yescharacteristic
520D12—34no—
521C4×D3—21no—
522C4×D3—21no—
523C4×D3—61no—
524C4×D3—61no—
525C4×D3—61no—
526C4×D3—61no—
527C4×D3—81no—
528C4×D3—121no—
529C4×D3—121no—
530C4×D3—122no—
531C4×D3—122no—
532C4×D3—122no—
533C4×D3—241no—
534C4×D3—241no—
535Dic6—21no—
536Dic6—21no—
537Dic6—21no—
538Dic6—61no—
539Dic6—61no—
540Dic6—61no—
541Dic6—61no—
542Dic6—61no—
543Dic6—61no—
544Dic6—61no—
545Dic6—61no—
546Dic6—81no—
547Dic6—121no—
548Dic6—121no—
549Dic6—121no—
550Dic6—121no—
551Dic6—122no—
552Dic6—122no—
553Dic6—122no—
554Dic6—122no—
555Dic6#23912yes—
556C3×C8—22no—
557C3×C8—21no—
558C3×C8—21no—
559C3×C8—61no—
560C3×C8—61no—
561C3⋊C8—21no—
562C3⋊C8—21no—
563C3⋊C8—61no—
564C3⋊C8—61no—
565C3⋊C8—121no—
566C2×C32#54611yescharacteristic
567C2×C32C22×Q1611yescharacteristic
568C2×C32#57711yescharacteristic
569C3⋊D3—22no—
570C3×D3—22no—
571C2×Q8—31no—
572C2×Q8—31no—
573C2×Q8—61no—
574C2×Q8—91no—
575C2×Q8—91no—
576C2×Q8—181no—
577C2×Q8—181no—
578C2×Q8—182no—
579C2×Q8—182no—
580C2×Q8—361no—
581C2×Q8—361no—
582C2×D4—91no—
583C22×C4—31no—
584C22×C4—61no—
585C22×C4—91no—
586C22×C4—181no—
587C22×C4—181no—
588C22×C4—181no—
589Q16—182no—
590Q16—361no—
591Q16—361no—
592C2×C8—31no—
593C2×C8—31no—
594C2×C8—91no—
595C2×C8—361no—
596C2×C8—361no—
597C2×C8C2×D3211yescharacteristic
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4—91no—
605C4⋊C4—181no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C4⋊C4—181no—
611C4⋊C4—181no—
612C4⋊C4C2×D3211yescharacteristic
613C4⋊C4C2×D3211yescharacteristic
614C22⋊C4—61no—
615C22⋊C4—91no—
616C22⋊C4—91no—
617C22⋊C4—181no—
618C22⋊C4—181no—
619C22⋊C4—181no—
620C42—31no—
621C42—61no—
622C42—181no—
623C22×C3—21no—
624C22×C3—32no—
625C22×C3—61no—
626C22×C3—61no—
627C22×C3C2×D3×D411yescharacteristic
628C22×C3C2×D3×D411yescharacteristic
629C2×D3—21no—
630C2×D3—21no—
631C2×D3—32no—
632C2×D3—32no—
633C2×D3—62no—
634C2×D3—61no—
635C2×D3—61no—
636C2×D3—61no—
637C2×D3—61no—
638C2×D3—121no—
639C2×D3—121no—
640C2×D3D3×Q1612yes—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—32no—
644C3×C4—41no—
645C3×C4—41no—
646C3×C4—41no—
647C3×C4—41no—
648C3×C4—62no—
649C3×C4—61no—
650C3×C4—61no—
651C3×C4—81no—
652C3×C4—81no—
653C3×C4—121no—
654C3×C4—121no—
655C3×C4—121no—
656C3×C4C2×#23911yescharacteristic
657C3×C4D3×#4111yescharacteristic
658C3×C4#100911yescharacteristic
659C3×C4#100911yescharacteristic
660Dic3—21no—
661Dic3—21no—
662Dic3—22no—
663Dic3—41no—
664Dic3—41no—
665Dic3—41no—
666Dic3—61no—
667Dic3—61no—
668Dic3—121no—
669Dic3—121no—
670Dic3—121no—
671Dic3—121no—
672Dic3—121no—
673Dic3—241no—
674Dic3—241no—
675Dic3D3×Q1612yes—
676C32#329911yescharacteristic, complemented, Sylow
677C23—31no—
678C23—91no—
679Q8—32no—
680Q8—61no—
681Q8—61no—
682Q8—61no—
683Q8—181no—
684Q8—181no—
685Q8—181no—
686Q8—181no—
687Q8—241no—
688Q8—362no—
689Q8—362no—
690D4—94no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—31no—
694C2×C4—31no—
695C2×C4—31no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—91no—
703C2×C4—181no—
704C2×C4—181no—
705C2×C4—181no—
706C2×C4—181no—
707C2×C4—241no—
708C2×C4—362no—
709C2×C4—362no—
710C2×C4—721no—
711C2×C4C22×D3211yescharacteristic
712C8—21no—
713C8—61no—
714C8—61no—
715C8—181no—
716C2×C3—21no—
717C2×C3—21no—
718C2×C3—21no—
719C2×C3—62no—
720C2×C3#563011yescharacteristic
721C2×C3#565411yescharacteristic
722C2×C3C2×D3×Q1611yescharacteristic
723C2×C3C2×D3×Q1611yescharacteristic
724C2×C3#577511yescharacteristic
725C2×C3#577511yescharacteristic
726D3—22no—
727D3—62no—
728D3—62no—
729D3—122no—
730C22—32no—
731C22—61no—
732C22—61no—
733C22—92no—
734C22—181no—
735C22—181no—
736C22D32×D411yescharacteristic
737C4—32no—
738C4—41no—
739C4—41no—
740C4—61no—
741C4—62no—
742C4—61no—
743C4—121no—
744C4—121no—
745C4—121no—
746C4—181no—
747C4—361no—
748C4—361no—
749C4#6430811yescharacteristic
750C4D3×#23911yescharacteristic
751C3—21no—
752C3#8111911yescharacteristic, complemented
753C3#8149011yescharacteristic, complemented
754C2—62no—
755C2—182no—
756C2#1059462011yescharacteristic
757C2#1059473311yescharacteristic
758C2D32×Q1611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radicalC2×#626D4
hypercenter#107D32
hypocenterC32#3299
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
3. #10592586C2semidirect
4. C3×#4884C2semidirect
5. C3×#4875C2semidirect
6. #10590952C2semidirect
8. #10590808C2semidirect
9. #10590672C2semidirect
10. #10590605C2semidirect
11. D3×#810C2semidirect
12. #10590579C2semidirect
13. #10590560C2semidirect
14. #10590481C2semidirect
15. #10590444C2semidirect
77. #4884D3semidirect
78. #4875D3semidirect
269. #626Q16semidirect
676. C32#3299semidirect
752. C3#81119semidirect
753. C3#81490semidirect

Maximal subgroups

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

subgroupindex
#105945372
#105943832
#105925862
C3×#48842
C3×#48752
#105909522
#105909062
#105908082
#105906722
#105906052
D3×#8102
#105905792
#105905602
#105904812
#105904442
#814903
#811193