Finite Group Databasebeta

← #11887630

Subgroups — #11887630

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#10594988C211yesmaximal, characteristic
2Dic6×#67C211yesmaximal, characteristic
3#10592815C211yesmaximal, characteristic, complemented
4C3×C8×#67C211yesmaximal, characteristic
5C2×C3×#816C211yesmaximal, characteristic, complemented
6#10591186C211yesmaximal, characteristic, complemented
7#10591135C211yesmaximal, characteristic, complemented
8#10590952C211yesmaximal, characteristic, complemented
9#10590890C211yesmaximal, characteristic, complemented
10#10590848C211yesmaximal, characteristic, complemented
11#10590808C211yesmaximal, characteristic, complemented
12#10590804C211yesmaximal, characteristic, complemented
13#10590793C211yesmaximal, characteristic, complemented
14#10590682C211yesmaximal, characteristic, complemented
15D3×#816C211yesmaximal, characteristic, complemented
16#79448—31nomaximal
17#78806—31nomaximal
18C22×C3×Dic6C2211yescharacteristic
19C2×D3×Dic6C2211yescharacteristic
20C22×C32×C8C2211yescharacteristic
21#64133C2211yescharacteristic
22#64133C2211yescharacteristic
23C2×#3746C2211yescharacteristic
24C3×C4×#67C2211yescharacteristic
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×D3×C8C2211yescharacteristic
27Dic3×#67—21no—
28Dic3×#67—21no—
29#63964—21no—
30#63964—21no—
31#63918C2211yescharacteristic
32#63899—21no—
33D3×C4⋊Dic3C2211yescharacteristic
34#63887—21no—
35#63866C2211yescharacteristic
36#63857C2211yescharacteristic
37#63856C2211yescharacteristic
38#63846—21no—
39#63844C2211yescharacteristic
40Dic3×Dic6C2211yescharacteristic
41#63839—21no—
42C2×#3719C2211yescharacteristic
43C2×#3719C2211yescharacteristic
44#63645C2211yescharacteristic
45#63643C2211yescharacteristic
46#63643C2211yescharacteristic
47C3×#830C2211yescharacteristic
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×#816C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×Dic3⋊C8C2211yescharacteristic
54C3×C8×Dic3C2211yescharacteristic
55#63575C2211yescharacteristic
56#63575C2211yescharacteristic
57#63567C2211yescharacteristic
58#63567C2211yescharacteristic
59#63566C2211yescharacteristic
60#63566C2211yescharacteristic
61Q8×#67—31no—
62#5543—31no—
63D4×Dic6—31no—
64#5511—31no—
65C3×C8×D4—31no—
66C2×C3×#103—31no—
67#5228—31no—
68#5116—31no—
69#5116—31no—
70#5116—31no—
71#5116—61no—
72C8×#67D311yescharacteristic
73C2×#816—31no—
74C2×#816D311yescharacteristic, complemented
75#4970—31no—
76#4850—31no—
77#4849—31no—
78#4813—31no—
79#4811—31no—
80#4809—31no—
81D3×#103—31no—
82#4795—31no—
83#4793—31no—
84#4792—31no—
85#4790—31no—
86#4739—31no—
87#4739—31no—
88#4722—31no—
89#4722—31no—
90C4×Dic12—31no—
91#4681—31no—
92C22×C32×C4C2311yescharacteristic
93C2×#634C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×C3×#67D411yescharacteristic
96C22×C3×Dic3—21no—
97C22×C3×Dic3—21no—
98C2×C3×C4×D3C2311yescharacteristic
99C2×C3×Dic6—22no—
100C2×C3×Dic6—21no—
101C2×C3×Dic6—41no—
102C2×C3×Dic6C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×#627—21no—
105C2×#627—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108D3×Dic6—22no—
109D3×Dic6—41no—
110C2×C32×C8—41no—
111C2×C32×C8C2311yescharacteristic
112C2×C32×C8C2311yescharacteristic
113#3757—21no—
114#3757—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118#3750—21no—
119#3746—41no—
120C3×#217D411yescharacteristic
121C3×(C2×D3)⋊C4D411yescharacteristic
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4D411yescharacteristic
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C3×D3×C8—41no—
130#3724—21no—
131#3724—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141Dic32—21no—
142#3719—22no—
143#3719—41no—
144#3299—91noSylow
145C22×C3×Q8—31no—
146C2×D3×Q8—31no—
147C22×Dic6—31no—
148C22×Dic6C2×D311yescharacteristic
149C22×C3×C8—21no—
150C22×C3×C8—31no—
151C22×C3×C8C2×D311yescharacteristic
152C22×C3×C8C2×D311yescharacteristic
153C3×C4×D4—31no—
154C2×C3×C4⋊C4—31no—
155#946—31no—
156#946—61no—
157Q8×Dic3—31no—
158#944—31no—
159#944—61no—
160C2×#216—31no—
161C2×#216—31no—
162D4×Dic3—61no—
163D4×Dic3—61no—
164C4×#67—61no—
165C4×#67—61no—
166C4×#67C2×D311yescharacteristic
167C2×C4⋊Dic3—31no—
168C2×C4⋊Dic3C2×D311yescharacteristic
169#924—31no—
170#924—31no—
171#924—31no—
172#924—31no—
173#924—31no—
174#924—31no—
175#924—61no—
176#924—61no—
177#924—61no—
178#924—61no—
179C2×Dic12—31no—
180C2×Dic12—31no—
181C2×Dic12—31no—
182C2×Dic12—31no—
183C2×Dic12—61no—
184C2×D3×C8C2×D311yescharacteristic
185#897—31no—
186#896—61no—
187D3×C4⋊C4—31no—
188#890—61no—
189#889—61no—
190#888—31no—
191#888—61no—
192#887—31no—
193#878—61no—
194#878—61no—
195#878—61no—
196#878—61no—
197#869—31no—
198#869—31no—
199C4×Dic6—31no—
200C4×Dic6—31no—
201C3×C4⋊C8—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×#103—31no—
205C3×#103—31no—
206C3×C22⋊C8—31no—
207C3×C22⋊C8—31no—
208C3×C4×C8—31no—
209#835—31no—
210#835—31no—
211#830C2×D311yescharacteristic
212(C2×D3)⋊C8C2×D311yescharacteristic
213#818—31no—
214#818—31no—
215#818—31no—
216#818—31no—
217#818—61no—
218#816—31no—
219#816—31no—
220#816—31no—
221#816—31no—
222#816—31no—
223#816—31no—
224#816—31no—
225#816—31no—
226#816—61no—
227#816—61no—
228#816C2×D311yescharacteristic
229#816C2×D311yescharacteristic
230#816C2×D311yescharacteristic
231#816C2×D311yescharacteristic
232Dic3⋊C8C2×D311yescharacteristic
233C8×Dic3C2×D311yescharacteristic
234#810—31no—
235#810—31no—
236#807—31no—
237#807—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3×D3C2×D411yescharacteristic
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4C2×D411yescharacteristic
243C2×C32×C4C2411yescharacteristic
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—21no—
248#634—21no—
249#634—21no—
250#634—21no—
251#634—21no—
252C3×#67Q1614yescomplemented
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—42no—
258C2×C3×Dic3—81no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×C4×D3—21no—
263C3×C4×D3—21no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6—42no—
268C3×Dic6#4112yes—
269#627—42no—
270#627—81no—
271D3×Dic3—42no—
272D3×Dic3—81no—
273C32×C8—21no—
274C32×C8—21no—
275C3×C3⋊C8—21no—
276C3×C3⋊C8—21no—
277#554—91no—
278D4×Q8—91no—
279#487—91no—
280#484—91no—
281#484—91no—
282#477—91no—
283#467—91no—
284#467—91no—
285#462—91no—
286#451—91no—
287#451—91no—
288C4×Q16—91no—
289C8×D4—31no—
290C2×#103—31no—
291C2×#103—91no—
292C2×C3×Q8—31no—
293C2×C3×Q8—31no—
294C2×C3×Q8—62no—
295C2×C3×Q8—61no—
296C2×C3×Q8—121no—
297C2×C3×D4—31no—
298C22×C3×C4—21no—
299C22×C3×C4—31no—
300C22×C3×C4—61no—
301C22×C3×C4—61no—
302C22×C3×C4C22×D311yescharacteristic
303C22×C3×C4C22×D311yescharacteristic
304C2×#67D1211yescharacteristic
305C22×Dic3—21no—
306C22×Dic3—21no—
307C22×Dic3—61no—
308C22×Dic3—61no—
309D3×Q8—62no—
310D3×Q8—121no—
311C2×C4×D3—61no—
312C2×C4×D3—61no—
313C2×C4×D3C22×D311yescharacteristic
314C2×Dic6—22no—
315C2×Dic6—21no—
316C2×Dic6—31no—
317C2×Dic6—31no—
318C2×Dic6—31no—
319C2×Dic6—31no—
320C2×Dic6—41no—
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—21no—
333C2×C3×C8—31no—
334C2×C3×C8—31no—
335C2×C3×C8—41no—
336C2×C3×C8—41no—
337C2×C3×C8—42no—
338C2×C3×C8—121no—
339C2×C3×C8C22×D311yescharacteristic
340C2×C3×C8C22×D311yescharacteristic
341C2×C3×C8C22×D311yescharacteristic
342C2×C3×C8C22×D311yescharacteristic
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—61no—
347C3×C22⋊C4—31no—
348C3×C22⋊C4—31no—
349C3×C42—31no—
350#217—61no—
351#217—61no—
352#217—61no—
353#217—61no—
354#217—61no—
355#217—61no—
356#217—121no—
357#217—121no—
358#217D1211yescharacteristic
359#216—62no—
360#216—121no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4D1211yescharacteristic
364C4⋊Dic3—21no—
365C4⋊Dic3—31no—
366C4⋊Dic3—31no—
367C4⋊Dic3—31no—
368C4⋊Dic3—31no—
369C4⋊Dic3—61no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3C22×D311yescharacteristic
378C4⋊Dic3C22×D311yescharacteristic
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—121no—
394Dic3⋊C4—121no—
395Dic3⋊C4D1211yescharacteristic
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3C22×D311yescharacteristic
401C2×C3⋊C8C22×D311yescharacteristic
402C2×C3⋊C8C22×D311yescharacteristic
403Dic12—62no—
404Dic12—121no—
405Dic12—121no—
406Dic12—122no—
407Dic12—121no—
408D3×C8—41no—
409C22×C32—21no—
410C22×C32—21no—
411C22×C32C2×Q1612yes—
412C22×C32C22×D411yescharacteristic
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3C2×Q1612yes—
416C32×C4—21no—
417C32×C4C2×#4111yescharacteristic
418C32×C4H(5,𝔽2)11yescharacteristic
419C3⋊Dic3—41no—
420C3⋊Dic3—41no—
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—31no—
431C22×Q8—91no—
432C2×Q16—91no—
433C2×Q16—91no—
434C2×Q16—91no—
435C22×C8—31no—
436C22×C8D3211yescharacteristic
437C4⋊Q8—91no—
438C4⋊Q8—91no—
439C4⋊Q8—181no—
440#125—181no—
441C22⋊Q8—91no—
442C22⋊Q8—91no—
443C22⋊Q8—91no—
444C22⋊Q8—91no—
445C22⋊Q8—181no—
446C22⋊Q8—181no—
447C22⋊Q8—181no—
448C22⋊Q8—181no—
449C4×Q8—91no—
450C4×Q8—91no—
451C4×D4—31no—
452C4×D4—181no—
453C4×D4—181no—
454C2×C4⋊C4—31no—
455C2×C4⋊C4—91no—
456#107—91no—
457#107—91no—
458#107—91no—
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—31no—
472C4×C8—31no—
473C23×C3—21no—
474C23×C3—31no—
475C23×C3C2×D1211yescharacteristic
476C23×C3D3×D411yescharacteristic
477C22×D3C2×D1211yescharacteristic
478C3×Q8—32no—
479C3×Q8—61no—
480C3×Q8—61no—
481C3×Q8—61no—
482C3×Q8—122no—
483C3×D4—34no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—31no—
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—122no—
502C2×C3×C4—241no—
503C2×C3×C4C2×D1211yescharacteristic
504C2×C3×C4D3×D411yescharacteristic
505C2×C3×C4C23×D311yescharacteristic
506C2×C3×C4C23×D311yescharacteristic
507#67Dic1214yescomplemented
508C2×Dic3—21no—
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—42no—
513C2×Dic3—61no—
514C2×Dic3—61no—
515C2×Dic3—61no—
516C2×Dic3—61no—
517C2×Dic3—61no—
518C2×Dic3—61no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—81no—
522C2×Dic3—121no—
523C2×Dic3—121no—
524C2×Dic3—121no—
525C2×Dic3—121no—
526C2×Dic3—122no—
527C2×Dic3—241no—
528C2×Dic3C2×D1211yescharacteristic
529C2×Dic3C2×D1211yescharacteristic
530C2×Dic3C2×D1211yescharacteristic
531C4×D3—21no—
532C4×D3—21no—
533C4×D3—122no—
534C4×D3—241no—
535Dic6—21no—
536Dic6—21no—
537Dic6—21no—
538Dic6—42no—
539Dic6—61no—
540Dic6—61no—
541Dic6—61no—
542Dic6—61no—
543Dic6—61no—
544Dic6—61no—
545Dic6—61no—
546Dic6—61no—
547Dic6—121no—
548Dic6—121no—
549Dic6—121no—
550Dic6—121no—
551Dic6—122no—
552Dic6—122no—
553Dic6—241no—
554Dic6—241no—
555Dic6#23512yes—
556C3×C8—22no—
557C3×C8—21no—
558C3×C8—21no—
559C3×C8—21no—
560C3×C8—21no—
561C3×C8—41no—
562C3×C8—61no—
563C3×C8—61no—
564C3⋊C8—21no—
565C3⋊C8—21no—
566C2×C32—22no—
567C2×C32#54611yescharacteristic
568C2×C32C22×Q1611yescharacteristic
569C2×C32#57711yescharacteristic
570C3×D3—22no—
571C2×Q8—31no—
572C2×Q8—31no—
573C2×Q8—62no—
574C2×Q8—61no—
575C2×Q8—91no—
576C2×Q8—91no—
577C2×Q8—121no—
578C2×Q8—181no—
579C2×Q8—181no—
580C2×Q8—182no—
581C2×Q8—361no—
582C2×D4—31no—
583C22×C4—31no—
584C22×C4—61no—
585C22×C4—61no—
586C22×C4—181no—
587C22×C4—181no—
588C22×C4C2×D3211yescharacteristic
589Q16—182no—
590Q16—361no—
591Q16—361no—
592C2×C8—31no—
593C2×C8—31no—
594C2×C8—41no—
595C2×C8—121no—
596C2×C8C2×D3211yescharacteristic
597C2×C8C2×D3211yescharacteristic
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—31no—
601C4⋊C4—61no—
602C4⋊C4—91no—
603C4⋊C4—91no—
604C4⋊C4—181no—
605C4⋊C4—181no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C4⋊C4—181no—
611C4⋊C4—181no—
612C4⋊C4—181no—
613C4⋊C4—181no—
614C22⋊C4—31no—
615C22⋊C4—31no—
616C22⋊C4—181no—
617C22⋊C4—181no—
618C22⋊C4—181no—
619C22⋊C4—181no—
620C42—31no—
621C42—181no—
622C42—181no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—22no—
629C22×C3—32no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—61no—
633C22×C3—61no—
634C22×C3C2×Dic1212yes—
635C22×C3D3×Q1612yes—
636C22×C3C22×D1211yescharacteristic
637C22×C3C2×D3×D411yescharacteristic
638C2×D3—21no—
639C2×D3—21no—
640C2×D3C2×Dic1212yes—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—21no—
644C3×C4—21no—
645C3×C4—32no—
646C3×C4—41no—
647C3×C4—61no—
648C3×C4—61no—
649C3×C4—62no—
650C3×C4—121no—
651C3×C4—121no—
652C3×C4—121no—
653C3×C4C2×#23511yescharacteristic
654C3×C4#100411yescharacteristic
655C3×C4#100411yescharacteristic
656C3×C4D3×#4111yescharacteristic
657Dic3—22no—
658Dic3—21no—
659Dic3—21no—
660Dic3—41no—
661Dic3—41no—
662Dic3—41no—
663Dic3—121no—
664Dic3—121no—
665Dic3—121no—
666Dic3—121no—
667Dic3—121no—
668Dic3—121no—
669Dic3—121no—
670Dic3—121no—
671Dic3—241no—
672Dic3—241no—
673Dic3—241no—
674Dic3—241no—
675Dic3C2×Dic1212yes—
676C32#329911yescharacteristic, complemented, Sylow
677C23—31no—
678C23D3×D1211yescharacteristic
679Q8—32no—
680Q8—61no—
681Q8—61no—
682Q8—61no—
683Q8—122no—
684Q8—181no—
685Q8—181no—
686Q8—181no—
687Q8—181no—
688Q8—362no—
689Q8—721no—
690D4—34no—
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—122no—
703C2×C4—181no—
704C2×C4—181no—
705C2×C4—181no—
706C2×C4—181no—
707C2×C4—241no—
708C2×C4—362no—
709C2×C4—721no—
710C2×C4D3×D1211yescharacteristic
711C2×C4C22×D3211yescharacteristic
712C8—21no—
713C8—21no—
714C8—61no—
715C8—61no—
716C2×C3—22no—
717C2×C3—22no—
718C2×C3—21no—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—42no—
722C2×C3—62no—
723C2×C3#549011yescharacteristic
724C2×C3#555411yescharacteristic
725C2×C3C22×Dic1211yescharacteristic
726C2×C3#575111yescharacteristic
727C2×C3#576211yescharacteristic
728C2×C3C2×D3×Q1611yescharacteristic
729D3—22no—
730C22—21no—
731C22—21no—
732C22—32no—
733C22—61no—
734C22—61no—
735C22D3×Dic1212yes—
736C22C2×D3×D1211yescharacteristic
737C4—21no—
738C4—32no—
739C4—61no—
740C4—62no—
741C4—61no—
742C4—121no—
743C4—121no—
744C4—121no—
745C4—361no—
746C4—361no—
747C4—361no—
748C4—361no—
749C4D3×#23511yescharacteristic
750C4#6433011yescharacteristic
751C3—21no—
752C3#7880611yescharacteristic, complemented
753C3#7944811yescharacteristic, complemented
754C2—22no—
755C2—62no—
756C2#1059467711yescharacteristic
757C2C2×D3×Dic1211yescharacteristic
758C2#1059507311yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
prime radicalC2×C3×#67D4
hypercenterC22×C8D32
hypocenterC32#3299
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
3. #10592815C2semidirect
5. C2×C3×#816C2semidirect
6. #10591186C2semidirect
7. #10591135C2semidirect
8. #10590952C2semidirect
9. #10590890C2semidirect
10. #10590848C2semidirect
11. #10590808C2semidirect
12. #10590804C2semidirect
13. #10590793C2semidirect
14. #10590682C2semidirect
15. D3×#816C2semidirect
74. C2×#816D3semidirect
252. C3×#67Q16semidirect
507. #67Dic12semidirect
676. C32#3299semidirect
752. C3#78806semidirect
753. C3#79448semidirect

Maximal subgroups

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

subgroupindex
#105949882
Dic6×#672
#105928152
C3×C8×#672
C2×C3×#8162
#105911862
#105911352
#105909522
#105908902
#105908482
#105908082
#105908042
#105907932
#105906822
D3×#8162
#794483
#788063