Finite Group Databasebeta

← #11887681

Subgroups — #11887681

Order 1152.

828 conjugacy classes of subgroups.

The subgroup lattice has 757 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594536C211yesmaximal, characteristic
2#10594383C211yesmaximal, characteristic
3#10592583C211yesmaximal, characteristic, complemented
4C3×#4884C211yesmaximal, characteristic, complemented
5C3×#4873C211yesmaximal, characteristic, complemented
6#10590950C211yesmaximal, characteristic, complemented
7#10590949C211yesmaximal, characteristic, complemented
8#10590890C211yesmaximal, characteristic, complemented
9#10590721C211yesmaximal, characteristic
10#10590601C211yesmaximal, characteristic, complemented
11D3×#810C211yesmaximal, characteristic, complemented
12#10590561C211yesmaximal, characteristic, complemented
13#10590557C211yesmaximal, characteristic, complemented
14#10590525C211yesmaximal, characteristic, complemented
15#10590518C211yesmaximal, characteristic, complemented
16#81490—31nomaximal
17#79735—31nomaximal
18C2×#3797C2211yescharacteristic
19C2×D3×Dic6C2211yescharacteristic
20#64106C2211yescharacteristic
21C4⋊C4×C3⋊D3C2211yescharacteristic
22C2×C3×Dic12C2211yescharacteristic
23C3×#897C2211yescharacteristic
24C3×D3×C4⋊C4C2211yescharacteristic
25C3×#887C2211yescharacteristic
26C3×#887C2211yescharacteristic
27#63918—21no—
28#63918C2211yescharacteristic
29C4×#626—21no—
30C4×#626C2211yescharacteristic
31#63895—21no—
32#63893—21no—
33#63880—21no—
34#63871C2211yescharacteristic
35#63867—21no—
36#63866C2211yescharacteristic
37#63865—21no—
38#63856C2211yescharacteristic
39#63851—21no—
40C2×#3719C2211yescharacteristic
41C2×#3718C2211yescharacteristic
42C2×#3710C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44C32×#107C2211yescharacteristic
45#63647C2211yescharacteristic
46#63643C2211yescharacteristic
47#63637C2211yescharacteristic
48#63634C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×C8×Dic3C2211yescharacteristic
52C3×#810C2211yescharacteristic
53C3×#810C2211yescharacteristic
54C3×#810C2211yescharacteristic
55C3×#807C2211yescharacteristic
56Dic3⋊(C3⋊C8)C2211yescharacteristic
57#63567C2211yescharacteristic
58#63566C2211yescharacteristic
59#63566C2211yescharacteristic
60#63565C2211yescharacteristic
61#5632—31no—
62#5579—31no—
63Q8×D12—31no—
64#5511—31no—
65C3×#484—31no—
66C3×C4×Q16—31no—
67#5186—31no—
68#5186—31no—
69#5051—31no—
70#5031—31no—
71#5021—31no—
72C2×#810—31no—
73#4887—31no—
74#4884—31no—
75#4884—31no—
76#4884—61no—
77#4884D311yescharacteristic, complemented
78#4875—31no—
79#4873D311yescharacteristic, complemented
80#4813—31no—
81#4813—31no—
82#4809—31no—
83D3×#103—31no—
84D3×#103—31no—
85D3×#103—31no—
86#4795—31no—
87#4792—31no—
88#4739—31no—
89#67⋊C8—31no—
90C8×D12—31no—
91#4681—31no—
92C2×C4×C3⋊D3—21no—
93C2×C4×C3⋊D3C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×C3×C4×D3—21no—
96C2×C3×C4×D3C2311yescharacteristic
97C2×C3×Dic6C2311yescharacteristic
98C2×C3×Dic6C2311yescharacteristic
99C2×C3×Dic6C2311yescharacteristic
100C2×#627—21no—
101C2×#627—21no—
102C2×#627—21no—
103C2×#626D411yescharacteristic
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—
114C4⋊(C3⋊Dic3)—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116#3750—21no—
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×(C2×D3)⋊C4—21no—
119C3×C4⋊Dic3—21no—
120C3×C4⋊Dic3C2311yescharacteristic
121C3×Dic3⋊C4—21no—
122C3×Dic3⋊C4—21no—
123C3×Dic3⋊C4—21no—
124C3×C4×Dic3—21no—
125C3×C4×Dic3—21no—
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C3×Dic12—22no—
130#3724—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3D411yescharacteristic
136#3722—21no—
137#3722D411yescharacteristic
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3D411yescharacteristic
140#3719—41no—
141#3718—41no—
142#3710—41no—
143D3×C3⋊C8—41no—
144#3299—91noSylow
145C2×D3×Q8—31no—
146C2×D3×Q8—31no—
147C2×D3×Q8—31no—
148C22×Dic6—31no—
149C2×C3×Q16—31no—
150C3×C22⋊Q8—31no—
151C3×C4×Q8—31no—
152C3×C4×Q8—31no—
153C2×C3×C4⋊C4—31no—
154#946—31no—
155#946—31no—
156#944—31no—
157C2×#216—31no—
158C2×#216—31no—
159C2×#216—31no—
160C4×#67—31no—
161C4×#67—61no—
162#924—31no—
163#924—61no—
164C22×C3⋊C8—31no—
165C2×Dic12—31no—
166C2×Dic12C2×D311yescharacteristic
167C2×D3×C8—31no—
168C2×D3×C8—31no—
169C2×D3×C8—31no—
170#897—31no—
171#897—31no—
172#897—31no—
173#897—61no—
174#897—61no—
175#897—61no—
176#897C2×D311yescharacteristic
177#896—61no—
178#896—61no—
179#896—61no—
180#896—61no—
181D3×C4⋊C4—31no—
182D3×C4⋊C4—31no—
183D3×C4⋊C4—61no—
184D3×C4⋊C4C2×D311yescharacteristic
185#889—61no—
186#888—31no—
187#888—61no—
188#887C2×D311yescharacteristic
189#887C2×D311yescharacteristic
190#67⋊C4—61no—
191#878—61no—
192C4×D12—31no—
193C4×D12—61no—
194C4×D12—61no—
195#870—61no—
196#869—31no—
197#869—31no—
198#869—61no—
199C3×#107—21no—
200C3×#107—31no—
201C3×#107C2×D311yescharacteristic
202C3×#107C2×D311yescharacteristic
203C3×#103—31no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#103—31no—
207C3×C22⋊C8—31no—
208C3×C4×C8—31no—
209#835—31no—
210#835—31no—
211#835—31no—
212(C2×D3)⋊C8—31no—
213(C2×D3)⋊C8—31no—
214(C2×D3)⋊C8—61no—
215(C2×D3)⋊C8C2×D311yescharacteristic
216#816—31no—
217#816—31no—
218#816—31no—
219#816—31no—
220#816—31no—
221#816—61no—
222#816C2×D311yescharacteristic
223Dic3⋊C8—31no—
224C8×Dic3C2×D311yescharacteristic
225#810—31no—
226#810—31no—
227#810—31no—
228#810—31no—
229#810—61no—
230#810C2×D311yescharacteristic
231#810C2×D311yescharacteristic
232#810C2×D311yescharacteristic
233#807—31no—
234#807—31no—
235#807—61no—
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—
248C4×C3⋊D3—81no—
249#634—21no—
250#634—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C3×C4×D3—21no—
259C3×C4×D3—21no—
260C3×C4×D3—81no—
261C3×Dic6—21no—
262C3×Dic6—21no—
263C3×Dic6—21no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266C3×Dic6#4112yes—
267#627—42no—
268#627—42no—
269#627—81no—
270#626Q1614yescomplemented
271#624—42no—
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—91no—
283#467—91no—
284#467—91no—
285#462—91no—
286#451—91no—
287#451—91no—
288C4×Q16—31no—
289C8×D4—91no—
290C2×#103—91no—
291C2×#103—91no—
292C2×C3×Q8—31no—
293C2×C3×Q8—31no—
294C2×C3×Q8—31no—
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×D3—121no—
316C2×C4×D3C22×D311yescharacteristic
317C2×Dic6—31no—
318C2×Dic6—31no—
319C2×Dic6—61no—
320C2×Dic6—62no—
321C2×Dic6—61no—
322C2×Dic6—61no—
323C2×Dic6—61no—
324C2×Dic6—61no—
325C2×Dic6—61no—
326C2×Dic6—61no—
327C2×Dic6—121no—
328C2×Dic6C22×D311yescharacteristic
329C2×Dic6C22×D311yescharacteristic
330C2×Dic6C22×D311yescharacteristic
331C3×Q16—62no—
332C2×C3×C8—21no—
333C2×C3×C8—31no—
334C2×C3×C8—31no—
335C2×C3×C8C22×D311yescharacteristic
336C2×C3×C8C22×D311yescharacteristic
337C3×C4⋊C4—21no—
338C3×C4⋊C4—21no—
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—
351C3×C42—61no—
352#217—31no—
353#217—61no—
354#216—121no—
355#216—121no—
356#216—121no—
357(C2×D3)⋊C4—21no—
358(C2×D3)⋊C4—31no—
359(C2×D3)⋊C4—31no—
360(C2×D3)⋊C4—31no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—121no—
367C4⋊Dic3—21no—
368C4⋊Dic3—31no—
369C4⋊Dic3—31no—
370C4⋊Dic3—31no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—121no—
379C4⋊Dic3C22×D311yescharacteristic
380Dic3⋊C4—21no—
381Dic3⋊C4—21no—
382Dic3⋊C4—21no—
383Dic3⋊C4—31no—
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—121no—
393C4×Dic3—21no—
394C4×Dic3—21no—
395C4×Dic3C22×D311yescharacteristic
396C2×C3⋊C8—31no—
397C2×C3⋊C8—31no—
398C2×C3⋊C8—61no—
399C2×C3⋊C8—121no—
400C2×C3⋊C8C22×D311yescharacteristic
401C2×C3⋊C8C22×D311yescharacteristic
402Dic12—22no—
403Dic12—121no—
404D3×C8—121no—
405D3×C8—121no—
406D3×C8—121no—
407C22×C32C22×D411yescharacteristic
408C2×C3⋊D3—21no—
409C2×C3⋊D3—21no—
410C2×C3⋊D3C2×Q1612yes—
411C2×C3×D3—21no—
412C2×C3×D3—21no—
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×Dic3—22no—
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3C2×Q1612yes—
428C22×Q8—91no—
429C22×Q8—91no—
430C2×Q16—31no—
431C2×Q16—91no—
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—91no—
441C22⋊Q8—91no—
442C22⋊Q8—91no—
443C22⋊Q8—181no—
444C22⋊Q8—181no—
445C22⋊Q8—181no—
446C22⋊Q8—181no—
447C4×Q8—31no—
448C4×Q8—31no—
449C4×D4—91no—
450C4×D4—181no—
451C4×D4—181no—
452C2×C4⋊C4—31no—
453C2×C4⋊C4—91no—
454#107—31no—
455#107—91no—
456#107D3211yescharacteristic
457C4⋊C8—91no—
458#103—31no—
459#103—31no—
460#103—31no—
461#103—31no—
462#103—91no—
463#103—91no—
464#103—91no—
465#103—91no—
466#103—91no—
467#103—91no—
468C22⋊C8—31no—
469C22⋊C8—91no—
470C4×C8—31no—
471C23×C3—31no—
472C22×D3—31no—
473C22×D3—31no—
474C22×D3—61no—
475C22×D3D3×D411yescharacteristic
476C3×Q8—32no—
477C3×Q8—61no—
478C3×Q8—61no—
479C3×Q8—61no—
480C3×Q8—61no—
481C3×Q8—61no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—31no—
488C2×C3×C4—31no—
489C2×C3×C4—31no—
490C2×C3×C4—41no—
491C2×C3×C4—41no—
492C2×C3×C4—61no—
493C2×C3×C4—61no—
494C2×C3×C4—61no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—241no—
499C2×C3×C4C23×D311yescharacteristic
500C2×C3×C4C23×D311yescharacteristic
501#67—34no—
502C2×Dic3—21no—
503C2×Dic3—21no—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—31no—
507C2×Dic3—31no—
508C2×Dic3—61no—
509C2×Dic3—61no—
510C2×Dic3—61no—
511C2×Dic3—61no—
512C2×Dic3—61no—
513C2×Dic3—121no—
514C2×Dic3—121no—
515C2×Dic3—122no—
516C2×Dic3D3×D411yescharacteristic
517C2×Dic3D3×D411yescharacteristic
518C2×Dic3D3×D411yescharacteristic
519D12—34no—
520C4×D3—21no—
521C4×D3—21no—
522C4×D3—61no—
523C4×D3—61no—
524C4×D3—61no—
525C4×D3—61no—
526C4×D3—81no—
527C4×D3—121no—
528C4×D3—121no—
529C4×D3—122no—
530C4×D3—122no—
531C4×D3—122no—
532C4×D3—241no—
533C4×D3—241no—
534C4×D3—242no—
535Dic6—21no—
536Dic6—21no—
537Dic6—21no—
538Dic6—21no—
539Dic6—21no—
540Dic6—61no—
541Dic6—61no—
542Dic6—61no—
543Dic6—61no—
544Dic6—121no—
545Dic6—121no—
546Dic6—122no—
547Dic6—122no—
548Dic6—122no—
549Dic6—122no—
550Dic6—241no—
551Dic6—241no—
552Dic6#23512yes—
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—31no—
571C2×Q8—91no—
572C2×Q8—181no—
573C2×Q8—181no—
574C2×Q8—181no—
575C2×Q8—182no—
576C2×Q8—182no—
577C2×Q8—361no—
578C2×Q8—361no—
579C2×D4—91no—
580C22×C4—31no—
581C22×C4—61no—
582C22×C4—91no—
583C22×C4—181no—
584C22×C4—181no—
585C22×C4—181no—
586Q16—62no—
587Q16—361no—
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—61no—
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⋊C4C2×D3211yescharacteristic
610C4⋊C4C2×D3211yescharacteristic
611C22⋊C4—61no—
612C22⋊C4—91no—
613C22⋊C4—91no—
614C22⋊C4—181no—
615C22⋊C4—181no—
616C22⋊C4—181no—
617C42—31no—
618C42—61no—
619C42—61no—
620C22×C3—21no—
621C22×C3—32no—
622C22×C3—61no—
623C22×C3—61no—
624C22×C3C2×D3×D411yescharacteristic
625C22×C3C2×D3×D411yescharacteristic
626C2×D3—21no—
627C2×D3—21no—
628C2×D3—32no—
629C2×D3—32no—
630C2×D3—62no—
631C2×D3—61no—
632C2×D3—61no—
633C2×D3—61no—
634C2×D3—61no—
635C2×D3—121no—
636C2×D3—121no—
637C2×D3D3×Q1612yes—
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—32no—
641C3×C4—41no—
642C3×C4—41no—
643C3×C4—41no—
644C3×C4—41no—
645C3×C4—62no—
646C3×C4—61no—
647C3×C4—61no—
648C3×C4—81no—
649C3×C4—81no—
650C3×C4—121no—
651C3×C4—121no—
652C3×C4—121no—
653C3×C4C2×#23511yescharacteristic
654C3×C4D3×#4111yescharacteristic
655C3×C4#100911yescharacteristic
656C3×C4#100911yescharacteristic
657Dic3—21no—
658Dic3—21no—
659Dic3—22no—
660Dic3—41no—
661Dic3—41no—
662Dic3—41no—
663Dic3—61no—
664Dic3—61no—
665Dic3—121no—
666Dic3—121no—
667Dic3—121no—
668Dic3—121no—
669Dic3—121no—
670Dic3—241no—
671Dic3—241no—
672Dic3D3×Q1612yes—
673C32#329911yescharacteristic, complemented, Sylow
674C23—31no—
675C23—91no—
676Q8—32no—
677Q8—61no—
678Q8—61no—
679Q8—61no—
680Q8—61no—
681Q8—61no—
682Q8—181no—
683Q8—181no—
684Q8—362no—
685Q8—362no—
686Q8—721no—
687D4—94no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—31no—
691C2×C4—31no—
692C2×C4—31no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—91no—
700C2×C4—181no—
701C2×C4—181no—
702C2×C4—181no—
703C2×C4—181no—
704C2×C4—241no—
705C2×C4—362no—
706C2×C4—362no—
707C2×C4—721no—
708C2×C4C22×D3211yescharacteristic
709C8—21no—
710C8—61no—
711C8—61no—
712C8—181no—
713C2×C3—21no—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—62no—
717C2×C3#555011yescharacteristic
718C2×C3#565411yescharacteristic
719C2×C3C2×D3×Q1611yescharacteristic
720C2×C3C2×D3×Q1611yescharacteristic
721C2×C3#577011yescharacteristic
722C2×C3#577511yescharacteristic
723D3—22no—
724D3—62no—
725D3—62no—
726D3—122no—
727C22—32no—
728C22—61no—
729C22—61no—
730C22—92no—
731C22—181no—
732C22—181no—
733C22D32×D411yescharacteristic
734C4—32no—
735C4—41no—
736C4—41no—
737C4—61no—
738C4—62no—
739C4—61no—
740C4—121no—
741C4—121no—
742C4—121no—
743C4—181no—
744C4—361no—
745C4—361no—
746C4D3×#23511yescharacteristic
747C4#6432011yescharacteristic
748C3—21no—
749C3#7973511yescharacteristic, complemented
750C3#8149011yescharacteristic, complemented
751C2—62no—
752C2—182no—
753C2#1059461911yescharacteristic
754C2#1059473611yescharacteristic
755C2D32×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. #10592583C2semidirect
4. C3×#4884C2semidirect
5. C3×#4873C2semidirect
6. #10590950C2semidirect
7. #10590949C2semidirect
8. #10590890C2semidirect
10. #10590601C2semidirect
11. D3×#810C2semidirect
12. #10590561C2semidirect
13. #10590557C2semidirect
14. #10590525C2semidirect
15. #10590518C2semidirect
77. #4884D3semidirect
79. #4873D3semidirect
270. #626Q16semidirect
673. C32#3299semidirect
749. C3#79735semidirect
750. C3#81490semidirect

Maximal subgroups

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

subgroupindex
#105945362
#105943832
#105925832
C3×#48842
C3×#48732
#105909502
#105909492
#105908902
#105907212
#105906012
D3×#8102
#105905612
#105905572
#105905252
#105905182
#814903
#797353