Finite Group Databasebeta

← #11887629

Subgroups — #11887629

Order 1152.

843 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594991C211yesmaximal, characteristic
2#10594803C211yesmaximal, characteristic
3C8×#638C211yesmaximal, characteristic
4C3×#5116C211yesmaximal, characteristic, complemented
5C2×C3×#816C211yesmaximal, characteristic, complemented
6#10591185C211yesmaximal, characteristic, complemented
7#10591132C211yesmaximal, characteristic, complemented
8#10590950C211yesmaximal, characteristic, complemented
9#10590901C211yesmaximal, characteristic, complemented
10#10590855C211yesmaximal, characteristic, complemented
11#10590817C211yesmaximal, characteristic, complemented
12#10590798C211yesmaximal, characteristic, complemented
13#10590790C211yesmaximal, characteristic, complemented
14#10590689C211yesmaximal, characteristic, complemented
15#10590672C211yesmaximal, characteristic, complemented
16#80781—31nomaximal
17#78806—31nomaximal
18C22×C3×Dic6C2211yescharacteristic
19C2×#3797C2211yescharacteristic
20C22×C32×C8C2211yescharacteristic
21C4×#638C2211yescharacteristic
22C2×C8×C3⋊D3C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C3×#924C2211yescharacteristic
25C3×#924C2211yescharacteristic
26C2×C3×Dic12C2211yescharacteristic
27#63964—21no—
28#63964—21no—
29#63952—21no—
30#63952—21no—
31#63919C2211yescharacteristic
32#63900C2211yescharacteristic
33#63895—21no—
34#63888—21no—
35#63873C2211yescharacteristic
36#63871C2211yescharacteristic
37#63871C2211yescharacteristic
38#63847—21no—
39#63843C2211yescharacteristic
40#63843C2211yescharacteristic
41#63839—21no—
42C2×#3718C2211yescharacteristic
43C2×#3718C2211yescharacteristic
44#63657C2211yescharacteristic
45#63647C2211yescharacteristic
46#63641C2211yescharacteristic
47C8×C3⋊Dic3C2211yescharacteristic
48C3×#818C2211yescharacteristic
49C3×#816C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×#816C2211yescharacteristic
54C3×#816C2211yescharacteristic
55#63576C2211yescharacteristic
56#63576C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59#63565C2211yescharacteristic
60#63565C2211yescharacteristic
61Q8×#67—31no—
62#5635—31no—
63#5632—31no—
64#5511—31no—
65C3×#467—31no—
66C2×C3×#103—31no—
67#5228—31no—
68#5186—31no—
69#5182—31no—
70#5116D311yescharacteristic, complemented
71C8×#67—31no—
72C8×#67—31no—
73C8×#67—61no—
74C2×#816D311yescharacteristic, complemented
75#5050—31no—
76#5044—31no—
77#4970—31no—
78#4884—31no—
79#4875—31no—
80#4813—31no—
81#4813—31no—
82#4811—31no—
83#4809—31no—
84D3×#103—31no—
85D3×#103—31no—
86#4795—31no—
87#4793—31no—
88#4792—31no—
89#4792—31no—
90#4790—31no—
91#4790—31no—
92C22×C32×C4C2311yescharacteristic
93C2×#638D411yescharacteristic
94C2×C4×C3⋊D3C2311yescharacteristic
95C22×C3×Dic3—21no—
96C22×C3×Dic3—21no—
97C2×C3×Dic6—22no—
98C2×C3×Dic6—21no—
99C2×C3×Dic6—41no—
100C2×C3×Dic6C2311yescharacteristic
101C2×C3×Dic6C2311yescharacteristic
102C2×C3×Dic6C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×#627—21no—
105C2×#627—21no—
106C2×#624—21no—
107C2×#624—21no—
108#3797—22no—
109#3797—41no—
110C2×C32×C8—41no—
111C2×C32×C8C2311yescharacteristic
112C2×C32×C8C2311yescharacteristic
113#3757D411yescharacteristic
114#3752D411yescharacteristic
115#3750D411yescharacteristic
116C4×C3⋊Dic3C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C8×C3⋊D3—41no—
120C3×#217—21no—
121C3×#217—21no—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic12—41no—
130#3724—21no—
131#3724—21no—
132#3724—21no—
133#3724—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138#3722—21no—
139#3722—21no—
140Dic32—21no—
141Dic32—21no—
142#3718—22no—
143#3718—41no—
144#3299—91noSylow
145C22×C3×Q8—31no—
146C2×D3×Q8—31no—
147C2×D3×Q8—31no—
148C22×Dic6C2×D311yescharacteristic
149C2×C3×Q16—31no—
150C22×C3×C8—21no—
151C22×C3×C8C2×D311yescharacteristic
152C22×C3×C8C2×D311yescharacteristic
153C3×C22⋊Q8—31no—
154C3×C22⋊Q8—31no—
155C2×C3×C4⋊C4—31no—
156#946—31no—
157#946—31no—
158#946—61no—
159Q8×Dic3—31no—
160Q8×Dic3—31no—
161#944—31no—
162#944—31no—
163#944—61no—
164C2×#216—31no—
165C2×#216—31no—
166C2×#216—31no—
167C2×#216—31no—
168C4×#67—31no—
169C4×#67—31no—
170C4×#67—61no—
171C4×#67—61no—
172C4×#67—61no—
173C2×C4⋊Dic3C2×D311yescharacteristic
174#924—61no—
175#924—61no—
176#924C2×D311yescharacteristic
177#924C2×D311yescharacteristic
178C2×Dic12C2×D311yescharacteristic
179C2×D3×C8—31no—
180C2×D3×C8—31no—
181C2×D3×C8—61no—
182#897—31no—
183#897—31no—
184#897—61no—
185#896—61no—
186#896—61no—
187D3×C4⋊C4—31no—
188D3×C4⋊C4—31no—
189#889—61no—
190#889—61no—
191#888—31no—
192#888—31no—
193#888—61no—
194#887—31no—
195#887—31no—
196#67⋊C4—61no—
197#67⋊C4—61no—
198#878—61no—
199#878—61no—
200C3×#107—31no—
201C3×#103—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#103—31no—
207#835—31no—
208#835—31no—
209#835—31no—
210#835—31no—
211#830—31no—
212#830—31no—
213#830—61no—
214(C2×D3)⋊C8—31no—
215(C2×D3)⋊C8—31no—
216(C2×D3)⋊C8—61no—
217#818C2×D311yescharacteristic
218#816C2×D311yescharacteristic
219#816C2×D311yescharacteristic
220#816C2×D311yescharacteristic
221#816C2×D311yescharacteristic
222#816C2×D311yescharacteristic
223#816C2×D311yescharacteristic
224Dic3⋊C8—31no—
225Dic3⋊C8—31no—
226Dic3⋊C8—61no—
227C8×Dic3—31no—
228C8×Dic3—31no—
229C8×Dic3—61no—
230#810—31no—
231#810—31no—
232#810—31no—
233#810—31no—
234#807—31no—
235#807—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
244#638Q1614yescomplemented
245C2×C3⋊Dic3C2×D411yescharacteristic
246C2×C3⋊Dic3C2×D411yescharacteristic
247C2×C3⋊Dic3C2×D411yescharacteristic
248C4×C3⋊D3—21no—
249C4×C3⋊D3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—42no—
259C2×C3×Dic3—81no—
260C3×Dic6—21no—
261C3×Dic6—21no—
262C3×Dic6—21no—
263C3×Dic6—21no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6—42no—
268C3×Dic6#4112yes—
269#627—42no—
270#627—81no—
271#624—42no—
272#624—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—31no—
284#467—91no—
285#462—91no—
286#451—91no—
287#451—91no—
288C4×Q16—91no—
289C8×D4—91no—
290C2×#103—31no—
291C2×#103—91no—
292C2×C3×Q8—31no—
293C2×C3×Q8—31no—
294C2×C3×Q8—31no—
295C2×C3×Q8—31no—
296C2×C3×Q8—62no—
297C2×C3×Q8—61no—
298C2×C3×Q8—121no—
299C22×C3×C4—21no—
300C22×C3×C4—61no—
301C22×C3×C4—61no—
302C22×C3×C4C22×D311yescharacteristic
303C22×C3×C4C22×D311yescharacteristic
304C2×#67—31no—
305C2×#67—31no—
306C2×#67—61no—
307C22×Dic3—21no—
308C22×Dic3—21no—
309D3×Q8—62no—
310D3×Q8—62no—
311D3×Q8—121no—
312D3×Q8—121no—
313C2×C4×D3—31no—
314C2×C4×D3—31no—
315C2×C4×D3—61no—
316C2×C4×D3—61no—
317C2×C4×D3—61no—
318C2×C4×D3—61no—
319C2×C4×D3—61no—
320C2×Dic6—22no—
321C2×Dic6—21no—
322C2×Dic6—41no—
323C2×Dic6—61no—
324C2×Dic6—61no—
325C2×Dic6—61no—
326C2×Dic6—61no—
327C2×Dic6C22×D311yescharacteristic
328C2×Dic6C22×D311yescharacteristic
329C2×Dic6C22×D311yescharacteristic
330C2×Dic6C22×D311yescharacteristic
331C3×Q16—121no—
332C2×C3×C8—21no—
333C2×C3×C8—21no—
334C2×C3×C8—41no—
335C2×C3×C8—41no—
336C2×C3×C8—42no—
337C2×C3×C8C22×D311yescharacteristic
338C2×C3×C8C22×D311yescharacteristic
339C2×C3×C8C22×D311yescharacteristic
340C2×C3×C8C22×D311yescharacteristic
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350#217—21no—
351#217—21no—
352#217—31no—
353#217—31no—
354#217—61no—
355#216—62no—
356#216—62no—
357#216—121no—
358#216—121no—
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—
366C4⋊Dic3—21no—
367C4⋊Dic3—61no—
368C4⋊Dic3—61no—
369C4⋊Dic3—61no—
370C4⋊Dic3—61no—
371C4⋊Dic3C22×D311yescharacteristic
372C4⋊Dic3C22×D311yescharacteristic
373C4⋊Dic3C22×D311yescharacteristic
374C4⋊Dic3C22×D311yescharacteristic
375Dic3⋊C4—21no—
376Dic3⋊C4—21no—
377Dic3⋊C4—31no—
378Dic3⋊C4—31no—
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—
392C4×Dic3—31no—
393C4×Dic3—31no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—61no—
404C2×C3⋊C8—61no—
405Dic12—41no—
406D3×C8—121no—
407D3×C8—121no—
408D3×C8—122no—
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—21no—
420C3⋊Dic3—21no—
421C3⋊Dic3C2×Q1612yes—
422C3×Dic3—22no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C3×Dic3—41no—
430C22×Q8—31no—
431C22×Q8—91no—
432C2×Q16—31no—
433C2×Q16—91no—
434C2×Q16—91no—
435C22×C8—91no—
436C22×C8D3211yescharacteristic
437C4⋊Q8—91no—
438C4⋊Q8—91no—
439C4⋊Q8—181no—
440#125—181no—
441C22⋊Q8—31no—
442C22⋊Q8—31no—
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—91no—
452C4×D4—181no—
453C4×D4—181no—
454C2×C4⋊C4—31no—
455C2×C4⋊C4—91no—
456#107—31no—
457#107—91no—
458#107—91no—
459C4⋊C8—91no—
460#103—31no—
461#103—31no—
462#103—31no—
463#103—31no—
464#103—31no—
465#103—31no—
466#103—91no—
467#103—91no—
468#103—91no—
469#103—91no—
470C22⋊C8—91no—
471C22⋊C8—91no—
472C4×C8—91no—
473C23×C3—21no—
474C23×C3D3×D411yescharacteristic
475C23×C3D3×D411yescharacteristic
476C22×D3—31no—
477C22×D3—31no—
478C22×D3—61no—
479C3×Q8—32no—
480C3×Q8—61no—
481C3×Q8—61no—
482C3×Q8—61no—
483C3×Q8—61no—
484C3×Q8—61no—
485C3×Q8—61no—
486C3×Q8—61no—
487C3×Q8—122no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
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—61no—
504C2×C3×C4—122no—
505C2×C3×C4—241no—
506C2×C3×C4D3×D411yescharacteristic
507C2×C3×C4D3×D411yescharacteristic
508C2×C3×C4C23×D311yescharacteristic
509C2×C3×C4C23×D311yescharacteristic
510#67—34no—
511#67—34no—
512#67—64no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—31no—
522C2×Dic3—31no—
523C2×Dic3—31no—
524C2×Dic3—31no—
525C2×Dic3—31no—
526C2×Dic3—31no—
527C2×Dic3—42no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—81no—
532C4×D3—61no—
533C4×D3—61no—
534C4×D3—61no—
535C4×D3—61no—
536C4×D3—121no—
537C4×D3—121no—
538C4×D3—122no—
539C4×D3—122no—
540C4×D3—241no—
541C4×D3—241no—
542Dic6—21no—
543Dic6—21no—
544Dic6—21no—
545Dic6—21no—
546Dic6—21no—
547Dic6—21no—
548Dic6—21no—
549Dic6—42no—
550Dic6—122no—
551Dic6—122no—
552Dic6—241no—
553Dic6—241no—
554Dic6#23512yes—
555C3×C8—22no—
556C3×C8—21no—
557C3×C8—21no—
558C3×C8—21no—
559C3×C8—21no—
560C3×C8—41no—
561C3⋊C8—61no—
562C3⋊C8—61no—
563C3⋊C8—61no—
564C3⋊C8—61no—
565C3⋊C8—121no—
566C3⋊C8—121no—
567C2×C32—22no—
568C2×C32#54611yescharacteristic
569C2×C32C22×Q1611yescharacteristic
570C2×C32#57711yescharacteristic
571C3⋊D3—22no—
572C2×Q8—31no—
573C2×Q8—31no—
574C2×Q8—31no—
575C2×Q8—31no—
576C2×Q8—62no—
577C2×Q8—61no—
578C2×Q8—121no—
579C2×Q8—181no—
580C2×Q8—181no—
581C2×Q8—182no—
582C2×Q8—361no—
583C2×D4—91no—
584C22×C4—61no—
585C22×C4—61no—
586C22×C4—91no—
587C22×C4—181no—
588C22×C4—181no—
589C22×C4C2×D3211yescharacteristic
590Q16—121no—
591Q16—182no—
592Q16—361no—
593C2×C8—41no—
594C2×C8—91no—
595C2×C8—91no—
596C2×C8—361no—
597C2×C8C2×D3211yescharacteristic
598C2×C8C2×D3211yescharacteristic
599C4⋊C4—31no—
600C4⋊C4—31no—
601C4⋊C4—31no—
602C4⋊C4—31no—
603C4⋊C4—61no—
604C4⋊C4—61no—
605C4⋊C4—61no—
606C4⋊C4—91no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C4⋊C4—181no—
611C4⋊C4—181no—
612C4⋊C4—181no—
613C4⋊C4—181no—
614C4⋊C4—181no—
615C22⋊C4—61no—
616C22⋊C4—61no—
617C22⋊C4—91no—
618C22⋊C4—91no—
619C22⋊C4—181no—
620C22⋊C4—181no—
621C42—91no—
622C42—181no—
623C42—181no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—22no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3D3×Q1612yes—
633C22×C3D3×Q1612yes—
634C22×C3C2×D3×D411yescharacteristic
635C22×C3C2×D3×D411yescharacteristic
636C2×D3—32no—
637C2×D3—32no—
638C2×D3—62no—
639C2×D3—61no—
640C2×D3—61no—
641C2×D3—61no—
642C2×D3—61no—
643C2×D3—121no—
644C2×D3—121no—
645C3×C4—21no—
646C3×C4—21no—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—41no—
650C3×C4—62no—
651C3×C4—121no—
652C3×C4—121no—
653C3×C4—121no—
654C3×C4—121no—
655C3×C4—121no—
656C3×C4—121no—
657C3×C4—121no—
658C3×C4C2×#23511yescharacteristic
659C3×C4#100411yescharacteristic
660C3×C4#100411yescharacteristic
661C3×C4D3×#4111yescharacteristic
662Dic3—22no—
663Dic3—32no—
664Dic3—32no—
665Dic3—41no—
666Dic3—41no—
667Dic3—41no—
668Dic3—41no—
669Dic3—41no—
670Dic3—41no—
671Dic3—41no—
672Dic3—62no—
673Dic3—61no—
674Dic3—61no—
675Dic3—61no—
676Dic3—61no—
677Dic3—121no—
678Dic3—121no—
679C32#329911yescharacteristic, complemented, Sylow
680C23—91no—
681C23#380211yescharacteristic
682Q8—32no—
683Q8—61no—
684Q8—61no—
685Q8—61no—
686Q8—61no—
687Q8—61no—
688Q8—61no—
689Q8—61no—
690Q8—122no—
691Q8—362no—
692Q8—721no—
693D4—94no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—91no—
705C2×C4—91no—
706C2×C4—91no—
707C2×C4—122no—
708C2×C4—181no—
709C2×C4—181no—
710C2×C4—241no—
711C2×C4—362no—
712C2×C4—721no—
713C2×C4#380211yescharacteristic
714C2×C4C22×D3211yescharacteristic
715C8—21no—
716C8—21no—
717C8—181no—
718C8—181no—
719C2×C3—22no—
720C2×C3—22no—
721C2×C3—21no—
722C2×C3—21no—
723C2×C3—21no—
724C2×C3—42no—
725C2×C3#549011yescharacteristic
726C2×C3#561011yescharacteristic
727C2×C3#576211yescharacteristic
728C2×C3C2×D3×Q1611yescharacteristic
729C2×C3C2×D3×Q1611yescharacteristic
730C2×C3#577011yescharacteristic
731D3—62no—
732D3—62no—
733D3—122no—
734C22—21no—
735C22—21no—
736C22—92no—
737C22—181no—
738C22—181no—
739C22#6380212yes—
740C22C2×#380211yescharacteristic
741C4—21no—
742C4—62no—
743C4—92no—
744C4—121no—
745C4—121no—
746C4—121no—
747C4—121no—
748C4—121no—
749C4—121no—
750C4—121no—
751C4—181no—
752C4—181no—
753C4D3×#23511yescharacteristic
754C4#6433011yescharacteristic
755C3—21no—
756C3#7880611yescharacteristic, complemented
757C3#8078111yescharacteristic, complemented
758C2—22no—
759C2—182no—
760C2#1059468611yescharacteristic
761C2C2×#6380211yescharacteristic
762C2#1059508311yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
prime radicalC2×#638D4
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
4. C3×#5116C2semidirect
5. C2×C3×#816C2semidirect
6. #10591185C2semidirect
7. #10591132C2semidirect
8. #10590950C2semidirect
9. #10590901C2semidirect
10. #10590855C2semidirect
11. #10590817C2semidirect
12. #10590798C2semidirect
13. #10590790C2semidirect
14. #10590689C2semidirect
15. #10590672C2semidirect
70. #5116D3semidirect
74. C2×#816D3semidirect
244. #638Q16semidirect
679. C32#3299semidirect
756. C3#78806semidirect
757. C3#80781semidirect

Maximal subgroups

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

subgroupindex
#105949912
#105948032
C8×#6382
C3×#51162
C2×C3×#8162
#105911852
#105911322
#105909502
#105909012
#105908552
#105908172
#105907982
#105907902
#105906892
#105906722
#807813
#788063