Finite Group Databasebeta

← #11872520

Subgroups — #11872520

Order 1152.

891 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596045C211yesmaximal, characteristic
2#10593867C211yesmaximal, characteristic, complemented
3C3×#5031C211yesmaximal, characteristic, complemented
4C3×#5022C211yesmaximal, characteristic, complemented
5#10591602C211yesmaximal, characteristic
6#10591602C211yesmaximal, characteristic
7#10591582C211yesmaximal, characteristic, complemented
8#10591581C211yesmaximal, characteristic, complemented
9#10590529C211yesmaximal, characteristic, complemented
10#10590528C211yesmaximal, characteristic, complemented
11#10590484C211yesmaximal, characteristic, complemented
12#10590483C211yesmaximal, characteristic, complemented
13#10590379C211yesmaximal, characteristic, complemented
14#10590308C211yesmaximal, characteristic, complemented
15#10590257C211yesmaximal, characteristic, complemented
16#81209—31nomaximal
17#80460—31nomaximal
18C2×#3832C2211yescharacteristic
19C32×C4×Q8C2211yescharacteristic
20Q8×C3⋊Dic3C2211yescharacteristic
21#64102—21no—
22#64102C2211yescharacteristic
23C4⋊C4×C3⋊D3—21no—
24C4⋊C4×C3⋊D3C2211yescharacteristic
25C4×C4⋊(C3⋊D3)—21no—
26C4×C4⋊(C3⋊D3)C2211yescharacteristic
27#64081—21no—
28#64081C2211yescharacteristic
29C2×C3×#216C2211yescharacteristic
30C2×C3×#216C2211yescharacteristic
31C3×#870C2211yescharacteristic
32C3×#869C2211yescharacteristic
33#63871C2211yescharacteristic
34#63871C2211yescharacteristic
35#63848—21no—
36#63848—21no—
37#63846—21no—
38#63846—21no—
39#63843C2211yescharacteristic
40#63843C2211yescharacteristic
41C2×#3717C2211yescharacteristic
42C2×#3717C2211yescharacteristic
43C3×#835C2211yescharacteristic
44C3×#835C2211yescharacteristic
45C3×#810C2211yescharacteristic
46C3×#810C2211yescharacteristic
47C3×#808C2211yescharacteristic
48C3×#807C2211yescharacteristic
49C3×C4⋊(C3⋊C8)C2211yescharacteristic
50C3×C4⋊(C3⋊C8)C2211yescharacteristic
51#63575C2211yescharacteristic
52#63573C2211yescharacteristic
53#63566C2211yescharacteristic
54#63566C2211yescharacteristic
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic
57#63557C2211yescharacteristic
58#63557C2211yescharacteristic
59#63555C2211yescharacteristic
60#63553C2211yescharacteristic
61#5731—31no—
62#5698—31no—
63#5574—31no—
64#5574—31no—
65#5574—61no—
66C3×#479—31no—
67C3×#462—31no—
68#5187—31no—
69#5187—31no—
70#5184—31no—
71Dic3×Q16—31no—
72#5083—31no—
73#5066—31no—
74#5031D311yescharacteristic, complemented
75#5022D311yescharacteristic, complemented
76#4889—31no—
77#4884—31no—
78#4862—31no—
79#4852—31no—
80#4847—31no—
81#4841—31no—
82#4840—31no—
83#4840—31no—
84#4817—31no—
85#4811—31no—
86#4808—31no—
87#4808—31no—
88#4805—31no—
89#4790—31no—
90#4789—31no—
91#4788—31no—
92C2×C32×Q8C2311yescharacteristic
93#3832—22no—
94#3832—22no—
95C2×C4⋊(C3⋊D3)—21no—
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4×C3⋊D3—21no—
98C2×C4×C3⋊D3—21no—
99C2×C4×C3⋊D3—21no—
100C2×C4×C3⋊D3—21no—
101C2×C4×C3⋊D3C2311yescharacteristic
102C2×C3×Dic6C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C32×C4⋊C4—21no—
105C32×C4⋊C4C2311yescharacteristic
106C32×C42—21no—
107C32×C42C2311yescharacteristic
108#3752—21no—
109#3752—21no—
110#3752D411yescharacteristic
111#3752D411yescharacteristic
112C4⋊(C3⋊Dic3)—21no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114#3750—21no—
115#3750D411yescharacteristic
116#3750D411yescharacteristic
117C4×C3⋊Dic3—21no—
118C4×C3⋊Dic3C2311yescharacteristic
119C3×#216—22no—
120C3×#216—22no—
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135#3722—21no—
136#3722—21no—
137Dic32—21no—
138Dic32—21no—
139#3717—22no—
140#3717—22no—
141#3120—91noSylow
142C2×#239—31no—
143C2×#239—31no—
144C2×#239—61no—
145C2×C3×Q16—31no—
146C2×C3×Q16—31no—
147C3×C4⋊Q8—31no—
148C3×#125—31no—
149C3×C4×Q8—21no—
150C3×C4×Q8C2×D311yescharacteristic
151C3×C4×Q8C2×D311yescharacteristic
152#946—31no—
153#946—31no—
154Q8×Dic3—31no—
155Q8×Dic3—31no—
156Q8×Dic3—31no—
157Q8×Dic3—31no—
158Q8×Dic3—61no—
159C2×#216C2×D311yescharacteristic
160C2×#216C2×D311yescharacteristic
161C2×#215—31no—
162C2×#215—31no—
163C2×#204—31no—
164C2×#204—31no—
165#898—61no—
166#898—61no—
167#898—61no—
168#898—61no—
169#897—31no—
170#897—31no—
171#893—31no—
172#893—31no—
173#893—61no—
174#893—61no—
175#893—61no—
176#893—62no—
177D3×C4⋊C4—31no—
178D3×C4⋊C4—31no—
179D3×C4⋊C4—61no—
180D3×C4⋊C4—61no—
181D3×C4⋊C4—61no—
182D3×C4⋊C4—62no—
183#890—61no—
184#890—61no—
185#889—61no—
186#889—61no—
187#887—31no—
188#887—31no—
189C4×D12—31no—
190C4×D12—31no—
191C4×D12—61no—
192C4×D12—61no—
193C4×D12—61no—
194C4×D12—62no—
195#872—31no—
196#872—31no—
197#872—61no—
198#872—61no—
199#872—61no—
200#872—62no—
201#870C2×D311yescharacteristic
202#869C2×D311yescharacteristic
203C3×#107—31no—
204C3×#106—31no—
205C3×C4⋊C8—31no—
206C3×C4⋊C8—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#103—31no—
211#835—31no—
212#835—31no—
213#835C2×D311yescharacteristic
214#835C2×D311yescharacteristic
215#821—31no—
216#821—31no—
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—31no—
221#818—31no—
222#817—31no—
223#816—31no—
224#816—31no—
225#815—31no—
226#815—31no—
227C8×Dic3—31no—
228C8×Dic3—31no—
229#810C2×D311yescharacteristic
230#810C2×D311yescharacteristic
231#809—31no—
232#809—31no—
233#808—31no—
234#808C2×D311yescharacteristic
235#807—31no—
236#807C2×D311yescharacteristic
237C4⋊(C3⋊C8)C2×D311yescharacteristic
238C4⋊(C3⋊C8)C2×D311yescharacteristic
239C22×C3⋊D3—21no—
240C22×C3⋊D3C2×D411yescharacteristic
241C32×Q8—21no—
242C32×Q8#4112yes—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2411yescharacteristic
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3C2×D411yescharacteristic
250C2×C3⋊Dic3C2×D411yescharacteristic
251C2×C3⋊Dic3C2×D411yescharacteristic
252C4⋊(C3⋊D3)—24no—
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)#4112yes—
255C4×C3⋊D3—24no—
256C4×C3⋊D3—21no—
257C4×C3⋊D3—21no—
258C4×C3⋊D3—81no—
259C4×C3⋊D3—81no—
260C4×C3⋊D3—81no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×C3⋊C8—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272C3×C3⋊C8—21no—
273#541—91no—
274#520—91no—
275#484—91no—
276#483—91no—
277#479—31no—
278#478—91no—
279#462—31no—
280#461—91no—
281#452—91no—
282#452—91no—
283#441—91no—
284#440—91no—
285C4×Q16—91no—
286C4×SD16—91no—
287#433—91no—
288C2×C3×Q8—21no—
289C2×C3×Q8—31no—
290C2×C3×Q8—31no—
291C2×C3×Q8C22×D311yescharacteristic
292C2×C3×Q8C22×D311yescharacteristic
293#239—62no—
294#239—62no—
295#239—64no—
296#239—64no—
297#239—62no—
298#239—62no—
299C2×D12—31no—
300C2×D12—31no—
301C2×D12—61no—
302C2×D12—61no—
303C2×D12—61no—
304C2×D12—62no—
305C2×C4×D3—31no—
306C2×C4×D3—31no—
307C2×C4×D3—61no—
308C2×C4×D3—61no—
309C2×C4×D3—61no—
310C2×C4×D3—62no—
311C2×C4×D3—61no—
312C2×C4×D3—61no—
313C2×C4×D3—61no—
314C2×C4×D3—61no—
315C2×C4×D3—62no—
316C2×C4×D3—62no—
317C2×C4×D3—62no—
318C2×C4×D3—61no—
319C2×C4×D3—61no—
320C2×Dic6C22×D311yescharacteristic
321C2×Dic6C22×D311yescharacteristic
322C3×Q16—62no—
323C3×Q16—62no—
324C2×C3×C8—31no—
325C2×C3×C8—31no—
326C2×C3×C8—31no—
327C2×C3×C8—31no—
328C3×C4⋊C4—22no—
329C3×C4⋊C4—21no—
330C3×C4⋊C4—21no—
331C3×C4⋊C4—21no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—61no—
335C3×C4⋊C4—61no—
336C3×C4⋊C4—61no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4C22×D311yescharacteristic
339C3×C4⋊C4C22×D311yescharacteristic
340C3×C42—22no—
341C3×C42—21no—
342C3×C42—21no—
343C3×C42—21no—
344C3×C42C22×D311yescharacteristic
345C3×C42C22×D311yescharacteristic
346#216—22no—
347#216—22no—
348#215—62no—
349#215—62no—
350(C2×D3)⋊C4—31no—
351(C2×D3)⋊C4—31no—
352(C2×D3)⋊C4—31no—
353(C2×D3)⋊C4—31no—
354(C2×D3)⋊C4—61no—
355(C2×D3)⋊C4—61no—
356(C2×D3)⋊C4—61no—
357(C2×D3)⋊C4—61no—
358(C2×D3)⋊C4—61no—
359(C2×D3)⋊C4—61no—
360(C2×D3)⋊C4—61no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—62no—
363(C2×D3)⋊C4—62no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366C4⋊Dic3—21no—
367C4⋊Dic3—21no—
368C4⋊Dic3—31no—
369C4⋊Dic3—31no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3—62no—
378C4⋊Dic3C22×D311yescharacteristic
379C4⋊Dic3C22×D311yescharacteristic
380Dic3⋊C4—21no—
381Dic3⋊C4—21no—
382Dic3⋊C4—31no—
383Dic3⋊C4—31no—
384Dic3⋊C4—31no—
385Dic3⋊C4—31no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—62no—
395C4×Dic3—31no—
396C4×Dic3—31no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3—61no—
404C4×Dic3—62no—
405C2×C3⋊C8C22×D311yescharacteristic
406C2×C3⋊C8C22×D311yescharacteristic
407C2×C3⋊C8C22×D311yescharacteristic
408C2×C3⋊C8C22×D311yescharacteristic
409#204—62no—
410#204—62no—
411C22×C32C22×D411yescharacteristic
412C2×C3⋊D3—21no—
413C2×C3⋊D3—22no—
414C2×C3⋊D3—21no—
415C2×C3⋊D3—21no—
416C2×C3⋊D3—41no—
417C2×C3⋊D3—41no—
418C32×C4—22no—
419C32×C4—21no—
420C32×C4—21no—
421C32×C4—41no—
422C32×C4C2×#4111yescharacteristic
423C32×C4C2×#4111yescharacteristic
424C3⋊Dic3—21no—
425C3⋊Dic3—21no—
426C3⋊Dic3—21no—
427C3⋊Dic3—41no—
428C3×Dic3—41no—
429C3×Dic3—41no—
430C3×Dic3—41no—
431C3×Dic3—41no—
432C2×#41—91no—
433C2×Q16—31no—
434C2×Q16—31no—
435C2×SD16—91no—
436C2×SD16—91no—
437C4⋊Q8—31no—
438#126—181no—
439#126—181no—
440#125—31no—
441#125—181no—
442#125—181no—
443C22⋊Q8—91no—
444C22⋊Q8—91no—
445C4×Q8—91no—
446C4×Q8—91no—
447C4×Q8—91no—
448C4×Q8D3211yescharacteristic
449C4×D4—91no—
450C4×D4—91no—
451C4×D4—181no—
452C4×D4—181no—
453#117—91no—
454#117—181no—
455C2×C4⋊C4—91no—
456C2×C4⋊C4—181no—
457#107—31no—
458#107—91no—
459#106—31no—
460#106—91no—
461C4⋊C8—31no—
462C4⋊C8—31no—
463#103—31no—
464#103—31no—
465#103—31no—
466#103—31no—
467#103—91no—
468#103—91no—
469#102—91no—
470#102—91no—
471C22⋊C8—91no—
472C22⋊C8—91no—
473#97—91no—
474C4×C8—91no—
475C22×D3—31no—
476C22×D3—31no—
477C22×D3—61no—
478C22×D3—62no—
479C22×D3—61no—
480C22×D3—61no—
481C3×Q8—22no—
482C3×Q8—21no—
483C3×Q8—21no—
484C3×Q8—22no—
485C3×Q8—61no—
486C3×Q8—61no—
487C3×Q8—61no—
488C3×Q8—61no—
489C3×Q8#23712yes—
490C3×Q8#23912yes—
491C2×C3×C4—22no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—22no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4D3×D411yescharacteristic
505C2×C3×C4D3×D411yescharacteristic
506C2×C3×C4D3×D411yescharacteristic
507C2×C3×C4D3×D411yescharacteristic
508C2×C3×C4C23×D311yescharacteristic
509C2×C3×C4C23×D311yescharacteristic
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—31no—
515C2×Dic3—31no—
516C2×Dic3—31no—
517C2×Dic3—31no—
518C2×Dic3—31no—
519C2×Dic3—31no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—62no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526D12—32no—
527D12—32no—
528D12—62no—
529D12—68no—
530D12—64no—
531D12—64no—
532D12—62no—
533D12—61no—
534D12—61no—
535C4×D3—68no—
536C4×D3—64no—
537C4×D3—64no—
538C4×D3—62no—
539C4×D3—62no—
540C4×D3—61no—
541C4×D3—61no—
542C4×D3—61no—
543C4×D3—61no—
544C4×D3—241no—
545C4×D3—241no—
546C4×D3—241no—
547C4×D3—241no—
548C4×D3—241no—
549C4×D3—241no—
550C4×D3—242no—
551C4×D3—242no—
552C4×D3—242no—
553Dic6—21no—
554Dic6—21no—
555Dic6—21no—
556Dic6—21no—
557C3×C8—61no—
558C3×C8—61no—
559C3×C8—61no—
560C3×C8—61no—
561C3⋊C8—21no—
562C3⋊C8—21no—
563C3⋊C8—21no—
564C3⋊C8—21no—
565C2×C32#52511yescharacteristic
566C2×C32#57711yescharacteristic
567C2×C32#57811yescharacteristic
568C3⋊D3—41no—
569C3⋊D3—42no—
570#41—182no—
571#41—182no—
572C2×Q8—31no—
573C2×Q8—31no—
574C2×Q8C2×D3211yescharacteristic
575C2×D4—91no—
576C2×D4—181no—
577C22×C4—91no—
578C22×C4—181no—
579C22×C4—181no—
580C22×C4—181no—
581C22×C4—181no—
582Q16—62no—
583Q16—62no—
584SD16—182no—
585SD16—182no—
586C2×C8—31no—
587C2×C8—31no—
588C2×C8—31no—
589C2×C8—31no—
590C4⋊C4—21no—
591C4⋊C4—31no—
592C4⋊C4—31no—
593C4⋊C4—61no—
594C4⋊C4—61no—
595C4⋊C4—61no—
596C4⋊C4—61no—
597C4⋊C4—91no—
598C4⋊C4—91no—
599C4⋊C4—91no—
600C4⋊C4—181no—
601C4⋊C4—181no—
602C4⋊C4—181no—
603C4⋊C4—181no—
604C4⋊C4—181no—
605C4⋊C4—181no—
606C4⋊C4C2×D3211yescharacteristic
607C22⋊C4—91no—
608C22⋊C4—91no—
609C22⋊C4—181no—
610C22⋊C4—181no—
611C22⋊C4—181no—
612C22⋊C4—181no—
613C42—21no—
614C42—91no—
615C42—181no—
616C42—181no—
617C42—181no—
618C42C2×D3211yescharacteristic
619C22×C3—21no—
620C22×C3C2×D3×D411yescharacteristic
621C22×C3C2×D3×D411yescharacteristic
622C2×D3—64no—
623C2×D3—62no—
624C2×D3—61no—
625C2×D3—61no—
626C2×D3—61no—
627C2×D3—61no—
628C2×D3—62no—
629C2×D3—61no—
630C2×D3—62no—
631C2×D3—61no—
632C2×D3—121no—
633C2×D3—121no—
634C2×D3—122no—
635C2×D3—122no—
636C2×D3—121no—
637C2×D3—121no—
638C2×D3—121no—
639C2×D3—121no—
640C3×C4—24no—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—21no—
644C3×C4—21no—
645C3×C4—22no—
646C3×C4—22no—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—41no—
650C3×C4—41no—
651C3×C4—42no—
652C3×C4—41no—
653C3×C4—41no—
654C3×C4—121no—
655C3×C4—121no—
656C3×C4—121no—
657C3×C4—121no—
658C3×C4C2×#23711yescharacteristic
659C3×C4C2×#23911yescharacteristic
660C3×C4D3×#4111yescharacteristic
661C3×C4D3×#4111yescharacteristic
662Dic3—41no—
663Dic3—41no—
664Dic3—41no—
665Dic3—41no—
666Dic3—62no—
667Dic3—61no—
668Dic3—61no—
669Dic3—61no—
670Dic3—61no—
671Dic3—61no—
672Dic3—61no—
673Dic3—121no—
674Dic3—121no—
675Dic3—122no—
676Dic3—121no—
677Dic3—121no—
678C32#312011yescharacteristic, complemented, Sylow
679C23—91no—
680C23—181no—
681Q8—21no—
682Q8—61no—
683Q8—61no—
684Q8—61no—
685Q8—61no—
686Q8#379612yes—
687D4—92no—
688D4—184no—
689D4—181no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—91no—
697C2×C4—91no—
698C2×C4—91no—
699C2×C4—184no—
700C2×C4—181no—
701C2×C4—181no—
702C2×C4—181no—
703C2×C4—721no—
704C2×C4—721no—
705C2×C4—721no—
706C2×C4#381111yescharacteristic
707C2×C4#381111yescharacteristic
708C2×C4C22×D3211yescharacteristic
709C8—61no—
710C8—61no—
711C8—61no—
712C8—61no—
713C2×C3—21no—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3#560611yescharacteristic
717C2×C3#562711yescharacteristic
718C2×C3#576611yescharacteristic
719C2×C3#577011yescharacteristic
720C2×C3#577811yescharacteristic
721C2×C3#577911yescharacteristic
722D3—122no—
723D3—124no—
724D3—121no—
725D3—122no—
726D3—121no—
727D3—122no—
728C22—181no—
729C22—182no—
730C22—181no—
731C22—181no—
732C22—361no—
733C22—361no—
734C22C2×#381111yescharacteristic
735C4—21no—
736C4—22no—
737C4—21no—
738C4—41no—
739C4—121no—
740C4—121no—
741C4—121no—
742C4—121no—
743C4—181no—
744C4—181no—
745C4—181no—
746C4—361no—
747C4C2×#379611yescharacteristic
748C4#6430611yescharacteristic
749C3—21no—
750C3#8046011yescharacteristic, complemented
751C3#8120911yescharacteristic, complemented
752C2—361no—
753C2—362no—
754C2#1059492211yescharacteristic
755C2#1059533711yescharacteristic
756C2#1059547311yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×#3832C22
hypercenterC4×Q8D32
hypocenterC32#3120
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. #10593867C2semidirect
3. C3×#5031C2semidirect
4. C3×#5022C2semidirect
7. #10591582C2semidirect
8. #10591581C2semidirect
9. #10590529C2semidirect
10. #10590528C2semidirect
11. #10590484C2semidirect
12. #10590483C2semidirect
13. #10590379C2semidirect
14. #10590308C2semidirect
15. #10590257C2semidirect
74. #5031D3semidirect
75. #5022D3semidirect
678. C32#3120semidirect
750. C3#80460semidirect
751. C3#81209semidirect

Maximal subgroups

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

subgroupindex
#105960452
#105938672
C3×#50312
C3×#50222
#105916022
#105915822
#105915812
#105905292
#105905282
#105904842
#105904832
#105903792
#105903082
#105902572
#812093
#804603