Finite Group Databasebeta

← #11870388

Subgroups — #11870388

Order 1152.

844 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595398C211yesmaximal, characteristic
2#10594511C211yesmaximal, characteristic, complemented
3#10592514C211yesmaximal, characteristic, complemented
4C3×#4815C211yesmaximal, characteristic, complemented
5C3×#4804C211yesmaximal, characteristic, complemented
6#10591553C211yesmaximal, characteristic, complemented
7#10591550C211yesmaximal, characteristic, complemented
8#10591549C211yesmaximal, characteristic, complemented
9#10590953C211yesmaximal, characteristic, complemented
10#10590676C211yesmaximal, characteristic, complemented
11D3×#817C211yesmaximal, characteristic, complemented
12#10590649C211yesmaximal, characteristic, complemented
13#10590512C211yesmaximal, characteristic, complemented
14#10590502C211yesmaximal, characteristic, complemented
15#10590436C211yesmaximal, characteristic, complemented
16#81521—31nomaximal
17#78844—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×#3798C2211yescharacteristic
20#64155C2211yescharacteristic
21#64101C2211yescharacteristic
22C3×#946C2211yescharacteristic
23C2×C3×D3×C8C2211yescharacteristic
24C3×#892C2211yescharacteristic
25C3×#892C2211yescharacteristic
26C4×#627—21no—
27#63916C2211yescharacteristic
28#63908C2211yescharacteristic
29#63906—21no—
30#63902—21no—
31#63900C2211yescharacteristic
32D3×C4⋊Dic3C2211yescharacteristic
33D3×C4⋊Dic3C2211yescharacteristic
34D3×C4⋊Dic3C2211yescharacteristic
35#63886—21no—
36#63885—21no—
37#63880—21no—
38#63880—21no—
39#63851—21no—
40C2×#3711C2211yescharacteristic
41C32×#103C2211yescharacteristic
42#63662C2211yescharacteristic
43#63647C2211yescharacteristic
44#63644C2211yescharacteristic
45#63634C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×#817C2211yescharacteristic
51C3×#809C2211yescharacteristic
52C3×#807C2211yescharacteristic
53#63574C2211yescharacteristic
54#63573C2211yescharacteristic
55#63573C2211yescharacteristic
56#63573C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59#63557C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61#5833—31no—
62#5629—31no—
63#5523—31no—
64#5523—31no—
65C3×#485—31no—
66C3×#416—31no—
67#5232—31no—
68#5110—31no—
69C2×#817—31no—
70#5043—31no—
71#5003—31no—
72#4995—31no—
73#4885—31no—
74#4881—31no—
75#4863—31no—
76D3×#106—31no—
77#4815—31no—
78#4815—31no—
79#4815—61no—
80#4815D311yescharacteristic, complemented
81#4805—31no—
82#4805—31no—
83#4805—31no—
84#4804D311yescharacteristic, complemented
85#4803—31no—
86#4779—31no—
87#4779—31no—
88#4777—31no—
89#4777—31no—
90#4735—31no—
91#4727—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C4×C3⋊D3C2311yescharacteristic
94C3×#239—22no—
95C3×#239—22no—
96C2×C3×D12—21no—
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×C4×D3C2311yescharacteristic
101C2×#627D411yescharacteristic
102C2×#626—21no—
103C2×#626D411yescharacteristic
104C2×#626D411yescharacteristic
105C2×#625—21no—
106C2×#625D411yescharacteristic
107C2×#624—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111#3798—22no—
112#3798—22no—
113C2×C32×C8C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115#3752—21no—
116#3752—21no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119#3750—21no—
120C4×C3⋊Dic3—21no—
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×C4×Dic3—21no—
130C3×C4×Dic3—21no—
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C3×D3×C8—22no—
134#3724—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140#3711—22no—
141#3099—91noSylow
142C2×C3×#41—31no—
143C2×#239C2×D311yescharacteristic
144C2×#235—31no—
145C2×#235—31no—
146C22×C3×C8—31no—
147C3×C22⋊Q8—31no—
148C3×#117—31no—
149C3×#117—31no—
150#946—31no—
151#946—31no—
152#946—61no—
153#946C2×D311yescharacteristic
154#939—61no—
155#939—61no—
156#938—31no—
157#938—31no—
158#930—31no—
159#930—61no—
160C2×C4⋊Dic3—31no—
161C2×C4⋊Dic3—31no—
162C2×C4⋊Dic3—31no—
163#924—61no—
164C2×#208—31no—
165C2×ΓL(1,𝔽25)—31no—
166C2×D3×C8C2×D311yescharacteristic
167#896—61no—
168#895—31no—
169#895—61no—
170#892—31no—
171#892—31no—
172#892—61no—
173#892C2×D311yescharacteristic
174#892C2×D311yescharacteristic
175D3×C4⋊C4—31no—
176D3×C4⋊C4—31no—
177D3×C4⋊C4—31no—
178D3×C4⋊C4—31no—
179D3×C4⋊C4—31no—
180#884—61no—
181#884—61no—
182#67⋊C4—61no—
183#67⋊C4—61no—
184#67⋊C4—61no—
185#67⋊C4—61no—
186C4×D12—61no—
187C4×D12—61no—
188C4×Dic6—61no—
189C4×Dic6—61no—
190C3×#107—31no—
191C3×#106—31no—
192C3×#103—21no—
193C3×#103—31no—
194C3×#103—31no—
195C3×#103C2×D311yescharacteristic
196C3×#103C2×D311yescharacteristic
197C3×#102—31no—
198C3×#102—31no—
199C3×C22⋊C8—31no—
200#835—31no—
201#835—31no—
202#835—61no—
203#835C2×D311yescharacteristic
204#835C2×D311yescharacteristic
205#832—31no—
206#832—31no—
207#830—31no—
208#821—31no—
209#821C2×D311yescharacteristic
210(C2×D3)⋊C8—31no—
211(C2×D3)⋊C8—31no—
212(C2×D3)⋊C8—31no—
213(C2×D3)⋊C8—31no—
214(C2×D3)⋊C8—31no—
215(C2×D3)⋊C8—61no—
216(C2×D3)⋊C8C2×D311yescharacteristic
217#817—31no—
218#817—31no—
219#817—31no—
220#817—31no—
221#817—31no—
222#817—61no—
223#817C2×D311yescharacteristic
224#809—31no—
225#809C2×D311yescharacteristic
226#808—31no—
227#808—31no—
228#808—31no—
229#808—31no—
230#808—31no—
231#807—31no—
232#807—31no—
233#807—61no—
234#807C2×D311yescharacteristic
235C22×C3⋊D3C2×D411yescharacteristic
236C22×C3×D3—21no—
237C22×C3×D3C2×D411yescharacteristic
238C22×C3×D3C2×D411yescharacteristic
239C32×Q8—21no—
240C32×Q8—21no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4C2411yescharacteristic
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3C2×D411yescharacteristic
247C4×C3⋊D3—21no—
248C4×C3⋊D3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C3×D12—21no—
255C3×D12—21no—
256C3×D12—42no—
257C3×C4×D3—21no—
258C3×C4×D3—21no—
259C3×C4×D3—42no—
260C3×C4×D3#4112yes—
261C3×C4×D3#4112yes—
262#627—22no—
263#626—22no—
264#626—22no—
265#626—81no—
266#625—22no—
267#625—81no—
268#624—81no—
269D3×Dic3—81no—
270D3×Dic3—81no—
271D3×Dic3—81no—
272C32×C8—21no—
273C3⋊(C3⋊C8)—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#537—91no—
277#520—91no—
278#485—31no—
279#485—91no—
280#483—91no—
281#483—91no—
282#482—91no—
283#482—91no—
284#481—91no—
285#481—91no—
286#428—91no—
287C2×#106—91no—
288#417—91no—
289#416—31no—
290#408—91no—
291C3×#41—62no—
292C3×#41—62no—
293C2×C3×Q8—21no—
294C2×C3×Q8C22×D311yescharacteristic
295C2×C3×Q8C22×D311yescharacteristic
296C2×C3×D4—31no—
297C2×C3×D4—61no—
298C22×C3×C4—31no—
299C22×C3×C4—31no—
300C22×C3×C4—61no—
301C2×#67—31no—
302C2×#67—31no—
303C2×#67—31no—
304C2×#67—31no—
305C2×#67—61no—
306C2×#67—61no—
307C2×#67—61no—
308C22×Dic3—61no—
309C22×Dic3—61no—
310C22×Dic3—61no—
311#239—22no—
312#239—22no—
313#235—62no—
314#235—62no—
315#235—62no—
316#235—62no—
317C2×D12—21no—
318C2×D12—31no—
319C2×D12—31no—
320C2×D12—61no—
321C2×D12C22×D311yescharacteristic
322C2×C4×D3—21no—
323C2×C4×D3—31no—
324C2×C4×D3—31no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3C22×D311yescharacteristic
332C2×C4×D3C22×D311yescharacteristic
333C2×Dic6—31no—
334C2×Dic6—31no—
335C2×C3×C8—21no—
336C2×C3×C8—31no—
337C2×C3×C8—31no—
338C2×C3×C8—62no—
339C2×C3×C8C22×D311yescharacteristic
340C2×C3×C8C22×D311yescharacteristic
341C3×C4⋊C4—21no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C22⋊C4—61no—
351C3×C42—61no—
352C3×C42—61no—
353#217—61no—
354#217—61no—
355(C2×D3)⋊C4—21no—
356(C2×D3)⋊C4—21no—
357(C2×D3)⋊C4—21no—
358(C2×D3)⋊C4—61no—
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—31no—
367C4⋊Dic3—31no—
368C4⋊Dic3—31no—
369C4⋊Dic3—31no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3C22×D311yescharacteristic
376C4⋊Dic3C22×D311yescharacteristic
377C4⋊Dic3C22×D311yescharacteristic
378Dic3⋊C4—21no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—121no—
387C4×Dic3—21no—
388C4×Dic3—21no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3—121no—
392#208—62no—
393C2×C3⋊C8—31no—
394C2×C3⋊C8—31no—
395C2×C3⋊C8—61no—
396C2×C3⋊C8C22×D311yescharacteristic
397C2×C3⋊C8C22×D311yescharacteristic
398ΓL(1,𝔽25)—62no—
399D3×C8—22no—
400C22×C32C22×D411yescharacteristic
401C2×C3⋊D3—21no—
402C2×C3⋊D3—21no—
403C2×C3⋊D3—21no—
404C2×C3×D3—21no—
405C2×C3×D3—21no—
406C2×C3×D3—21no—
407C2×C3×D3—21no—
408C2×C3×D3—21no—
409C2×C3×D3—41no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3#12312yes—
413C32×C4—41no—
414C32×C4—41no—
415C32×C4C2×#4111yescharacteristic
416C32×C4C2×#4111yescharacteristic
417C3⋊Dic3—21no—
418C3⋊Dic3—41no—
419C3⋊Dic3—41no—
420C3×Dic3—21no—
421C3×Dic3—41no—
422C3×Dic3—41no—
423C3×Dic3—41no—
424C3×Dic3#12312yes—
425C2×#41—31no—
426C2×#41—91no—
427C2×M16—91no—
428C22×C8—31no—
429C22⋊Q8—31no—
430C22⋊Q8—91no—
431C22⋊Q8—181no—
432#121—91no—
433#121—91no—
434#121—181no—
435#121—181no—
436#121—181no—
437C4×Q8—181no—
438C4×D4—181no—
439C4×D4—181no—
440C4×D4—181no—
441#117—31no—
442#117—31no—
443#117—91no—
444C2×C4⋊C4—91no—
445C2×C4⋊C4—91no—
446C2×C4⋊C4—91no—
447C2×C4⋊C4—91no—
448#107—31no—
449#107—91no—
450#106—31no—
451#106—91no—
452#106—91no—
453#106—91no—
454#106—91no—
455#106—91no—
456#103—31no—
457#103—31no—
458#103—91no—
459#103D3211yescharacteristic
460#102—31no—
461#102—31no—
462#102—91no—
463#102—91no—
464C22⋊C8—31no—
465C22⋊C8—91no—
466C22⋊C8—91no—
467C22⋊C8—91no—
468C23×C3—31no—
469C23×C3—31no—
470C23×C3—61no—
471C22×D3—21no—
472C22×D3—31no—
473C22×D3—31no—
474C22×D3—61no—
475C22×D3D3×D411yescharacteristic
476C22×D3D3×D411yescharacteristic
477C3×Q8—21no—
478C3×Q8—21no—
479C3×Q8—21no—
480C3×Q8—21no—
481C3×Q8—41no—
482C3×Q8—41no—
483C3×D4—61no—
484C3×D4—61no—
485C3×D4—122no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—31no—
492C2×C3×C4—32no—
493C2×C3×C4—32no—
494C2×C3×C4—31no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—122no—
503C2×C3×C4C23×D311yescharacteristic
504C2×C3×C4C23×D311yescharacteristic
505#67—62no—
506#67—62no—
507#67—62no—
508#67—62no—
509#67—241no—
510#67—241no—
511#67—241no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—31no—
516C2×Dic3—31no—
517C2×Dic3—61no—
518C2×Dic3—61no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—121no—
523C2×Dic3—121no—
524C2×Dic3—241no—
525C2×Dic3—241no—
526C2×Dic3—241no—
527C2×Dic3D3×D411yescharacteristic
528C2×Dic3D3×D411yescharacteristic
529D12—21no—
530D12—21no—
531D12—42no—
532D12—62no—
533D12—62no—
534D12—241no—
535C4×D3—21no—
536C4×D3—21no—
537C4×D3—42no—
538C4×D3—61no—
539C4×D3—61no—
540C4×D3—61no—
541C4×D3—61no—
542C4×D3—121no—
543C4×D3—121no—
544C4×D3—241no—
545C4×D3—241no—
546C4×D3—241no—
547C4×D3—241no—
548C4×D3—241no—
549C4×D3#23512yes—
550C4×D3#23712yes—
551Dic6—62no—
552Dic6—62no—
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×C32C2×#12311yescharacteristic
564C2×C32#57711yescharacteristic
565C2×C32#57711yescharacteristic
566C3⋊D3—41no—
567C3×D3—22no—
568C3×D3—41no—
569C3×D3—81no—
570#41—62no—
571#41—62no—
572#41—182no—
573#41—182no—
574C2×Q8—91no—
575C2×Q8C2×D3211yescharacteristic
576C2×D4—31no—
577C2×D4—61no—
578C2×D4—91no—
579C2×D4—91no—
580C2×D4—91no—
581C2×D4—181no—
582C2×D4—181no—
583C22×C4—31no—
584C22×C4—31no—
585C22×C4—61no—
586C22×C4—91no—
587C22×C4—181no—
588C22×C4—181no—
589C22×C4—181no—
590C22×C4—181no—
591M16—182no—
592C2×C8—31no—
593C2×C8—31no—
594C2×C8—62no—
595C2×C8—91no—
596C2×C8C2×D3211yescharacteristic
597C4⋊C4—31no—
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—61no—
601C4⋊C4—91no—
602C4⋊C4—91no—
603C4⋊C4—181no—
604C4⋊C4—181no—
605C4⋊C4—181no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4C2×D3211yescharacteristic
609C22⋊C4—61no—
610C22⋊C4—61no—
611C22⋊C4—61no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C22⋊C4—181no—
616C42—61no—
617C42—61no—
618C42—181no—
619C22×C3—21no—
620C22×C3—32no—
621C22×C3—61no—
622C22×C3—61no—
623C22×C3—61no—
624C22×C3—61no—
625C22×C3—61no—
626C22×C3—121no—
627C22×C3—121no—
628C22×C3—121no—
629C22×C3C2×D3×D411yescharacteristic
630C22×C3C2×D3×D411yescharacteristic
631C2×D3—21no—
632C2×D3—21no—
633C2×D3—21no—
634C2×D3—21no—
635C2×D3—21no—
636C2×D3—41no—
637C2×D3—41no—
638C2×D3—41no—
639C2×D3—61no—
640C2×D3—61no—
641C2×D3—61no—
642C2×D3—61no—
643C2×D3—61no—
644C2×D3—61no—
645C2×D3—121no—
646C2×D3—121no—
647C2×D3—121no—
648C2×D3#88312yes—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—32no—
652C3×C4—41no—
653C3×C4—41no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4—61no—
657C3×C4—81no—
658C3×C4—81no—
659C3×C4—121no—
660C3×C4—121no—
661C3×C4—121no—
662C3×C4C2×#23511yescharacteristic
663C3×C4C2×#23711yescharacteristic
664C3×C4D3×#4111yescharacteristic
665C3×C4D3×#4111yescharacteristic
666Dic3—21no—
667Dic3—41no—
668Dic3—41no—
669Dic3—41no—
670Dic3—61no—
671Dic3—61no—
672Dic3—121no—
673Dic3—121no—
674Dic3—121no—
675Dic3—121no—
676Dic3—121no—
677Dic3—241no—
678Dic3—241no—
679Dic3#88312yes—
680C32#309911yescharacteristic, complemented, Sylow
681C23—31no—
682C23—31no—
683C23—61no—
684C23—91no—
685Q8—21no—
686Q8—21no—
687Q8—182no—
688D4—61no—
689D4—61no—
690D4—122no—
691D4—182no—
692D4—182no—
693D4—182no—
694D4—721no—
695D4—721no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—31no—
699C2×C4—32no—
700C2×C4—32no—
701C2×C4—31no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—91no—
708C2×C4—122no—
709C2×C4—181no—
710C2×C4—181no—
711C2×C4—181no—
712C2×C4—181no—
713C2×C4—721no—
714C2×C4—721no—
715C2×C4—721no—
716C2×C4—721no—
717C2×C4C22×D3211yescharacteristic
718C8—21no—
719C8—61no—
720C8—61no—
721C8—181no—
722C2×C3—21no—
723C2×C3—21no—
724C2×C3—21no—
725C2×C3—62no—
726C2×C3—121no—
727C2×C3—241no—
728C2×C3C2×#88311yescharacteristic
729C2×C3D3×#12311yescharacteristic
730C2×C3#577011yescharacteristic
731C2×C3#577011yescharacteristic
732C2×C3#577011yescharacteristic
733C2×C3#577811yescharacteristic
734D3—22no—
735D3—41no—
736D3—81no—
737D3—121no—
738D3—121no—
739D3—241no—
740C22—32no—
741C22—61no—
742C22—61no—
743C22—61no—
744C22—61no—
745C22—61no—
746C22—121no—
747C22—121no—
748C22—121no—
749C22—181no—
750C22—181no—
751C22—181no—
752C22D32×D411yescharacteristic
753C4—32no—
754C4—41no—
755C4—41no—
756C4—61no—
757C4—121no—
758C4—121no—
759C4—121no—
760C4—181no—
761C4—361no—
762C4—361no—
763C4D3×#23511yescharacteristic
764C4D3×#23711yescharacteristic
765C3—21no—
766C3#7884411yescharacteristic, complemented
767C3#8152111yescharacteristic, complemented
768C2—62no—
769C2—121no—
770C2—241no—
771C2—361no—
772C2D3×#88311yescharacteristic
773C2#1059475711yescharacteristic
774C2#1059477011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radical#10595398C2
hypercenter#103D32
hypocenterC32#3099
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
2. #10594511C2semidirect
3. #10592514C2semidirect
4. C3×#4815C2semidirect
5. C3×#4804C2semidirect
6. #10591553C2semidirect
7. #10591550C2semidirect
8. #10591549C2semidirect
9. #10590953C2semidirect
10. #10590676C2semidirect
11. D3×#817C2semidirect
12. #10590649C2semidirect
13. #10590512C2semidirect
14. #10590502C2semidirect
15. #10590436C2semidirect
80. #4815D3semidirect
84. #4804D3semidirect
680. C32#3099semidirect
766. C3#78844semidirect
767. C3#81521semidirect

Maximal subgroups

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

subgroupindex
#105953982
#105945112
#105925142
C3×#48152
C3×#48042
#105915532
#105915502
#105915492
#105909532
#105906762
D3×#8172
#105906492
#105905122
#105905022
#105904362
#815213
#788443