Finite Group Databasebeta

← #11872943

Subgroups — #11872943

Order 1152.

835 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5561C211yesmaximal, characteristic, complemented
2#10593890C211yesmaximal, characteristic, complemented
3C4×#3753C211yesmaximal, characteristic, complemented
4C3×#5018C211yesmaximal, characteristic, complemented
5#10591521C211yesmaximal, characteristic
6#10591442C211yesmaximal, characteristic, complemented
7#10591432C211yesmaximal, characteristic, complemented
8#10591413C211yesmaximal, characteristic, complemented
9#10590616C211yesmaximal, characteristic, complemented
10#10590489C211yesmaximal, characteristic, complemented
11#10590464C211yesmaximal, characteristic, complemented
12#10590440C211yesmaximal, characteristic, complemented
13C4×#3718C211yesmaximal, characteristic, complemented
14#10590362C211yesmaximal, characteristic, complemented
15#10590265C211yesmaximal, characteristic, complemented
16#83461—31nomaximal
17#79813—31nomaximal
18C2×#3799C2211yescharacteristic
19C32×C4×D4C2211yescharacteristic
20C2×#3753C2211yescharacteristic
21C4×C4⋊(C3⋊D3)C2211yescharacteristic
22C3×#938C2211yescharacteristic
23C3×#936C2211yescharacteristic
24C2×C3×#214C2211yescharacteristic
25C3×#929—21no—
26C3×#924—21no—
27C3×#897C2211yescharacteristic
28C3×#888C2211yescharacteristic
29C3×#885—21no—
30C3×#879—21no—
31C3×#872C2211yescharacteristic
32C3×C4×Dic6C2211yescharacteristic
33C3×C4×Dic6C2211yescharacteristic
34#63894C2211yescharacteristic
35D3×C4⋊Dic3C2211yescharacteristic
36#63883—21no—
37#63881—21no—
38#63880—21no—
39Dic3×Dic6C2211yescharacteristic
40#63836—21no—
41C2×#3718C2211yescharacteristic
42C2×#3717C2211yescharacteristic
43#63659C2211yescharacteristic
44#63636C2211yescharacteristic
45#63634C2211yescharacteristic
46C4×C3⋊(C3⋊C8)C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#810C2211yescharacteristic
49C3×#807C2211yescharacteristic
50C3×#803C2211yescharacteristic
51#63576C2211yescharacteristic
52#63575C2211yescharacteristic
53Dic3⋊(C3⋊C8)C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63566C2211yescharacteristic
56#63565C2211yescharacteristic
57#63565C2211yescharacteristic
58#63564C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C3×#542—31no—
62#5574—31no—
63#5561D311yescharacteristic, complemented
64#5523—31no—
65C3×#440—31no—
66#5172—31no—
67#5166—31no—
68#5091—31no—
69#5087—31no—
70#5057—31no—
71#5054—31no—
72#5047—31no—
73#5044—31no—
74#5037—31no—
75#5033—31no—
76C4×#216—31no—
77C4×#216—31no—
78#5026—31no—
79#5018D311yescharacteristic, complemented
80C4×#213—31no—
81C4×#213—31no—
82C4×#213—61no—
83#5000—31no—
84#4890—31no—
85#4884—31no—
86#4808—31no—
87#4793—31no—
88#4787—31no—
89#4774—31no—
90#4710—31no—
91#4709—31no—
92C2×C32×D4C2311yescharacteristic
93C22×C32×C4—21no—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×C3×#67—21no—
97C2×C3×C4×D3C2311yescharacteristic
98C2×C3×Dic6—21no—
99C2×C3×Dic6C2311yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
101C2×#626—21no—
102C2×#624—21no—
103C2×#624—21no—
104C2×D3×Dic3—21no—
105#3799—22no—
106#3799—22no—
107C32×C4⋊C4C2311yescharacteristic
108C32×C22⋊C4—21no—
109C32×C42C2311yescharacteristic
110#3753—22no—
111#3752—21no—
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113C2×C3⋊(C3⋊C8)C2311yescharacteristic
114C2×C3⋊(C3⋊C8)C2311yescharacteristic
115C3×#217—21no—
116C3×#217—21no—
117C3×#217—21no—
118C3×#214—22no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4D411yescharacteristic
121C3×(C2×D3)⋊C4D411yescharacteristic
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4D411yescharacteristic
129C3×Dic3⋊C4D411yescharacteristic
130C3×C4×Dic3—21no—
131C3×C4×Dic3—21no—
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137#3722—21no—
138Dic32—21no—
139#3718—22no—
140#3717—22no—
141#3124—91noSylow
142C2×#239—31no—
143C2×#235—31no—
144C2×C3×SD16—31no—
145C3×C4⋊Q8—31no—
146C3×#126—61no—
147C3×#124—31no—
148C3×#124—61no—
149C3×#123—61no—
150C3×C22⋊Q8—31no—
151C3×C22⋊Q8—61no—
152C3×#121—31no—
153C3×C4×Q8—31no—
154C3×C4×Q8—31no—
155C3×C4×D4—21no—
156C3×C4×D4C2×D311yescharacteristic
157C3×C4×D4C2×D311yescharacteristic
158C3×#117—31no—
159Q8×Dic3—31no—
160C2×#216—31no—
161C2×#216—31no—
162C2×#215—31no—
163#938C2×D311yescharacteristic
164#936C2×D311yescharacteristic
165C2×#214C2×D311yescharacteristic
166C2×#213—31no—
167C2×#213—31no—
168C2×#213—61no—
169#929—21no—
170C2×C4⋊Dic3—31no—
171#924—21no—
172C2×#204—31no—
173#897C2×D311yescharacteristic
174#893—31no—
175#893—61no—
176#892—61no—
177D3×C4⋊C4—31no—
178D3×C4⋊C4—61no—
179D3×C4⋊C4—61no—
180#888C2×D311yescharacteristic
181#885—21no—
182#67⋊C4—61no—
183#67⋊C4—61no—
184#879—21no—
185C4×D12—31no—
186C4×D12—31no—
187C4×D12—31no—
188C4×D12—61no—
189C4×D12—61no—
190#872—61no—
191#872C2×D311yescharacteristic
192C4×Dic6—31no—
193C4×Dic6C2×D311yescharacteristic
194C4×Dic6C2×D311yescharacteristic
195C3×#107—31no—
196C3×#103—31no—
197C3×#102—31no—
198C3×#97—31no—
199#835—31no—
200#835—31no—
201#835—31no—
202#832—31no—
203#832—31no—
204#832—61no—
205#832C2×D311yescharacteristic
206#830—31no—
207#830—31no—
208#821—31no—
209(C2×D3)⋊C8—31no—
210(C2×D3)⋊C8—31no—
211#818—31no—
212#816—31no—
213Dic3⋊C8—31no—
214Dic3⋊C8—31no—
215#810—31no—
216#810—31no—
217#810C2×D311yescharacteristic
218#809—31no—
219#809—31no—
220#809—31no—
221#809—61no—
222#807—31no—
223#807—31no—
224#807—31no—
225#807—31no—
226#807—31no—
227#807—61no—
228#807C2×D311yescharacteristic
229C4⋊(C3⋊C8)—31no—
230C4⋊(C3⋊C8)—31no—
231#803C2×D311yescharacteristic
232C4×C3⋊C8—31no—
233C4×C3⋊C8—31no—
234C4×C3⋊C8—61no—
235C23×C32—21no—
236C22×C3⋊D3—21no—
237C22×C3×D3C2×D411yescharacteristic
238C32×D4—21no—
239C32×D4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—81no—
242C2×C32×C4C2×D411yescharacteristic
243C2×C32×C4C2×D411yescharacteristic
244C2×C32×C4C2411yescharacteristic
245C2×C3⋊Dic3—21no—
246C4⋊(C3⋊D3)—21no—
247C4⋊(C3⋊D3)#4112yes—
248C4×C3⋊D3—81no—
249C3×#67—81no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C3×C4×D3—21no—
258C3×C4×D3—21no—
259C3×Dic6—21no—
260C3×Dic6—21no—
261C3×Dic6—21no—
262C3×Dic6—81no—
263C3×Dic6#4112yes—
264#626—24no—
265#624—24no—
266#624—81no—
267D3×Dic3—81no—
268C3⋊(C3⋊C8)—21no—
269C3⋊(C3⋊C8)—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272#542—31no—
273#520—91no—
274#484—91no—
275#480—91no—
276#477—91no—
277#474—91no—
278#464—91no—
279#463—91no—
280#452—91no—
281#449—91no—
282#440—31no—
283#440—91no—
284C4×Q16—91no—
285C4×D8—91no—
286#433—91no—
287C2×C3×Q8—31no—
288C2×C3×Q8—31no—
289C2×C3×Q8—61no—
290C2×C3×D4—21no—
291C2×C3×D4—61no—
292C2×C3×D4C22×D311yescharacteristic
293C2×C3×D4C22×D311yescharacteristic
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—31no—
297C22×C3×C4—41no—
298C2×#67—21no—
299C2×#67—61no—
300C22×Dic3—61no—
301#239—62no—
302#239—62no—
303#235—62no—
304#235—62no—
305C2×D12—31no—
306C2×D12—31no—
307C2×D12—61no—
308C2×D12—61no—
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—61no—
316C2×C4×D3—121no—
317C2×C4×D3C22×D311yescharacteristic
318C2×Dic6—21no—
319C2×Dic6C22×D311yescharacteristic
320C2×Dic6C22×D311yescharacteristic
321C3×SD16—62no—
322C2×C3×C8—31no—
323C2×C3×C8—31no—
324C3×C4⋊C4—21no—
325C3×C4⋊C4—31no—
326C3×C4⋊C4—31no—
327C3×C4⋊C4—31no—
328C3×C4⋊C4—31no—
329C3×C4⋊C4—61no—
330C3×C4⋊C4—61no—
331C3×C4⋊C4—61no—
332C3×C4⋊C4—61no—
333C3×C4⋊C4C22×D311yescharacteristic
334C3×C4⋊C4C22×D311yescharacteristic
335C3×C22⋊C4—21no—
336C3×C22⋊C4—21no—
337C3×C22⋊C4—31no—
338C3×C22⋊C4—31no—
339C3×C22⋊C4—41no—
340C3×C22⋊C4—61no—
341C3×C22⋊C4—61no—
342C3×C22⋊C4—61no—
343C3×C22⋊C4—61no—
344C3×C42—21no—
345C3×C42—31no—
346C3×C42—61no—
347C3×C42—61no—
348C3×C42C22×D311yescharacteristic
349C3×C42C22×D311yescharacteristic
350#217—21no—
351#217—21no—
352#217—21no—
353#216—62no—
354#216—62no—
355#215—62no—
356#214—22no—
357#213—62no—
358#213—62no—
359#213—64no—
360(C2×D3)⋊C4—21no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—121no—
366(C2×D3)⋊C4#6711yescharacteristic
367(C2×D3)⋊C4#6711yescharacteristic
368C4⋊Dic3—21no—
369C4⋊Dic3—31no—
370C4⋊Dic3—31no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3C22×D311yescharacteristic
375C4⋊Dic3C22×D311yescharacteristic
376Dic3⋊C4—21no—
377Dic3⋊C4—21no—
378Dic3⋊C4—21no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4#6711yescharacteristic
382Dic3⋊C4#6711yescharacteristic
383C4×Dic3—21no—
384C4×Dic3—21no—
385C4×Dic3—61no—
386C4×Dic3—61no—
387C4×Dic3C22×D311yescharacteristic
388C2×C3⋊C8—31no—
389C2×C3⋊C8—31no—
390C2×C3⋊C8—31no—
391C2×C3⋊C8—31no—
392C2×C3⋊C8—61no—
393C2×C3⋊C8—61no—
394C2×C3⋊C8C22×D311yescharacteristic
395C2×C3⋊C8C22×D311yescharacteristic
396#204—62no—
397C22×C32—41no—
398C22×C32—41no—
399C22×C32—41no—
400C22×C32C22×D411yescharacteristic
401C2×C3⋊D3—22no—
402C2×C3⋊D3—41no—
403C2×C3⋊D3—41no—
404C2×C3×D3—21no—
405C2×C3×D3—21no—
406C2×C3×D3—21no—
407C32×C4—21no—
408C32×C4—21no—
409C32×C4—41no—
410C32×C4C2×#4111yescharacteristic
411C32×C4C2×#4111yescharacteristic
412C3⋊Dic3—41no—
413C3×Dic3—21no—
414C3×Dic3—22no—
415C3×Dic3—21no—
416C3×Dic3—21no—
417C3×Dic3—41no—
418C3×Dic3—41no—
419C3×Dic3—41no—
420C2×#41—91no—
421C2×Q16—91no—
422C2×SD16—31no—
423C2×SD16—91no—
424C2×D8—91no—
425C4⋊Q8—31no—
426#126—61no—
427#124—31no—
428#124—61no—
429#123—61no—
430C22⋊Q8—31no—
431C22⋊Q8—61no—
432#121—31no—
433C4×Q8—31no—
434C4×Q8—31no—
435C4×Q8—91no—
436C4×D4—91no—
437C4×D4—91no—
438C4×D4—181no—
439C4×D4—181no—
440C4×D4D3211yescharacteristic
441#117—31no—
442#117—181no—
443C2×C4⋊C4—91no—
444C2×C4⋊C4—181no—
445#107—31no—
446#107—91no—
447#107—91no—
448#107—91no—
449C4⋊C8—91no—
450C4⋊C8—91no—
451#103—31no—
452#103—91no—
453#103—91no—
454#103—91no—
455#102—31no—
456#102—91no—
457#102—91no—
458#102—91no—
459C22⋊C8—91no—
460C22⋊C8—91no—
461#97—31no—
462C4×C8—91no—
463C23×C3—21no—
464C23×C3—21no—
465C23×C3—31no—
466C23×C3—41no—
467C22×D3—61no—
468C22×D3—61no—
469C22×D3—121no—
470C22×D3C2×#6711yescharacteristic
471C3×Q8—32no—
472C3×Q8—61no—
473C3×Q8—61no—
474C3×Q8—61no—
475C3×Q8—241no—
476C3×D4—22no—
477C3×D4—21no—
478C3×D4—21no—
479C3×D4—21no—
480C3×D4—21no—
481C3×D4—41no—
482C3×D4—241no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—31no—
489C2×C3×C4—31no—
490C2×C3×C4—31no—
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—81no—
499C2×C3×C4—81no—
500C2×C3×C4—82no—
501C2×C3×C4D3×D411yescharacteristic
502C2×C3×C4D3×D411yescharacteristic
503C2×C3×C4C2×#6711yescharacteristic
504C2×C3×C4C2×#6711yescharacteristic
505C2×C3×C4C23×D311yescharacteristic
506C2×C3×C4C23×D311yescharacteristic
507#67—64no—
508#67—81no—
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—61no—
514C2×Dic3—61no—
515C2×Dic3—121no—
516C2×Dic3—241no—
517C2×Dic3C2×#6711yescharacteristic
518C2×Dic3C2×#6711yescharacteristic
519C2×Dic3C2×#6711yescharacteristic
520D12—32no—
521D12—32no—
522D12—62no—
523D12—64no—
524D12—61no—
525D12—61no—
526D12—121no—
527C4×D3—21no—
528C4×D3—21no—
529C4×D3—64no—
530C4×D3—64no—
531C4×D3—241no—
532C4×D3—241no—
533C4×D3—241no—
534C4×D3—241no—
535C4×D3—241no—
536C4×D3—242no—
537Dic6—21no—
538Dic6—21no—
539Dic6—21no—
540Dic6—81no—
541Dic6#23512yes—
542C3×C8—61no—
543C3×C8—61no—
544C3⋊C8—21no—
545C3⋊C8—21no—
546C3⋊C8—62no—
547C3⋊C8—61no—
548C3⋊C8—61no—
549C3⋊C8—61no—
550C3⋊C8—61no—
551C3⋊C8—121no—
552C2×C32—81no—
553C2×C32#52511yescharacteristic
554C2×C32#57611yescharacteristic
555C2×C32#57811yescharacteristic
556C3⋊D3—42no—
557C3×D3—41no—
558#41—182no—
559#41—182no—
560C2×Q8—31no—
561C2×Q8—31no—
562C2×Q8—61no—
563C2×D4—61no—
564C2×D4—91no—
565C2×D4—181no—
566C2×D4C2×D3211yescharacteristic
567C22×C4—21no—
568C22×C4—31no—
569C22×C4—181no—
570C22×C4—181no—
571C22×C4—181no—
572C22×C4—181no—
573Q16—182no—
574SD16—62no—
575SD16—182no—
576D8—182no—
577C2×C8—31no—
578C2×C8—31no—
579C2×C8—91no—
580C2×C8—91no—
581C4⋊C4—31no—
582C4⋊C4—31no—
583C4⋊C4—31no—
584C4⋊C4—31no—
585C4⋊C4—61no—
586C4⋊C4—61no—
587C4⋊C4—61no—
588C4⋊C4—61no—
589C4⋊C4—91no—
590C4⋊C4—181no—
591C4⋊C4—181no—
592C4⋊C4C2×D3211yescharacteristic
593C22⋊C4—21no—
594C22⋊C4—31no—
595C22⋊C4—31no—
596C22⋊C4—61no—
597C22⋊C4—61no—
598C22⋊C4—61no—
599C22⋊C4—61no—
600C22⋊C4—181no—
601C22⋊C4—181no—
602C42—31no—
603C42—61no—
604C42—61no—
605C42—181no—
606C42C2×D3211yescharacteristic
607C22×C3—21no—
608C22×C3—42no—
609C22×C3—41no—
610C22×C3—41no—
611C22×C3—41no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3—41no—
615C22×C3—61no—
616C22×C3—61no—
617C22×C3—61no—
618C22×C3—81no—
619C22×C3—81no—
620C22×C3C2×D3×D411yescharacteristic
621C22×C3C22×#6711yescharacteristic
622C2×D3—21no—
623C2×D3—21no—
624C2×D3—21no—
625C2×D3—62no—
626C2×D3—62no—
627C2×D3—122no—
628C2×D3—121no—
629C2×D3—121no—
630C2×D3—121no—
631C2×D3—121no—
632C2×D3—241no—
633C2×D3—241no—
634C3×C4—22no—
635C3×C4—21no—
636C3×C4—21no—
637C3×C4—21no—
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—21no—
641C3×C4—41no—
642C3×C4—41no—
643C3×C4—41no—
644C3×C4—61no—
645C3×C4—61no—
646C3×C4—61no—
647C3×C4—62no—
648C3×C4—81no—
649C3×C4—121no—
650C3×C4—121no—
651C3×C4—121no—
652C3×C4C2×#23511yescharacteristic
653C3×C4D3×#4111yescharacteristic
654C3×C4D3×#4111yescharacteristic
655C3×C4D3×#4111yescharacteristic
656Dic3—22no—
657Dic3—21no—
658Dic3—21no—
659Dic3—21no—
660Dic3—41no—
661Dic3—41no—
662Dic3—41no—
663Dic3—121no—
664Dic3—121no—
665Dic3—241no—
666C32#312411yescharacteristic, complemented, Sylow
667C23—21no—
668C23—31no—
669C23—181no—
670Q8—32no—
671Q8—61no—
672Q8—61no—
673Q8—61no—
674Q8—241no—
675D4—21no—
676D4—21no—
677D4—92no—
678D4—184no—
679D4—181no—
680D4—241no—
681C2×C4—21no—
682C2×C4—31no—
683C2×C4—31no—
684C2×C4—31no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—81no—
692C2×C4—184no—
693C2×C4—181no—
694C2×C4—721no—
695C2×C4—721no—
696C2×C4—721no—
697C2×C4D3×#6711yescharacteristic
698C2×C4D3×#6711yescharacteristic
699C2×C4C22×D3211yescharacteristic
700C8—61no—
701C8—61no—
702C8—181no—
703C8—181no—
704C2×C3—21no—
705C2×C3—21no—
706C2×C3—21no—
707C2×C3—82no—
708C2×C3—81no—
709C2×C3—81no—
710C2×C3—121no—
711C2×C3#554711yescharacteristic
712C2×C3#577411yescharacteristic
713C2×C3#577911yescharacteristic
714C2×C3#582811yescharacteristic
715C2×C3#583511yescharacteristic
716C2×C3#583811yescharacteristic
717D3—41no—
718D3—122no—
719D3—122no—
720D3—242no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—61no—
725C22—61no—
726C22—61no—
727C22—182no—
728C22—361no—
729C22—361no—
730C22C2×D3×#6711yescharacteristic
731C4—21no—
732C4—21no—
733C4—41no—
734C4—61no—
735C4—61no—
736C4—61no—
737C4—62no—
738C4—121no—
739C4—121no—
740C4—121no—
741C4—361no—
742C4D3×#23511yescharacteristic
743C4#6430611yescharacteristic
744C3—21no—
745C3#7981311yescharacteristic, complemented
746C3#8346111yescharacteristic, complemented
747C2—81no—
748C2—121no—
749C2—362no—
750C2#1059506011yescharacteristic
751C2#1059509711yescharacteristic
752C2#1059546511yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radical#10591521C2
hypercenterC4×D4D32
hypocenterC32#3124
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×#5561C2semidirect
2. #10593890C2semidirect
3. C4×#3753C2semidirect
4. C3×#5018C2semidirect
6. #10591442C2semidirect
7. #10591432C2semidirect
8. #10591413C2semidirect
9. #10590616C2semidirect
10. #10590489C2semidirect
11. #10590464C2semidirect
12. #10590440C2semidirect
13. C4×#3718C2semidirect
14. #10590362C2semidirect
15. #10590265C2semidirect
63. #5561D3semidirect
79. #5018D3semidirect
666. C32#3124semidirect
745. C3#79813semidirect
746. C3#83461semidirect

Maximal subgroups

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

subgroupindex
C3×#55612
#105938902
C4×#37532
C3×#50182
#105915212
#105914422
#105914322
#105914132
#105906162
#105904892
#105904642
#105904402
C4×#37182
#105903622
#105902652
#834613
#798133