Finite Group Databasebeta

← #11872936

Subgroups — #11872936

Order 1152.

830 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5546C211yesmaximal, characteristic, complemented
2#10593877C211yesmaximal, characteristic, complemented
3#10592715C211yesmaximal, characteristic, complemented
4C3×#5007C211yesmaximal, characteristic, complemented
5#10591463C211yesmaximal, characteristic, complemented
6#10591452C211yesmaximal, characteristic
7#10591405C211yesmaximal, characteristic, complemented
8#10591400C211yesmaximal, characteristic, complemented
9#10590481C211yesmaximal, characteristic, complemented
10#10590457C211yesmaximal, characteristic, complemented
11#10590427C211yesmaximal, characteristic, complemented
12#10590422C211yesmaximal, characteristic, complemented
13#10590368C211yesmaximal, characteristic, complemented
14#10590310C211yesmaximal, characteristic, complemented
15#10590253C211yesmaximal, characteristic, complemented
16#82569—31nomaximal
17#80953—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C32×C4×D4C2211yescharacteristic
20C2×#3754C2211yescharacteristic
21C2×#3753C2211yescharacteristic
22#64084C2211yescharacteristic
23C3×D4×Dic3C2211yescharacteristic
24C3×C4×#67—21no—
25C2×C3×Dic3⋊C4—21no—
26C3×D3×C4⋊C4C2211yescharacteristic
27C3×#887C2211yescharacteristic
28C3×#67⋊C4—21no—
29C3×#877—21no—
30C3×#872C2211yescharacteristic
31C3×#869C2211yescharacteristic
32C3×C4×Dic6C2211yescharacteristic
33#63909C2211yescharacteristic
34#63907—21no—
35#63894C2211yescharacteristic
36#63888—21no—
37#63857C2211yescharacteristic
38#63854—21no—
39#63848—21no—
40#63844C2211yescharacteristic
41C2×#3719C2211yescharacteristic
42C2×#3717C2211yescharacteristic
43#63637C2211yescharacteristic
44#63636C2211yescharacteristic
45C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#807C2211yescharacteristic
49C3×#807C2211yescharacteristic
50C3×C4⋊(C3⋊C8)C2211yescharacteristic
51#63576C2211yescharacteristic
52#63576C2211yescharacteristic
53#63567C2211yescharacteristic
54#63565C2211yescharacteristic
55#63565C2211yescharacteristic
56#63564C2211yescharacteristic
57(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
58(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#520—31no—
62#5733—31no—
63#5546D311yescharacteristic, complemented
64#5534—31no—
65C3×#474—31no—
66#5239—31no—
67#5238—31no—
68#5091—31no—
69C4×#216—31no—
70#5028—31no—
71#5026—31no—
72#5021—31no—
73#5018—31no—
74#5016—31no—
75#5016—31no—
76#5016—61no—
77C4×#213—31no—
78#5007D311yescharacteristic, complemented
79#5000—31no—
80#4970—31no—
81#4967—31no—
82#4889—31no—
83#4884—31no—
84#4882—31no—
85#4873—31no—
86#4845—31no—
87#4840—31no—
88#4783—31no—
89#4781—31no—
90#4757—31no—
91#4756—31no—
92C2×C32×D4C2311yescharacteristic
93C22×C32×C4—21no—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×#634C2311yescharacteristic
96C2×C3×#67—21no—
97C22×C3×Dic3—21no—
98C22×C3×Dic3—21no—
99C3×#237—22no—
100C3×#237—22no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6—21no—
104C2×C3×Dic6C2311yescharacteristic
105C2×#626—21no—
106C2×#624—21no—
107C32×C4⋊C4C2311yescharacteristic
108C32×C22⋊C4—21no—
109C32×C42C2311yescharacteristic
110#3754—22no—
111#3753—22no—
112#3752—21no—
113#3752—21no—
114C2×C3⋊(C3⋊C8)C2311yescharacteristic
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C3×#217—21no—
117C3×(C2×D3)⋊C4D411yescharacteristic
118C3×(C2×D3)⋊C4D411yescharacteristic
119C3×C4⋊Dic3—21no—
120C3×C4⋊Dic3C2311yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×Dic3⋊C4—21no—
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4D411yescharacteristic
127C3×Dic3⋊C4D411yescharacteristic
128C3×C4×Dic3—21no—
129C3×C4×Dic3—21no—
130C3×C4×Dic3C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133#3724—21no—
134Dic3⋊Dic3—21no—
135#3722—21no—
136#3722—21no—
137(C2×D3)⋊Dic3—21no—
138Dic32—21no—
139#3719—22no—
140#3717—22no—
141#3124—91noSylow
142C2×C3×#41—31no—
143C2×#237C2×D311yescharacteristic
144C3×C4⋊Q8—31no—
145C3×C4×Q8—31no—
146C3×C4×Q8—31no—
147C3×C4×D4—21no—
148C3×C4×D4—31no—
149C3×C4×D4—61no—
150C3×C4×D4—61no—
151C3×C4×D4C2×D311yescharacteristic
152C3×C4×D4C2×D311yescharacteristic
153C3×#117—31no—
154C3×#117—61no—
155C2×C3×C4⋊C4—31no—
156C2×C3×C4⋊C4—61no—
157#947—61no—
158#946—61no—
159C2×#216—31no—
160C2×#215—31no—
161D4×Dic3C2×D311yescharacteristic
162C2×#214—31no—
163C2×#214—31no—
164C2×#214—61no—
165C2×#213—31no—
166C2×#213—31no—
167C2×#213—61no—
168#930—31no—
169C4×#67—21no—
170#924—31no—
171C2×Dic3⋊C4—21no—
172C2×Dic12—31no—
173C2×#204—31no—
174#898—61no—
175#898—61no—
176#897—31no—
177#896—61no—
178#895—31no—
179#894—61no—
180#893—31no—
181D3×C4⋊C4C2×D311yescharacteristic
182#887—31no—
183#887C2×D311yescharacteristic
184#885—61no—
185#883—61no—
186#67⋊C4—21no—
187#877—21no—
188#875—31no—
189#875—31no—
190#875—61no—
191C4×D12—31no—
192#872C2×D311yescharacteristic
193#869C2×D311yescharacteristic
194C4×Dic6—31no—
195C4×Dic6C2×D311yescharacteristic
196C3×#107—31no—
197C3×#107—31no—
198C3×C4⋊C8—31no—
199C3×#102—31no—
200C3×#102—31no—
201#835—31no—
202#835—31no—
203#832C2×D311yescharacteristic
204#832C2×D311yescharacteristic
205#830—31no—
206#830—31no—
207#821—31no—
208(C2×D3)⋊C8—31no—
209(C2×D3)⋊C8—31no—
210#816—31no—
211#815—31no—
212C8×Dic3—31no—
213#810—31no—
214#810—31no—
215#810—31no—
216#810—31no—
217#810—31no—
218#810—61no—
219#809—31no—
220#809—31no—
221#809—31no—
222#809—61no—
223#807—31no—
224#807—31no—
225#807—31no—
226#807—31no—
227#807C2×D311yescharacteristic
228#807C2×D311yescharacteristic
229C4⋊(C3⋊C8)—31no—
230C4⋊(C3⋊C8)—31no—
231C4⋊(C3⋊C8)—61no—
232C4⋊(C3⋊C8)C2×D311yescharacteristic
233#803—31no—
234C4×C3⋊C8—31no—
235C23×C32—21no—
236C22×C3⋊D3—21no—
237C22×C3×D3C2×D411yescharacteristic
238C32×D4—21no—
239C32×D4#4112yes—
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)—21no—
248#634—21no—
249#634—21no—
250C3×#67—24no—
251C2×C3×Dic3—24no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—81no—
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C3×C4×D3—21no—
261C3×C4×D3—21no—
262C3×C4×D3—81no—
263C3×Dic6—21no—
264C3×Dic6—81no—
265C3×Dic6#4112yes—
266#626—81no—
267#624—81no—
268C3⋊(C3⋊C8)—21no—
269C3⋊(C3⋊C8)—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272#542—91no—
273#520—31no—
274#484—91no—
275#480—91no—
276#477—91no—
277#474—31no—
278#464—91no—
279#463—91no—
280#452—91no—
281#449—91no—
282#440—91no—
283#440—91no—
284C4×Q16—91no—
285C4×D8—91no—
286#433—91no—
287C3×#41—62no—
288C3×#41—62no—
289C2×C3×Q8—31no—
290C2×C3×Q8—61no—
291C2×C3×D4—21no—
292C2×C3×D4—61no—
293C2×C3×D4C22×D311yescharacteristic
294C2×C3×D4C22×D311yescharacteristic
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—31no—
298C22×C3×C4—41no—
299C22×C3×C4—61no—
300C22×C3×C4—61no—
301C22×C3×C4—61no—
302C2×#67—21no—
303C2×#67—61no—
304C22×Dic3—21no—
305C22×Dic3—21no—
306#237—22no—
307#237—22no—
308C2×D12—31no—
309C2×D12—31no—
310C2×D12—61no—
311C2×D12—61no—
312C2×C4×D3—21no—
313C2×C4×D3—61no—
314C2×C4×D3—61no—
315C2×C4×D3C22×D311yescharacteristic
316C2×Dic6—21no—
317C2×Dic6—31no—
318C2×Dic6—31no—
319C2×Dic6—61no—
320C2×Dic6C22×D311yescharacteristic
321C2×C3×C8—31no—
322C2×C3×C8—31no—
323C3×C4⋊C4—21no—
324C3×C4⋊C4—31no—
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×C42—21no—
342C3×C42—31no—
343C3×C42—61no—
344C3×C42—61no—
345C3×C42C22×D311yescharacteristic
346C3×C42C22×D311yescharacteristic
347#217—21no—
348#217—61no—
349#216—62no—
350#215—62no—
351#214—62no—
352#214—62no—
353#214—122no—
354#213—62no—
355#213—62no—
356#213—122no—
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—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—121no—
367(C2×D3)⋊C4—121no—
368(C2×D3)⋊C4#6711yescharacteristic
369(C2×D3)⋊C4#6711yescharacteristic
370C4⋊Dic3—21no—
371C4⋊Dic3—61no—
372C4⋊Dic3C22×D311yescharacteristic
373C4⋊Dic3C22×D311yescharacteristic
374C4⋊Dic3C22×D311yescharacteristic
375Dic3⋊C4—21no—
376Dic3⋊C4—21no—
377Dic3⋊C4—21no—
378Dic3⋊C4—61no—
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
396Dic12—62no—
397#204—62no—
398C22×C32—22no—
399C22×C32—41no—
400C22×C32—41no—
401C22×C32C22×D411yescharacteristic
402C2×C3⋊D3—41no—
403C2×C3⋊D3—41no—
404C2×C3⋊D3—41no—
405C2×C3×D3—21no—
406C2×C3×D3—21no—
407C2×C3×D3—21no—
408C32×C4—21no—
409C32×C4—21no—
410C32×C4—41no—
411C32×C4C2×#4111yescharacteristic
412C32×C4C2×#4111yescharacteristic
413C3⋊Dic3—41no—
414C3×Dic3—22no—
415C3×Dic3—21no—
416C3×Dic3—21no—
417C3×Dic3—21no—
418C3×Dic3—41no—
419C3×Dic3—41no—
420C3×Dic3—41no—
421C2×#41—31no—
422C2×Q16—91no—
423C2×SD16—91no—
424C2×SD16—91no—
425C2×D8—91no—
426C4⋊Q8—31no—
427#126—181no—
428#124—91no—
429#124—181no—
430#123—181no—
431C22⋊Q8—91no—
432C22⋊Q8—181no—
433#121—91no—
434C4×Q8—31no—
435C4×Q8—31no—
436C4×Q8—91no—
437C4×D4—31no—
438C4×D4—61no—
439C4×D4—61no—
440C4×D4—91no—
441C4×D4D3211yescharacteristic
442#117—31no—
443#117—61no—
444C2×C4⋊C4—31no—
445C2×C4⋊C4—61no—
446#107—31no—
447#107—31no—
448#107—91no—
449#107—91no—
450C4⋊C8—31no—
451C4⋊C8—91no—
452#103—91no—
453#103—91no—
454#103—91no—
455#103—91no—
456#102—31no—
457#102—31no—
458#102—91no—
459#102—91no—
460C22⋊C8—91no—
461C22⋊C8—91no—
462#97—91no—
463C4×C8—91no—
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—31no—
467C23×C3—41no—
468C22×D3—61no—
469C22×D3—61no—
470C22×D3—121no—
471C22×D3C2×#6711yescharacteristic
472C3×Q8—32no—
473C3×Q8—61no—
474C3×Q8—241no—
475C3×D4—21no—
476C3×D4—21no—
477C3×D4—22no—
478C3×D4—41no—
479C3×D4—64no—
480C3×D4#23512yes—
481C3×D4#23912yes—
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—64no—
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×C4—241no—
502C2×C3×C4—241no—
503C2×C3×C4D3×D411yescharacteristic
504C2×C3×C4D3×D411yescharacteristic
505C2×C3×C4C2×#6711yescharacteristic
506C2×C3×C4C2×#6711yescharacteristic
507C2×C3×C4C23×D311yescharacteristic
508C2×C3×C4C23×D311yescharacteristic
509#67—24no—
510#67—241no—
511C2×Dic3—24no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—61no—
517C2×Dic3—61no—
518C2×Dic3—81no—
519C2×Dic3—121no—
520C2×Dic3C2×#6711yescharacteristic
521C2×Dic3C2×#6711yescharacteristic
522C2×Dic3C2×#6711yescharacteristic
523D12—61no—
524D12—61no—
525D12—61no—
526D12—61no—
527D12—121no—
528D12—121no—
529D12—241no—
530C4×D3—21no—
531C4×D3—21no—
532C4×D3—81no—
533C4×D3—241no—
534C4×D3—241no—
535Dic6—21no—
536Dic6—61no—
537Dic6—61no—
538Dic6—61no—
539Dic6—61no—
540Dic6—81no—
541Dic6—121no—
542Dic6—121no—
543Dic6#23512yes—
544C3×C8—61no—
545C3×C8—61no—
546C3⋊C8—21no—
547C3⋊C8—21no—
548C3⋊C8—61no—
549C3⋊C8—61no—
550C3⋊C8—61no—
551C3⋊C8—61no—
552C3⋊C8—121no—
553C3⋊C8—121no—
554C2×C32—42no—
555C2×C32#52511yescharacteristic
556C2×C32#57611yescharacteristic
557C2×C32#57811yescharacteristic
558C3⋊D3—81no—
559C3×D3—41no—
560#41—62no—
561#41—62no—
562C2×Q8—31no—
563C2×Q8—61no—
564C2×Q8—91no—
565C2×D4—61no—
566C2×D4—91no—
567C2×D4—181no—
568C2×D4C2×D3211yescharacteristic
569C22×C4—21no—
570C22×C4—31no—
571C22×C4—61no—
572C22×C4—61no—
573C22×C4—61no—
574C22×C4—181no—
575Q16—182no—
576SD16—182no—
577SD16—182no—
578D8—182no—
579C2×C8—31no—
580C2×C8—31no—
581C2×C8—91no—
582C2×C8—91no—
583C4⋊C4—31no—
584C4⋊C4—31no—
585C4⋊C4—31no—
586C4⋊C4—31no—
587C4⋊C4—31no—
588C4⋊C4—61no—
589C4⋊C4—61no—
590C4⋊C4—61no—
591C4⋊C4—61no—
592C4⋊C4—181no—
593C4⋊C4—181no—
594C4⋊C4C2×D3211yescharacteristic
595C22⋊C4—21no—
596C22⋊C4—31no—
597C22⋊C4—31no—
598C22⋊C4—61no—
599C22⋊C4—181no—
600C22⋊C4—181no—
601C22⋊C4—181no—
602C22⋊C4—181no—
603C22⋊C4—181no—
604C42—31no—
605C42—61no—
606C42—61no—
607C42—181no—
608C42C2×D3211yescharacteristic
609C22×C3—22no—
610C22×C3—22no—
611C22×C3—21no—
612C22×C3—42no—
613C22×C3—41no—
614C22×C3—41no—
615C22×C3—41no—
616C22×C3—41no—
617C22×C3—61no—
618C22×C3—61no—
619C22×C3—61no—
620C22×C3—81no—
621C22×C3—81no—
622C22×C3C2×D3×D411yescharacteristic
623C22×C3C22×#6711yescharacteristic
624C2×D3—21no—
625C2×D3—21no—
626C2×D3—21no—
627C2×D3—121no—
628C2×D3—121no—
629C2×D3—121no—
630C2×D3—121no—
631C2×D3—121no—
632C2×D3—121no—
633C2×D3—241no—
634C2×D3—241no—
635C2×D3—241no—
636C3×C4—21no—
637C3×C4—21no—
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—41no—
643C3×C4—41no—
644C3×C4—41no—
645C3×C4—41no—
646C3×C4—61no—
647C3×C4—61no—
648C3×C4—61no—
649C3×C4—62no—
650C3×C4—81no—
651C3×C4—121no—
652C3×C4—121no—
653C3×C4—121no—
654C3×C4C2×#23511yescharacteristic
655C3×C4C2×#23511yescharacteristic
656C3×C4C2×#23911yescharacteristic
657C3×C4D3×#4111yescharacteristic
658Dic3—22no—
659Dic3—21no—
660Dic3—21no—
661Dic3—21no—
662Dic3—41no—
663Dic3—41no—
664Dic3—41no—
665Dic3—121no—
666Dic3—121no—
667Dic3—241no—
668C32#312411yescharacteristic, complemented, Sylow
669C23—21no—
670C23—31no—
671C23—181no—
672Q8—32no—
673Q8—61no—
674Q8—181no—
675Q8—181no—
676Q8—241no—
677D4—21no—
678D4—64no—
679D4—181no—
680D4—181no—
681D4—721no—
682D4#379912yes—
683C2×C4—21no—
684C2×C4—31no—
685C2×C4—31no—
686C2×C4—31no—
687C2×C4—64no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—81no—
695C2×C4—181no—
696C2×C4—241no—
697C2×C4—241no—
698C2×C4—721no—
699C2×C4D3×#6711yescharacteristic
700C2×C4D3×#6711yescharacteristic
701C2×C4C22×D3211yescharacteristic
702C8—61no—
703C8—61no—
704C8—181no—
705C8—181no—
706C2×C3—21no—
707C2×C3—21no—
708C2×C3—21no—
709C2×C3—42no—
710C2×C3—42no—
711C2×C3—82no—
712C2×C3—121no—
713C2×C3#562711yescharacteristic
714C2×C3#575711yescharacteristic
715C2×C3#577911yescharacteristic
716C2×C3#579111yescharacteristic
717C2×C3#583511yescharacteristic
718C2×C3#583811yescharacteristic
719D3—41no—
720D3—241no—
721D3—241no—
722D3—481no—
723C22—22no—
724C22—41no—
725C22—41no—
726C22—61no—
727C22—61no—
728C22—61no—
729C22—361no—
730C22—361no—
731C22—361no—
732C22C2×D3×#6711yescharacteristic
733C4—21no—
734C4—21no—
735C4—41no—
736C4—61no—
737C4—61no—
738C4—61no—
739C4—62no—
740C4—121no—
741C4—121no—
742C4—121no—
743C4—361no—
744C4C2×#379911yescharacteristic
745C4D3×#23511yescharacteristic
746C3—21no—
747C3#8095311yescharacteristic, complemented
748C3#8256911yescharacteristic, complemented
749C2—42no—
750C2—121no—
751C2—721no—
752C2#1059500511yescharacteristic
753C2#1059509611yescharacteristic
754C2#1059546511yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radical#10591452C2
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×#5546C2semidirect
2. #10593877C2semidirect
3. #10592715C2semidirect
4. C3×#5007C2semidirect
5. #10591463C2semidirect
7. #10591405C2semidirect
8. #10591400C2semidirect
9. #10590481C2semidirect
10. #10590457C2semidirect
11. #10590427C2semidirect
12. #10590422C2semidirect
13. #10590368C2semidirect
14. #10590310C2semidirect
15. #10590253C2semidirect
63. #5546D3semidirect
78. #5007D3semidirect
668. C32#3124semidirect
747. C3#80953semidirect
748. C3#82569semidirect

Maximal subgroups

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

subgroupindex
C3×#55462
#105938772
#105927152
C3×#50072
#105914632
#105914522
#105914052
#105914002
#105904812
#105904572
#105904272
#105904222
#105903682
#105903102
#105902532
#825693
#809533