Finite Group Databasebeta

← #11872952

Subgroups — #11872952

Order 1152.

828 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5582C211yesmaximal, characteristic, complemented
2#10593890C211yesmaximal, characteristic, complemented
3#10592725C211yesmaximal, characteristic, complemented
4C3×C4×#216C211yesmaximal, characteristic, complemented
5#10591657C211yesmaximal, characteristic, complemented
6#10591578C211yesmaximal, characteristic, complemented
7#10591568C211yesmaximal, characteristic, complemented
8#10591551C211yesmaximal, characteristic, complemented
9#10590615C211yesmaximal, characteristic
10#10590489C211yesmaximal, characteristic, complemented
11#10590464C211yesmaximal, characteristic, complemented
12#10590438C211yesmaximal, characteristic, complemented
13#10590358C211yesmaximal, characteristic, complemented
14C4×#3714C211yesmaximal, characteristic, complemented
15#10590264C211yesmaximal, characteristic, complemented
16#83461—31nomaximal
17#79749—31nomaximal
18C2×#3799C2211yescharacteristic
19C32×C4×Q8C2211yescharacteristic
20C2×#3755C2211yescharacteristic
21C4×C4⋊(C3⋊D3)C2211yescharacteristic
22C3×#947C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic
25C3×#896—21no—
26C3×#895C2211yescharacteristic
27C3×#894—21no—
28C3×#888C2211yescharacteristic
29C3×#876—21no—
30C3×#875—21no—
31C3×C4×D12C2211yescharacteristic
32C3×#872C2211yescharacteristic
33C3×C4×Dic6C2211yescharacteristic
34#63894C2211yescharacteristic
35D3×C4⋊Dic3C2211yescharacteristic
36#63883—21no—
37#63881—21no—
38#63880—21no—
39Dic3×Dic6C2211yescharacteristic
40#63836—21no—
41C2×#3715C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43#63662C2211yescharacteristic
44#63636C2211yescharacteristic
45#63634C2211yescharacteristic
46#63630C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#810C2211yescharacteristic
49C3×#807C2211yescharacteristic
50C3×C4×C3⋊C8C2211yescharacteristic
51#63576C2211yescharacteristic
52#63575C2211yescharacteristic
53Dic3⋊(C3⋊C8)C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63565C2211yescharacteristic
56#63564C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C3×#542—31no—
62#5582D311yescharacteristic, complemented
63#5574—31no—
64#5523—31no—
65C3×C4×Q16—31no—
66#5187—31no—
67#5185—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×#216D311yescharacteristic, complemented
77#5026—31no—
78#5026—31no—
79#5026—31no—
80#5026—61no—
81#5018—31no—
82C4×#213—31no—
83#5000—31no—
84#4890—31no—
85#4882—31no—
86#4819—31no—
87#4811—31no—
88#4810—31no—
89#4793—31no—
90C4×D24—31no—
91#4690—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3—21no—
95C2×C3×D12—21no—
96C2×C3×D12C2311yescharacteristic
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3C2311yescharacteristic
99C2×C3×Dic6—21no—
100C2×C3×Dic6C2311yescharacteristic
101C2×#626—21no—
102C2×#624—21no—
103C2×#624—21no—
104C2×D3×Dic3—21no—
105#3799—22no—
106#3799—22no—
107C32×C4⋊C4—21no—
108C32×C4⋊C4C2311yescharacteristic
109C32×C42—21no—
110C32×C42C2311yescharacteristic
111#3755—22no—
112#3752—21no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C2×C3⋊(C3⋊C8)C2311yescharacteristic
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C3×#216—22no—
117C3×(C2×D3)⋊C4—21no—
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4D411yescharacteristic
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4D411yescharacteristic
130C3×Dic3⋊C4D411yescharacteristic
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#3715—22no—
140#3714—22no—
141#3124—91noSylow
142C2×#239—31no—
143C2×#235—31no—
144C2×C3×Q16—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—21no—
154C3×C4×Q8—31no—
155C3×C4×Q8C2×D311yescharacteristic
156C3×C4×Q8C2×D311yescharacteristic
157C3×C4×D4—31no—
158C3×#117—31no—
159#947C2×D311yescharacteristic
160#946C2×D311yescharacteristic
161Q8×Dic3—31no—
162C2×#216C2×D311yescharacteristic
163C2×#215—31no—
164C2×#215—31no—
165C2×#215—31no—
166C2×#215—61no—
167C2×#214—31no—
168C2×#213—31no—
169C2×C4⋊Dic3—31no—
170C2×D24—31no—
171#896—21no—
172#895C2×D311yescharacteristic
173#894—21no—
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#67⋊C4—61no—
182#67⋊C4—61no—
183#876—21no—
184#875—21no—
185C4×D12—31no—
186C4×D12—31no—
187C4×D12—31no—
188C4×D12—61no—
189C4×D12—61no—
190C4×D12C2×D311yescharacteristic
191#872—61no—
192#872C2×D311yescharacteristic
193C4×Dic6—31no—
194C4×Dic6C2×D311yescharacteristic
195C3×#107—31no—
196C3×#103—31no—
197C3×#103—31no—
198C3×C4×C8—31no—
199#835—31no—
200#835—31no—
201#835—31no—
202#835—61no—
203#835C2×D311yescharacteristic
204#832—31no—
205#832—31no—
206#830—31no—
207#830—31no—
208#821—31no—
209#821—31no—
210(C2×D3)⋊C8—31no—
211(C2×D3)⋊C8—31no—
212#818—31no—
213Dic3⋊C8—31no—
214Dic3⋊C8—31no—
215#810—31no—
216#810C2×D311yescharacteristic
217#809—31no—
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#803—31no—
232#803—31no—
233#803—61no—
234C4×C3⋊C8C2×D311yescharacteristic
235C22×C3⋊D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3C2×D411yescharacteristic
238C32×Q8—21no—
239C32×Q8—21no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
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—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C3×D12—21no—
256C3×D12—21no—
257C3×D12—81no—
258C3×C4×D3—21no—
259C3×C4×D3—21no—
260C3×C4×D3—81no—
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—91no—
283#440—91no—
284C4×Q16—31no—
285C4×D8—91no—
286#433—91no—
287C2×C3×Q8—21no—
288C2×C3×Q8—31no—
289C2×C3×Q8—61no—
290C2×C3×Q8C22×D311yescharacteristic
291C2×C3×Q8C22×D311yescharacteristic
292C2×C3×D4—31no—
293C2×C3×D4—61no—
294C22×C3×C4—31no—
295C22×C3×C4—61no—
296C2×#67—61no—
297C22×Dic3—61no—
298#239—62no—
299#239—62no—
300#235—62no—
301#235—62no—
302C2×D12—21no—
303C2×D12—31no—
304C2×D12—31no—
305C2×D12—61no—
306C2×D12—61no—
307C2×D12C22×D311yescharacteristic
308C2×C4×D3—21no—
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
320C3×Q16—62no—
321C2×C3×C8—31no—
322C2×C3×C8—31no—
323C3×C4⋊C4—21no—
324C3×C4⋊C4—21no—
325C3×C4⋊C4—21no—
326C3×C4⋊C4—31no—
327C3×C4⋊C4—31no—
328C3×C4⋊C4—31no—
329C3×C4⋊C4—31no—
330C3×C4⋊C4—41no—
331C3×C4⋊C4—61no—
332C3×C4⋊C4—61no—
333C3×C4⋊C4—61no—
334C3×C4⋊C4C22×D311yescharacteristic
335C3×C4⋊C4C22×D311yescharacteristic
336C3×C22⋊C4—31no—
337C3×C22⋊C4—31no—
338C3×C22⋊C4—61no—
339C3×C22⋊C4—61no—
340C3×C22⋊C4—61no—
341C3×C22⋊C4—61no—
342C3×C22⋊C4—61no—
343C3×C42—21no—
344C3×C42—21no—
345C3×C42—21no—
346C3×C42—31no—
347C3×C42—41no—
348C3×C42—61no—
349C3×C42C22×D311yescharacteristic
350C3×C42C22×D311yescharacteristic
351#216—22no—
352#215—62no—
353#215—62no—
354#215—62no—
355#215—64no—
356#214—62no—
357#213—62no—
358(C2×D3)⋊C4—21no—
359(C2×D3)⋊C4—21no—
360(C2×D3)⋊C4—21no—
361(C2×D3)⋊C4—21no—
362(C2×D3)⋊C4—21no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—121no—
368(C2×D3)⋊C4#6711yescharacteristic
369(C2×D3)⋊C4#6711yescharacteristic
370C4⋊Dic3—31no—
371C4⋊Dic3—31no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3C22×D311yescharacteristic
376C4⋊Dic3C22×D311yescharacteristic
377Dic3⋊C4—21no—
378Dic3⋊C4—21no—
379Dic3⋊C4—21no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4#6711yescharacteristic
383Dic3⋊C4#6711yescharacteristic
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
396D24—62no—
397C22×C32C22×D411yescharacteristic
398C2×C3⋊D3—22no—
399C2×C3⋊D3—41no—
400C2×C3⋊D3—41no—
401C2×C3×D3—21no—
402C2×C3×D3—21no—
403C2×C3×D3—21no—
404C2×C3×D3—41no—
405C2×C3×D3—41no—
406C2×C3×D3—41no—
407C32×C4—21no—
408C32×C4—21no—
409C32×C4—41no—
410C32×C4—41no—
411C32×C4C2×#4111yescharacteristic
412C32×C4C2×#4111yescharacteristic
413C3⋊Dic3—41no—
414C3×Dic3—21no—
415C3×Dic3—22no—
416C3×Dic3—21no—
417C3×Dic3—21no—
418C3×Dic3—41no—
419C3×Dic3—41no—
420C2×#41—91no—
421C2×Q16—31no—
422C2×SD16—91no—
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—91no—
435C4×Q8D3211yescharacteristic
436C4×D4—31no—
437C4×D4—91no—
438C4×D4—91no—
439C4×D4—181no—
440C4×D4—181no—
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—31no—
453#103—91no—
454#103—91no—
455#102—91no—
456#102—91no—
457#102—91no—
458#102—91no—
459C22⋊C8—91no—
460C22⋊C8—91no—
461#97—91no—
462C4×C8—31no—
463C23×C3—31no—
464C23×C3—61no—
465C22×D3—21no—
466C22×D3—61no—
467C22×D3—61no—
468C22×D3—121no—
469C22×D3C2×#6711yescharacteristic
470C3×Q8—22no—
471C3×Q8—21no—
472C3×Q8—21no—
473C3×Q8—21no—
474C3×Q8—21no—
475C3×Q8—32no—
476C3×Q8—41no—
477C3×Q8—61no—
478C3×Q8—241no—
479C3×D4—61no—
480C3×D4—61no—
481C3×D4—241no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—31no—
490C2×C3×C4—31no—
491C2×C3×C4—31no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—61no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—241no—
500C2×C3×C4D3×D411yescharacteristic
501C2×C3×C4D3×D411yescharacteristic
502C2×C3×C4C2×#6711yescharacteristic
503C2×C3×C4C2×#6711yescharacteristic
504C2×C3×C4C23×D311yescharacteristic
505C2×C3×C4C23×D311yescharacteristic
506#67—64no—
507C2×Dic3—21no—
508C2×Dic3—21no—
509C2×Dic3—21no—
510C2×Dic3—61no—
511C2×Dic3—61no—
512C2×Dic3—121no—
513C2×Dic3—241no—
514C2×Dic3C2×#6711yescharacteristic
515C2×Dic3C2×#6711yescharacteristic
516C2×Dic3C2×#6711yescharacteristic
517D12—21no—
518D12—21no—
519D12—32no—
520D12—32no—
521D12—62no—
522D12—64no—
523D12—61no—
524D12—61no—
525D12—81no—
526D12—121no—
527C4×D3—21no—
528C4×D3—21no—
529C4×D3—64no—
530C4×D3—64no—
531C4×D3—81no—
532C4×D3—241no—
533C4×D3—241no—
534C4×D3—241no—
535C4×D3—241no—
536C4×D3—241no—
537C4×D3—242no—
538Dic6—21no—
539Dic6—81no—
540Dic6#23512yes—
541C3×C8—61no—
542C3×C8—61no—
543C3⋊C8—21no—
544C3⋊C8—21no—
545C3⋊C8—62no—
546C3⋊C8—61no—
547C3⋊C8—61no—
548C3⋊C8—61no—
549C3⋊C8—61no—
550C3⋊C8—121no—
551C2×C32#52511yescharacteristic
552C2×C32#57611yescharacteristic
553C2×C32#57811yescharacteristic
554C3⋊D3—42no—
555C3×D3—41no—
556C3×D3—81no—
557#41—182no—
558#41—182no—
559C2×Q8—31no—
560C2×Q8—61no—
561C2×Q8C2×D3211yescharacteristic
562C2×D4—31no—
563C2×D4—61no—
564C2×D4—91no—
565C2×D4—181no—
566C22×C4—31no—
567C22×C4—61no—
568C22×C4—181no—
569C22×C4—181no—
570C22×C4—181no—
571C22×C4—181no—
572Q16—62no—
573SD16—182no—
574SD16—182no—
575D8—182no—
576C2×C8—31no—
577C2×C8—31no—
578C2×C8—91no—
579C2×C8—91no—
580C4⋊C4—21no—
581C4⋊C4—31no—
582C4⋊C4—31no—
583C4⋊C4—31no—
584C4⋊C4—31no—
585C4⋊C4—61no—
586C4⋊C4—61no—
587C4⋊C4—61no—
588C4⋊C4—91no—
589C4⋊C4—181no—
590C4⋊C4—181no—
591C4⋊C4C2×D3211yescharacteristic
592C22⋊C4—31no—
593C22⋊C4—31no—
594C22⋊C4—61no—
595C22⋊C4—61no—
596C22⋊C4—61no—
597C22⋊C4—61no—
598C22⋊C4—61no—
599C22⋊C4—181no—
600C22⋊C4—181no—
601C42—21no—
602C42—31no—
603C42—61no—
604C42—181no—
605C42C2×D3211yescharacteristic
606C22×C3—21no—
607C22×C3—61no—
608C22×C3—61no—
609C22×C3—61no—
610C22×C3—121no—
611C22×C3—121no—
612C22×C3—121no—
613C22×C3C2×D3×D411yescharacteristic
614C22×C3C22×#6711yescharacteristic
615C2×D3—21no—
616C2×D3—21no—
617C2×D3—21no—
618C2×D3—41no—
619C2×D3—41no—
620C2×D3—41no—
621C2×D3—62no—
622C2×D3—62no—
623C2×D3—122no—
624C2×D3—121no—
625C2×D3—121no—
626C2×D3—121no—
627C2×D3—121no—
628C2×D3—241no—
629C2×D3—241no—
630C3×C4—21no—
631C3×C4—21no—
632C3×C4—21no—
633C3×C4—21no—
634C3×C4—21no—
635C3×C4—21no—
636C3×C4—41no—
637C3×C4—41no—
638C3×C4—42no—
639C3×C4—41no—
640C3×C4—41no—
641C3×C4—41no—
642C3×C4—41no—
643C3×C4—61no—
644C3×C4—61no—
645C3×C4—61no—
646C3×C4—62no—
647C3×C4—81no—
648C3×C4—121no—
649C3×C4—121no—
650C3×C4C2×#23511yescharacteristic
651C3×C4D3×#4111yescharacteristic
652C3×C4D3×#4111yescharacteristic
653C3×C4D3×#4111yescharacteristic
654Dic3—22no—
655Dic3—21no—
656Dic3—21no—
657Dic3—21no—
658Dic3—41no—
659Dic3—41no—
660Dic3—121no—
661Dic3—121no—
662Dic3—241no—
663C32#312411yescharacteristic, complemented, Sylow
664C23—31no—
665C23—61no—
666C23—181no—
667Q8—21no—
668Q8—21no—
669Q8—32no—
670Q8—61no—
671Q8—241no—
672D4—61no—
673D4—61no—
674D4—92no—
675D4—184no—
676D4—181no—
677D4—241no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—31no—
681C2×C4—31no—
682C2×C4—31no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—184no—
689C2×C4—181no—
690C2×C4—241no—
691C2×C4—721no—
692C2×C4—721no—
693C2×C4—721no—
694C2×C4D3×#6711yescharacteristic
695C2×C4D3×#6711yescharacteristic
696C2×C4C22×D3211yescharacteristic
697C8—61no—
698C8—61no—
699C8—181no—
700C8—181no—
701C2×C3—21no—
702C2×C3—21no—
703C2×C3—21no—
704C2×C3—121no—
705C2×C3—241no—
706C2×C3#554711yescharacteristic
707C2×C3#576611yescharacteristic
708C2×C3#576911yescharacteristic
709C2×C3#582811yescharacteristic
710C2×C3#583511yescharacteristic
711C2×C3#583811yescharacteristic
712D3—41no—
713D3—81no—
714D3—122no—
715D3—122no—
716D3—242no—
717C22—61no—
718C22—61no—
719C22—61no—
720C22—121no—
721C22—121no—
722C22—121no—
723C22—182no—
724C22—361no—
725C22—361no—
726C22C2×D3×#6711yescharacteristic
727C4—21no—
728C4—21no—
729C4—41no—
730C4—41no—
731C4—61no—
732C4—61no—
733C4—62no—
734C4—61no—
735C4—121no—
736C4—121no—
737C4—361no—
738C4D3×#23511yescharacteristic
739C4#6430611yescharacteristic
740C3—21no—
741C3#7974911yescharacteristic, complemented
742C3#8346111yescharacteristic, complemented
743C2—121no—
744C2—241no—
745C2—362no—
746C2#1059506011yescharacteristic
747C2#1059532711yescharacteristic
748C2#1059545611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radical#10590615C2
hypercenterC4×Q8D32
hypocenterC32#3124
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
1. C3×#5582C2semidirect
2. #10593890C2semidirect
3. #10592725C2semidirect
4. C3×C4×#216C2semidirect
5. #10591657C2semidirect
6. #10591578C2semidirect
7. #10591568C2semidirect
8. #10591551C2semidirect
10. #10590489C2semidirect
11. #10590464C2semidirect
12. #10590438C2semidirect
13. #10590358C2semidirect
14. C4×#3714C2semidirect
15. #10590264C2semidirect
62. #5582D3semidirect
76. C4×#216D3semidirect
663. C32#3124semidirect
741. C3#79749semidirect
742. C3#83461semidirect

Maximal subgroups

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

subgroupindex
C3×#55822
#105938902
#105927252
C3×C4×#2162
#105916572
#105915782
#105915682
#105915512
#105906152
#105904892
#105904642
#105904382
#105903582
C4×#37142
#105902642
#834613
#797493