Finite Group Databasebeta

← #11889437

Subgroups — #11889437

Order 1152.

806 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5581C211yesmaximal, characteristic
2#10593904C211yesmaximal, characteristic
3#10592729C211yesmaximal, characteristic, complemented
4C3×#5031C211yesmaximal, characteristic, complemented
5#10591653C211yesmaximal, characteristic, complemented
6#10591653C211yesmaximal, characteristic, complemented
7#10591638C211yesmaximal, characteristic, complemented
8#10591635C211yesmaximal, characteristic, complemented
9#10590600C211yesmaximal, characteristic, complemented
10D3×#810C211yesmaximal, characteristic, complemented
11#10590519C211yesmaximal, characteristic, complemented
12#10590516C211yesmaximal, characteristic, complemented
13#10590330C211yesmaximal, characteristic
14#10590292C211yesmaximal, characteristic, complemented
15#10590291C211yesmaximal, characteristic, complemented
16#83603—31nomaximal
17#80493—31nomaximal
18C2×D3×Dic6C2211yescharacteristic
19C2×D3×Dic6C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic
21C2×#3756C2211yescharacteristic
22C4×#634C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C2×C3×#216C2211yescharacteristic
26C2×C3×#216C2211yescharacteristic
27C3×#894—21no—
28C3×#892C2211yescharacteristic
29C3×D3×C4⋊C4C2211yescharacteristic
30C3×#889—21no—
31C3×#876—21no—
32C3×C4×D12C2211yescharacteristic
33C3×#872—21no—
34C3×#870C2211yescharacteristic
35C3×#869C2211yescharacteristic
36#63919—21no—
37#63899—21no—
38#63899—21no—
39#63898—21no—
40#63856C2211yescharacteristic
41#63856C2211yescharacteristic
42C2×#3711C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44#63662C2211yescharacteristic
45#63637C2211yescharacteristic
46#63635C2211yescharacteristic
47#63630C2211yescharacteristic
48C3×#810C2211yescharacteristic
49C3×#810C2211yescharacteristic
50C3×C4⋊(C3⋊C8)C2211yescharacteristic
51#63575C2211yescharacteristic
52#63573C2211yescharacteristic
53#63567C2211yescharacteristic
54#63567C2211yescharacteristic
55#63565C2211yescharacteristic
56#63565C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C3×#552—31no—
62#5727—31no—
63#5581D311yescharacteristic
64D4×Dic6—31no—
65C3×#462—31no—
66#5189—31no—
67#5188—31no—
68#5186—31no—
69#5186—31no—
70#5082—31no—
71#5069—31no—
72#5063—31no—
73#5052—31no—
74#5051—31no—
75#5050—31no—
76#5050—31no—
77#5031D311yescharacteristic, complemented
78#5030—31no—
79#5030—31no—
80#5030—61no—
81#5011—31no—
82#5004—31no—
83#4996—31no—
84#4971—31no—
85C2×#810—31no—
86#4836—31no—
87#4829—31no—
88#4814—31no—
89#4805—31no—
90#4802—31no—
91D3×#103—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×#634C2311yescharacteristic
94C2×C3×D12D411yescharacteristic
95C2×C3×C4×D3—21no—
96C2×C3×C4×D3C2311yescharacteristic
97C2×C3×C4×D3C2311yescharacteristic
98C2×C3×Dic6C2311yescharacteristic
99C2×C3×Dic6C2311yescharacteristic
100C2×#627—21no—
101C2×#627—21no—
102C2×D3×Dic3—21no—
103C2×D3×Dic3—21no—
104D3×Dic6—22no—
105D3×Dic6—22no—
106D3×Dic6—41no—
107D3×Dic6—41no—
108C32×C4⋊C4—21no—
109C32×C4⋊C4C2311yescharacteristic
110C32×C42—21no—
111C32×C42C2311yescharacteristic
112#3756—22no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114#3750—21no—
115C4×C3⋊Dic3—21no—
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×#216—41no—
119C3×#216—41no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×(C2×D3)⋊C4D411yescharacteristic
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3D411yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×C4×Dic3—21no—
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138#3724—21no—
139#3724—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142#3711—41no—
143D3×C3⋊C8—41no—
144#3312—91noSylow
145C2×D3×Q8—31no—
146C2×D3×Q8—31no—
147C22×Dic6—31no—
148C22×Dic6—31no—
149C2×C3×Q16—31no—
150C2×C3×Q16—31no—
151C3×C4⋊Q8—31no—
152C3×#126—61no—
153C3×#125—31no—
154C3×#125—61no—
155C3×#123—61no—
156C3×C22⋊Q8—31no—
157C3×C22⋊Q8—31no—
158C3×C4×Q8—21no—
159C3×C4×Q8C2×D311yescharacteristic
160C3×C4×Q8C2×D311yescharacteristic
161C3×C4×D4—31no—
162C3×#117—31no—
163C3×#117—61no—
164C2×C3×C4⋊C4—31no—
165#946—31no—
166#946—31no—
167#946C2×D311yescharacteristic
168#946C2×D311yescharacteristic
169C2×#216—31no—
170C2×#216—31no—
171C2×#216—61no—
172C2×#216C2×D311yescharacteristic
173C2×#216C2×D311yescharacteristic
174D4×Dic3—61no—
175#924—31no—
176#924—31no—
177C2×#208—31no—
178C22×C3⋊C8—31no—
179C2×ΓL(1,𝔽25)—31no—
180C2×D3×C8—31no—
181#896—61no—
182#896—61no—
183#894—21no—
184#893—61no—
185#892C2×D311yescharacteristic
186D3×C4⋊C4C2×D311yescharacteristic
187#889—21no—
188#888—61no—
189#888—61no—
190#878—61no—
191#878—61no—
192#876—21no—
193C4×D12C2×D311yescharacteristic
194#872—21no—
195#870C2×D311yescharacteristic
196#869C2×D311yescharacteristic
197C4×Dic6—31no—
198C4×Dic6—31no—
199C4×Dic6—61no—
200C3×C4⋊C8—31no—
201C3×#103—31no—
202C3×#103—31no—
203#835—31no—
204#835—31no—
205#835—31no—
206#835—31no—
207#835—31no—
208#835—31no—
209#835—61no—
210#830—31no—
211#830—31no—
212(C2×D3)⋊C8—31no—
213(C2×D3)⋊C8—31no—
214#818—31no—
215#817—31no—
216#816—31no—
217#816—31no—
218#810—31no—
219#810—31no—
220#810—31no—
221#810—31no—
222#810—31no—
223#810—31no—
224#810—31no—
225#810—31no—
226#810—61no—
227#810C2×D311yescharacteristic
228#810C2×D311yescharacteristic
229#808—31no—
230#808—31no—
231#808—31no—
232#808—61no—
233#807—31no—
234C4⋊(C3⋊C8)C2×D311yescharacteristic
235#803—31no—
236#803—31no—
237#803—61no—
238C22×C3×D3C2×D411yescharacteristic
239C22×C3×D3C2×D411yescharacteristic
240C32×Q8—21no—
241C32×Q8—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2411yescharacteristic
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249#634—21no—
250#634#4112yes—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C3×D12—22no—
258C3×C4×D3—21no—
259C3×C4×D3—21no—
260C3×C4×D3—21no—
261C3×C4×D3—21no—
262C3×C4×D3—42no—
263C3×Dic6—21no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267#627—42no—
268#627—42no—
269D3×Dic3—42no—
270D3×Dic3—42no—
271C3⋊(C3⋊C8)—21no—
272C3⋊(C3⋊C8)—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#552—31no—
276D4×Q8—91no—
277#491—91no—
278#485—91no—
279#483—91no—
280#479—91no—
281#470—91no—
282#467—91no—
283#462—31no—
284#451—91no—
285#451—91no—
286#441—91no—
287#435—91no—
288#419—91no—
289C2×#103—91no—
290C2×C3×Q8—21no—
291C2×C3×Q8—31no—
292C2×C3×Q8—31no—
293C2×C3×Q8C22×D311yescharacteristic
294C2×C3×Q8C22×D311yescharacteristic
295C2×C3×D4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—31no—
298C22×C3×C4—61no—
299C22×Dic3—61no—
300C22×Dic3—61no—
301D3×Q8—62no—
302D3×Q8—62no—
303D3×Q8—121no—
304D3×Q8—121no—
305C2×D12#6711yescharacteristic
306C2×C4×D3—21no—
307C2×C4×D3—61no—
308C2×C4×D3—61no—
309C2×C4×D3C22×D311yescharacteristic
310C2×C4×D3C22×D311yescharacteristic
311C2×Dic6—31no—
312C2×Dic6—31no—
313C2×Dic6—61no—
314C2×Dic6—62no—
315C2×Dic6—62no—
316C2×Dic6—61no—
317C2×Dic6—61no—
318C2×Dic6—61no—
319C2×Dic6—61no—
320C2×Dic6—121no—
321C2×Dic6—121no—
322C2×Dic6C22×D311yescharacteristic
323C2×Dic6C22×D311yescharacteristic
324C3×Q16—121no—
325C3×Q16—121no—
326C2×C3×C8—31no—
327C2×C3×C8—31no—
328C3×C4⋊C4—21no—
329C3×C4⋊C4—21no—
330C3×C4⋊C4—21no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—41no—
335C3×C4⋊C4—61no—
336C3×C4⋊C4—61no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4C22×D311yescharacteristic
343C3×C4⋊C4C22×D311yescharacteristic
344C3×C22⋊C4—31no—
345C3×C22⋊C4—31no—
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C42—21no—
350C3×C42—21no—
351C3×C42—21no—
352C3×C42—41no—
353C3×C42—61no—
354C3×C42C22×D311yescharacteristic
355C3×C42C22×D311yescharacteristic
356#217—61no—
357#217—61no—
358#216—41no—
359#216—41no—
360#216—62no—
361#216—62no—
362#216—64no—
363(C2×D3)⋊C4—21no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4#6711yescharacteristic
369(C2×D3)⋊C4#6711yescharacteristic
370C4⋊Dic3—21no—
371C4⋊Dic3—21no—
372C4⋊Dic3—31no—
373C4⋊Dic3—31no—
374C4⋊Dic3—61no—
375C4⋊Dic3#6711yescharacteristic
376C4⋊Dic3C22×D311yescharacteristic
377C4⋊Dic3C22×D311yescharacteristic
378Dic3⋊C4—21no—
379Dic3⋊C4—21no—
380Dic3⋊C4—21no—
381Dic3⋊C4—21no—
382Dic3⋊C4—21no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—121no—
390C4×Dic3—21no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—121no—
394#208—121no—
395C2×C3⋊C8—31no—
396C2×C3⋊C8—31no—
397C2×C3⋊C8—31no—
398C2×C3⋊C8—31no—
399C2×C3⋊C8—61no—
400C2×C3⋊C8—61no—
401C2×C3⋊C8—121no—
402C2×C3⋊C8C22×D311yescharacteristic
403C2×C3⋊C8C22×D311yescharacteristic
404ΓL(1,𝔽25)—121no—
405D3×C8—121no—
406C22×C32C22×D411yescharacteristic
407C2×C3×D3—21no—
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3#13712yes—
413C32×C4—21no—
414C32×C4—21no—
415C32×C4—41no—
416C32×C4—41no—
417C32×C4C2×#4111yescharacteristic
418C32×C4H(5,𝔽2)11yescharacteristic
419C3⋊Dic3—22no—
420C3⋊Dic3—41no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C22×Q8—91no—
428C22×Q8—91no—
429C2×Q16—31no—
430C2×Q16—31no—
431C2×Q16—91no—
432C2×M16—91no—
433C22×C8—91no—
434C4⋊Q8—31no—
435C4⋊Q8—181no—
436#126—61no—
437#125—31no—
438#125—61no—
439#123—61no—
440C22⋊Q8—31no—
441C22⋊Q8—31no—
442C22⋊Q8—91no—
443C22⋊Q8—91no—
444C22⋊Q8—181no—
445C22⋊Q8—181no—
446C4×Q8—91no—
447C4×Q8D3211yescharacteristic
448C4×D4—31no—
449C4×D4—181no—
450#117—31no—
451#117—61no—
452C2×C4⋊C4—31no—
453#107—91no—
454#106—91no—
455#106—91no—
456C4⋊C8—31no—
457#103—31no—
458#103—31no—
459#103—91no—
460#103—91no—
461#103—91no—
462#103—91no—
463#103—91no—
464#103—91no—
465#103—91no—
466#103—91no—
467C22⋊C8—91no—
468C22⋊C8—91no—
469#97—91no—
470C23×C3—31no—
471C23×C3—31no—
472C22×D3C2×#6711yescharacteristic
473C22×D3C2×#6711yescharacteristic
474C3×Q8—22no—
475C3×Q8—21no—
476C3×Q8—21no—
477C3×Q8—21no—
478C3×Q8—21no—
479C3×Q8—41no—
480C3×Q8—61no—
481C3×Q8—61no—
482C3×Q8—61no—
483C3×Q8—61no—
484C3×D4—62no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—31no—
493C2×C3×C4—31no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—122no—
505C2×C3×C4D3×D411yescharacteristic
506C2×C3×C4D3×D411yescharacteristic
507C2×C3×C4C2×#6711yescharacteristic
508C2×C3×C4C2×#6711yescharacteristic
509C2×C3×C4C23×D311yescharacteristic
510C2×C3×C4C23×D311yescharacteristic
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—61no—
516C2×Dic3—61no—
517C2×Dic3—61no—
518C2×Dic3—61no—
519C2×Dic3—121no—
520C2×Dic3—121no—
521C2×Dic3—122no—
522C2×Dic3—122no—
523C2×Dic3C2×#6711yescharacteristic
524C2×Dic3C2×#6711yescharacteristic
525D12—22no—
526C4×D3—21no—
527C4×D3—21no—
528C4×D3—21no—
529C4×D3—21no—
530C4×D3—42no—
531C4×D3—122no—
532C4×D3—122no—
533Dic6—21no—
534Dic6—21no—
535Dic6—21no—
536Dic6—21no—
537Dic6—32no—
538Dic6—32no—
539Dic6—62no—
540Dic6—61no—
541Dic6—61no—
542Dic6—121no—
543Dic6—122no—
544Dic6—122no—
545Dic6—122no—
546Dic6—122no—
547C3×C8—61no—
548C3×C8—61no—
549C3⋊C8—21no—
550C3⋊C8—21no—
551C3⋊C8—62no—
552C3⋊C8—61no—
553C3⋊C8—61no—
554C3⋊C8—61no—
555C3⋊C8—61no—
556C3⋊C8—121no—
557C2×C32#54611yescharacteristic
558C2×C32C2×#13711yescharacteristic
559C2×C32#57811yescharacteristic
560C3×D3—22no—
561C3×D3—41no—
562C2×Q8—31no—
563C2×Q8—31no—
564C2×Q8—91no—
565C2×Q8—181no—
566C2×Q8—181no—
567C2×Q8—182no—
568C2×Q8—182no—
569C2×Q8—361no—
570C2×Q8—361no—
571C2×Q8C2×D3211yescharacteristic
572C2×D4—31no—
573C22×C4—31no—
574C22×C4—31no—
575C22×C4—61no—
576C22×C4—181no—
577C22×C4—181no—
578Q16—121no—
579Q16—121no—
580Q16—182no—
581M16—361no—
582C2×C8—31no—
583C2×C8—31no—
584C2×C8—91no—
585C2×C8—91no—
586C2×C8—361no—
587C4⋊C4—21no—
588C4⋊C4—31no—
589C4⋊C4—31no—
590C4⋊C4—31no—
591C4⋊C4—61no—
592C4⋊C4—61no—
593C4⋊C4—61no—
594C4⋊C4—61no—
595C4⋊C4—61no—
596C4⋊C4—61no—
597C4⋊C4—61no—
598C4⋊C4—91no—
599C4⋊C4—181no—
600C4⋊C4—181no—
601C4⋊C4—181no—
602C4⋊C4C2×D3211yescharacteristic
603C22⋊C4—31no—
604C22⋊C4—31no—
605C22⋊C4—61no—
606C22⋊C4—61no—
607C22⋊C4—61no—
608C22⋊C4—181no—
609C22⋊C4—181no—
610C42—21no—
611C42—61no—
612C42—181no—
613C42C2×D3211yescharacteristic
614C22×C3—21no—
615C22×C3—32no—
616C22×C3—61no—
617C22×C3—61no—
618C22×C3—61no—
619C22×C3—61no—
620C22×C3—61no—
621C22×C3C2×D3×D411yescharacteristic
622C22×C3C22×#6711yescharacteristic
623C2×D3—21no—
624C2×D3—21no—
625C2×D3—21no—
626C2×D3—21no—
627C2×D3—21no—
628C2×D3#95112yes—
629C3×C4—21no—
630C3×C4—21no—
631C3×C4—21no—
632C3×C4—21no—
633C3×C4—21no—
634C3×C4—21no—
635C3×C4—41no—
636C3×C4—41no—
637C3×C4—42no—
638C3×C4—41no—
639C3×C4—41no—
640C3×C4—41no—
641C3×C4—41no—
642C3×C4—61no—
643C3×C4—61no—
644C3×C4—81no—
645C3×C4—121no—
646C3×C4—121no—
647C3×C4—121no—
648C3×C4—121no—
649C3×C4#100411yescharacteristic
650C3×C4D3×#4111yescharacteristic
651C3×C4D3×#4111yescharacteristic
652C3×C4#100911yescharacteristic
653Dic3—21no—
654Dic3—21no—
655Dic3—41no—
656Dic3—41no—
657Dic3—41no—
658Dic3—41no—
659Dic3—62no—
660Dic3—62no—
661Dic3—122no—
662Dic3—121no—
663Dic3—121no—
664Dic3—241no—
665C32#331211yescharacteristic, complemented, Sylow
666C23—31no—
667C23—31no—
668Q8—21no—
669Q8—21no—
670Q8—61no—
671Q8—61no—
672Q8—61no—
673Q8—61no—
674Q8—92no—
675Q8—181no—
676Q8—362no—
677Q8—362no—
678D4—62no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—31no—
682C2×C4—31no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—122no—
692C2×C4—181no—
693C2×C4—181no—
694C2×C4—362no—
695C2×C4—362no—
696C2×C4D3×#6711yescharacteristic
697C2×C4D3×#6711yescharacteristic
698C2×C4C22×D3211yescharacteristic
699C8—61no—
700C8—61no—
701C8—181no—
702C8—181no—
703C2×C3—21no—
704C2×C3—21no—
705C2×C3—21no—
706C2×C3—62no—
707C2×C3—121no—
708C2×C3#561211yescharacteristic
709C2×C3#576611yescharacteristic
710C2×C3D3×#13711yescharacteristic
711C2×C3C2×#95111yescharacteristic
712C2×C3#582911yescharacteristic
713C2×C3#583811yescharacteristic
714D3—22no—
715D3—41no—
716C22—32no—
717C22—61no—
718C22—61no—
719C22—61no—
720C22—61no—
721C22—61no—
722C22C2×D3×#6711yescharacteristic
723C4—21no—
724C4—21no—
725C4—41no—
726C4—41no—
727C4—61no—
728C4—61no—
729C4—121no—
730C4—121no—
731C4—121no—
732C4—121no—
733C4—182no—
734C4—361no—
735C4#6430611yescharacteristic
736C4#6430711yescharacteristic
737C3—21no—
738C3#8049311yescharacteristic, complemented
739C3#8360311yescharacteristic, complemented
740C2—62no—
741C2—121no—
742C2#1059507011yescharacteristic
743C2#1059532711yescharacteristic
744C2D3×#95111yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×C3×D12D4
hypercenterC4×Q8D32
hypocenterC32#3312
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
3. #10592729C2semidirect
4. C3×#5031C2semidirect
5. #10591653C2semidirect
6. #10591653C2semidirect
7. #10591638C2semidirect
8. #10591635C2semidirect
9. #10590600C2semidirect
10. D3×#810C2semidirect
11. #10590519C2semidirect
12. #10590516C2semidirect
14. #10590292C2semidirect
15. #10590291C2semidirect
77. #5031D3semidirect
665. C32#3312semidirect
738. C3#80493semidirect
739. C3#83603semidirect

Maximal subgroups

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

subgroupindex
C3×#55812
#105939042
#105927292
C3×#50312
#105916532
#105916382
#105916352
#105906002
D3×#8102
#105905192
#105905162
#105903302
#105902922
#105902912
#836033
#804933