Finite Group Databasebeta

← #11889435

Subgroups — #11889435

Order 1152.

814 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
1#10593947C211yesmaximal, characteristic
2#10593903C211yesmaximal, characteristic
3#10592535C211yesmaximal, characteristic
4C3×#4849C211yesmaximal, characteristic, complemented
5C3×#4829C211yesmaximal, characteristic, complemented
6#10590950C211yesmaximal, characteristic, complemented
7#10590950C211yesmaximal, characteristic, complemented
8#10590858C211yesmaximal, characteristic, complemented
9#10590857C211yesmaximal, characteristic, complemented
10#10590715C211yesmaximal, characteristic, complemented
11#10590691C211yesmaximal, characteristic, complemented
12#10590686C211yesmaximal, characteristic, complemented
13#10590672C211yesmaximal, characteristic, complemented
14#10590381C211yesmaximal, characteristic, complemented
15#10590291C211yesmaximal, characteristic, complemented
16#81248—31nomaximal
17#80493—31nomaximal
18C2×#3797C2211yescharacteristic
19C2×#3797C2211yescharacteristic
20C2×#3743C2211yescharacteristic
21C2×C8×C3⋊D3C2211yescharacteristic
22C4×C4⋊(C3⋊D3)C2211yescharacteristic
23C2×C3×Dic12C2211yescharacteristic
24C2×C3×Dic12C2211yescharacteristic
25C3×#870C2211yescharacteristic
26C3×#869C2211yescharacteristic
27C3×C4×Dic6C2211yescharacteristic
28C3×C4×Dic6C2211yescharacteristic
29#63918—21no—
30#63900C2211yescharacteristic
31#63897—21no—
32#63895—21no—
33#63895—21no—
34#63894—21no—
35#63871C2211yescharacteristic
36#63871C2211yescharacteristic
37#63871C2211yescharacteristic
38#63871C2211yescharacteristic
39#63868—21no—
40#63849C2211yescharacteristic
41#63845—21no—
42#63836—21no—
43C2×#3718C2211yescharacteristic
44C32×C4⋊C8C2211yescharacteristic
45#63647C2211yescharacteristic
46#63647C2211yescharacteristic
47#63630C2211yescharacteristic
48C3×#818C2211yescharacteristic
49C3×#817C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×#816C2211yescharacteristic
54#63574C2211yescharacteristic
55#63565C2211yescharacteristic
56#63565C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59#63565C2211yescharacteristic
60#63565C2211yescharacteristic
61#5727—31no—
62#5694—31no—
63#5581—31no—
64Q8×D12—31no—
65C3×#479—31no—
66C3×#462—31no—
67#5189—31no—
68#5188—31no—
69#5186—31no—
70#5186—31no—
71#5082—31no—
72#5069—31no—
73#5030—31no—
74#5030—31no—
75#4888—31no—
76#4887—31no—
77#4867—31no—
78#4862—31no—
79#4849D311yescharacteristic, complemented
80#4836—31no—
81#4836—31no—
82#4836—61no—
83#4829D311yescharacteristic, complemented
84#4814—31no—
85#4809—31no—
86#4809—31no—
87#4805—31no—
88#4802—31no—
89#4802—31no—
90D3×#103—31no—
91D3×#103—31no—
92C2×C4⋊(C3⋊D3)D411yescharacteristic
93C2×C4×C3⋊D3C2311yescharacteristic
94C2×C4×C3⋊D3C2311yescharacteristic
95C2×C3×Dic6C2311yescharacteristic
96C2×C3×Dic6C2311yescharacteristic
97C2×C3×Dic6C2311yescharacteristic
98C2×C3×Dic6C2311yescharacteristic
99C2×#627—21no—
100C2×#627—21no—
101C2×#624—21no—
102C2×#624—21no—
103C2×#624—21no—
104#3797—22no—
105#3797—22no—
106#3797—41no—
107#3797—41no—
108C2×C32×C8C2311yescharacteristic
109C2×C32×C8C2311yescharacteristic
110C32×C42C2311yescharacteristic
111#3752D411yescharacteristic
112#3752D411yescharacteristic
113C4⋊(C3⋊Dic3)D411yescharacteristic
114C2×C3⋊(C3⋊C8)C2311yescharacteristic
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116#3743—41no—
117C8×C3⋊D3—41no—
118C3×C4⋊Dic3—21no—
119C3×C4⋊Dic3—21no—
120C3×C4⋊Dic3C2311yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×C4×Dic3—21no—
129C3×C4×Dic3—21no—
130C3×Dic12—41no—
131C3×Dic12—41no—
132#3724—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137#3722—21no—
138#3722—21no—
139#3722—21no—
140#3722—21no—
141#3722—21no—
142Dic32—21no—
143#3718—22no—
144#3312—91noSylow
145C2×D3×Q8—31no—
146C2×D3×Q8—31no—
147C2×D3×Q8—31no—
148C2×D3×Q8—31no—
149C2×C3×Q16—31no—
150C2×C3×Q16—31no—
151C3×C4⋊Q8—31no—
152C3×#125—31no—
153C3×C4×Q8—31no—
154C3×C4×Q8—31no—
155#946—31no—
156#946—31no—
157#946—31no—
158#946—31no—
159C2×#216—31no—
160C2×#216—31no—
161C2×Dic12C2×D311yescharacteristic
162C2×Dic12C2×D311yescharacteristic
163C2×ΓL(1,𝔽25)—31no—
164C2×ΓL(1,𝔽25)—31no—
165C2×ΓL(1,𝔽25)—61no—
166C2×D3×C8—31no—
167C2×D3×C8—31no—
168C2×D3×C8—61no—
169#898—61no—
170#897—31no—
171#897—31no—
172#897—31no—
173#897—31no—
174#897—61no—
175#897—61no—
176#896—61no—
177#896—61no—
178#894—61no—
179#894—61no—
180#893—61no—
181#892—31no—
182#892—31no—
183#892—61no—
184D3×C4⋊C4—31no—
185D3×C4⋊C4—31no—
186#890—61no—
187#889—61no—
188#888—61no—
189#876—61no—
190C4×D12—31no—
191C4×D12—31no—
192C4×D12—61no—
193C4×D12—61no—
194#872—61no—
195#870C2×D311yescharacteristic
196#869—61no—
197#869C2×D311yescharacteristic
198C4×Dic6C2×D311yescharacteristic
199C4×Dic6C2×D311yescharacteristic
200C3×#107—31no—
201C3×#106—31no—
202C3×C4⋊C8—21no—
203C3×C4⋊C8C2×D311yescharacteristic
204C3×C4⋊C8C2×D311yescharacteristic
205C3×#103—31no—
206C3×#103—31no—
207C3×#103—31no—
208C3×#103—31no—
209#835—31no—
210#835—31no—
211#835—31no—
212#835—31no—
213#835—31no—
214#835—31no—
215(C2×D3)⋊C8—31no—
216(C2×D3)⋊C8—31no—
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—61no—
220(C2×D3)⋊C8—61no—
221#818C2×D311yescharacteristic
222#817C2×D311yescharacteristic
223#816C2×D311yescharacteristic
224#816C2×D311yescharacteristic
225#816C2×D311yescharacteristic
226#816C2×D311yescharacteristic
227#810—31no—
228#810—31no—
229#810—31no—
230#810—31no—
231#810—31no—
232#810—31no—
233#808—31no—
234#808—31no—
235#803—31no—
236#803—31no—
237#803—61no—
238C22×C3⋊D3C2×D411yescharacteristic
239C22×C3⋊D3C2×D411yescharacteristic
240C2×C32×C4C2×D411yescharacteristic
241C2×C32×C4C2×D411yescharacteristic
242C2×C32×C4C2411yescharacteristic
243C2×C3⋊Dic3C2×D411yescharacteristic
244C2×C3⋊Dic3C2×D411yescharacteristic
245C4⋊(C3⋊D3)—22no—
246C4×C3⋊D3—21no—
247C4×C3⋊D3—21no—
248C4×C3⋊D3—21no—
249C4×C3⋊D3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C3×Dic6—21no—
259C3×Dic6—21no—
260C3×Dic6—21no—
261C3×Dic6—21no—
262C3×Dic6—21no—
263C3×Dic6—21no—
264C3×Dic6—21no—
265C3×Dic6#4112yes—
266#627—42no—
267#627—42no—
268#624—42no—
269#624—42no—
270#624—42no—
271C32×C8—21no—
272C32×C8—21no—
273C3⋊(C3⋊C8)—21no—
274C3⋊(C3⋊C8)—21no—
275#552—91no—
276D4×Q8—91no—
277#491—91no—
278#485—91no—
279#483—91no—
280#479—31no—
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—31no—
291C2×C3×Q8—31no—
292C2×C3×Q8—31no—
293C2×C3×Q8—31no—
294D3×Q8—62no—
295D3×Q8—62no—
296D3×Q8—62no—
297D3×Q8—62no—
298D3×Q8—121no—
299D3×Q8—121no—
300D3×Q8—121no—
301D3×Q8—121no—
302C2×D12—31no—
303C2×D12—31no—
304C2×D12—61no—
305C2×C4×D3—31no—
306C2×C4×D3—31no—
307C2×C4×D3—31no—
308C2×C4×D3—31no—
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—61no—
317C2×Dic6—61no—
318C2×Dic6—61no—
319C2×Dic6—61no—
320C2×Dic6—61no—
321C2×Dic6C22×D311yescharacteristic
322C2×Dic6C22×D311yescharacteristic
323C2×Dic6C22×D311yescharacteristic
324C2×Dic6C22×D311yescharacteristic
325C3×Q16—121no—
326C3×Q16—121no—
327C2×C3×C8—21no—
328C2×C3×C8—21no—
329C2×C3×C8C22×D311yescharacteristic
330C2×C3×C8C22×D311yescharacteristic
331C2×C3×C8C22×D311yescharacteristic
332C2×C3×C8C22×D311yescharacteristic
333C3×C4⋊C4—31no—
334C3×C4⋊C4—31no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4—61no—
343C3×C42—21no—
344C3×C42—61no—
345C3×C42—61no—
346C3×C42C22×D311yescharacteristic
347C3×C42C22×D311yescharacteristic
348#216—62no—
349#216—62no—
350(C2×D3)⋊C4—31no—
351(C2×D3)⋊C4—31no—
352(C2×D3)⋊C4—31no—
353(C2×D3)⋊C4—31no—
354(C2×D3)⋊C4—61no—
355(C2×D3)⋊C4—61no—
356(C2×D3)⋊C4—61no—
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—
366C4⋊Dic3—21no—
367C4⋊Dic3—21no—
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
378C4⋊Dic3C22×D311yescharacteristic
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—
389C4×Dic3—21no—
390C4×Dic3—21no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C2×C3⋊C8—31no—
394C2×C3⋊C8—31no—
395C2×C3⋊C8—31no—
396C2×C3⋊C8—31no—
397C2×C3⋊C8—61no—
398C2×C3⋊C8—61no—
399Dic12—41no—
400Dic12—41no—
401ΓL(1,𝔽25)—121no—
402ΓL(1,𝔽25)—121no—
403ΓL(1,𝔽25)—122no—
404D3×C8—121no—
405D3×C8—121no—
406D3×C8—122no—
407C22×C32C22×D411yescharacteristic
408C2×C3⋊D3—21no—
409C2×C3⋊D3—21no—
410C2×C3⋊D3—21no—
411C2×C3⋊D3—21no—
412C2×C3⋊D3—21no—
413C2×C3⋊D3#13712yes—
414C32×C4—21no—
415C32×C4—21no—
416C32×C4C2×#4111yescharacteristic
417C32×C4H(5,𝔽2)11yescharacteristic
418C3⋊Dic3—21no—
419C3⋊Dic3—21no—
420C3×Dic3—22no—
421C3×Dic3—41no—
422C3×Dic3—41no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C22×Q8—91no—
429C22×Q8—91no—
430C2×Q16—31no—
431C2×Q16—31no—
432C2×Q16—91no—
433C2×M16—91no—
434C22×C8—91no—
435C4⋊Q8—31no—
436C4⋊Q8—181no—
437#126—181no—
438#125—31no—
439#125—181no—
440#123—181no—
441C22⋊Q8—91no—
442C22⋊Q8—91no—
443C22⋊Q8—91no—
444C22⋊Q8—91no—
445C22⋊Q8—181no—
446C22⋊Q8—181no—
447C4×Q8—31no—
448C4×Q8—31no—
449C4×D4—91no—
450C4×D4—181no—
451#117—91no—
452#117—181no—
453C2×C4⋊C4—91no—
454#107—31no—
455#106—31no—
456#106—91no—
457C4⋊C8D3211yescharacteristic
458#103—31no—
459#103—31no—
460#103—31no—
461#103—31no—
462#103—91no—
463#103—91no—
464#103—91no—
465#103—91no—
466#103—91no—
467#103—91no—
468C22⋊C8—91no—
469C22⋊C8—91no—
470#97—91no—
471C22×D3—31no—
472C22×D3—31no—
473C22×D3—31no—
474C22×D3—31no—
475C22×D3—61no—
476C22×D3—61no—
477C3×Q8—32no—
478C3×Q8—61no—
479C3×Q8—61no—
480C3×Q8—61no—
481C3×Q8—61no—
482C3×Q8—61no—
483C3×Q8—61no—
484C3×Q8—61no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—61no—
489C2×C3×C4—61no—
490C2×C3×C4—61no—
491C2×C3×C4—61no—
492C2×C3×C4—61no—
493C2×C3×C4—61no—
494C2×C3×C4—61no—
495C2×C3×C4—61no—
496C2×C3×C4D3×D411yescharacteristic
497C2×C3×C4D3×D411yescharacteristic
498C2×C3×C4D3×D411yescharacteristic
499C2×C3×C4D3×D411yescharacteristic
500C2×C3×C4C23×D311yescharacteristic
501C2×C3×C4C23×D311yescharacteristic
502C2×Dic3—21no—
503C2×Dic3—21no—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—21no—
507C2×Dic3—21no—
508C2×Dic3—21no—
509C2×Dic3—21no—
510C2×Dic3—31no—
511C2×Dic3—31no—
512C2×Dic3—31no—
513C2×Dic3—31no—
514C2×Dic3—61no—
515C2×Dic3—61no—
516D12—62no—
517D12—62no—
518D12—122no—
519C4×D3—61no—
520C4×D3—61no—
521C4×D3—61no—
522C4×D3—61no—
523C4×D3—61no—
524C4×D3—61no—
525C4×D3—61no—
526C4×D3—61no—
527C4×D3—121no—
528C4×D3—121no—
529C4×D3—121no—
530C4×D3—121no—
531C4×D3—122no—
532C4×D3—122no—
533C4×D3—122no—
534C4×D3—122no—
535C4×D3—122no—
536C4×D3—122no—
537Dic6—21no—
538Dic6—21no—
539Dic6—21no—
540Dic6—21no—
541Dic6—21no—
542Dic6—21no—
543Dic6—21no—
544Dic6—122no—
545Dic6—122no—
546Dic6—122no—
547Dic6—122no—
548Dic6#23912yes—
549C3×C8—21no—
550C3×C8—21no—
551C3×C8—21no—
552C3×C8—21no—
553C3×C8—41no—
554C3×C8—41no—
555C3⋊C8—62no—
556C3⋊C8—61no—
557C3⋊C8—61no—
558C3⋊C8—61no—
559C3⋊C8—61no—
560C3⋊C8—121no—
561C2×C32#54611yescharacteristic
562C2×C32C2×#13711yescharacteristic
563C2×C32#57811yescharacteristic
564C3⋊D3—22no—
565C3⋊D3—41no—
566C2×Q8—31no—
567C2×Q8—31no—
568C2×Q8—31no—
569C2×Q8—31no—
570C2×Q8—181no—
571C2×Q8—181no—
572C2×Q8—182no—
573C2×Q8—182no—
574C2×Q8—361no—
575C2×Q8—361no—
576C2×D4—91no—
577C22×C4—91no—
578C22×C4—91no—
579C22×C4—181no—
580C22×C4—181no—
581C22×C4—181no—
582Q16—121no—
583Q16—121no—
584Q16—182no—
585M16—361no—
586C2×C8—91no—
587C2×C8—91no—
588C2×C8—361no—
589C2×C8C2×D3211yescharacteristic
590C2×C8C2×D3211yescharacteristic
591C4⋊C4—31no—
592C4⋊C4—31no—
593C4⋊C4—31no—
594C4⋊C4—31no—
595C4⋊C4—61no—
596C4⋊C4—61no—
597C4⋊C4—61no—
598C4⋊C4—61no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4—91no—
602C4⋊C4—181no—
603C4⋊C4—181no—
604C4⋊C4—181no—
605C4⋊C4—181no—
606C4⋊C4—181no—
607C22⋊C4—91no—
608C22⋊C4—91no—
609C22⋊C4—181no—
610C22⋊C4—181no—
611C22⋊C4—181no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C42—61no—
615C42—61no—
616C42—181no—
617C42C2×D3211yescharacteristic
618C22×C3—21no—
619C22×C3C2×D3×D411yescharacteristic
620C22×C3C2×D3×D411yescharacteristic
621C2×D3—32no—
622C2×D3—32no—
623C2×D3—62no—
624C2×D3—61no—
625C2×D3—61no—
626C2×D3—61no—
627C2×D3—61no—
628C2×D3—61no—
629C2×D3—61no—
630C2×D3—61no—
631C2×D3—61no—
632C2×D3—61no—
633C2×D3—61no—
634C2×D3—121no—
635C2×D3—121no—
636C2×D3—121no—
637C2×D3—121no—
638C2×D3—121no—
639C3×C4—21no—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—21no—
644C3×C4—21no—
645C3×C4—41no—
646C3×C4—41no—
647C3×C4—62no—
648C3×C4—121no—
649C3×C4—121no—
650C3×C4—121no—
651C3×C4—121no—
652C3×C4—121no—
653C3×C4—121no—
654C3×C4—121no—
655C3×C4#100411yescharacteristic
656C3×C4C2×#23911yescharacteristic
657C3×C4D3×#4111yescharacteristic
658C3×C4#100911yescharacteristic
659Dic3—22no—
660Dic3—41no—
661Dic3—41no—
662Dic3—41no—
663Dic3—41no—
664Dic3—41no—
665Dic3—41no—
666Dic3—41no—
667Dic3—61no—
668Dic3—61no—
669Dic3—61no—
670Dic3—61no—
671Dic3—121no—
672Dic3—121no—
673C32#331211yescharacteristic, complemented, Sylow
674C23—91no—
675C23—91no—
676Q8—32no—
677Q8—61no—
678Q8—61no—
679Q8—61no—
680Q8—61no—
681Q8—61no—
682Q8—61no—
683Q8—61no—
684Q8—362no—
685Q8—362no—
686D4—182no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—91no—
696C2×C4—91no—
697C2×C4—181no—
698C2×C4—181no—
699C2×C4—181no—
700C2×C4—181no—
701C2×C4—362no—
702C2×C4—362no—
703C2×C4—362no—
704C2×C4#380211yescharacteristic
705C2×C4#380211yescharacteristic
706C2×C4C22×D3211yescharacteristic
707C8—21no—
708C8—21no—
709C8—181no—
710C8—181no—
711C2×C3—21no—
712C2×C3—21no—
713C2×C3—21no—
714C2×C3#561211yescharacteristic
715C2×C3#563011yescharacteristic
716C2×C3#576611yescharacteristic
717C2×C3#577111yescharacteristic
718C2×C3D3×#13711yescharacteristic
719C2×C3D3×#13711yescharacteristic
720D3—62no—
721D3—62no—
722D3—122no—
723D3—121no—
724D3—121no—
725D3—241no—
726C22—92no—
727C22—181no—
728C22—181no—
729C22—181no—
730C22—181no—
731C22—181no—
732C22C2×#380211yescharacteristic
733C4—21no—
734C4—21no—
735C4—62no—
736C4—121no—
737C4—121no—
738C4—121no—
739C4—121no—
740C4—121no—
741C4—121no—
742C4—121no—
743C4—181no—
744C4—181no—
745C4#6431411yescharacteristic
746C4D3×#23911yescharacteristic
747C3—21no—
748C3#8049311yescharacteristic, complemented
749C3#8124811yescharacteristic, complemented
750C2—182no—
751C2—361no—
752C2#1059463311yescharacteristic
753C2#1059470311yescharacteristic
754C2#1059471711yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC2×C4⋊(C3⋊D3)D4
hypercenterC4⋊C8D32
hypocenterC32#3312
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
4. C3×#4849C2semidirect
5. C3×#4829C2semidirect
6. #10590950C2semidirect
7. #10590950C2semidirect
8. #10590858C2semidirect
9. #10590857C2semidirect
10. #10590715C2semidirect
11. #10590691C2semidirect
12. #10590686C2semidirect
13. #10590672C2semidirect
14. #10590381C2semidirect
15. #10590291C2semidirect
79. #4849D3semidirect
83. #4829D3semidirect
673. C32#3312semidirect
748. C3#80493semidirect
749. C3#81248semidirect

Maximal subgroups

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

subgroupindex
#105939472
#105939032
#105925352
C3×#48492
C3×#48292
#105909502
#105908582
#105908572
#105907152
#105906912
#105906862
#105906722
#105903812
#105902912
#812483
#804933