Finite Group Databasebeta

← #11889395

Subgroups — #11889395

Order 1152.

827 conjugacy classes of subgroups.

The subgroup lattice has 755 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#626C211yesmaximal, characteristic
2#10594457C211yesmaximal, characteristic
3#10592501C211yesmaximal, characteristic, complemented
4C3×#4809C211yesmaximal, characteristic, complemented
5C3×#4799C211yesmaximal, characteristic, complemented
6#10591603C211yesmaximal, characteristic, complemented
7#10591576C211yesmaximal, characteristic, complemented
8D3×#835C211yesmaximal, characteristic, complemented
9#10590907C211yesmaximal, characteristic
10#10590858C211yesmaximal, characteristic, complemented
11#10590800C211yesmaximal, characteristic, complemented
12#10590674C211yesmaximal, characteristic, complemented
13#10590579C211yesmaximal, characteristic, complemented
14#10590562C211yesmaximal, characteristic, complemented
15#10590526C211yesmaximal, characteristic, complemented
16#81248—31nomaximal
17#80195—31nomaximal
18C2×Q8×C3⋊D3C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×#3743C2211yescharacteristic
21#64101C2211yescharacteristic
22C3×Q8×Dic3C2211yescharacteristic
23C2×C3×#216C2211yescharacteristic
24C2×C3×Dic12C2211yescharacteristic
25C3×#897C2211yescharacteristic
26C3×#890C2211yescharacteristic
27C4×#626—21no—
28C4×#626C2211yescharacteristic
29#63890—21no—
30D3×C4⋊Dic3C2211yescharacteristic
31#63878—21no—
32#63872—21no—
33#63871—21no—
34#63871C2211yescharacteristic
35#63871C2211yescharacteristic
36#63866—21no—
37#63866C2211yescharacteristic
38#63857—21no—
39#63857C2211yescharacteristic
40#63848—21no—
41Dic3×Dic6C2211yescharacteristic
42C2×#3719C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44C32×#103C2211yescharacteristic
45#63662C2211yescharacteristic
46#63643C2211yescharacteristic
47#63637C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×#817C2211yescharacteristic
51C3×Dic3⋊C8C2211yescharacteristic
52C3×#810C2211yescharacteristic
53C3×#807C2211yescharacteristic
54#63573C2211yescharacteristic
55#63567C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59#63557C2211yescharacteristic
60#63554C2211yescharacteristic
61Q8×#67—31no—
62#5694—31no—
63#5642—31no—
64Q8×D12—31no—
65C3×#479—31no—
66C3×#451—31no—
67C2×#835—31no—
68#5189—31no—
69#5186—31no—
70#5184—31no—
71#5182—31no—
72#5069—31no—
73#5051—31no—
74#5030—31no—
75#4888—31no—
76#4887—31no—
77#4867—31no—
78#4862—31no—
79#4849—31no—
80#4836—31no—
81#4815—31no—
82#4809—31no—
83#4809D311yescharacteristic, complemented
84#4802—31no—
85#4802—31no—
86#4802—61no—
87D3×#103—31no—
88#4799D311yescharacteristic, complemented
89#4797—31no—
90#4730—31no—
91#4721—31no—
92C2×C32×Q8C2311yescharacteristic
93Q8×C3⋊D3—22no—
94Q8×C3⋊D3—41no—
95C2×C4×C3⋊D3—21no—
96C2×C4×C3⋊D3C2311yescharacteristic
97C2×#634—21no—
98C2×#634C2311yescharacteristic
99C3×D3×Q8—22no—
100C3×D3×Q8—41no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6—21no—
104C2×C3×Dic6C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×#626D411yescharacteristic
107C2×D3×Dic3—21no—
108C2×C32×C8C2311yescharacteristic
109C32×C4⋊C4C2311yescharacteristic
110#3752—21no—
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112C4×C3⋊Dic3—21no—
113C2×C3⋊(C3⋊C8)C2311yescharacteristic
114#3743—41no—
115C3×#216—22no—
116C3×(C2×D3)⋊C4—21no—
117C3×C4⋊Dic3—21no—
118C3×C4⋊Dic3—21no—
119C3×C4⋊Dic3—21no—
120C3×C4⋊Dic3C2311yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×Dic3⋊C4—21no—
123C3×C4×Dic3—21no—
124C3×C4×Dic3C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127C3×Dic12—41no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3D411yescharacteristic
136#3722—21no—
137#3722—21no—
138#3722D411yescharacteristic
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3D411yescharacteristic
141Dic32—21no—
142#3719—41no—
143D3×C3⋊C8—41no—
144#3312—91noSylow
145C22×C3×Q8—31no—
146C2×D3×Q8—31no—
147C2×D3×Q8—31no—
148C2×D3×Q8—61no—
149C2×D3×Q8C2×D311yescharacteristic
150C2×C3×Q16—31no—
151C2×C3×Q16—31no—
152C3×#125—31no—
153C3×C22⋊Q8—31no—
154C3×C4×Q8—31no—
155#946—31no—
156#946—31no—
157#946—61no—
158Q8×Dic3—31no—
159Q8×Dic3C2×D311yescharacteristic
160#944—31no—
161#944—61no—
162C2×#216—31no—
163C2×#216C2×D311yescharacteristic
164C4×#67—31no—
165C4×#67—61no—
166C2×C4⋊Dic3—31no—
167#924—31no—
168#924—61no—
169C22×C3⋊C8—31no—
170C2×Dic12—31no—
171C2×Dic12C2×D311yescharacteristic
172C2×ΓL(1,𝔽25)—31no—
173C2×ΓL(1,𝔽25)—31no—
174C2×ΓL(1,𝔽25)—61no—
175C2×D3×C8—31no—
176#898—61no—
177#898—61no—
178#897—31no—
179#897—31no—
180#897—31no—
181#897—61no—
182#897—61no—
183#897C2×D311yescharacteristic
184#894—61no—
185#892—31no—
186#892—31no—
187#892—61no—
188#892—61no—
189D3×C4⋊C4—31no—
190#890—61no—
191#890—61no—
192#890C2×D311yescharacteristic
193#886—61no—
194#877—61no—
195C4×D12—31no—
196C4×D12—61no—
197#869—31no—
198#869—61no—
199C4×Dic6—31no—
200C3×#107—31no—
201C3×#106—31no—
202C3×C4⋊C8—31no—
203C3×#103—21no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#103C2×D311yescharacteristic
207C3×#103C2×D311yescharacteristic
208C3×C22⋊C8—31no—
209#835—31no—
210#835—31no—
211#835—31no—
212#835—31no—
213#835—31no—
214#835—61no—
215#835C2×D311yescharacteristic
216(C2×D3)⋊C8—31no—
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8C2×D311yescharacteristic
219#817—31no—
220#817C2×D311yescharacteristic
221#816—31no—
222#816—31no—
223#816—31no—
224#816—31no—
225#816—61no—
226#815—31no—
227Dic3⋊C8C2×D311yescharacteristic
228#810—31no—
229#810—31no—
230#810—31no—
231#810—31no—
232#810—31no—
233#810—61no—
234#810C2×D311yescharacteristic
235#808—31no—
236#807C2×D311yescharacteristic
237#803—31no—
238C22×C3⋊D3C2×D411yescharacteristic
239C22×C3×D3C2×D411yescharacteristic
240C32×Q8—21no—
241C32×Q8#4112yes—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C2411yescharacteristic
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3C2×D411yescharacteristic
248C4×C3⋊D3—21no—
249C4×C3⋊D3—21no—
250C4×C3⋊D3—42no—
251#634—21no—
252#634—21no—
253#634—42no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×C4×D3—21no—
262C3×C4×D3—21no—
263C3×C4×D3—42no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C3×Dic6—42no—
269#626—22no—
270D3×Dic3—42no—
271C32×C8—21no—
272C3⋊(C3⋊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—91no—
284#451—31no—
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×Q8—61no—
294C2×C3×Q8—62no—
295C2×C3×Q8—121no—
296C2×C3×Q8C22×D311yescharacteristic
297C2×C3×Q8C22×D311yescharacteristic
298C22×C3×C4—31no—
299C22×C3×C4—61no—
300C2×#67—31no—
301C22×Dic3—61no—
302D3×Q8—22no—
303D3×Q8—41no—
304D3×Q8—64no—
305D3×Q8—62no—
306D3×Q8—62no—
307D3×Q8—121no—
308D3×Q8—121no—
309D3×Q8—122no—
310C2×D12—31no—
311C2×C4×D3—21no—
312C2×C4×D3—31no—
313C2×C4×D3—31no—
314C2×C4×D3—61no—
315C2×C4×D3—61no—
316C2×C4×D3—61no—
317C2×C4×D3—61no—
318C2×C4×D3—121no—
319C2×C4×D3C22×D311yescharacteristic
320C2×Dic6—21no—
321C2×Dic6—31no—
322C2×Dic6—31no—
323C2×Dic6—61no—
324C2×Dic6—61no—
325C2×Dic6—61no—
326C2×Dic6—121no—
327C2×Dic6C22×D311yescharacteristic
328C2×Dic6C22×D311yescharacteristic
329C3×Q16—62no—
330C3×Q16—121no—
331C2×C3×C8—21no—
332C2×C3×C8—31no—
333C2×C3×C8—31no—
334C2×C3×C8C22×D311yescharacteristic
335C2×C3×C8C22×D311yescharacteristic
336C3×C4⋊C4—21no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4C22×D311yescharacteristic
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C22⋊C4—61no—
346C3×C42—31no—
347C3×C42—61no—
348#217—31no—
349#217—61no—
350#216—22no—
351#216—121no—
352(C2×D3)⋊C4—21no—
353(C2×D3)⋊C4—31no—
354(C2×D3)⋊C4—31no—
355(C2×D3)⋊C4—31no—
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—121no—
364C4⋊Dic3—21no—
365C4⋊Dic3—21no—
366C4⋊Dic3—21no—
367C4⋊Dic3—31no—
368C4⋊Dic3—31no—
369C4⋊Dic3—31no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3C22×D311yescharacteristic
379C4⋊Dic3C22×D311yescharacteristic
380Dic3⋊C4—21no—
381Dic3⋊C4—31no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389C4×Dic3—21no—
390C4×Dic3—61no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—121no—
395C4×Dic3C22×D311yescharacteristic
396C2×C3⋊C8—31no—
397C2×C3⋊C8—31no—
398C2×C3⋊C8—61no—
399C2×C3⋊C8—121no—
400C2×C3⋊C8C22×D311yescharacteristic
401C2×C3⋊C8C22×D311yescharacteristic
402Dic12—41no—
403Dic12—121no—
404ΓL(1,𝔽25)—121no—
405ΓL(1,𝔽25)—121no—
406ΓL(1,𝔽25)—122no—
407D3×C8—121no—
408C22×C32C22×D411yescharacteristic
409C2×C3⋊D3—21no—
410C2×C3⋊D3—21no—
411C2×C3⋊D3—21no—
412C2×C3×D3—21no—
413C2×C3×D3—21no—
414C2×C3×D3#13712yes—
415C32×C4—22no—
416C32×C4—41no—
417C32×C4C2×#4111yescharacteristic
418C32×C4H(5,𝔽2)11yescharacteristic
419C3⋊Dic3—21no—
420C3⋊Dic3—41no—
421C3⋊Dic3—41no—
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3—21no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C22×Q8—31no—
430C22×Q8—91no—
431C2×Q16—31no—
432C2×Q16—31no—
433C2×Q16—91no—
434C2×M16—91no—
435C22×C8—91no—
436C4⋊Q8—91no—
437C4⋊Q8—181no—
438#126—181no—
439#125—31no—
440#125—181no—
441#123—181no—
442C22⋊Q8—31no—
443C22⋊Q8—91no—
444C22⋊Q8—91no—
445C22⋊Q8—91no—
446C22⋊Q8—181no—
447C22⋊Q8—181no—
448C4×Q8—31no—
449C4×Q8—91no—
450C4×D4—91no—
451C4×D4—181no—
452#117—91no—
453#117—181no—
454C2×C4⋊C4—91no—
455#107—31no—
456#106—31no—
457#106—91no—
458C4⋊C8—31no—
459#103—31no—
460#103—31no—
461#103—91no—
462#103—91no—
463#103—91no—
464#103—91no—
465#103—91no—
466#103—91no—
467#103—91no—
468#103D3211yescharacteristic
469C22⋊C8—31no—
470C22⋊C8—91no—
471#97—91no—
472C23×C3—31no—
473C22×D3—31no—
474C22×D3—31no—
475C22×D3—61no—
476C22×D3D3×D411yescharacteristic
477C3×Q8—21no—
478C3×Q8—21no—
479C3×Q8—22no—
480C3×Q8—41no—
481C3×Q8—61no—
482C3×Q8—61no—
483C3×Q8—61no—
484C3×Q8—61no—
485C3×Q8—122no—
486C3×Q8#23712yes—
487C3×Q8#23912yes—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—31no—
494C2×C3×C4—31no—
495C2×C3×C4—31no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
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×C4C23×D311yescharacteristic
506C2×C3×C4C23×D311yescharacteristic
507#67—62no—
508C2×Dic3—21no—
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—31no—
513C2×Dic3—31no—
514C2×Dic3—61no—
515C2×Dic3—61no—
516C2×Dic3—61no—
517C2×Dic3—61no—
518C2×Dic3—61no—
519C2×Dic3—121no—
520C2×Dic3—121no—
521C2×Dic3—122no—
522C2×Dic3D3×D411yescharacteristic
523C2×Dic3D3×D411yescharacteristic
524C2×Dic3D3×D411yescharacteristic
525D12—62no—
526C4×D3—21no—
527C4×D3—21no—
528C4×D3—42no—
529C4×D3—62no—
530C4×D3—62no—
531C4×D3—61no—
532C4×D3—61no—
533C4×D3—61no—
534C4×D3—61no—
535C4×D3—122no—
536C4×D3—122no—
537C4×D3—124no—
538C4×D3—122no—
539Dic6—21no—
540Dic6—21no—
541Dic6—21no—
542Dic6—21no—
543Dic6—42no—
544Dic6—62no—
545Dic6—61no—
546Dic6—61no—
547Dic6—61no—
548Dic6—61no—
549Dic6—121no—
550Dic6—122no—
551Dic6—122no—
552Dic6—124no—
553C3×C8—21no—
554C3×C8—21no—
555C3×C8—41no—
556C3×C8—61no—
557C3×C8—61no—
558C3⋊C8—21no—
559C3⋊C8—21no—
560C3⋊C8—61no—
561C3⋊C8—61no—
562C3⋊C8—121no—
563C2×C32#54611yescharacteristic
564C2×C32C2×#13711yescharacteristic
565C2×C32#57811yescharacteristic
566C3⋊D3—41no—
567C3×D3—22no—
568C2×Q8—31no—
569C2×Q8—31no—
570C2×Q8—61no—
571C2×Q8—62no—
572C2×Q8—91no—
573C2×Q8—121no—
574C2×Q8—181no—
575C2×Q8—182no—
576C2×Q8—361no—
577C2×Q8C2×D3211yescharacteristic
578C2×D4—91no—
579C22×C4—31no—
580C22×C4—61no—
581C22×C4—91no—
582C22×C4—181no—
583C22×C4—181no—
584Q16—62no—
585Q16—121no—
586Q16—361no—
587M16—361no—
588C2×C8—31no—
589C2×C8—31no—
590C2×C8—91no—
591C2×C8—361no—
592C2×C8C2×D3211yescharacteristic
593C4⋊C4—31no—
594C4⋊C4—31no—
595C4⋊C4—61no—
596C4⋊C4—61no—
597C4⋊C4—61no—
598C4⋊C4—61no—
599C4⋊C4—91no—
600C4⋊C4—91no—
601C4⋊C4—181no—
602C4⋊C4—181no—
603C4⋊C4—181no—
604C4⋊C4—181no—
605C4⋊C4—181no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4C2×D3211yescharacteristic
609C22⋊C4—61no—
610C22⋊C4—91no—
611C22⋊C4—91no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C22⋊C4—181no—
616C42—31no—
617C42—61no—
618C42—181no—
619C42—181no—
620C22×C3—21no—
621C22×C3—32no—
622C22×C3—61no—
623C22×C3—61no—
624C22×C3C2×D3×D411yescharacteristic
625C22×C3C2×D3×D411yescharacteristic
626C2×D3—21no—
627C2×D3—21no—
628C2×D3—62no—
629C2×D3—61no—
630C2×D3—61no—
631C2×D3—61no—
632C2×D3—61no—
633C2×D3—61no—
634C2×D3—61no—
635C2×D3—121no—
636C2×D3—121no—
637C2×D3#91812yes—
638C3×C4—22no—
639C3×C4—22no—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—42no—
643C3×C4—41no—
644C3×C4—41no—
645C3×C4—61no—
646C3×C4—61no—
647C3×C4—61no—
648C3×C4—81no—
649C3×C4—121no—
650C3×C4—121no—
651C3×C4—121no—
652C3×C4—121no—
653C3×C4C2×#23711yescharacteristic
654C3×C4#100411yescharacteristic
655C3×C4C2×#23911yescharacteristic
656C3×C4#100911yescharacteristic
657Dic3—21no—
658Dic3—21no—
659Dic3—21no—
660Dic3—41no—
661Dic3—41no—
662Dic3—41no—
663Dic3—41no—
664Dic3—62no—
665Dic3—61no—
666Dic3—61no—
667Dic3—122no—
668Dic3—121no—
669Dic3—121no—
670Dic3—121no—
671Dic3—121no—
672Dic3—241no—
673C32#331211yescharacteristic, complemented, Sylow
674C23—31no—
675C23—91no—
676Q8—21no—
677Q8—61no—
678Q8—61no—
679Q8—61no—
680Q8—61no—
681Q8—122no—
682Q8—181no—
683Q8—181no—
684Q8—362no—
685Q8#379612yes—
686D4—182no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—31no—
690C2×C4—31no—
691C2×C4—31no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—91no—
699C2×C4—122no—
700C2×C4—181no—
701C2×C4—181no—
702C2×C4—181no—
703C2×C4—181no—
704C2×C4—362no—
705C2×C4—362no—
706C2×C4C22×D3211yescharacteristic
707C8—21no—
708C8—61no—
709C8—61no—
710C8—181no—
711C2×C3—21no—
712C2×C3—21no—
713C2×C3—21no—
714C2×C3—62no—
715C2×C3#559111yescharacteristic
716C2×C3#563011yescharacteristic
717C2×C3C2×#91811yescharacteristic
718C2×C3#577111yescharacteristic
719C2×C3D3×#13711yescharacteristic
720C2×C3#577911yescharacteristic
721D3—22no—
722D3—122no—
723D3—121no—
724D3—121no—
725C22—32no—
726C22—61no—
727C22—61no—
728C22—181no—
729C22—181no—
730C22—181no—
731C22D32×D411yescharacteristic
732C4—22no—
733C4—41no—
734C4—61no—
735C4—61no—
736C4—61no—
737C4—121no—
738C4—121no—
739C4—121no—
740C4—121no—
741C4—181no—
742C4—361no—
743C4—361no—
744C4C2×#379611yescharacteristic
745C4#6431411yescharacteristic
746C3—21no—
747C3#8019511yescharacteristic, complemented
748C3#8124811yescharacteristic, complemented
749C2—62no—
750C2—361no—
751C2#1059406311yescharacteristic
752C2#1059475611yescharacteristic
753C2D3×#91811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×#626D4
hypercenter#103D32
hypocenterC32#3312
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
3. #10592501C2semidirect
4. C3×#4809C2semidirect
5. C3×#4799C2semidirect
6. #10591603C2semidirect
7. #10591576C2semidirect
8. D3×#835C2semidirect
10. #10590858C2semidirect
11. #10590800C2semidirect
12. #10590674C2semidirect
13. #10590579C2semidirect
14. #10590562C2semidirect
15. #10590526C2semidirect
83. #4809D3semidirect
88. #4799D3semidirect
673. C32#3312semidirect
747. C3#80195semidirect
748. C3#81248semidirect

Maximal subgroups

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

subgroupindex
Q8×#6262
#105944572
#105925012
C3×#48092
C3×#47992
#105916032
#105915762
D3×#8352
#105909072
#105908582
#105908002
#105906742
#105905792
#105905622
#105905262
#812483
#801953