Finite Group Databasebeta

← #11889384

Subgroups — #11889384

Order 1152.

892 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#638C211yesmaximal, characteristic
2#10594970C211yesmaximal, characteristic
3C3×#5228C211yesmaximal, characteristic, complemented
4C3×#5225C211yesmaximal, characteristic, complemented
5#10591616C211yesmaximal, characteristic, complemented
6#10591615C211yesmaximal, characteristic, complemented
7#10591603C211yesmaximal, characteristic, complemented
8#10591601C211yesmaximal, characteristic, complemented
9#10591582C211yesmaximal, characteristic, complemented
10#10591580C211yesmaximal, characteristic, complemented
11#10591553C211yesmaximal, characteristic, complemented
12#10591552C211yesmaximal, characteristic, complemented
13#10591149C211yesmaximal, characteristic
14#10591134C211yesmaximal, characteristic, complemented
15#10591121C211yesmaximal, characteristic, complemented
16#80196—31nomaximal
17#78966—31nomaximal
18C22×C32×Q8C2211yescharacteristic
19C2×Q8×C3⋊D3C2211yescharacteristic
20#64155—21no—
21#64155C2211yescharacteristic
22Q8×C3⋊Dic3C2211yescharacteristic
23#64153—21no—
24#64153C2211yescharacteristic
25C4×#638—21no—
26C4×#638C2211yescharacteristic
27#64133—21no—
28#64133C2211yescharacteristic
29C2×C3×#216C2211yescharacteristic
30C2×C3×#216C2211yescharacteristic
31C3×#926C2211yescharacteristic
32C3×#924C2211yescharacteristic
33C2×C3×#208C2211yescharacteristic
34#63975—21no—
35#63956—21no—
36#63900C2211yescharacteristic
37#63872C2211yescharacteristic
38#63871C2211yescharacteristic
39#63867—21no—
40#63843C2211yescharacteristic
41#63836—21no—
42C2×#3719C2211yescharacteristic
43C2×#3710C2211yescharacteristic
44C3×#835C2211yescharacteristic
45C3×#835C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#830C2211yescharacteristic
51#63575C2211yescharacteristic
52#63573C2211yescharacteristic
53#63573C2211yescharacteristic
54#63572C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63567C2211yescharacteristic
58#63566C2211yescharacteristic
59#63557C2211yescharacteristic
60#63555C2211yescharacteristic
61Q8×#67—31no—
62Q8×#67—31no—
63Q8×#67—61no—
64#5639—31no—
65#5529—31no—
66C3×#451—31no—
67C3×#419—31no—
68#5228D311yescharacteristic, complemented
69#5225D311yescharacteristic, complemented
70#5188—31no—
71#5186—31no—
72#5184—31no—
73#5182—31no—
74#5137—31no—
75#5127—31no—
76#5052—31no—
77#4996—31no—
78#4813—31no—
79#4809—31no—
80#4805—31no—
81#4805—31no—
82D3×#103—31no—
83D3×#103—31no—
84#4799—31no—
85#4797—31no—
86#4797—31no—
87#4796—31no—
88#4795—31no—
89#4789—31no—
90#4728—31no—
91#4723—31no—
92C2×C32×Q8—21no—
93C2×C32×Q8—22no—
94C2×C32×Q8—41no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97C22×C32×C4—21no—
98C22×C32×C4C2311yescharacteristic
99C2×#638D411yescharacteristic
100Q8×C3⋊D3—22no—
101Q8×C3⋊D3—41no—
102C2×C4×C3⋊D3—21no—
103C2×C4×C3⋊D3C2311yescharacteristic
104C2×#634—21no—
105C2×#634C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×#624—21no—
108#3757—21no—
109#3757D411yescharacteristic
110#3752—21no—
111#3752D411yescharacteristic
112C4⋊(C3⋊Dic3)—21no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114#3750—21no—
115#3750—21no—
116#3750—21no—
117#3750—21no—
118#3750D411yescharacteristic
119C4×C3⋊Dic3—21no—
120C4×C3⋊Dic3C2311yescharacteristic
121C3×#217—21no—
122C3×#217—21no—
123C3×#216—22no—
124C3×#216—41no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×C4×Dic3—21no—
130C3×#208—41no—
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135#3724—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140#3722—21no—
141Dic32—21no—
142#3719—41no—
143#3710—41no—
144#3312—91noSylow
145C22×C3×Q8—21no—
146C22×C3×Q8C2×D311yescharacteristic
147C22×C3×Q8C2×D311yescharacteristic
148C2×D3×Q8—31no—
149C2×D3×Q8—31no—
150C2×D3×Q8—61no—
151C2×C3×Q16—31no—
152C2×C3×Q16—31no—
153C2×C3×M16—31no—
154C3×C22⋊Q8—31no—
155C3×#117—31no—
156#946—31no—
157#946—31no—
158#946—31no—
159#946—61no—
160#946—61no—
161#946—61no—
162#946—62no—
163Q8×Dic3—31no—
164Q8×Dic3—31no—
165Q8×Dic3—31no—
166Q8×Dic3—61no—
167#944—31no—
168#944—31no—
169#944—61no—
170#944—61no—
171#944—61no—
172#944—62no—
173C2×#216—31no—
174C2×#216C2×D311yescharacteristic
175C2×#216C2×D311yescharacteristic
176C4×#67—31no—
177C4×#67—31no—
178C4×#67—61no—
179C4×#67—61no—
180C4×#67—61no—
181C4×#67—62no—
182#926C2×D311yescharacteristic
183#924—31no—
184#924—31no—
185#924—61no—
186#924—61no—
187#924—61no—
188#924—62no—
189#924C2×D311yescharacteristic
190C2×#208C2×D311yescharacteristic
191C2×Dic12—31no—
192C2×D3×C8—31no—
193C2×D3×C8—31no—
194#897—31no—
195#892—61no—
196D3×C4⋊C4—31no—
197D3×C4⋊C4—31no—
198#890—31no—
199#890—31no—
200#889—61no—
201#887—31no—
202#883—61no—
203#883—61no—
204#879—61no—
205#879—61no—
206#872—61no—
207#870—61no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#103—31no—
212C3×#103—31no—
213C3×#103—31no—
214C3×C22⋊C8—31no—
215#835—31no—
216#835C2×D311yescharacteristic
217#835C2×D311yescharacteristic
218#835C2×D311yescharacteristic
219#835C2×D311yescharacteristic
220#835C2×D311yescharacteristic
221#835C2×D311yescharacteristic
222#830C2×D311yescharacteristic
223(C2×D3)⋊C8—31no—
224(C2×D3)⋊C8—31no—
225#818—31no—
226#817—31no—
227#817—31no—
228#816—31no—
229#816—31no—
230#816—31no—
231#816—31no—
232#815—31no—
233#815—31no—
234Dic3⋊C8—31no—
235Dic3⋊C8—31no—
236#810—31no—
237#810—31no—
238#810—31no—
239#808—31no—
240#808—31no—
241#807—31no—
242C23×C32C2×D411yescharacteristic
243C22×C3⋊D3C2×D411yescharacteristic
244C32×Q8—21no—
245C32×Q8—21no—
246C32×Q8—21no—
247C32×Q8—42no—
248C32×Q8#4112yes—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—42no—
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2411yescharacteristic
256#638—22no—
257C2×C3⋊Dic3—21no—
258C2×C3⋊Dic3—21no—
259C2×C3⋊Dic3C2×D411yescharacteristic
260C2×C3⋊Dic3C2×D411yescharacteristic
261C2×C3⋊Dic3C2×D411yescharacteristic
262C4×C3⋊D3—21no—
263C4×C3⋊D3—21no—
264C4×C3⋊D3—42no—
265#634—21no—
266#634—21no—
267#634—42no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C3×Dic6—21no—
273C3×Dic6—21no—
274#624—42no—
275C3×C3⋊C8—21no—
276C3×C3⋊C8—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#552—91no—
280D4×Q8—91no—
281#491—91no—
282#485—91no—
283#483—91no—
284#479—91no—
285#470—91no—
286#467—91no—
287#462—91no—
288#451—31no—
289#451—91no—
290#441—91no—
291#435—91no—
292#419—31no—
293C2×#103—91no—
294C2×C3×Q8—22no—
295C2×C3×Q8—21no—
296C2×C3×Q8—21no—
297C2×C3×Q8—22no—
298C2×C3×Q8—22no—
299C2×C3×Q8—21no—
300C2×C3×Q8—21no—
301C2×C3×Q8—31no—
302C2×C3×Q8—42no—
303C2×C3×Q8—41no—
304C2×C3×Q8—41no—
305C2×C3×Q8—42no—
306C2×C3×Q8C22×D311yescharacteristic
307C2×C3×Q8C22×D311yescharacteristic
308C2×C3×Q8C22×D311yescharacteristic
309C2×C3×Q8C22×D311yescharacteristic
310C22×C3×C4—22no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4C22×D311yescharacteristic
315C22×C3×C4C22×D311yescharacteristic
316C2×#67—31no—
317C2×#67—31no—
318C2×#67—61no—
319D3×Q8—62no—
320D3×Q8—62no—
321D3×Q8—122no—
322D3×Q8—121no—
323D3×Q8—121no—
324D3×Q8—122no—
325C2×C4×D3—31no—
326C2×C4×D3—31no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—62no—
333C2×Dic6—31no—
334C2×Dic6—31no—
335C2×Dic6—61no—
336C2×Dic6—61no—
337C2×Dic6—61no—
338C2×Dic6—62no—
339C2×Dic6C22×D311yescharacteristic
340C3×Q16—62no—
341C3×Q16—121no—
342C3×M16—121no—
343C2×C3×C8—31no—
344C2×C3×C8—31no—
345C2×C3×C8—31no—
346C2×C3×C8—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C42—61no—
354#217—21no—
355#217—21no—
356#217—31no—
357#217—31no—
358#217—61no—
359#217—62no—
360#217—61no—
361#217—61no—
362#216—22no—
363#216—41no—
364#216—121no—
365(C2×D3)⋊C4—31no—
366(C2×D3)⋊C4—31no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—62no—
373C4⋊Dic3—31no—
374C4⋊Dic3—31no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—62no—
383C4⋊Dic3C22×D311yescharacteristic
384C4⋊Dic3C22×D311yescharacteristic
385C4⋊Dic3C22×D311yescharacteristic
386Dic3⋊C4—21no—
387Dic3⋊C4—31no—
388Dic3⋊C4—31no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—62no—
403Dic3⋊C4—62no—
404Dic3⋊C4—62no—
405Dic3⋊C4—62no—
406Dic3⋊C4—61no—
407Dic3⋊C4—61no—
408C4×Dic3—21no—
409C4×Dic3—31no—
410C4×Dic3—31no—
411C4×Dic3—61no—
412C4×Dic3—61no—
413C4×Dic3—61no—
414C4×Dic3—61no—
415C4×Dic3—61no—
416C4×Dic3—62no—
417#208—41no—
418C2×C3⋊C8C22×D311yescharacteristic
419C2×C3⋊C8C22×D311yescharacteristic
420C2×C3⋊C8C22×D311yescharacteristic
421C2×C3⋊C8C22×D311yescharacteristic
422Dic12—121no—
423D3×C8—121no—
424D3×C8—121no—
425C22×C32—21no—
426C22×C32—21no—
427C22×C32—21no—
428C22×C32C22×D411yescharacteristic
429C2×C3⋊D3—21no—
430C2×C3⋊D3—21no—
431C2×C3⋊D3#13712yes—
432C32×C4—22no—
433C32×C4—21no—
434C32×C4—41no—
435C32×C4C2×#4111yescharacteristic
436C32×C4H(5,𝔽2)11yescharacteristic
437C3⋊Dic3—21no—
438C3⋊Dic3—21no—
439C3⋊Dic3—21no—
440C3⋊Dic3—41no—
441C3⋊Dic3—41no—
442C3×Dic3—41no—
443C3×Dic3—41no—
444C3×Dic3—41no—
445C3×Dic3—41no—
446C22×Q8—91no—
447C22×Q8D3211yescharacteristic
448C2×Q16—31no—
449C2×Q16—31no—
450C2×Q16—91no—
451C2×M16—31no—
452C22×C8—91no—
453C4⋊Q8—91no—
454C4⋊Q8—181no—
455#126—181no—
456#125—91no—
457#125—181no—
458#123—181no—
459C22⋊Q8—31no—
460C22⋊Q8—91no—
461C22⋊Q8—91no—
462C22⋊Q8—91no—
463C22⋊Q8—181no—
464C22⋊Q8—181no—
465C4×Q8—91no—
466C4×Q8—91no—
467C4×D4—91no—
468C4×D4—181no—
469#117—31no—
470#117—181no—
471C2×C4⋊C4—91no—
472#107—91no—
473#106—91no—
474#106—91no—
475C4⋊C8—91no—
476#103—31no—
477#103—31no—
478#103—31no—
479#103—31no—
480#103—31no—
481#103—31no—
482#103—91no—
483#103—91no—
484#103—91no—
485#103—91no—
486C22⋊C8—31no—
487C22⋊C8—91no—
488#97—91no—
489C23×C3—21no—
490C23×C3D3×D411yescharacteristic
491C23×C3D3×D411yescharacteristic
492C22×D3—31no—
493C22×D3—31no—
494C22×D3—61no—
495C3×Q8—22no—
496C3×Q8—21no—
497C3×Q8—21no—
498C3×Q8—21no—
499C3×Q8—21no—
500C3×Q8—21no—
501C3×Q8—21no—
502C3×Q8—22no—
503C3×Q8—41no—
504C3×Q8—41no—
505C3×Q8—42no—
506C3×Q8—42no—
507C3×Q8—44no—
508C3×Q8—61no—
509C3×Q8—61no—
510C3×Q8#23512yes—
511C3×Q8#23712yes—
512C2×C3×C4—22no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—22no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—42no—
527C2×C3×C4—42no—
528C2×C3×C4—44no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4D3×D411yescharacteristic
534C2×C3×C4D3×D411yescharacteristic
535C2×C3×C4C23×D311yescharacteristic
536C2×C3×C4C23×D311yescharacteristic
537#67—62no—
538#67—62no—
539#67—64no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—31no—
545C2×Dic3—31no—
546C2×Dic3—31no—
547C2×Dic3—31no—
548C2×Dic3—31no—
549C2×Dic3—31no—
550C2×Dic3—61no—
551C2×Dic3—61no—
552C2×Dic3—61no—
553C2×Dic3—62no—
554C2×Dic3—62no—
555C2×Dic3—61no—
556C2×Dic3—61no—
557C2×Dic3—61no—
558C2×Dic3—61no—
559C4×D3—61no—
560C4×D3—61no—
561C4×D3—61no—
562C4×D3—61no—
563C4×D3—121no—
564C4×D3—121no—
565C4×D3—122no—
566C4×D3—122no—
567C4×D3—122no—
568C4×D3—122no—
569C4×D3—124no—
570Dic6—21no—
571Dic6—21no—
572Dic6—61no—
573Dic6—61no—
574Dic6—61no—
575Dic6—61no—
576Dic6—121no—
577Dic6—121no—
578Dic6—122no—
579Dic6—122no—
580Dic6—124no—
581C3×C8—61no—
582C3×C8—61no—
583C3×C8—61no—
584C3×C8—61no—
585C3⋊C8—21no—
586C3⋊C8—21no—
587C3⋊C8—21no—
588C3⋊C8—21no—
589C2×C32—41no—
590C2×C32#54611yescharacteristic
591C2×C32C2×#13711yescharacteristic
592C2×C32#57811yescharacteristic
593C3⋊D3—22no—
594C2×Q8—21no—
595C2×Q8—22no—
596C2×Q8—31no—
597C2×Q8—41no—
598C2×Q8—91no—
599C2×Q8—181no—
600C2×Q8—182no—
601C2×Q8—361no—
602C2×Q8C2×D3211yescharacteristic
603C2×Q8C2×D3211yescharacteristic
604C2×D4—91no—
605C22×C4—21no—
606C22×C4—91no—
607C22×C4—181no—
608C22×C4—181no—
609C22×C4C2×D3211yescharacteristic
610Q16—62no—
611Q16—121no—
612Q16—361no—
613M16—121no—
614C2×C8—31no—
615C2×C8—31no—
616C2×C8—31no—
617C2×C8—31no—
618C2×C8—361no—
619C4⋊C4—31no—
620C4⋊C4—31no—
621C4⋊C4—31no—
622C4⋊C4—61no—
623C4⋊C4—91no—
624C4⋊C4—91no—
625C4⋊C4—181no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C4⋊C4—181no—
629C4⋊C4—181no—
630C4⋊C4—181no—
631C4⋊C4—181no—
632C4⋊C4—181no—
633C4⋊C4—181no—
634C4⋊C4—181no—
635C22⋊C4—61no—
636C22⋊C4—61no—
637C22⋊C4—91no—
638C22⋊C4—91no—
639C22⋊C4—181no—
640C22⋊C4—181no—
641C22⋊C4—181no—
642C42—61no—
643C42—91no—
644C42—181no—
645C42—181no—
646C22×C3—22no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3C2×D3×D411yescharacteristic
657C22×C3C2×D3×D411yescharacteristic
658C2×D3—32no—
659C2×D3—32no—
660C2×D3—62no—
661C2×D3—61no—
662C2×D3—61no—
663C2×D3—61no—
664C2×D3—61no—
665C2×D3—121no—
666C2×D3—121no—
667C3×C4—24no—
668C3×C4—22no—
669C3×C4—21no—
670C3×C4—22no—
671C3×C4—21no—
672C3×C4—21no—
673C3×C4—21no—
674C3×C4—41no—
675C3×C4—42no—
676C3×C4—41no—
677C3×C4—41no—
678C3×C4—121no—
679C3×C4—121no—
680C3×C4—121no—
681C3×C4—121no—
682C3×C4C2×#23511yescharacteristic
683C3×C4C2×#23711yescharacteristic
684C3×C4#100411yescharacteristic
685C3×C4#100411yescharacteristic
686Dic3—41no—
687Dic3—41no—
688Dic3—41no—
689Dic3—41no—
690Dic3—62no—
691Dic3—61no—
692Dic3—61no—
693Dic3—61no—
694Dic3—61no—
695Dic3—61no—
696Dic3—61no—
697Dic3—121no—
698Dic3—121no—
699Dic3—122no—
700Dic3—122no—
701Dic3—121no—
702Dic3—121no—
703Dic3—121no—
704Dic3—121no—
705C32#331211yescharacteristic, complemented, Sylow
706C23—91no—
707C23#381111yescharacteristic
708Q8—21no—
709Q8—21no—
710Q8—21no—
711Q8—42no—
712Q8—61no—
713Q8—61no—
714Q8—181no—
715Q8—181no—
716Q8—362no—
717Q8#380412yes—
718D4—182no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—42no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—91no—
729C2×C4—91no—
730C2×C4—91no—
731C2×C4—181no—
732C2×C4—181no—
733C2×C4—181no—
734C2×C4—181no—
735C2×C4—362no—
736C2×C4—362no—
737C2×C4#381111yescharacteristic
738C2×C4C22×D3211yescharacteristic
739C8—61no—
740C8—61no—
741C8—61no—
742C8—61no—
743C2×C3—21no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—42no—
747C2×C3—41no—
748C2×C3—41no—
749C2×C3#549011yescharacteristic
750C2×C3#559111yescharacteristic
751C2×C3#576611yescharacteristic
752C2×C3D3×#13711yescharacteristic
753C2×C3D3×#13711yescharacteristic
754C2×C3#577911yescharacteristic
755D3—62no—
756D3—62no—
757D3—122no—
758C22—21no—
759C22—21no—
760C22—21no—
761C22—92no—
762C22—181no—
763C22—181no—
764C22C2×#381111yescharacteristic
765C4—21no—
766C4—22no—
767C4—41no—
768C4—121no—
769C4—121no—
770C4—121no—
771C4—121no—
772C4—181no—
773C4—181no—
774C4—181no—
775C4—361no—
776C4—361no—
777C4C2×#380411yescharacteristic
778C4#6433011yescharacteristic
779C3—21no—
780C3#7896611yescharacteristic, complemented
781C3#8019611yescharacteristic, complemented
782C2—41no—
783C2—182no—
784C2#1059532211yescharacteristic
785C2#1059533711yescharacteristic
786C2#1059550011yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radicalC2×#638D4
hypercenterC22×Q8D32
hypocenterC32#3312
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
3. C3×#5228C2semidirect
4. C3×#5225C2semidirect
5. #10591616C2semidirect
6. #10591615C2semidirect
7. #10591603C2semidirect
8. #10591601C2semidirect
9. #10591582C2semidirect
10. #10591580C2semidirect
11. #10591553C2semidirect
12. #10591552C2semidirect
14. #10591134C2semidirect
15. #10591121C2semidirect
68. #5228D3semidirect
69. #5225D3semidirect
705. C32#3312semidirect
780. C3#78966semidirect
781. C3#80196semidirect

Maximal subgroups

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

subgroupindex
Q8×#6382
#105949702
C3×#52282
C3×#52252
#105916162
#105916152
#105916032
#105916012
#105915822
#105915802
#105915532
#105915522
#105911492
#105911342
#105911212
#801963
#789663