Finite Group Databasebeta

← Q8×#3804 #11903756

Subgroups — Q8×#3804 #11903756

Order 1152.

2276 conjugacy classes of subgroups.

The subgroup lattice has 781 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#638C211yesmaximal, characteristic, complemented
2C3×Q8×#67C211yesmaximal, characteristic, complemented
3C2×C3×Q8×Dic3C211yesmaximal, characteristic, complemented
4#10595420C213yesmaximal, complemented
5Q8×#627C211yesmaximal, characteristic, complemented
6Q8×#626C211yesmaximal, characteristic, complemented
7#10595374C213yesmaximal, complemented
8Q8×#624C211yesmaximal, characteristic, complemented
9#10595371C213yesmaximal, complemented
10#10595367C213yesmaximal, complemented
11D3×Q8×Dic3C211yesmaximal, characteristic, complemented
12#10594991C213yesmaximal, complemented
13#10594988C213yesmaximal, complemented
14C4×#3804C213yesmaximal
15#10594808C213yesmaximal, complemented
16Q8×#237—31nomaximal
17Q8×#235—31nomaximal
18C22×C32×Q8C2211yescharacteristic
19C2×Q8×C3⋊D3C2211yescharacteristic
20C2×C3×D3×Q8C2211yescharacteristic
21C2×#3804C2211yescharacteristic
22#64155C2213yes—
23Q8×C3⋊Dic3C2211yescharacteristic
24#64153C2213yes—
25C4×#638C2213yes—
26#64133C2213yes—
27C3×#946C2213yes—
28C3×Q8×Dic3C2211yescharacteristic
29C3×Q8×Dic3C2213yes—
30C3×Q8×Dic3C2213yes—
31C3×Q8×Dic3C2211yescharacteristic
32C3×Q8×Dic3C2211yescharacteristic
33C3×#944C2213yes—
34C3×C4×#67C2213yes—
35C2×C3×C4⋊Dic3C2213yes—
36C3×#924C2213yes—
37C2×C3×C4×Dic3C2213yes—
38Dic3×#67C2213yes—
39#63964C2216yes—
40#63955C2213yes—
41#63952C2213yes—
42#63919C2213yes—
43#63918C2213yes—
44#63918C2213yes—
45C4×#627C2213yes—
46C4×#626C2213yes—
47#63900C2213yes—
48#63899C2216yes—
49#63895C2216yes—
50D3×C4⋊Dic3C2213yes—
51C4×#624C2213yes—
52#63880C2213yes—
53#63877C2213yes—
54C4×D3×Dic3C2213yes—
55#63871C2213yes—
56#63867C2216yes—
57#63866C2213yes—
58#63857C2213yes—
59#63847C2216yes—
60#63846C2216yes—
61#63844C2213yes—
62#63844C2213yes—
63#63843C2213yes—
64Dic3×Dic6C2213yes—
65#63837C2216yes—
66#63837C2213yes—
67#63836C2213yes—
68C3×D4×Q8—31no—
69C2×C3×C4×Q8—31no—
70Q8×#67—31no—
71Q8×#67—31no—
72Q8×#67—31no—
73Q8×#67—61no—
74Q8×#67D311yescharacteristic, complemented
75C2×Q8×Dic3—31no—
76C2×Q8×Dic3D311yescharacteristic, complemented
77#5728—33no—
78#5721—33no—
79#5635—33no—
80#5635—33no—
81#5622—33no—
82#5622—33no—
83#5579—33no—
84#5578—33no—
85#5578—33no—
86Q8×D12—31no—
87C4×D3×Q8—31no—
88C4×D3×Q8—31no—
89C4×D3×Q8—31no—
90#5567—33no—
91Q8×Dic6—31no—
92Q8×Dic6—31no—
93#5543—33no—
94C4×#237—33no—
95#5511—33no—
96#5511—33no—
97C4×#235—33no—
98#5470—33no—
99C2×C32×Q8—24no—
100C2×C32×Q8C2313yes—
101C2×C32×Q8C2311yescharacteristic
102C22×C32×C4C2313yes—
103C2×#638C2311yescharacteristic
104Q8×C3⋊D3—24no—
105C2×C4×C3⋊D3C2313yes—
106C2×#634C2313yes—
107C2×C3×#67C2311yescharacteristic
108C22×C3×Dic3C2313yes—
109C22×C3×Dic3C2311yescharacteristic
110C3×D3×Q8—24no—
111C2×C3×C4×D3C2313yes—
112C2×C3×Dic6C2313yes—
113C2×#627C2316yes—
114C2×#627C2311yescharacteristic
115C2×#626C2311yescharacteristic
116C2×#624C2313yes—
117C2×#624C2311yescharacteristic
118#3804Q818yesdirect product factor
119C2×D3×Dic3C2313yes—
120C2×D3×Dic3C2311yescharacteristic
121#3757C2313yes—
122#3752C2313yes—
123C4⋊(C3⋊Dic3)C2313yes—
124#3750C2316yes—
125#3750C2313yes—
126C4×C3⋊Dic3C2313yes—
127C3×#217C2313yes—
128C3×(C2×D3)⋊C4C2313yes—
129C3×C4⋊Dic3C2313yes—
130C3×C4⋊Dic3C2313yes—
131C3×C4⋊Dic3C2316yes—
132C3×C4⋊Dic3C2313yes—
133C3×Dic3⋊C4C2316yes—
134C3×Dic3⋊C4C2313yes—
135C3×C4×Dic3C2313yes—
136C3×C4×Dic3C2313yes—
137C3×C4×Dic3C2313yes—
138C3×C4×Dic3C2313yes—
139C3×C4×Dic3C2313yes—
140#3724C2316yes—
141#3724C2313yes—
142Dic3⋊Dic3C2313yes—
143Dic3⋊Dic3C2316yes—
144Dic3⋊Dic3C2313yes—
145Dic3⋊Dic3C2316yes—
146Dic3⋊Dic3C2313yes—
147#3722C2313yes—
148(C2×D3)⋊Dic3C2313yes—
149Dic32C2313yes—
150Dic32C2313yes—
151Dic32C2313yes—
152Dic32C2313yes—
153Q8×#41—91noSylow
154C22×C3×Q8—21no—
155C22×C3×Q8—31no—
156C22×C3×Q8C2×D311yescharacteristic
157C22×C3×Q8C2×D311yescharacteristic
158C2×D3×Q8—31no—
159C2×D3×Q8—31no—
160C2×D3×Q8—61no—
161C2×D3×Q8C2×D311yescharacteristic
162C2×#237—31no—
163C2×#235—31no—
164C3×C4⋊Q8—33no—
165C3×C22⋊Q8—33no—
166C3×C22⋊Q8—33no—
167C3×C4×Q8—31no—
168C3×C4×Q8—31no—
169C3×C4×Q8—33no—
170C3×C4×Q8—31no—
171C3×C4×Q8—33no—
172C3×C4×D4—33no—
173C2×C3×C4⋊C4—33no—
174C2×C3×C42—33no—
175#946—33no—
176#946—33no—
177#946—33no—
178#946—63no—
179#946C2×D313yes—
180Q8×Dic3—31no—
181Q8×Dic3—31no—
182Q8×Dic3—33no—
183Q8×Dic3—33no—
184Q8×Dic3—61no—
185Q8×Dic3C2×D313yes—
186Q8×Dic3C2×D313yes—
187Q8×Dic3C2×D311yescharacteristic
188Q8×Dic3C2×D311yescharacteristic
189Q8×Dic3C2×D311yescharacteristic
190#944—33no—
191#944—33no—
192#944—33no—
193#944—63no—
194#944C2×D313yes—
195D4×Dic3—33no—
196C4×#67—33no—
197C4×#67—33no—
198C4×#67—33no—
199C4×#67—33no—
200C4×#67—33no—
201C4×#67—63no—
202C4×#67C2×D313yes—
203#926—33no—
204C2×C4⋊Dic3—33no—
205C2×C4⋊Dic3C2×D313yes—
206#924—33no—
207#924—33no—
208#924—36no—
209#924—33no—
210#924—63no—
211#924C2×D313yes—
212C2×C4×Dic3—33no—
213C2×C4×Dic3C2×D313yes—
214#897—33no—
215#897—33no—
216#897—36no—
217#896—36no—
218#896—36no—
219#892—33no—
220D3×C4⋊C4—33no—
221D3×C4⋊C4—33no—
222D3×C4⋊C4—33no—
223#890—36no—
224#889—36no—
225#889—36no—
226#889—36no—
227#889—36no—
228#888—33no—
229#888—33no—
230#888—33no—
231#888—33no—
232#887—33no—
233#887—33no—
234#887—36no—
235#887—33no—
236#887—33no—
237#67⋊C4—33no—
238#67⋊C4—33no—
239#878—36no—
240#878—36no—
241#877—33no—
242#877—33no—
243C4×D12—33no—
244C4×D12—33no—
245#872—33no—
246#872—33no—
247C42×D3—33no—
248C42×D3—33no—
249C42×D3—33no—
250#870—36no—
251#869—33no—
252#869—33no—
253#869—33no—
254C4×Dic6—33no—
255C4×Dic6—33no—
256C4×Dic6—33no—
257C4×Dic6—36no—
258C4×Dic6—33no—
259C4×Dic6—33no—
260C4×Dic6—33no—
261C23×C32C2411yescharacteristic
262C22×C3⋊D3C2411yescharacteristic
263C22×C3×D3C2411yescharacteristic
264C32×Q8—26no—
265C32×Q8#4114yescomplemented
266C2×C32×C4—26no—
267C2×C32×C4C2413yes—
268C2×C32×C4C2413yes—
269#638C2×Q814yescomplemented
270C2×C3⋊Dic3C2413yes—
271C2×C3⋊Dic3C2413yes—
272C2×C3⋊Dic3C2411yescharacteristic
273C4×C3⋊D3—26no—
274#634—26no—
275C3×#67C2×Q814yescomplemented
276C2×C3×Dic3—43no—
277C2×C3×Dic3C2×Q814yescomplemented
278C2×C3×Dic3C2413yes—
279C2×C3×Dic3C2413yes—
280C2×C3×Dic3C2413yes—
281C2×C3×Dic3C2413yes—
282C2×C3×Dic3C2411yescharacteristic
283C2×C3×Dic3C2411yescharacteristic
284C2×C3×Dic3C2411yescharacteristic
285C3×C4×D3—26no—
286C3×Dic6—26no—
287#627—46no—
288#627C2×Q814yescomplemented
289#626C2×Q814yescomplemented
290#624—43no—
291#624C2×Q814yescomplemented
292D3×Dic3—43no—
293D3×Dic3C2×Q814yescomplemented
294Q82—91no—
295#557—93no—
296#554—93no—
297#554—93no—
298#554—93no—
299D4×Q8—31no—
300D4×Q8—91no—
301D4×Q8—91no—
302#533—93no—
303#533—93no—
304#533—93no—
305C4×#41—93no—
306C2×C4×Q8—31no—
307C2×C4×Q8—91no—
308C2×C4×Q8—91no—
309C2×C3×Q8—24no—
310C2×C3×Q8—24no—
311C2×C3×Q8—21no—
312C2×C3×Q8—23no—
313C2×C3×Q8—33no—
314C2×C3×Q8—44no—
315C2×C3×Q8—64no—
316C2×C3×Q8C22×D313yes—
317C2×C3×Q8C22×D313yes—
318C2×C3×Q8C22×D311yescharacteristic
319C2×C3×Q8C22×D311yescharacteristic
320C2×C3×D4—31no—
321C22×C3×C4—23no—
322C22×C3×C4—31no—
323C22×C3×C4—33no—
324C22×C3×C4—33no—
325C22×C3×C4C22×D313yes—
326C22×C3×C4C22×D313yes—
327C2×#67—31no—
328C2×#67—31no—
329C2×#67—31no—
330C2×#67—61no—
331C2×#67C22×D311yescharacteristic
332C22×Dic3—31no—
333C22×Dic3—33no—
334C22×Dic3C22×D313yes—
335C22×Dic3C22×D311yescharacteristic
336D3×Q8—24no—
337D3×Q8—64no—
338D3×Q8—64no—
339D3×Q8—124no—
340#237—38no—
341#235—38no—
342C2×D12—31no—
343C2×C4×D3—31no—
344C2×C4×D3—31no—
345C2×C4×D3—31no—
346C2×C4×D3—33no—
347C2×C4×D3—33no—
348C2×C4×D3—33no—
349C2×C4×D3—33no—
350C2×C4×D3—33no—
351C2×C4×D3—63no—
352C2×C4×D3C22×D313yes—
353C2×Dic6—31no—
354C2×Dic6—31no—
355C2×Dic6—33no—
356C2×Dic6—33no—
357C2×Dic6—36no—
358C2×Dic6—36no—
359C2×Dic6—63no—
360C2×Dic6C22×D313yes—
361C3×C4⋊C4—33no—
362C3×C4⋊C4—33no—
363C3×C4⋊C4—36no—
364C3×C4⋊C4—33no—
365C3×C4⋊C4—33no—
366C3×C4⋊C4—36no—
367C3×C22⋊C4—33no—
368C3×C22⋊C4—33no—
369C3×C42—33no—
370C3×C42—33no—
371C3×C42—33no—
372C3×C42—33no—
373C3×C42—33no—
374#217—33no—
375#217—33no—
376#217—33no—
377#217—63no—
378#217C22×D313yes—
379(C2×D3)⋊C4—33no—
380(C2×D3)⋊C4—33no—
381(C2×D3)⋊C4—33no—
382(C2×D3)⋊C4—33no—
383(C2×D3)⋊C4—33no—
384(C2×D3)⋊C4—63no—
385(C2×D3)⋊C4C22×D313yes—
386C4⋊Dic3—33no—
387C4⋊Dic3—33no—
388C4⋊Dic3—33no—
389C4⋊Dic3—33no—
390C4⋊Dic3—33no—
391C4⋊Dic3—36no—
392C4⋊Dic3—36no—
393C4⋊Dic3—63no—
394C4⋊Dic3C22×D313yes—
395C4⋊Dic3C22×D313yes—
396C4⋊Dic3C22×D313yes—
397C4⋊Dic3C22×D316yes—
398Dic3⋊C4—36no—
399Dic3⋊C4—33no—
400Dic3⋊C4—33no—
401Dic3⋊C4—36no—
402Dic3⋊C4—36no—
403Dic3⋊C4—36no—
404Dic3⋊C4—33no—
405Dic3⋊C4—33no—
406Dic3⋊C4—33no—
407Dic3⋊C4—33no—
408Dic3⋊C4—36no—
409Dic3⋊C4—33no—
410Dic3⋊C4—36no—
411Dic3⋊C4—66no—
412Dic3⋊C4—63no—
413Dic3⋊C4C22×D316yes—
414Dic3⋊C4C22×D313yes—
415C4×Dic3—33no—
416C4×Dic3—33no—
417C4×Dic3—33no—
418C4×Dic3—33no—
419C4×Dic3—33no—
420C4×Dic3—33no—
421C4×Dic3—33no—
422C4×Dic3—33no—
423C4×Dic3—33no—
424C4×Dic3—33no—
425C4×Dic3—63no—
426C4×Dic3C22×D313yes—
427C4×Dic3C22×D313yes—
428C4×Dic3C22×D313yes—
429C4×Dic3C22×D313yes—
430C4×Dic3C22×D313yes—
431C22×C32—21no—
432C22×C32—21no—
433C22×C32C22×Q812yes—
434C22×C32C2511yescharacteristic
435C2×C3⋊D3—21no—
436C2×C3⋊D3—21no—
437C2×C3⋊D3C22×Q812yes—
438C2×C3×D3—21no—
439C2×C3×D3—21no—
440C2×C3×D3C22×Q812yes—
441C32×C4—23no—
442C32×C4C2×#4116yes—
443C3⋊Dic3—23no—
444C3⋊Dic3—23no—
445C3⋊Dic3C22×Q812yes—
446C3×Dic3—23no—
447C3×Dic3—23no—
448C3×Dic3—23no—
449C3×Dic3—23no—
450C3×Dic3C22×Q812yes—
451C3×Dic3C22×Q812yes—
452C3×Dic3C22×Q812yes—
453C2×#41—91no—
454C22×Q8—31no—
455C22×Q8—91no—
456C22×Q8D3211yescharacteristic
457C4⋊Q8—33no—
458C4⋊Q8—93no—
459C4⋊Q8—93no—
460C4⋊Q8—93no—
461C4⋊Q8—93no—
462C4⋊Q8—93no—
463#125—96no—
464#125—96no—
465#125—96no—
466C22⋊Q8—33no—
467C22⋊Q8—33no—
468C22⋊Q8—96no—
469C22⋊Q8—96no—
470C22⋊Q8—96no—
471C22⋊Q8—93no—
472C22⋊Q8—93no—
473C22⋊Q8—93no—
474C22⋊Q8—93no—
475C4×Q8—31no—
476C4×Q8—33no—
477C4×Q8—31no—
478C4×Q8—33no—
479C4×Q8—31no—
480C4×Q8—93no—
481C4×Q8—93no—
482C4×Q8—93no—
483C4×Q8—93no—
484C4×Q8—96no—
485C4×Q8—93no—
486C4×Q8—93no—
487C4×Q8—91no—
488C4×D4—33no—
489C4×D4—93no—
490C4×D4—93no—
491C4×D4—93no—
492C4×D4—93no—
493C4×D4—93no—
494#117—93no—
495#117—93no—
496#117—93no—
497C2×C4⋊C4—33no—
498C2×C4⋊C4—93no—
499C2×C4⋊C4—93no—
500C2×C42—33no—
501C2×C42—93no—
502C2×C42—93no—
503C23×C3—21no—
504C23×C3—31no—
505C23×C3C23×D311yescharacteristic
506C23×C3C23×D311yescharacteristic
507C22×D3—31no—
508C22×D3—31no—
509C22×D3—61no—
510C22×D3C23×D311yescharacteristic
511C3×Q8—26no—
512C3×Q8—26no—
513C3×Q8—24no—
514C3×Q8—46no—
515C3×Q8—66no—
516C3×Q8#23514yescomplemented
517C3×Q8#23714yescomplemented
518C3×D4—34no—
519C2×C3×C4—26no—
520C2×C3×C4—26no—
521C2×C3×C4—23no—
522C2×C3×C4—23no—
523C2×C3×C4—34no—
524C2×C3×C4—31no—
525C2×C3×C4—31no—
526C2×C3×C4—31no—
527C2×C3×C4—33no—
528C2×C3×C4—33no—
529C2×C3×C4—33no—
530C2×C3×C4—33no—
531C2×C3×C4—46no—
532C2×C3×C4—66no—
533C2×C3×C4—123no—
534C2×C3×C4C23×D313yes—
535C2×C3×C4C23×D313yes—
536C2×C3×C4C23×D313yes—
537C2×C3×C4C23×D313yes—
538#67—34no—
539#67—34no—
540#67—34no—
541#67—64no—
542#67D3×Q814yescomplemented
543C2×Dic3—31no—
544C2×Dic3—31no—
545C2×Dic3—34no—
546C2×Dic3—33no—
547C2×Dic3—33no—
548C2×Dic3—33no—
549C2×Dic3—33no—
550C2×Dic3—43no—
551C2×Dic3—61no—
552C2×Dic3—63no—
553C2×Dic3—63no—
554C2×Dic3—123no—
555C2×Dic3D3×Q814yescomplemented
556C2×Dic3C23×D313yes—
557C2×Dic3C23×D313yes—
558C2×Dic3C23×D313yes—
559C2×Dic3C23×D313yes—
560C2×Dic3C23×D311yescharacteristic
561C2×Dic3C23×D311yescharacteristic
562C2×Dic3C23×D311yescharacteristic
563D12—34no—
564C4×D3—26no—
565C4×D3—34no—
566C4×D3—34no—
567C4×D3—34no—
568C4×D3—66no—
569C4×D3—66no—
570C4×D3—126no—
571C4×D3—123no—
572C4×D3—123no—
573C4×D3—123no—
574Dic6—26no—
575Dic6—34no—
576Dic6—34no—
577Dic6—66no—
578Dic6—66no—
579Dic6—126no—
580Dic6—126no—
581Dic6—126no—
582C2×C32—22no—
583C2×C32C23×Q811yescharacteristic
584C2×C32C22×#4111yescharacteristic
585C2×C32#58511yescharacteristic
586C3⋊D3—22no—
587C3×D3—22no—
588#41—98no—
589C2×Q8—24no—
590C2×Q8—33no—
591C2×Q8—64no—
592C2×Q8—91no—
593C2×Q8—96no—
594C2×Q8—93no—
595C2×Q8—184no—
596C2×Q8C2×D3213yes—
597C2×Q8C2×D3211yescharacteristic
598C2×D4—31no—
599C2×D4—91no—
600C2×D4—91no—
601C22×C4—31no—
602C22×C4—33no—
603C22×C4—33no—
604C22×C4—91no—
605C22×C4—93no—
606C22×C4—91no—
607C22×C4—93no—
608C22×C4—93no—
609C22×C4C2×D3213yes—
610C4⋊C4—33no—
611C4⋊C4—36no—
612C4⋊C4—33no—
613C4⋊C4—33no—
614C4⋊C4—33no—
615C4⋊C4—36no—
616C4⋊C4—96no—
617C4⋊C4—96no—
618C4⋊C4—93no—
619C4⋊C4—93no—
620C4⋊C4—93no—
621C4⋊C4—93no—
622C4⋊C4—96no—
623C4⋊C4—93no—
624C4⋊C4—93no—
625C4⋊C4—96no—
626C22⋊C4—33no—
627C22⋊C4—33no—
628C22⋊C4—93no—
629C22⋊C4—93no—
630C22⋊C4—93no—
631C22⋊C4—93no—
632C42—33no—
633C42—33no—
634C42—33no—
635C42—33no—
636C42—33no—
637C42—93no—
638C42—93no—
639C42—93no—
640C42—93no—
641C42—93no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—22no—
647C22×C3—21no—
648C22×C3—32no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—61no—
652C22×C3—61no—
653C22×C3C2×D3×Q812yes—
654C22×C3C2×D3×Q812yes—
655C22×C3C24×D311yescharacteristic
656C22×C3C24×D311yescharacteristic
657C2×D3—21no—
658C2×D3—21no—
659C2×D3—32no—
660C2×D3—32no—
661C2×D3—62no—
662C2×D3—61no—
663C2×D3—61no—
664C2×D3—61no—
665C2×D3—61no—
666C2×D3—121no—
667C2×D3—121no—
668C2×D3C2×D3×Q812yes—
669C3×C4—23no—
670C3×C4—23no—
671C3×C4—26no—
672C3×C4—32no—
673C3×C4—32no—
674C3×C4—32no—
675C3×C4—43no—
676C3×C4—63no—
677C3×C4—63no—
678C3×C4—63no—
679C3×C4—63no—
680C3×C4C2×#23516yes—
681C3×C4C2×#23716yes—
682Dic3—23no—
683Dic3—23no—
684Dic3—23no—
685Dic3—23no—
686Dic3—32no—
687Dic3—32no—
688Dic3—62no—
689Dic3—63no—
690Dic3—63no—
691Dic3—63no—
692Dic3—63no—
693Dic3—123no—
694Dic3—123no—
695Dic3C2×D3×Q812yes—
696Dic3C2×D3×Q812yes—
697Dic3C2×D3×Q812yes—
698C32Q8×#4111yescharacteristic, complemented, Sylow
699C23—31no—
700C23—91no—
701C23C22×D3211yescharacteristic
702Q8—26no—
703Q8—66no—
704Q8—94no—
705Q8—186no—
706Q8—366no—
707Q8#380414yesdirect product factor
708D4—34no—
709D4—94no—
710D4—94no—
711C2×C4—26no—
712C2×C4—34no—
713C2×C4—31no—
714C2×C4—31no—
715C2×C4—31no—
716C2×C4—33no—
717C2×C4—33no—
718C2×C4—33no—
719C2×C4—33no—
720C2×C4—66no—
721C2×C4—94no—
722C2×C4—94no—
723C2×C4—91no—
724C2×C4—93no—
725C2×C4—93no—
726C2×C4—123no—
727C2×C4—186no—
728C2×C4—363no—
729C2×C4—363no—
730C2×C4C22×D3213yes—
731C2×C4C22×D3213yes—
732C2×C3—22no—
733C2×C3—22no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—42no—
738C2×C3—62no—
739C2×C3C22×#23511yescharacteristic
740C2×C3C22×#23711yescharacteristic
741C2×C3C22×D3×Q811yescharacteristic
742C2×C3C22×D3×Q811yescharacteristic
743C2×C3#596411yescharacteristic
744C2×C3#596811yescharacteristic
745D3—22no—
746D3—62no—
747D3—62no—
748D3—122no—
749C22—21no—
750C22—21no—
751C22—32no—
752C22—61no—
753C22—61no—
754C22—92no—
755C22—181no—
756C22—181no—
757C22D32×Q812yes—
758C22C23×D3211yescharacteristic
759C4—23no—
760C4—32no—
761C4—32no—
762C4—32no—
763C4—63no—
764C4—63no—
765C4—63no—
766C4—63no—
767C4—92no—
768C4—183no—
769C4—183no—
770C4C2×#380416yes—
771C3—21no—
772C3Q8×#23511yescharacteristic, complemented
773C3Q8×#23711yescharacteristic, complemented
774C2—22no—
775C2—62no—
776C2—182no—
777C2C2×D32×Q811yescharacteristic
778C2#1059668811yescharacteristic
779C2C22×#380411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC22×C32×Q8C22
prime radicalC2×#3804C22
hypercenterC22×Q8D32
hypocenterC32Q8×#41
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. Q8×#638C2semidirect
2. C3×Q8×#67C2semidirect
3. C2×C3×Q8×Dic3C2semidirect
4. #10595420C2semidirect
5. Q8×#627C2semidirect
6. Q8×#626C2semidirect
7. #10595374C2semidirect
8. Q8×#624C2semidirect
9. #10595371C2semidirect
10. #10595367C2semidirect
11. D3×Q8×Dic3C2semidirect
12. #10594991C2semidirect
13. #10594988C2semidirect
15. #10594808C2semidirect
74. Q8×#67D3semidirect
76. C2×Q8×Dic3D3semidirect
118. #3804Q8direct (N × H)
265. C32×Q8#41semidirect
269. #638C2×Q8semidirect
275. C3×#67C2×Q8semidirect
277. C2×C3×Dic3C2×Q8semidirect
288. #627C2×Q8semidirect
289. #626C2×Q8semidirect
291. #624C2×Q8semidirect
293. D3×Dic3C2×Q8semidirect
516. C3×Q8#235semidirect
517. C3×Q8#237semidirect
542. #67D3×Q8semidirect
555. C2×Dic3D3×Q8semidirect
698. C32Q8×#41semidirect
707. Q8#3804direct (N × H)
772. C3Q8×#235semidirect
773. C3Q8×#237semidirect

Maximal subgroups

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

subgroupindex
Q8×#6382
C3×Q8×#672
C2×C3×Q8×Dic32
#105954202
Q8×#6272
Q8×#6262
#105953742
Q8×#6242
#105953712
#105953672
D3×Q8×Dic32
#105949912
#105949882
C4×#38042
#105948082
Q8×#2373
Q8×#2353