Finite Group Databasebeta

← #14458640

Subgroups — #14458640

Order 1920.

816 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65973C211yesmaximal, characteristic, complemented
2#11754665C211yesmaximal, characteristic
3#11751148C211yesmaximal, characteristic, complemented
4C5×#5048C211yesmaximal, characteristic, complemented
5#11749397C211yesmaximal, characteristic, complemented
6#11749311C211yesmaximal, characteristic, complemented
7#11749292C211yesmaximal, characteristic, complemented
8#11749221C211yesmaximal, characteristic, complemented
9C3⋊C8×C22⋊D5C211yesmaximal, characteristic, complemented
10#11748411C211yesmaximal, characteristic, complemented
11#11748383C211yesmaximal, characteristic, complemented
12D5×#809C211yesmaximal, characteristic, complemented
13#11747244C211yesmaximal, characteristic, complemented
14#11747168C211yesmaximal, characteristic, complemented
15#11747142C211yesmaximal, characteristic, complemented
16#10612402—31nomaximal, Hall
17C2×#6817C2211yescharacteristic
18C2×D5×D12C2211yescharacteristic
19C3×C5×C22⋊Q8C2211yescharacteristic, complemented
20C2×#6718C2211yescharacteristic, complemented
21C2×#6717C2211yescharacteristic
22C2×C5×#215C2211yescharacteristic
23C5×#930C2211yescharacteristic
24C22×C5×C3⋊C8C2211yescharacteristic, complemented
25C3×#4092C2211yescharacteristic
26C3×Q8×Dic5C2211yescharacteristic, complemented
27C3×C4×C22⋊D5C2211yescharacteristic
28C3×#4072C2211yescharacteristic, complemented
29C3×#4038—21no—
30C3×D5×C4⋊C4C2211yescharacteristic
31C3×#4036C2211yescharacteristic, complemented
32C3×#4035—21no—
33C3×#4029—21no—
34C3×#4025—21no—
35#91577—21no—
36#91557—21no—
37#91473—21no—
38#91418C2211yescharacteristic
39#91373C2211yescharacteristic
40#91360C2211yescharacteristic
41#91355—21no—
42C2×D5×C3⋊C8C2211yescharacteristic
43#91114C2211yescharacteristic, complemented
44#91094C2211yescharacteristic, complemented
45#91093C2211yescharacteristic
46C5×#835C2211yescharacteristic, complemented
47C5×#809C2211yescharacteristic
48C5×#808C2211yescharacteristic, complemented
49#90989C2211yescharacteristic, complemented
50#90986C2211yescharacteristic, complemented
51#90982C2211yescharacteristic, complemented
52#90974C2211yescharacteristic, complemented
53#90974C2211yescharacteristic, complemented
54#90968C2211yescharacteristic
55#90968C2211yescharacteristic
56#90966C2211yescharacteristic
57#90966C2211yescharacteristic
58#90955C2211yescharacteristic
59Dic5×C3⋊C8C2211yescharacteristic, complemented
60#83598—51nomaximal, Hall
61#65973D311yescharacteristic, complemented
62#65946—31no—
63C5×#465—31no—
64#65458—31no—
65#65455—31no—
66#65402—31no—
67C8×C22⋊D5—31no—
68#65336—31no—
69#65324—31no—
70#65160—31no—
71#65151—31no—
72#65102—31no—
73#65077—31no—
74D5×#102—31no—
75#65057—31no—
76C22×D3×D5—21no—
77C2×C3×C5×Q8C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C2×#1220—21no—
80#6817—22no—
81#6817—41no—
82C2×D60C2311yescharacteristic
83C2×C4×D15—21no—
84C2×Dic30C2311yescharacteristic
85C2×C5×#67—21no—
86C2×C5×D12C2311yescharacteristic
87C2×C3×C22⋊D5D411yescharacteristic
88C2×C3×C4×D5—21no—
89C2×C3×C4×D5C2311yescharacteristic
90C2×#1203—21no—
91C2×#1200—21no—
92D5×D12—22no—
93D5×D12—41no—
94C3×C5×C4⋊C4—21no—
95C3×C5×C4⋊C4C2311yescharacteristic
96C3×C5×C22⋊C4—21no—
97#6718—41no—
98#6717—22no—
99C2×C3⋊#168C2311yescharacteristic
100C2×C3⋊#168C2311yescharacteristic
101C5×#215—41no—
102C5×(C2×D3)⋊C4—21no—
103C5×C4⋊Dic3C2311yescharacteristic
104C2×C5×C3⋊C8—41no—
105C2×C5×C3⋊C8C2311yescharacteristic
106C2×C5×C3⋊C8C2311yescharacteristic
107C3×C22⋊Dic5—21no—
108C3×C22⋊Dic5D411yescharacteristic
109C3×#685—21no—
110C3×#685D411yescharacteristic
111C3×C4⋊Dic5—21no—
112C3×C4⋊Dic5—21no—
113C3×C4⋊Dic5C2311yescharacteristic
114C3×C4⋊Dic5C2311yescharacteristic
115C3×#683—21no—
116C3×#683—21no—
117C3×#683—21no—
118C3×#683D411yescharacteristic
119C3×C4×Dic5—21no—
120C3×C4×Dic5—21no—
121C3×C4×Dic5C2311yescharacteristic
122Dic3⋊Dic5—21no—
123#6667—21no—
124(C2×D3)⋊Dic5—21no—
125(C2×D3)⋊Dic5—21no—
126#6665—21no—
127D5×C3⋊C8—41no—
128C3×#552—51no—
129#5550—51no—
130#5068—51no—
131#5066—51no—
132#5051—51no—
133#5048D511yescharacteristic, complemented
134#5047—51no—
135#5046—51no—
136#5028—51no—
137C4×#215—51no—
138D4×C3⋊C8—51no—
139#5003—51no—
140#5002—51no—
141#4971—51no—
142C2×#809—51no—
143C2×D4×D5—31no—
144C2×#709—31no—
145C2×C5×SD16—31no—
146C22×C5×C8—31no—
147C5×C22⋊Q8C2×D311yescharacteristic, complemented
148C5×#121—31no—
149#4092C2×D311yescharacteristic
150Q8×Dic5C2×D311yescharacteristic, complemented
151C2×#689—31no—
152C2×#688—31no—
153#4084—61no—
154#4083—61no—
155#4082—31no—
156C4×C22⋊D5C2×D311yescharacteristic
157#4072C2×D311yescharacteristic, complemented
158C2×C8×D5—31no—
159#4043—31no—
160#4039—31no—
161#4038—21no—
162D5×C4⋊C4C2×D311yescharacteristic
163#4036C2×D311yescharacteristic, complemented
164#4035—21no—
165#4029—21no—
166#4029—61no—
167D5×C22⋊C4—61no—
168#4025—21no—
169C5×#106—31no—
170C5×#103—31no—
171C5×#102—31no—
172#3964—31no—
173#3964—31no—
174C22⋊#168—31no—
175#3953—31no—
176#3953—31no—
177#3952—31no—
178#3948—31no—
179#3948—31no—
180#3946—31no—
181C8×Dic5—31no—
182#3942—31no—
183#3941—31no—
184#3940—31no—
185#3939—31no—
186#3296—151noSylow
187C23×C3×C5C2×D411yescharacteristic
188C22×D15—21no—
189C22×C5×D3—21no—
190C22×C3×D5C2×D411yescharacteristic
191C2×D3×D5—42no—
192C2×D3×D5—42no—
193C2×D3×D5—81no—
194C3×C5×Q8—21no—
195C3×C5×Q8—21no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5C2×D411yescharacteristic
201C2×C3×C4×C5C2411yescharacteristic
202#1220—42no—
203C2×Dic15—21no—
204D60—21no—
205D60#4112yes—
206C4×D15—42no—
207Dic30—21no—
208Dic30—21no—
209C5×#67—81no—
210C2×C5×Dic3—21no—
211C5×D12—21no—
212C5×D12—21no—
213C3×C22⋊D5—22no—
214C2×C3×Dic5—21no—
215C2×C3×Dic5—21no—
216C2×C3×Dic5C2×D411yescharacteristic
217C2×C3×Dic5C2×D411yescharacteristic
218C2×C3×Dic5C2×D411yescharacteristic
219C3×C4×D5—21no—
220C3×C4×D5—21no—
221C3×C4×D5—42no—
222#1203—42no—
223#1200—81no—
224C3⋊#168—21no—
225C3⋊#168—21no—
226C5×C3⋊C8—21no—
227C5×C3⋊C8—21no—
228C2×#235—51no—
229C22×D12—51no—
230C3×#126—101no—
231C3×#125—51no—
232C3×#125—101no—
233C3×#123—101no—
234C3×C22⋊Q8—51no—
235C3×C22⋊Q8C2×D511yescharacteristic, complemented
236C3×C4×Q8—51no—
237C3×C4×D4—51no—
238C3×#117—51no—
239C3×#117—101no—
240C2×C3×C4⋊C4—51no—
241C2×#216—51no—
242C2×#215—51no—
243C2×#215C2×D511yescharacteristic
244#937—101no—
245#930C2×D511yescharacteristic
246#924—51no—
247C22×C3⋊C8—51no—
248C22×C3⋊C8C2×D511yescharacteristic, complemented
249#894—101no—
250#884—101no—
251D3×C22⋊C4—101no—
252#875—51no—
253C4×D12—51no—
254#835C2×D511yescharacteristic, complemented
255#830—51no—
256#830—51no—
257#810—51no—
258#810—51no—
259#810—51no—
260#809—51no—
261#809—51no—
262#809—51no—
263#809—51no—
264#809—51no—
265#809C2×D511yescharacteristic
266#808—51no—
267#808C2×D511yescharacteristic, complemented
268#807—51no—
269C4⋊(C3⋊C8)—51no—
270C4×C3⋊C8—51no—
271C23×D5—61no—
272C2×C5×Q8C22×D311yescharacteristic
273C2×C5×D4—31no—
274C2×C5×D4—61no—
275C22×C4×C5C22×D311yescharacteristic
276C2×C22⋊D5—61no—
277C2×C22⋊D5—61no—
278C2×C22⋊D5#6711yescharacteristic
279D4×D5—62no—
280D4×D5—121no—
281#709—62no—
282#709—121no—
283C2×D20—31no—
284C2×C4×D5—21no—
285C2×C4×D5—61no—
286C2×C4×D5—61no—
287C2×C4×D5C22×D311yescharacteristic
288C2×Dic10—31no—
289C5×SD16—121no—
290C2×C5×C8—31no—
291C2×C5×C8—31no—
292C2×C5×C8—121no—
293C5×C4⋊C4—21no—
294C5×C4⋊C4—31no—
295C5×C4⋊C4C22×D311yescharacteristic
296C5×C22⋊C4—21no—
297C5×C22⋊C4—61no—
298C22⋊Dic5—21no—
299C22⋊Dic5—61no—
300C22⋊Dic5—61no—
301C22⋊Dic5#6711yescharacteristic
302#689—121no—
303#688—62no—
304#685—21no—
305#685—61no—
306#685—61no—
307#685#6711yescharacteristic
308C4⋊Dic5—21no—
309C4⋊Dic5—21no—
310C4⋊Dic5—61no—
311C4⋊Dic5C22×D311yescharacteristic
312C4⋊Dic5C22×D311yescharacteristic
313#683—21no—
314#683—21no—
315#683—21no—
316#683#6711yescharacteristic
317C4×Dic5—21no—
318C4×Dic5—21no—
319C4×Dic5C22×D311yescharacteristic
320C2×#168—31no—
321C2×#168—31no—
322C8×D5—121no—
323#552—51no—
324#546—151no—
325#488—151no—
326#483—151no—
327#482—151no—
328#478—151no—
329#467—151no—
330#465—31no—
331#464—151no—
332#452—151no—
333#450—151no—
334C4×SD16—151no—
335C8×D4—151no—
336#416—151no—
337C2×#102—151no—
338C22×C3×C5—21no—
339C22×C3×C5—21no—
340C22×C3×C5—21no—
341C22×C3×C5C22×D411yescharacteristic
342C2×D15—22no—
343C2×D15—41no—
344C2×D15—41no—
345C2×C5×D3—41no—
346C2×C5×D3—41no—
347C2×C5×D3—41no—
348C2×C3×D5—21no—
349C2×C3×D5—21no—
350C2×C3×D5#13512yes—
351D3×D5—84no—
352C3×C4×C5—21no—
353C3×C4×C5—41no—
354C3×C4×C5—41no—
355C3×C4×C5C2×#4111yescharacteristic
356C3×C4×C5H(5,𝔽2)11yescharacteristic
357Dic15—41no—
358C3×Dic5—21no—
359C3×Dic5—21no—
360C3×Dic5—21no—
361C3×Dic5—41no—
362C3×Dic5—41no—
363C5×Dic3—41no—
364C23×D3—101no—
365C2×C3×Q8C22×D511yescharacteristic
366C2×C3×D4—51no—
367C22×C3×C4—51no—
368C22×C3×C4—101no—
369C22×C3×C4C22×D511yescharacteristic
370C2×#67—21no—
371C2×#67—101no—
372#235—102no—
373#235—201no—
374C2×D12—51no—
375C2×D12—102no—
376C2×D12—101no—
377C2×D12—201no—
378C2×D12C22×D511yescharacteristic
379C2×C4×D3—101no—
380C2×C4×D3—101no—
381C2×Dic6—51no—
382C3×C4⋊C4—21no—
383C3×C4⋊C4—51no—
384C3×C4⋊C4—51no—
385C3×C4⋊C4—51no—
386C3×C4⋊C4—101no—
387C3×C4⋊C4—101no—
388C3×C4⋊C4—101no—
389C3×C4⋊C4—101no—
390C3×C4⋊C4—101no—
391C3×C4⋊C4C22×D511yescharacteristic
392C3×C22⋊C4—21no—
393C3×C22⋊C4—51no—
394C3×C22⋊C4—51no—
395C3×C22⋊C4—101no—
396C3×C22⋊C4—101no—
397C3×C42—51no—
398C3×C42—101no—
399C3×C42—101no—
400#217—101no—
401#216—201no—
402#215—41no—
403#215—102no—
404(C2×D3)⋊C4—21no—
405(C2×D3)⋊C4—101no—
406(C2×D3)⋊C4—101no—
407(C2×D3)⋊C4—101no—
408C4⋊Dic3C22×D511yescharacteristic
409Dic3⋊C4—101no—
410C2×C3⋊C8—41no—
411C2×C3⋊C8—51no—
412C2×C3⋊C8—51no—
413C2×C3⋊C8—201no—
414C2×C3⋊C8C22×D511yescharacteristic
415C2×C3⋊C8C22×D511yescharacteristic
416C23×C5—61no—
417C23×C5C2×#6711yescharacteristic
418C22×D5—61no—
419C22×D5—122no—
420C22×D5—122no—
421C22×D5—241no—
422C22×D5C2×#6711yescharacteristic
423C5×Q8—21no—
424C5×Q8—21no—
425C5×D4—61no—
426C5×D4—61no—
427C5×D4—241no—
428C2×C4×C5—21no—
429C2×C4×C5—21no—
430C2×C4×C5—21no—
431C2×C4×C5—21no—
432C2×C4×C5—61no—
433C2×C4×C5C2×#6711yescharacteristic
434C2×C4×C5C23×D311yescharacteristic
435C22⋊D5—22no—
436C22⋊D5—122no—
437C22⋊D5—122no—
438C2×Dic5—21no—
439C2×Dic5—21no—
440C2×Dic5—61no—
441C2×Dic5C2×#6711yescharacteristic
442C2×Dic5C2×#6711yescharacteristic
443C2×Dic5C2×#6711yescharacteristic
444D20—32no—
445D20—61no—
446C4×D5—21no—
447C4×D5—21no—
448C4×D5—42no—
449C4×D5—122no—
450C4×D5—241no—
451Dic10—61no—
452Dic10—61no—
453C5×C8—61no—
454C5×C8—61no—
455#168—61no—
456#168—61no—
457C2×#41—151no—
458C22×D4—151no—
459C2×Q16—151no—
460C2×SD16—31no—
461C2×SD16—151no—
462C22×C8—31no—
463C22×C8—151no—
464#126—101no—
465#125—51no—
466#125—101no—
467#124—151no—
468#123—101no—
469#123—301no—
470C22⋊Q8—51no—
471C22⋊Q8—151no—
472C22⋊Q8D3×D511yescharacteristic, complemented
473#121—31no—
474#121—301no—
475#120—301no—
476C4×Q8—51no—
477C4×D4—51no—
478C4×D4—151no—
479#117—51no—
480#117—101no—
481C2×C4⋊C4—51no—
482C2×C22⋊C4—301no—
483#107—151no—
484#106—31no—
485#106—151no—
486C4⋊C8—151no—
487#103—31no—
488#103—151no—
489#103—151no—
490#103—151no—
491#102—31no—
492#102—151no—
493#102—151no—
494#102—151no—
495#102—151no—
496#102—151no—
497C22⋊C8—151no—
498C22⋊C8—151no—
499C4×C8—151no—
500C2×C3×C5—41no—
501C2×C3×C5#54611yescharacteristic
502C2×C3×C5C2×#13511yescharacteristic
503C2×C3×C5#57711yescharacteristic
504D15—42no—
505C3×D5—22no—
506C5×D3—81no—
507C23×C3—51no—
508C23×C3D4×D511yescharacteristic
509C22×D3—21no—
510C22×D3—101no—
511C22×D3—202no—
512C22×D3—202no—
513C22×D3—401no—
514C3×Q8—21no—
515C3×Q8—21no—
516C3×D4—102no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—51no—
522C2×C3×C4—51no—
523C2×C3×C4—51no—
524C2×C3×C4—101no—
525C2×C3×C4—101no—
526C2×C3×C4—101no—
527C2×C3×C4—101no—
528C2×C3×C4—202no—
529C2×C3×C4D4×D511yescharacteristic
530C2×C3×C4C23×D511yescharacteristic
531#67—81no—
532#67—202no—
533C2×Dic3—21no—
534C2×Dic3—101no—
535D12—21no—
536D12—21no—
537D12—52no—
538D12—101no—
539D12—202no—
540C4×D3—202no—
541C4×D3—401no—
542Dic6—101no—
543Dic6—101no—
544C3⋊C8—21no—
545C3⋊C8—21no—
546C3⋊C8—101no—
547C3⋊C8—101no—
548C22×C5—21no—
549C22×C5—21no—
550C22×C5—21no—
551C22×C5—121no—
552C22×C5—121no—
553C22×C5—121no—
554C22×C5C22×#6711yescharacteristic
555C2×D5—21no—
556C2×D5—21no—
557C2×D5—62no—
558C2×D5—121no—
559C2×D5—121no—
560C2×D5—244no—
561C2×D5#95012yes—
562C4×C5—21no—
563C4×C5—41no—
564C4×C5—41no—
565C4×C5—121no—
566C4×C5D3×#4111yescharacteristic
567C4×C5#100911yescharacteristic
568Dic5—21no—
569Dic5—21no—
570Dic5—21no—
571Dic5—41no—
572Dic5—41no—
573Dic5—121no—
574C24—301no—
575#41—302no—
576#41—601no—
577C2×Q8—151no—
578C2×Q8C2×D3×D511yescharacteristic
579C2×D4—31no—
580C2×D4—51no—
581C2×D4—61no—
582C2×D4—151no—
583C2×D4—301no—
584C2×D4—302no—
585C2×D4—301no—
586C2×D4—601no—
587C22×C4—51no—
588C22×C4—101no—
589C22×C4—301no—
590C22×C4—301no—
591C22×C4C2×D3×D511yescharacteristic
592Q16—601no—
593SD16—121no—
594SD16—302no—
595C2×C8—31no—
596C2×C8—31no—
597C2×C8—121no—
598C2×C8—151no—
599C2×C8—151no—
600C2×C8—601no—
601C4⋊C4—21no—
602C4⋊C4—31no—
603C4⋊C4—51no—
604C4⋊C4—51no—
605C4⋊C4—51no—
606C4⋊C4—101no—
607C4⋊C4—101no—
608C4⋊C4—101no—
609C4⋊C4—101no—
610C4⋊C4—101no—
611C4⋊C4—301no—
612C4⋊C4C2×D3×D511yescharacteristic
613C22⋊C4—21no—
614C22⋊C4—51no—
615C22⋊C4—51no—
616C22⋊C4—61no—
617C22⋊C4—101no—
618C22⋊C4—101no—
619C22⋊C4—301no—
620C22⋊C4—301no—
621C22⋊C4—301no—
622C22⋊C4—301no—
623C42—51no—
624C42—101no—
625C42—101no—
626C3×C5#329611yescharacteristic, complemented, Hall
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—52no—
631C22×C3—101no—
632C22×C3—101no—
633C22×C3C2×D4×D511yescharacteristic
634C2×D3—41no—
635C2×D3—41no—
636C2×D3—41no—
637C2×D3—102no—
638C2×D3—201no—
639C2×D3—201no—
640C2×D3—404no—
641C3×C4—21no—
642C3×C4—41no—
643C3×C4—41no—
644C3×C4—101no—
645C3×C4—101no—
646C3×C4—101no—
647C3×C4—201no—
648C3×C4—201no—
649C3×C4#414411yescharacteristic
650C3×C4D5×#4111yescharacteristic
651Dic3—41no—
652Dic3—201no—
653C2×C5—41no—
654C2×C5—241no—
655C2×C5C2×#95011yescharacteristic
656C2×C5#582911yescharacteristic
657C2×C5#583711yescharacteristic
658D5—22no—
659D5—122no—
660C23—51no—
661C23—61no—
662C23—301no—
663C23—602no—
664C23—602no—
665C23—1201no—
666C23D5×#6711yescharacteristic
667Q8—21no—
668Q8—21no—
669Q8—301no—
670Q8—301no—
671D4—61no—
672D4—61no—
673D4—102no—
674D4—152no—
675D4—241no—
676D4—301no—
677D4—602no—
678D4—602no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—51no—
684C2×C4—51no—
685C2×C4—51no—
686C2×C4—61no—
687C2×C4—101no—
688C2×C4—101no—
689C2×C4—101no—
690C2×C4—101no—
691C2×C4—202no—
692C2×C4—301no—
693C2×C4—602no—
694C2×C4—1201no—
695C2×C4D5×#6711yescharacteristic
696C2×C4C22×D3×D511yescharacteristic
697C8—61no—
698C8—61no—
699C8—301no—
700C8—301no—
701C2×C3—41no—
702C2×C3—102no—
703C2×C3#6594411yescharacteristic
704C2×C3#6609611yescharacteristic
705C2×C3D5×#13511yescharacteristic
706D3—81no—
707D3—202no—
708C5#8359811yescharacteristic, complemented, Sylow
709C22—21no—
710C22—21no—
711C22—21no—
712C22—52no—
713C22—101no—
714C22—101no—
715C22—121no—
716C22—121no—
717C22—121no—
718C22—302no—
719C22—601no—
720C22—601no—
721C22—1204no—
722C22C2×D5×#6711yescharacteristic
723C4—21no—
724C4—41no—
725C4—41no—
726C4—101no—
727C4—101no—
728C4—101no—
729C4—121no—
730C4—201no—
731C4—201no—
732C4—601no—
733C4#9202411yescharacteristic
734C4#9202711yescharacteristic
735C3#1061240211yescharacteristic, complemented, Sylow
736C2—41no—
737C2—102no—
738C2—241no—
739C2—602no—
740C2#1175506411yescharacteristic
741C2#1175508511yescharacteristic
742C2D5×#95011yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C22⋊Q8C22
socleC22×C3×C5C22×D4
prime radical#11754665C2
hypercenterC22⋊Q8D3×D5
hypocenterC3×C5#3296
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#65973C2semidirect
3. #11751148C2semidirect
4. C5×#5048C2semidirect
5. #11749397C2semidirect
6. #11749311C2semidirect
7. #11749292C2semidirect
8. #11749221C2semidirect
9. C3⋊C8×C22⋊D5C2semidirect
10. #11748411C2semidirect
11. #11748383C2semidirect
12. D5×#809C2semidirect
13. #11747244C2semidirect
14. #11747168C2semidirect
15. #11747142C2semidirect
19. C3×C5×C22⋊Q8C22semidirect
20. C2×#6718C22semidirect
24. C22×C5×C3⋊C8C22semidirect
26. C3×Q8×Dic5C22semidirect
28. C3×#4072C22semidirect
31. C3×#4036C22semidirect
43. #91114C22semidirect
44. #91094C22semidirect
46. C5×#835C22semidirect
48. C5×#808C22semidirect
49. #90989C22semidirect
50. #90986C22semidirect
51. #90982C22semidirect
52. #90974C22semidirect
53. #90974C22semidirect
59. Dic5×C3⋊C8C22semidirect
61. #65973D3semidirect
133. #5048D5semidirect
147. C5×C22⋊Q8C2×D3semidirect
150. Q8×Dic5C2×D3semidirect
157. #4072C2×D3semidirect
163. #4036C2×D3semidirect
235. C3×C22⋊Q8C2×D5semidirect
248. C22×C3⋊C8C2×D5semidirect
254. #835C2×D5semidirect
267. #808C2×D5semidirect
472. C22⋊Q8D3×D5semidirect
626. C3×C5#3296semidirect
708. C5#83598semidirect
735. C3#10612402semidirect

Maximal subgroups

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

subgroupindex
C3×#659732
#117546652
#117511482
C5×#50482
#117493972
#117493112
#117492922
#117492212
C3⋊C8×C22⋊D52
#117484112
#117483832
D5×#8092
#117472442
#117471682
#117471422
#106124023
#835985