Finite Group Databasebeta

← #14458713

Subgroups — #14458713

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
1C5×#5642C211yesmaximal, characteristic, complemented
2#11754305C211yesmaximal, characteristic
3#11751152C211yesmaximal, characteristic, complemented
4C3×#65335C211yesmaximal, characteristic, complemented
5#11749403C211yesmaximal, characteristic, complemented
6#11749325C211yesmaximal, characteristic, complemented
7#11749274C211yesmaximal, characteristic, complemented
8Dic3×#688C211yesmaximal, characteristic, complemented
9#67⋊#168C211yesmaximal, characteristic, complemented
10#11748444C211yesmaximal, characteristic, complemented
11C2×#90964C211yesmaximal, characteristic, complemented
12#11747502C211yesmaximal, characteristic, complemented
13#11747374C211yesmaximal, characteristic, complemented
14#11747322C211yesmaximal, characteristic, complemented
15#11747249C211yesmaximal, characteristic, complemented
16#10615329—31nomaximal, Hall
17C22×C3×D20C2211yescharacteristic
18C2×#6765C2211yescharacteristic
19C3×C5×C22⋊Q8C2211yescharacteristic
20C2×#6718C2211yescharacteristic, complemented
21#91813C2211yescharacteristic
22C22×C3⋊#168C2211yescharacteristic
23C5×#946C2211yescharacteristic, complemented
24C5×Q8×Dic3C2211yescharacteristic, complemented
25C4×C5×#67C2211yescharacteristic
26C2×C5×C4⋊Dic3C2211yescharacteristic
27C5×#898—21no—
28C5×#892C2211yescharacteristic, complemented
29C5×#890—21no—
30C5×#890C2211yescharacteristic, complemented
31C5×#886—21no—
32C5×#877—21no—
33C2×C3×#688C2211yescharacteristic
34C2×C3×#688C2211yescharacteristic
35#91563—21no—
36D5×#217—21no—
37#91456C2211yescharacteristic
38Dic3×D20C2211yescharacteristic
39#91408—21no—
40#91407—21no—
41#91364C2211yescharacteristic
42C2×D3×#168C2211yescharacteristic, complemented
43#91119C2211yescharacteristic, complemented
44#91094C2211yescharacteristic, complemented
45#91091C2211yescharacteristic, complemented
46C3×C22⋊#168C2211yescharacteristic
47C3×#3941C2211yescharacteristic
48C3×#3941C2211yescharacteristic
49#90985C2211yescharacteristic, complemented
50#90985C2211yescharacteristic, complemented
51Dic3⋊#168C2211yescharacteristic, complemented
52#90975C2211yescharacteristic, complemented
53#90975C2211yescharacteristic, complemented
54#90964C2211yescharacteristic
55#90964C2211yescharacteristic
56#90964C2211yescharacteristic
57#90964C2211yescharacteristic
58(C2×D3)⋊#168C2211yescharacteristic, complemented
59Dic3×#168C2211yescharacteristic, complemented
60#80159—51nomaximal, Hall
61C5×#552—31no—
62#65884—31no—
63#65357—31no—
64#65355—31no—
65#65340—31no—
66#65337—31no—
67#65336—31no—
68#65335D311yescharacteristic, complemented
69#65317—31no—
70C4×#688—31no—
71D4×#168—31no—
72#65292—31no—
73#65291—31no—
74#65260—31no—
75C2×#3941—31no—
76C23×C3×D5—21no—
77C2×C3×C5×Q8C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C2×Dic30C2311yescharacteristic
80C2×C5×#67D411yescharacteristic
81C22×C5×Dic3—21no—
82C2×C4×C5×D3C2311yescharacteristic
83C2×C3×D20—22no—
84C2×C3×D20—21no—
85C2×C3×D20—41no—
86C2×C3×D20C2311yescharacteristic
87C2×C3×D20C2311yescharacteristic
88C2×#1201—21no—
89C2×#1201—21no—
90C2×D5×Dic3—21no—
91C2×D5×Dic3—21no—
92#6765—22no—
93#6765—41no—
94C3×C5×C4⋊C4—21no—
95C3×C5×C4⋊C4C2311yescharacteristic
96C3×C5×C22⋊C4—21no—
97#6719—21no—
98#6718—41no—
99C4⋊Dic15C2311yescharacteristic
100#6712—21no—
101C2×C3⋊#168—41no—
102C2×C3⋊#168C2311yescharacteristic
103C2×C3⋊#168C2311yescharacteristic
104C5×#217D411yescharacteristic
105C5×(C2×D3)⋊C4—21no—
106C5×(C2×D3)⋊C4—21no—
107C5×(C2×D3)⋊C4D411yescharacteristic
108C5×C4⋊Dic3—21no—
109C5×C4⋊Dic3—21no—
110C5×C4⋊Dic3—21no—
111C5×C4⋊Dic3C2311yescharacteristic
112C5×C4⋊Dic3C2311yescharacteristic
113C5×Dic3⋊C4—21no—
114C5×Dic3⋊C4—21no—
115C5×Dic3⋊C4D411yescharacteristic
116C4×C5×Dic3—21no—
117C4×C5×Dic3—21no—
118C4×C5×Dic3C2311yescharacteristic
119C3×#688—22no—
120C3×#688—41no—
121C2×C3×#168C2311yescharacteristic
122C2×C3×#168C2311yescharacteristic
123#6665—21no—
124#6665—21no—
125#6665—21no—
126#6665—21no—
127D3×#168—41no—
128#5806—51no—
129#5642D511yescharacteristic, complemented
130C3×#450—51no—
131C2×#832—51no—
132#5173—51no—
133#5171—51no—
134#5166—51no—
135Dic3×SD16—51no—
136#5051—51no—
137#4779—51no—
138#4772—51no—
139#4768—51no—
140#4763—51no—
141#67⋊C8—51no—
142#4721—51no—
143C2×#709—31no—
144C22×D20C2×D311yescharacteristic
145C5×#126—61no—
146C5×#125—31no—
147C5×#125—61no—
148C5×#123—61no—
149C5×C22⋊Q8—31no—
150C5×C22⋊Q8C2×D311yescharacteristic
151C4×C5×Q8—31no—
152C4×C5×D4—31no—
153C5×#117—31no—
154C5×#117—61no—
155C2×C5×C4⋊C4—31no—
156C2×#689—31no—
157C2×#688C2×D311yescharacteristic
158C2×#688C2×D311yescharacteristic
159#4083—61no—
160#4076—31no—
161#4070—31no—
162C22×#168—31no—
163C22×#168—31no—
164#4040—61no—
165#4030—61no—
166D5×C22⋊C4—61no—
167#4021—31no—
168C4×D20—31no—
169#3967—31no—
170C22⋊#168—31no—
171C22⋊#168C2×D311yescharacteristic
172#3942—31no—
173#3942—31no—
174#3942—31no—
175#3941—31no—
176#3941—31no—
177#3941—31no—
178#3941—31no—
179#3941C2×D311yescharacteristic
180#3941C2×D311yescharacteristic
181#3940—31no—
182#3940—31no—
183#3939—31no—
184C4⋊#168—31no—
185C4×#168—31no—
186#3296—151noSylow
187C23×C3×C5C2×D411yescharacteristic
188C22×C5×D3C2×D411yescharacteristic
189C22×C3×D5—21no—
190C22×C3×D5—21no—
191C22×C3×D5—42no—
192C22×C3×D5—42no—
193C22×C3×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
202C2×Dic15—21no—
203C2×Dic15—21no—
204Dic30—21no—
205Dic30—21no—
206C5×#67—22no—
207C2×C5×Dic3—21no—
208C2×C5×Dic3—21no—
209C2×C5×Dic3—42no—
210C2×C5×Dic3C2×D411yescharacteristic
211C2×C5×Dic3C2×D411yescharacteristic
212C2×C5×Dic3C2×D411yescharacteristic
213C4×C5×D3—21no—
214C4×C5×D3—21no—
215C3×D20—21no—
216C3×D20—21no—
217C3×D20—21no—
218C3×D20—42no—
219C3×D20#4112yes—
220#1201—42no—
221#1201—81no—
222D5×Dic3—42no—
223D5×Dic3—81no—
224C3⋊#168—21no—
225C3⋊#168—21no—
226C3×#168—21no—
227C3×#168—21no—
228C22×C3×D4—51no—
229C2×#237—51no—
230C2×C3×SD16—51no—
231C2×C3×SD16—51no—
232C3×C22⋊Q8C2×D511yescharacteristic
233#953—101no—
234C2×#217—101no—
235#946C2×D511yescharacteristic, complemented
236Q8×Dic3C2×D511yescharacteristic, complemented
237C2×#216—51no—
238#939—101no—
239#938—51no—
240#936—51no—
241#935—101no—
242D4×Dic3—51no—
243C4×#67C2×D511yescharacteristic
244C2×C4⋊Dic3C2×D511yescharacteristic
245#924—51no—
246C22×C3⋊C8—51no—
247C2×D3×C8—51no—
248#898—21no—
249#892C2×D511yescharacteristic, complemented
250#890—21no—
251#890C2×D511yescharacteristic, complemented
252#886—21no—
253#877—21no—
254C3×#102—51no—
255C3×#102—51no—
256C3×C22⋊C8—51no—
257#835—51no—
258#832—51no—
259#832—51no—
260#832—51no—
261#832—51no—
262(C2×D3)⋊C8—51no—
263#817—51no—
264#817—51no—
265#816—51no—
266#816—51no—
267Dic3⋊C8—51no—
268C8×Dic3—51no—
269#810—51no—
270#807—51no—
271C23×D5—21no—
272C2×C5×Q8C22×D311yescharacteristic
273C2×C5×D4—31no—
274C22×C4×C5—31no—
275C22×C4×C5—61no—
276C22×C4×C5C22×D311yescharacteristic
277C2×C22⋊D5—61no—
278C2×C22⋊D5—61no—
279#709—62no—
280#709—121no—
281C2×D20—22no—
282C2×D20—21no—
283C2×D20—41no—
284C2×D20C22×D311yescharacteristic
285C2×D20C22×D311yescharacteristic
286C2×C4×D5—61no—
287C2×C4×D5—61no—
288C2×Dic10—31no—
289C5×C4⋊C4—21no—
290C5×C4⋊C4—31no—
291C5×C4⋊C4—31no—
292C5×C4⋊C4—31no—
293C5×C4⋊C4—61no—
294C5×C4⋊C4—61no—
295C5×C4⋊C4—61no—
296C5×C4⋊C4—61no—
297C5×C4⋊C4—61no—
298C5×C4⋊C4C22×D311yescharacteristic
299C5×C22⋊C4—21no—
300C5×C22⋊C4—31no—
301C5×C22⋊C4—31no—
302C5×C22⋊C4—61no—
303C5×C22⋊C4—61no—
304C42×C5—31no—
305C42×C5—61no—
306C42×C5—61no—
307C22⋊Dic5—61no—
308#689—121no—
309#688—22no—
310#688—41no—
311#685—61no—
312#685—61no—
313#685—61no—
314#685—61no—
315C4⋊Dic5—31no—
316#683—61no—
317C2×#168—31no—
318C2×#168—31no—
319C2×#168—121no—
320C2×#168—121no—
321C2×#168C22×D311yescharacteristic
322C2×#168C22×D311yescharacteristic
323#552—31no—
324#546—151no—
325#488—151no—
326#483—151no—
327#482—151no—
328#478—151no—
329#467—151no—
330#465—151no—
331#464—151no—
332#452—151no—
333#450—51no—
334C4×SD16—151no—
335C8×D4—151no—
336#416—151no—
337C2×#102—151no—
338C22×C3×C5—21no—
339C22×C3×C5—21no—
340C22×C3×C5#13512yes—
341C22×C3×C5C22×D411yescharacteristic
342C2×C5×D3—21no—
343C2×C5×D3—21no—
344C2×C5×D3—21no—
345C2×C3×D5—22no—
346C2×C3×D5—41no—
347C2×C3×D5—41no—
348C2×C3×D5—41no—
349C2×C3×D5—41no—
350C2×C3×D5—41no—
351C2×C3×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—
358Dic15—41no—
359C5×Dic3—21no—
360C5×Dic3—21no—
361C5×Dic3—21no—
362C5×Dic3—41no—
363C5×Dic3—41no—
364C24×C3—101no—
365C2×C3×Q8C22×D511yescharacteristic
366C2×C3×D4—51no—
367C2×C3×D4—51no—
368C2×C3×D4—102no—
369C2×C3×D4—101no—
370C2×C3×D4—201no—
371C22×C3×C4C22×D511yescharacteristic
372C2×#67—101no—
373C2×#67—101no—
374C2×#67C22⋊D511yescharacteristic
375C22×Dic3—21no—
376C22×Dic3—101no—
377C22×Dic3—101no—
378#237—102no—
379#237—201no—
380C2×C4×D3C22×D511yescharacteristic
381C2×Dic6—51no—
382C3×SD16—102no—
383C3×SD16—201no—
384C2×C3×C8—51no—
385C2×C3×C8—51no—
386C3×C4⋊C4—21no—
387C3×C4⋊C4C22×D511yescharacteristic
388C3×C22⋊C4—21no—
389#217—101no—
390#217—101no—
391#217—101no—
392#217—101no—
393#217—101no—
394#217C22⋊D511yescharacteristic
395#216—201no—
396(C2×D3)⋊C4—21no—
397(C2×D3)⋊C4—21no—
398(C2×D3)⋊C4C22⋊D511yescharacteristic
399C4⋊Dic3—21no—
400C4⋊Dic3—21no—
401C4⋊Dic3—21no—
402C4⋊Dic3—51no—
403C4⋊Dic3C22×D511yescharacteristic
404C4⋊Dic3C22×D511yescharacteristic
405Dic3⋊C4—21no—
406Dic3⋊C4—21no—
407Dic3⋊C4—101no—
408Dic3⋊C4C22⋊D511yescharacteristic
409C4×Dic3—21no—
410C4×Dic3—21no—
411C4×Dic3C22×D511yescharacteristic
412C2×C3⋊C8—51no—
413C2×C3⋊C8—51no—
414C2×C3⋊C8—201no—
415D3×C8—201no—
416C23×C5—31no—
417C23×C5D3×D411yescharacteristic
418C22×D5—21no—
419C22×D5—21no—
420C22×D5—42no—
421C22×D5—42no—
422C22×D5—81no—
423C5×Q8—21no—
424C5×Q8—21no—
425C5×D4—62no—
426C2×C4×C5—21no—
427C2×C4×C5—21no—
428C2×C4×C5—21no—
429C2×C4×C5—21no—
430C2×C4×C5—31no—
431C2×C4×C5—31no—
432C2×C4×C5—31no—
433C2×C4×C5—61no—
434C2×C4×C5—61no—
435C2×C4×C5—61no—
436C2×C4×C5—61no—
437C2×C4×C5—122no—
438C2×C4×C5D3×D411yescharacteristic
439C2×C4×C5C23×D311yescharacteristic
440C22⋊D5—122no—
441C22⋊D5—241no—
442C2×Dic5—61no—
443C2×Dic5—61no—
444D20—21no—
445D20—21no—
446D20—21no—
447D20—42no—
448D20#23712yes—
449C4×D5—122no—
450C4×D5—241no—
451Dic10—61no—
452Dic10—61no—
453#168—21no—
454#168—21no—
455#168—61no—
456#168—61no—
457C2×#41—151no—
458C22×D4—51no—
459C2×Q16—151no—
460C2×SD16—51no—
461C2×SD16—51no—
462C22×C8—151no—
463C22×C8—151no—
464#126—61no—
465#125—31no—
466#125—61no—
467#124—151no—
468#123—61no—
469#123—301no—
470C22⋊Q8—31no—
471C22⋊Q8—151no—
472C22⋊Q8D3×D511yescharacteristic
473#121—151no—
474#121—301no—
475#120—301no—
476C4×Q8—31no—
477C4×D4—31no—
478C4×D4—151no—
479#117—31no—
480#117—61no—
481C2×C4⋊C4—31no—
482C2×C22⋊C4—301no—
483#107—151no—
484#106—151no—
485#106—151no—
486C4⋊C8—151no—
487#103—151no—
488#103—151no—
489#103—151no—
490#103—151no—
491#102—51no—
492#102—51no—
493#102—151no—
494#102—151no—
495#102—151no—
496#102—151no—
497C22⋊C8—51no—
498C22⋊C8—151no—
499C4×C8—151no—
500C2×C3×C5—22no—
501C2×C3×C5#54611yescharacteristic
502C2×C3×C5C2×#13511yescharacteristic
503C2×C3×C5#57711yescharacteristic
504C3×D5—42no—
505C3×D5—81no—
506C5×D3—41no—
507C23×C3—101no—
508C23×C3—101no—
509C23×C3—202no—
510C23×C3—202no—
511C23×C3—401no—
512C23×C3C2×C22⋊D511yescharacteristic
513C22×D3C2×C22⋊D511yescharacteristic
514C3×Q8—21no—
515C3×Q8—21no—
516C3×D4—52no—
517C3×D4—101no—
518C3×D4—101no—
519C3×D4—101no—
520C3×D4—202no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4C2×C22⋊D511yescharacteristic
526C2×C3×C4C23×D511yescharacteristic
527#67—22no—
528#67—202no—
529#67—401no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—42no—
533C2×Dic3—101no—
534C2×Dic3—101no—
535C2×Dic3—202no—
536C2×Dic3—401no—
537C2×Dic3C2×C22⋊D511yescharacteristic
538C2×Dic3C2×C22⋊D511yescharacteristic
539C2×Dic3C2×C22⋊D511yescharacteristic
540C4×D3—21no—
541C4×D3—21no—
542Dic6—101no—
543Dic6—101no—
544C3×C8—101no—
545C3×C8—101no—
546C3⋊C8—101no—
547C3⋊C8—101no—
548C22×C5—21no—
549C22×C5—21no—
550C22×C5—61no—
551C22×C5—61no—
552C22×C5—61no—
553C22×C5#91612yes—
554C22×C5C2×D3×D411yescharacteristic
555C2×D5—22no—
556C2×D5—41no—
557C2×D5—41no—
558C2×D5—41no—
559C2×D5—41no—
560C2×D5—41no—
561C2×D5—84no—
562C4×C5—21no—
563C4×C5—41no—
564C4×C5—41no—
565C4×C5—61no—
566C4×C5—61no—
567C4×C5—61no—
568C4×C5—121no—
569C4×C5—121no—
570C4×C5C2×#23711yescharacteristic
571C4×C5#100411yescharacteristic
572Dic5—121no—
573Dic5—121no—
574C24—101no—
575#41—302no—
576#41—601no—
577C2×Q8—151no—
578C2×Q8C2×D3×D511yescharacteristic
579C2×D4—31no—
580C2×D4—51no—
581C2×D4—51no—
582C2×D4—102no—
583C2×D4—101no—
584C2×D4—201no—
585C2×D4—301no—
586C2×D4—301no—
587C22×C4—31no—
588C22×C4—61no—
589C22×C4—301no—
590C22×C4—301no—
591C22×C4C2×D3×D511yescharacteristic
592Q16—601no—
593SD16—102no—
594SD16—201no—
595C2×C8—51no—
596C2×C8—51no—
597C2×C8—151no—
598C2×C8—151no—
599C2×C8—601no—
600C2×C8—601no—
601C4⋊C4—21no—
602C4⋊C4—31no—
603C4⋊C4—31no—
604C4⋊C4—31no—
605C4⋊C4—61no—
606C4⋊C4—61no—
607C4⋊C4—61no—
608C4⋊C4—61no—
609C4⋊C4—61no—
610C4⋊C4—151no—
611C4⋊C4—301no—
612C4⋊C4C2×D3×D511yescharacteristic
613C22⋊C4—21no—
614C22⋊C4—31no—
615C22⋊C4—31no—
616C22⋊C4—61no—
617C22⋊C4—61no—
618C22⋊C4—301no—
619C22⋊C4—301no—
620C22⋊C4—301no—
621C22⋊C4—301no—
622C22⋊C4—301no—
623C42—31no—
624C42—61no—
625C42—61no—
626C3×C5#329611yescharacteristic, complemented, Hall
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—102no—
630C22×C3—201no—
631C22×C3—201no—
632C22×C3—201no—
633C22×C3—201no—
634C22×C3—201no—
635C22×C3—404no—
636C22×C3#409612yes—
637C22×C3C22×C22⋊D511yescharacteristic
638C2×D3—21no—
639C2×D3—21no—
640C2×D3—21no—
641C3×C4—21no—
642C3×C4—41no—
643C3×C4—41no—
644C3×C4D5×#4111yescharacteristic
645C3×C4#414911yescharacteristic
646Dic3—21no—
647Dic3—21no—
648Dic3—21no—
649Dic3—41no—
650Dic3—41no—
651Dic3—201no—
652Dic3—201no—
653C2×C5—22no—
654C2×C5—121no—
655C2×C5#559111yescharacteristic
656C2×C5C2×#91611yescharacteristic
657C2×C5#577511yescharacteristic
658D5—42no—
659D5—81no—
660C23—31no—
661C23—101no—
662C23—101no—
663C23—202no—
664C23—202no—
665C23—401no—
666C23D3×C22⋊D511yescharacteristic
667Q8—21no—
668Q8—21no—
669Q8—301no—
670Q8—301no—
671D4—52no—
672D4—62no—
673D4—101no—
674D4—101no—
675D4—101no—
676D4—202no—
677D4—602no—
678D4—1201no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—31no—
684C2×C4—31no—
685C2×C4—31no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—122no—
691C2×C4—301no—
692C2×C4—301no—
693C2×C4—602no—
694C2×C4—1201no—
695C2×C4D3×C22⋊D511yescharacteristic
696C2×C4C22×D3×D511yescharacteristic
697C8—101no—
698C8—101no—
699C8—301no—
700C8—301no—
701C2×C3—22no—
702C2×C3—202no—
703C2×C3—401no—
704C2×C3C2×#409611yescharacteristic
705C2×C3#6616311yescharacteristic
706C2×C3#6617111yescharacteristic
707D3—41no—
708C5#8015911yescharacteristic, complemented, Sylow
709C22—21no—
710C22—21no—
711C22—61no—
712C22—61no—
713C22—61no—
714C22—102no—
715C22—201no—
716C22—201no—
717C22—201no—
718C22—201no—
719C22—201no—
720C22—404no—
721C22#9151712yes—
722C22C2×D3×C22⋊D511yescharacteristic
723C4—21no—
724C4—41no—
725C4—41no—
726C4—61no—
727C4—61no—
728C4—61no—
729C4—121no—
730C4—121no—
731C4—601no—
732C4—601no—
733C4D5×#23711yescharacteristic
734C4#9202611yescharacteristic
735C3#1061532911yescharacteristic, complemented, Sylow
736C2—22no—
737C2—121no—
738C2—202no—
739C2—401no—
740C2#1175506611yescharacteristic
741C2C2×#9151711yescharacteristic
742C2#1175532411yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C22⋊Q8C22
socleC22×C3×C5C22×D4
prime radical#11754305C2
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. C5×#5642C2semidirect
3. #11751152C2semidirect
4. C3×#65335C2semidirect
5. #11749403C2semidirect
6. #11749325C2semidirect
7. #11749274C2semidirect
8. Dic3×#688C2semidirect
9. #67⋊#168C2semidirect
10. #11748444C2semidirect
11. C2×#90964C2semidirect
12. #11747502C2semidirect
13. #11747374C2semidirect
14. #11747322C2semidirect
15. #11747249C2semidirect
20. C2×#6718C22semidirect
23. C5×#946C22semidirect
24. C5×Q8×Dic3C22semidirect
28. C5×#892C22semidirect
30. C5×#890C22semidirect
42. C2×D3×#168C22semidirect
43. #91119C22semidirect
44. #91094C22semidirect
45. #91091C22semidirect
49. #90985C22semidirect
50. #90985C22semidirect
51. Dic3⋊#168C22semidirect
52. #90975C22semidirect
53. #90975C22semidirect
58. (C2×D3)⋊#168C22semidirect
59. Dic3×#168C22semidirect
68. #65335D3semidirect
129. #5642D5semidirect
235. #946C2×D5semidirect
236. Q8×Dic3C2×D5semidirect
249. #892C2×D5semidirect
251. #890C2×D5semidirect
626. C3×C5#3296semidirect
708. C5#80159semidirect
735. C3#10615329semidirect

Maximal subgroups

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

subgroupindex
C5×#56422
#117543052
#117511522
C3×#653352
#117494032
#117493252
#117492742
Dic3×#6882
#67⋊#1682
#117484442
C2×#909642
#117475022
#117473742
#117473222
#117472492
#106153293
#801595