Finite Group Databasebeta

← #14458705

Subgroups — #14458705

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
1#11756309C211yesmaximal, characteristic
2C3×#65875C211yesmaximal, characteristic, complemented
3C5×D4×C3⋊C8C211yesmaximal, characteristic, complemented
4#11748560C211yesmaximal, characteristic, complemented
5#11748552C211yesmaximal, characteristic, complemented
6#11748551C211yesmaximal, characteristic, complemented
7#11748541C211yesmaximal, characteristic, complemented
8#11748452C211yesmaximal, characteristic, complemented
9#11748450C211yesmaximal, characteristic, complemented
10#11748411C211yesmaximal, characteristic, complemented
11C2×#90968C211yesmaximal, characteristic, complemented
12#11747065C211yesmaximal, characteristic, complemented
13C4×#6658C211yesmaximal, characteristic, complemented
14#11746951C211yesmaximal, characteristic, complemented
15#11746933C211yesmaximal, characteristic, complemented
16#10611171—31nomaximal, Hall
17C2×#6817C2211yescharacteristic
18C22×D60C2211yescharacteristic
19C3×C4×C5×D4C2211yescharacteristic
20#91826—21no—
21#91819C2211yescharacteristic
22#91813C2211yescharacteristic
23#91783—21no—
24#91773—21no—
25C22⋊C4×D15—21no—
26#91764C2211yescharacteristic
27C4×D60C2211yescharacteristic
28C22×C5×C3⋊C8C2211yescharacteristic
29C22×C5×C3⋊C8C2211yescharacteristic, complemented
30C3×#4081—21no—
31C3×#4072C2211yescharacteristic, complemented
32C2×C3×C4⋊Dic5C2211yescharacteristic
33C3×#4070C2211yescharacteristic
34C3×#4070C2211yescharacteristic, complemented
35C3×#4035—21no—
36C3×#4025—21no—
37C3×#4023—21no—
38C3×#4016C2211yescharacteristic, complemented
39C3×C4×Dic10C2211yescharacteristic, complemented
40C2×#6662C2211yescharacteristic, complemented
41C2×#6658C2211yescharacteristic
42C2×#6658C2211yescharacteristic
43C5×#830C2211yescharacteristic
44C5×#830C2211yescharacteristic, complemented
45C5×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
46C4×C5×C3⋊C8C2211yescharacteristic, complemented
47#90990C2211yescharacteristic, complemented
48#90987C2211yescharacteristic, complemented
49#90987C2211yescharacteristic, complemented
50#90974C2211yescharacteristic, complemented
51#90974C2211yescharacteristic, complemented
52#90974C2211yescharacteristic, complemented
53#90971C2211yescharacteristic, complemented
54#90968C2211yescharacteristic
55#90968C2211yescharacteristic
56#90968C2211yescharacteristic
57#90968C2211yescharacteristic
58#90968C2211yescharacteristic
59#90968C2211yescharacteristic
60#83598—51nomaximal, Hall
61#65884—31no—
62#65875D311yescharacteristic, complemented
63C5×C8×D4—31no—
64#65405—31no—
65#65403—31no—
66#65402—31no—
67C2×#3953—31no—
68#65136—31no—
69#65134—31no—
70#65026—31no—
71#65022—31no—
72#65020—31no—
73#65010—31no—
74#64986—31no—
75C4×#677—31no—
76C23×D15—21no—
77C2×C3×C5×D4D411yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×C3×C4×C5C2311yescharacteristic
80C2×#1220—21no—
81C2×#1220—21no—
82#6817—22no—
83#6817—41no—
84C2×D60—22no—
85C2×D60—21no—
86C2×D60—41no—
87C2×D60C2311yescharacteristic
88C2×D60C2311yescharacteristic
89C2×C4×D15—21no—
90C2×C4×D15—21no—
91C2×Dic30C2311yescharacteristic
92C22×C3×Dic5—21no—
93C2×C3×Dic10C2311yescharacteristic
94C3×C5×C4⋊C4D411yescharacteristic
95C3×C5×C22⋊C4D411yescharacteristic
96C3×C5×C22⋊C4D411yescharacteristic
97C3×C42×C5C2311yescharacteristic
98#6719—21no—
99#6714—21no—
100#6714—21no—
101#6714—21no—
102#6714—21no—
103C4⋊Dic15C2311yescharacteristic
104#6712—21no—
105C2×C5×C3⋊C8—41no—
106C2×C5×C3⋊C8—41no—
107C2×C5×C3⋊C8C2311yescharacteristic
108C2×C5×C3⋊C8C2311yescharacteristic
109C2×C5×C3⋊C8C2311yescharacteristic
110C2×C5×C3⋊C8C2311yescharacteristic
111C3×C22⋊Dic5—21no—
112C3×C22⋊Dic5—21no—
113C3×C22⋊Dic5—21no—
114C3×C4⋊Dic5—21no—
115C3×C4⋊Dic5C2311yescharacteristic
116C3×C4⋊Dic5C2311yescharacteristic
117C3×C4⋊Dic5C2311yescharacteristic
118C3×#683—21no—
119C3×#683—21no—
120C3×#683—21no—
121C3×#683—21no—
122C3×#683—21no—
123C3×C4×Dic5—21no—
124C3×C4×Dic5—21no—
125#6662—41no—
126#6658—22no—
127#6658—41no—
128C3×#552—51no—
129#5550—51no—
130#5068—51no—
131#5066—51no—
132#5051—51no—
133#5048—51no—
134#5047—51no—
135#5046—51no—
136#5028—51no—
137C4×#215—51no—
138D4×C3⋊C8D511yescharacteristic, complemented
139#5003—51no—
140#5002—51no—
141#4971—51no—
142C2×#809—51no—
143C2×#709—31no—
144C22×D20—31no—
145C22×C5×C8—31no—
146C22×C5×C8—31no—
147C4×C5×D4C2×D311yescharacteristic
148#4083—61no—
149#4081—21no—
150#4076—31no—
151#4072C2×D311yescharacteristic, complemented
152C2×C4⋊Dic5C2×D311yescharacteristic
153#4070—31no—
154#4070C2×D311yescharacteristic
155#4070C2×D311yescharacteristic, complemented
156C2×Dic20—31no—
157C2×#677—31no—
158C2×#677—31no—
159#4040—61no—
160#4035—21no—
161#4030—61no—
162D5×C22⋊C4—61no—
163#4025—21no—
164#4023—21no—
165#4021—31no—
166C4×D20—31no—
167#4016C2×D311yescharacteristic, complemented
168C4×Dic10C2×D311yescharacteristic, complemented
169C5×C4⋊C8—31no—
170C5×C22⋊C8—31no—
171C5×C22⋊C8—31no—
172C4×C5×C8—31no—
173#3953—31no—
174#3953—31no—
175#3953—31no—
176#3953—31no—
177#3953—31no—
178#3953—31no—
179#3950—31no—
180#3949—31no—
181#3949—31no—
182#3948—31no—
183#3948—31no—
184#3948—31no—
185#3948—31no—
186#3296—151noSylow
187C23×C3×C5C2×D411yescharacteristic
188C23×C3×C5C2×D411yescharacteristic
189C22×D15—21no—
190C22×D15—21no—
191C22×D15—42no—
192C22×D15—42no—
193C22×D15—81no—
194C3×C5×D4—22no—
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5C2×D411yescharacteristic
200C2×C3×C4×C5C2×D411yescharacteristic
201C2×C3×C4×C5C2×D411yescharacteristic
202C2×C3×C4×C5C2×D411yescharacteristic
203C2×C3×C4×C5C2411yescharacteristic
204#1220—42no—
205#1220—81no—
206C2×Dic15—21no—
207C2×Dic15—21no—
208D60—21no—
209D60—21no—
210D60—21no—
211D60—42no—
212D60#4112yes—
213C4×D15—42no—
214C4×D15—81no—
215Dic30—21no—
216Dic30—21no—
217C2×C3×Dic5—21no—
218C2×C3×Dic5—21no—
219C2×C3×Dic5—21no—
220C2×C3×Dic5—21no—
221C2×C3×Dic5—42no—
222C3×Dic10—21no—
223C3×Dic10—21no—
224C5×C3⋊C8—21no—
225C5×C3⋊C8—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⋊Q8—51no—
236C3×C4×Q8—51no—
237C3×C4×D4C2×D511yescharacteristic
238C3×#117—51no—
239C3×#117—101no—
240C2×C3×C4⋊C4—51no—
241C2×#216—51no—
242C2×#215—51no—
243C2×#215—51no—
244#937—101no—
245#930—51no—
246#924—51no—
247C22×C3⋊C8C2×D511yescharacteristic
248C22×C3⋊C8C2×D511yescharacteristic, complemented
249#894—101no—
250#884—101no—
251D3×C22⋊C4—101no—
252#875—51no—
253C4×D12—51no—
254#835—51no—
255#830C2×D511yescharacteristic
256#830C2×D511yescharacteristic, complemented
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#809—51no—
266#808—51no—
267#808—51no—
268#807—51no—
269C4⋊(C3⋊C8)C2×D511yescharacteristic, complemented
270C4×C3⋊C8C2×D511yescharacteristic, complemented
271C23×D5—61no—
272C2×C5×D4#6711yescharacteristic
273C22×C4×C5C22×D311yescharacteristic
274C22×C4×C5C22×D311yescharacteristic
275C2×C22⋊D5—61no—
276C2×C22⋊D5—61no—
277C22×Dic5—21no—
278#709—62no—
279#709—121no—
280C2×D20—31no—
281C2×D20—31no—
282C2×D20—62no—
283C2×D20—61no—
284C2×D20—121no—
285C2×C4×D5—61no—
286C2×C4×D5—61no—
287C2×Dic10—31no—
288C2×Dic10C22×D311yescharacteristic
289C2×C5×C8—31no—
290C2×C5×C8—31no—
291C2×C5×C8—31no—
292C2×C5×C8—31no—
293C2×C5×C8—121no—
294C2×C5×C8—121no—
295C5×C4⋊C4#6711yescharacteristic
296C5×C22⋊C4#6711yescharacteristic
297C5×C22⋊C4#6711yescharacteristic
298C42×C5C22×D311yescharacteristic
299C22⋊Dic5—21no—
300C22⋊Dic5—21no—
301C22⋊Dic5—21no—
302C22⋊Dic5—61no—
303#685—61no—
304#685—61no—
305#685—61no—
306#685—61no—
307C4⋊Dic5—21no—
308C4⋊Dic5—31no—
309C4⋊Dic5C22×D311yescharacteristic
310C4⋊Dic5C22×D311yescharacteristic
311C4⋊Dic5C22×D311yescharacteristic
312#683—21no—
313#683—21no—
314#683—21no—
315#683—21no—
316#683—21no—
317#683—61no—
318C4×Dic5—21no—
319C4×Dic5—21no—
320Dic20—121no—
321#677—62no—
322#677—121no—
323#552—51no—
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—151no—
334C4×SD16—151no—
335C8×D4—31no—
336#416—151no—
337C2×#102—151no—
338C22×C3×C5—21no—
339C22×C3×C5—21no—
340C22×C3×C5—21no—
341C22×C3×C5—21no—
342C22×C3×C5—21no—
343C22×C3×C5#13512yes—
344C22×C3×C5C22×D411yescharacteristic
345C2×D15—22no—
346C2×D15—41no—
347C2×D15—41no—
348C2×D15—41no—
349C2×D15—41no—
350C2×D15—41no—
351C2×D15—84no—
352C3×C4×C5—21no—
353C3×C4×C5—21no—
354C3×C4×C5—21no—
355C3×C4×C5—21no—
356C3×C4×C5C2×#4111yescharacteristic
357C3×C4×C5H(5,𝔽2)11yescharacteristic
358Dic15—41no—
359Dic15—41no—
360C3×Dic5—41no—
361C3×Dic5—41no—
362C3×Dic5—41no—
363C3×Dic5—41no—
364C23×D3—101no—
365C2×C3×Q8—51no—
366C2×C3×D4D2011yescharacteristic
367C22×C3×C4—101no—
368C22×C3×C4C22×D511yescharacteristic
369C22×C3×C4C22×D511yescharacteristic
370C2×#67—101no—
371C2×#67—101no—
372#235—102no—
373#235—201no—
374C2×D12—51no—
375C2×D12—51no—
376C2×D12—102no—
377C2×D12—101no—
378C2×D12—201no—
379C2×C4×D3—101no—
380C2×C4×D3—101no—
381C2×Dic6—51no—
382C3×C4⋊C4—51no—
383C3×C4⋊C4—51no—
384C3×C4⋊C4—51no—
385C3×C4⋊C4—101no—
386C3×C4⋊C4—101no—
387C3×C4⋊C4—101no—
388C3×C4⋊C4—101no—
389C3×C4⋊C4—101no—
390C3×C4⋊C4—101no—
391C3×C4⋊C4D2011yescharacteristic
392C3×C22⋊C4—101no—
393C3×C22⋊C4—101no—
394C3×C22⋊C4—101no—
395C3×C22⋊C4D2011yescharacteristic
396C3×C22⋊C4D2011yescharacteristic
397C3×C42—101no—
398C3×C42—101no—
399C3×C42C22×D511yescharacteristic
400#217—101no—
401#216—201no—
402#215—102no—
403#215—201no—
404(C2×D3)⋊C4—101no—
405(C2×D3)⋊C4—101no—
406(C2×D3)⋊C4—101no—
407(C2×D3)⋊C4—101no—
408C4⋊Dic3—51no—
409Dic3⋊C4—101no—
410C2×C3⋊C8—41no—
411C2×C3⋊C8—41no—
412C2×C3⋊C8C22×D511yescharacteristic
413C2×C3⋊C8C22×D511yescharacteristic
414C2×C3⋊C8C22×D511yescharacteristic
415C2×C3⋊C8C22×D511yescharacteristic
416C23×C5C2×#6711yescharacteristic
417C23×C5C2×#6711yescharacteristic
418C22×D5—61no—
419C22×D5—61no—
420C22×D5—122no—
421C22×D5—122no—
422C22×D5—241no—
423C5×D4—22no—
424C2×C4×C5—21no—
425C2×C4×C5—21no—
426C2×C4×C5—21no—
427C2×C4×C5—21no—
428C2×C4×C5C2×#6711yescharacteristic
429C2×C4×C5C2×#6711yescharacteristic
430C2×C4×C5C2×#6711yescharacteristic
431C2×C4×C5C2×#6711yescharacteristic
432C2×C4×C5C23×D311yescharacteristic
433C22⋊D5—122no—
434C22⋊D5—241no—
435C2×Dic5—21no—
436C2×Dic5—21no—
437C2×Dic5—21no—
438C2×Dic5—21no—
439C2×Dic5—42no—
440C2×Dic5—61no—
441C2×Dic5—61no—
442D20—32no—
443D20—61no—
444D20—61no—
445D20—61no—
446D20—122no—
447C4×D5—122no—
448C4×D5—241no—
449Dic10—21no—
450Dic10—21no—
451Dic10—61no—
452Dic10—61no—
453C5×C8—61no—
454C5×C8—61no—
455C5×C8—61no—
456C5×C8—61no—
457C2×#41—151no—
458C22×D4—151no—
459C2×Q16—151no—
460C2×SD16—151no—
461C2×SD16—151no—
462C22×C8—31no—
463C22×C8—31no—
464#126—101no—
465#125—51no—
466#125—101no—
467#124—151no—
468#123—101no—
469#123—301no—
470C22⋊Q8—51no—
471C22⋊Q8—51no—
472C22⋊Q8—151no—
473#121—151no—
474#121—301no—
475#120—301no—
476C4×Q8—51no—
477C4×D4—151no—
478C4×D4D3×D511yescharacteristic
479#117—51no—
480#117—101no—
481C2×C4⋊C4—51no—
482C2×C22⋊C4—301no—
483#107—151no—
484#106—151no—
485#106—151no—
486C4⋊C8—31no—
487#103—151no—
488#103—151no—
489#103—151no—
490#103—151no—
491#102—151no—
492#102—151no—
493#102—151no—
494#102—151no—
495#102—151no—
496#102—151no—
497C22⋊C8—31no—
498C22⋊C8—31no—
499C4×C8—31no—
500C2×C3×C5—22no—
501C2×C3×C5—41no—
502C2×C3×C5#54611yescharacteristic
503C2×C3×C5C2×#13511yescharacteristic
504C2×C3×C5#57711yescharacteristic
505D15—42no—
506D15—81no—
507C23×C3C2×D2011yescharacteristic
508C23×C3C2×D2011yescharacteristic
509C22×D3—101no—
510C22×D3—101no—
511C22×D3—202no—
512C22×D3—202no—
513C22×D3—401no—
514C3×Q8—101no—
515C3×Q8—101no—
516C3×D4—22no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—101no—
522C2×C3×C4—101no—
523C2×C3×C4—101no—
524C2×C3×C4—101no—
525C2×C3×C4—202no—
526C2×C3×C4C2×D2011yescharacteristic
527C2×C3×C4C2×D2011yescharacteristic
528C2×C3×C4C2×D2011yescharacteristic
529C2×C3×C4C2×D2011yescharacteristic
530C2×C3×C4C23×D511yescharacteristic
531#67—202no—
532#67—401no—
533C2×Dic3—101no—
534C2×Dic3—101no—
535D12—52no—
536D12—101no—
537D12—101no—
538D12—101no—
539D12—202no—
540C4×D3—202no—
541C4×D3—401no—
542Dic6—101no—
543Dic6—101no—
544C3⋊C8—21no—
545C3⋊C8—21no—
546C3⋊C8—21no—
547C3⋊C8—21no—
548C22×C5—21no—
549C22×C5—21no—
550C22×C5—21no—
551C22×C5—21no—
552C22×C5—21no—
553C22×C5#95012yes—
554C22×C5C22×#6711yescharacteristic
555C2×D5—62no—
556C2×D5—121no—
557C2×D5—121no—
558C2×D5—121no—
559C2×D5—121no—
560C2×D5—121no—
561C2×D5—244no—
562C4×C5—21no—
563C4×C5—21no—
564C4×C5—21no—
565C4×C5—21no—
566C4×C5D3×#4111yescharacteristic
567C4×C5#100911yescharacteristic
568Dic5—41no—
569Dic5—41no—
570Dic5—41no—
571Dic5—41no—
572Dic5—121no—
573Dic5—121no—
574C24—301no—
575#41—302no—
576#41—601no—
577C2×Q8—51no—
578C2×Q8—151no—
579C2×D4—151no—
580C2×D4—151no—
581C2×D4—302no—
582C2×D4—301no—
583C2×D4—301no—
584C2×D4—301no—
585C2×D4—601no—
586C2×D4#120211yescharacteristic
587C22×C4—101no—
588C22×C4—301no—
589C22×C4—301no—
590C22×C4C2×D3×D511yescharacteristic
591C22×C4C2×D3×D511yescharacteristic
592Q16—601no—
593SD16—302no—
594SD16—601no—
595C2×C8—31no—
596C2×C8—31no—
597C2×C8—31no—
598C2×C8—31no—
599C2×C8—121no—
600C2×C8—121no—
601C4⋊C4—51no—
602C4⋊C4—51no—
603C4⋊C4—51no—
604C4⋊C4—101no—
605C4⋊C4—101no—
606C4⋊C4—101no—
607C4⋊C4—101no—
608C4⋊C4—101no—
609C4⋊C4—101no—
610C4⋊C4—151no—
611C4⋊C4—301no—
612C4⋊C4#120211yescharacteristic
613C22⋊C4—101no—
614C22⋊C4—101no—
615C22⋊C4—101no—
616C22⋊C4—301no—
617C22⋊C4—301no—
618C22⋊C4—301no—
619C22⋊C4—301no—
620C22⋊C4—301no—
621C22⋊C4#120211yescharacteristic
622C22⋊C4#120211yescharacteristic
623C42—101no—
624C42—101no—
625C42C2×D3×D511yescharacteristic
626C3×C5#329611yescharacteristic, complemented, Hall
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3#405012yes—
633C22×C3C22×D2011yescharacteristic
634C2×D3—102no—
635C2×D3—201no—
636C2×D3—201no—
637C2×D3—201no—
638C2×D3—201no—
639C2×D3—201no—
640C2×D3—404no—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—21no—
644C3×C4—21no—
645C3×C4—201no—
646C3×C4—201no—
647C3×C4—201no—
648C3×C4—201no—
649C3×C4#414411yescharacteristic
650C3×C4D5×#4111yescharacteristic
651Dic3—201no—
652Dic3—201no—
653C2×C5—22no—
654C2×C5—41no—
655C2×C5C2×#95011yescharacteristic
656C2×C5#582911yescharacteristic
657C2×C5#583711yescharacteristic
658D5—122no—
659D5—241no—
660C23—301no—
661C23—301no—
662C23—602no—
663C23—602no—
664C23—1201no—
665C23C2×#120211yescharacteristic
666C23C2×#120211yescharacteristic
667Q8—101no—
668Q8—101no—
669Q8—301no—
670Q8—301no—
671D4—22no—
672D4—152no—
673D4—301no—
674D4—301no—
675D4—301no—
676D4—602no—
677D4—602no—
678D4—1201no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—101no—
684C2×C4—101no—
685C2×C4—101no—
686C2×C4—101no—
687C2×C4—202no—
688C2×C4—301no—
689C2×C4—301no—
690C2×C4—602no—
691C2×C4—1201no—
692C2×C4C2×#120211yescharacteristic
693C2×C4C2×#120211yescharacteristic
694C2×C4C2×#120211yescharacteristic
695C2×C4C2×#120211yescharacteristic
696C2×C4C22×D3×D511yescharacteristic
697C8—61no—
698C8—61no—
699C8—61no—
700C8—61no—
701C2×C3—22no—
702C2×C3—41no—
703C2×C3#6588811yescharacteristic
704C2×C3C2×#405011yescharacteristic
705C2×C3#6608511yescharacteristic
706D3—202no—
707D3—401no—
708C5#8359811yescharacteristic, complemented, Sylow
709C22—21no—
710C22—21no—
711C22—21no—
712C22—21no—
713C22—21no—
714C22—302no—
715C22—601no—
716C22—601no—
717C22—601no—
718C22—601no—
719C22—601no—
720C22—1204no—
721C22#9131112yes—
722C22C22×#120211yescharacteristic
723C4—21no—
724C4—21no—
725C4—21no—
726C4—21no—
727C4—201no—
728C4—201no—
729C4—201no—
730C4—201no—
731C4—601no—
732C4—601no—
733C4#9202411yescharacteristic
734C4#9202711yescharacteristic
735C3#1061117111yescharacteristic, complemented, Sylow
736C2—22no—
737C2—41no—
738C2—602no—
739C2—1201no—
740C2C2×#9131111yescharacteristic
741C2#1175498011yescharacteristic
742C2#1175531011yescharacteristic
subgroupG/H
centerC22C22×#1202
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radical#11756309C2
hypercenterC4×D4D3×D5
hypocenterC3×C5#3296
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C3×#65875C2semidirect
3. C5×D4×C3⋊C8C2semidirect
4. #11748560C2semidirect
5. #11748552C2semidirect
6. #11748551C2semidirect
7. #11748541C2semidirect
8. #11748452C2semidirect
9. #11748450C2semidirect
10. #11748411C2semidirect
11. C2×#90968C2semidirect
12. #11747065C2semidirect
13. C4×#6658C2semidirect
14. #11746951C2semidirect
15. #11746933C2semidirect
29. C22×C5×C3⋊C8C22semidirect
31. C3×#4072C22semidirect
34. C3×#4070C22semidirect
38. C3×#4016C22semidirect
39. C3×C4×Dic10C22semidirect
40. C2×#6662C22semidirect
44. C5×#830C22semidirect
45. C5×C4⋊(C3⋊C8)C22semidirect
46. C4×C5×C3⋊C8C22semidirect
47. #90990C22semidirect
48. #90987C22semidirect
49. #90987C22semidirect
50. #90974C22semidirect
51. #90974C22semidirect
52. #90974C22semidirect
53. #90971C22semidirect
62. #65875D3semidirect
138. D4×C3⋊C8D5semidirect
151. #4072C2×D3semidirect
155. #4070C2×D3semidirect
167. #4016C2×D3semidirect
168. C4×Dic10C2×D3semidirect
248. C22×C3⋊C8C2×D5semidirect
256. #830C2×D5semidirect
269. C4⋊(C3⋊C8)C2×D5semidirect
270. C4×C3⋊C8C2×D5semidirect
626. C3×C5#3296semidirect
708. C5#83598semidirect
735. C3#10611171semidirect

Maximal subgroups

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

subgroupindex
#117563092
C3×#658752
C5×D4×C3⋊C82
#117485602
#117485522
#117485512
#117485412
#117484522
#117484502
#117484112
C2×#909682
#117470652
C4×#66582
#117469512
#117469332
#106111713
#835985