Finite Group Databasebeta

← #14417036

Subgroups — #14417036

Order 1920.

1012 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91803C211yesmaximal, characteristic
2#11755149C211yesmaximal, characteristic, complemented
3#11754922C211yesmaximal, characteristic, complemented
4C5×#5164C211yesmaximal, characteristic, complemented
5C3×SD16×Dic5C211yesmaximal, characteristic, complemented
6#11749232C211yesmaximal, characteristic, complemented
7#11749225C211yesmaximal, characteristic, complemented
8#11749215C211yesmaximal, characteristic, complemented
9#11748986C211yesmaximal, characteristic, complemented
10#11748979C211yesmaximal, characteristic, complemented
11#11748957C211yesmaximal, characteristic, complemented
12#11748053C211yesmaximal, characteristic, complemented
13#11747796C211yesmaximal, characteristic, complemented
14#11747766C211yesmaximal, characteristic, complemented
15#11747638C211yesmaximal, characteristic, complemented
16#10611506—31nomaximal, Hall
17C2×#6821C2211yescharacteristic
18C2×D4×D15C2211yescharacteristic
19C2×C3×C5×SD16C2211yescharacteristic
20C2×#6717C2211yescharacteristic
21C2×#6715C2211yescharacteristic
22#91803C418yescomplemented
23C2×D120C2211yescharacteristic
24C2×#6705C2211yescharacteristic
25C5×Q8×Dic3C2211yescharacteristic, complemented
26C5×D4×Dic3C2211yescharacteristic
27C3×Q8×Dic5C2211yescharacteristic, complemented
28C3×D4×Dic5C2211yescharacteristic
29#91561—21no—
30#91556—21no—
31#91552—21no—
32C2×#6667—21no—
33#91437—21no—
34#91437C2211yescharacteristic
35#91428—21no—
36#91428C2211yescharacteristic
37#91428C2211yescharacteristic, complemented
38#91418—21no—
39#91418C2211yescharacteristic
40#91418C2211yescharacteristic, complemented
41#91386—21no—
42#91386C2211yescharacteristic
43#91347C2211yescharacteristic
44C2×#6648C2211yescharacteristic
45C5×#835C2211yescharacteristic, complemented
46C5×#832C2211yescharacteristic
47C5×#818C2211yescharacteristic, complemented
48C5×#815C2211yescharacteristic, complemented
49C3×#3967C2211yescharacteristic, complemented
50C3×#3964C2211yescharacteristic
51C3×#3949C2211yescharacteristic, complemented
52C3×C8×Dic5C2211yescharacteristic, complemented
53#90989C2211yescharacteristic, complemented
54#90986C2211yescharacteristic, complemented
55#90969C2211yescharacteristic
56#90969C2211yescharacteristic, complemented
57#90968C2211yescharacteristic
58#90968C2211yescharacteristic, complemented
59#90952C2211yescharacteristic, complemented
60Dic3×#168C2211yescharacteristic, complemented
61#79647—51nomaximal, Hall
62C2×#4060—31no—
63#65908—31no—
64#65879—31no—
65C5×#440—31no—
66SD16×Dic5D311yescharacteristic, complemented
67C4×#688—31no—
68C4×#686—31no—
69#65170—31no—
70#65161—31no—
71#65106—31no—
72#65093—31no—
73#65074—31no—
74D5×#102—31no—
75#65000—31no—
76#64997—31no—
77C23×D15—21no—
78C2×C3×C5×Q8C2311yescharacteristic
79C2×C3×C5×D4C2311yescharacteristic
80C2×#1220—21no—
81#6821—22no—
82#6821C2×C414yescomplemented
83D4×D15—22no—
84D4×D15C2×C414yescomplemented
85C2×D60—21no—
86C2×D60C2311yescharacteristic
87C2×D60C2311yescharacteristic
88C2×C4×D15—21no—
89C2×C4×D15C2311yescharacteristic
90C22×C5×Dic3—21no—
91C22×C3×Dic5—21no—
92C2×#1200—21no—
93C2×#1200—21no—
94C2×#1200—21no—
95C2×#1200—21no—
96C2×#1200—21no—
97C3×C5×SD16C2×C414yescomplemented
98C2×C3×C5×C8C2311yescharacteristic
99#6717C2×C414yescomplemented
100#6715C2×C414yescomplemented
101C2×C3⋊#168C2311yescharacteristic
102D120C2×C414yescomplemented
103#6705C2×C414yescomplemented
104C5×#217—21no—
105C5×C4⋊Dic3—21no—
106C5×C4⋊Dic3C2311yescharacteristic
107C5×C4⋊Dic3C2311yescharacteristic
108C4×C5×Dic3—21no—
109C4×C5×Dic3C2311yescharacteristic
110C2×C5×C3⋊C8C2311yescharacteristic
111C3×C22⋊Dic5—21no—
112C3×C4⋊Dic5—21no—
113C3×C4⋊Dic5C2311yescharacteristic
114C3×C4⋊Dic5C2311yescharacteristic
115C3×C4×Dic5—21no—
116C3×C4×Dic5C2311yescharacteristic
117C2×C3×#168C2311yescharacteristic
118#6669—21no—
119#6669D411yescharacteristic
120#6669D411yescharacteristic
121#6667—21no—
122#6667—21no—
123#6667—21no—
124#6667—21no—
125#6667—21no—
126#6667D411yescharacteristic
127#6667D411yescharacteristic
128Dic3×Dic5—21no—
129#6648—22no—
130C2×#914—51no—
131#5574—51no—
132#5545—51no—
133C3×C4×SD16—51no—
134#5164D511yescharacteristic, complemented
135#5026—51no—
136#5014—51no—
137#4869—51no—
138#4861—51no—
139#4804—51no—
140#4788—51no—
141D3×#102—51no—
142#4756—51no—
143C4×D24—51no—
144#4689—51no—
145C2×#713—31no—
146C2×D4×D5—31no—
147C2×C5×SD16C2×D311yescharacteristic
148C4×C5×Q8—31no—
149C4×C5×D4—31no—
150Q8×Dic5C2×D311yescharacteristic, complemented
151C2×#688—31no—
152D4×Dic5C2×D311yescharacteristic
153C2×#686—31no—
154C4×C22⋊D5—61no—
155C2×#685—61no—
156#4060—38no—
157C2×D40—31no—
158C2×#676—31no—
159C2×C8×D5—31no—
160#4039—31no—
161#4039—31no—
162#4039—61no—
163#4038—31no—
164D5×C4⋊C4—31no—
165D5×C4⋊C4—61no—
166#4027—61no—
167D5×C22⋊C4—61no—
168C4×D20—31no—
169C4×D20—31no—
170C4×D20—61no—
171#4018—31no—
172#4018—61no—
173C5×#107—31no—
174C5×#103—31no—
175C5×#102—31no—
176C5×#97—31no—
177#3967C2×D311yescharacteristic, complemented
178#3964C2×D311yescharacteristic
179#3953—31no—
180#3953—31no—
181#3949C2×D311yescharacteristic, complemented
182#3947—31no—
183C8×Dic5C2×D311yescharacteristic, complemented
184#3941—31no—
185#3941—31no—
186#3940—31no—
187#3939—31no—
188C4×#168—31no—
189#2946—151noSylow
190C23×C3×C5—21no—
191C22×D15—21no—
192C22×D15—21no—
193C22×D15—24no—
194C22×D15—81no—
195C22×D15—81no—
196C22×D15C2×D411yescharacteristic
197C3×C5×Q8—21no—
198C3×C5×Q8C22×C412yes—
199C3×C5×D4—21no—
200C3×C5×D4C22×C412yes—
201C2×C3×C4×C5—21no—
202C2×C3×C4×C5C2411yescharacteristic
203#1220—24no—
204C2×Dic15C2×D411yescharacteristic
205D60—24no—
206D60—21no—
207D60—21no—
208D60C22×C412yes—
209D60C22×C412yes—
210C4×D15—24no—
211C4×D15C22×C412yes—
212C4×D15#4112yes—
213C2×C5×Dic3—21no—
214C2×C5×Dic3—21no—
215C2×C5×Dic3—81no—
216C2×C5×Dic3C2×D411yescharacteristic
217C2×C5×Dic3C2×D411yescharacteristic
218C2×C3×Dic5—21no—
219C2×C3×Dic5—21no—
220C2×C3×Dic5—81no—
221C2×C3×Dic5C2×D411yescharacteristic
222C2×C3×Dic5C2×D411yescharacteristic
223#1200—81no—
224#1200—81no—
225#1200—81no—
226#1200—81no—
227#1200—81no—
228C3×C5×C8C22×C412yes—
229C3⋊#168C22×C412yes—
230C3×#168—21no—
231C5×C3⋊C8—21no—
232C2×#239—51no—
233C2×D3×D4—51no—
234C2×C3×SD16C2×D511yescharacteristic
235C3×C4×Q8—51no—
236C3×C4×D4—51no—
237Q8×Dic3C2×D511yescharacteristic, complemented
238C2×#215—51no—
239D4×Dic3C2×D511yescharacteristic
240C2×#213—51no—
241C4×#67—101no—
242C2×(C2×D3)⋊C4—101no—
243#914—58no—
244C2×D24—51no—
245C2×ΓL(1,𝔽25)—51no—
246C2×D3×C8—51no—
247#893—51no—
248#893—51no—
249#893—101no—
250#892—51no—
251D3×C4⋊C4—51no—
252D3×C4⋊C4—101no—
253#67⋊C4—101no—
254D3×C22⋊C4—101no—
255C4×D12—51no—
256C4×D12—51no—
257C4×D12—101no—
258#872—51no—
259#872—101no—
260C3×#106—51no—
261C3×#103—51no—
262C3×#102—51no—
263C3×C4×C8—51no—
264#835C2×D511yescharacteristic, complemented
265#832C2×D511yescharacteristic
266#821—51no—
267#821—51no—
268#818C2×D511yescharacteristic, complemented
269#815C2×D511yescharacteristic, complemented
270C8×Dic3—51no—
271#809—51no—
272#809—51no—
273#808—51no—
274#807—51no—
275#803—51no—
276C23×D5—61no—
277C2×C5×Q8C22×D311yescharacteristic
278C2×C5×D4C22×D311yescharacteristic
279C22×C4×C5—61no—
280C2×C22⋊D5—61no—
281C22×Dic5—21no—
282#713—34no—
283#713—62no—
284D4×D5—34no—
285D4×D5—62no—
286C2×D20—31no—
287C2×D20—31no—
288C2×D20—61no—
289C2×C4×D5—31no—
290C2×C4×D5—61no—
291C2×C4×D5—61no—
292C2×C4×D5—61no—
293C2×C4×D5—61no—
294C2×C4×D5—61no—
295C2×C4×D5—61no—
296C5×SD16C4×D314yescomplemented
297C2×C5×C8—31no—
298C2×C5×C8C22×D311yescharacteristic
299C5×C4⋊C4—31no—
300C5×C4⋊C4—31no—
301C5×C4⋊C4—61no—
302C5×C22⋊C4—61no—
303C42×C5—31no—
304C42×C5—61no—
305C22⋊Dic5—21no—
306#688—34no—
307#686—34no—
308#685—31no—
309#685—31no—
310#685—61no—
311#685—61no—
312#685—61no—
313#685—61no—
314#685—61no—
315C4⋊Dic5—21no—
316C4⋊Dic5C22×D311yescharacteristic
317C4⋊Dic5C22×D311yescharacteristic
318#683—31no—
319#683—31no—
320#683—61no—
321C4×Dic5—21no—
322C4×Dic5—61no—
323C4×Dic5C22×D311yescharacteristic
324C2×#168—31no—
325C2×#168C22×D311yescharacteristic
326D40—34no—
327#676—34no—
328C8×D5—62no—
329C2×AGL(1,ℤ/8)—151no—
330#520—151no—
331#518—151no—
332#442—151no—
333#442—151no—
334#440—31no—
335#440—151no—
336C4×SD16—51no—
337C4×SD16—151no—
338C4×D8—151no—
339C4×D8—151no—
340#428—151no—
341#416—151no—
342C2×#102—151no—
343#405—151no—
344C22×C3×C5—22no—
345C22×C3×C5—41no—
346C22×C3×C5—41no—
347C22×C3×C5C22×D411yescharacteristic
348C2×D15—21no—
349C2×D15—21no—
350C2×D15—22no—
351C2×D15—22no—
352C2×D15—41no—
353C2×D15—41no—
354C2×D15—41no—
355C2×D15—41no—
356C2×D15—84no—
357C2×D15C4×D412yes—
358C3×C4×C5—22no—
359C3×C4×C5C23×C411yescharacteristic
360C3×C4×C5C2×#4111yescharacteristic
361Dic15C4×D412yes—
362C3×Dic5—21no—
363C3×Dic5—21no—
364C3×Dic5—41no—
365C3×Dic5—41no—
366C5×Dic3—21no—
367C5×Dic3—21no—
368C5×Dic3—41no—
369C5×Dic3—41no—
370C23×D3—101no—
371C2×C3×Q8C22×D511yescharacteristic
372C2×C3×D4C22×D511yescharacteristic
373C22×C3×C4—101no—
374C2×#67—101no—
375C22×Dic3—21no—
376#239—54no—
377#239—102no—
378D3×D4—54no—
379D3×D4—102no—
380C2×D12—51no—
381C2×D12—51no—
382C2×D12—101no—
383C2×C4×D3—51no—
384C2×C4×D3—101no—
385C2×C4×D3—101no—
386C2×C4×D3—101no—
387C2×C4×D3—101no—
388C2×C4×D3—101no—
389C2×C4×D3—101no—
390C3×SD16C4×D514yescomplemented
391C2×C3×C8—51no—
392C2×C3×C8C22×D511yescharacteristic
393C3×C4⋊C4—51no—
394C3×C4⋊C4—51no—
395C3×C4⋊C4—101no—
396C3×C22⋊C4—101no—
397C3×C42—51no—
398C3×C42—101no—
399#217—21no—
400#215—54no—
401#213—54no—
402(C2×D3)⋊C4—51no—
403(C2×D3)⋊C4—51no—
404(C2×D3)⋊C4—101no—
405(C2×D3)⋊C4—101no—
406(C2×D3)⋊C4—101no—
407(C2×D3)⋊C4—101no—
408(C2×D3)⋊C4—101no—
409C4⋊Dic3—21no—
410C4⋊Dic3C22×D511yescharacteristic
411C4⋊Dic3C22×D511yescharacteristic
412Dic3⋊C4—51no—
413Dic3⋊C4—51no—
414Dic3⋊C4—101no—
415C4×Dic3—21no—
416C4×Dic3—101no—
417C4×Dic3C22×D511yescharacteristic
418C2×C3⋊C8—51no—
419C2×C3⋊C8C22×D511yescharacteristic
420D24—54no—
421ΓL(1,𝔽25)—54no—
422D3×C8—102no—
423C23×C5—21no—
424C22×D5—31no—
425C22×D5—64no—
426C22×D5—61no—
427C22×D5—61no—
428C22×D5—241no—
429C22×D5—241no—
430C5×Q8—21no—
431C5×Q8C2×C4×D312yes—
432C5×D4—21no—
433C5×D4C2×C4×D312yes—
434C2×C4×C5—21no—
435C2×C4×C5—31no—
436C2×C4×C5—31no—
437C2×C4×C5—61no—
438C2×C4×C5—61no—
439C2×C4×C5—241no—
440C2×C4×C5C23×D311yescharacteristic
441C22⋊D5—64no—
442C2×Dic5—21no—
443C2×Dic5—21no—
444C2×Dic5—31no—
445C2×Dic5—81no—
446C2×Dic5D3×D411yescharacteristic
447C2×Dic5D3×D411yescharacteristic
448D20—32no—
449D20—32no—
450D20—64no—
451D20—61no—
452D20—61no—
453C4×D5—32no—
454C4×D5—32no—
455C4×D5—64no—
456C4×D5—241no—
457C4×D5—241no—
458C4×D5—241no—
459C4×D5—241no—
460C4×D5—241no—
461C5×C8—61no—
462C5×C8C2×C4×D312yes—
463#168—21no—
464#168—32no—
465C2×#41—151no—
466C22×D4—151no—
467AGL(1,ℤ/8)—158no—
468C2×SD16—151no—
469C2×SD16D3×D511yescharacteristic
470C2×D8—151no—
471C2×D8—151no—
472C2×M16—151no—
473C22×C8—151no—
474C4×Q8—31no—
475C4×Q8—51no—
476C4×D4—31no—
477C4×D4—51no—
478C4×D4—151no—
479C4×D4—151no—
480C4×D4—151no—
481C4×D4—151no—
482C4×D4—301no—
483C4×D4—301no—
484C4×D4—301no—
485C4×D4—301no—
486#117—151no—
487#117—151no—
488#117—301no—
489C2×C4⋊C4—151no—
490C2×C4⋊C4—301no—
491C2×C22⋊C4—301no—
492C2×C22⋊C4—301no—
493#107—31no—
494#107—151no—
495#106—51no—
496#106—151no—
497#103—31no—
498#103—51no—
499#102—31no—
500#102—51no—
501#102—151no—
502#102—151no—
503#102—151no—
504#102—151no—
505#97—31no—
506#97—151no—
507C4×C8—51no—
508C4×C8—151no—
509C2×C3×C5—42no—
510C2×C3×C5C2×C4×D411yescharacteristic
511C2×C3×C5#57611yescharacteristic
512C2×C3×C5#57711yescharacteristic
513D15—22no—
514D15—42no—
515D15—42no—
516C23×C3—21no—
517C22×D3—51no—
518C22×D3—104no—
519C22×D3—101no—
520C22×D3—101no—
521C22×D3—401no—
522C22×D3—401no—
523C3×Q8—21no—
524C3×Q8C2×C4×D512yes—
525C3×D4—21no—
526C3×D4C2×C4×D512yes—
527C2×C3×C4—21no—
528C2×C3×C4—51no—
529C2×C3×C4—51no—
530C2×C3×C4—101no—
531C2×C3×C4—101no—
532C2×C3×C4—401no—
533C2×C3×C4C23×D511yescharacteristic
534#67—104no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—51no—
538C2×Dic3—81no—
539C2×Dic3D4×D511yescharacteristic
540C2×Dic3D4×D511yescharacteristic
541D12—52no—
542D12—52no—
543D12—104no—
544D12—101no—
545D12—101no—
546C4×D3—52no—
547C4×D3—52no—
548C4×D3—104no—
549C4×D3—401no—
550C4×D3—401no—
551C4×D3—401no—
552C4×D3—401no—
553C4×D3—401no—
554C3×C8—101no—
555C3×C8C2×C4×D512yes—
556C3⋊C8—21no—
557C3⋊C8—52no—
558C22×C5—22no—
559C22×C5—41no—
560C22×C5—41no—
561C22×C5C2×D3×D411yescharacteristic
562C2×D5—32no—
563C2×D5—61no—
564C2×D5—61no—
565C2×D5—62no—
566C2×D5—62no—
567C2×D5—121no—
568C2×D5—121no—
569C2×D5—121no—
570C2×D5—121no—
571C2×D5—244no—
572C4×C5—22no—
573C4×C5—61no—
574C4×C5—61no—
575C4×C5—121no—
576C4×C5—121no—
577C4×C5C22×C4×D311yescharacteristic
578C4×C5D3×#4111yescharacteristic
579Dic5—21no—
580Dic5—21no—
581Dic5—32no—
582Dic5—41no—
583Dic5—41no—
584C24—301no—
585#41—154no—
586#41—302no—
587C2×Q8C2×D3×D511yescharacteristic
588C2×D4—154no—
589C2×D4—151no—
590C2×D4—151no—
591C2×D4—301no—
592C2×D4—302no—
593C2×D4—301no—
594C2×D4C2×D3×D511yescharacteristic
595C22×C4—61no—
596C22×C4—101no—
597C22×C4—151no—
598C22×C4—301no—
599C22×C4—301no—
600C22×C4—301no—
601C22×C4—301no—
602C22×C4—301no—
603C22×C4—301no—
604SD16—154no—
605SD16#120014yescomplemented
606D8—154no—
607D8—154no—
608M16—154no—
609C2×C8—31no—
610C2×C8—51no—
611C2×C8—151no—
612C2×C8—302no—
613C2×C8C2×D3×D511yescharacteristic
614C4⋊C4—31no—
615C4⋊C4—31no—
616C4⋊C4—51no—
617C4⋊C4—51no—
618C4⋊C4—61no—
619C4⋊C4—101no—
620C4⋊C4—151no—
621C4⋊C4—151no—
622C4⋊C4—301no—
623C22⋊C4—61no—
624C22⋊C4—101no—
625C22⋊C4—151no—
626C22⋊C4—151no—
627C22⋊C4—301no—
628C22⋊C4—301no—
629C22⋊C4—301no—
630C22⋊C4—301no—
631C22⋊C4—301no—
632C42—31no—
633C42—51no—
634C42—61no—
635C42—101no—
636C42—301no—
637C3×C5#294611yescharacteristic, complemented, Hall
638C22×C3—22no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3C2×D4×D511yescharacteristic
642C2×D3—52no—
643C2×D3—101no—
644C2×D3—101no—
645C2×D3—102no—
646C2×D3—102no—
647C2×D3—201no—
648C2×D3—201no—
649C2×D3—201no—
650C2×D3—201no—
651C2×D3—404no—
652C3×C4—22no—
653C3×C4—101no—
654C3×C4—101no—
655C3×C4—201no—
656C3×C4—201no—
657C3×C4C22×C4×D511yescharacteristic
658C3×C4D5×#4111yescharacteristic
659Dic3—21no—
660Dic3—21no—
661Dic3—41no—
662Dic3—41no—
663Dic3—52no—
664C2×C5—42no—
665C2×C5C4×D3×D411yescharacteristic
666C2×C5#576211yescharacteristic
667C2×C5#576911yescharacteristic
668D5—62no—
669D5—122no—
670D5—122no—
671C23—21no—
672C23—151no—
673C23—304no—
674C23—301no—
675C23—301no—
676C23—1201no—
677C23—1201no—
678Q8—21no—
679Q8C2×#120012yes—
680D4—21no—
681D4—152no—
682D4—152no—
683D4—304no—
684D4—304no—
685D4—301no—
686D4—301no—
687D4C2×#120012yes—
688C2×C4—21no—
689C2×C4—31no—
690C2×C4—31no—
691C2×C4—51no—
692C2×C4—51no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—101no—
696C2×C4—101no—
697C2×C4—151no—
698C2×C4—152no—
699C2×C4—152no—
700C2×C4—241no—
701C2×C4—304no—
702C2×C4—401no—
703C2×C4—1201no—
704C2×C4—1201no—
705C2×C4—1201no—
706C2×C4—1201no—
707C2×C4—1201no—
708C2×C4C22×D3×D511yescharacteristic
709C8—61no—
710C8—101no—
711C8—152no—
712C8C2×#120012yes—
713C2×C3—42no—
714C2×C3C4×D4×D511yescharacteristic
715C2×C3#6610811yescharacteristic
716C2×C3#6611211yescharacteristic
717D3—102no—
718D3—202no—
719D3—202no—
720C5#7964711yescharacteristic, complemented, Sylow
721C22—22no—
722C22—41no—
723C22—41no—
724C22—152no—
725C22—301no—
726C22—301no—
727C22—302no—
728C22—302no—
729C22—601no—
730C22—601no—
731C22—601no—
732C22—601no—
733C22—1204no—
734C22D3×D4×D511yescharacteristic
735C4—22no—
736C4—61no—
737C4—61no—
738C4—101no—
739C4—101no—
740C4—121no—
741C4—121no—
742C4—152no—
743C4—201no—
744C4—201no—
745C4#9202411yescharacteristic
746C4C22×#120011yescharacteristic
747C3#1061150611yescharacteristic, complemented, Sylow
748C2—42no—
749C2—302no—
750C2—602no—
751C2—602no—
752C2#1175408411yescharacteristic
753C2#1175409311yescharacteristic
754C2D4×#120011yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×SD16C22
socleC22×C3×C5C22×D4
prime radicalC2×#91803C2
cosocleC2×C3×C4×C5C24
hypercenterC2×SD16D3×D5
hypocenterC3×C5#2946
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
2. #11755149C2semidirect
3. #11754922C2semidirect
4. C5×#5164C2semidirect
5. C3×SD16×Dic5C2semidirect
6. #11749232C2semidirect
7. #11749225C2semidirect
8. #11749215C2semidirect
9. #11748986C2semidirect
10. #11748979C2semidirect
11. #11748957C2semidirect
12. #11748053C2semidirect
13. #11747796C2semidirect
14. #11747766C2semidirect
15. #11747638C2semidirect
22. #91803C4semidirect
25. C5×Q8×Dic3C22semidirect
27. C3×Q8×Dic5C22semidirect
37. #91428C22semidirect
40. #91418C22semidirect
45. C5×#835C22semidirect
47. C5×#818C22semidirect
48. C5×#815C22semidirect
49. C3×#3967C22semidirect
51. C3×#3949C22semidirect
52. C3×C8×Dic5C22semidirect
53. #90989C22semidirect
54. #90986C22semidirect
56. #90969C22semidirect
58. #90968C22semidirect
59. #90952C22semidirect
60. Dic3×#168C22semidirect
66. SD16×Dic5D3semidirect
82. #6821C2×C4semidirect
84. D4×D15C2×C4semidirect
97. C3×C5×SD16C2×C4semidirect
99. #6717C2×C4semidirect
100. #6715C2×C4semidirect
102. D120C2×C4semidirect
103. #6705C2×C4semidirect
134. #5164D5semidirect
150. Q8×Dic5C2×D3semidirect
177. #3967C2×D3semidirect
181. #3949C2×D3semidirect
183. C8×Dic5C2×D3semidirect
237. Q8×Dic3C2×D5semidirect
264. #835C2×D5semidirect
268. #818C2×D5semidirect
269. #815C2×D5semidirect
296. C5×SD16C4×D3semidirect
390. C3×SD16C4×D5semidirect
605. SD16#1200semidirect
637. C3×C5#2946semidirect
720. C5#79647semidirect
747. C3#10611506semidirect

Maximal subgroups

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

subgroupindex
C2×#918032
#117551492
#117549222
C5×#51642
C3×SD16×Dic52
#117492322
#117492252
#117492152
#117489862
#117489792
#117489572
#117480532
#117477962
#117477662
#117476382
#106115063
#796475