Finite Group Databasebeta

← #11910381

Subgroups — #11910381

Order 1152.

2214 conjugacy classes of subgroups.

The subgroup lattice has 799 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596143C211yesmaximal, characteristic, complemented
2C3×#5683C211yesmaximal, characteristic, complemented
3C3×#5668C211yesmaximal, characteristic, complemented
4#10595393C212yesmaximal, complemented
5#10595359C212yesmaximal, complemented
6#10595259C212yesmaximal, complemented
7#10595154C212yesmaximal, complemented
8#10594234C214yesmaximal, complemented
9#10594172C214yesmaximal, complemented
10#10594087C214yesmaximal, complemented
11#10594054C214yesmaximal, complemented
12#10593985C212yesmaximal, complemented
13#10593921C212yesmaximal, complemented
14#87085—31nomaximal
15#86248—31nomaximal
16C2×C3×#239C2211yescharacteristic, complemented
17C2×C3×#237C2211yescharacteristic
18C22×D3×Dic3C2212yescomplemented
19C2×#3795C2212yes—
20C32×#124C2211yescharacteristic
21#64153C2212yescomplemented
22#64144C2212yes—
23#64088C2214yescomplemented
24#64087C2214yescomplemented
25#64079C2212yescomplemented
26C3×#947C2212yes—
27C3×#944C2211yescharacteristic, complemented
28C3×#940C2211yescharacteristic
29C3×#937C2212yes—
30C3×#885C2214yes—
31C3×#884C2214yescomplemented
32C3×#882C2214yes—
33C3×#67⋊C4C2214yescomplemented
34C3×#875C2212yes—
35C3×#875C2211yescharacteristic, complemented
36C3×C42×D3C2211yescharacteristic, complemented
37#63980C2214yes—
38#63976C2214yescomplemented
39#63976C2212yescomplemented
40Dic3×#67C2214yes—
41#63970C2214yes—
42#63970C2214yes—
43#63969C2214yescomplemented
44#63962C2212yescomplemented
45#63955C2212yescomplemented
46#63914C2212yes—
47#63908C2212yes—
48#63905C2214yescomplemented
49#63896C2214yescomplemented
50Dic3×D12C2212yes—
51#63891C2214yescomplemented
52#63891C2214yescomplemented
53#63887C2214yescomplemented
54#63887C2214yescomplemented
55#63885C2214yes—
56#63885C2214yescomplemented
57#63885C2214yescomplemented
58#63884C2214yes—
59#63879C2214yescomplemented
60#63879C2214yescomplemented
61#63877C2214yescomplemented
62C4×D3×Dic3C2212yescomplemented
63#63867C2214yescomplemented
64#63862C2214yescomplemented
65#63860C2212yescomplemented
66#63859C2214yescomplemented
67#63856C2212yescomplemented
68Dic3×Dic6C2212yescomplemented
69C3×H(3,𝔽4)—31no—
70C3×#532—31no—
71#5832—32no—
72#5828—32no—
73#5735—32no—
74#5720—32no—
75#5684—34no—
76#5684—32no—
77#5684—32no—
78#5683D311yescharacteristic, complemented
79#5680—34no—
80#5680—32no—
81#5672—31no—
82#5672—31no—
83#5672—32no—
84#5672—61no—
85#5668—32no—
86#5668D311yescharacteristic, complemented
87#5621—34no—
88#5620—34no—
89#5595—32no—
90#5595—34no—
91#5586—32no—
92#5586—34no—
93#5547—34no—
94#5538—34no—
95#5479—32no—
96C23×C3×D3C2312yes—
97C2×C32×Q8C2311yescharacteristic
98C2×C32×D4C2311yescharacteristic
99C22×C3⋊Dic3C2312yes—
100C2×#634C2312yes—
101C2×C3×#67C2314yes—
102C2×C3×#67C2314yes—
103C2×C3×#67C2312yes—
104C22×C3×Dic3C2312yes—
105C3×#239—42no—
106C3×#237—42no—
107C2×C3×D12C2312yes—
108C2×C3×D12C2312yes—
109C2×C3×D12C2312yes—
110C2×C3×D12C2311yescharacteristic
111C2×C3×C4×D3C2312yes—
112C2×C3×C4×D3C2311yescharacteristic
113C2×C3×C4×D3C2312yes—
114C2×C3×Dic6C2312yes—
115C2×C3×Dic6C2311yescharacteristic
116C2×#625C2314yes—
117C2×#625C2314yes—
118C2×#625C2314yes—
119C2×D3×Dic3—44no—
120C2×D3×Dic3C2314yes—
121C2×D3×Dic3C2314yes—
122C2×D3×Dic3C2314yes—
123#3795—44no—
124C32×C22⋊C4C2314yes—
125C32×C42C2311yescharacteristic
126#3757C2314yes—
127#3757C2312yes—
128C4⋊(C3⋊Dic3)C2312yes—
129C4⋊(C3⋊Dic3)C2312yes—
130#3750C2314yes—
131#3750C2314yes—
132#3750C2314yes—
133C4×C3⋊Dic3C2312yes—
134C3×#217C2312yes—
135C3×(C2×D3)⋊C4C2314yes—
136C3×(C2×D3)⋊C4C2314yes—
137C3×(C2×D3)⋊C4C2314yes—
138C3×(C2×D3)⋊C4C2314yes—
139C3×Dic3⋊C4C2314yes—
140C3×C4×Dic3C2312yes—
141C3×C4×Dic3C2312yes—
142C3×C4×Dic3C2311yescharacteristic
143#3724C2314yes—
144Dic3⋊Dic3C2314yes—
145Dic3⋊Dic3C2314yes—
146Dic3⋊Dic3C2314yes—
147(C2×D3)⋊Dic3C2314yes—
148(C2×D3)⋊Dic3C2314yes—
149(C2×D3)⋊Dic3C2314yes—
150(C2×D3)⋊Dic3C2314yes—
151(C2×D3)⋊Dic3C2314yes—
152Dic32C2314yes—
153#3529—91noSylow
154C2×C3×#41—31no—
155C2×C3×#41—31no—
156C23×Dic3—32no—
157C2×#239C2×D311yescharacteristic, complemented
158C2×#237—32no—
159C2×#237C2×D311yescharacteristic
160C2×#235—32no—
161C22×C4×D3—32no—
162C3×C4⋊Q8—31no—
163C3×#127—31no—
164C3×#124—21no—
165C3×#124—32no—
166C3×#124—34no—
167C3×#124—32no—
168C3×#124—31no—
169C3×#124C2×D311yescharacteristic
170C3×#124C2×D311yescharacteristic
171C3×#121—34no—
172C3×#120—32no—
173C3×#120—34no—
174C3×C4×D4—34no—
175C2×C3×C42—31no—
176#953—32no—
177#953—34no—
178#947C2×D312yes—
179#946—32no—
180#946—34no—
181#946—34no—
182Q8×Dic3—32no—
183#944—32no—
184#944—32no—
185#944—62no—
186#944C2×D311yescharacteristic, complemented
187#940—32no—
188#940—32no—
189#940C2×D311yescharacteristic
190#939—34no—
191#939—34no—
192#939—34no—
193#939—34no—
194#939—34no—
195#939—34no—
196#939—34no—
197#938—34no—
198#938—34no—
199#938—32no—
200#937—34no—
201#937—32no—
202#937C2×D312yes—
203#936—32no—
204#935—32no—
205#935—32no—
206#935—34no—
207#935—32no—
208#935—34no—
209#935—62no—
210D4×Dic3—34no—
211D4×Dic3—32no—
212#930—32no—
213#929—34no—
214C4×#67—34no—
215C4×#67—34no—
216C4×#67—34no—
217#926—32no—
218#924—32no—
219C2×C4×Dic3—32no—
220#898—34no—
221#896—34no—
222#894—34no—
223#889—34no—
224#886—32no—
225#886—34no—
226#886—34no—
227#885C2×D314yes—
228#884—34no—
229#884—34no—
230#884—34no—
231#884C2×D314yescomplemented
232#883—34no—
233#883—34no—
234#883—34no—
235#883—34no—
236#882C2×D314yes—
237#67⋊C4—34no—
238#67⋊C4—34no—
239#67⋊C4C2×D314yescomplemented
240#879—34no—
241#879—34no—
242#879—34no—
243#879—34no—
244#879—64no—
245#878—34no—
246#878—34no—
247#878—34no—
248#878—34no—
249#878—34no—
250#878—64no—
251#877—32no—
252#877—34no—
253#876—34no—
254#875—32no—
255#875C2×D312yes—
256#875C2×D311yescharacteristic, complemented
257C4×D12—32no—
258#872—34no—
259C42×D3—32no—
260C42×D3C2×D311yescharacteristic, complemented
261#870—32no—
262#870—32no—
263#870—34no—
264#870—62no—
265C4×Dic6—32no—
266C23×C32C2412yes—
267C22×C3×D3—44no—
268C22×C3×D3—42no—
269C22×C3×D3C2414yes—
270C22×C3×D3C2411yescharacteristic
271C22×C3×D3C2412yes—
272C32×Q8—41no—
273C32×D4—41no—
274C2×C32×C4C2412yes—
275C2×C32×C4C2411yescharacteristic
276C2×C32×C4C2412yes—
277C2×C3⋊Dic3—42no—
278C2×C3⋊Dic3C2414yes—
279C2×C3⋊Dic3C2414yes—
280#634—42no—
281C3×#67—42no—
282C3×#67—44no—
283C3×#67—44no—
284C2×C3×Dic3—24no—
285C2×C3×Dic3C2414yes—
286C2×C3×Dic3C2412yes—
287C2×C3×Dic3C2412yes—
288C2×C3×Dic3C2411yescharacteristic
289C3×D12—42no—
290C3×D12—42no—
291C3×D12—41no—
292C3×D12—42no—
293C3×C4×D3—24no—
294C3×C4×D3—22no—
295C3×C4×D3—42no—
296C3×Dic6—42no—
297C3×Dic6—41no—
298#625—44no—
299#625—44no—
300#625—44no—
301D3×Dic3—28no—
302D3×Dic3—44no—
303D3×Dic3—44no—
304#563—92no—
305#563—91no—
306#562—94no—
307#562—92no—
308H(3,𝔽4)—31no—
309#560—94no—
310#560—92no—
311#532—31no—
312#532—92no—
313#529—92no—
314#529—94no—
315#525—94no—
316#525—92no—
317C24×C3—32no—
318C23×D3C22×D312yes—
319C3×#41—122no—
320C3×#41—122no—
321C2×C3×Q8—21no—
322C2×C3×Q8—32no—
323C2×C3×Q8—31no—
324C2×C3×Q8C22×D311yescharacteristic
325C2×C3×Q8C22×D311yescharacteristic
326C2×C3×D4—21no—
327C2×C3×D4—34no—
328C2×C3×D4—32no—
329C2×C3×D4—34no—
330C2×C3×D4—32no—
331C2×C3×D4—32no—
332C2×C3×D4—32no—
333C2×C3×D4—31no—
334C2×C3×D4C22×D311yescharacteristic
335C2×C3×D4C22×D311yescharacteristic
336C22×C3×C4—32no—
337C22×C3×C4—32no—
338C22×C3×C4—31no—
339C22×C3×C4—32no—
340C2×#67—34no—
341C2×#67—34no—
342C2×#67—34no—
343C2×#67—34no—
344C2×#67—34no—
345C2×#67—34no—
346C2×#67C22×D314yes—
347C2×#67C22×D314yes—
348C2×#67C22×D312yes—
349C22×Dic3—32no—
350C22×Dic3—32no—
351C22×Dic3—34no—
352C22×Dic3—34no—
353C22×Dic3—34no—
354C22×Dic3—62no—
355C22×Dic3—124no—
356C22×Dic3C22×D312yes—
357#239—42no—
358#237—42no—
359#237—124no—
360#235—124no—
361C2×D12C22×D312yes—
362C2×D12C22×D312yes—
363C2×D12C22×D311yescharacteristic
364C2×D12C22×D312yes—
365C2×C4×D3—34no—
366C2×C4×D3—34no—
367C2×C4×D3—34no—
368C2×C4×D3—124no—
369C2×C4×D3C22×D312yes—
370C2×C4×D3C22×D311yescharacteristic
371C2×C4×D3C22×D312yes—
372C2×Dic6—32no—
373C2×Dic6—32no—
374C2×Dic6—62no—
375C2×Dic6C22×D312yes—
376C2×Dic6C22×D311yescharacteristic
377C3×C4⋊C4—34no—
378C3×C22⋊C4—24no—
379C3×C22⋊C4—32no—
380C3×C22⋊C4—34no—
381C3×C22⋊C4—34no—
382C3×C22⋊C4—34no—
383C3×C22⋊C4—34no—
384C3×C22⋊C4C22×D314yes—
385C3×C22⋊C4C22×D314yes—
386C3×C42—21no—
387C3×C42—32no—
388C3×C42—32no—
389C3×C42—31no—
390C3×C42C22×D311yescharacteristic
391C3×C42C22×D311yescharacteristic
392#217—32no—
393#217—34no—
394#217—34no—
395#217—32no—
396#217—34no—
397#217—34no—
398#217—34no—
399#217—34no—
400#217—34no—
401#217—64no—
402#217—62no—
403#217C22×D312yes—
404(C2×D3)⋊C4—34no—
405(C2×D3)⋊C4—34no—
406(C2×D3)⋊C4—34no—
407(C2×D3)⋊C4—34no—
408(C2×D3)⋊C4—34no—
409(C2×D3)⋊C4C22×D314yes—
410(C2×D3)⋊C4C22×D314yes—
411(C2×D3)⋊C4C22×D314yes—
412(C2×D3)⋊C4C22×D314yes—
413C4⋊Dic3—32no—
414C4⋊Dic3—32no—
415C4⋊Dic3—32no—
416C4⋊Dic3—32no—
417C4⋊Dic3—34no—
418C4⋊Dic3—34no—
419C4⋊Dic3—34no—
420C4⋊Dic3—62no—
421C4⋊Dic3—62no—
422Dic3⋊C4—34no—
423Dic3⋊C4—34no—
424Dic3⋊C4—34no—
425Dic3⋊C4—34no—
426Dic3⋊C4—34no—
427Dic3⋊C4—34no—
428Dic3⋊C4—34no—
429Dic3⋊C4—34no—
430Dic3⋊C4—34no—
431Dic3⋊C4—34no—
432Dic3⋊C4—34no—
433Dic3⋊C4—64no—
434Dic3⋊C4—64no—
435Dic3⋊C4—64no—
436Dic3⋊C4C22×D314yes—
437C4×Dic3—32no—
438C4×Dic3—32no—
439C4×Dic3—34no—
440C4×Dic3—34no—
441C4×Dic3—62no—
442C4×Dic3C22×D312yes—
443C4×Dic3C22×D311yescharacteristic
444C4×Dic3C22×D312yes—
445C22×C32—22no—
446C22×C32—24no—
447C22×C32C2511yescharacteristic
448C2×C3×D3—24no—
449C2×C3×D3—22no—
450C2×C3×D3—21no—
451C2×C3×D3—24no—
452C2×C3×D3—22no—
453C2×C3×D3—24no—
454C2×C3×D3—24no—
455C2×C3×D3—48no—
456C32×C4—21no—
457C32×C4—22no—
458C32×C4—22no—
459C3⋊Dic3—24no—
460C3⋊Dic3—24no—
461C3×Dic3—22no—
462C3×Dic3—24no—
463C3×Dic3—22no—
464C3×Dic3H(5,𝔽2)12yes—
465C2×#41—31no—
466C2×#41—31no—
467C2×#41—92no—
468C23×C4—92no—
469C4⋊Q8—31no—
470C4⋊Q8—92no—
471#127—31no—
472#127—92no—
473#126—94no—
474#126—94no—
475#126—94no—
476#125—94no—
477#125—92no—
478#124—32no—
479#124—34no—
480#124—32no—
481#124—31no—
482#124—92no—
483#124D3211yescharacteristic
484#123—94no—
485#123—94no—
486#123—94no—
487#123—92no—
488#123—94no—
489#123—94no—
490#123—92no—
491C22⋊Q8—94no—
492C22⋊Q8—94no—
493C22⋊Q8—94no—
494C22⋊Q8—92no—
495C22⋊Q8—94no—
496#121—34no—
497#121—94no—
498#121—94no—
499#121—94no—
500#121—92no—
501#121—94no—
502#121—94no—
503#121—94no—
504#120—32no—
505#120—34no—
506#120—94no—
507#120—92no—
508C4×Q8—92no—
509C4×D4—34no—
510C4×D4—92no—
511C4×D4—94no—
512C4×D4—94no—
513C4×D4—94no—
514#117—94no—
515#117—92no—
516C2×C42—31no—
517C2×C42—92no—
518C23×C3—22no—
519C23×C3—31no—
520C23×C3—34no—
521C23×C3—32no—
522C23×C3—122no—
523C23×C3—124no—
524C23×C3C23×D312yes—
525C23×C3C23×D312yes—
526C22×D3—42no—
527C22×D3—44no—
528C22×D3C23×D311yescharacteristic
529C22×D3C23×D314yes—
530C22×D3C23×D312yes—
531C3×Q8—41no—
532C3×Q8—41no—
533C3×Q8—81no—
534C3×Q8—122no—
535C3×Q8—121no—
536C3×D4—41no—
537C3×D4—41no—
538C3×D4—81no—
539C3×D4—122no—
540C3×D4—122no—
541C3×D4—122no—
542C3×D4—121no—
543C3×D4—124no—
544C3×D4—124no—
545C3×D4—122no—
546C2×C3×C4—22no—
547C2×C3×C4—21no—
548C2×C3×C4—22no—
549C2×C3×C4—31no—
550C2×C3×C4—34no—
551C2×C3×C4—32no—
552C2×C3×C4—32no—
553C2×C3×C4—64no—
554C2×C3×C4—62no—
555C2×C3×C4—64no—
556C2×C3×C4—122no—
557C2×C3×C4C23×D312yes—
558C2×C3×C4C23×D312yes—
559C2×C3×C4C23×D311yescharacteristic
560C2×C3×C4C23×D312yes—
561C2×C3×C4C23×D311yescharacteristic
562C2×C3×C4C23×D312yes—
563#67—42no—
564#67—44no—
565#67—44no—
566#67—124no—
567#67—124no—
568#67—124no—
569#67—124no—
570#67—124no—
571#67—124no—
572C2×Dic3—24no—
573C2×Dic3—34no—
574C2×Dic3—34no—
575C2×Dic3—34no—
576C2×Dic3—34no—
577C2×Dic3—64no—
578C2×Dic3—64no—
579C2×Dic3—68no—
580C2×Dic3—124no—
581C2×Dic3—124no—
582C2×Dic3—122no—
583C2×Dic3—122no—
584C2×Dic3—242no—
585C2×Dic3C23×D314yes—
586C2×Dic3C23×D312yes—
587C2×Dic3C23×D312yes—
588C2×Dic3C23×D311yescharacteristic
589D12—42no—
590D12—42no—
591D12—41no—
592D12—42no—
593C4×D3—22no—
594C4×D3—24no—
595C4×D3—42no—
596C4×D3—68no—
597C4×D3—124no—
598C4×D3—124no—
599Dic6—42no—
600Dic6—41no—
601Dic6—122no—
602Dic6—122no—
603Dic6—242no—
604C2×C32—42no—
605C2×C32C2×H(5,𝔽2)11yescharacteristic
606C2×C32#58512yes—
607C3×D3—42no—
608C3×D3—41no—
609C3×D3—44no—
610C24—32no—
611#41—122no—
612#41—122no—
613#41—364no—
614C2×Q8—32no—
615C2×Q8—31no—
616C2×Q8—92no—
617C2×Q8C2×D3211yescharacteristic
618C2×D4—34no—
619C2×D4—34no—
620C2×D4—32no—
621C2×D4—32no—
622C2×D4—32no—
623C2×D4—32no—
624C2×D4—31no—
625C2×D4—94no—
626C2×D4—94no—
627C2×D4—94no—
628C2×D4C2×D3211yescharacteristic
629C22×C4—32no—
630C22×C4—31no—
631C22×C4—32no—
632C22×C4—32no—
633C22×C4—94no—
634C22×C4—94no—
635C22×C4—94no—
636C22×C4—92no—
637C22×C4—364no—
638C4⋊C4—34no—
639C4⋊C4—94no—
640C4⋊C4—94no—
641C4⋊C4—94no—
642C4⋊C4—94no—
643C4⋊C4—94no—
644C4⋊C4—94no—
645C4⋊C4—94no—
646C4⋊C4—92no—
647C4⋊C4—92no—
648C22⋊C4—32no—
649C22⋊C4—34no—
650C22⋊C4—34no—
651C22⋊C4—34no—
652C22⋊C4—34no—
653C22⋊C4—94no—
654C22⋊C4—94no—
655C22⋊C4—94no—
656C22⋊C4—94no—
657C22⋊C4—94no—
658C22⋊C4—92no—
659C22⋊C4—94no—
660C22⋊C4C2×D3214yes—
661C42—32no—
662C42—31no—
663C42—32no—
664C42—94no—
665C42—92no—
666C42C2×D3211yescharacteristic
667C22×C3—22no—
668C22×C3—24no—
669C22×C3—22no—
670C22×C3—24no—
671C22×C3—21no—
672C22×C3—42no—
673C22×C3—44no—
674C22×C3—64no—
675C22×C3—64no—
676C22×C3—64no—
677C22×C3—62no—
678C22×C3—61no—
679C22×C3—64no—
680C22×C3—62no—
681C22×C3—128no—
682C22×C3C24×D311yescharacteristic
683C22×C3C24×D311yescharacteristic
684C2×D3—21no—
685C2×D3—22no—
686C2×D3—22no—
687C2×D3—24no—
688C2×D3—24no—
689C2×D3—24no—
690C2×D3—24no—
691C2×D3—48no—
692C3×C4—21no—
693C3×C4—22no—
694C3×C4—22no—
695C3×C4—22no—
696C3×C4—21no—
697C3×C4—22no—
698C3×C4—32no—
699C3×C4—42no—
700C3×C4—41no—
701C3×C4—42no—
702C3×C4—64no—
703C3×C4—62no—
704C3×C4—62no—
705Dic3—22no—
706Dic3—22no—
707Dic3—24no—
708Dic3—64no—
709Dic3—64no—
710Dic3—64no—
711Dic3—64no—
712Dic3—124no—
713Dic3—124no—
714Dic3#100412yes—
715C32#352911yescharacteristic, complemented, Sylow
716C23—34no—
717C23—32no—
718C23—31no—
719C23—122no—
720C23—124no—
721C23C22×D3212yes—
722Q8—41no—
723Q8—121no—
724Q8—122no—
725Q8—362no—
726D4—41no—
727D4—121no—
728D4—122no—
729D4—122no—
730D4—122no—
731D4—122no—
732D4—124no—
733D4—124no—
734D4—364no—
735D4—364no—
736D4—364no—
737C2×C4—31no—
738C2×C4—32no—
739C2×C4—34no—
740C2×C4—32no—
741C2×C4—62no—
742C2×C4—64no—
743C2×C4—64no—
744C2×C4—94no—
745C2×C4—94no—
746C2×C4—122no—
747C2×C4—188no—
748C2×C4—364no—
749C2×C4—364no—
750C2×C4—362no—
751C2×C4C22×D3212yes—
752C2×C4C22×D3212yes—
753C2×C4C22×D3211yescharacteristic
754C2×C3—21no—
755C2×C3—22no—
756C2×C3—42no—
757C2×C3—42no—
758C2×C3—82no—
759C2×C3—122no—
760C2×C3—121no—
761C2×C3—124no—
762C2×C3C2×#100411yescharacteristic
763C2×C3#596412yes—
764C2×C3D3×H(5,𝔽2)11yescharacteristic
765C2×C3#596612yes—
766D3—44no—
767D3—41no—
768D3—42no—
769C22—22no—
770C22—24no—
771C22—61no—
772C22—62no—
773C22—64no—
774C22—62no—
775C22—64no—
776C22—64no—
777C22—64no—
778C22—128no—
779C22C23×D3211yescharacteristic
780C4—21no—
781C4—22no—
782C4—22no—
783C4—32no—
784C4—62no—
785C4—62no—
786C4—64no—
787C4—184no—
788C4—184no—
789C3—21no—
790C3#8624811yescharacteristic, complemented
791C3#8708511yescharacteristic, complemented
792C2—42no—
793C2—124no—
794C2—121no—
795C2—122no—
796C2D3×#100411yescharacteristic
797C2#1059669612yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#124C22
hypercenter#124D32
hypocenterC32#3529
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #10596143C2semidirect
2. C3×#5683C2semidirect
3. C3×#5668C2semidirect
4. #10595393C2semidirect
5. #10595359C2semidirect
6. #10595259C2semidirect
7. #10595154C2semidirect
8. #10594234C2semidirect
9. #10594172C2semidirect
10. #10594087C2semidirect
11. #10594054C2semidirect
12. #10593985C2semidirect
13. #10593921C2semidirect
16. C2×C3×#239C22semidirect
18. C22×D3×Dic3C22semidirect
21. #64153C22semidirect
23. #64088C22semidirect
24. #64087C22semidirect
25. #64079C22semidirect
27. C3×#944C22semidirect
31. C3×#884C22semidirect
33. C3×#67⋊C4C22semidirect
35. C3×#875C22semidirect
36. C3×C42×D3C22semidirect
38. #63976C22semidirect
39. #63976C22semidirect
43. #63969C22semidirect
44. #63962C22semidirect
45. #63955C22semidirect
48. #63905C22semidirect
49. #63896C22semidirect
51. #63891C22semidirect
52. #63891C22semidirect
53. #63887C22semidirect
54. #63887C22semidirect
56. #63885C22semidirect
57. #63885C22semidirect
59. #63879C22semidirect
60. #63879C22semidirect
61. #63877C22semidirect
62. C4×D3×Dic3C22semidirect
63. #63867C22semidirect
64. #63862C22semidirect
65. #63860C22semidirect
66. #63859C22semidirect
67. #63856C22semidirect
68. Dic3×Dic6C22semidirect
78. #5683D3semidirect
86. #5668D3semidirect
157. C2×#239C2×D3semidirect
186. #944C2×D3semidirect
231. #884C2×D3semidirect
239. #67⋊C4C2×D3semidirect
256. #875C2×D3semidirect
260. C42×D3C2×D3semidirect
715. C32#3529semidirect
790. C3#86248semidirect
791. C3#87085semidirect

Maximal subgroups

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

subgroupindex
#105961432
C3×#56832
C3×#56682
#105953932
#105953592
#105952592
#105951542
#105942342
#105941722
#105940872
#105940542
#105939852
#105939212
#870853
#862483