Finite Group Databasebeta

← #11910379

Subgroups — #11910379

Order 1152.

2246 conjugacy classes of subgroups.

The subgroup lattice has 807 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596154C211yesmaximal, characteristic, complemented
2C3×#5672C211yesmaximal, characteristic, complemented
3C3×#5668C211yesmaximal, characteristic, complemented
4#10595360C212yesmaximal, complemented
5#10595352C212yesmaximal, complemented
6#10595266C212yesmaximal, complemented
7#10595159C212yesmaximal, complemented
8#10594242C214yesmaximal, complemented
9#10594174C214yesmaximal, complemented
10#10594089C214yesmaximal, complemented
11#10594066C214yesmaximal, complemented
12#10593976C212yesmaximal, complemented
13#10593953C212yesmaximal, complemented
14#87115—31nomaximal
15#86248—31nomaximal
16C2×C3×#239C2211yescharacteristic, complemented
17C2×C3×#237C2211yescharacteristic
18C22×#624C2212yescomplemented
19C2×#3799C2212yes—
20C32×#124C2211yescharacteristic
21#64156C2212yes—
22#64146C2212yes—
23#64094C2214yes—
24#64091C2214yes—
25#64084C2212yes—
26C3×#944C2211yescharacteristic, complemented
27C3×#944C2212yescomplemented
28C3×#940C2211yescharacteristic
29C3×#935C2212yes—
30C3×#884C2214yescomplemented
31C3×#67⋊C4C2214yescomplemented
32C3×#879C2214yescomplemented
33C3×#878C2214yescomplemented
34C3×#875C2211yescharacteristic, complemented
35C3×C42×D3C2211yescharacteristic, complemented
36C3×#870C2212yescomplemented
37#63981C2214yescomplemented
38#63981C2212yescomplemented
39#63978C2214yes—
40#63971C2214yes—
41#63969C2214yescomplemented
42#63961C2212yescomplemented
43#63958C2214yes—
44#63955C2212yescomplemented
45#63952C2214yes—
46#63911C2212yes—
47#63910C2214yes—
48#63909C2212yes—
49#63904C2214yescomplemented
50#63904C2214yescomplemented
51#63897C2214yes—
52#63896C2214yescomplemented
53#63894C2212yes—
54#63890C2214yescomplemented
55#63888C2214yescomplemented
56#63888C2214yescomplemented
57#63886C2214yescomplemented
58#63886C2214yescomplemented
59C4×D3×Dic3C2212yescomplemented
60#63870C2214yescomplemented
61#63868C2214yescomplemented
62#63868C2214yescomplemented
63#63863C2212yescomplemented
64#63857C2212yescomplemented
65#63854C2214yescomplemented
66#63850C2214yescomplemented
67#63844C2212yescomplemented
68#63836C2214yescomplemented
69C3×#563—31no—
70C3×#532—31no—
71#5832—32no—
72#5828—32no—
73#5735—32no—
74#5735—32no—
75#5725—32no—
76#5720—32no—
77#5711—34no—
78#5706—34no—
79#5700—32no—
80#5691—32no—
81#5684—32no—
82#5683—31no—
83#5683—31no—
84#5683—61no—
85#5672D311yescharacteristic, complemented
86#5668D311yescharacteristic, complemented
87#5666—32no—
88#5656—32no—
89#5647—34no—
90#5627—34no—
91#5621—34no—
92#5620—34no—
93#5547—34no—
94#5538—34no—
95#5479—32no—
96C23×C3⋊D3C2312yes—
97C2×C32×Q8C2311yescharacteristic
98C2×C32×D4C2311yescharacteristic
99C2×#638C2314yes—
100C2×C4⋊(C3⋊D3)C2312yes—
101C2×C4⋊(C3⋊D3)C2312yes—
102C2×#634C2312yes—
103C2×C3×#67C2314yes—
104C2×C3×#67C2312yes—
105C22×C3×Dic3C2312yes—
106C22×C3×Dic3C2312yes—
107C3×#239—42no—
108C3×#237—42no—
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×#626C2314yes—
117C2×#626C2314yes—
118C2×#626C2314yes—
119C2×#624—44no—
120C2×#624C2314yes—
121C2×#624C2314yes—
122C2×D3×Dic3C2314yes—
123#3799—44no—
124C32×C22⋊C4C2314yes—
125C32×C42C2311yescharacteristic
126#3757C2312yes—
127#3752C2314yes—
128#3752C2314yes—
129#3752C2314yes—
130C4×C3⋊Dic3C2312yes—
131C3×#217C2314yes—
132C3×#217C2312yes—
133C3×(C2×D3)⋊C4C2314yes—
134C3×C4⋊Dic3C2312yes—
135C3×C4⋊Dic3C2312yes—
136C3×Dic3⋊C4C2314yes—
137C3×Dic3⋊C4C2314yes—
138C3×Dic3⋊C4C2314yes—
139C3×Dic3⋊C4C2314yes—
140C3×C4×Dic3C2312yes—
141C3×C4×Dic3C2312yes—
142C3×C4×Dic3C2311yescharacteristic
143#3724C2314yes—
144#3724C2314yes—
145Dic3⋊Dic3C2314yes—
146Dic3⋊Dic3C2314yes—
147#3722C2314yes—
148#3722C2314yes—
149#3722C2314yes—
150(C2×D3)⋊Dic3C2314yes—
151(C2×D3)⋊Dic3C2314yes—
152Dic32C2314yes—
153#3529—91noSylow
154C2×C3×#41—31no—
155C2×C3×#41—31no—
156C2×#239—32no—
157C2×#239C2×D311yescharacteristic, complemented
158C2×#237C2×D311yescharacteristic
159C2×#235—32no—
160C22×C4×D3—32no—
161C22×C4×D3—32no—
162C3×C4⋊Q8—32no—
163C3×C4⋊Q8—31no—
164C3×#127—31no—
165C3×#126—34no—
166C3×#125—32no—
167C3×#124—21no—
168C3×#124—31no—
169C3×#124C2×D311yescharacteristic
170C3×#124C2×D311yescharacteristic
171C3×#123—32no—
172C3×C22⋊Q8—34no—
173C3×#121—34no—
174C3×C4×D4—34no—
175C2×C3×C42—31no—
176#947—32no—
177#947—32no—
178#947—32no—
179#947—62no—
180#946—34no—
181#946—34no—
182#944C2×D311yescharacteristic, complemented
183#944C2×D312yescomplemented
184#940—32no—
185#940C2×D311yescharacteristic
186#939—34no—
187#939—34no—
188#939—34no—
189#939—34no—
190#938—34no—
191#937—32no—
192#937—32no—
193#937—34no—
194#937—32no—
195#937—62no—
196#936—32no—
197#935—32no—
198#935—34no—
199#935C2×D312yes—
200#930—34no—
201#930—32no—
202#929—32no—
203#929—34no—
204C4×#67—34no—
205C4×#67—34no—
206C4×#67—34no—
207#926—32no—
208#924—32no—
209C2×C4×Dic3—32no—
210#898—34no—
211#898—34no—
212#897—32no—
213#896—34no—
214#896—34no—
215#896—34no—
216#895—34no—
217#895—34no—
218#895—32no—
219#895—34no—
220#894—34no—
221#894—34no—
222#894—34no—
223#894—34no—
224#894—34no—
225#893—34no—
226#893—34no—
227#893—32no—
228#892—34no—
229#889—34no—
230#889—34no—
231#887—32no—
232#886—34no—
233#885—34no—
234#885—34no—
235#885—64no—
236#884—34no—
237#884—34no—
238#884—34no—
239#884C2×D314yescomplemented
240#883—34no—
241#883—34no—
242#882—32no—
243#882—34no—
244#882—34no—
245#882—34no—
246#882—64no—
247#67⋊C4—34no—
248#67⋊C4C2×D314yescomplemented
249#879C2×D314yescomplemented
250#878—34no—
251#878C2×D314yescomplemented
252#877—32no—
253#876—34no—
254#876—34no—
255#875—32no—
256#875—32no—
257#875—62no—
258#875C2×D311yescharacteristic, complemented
259#874—32no—
260C4×D12—32no—
261#872—34no—
262C42×D3—32no—
263C42×D3C2×D311yescharacteristic, complemented
264#870C2×D312yescomplemented
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—
277#638—44no—
278C2×C3⋊Dic3C2414yes—
279C4⋊(C3⋊D3)—42no—
280C4⋊(C3⋊D3)—42no—
281#634—42no—
282C3×#67—42no—
283C3×#67—44no—
284C2×C3×Dic3—24no—
285C2×C3×Dic3—42no—
286C2×C3×Dic3C2414yes—
287C2×C3×Dic3C2414yes—
288C2×C3×Dic3C2412yes—
289C2×C3×Dic3C2412yes—
290C2×C3×Dic3C2411yescharacteristic
291C3×D12—42no—
292C3×D12—41no—
293C3×C4×D3—24no—
294C3×C4×D3—22no—
295C3×C4×D3—42no—
296C3×Dic6—42no—
297C3×Dic6—41no—
298#626—44no—
299#626—44no—
300#626—44no—
301#624—28no—
302#624—44no—
303D3×Dic3—44no—
304#563—31no—
305#563—92no—
306#562—94no—
307#562—92no—
308H(3,𝔽4)—91no—
309#560—94no—
310#560—92no—
311#532—31no—
312#532—92no—
313#529—92no—
314#529—94no—
315#525—94no—
316#525—92no—
317C23×D3—32no—
318C23×D3—32no—
319C23×D3—62no—
320C3×#41—122no—
321C3×#41—122no—
322C2×C3×Q8—21no—
323C2×C3×Q8—31no—
324C2×C3×Q8—32no—
325C2×C3×Q8C22×D311yescharacteristic
326C2×C3×Q8C22×D311yescharacteristic
327C2×C3×D4—21no—
328C2×C3×D4—32no—
329C2×C3×D4—34no—
330C2×C3×D4—32no—
331C2×C3×D4—31no—
332C2×C3×D4C22×D311yescharacteristic
333C2×C3×D4C22×D311yescharacteristic
334C22×C3×C4—32no—
335C22×C3×C4—32no—
336C22×C3×C4—32no—
337C22×C3×C4—31no—
338C22×C3×C4—32no—
339C2×#67—34no—
340C2×#67—34no—
341C2×#67—34no—
342C2×#67—34no—
343C2×#67—34no—
344C2×#67—64no—
345C2×#67C22×D314yes—
346C2×#67C22×D312yes—
347C22×Dic3—34no—
348C22×Dic3C22×D312yes—
349C22×Dic3C22×D312yes—
350#239—42no—
351#239—124no—
352#237—42no—
353#235—124no—
354C2×D12—34no—
355C2×D12—34no—
356C2×D12—34no—
357C2×D12—32no—
358C2×D12—32no—
359C2×D12—32no—
360C2×D12—32no—
361C2×D12—62no—
362C2×D12—62no—
363C2×D12C22×D312yes—
364C2×D12C22×D311yescharacteristic
365C2×C4×D3—34no—
366C2×C4×D3—34no—
367C2×C4×D3—34no—
368C2×C4×D3—34no—
369C2×C4×D3—34no—
370C2×C4×D3—124no—
371C2×C4×D3—124no—
372C2×C4×D3C22×D312yes—
373C2×C4×D3C22×D311yescharacteristic
374C2×C4×D3C22×D312yes—
375C2×Dic6—32no—
376C2×Dic6—32no—
377C2×Dic6—62no—
378C2×Dic6C22×D311yescharacteristic
379C2×Dic6C22×D312yes—
380C3×C4⋊C4—32no—
381C3×C4⋊C4—34no—
382C3×C4⋊C4—34no—
383C3×C4⋊C4—34no—
384C3×C4⋊C4—32no—
385C3×C4⋊C4—34no—
386C3×C22⋊C4—24no—
387C3×C22⋊C4—32no—
388C3×C22⋊C4—34no—
389C3×C22⋊C4—34no—
390C3×C22⋊C4C22×D314yes—
391C3×C22⋊C4C22×D314yes—
392C3×C42—21no—
393C3×C42—32no—
394C3×C42—32no—
395C3×C42—31no—
396C3×C42C22×D311yescharacteristic
397C3×C42C22×D311yescharacteristic
398#217—32no—
399#217—32no—
400#217—34no—
401#217—34no—
402#217—62no—
403#217C22×D314yes—
404#217C22×D312yes—
405(C2×D3)⋊C4—34no—
406(C2×D3)⋊C4—34no—
407(C2×D3)⋊C4—34no—
408(C2×D3)⋊C4—34no—
409(C2×D3)⋊C4—34no—
410(C2×D3)⋊C4—34no—
411(C2×D3)⋊C4—34no—
412(C2×D3)⋊C4—34no—
413(C2×D3)⋊C4—34no—
414(C2×D3)⋊C4—34no—
415(C2×D3)⋊C4—34no—
416(C2×D3)⋊C4—34no—
417(C2×D3)⋊C4—34no—
418(C2×D3)⋊C4—34no—
419(C2×D3)⋊C4—64no—
420(C2×D3)⋊C4—64no—
421(C2×D3)⋊C4—64no—
422(C2×D3)⋊C4C22×D314yes—
423C4⋊Dic3—34no—
424C4⋊Dic3—34no—
425C4⋊Dic3C22×D312yes—
426C4⋊Dic3C22×D312yes—
427Dic3⋊C4—34no—
428Dic3⋊C4—34no—
429Dic3⋊C4—34no—
430Dic3⋊C4—34no—
431Dic3⋊C4—34no—
432Dic3⋊C4—34no—
433Dic3⋊C4C22×D314yes—
434Dic3⋊C4C22×D314yes—
435Dic3⋊C4C22×D314yes—
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—24no—
450C2×C3⋊D3—24no—
451C2×C3⋊D3—48no—
452C2×C3×D3—22no—
453C2×C3×D3—21no—
454C2×C3×D3—24no—
455C2×C3×D3—22no—
456C32×C4—22no—
457C32×C4—21no—
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—32no—
471#127—31no—
472#127—92no—
473#126—34no—
474#126—94no—
475#126—94no—
476#125—32no—
477#125—94no—
478#124—31no—
479#124—92no—
480#124—92no—
481#124—94no—
482#124—92no—
483#124D3211yescharacteristic
484#123—32no—
485#123—94no—
486#123—94no—
487#123—94no—
488#123—94no—
489#123—94no—
490#123—92no—
491C22⋊Q8—34no—
492C22⋊Q8—94no—
493C22⋊Q8—92no—
494C22⋊Q8—94no—
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—92no—
505#120—94no—
506#120—92no—
507#120—94no—
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—32no—
521C23×C3C23×D312yes—
522C23×C3C23×D312yes—
523C22×D3—34no—
524C22×D3—34no—
525C22×D3—64no—
526C22×D3—122no—
527C22×D3—122no—
528C22×D3—124no—
529C22×D3—124no—
530C22×D3—242no—
531C22×D3—244no—
532C22×D3C23×D311yescharacteristic
533C22×D3C23×D312yes—
534C3×Q8—41no—
535C3×Q8—41no—
536C3×Q8—81no—
537C3×Q8—122no—
538C3×Q8—121no—
539C3×D4—41no—
540C3×D4—41no—
541C3×D4—81no—
542C3×D4—122no—
543C3×D4—121no—
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—34no—
554C2×C3×C4—64no—
555C2×C3×C4—62no—
556C2×C3×C4—64no—
557C2×C3×C4—122no—
558C2×C3×C4—122no—
559C2×C3×C4C23×D312yes—
560C2×C3×C4C23×D312yes—
561C2×C3×C4C23×D311yescharacteristic
562C2×C3×C4C23×D312yes—
563C2×C3×C4C23×D311yescharacteristic
564C2×C3×C4C23×D312yes—
565#67—42no—
566#67—44no—
567#67—124no—
568#67—124no—
569#67—124no—
570#67—124no—
571#67—124no—
572#67—244no—
573C2×Dic3—24no—
574C2×Dic3—34no—
575C2×Dic3—34no—
576C2×Dic3—42no—
577C2×Dic3—64no—
578C2×Dic3—124no—
579C2×Dic3C23×D314yes—
580C2×Dic3C23×D312yes—
581C2×Dic3C23×D312yes—
582C2×Dic3C23×D314yes—
583C2×Dic3C23×D311yescharacteristic
584D12—41no—
585D12—42no—
586D12—122no—
587D12—122no—
588D12—122no—
589D12—122no—
590D12—124no—
591D12—124no—
592D12—124no—
593D12—242no—
594D12—242no—
595C4×D3—22no—
596C4×D3—24no—
597C4×D3—42no—
598C4×D3—68no—
599C4×D3—68no—
600C4×D3—124no—
601C4×D3—124no—
602C4×D3—124no—
603Dic6—42no—
604Dic6—41no—
605Dic6—122no—
606Dic6—122no—
607Dic6—242no—
608C2×C32—42no—
609C2×C32C2×H(5,𝔽2)11yescharacteristic
610C2×C32#58512yes—
611C3⋊D3—44no—
612C3×D3—42no—
613C3×D3—41no—
614C24—92no—
615#41—122no—
616#41—122no—
617#41—364no—
618C2×Q8—32no—
619C2×Q8—31no—
620C2×Q8—92no—
621C2×Q8C2×D3211yescharacteristic
622C2×D4—34no—
623C2×D4—32no—
624C2×D4—32no—
625C2×D4—31no—
626C2×D4—94no—
627C2×D4—94no—
628C2×D4—94no—
629C2×D4—94no—
630C2×D4—92no—
631C2×D4—92no—
632C2×D4C2×D3211yescharacteristic
633C22×C4—32no—
634C22×C4—32no—
635C22×C4—31no—
636C22×C4—32no—
637C22×C4—32no—
638C22×C4—94no—
639C22×C4—94no—
640C22×C4—94no—
641C22×C4—364no—
642C4⋊C4—34no—
643C4⋊C4—34no—
644C4⋊C4—34no—
645C4⋊C4—34no—
646C4⋊C4—32no—
647C4⋊C4—32no—
648C4⋊C4—94no—
649C4⋊C4—94no—
650C4⋊C4—94no—
651C4⋊C4—94no—
652C22⋊C4—32no—
653C22⋊C4—34no—
654C22⋊C4—34no—
655C22⋊C4—94no—
656C22⋊C4—94no—
657C22⋊C4—94no—
658C22⋊C4—94no—
659C22⋊C4—94no—
660C22⋊C4—92no—
661C22⋊C4—94no—
662C22⋊C4—94no—
663C22⋊C4—94no—
664C22⋊C4C2×D3214yes—
665C42—32no—
666C42—31no—
667C42—32no—
668C42—94no—
669C42—92no—
670C42C2×D3211yescharacteristic
671C22×C3—22no—
672C22×C3—24no—
673C22×C3—22no—
674C22×C3—24no—
675C22×C3—21no—
676C22×C3—44no—
677C22×C3—42no—
678C22×C3—62no—
679C22×C3—61no—
680C22×C3—64no—
681C22×C3—62no—
682C22×C3C24×D311yescharacteristic
683C22×C3C24×D311yescharacteristic
684C2×D3—22no—
685C2×D3—21no—
686C2×D3—22no—
687C2×D3—24no—
688C2×D3—64no—
689C2×D3—64no—
690C2×D3—64no—
691C2×D3—64no—
692C2×D3—64no—
693C2×D3—64no—
694C2×D3—124no—
695C2×D3—124no—
696C2×D3—124no—
697C2×D3—128no—
698C2×D3—128no—
699C2×D3—248no—
700C3×C4—21no—
701C3×C4—22no—
702C3×C4—22no—
703C3×C4—22no—
704C3×C4—21no—
705C3×C4—22no—
706C3×C4—32no—
707C3×C4—42no—
708C3×C4—42no—
709C3×C4—41no—
710C3×C4—64no—
711C3×C4—64no—
712C3×C4—62no—
713C3×C4—62no—
714Dic3—22no—
715Dic3—22no—
716Dic3—24no—
717Dic3—24no—
718Dic3—64no—
719Dic3—64no—
720Dic3—124no—
721Dic3#100412yes—
722C32#352911yescharacteristic, complemented, Sylow
723C23—32no—
724C23—31no—
725C23—94no—
726C23—362no—
727C23—364no—
728C23C22×D3212yes—
729Q8—41no—
730Q8—121no—
731Q8—122no—
732Q8—362no—
733D4—41no—
734D4—121no—
735D4—122no—
736D4—122no—
737D4—124no—
738D4—362no—
739D4—362no—
740D4—364no—
741D4—364no—
742D4—364no—
743D4—364no—
744C2×C4—31no—
745C2×C4—32no—
746C2×C4—34no—
747C2×C4—32no—
748C2×C4—34no—
749C2×C4—62no—
750C2×C4—64no—
751C2×C4—64no—
752C2×C4—94no—
753C2×C4—122no—
754C2×C4—122no—
755C2×C4—188no—
756C2×C4—364no—
757C2×C4—364no—
758C2×C4C22×D3212yes—
759C2×C4C22×D3212yes—
760C2×C4C22×D3211yescharacteristic
761C2×C3—21no—
762C2×C3—22no—
763C2×C3—42no—
764C2×C3—42no—
765C2×C3—82no—
766C2×C3—122no—
767C2×C3—121no—
768C2×C3C2×#100411yescharacteristic
769C2×C3#596412yes—
770C2×C3D3×H(5,𝔽2)11yescharacteristic
771C2×C3#596812yes—
772D3—42no—
773D3—41no—
774D3—124no—
775D3—124no—
776D3—244no—
777C22—22no—
778C22—24no—
779C22—61no—
780C22—62no—
781C22—62no—
782C22—64no—
783C22—184no—
784C22—184no—
785C22—184no—
786C22—368no—
787C22C23×D3211yescharacteristic
788C4—21no—
789C4—22no—
790C4—22no—
791C4—32no—
792C4—62no—
793C4—64no—
794C4—62no—
795C4—64no—
796C4—184no—
797C3—21no—
798C3#8624811yescharacteristic, complemented
799C3#8711511yescharacteristic, complemented
800C2—42no—
801C2—121no—
802C2—122no—
803C2—364no—
804C2D3×#100411yescharacteristic
805C2#1059669712yes—
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. #10596154C2semidirect
2. C3×#5672C2semidirect
3. C3×#5668C2semidirect
4. #10595360C2semidirect
5. #10595352C2semidirect
6. #10595266C2semidirect
7. #10595159C2semidirect
8. #10594242C2semidirect
9. #10594174C2semidirect
10. #10594089C2semidirect
11. #10594066C2semidirect
12. #10593976C2semidirect
13. #10593953C2semidirect
16. C2×C3×#239C22semidirect
18. C22×#624C22semidirect
26. C3×#944C22semidirect
27. C3×#944C22semidirect
30. C3×#884C22semidirect
31. C3×#67⋊C4C22semidirect
32. C3×#879C22semidirect
33. C3×#878C22semidirect
34. C3×#875C22semidirect
35. C3×C42×D3C22semidirect
36. C3×#870C22semidirect
37. #63981C22semidirect
38. #63981C22semidirect
41. #63969C22semidirect
42. #63961C22semidirect
44. #63955C22semidirect
49. #63904C22semidirect
50. #63904C22semidirect
52. #63896C22semidirect
54. #63890C22semidirect
55. #63888C22semidirect
56. #63888C22semidirect
57. #63886C22semidirect
58. #63886C22semidirect
59. C4×D3×Dic3C22semidirect
60. #63870C22semidirect
61. #63868C22semidirect
62. #63868C22semidirect
63. #63863C22semidirect
64. #63857C22semidirect
65. #63854C22semidirect
66. #63850C22semidirect
67. #63844C22semidirect
68. #63836C22semidirect
85. #5672D3semidirect
86. #5668D3semidirect
157. C2×#239C2×D3semidirect
182. #944C2×D3semidirect
183. #944C2×D3semidirect
239. #884C2×D3semidirect
248. #67⋊C4C2×D3semidirect
249. #879C2×D3semidirect
251. #878C2×D3semidirect
258. #875C2×D3semidirect
263. C42×D3C2×D3semidirect
264. #870C2×D3semidirect
722. C32#3529semidirect
798. C3#86248semidirect
799. C3#87115semidirect

Maximal subgroups

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

subgroupindex
#105961542
C3×#56722
C3×#56682
#105953602
#105953522
#105952662
#105951592
#105942422
#105941742
#105940892
#105940662
#105939762
#105939532
#871153
#862483