Finite Group Databasebeta

← #7685306

Subgroups — #7685306

Order 512.

5716 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59862C216yesmaximal, complemented
2#59488C216yesmaximal, complemented
3#59378C213yesmaximal, complemented
4#45380C213yesmaximal, complemented
5#45251C213yesmaximal, complemented
6#45019C216yesmaximal, complemented
7#39566C216yesmaximal, complemented
8#39070C216yesmaximal, complemented
9#36585C212yesmaximal, complemented
10#36483C211yesmaximal, characteristic, complemented
11#36431C212yesmaximal, complemented
12#36291C216yesmaximal, complemented
13#36082C211yesmaximal, characteristic
14#35983C212yesmaximal, complemented
15#35854C211yesmaximal, characteristic, complemented
16#34906C213yesmaximal, complemented
17#34263C212yesmaximal, complemented
18#34258C212yesmaximal, complemented
19C4×#548C212yesmaximal, complemented
20C22×H(5,𝔽2)C2211yescharacteristic
21C2×#557C2211yescharacteristic, complemented
22C2×#548C2212yes—
23C2×#548C2211yescharacteristic
24C2×#520C2212yes—
25C2×C4×#41C2212yes—
26C22×C4×Q8C2211yescharacteristic, complemented
27#2860C2216yescomplemented
28#2854C2213yescomplemented
29#2851C2216yescomplemented
30#2796C22112yescomplemented
31#2789C2216yescomplemented
32#2760C2216yescomplemented
33#2751C22112yescomplemented
34#2746C22112yescomplemented
35#2740C22112yescomplemented
36#2736C2216yescomplemented
37#2735C22112yescomplemented
38#2697C2216yescomplemented
39#2640C2213yescomplemented
40#2625C2216yescomplemented
41#2616C2213yes—
42#2609C2216yescomplemented
43#2607C2213yescomplemented
44#2602C2216yescomplemented
45#2600C2213yescomplemented
46#2595C2216yescomplemented
47#2595C22112yescomplemented
48#2592C2213yescomplemented
49#2588C2216yescomplemented
50#2580C2216yescomplemented
51#2578C2216yescomplemented
52#2576C22112yescomplemented
53#2566C2216yescomplemented
54#2563C2213yescomplemented
55#2561C22112yescomplemented
56#2560C2216yescomplemented
57#2523C2211yescharacteristic, complemented
58#2516C22112yescomplemented
59#2513C2216yescomplemented
60#2513C2216yescomplemented
61#2513C2216yescomplemented
62#2503C2216yescomplemented
63#2501C2213yescomplemented
64#2494C2216yescomplemented
65#2494C2216yescomplemented
66#2494C2216yescomplemented
67#2490C2216yescomplemented
68#2489C2216yescomplemented
69#2487C2216yescomplemented
70#2486C2213yescomplemented
71#2483C2216yescomplemented
72#2482C22112yescomplemented
73#2480C22112yescomplemented
74#2471C22112yescomplemented
75#2467C2216yescomplemented
76#2463C2213yescomplemented
77#2454C2216yescomplemented
78#2452C2216yescomplemented
79#2448C2216yescomplemented
80#2447C2216yescomplemented
81#2447C2216yescomplemented
82#2441C2216yescomplemented
83#2439C2216yescomplemented
84#2435C2213yes—
85#2435C2216yes—
86#2423C2216yescomplemented
87#2420C2216yescomplemented
88#2420C2216yescomplemented
89#2418C22112yescomplemented
90#2408C2213yes—
91#2408C2216yes—
92#2398C2213yescomplemented
93#2395C2216yescomplemented
94#2388C2213yes—
95#2367C2216yescomplemented
96#2362C2216yescomplemented
97#2361C2216yescomplemented
98#2358C2216yescomplemented
99#2357C2216yescomplemented
100#2354C2216yescomplemented
101#2352C2216yescomplemented
102#2351C2212yescomplemented
103#2351C2212yescomplemented
104#2351C2212yescomplemented
105Q8×C4⋊C4C2212yescomplemented
106#2345C2216yescomplemented
107#2344C2216yescomplemented
108#2342C22112yescomplemented
109#2341C2212yes—
110#2341C2212yes—
111#2341C2212yes—
112#2341C2212yes—
113#2341C2212yes—
114#2341C2211yescharacteristic
115Q8×C22⋊C4C2212yescomplemented
116Q8×C22⋊C4C2211yescharacteristic, complemented
117D4×C22⋊C4C2216yes—
118D4×C22⋊C4C2216yes—
119D4×C22⋊C4C2216yes—
120D4×C22⋊C4C2216yes—
121#2319C2216yescomplemented
122#2314C2216yescomplemented
123#2311C2216yes—
124#2309C2216yes—
125C4×#126C2216yescomplemented
126C4×#124C2216yescomplemented
127C4×C22⋊Q8C2216yescomplemented
128C4×C22⋊Q8C2216yescomplemented
129C4×#123C2213yescomplemented
130C4×#121C2216yescomplemented
131#2298C2216yescomplemented
132#2297C2216yes—
133#2293C2216yescomplemented
134C2×#390C2216yes—
135#2276C2211yescharacteristic, complemented
136C42×Q8C2212yescomplemented
137C42×D4C2216yescomplemented
138C2×H(5,𝔽2)—216no—
139C2×H(5,𝔽2)—44no—
140C22×#41C2311yescharacteristic
141C22×#41C2313yes—
142C22×#41C2312yes—
143C23×Q8C2311yescharacteristic
144C23×D4C2316yes—
145C23×D4C2313yes—
146#557—44no—
147#548—216no—
148#548—44no—
149C2×C4⋊Q8C2313yes—
150C2×#126C2316yes—
151C2×#125C2316yes—
152C2×#124C2316yes—
153C2×#124C2313yes—
154C2×#123C2313yes—
155C2×#123C2316yes—
156C2×C22⋊Q8C2316yes—
157C2×C22⋊Q8C2316yes—
158C2×C22⋊Q8C2313yes—
159C2×#121C2316yes—
160C2×#121C2313yes—
161C2×#120C2316yes—
162#520—216no—
163C4×#41—48no—
164C2×C4×Q8—44no—
165C2×C4×Q8C2312yes—
166C2×C4×Q8C2312yes—
167C2×C4×Q8C2312yes—
168C2×C4×Q8C2311yescharacteristic
169C2×C4×Q8C2312yes—
170C2×C4×Q8C2312yes—
171C2×C4×Q8C2313yes—
172C2×C4×Q8C2316yes—
173C2×C4×D4C2316yes—
174C2×C4×D4C2316yes—
175C2×C4×D4C2316yes—
176C2×C4×D4C2313yes—
177C2×C4×D4C2316yes—
178C2×C4×D4C2316yes—
179C2×C4×D4C2316yes—
180C2×C4×D4C2316yes—
181C2×#117C2316yes—
182C2×#117C2316yes—
183C2×#117C23112yes—
184C22×C4⋊C4C2316yes—
185C22×C4⋊C4C2313yes—
186C22×C22⋊C4C23112yes—
187C22×C22⋊C4C23112yes—
188C22×C42C2316yes—
189C22×C42C2313yes—
190#401C23112yes—
191#400C2316yes—
192#400C2316yes—
193#400C23112yes—
194#399C23112yes—
195#399C2316yes—
196#399C23112yes—
197#398C2316yes—
198#398C2316yes—
199#397C2316yes—
200#397C23112yes—
201#397C23112yes—
202#397C2316yes—
203#397C2313yes—
204#397C23112yes—
205#397C23112yes—
206#397C2311yescharacteristic
207#397C2312yes—
208#397C23112yes—
209#397C2316yes—
210#397C23112yes—
211#396C23112yes—
212#396C23112yes—
213#395C2313yes—
214#394C2316yes—
215#394C2316yes—
216#394C2313yes—
217#394C23112yes—
218#394C2316yes—
219#394C2316yes—
220#394C2316yes—
221#393C2313yes—
222#393C2316yes—
223#393C23112yes—
224#393C2313yes—
225#393C2311yescharacteristic
226#392C2313yes—
227#392C2316yes—
228#391C2316yes—
229#391C2316yes—
230#391C2312yes—
231#391C2316yes—
232#391C2316yes—
233#391C2316yes—
234#390C2316yes—
235#390C2316yes—
236#390C2316yes—
237#390C23112yes—
238#390C2316yes—
239#390C2316yes—
240#390C2316yes—
241#390C2316yes—
242#390C2316yes—
243#390C2316yes—
244#390C2316yes—
245#390C2316yes—
246#390C2316yes—
247#390C2316yes—
248#390C2316yes—
249#389C2316yes—
250#389C2316yes—
251#389C2316yes—
252#389C2316yes—
253#389C2316yes—
254#389C2316yes—
255#389C2316yes—
256#389C2316yes—
257#389C2316yes—
258#388C2316yes—
259#388C2316yes—
260#388C2316yes—
261#388C2316yes—
262#388C2316yes—
263#388C2316yes—
264#388C23112yes—
265#388C23112yes—
266#388C23112yes—
267#388C23112yes—
268#388C2316yes—
269#388C2316yes—
270#388C23112yes—
271#388C23112yes—
272#388C23112yes—
273#388C23112yes—
274#388C23112yes—
275#388C23112yes—
276#387C2316yes—
277#387C2316yes—
278#387C2316yes—
279#387C2312yes—
280#387C2316yes—
281#387C23112yes—
282#387C2316yes—
283#387C2316yes—
284#387C2316yes—
285#387C2312yes—
286#387C23112yes—
287#387C2316yes—
288#387C23112yes—
289#386C2316yes—
290#386C23112yes—
291#386C23112yes—
292#386C2316yes—
293#386C2316yes—
294#386C2316yes—
295#386C2313yes—
296#386C23112yes—
297#386C23112yes—
298#385C2316yes—
299#385C23112yes—
300#385C23112yes—
301#385C2316yes—
302#385C23112yes—
303#385C23112yes—
304#385C2311yescharacteristic
305#384C2316yes—
306#383C2312yes—
307#382C2316yes—
308#382C2316yes—
309#382C2316yes—
310#382C2316yes—
311#381C23112yes—
312#381C23112yes—
313#381C23112yes—
314#381C2313yes—
315#380C2316yes—
316#380C2316yes—
317#380C2316yes—
318#380C2316yes—
319#380C2316yes—
320#380C2316yes—
321#380C23112yes—
322#380C2316yes—
323#380C2313yes—
324#380C2313yes—
325#379C2316yes—
326#379C23112yes—
327#379C23112yes—
328#379C23112yes—
329C4×C4⋊C4C2316yes—
330C4×C4⋊C4C2316yes—
331C4×C4⋊C4C2316yes—
332C4×C4⋊C4C2316yes—
333C4×C4⋊C4C2313yes—
334C4×C4⋊C4C2316yes—
335C4×C4⋊C4C2316yes—
336C4×C4⋊C4C2316yes—
337C4×C4⋊C4C2316yes—
338C4×C4⋊C4C2316yes—
339C4×C4⋊C4C2316yes—
340C4×C22⋊C4C2313yes—
341C4×C22⋊C4C2316yes—
342C4×C22⋊C4C2316yes—
343C4×C22⋊C4C2316yes—
344C4×C22⋊C4C23112yes—
345C4×C22⋊C4C23112yes—
346C4×C22⋊C4C2316yes—
347C4×C22⋊C4C2316yes—
348C4×C22⋊C4C2316yes—
349C4×C22⋊C4C2316yes—
350C4×C22⋊C4C2313yes—
351C4×C22⋊C4C2316yes—
352C4×C22⋊C4C2316yes—
353C4×C22⋊C4C2312yes—
354#376C2313yes—
355C43C2316yes—
356C25C2416yes—
357H(5,𝔽2)—464no—
358C2×#41—28no—
359C2×#41—28no—
360C2×#41—28no—
361C2×#41—24no—
362C2×#41—224no—
363C2×#41—46no—
364C2×#41#41116yes—
365C22×Q8—28no—
366C22×Q8—24no—
367C22×Q8C2413yes—
368C22×Q8C2411yescharacteristic
369C22×Q8C2413yes—
370C22×Q8C2411yescharacteristic
371C22×D4—224no—
372C22×D4—224no—
373C22×D4—224no—
374C22×D4—412no—
375C22×D4—46no—
376C22×D4C2413yes—
377C22×D4C2416yes—
378C22×D4C2413yes—
379C22×D4C2416yes—
380C22×D4C2416yes—
381C22×D4C2413yes—
382C23×C4C2413yes—
383C23×C4C2413yes—
384C23×C4C2411yescharacteristic
385C23×C4C2416yes—
386C23×C4C24112yes—
387C23×C4C2416yes—
388C23×C4C2413yes—
389C23×C4C2416yes—
390C4⋊Q8—46no—
391#126—412no—
392#125—412no—
393#124—224no—
394#124—46no—
395#123—46no—
396#123—86no—
397C22⋊Q8—224no—
398C22⋊Q8—412no—
399C22⋊Q8—46no—
400#121—224no—
401#121—46no—
402#120—412no—
403C4×Q8—28no—
404C4×Q8—28no—
405C4×Q8—28no—
406C4×Q8—28no—
407C4×Q8—28no—
408C4×Q8—24no—
409C4×Q8—46no—
410C4×Q8—412no—
411C4×D4—224no—
412C4×D4—224no—
413C4×D4—224no—
414C4×D4—412no—
415C4×D4—412no—
416C4×D4—46no—
417C4×D4—412no—
418C4×D4—412no—
419#117—224no—
420#117—412no—
421#117—812no—
422C2×C4⋊C4—224no—
423C2×C4⋊C4—46no—
424C2×C4⋊C4C2416yes—
425C2×C4⋊C4C2416yes—
426C2×C4⋊C4C2416yes—
427C2×C4⋊C4C2416yes—
428C2×C4⋊C4C2412yes—
429C2×C4⋊C4C2416yes—
430C2×C4⋊C4C2416yes—
431C2×C4⋊C4C2416yes—
432C2×C4⋊C4C2413yes—
433C2×C4⋊C4C2416yes—
434C2×C4⋊C4C2412yes—
435C2×C4⋊C4C2416yes—
436C2×C4⋊C4C2416yes—
437C2×C4⋊C4C24112yes—
438C2×C4⋊C4C2413yes—
439C2×C4⋊C4C2416yes—
440C2×C4⋊C4C2411yescharacteristic
441C2×C4⋊C4C2416yes—
442C2×C4⋊C4C2416yes—
443C2×C4⋊C4C2416yes—
444C2×C4⋊C4C2416yes—
445C2×C4⋊C4C2416yes—
446C2×C4⋊C4C2416yes—
447C2×C22⋊C4—424no—
448C2×C22⋊C4—812no—
449C2×C22⋊C4C2416yes—
450C2×C22⋊C4C2416yes—
451C2×C22⋊C4C2416yes—
452C2×C22⋊C4C2416yes—
453C2×C22⋊C4C2412yes—
454C2×C22⋊C4C2412yes—
455C2×C22⋊C4C2416yes—
456C2×C22⋊C4C24112yes—
457C2×C22⋊C4C2411yescharacteristic
458C2×C22⋊C4C2416yes—
459C2×C22⋊C4C2416yes—
460C2×C22⋊C4C24112yes—
461C2×C22⋊C4C24112yes—
462C2×C22⋊C4C24112yes—
463C2×C22⋊C4C24112yes—
464C2×C22⋊C4C2416yes—
465C2×C22⋊C4C24112yes—
466C2×C22⋊C4C2411yescharacteristic
467C2×C22⋊C4C2413yes—
468C2×C22⋊C4C2416yes—
469C2×C22⋊C4C2416yes—
470C2×C22⋊C4C24112yes—
471C2×C22⋊C4C2416yes—
472C2×C22⋊C4C2416yes—
473C2×C22⋊C4C2416yes—
474C2×C22⋊C4C2416yes—
475C2×C22⋊C4C2413yes—
476C2×C22⋊C4C2416yes—
477C2×C22⋊C4C2416yes—
478C2×C22⋊C4C2416yes—
479C2×C42—46no—
480C2×C42—412no—
481C2×C42C2416yes—
482C2×C42C2416yes—
483C2×C42C2413yes—
484C2×C42C2416yes—
485C2×C42C2416yes—
486C2×C42C2416yes—
487C2×C42C2412yes—
488C2×C42C2416yes—
489C2×C42C2416yes—
490C2×C42C2416yes—
491C2×C42C2416yes—
492C2×C42C2416yes—
493C2×C42C2416yes—
494C2×C42C2412yes—
495#95C2411yescharacteristic
496#95C2416yes—
497#95C2413yes—
498#95C2412yes—
499#95C2412yes—
500#95C2411yescharacteristic
501#95C2412yes—
502#95C2412yes—
503#95C2412yes—
504#95C2412yes—
505#95C2416yes—
506#95C2416yes—
507#95C2416yes—
508#95C2416yes—
509#95C2416yes—
510#95C2416yes—
511#95C2416yes—
512#95C2416yes—
513#95C2416yes—
514#95C2413yes—
515#95C24112yes—
516#95C24112yes—
517#95C2416yes—
518#95C24112yes—
519#95C24112yes—
520#95C2412yes—
521#95C2412yes—
522#95C2416yes—
523#95C2416yes—
524#95C2416yes—
525#95C2416yes—
526#95C24112yes—
527C24—224no—
528C24—46no—
529C24—412no—
530C24—46no—
531C24—46no—
532C24C2513yes—
533C24C2516yes—
534C24C2511yescharacteristic
535#41—264no—
536#41—448no—
537#41—416no—
538C2×Q8—212no—
539C2×Q8—24no—
540C2×Q8—26no—
541C2×Q8—41no—
542C2×Q8—43no—
543C2×Q8—46no—
544C2×Q8—416no—
545C2×Q8C2×#4118yes—
546C2×Q8H(5,𝔽2)14yes—
547C2×D4—212no—
548C2×D4—212no—
549C2×D4—212no—
550C2×D4—212no—
551C2×D4—26no—
552C2×D4—212no—
553C2×D4—212no—
554C2×D4—212no—
555C2×D4—212no—
556C2×D4—26no—
557C2×D4—496no—
558C2×D4—46no—
559C2×D4—46no—
560C2×D4—43no—
561C2×D4—43no—
562C2×D4—43no—
563C2×D4—448no—
564C2×D4C2×#41124yes—
565C22×C4—212no—
566C22×C4—212no—
567C22×C4—224no—
568C22×C4—26no—
569C22×C4—212no—
570C22×C4—212no—
571C22×C4—26no—
572C22×C4—26no—
573C22×C4—24no—
574C22×C4—212no—
575C22×C4—41no—
576C22×C4—43no—
577C22×C4—46no—
578C22×C4—46no—
579C22×C4—412no—
580C22×C4—46no—
581C22×C4—412no—
582C22×C4—46no—
583C22×C4—46no—
584C22×C4—43no—
585C22×C4C2×#41124yes—
586C22×C4C2511yescharacteristic
587C22×C4C2516yes—
588C22×C4C2511yescharacteristic
589C22×C4C2516yes—
590C22×C4C2513yes—
591C22×C4C2516yes—
592C22×C4C2512yes—
593C22×C4C2512yes—
594C22×C4C2512yes—
595C22×C4C2516yes—
596C22×C4C2512yes—
597C22×C4C2516yes—
598C22×C4C2513yes—
599C22×C4C2512yes—
600C22×C4C2512yes—
601C22×C4C2513yes—
602C4⋊C4—212no—
603C4⋊C4—212no—
604C4⋊C4—212no—
605C4⋊C4—24no—
606C4⋊C4—212no—
607C4⋊C4—212no—
608C4⋊C4—212no—
609C4⋊C4—212no—
610C4⋊C4—26no—
611C4⋊C4—212no—
612C4⋊C4—24no—
613C4⋊C4—46no—
614C4⋊C4—46no—
615C4⋊C4—412no—
616C4⋊C4—46no—
617C4⋊C4—43no—
618C4⋊C4—41no—
619C4⋊C4—46no—
620C4⋊C4—46no—
621C4⋊C4—46no—
622C4⋊C4—46no—
623C4⋊C4—46no—
624C4⋊C4—46no—
625C22⋊C4—212no—
626C22⋊C4—212no—
627C22⋊C4—212no—
628C22⋊C4—224no—
629C22⋊C4—24no—
630C22⋊C4—22no—
631C22⋊C4—24no—
632C22⋊C4—212no—
633C22⋊C4—212no—
634C22⋊C4—412no—
635C22⋊C4—412no—
636C22⋊C4—46no—
637C22⋊C4—46no—
638C22⋊C4—412no—
639C22⋊C4—412no—
640C22⋊C4—412no—
641C22⋊C4—46no—
642C22⋊C4—46no—
643C22⋊C4—46no—
644C22⋊C4—41no—
645C22⋊C4—43no—
646C22⋊C4—46no—
647C22⋊C4—412no—
648C22⋊C4—46no—
649C22⋊C4—46no—
650C22⋊C4—46no—
651C22⋊C4—46no—
652C22⋊C4—43no—
653C22⋊C4—46no—
654C22⋊C4—46no—
655C42—212no—
656C42—212no—
657C42—212no—
658C42—212no—
659C42—212no—
660C42—26no—
661C42—24no—
662C42—42no—
663C42—46no—
664C42—46no—
665C42—46no—
666C42—46no—
667C42—46no—
668C42—46no—
669C23—22no—
670C23—26no—
671C23—26no—
672C23—21no—
673C23—26no—
674C23—22no—
675C23—26no—
676C23—26no—
677C23—26no—
678C23—21no—
679C23—26no—
680C23—23no—
681C23—26no—
682C23—23no—
683C23—23no—
684C23—424no—
685C23—824no—
686C23—824no—
687C23—166no—
688C23—166no—
689C23C22×#41112yes—
690C23#58512yes—
691C23C2611yescharacteristic
692Q8—44no—
693Q8—412no—
694Q8—86no—
695Q8#551116yes—
696D4—248no—
697D4—424no—
698D4—424no—
699D4—412no—
700D4—412no—
701D4—86no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—248no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—26no—
711C2×C4—26no—
712C2×C4—26no—
713C2×C4—26no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—26no—
718C2×C4—26no—
719C2×C4—23no—
720C2×C4—23no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—26no—
726C2×C4—26no—
727C2×C4—26no—
728C2×C4—26no—
729C2×C4—22no—
730C2×C4—26no—
731C2×C4—22no—
732C2×C4—23no—
733C2×C4—26no—
734C2×C4—22no—
735C2×C4—26no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—26no—
739C2×C4—23no—
740C2×C4—26no—
741C2×C4—22no—
742C2×C4—26no—
743C2×C4—44no—
744C2×C4—412no—
745C2×C4—412no—
746C2×C4—812no—
747C2×C4—824no—
748C2×C4—86no—
749C2×C4—812no—
750C2×C4C22×#4114yes—
751C2×C4C22×#41112yes—
752C2×C4C2×H(5,𝔽2)16yes—
753C2×C4#58514yes—
754C22—212no—
755C22—24no—
756C22—212no—
757C22—22no—
758C22—212no—
759C22—42no—
760C22—46no—
761C22—41no—
762C22—46no—
763C22—46no—
764C22—46no—
765C22—41no—
766C22—46no—
767C22—43no—
768C22—46no—
769C22—43no—
770C22—43no—
771C22—1624no—
772C22C23×#4112yes—
773C22C22×H(5,𝔽2)11yescharacteristic
774C22C2×#58512yes—
775C22C2×#58511yescharacteristic
776C22H(7,𝔽2)11yescharacteristic
777C4—24no—
778C4—24no—
779C4—42no—
780C4—46no—
781C4—46no—
782C4—46no—
783C4—41no—
784C4—42no—
785C4—42no—
786C4—46no—
787C4—46no—
788C4—42no—
789C4—43no—
790C4—41no—
791C4—43no—
792C4C2×#551112yes—
793C2—42no—
794C2—412no—
795C2—83no—
796C2C22×#55111yescharacteristic
797C2#6281012yes—
798C2#6289911yescharacteristic
799C2#6301012yes—
800C2#6302011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36082C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59862C2semidirect
2. #59488C2semidirect
3. #59378C2semidirect
4. #45380C2semidirect
5. #45251C2semidirect
6. #45019C2semidirect
7. #39566C2semidirect
8. #39070C2semidirect
9. #36585C2semidirect
10. #36483C2semidirect
11. #36431C2semidirect
12. #36291C2semidirect
14. #35983C2semidirect
15. #35854C2semidirect
16. #34906C2semidirect
17. #34263C2semidirect
18. #34258C2semidirect
19. C4×#548C2semidirect
21. C2×#557C22semidirect
26. C22×C4×Q8C22semidirect
27. #2860C22semidirect
28. #2854C22semidirect
29. #2851C22semidirect
30. #2796C22semidirect
31. #2789C22semidirect
32. #2760C22semidirect
33. #2751C22semidirect
34. #2746C22semidirect
35. #2740C22semidirect
36. #2736C22semidirect
37. #2735C22semidirect
38. #2697C22semidirect
39. #2640C22semidirect
40. #2625C22semidirect
42. #2609C22semidirect
43. #2607C22semidirect
44. #2602C22semidirect
45. #2600C22semidirect
46. #2595C22semidirect
47. #2595C22semidirect
48. #2592C22semidirect
49. #2588C22semidirect
50. #2580C22semidirect
51. #2578C22semidirect
52. #2576C22semidirect
53. #2566C22semidirect
54. #2563C22semidirect
55. #2561C22semidirect
56. #2560C22semidirect
57. #2523C22semidirect
58. #2516C22semidirect
59. #2513C22semidirect
60. #2513C22semidirect
61. #2513C22semidirect
62. #2503C22semidirect
63. #2501C22semidirect
64. #2494C22semidirect
65. #2494C22semidirect
66. #2494C22semidirect
67. #2490C22semidirect
68. #2489C22semidirect
69. #2487C22semidirect
70. #2486C22semidirect
71. #2483C22semidirect
72. #2482C22semidirect
73. #2480C22semidirect
74. #2471C22semidirect
75. #2467C22semidirect
76. #2463C22semidirect
77. #2454C22semidirect
78. #2452C22semidirect
79. #2448C22semidirect
80. #2447C22semidirect
81. #2447C22semidirect
82. #2441C22semidirect
83. #2439C22semidirect
86. #2423C22semidirect
87. #2420C22semidirect
88. #2420C22semidirect
89. #2418C22semidirect
92. #2398C22semidirect
93. #2395C22semidirect
95. #2367C22semidirect
96. #2362C22semidirect
97. #2361C22semidirect
98. #2358C22semidirect
99. #2357C22semidirect
100. #2354C22semidirect
101. #2352C22semidirect
102. #2351C22semidirect
103. #2351C22semidirect
104. #2351C22semidirect
105. Q8×C4⋊C4C22semidirect
106. #2345C22semidirect
107. #2344C22semidirect
108. #2342C22semidirect
115. Q8×C22⋊C4C22semidirect
116. Q8×C22⋊C4C22semidirect
121. #2319C22semidirect
122. #2314C22semidirect
125. C4×#126C22semidirect
126. C4×#124C22semidirect
127. C4×C22⋊Q8C22semidirect
128. C4×C22⋊Q8C22semidirect
129. C4×#123C22semidirect
130. C4×#121C22semidirect
131. #2298C22semidirect
133. #2293C22semidirect
135. #2276C22semidirect
136. C42×Q8C22semidirect
137. C42×D4C22semidirect

Maximal subgroups

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

subgroupindex
#598622
#594882
#593782
#453802
#452512
#450192
#395662
#390702
#365852
#364832
#364312
#362912
#360822
#359832
#358542
#349062
#342632
#342582
C4×#5482