Finite Group Databasebeta

← #7655104

Subgroups — #7655104

Order 512.

8796 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3517C211yesmaximal, characteristic, complemented
2C2×D4×#41C211yesmaximal, characteristic, complemented
3#42438C2112yesmaximal, complemented
4#39862C2112yesmaximal, complemented
5#39362C213yesmaximal, complemented
6#39361C213yesmaximal, complemented
7#38956C213yesmaximal, complemented
8#38951C213yesmaximal, complemented
9#37616C213yesmaximal, complemented
10#36592C211yesmaximal, characteristic, complemented
11#36583C211yesmaximal, characteristic, complemented
12#36465C211yesmaximal, characteristic, complemented
13#36446C211yesmaximal, characteristic, complemented
14#36429C214yesmaximal, complemented
15#35831C214yesmaximal, complemented
16#35293C213yesmaximal, complemented
17#35165C213yesmaximal, complemented
18#34965C213yesmaximal, complemented
19#34129C211yesmaximal, characteristic, complemented
20C23×#41C2212yes—
21#3517—216no—
22C2×#557C2211yescharacteristic, complemented
23C2×#553C2216yescomplemented
24D4×#41—216no—
25C2×#550C2212yes—
26C2×#550C2211yescharacteristic
27C2×#550C2213yescomplemented
28C2×#550C2211yescharacteristic, complemented
29C2×#550C2214yescomplemented
30C2×D4×Q8C2211yescharacteristic
31C2×#548C2212yes—
32C2×#548C2214yescomplemented
33C2×#547C2213yes—
34C2×#547C2213yescomplemented
35C2×#546C2216yes—
36C2×D42C2213yes—
37C2×#540C2216yescomplemented
38C2×#535C2216yes—
39C2×#532C2213yes—
40C2×#532C2213yescomplemented
41C2×#529C2213yescomplemented
42C2×#525C2216yes—
43C2×#520C2212yescomplemented
44C2×C4×#41C2211yescharacteristic
45C22×C4×D4C2213yes—
46#2867C2213yescomplemented
47#2862C2213yescomplemented
48#2858C2213yescomplemented
49#2858C2213yescomplemented
50#2847C22112yescomplemented
51#2813C22112yescomplemented
52#2706C22124yescomplemented
53#2703C22124yescomplemented
54#2678C22124yescomplemented
55#2669C22124yescomplemented
56#2636C22112yescomplemented
57#2620C2216yescomplemented
58#2620C22112yescomplemented
59#2619C2216yescomplemented
60#2619C22112yescomplemented
61#2617C22112yescomplemented
62#2603C22112yescomplemented
63#2568C2213yescomplemented
64#2566C2211yescharacteristic
65#2566C2213yescomplemented
66#2548C2213yescomplemented
67#2547C2213yes—
68#2547C2213yescomplemented
69#2544C2213yes—
70#2544C2216yescomplemented
71#2544C2213yescomplemented
72#2544C22112yescomplemented
73#2542C2213yescomplemented
74#2541C2213yes—
75#2541C2213yescomplemented
76#2541C22112yescomplemented
77#2541C2213yescomplemented
78#2540C22112yescomplemented
79#2537C22112yescomplemented
80#2535C22112yescomplemented
81#2504C2213yescomplemented
82#2502C2213yescomplemented
83#2490C22112yescomplemented
84#2489C22112yescomplemented
85#2435C2213yes—
86#2433C2213yes—
87#2433C22112yescomplemented
88#2431C2216yescomplemented
89#2431C22112yescomplemented
90#2431C2216yescomplemented
91#2431C22112yescomplemented
92#2428C22112yescomplemented
93#2427C22112yescomplemented
94#2417C22112yescomplemented
95#2416C22112yescomplemented
96#2411C22112yescomplemented
97#2408C22112yescomplemented
98#2407C22112yescomplemented
99#2407C22112yescomplemented
100#2392C22112yescomplemented
101#2354C2216yescomplemented
102Q8×C4⋊C4C2212yescomplemented
103#2346C2216yescomplemented
104#2341C2212yes—
105#2341C2214yescomplemented
106Q8×C22⋊C4C2214yescomplemented
107#2328C22112yescomplemented
108#2311C2216yescomplemented
109C4×#127C2213yes—
110C4×#127C2213yescomplemented
111C4×#124C2213yes—
112C4×#124C2213yescomplemented
113C4×#120C22112yescomplemented
114#2293C2213yescomplemented
115#2293C2213yescomplemented
116#2285C2213yescomplemented
117C42×Q8C2211yescharacteristic, complemented
118C42×Q8C2211yescharacteristic, complemented
119C4×#117C2213yescomplemented
120C22×#41—216no—
121C22×#41—416no—
122C22×#41C2312yes—
123C22×#41C2312yes—
124C22×#41C2311yescharacteristic
125C22×#41C2316yes—
126C22×#41C2316yes—
127C22×#41C2316yes—
128C23×Q8C2312yes—
129C23×D4C2313yes—
130C23×D4C2316yes—
131C24×C4C2316yes—
132#557—28no—
133#553—248no—
134#550—216no—
135#550—28no—
136#550—28no—
137#550—224no—
138#550—416no—
139D4×Q8—28no—
140#548—216no—
141#548—416no—
142#547—224no—
143#547—224no—
144#546—248no—
145D42—224no—
146#540—248no—
147#535—424no—
148#532—224no—
149#532—224no—
150C2×C4⋊Q8C2313yes—
151C2×C4⋊Q8C2313yes—
152C2×#127C2313yes—
153C2×#127C2313yes—
154C2×#127C2313yes—
155C2×#127C2316yes—
156C2×#127C2313yes—
157C2×#127C23112yes—
158C2×#127C2316yes—
159C2×#127C23112yes—
160#529—224no—
161C2×#126C2316yes—
162C2×#125C2311yescharacteristic
163C2×#125C2316yes—
164C2×#124C2316yes—
165C2×#124C2313yes—
166C2×#124C2313yes—
167C2×#124C2313yes—
168C2×#124C2316yes—
169C2×#124C23112yes—
170#525—248no—
171C2×#123C2316yes—
172C2×#123C23112yes—
173C2×#123C23112yes—
174C2×C22⋊Q8C2313yes—
175C2×C22⋊Q8C2316yes—
176C2×C22⋊Q8C2316yes—
177C2×C22⋊Q8C23112yes—
178C2×#121C2316yes—
179C2×#121C2316yes—
180C2×#121C2313yes—
181C2×#121C2316yes—
182C2×#121C2316yes—
183C2×#121C2316yes—
184C2×#121C2316yes—
185C2×#121C2316yes—
186C2×#121C23112yes—
187C2×#121C2316yes—
188C2×#121C23112yes—
189C2×#121C23112yes—
190C2×#121C23112yes—
191C2×#121C23124yes—
192C2×#120C23112yes—
193C2×#120C23124yes—
194C2×#120C23112yes—
195#520—216no—
196C4×#41D4116yescomplemented
197C2×C4×Q8C2313yes—
198C2×C4×Q8C2312yes—
199C2×C4×Q8C2312yes—
200C2×C4×Q8C2312yes—
201C2×C4×Q8C2311yescharacteristic
202C2×C4×Q8C2311yescharacteristic
203C2×C4×D4—224no—
204C2×C4×D4C2313yes—
205C2×C4×D4C2313yes—
206C2×C4×D4C2313yes—
207C2×C4×D4C2311yescharacteristic
208C2×C4×D4C2313yes—
209C2×C4×D4C2316yes—
210C2×C4×D4C2316yes—
211C2×C4×D4C2316yes—
212C2×C4×D4C2316yes—
213C2×C4×D4C2316yes—
214C2×C4×D4C2316yes—
215C2×C4×D4C2316yes—
216C2×C4×D4C23112yes—
217C2×C4×D4C23112yes—
218C2×C4×D4C2313yes—
219C2×C4×D4C2313yes—
220C2×#117C2316yes—
221C2×#117C2316yes—
222C2×#117C2316yes—
223C2×#117C2313yes—
224C22×C4⋊C4C2313yes—
225C22×C4⋊C4C2316yes—
226C22×C22⋊C4C2316yes—
227C22×C42C2313yes—
228#400C23112yes—
229#399C23112yes—
230#398C23112yes—
231#397C23112yes—
232#397C23112yes—
233#397C23112yes—
234#396C2314yes—
235#396C23112yes—
236#396C23124yes—
237#394C23112yes—
238#394C23112yes—
239#394C23124yes—
240#394C23112yes—
241#394C23124yes—
242#394C23124yes—
243#394C23112yes—
244#392C23112yes—
245#392C23112yes—
246#392C23112yes—
247#392C23124yes—
248#392C23124yes—
249#392C23124yes—
250#392C23112yes—
251#391C2313yes—
252#391C2316yes—
253#391C23112yes—
254#391C23112yes—
255#391C2313yes—
256#390C2311yescharacteristic
257#390C2313yes—
258#390C23112yes—
259#390C2313yes—
260#390C2313yes—
261#390C23112yes—
262#390C2311yescharacteristic
263#390C2313yes—
264#390C2316yes—
265#390C23112yes—
266#390C23112yes—
267#390C2316yes—
268#390C2316yes—
269#390C23112yes—
270#390C23112yes—
271#389C2316yes—
272#389C2316yes—
273#388C23112yes—
274#388C23112yes—
275#388C23112yes—
276#388C23112yes—
277#386C23124yes—
278#386C23112yes—
279#386C23124yes—
280#386C23124yes—
281#386C23124yes—
282#386C23112yes—
283#386C23112yes—
284#385C2314yes—
285#385C23112yes—
286#385C23112yes—
287#384C2313yes—
288#384C2311yescharacteristic
289#384C2316yes—
290#382C2311yescharacteristic
291#382C2313yes—
292#382C23112yes—
293#382C2316yes—
294#380C23124yes—
295#380C2316yes—
296#380C23112yes—
297#380C23112yes—
298#380C2316yes—
299#379C23112yes—
300C4×C4⋊C4C2311yescharacteristic
301C4×C4⋊C4C2313yes—
302C4×C4⋊C4C2313yes—
303C4×C4⋊C4C2316yes—
304C4×C4⋊C4C2316yes—
305C4×C4⋊C4C2316yes—
306C4×C4⋊C4C2313yes—
307C4×C22⋊C4C23112yes—
308C4×C22⋊C4C2316yes—
309C4×C22⋊C4C23112yes—
310C4×C22⋊C4C2313yes—
311C4×C22⋊C4C2313yes—
312#376C2316yes—
313C43C2313yes—
314C43C2313yes—
315C25C2416yes—
316C2×#41—28no—
317C2×#41—28no—
318C2×#41—28no—
319C2×#41—216no—
320C2×#41—216no—
321C2×#41—224no—
322C2×#41—224no—
323C2×#41—224no—
324C2×#41—424no—
325C2×#41—424no—
326C2×#41—412no—
327C2×#41—412no—
328C2×#41—4128no—
329C2×#41C2×D418yes—
330C22×Q8—28no—
331C22×Q8—216no—
332C22×Q8C2413yes—
333C22×Q8C2416yes—
334C22×Q8C2411yescharacteristic
335C22×D4—224no—
336C22×D4—212no—
337C22×D4—212no—
338C22×D4—46no—
339C22×D4—424no—
340C22×D4C2416yes—
341C22×D4C2413yes—
342C22×D4C2413yes—
343C22×D4C2416yes—
344C22×D4C2416yes—
345C22×D4C2413yes—
346C22×D4C2411yescharacteristic
347C22×D4C24112yes—
348C22×D4C2416yes—
349C22×D4C2416yes—
350C22×D4C24112yes—
351C22×D4C2416yes—
352C22×D4C24112yes—
353C22×D4C24112yes—
354C22×D4C24124yes—
355C23×C4—224no—
356C23×C4—424no—
357C23×C4C2416yes—
358C23×C4C2416yes—
359C23×C4C2416yes—
360C23×C4C2413yes—
361C23×C4C2413yes—
362C23×C4C2416yes—
363C23×C4C24112yes—
364C23×C4C2412yes—
365C23×C4C2416yes—
366C23×C4C2413yes—
367C4⋊Q8—212no—
368C4⋊Q8—212no—
369#127—224no—
370#127—212no—
371#127—212no—
372#127—212no—
373#127—424no—
374#127—46no—
375#127—412no—
376#127—424no—
377#126—224no—
378#125—224no—
379#125—24no—
380#124—212no—
381#124—212no—
382#124—224no—
383#124—46no—
384#124—412no—
385#124—424no—
386#123—224no—
387#123—248no—
388#123—248no—
389C22⋊Q8—212no—
390C22⋊Q8—224no—
391C22⋊Q8—224no—
392C22⋊Q8—424no—
393#121—224no—
394#121—212no—
395#121—224no—
396#121—224no—
397#121—224no—
398#121—224no—
399#121—224no—
400#121—224no—
401#121—224no—
402#121—248no—
403#121—448no—
404#121—424no—
405#121—424no—
406#121—424no—
407#120—248no—
408#120—424no—
409#120—448no—
410C4×Q8—28no—
411C4×Q8—28no—
412C4×Q8—28no—
413C4×Q8—212no—
414C4×Q8C2×D418yes—
415C4×Q8C2×D418yes—
416C4×D4—224no—
417C4×D4—224no—
418C4×D4—24no—
419C4×D4—224no—
420C4×D4—212no—
421C4×D4—212no—
422C4×D4—224no—
423C4×D4—212no—
424C4×D4—224no—
425C4×D4—224no—
426C4×D4—212no—
427C4×D4—224no—
428C4×D4—424no—
429C4×D4—424no—
430C4×D4C2×D4124yes—
431C4×D4C2×D4124yes—
432#117—224no—
433#117—412no—
434#117—412no—
435#117C2×D4124yes—
436C2×C4⋊C4—212no—
437C2×C4⋊C4—224no—
438C2×C4⋊C4C2411yescharacteristic
439C2×C4⋊C4C2416yes—
440C2×C4⋊C4C2413yes—
441C2×C4⋊C4C2416yes—
442C2×C4⋊C4C2416yes—
443C2×C4⋊C4C2412yes—
444C2×C4⋊C4C2412yes—
445C2×C4⋊C4C2411yescharacteristic
446C2×C4⋊C4C2412yes—
447C2×C4⋊C4C2416yes—
448C2×C4⋊C4C2416yes—
449C2×C4⋊C4C2411yescharacteristic
450C2×C4⋊C4C2416yes—
451C2×C4⋊C4C2416yes—
452C2×C4⋊C4C2416yes—
453C2×C4⋊C4C24112yes—
454C2×C4⋊C4C2416yes—
455C2×C4⋊C4C2414yes—
456C2×C4⋊C4C24112yes—
457C2×C4⋊C4C2413yes—
458C2×C4⋊C4C2413yes—
459C2×C22⋊C4—224no—
460C2×C22⋊C4C2412yes—
461C2×C22⋊C4C2416yes—
462C2×C22⋊C4C2416yes—
463C2×C22⋊C4C2416yes—
464C2×C22⋊C4C2416yes—
465C2×C22⋊C4C2416yes—
466C2×C22⋊C4C2416yes—
467C2×C22⋊C4C2416yes—
468C2×C22⋊C4C24112yes—
469C2×C22⋊C4C2416yes—
470C2×C22⋊C4C2416yes—
471C2×C22⋊C4C2414yes—
472C2×C22⋊C4C24112yes—
473C2×C22⋊C4C24112yes—
474C2×C22⋊C4C2416yes—
475C2×C22⋊C4C2414yes—
476C2×C22⋊C4C24112yes—
477C2×C22⋊C4C24112yes—
478C2×C22⋊C4C24112yes—
479C2×C22⋊C4C24124yes—
480C2×C22⋊C4C24112yes—
481C2×C22⋊C4C24124yes—
482C2×C22⋊C4C24112yes—
483C2×C22⋊C4C2416yes—
484C2×C42C2×D4124yes—
485C2×C42C2413yes—
486C2×C42C2413yes—
487C2×C42C2416yes—
488C2×C42C2416yes—
489C2×C42C2416yes—
490C2×C42C2416yes—
491C2×C42C2411yescharacteristic
492C2×C42C2411yescharacteristic
493C2×C42C2416yes—
494C2×C42C2413yes—
495C2×C42C2413yes—
496C2×C42C2413yes—
497C2×C42C2411yescharacteristic
498#95C2412yes—
499#95C2416yes—
500#95C2416yes—
501#95C2416yes—
502#95C2414yes—
503#95C24112yes—
504#95C24112yes—
505#95C24112yes—
506#95C2416yes—
507#95C2416yes—
508#95C24124yes—
509C24—212no—
510C24—212no—
511C24—412no—
512C24—46no—
513C24—412no—
514C24C2516yes—
515C24C2516yes—
516C24C2513yes—
517C24C2512yes—
518#41—232no—
519#41—496no—
520#41—496no—
521#41—432no—
522#41—432no—
523#41—848no—
524C2×Q8—26no—
525C2×Q8—212no—
526C2×Q8—224no—
527C2×Q8—26no—
528C2×Q8—26no—
529C2×Q8—432no—
530C2×Q8C22×D414yes—
531C2×Q8H(5,𝔽2)18yes—
532C2×D4—224no—
533C2×D4—212no—
534C2×D4—212no—
535C2×D4—224no—
536C2×D4—224no—
537C2×D4—22no—
538C2×D4—212no—
539C2×D4—26no—
540C2×D4—212no—
541C2×D4—26no—
542C2×D4—212no—
543C2×D4—212no—
544C2×D4—212no—
545C2×D4—212no—
546C2×D4—224no—
547C2×D4—224no—
548C2×D4—26no—
549C2×D4—26no—
550C2×D4—22no—
551C2×D4—26no—
552C2×D4—26no—
553C2×D4—224no—
554C2×D4—448no—
555C2×D4—46no—
556C2×D4—424no—
557C2×D4—412no—
558C2×D4—412no—
559C2×D4—412no—
560C2×D4—412no—
561C2×D4—412no—
562C2×D4—412no—
563C2×D4—412no—
564C2×D4—412no—
565C2×D4—412no—
566C2×D4—424no—
567C2×D4—424no—
568C2×D4—424no—
569C2×D4—496no—
570C2×D4C22×D4112yes—
571C2×D4H(5,𝔽2)14yes—
572C22×C4—26no—
573C22×C4—212no—
574C22×C4—26no—
575C22×C4—212no—
576C22×C4—212no—
577C22×C4—24no—
578C22×C4—212no—
579C22×C4—212no—
580C22×C4—212no—
581C22×C4—224no—
582C22×C4—224no—
583C22×C4—224no—
584C22×C4—224no—
585C22×C4—46no—
586C22×C4—44no—
587C22×C4—412no—
588C22×C4—412no—
589C22×C4—412no—
590C22×C4—412no—
591C22×C4—496no—
592C22×C4C22×D4112yes—
593C22×C4C22×D4112yes—
594C22×C4C22×D4112yes—
595C22×C4C2516yes—
596C22×C4C2512yes—
597C22×C4C2516yes—
598C22×C4C2512yes—
599C22×C4C2516yes—
600C22×C4C2512yes—
601C22×C4C2516yes—
602C22×C4C2512yes—
603C22×C4C2511yescharacteristic
604C22×C4C2513yes—
605C22×C4C2513yes—
606C22×C4C2511yescharacteristic
607C22×C4C2512yes—
608C22×C4C2513yes—
609C22×C4C2511yescharacteristic
610C4⋊C4—22no—
611C4⋊C4—212no—
612C4⋊C4—26no—
613C4⋊C4—212no—
614C4⋊C4—212no—
615C4⋊C4—24no—
616C4⋊C4—22no—
617C4⋊C4—24no—
618C4⋊C4—212no—
619C4⋊C4—212no—
620C4⋊C4—22no—
621C4⋊C4—212no—
622C4⋊C4—212no—
623C4⋊C4—212no—
624C4⋊C4—24no—
625C4⋊C4—46no—
626C4⋊C4—412no—
627C4⋊C4—44no—
628C4⋊C4—412no—
629C4⋊C4C22×D4112yes—
630C4⋊C4C22×D4112yes—
631C22⋊C4—212no—
632C22⋊C4—224no—
633C22⋊C4—24no—
634C22⋊C4—212no—
635C22⋊C4—212no—
636C22⋊C4—212no—
637C22⋊C4—212no—
638C22⋊C4—212no—
639C22⋊C4—212no—
640C22⋊C4—224no—
641C22⋊C4—212no—
642C22⋊C4—212no—
643C22⋊C4—28no—
644C22⋊C4—46no—
645C22⋊C4—412no—
646C22⋊C4—44no—
647C22⋊C4—412no—
648C22⋊C4—412no—
649C22⋊C4—412no—
650C22⋊C4—412no—
651C22⋊C4—424no—
652C22⋊C4—424no—
653C22⋊C4—412no—
654C22⋊C4C22×D4124yes—
655C42—212no—
656C42—26no—
657C42—26no—
658C42—212no—
659C42—212no—
660C42—212no—
661C42—22no—
662C42—22no—
663C42—46no—
664C42C22×D414yes—
665C42C22×D4112yes—
666C42C22×D4112yes—
667C42C22×D4112yes—
668C23—22no—
669C23—23no—
670C23—24no—
671C23—26no—
672C23—26no—
673C23—24no—
674C23—23no—
675C23—22no—
676C23—26no—
677C23—26no—
678C23—212no—
679C23—26no—
680C23—212no—
681C23—26no—
682C23—26no—
683C23—212no—
684C23—26no—
685C23—212no—
686C23—424no—
687C23—424no—
688C23—824no—
689C23—812no—
690C23—824no—
691C23C23×D416yes—
692C23C2×H(5,𝔽2)14yes—
693C23C2611yescharacteristic
694Q8—424no—
695Q8—412no—
696Q8#535116yescomplemented
697D4—224no—
698D4—28no—
699D4—424no—
700D4—448no—
701D4—424no—
702D4—424no—
703D4—412no—
704D4—412no—
705D4—824no—
706D4—812no—
707D4—812no—
708D4—824no—
709D4—812no—
710D4—824no—
711D4—1624no—
712C2×C4—22no—
713C2×C4—23no—
714C2×C4—22no—
715C2×C4—26no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—23no—
719C2×C4—224no—
720C2×C4—224no—
721C2×C4—22no—
722C2×C4—26no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—26no—
726C2×C4—22no—
727C2×C4—26no—
728C2×C4—26no—
729C2×C4—26no—
730C2×C4—26no—
731C2×C4—26no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—212no—
735C2×C4—22no—
736C2×C4—26no—
737C2×C4—22no—
738C2×C4—26no—
739C2×C4—24no—
740C2×C4—26no—
741C2×C4—412no—
742C2×C4—48no—
743C2×C4—424no—
744C2×C4—424no—
745C2×C4—424no—
746C2×C4—424no—
747C2×C4—424no—
748C2×C4—824no—
749C2×C4C23×D412yes—
750C2×C4C23×D412yes—
751C2×C4C23×D416yes—
752C2×C4C23×D416yes—
753C2×C4C23×D416yes—
754C2×C4C23×D412yes—
755C2×C4C2×H(5,𝔽2)112yes—
756C2×C4C2×H(5,𝔽2)12yes—
757C2×C4#58514yes—
758C2×C4#58512yes—
759C22—28no—
760C22—26no—
761C22—24no—
762C22—26no—
763C22—26no—
764C22—46no—
765C22—46no—
766C22—44no—
767C22—42no—
768C22—42no—
769C22—412no—
770C22—412no—
771C22—412no—
772C22—412no—
773C22—46no—
774C22—46no—
775C22—46no—
776C22—46no—
777C22—46no—
778C22—46no—
779C22—848no—
780C22C24×D411yescharacteristic
781C22C22×H(5,𝔽2)11yescharacteristic
782C22C22×H(5,𝔽2)12yes—
783C22C2×#58512yes—
784C22C2×#58511yescharacteristic
785C4—24no—
786C4—26no—
787C4—22no—
788C4—26no—
789C4—22no—
790C4—46no—
791C4—46no—
792C4—42no—
793C4—46no—
794C4—42no—
795C4—42no—
796C4—42no—
797C4—46no—
798C4C2×#535112yes—
799C4#348814yes—
800C2—46no—
801C2—44no—
802C2—86no—
803C2—86no—
804C2C22×#53511yescharacteristic
805C2C2×#348811yescharacteristic
806C2#6281211yescharacteristic
807C2#6301412yes—
808C2#6301912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3517C2semidirect
2. C2×D4×#41C2semidirect
3. #42438C2semidirect
4. #39862C2semidirect
5. #39362C2semidirect
6. #39361C2semidirect
7. #38956C2semidirect
8. #38951C2semidirect
9. #37616C2semidirect
10. #36592C2semidirect
11. #36583C2semidirect
12. #36465C2semidirect
13. #36446C2semidirect
14. #36429C2semidirect
15. #35831C2semidirect
16. #35293C2semidirect
17. #35165C2semidirect
18. #34965C2semidirect
19. #34129C2semidirect
22. C2×#557C22semidirect
23. C2×#553C22semidirect
27. C2×#550C22semidirect
28. C2×#550C22semidirect
29. C2×#550C22semidirect
32. C2×#548C22semidirect
34. C2×#547C22semidirect
37. C2×#540C22semidirect
40. C2×#532C22semidirect
41. C2×#529C22semidirect
43. C2×#520C22semidirect
46. #2867C22semidirect
47. #2862C22semidirect
48. #2858C22semidirect
49. #2858C22semidirect
50. #2847C22semidirect
51. #2813C22semidirect
52. #2706C22semidirect
53. #2703C22semidirect
54. #2678C22semidirect
55. #2669C22semidirect
56. #2636C22semidirect
57. #2620C22semidirect
58. #2620C22semidirect
59. #2619C22semidirect
60. #2619C22semidirect
61. #2617C22semidirect
62. #2603C22semidirect
63. #2568C22semidirect
65. #2566C22semidirect
66. #2548C22semidirect
68. #2547C22semidirect
70. #2544C22semidirect
71. #2544C22semidirect
72. #2544C22semidirect
73. #2542C22semidirect
75. #2541C22semidirect
76. #2541C22semidirect
77. #2541C22semidirect
78. #2540C22semidirect
79. #2537C22semidirect
80. #2535C22semidirect
81. #2504C22semidirect
82. #2502C22semidirect
83. #2490C22semidirect
84. #2489C22semidirect
87. #2433C22semidirect
88. #2431C22semidirect
89. #2431C22semidirect
90. #2431C22semidirect
91. #2431C22semidirect
92. #2428C22semidirect
93. #2427C22semidirect
94. #2417C22semidirect
95. #2416C22semidirect
96. #2411C22semidirect
97. #2408C22semidirect
98. #2407C22semidirect
99. #2407C22semidirect
100. #2392C22semidirect
101. #2354C22semidirect
102. Q8×C4⋊C4C22semidirect
103. #2346C22semidirect
105. #2341C22semidirect
106. Q8×C22⋊C4C22semidirect
107. #2328C22semidirect
108. #2311C22semidirect
110. C4×#127C22semidirect
112. C4×#124C22semidirect
113. C4×#120C22semidirect
114. #2293C22semidirect
115. #2293C22semidirect
116. #2285C22semidirect
117. C42×Q8C22semidirect
118. C42×Q8C22semidirect
119. C4×#117C22semidirect
196. C4×#41D4semidirect
696. Q8#535semidirect

Maximal subgroups

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

subgroupindex
C2×#35172
C2×D4×#412
#424382
#398622
#393622
#393612
#389562
#389512
#376162
#365922
#365832
#364652
#364462
#364292
#358312
#352932
#351652
#349652
#341292