Finite Group Databasebeta

← #7631024

Subgroups — #7631024

Order 512.

6654 conjugacy classes of subgroups.

The subgroup lattice has 831 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36644C211yesmaximal, characteristic, complemented
2#36635C211yesmaximal, characteristic, complemented
3#36624C214yesmaximal, complemented
4#36587C214yesmaximal, complemented
5#36498C214yesmaximal, complemented
6#36463C214yesmaximal, complemented
7#36211C212yesmaximal, complemented
8#36194C212yesmaximal, complemented
9#36149C212yesmaximal, complemented
10#36147C218yesmaximal, complemented
11#36128C212yesmaximal, complemented
12#36101C214yesmaximal, complemented
13#35237C212yesmaximal, complemented
14#35197C214yesmaximal, complemented
15#35081C214yesmaximal, complemented
16#35044C218yesmaximal, complemented
17#34330C214yesmaximal, complemented
18#34236C212yesmaximal, complemented
19C2×C42×D4C211yesmaximal, characteristic, complemented
20C2×#550C2214yes—
21C2×#532C2212yes—
22C2×#532C2214yes—
23C2×#532C2214yescomplemented
24C2×#525C2218yes—
25C22×C4×D4C2212yes—
26C22×C4×D4C2211yescharacteristic
27C23×C42C2212yes—
28#2868C2211yescharacteristic, complemented
29#2867C2211yescharacteristic, complemented
30#2864C2212yescomplemented
31#2863C2214yescomplemented
32#2862C2211yescharacteristic, complemented
33#2859C2211yescharacteristic, complemented
34#2858C2212yescomplemented
35#2858C2214yescomplemented
36#2857C2212yes—
37#2857C2214yescomplemented
38#2856C2214yes—
39#2856C2212yes—
40#2856C2212yes—
41#2856C2214yescomplemented
42#2855C2214yes—
43#2854C2218yescomplemented
44#2854C2218yescomplemented
45#2851C2212yes—
46#2850C2218yes—
47#2850C2218yescomplemented
48#2847C2218yes—
49#2847C2218yes—
50#2648C22116yescomplemented
51#2631C2218yes—
52#2597C22116yescomplemented
53#2571C2214yescomplemented
54#2563C2214yes—
55#2557C22116yescomplemented
56#2548C2214yescomplemented
57#2541C2214yes—
58#2541C2214yes—
59#2538C2214yes—
60#2535C2214yes—
61#2535C2214yes—
62#2513C2218yescomplemented
63#2513C2218yescomplemented
64#2504C2214yes—
65#2497C2218yescomplemented
66#2492C2218yescomplemented
67#2490C2218yescomplemented
68#2459C22116yescomplemented
69#2457C22116yescomplemented
70#2456C22116yes—
71#2447C2218yescomplemented
72#2445C2218yes—
73#2444C22116yes—
74#2439C2218yescomplemented
75#2433C2214yes—
76#2431C2218yescomplemented
77#2428C2218yescomplemented
78#2428C2218yescomplemented
79#2427C2218yescomplemented
80#2424C22116yes—
81#2420C2218yescomplemented
82#2420C2218yescomplemented
83#2414C2218yes—
84#2407C2218yes—
85#2404C2218yes—
86#2369C2214yescomplemented
87#2366C2218yes—
88#2366C2214yescomplemented
89#2366C2214yescomplemented
90#2364C22116yescomplemented
91#2363C2218yescomplemented
92#2361C2218yes—
93#2357C2218yescomplemented
94#2357C2214yescomplemented
95#2355C2214yescomplemented
96#2354C2214yes—
97#2349C2214yescomplemented
98#2339C2218yes—
99#2339C2218yescomplemented
100#2337C2218yescomplemented
101#2333C22116yescomplemented
102#2328C2218yes—
103#2319C2214yescomplemented
104C4×C4⋊Q8C2212yescomplemented
105C4×#127C2214yescomplemented
106C4×#127C2212yescomplemented
107C4×#127C2212yescomplemented
108C4×#125C2212yescomplemented
109C4×C22⋊Q8C2214yes—
110C4×#121C2218yes—
111C4×#121C2218yes—
112C4×#121C2218yescomplemented
113C4×#121C2218yescomplemented
114#2297C2218yescomplemented
115#2295C2214yescomplemented
116#2285C2214yescomplemented
117#2283C2212yes—
118#2275C2214yescomplemented
119C42×D4C2212yes—
120C42×D4C2212yes—
121C42×D4C2212yes—
122C42×D4C2212yes—
123C42×D4C2212yes—
124C42×D4C2212yes—
125C42×D4C2214yes—
126C2×C4×C4⋊C4C2211yescharacteristic
127C2×C4×C4⋊C4C2212yes—
128C2×C4×C22⋊C4C2212yes—
129C2×C4×C22⋊C4C2214yes—
130C2×C43C2211yescharacteristic
131C22×#41C2314yes—
132C22×#41C2318yes—
133C23×D4C2311yescharacteristic
134C24×C4C2314yes—
135C24×C4C2312yes—
136#550—232no—
137#532—216no—
138#532—416no—
139#532—416no—
140C2×C4⋊Q8C2312yes—
141C2×C4⋊Q8C2312yes—
142C2×C4⋊Q8C2314yes—
143C2×#127C2312yes—
144C2×#127C2314yes—
145C2×#127C2318yes—
146C2×#127C2312yes—
147C2×#127C2312yes—
148C2×#127C2314yes—
149C2×#125C2312yes—
150C2×#124C2314yes—
151C2×#124C2318yes—
152C2×#124C2318yes—
153#525—432no—
154C2×#123C23116yes—
155C2×C22⋊Q8C2314yes—
156C2×C22⋊Q8C2318yes—
157C2×#121C23116yes—
158C2×#121C2314yes—
159C2×#121C2318yes—
160C2×#121C2318yes—
161C2×#121C2314yes—
162C2×#121C2318yes—
163C2×#121C2318yes—
164C2×#121C2318yes—
165C2×#121C2318yes—
166C2×#121C2318yes—
167C2×#120C23116yes—
168C2×C4×Q8C2314yes—
169C2×C4×D4—216no—
170C2×C4×D4—28no—
171C2×C4×D4C2314yes—
172C2×C4×D4C2314yes—
173C2×C4×D4C2312yes—
174C2×C4×D4C2312yes—
175C2×C4×D4C2318yes—
176C2×C4×D4C2312yes—
177C2×C4×D4C2312yes—
178C2×C4×D4C2314yes—
179C2×C4×D4C2312yes—
180C2×C4×D4C2314yes—
181C2×C4×D4C2312yes—
182C2×C4×D4C2312yes—
183C2×C4×D4C2318yes—
184C2×C4×D4C2318yes—
185C2×C4×D4C23116yes—
186C2×C4×D4C2318yes—
187C2×C4×D4C2318yes—
188C2×C4×D4C23116yes—
189C2×C4×D4C2312yes—
190C2×#117C2318yes—
191C22×C4⋊C4C2312yes—
192C22×C4⋊C4C2311yescharacteristic
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2314yes—
195C22×C42—48no—
196C22×C42C2312yes—
197C22×C42C2311yescharacteristic
198C22×C42C2312yes—
199C22×C42C2314yes—
200C22×C42C2314yes—
201C22×C42C2314yes—
202C22×C42C2311yescharacteristic
203C22×C42C2314yes—
204C22×C42C2312yes—
205C22×C42C2314yes—
206C22×C42C2311yescharacteristic
207#400C23116yes—
208#397C2318yes—
209#397C2318yes—
210#397C23116yes—
211#397C23116yes—
212#396C23116yes—
213#394C23116yes—
214#394C23116yes—
215#394C23116yes—
216#393C23116yes—
217#392C23116yes—
218#392C2318yes—
219#392C2318yes—
220#392C23116yes—
221#391C2314yes—
222#391C23116yes—
223#391C2318yes—
224#391C2314yes—
225#391C2314yes—
226#391C2314yes—
227#390C2318yes—
228#390C2318yes—
229#390C2318yes—
230#390C2314yes—
231#390C2318yes—
232#390C2318yes—
233#390C2314yes—
234#390C2318yes—
235#390C2318yes—
236#390C2318yes—
237#390C23116yes—
238#390C2318yes—
239#390C2318yes—
240#390C2318yes—
241#389C2314yes—
242#389C2314yes—
243#389C2314yes—
244#389C2318yes—
245#389C2318yes—
246#389C2314yes—
247#389C2318yes—
248#389C2314yes—
249#389C2314yes—
250#388C23116yes—
251#388C23116yes—
252#388C23116yes—
253#388C23116yes—
254#388C23116yes—
255#388C23116yes—
256#388C23116yes—
257#387C2318yes—
258#387C2318yes—
259#387C23116yes—
260#387C2318yes—
261#387C2318yes—
262#386C23116yes—
263#386C23116yes—
264#386C23116yes—
265#386C23116yes—
266#386C23116yes—
267#386C23116yes—
268#386C23116yes—
269#386C23116yes—
270#386C23116yes—
271#386C23116yes—
272#386C23116yes—
273#385C23116yes—
274#385C2318yes—
275#384C2314yes—
276#384C2312yes—
277#384C2312yes—
278#384C2312yes—
279#383C2314yes—
280#382C2312yes—
281#382C2318yes—
282#382C2318yes—
283#382C2312yes—
284#382C2312yes—
285#381C2318yes—
286#381C23116yes—
287#381C2314yes—
288#380C2318yes—
289#380C2318yes—
290#380C2318yes—
291#380C2314yes—
292#380C2314yes—
293#380C2318yes—
294#380C2318yes—
295C4×C4⋊C4C2314yes—
296C4×C4⋊C4C2318yes—
297C4×C4⋊C4C2314yes—
298C4×C4⋊C4C2312yes—
299C4×C4⋊C4C2311yescharacteristic
300C4×C4⋊C4C2312yes—
301C4×C4⋊C4C2314yes—
302C4×C4⋊C4C2312yes—
303C4×C4⋊C4C2318yes—
304C4×C4⋊C4C2312yes—
305C4×C4⋊C4C2318yes—
306C4×C4⋊C4C2312yes—
307C4×C4⋊C4C2318yes—
308C4×C4⋊C4C2312yes—
309C4×C4⋊C4C2314yes—
310C4×C4⋊C4C2312yes—
311C4×C4⋊C4C2311yescharacteristic
312C4×C22⋊C4C2314yes—
313C4×C22⋊C4C23116yes—
314C4×C22⋊C4C2318yes—
315C4×C22⋊C4C2314yes—
316C4×C22⋊C4C23116yes—
317C4×C22⋊C4C2314yes—
318C4×C22⋊C4C2314yes—
319C4×C22⋊C4C2314yes—
320C4×C22⋊C4C2314yes—
321C4×C22⋊C4C2314yes—
322C4×C22⋊C4C2314yes—
323C4×C22⋊C4C2314yes—
324C4×C22⋊C4C2314yes—
325C4×C22⋊C4C2314yes—
326C4×C22⋊C4C2314yes—
327C4×C22⋊C4C2314yes—
328#376C2314yes—
329C2×#95C2312yes—
330C2×#95C2318yes—
331C2×#95C2314yes—
332C43C2311yescharacteristic
333C43C2311yescharacteristic
334C43C2311yescharacteristic
335C43C2312yes—
336C43C2311yescharacteristic
337C43C2312yes—
338C25C2412yes—
339C2×#41—216no—
340C2×#41—232no—
341C2×#41—416no—
342C2×#41—416no—
343C2×#41—416no—
344C22×Q8C2414yes—
345C22×Q8C2414yes—
346C22×D4—28no—
347C22×D4—24no—
348C22×D4C2412yes—
349C22×D4C2414yes—
350C22×D4C2414yes—
351C22×D4C2418yes—
352C22×D4C2418yes—
353C22×D4C2412yes—
354C22×D4C24116yes—
355C22×D4C2418yes—
356C22×D4C24116yes—
357C22×D4C2414yes—
358C23×C4—216no—
359C23×C4—28no—
360C23×C4—216no—
361C23×C4—44no—
362C23×C4—48no—
363C23×C4—44no—
364C23×C4C2414yes—
365C23×C4C2414yes—
366C23×C4C2412yes—
367C23×C4C2414yes—
368C23×C4C2414yes—
369C23×C4C2414yes—
370C23×C4C2411yescharacteristic
371C23×C4C2411yescharacteristic
372C23×C4C2414yes—
373C23×C4C2411yescharacteristic
374C23×C4C2412yes—
375C23×C4C2412yes—
376C23×C4C2418yes—
377C23×C4C24116yes—
378C23×C4C2414yes—
379C4⋊Q8—28no—
380C4⋊Q8—28no—
381C4⋊Q8—48no—
382#127—232no—
383#127—28no—
384#127—216no—
385#127—28no—
386#127—44no—
387#127—48no—
388#125—44no—
389#124—216no—
390#124—416no—
391#124—416no—
392#123—432no—
393C22⋊Q8—216no—
394C22⋊Q8—416no—
395#121—216no—
396#121—216no—
397#121—232no—
398#121—232no—
399#121—264no—
400#121—416no—
401#121—416no—
402#121—416no—
403#121—416no—
404#121—416no—
405#120—432no—
406C4×Q8—216no—
407C4×D4—28no—
408C4×D4—216no—
409C4×D4—28no—
410C4×D4—232no—
411C4×D4—216no—
412C4×D4—28no—
413C4×D4—28no—
414C4×D4—28no—
415C4×D4—28no—
416C4×D4—28no—
417C4×D4—216no—
418C4×D4—216no—
419C4×D4—416no—
420C4×D4—416no—
421C4×D4—416no—
422C4×D4—416no—
423C4×D4—432no—
424C4×D4—432no—
425C4×D4#41116yescomplemented
426#117—416no—
427C2×C4⋊C4—24no—
428C2×C4⋊C4—28no—
429C2×C4⋊C4C2412yes—
430C2×C4⋊C4C2414yes—
431C2×C4⋊C4C2412yes—
432C2×C4⋊C4C2412yes—
433C2×C4⋊C4C2414yes—
434C2×C4⋊C4C2418yes—
435C2×C4⋊C4C2414yes—
436C2×C4⋊C4C2414yes—
437C2×C4⋊C4C2418yes—
438C2×C4⋊C4C2414yes—
439C2×C4⋊C4C2414yes—
440C2×C4⋊C4C2414yes—
441C2×C4⋊C4C2418yes—
442C2×C4⋊C4C2414yes—
443C2×C4⋊C4C2418yes—
444C2×C4⋊C4C24116yes—
445C2×C4⋊C4C2418yes—
446C2×C4⋊C4C2412yes—
447C2×C22⋊C4—28no—
448C2×C22⋊C4—216no—
449C2×C22⋊C4C2414yes—
450C2×C22⋊C4C2414yes—
451C2×C22⋊C4C2414yes—
452C2×C22⋊C4C2414yes—
453C2×C22⋊C4C2414yes—
454C2×C22⋊C4C2418yes—
455C2×C22⋊C4C24116yes—
456C2×C22⋊C4C24116yes—
457C2×C22⋊C4C2418yes—
458C2×C22⋊C4C2418yes—
459C2×C22⋊C4C24116yes—
460C2×C22⋊C4C24116yes—
461C2×C22⋊C4C24116yes—
462C2×C22⋊C4C24116yes—
463C2×C22⋊C4C24116yes—
464C2×C22⋊C4C24116yes—
465C2×C22⋊C4C24116yes—
466C2×C22⋊C4C2414yes—
467C2×C42—28no—
468C2×C42—28no—
469C2×C42—216no—
470C2×C42—24no—
471C2×C42—48no—
472C2×C42—48no—
473C2×C42—48no—
474C2×C42—44no—
475C2×C42—48no—
476C2×C42—42no—
477C2×C42#4118yescomplemented
478C2×C42C2412yes—
479C2×C42C2412yes—
480C2×C42C2412yes—
481C2×C42C2412yes—
482C2×C42C2412yes—
483C2×C42C2414yes—
484C2×C42C2414yes—
485C2×C42C2418yes—
486C2×C42C2412yes—
487C2×C42C2414yes—
488C2×C42C2411yescharacteristic
489C2×C42C2412yes—
490C2×C42C2411yescharacteristic
491C2×C42C2411yescharacteristic
492C2×C42C2412yes—
493C2×C42C24116yes—
494C2×C42C2412yes—
495C2×C42C2412yes—
496C2×C42C2414yes—
497C2×C42C2414yes—
498C2×C42C2412yes—
499C2×C42C2411yescharacteristic
500C2×C42C2411yescharacteristic
501C2×C42C2412yes—
502C2×C42C2411yescharacteristic
503C2×C42C2411yescharacteristic
504C2×C42C2411yescharacteristic
505#95C2412yes—
506#95C2414yes—
507#95C2412yes—
508#95C2414yes—
509#95C2414yes—
510#95C2414yes—
511#95C2414yes—
512#95C2414yes—
513#95C24116yes—
514#95C2418yes—
515#95C2414yes—
516#95C2418yes—
517#95C24116yes—
518#95C2414yes—
519#95C2414yes—
520#95C24116yes—
521#95C24116yes—
522#95C2418yes—
523#95C2418yes—
524#95C2418yes—
525C24—28no—
526C24—24no—
527C24—28no—
528C24—42no—
529C24—42no—
530C24C2518yes—
531C24C2514yes—
532C24C2511yescharacteristic
533#41—832no—
534#41—864no—
535C2×Q8—28no—
536C2×Q8—28no—
537C2×Q8—28no—
538C2×Q8—28no—
539C2×Q8—48no—
540C2×D4—232no—
541C2×D4—28no—
542C2×D4—216no—
543C2×D4—232no—
544C2×D4—232no—
545C2×D4—232no—
546C2×D4—24no—
547C2×D4—24no—
548C2×D4—24no—
549C2×D4—28no—
550C2×D4—28no—
551C2×D4—216no—
552C2×D4—216no—
553C2×D4—216no—
554C2×D4—28no—
555C2×D4—28no—
556C2×D4—216no—
557C2×D4—216no—
558C2×D4—28no—
559C2×D4—416no—
560C2×D4—48no—
561C2×D4—416no—
562C2×D4—416no—
563C2×D4—416no—
564C2×D4—48no—
565C2×D4—48no—
566C2×D4C2×#4118yes—
567C22×C4—24no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—22no—
571C22×C4—24no—
572C22×C4—28no—
573C22×C4—28no—
574C22×C4—22no—
575C22×C4—24no—
576C22×C4—28no—
577C22×C4—24no—
578C22×C4—28no—
579C22×C4—24no—
580C22×C4—28no—
581C22×C4—28no—
582C22×C4—28no—
583C22×C4—28no—
584C22×C4—28no—
585C22×C4—28no—
586C22×C4—28no—
587C22×C4—28no—
588C22×C4—28no—
589C22×C4—28no—
590C22×C4—28no—
591C22×C4—216no—
592C22×C4—232no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—44no—
600C22×C4—42no—
601C22×C4—464no—
602C22×C4—416no—
603C22×C4—416no—
604C22×C4—416no—
605C22×C4—432no—
606C22×C4C2×#4114yes—
607C22×C4C2×#4114yes—
608C22×C4C2×#4114yes—
609C22×C4C2×#41116yes—
610C22×C4H(5,𝔽2)18yes—
611C22×C4C2514yes—
612C22×C4C2518yes—
613C22×C4C2518yes—
614C22×C4C2512yes—
615C22×C4C2514yes—
616C22×C4C2518yes—
617C22×C4C2511yescharacteristic
618C22×C4C2511yescharacteristic
619C22×C4C2511yescharacteristic
620C22×C4C2514yes—
621C22×C4C2511yescharacteristic
622C22×C4C2512yes—
623C22×C4C2512yes—
624C22×C4C2511yescharacteristic
625C22×C4C2512yes—
626C22×C4C2511yescharacteristic
627C4⋊C4—28no—
628C4⋊C4—24no—
629C4⋊C4—24no—
630C4⋊C4—24no—
631C4⋊C4—28no—
632C4⋊C4—28no—
633C4⋊C4—28no—
634C4⋊C4—216no—
635C4⋊C4—28no—
636C4⋊C4—216no—
637C4⋊C4—28no—
638C4⋊C4—28no—
639C4⋊C4—216no—
640C4⋊C4—28no—
641C4⋊C4—48no—
642C4⋊C4—416no—
643C4⋊C4—48no—
644C4⋊C4C2×#4118yes—
645C22⋊C4—28no—
646C22⋊C4—216no—
647C22⋊C4—28no—
648C22⋊C4—28no—
649C22⋊C4—28no—
650C22⋊C4—28no—
651C22⋊C4—232no—
652C22⋊C4—216no—
653C22⋊C4—216no—
654C22⋊C4—232no—
655C22⋊C4—416no—
656C22⋊C4—416no—
657C22⋊C4—416no—
658C22⋊C4—416no—
659C22⋊C4—416no—
660C22⋊C4—416no—
661C22⋊C4—416no—
662C22⋊C4C2×#41116yes—
663C42—24no—
664C42—24no—
665C42—24no—
666C42—216no—
667C42—22no—
668C42—24no—
669C42—28no—
670C42—28no—
671C42—28no—
672C42—24no—
673C42—24no—
674C42—24no—
675C42—24no—
676C42—22no—
677C42—22no—
678C42—42no—
679C42—44no—
680C42—42no—
681C42—44no—
682C42—42no—
683C42—416no—
684C42C2×#4118yes—
685C42C2×#4114yes—
686C42C2×#4114yes—
687C42C2×#4114yes—
688C42C2×#4114yes—
689C42H(5,𝔽2)14yes—
690C23—22no—
691C23—21no—
692C23—21no—
693C23—216no—
694C23—24no—
695C23—24no—
696C23—24no—
697C23—24no—
698C23—24no—
699C23—24no—
700C23—28no—
701C23—216no—
702C23—216no—
703C23—28no—
704C23—28no—
705C23—416no—
706C23—416no—
707C23—48no—
708C23—48no—
709C23C22×#4118yes—
710C23C22×#4112yes—
711C23C2×H(5,𝔽2)14yes—
712C23C2611yescharacteristic
713Q8—416no—
714Q8—88no—
715D4—216no—
716D4—216no—
717D4—432no—
718D4—416no—
719D4—416no—
720D4—432no—
721D4—816no—
722D4—88no—
723D4—832no—
724D4—832no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—24no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—24no—
734C2×C4—22no—
735C2×C4—21no—
736C2×C4—28no—
737C2×C4—28no—
738C2×C4—28no—
739C2×C4—216no—
740C2×C4—232no—
741C2×C4—22no—
742C2×C4—28no—
743C2×C4—28no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—28no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—22no—
750C2×C4—28no—
751C2×C4—216no—
752C2×C4—28no—
753C2×C4—28no—
754C2×C4—24no—
755C2×C4—22no—
756C2×C4—24no—
757C2×C4—28no—
758C2×C4—416no—
759C2×C4—48no—
760C2×C4—416no—
761C2×C4—416no—
762C2×C4—416no—
763C2×C4—48no—
764C2×C4—416no—
765C2×C4—416no—
766C2×C4—832no—
767C2×C4—816no—
768C2×C4C22×#4114yes—
769C2×C4C22×#4112yes—
770C2×C4C22×#4112yes—
771C2×C4C22×#4112yes—
772C2×C4C22×#4112yes—
773C2×C4C22×#4118yes—
774C2×C4C22×#4114yes—
775C2×C4C22×#4112yes—
776C2×C4C22×#4112yes—
777C2×C4C22×#4114yes—
778C2×C4C2×H(5,𝔽2)14yes—
779C2×C4C2×H(5,𝔽2)12yes—
780C2×C4C2×H(5,𝔽2)14yes—
781C2×C4C2×H(5,𝔽2)14yes—
782C2×C4#58512yes—
783C22—22no—
784C22—24no—
785C22—24no—
786C22—22no—
787C22—28no—
788C22—28no—
789C22—28no—
790C22—432no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—44no—
795C22—48no—
796C22—416no—
797C22—48no—
798C22—416no—
799C22—48no—
800C22#350814yes—
801C22C23×#4111yescharacteristic
802C22C23×#4112yes—
803C22C22×H(5,𝔽2)11yescharacteristic
804C22C22×H(5,𝔽2)12yes—
805C22C2×#58511yescharacteristic
806C4—22no—
807C4—24no—
808C4—28no—
809C4—22no—
810C4—22no—
811C4—24no—
812C4—22no—
813C4—44no—
814C4—44no—
815C4—48no—
816C4—48no—
817C4—42no—
818C4—48no—
819C4#344414yes—
820C4#350614yes—
821C4#351918yes—
822C2—24no—
823C2—48no—
824C2—88no—
825C2C2×#344411yescharacteristic
826C2C2×#350611yescharacteristic
827C2C2×#351912yes—
828C2C2×#350811yescharacteristic
829C2#6280012yes—
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. #36644C2semidirect
2. #36635C2semidirect
3. #36624C2semidirect
4. #36587C2semidirect
5. #36498C2semidirect
6. #36463C2semidirect
7. #36211C2semidirect
8. #36194C2semidirect
9. #36149C2semidirect
10. #36147C2semidirect
11. #36128C2semidirect
12. #36101C2semidirect
13. #35237C2semidirect
14. #35197C2semidirect
15. #35081C2semidirect
16. #35044C2semidirect
17. #34330C2semidirect
18. #34236C2semidirect
19. C2×C42×D4C2semidirect
23. C2×#532C22semidirect
28. #2868C22semidirect
29. #2867C22semidirect
30. #2864C22semidirect
31. #2863C22semidirect
32. #2862C22semidirect
33. #2859C22semidirect
34. #2858C22semidirect
35. #2858C22semidirect
37. #2857C22semidirect
41. #2856C22semidirect
43. #2854C22semidirect
44. #2854C22semidirect
47. #2850C22semidirect
50. #2648C22semidirect
52. #2597C22semidirect
53. #2571C22semidirect
55. #2557C22semidirect
56. #2548C22semidirect
62. #2513C22semidirect
63. #2513C22semidirect
65. #2497C22semidirect
66. #2492C22semidirect
67. #2490C22semidirect
68. #2459C22semidirect
69. #2457C22semidirect
71. #2447C22semidirect
74. #2439C22semidirect
76. #2431C22semidirect
77. #2428C22semidirect
78. #2428C22semidirect
79. #2427C22semidirect
81. #2420C22semidirect
82. #2420C22semidirect
86. #2369C22semidirect
88. #2366C22semidirect
89. #2366C22semidirect
90. #2364C22semidirect
91. #2363C22semidirect
93. #2357C22semidirect
94. #2357C22semidirect
95. #2355C22semidirect
97. #2349C22semidirect
99. #2339C22semidirect
100. #2337C22semidirect
101. #2333C22semidirect
103. #2319C22semidirect
104. C4×C4⋊Q8C22semidirect
105. C4×#127C22semidirect
106. C4×#127C22semidirect
107. C4×#127C22semidirect
108. C4×#125C22semidirect
112. C4×#121C22semidirect
113. C4×#121C22semidirect
114. #2297C22semidirect
115. #2295C22semidirect
116. #2285C22semidirect
118. #2275C22semidirect
425. C4×D4#41semidirect
477. C2×C42#41semidirect

Maximal subgroups

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

subgroupindex
#366442
#366352
#366242
#365872
#364982
#364632
#362112
#361942
#361492
#361472
#361282
#361012
#352372
#351972
#350812
#350442
#343302
#342362
C2×C42×D42