Finite Group Databasebeta

← #7630720

Subgroups — #7630720

Order 512.

5170 conjugacy classes of subgroups.

The subgroup lattice has 875 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36068C218yesmaximal, complemented
2#35999C218yesmaximal, complemented
3#35988C218yesmaximal, complemented
4#35977C218yesmaximal, complemented
5#35098C214yesmaximal, complemented
6#35090C211yesmaximal, characteristic, complemented
7#35089C211yesmaximal, characteristic
8#35042C214yesmaximal, complemented
9#35024C214yesmaximal, complemented
10#34995C212yesmaximal, complemented
11#34994C211yesmaximal, characteristic, complemented
12#34993C211yesmaximal, characteristic
13#34584C214yesmaximal, complemented
14C2×#2623C212yesmaximal, complemented
15#34273C211yesmaximal, characteristic
16#34270C211yesmaximal, characteristic, complemented
17#34251C212yesmaximal, complemented
18#34199C212yesmaximal, complemented
19C2×#2274C211yesmaximal, characteristic, complemented
20C2×#543C2211yescharacteristic
21C2×#534C2211yescharacteristic
22C22×#123C2212yes—
23C2×#518C2212yes—
24C22×#117C2211yescharacteristic
25C22×#117C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27#2855C2214yescomplemented
28#2854C2214yes—
29#2852C2218yescomplemented
30#2851C2214yescomplemented
31#2850C2214yes—
32#2655C2218yescomplemented
33#2654C2218yescomplemented
34#2651C2218yescomplemented
35#2650C2218yescomplemented
36#2646C2214yescomplemented
37#2643C2218yescomplemented
38#2639C2214yes—
39#2627C2214yescomplemented
40#2623C2218yes—
41#2623C2218yes—
42#2623C2214yescomplemented
43#2623C2214yescomplemented
44#2623C2214yescomplemented
45#2623C2214yescomplemented
46#2618C2214yes—
47#2597C2218yescomplemented
48#2596C2218yescomplemented
49#2596C2218yescomplemented
50#2594C2218yescomplemented
51#2590C2218yescomplemented
52#2589C2218yescomplemented
53#2577C2218yescomplemented
54#2575C2218yescomplemented
55#2533C2218yescomplemented
56#2532C2218yescomplemented
57#2525C2218yescomplemented
58#2524C2218yescomplemented
59#2522C2218yescomplemented
60#2521C2218yescomplemented
61#2520C2218yescomplemented
62#2519C2218yescomplemented
63#2516C2218yescomplemented
64#2515C2218yescomplemented
65#2514C2214yescomplemented
66#2513C2214yescomplemented
67#2510C2218yes—
68#2509C2214yescomplemented
69#2508C2214yescomplemented
70#2505C2218yescomplemented
71#2493C2218yescomplemented
72#2488C2218yes—
73#2481C2218yes—
74#2480C2218yescomplemented
75#2479C2218yescomplemented
76#2478C2218yescomplemented
77#2473C2218yescomplemented
78#2472C2218yes—
79#2454C2214yescomplemented
80#2453C2214yescomplemented
81#2448C2214yescomplemented
82#2447C2214yescomplemented
83#2438C2218yescomplemented
84#2438C2218yescomplemented
85#2413C2214yes—
86#2413C2214yes—
87#2411C2214yes—
88#2411C2214yes—
89#2402C2218yescomplemented
90#2401C2218yescomplemented
91#2396C2218yescomplemented
92#2395C2218yescomplemented
93C2×#400C2214yescomplemented
94C2×#399C2214yescomplemented
95C2×#398C2214yescomplemented
96C2×#397C2214yescomplemented
97#2368C2218yescomplemented
98#2360C2218yescomplemented
99#2359C2218yes—
100#2359C2218yes—
101#2359C2218yes—
102#2358C2218yes—
103#2353C2218yes—
104#2352C2218yes—
105#2344C2214yescomplemented
106#2344C2214yescomplemented
107#2343C2218yescomplemented
108#2342C2214yescomplemented
109#2342C2218yescomplemented
110#2342C2214yescomplemented
111#2329C2214yescomplemented
112#2325C2214yes—
113#2322C2218yescomplemented
114#2318C2218yescomplemented
115#2315C2211yescharacteristic
116#2315C2211yescharacteristic
117#2315C2212yes—
118#2315C2212yes—
119#2308C2212yes—
120#2308C2212yes—
121C4×C22⋊Q8C2214yescomplemented
122C4×#123C2218yescomplemented
123C4×#121C2214yes—
124#2290C2218yescomplemented
125C2×#386C2212yes—
126C2×#386C2212yes—
127C2×#385C2212yes—
128C2×#385C2212yes—
129C2×#381C2212yes—
130#2274C2218yescomplemented
131#2274C2218yescomplemented
132#2273C2212yes—
133C2×C4×C4⋊C4C2212yescomplemented
134C2×C4×C4⋊C4C2212yescomplemented
135C2×C4×C4⋊C4C2212yescomplemented
136C2×C4×C4⋊C4C2212yescomplemented
137C2×C4×C22⋊C4C2211yescharacteristic
138C2×C4×C22⋊C4C2211yescharacteristic
139C2×C4×C22⋊C4C2211yescharacteristic
140C2×C4×C22⋊C4C2211yescharacteristic
141C23×D4C2312yes—
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145#543—28no—
146#534—28no—
147C2×#126C2318yes—
148C2×#125C2314yes—
149C2×#124C2314yes—
150C2×#123—216no—
151C2×#123C2314yes—
152C2×#123C2314yes—
153C2×#123C2314yes—
154C2×#123C2314yes—
155C2×#123C2314yes—
156C2×C22⋊Q8C2314yes—
157C2×C22⋊Q8C2318yes—
158C2×#121C2314yes—
159C2×#120C2314yes—
160#518—216no—
161C2×C4×Q8C2314yes—
162C2×C4×D4C2318yes—
163C2×C4×D4C2318yes—
164C2×C4×D4C2314yes—
165C2×#117—28no—
166C2×#117—28no—
167C2×#117C2314yes—
168C2×#117C2314yes—
169C2×#117C2314yes—
170C2×#117C2314yes—
171C2×#117C2314yes—
172C2×#117C2318yes—
173C22×C4⋊C4—28no—
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2312yes—
176C22×C4⋊C4C2312yes—
177C22×C4⋊C4C2312yes—
178C22×C4⋊C4C2314yes—
179C22×C4⋊C4C2314yes—
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2311yescharacteristic
182C22×C4⋊C4C2311yescharacteristic
183C22×C4⋊C4C2311yescharacteristic
184C22×C4⋊C4C2314yes—
185C22×C4⋊C4C2314yes—
186C22×C22⋊C4C2311yescharacteristic
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2314yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2314yes—
195C22×C22⋊C4C2314yes—
196C22×C22⋊C4C2311yescharacteristic
197C22×C22⋊C4C2311yescharacteristic
198C22×C42C2312yes—
199C22×C42C2312yes—
200C22×C42C2312yes—
201C22×C42C2312yes—
202C22×C42C2312yes—
203C22×C42C2312yes—
204#401C2318yes—
205#400C2318yes—
206#400C2318yes—
207#400C2318yes—
208#400C2318yes—
209#400C2318yes—
210#400C2318yes—
211#400C2318yes—
212#400C2318yes—
213#400C2318yes—
214#400C2318yes—
215#400C2318yes—
216#399C2318yes—
217#399C2318yes—
218#399C2318yes—
219#399C2318yes—
220#398C2318yes—
221#398C2318yes—
222#398C2318yes—
223#398C2318yes—
224#398C2318yes—
225#398C2318yes—
226#398C2318yes—
227#398C2318yes—
228#398C2318yes—
229#397C2318yes—
230#397C2318yes—
231#397C2318yes—
232#397C2318yes—
233#397C2318yes—
234#397C2318yes—
235#397C2318yes—
236#397C2318yes—
237#396C2318yes—
238#396C2318yes—
239#396C2318yes—
240#395C2318yes—
241#394C2318yes—
242#394C2318yes—
243#393C2318yes—
244#391C2318yes—
245#391C2314yes—
246#391C2314yes—
247#391C2314yes—
248#391C2314yes—
249#390C2314yes—
250#390C2314yes—
251#390C2314yes—
252#390C2314yes—
253#389C2318yes—
254#389C2318yes—
255#389C2318yes—
256#389C2314yes—
257#389C2314yes—
258#389C2314yes—
259#389C2314yes—
260#389C2314yes—
261#389C2314yes—
262#389C2314yes—
263#389C2314yes—
264#388C2318yes—
265#388C2318yes—
266#388C2318yes—
267#388C2318yes—
268#388C2318yes—
269#388C2318yes—
270#388C2318yes—
271#388C2318yes—
272#388C2318yes—
273#388C2318yes—
274#388C2318yes—
275#388C2318yes—
276#388C2318yes—
277#388C2318yes—
278#388C2318yes—
279#388C2318yes—
280#388C2318yes—
281#387C2318yes—
282#387C2318yes—
283#387C2318yes—
284#387C2318yes—
285#387C2318yes—
286#387C2318yes—
287#387C2318yes—
288#387C2318yes—
289#387C2318yes—
290#387C2318yes—
291#387C2318yes—
292#387C2318yes—
293#387C2318yes—
294#387C2318yes—
295#387C2318yes—
296#387C2318yes—
297#387C2318yes—
298#387C2318yes—
299#387C2318yes—
300#386C2318yes—
301#386C2318yes—
302#386C2314yes—
303#386C2314yes—
304#386C2318yes—
305#386C2314yes—
306#386C2314yes—
307#386C2318yes—
308#386C2318yes—
309#386C2318yes—
310#386C2314yes—
311#386C2314yes—
312#385C2318yes—
313#385C2318yes—
314#385C2318yes—
315#385C2318yes—
316#385C2318yes—
317#385C2314yes—
318#385C2314yes—
319#385C2314yes—
320#385C2318yes—
321#385C2318yes—
322#385C2318yes—
323#385C2314yes—
324#385C2318yes—
325#385C2318yes—
326#385C2314yes—
327#385C2314yes—
328#383C2318yes—
329#383C2318yes—
330#382C2318yes—
331#382C2314yes—
332#382C2314yes—
333#381C2314yes—
334#381C2314yes—
335#381C2318yes—
336#381C2314yes—
337#381C2314yes—
338#381C2314yes—
339#381C2314yes—
340#380C2314yes—
341#380C2314yes—
342#380C2314yes—
343#380C2314yes—
344#380C2318yes—
345#380C2318yes—
346#379C2314yes—
347#379C2314yes—
348C4×C4⋊C4C2314yes—
349C4×C4⋊C4C2314yes—
350C4×C4⋊C4C2318yes—
351C4×C4⋊C4C2318yes—
352C4×C4⋊C4C2318yes—
353C4×C4⋊C4C2314yes—
354C4×C4⋊C4C2318yes—
355C4×C4⋊C4C2314yes—
356C4×C4⋊C4C2318yes—
357C4×C4⋊C4C2318yes—
358C4×C4⋊C4C2314yes—
359C4×C4⋊C4C2314yes—
360C4×C4⋊C4C2318yes—
361C4×C4⋊C4C2318yes—
362C4×C4⋊C4C2318yes—
363C4×C4⋊C4C2318yes—
364C4×C22⋊C4C2318yes—
365C4×C22⋊C4C2318yes—
366C4×C22⋊C4C2318yes—
367C4×C22⋊C4C2318yes—
368C4×C22⋊C4C2318yes—
369C4×C22⋊C4C2314yes—
370C4×C22⋊C4C2314yes—
371C4×C22⋊C4C2318yes—
372C4×C22⋊C4C2318yes—
373C4×C22⋊C4C2318yes—
374C4×C22⋊C4C2318yes—
375C4×C22⋊C4C2318yes—
376#376C2318yes—
377C2×#95C2312yes—
378C2×#95C2312yes—
379C2×#95C2314yes—
380C2×#95C2314yes—
381C2×#95C2314yes—
382C2×#95C2314yes—
383C2×#95C2314yes—
384C2×#95C2314yes—
385C2×#95C2312yes—
386C2×#95C2312yes—
387C25C2412yes—
388C25C2411yescharacteristic
389C22×Q8C2414yes—
390C22×D4—28no—
391C22×D4—28no—
392C22×D4—28no—
393C22×D4C2414yes—
394C22×D4C2414yes—
395C22×D4C2414yes—
396C23×C4—24no—
397C23×C4—24no—
398C23×C4—24no—
399C23×C4—24no—
400C23×C4—82no—
401C23×C4—82no—
402C23×C4#4118yes—
403C23×C4C2412yes—
404C23×C4C2412yes—
405C23×C4C2412yes—
406C23×C4C2411yescharacteristic
407C23×C4C2411yescharacteristic
408C23×C4C2412yes—
409C23×C4C2414yes—
410C23×C4C2414yes—
411C23×C4C2412yes—
412C23×C4C2414yes—
413C23×C4C2414yes—
414C23×C4C2412yes—
415C23×C4C2412yes—
416C23×C4C2418yes—
417C23×C4C2411yescharacteristic
418C23×C4C2411yescharacteristic
419C23×C4C2411yescharacteristic
420C23×C4C2411yescharacteristic
421C23×C4C2412yes—
422C23×C4C2412yes—
423#126—88no—
424#125—84no—
425#124—84no—
426#123—216no—
427#123—216no—
428#123—216no—
429#123—216no—
430#123—216no—
431C22⋊Q8—216no—
432C22⋊Q8—232no—
433#121—216no—
434#120—216no—
435C4×Q8—84no—
436C4×D4—232no—
437C4×D4—232no—
438C4×D4—84no—
439#117—216no—
440#117—216no—
441#117—216no—
442#117—216no—
443#117—216no—
444#117—88no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—216no—
450C2×C4⋊C4—216no—
451C2×C4⋊C4—28no—
452C2×C4⋊C4—28no—
453C2×C4⋊C4—28no—
454C2×C4⋊C4—28no—
455C2×C4⋊C4—84no—
456C2×C4⋊C4—84no—
457C2×C4⋊C4C2412yes—
458C2×C4⋊C4C2412yes—
459C2×C4⋊C4C2414yes—
460C2×C4⋊C4C2414yes—
461C2×C4⋊C4C2412yes—
462C2×C4⋊C4C2412yes—
463C2×C4⋊C4C2414yes—
464C2×C4⋊C4C2414yes—
465C2×C4⋊C4C2418yes—
466C2×C4⋊C4C2414yes—
467C2×C4⋊C4C2414yes—
468C2×C4⋊C4C2414yes—
469C2×C4⋊C4C2414yes—
470C2×C4⋊C4C2418yes—
471C2×C4⋊C4C2414yes—
472C2×C4⋊C4C2414yes—
473C2×C4⋊C4C2418yes—
474C2×C4⋊C4C2418yes—
475C2×C4⋊C4C2418yes—
476C2×C4⋊C4C2418yes—
477C2×C4⋊C4C2418yes—
478C2×C4⋊C4C2418yes—
479C2×C4⋊C4C2414yes—
480C2×C4⋊C4C2414yes—
481C2×C4⋊C4C2418yes—
482C2×C4⋊C4C2418yes—
483C2×C4⋊C4C2414yes—
484C2×C4⋊C4C2414yes—
485C2×C4⋊C4C2418yes—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—28no—
489C2×C22⋊C4—28no—
490C2×C22⋊C4—28no—
491C2×C22⋊C4—28no—
492C2×C22⋊C4—28no—
493C2×C22⋊C4—216no—
494C2×C22⋊C4—84no—
495C2×C22⋊C4—84no—
496C2×C22⋊C4#4118yes—
497C2×C22⋊C4#4118yes—
498C2×C22⋊C4C2414yes—
499C2×C22⋊C4C2414yes—
500C2×C22⋊C4C2414yes—
501C2×C22⋊C4C2414yes—
502C2×C22⋊C4C2418yes—
503C2×C22⋊C4C2414yes—
504C2×C22⋊C4C2414yes—
505C2×C22⋊C4C2414yes—
506C2×C22⋊C4C2414yes—
507C2×C22⋊C4C2414yes—
508C2×C22⋊C4C2414yes—
509C2×C22⋊C4C2414yes—
510C2×C22⋊C4C2414yes—
511C2×C22⋊C4C2418yes—
512C2×C22⋊C4C2418yes—
513C2×C22⋊C4C2418yes—
514C2×C22⋊C4C2418yes—
515C2×C22⋊C4C2418yes—
516C2×C22⋊C4C2418yes—
517C2×C22⋊C4C2418yes—
518C2×C22⋊C4C2418yes—
519C2×C22⋊C4C2418yes—
520C2×C22⋊C4C2414yes—
521C2×C22⋊C4C2414yes—
522C2×C42—28no—
523C2×C42—28no—
524C2×C42—82no—
525C2×C42—82no—
526C2×C42—82no—
527C2×C42—82no—
528C2×C42C2418yes—
529C2×C42C2414yes—
530C2×C42C2414yes—
531C2×C42C2418yes—
532C2×C42C2418yes—
533C2×C42C2418yes—
534C2×C42C2414yes—
535C2×C42C2414yes—
536C2×C42C2414yes—
537C2×C42C2414yes—
538C2×C42C2418yes—
539C2×C42C2418yes—
540#95C2418yes—
541#95C2418yes—
542#95C2414yes—
543#95C2414yes—
544#95C2418yes—
545#95C2418yes—
546#95C2414yes—
547#95C2414yes—
548#95C2418yes—
549#95C2418yes—
550#95C2418yes—
551#95C2418yes—
552#95C2418yes—
553#95C2418yes—
554#95C2418yes—
555#95C2418yes—
556#95C2418yes—
557#95C2418yes—
558#95C2418yes—
559#95C2418yes—
560#95C2418yes—
561#95C2418yes—
562#95C2418yes—
563#95C2418yes—
564#95C2418yes—
565#95C2418yes—
566#95C2418yes—
567#95C2418yes—
568#95C2418yes—
569#95C2418yes—
570C24—24no—
571C24—24no—
572C24—24no—
573C24—42no—
574C24—42no—
575C24—44no—
576C24—44no—
577C24C2×#4114yes—
578C24C2×#4114yes—
579C24C2×#4114yes—
580C24C2514yes—
581C24C2512yes—
582C24C2511yescharacteristic
583C2×Q8—28no—
584C2×Q8—44no—
585C2×Q8—44no—
586C2×D4—28no—
587C2×D4—28no—
588C2×D4—28no—
589C2×D4—28no—
590C2×D4—28no—
591C2×D4—28no—
592C2×D4—28no—
593C2×D4—44no—
594C2×D4—44no—
595C2×D4—432no—
596C22×C4—232no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—24no—
602C22×C4—24no—
603C22×C4—24no—
604C22×C4—24no—
605C22×C4—24no—
606C22×C4—24no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—24no—
612C22×C4—24no—
613C22×C4—24no—
614C22×C4—24no—
615C22×C4—24no—
616C22×C4—28no—
617C22×C4—28no—
618C22×C4—28no—
619C22×C4—28no—
620C22×C4—216no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—44no—
634C22×C4—44no—
635C22×C4—44no—
636C22×C4—44no—
637C22×C4—44no—
638C22×C4—44no—
639C22×C4—44no—
640C22×C4—48no—
641C22×C4—48no—
642C22×C4—44no—
643C22×C4—44no—
644C22×C4—44no—
645C22×C4—88no—
646C22×C4—88no—
647C22×C4C2×#4118yes—
648C22×C4C2×#4118yes—
649C22×C4C2×#4114yes—
650C22×C4C2×#4114yes—
651C22×C4C2×#4118yes—
652C22×C4C2×#4118yes—
653C22×C4C2514yes—
654C22×C4C2514yes—
655C22×C4C2518yes—
656C22×C4C2518yes—
657C22×C4C2514yes—
658C22×C4C2514yes—
659C22×C4C2512yes—
660C22×C4C2512yes—
661C22×C4C2512yes—
662C22×C4C2512yes—
663C22×C4C2514yes—
664C22×C4C2514yes—
665C22×C4C2514yes—
666C22×C4C2512yes—
667C22×C4C2511yescharacteristic
668C22×C4C2511yescharacteristic
669C4⋊C4—24no—
670C4⋊C4—24no—
671C4⋊C4—28no—
672C4⋊C4—28no—
673C4⋊C4—24no—
674C4⋊C4—24no—
675C4⋊C4—28no—
676C4⋊C4—28no—
677C4⋊C4—216no—
678C4⋊C4—28no—
679C4⋊C4—28no—
680C4⋊C4—28no—
681C4⋊C4—28no—
682C4⋊C4—216no—
683C4⋊C4—28no—
684C4⋊C4—28no—
685C4⋊C4—216no—
686C4⋊C4—48no—
687C4⋊C4—48no—
688C4⋊C4—48no—
689C4⋊C4—48no—
690C4⋊C4—44no—
691C4⋊C4—44no—
692C4⋊C4—48no—
693C4⋊C4—48no—
694C4⋊C4—48no—
695C4⋊C4—44no—
696C4⋊C4—44no—
697C4⋊C4—48no—
698C22⋊C4—28no—
699C22⋊C4—28no—
700C22⋊C4—28no—
701C22⋊C4—28no—
702C22⋊C4—28no—
703C22⋊C4—28no—
704C22⋊C4—28no—
705C22⋊C4—28no—
706C22⋊C4—216no—
707C22⋊C4—28no—
708C22⋊C4—28no—
709C22⋊C4—28no—
710C22⋊C4—28no—
711C22⋊C4—216no—
712C22⋊C4—48no—
713C22⋊C4—48no—
714C22⋊C4—48no—
715C22⋊C4—48no—
716C22⋊C4—48no—
717C22⋊C4—48no—
718C22⋊C4—48no—
719C22⋊C4—48no—
720C22⋊C4C2×#41116yes—
721C22⋊C4C2×#41116yes—
722C42—216no—
723C42—28no—
724C42—28no—
725C42—216no—
726C42—48no—
727C42—44no—
728C42—44no—
729C42—44no—
730C42—44no—
731C42—48no—
732C42—48no—
733C42—48no—
734C23—22no—
735C23—24no—
736C23—22no—
737C23—24no—
738C23—24no—
739C23—24no—
740C23—24no—
741C23—28no—
742C23—28no—
743C23—44no—
744C23—48no—
745C23—48no—
746C23—44no—
747C23—48no—
748C23—88no—
749C23—88no—
750C23—84no—
751C23—84no—
752C23#529116yes—
753C23C22×#4114yes—
754C23C22×#4114yes—
755C23C22×#4112yes—
756C23C22×#4112yes—
757C23C22×#4112yes—
758C23C22×#4114yes—
759C23C2611yescharacteristic
760Q8—88no—
761D4—416no—
762D4—416no—
763D4—88no—
764C2×C4—22no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—216no—
775C2×C4—216no—
776C2×C4—28no—
777C2×C4—28no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—28no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—28no—
785C2×C4—24no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—28no—
800C2×C4—28no—
801C2×C4—28no—
802C2×C4—28no—
803C2×C4—28no—
804C2×C4—24no—
805C2×C4—24no—
806C2×C4—28no—
807C2×C4—48no—
808C2×C4—48no—
809C2×C4—48no—
810C2×C4—48no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—44no—
815C2×C4—48no—
816C2×C4—816no—
817C2×C4—88no—
818C2×C4—88no—
819C2×C4—84no—
820C2×C4—84no—
821C2×C4—88no—
822C2×C4—88no—
823C2×C4C22×#4118yes—
824C2×C4C22×#4118yes—
825C2×C4C22×#4114yes—
826C2×C4C22×#4112yes—
827C2×C4C22×#4112yes—
828C22—24no—
829C22—24no—
830C22—28no—
831C22—28no—
832C22—22no—
833C22—24no—
834C22—24no—
835C22—22no—
836C22—416no—
837C22—48no—
838C22—48no—
839C22—44no—
840C22—44no—
841C22—44no—
842C22—168no—
843C22C2×#52918yes—
844C22C2×#52914yes—
845C22C23×#4111yescharacteristic
846C22C23×#4111yescharacteristic
847C22C23×#4111yescharacteristic
848C22H(7,𝔽2)12yes—
849C222−1+612yes—
850C4—28no—
851C4—28no—
852C4—24no—
853C4—22no—
854C4—22no—
855C4—44no—
856C4—44no—
857C4—48no—
858C4—48no—
859C4—42no—
860C4—42no—
861C4—42no—
862C4—42no—
863C4—44no—
864C4—44no—
865C4—44no—
866C2—28no—
867C2—24no—
868C2—84no—
869C2C22×#52911yescharacteristic
870C2#6284712yes—
871C2#6284712yes—
872C2#6285511yescharacteristic
873C2#6286011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#534C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36068C2semidirect
2. #35999C2semidirect
3. #35988C2semidirect
4. #35977C2semidirect
5. #35098C2semidirect
6. #35090C2semidirect
8. #35042C2semidirect
9. #35024C2semidirect
10. #34995C2semidirect
11. #34994C2semidirect
13. #34584C2semidirect
14. C2×#2623C2semidirect
16. #34270C2semidirect
17. #34251C2semidirect
18. #34199C2semidirect
19. C2×#2274C2semidirect
27. #2855C22semidirect
29. #2852C22semidirect
30. #2851C22semidirect
32. #2655C22semidirect
33. #2654C22semidirect
34. #2651C22semidirect
35. #2650C22semidirect
36. #2646C22semidirect
37. #2643C22semidirect
39. #2627C22semidirect
42. #2623C22semidirect
43. #2623C22semidirect
44. #2623C22semidirect
45. #2623C22semidirect
47. #2597C22semidirect
48. #2596C22semidirect
49. #2596C22semidirect
50. #2594C22semidirect
51. #2590C22semidirect
52. #2589C22semidirect
53. #2577C22semidirect
54. #2575C22semidirect
55. #2533C22semidirect
56. #2532C22semidirect
57. #2525C22semidirect
58. #2524C22semidirect
59. #2522C22semidirect
60. #2521C22semidirect
61. #2520C22semidirect
62. #2519C22semidirect
63. #2516C22semidirect
64. #2515C22semidirect
65. #2514C22semidirect
66. #2513C22semidirect
68. #2509C22semidirect
69. #2508C22semidirect
70. #2505C22semidirect
71. #2493C22semidirect
74. #2480C22semidirect
75. #2479C22semidirect
76. #2478C22semidirect
77. #2473C22semidirect
79. #2454C22semidirect
80. #2453C22semidirect
81. #2448C22semidirect
82. #2447C22semidirect
83. #2438C22semidirect
84. #2438C22semidirect
89. #2402C22semidirect
90. #2401C22semidirect
91. #2396C22semidirect
92. #2395C22semidirect
93. C2×#400C22semidirect
94. C2×#399C22semidirect
95. C2×#398C22semidirect
96. C2×#397C22semidirect
97. #2368C22semidirect
98. #2360C22semidirect
105. #2344C22semidirect
106. #2344C22semidirect
107. #2343C22semidirect
108. #2342C22semidirect
109. #2342C22semidirect
110. #2342C22semidirect
111. #2329C22semidirect
113. #2322C22semidirect
114. #2318C22semidirect
121. C4×C22⋊Q8C22semidirect
122. C4×#123C22semidirect
124. #2290C22semidirect
130. #2274C22semidirect
131. #2274C22semidirect
133. C2×C4×C4⋊C4C22semidirect
134. C2×C4×C4⋊C4C22semidirect
135. C2×C4×C4⋊C4C22semidirect
136. C2×C4×C4⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#360682
#359992
#359882
#359772
#350982
#350902
#350892
#350422
#350242
#349952
#349942
#349932
#345842
C2×#26232
#342732
#342702
#342512
#341992
C2×#22742