Finite Group Databasebeta

← #7632119

Subgroups — #7632119

Order 512.

7280 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3507C211yesmaximal, characteristic, complemented
2C22×#556C211yesmaximal, characteristic, complemented
3#36271C218yesmaximal, complemented
4#36268C218yesmaximal, complemented
5#36048C214yesmaximal, complemented
6#35956C214yesmaximal, complemented
7#35938C214yesmaximal, complemented
8#35909C214yesmaximal, complemented
9#35677C212yesmaximal, complemented
10#35667C212yesmaximal, complemented
11#35469C214yesmaximal, complemented
12#35397C214yesmaximal, complemented
13#35338C211yesmaximal, characteristic, complemented
14#35329C211yesmaximal, characteristic
15#35145C214yesmaximal, complemented
16#34955C211yesmaximal, characteristic, complemented
17#34953C211yesmaximal, characteristic, complemented
18#34877C214yesmaximal, complemented
19#34266C212yesmaximal, complemented
20#34265C212yesmaximal, complemented
21C4×#519C211yesmaximal, characteristic, complemented
22#3507—216no—
23C2×#559C2212yescomplemented
24C2×#557C2212yescomplemented
25C2×#556—216no—
26C2×#556C2214yes—
27C2×#556C2214yes—
28C2×#556C2214yes—
29C2×#556C2214yes—
30C2×#556C2214yescomplemented
31C2×#556C2212yescomplemented
32C2×#554C2212yescomplemented
33C2×#552C2214yescomplemented
34C2×#539C2214yes—
35C2×#536C2212yes—
36C2×#536C2212yes—
37C2×#535C2212yes—
38C2×#533C2211yescharacteristic
39C2×#532C2211yescharacteristic
40C22×C4⋊Q8C2211yescharacteristic
41C2×#529C2214yes—
42C22×#126C2212yes—
43C22×#126C2212yes—
44C22×#124C2211yescharacteristic
45C22×#124C2211yescharacteristic
46C22×C22⋊Q8C2212yes—
47C2×#520C2212yes—
48C2×#519C2212yes—
49C22×C4×Q8C2211yescharacteristic
50C22×C4×Q8C2211yescharacteristic
51C22×C4×Q8C2211yescharacteristic
52C22×C4×D4C2211yescharacteristic
53C22×#117C2212yes—
54#2861C2214yes—
55#2860C22116yescomplemented
56#2858C2214yes—
57#2664C2218yescomplemented
58#2662C2218yescomplemented
59#2658C2212yes—
60#2657C2212yes—
61#2640C2212yes—
62#2640C2212yes—
63#2611C2218yescomplemented
64#2610C2218yescomplemented
65#2604C2218yescomplemented
66#2603C2218yescomplemented
67#2601C22116yescomplemented
68#2601C22116yescomplemented
69#2592C2214yes—
70#2592C2214yes—
71#2592C2214yescomplemented
72#2591C2212yes—
73#2591C2212yes—
74#2584C2214yescomplemented
75#2583C2212yes—
76#2583C2212yes—
77#2568C2212yescomplemented
78#2567C2212yescomplemented
79#2561C2214yes—
80#2561C2214yes—
81#2560C22116yescomplemented
82#2560C22116yescomplemented
83#2556C22116yescomplemented
84#2554C22116yescomplemented
85#2548C2218yes—
86#2548C2212yescomplemented
87#2546C2212yescomplemented
88#2546C2218yescomplemented
89#2545C2218yes—
90#2545C2218yescomplemented
91#2540C2214yes—
92#2540C2214yes—
93#2539C2214yes—
94#2539C2214yes—
95#2519C22116yescomplemented
96#2512C22116yescomplemented
97#2504C2212yes—
98#2502C2212yes—
99#2461C22116yescomplemented
100#2452C22116yescomplemented
101#2436C2212yes—
102#2434C2212yes—
103#2429C2218yescomplemented
104#2429C2218yescomplemented
105#2426C2218yes—
106#2426C2218yes—
107#2413C2218yes—
108#2413C2218yes—
109#2411C2218yes—
110#2411C2218yes—
111#2399C2214yescomplemented
112#2398C2214yescomplemented
113#2396C2218yescomplemented
114#2392C2218yescomplemented
115#2367C2218yes—
116#2367C2218yescomplemented
117#2366C2218yes—
118#2365C2218yescomplemented
119#2363C2218yes—
120#2362C2218yescomplemented
121#2361C2218yes—
122#2360C2218yescomplemented
123#2322C2218yes—
124#2321C2218yes—
125#2310C2212yes—
126#2309C2212yes—
127C4×C4⋊Q8C2214yescomplemented
128C4×#124C2214yescomplemented
129C4×#123C2218yes—
130C4×#120C2218yes—
131#2297C2212yes—
132#2297C2212yes—
133#2296C2212yes—
134#2296C2212yes—
135#2293C22116yescomplemented
136#2276C2214yescomplemented
137#2276C2214yescomplemented
138#2274C2214yes—
139#2274C2212yes—
140C42×Q8C2214yescomplemented
141C42×Q8C2214yescomplemented
142C4×#117C2211yescharacteristic
143C4×#117C2211yescharacteristic
144C4×#117C2214yes—
145C22×#41C2312yes—
146C23×Q8C2311yescharacteristic
147C23×Q8C2311yescharacteristic
148C23×Q8C2311yescharacteristic
149C23×D4C2311yescharacteristic
150C24×C4C2312yes—
151#559—216no—
152#557—216no—
153#556—232no—
154#556—232no—
155#556—232no—
156#556—232no—
157#556—216no—
158#556—232no—
159#554—216no—
160#552—232no—
161#539—232no—
162#536—216no—
163#536—216no—
164#535—216no—
165#533—28no—
166#532—28no—
167C2×C4⋊Q8—28no—
168C2×C4⋊Q8C2311yescharacteristic
169C2×C4⋊Q8C2311yescharacteristic
170C2×C4⋊Q8C2314yes—
171C2×C4⋊Q8C2311yescharacteristic
172C2×C4⋊Q8C2314yes—
173C2×C4⋊Q8C2314yes—
174C2×C4⋊Q8C2314yes—
175C2×C4⋊Q8C2314yes—
176C2×#127C2314yes—
177C2×#127C2311yescharacteristic
178#529—232no—
179C2×#126—216no—
180C2×#126—216no—
181C2×#126C2318yes—
182C2×#126C2318yes—
183C2×#126C2318yes—
184C2×#126C2318yes—
185C2×#126C2318yes—
186C2×#126C2318yes—
187C2×#125C2312yes—
188C2×#125C2314yes—
189C2×#125C2318yes—
190C2×#124—28no—
191C2×#124—28no—
192C2×#124C2312yes—
193C2×#124C2312yes—
194C2×#124C2312yes—
195C2×#124C2314yes—
196C2×#124C2314yes—
197C2×#124C2312yes—
198C2×#124C2314yes—
199C2×#124C2312yes—
200C2×#124C2314yes—
201C2×#124C2314yes—
202C2×#124C2314yes—
203C2×#124C2314yes—
204C2×#123C2318yes—
205C2×#123C2318yes—
206C2×#123C2318yes—
207C2×C22⋊Q8—216no—
208C2×C22⋊Q8C2318yes—
209C2×C22⋊Q8C2318yes—
210C2×C22⋊Q8C2312yes—
211C2×C22⋊Q8C2312yes—
212C2×C22⋊Q8C2318yes—
213C2×C22⋊Q8C2318yes—
214C2×C22⋊Q8C2314yes—
215C2×C22⋊Q8C2314yes—
216C2×#121C2312yes—
217C2×#121C2318yes—
218C2×#121C2312yes—
219C2×#120C2318yes—
220#520—216no—
221#519—216no—
222C2×C4×Q8—28no—
223C2×C4×Q8—28no—
224C2×C4×Q8D4116yescomplemented
225C2×C4×Q8C2312yes—
226C2×C4×Q8C2312yes—
227C2×C4×Q8C2312yes—
228C2×C4×Q8C2312yes—
229C2×C4×Q8C2312yes—
230C2×C4×Q8C2312yes—
231C2×C4×Q8C2314yes—
232C2×C4×Q8C2314yes—
233C2×C4×Q8C2314yes—
234C2×C4×Q8C2314yes—
235C2×C4×Q8C2318yes—
236C2×C4×Q8C2318yes—
237C2×C4×Q8C2312yes—
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2312yes—
241C2×C4×D4—28no—
242C2×C4×D4C2318yes—
243C2×C4×D4C2314yes—
244C2×C4×D4C2314yes—
245C2×C4×D4C2314yes—
246C2×C4×D4C2314yes—
247C2×C4×D4C2312yes—
248C2×C4×D4C2312yes—
249C2×C4×D4C23116yes—
250C2×#117—216no—
251C2×#117C2312yes—
252C2×#117C2312yes—
253C2×#117C2318yes—
254C2×#117C2318yes—
255C2×#117C2318yes—
256C2×#117C2314yes—
257C2×#117C2318yes—
258C2×#117C2312yes—
259C22×C4⋊C4C2312yes—
260C22×C4⋊C4C2311yescharacteristic
261C22×C4⋊C4C2311yescharacteristic
262C22×C4⋊C4C2314yes—
263C22×C4⋊C4C2312yes—
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2312yes—
266C22×C4⋊C4C2311yescharacteristic
267C22×C4⋊C4C2312yes—
268C22×C22⋊C4C2312yes—
269C22×C22⋊C4C2312yes—
270C22×C22⋊C4C2312yes—
271C22×C22⋊C4C2312yes—
272C22×C22⋊C4C2312yes—
273C22×C42C2312yes—
274C22×C42C2311yescharacteristic
275C22×C42C2311yescharacteristic
276C22×C42C2312yes—
277C22×C42C2311yescharacteristic
278#400C2314yes—
279#400C2314yes—
280#399C2318yes—
281#399C2318yes—
282#398C23116yes—
283#398C23116yes—
284#398C2314yes—
285#398C2314yes—
286#398C2318yes—
287#397C2318yes—
288#397C2318yes—
289#397C2318yes—
290#396C23116yes—
291#396C23116yes—
292#396C23116yes—
293#396C23116yes—
294#395C2314yes—
295#395C2314yes—
296#395C2318yes—
297#394C23116yes—
298#394C23116yes—
299#394C2314yes—
300#394C2314yes—
301#393C2318yes—
302#393C2318yes—
303#393C2318yes—
304#392C2318yes—
305#392C2318yes—
306#391C2314yes—
307#391C2314yes—
308#391C2318yes—
309#391C2314yes—
310#391C2314yes—
311#391C2314yes—
312#391C2314yes—
313#391C2314yes—
314#390C23116yes—
315#390C2318yes—
316#390C2314yes—
317#390C2314yes—
318#390C23116yes—
319#390C2314yes—
320#390C2314yes—
321#390C23116yes—
322#390C23116yes—
323#390C23116yes—
324#390C2314yes—
325#389C2318yes—
326#389C2318yes—
327#389C2314yes—
328#389C2314yes—
329#389C23116yes—
330#389C2314yes—
331#389C2314yes—
332#389C23116yes—
333#389C23116yes—
334#388C23116yes—
335#388C23116yes—
336#388C23116yes—
337#388C23116yes—
338#388C23116yes—
339#388C23116yes—
340#388C23116yes—
341#388C23116yes—
342#388C23116yes—
343#388C2318yes—
344#388C2318yes—
345#388C23116yes—
346#387C23116yes—
347#387C23116yes—
348#386C23116yes—
349#386C23116yes—
350#386C2314yes—
351#386C2314yes—
352#386C2314yes—
353#386C2314yes—
354#385C2314yes—
355#385C2314yes—
356#385C23116yes—
357#385C2314yes—
358#385C2314yes—
359#385C23116yes—
360#384C2314yes—
361#382C2314yes—
362#381C2318yes—
363#379C2318yes—
364C4×C4⋊C4C23116yes—
365C4×C4⋊C4C2318yes—
366C4×C4⋊C4C2318yes—
367C4×C4⋊C4C2312yes—
368C4×C4⋊C4C2312yes—
369C4×C4⋊C4C2312yes—
370C4×C4⋊C4C2312yes—
371C4×C4⋊C4C2318yes—
372C4×C4⋊C4C2318yes—
373C4×C4⋊C4C23116yes—
374C4×C4⋊C4C2318yes—
375C4×C4⋊C4C2318yes—
376C4×C4⋊C4C23116yes—
377C4×C22⋊C4C23116yes—
378C4×C22⋊C4C23116yes—
379C4×C22⋊C4C2312yes—
380C4×C22⋊C4C2312yes—
381C4×C22⋊C4C2318yes—
382C4×C22⋊C4C2312yes—
383C4×C22⋊C4C2318yes—
384C4×C22⋊C4C2318yes—
385C4×C22⋊C4C2312yes—
386#376C2318yes—
387#376C2312yes—
388#376C2312yes—
389C43C2312yes—
390C43C2318yes—
391C43C2312yes—
392C25C2412yes—
393C2×#41—28no—
394C2×#41—28no—
395C2×#41—28no—
396C22×Q8—24no—
397C22×Q8—24no—
398C22×Q8—28no—
399C22×Q8—28no—
400C22×Q8—44no—
401C22×Q8C2×D418yes—
402C22×Q8C2412yes—
403C22×Q8C2412yes—
404C22×Q8C2412yes—
405C22×Q8C2412yes—
406C22×Q8C2412yes—
407C22×Q8C2412yes—
408C22×Q8C2412yes—
409C22×Q8C2412yes—
410C22×Q8C2412yes—
411C22×D4—24no—
412C22×D4—28no—
413C22×D4C2414yes—
414C22×D4C2412yes—
415C22×D4C2412yes—
416C22×D4C2412yes—
417C22×D4C2412yes—
418C22×D4C24116yes—
419C22×D4C2412yes—
420C23×C4—28no—
421C23×C4—48no—
422C23×C4C2412yes—
423C23×C4C2411yescharacteristic
424C23×C4C2414yes—
425C23×C4C2418yes—
426C23×C4C2412yes—
427C23×C4C2411yescharacteristic
428C23×C4C2411yescharacteristic
429C23×C4C2411yescharacteristic
430C23×C4C2418yes—
431C23×C4C2411yescharacteristic
432C23×C4C2411yescharacteristic
433C23×C4C2412yes—
434C23×C4C2411yescharacteristic
435C4⋊Q8—216no—
436C4⋊Q8—216no—
437C4⋊Q8—216no—
438C4⋊Q8—24no—
439C4⋊Q8—24no—
440C4⋊Q8—24no—
441C4⋊Q8—216no—
442C4⋊Q8—48no—
443#127—24no—
444#127—216no—
445#126—232no—
446#126—232no—
447#126—232no—
448#126—232no—
449#126—232no—
450#126—232no—
451#125—232no—
452#125—216no—
453#125—28no—
454#124—216no—
455#124—216no—
456#124—216no—
457#124—28no—
458#124—28no—
459#124—28no—
460#124—28no—
461#124—216no—
462#124—28no—
463#124—216no—
464#124—216no—
465#124—48no—
466#123—232no—
467#123—232no—
468#123—232no—
469C22⋊Q8—216no—
470C22⋊Q8—216no—
471C22⋊Q8—28no—
472C22⋊Q8—28no—
473C22⋊Q8—232no—
474C22⋊Q8—232no—
475C22⋊Q8—232no—
476C22⋊Q8—232no—
477#121—28no—
478#121—28no—
479#121—232no—
480#120—232no—
481C4×Q8—216no—
482C4×Q8—216no—
483C4×Q8—216no—
484C4×Q8—232no—
485C4×Q8—28no—
486C4×Q8—28no—
487C4×Q8—28no—
488C4×Q8—28no—
489C4×Q8—216no—
490C4×Q8—28no—
491C4×Q8—28no—
492C4×Q8—232no—
493C4×Q8C2×D4116yes—
494C4×Q8C2×D4116yes—
495C4×Q8C2×D4116yes—
496C4×Q8C2×D4116yes—
497C4×D4—232no—
498C4×D4—216no—
499C4×D4—216no—
500C4×D4—216no—
501C4×D4—216no—
502C4×D4—28no—
503C4×D4—28no—
504C4×D4—432no—
505#117—28no—
506#117—28no—
507#117—216no—
508#117—232no—
509#117—232no—
510#117—232no—
511#117—232no—
512#117#41116yes—
513C2×C4⋊C4—24no—
514C2×C4⋊C4—28no—
515C2×C4⋊C4—28no—
516C2×C4⋊C4—24no—
517C2×C4⋊C4—24no—
518C2×C4⋊C4—28no—
519C2×C4⋊C4—216no—
520C2×C4⋊C4C2×D418yes—
521C2×C4⋊C4C2×D4116yes—
522C2×C4⋊C4C2412yes—
523C2×C4⋊C4C2412yes—
524C2×C4⋊C4C2412yes—
525C2×C4⋊C4C2418yes—
526C2×C4⋊C4C2418yes—
527C2×C4⋊C4C2418yes—
528C2×C4⋊C4C2412yes—
529C2×C4⋊C4C2412yes—
530C2×C4⋊C4C2412yes—
531C2×C4⋊C4C2412yes—
532C2×C4⋊C4C2418yes—
533C2×C4⋊C4C2412yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C24116yes—
537C2×C4⋊C4C2418yes—
538C2×C4⋊C4C2412yes—
539C2×C4⋊C4C2418yes—
540C2×C4⋊C4C2412yes—
541C2×C4⋊C4C2412yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2418yes—
544C2×C4⋊C4C2412yes—
545C2×C4⋊C4C24116yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2418yes—
548C2×C4⋊C4C2418yes—
549C2×C4⋊C4C2412yes—
550C2×C4⋊C4C2412yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2414yes—
554C2×C22⋊C4—28no—
555C2×C22⋊C4—28no—
556C2×C22⋊C4—28no—
557C2×C22⋊C4—28no—
558C2×C22⋊C4—28no—
559C2×C22⋊C4C2414yes—
560C2×C22⋊C4C2418yes—
561C2×C22⋊C4C2414yes—
562C2×C22⋊C4C2418yes—
563C2×C22⋊C4C2414yes—
564C2×C22⋊C4C2418yes—
565C2×C22⋊C4C2414yes—
566C2×C22⋊C4C2414yes—
567C2×C22⋊C4C2414yes—
568C2×C22⋊C4C2414yes—
569C2×C22⋊C4C2418yes—
570C2×C22⋊C4C2418yes—
571C2×C22⋊C4C2418yes—
572C2×C22⋊C4C2414yes—
573C2×C22⋊C4C2418yes—
574C2×C22⋊C4C24116yes—
575C2×C22⋊C4C24116yes—
576C2×C22⋊C4C24116yes—
577C2×C22⋊C4C2418yes—
578C2×C22⋊C4C2418yes—
579C2×C22⋊C4C24116yes—
580C2×C22⋊C4C2418yes—
581C2×C22⋊C4C2414yes—
582C2×C42—28no—
583C2×C42—24no—
584C2×C42—24no—
585C2×C42C2×D4116yes—
586C2×C42C2×D418yes—
587C2×C42C2418yes—
588C2×C42C2418yes—
589C2×C42C2414yes—
590C2×C42C2414yes—
591C2×C42C24116yes—
592C2×C42C2412yes—
593C2×C42C2412yes—
594C2×C42C2412yes—
595C2×C42C2412yes—
596C2×C42C24116yes—
597C2×C42C2414yes—
598C2×C42C2414yes—
599C2×C42C2414yes—
600C2×C42C2414yes—
601C2×C42C2414yes—
602C2×C42C2414yes—
603C2×C42C2411yescharacteristic
604C2×C42C2411yescharacteristic
605C2×C42C2411yescharacteristic
606C2×C42C2411yescharacteristic
607C2×C42C2414yes—
608#95C2414yes—
609#95C2414yes—
610#95C24116yes—
611#95C2414yes—
612#95C2414yes—
613#95C2418yes—
614#95C2418yes—
615#95C2418yes—
616#95C2418yes—
617#95C24116yes—
618#95C2418yes—
619#95C2418yes—
620#95C24116yes—
621#95C2418yes—
622#95C2418yes—
623C24—24no—
624C24—28no—
625C24—44no—
626C24—44no—
627C24C2514yes—
628C24C2514yes—
629C24C2511yescharacteristic
630#41—432no—
631C2×Q8—232no—
632C2×Q8—24no—
633C2×Q8—24no—
634C2×Q8—24no—
635C2×Q8—24no—
636C2×Q8—24no—
637C2×Q8—24no—
638C2×Q8—24no—
639C2×Q8—28no—
640C2×Q8—28no—
641C2×Q8—28no—
642C2×Q8—24no—
643C2×Q8—28no—
644C2×Q8—24no—
645C2×Q8—24no—
646C2×Q8—24no—
647C2×Q8—42no—
648C2×Q8—42no—
649C2×Q8—44no—
650C2×Q8—44no—
651C2×Q8—416no—
652C2×Q8—416no—
653C2×Q8C22×D418yes—
654C2×Q8C22×D418yes—
655C2×D4—28no—
656C2×D4—28no—
657C2×D4—28no—
658C2×D4—24no—
659C2×D4—24no—
660C2×D4—24no—
661C2×D4—24no—
662C2×D4—24no—
663C2×D4—28no—
664C2×D4—24no—
665C2×D4—28no—
666C2×D4—24no—
667C2×D4—232no—
668C2×D4—44no—
669C2×D4—416no—
670C2×D4—44no—
671C2×D4—416no—
672C2×D4—416no—
673C22×C4—22no—
674C22×C4—28no—
675C22×C4—24no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—24no—
680C22×C4—28no—
681C22×C4—28no—
682C22×C4—216no—
683C22×C4—28no—
684C22×C4—28no—
685C22×C4—216no—
686C22×C4—216no—
687C22×C4—44no—
688C22×C4—48no—
689C22×C4—42no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—42no—
694C22×C4—416no—
695C22×C4—432no—
696C22×C4C22×D418yes—
697C22×C4C22×D418yes—
698C22×C4C22×D414yes—
699C22×C4C22×D414yes—
700C22×C4C22×D414yes—
701C22×C4C2×#4118yes—
702C22×C4C2518yes—
703C22×C4C2512yes—
704C22×C4C2514yes—
705C22×C4C2512yes—
706C22×C4C2514yes—
707C22×C4C2512yes—
708C22×C4C2514yes—
709C22×C4C2514yes—
710C22×C4C2511yescharacteristic
711C22×C4C2514yes—
712C22×C4C2511yescharacteristic
713C22×C4C2511yescharacteristic
714C22×C4C2511yescharacteristic
715C22×C4C2514yes—
716C22×C4C2518yes—
717C22×C4C2512yes—
718C22×C4C2511yescharacteristic
719C22×C4C2511yescharacteristic
720C4⋊C4—24no—
721C4⋊C4—24no—
722C4⋊C4—24no—
723C4⋊C4—216no—
724C4⋊C4—216no—
725C4⋊C4—216no—
726C4⋊C4—24no—
727C4⋊C4—24no—
728C4⋊C4—24no—
729C4⋊C4—24no—
730C4⋊C4—216no—
731C4⋊C4—24no—
732C4⋊C4—28no—
733C4⋊C4—216no—
734C4⋊C4—24no—
735C4⋊C4—24no—
736C4⋊C4—24no—
737C4⋊C4—28no—
738C4⋊C4—216no—
739C4⋊C4—24no—
740C4⋊C4—232no—
741C4⋊C4—28no—
742C4⋊C4—232no—
743C4⋊C4—216no—
744C4⋊C4—48no—
745C4⋊C4—48no—
746C4⋊C4—48no—
747C4⋊C4C22×D418yes—
748C4⋊C4C22×D418yes—
749C4⋊C4C22×D4116yes—
750C4⋊C4C22×D4116yes—
751C4⋊C4C2×#41116yes—
752C22⋊C4—28no—
753C22⋊C4—28no—
754C22⋊C4—216no—
755C22⋊C4—28no—
756C22⋊C4—28no—
757C22⋊C4—216no—
758C22⋊C4—216no—
759C22⋊C4—28no—
760C22⋊C4—28no—
761C22⋊C4—28no—
762C22⋊C4—216no—
763C22⋊C4—216no—
764C22⋊C4—28no—
765C22⋊C4—216no—
766C22⋊C4—232no—
767C22⋊C4—232no—
768C22⋊C4—216no—
769C22⋊C4—48no—
770C22⋊C4—48no—
771C22⋊C4—416no—
772C22⋊C4—416no—
773C22⋊C4—48no—
774C22⋊C4C2×#41116yes—
775C42—216no—
776C42—24no—
777C42—24no—
778C42—24no—
779C42—24no—
780C42—216no—
781C42—28no—
782C42—232no—
783C42—28no—
784C42—44no—
785C42—44no—
786C42—416no—
787C42—44no—
788C42—44no—
789C42C22×D4116yes—
790C42C22×D4116yes—
791C42C22×D414yes—
792C42C22×D414yes—
793C42C22×D414yes—
794C42C22×D414yes—
795C42C2×#41116yes—
796C23—22no—
797C23—22no—
798C23—24no—
799C23—24no—
800C23—24no—
801C23—28no—
802C23—24no—
803C23—28no—
804C23—28no—
805C23—28no—
806C23—28no—
807C23—48no—
808C23—48no—
809C23—48no—
810C23—816no—
811C23C23×D412yes—
812C23C22×#4114yes—
813C23C2611yescharacteristic
814Q8—216no—
815Q8—216no—
816Q8—48no—
817Q8—48no—
818Q8—48no—
819Q8—48no—
820Q8—48no—
821Q8—48no—
822Q8—84no—
823D4—48no—
824D4—416no—
825D4—48no—
826D4—48no—
827D4—48no—
828D4—832no—
829D4—84no—
830C2×C4—28no—
831C2×C4—22no—
832C2×C4—28no—
833C2×C4—28no—
834C2×C4—28no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—28no—
840C2×C4—22no—
841C2×C4—216no—
842C2×C4—22no—
843C2×C4—24no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—24no—
847C2×C4—24no—
848C2×C4—24no—
849C2×C4—28no—
850C2×C4—24no—
851C2×C4—28no—
852C2×C4—24no—
853C2×C4—28no—
854C2×C4—22no—
855C2×C4—28no—
856C2×C4—22no—
857C2×C4—28no—
858C2×C4—24no—
859C2×C4—24no—
860C2×C4—28no—
861C2×C4—48no—
862C2×C4—44no—
863C2×C4—44no—
864C2×C4—432no—
865C2×C4—44no—
866C2×C4—44no—
867C2×C4—44no—
868C2×C4—48no—
869C2×C4—416no—
870C2×C4—816no—
871C2×C4#532116yes—
872C2×C4C23×D418yes—
873C2×C4C23×D412yes—
874C2×C4C23×D412yes—
875C2×C4C23×D418yes—
876C2×C4C23×D412yes—
877C2×C4C23×D412yes—
878C2×C4C23×D412yes—
879C2×C4C23×D412yes—
880C2×C4C22×#41116yes—
881C2×C4C22×#4114yes—
882C2×C4C22×#4114yes—
883C2×C4#58514yes—
884C22—28no—
885C22—22no—
886C22—22no—
887C22—48no—
888C22—416no—
889C22—48no—
890C22—44no—
891C22—44no—
892C22—44no—
893C22—44no—
894C22—44no—
895C22—44no—
896C22—816no—
897C22C2×#53214yes—
898C22C24×D411yescharacteristic
899C22C23×#4112yes—
900C22C2×#58512yes—
901C222−1+612yes—
902C4—216no—
903C4—24no—
904C4—28no—
905C4—22no—
906C4—22no—
907C4—22no—
908C4—22no—
909C4—28no—
910C4—48no—
911C4—42no—
912C4—44no—
913C4—42no—
914C4—42no—
915C4—44no—
916C4—44no—
917C4—44no—
918C4C2×#53214yes—
919C4C2×#53214yes—
920C2—24no—
921C2—84no—
922C2—84no—
923C2C22×#53211yescharacteristic
924C2#6281111yescharacteristic
925C2#6284811yescharacteristic
926C2#6299514yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35329C2
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×#3507C2semidirect
2. C22×#556C2semidirect
3. #36271C2semidirect
4. #36268C2semidirect
5. #36048C2semidirect
6. #35956C2semidirect
7. #35938C2semidirect
8. #35909C2semidirect
9. #35677C2semidirect
10. #35667C2semidirect
11. #35469C2semidirect
12. #35397C2semidirect
13. #35338C2semidirect
15. #35145C2semidirect
16. #34955C2semidirect
17. #34953C2semidirect
18. #34877C2semidirect
19. #34266C2semidirect
20. #34265C2semidirect
21. C4×#519C2semidirect
23. C2×#559C22semidirect
24. C2×#557C22semidirect
30. C2×#556C22semidirect
31. C2×#556C22semidirect
32. C2×#554C22semidirect
33. C2×#552C22semidirect
55. #2860C22semidirect
57. #2664C22semidirect
58. #2662C22semidirect
63. #2611C22semidirect
64. #2610C22semidirect
65. #2604C22semidirect
66. #2603C22semidirect
67. #2601C22semidirect
68. #2601C22semidirect
71. #2592C22semidirect
74. #2584C22semidirect
77. #2568C22semidirect
78. #2567C22semidirect
81. #2560C22semidirect
82. #2560C22semidirect
83. #2556C22semidirect
84. #2554C22semidirect
86. #2548C22semidirect
87. #2546C22semidirect
88. #2546C22semidirect
90. #2545C22semidirect
95. #2519C22semidirect
96. #2512C22semidirect
99. #2461C22semidirect
100. #2452C22semidirect
103. #2429C22semidirect
104. #2429C22semidirect
111. #2399C22semidirect
112. #2398C22semidirect
113. #2396C22semidirect
114. #2392C22semidirect
116. #2367C22semidirect
118. #2365C22semidirect
120. #2362C22semidirect
122. #2360C22semidirect
127. C4×C4⋊Q8C22semidirect
128. C4×#124C22semidirect
135. #2293C22semidirect
136. #2276C22semidirect
137. #2276C22semidirect
140. C42×Q8C22semidirect
141. C42×Q8C22semidirect
224. C2×C4×Q8D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35072
C22×#5562
#362712
#362682
#360482
#359562
#359382
#359092
#356772
#356672
#354692
#353972
#353382
#353292
#351452
#349552
#349532
#348772
#342662
#342652
C4×#5192