Finite Group Databasebeta

← #7633260

Subgroups — #7633260

Order 512.

7752 conjugacy classes of subgroups.

The subgroup lattice has 1046 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3509C211yesmaximal, characteristic, complemented
2C2×C4×2−1+4C211yesmaximal, characteristic
3#36545C214yesmaximal, complemented
4#36405C214yesmaximal, complemented
5#36375C218yesmaximal, complemented
6#36021C218yesmaximal, complemented
7#35846C214yesmaximal, complemented
8#35749C214yesmaximal, complemented
9#35670C214yesmaximal, complemented
10#35666C212yesmaximal
11#35622C214yesmaximal, complemented
12#35619C212yesmaximal, complemented
13#35316C211yesmaximal, characteristic, complemented
14#35248C212yesmaximal, complemented
15#35200C212yesmaximal, complemented
16#35179C211yesmaximal, characteristic, complemented
17#34979C212yesmaximal, complemented
18#34953C212yesmaximal, complemented
19#34947C211yesmaximal, characteristic, complemented
20C2×#2546C211yesmaximal, characteristic, complemented
21#34276C212yesmaximal, complemented
22#34209C212yesmaximal, complemented
23#34121C211yesmaximal, characteristic, complemented
24C22×2−1+4C2211yescharacteristic
25#3509—216no—
26C2×#557C2212yes—
27C2×#557C2212yes—
28C2×#556C2212yes—
29C2×#556C2212yes—
30C2×#552C2214yes—
31C2×#552C2214yes—
32C2×#541C2214yes—
33C2×#536C2212yes—
34C2×#536C2212yes—
35C2×#533C2211yescharacteristic
36C2×#533C2212yes—
37C2×#533C2212yes—
38C22×C4⋊Q8C2212yes—
39C22×C4⋊Q8C2211yescharacteristic
40C4×2−1+4—216no—
41C2×#520C2212yes—
42C2×#520C2211yescharacteristic
43C2×#520C2212yes—
44C2×#520C2214yes—
45C2×#520C2211yescharacteristic
46C2×#519C2212yes—
47C2×#519C2212yes—
48C2×#519C2211yescharacteristic
49C2×#519C2212yes—
50C2×C4×#41C2214yes—
51C2×C4×#41C2212yes—
52C2×C4×#41C2212yes—
53C2×C4×#41C2211yescharacteristic
54C2×C4×#41C2211yescharacteristic
55C22×C4×Q8C2211yescharacteristic
56C22×C4×Q8C2212yes—
57C22×C4×Q8C2212yes—
58#2857C2214yes—
59#2855C2214yes—
60#2855C2218yes—
61#2851C2218yes—
62#2638C2218yes—
63#2634C2218yes—
64#2627C2214yes—
65#2621C2214yes—
66#2611C2218yes—
67#2599C2218yes—
68#2584C2218yes—
69#2583C2218yes—
70#2582C2214yes—
71#2581C2214yes—
72#2581C2218yes—
73#2568C2212yes—
74#2568C2211yescharacteristic
75#2567C2212yes—
76#2567C2211yescharacteristic
77#2566C2212yes—
78#2565C2214yes—
79#2565C2212yes—
80#2564C2214yes—
81#2563C2211yescharacteristic
82#2547C2212yes—
83#2547C2212yes—
84#2546C2214yes—
85#2546C2214yes—
86#2546C2214yes—
87#2546C2212yes—
88#2546C2212yes—
89#2546C2212yes—
90#2546C2212yes—
91#2542C2211yescharacteristic
92#2503C2214yes—
93#2502C2214yes—
94#2499C2214yes—
95#2499C2214yes—
96#2486C2214yes—
97#2486C2214yes—
98#2485C2218yes—
99#2484C2218yes—
100#2478C22116yes—
101#2478C22116yes—
102#2475C22116yes—
103#2473C22116yes—
104#2468C22116yes—
105#2466C22116yes—
106#2462C22116yes—
107#2462C22116yes—
108#2447C2218yes—
109#2446C2218yes—
110#2434C2214yes—
111#2434C2214yes—
112#2434C2218yes—
113#2432C2218yes—
114#2432C2214yes—
115#2432C2214yes—
116#2419C22116yes—
117#2417C2214yes—
118#2415C2218yes—
119#2406C22116yes—
120#2399C2218yes—
121#2396C2214yes—
122#2395C2218yes—
123C2×#398C2214yes—
124#2365C2218yes—
125#2365C2218yes—
126#2362C2218yes—
127#2360C2218yes—
128#2359C22116yes—
129#2357C2212yes—
130#2356C2212yes—
131#2355C2212yes—
132#2354C2212yes—
133#2353C2214yes—
134#2352C2214yes—
135#2344C22116yes—
136#2327C2214yes—
137#2327C2214yes—
138#2327C2214yes—
139#2326C2214yes—
140#2317C2212yes—
141#2310C2212yes—
142#2310C2212yes—
143C4×C4⋊Q8C2214yes—
144C4×C4⋊Q8C2214yes—
145C4×C4⋊Q8C2214yes—
146C4×#124C2214yes—
147C4×C22⋊Q8C2218yes—
148C4×C22⋊Q8C2214yes—
149#2298C2214yes—
150#2297C2212yes—
151#2297C2212yes—
152#2296C2218yes—
153C2×#391C2212yes—
154C2×#389C2214yes—
155#2285C2212yes—
156#2285C2211yescharacteristic
157#2283C2212yes—
158C4×#117C2212yes—
159C4×#117C2212yes—
160C2×C4×C4⋊C4C2211yescharacteristic
161C2×2−1+4—28no—
162C2×2−1+4—28no—
163C2×2−1+4—28no—
164C22×#41C2314yes—
165C22×#41C2312yes—
166C22×#41C2312yes—
167C22×#41C2311yescharacteristic
168C22×#41C2311yescharacteristic
169C23×Q8C2312yes—
170C23×Q8C2312yes—
171C23×Q8C2312yes—
172C23×Q8C2311yescharacteristic
173#557—216no—
174#557—216no—
175#556—216no—
176#556—216no—
177#552—232no—
178#552—232no—
179#541—232no—
180#536—216no—
181#536—216no—
182#533—28no—
183#533—216no—
184#533—216no—
185C2×C4⋊Q8—216no—
186C2×C4⋊Q8—28no—
187C2×C4⋊Q8C2314yes—
188C2×C4⋊Q8C2314yes—
189C2×C4⋊Q8C2311yescharacteristic
190C2×C4⋊Q8C2311yescharacteristic
191C2×C4⋊Q8C2314yes—
192C2×C4⋊Q8C2312yes—
193C2×C4⋊Q8C2318yes—
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2312yes—
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2314yes—
198C2×#126C2318yes—
199C2×#126C2318yes—
200C2×#125C2312yes—
201C2×#125C2314yes—
202C2×#125C2314yes—
203C2×#125C2318yes—
204C2×#125C2318yes—
205C2×#124C2314yes—
206C2×#124C2314yes—
207C2×#123C2318yes—
208C2×#123C2318yes—
209C2×C22⋊Q8C2312yes—
210C2×C22⋊Q8C2314yes—
211C2×C22⋊Q8C2314yes—
212C2×C22⋊Q8C2312yes—
213C2×C22⋊Q8C2318yes—
214C2×C22⋊Q8C2314yes—
215C2×C22⋊Q8C2314yes—
216C2×C22⋊Q8C2314yes—
217#520—28no—
218#520—232no—
219#520—216no—
220#520—28no—
221#520—216no—
222#519—216no—
223#519—28no—
224#519—216no—
225#519—216no—
226C4×#41—232no—
227C4×#41—216no—
228C4×#41—28no—
229C4×#41—216no—
230C4×#41D4116yes—
231C2×C4×Q8—216no—
232C2×C4×Q8—28no—
233C2×C4×Q8—216no—
234C2×C4×Q8C2314yes—
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2312yes—
238C2×C4×Q8C2314yes—
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2314yes—
244C2×C4×Q8C2312yes—
245C2×C4×Q8C2312yes—
246C2×C4×Q8C2314yes—
247C2×C4×Q8C2312yes—
248C2×C4×Q8C2312yes—
249C2×C4×Q8C2314yes—
250C2×C4×Q8C2314yes—
251C2×C4×Q8C2314yes—
252C2×C4×Q8C2312yes—
253C2×C4×Q8C2312yes—
254C2×C4×Q8C2314yes—
255C2×C4×Q8C2312yes—
256C2×C4×Q8C2314yes—
257C2×C4×Q8C2314yes—
258C2×C4×Q8C2311yescharacteristic
259C2×C4×Q8C2311yescharacteristic
260C2×C4×D4C2311yescharacteristic
261C2×C4×D4C2312yes—
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2312yes—
264C2×C4×D4C2314yes—
265C2×C4×D4C2314yes—
266C2×C4×D4C2314yes—
267C2×C4×D4C2312yes—
268C2×C4×D4C2314yes—
269C2×C4×D4C2312yes—
270C2×C4×D4C2314yes—
271C2×C4×D4C2314yes—
272C2×C4×D4C2312yes—
273C2×C4×D4C2312yes—
274C2×C4×D4C2311yescharacteristic
275C2×C4×D4C2311yescharacteristic
276C2×#117C2312yes—
277C2×#117C2311yescharacteristic
278C2×#117C2312yes—
279C2×#117C2314yes—
280C2×#117C2314yes—
281C2×#117C2318yes—
282C2×#117C2314yes—
283C2×#117C2312yes—
284C2×#117C2312yes—
285C2×#117C2314yes—
286C2×#117C2314yes—
287C2×#117C2314yes—
288C2×#117C2314yes—
289C2×#117C2312yes—
290C2×#117C2314yes—
291C2×#117C2311yescharacteristic
292C2×#117C2312yes—
293C22×C4⋊C4C2311yescharacteristic
294C22×C4⋊C4C2314yes—
295C22×C4⋊C4C2318yes—
296C22×C4⋊C4C2312yes—
297C22×C4⋊C4C2312yes—
298C22×C4⋊C4C2312yes—
299C22×C4⋊C4C2312yes—
300C22×C4⋊C4C2314yes—
301C22×C4⋊C4C2312yes—
302C22×C4⋊C4C2312yes—
303C22×C42C2314yes—
304C22×C42C2312yes—
305C22×C42C2314yes—
306C22×C42C2312yes—
307C22×C42C2312yes—
308C22×C42C2311yescharacteristic
309C22×C42C2312yes—
310#400C2314yes—
311#400C2318yes—
312#400C23116yes—
313#399C2314yes—
314#398C23116yes—
315#398C2318yes—
316#398C2318yes—
317#398C2318yes—
318#398C23116yes—
319#398C2318yes—
320#398C2318yes—
321#398C23116yes—
322#397C2318yes—
323#397C2318yes—
324#397C23116yes—
325#397C23116yes—
326#396C2318yes—
327#395C2314yes—
328#395C2318yes—
329#395C23116yes—
330#395C23116yes—
331#394C23116yes—
332#394C23116yes—
333#393C2314yes—
334#391C2312yes—
335#391C2314yes—
336#391C2314yes—
337#391C2314yes—
338#391C2314yes—
339#391C2314yes—
340#391C2312yes—
341#391C2318yes—
342#391C2318yes—
343#391C2314yes—
344#391C2318yes—
345#391C2314yes—
346#391C2314yes—
347#391C2318yes—
348#390C2312yes—
349#390C2312yes—
350#390C2314yes—
351#389C23116yes—
352#389C23116yes—
353#389C23116yes—
354#389C2318yes—
355#389C2314yes—
356#389C2318yes—
357#389C2318yes—
358#389C2318yes—
359#389C2318yes—
360#389C2318yes—
361#389C23116yes—
362#388C23116yes—
363#388C2318yes—
364#388C2318yes—
365#388C23116yes—
366#387C2318yes—
367#387C23116yes—
368#387C23116yes—
369#387C23116yes—
370#387C23116yes—
371#387C23116yes—
372#387C23116yes—
373#387C23116yes—
374#387C23116yes—
375#387C2318yes—
376#387C2318yes—
377#387C23116yes—
378#386C2318yes—
379#386C2318yes—
380#385C2318yes—
381#385C2318yes—
382#385C23116yes—
383#385C23116yes—
384#385C23116yes—
385#385C23116yes—
386#385C23116yes—
387#385C23116yes—
388#384C2312yes—
389#384C2312yes—
390#384C2314yes—
391#384C2312yes—
392#383C2314yes—
393#382C2312yes—
394#382C2314yes—
395#382C2312yes—
396#382C2314yes—
397#382C2312yes—
398#381C2318yes—
399#381C2318yes—
400#381C23116yes—
401#381C2314yes—
402#380C2314yes—
403#380C2318yes—
404#380C2318yes—
405#380C2312yes—
406#380C2314yes—
407#380C2318yes—
408#380C2312yes—
409C4×C4⋊C4C23116yes—
410C4×C4⋊C4C23116yes—
411C4×C4⋊C4C23116yes—
412C4×C4⋊C4C2311yescharacteristic
413C4×C4⋊C4C2312yes—
414C4×C4⋊C4C2312yes—
415C4×C4⋊C4C2312yes—
416C4×C4⋊C4C2311yescharacteristic
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2312yes—
419C4×C4⋊C4C2314yes—
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2312yes—
422C4×C4⋊C4C2318yes—
423C4×C22⋊C4C2314yes—
424C4×C22⋊C4C2318yes—
425C4×C22⋊C4C23116yes—
426C4×C22⋊C4C2318yes—
427C4×C22⋊C4C2314yes—
428C4×C22⋊C4C2314yes—
429#376C2314yes—
430#376C2314yes—
431C2×#95C2312yes—
432C2×#95C2318yes—
433C43C2314yes—
4342−1+4—2128no—
435C2×#41—28no—
436C2×#41—28no—
437C2×#41—216no—
438C2×#41—28no—
439C2×#41—216no—
440C2×#41—28no—
441C2×#41—28no—
442C2×#41—24no—
443C2×#41—216no—
444C2×#41—28no—
445C2×#41—24no—
446C2×#41—24no—
447C2×#41—24no—
448C2×#41C2×D418yes—
449C2×#41#4118yes—
450C22×Q8—28no—
451C22×Q8—28no—
452C22×Q8—28no—
453C22×Q8—28no—
454C22×Q8—28no—
455C22×Q8—24no—
456C22×Q8—28no—
457C22×Q8—28no—
458C22×Q8—24no—
459C22×Q8—28no—
460C22×Q8—28no—
461C22×Q8#4118yes—
462C22×Q8C2414yes—
463C22×Q8C2412yes—
464C22×Q8C2414yes—
465C22×Q8C2414yes—
466C22×Q8C2411yescharacteristic
467C22×Q8C2411yescharacteristic
468C22×Q8C2412yes—
469C22×Q8C2412yes—
470C22×Q8C2412yes—
471C22×D4C2414yes—
472C22×D4C2412yes—
473C22×D4C2411yescharacteristic
474C22×D4C2412yes—
475C22×D4C2411yescharacteristic
476C23×C4C2414yes—
477C23×C4C2414yes—
478C23×C4C2414yes—
479C23×C4C2412yes—
480C23×C4C2414yes—
481C23×C4C2411yescharacteristic
482C23×C4C2412yes—
483C23×C4C2412yes—
484C23×C4C2412yes—
485C23×C4C2412yes—
486C23×C4C2412yes—
487C23×C4C2414yes—
488C23×C4C2412yes—
489C23×C4C2414yes—
490C23×C4C2411yescharacteristic
491C23×C4C2412yes—
492C23×C4C2411yescharacteristic
493C4⋊Q8—216no—
494C4⋊Q8—216no—
495C4⋊Q8—216no—
496C4⋊Q8—232no—
497C4⋊Q8—216no—
498C4⋊Q8—28no—
499C4⋊Q8—28no—
500C4⋊Q8—28no—
501C4⋊Q8—28no—
502C4⋊Q8—24no—
503C4⋊Q8—24no—
504#126—232no—
505#126—232no—
506#125—232no—
507#125—232no—
508#125—28no—
509#125—216no—
510#125—216no—
511#124—216no—
512#124—216no—
513#123—232no—
514#123—232no—
515C22⋊Q8—216no—
516C22⋊Q8—216no—
517C22⋊Q8—28no—
518C22⋊Q8—28no—
519C22⋊Q8—216no—
520C22⋊Q8—216no—
521C22⋊Q8—232no—
522C22⋊Q8—216no—
523C4×Q8—28no—
524C4×Q8—28no—
525C4×Q8—216no—
526C4×Q8—28no—
527C4×Q8—216no—
528C4×Q8—216no—
529C4×Q8—216no—
530C4×Q8—216no—
531C4×Q8—28no—
532C4×Q8—28no—
533C4×Q8—24no—
534C4×Q8—216no—
535C4×Q8—28no—
536C4×Q8—28no—
537C4×Q8—28no—
538C4×Q8—28no—
539C4×Q8—28no—
540C4×Q8—24no—
541C4×Q8—216no—
542C4×Q8—216no—
543C4×Q8—216no—
544C4×Q8—216no—
545C4×Q8—28no—
546C4×Q8—28no—
547C4×Q8C2×D418yes—
548C4×Q8C2×D418yes—
549C4×D4—216no—
550C4×D4—28no—
551C4×D4—28no—
552C4×D4—216no—
553C4×D4—28no—
554C4×D4—216no—
555C4×D4—216no—
556C4×D4—216no—
557C4×D4—216no—
558C4×D4—24no—
559C4×D4—28no—
560C4×D4—24no—
561C4×D4C2×D4116yes—
562C4×D4C2×D418yes—
563C4×D4C2×D4116yes—
564C4×D4C2×D418yes—
565#117—28no—
566#117—24no—
567#117—28no—
568#117—216no—
569#117—216no—
570#117—28no—
571#117—28no—
572#117—216no—
573#117—216no—
574#117—216no—
575#117—216no—
576#117—216no—
577#117—232no—
578#117—216no—
579#117—28no—
580#117C2×D418yes—
581#117C2×D4116yes—
582C2×C4⋊C4—28no—
583C2×C4⋊C4—216no—
584C2×C4⋊C4—28no—
585C2×C4⋊C4—24no—
586C2×C4⋊C4—28no—
587C2×C4⋊C4—28no—
588C2×C4⋊C4—232no—
589C2×C4⋊C4—28no—
590C2×C4⋊C4—216no—
591C2×C4⋊C4—28no—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C24116yes—
606C2×C4⋊C4C24116yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2418yes—
617C2×C4⋊C4C2418yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2418yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C24116yes—
625C2×C4⋊C4C2418yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C24116yes—
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C22⋊C4C2412yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2412yes—
637C2×C22⋊C4C2412yes—
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2414yes—
640C2×C22⋊C4C2418yes—
641C2×C22⋊C4C2418yes—
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2418yes—
644C2×C22⋊C4C24116yes—
645C2×C22⋊C4C2418yes—
646C2×C22⋊C4C2418yes—
647C2×C22⋊C4C2418yes—
648C2×C22⋊C4C2412yes—
649C2×C22⋊C4C2412yes—
650C2×C22⋊C4C2412yes—
651C2×C42—28no—
652C2×C42—216no—
653C2×C42—28no—
654C2×C42—216no—
655C2×C42—28no—
656C2×C42C2×D418yes—
657C2×C42C2×D4116yes—
658C2×C42C2414yes—
659C2×C42C2414yes—
660C2×C42C2414yes—
661C2×C42C2412yes—
662C2×C42C2414yes—
663C2×C42C2412yes—
664C2×C42C2414yes—
665C2×C42C2418yes—
666C2×C42C2418yes—
667C2×C42C2414yes—
668C2×C42C2414yes—
669C2×C42C2418yes—
670C2×C42C2414yes—
671C2×C42C2412yes—
672C2×C42C2412yes—
673C2×C42C2412yes—
674C2×C42C2414yes—
675C2×C42C2418yes—
676C2×C42C2412yes—
677C2×C42C2412yes—
678C2×C42C2411yescharacteristic
679C2×C42C2411yescharacteristic
680C2×C42C2412yes—
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683#95C2412yes—
684#95C24116yes—
685#95C2412yes—
686#95C2414yes—
687#95C24116yes—
688#95C2414yes—
689#95C2418yes—
690#95C2418yes—
691#95C2418yes—
692#95C2418yes—
693#95C24116yes—
694#95C2418yes—
695#95C2418yes—
696#95C2418yes—
697#95C2418yes—
698#95C24116yes—
699#95C24116yes—
700#95C2414yes—
701#95C24116yes—
702#95C24116yes—
703C24C2512yes—
704C24C2512yes—
705C24C2511yescharacteristic
706#41—2128no—
707#41—264no—
708#41—264no—
709#41—232no—
710#41—232no—
711C2×Q8—264no—
712C2×Q8—264no—
713C2×Q8—232no—
714C2×Q8—28no—
715C2×Q8—24no—
716C2×Q8—22no—
717C2×Q8—24no—
718C2×Q8—24no—
719C2×Q8—24no—
720C2×Q8—28no—
721C2×Q8—28no—
722C2×Q8—28no—
723C2×Q8—28no—
724C2×Q8—22no—
725C2×Q8—22no—
726C2×Q8—24no—
727C2×Q8—22no—
728C2×Q8—24no—
729C2×Q8—28no—
730C2×Q8—28no—
731C2×Q8—28no—
732C2×Q8—28no—
733C2×Q8—28no—
734C2×Q8—44no—
735C2×Q8—432no—
736C2×Q8C22×D414yes—
737C2×Q8C2×#4114yes—
738C2×Q8C2×#4118yes—
739C2×Q8C2×#4118yes—
740C2×D4—28no—
741C2×D4—24no—
742C2×D4—28no—
743C2×D4—24no—
744C2×D4—24no—
745C2×D4—24no—
746C2×D4—22no—
747C2×D4—28no—
748C2×D4—22no—
749C2×D4—22no—
750C2×D4—22no—
751C2×D4C22×D418yes—
752C2×D4C22×D414yes—
753C2×D4C2×#4118yes—
754C2×D4C2×#4114yes—
755C22×C4—28no—
756C22×C4—24no—
757C22×C4—28no—
758C22×C4—24no—
759C22×C4—28no—
760C22×C4—24no—
761C22×C4—28no—
762C22×C4—28no—
763C22×C4—28no—
764C22×C4—24no—
765C22×C4—24no—
766C22×C4—24no—
767C22×C4—24no—
768C22×C4—28no—
769C22×C4—28no—
770C22×C4—28no—
771C22×C4—28no—
772C22×C4—28no—
773C22×C4—28no—
774C22×C4—24no—
775C22×C4—24no—
776C22×C4—28no—
777C22×C4—28no—
778C22×C4—28no—
779C22×C4—24no—
780C22×C4—44no—
781C22×C4—44no—
782C22×C4—42no—
783C22×C4—48no—
784C22×C4—44no—
785C22×C4—44no—
786C22×C4—48no—
787C22×C4C22×D414yes—
788C22×C4C22×D418yes—
789C22×C4C22×D418yes—
790C22×C4C22×D414yes—
791C22×C4C22×D418yes—
792C22×C4C22×D414yes—
793C22×C4C2×#4118yes—
794C22×C4C2×#4118yes—
795C22×C4C2×#4114yes—
796C22×C4C2×#4114yes—
797C22×C4C2514yes—
798C22×C4C2518yes—
799C22×C4C2512yes—
800C22×C4C2514yes—
801C22×C4C2512yes—
802C22×C4C2514yes—
803C22×C4C2514yes—
804C22×C4C2518yes—
805C22×C4C2511yescharacteristic
806C22×C4C2512yes—
807C22×C4C2512yes—
808C22×C4C2512yes—
809C22×C4C2511yescharacteristic
810C22×C4C2511yescharacteristic
811C22×C4C2514yes—
812C22×C4C2512yes—
813C22×C4C2514yes—
814C22×C4C2511yescharacteristic
815C22×C4C2511yescharacteristic
816C22×C4C2511yescharacteristic
817C4⋊C4—28no—
818C4⋊C4—28no—
819C4⋊C4—28no—
820C4⋊C4—28no—
821C4⋊C4—24no—
822C4⋊C4—28no—
823C4⋊C4—24no—
824C4⋊C4—22no—
825C4⋊C4—24no—
826C4⋊C4—28no—
827C4⋊C4—28no—
828C4⋊C4—28no—
829C4⋊C4—28no—
830C4⋊C4—28no—
831C4⋊C4—24no—
832C4⋊C4—22no—
833C4⋊C4—24no—
834C4⋊C4—24no—
835C4⋊C4—24no—
836C4⋊C4—24no—
837C4⋊C4—216no—
838C4⋊C4—216no—
839C4⋊C4—216no—
840C4⋊C4—216no—
841C4⋊C4—28no—
842C4⋊C4—28no—
843C4⋊C4—232no—
844C4⋊C4—232no—
845C4⋊C4—28no—
846C4⋊C4—232no—
847C4⋊C4—28no—
848C4⋊C4—24no—
849C4⋊C4—28no—
850C4⋊C4—216no—
851C4⋊C4—48no—
852C4⋊C4—44no—
853C4⋊C4—416no—
854C4⋊C4C22×D414yes—
855C4⋊C4C22×D418yes—
856C4⋊C4C22×D414yes—
857C4⋊C4C22×D418yes—
858C4⋊C42−1+418yescomplemented
859C22⋊C4—28no—
860C22⋊C4—24no—
861C22⋊C4—28no—
862C22⋊C4—216no—
863C22⋊C4—216no—
864C22⋊C4—28no—
865C22⋊C4—232no—
866C22⋊C4—24no—
867C22⋊C4—28no—
868C22⋊C4—24no—
869C22⋊C4—216no—
870C22⋊C4—216no—
871C22⋊C4—48no—
872C22⋊C4—48no—
873C22⋊C4C22×D418yes—
874C22⋊C4C22×D418yes—
875C22⋊C4C22×D418yes—
876C42—28no—
877C42—24no—
878C42—28no—
879C42—24no—
880C42—28no—
881C42—28no—
882C42—28no—
883C42—28no—
884C42—24no—
885C42—216no—
886C42—216no—
887C42—28no—
888C42—24no—
889C42—28no—
890C42—24no—
891C42—28no—
892C42—216no—
893C42—48no—
894C42C22×D418yes—
895C42C22×D414yes—
896C42C22×D414yes—
897C42C22×D418yes—
898C42C22×D414yes—
899C42C22×D418yes—
900C42C22×D414yes—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—24no—
908C23—24no—
909C23—24no—
910C23—24no—
911C23C23×D414yes—
912C23C23×D412yes—
913C23C22×#4114yes—
914C23C22×#4112yes—
915C23C22×#4112yes—
916C23C2611yescharacteristic
917Q8—232no—
918Q8—28no—
919Q8—28no—
920Q8—216no—
921Q8—216no—
922Q8—48no—
923Q8—416no—
924Q8—416no—
925Q8—48no—
926D4—232no—
927D4—216no—
928D4—216no—
929D4—28no—
930D4—28no—
931C2×C4—232no—
932C2×C4—232no—
933C2×C4—24no—
934C2×C4—22no—
935C2×C4—24no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—22no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—216no—
947C2×C4—216no—
948C2×C4—216no—
949C2×C4—28no—
950C2×C4—216no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—24no—
954C2×C4—24no—
955C2×C4—24no—
956C2×C4—28no—
957C2×C4—24no—
958C2×C4—28no—
959C2×C4—28no—
960C2×C4—28no—
961C2×C4—28no—
962C2×C4—28no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—28no—
966C2×C4—24no—
967C2×C4—28no—
968C2×C4—24no—
969C2×C4—28no—
970C2×C4—44no—
971C2×C4—48no—
972C2×C4—416no—
973C2×C4—416no—
974C2×C4—48no—
975C2×C4—88no—
976C2×C4—84no—
977C2×C4—84no—
978C2×C4—88no—
979C2×C4#525116yes—
980C2×C4C23×D414yes—
981C2×C4C23×D414yes—
982C2×C4C23×D412yes—
983C2×C4C23×D412yes—
984C2×C4C23×D414yes—
985C2×C4C23×D412yes—
986C2×C4C23×D412yes—
987C2×C4C23×D412yes—
988C2×C4C23×D412yes—
989C2×C4C22×#4118yes—
990C2×C4C22×#4114yes—
991C2×C4C22×#4112yes—
992C2×C4C22×#4112yes—
993C2×C4C22×#4112yes—
994C2×C4C22×#4112yes—
995C2×C4C2×2−1+418yes—
996C2×C4C2×2−1+414yes—
997C22—24no—
998C22—24no—
999C22—22no—
1000C22—22no—
1001C22—28no—
1002C22—24no—
1003C22—24no—
1004C22—24no—
1005C22—24no—
1006C22—44no—
1007C22—44no—
1008C22—44no—
1009C22—42no—
1010C22—42no—
1011C22C2×#52514yes—
1012C22C24×D411yescharacteristic
1013C22C23×#4111yescharacteristic
1014C22C23×#4111yescharacteristic
1015C22C22×2−1+412yes—
1016C222−1+612yes—
1017C4—28no—
1018C4—24no—
1019C4—22no—
1020C4—22no—
1021C4—24no—
1022C4—22no—
1023C4—24no—
1024C4—28no—
1025C4—24no—
1026C4—44no—
1027C4—48no—
1028C4—42no—
1029C4—44no—
1030C4—44no—
1031C4—42no—
1032C4—44no—
1033C4—48no—
1034C4C2×#52514yes—
1035C4C2×#52514yes—
1036C4#349914yes—
1037C2—24no—
1038C2—44no—
1039C2—44no—
1040C2C22×#52511yescharacteristic
1041C2C2×#349911yescharacteristic
1042C2#6285911yescharacteristic
1043C2#6299812yes—
1044C2#6300112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×2−1+4C22
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×#3509C2semidirect
3. #36545C2semidirect
4. #36405C2semidirect
5. #36375C2semidirect
6. #36021C2semidirect
7. #35846C2semidirect
8. #35749C2semidirect
9. #35670C2semidirect
11. #35622C2semidirect
12. #35619C2semidirect
13. #35316C2semidirect
14. #35248C2semidirect
15. #35200C2semidirect
16. #35179C2semidirect
17. #34979C2semidirect
18. #34953C2semidirect
19. #34947C2semidirect
20. C2×#2546C2semidirect
21. #34276C2semidirect
22. #34209C2semidirect
23. #34121C2semidirect
858. C4⋊C42−1+4semidirect

Maximal subgroups

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

subgroupindex
C2×#35092
C2×C4×2−1+42
#365452
#364052
#363752
#360212
#358462
#357492
#356702
#356662
#356222
#356192
#353162
#352482
#352002
#351792
#349792
#349532
#349472
C2×#25462
#342762
#342092
#341212