Finite Group Databasebeta

← #7674791

Subgroups — #7674791

Order 512.

5058 conjugacy classes of subgroups.

The subgroup lattice has 1031 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59288C214yesmaximal, complemented
2#59254C214yesmaximal, complemented
3#59205C214yesmaximal, complemented
4#59197C214yesmaximal, complemented
5#44460C214yesmaximal, complemented
6#44081C214yesmaximal, complemented
7#43513C214yesmaximal, complemented
8#43509C214yesmaximal, complemented
9#38973C214yesmaximal, complemented
10#38223C218yesmaximal, complemented
11#36254C214yesmaximal, complemented
12#35368C212yesmaximal, complemented
13#35360C212yesmaximal
14#35020C211yesmaximal, characteristic, complemented
15#34995C212yesmaximal, complemented
16C2×#2487C211yesmaximal, characteristic, complemented
17C2×#2487C211yesmaximal, characteristic, complemented
18#34251C212yesmaximal, complemented
19#34185C211yesmaximal, characteristic, complemented
20#34181C211yesmaximal, characteristic, complemented
21C2×#2345C211yesmaximal, characteristic, complemented
22C4×#534C211yesmaximal, characteristic
23C2×#534C2211yescharacteristic
24C2×#518C2212yes—
25C22×C4×D4C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27C23×C4⋊C4C2211yescharacteristic
28#2852C2218yescomplemented
29#2851C2214yescomplemented
30#2776C2218yescomplemented
31#2773C2218yescomplemented
32#2773C2218yescomplemented
33#2771C2218yescomplemented
34#2767C2218yescomplemented
35#2766C2218yescomplemented
36#2747C2218yescomplemented
37#2743C2218yescomplemented
38#2741C2218yescomplemented
39#2738C2218yescomplemented
40#2738C2218yescomplemented
41#2694C2218yescomplemented
42#2646C2214yescomplemented
43#2643C2218yescomplemented
44#2611C2218yescomplemented
45#2596C2218yescomplemented
46#2575C2218yescomplemented
47#2570C2214yescomplemented
48#2569C2218yescomplemented
49#2569C2214yescomplemented
50#2569C2214yescomplemented
51#2562C2214yescomplemented
52#2553C2218yescomplemented
53#2533C2218yescomplemented
54#2533C2218yescomplemented
55#2533C2218yescomplemented
56#2530C2218yescomplemented
57#2519C2218yescomplemented
58#2510C2218yes—
59#2508C2214yescomplemented
60#2506C2214yescomplemented
61#2505C2218yescomplemented
62#2505C2218yescomplemented
63#2498C2218yes—
64#2498C2218yescomplemented
65#2496C2214yescomplemented
66#2495C2214yescomplemented
67#2495C2214yescomplemented
68#2494C2214yescomplemented
69#2493C2218yescomplemented
70#2493C2218yescomplemented
71#2487C2214yes—
72#2487C2214yes—
73#2487C2214yes—
74#2487C2214yes—
75#2487C2212yescomplemented
76#2487C2212yescomplemented
77#2487C2214yescomplemented
78#2487C2214yescomplemented
79#2487C2212yescomplemented
80#2487C2212yescomplemented
81#2486C2214yescomplemented
82#2485C2214yescomplemented
83#2481C2218yes—
84#2480C2218yescomplemented
85#2479C2218yescomplemented
86#2473C2218yescomplemented
87#2473C2218yescomplemented
88#2444C2218yes—
89#2443C2218yes—
90#2442C2218yescomplemented
91#2442C2214yescomplemented
92#2442C2214yescomplemented
93#2442C2214yescomplemented
94#2441C2214yescomplemented
95#2419C2218yes—
96#2418C2218yes—
97#2412C2218yes—
98C2×#400C2212yescomplemented
99C2×#400C2212yescomplemented
100C2×#399C2212yescomplemented
101C2×#399C2212yescomplemented
102#2370C2214yescomplemented
103#2353C2218yes—
104#2353C2214yes—
105#2353C2214yescomplemented
106#2352C2218yes—
107#2352C2214yes—
108#2352C2214yescomplemented
109#2352C2214yescomplemented
110#2349C2214yes—
111#2349C2214yescomplemented
112D4×C4⋊C4C2214yes—
113D4×C4⋊C4C2214yescomplemented
114#2346C2214yescomplemented
115#2345C2214yescomplemented
116#2345C2214yescomplemented
117#2345C2214yescomplemented
118#2345C2214yescomplemented
119#2344C2214yescomplemented
120#2343C2218yescomplemented
121#2342C2218yescomplemented
122#2325C2214yes—
123#2322C2212yes—
124#2322C2212yes—
125#2321C2212yes—
126#2321C2212yes—
127#2318C2218yescomplemented
128#2316C2212yescomplemented
129#2315C2212yes—
130#2315C2211yescharacteristic
131#2315C2212yes—
132#2315C2212yes—
133#2315C2212yescomplemented
134#2313C2212yescomplemented
135#2312C2212yescomplemented
136#2308C2212yes—
137#2308C2211yescharacteristic
138#2308C2211yescharacteristic
139C4×#123C2212yes—
140C4×#123C2212yes—
141C4×#121C2214yes—
142C4×#120C2212yes—
143C4×#120C2212yes—
144C2×#389C2212yescomplemented
145C2×#389C2212yescomplemented
146C2×#389C2212yescomplemented
147#2290C2218yescomplemented
148C2×#387C2214yescomplemented
149C2×#386C2212yes—
150C2×#386C2212yes—
151C2×#385C2212yes—
152C2×#385C2212yes—
153#2285C2212yescomplemented
154#2283C2212yescomplemented
155#2280C2212yescomplemented
156C2×#380C2212yes—
157C2×#380C2211yescharacteristic
158C2×#380C2211yescharacteristic
159C2×#380C2211yescharacteristic
160C2×#380C2212yescomplemented
161C2×#380C2212yescomplemented
162C2×#380C2212yescomplemented
163#2273C2212yes—
164C2×C4×C4⋊C4C2212yescomplemented
165C2×C4×C22⋊C4C2211yescharacteristic
166C2×C4×C22⋊C4C2212yes—
167C23×D4C2311yescharacteristic
168C23×D4C2311yescharacteristic
169C24×C4C2311yescharacteristic
170C24×C4C2311yescharacteristic
171C24×C4C2312yes—
172C24×C4C2311yescharacteristic
173#534—28no—
174C2×#126C2318yes—
175C2×#125C2314yes—
176C2×#125C2318yes—
177C2×#123C2312yes—
178C2×#123C2312yes—
179C2×#123C2318yes—
180C2×#121C2314yes—
181C2×#120C2312yes—
182C2×#120C2312yes—
183#518—216no—
184C2×C4×D4—28no—
185C2×C4×D4—28no—
186C2×C4×D4C2318yes—
187C2×C4×D4C2312yes—
188C2×C4×D4C2312yes—
189C2×C4×D4C2312yes—
190C2×C4×D4C2312yes—
191C2×C4×D4C2312yes—
192C2×C4×D4C2318yes—
193C2×C4×D4C2312yes—
194C2×C4×D4C2312yes—
195C2×C4×D4C2312yes—
196C2×C4×D4C2314yes—
197C2×#117C2314yes—
198C2×#117C2314yes—
199C2×#117C2318yes—
200C22×C4⋊C4—28no—
201C22×C4⋊C4C2311yescharacteristic
202C22×C4⋊C4C2311yescharacteristic
203C22×C4⋊C4C2312yes—
204C22×C4⋊C4C2312yes—
205C22×C4⋊C4C2312yes—
206C22×C4⋊C4C2312yes—
207C22×C4⋊C4C2311yescharacteristic
208C22×C4⋊C4C2312yes—
209C22×C4⋊C4C2311yescharacteristic
210C22×C4⋊C4C2314yes—
211C22×C4⋊C4C2312yes—
212C22×C4⋊C4C2312yes—
213C22×C4⋊C4C2312yes—
214C22×C4⋊C4C2314yes—
215C22×C4⋊C4C2314yes—
216C22×C4⋊C4C2314yes—
217C22×C22⋊C4C2311yescharacteristic
218C22×C22⋊C4C2311yescharacteristic
219C22×C22⋊C4C2312yes—
220C22×C22⋊C4C2311yescharacteristic
221C22×C22⋊C4C2312yes—
222C22×C22⋊C4C2311yescharacteristic
223C22×C22⋊C4C2312yes—
224C22×C22⋊C4C2311yescharacteristic
225C22×C22⋊C4C2311yescharacteristic
226C22×C22⋊C4C2314yes—
227C22×C22⋊C4C2314yes—
228C22×C22⋊C4C2314yes—
229C22×C42C2311yescharacteristic
230C22×C42C2311yescharacteristic
231C22×C42C2312yes—
232C22×C42C2314yes—
233#401C2318yes—
234#400C2318yes—
235#400C2318yes—
236#400C2318yes—
237#400C2318yes—
238#400C2318yes—
239#400C2314yes—
240#400C2318yes—
241#400C2314yes—
242#400C2318yes—
243#400C2318yes—
244#400C2318yes—
245#400C2318yes—
246#400C2318yes—
247#400C2314yes—
248#400C2314yes—
249#400C2318yes—
250#399C2314yes—
251#399C2314yes—
252#399C2318yes—
253#399C2314yes—
254#399C2314yes—
255#399C2318yes—
256#399C2318yes—
257#398C2318yes—
258#398C2318yes—
259#398C2318yes—
260#398C2318yes—
261#398C2318yes—
262#398C2318yes—
263#398C2318yes—
264#397C2318yes—
265#397C2318yes—
266#397C2318yes—
267#397C2318yes—
268#397C2318yes—
269#397C2318yes—
270#396C2318yes—
271#394C2318yes—
272#394C2318yes—
273#390C2314yes—
274#389C2314yes—
275#389C2314yes—
276#389C2318yes—
277#389C2318yes—
278#389C2314yes—
279#389C2314yes—
280#389C2314yes—
281#389C2318yes—
282#389C2314yes—
283#389C2314yes—
284#389C2318yes—
285#389C2318yes—
286#389C2318yes—
287#389C2314yes—
288#389C2314yes—
289#389C2318yes—
290#388C2318yes—
291#388C2318yes—
292#388C2318yes—
293#388C2318yes—
294#388C2318yes—
295#388C2318yes—
296#388C2314yes—
297#388C2314yes—
298#388C2314yes—
299#388C2314yes—
300#388C2318yes—
301#388C2318yes—
302#388C2318yes—
303#388C2318yes—
304#388C2318yes—
305#387C2318yes—
306#387C2318yes—
307#387C2318yes—
308#387C2318yes—
309#387C2318yes—
310#387C2318yes—
311#387C2318yes—
312#387C2318yes—
313#387C2318yes—
314#387C2318yes—
315#387C2318yes—
316#387C2318yes—
317#387C2318yes—
318#387C2314yes—
319#387C2314yes—
320#387C2318yes—
321#387C2318yes—
322#387C2318yes—
323#387C2318yes—
324#387C2318yes—
325#387C2318yes—
326#387C2318yes—
327#387C2318yes—
328#386C2314yes—
329#386C2312yes—
330#386C2312yes—
331#386C2312yes—
332#386C2312yes—
333#386C2314yes—
334#386C2318yes—
335#386C2318yes—
336#386C2314yes—
337#386C2314yes—
338#386C2314yes—
339#386C2314yes—
340#386C2318yes—
341#386C2318yes—
342#386C2314yes—
343#386C2318yes—
344#386C2314yes—
345#385C2312yes—
346#385C2318yes—
347#385C2318yes—
348#385C2318yes—
349#385C2318yes—
350#385C2312yes—
351#385C2312yes—
352#385C2312yes—
353#385C2318yes—
354#385C2318yes—
355#385C2318yes—
356#385C2318yes—
357#385C2318yes—
358#385C2314yes—
359#385C2314yes—
360#385C2314yes—
361#385C2314yes—
362#385C2318yes—
363#385C2314yes—
364#385C2318yes—
365#385C2314yes—
366#384C2314yes—
367#383C2318yes—
368#383C2318yes—
369#383C2314yes—
370#382C2314yes—
371#382C2314yes—
372#382C2318yes—
373#382C2318yes—
374#382C2314yes—
375#381C2314yes—
376#381C2312yes—
377#381C2312yes—
378#381C2318yes—
379#381C2318yes—
380#381C2314yes—
381#380C2314yes—
382#380C2314yes—
383#380C2314yes—
384#380C2314yes—
385#380C2312yes—
386#380C2312yes—
387#380C2314yes—
388#380C2318yes—
389#380C2312yes—
390#380C2318yes—
391#380C2318yes—
392#380C2314yes—
393#380C2314yes—
394#380C2312yes—
395#380C2318yes—
396#380C2312yes—
397#380C2312yes—
398#380C2312yes—
399#380C2312yes—
400#380C2318yes—
401#380C2314yes—
402#380C2312yes—
403#380C2312yes—
404#380C2314yes—
405#380C2312yes—
406#380C2312yes—
407#380C2314yes—
408#380C2318yes—
409#380C2318yes—
410#379C2314yes—
411#379C2312yes—
412#379C2312yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2318yes—
416C4×C4⋊C4C2318yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2314yes—
419C4×C4⋊C4C2314yes—
420C4×C4⋊C4C2314yes—
421C4×C22⋊C4C2314yes—
422C4×C22⋊C4C2314yes—
423C4×C22⋊C4C2312yes—
424C4×C22⋊C4C2312yes—
425C4×C22⋊C4C2318yes—
426C4×C22⋊C4C2318yes—
427C4×C22⋊C4C2318yes—
428C4×C22⋊C4C2318yes—
429C4×C22⋊C4C2314yes—
430C4×C22⋊C4C2318yes—
431C4×C22⋊C4C2312yes—
432C4×C22⋊C4C2312yes—
433C4×C22⋊C4C2314yes—
434C4×C22⋊C4C2314yes—
435#376C2318yes—
436#376C2314yes—
437C2×#95C2312yes—
438C2×#95C2312yes—
439C2×#95C2314yes—
440C2×#95C2314yes—
441C2×#95C2312yes—
442C2×#95C2314yes—
443C2×#95C2314yes—
444C2×#95C2312yes—
445C2×#95C2314yes—
446C2×#95C2314yes—
447C2×#95C2314yes—
448C25C2411yescharacteristic
449C25C2411yescharacteristic
450C25C2411yescharacteristic
451C22×D4—24no—
452C22×D4—24no—
453C22×D4—24no—
454C22×D4—24no—
455C22×D4—24no—
456C22×D4#4118yes—
457C22×D4C2412yes—
458C22×D4C2412yes—
459C22×D4C2412yes—
460C22×D4C2412yes—
461C22×D4C2414yes—
462C23×C4—28no—
463C23×C4—24no—
464C23×C4—24no—
465C23×C4—44no—
466C23×C4—44no—
467C23×C4—44no—
468C23×C4—84no—
469C23×C4#4118yes—
470C23×C4C2412yes—
471C23×C4C2411yescharacteristic
472C23×C4C2412yes—
473C23×C4C2411yescharacteristic
474C23×C4C2411yescharacteristic
475C23×C4C2411yescharacteristic
476C23×C4C2411yescharacteristic
477C23×C4C2411yescharacteristic
478C23×C4C2411yescharacteristic
479C23×C4C2414yes—
480C23×C4C2414yes—
481C23×C4C2414yes—
482C23×C4C2414yes—
483C23×C4C2414yes—
484C23×C4C2412yes—
485C23×C4C2418yes—
486C23×C4C2411yescharacteristic
487C23×C4C2411yescharacteristic
488C23×C4C2412yes—
489C23×C4C2412yes—
490C23×C4C2412yes—
491C23×C4C2412yes—
492C23×C4C2412yes—
493C23×C4C2411yescharacteristic
494C23×C4C2411yescharacteristic
495C23×C4C2411yescharacteristic
496#126—88no—
497#125—48no—
498#125—88no—
499#123—28no—
500#123—28no—
501#123—88no—
502#121—216no—
503#120—28no—
504#120—28no—
505C4×D4—232no—
506C4×D4—232no—
507C4×D4—28no—
508C4×D4—28no—
509C4×D4—28no—
510C4×D4—28no—
511C4×D4—28no—
512C4×D4—28no—
513C4×D4—28no—
514C4×D4—28no—
515C4×D4—48no—
516#117—216no—
517#117—48no—
518#117—88no—
519C2×C4⋊C4—24no—
520C2×C4⋊C4—24no—
521C2×C4⋊C4—28no—
522C2×C4⋊C4—28no—
523C2×C4⋊C4—28no—
524C2×C4⋊C4—28no—
525C2×C4⋊C4—28no—
526C2×C4⋊C4—24no—
527C2×C4⋊C4—24no—
528C2×C4⋊C4—44no—
529C2×C4⋊C4—48no—
530C2×C4⋊C4—44no—
531C2×C4⋊C4—44no—
532C2×C4⋊C4—84no—
533C2×C4⋊C4—84no—
534C2×C4⋊C4—84no—
535C2×C4⋊C4C2412yes—
536C2×C4⋊C4C2412yes—
537C2×C4⋊C4C2412yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2412yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2412yes—
545C2×C4⋊C4C2412yes—
546C2×C4⋊C4C2412yes—
547C2×C4⋊C4C2412yes—
548C2×C4⋊C4C2418yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2418yes—
551C2×C4⋊C4C2418yes—
552C2×C4⋊C4C2418yes—
553C2×C4⋊C4C2418yes—
554C2×C4⋊C4C2418yes—
555C2×C4⋊C4C2418yes—
556C2×C4⋊C4C2414yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2418yes—
560C2×C4⋊C4C2418yes—
561C2×C4⋊C4C2414yes—
562C2×C4⋊C4C2418yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2418yes—
565C2×C4⋊C4C2418yes—
566C2×C4⋊C4C2418yes—
567C2×C22⋊C4—24no—
568C2×C22⋊C4—24no—
569C2×C22⋊C4—216no—
570C2×C22⋊C4—28no—
571C2×C22⋊C4—28no—
572C2×C22⋊C4—24no—
573C2×C22⋊C4—24no—
574C2×C22⋊C4—28no—
575C2×C22⋊C4—24no—
576C2×C22⋊C4—24no—
577C2×C22⋊C4—84no—
578C2×C22⋊C4—84no—
579C2×C22⋊C4C2414yes—
580C2×C22⋊C4C2414yes—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C2412yes—
583C2×C22⋊C4C2412yes—
584C2×C22⋊C4C2412yes—
585C2×C22⋊C4C2412yes—
586C2×C22⋊C4C2414yes—
587C2×C22⋊C4C2418yes—
588C2×C22⋊C4C2412yes—
589C2×C22⋊C4C2412yes—
590C2×C22⋊C4C2412yes—
591C2×C22⋊C4C2412yes—
592C2×C22⋊C4C2412yes—
593C2×C22⋊C4C2412yes—
594C2×C22⋊C4C2412yes—
595C2×C22⋊C4C2412yes—
596C2×C22⋊C4C2414yes—
597C2×C22⋊C4C2414yes—
598C2×C22⋊C4C2414yes—
599C2×C22⋊C4C2414yes—
600C2×C22⋊C4C2418yes—
601C2×C22⋊C4C2418yes—
602C2×C22⋊C4C2418yes—
603C2×C22⋊C4C2418yes—
604C2×C22⋊C4C2414yes—
605C2×C22⋊C4C2418yes—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2414yes—
608C2×C22⋊C4C2418yes—
609C2×C22⋊C4C2414yes—
610C2×C42—24no—
611C2×C42—24no—
612C2×C42—44no—
613C2×C42—84no—
614C2×C42C2418yes—
615C2×C42C2412yes—
616C2×C42C2412yes—
617C2×C42C2412yes—
618C2×C42C2412yes—
619C2×C42C2414yes—
620C2×C42C2418yes—
621C2×C42C2418yes—
622C2×C42C2418yes—
623C2×C42C2418yes—
624C2×C42C2414yes—
625#95C2414yes—
626#95C2414yes—
627#95C2414yes—
628#95C2414yes—
629#95C2418yes—
630#95C2418yes—
631#95C2418yes—
632#95C2418yes—
633#95C2414yes—
634#95C2414yes—
635#95C2418yes—
636#95C2418yes—
637#95C2418yes—
638#95C2418yes—
639#95C2418yes—
640#95C2414yes—
641#95C2418yes—
642#95C2414yes—
643#95C2418yes—
644#95C2418yes—
645#95C2418yes—
646#95C2414yes—
647#95C2418yes—
648#95C2418yes—
649#95C2418yes—
650#95C2418yes—
651#95C2414yes—
652#95C2418yes—
653#95C2414yes—
654#95C2414yes—
655#95C2414yes—
656#95C2418yes—
657#95C2418yes—
658#95C2414yes—
659#95C2418yes—
660#95C2418yes—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—42no—
667C24—42no—
668C24—42no—
669C24—42no—
670C24—42no—
671C24—42no—
672C24C2×#4114yes—
673C24C2×#4114yes—
674C24C2×#4114yes—
675C242−1+414yes—
676C24C2512yes—
677C24C2512yes—
678C24C2511yescharacteristic
679C24C2511yescharacteristic
680C24C2511yescharacteristic
681C2×D4—232no—
682C2×D4—24no—
683C2×D4—24no—
684C2×D4—24no—
685C2×D4—24no—
686C2×D4—24no—
687C2×D4—24no—
688C2×D4—24no—
689C2×D4—24no—
690C2×D4—24no—
691C2×D4—24no—
692C2×D4—28no—
693C2×D4—44no—
694C2×D4—44no—
695C2×D4—416no—
696C2×D4C2×#4118yes—
697C2×D4C2×#4118yes—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—24no—
701C22×C4—24no—
702C22×C4—24no—
703C22×C4—22no—
704C22×C4—24no—
705C22×C4—24no—
706C22×C4—22no—
707C22×C4—24no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—216no—
714C22×C4—28no—
715C22×C4—28no—
716C22×C4—24no—
717C22×C4—28no—
718C22×C4—28no—
719C22×C4—28no—
720C22×C4—24no—
721C22×C4—24no—
722C22×C4—28no—
723C22×C4—28no—
724C22×C4—24no—
725C22×C4—24no—
726C22×C4—416no—
727C22×C4—42no—
728C22×C4—42no—
729C22×C4—44no—
730C22×C4—44no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—42no—
735C22×C4—44no—
736C22×C4—44no—
737C22×C4—44no—
738C22×C4—44no—
739C22×C4—44no—
740C22×C4—44no—
741C22×C4—44no—
742C22×C4—48no—
743C22×C4—44no—
744C22×C4—42no—
745C22×C4—42no—
746C22×C4—42no—
747C22×C4—44no—
748C22×C4—44no—
749C22×C4—48no—
750C22×C4—44no—
751C22×C4—44no—
752C22×C4—42no—
753C22×C4—42no—
754C22×C4—88no—
755C22×C4—88no—
756C22×C4—816no—
757C22×C4C2×#4114yes—
758C22×C4C2×#4114yes—
759C22×C4C2×#4114yes—
760C22×C4C2×#4114yes—
761C22×C4C2×#4114yes—
762C22×C4C2×#4114yes—
763C22×C4C2×#4114yes—
764C22×C4C2512yes—
765C22×C4C2512yes—
766C22×C4C2512yes—
767C22×C4C2514yes—
768C22×C4C2518yes—
769C22×C4C2518yes—
770C22×C4C2514yes—
771C22×C4C2514yes—
772C22×C4C2518yes—
773C22×C4C2514yes—
774C22×C4C2512yes—
775C22×C4C2512yes—
776C22×C4C2512yes—
777C22×C4C2511yescharacteristic
778C22×C4C2511yescharacteristic
779C22×C4C2511yescharacteristic
780C22×C4C2511yescharacteristic
781C4⋊C4—28no—
782C4⋊C4—28no—
783C4⋊C4—24no—
784C4⋊C4—24no—
785C4⋊C4—24no—
786C4⋊C4—24no—
787C4⋊C4—24no—
788C4⋊C4—24no—
789C4⋊C4—24no—
790C4⋊C4—24no—
791C4⋊C4—216no—
792C4⋊C4—28no—
793C4⋊C4—28no—
794C4⋊C4—28no—
795C4⋊C4—28no—
796C4⋊C4—44no—
797C4⋊C4—44no—
798C4⋊C4—44no—
799C4⋊C4—48no—
800C4⋊C4—48no—
801C4⋊C4—48no—
802C4⋊C4—48no—
803C4⋊C4—48no—
804C4⋊C4—48no—
805C4⋊C4—48no—
806C4⋊C4—48no—
807C4⋊C4—44no—
808C4⋊C4—48no—
809C4⋊C4—48no—
810C4⋊C4—48no—
811C4⋊C4—44no—
812C4⋊C4—48no—
813C22⋊C4—28no—
814C22⋊C4—28no—
815C22⋊C4—24no—
816C22⋊C4—24no—
817C22⋊C4—24no—
818C22⋊C4—24no—
819C22⋊C4—216no—
820C22⋊C4—28no—
821C22⋊C4—28no—
822C22⋊C4—24no—
823C22⋊C4—24no—
824C22⋊C4—28no—
825C22⋊C4—24no—
826C22⋊C4—28no—
827C22⋊C4—28no—
828C22⋊C4—24no—
829C22⋊C4—24no—
830C22⋊C4—24no—
831C22⋊C4—24no—
832C22⋊C4—24no—
833C22⋊C4—28no—
834C22⋊C4—48no—
835C22⋊C4—48no—
836C22⋊C4—48no—
837C22⋊C4—48no—
838C22⋊C4—48no—
839C22⋊C4—44no—
840C22⋊C4—44no—
841C22⋊C4—44no—
842C22⋊C4—48no—
843C22⋊C4—44no—
844C42—24no—
845C42—24no—
846C42—24no—
847C42—24no—
848C42—216no—
849C42—28no—
850C42—44no—
851C42—48no—
852C42—48no—
853C42—48no—
854C42—48no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—24no—
864C23—24no—
865C23—28no—
866C23—22no—
867C23—22no—
868C23—22no—
869C23—24no—
870C23—24no—
871C23—44no—
872C23—44no—
873C23—48no—
874C23—48no—
875C23—48no—
876C23—48no—
877C23—44no—
878C23—82no—
879C23—82no—
880C23—84no—
881C23—82no—
882C23—82no—
883C23—84no—
884C23#552116yes—
885C23C22×#4114yes—
886C23C22×#4112yes—
887C23C22×#4112yes—
888C23C22×#4112yes—
889C23C22×#4112yes—
890C23C22×#4112yes—
891C23C22×#4112yes—
892C23C2×2−1+412yes—
893C23C2×2−1+412yes—
894C23C2×2−1+412yes—
895C23C2611yescharacteristic
896D4—216no—
897D4—216no—
898D4—48no—
899D4—48no—
900D4—88no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—28no—
907C2×C4—28no—
908C2×C4—28no—
909C2×C4—28no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—28no—
914C2×C4—28no—
915C2×C4—24no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—24no—
920C2×C4—24no—
921C2×C4—24no—
922C2×C4—28no—
923C2×C4—22no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—24no—
927C2×C4—28no—
928C2×C4—28no—
929C2×C4—24no—
930C2×C4—28no—
931C2×C4—24no—
932C2×C4—28no—
933C2×C4—24no—
934C2×C4—24no—
935C2×C4—24no—
936C2×C4—28no—
937C2×C4—24no—
938C2×C4—28no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—24no—
942C2×C4—44no—
943C2×C4—44no—
944C2×C4—44no—
945C2×C4—48no—
946C2×C4—48no—
947C2×C4—48no—
948C2×C4—44no—
949C2×C4—48no—
950C2×C4—48no—
951C2×C4—84no—
952C2×C4—84no—
953C2×C4—88no—
954C2×C4—88no—
955C2×C4—816no—
956C2×C4—84no—
957C2×C4—82no—
958C2×C4—82no—
959C2×C4—88no—
960C2×C4—82no—
961C2×C4—82no—
962C2×C4—88no—
963C2×C4—88no—
964C2×C4C22×#4114yes—
965C2×C4C22×#4112yes—
966C2×C4C22×#4112yes—
967C2×C4C22×#4112yes—
968C2×C4C22×#4112yes—
969C2×C4#58514yes—
970C22—24no—
971C22—24no—
972C22—24no—
973C22—22no—
974C22—22no—
975C22—22no—
976C22—22no—
977C22—22no—
978C22—22no—
979C22—24no—
980C22—24no—
981C22—24no—
982C22—28no—
983C22—24no—
984C22—416no—
985C22—42no—
986C22—42no—
987C22—44no—
988C22—44no—
989C22—42no—
990C22—42no—
991C22—44no—
992C22—42no—
993C22—88no—
994C22—88no—
995C22C2×#55214yes—
996C22C2×#55214yes—
997C22C2×#55214yes—
998C22C23×#4111yescharacteristic
999C22C23×#4111yescharacteristic
1000C22C22×2−1+411yescharacteristic
1001C22C2×#58512yes—
1002C22H(7,𝔽2)12yes—
1003C4—22no—
1004C4—22no—
1005C4—22no—
1006C4—24no—
1007C4—48no—
1008C4—48no—
1009C4—44no—
1010C4—42no—
1011C4—42no—
1012C4—44no—
1013C4—44no—
1014C4—42no—
1015C4—42no—
1016C4—44no—
1017C4—48no—
1018C4—42no—
1019C4#349114yes—
1020C2—24no—
1021C2—24no—
1022C2—24no—
1023C2—44no—
1024C2—82no—
1025C2C22×#55211yescharacteristic
1026C2C2×#349111yescharacteristic
1027C2#6285511yescharacteristic
1028C2#6290212yes—
1029C2#6299212yes—
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. #59288C2semidirect
2. #59254C2semidirect
3. #59205C2semidirect
4. #59197C2semidirect
5. #44460C2semidirect
6. #44081C2semidirect
7. #43513C2semidirect
8. #43509C2semidirect
9. #38973C2semidirect
10. #38223C2semidirect
11. #36254C2semidirect
12. #35368C2semidirect
14. #35020C2semidirect
15. #34995C2semidirect
16. C2×#2487C2semidirect
17. C2×#2487C2semidirect
18. #34251C2semidirect
19. #34185C2semidirect
20. #34181C2semidirect
21. C2×#2345C2semidirect
28. #2852C22semidirect
29. #2851C22semidirect
30. #2776C22semidirect
31. #2773C22semidirect
32. #2773C22semidirect
33. #2771C22semidirect
34. #2767C22semidirect
35. #2766C22semidirect
36. #2747C22semidirect
37. #2743C22semidirect
38. #2741C22semidirect
39. #2738C22semidirect
40. #2738C22semidirect
41. #2694C22semidirect
42. #2646C22semidirect
43. #2643C22semidirect
44. #2611C22semidirect
45. #2596C22semidirect
46. #2575C22semidirect
47. #2570C22semidirect
48. #2569C22semidirect
49. #2569C22semidirect
50. #2569C22semidirect
51. #2562C22semidirect
52. #2553C22semidirect
53. #2533C22semidirect
54. #2533C22semidirect
55. #2533C22semidirect
56. #2530C22semidirect
57. #2519C22semidirect
59. #2508C22semidirect
60. #2506C22semidirect
61. #2505C22semidirect
62. #2505C22semidirect
64. #2498C22semidirect
65. #2496C22semidirect
66. #2495C22semidirect
67. #2495C22semidirect
68. #2494C22semidirect
69. #2493C22semidirect
70. #2493C22semidirect
75. #2487C22semidirect
76. #2487C22semidirect
77. #2487C22semidirect
78. #2487C22semidirect
79. #2487C22semidirect
80. #2487C22semidirect
81. #2486C22semidirect
82. #2485C22semidirect
84. #2480C22semidirect
85. #2479C22semidirect
86. #2473C22semidirect
87. #2473C22semidirect
90. #2442C22semidirect
91. #2442C22semidirect
92. #2442C22semidirect
93. #2442C22semidirect
94. #2441C22semidirect
98. C2×#400C22semidirect
99. C2×#400C22semidirect
100. C2×#399C22semidirect
101. C2×#399C22semidirect
102. #2370C22semidirect
105. #2353C22semidirect
108. #2352C22semidirect
109. #2352C22semidirect
111. #2349C22semidirect
113. D4×C4⋊C4C22semidirect
114. #2346C22semidirect
115. #2345C22semidirect
116. #2345C22semidirect
117. #2345C22semidirect
118. #2345C22semidirect
119. #2344C22semidirect
120. #2343C22semidirect
121. #2342C22semidirect
127. #2318C22semidirect
128. #2316C22semidirect
133. #2315C22semidirect
134. #2313C22semidirect
135. #2312C22semidirect
144. C2×#389C22semidirect
145. C2×#389C22semidirect
146. C2×#389C22semidirect
147. #2290C22semidirect
148. C2×#387C22semidirect
153. #2285C22semidirect
154. #2283C22semidirect
155. #2280C22semidirect
160. C2×#380C22semidirect
161. C2×#380C22semidirect
162. C2×#380C22semidirect
164. C2×C4×C4⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#592882
#592542
#592052
#591972
#444602
#440812
#435132
#435092
#389732
#382232
#362542
#353682
#353602
#350202
#349952
C2×#24872
#342512
#341852
#341812
C2×#23452
C4×#5342