Finite Group Databasebeta

← #7631661

Subgroups — #7631661

Order 512.

5468 conjugacy classes of subgroups.

The subgroup lattice has 1029 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36294C214yesmaximal, complemented
2#36291C214yesmaximal, complemented
3#36171C214yesmaximal, complemented
4#36168C214yesmaximal, complemented
5#36034C214yesmaximal, complemented
6#35848C218yesmaximal, complemented
7#35837C214yesmaximal, complemented
8#35388C218yesmaximal, complemented
9#35370C212yesmaximal, complemented
10#35360C212yesmaximal, complemented
11#35029C214yesmaximal, complemented
12#35020C211yesmaximal, characteristic, complemented
13#35000C211yesmaximal, characteristic
14#34788C214yesmaximal, complemented
15C2×#2504C211yesmaximal, characteristic, complemented
16C2×#2487C211yesmaximal, characteristic, complemented
17#34273C212yesmaximal, complemented
18#34251C212yesmaximal, complemented
19#34205C211yesmaximal, characteristic, complemented
20C2×#2345C211yesmaximal, characteristic, complemented
21C4×#518C211yesmaximal, characteristic, complemented
22C2×#534C2212yes—
23C22×#121C2211yescharacteristic
24C2×#518C2211yescharacteristic
25C2×#518C2212yes—
26C2×#518C2211yescharacteristic
27C22×C4×D4C2211yescharacteristic
28C23×C4⋊C4C2211yescharacteristic
29#2864C2214yescomplemented
30#2860C2214yescomplemented
31#2854C2212yes—
32#2854C2214yescomplemented
33#2851C2214yescomplemented
34#2851C2214yescomplemented
35#2847C2212yes—
36#2654C2218yescomplemented
37#2649C2218yescomplemented
38#2646C2214yescomplemented
39#2618C2212yes—
40#2617C2212yes—
41#2596C2218yescomplemented
42#2595C2218yescomplemented
43#2578C2218yescomplemented
44#2575C2218yescomplemented
45#2573C2218yescomplemented
46#2569C2214yescomplemented
47#2569C2214yescomplemented
48#2553C2218yescomplemented
49#2543C2214yes—
50#2534C2214yes—
51#2531C2218yescomplemented
52#2530C2218yescomplemented
53#2529C2218yescomplemented
54#2528C2218yescomplemented
55#2525C2218yescomplemented
56#2524C2218yescomplemented
57#2517C2218yescomplemented
58#2516C2218yescomplemented
59#2516C2218yescomplemented
60#2513C2214yescomplemented
61#2510C2218yescomplemented
62#2510C2218yescomplemented
63#2510C2218yescomplemented
64#2509C2214yescomplemented
65#2508C2214yescomplemented
66#2504C2214yes—
67#2504C2214yes—
68#2504C2214yescomplemented
69#2504C2212yescomplemented
70#2504C2212yescomplemented
71#2498C2218yescomplemented
72#2495C2214yescomplemented
73#2494C2214yescomplemented
74#2493C2218yescomplemented
75#2490C2214yescomplemented
76#2487C2214yes—
77#2487C2214yes—
78#2487C2214yescomplemented
79#2487C2212yescomplemented
80#2487C2212yescomplemented
81#2486C2212yes—
82#2481C2218yescomplemented
83#2481C2218yescomplemented
84#2480C2218yescomplemented
85#2478C2218yescomplemented
86#2471C2218yescomplemented
87#2467C2218yescomplemented
88#2454C2214yescomplemented
89#2444C2218yescomplemented
90#2443C2218yescomplemented
91#2442C2214yescomplemented
92#2442C2214yescomplemented
93#2420C2214yescomplemented
94#2419C2218yes—
95#2419C2218yescomplemented
96#2418C2218yes—
97#2416C2214yes—
98#2412C2218yescomplemented
99#2408C2212yes—
100#2401C2218yescomplemented
101#2395C2218yescomplemented
102C2×#400C2212yescomplemented
103C2×#399C2212yescomplemented
104C2×#397C2214yescomplemented
105#2364C2214yes—
106#2361C2214yes—
107#2359C2218yes—
108#2359C2218yescomplemented
109#2358C2218yes—
110#2358C2218yescomplemented
111#2353C2218yescomplemented
112#2352C2218yescomplemented
113#2345C2214yescomplemented
114#2345C2214yescomplemented
115#2345C2214yescomplemented
116#2345C2214yescomplemented
117#2344C2212yescomplemented
118#2343C2218yescomplemented
119#2342C2214yescomplemented
120#2342C2218yescomplemented
121D4×C22⋊C4C2212yescomplemented
122#2325C2214yescomplemented
123#2325C2218yescomplemented
124#2318C2218yescomplemented
125#2315C2212yes—
126#2315C2212yes—
127#2308C2212yes—
128#2308C2212yes—
129C4×#125C2214yescomplemented
130C4×#121C2218yescomplemented
131C4×#121C2214yescomplemented
132C4×#121C2214yescomplemented
133#2293C2214yescomplemented
134C2×#390C2212yescomplemented
135C2×#389C2212yescomplemented
136C2×#389C2212yescomplemented
137#2290C2218yescomplemented
138C2×#387C2214yescomplemented
139C2×#386C2212yes—
140C2×#386C2212yes—
141C2×#386C2212yes—
142C2×#385C2212yes—
143#2283C2214yescomplemented
144C2×#382C2212yescomplemented
145C2×#380C2212yes—
146C2×#380C2211yescharacteristic
147C2×#380C2211yescharacteristic
148C2×#380C2212yescomplemented
149#2275C2214yes—
150#2275C2214yescomplemented
151#2274C2212yescomplemented
152#2273C2211yescharacteristic
153#2273C2211yescharacteristic
154#2273C2212yescomplemented
155C42×D4C2214yes—
156C42×D4C2214yescomplemented
157C4×#117C2212yescomplemented
158C2×C4×C4⋊C4C2212yescomplemented
159C2×C4×C22⋊C4C2211yescharacteristic
160C2×C4×C22⋊C4C2212yes—
161C2×C4×C22⋊C4C2211yescharacteristic
162C2×C4×C22⋊C4C2212yescomplemented
163C23×D4C2312yes—
164C23×D4C2311yescharacteristic
165C23×D4C2311yescharacteristic
166C24×C4C2311yescharacteristic
167C24×C4C2312yes—
168C24×C4C2311yescharacteristic
169#534—216no—
170C2×#126C2318yes—
171C2×#125C2314yes—
172C2×#123C2314yes—
173C2×#123C2314yes—
174C2×#123C2318yes—
175C2×#121—28no—
176C2×#121C2312yes—
177C2×#121C2318yes—
178C2×#121C2312yes—
179C2×#121C2312yes—
180C2×#121C2312yes—
181C2×#121C2314yes—
182C2×#120C2314yes—
183C2×#120C2314yes—
184#518—28no—
185#518—28no—
186#518—216no—
187C2×C4×D4—28no—
188C2×C4×D4C2318yes—
189C2×C4×D4C2314yes—
190C2×C4×D4C2318yes—
191C2×C4×D4C2314yes—
192C2×C4×D4C2312yes—
193C2×C4×D4C2312yes—
194C2×C4×D4C2312yes—
195C2×C4×D4C2312yes—
196C2×C4×D4C2314yes—
197C2×C4×D4C2314yes—
198C2×C4×D4C2314yes—
199C2×C4×D4C2318yes—
200C2×#117C2314yes—
201C2×#117C2312yes—
202C2×#117C2312yes—
203C2×#117C2318yes—
204C22×C4⋊C4—28no—
205C22×C4⋊C4C2311yescharacteristic
206C22×C4⋊C4C2312yes—
207C22×C4⋊C4C2312yes—
208C22×C4⋊C4C2312yes—
209C22×C4⋊C4C2312yes—
210C22×C4⋊C4C2311yescharacteristic
211C22×C4⋊C4C2311yescharacteristic
212C22×C4⋊C4C2312yes—
213C22×C4⋊C4C2311yescharacteristic
214C22×C4⋊C4C2312yes—
215C22×C4⋊C4C2312yes—
216C22×C4⋊C4C2314yes—
217C22×C4⋊C4C2314yes—
218C22×C22⋊C4C2311yescharacteristic
219C22×C22⋊C4C2311yescharacteristic
220C22×C22⋊C4C2312yes—
221C22×C22⋊C4C2312yes—
222C22×C22⋊C4C2311yescharacteristic
223C22×C22⋊C4C2311yescharacteristic
224C22×C22⋊C4C2314yes—
225C22×C22⋊C4C2312yes—
226C22×C22⋊C4C2312yes—
227C22×C22⋊C4C2311yescharacteristic
228C22×C22⋊C4C2312yes—
229C22×C22⋊C4C2314yes—
230C22×C22⋊C4C2314yes—
231C22×C22⋊C4C2314yes—
232C22×C22⋊C4C2311yescharacteristic
233C22×C42C2311yescharacteristic
234C22×C42C2312yes—
235C22×C42C2314yes—
236C22×C42C2312yes—
237C22×C42C2314yes—
238#401C2318yes—
239#400C2318yes—
240#400C2318yes—
241#400C2314yes—
242#400C2318yes—
243#400C2318yes—
244#400C2318yes—
245#400C2318yes—
246#400C2314yes—
247#400C2318yes—
248#399C2318yes—
249#399C2318yes—
250#399C2314yes—
251#399C2314yes—
252#398C2318yes—
253#398C2318yes—
254#398C2314yes—
255#398C2318yes—
256#397C2318yes—
257#397C2314yes—
258#397C2318yes—
259#397C2318yes—
260#397C2318yes—
261#397C2318yes—
262#397C2318yes—
263#397C2318yes—
264#397C2318yes—
265#397C2318yes—
266#397C2318yes—
267#396C2318yes—
268#396C2318yes—
269#394C2318yes—
270#394C2314yes—
271#394C2318yes—
272#394C2318yes—
273#392C2314yes—
274#390C2314yes—
275#390C2318yes—
276#390C2314yes—
277#390C2314yes—
278#390C2318yes—
279#390C2314yes—
280#389C2314yes—
281#389C2314yes—
282#389C2318yes—
283#389C2314yes—
284#389C2314yes—
285#389C2314yes—
286#389C2314yes—
287#389C2318yes—
288#389C2314yes—
289#389C2314yes—
290#389C2318yes—
291#388C2318yes—
292#388C2318yes—
293#388C2318yes—
294#388C2318yes—
295#388C2318yes—
296#388C2318yes—
297#388C2318yes—
298#388C2318yes—
299#388C2318yes—
300#388C2318yes—
301#388C2318yes—
302#388C2318yes—
303#388C2318yes—
304#388C2318yes—
305#388C2318yes—
306#388C2318yes—
307#387C2318yes—
308#387C2318yes—
309#387C2318yes—
310#387C2318yes—
311#387C2318yes—
312#387C2318yes—
313#387C2318yes—
314#387C2318yes—
315#387C2318yes—
316#387C2318yes—
317#387C2318yes—
318#387C2318yes—
319#387C2318yes—
320#387C2318yes—
321#387C2318yes—
322#387C2318yes—
323#387C2318yes—
324#387C2318yes—
325#386C2318yes—
326#386C2318yes—
327#386C2314yes—
328#386C2314yes—
329#386C2318yes—
330#386C2314yes—
331#386C2318yes—
332#386C2318yes—
333#386C2314yes—
334#386C2314yes—
335#386C2318yes—
336#386C2318yes—
337#386C2318yes—
338#386C2318yes—
339#386C2318yes—
340#386C2318yes—
341#386C2314yes—
342#386C2314yes—
343#386C2314yes—
344#385C2318yes—
345#385C2318yes—
346#385C2318yes—
347#385C2318yes—
348#385C2318yes—
349#385C2314yes—
350#385C2318yes—
351#385C2318yes—
352#385C2318yes—
353#385C2318yes—
354#385C2314yes—
355#383C2318yes—
356#383C2318yes—
357#382C2314yes—
358#382C2318yes—
359#382C2318yes—
360#382C2314yes—
361#382C2314yes—
362#381C2314yes—
363#381C2314yes—
364#381C2318yes—
365#381C2318yes—
366#380C2312yes—
367#380C2312yes—
368#380C2318yes—
369#380C2318yes—
370#380C2318yes—
371#380C2318yes—
372#380C2314yes—
373#380C2312yes—
374#380C2312yes—
375#380C2312yes—
376#380C2314yes—
377#380C2312yes—
378#380C2312yes—
379#380C2318yes—
380#380C2318yes—
381#380C2312yes—
382#380C2314yes—
383#379C2314yes—
384#379C2314yes—
385C4×C4⋊C4C2318yes—
386C4×C4⋊C4C2314yes—
387C4×C4⋊C4C2314yes—
388C4×C4⋊C4C2318yes—
389C4×C4⋊C4C2314yes—
390C4×C4⋊C4C2314yes—
391C4×C4⋊C4C2314yes—
392C4×C4⋊C4C2318yes—
393C4×C4⋊C4C2314yes—
394C4×C4⋊C4C2314yes—
395C4×C4⋊C4C2314yes—
396C4×C4⋊C4C2314yes—
397C4×C22⋊C4C2312yes—
398C4×C22⋊C4C2312yes—
399C4×C22⋊C4C2318yes—
400C4×C22⋊C4C2314yes—
401C4×C22⋊C4C2314yes—
402C4×C22⋊C4C2314yes—
403C4×C22⋊C4C2318yes—
404C4×C22⋊C4C2312yes—
405C4×C22⋊C4C2314yes—
406C4×C22⋊C4C2312yes—
407C4×C22⋊C4C2318yes—
408C4×C22⋊C4C2318yes—
409C4×C22⋊C4C2312yes—
410C4×C22⋊C4C2312yes—
411C4×C22⋊C4C2312yes—
412C4×C22⋊C4C2312yes—
413C4×C22⋊C4C2318yes—
414C4×C22⋊C4C2318yes—
415C4×C22⋊C4C2314yes—
416C4×C22⋊C4C2314yes—
417C4×C22⋊C4C2312yes—
418C4×C22⋊C4C2312yes—
419C4×C22⋊C4C2314yes—
420C4×C22⋊C4C2314yes—
421C4×C22⋊C4C2312yes—
422C4×C22⋊C4C2314yes—
423C4×C22⋊C4C2312yes—
424C4×C22⋊C4C2314yes—
425#376C2318yes—
426#376C2314yes—
427C2×#95C2312yes—
428C2×#95C2312yes—
429C2×#95C2314yes—
430C2×#95C2312yes—
431C2×#95C2314yes—
432C2×#95C2314yes—
433C2×#95C2314yes—
434C2×#95C2314yes—
435C2×#95C2312yes—
436C2×#95C2314yes—
437C2×#95C2314yes—
438C43C2314yes—
439C25C2412yes—
440C25C2411yescharacteristic
441C25C2411yescharacteristic
442C22×D4—24no—
443C22×D4—24no—
444C22×D4—28no—
445C22×D4—28no—
446C22×D4—28no—
447C22×D4—24no—
448C22×D4—44no—
449C22×D4#4118yes—
450C22×D4C2414yes—
451C22×D4C2414yes—
452C22×D4C2412yes—
453C22×D4C2412yes—
454C22×D4C2412yes—
455C22×D4C2418yes—
456C22×D4C2412yes—
457C23×C4—28no—
458C23×C4—24no—
459C23×C4—44no—
460C23×C4—44no—
461C23×C4—84no—
462C23×C4#4118yes—
463C23×C4C2412yes—
464C23×C4C2412yes—
465C23×C4C2411yescharacteristic
466C23×C4C2411yescharacteristic
467C23×C4C2411yescharacteristic
468C23×C4C2411yescharacteristic
469C23×C4C2412yes—
470C23×C4C2412yes—
471C23×C4C2411yescharacteristic
472C23×C4C2414yes—
473C23×C4C2414yes—
474C23×C4C2414yes—
475C23×C4C2412yes—
476C23×C4C2414yes—
477C23×C4C2411yescharacteristic
478C23×C4C2418yes—
479C23×C4C2414yes—
480C23×C4C2414yes—
481C23×C4C2412yes—
482C23×C4C2412yes—
483C23×C4C2412yes—
484C23×C4C2411yescharacteristic
485C23×C4C2411yescharacteristic
486C23×C4C2412yes—
487C23×C4C2411yescharacteristic
488#126—88no—
489#125—48no—
490#123—216no—
491#123—216no—
492#123—88no—
493#121—232no—
494#121—28no—
495#121—28no—
496#121—28no—
497#121—28no—
498#121—48no—
499#120—216no—
500#120—216no—
501C4×D4—216no—
502C4×D4—216no—
503C4×D4—28no—
504C4×D4—28no—
505C4×D4—28no—
506C4×D4—28no—
507C4×D4—216no—
508C4×D4—232no—
509C4×D4—216no—
510C4×D4—232no—
511C4×D4—48no—
512C4×D4—88no—
513#117—28no—
514#117—216no—
515#117—28no—
516#117—88no—
517C2×C4⋊C4—24no—
518C2×C4⋊C4—24no—
519C2×C4⋊C4—28no—
520C2×C4⋊C4—28no—
521C2×C4⋊C4—28no—
522C2×C4⋊C4—28no—
523C2×C4⋊C4—28no—
524C2×C4⋊C4—24no—
525C2×C4⋊C4—24no—
526C2×C4⋊C4—44no—
527C2×C4⋊C4—44no—
528C2×C4⋊C4—84no—
529C2×C4⋊C4—84no—
530C2×C4⋊C4C2412yes—
531C2×C4⋊C4C2412yes—
532C2×C4⋊C4C2412yes—
533C2×C4⋊C4C2414yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C2412yes—
536C2×C4⋊C4C2412yes—
537C2×C4⋊C4C2412yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2412yes—
540C2×C4⋊C4C2412yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2418yes—
545C2×C4⋊C4C2418yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2418yes—
548C2×C4⋊C4C2418yes—
549C2×C4⋊C4C2418yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2418yes—
553C2×C4⋊C4C2418yes—
554C2×C4⋊C4C2418yes—
555C2×C4⋊C4C2418yes—
556C2×C22⋊C4—24no—
557C2×C22⋊C4—28no—
558C2×C22⋊C4—24no—
559C2×C22⋊C4—24no—
560C2×C22⋊C4—28no—
561C2×C22⋊C4—24no—
562C2×C22⋊C4—28no—
563C2×C22⋊C4—24no—
564C2×C22⋊C4—28no—
565C2×C22⋊C4—216no—
566C2×C22⋊C4—28no—
567C2×C22⋊C4—84no—
568C2×C22⋊C4—84no—
569C2×C22⋊C4—84no—
570C2×C22⋊C4#4118yes—
571C2×C22⋊C4C2412yes—
572C2×C22⋊C4C2412yes—
573C2×C22⋊C4C2412yes—
574C2×C22⋊C4C2414yes—
575C2×C22⋊C4C2412yes—
576C2×C22⋊C4C2412yes—
577C2×C22⋊C4C2412yes—
578C2×C22⋊C4C2412yes—
579C2×C22⋊C4C2412yes—
580C2×C22⋊C4C2414yes—
581C2×C22⋊C4C2412yes—
582C2×C22⋊C4C2414yes—
583C2×C22⋊C4C2412yes—
584C2×C22⋊C4C2414yes—
585C2×C22⋊C4C2418yes—
586C2×C22⋊C4C2414yes—
587C2×C22⋊C4C2414yes—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2414yes—
590C2×C22⋊C4C2418yes—
591C2×C22⋊C4C2418yes—
592C2×C22⋊C4C2418yes—
593C2×C22⋊C4C2418yes—
594C2×C22⋊C4C2418yes—
595C2×C22⋊C4C2418yes—
596C2×C22⋊C4C2418yes—
597C2×C22⋊C4C2418yes—
598C2×C22⋊C4C2418yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2418yes—
601C2×C22⋊C4C2418yes—
602C2×C22⋊C4C2412yes—
603C2×C22⋊C4C2412yes—
604C2×C42—24no—
605C2×C42—44no—
606C2×C42—48no—
607C2×C42—44no—
608C2×C42—84no—
609C2×C42C2414yes—
610C2×C42C2414yes—
611C2×C42C2418yes—
612C2×C42C2412yes—
613C2×C42C2412yes—
614C2×C42C2414yes—
615C2×C42C2414yes—
616C2×C42C2414yes—
617C2×C42C2418yes—
618C2×C42C2418yes—
619C2×C42C2414yes—
620C2×C42C2414yes—
621C2×C42C2414yes—
622C2×C42C2414yes—
623C2×C42C2414yes—
624#95C2414yes—
625#95C2414yes—
626#95C2418yes—
627#95C2418yes—
628#95C2414yes—
629#95C2414yes—
630#95C2414yes—
631#95C2414yes—
632#95C2414yes—
633#95C2418yes—
634#95C2418yes—
635#95C2418yes—
636#95C2418yes—
637#95C2418yes—
638#95C2418yes—
639#95C2418yes—
640#95C2414yes—
641#95C2414yes—
642#95C2414yes—
643#95C2418yes—
644#95C2418yes—
645#95C2418yes—
646#95C2414yes—
647#95C2414yes—
648#95C2418yes—
649#95C2418yes—
650#95C2418yes—
651#95C2418yes—
652#95C2418yes—
653#95C2418yes—
654#95C2418yes—
655#95C2418yes—
656C24—22no—
657C24—22no—
658C24—24no—
659C24—24no—
660C24—24no—
661C24—42no—
662C24—42no—
663C24—42no—
664C24—42no—
665C24—44no—
666C24—44no—
667C24C2×#4114yes—
668C24C2×#4114yes—
669C24C2×#4114yes—
670C24C2×#4114yes—
671C24C2514yes—
672C24C2512yes—
673C24C2511yescharacteristic
674C24C2511yescharacteristic
675C24C2511yescharacteristic
676C2×D4—232no—
677C2×D4—24no—
678C2×D4—24no—
679C2×D4—24no—
680C2×D4—24no—
681C2×D4—28no—
682C2×D4—28no—
683C2×D4—28no—
684C2×D4—28no—
685C2×D4—28no—
686C2×D4—28no—
687C2×D4—216no—
688C2×D4—24no—
689C2×D4—24no—
690C2×D4—28no—
691C2×D4—48no—
692C2×D4—48no—
693C2×D4—44no—
694C2×D4—432no—
695C2×D4—88no—
696C2×D4C2×#4118yes—
697C2×D4C2×#4118yes—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—24no—
701C22×C4—24no—
702C22×C4—24no—
703C22×C4—24no—
704C22×C4—24no—
705C22×C4—24no—
706C22×C4—24no—
707C22×C4—24no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—28no—
711C22×C4—24no—
712C22×C4—24no—
713C22×C4—28no—
714C22×C4—24no—
715C22×C4—28no—
716C22×C4—28no—
717C22×C4—28no—
718C22×C4—24no—
719C22×C4—28no—
720C22×C4—28no—
721C22×C4—216no—
722C22×C4—24no—
723C22×C4—416no—
724C22×C4—42no—
725C22×C4—42no—
726C22×C4—44no—
727C22×C4—44no—
728C22×C4—42no—
729C22×C4—42no—
730C22×C4—42no—
731C22×C4—44no—
732C22×C4—42no—
733C22×C4—44no—
734C22×C4—42no—
735C22×C4—42no—
736C22×C4—44no—
737C22×C4—42no—
738C22×C4—42no—
739C22×C4—44no—
740C22×C4—44no—
741C22×C4—44no—
742C22×C4—44no—
743C22×C4—44no—
744C22×C4—44no—
745C22×C4—42no—
746C22×C4—42no—
747C22×C4—44no—
748C22×C4—48no—
749C22×C4—48no—
750C22×C4—44no—
751C22×C4—44no—
752C22×C4—44no—
753C22×C4—42no—
754C22×C4—88no—
755C22×C4—816no—
756C22×C4C2×#4114yes—
757C22×C4C2×#4114yes—
758C22×C4C2×#4114yes—
759C22×C4C2×#4114yes—
760C22×C4C2×#4114yes—
761C22×C4C2×#4114yes—
762C22×C4C2×#4118yes—
763C22×C4C2×#4114yes—
764C22×C4C2512yes—
765C22×C4C2514yes—
766C22×C4C2514yes—
767C22×C4C2514yes—
768C22×C4C2514yes—
769C22×C4C2514yes—
770C22×C4C2518yes—
771C22×C4C2518yes—
772C22×C4C2514yes—
773C22×C4C2512yes—
774C22×C4C2511yescharacteristic
775C22×C4C2511yescharacteristic
776C22×C4C2514yes—
777C22×C4C2512yes—
778C22×C4C2511yescharacteristic
779C22×C4C2511yescharacteristic
780C4⋊C4—28no—
781C4⋊C4—24no—
782C4⋊C4—24no—
783C4⋊C4—28no—
784C4⋊C4—24no—
785C4⋊C4—24no—
786C4⋊C4—24no—
787C4⋊C4—24no—
788C4⋊C4—24no—
789C4⋊C4—24no—
790C4⋊C4—28no—
791C4⋊C4—216no—
792C4⋊C4—28no—
793C4⋊C4—216no—
794C4⋊C4—28no—
795C4⋊C4—28no—
796C4⋊C4—44no—
797C4⋊C4—44no—
798C4⋊C4—48no—
799C4⋊C4—48no—
800C4⋊C4—48no—
801C4⋊C4—48no—
802C4⋊C4—48no—
803C4⋊C4—48no—
804C4⋊C4—48no—
805C4⋊C4—48no—
806C22⋊C4—24no—
807C22⋊C4—24no—
808C22⋊C4—28no—
809C22⋊C4—24no—
810C22⋊C4—24no—
811C22⋊C4—24no—
812C22⋊C4—28no—
813C22⋊C4—24no—
814C22⋊C4—24no—
815C22⋊C4—28no—
816C22⋊C4—24no—
817C22⋊C4—28no—
818C22⋊C4—28no—
819C22⋊C4—216no—
820C22⋊C4—24no—
821C22⋊C4—24no—
822C22⋊C4—28no—
823C22⋊C4—216no—
824C22⋊C4—28no—
825C22⋊C4—28no—
826C22⋊C4—216no—
827C22⋊C4—48no—
828C22⋊C4—48no—
829C22⋊C4—48no—
830C22⋊C4—48no—
831C22⋊C4—48no—
832C22⋊C4—48no—
833C22⋊C4—48no—
834C22⋊C4—48no—
835C22⋊C4—48no—
836C22⋊C4—48no—
837C22⋊C4C2×#4118yes—
838C22⋊C4C2×#4118yes—
839C42—24no—
840C42—24no—
841C42—28no—
842C42—216no—
843C42—28no—
844C42—28no—
845C42—28no—
846C42—44no—
847C42—44no—
848C42—44no—
849C42—44no—
850C42—48no—
851C42—48no—
852C42—44no—
853C42—44no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—24no—
863C23—24no—
864C23—28no—
865C23—24no—
866C23—24no—
867C23—24no—
868C23—28no—
869C23—28no—
870C23—44no—
871C23—44no—
872C23—48no—
873C23—48no—
874C23—48no—
875C23—48no—
876C23—82no—
877C23—84no—
878C23—82no—
879C23—84no—
880C23—88no—
881C23—88no—
882C23—84no—
883C23#529116yes—
884C23C22×#4114yes—
885C23C22×#4112yes—
886C23C22×#4112yes—
887C23C22×#4112yes—
888C23C22×#4112yes—
889C23C22×#4112yes—
890C23C22×#4112yes—
891C23C22×#4112yes—
892C23C22×#4112yes—
893C23C22×#4112yes—
894C23C2611yescharacteristic
895D4—216no—
896D4—216no—
897D4—416no—
898D4—416no—
899D4—48no—
900D4—84no—
901D4—816no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—24no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—24no—
909C2×C4—28no—
910C2×C4—28no—
911C2×C4—28no—
912C2×C4—28no—
913C2×C4—22no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—28no—
919C2×C4—28no—
920C2×C4—22no—
921C2×C4—24no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—24no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—28no—
930C2×C4—28no—
931C2×C4—24no—
932C2×C4—24no—
933C2×C4—24no—
934C2×C4—28no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—24no—
938C2×C4—24no—
939C2×C4—28no—
940C2×C4—24no—
941C2×C4—44no—
942C2×C4—44no—
943C2×C4—44no—
944C2×C4—48no—
945C2×C4—48no—
946C2×C4—48no—
947C2×C4—48no—
948C2×C4—48no—
949C2×C4—88no—
950C2×C4—816no—
951C2×C4—84no—
952C2×C4—84no—
953C2×C4—88no—
954C2×C4—84no—
955C2×C4—84no—
956C2×C4—88no—
957C2×C4—88no—
958C2×C4—82no—
959C2×C4—82no—
960C2×C4—88no—
961C2×C4—88no—
962C2×C4C22×#4118yes—
963C2×C4C22×#4114yes—
964C2×C4C22×#4112yes—
965C2×C4C22×#4112yes—
966C2×C4C22×#4112yes—
967C2×C4C22×#4112yes—
968C2×C4#58514yes—
969C22—24no—
970C22—24no—
971C22—24no—
972C22—24no—
973C22—24no—
974C22—24no—
975C22—22no—
976C22—22no—
977C22—22no—
978C22—22no—
979C22—22no—
980C22—22no—
981C22—28no—
982C22—24no—
983C22—416no—
984C22—44no—
985C22—42no—
986C22—42no—
987C22—48no—
988C22—48no—
989C22—44no—
990C22—44no—
991C22—44no—
992C22—88no—
993C22—168no—
994C22C2×#52914yes—
995C22C2×#52914yes—
996C22C2×#52914yes—
997C22C23×#4111yescharacteristic
998C22C23×#4111yescharacteristic
999C22C23×#4111yescharacteristic
1000C22C2×#58512yes—
1001C22H(7,𝔽2)12yes—
1002C4—28no—
1003C4—22no—
1004C4—22no—
1005C4—22no—
1006C4—24no—
1007C4—44no—
1008C4—48no—
1009C4—44no—
1010C4—44no—
1011C4—48no—
1012C4—42no—
1013C4—44no—
1014C4—44no—
1015C4—42no—
1016C4—44no—
1017C4#349114yes—
1018C2—24no—
1019C2—24no—
1020C2—24no—
1021C2—44no—
1022C2—84no—
1023C2C22×#52911yescharacteristic
1024C2C2×#349111yescharacteristic
1025C2#6285511yescharacteristic
1026C2#6299212yes—
1027C2#6299212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35000C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36294C2semidirect
2. #36291C2semidirect
3. #36171C2semidirect
4. #36168C2semidirect
5. #36034C2semidirect
6. #35848C2semidirect
7. #35837C2semidirect
8. #35388C2semidirect
9. #35370C2semidirect
10. #35360C2semidirect
11. #35029C2semidirect
12. #35020C2semidirect
14. #34788C2semidirect
15. C2×#2504C2semidirect
16. C2×#2487C2semidirect
17. #34273C2semidirect
18. #34251C2semidirect
19. #34205C2semidirect
20. C2×#2345C2semidirect
21. C4×#518C2semidirect
29. #2864C22semidirect
30. #2860C22semidirect
32. #2854C22semidirect
33. #2851C22semidirect
34. #2851C22semidirect
36. #2654C22semidirect
37. #2649C22semidirect
38. #2646C22semidirect
41. #2596C22semidirect
42. #2595C22semidirect
43. #2578C22semidirect
44. #2575C22semidirect
45. #2573C22semidirect
46. #2569C22semidirect
47. #2569C22semidirect
48. #2553C22semidirect
51. #2531C22semidirect
52. #2530C22semidirect
53. #2529C22semidirect
54. #2528C22semidirect
55. #2525C22semidirect
56. #2524C22semidirect
57. #2517C22semidirect
58. #2516C22semidirect
59. #2516C22semidirect
60. #2513C22semidirect
61. #2510C22semidirect
62. #2510C22semidirect
63. #2510C22semidirect
64. #2509C22semidirect
65. #2508C22semidirect
68. #2504C22semidirect
69. #2504C22semidirect
70. #2504C22semidirect
71. #2498C22semidirect
72. #2495C22semidirect
73. #2494C22semidirect
74. #2493C22semidirect
75. #2490C22semidirect
78. #2487C22semidirect
79. #2487C22semidirect
80. #2487C22semidirect
82. #2481C22semidirect
83. #2481C22semidirect
84. #2480C22semidirect
85. #2478C22semidirect
86. #2471C22semidirect
87. #2467C22semidirect
88. #2454C22semidirect
89. #2444C22semidirect
90. #2443C22semidirect
91. #2442C22semidirect
92. #2442C22semidirect
93. #2420C22semidirect
95. #2419C22semidirect
98. #2412C22semidirect
100. #2401C22semidirect
101. #2395C22semidirect
102. C2×#400C22semidirect
103. C2×#399C22semidirect
104. C2×#397C22semidirect
108. #2359C22semidirect
110. #2358C22semidirect
111. #2353C22semidirect
112. #2352C22semidirect
113. #2345C22semidirect
114. #2345C22semidirect
115. #2345C22semidirect
116. #2345C22semidirect
117. #2344C22semidirect
118. #2343C22semidirect
119. #2342C22semidirect
120. #2342C22semidirect
121. D4×C22⋊C4C22semidirect
122. #2325C22semidirect
123. #2325C22semidirect
124. #2318C22semidirect
129. C4×#125C22semidirect
130. C4×#121C22semidirect
131. C4×#121C22semidirect
132. C4×#121C22semidirect
133. #2293C22semidirect
134. C2×#390C22semidirect
135. C2×#389C22semidirect
136. C2×#389C22semidirect
137. #2290C22semidirect
138. C2×#387C22semidirect
143. #2283C22semidirect
144. C2×#382C22semidirect
148. C2×#380C22semidirect
150. #2275C22semidirect
151. #2274C22semidirect
154. #2273C22semidirect
156. C42×D4C22semidirect
157. C4×#117C22semidirect
158. C2×C4×C4⋊C4C22semidirect
162. C2×C4×C22⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#362942
#362912
#361712
#361682
#360342
#358482
#358372
#353882
#353702
#353602
#350292
#350202
#350002
#347882
C2×#25042
C2×#24872
#342732
#342512
#342052
C2×#23452
C4×#5182