Finite Group Databasebeta

← #7625760

Subgroups — #7625760

Order 512.

7326 conjugacy classes of subgroups.

The subgroup lattice has 1127 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3510C211yesmaximal, characteristic
2#34331C214yesmaximal, complemented
3#34329C214yesmaximal, complemented
4#34326C214yesmaximal, complemented
5#34324C214yesmaximal, complemented
6#34303C218yesmaximal, complemented
7#34296C218yesmaximal, complemented
8#34279C214yesmaximal, complemented
9#34269C211yesmaximal, characteristic
10#34268C211yesmaximal, characteristic, complemented
11#34255C211yesmaximal, characteristic, complemented
12#34254C211yesmaximal, characteristic, complemented
13#34220C214yesmaximal, complemented
14#34214C211yesmaximal, characteristic, complemented
15#34211C211yesmaximal, characteristic, complemented
16#34188C211yesmaximal, characteristic, complemented
17C4×#542C214yesmaximal, complemented
18C4×#536C211yesmaximal, characteristic, complemented
19C4×#535C211yesmaximal, characteristic
20#34084C214yesmaximal, complemented
21#34074C211yesmaximal, characteristic, complemented
22C2×#2326C211yesmaximal, characteristic, complemented
23C4×#519C211yesmaximal, characteristic, complemented
24C4×#518C211yesmaximal, characteristic, complemented
25#33999C211yesmaximal, characteristic, complemented
26#3510C4132yescomplemented
27C2×#559C2214yes—
28C2×#556C2214yes—
29C2×#551C2218yes—
30C2×#542C2214yes—
31C2×#536C2211yescharacteristic
32C2×#535C2211yescharacteristic
33C2×#533C2211yescharacteristic
34C2×#529C2214yes—
35C22×#124C2211yescharacteristic
36C2×#519C2211yescharacteristic
37C2×#519C2211yescharacteristic
38C2×#518C2211yescharacteristic
39C2×#518C2211yescharacteristic
40C2×C4×#41C2211yescharacteristic
41C2×C4×#41C2211yescharacteristic
42C2×C4×#41C2211yescharacteristic
43C22×C4×Q8C2211yescharacteristic
44C22×C4×D4C2211yescharacteristic
45#2374C2218yescomplemented
46#2373C2218yescomplemented
47#2373C2218yescomplemented
48#2373C2218yescomplemented
49#2373C2218yescomplemented
50#2372C2218yescomplemented
51#2368C2218yescomplemented
52#2367C2214yes—
53#2367C2214yes—
54#2367C2214yes—
55#2367C2214yescomplemented
56#2367C2218yescomplemented
57#2366C2214yes—
58#2365C2214yescomplemented
59#2362C2218yescomplemented
60#2360C2218yes—
61#2359C2218yes—
62#2359C2218yescomplemented
63#2359C2218yescomplemented
64#2359C2218yescomplemented
65#2358C2218yes—
66#2357C2214yes—
67#2356C2214yescomplemented
68#2355C2214yescomplemented
69#2355C2214yescomplemented
70#2355C2214yescomplemented
71#2354C2214yes—
72#2354C2214yescomplemented
73#2353C2218yescomplemented
74#2352C2218yes—
75Q8×C4⋊C4C2214yescomplemented
76#2349C2218yescomplemented
77#2346C2218yescomplemented
78#2343C2218yes—
79#2343C2218yescomplemented
80#2342C2218yes—
81#2342C2218yes—
82#2337C2218yescomplemented
83#2335C2218yescomplemented
84#2335C2218yescomplemented
85#2335C2218yescomplemented
86#2334C2218yescomplemented
87#2334C2218yescomplemented
88#2334C2218yescomplemented
89#2332C2218yescomplemented
90#2331C2212yescomplemented
91#2331C2212yescomplemented
92#2330C2212yescomplemented
93#2330C2212yescomplemented
94#2330C2214yescomplemented
95#2329C2214yes—
96#2329C2214yes—
97#2328C2212yes—
98#2327C2212yescomplemented
99#2326C2214yes—
100#2326C2214yes—
101#2326C2212yes—
102#2326C2212yes—
103#2326C2212yes—
104#2326C2212yes—
105#2326C2212yes—
106#2326C2214yes—
107#2326C2212yescomplemented
108#2324C2214yes—
109#2324C2214yes—
110#2323C2214yescomplemented
111#2323C2214yescomplemented
112#2322C2214yes—
113#2321C2214yes—
114#2320C2214yescomplemented
115#2319C2214yes—
116#2317C2211yescharacteristic
117#2317C2211yescharacteristic
118#2314C2214yescomplemented
119#2311C2211yescharacteristic
120#2311C2211yescharacteristic
121#2310C2211yescharacteristic
122#2309C2211yescharacteristic
123C4×C4⋊Q8C2212yescomplemented
124C4×C4⋊Q8C2214yescomplemented
125C4×#127C2212yes—
126C4×#126C2218yescomplemented
127C4×#124C2212yes—
128C4×#124C2214yes—
129C4×#124C2212yescomplemented
130C4×#124C2218yescomplemented
131C4×C22⋊Q8C2218yescomplemented
132C4×C22⋊Q8C2214yescomplemented
133C4×C22⋊Q8C2214yescomplemented
134C4×#123C2214yes—
135C4×#123C2218yescomplemented
136C4×#121C2214yes—
137C4×#121C2214yes—
138C4×#120C2214yes—
139#2298C2218yescomplemented
140#2296C2211yescharacteristic
141#2296C2211yescharacteristic
142#2296C2218yescomplemented
143#2295C2214yescomplemented
144#2295C2214yescomplemented
145#2295C2214yescomplemented
146C2×#391C2211yescharacteristic
147#2293C2214yes—
148#2293C2218yescomplemented
149C2×#390C2211yescharacteristic
150#2290C2218yescomplemented
151C2×#388C2214yes—
152C2×#385C2214yes—
153#2285C2211yescharacteristic
154#2285C2214yescomplemented
155C2×#384C2211yescharacteristic
156#2276C2212yescomplemented
157#2276C2214yescomplemented
158#2276C2212yescomplemented
159#2276C2214yescomplemented
160#2275C2214yes—
161#2275C2214yes—
162#2275C2214yes—
163#2275C2214yes—
164#2275C2212yescomplemented
165#2275C2212yescomplemented
166#2274C2211yescharacteristic
167#2274C2211yescharacteristic
168#2274C2211yescharacteristic
169#2274C2211yescharacteristic
170#2274C2214yes—
171#2273C2214yes—
172C42×Q8C2214yescomplemented
173C42×Q8C2214yescomplemented
174C42×D4C2214yes—
175C42×D4C2214yes—
176C4×#117C2211yescharacteristic
177C4×#117C2211yescharacteristic
178C4×#117C2211yescharacteristic
179C4×#117C2211yescharacteristic
180C4×#117C2211yescharacteristic
181C4×#117C2214yes—
182C4×#117C2212yescomplemented
183C4×#117C2212yescomplemented
184C4×#117C2212yescomplemented
185C2×C4×C22⋊C4C2214yes—
186C2×#376C2211yescharacteristic
187C2×#376C2212yescomplemented
188C22×#41C2311yescharacteristic
189C23×Q8C2311yescharacteristic
190C23×D4C2311yescharacteristic
191C24×C4C2312yes—
192#559C2×C4164yescomplemented
193#556C2×C4164yescomplemented
194#551C2×C41128yescomplemented
195#542C2×C4164yescomplemented
196#536C2×C4116yescomplemented
197#535C2×C4116yes—
198#533C2×C4116yescomplemented
199C2×C4⋊Q8C2312yes—
200C2×C4⋊Q8C2312yes—
201C2×#127C2312yes—
202#529C2×C4164yescomplemented
203C2×#126C2318yes—
204C2×#126C2318yes—
205C2×#125C2312yes—
206C2×#124C2×C4116yescomplemented
207C2×#124C2312yes—
208C2×#124C2314yes—
209C2×#124C2312yes—
210C2×#124C2312yes—
211C2×#124C2312yes—
212C2×#124C2318yes—
213C2×#123C2314yes—
214C2×#123C2318yes—
215C2×#123C2318yes—
216C2×C22⋊Q8C2314yes—
217C2×C22⋊Q8C2314yes—
218C2×C22⋊Q8C2318yes—
219C2×#121C2314yes—
220C2×#120C2314yes—
221#519—28no—
222#519C2×C4116yescomplemented
223#518—28no—
224#518C2×C4116yescomplemented
225C4×#41—28no—
226C4×#41—28no—
227C4×#41C2×C4116yescomplemented
228C2×C4×Q8—28no—
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2312yes—
231C2×C4×Q8C2312yes—
232C2×C4×Q8C2314yes—
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2314yes—
238C2×C4×Q8C2318yes—
239C2×C4×Q8C2314yes—
240C2×C4×Q8C2314yes—
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2314yes—
243C2×C4×D4—28no—
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2312yes—
246C2×C4×D4C2312yes—
247C2×C4×D4C2312yes—
248C2×C4×D4C2312yes—
249C2×C4×D4C2314yes—
250C2×C4×D4C2312yes—
251C2×C4×D4C2312yes—
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2314yes—
254C2×C4×D4C2312yes—
255C2×C4×D4C2314yes—
256C2×C4×D4C2318yes—
257C2×C4×D4C2318yes—
258C2×C4×D4C2314yes—
259C2×C4×D4C2314yes—
260C2×C4×D4C2314yes—
261C2×C4×D4C2318yes—
262C2×C4×D4C2312yes—
263C2×#117C2311yescharacteristic
264C2×#117C2311yescharacteristic
265C2×#117C2311yescharacteristic
266C2×#117C2312yes—
267C2×#117C2312yes—
268C2×#117C2314yes—
269C2×#117C2318yes—
270C2×#117C2318yes—
271C2×#117C2311yescharacteristic
272C2×#117C2311yescharacteristic
273C2×#117C2314yes—
274C2×#117C2311yescharacteristic
275C2×#117C2312yes—
276C2×#117C2318yes—
277C2×#117C2311yescharacteristic
278C22×C4⋊C4C2311yescharacteristic
279C22×C4⋊C4C2311yescharacteristic
280C22×C4⋊C4C2312yes—
281C22×C4⋊C4C2314yes—
282C22×C22⋊C4C2312yes—
283C22×C22⋊C4C2314yes—
284C22×C22⋊C4C2314yes—
285C22×C22⋊C4C2314yes—
286C22×C22⋊C4C2314yes—
287C22×C42C2312yes—
288C22×C42C2311yescharacteristic
289C22×C42C2312yes—
290C22×C42C2312yes—
291C22×C42C2318yes—
292C22×C42C2311yescharacteristic
293C22×C42C2312yes—
294C22×C42C2311yescharacteristic
295#391C2312yes—
296#391C2312yes—
297#391C2318yes—
298#391C2314yes—
299#391C2312yes—
300#391C2312yes—
301#391C2312yes—
302#391C2312yes—
303#391C2314yes—
304#391C2314yes—
305#391C2314yes—
306#391C2314yes—
307#391C2314yes—
308#390C2312yes—
309#390C2312yes—
310#390C2318yes—
311#390C2314yes—
312#390C2312yes—
313#390C2312yes—
314#390C2312yes—
315#390C2312yes—
316#390C2318yes—
317#390C2314yes—
318#389C2314yes—
319#389C2314yes—
320#389C2318yes—
321#389C2318yes—
322#389C2312yes—
323#389C2312yes—
324#389C2312yes—
325#389C2318yes—
326#389C2312yes—
327#389C2314yes—
328#389C2314yes—
329#389C2314yes—
330#389C2314yes—
331#389C2318yes—
332#389C2318yes—
333#388C2318yes—
334#388C2318yes—
335#388C2318yes—
336#388C2318yes—
337#388C2318yes—
338#388C2318yes—
339#388C2318yes—
340#388C2318yes—
341#388C2318yes—
342#388C2318yes—
343#388C2318yes—
344#388C2318yes—
345#388C2318yes—
346#388C2318yes—
347#388C2318yes—
348#388C2318yes—
349#388C2318yes—
350#388C2318yes—
351#388C2318yes—
352#388C2318yes—
353#388C2318yes—
354#388C2318yes—
355#387C2314yes—
356#387C2318yes—
357#387C2318yes—
358#387C2318yes—
359#387C2318yes—
360#387C2318yes—
361#387C2318yes—
362#387C2318yes—
363#387C2314yes—
364#387C2314yes—
365#387C2314yes—
366#387C2314yes—
367#387C2314yes—
368#387C2314yes—
369#387C2314yes—
370#387C2318yes—
371#387C2318yes—
372#387C2318yes—
373#387C2318yes—
374#387C2318yes—
375#386C2314yes—
376#386C2314yes—
377#386C2318yes—
378#386C2318yes—
379#386C2318yes—
380#386C2318yes—
381#385C2314yes—
382#385C2314yes—
383#385C2318yes—
384#385C2318yes—
385#385C2318yes—
386#385C2318yes—
387#385C2318yes—
388#385C2318yes—
389#385C2318yes—
390#385C2318yes—
391#385C2318yes—
392#385C2314yes—
393#385C2314yes—
394#385C2318yes—
395#384C2312yes—
396#384C2312yes—
397#384C2312yes—
398#384C2312yes—
399#384C2312yes—
400#384C2314yes—
401#383C2318yes—
402#382C2312yes—
403#382C2312yes—
404#382C2312yes—
405#382C2318yes—
406#382C2318yes—
407#381C2314yes—
408#381C2318yes—
409#380C2314yes—
410#380C2314yes—
411#380C2318yes—
412#380C2314yes—
413#380C2318yes—
414#379C2314yes—
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2318yes—
417C4×C4⋊C4C2318yes—
418C4×C4⋊C4C2314yes—
419C4×C4⋊C4C2314yes—
420C4×C4⋊C4C2318yes—
421C4×C4⋊C4C2314yes—
422C4×C4⋊C4C2314yes—
423C4×C4⋊C4C2312yes—
424C4×C4⋊C4C2312yes—
425C4×C4⋊C4C2312yes—
426C4×C4⋊C4C2312yes—
427C4×C4⋊C4C2318yes—
428C4×C4⋊C4C2314yes—
429C4×C4⋊C4C2314yes—
430C4×C4⋊C4C2314yes—
431C4×C4⋊C4C2318yes—
432C4×C4⋊C4C2318yes—
433C4×C4⋊C4C2318yes—
434C4×C4⋊C4C2318yes—
435C4×C4⋊C4C2312yes—
436C4×C4⋊C4C2314yes—
437C4×C4⋊C4C2314yes—
438C4×C4⋊C4C2318yes—
439C4×C4⋊C4C2312yes—
440C4×C4⋊C4C2314yes—
441C4×C4⋊C4C2314yes—
442C4×C4⋊C4C2314yes—
443C4×C4⋊C4C2314yes—
444C4×C4⋊C4C2312yes—
445C4×C4⋊C4C2314yes—
446C4×C4⋊C4C2312yes—
447C4×C4⋊C4C2318yes—
448C4×C4⋊C4C2318yes—
449C4×C4⋊C4C2314yes—
450C4×C4⋊C4C2314yes—
451C4×C4⋊C4C2312yes—
452C4×C4⋊C4C2312yes—
453C4×C22⋊C4C2318yes—
454C4×C22⋊C4C2318yes—
455C4×C22⋊C4C2318yes—
456C4×C22⋊C4C2312yes—
457C4×C22⋊C4C2312yes—
458C4×C22⋊C4C2312yes—
459C4×C22⋊C4C2312yes—
460C4×C22⋊C4C2318yes—
461C4×C22⋊C4C2318yes—
462C4×C22⋊C4C2314yes—
463C4×C22⋊C4C2314yes—
464C4×C22⋊C4C2314yes—
465C4×C22⋊C4C2314yes—
466C4×C22⋊C4C2314yes—
467C4×C22⋊C4C2314yes—
468C4×C22⋊C4C2314yes—
469C4×C22⋊C4C2318yes—
470C4×C22⋊C4C2318yes—
471C4×C22⋊C4C2314yes—
472C4×C22⋊C4C2318yes—
473C4×C22⋊C4C2318yes—
474C4×C22⋊C4C2318yes—
475C4×C22⋊C4C2318yes—
476C4×C22⋊C4C2314yes—
477C4×C22⋊C4C2314yes—
478C4×C22⋊C4C2314yes—
479C4×C22⋊C4C2318yes—
480C4×C22⋊C4C2318yes—
481C4×C22⋊C4C2314yes—
482C4×C22⋊C4C2312yes—
483C4×C22⋊C4C2312yes—
484#376C2312yes—
485#376C2311yescharacteristic
486#376C2311yescharacteristic
487#376C2312yes—
488#376C2311yescharacteristic
489#376C2311yescharacteristic
490#376C2312yes—
491#376C2312yes—
492#376C2312yes—
493#376C2312yes—
494#376C2318yes—
495#376C2314yes—
496#376C2314yes—
497#376C2318yes—
498#376C2312yes—
499C2×#95C2312yes—
500C2×#95C2312yes—
501C2×#95C2314yes—
502C2×#95C2318yes—
503C2×#95C2314yes—
504C2×#95C2314yes—
505C43C2318yes—
506C43C2312yes—
507C43C2312yes—
508C43C2312yes—
509C43C2312yes—
510C43C2312yes—
511C25C2412yes—
512C2×#41—24no—
513C2×#41—24no—
514C2×#41C22×C418yes—
515C22×Q8—24no—
516C22×Q8—24no—
517C22×Q8C22×C418yes—
518C22×Q8C2412yes—
519C22×Q8C2412yes—
520C22×Q8C2411yescharacteristic
521C22×Q8C2414yes—
522C22×D4—24no—
523C22×D4—24no—
524C22×D4C22×C418yes—
525C22×D4C2412yes—
526C22×D4C2412yes—
527C22×D4C2412yes—
528C22×D4C2411yescharacteristic
529C22×D4C2418yes—
530C23×C4—28no—
531C23×C4—84no—
532C23×C4C2412yes—
533C23×C4C2412yes—
534C23×C4C2412yes—
535C23×C4C2412yes—
536C23×C4C2412yes—
537C23×C4C2418yes—
538C23×C4C2412yes—
539C23×C4C2414yes—
540C23×C4C2414yes—
541C23×C4C2414yes—
542C23×C4C2412yes—
543C23×C4C2412yes—
544C23×C4C2418yes—
545C23×C4C2414yes—
546C23×C4C2411yescharacteristic
547C23×C4C2411yescharacteristic
548C23×C4C2411yescharacteristic
549C4⋊Q8C22×C4116yescomplemented
550C4⋊Q8C22×C4116yescomplemented
551#127C22×C4116yes—
552#126C22×C4164yescomplemented
553#126C22×C4164yescomplemented
554#125C22×C4116yescomplemented
555#124C22×C4116yes—
556#124C22×C4116yes—
557#124C22×C4132yes—
558#124C22×C4116yes—
559#124C22×C4116yescomplemented
560#124C22×C4164yescomplemented
561#123C22×C4132yes—
562#123C22×C4164yescomplemented
563#123C22×C4164yescomplemented
564C22⋊Q8C22×C4132yes—
565C22⋊Q8C22×C4132yescomplemented
566C22⋊Q8C22×C4164yescomplemented
567#121C22×C4132yes—
568#120C22×C4132yes—
569C4×Q8—28no—
570C4×Q8—216no—
571C4×Q8—28no—
572C4×Q8—28no—
573C4×Q8—28no—
574C4×Q8—28no—
575C4×Q8—24no—
576C4×Q8—24no—
577C4×Q8—216no—
578C4×Q8—88no—
579C4×Q8C22×C4116yescomplemented
580C4×Q8C22×C4132yescomplemented
581C4×Q8C22×C4132yescomplemented
582C4×Q8C22×C4132yescomplemented
583C4×D4—28no—
584C4×D4—28no—
585C4×D4—28no—
586C4×D4—216no—
587C4×D4—216no—
588C4×D4—28no—
589C4×D4—28no—
590C4×D4—28no—
591C4×D4—28no—
592C4×D4—24no—
593C4×D4—24no—
594C4×D4—216no—
595C4×D4—88no—
596C4×D4—88no—
597C4×D4C22×C4132yes—
598C4×D4C22×C4132yes—
599C4×D4C22×C4132yes—
600C4×D4C22×C4116yescomplemented
601C4×D4C22×C4164yescomplemented
602#117—24no—
603#117—24no—
604#117—24no—
605#117—216no—
606#117—28no—
607#117—28no—
608#117—88no—
609#117—88no—
610#117C22×C418yes—
611#117C22×C418yes—
612#117C22×C418yes—
613#117C22×C4132yes—
614#117C22×C4116yescomplemented
615#117C22×C4164yescomplemented
616#117#4118yes—
617C2×C4⋊C4—24no—
618C2×C4⋊C4—28no—
619C2×C4⋊C4—24no—
620C2×C4⋊C4—84no—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2418yes—
635C2×C4⋊C4C2418yes—
636C2×C4⋊C4C2418yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2418yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2412yes—
655C2×C22⋊C4—28no—
656C2×C22⋊C4—216no—
657C2×C22⋊C4—84no—
658C2×C22⋊C4C22×C4132yes—
659C2×C22⋊C4C22×C4132yes—
660C2×C22⋊C4C2412yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2418yes—
663C2×C22⋊C4C2414yes—
664C2×C22⋊C4C2412yes—
665C2×C22⋊C4C2412yes—
666C2×C22⋊C4C2412yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2412yes—
669C2×C22⋊C4C2418yes—
670C2×C22⋊C4C2418yes—
671C2×C22⋊C4C2418yes—
672C2×C22⋊C4C2418yes—
673C2×C22⋊C4C2418yes—
674C2×C22⋊C4C2418yes—
675C2×C22⋊C4C2412yes—
676C2×C22⋊C4C2412yes—
677C2×C22⋊C4C2418yes—
678C2×C22⋊C4C2418yes—
679C2×C22⋊C4C2418yes—
680C2×C22⋊C4C2412yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2418yes—
683C2×C22⋊C4C2418yes—
684C2×C22⋊C4C2412yes—
685C2×C42—28no—
686C2×C42—24no—
687C2×C42—28no—
688C2×C42—28no—
689C2×C42—88no—
690C2×C42C22×C418yes—
691C2×C42C22×C4116yescomplemented
692C2×C42#4118yes—
693C2×C42C2412yes—
694C2×C42C2411yescharacteristic
695C2×C42C2412yes—
696C2×C42C2418yes—
697C2×C42C2412yes—
698C2×C42C2412yes—
699C2×C42C2414yes—
700C2×C42C2412yes—
701C2×C42C2412yes—
702C2×C42C2414yes—
703C2×C42C2414yes—
704C2×C42C2411yescharacteristic
705C2×C42C2414yes—
706C2×C42C2418yes—
707C2×C42C2418yes—
708C2×C42C2414yes—
709C2×C42C2418yes—
710C2×C42C2414yes—
711C2×C42C2418yes—
712C2×C42C2414yes—
713C2×C42C2414yes—
714C2×C42C2414yes—
715C2×C42C2414yes—
716C2×C42C2414yes—
717C2×C42C2414yes—
718C2×C42C2414yes—
719C2×C42C2412yes—
720C2×C42C2418yes—
721C2×C42C2414yes—
722C2×C42C2411yescharacteristic
723C2×C42C2412yes—
724C2×C42C2412yes—
725C2×C42C2412yes—
726C2×C42C2411yescharacteristic
727C2×C42C2412yes—
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732#95C2412yes—
733#95C2412yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2412yes—
740#95C2412yes—
741#95C2412yes—
742#95C2414yes—
743#95C2414yes—
744#95C2412yes—
745#95C2412yes—
746#95C2412yes—
747#95C2418yes—
748#95C2418yes—
749#95C2418yes—
750#95C2418yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2418yes—
755#95C2418yes—
756#95C2414yes—
757#95C2418yes—
758#95C2418yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2418yes—
763#95C2414yes—
764#95C2414yes—
765#95C2418yes—
766#95C2418yes—
767#95C2418yes—
768C24—24no—
769C24—24no—
770C24—44no—
771C24—44no—
772C24C23×C418yes—
773C24C2514yes—
774C24C2512yes—
775C24C2511yescharacteristic
776#41—232no—
777C2×Q8—232no—
778C2×Q8—24no—
779C2×Q8—24no—
780C2×Q8—24no—
781C2×Q8—24no—
782C2×Q8—22no—
783C2×Q8—22no—
784C2×Q8—44no—
785C2×Q8—44no—
786C2×Q8C23×C418yes—
787C2×Q8C23×C418yes—
788C2×Q8C23×C414yes—
789C2×Q8C23×C4116yes—
790C2×D4—24no—
791C2×D4—24no—
792C2×D4—232no—
793C2×D4—24no—
794C2×D4—24no—
795C2×D4—24no—
796C2×D4—24no—
797C2×D4—22no—
798C2×D4—22no—
799C2×D4—48no—
800C2×D4—48no—
801C2×D4C23×C418yes—
802C2×D4C23×C418yes—
803C2×D4C23×C418yes—
804C2×D4C23×C414yes—
805C2×D4C23×C4132yes—
806C22×C4—24no—
807C22×C4—24no—
808C22×C4—24no—
809C22×C4—24no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—24no—
813C22×C4—28no—
814C22×C4—28no—
815C22×C4—24no—
816C22×C4—24no—
817C22×C4—216no—
818C22×C4—28no—
819C22×C4—48no—
820C22×C4—48no—
821C22×C4—42no—
822C22×C4—44no—
823C22×C4—42no—
824C22×C4—42no—
825C22×C4—48no—
826C22×C4—44no—
827C22×C4—42no—
828C22×C4—48no—
829C22×C4—42no—
830C22×C4—44no—
831C22×C4—44no—
832C22×C4—44no—
833C22×C4—44no—
834C22×C4—48no—
835C22×C4—44no—
836C22×C4—48no—
837C22×C4—44no—
838C22×C4—42no—
839C22×C4—816no—
840C22×C4C23×C418yes—
841C22×C4C23×C418yes—
842C22×C4C23×C418yes—
843C22×C4C23×C4116yes—
844C22×C4C23×C4132yes—
845C22×C4C23×C414yes—
846C22×C4C2×#4114yes—
847C22×C4C2×#4114yes—
848C22×C4C2×#4114yes—
849C22×C4C2×#4114yes—
850C22×C4C2512yes—
851C22×C4C2512yes—
852C22×C4C2514yes—
853C22×C4C2512yes—
854C22×C4C2514yes—
855C22×C4C2514yes—
856C22×C4C2512yes—
857C22×C4C2514yes—
858C22×C4C2514yes—
859C22×C4C2514yes—
860C22×C4C2514yes—
861C22×C4C2512yes—
862C22×C4C2512yes—
863C22×C4C2514yes—
864C22×C4C2512yes—
865C22×C4C2511yescharacteristic
866C22×C4C2511yescharacteristic
867C22×C4C2511yescharacteristic
868C22×C4C2514yes—
869C22×C4C2511yescharacteristic
870C22×C4C2511yescharacteristic
871C22×C4C2511yescharacteristic
872C4⋊C4—24no—
873C4⋊C4—24no—
874C4⋊C4—28no—
875C4⋊C4—28no—
876C4⋊C4—24no—
877C4⋊C4—24no—
878C4⋊C4—24no—
879C4⋊C4—24no—
880C4⋊C4—28no—
881C4⋊C4—24no—
882C4⋊C4—22no—
883C4⋊C4—22no—
884C4⋊C4—216no—
885C4⋊C4—24no—
886C4⋊C4—48no—
887C4⋊C4—48no—
888C4⋊C4—44no—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C4⋊C4—44no—
892C4⋊C4—44no—
893C4⋊C4—48no—
894C4⋊C4—44no—
895C4⋊C4—48no—
896C4⋊C4C23×C418yes—
897C4⋊C4C23×C418yes—
898C4⋊C4C23×C418yes—
899C4⋊C4C23×C4132yes—
900C4⋊C4C23×C4116yes—
901C4⋊C4C23×C4116yes—
902C4⋊C4C23×C4132yes—
903C4⋊C4C23×C4116yes—
904C4⋊C4C23×C4116yes—
905C4⋊C4C2×#4118yes—
906C22⋊C4—24no—
907C22⋊C4—24no—
908C22⋊C4—24no—
909C22⋊C4—216no—
910C22⋊C4—28no—
911C22⋊C4—28no—
912C22⋊C4—24no—
913C22⋊C4—28no—
914C22⋊C4—24no—
915C22⋊C4—48no—
916C22⋊C4—48no—
917C22⋊C4—48no—
918C22⋊C4—48no—
919C22⋊C4—48no—
920C22⋊C4—48no—
921C22⋊C4C23×C418yes—
922C22⋊C4C23×C418yes—
923C22⋊C4C23×C4132yes—
924C22⋊C4C23×C4132yes—
925C22⋊C4C23×C4132yes—
926C22⋊C4C23×C418yes—
927C22⋊C4C23×C4116yes—
928C22⋊C4C23×C4132yes—
929C22⋊C4C23×C4132yes—
930C22⋊C4C2×#4118yes—
931C42—22no—
932C42—22no—
933C42—24no—
934C42—28no—
935C42—24no—
936C42—24no—
937C42—24no—
938C42—28no—
939C42—28no—
940C42—24no—
941C42—216no—
942C42—24no—
943C42—44no—
944C42—44no—
945C42—48no—
946C42—48no—
947C42—44no—
948C42—44no—
949C42—44no—
950C42—44no—
951C42—44no—
952C42—48no—
953C42—44no—
954C42—44no—
955C42—48no—
956C42—44no—
957C42C23×C414yes—
958C42C23×C414yes—
959C42C23×C418yes—
960C42C23×C418yes—
961C42C23×C4116yes—
962C42C23×C4132yes—
963C42C23×C418yes—
964C42C23×C418yes—
965C42C2×#4114yes—
966C42C2×#4118yes—
967C42C2×#4114yes—
968C42C2×#4114yes—
969C42C2×#4114yes—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—24no—
975C23—24no—
976C23—24no—
977C23—28no—
978C23—28no—
979C23—24no—
980C23—216no—
981C23—416no—
982C23—84no—
983C23—88no—
984C23—84no—
985C23C24×C418yes—
986C23C24×C414yes—
987C23C24×C412yes—
988C23C22×#4112yes—
989C23C22×#4112yes—
990C23C2611yescharacteristic
991Q8—216no—
992Q8—216no—
993Q8—28no—
994Q8—416no—
995D4—216no—
996D4—216no—
997D4—216no—
998D4—28no—
999D4—432no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—24no—
1003C2×C4—24no—
1004C2×C4—24no—
1005C2×C4—24no—
1006C2×C4—22no—
1007C2×C4—24no—
1008C2×C4—24no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—24no—
1014C2×C4—22no—
1015C2×C4—24no—
1016C2×C4—22no—
1017C2×C4—24no—
1018C2×C4—24no—
1019C2×C4—22no—
1020C2×C4—216no—
1021C2×C4—216no—
1022C2×C4—22no—
1023C2×C4—24no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—24no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—22no—
1033C2×C4—28no—
1034C2×C4—24no—
1035C2×C4—28no—
1036C2×C4—22no—
1037C2×C4—24no—
1038C2×C4—22no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—22no—
1042C2×C4—44no—
1043C2×C4—416no—
1044C2×C4—432no—
1045C2×C4—48no—
1046C2×C4—44no—
1047C2×C4—416no—
1048C2×C4—84no—
1049C2×C4—816no—
1050C2×C4—88no—
1051C2×C4—84no—
1052C2×C4—88no—
1053C2×C4—84no—
1054C2×C4—84no—
1055C2×C4—84no—
1056C2×C4C4×#41116yes—
1057C2×C4C24×C414yes—
1058C2×C4C24×C418yes—
1059C2×C4C24×C418yes—
1060C2×C4C24×C418yes—
1061C2×C4C24×C414yes—
1062C2×C4C24×C414yes—
1063C2×C4C24×C418yes—
1064C2×C4C24×C412yes—
1065C2×C4C24×C412yes—
1066C2×C4C22×#4112yes—
1067C2×C4C22×#4112yes—
1068C2×C4C22×#4118yes—
1069C2×C4C22×#4112yes—
1070C2×C4C22×#4112yes—
1071C2×C4C22×#4112yes—
1072C2×C4C22×#4112yes—
1073C2×C4C22×#4112yes—
1074C2×C4C22×#4112yes—
1075C22—22no—
1076C22—24no—
1077C22—22no—
1078C22—24no—
1079C22—24no—
1080C22—28no—
1081C22—28no—
1082C22—216no—
1083C22—44no—
1084C22—42no—
1085C22—44no—
1086C22—48no—
1087C22—42no—
1088C22—44no—
1089C22—816no—
1090C22C2×C4×#4114yes—
1091C22C25×C411yescharacteristic
1092C22C23×#4111yescharacteristic
1093C22C23×#4111yescharacteristic
1094C22H(7,𝔽2)12yes—
1095C222−1+612yes—
1096C4—22no—
1097C4—22no—
1098C4—28no—
1099C4—22no—
1100C4—22no—
1101C4—24no—
1102C4—28no—
1103C4—28no—
1104C4—24no—
1105C4—28no—
1106C4—24no—
1107C4—28no—
1108C4—44no—
1109C4—42no—
1110C4—44no—
1111C4—44no—
1112C4—42no—
1113C4—44no—
1114C4—42no—
1115C4—42no—
1116C4C2×C4×#4114yes—
1117C4C2×C4×#4114yes—
1118C2—24no—
1119C2—44no—
1120C2—48no—
1121C2C22×C4×#4111yescharacteristic
1122C2#6265412yes—
1123C2#6285511yescharacteristic
1124C2#6285712yes—
1125C2#6286011yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC23C26
commutatorC22C25×C4
prime radicalC2×#535C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34331C2semidirect
3. #34329C2semidirect
4. #34326C2semidirect
5. #34324C2semidirect
6. #34303C2semidirect
7. #34296C2semidirect
8. #34279C2semidirect
10. #34268C2semidirect
11. #34255C2semidirect
12. #34254C2semidirect
13. #34220C2semidirect
14. #34214C2semidirect
15. #34211C2semidirect
16. #34188C2semidirect
17. C4×#542C2semidirect
18. C4×#536C2semidirect
20. #34084C2semidirect
21. #34074C2semidirect
22. C2×#2326C2semidirect
23. C4×#519C2semidirect
24. C4×#518C2semidirect
25. #33999C2semidirect
26. #3510C4semidirect
45. #2374C22semidirect
46. #2373C22semidirect
47. #2373C22semidirect
48. #2373C22semidirect
49. #2373C22semidirect
50. #2372C22semidirect
51. #2368C22semidirect
55. #2367C22semidirect
56. #2367C22semidirect
58. #2365C22semidirect
59. #2362C22semidirect
62. #2359C22semidirect
63. #2359C22semidirect
64. #2359C22semidirect
67. #2356C22semidirect
68. #2355C22semidirect
69. #2355C22semidirect
70. #2355C22semidirect
72. #2354C22semidirect
73. #2353C22semidirect
75. Q8×C4⋊C4C22semidirect
76. #2349C22semidirect
77. #2346C22semidirect
79. #2343C22semidirect
82. #2337C22semidirect
83. #2335C22semidirect
84. #2335C22semidirect
85. #2335C22semidirect
86. #2334C22semidirect
87. #2334C22semidirect
88. #2334C22semidirect
89. #2332C22semidirect
90. #2331C22semidirect
91. #2331C22semidirect
92. #2330C22semidirect
93. #2330C22semidirect
94. #2330C22semidirect
98. #2327C22semidirect
107. #2326C22semidirect
110. #2323C22semidirect
111. #2323C22semidirect
114. #2320C22semidirect
118. #2314C22semidirect
123. C4×C4⋊Q8C22semidirect
124. C4×C4⋊Q8C22semidirect
126. C4×#126C22semidirect
129. C4×#124C22semidirect
130. C4×#124C22semidirect
131. C4×C22⋊Q8C22semidirect
132. C4×C22⋊Q8C22semidirect
133. C4×C22⋊Q8C22semidirect
135. C4×#123C22semidirect
139. #2298C22semidirect
142. #2296C22semidirect
143. #2295C22semidirect
144. #2295C22semidirect
145. #2295C22semidirect
148. #2293C22semidirect
150. #2290C22semidirect
154. #2285C22semidirect
156. #2276C22semidirect
157. #2276C22semidirect
158. #2276C22semidirect
159. #2276C22semidirect
164. #2275C22semidirect
165. #2275C22semidirect
172. C42×Q8C22semidirect
173. C42×Q8C22semidirect
182. C4×#117C22semidirect
183. C4×#117C22semidirect
184. C4×#117C22semidirect
187. C2×#376C22semidirect
192. #559C2×C4semidirect
193. #556C2×C4semidirect
194. #551C2×C4semidirect
195. #542C2×C4semidirect
196. #536C2×C4semidirect
198. #533C2×C4semidirect
202. #529C2×C4semidirect
206. C2×#124C2×C4semidirect
222. #519C2×C4semidirect
224. #518C2×C4semidirect
227. C4×#41C2×C4semidirect
549. C4⋊Q8C22×C4semidirect
550. C4⋊Q8C22×C4semidirect
552. #126C22×C4semidirect
553. #126C22×C4semidirect
554. #125C22×C4semidirect
559. #124C22×C4semidirect
560. #124C22×C4semidirect
562. #123C22×C4semidirect
563. #123C22×C4semidirect
565. C22⋊Q8C22×C4semidirect
566. C22⋊Q8C22×C4semidirect
579. C4×Q8C22×C4semidirect
580. C4×Q8C22×C4semidirect
581. C4×Q8C22×C4semidirect
582. C4×Q8C22×C4semidirect
600. C4×D4C22×C4semidirect
601. C4×D4C22×C4semidirect
614. #117C22×C4semidirect
615. #117C22×C4semidirect
691. C2×C42C22×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#35102
#343312
#343292
#343262
#343242
#343032
#342962
#342792
#342692
#342682
#342552
#342542
#342202
#342142
#342112
#341882
C4×#5422
C4×#5362
C4×#5352
#340842
#340742
C2×#23262
C4×#5192
C4×#5182
#339992