Finite Group Databasebeta

← #7681048

Subgroups — #7681048

Order 512.

7900 conjugacy classes of subgroups.

The subgroup lattice has 1309 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3509C211yesmaximal, characteristic, complemented
2C22×#536C211yesmaximal, characteristic
3#59148C214yesmaximal, complemented
4#59144C214yesmaximal, complemented
5#59012C218yesmaximal, complemented
6#45323C214yesmaximal, complemented
7#45144C214yesmaximal, complemented
8#44761C218yesmaximal, complemented
9#39435C214yesmaximal, complemented
10#37783C214yesmaximal, complemented
11#37663C214yesmaximal, complemented
12#36130C214yesmaximal, complemented
13#35673C211yesmaximal, characteristic, complemented
14#35667C211yesmaximal, characteristic, complemented
15#35667C211yesmaximal, characteristic, complemented
16#35628C211yesmaximal, characteristic, complemented
17#35316C211yesmaximal, characteristic, complemented
18#35307C211yesmaximal, characteristic, complemented
19#35305C211yesmaximal, characteristic
20#34739C211yesmaximal, characteristic, complemented
21C2×#2434C211yesmaximal, characteristic, complemented
22#34268C211yesmaximal, characteristic, complemented
23#34203C211yesmaximal, characteristic, complemented
24#34173C211yesmaximal, characteristic, complemented
25C22⋊C4×#41C211yesmaximal, characteristic
26C23×#41C2211yescharacteristic
27C24×Q8C2211yescharacteristic
28#3509—216no—
29C2×#557C2214yescomplemented
30C2×#556C2214yescomplemented
31C2×#552C2218yescomplemented
32C2×#541C2214yescomplemented
33C2×#536—216no—
34C2×#536C2214yes—
35C2×#536C2212yes—
36C2×#536C2211yescharacteristic
37C2×#536C2211yescharacteristic
38C2×#536C2211yescharacteristic
39C2×#536C2212yes—
40C2×#536C2214yes—
41C2×#536C2211yescharacteristic
42C2×#536C2211yescharacteristic
43C2×#536C2211yescharacteristic
44C2×#533C2214yescomplemented
45C2×#533C2211yescharacteristic, complemented
46C22×C4⋊Q8C2212yes—
47C22×C4⋊Q8C2211yescharacteristic, complemented
48C22×C4⋊Q8C2211yescharacteristic, complemented
49C22×#124C2212yes—
50C22×#123C2214yes—
51C22×C22⋊Q8C2214yes—
52C22×C22⋊Q8C2211yescharacteristic
53C2×#519C2211yescharacteristic, complemented
54C2×#519C2211yescharacteristic, complemented
55C2×#519C2211yescharacteristic, complemented
56C2×C4×#41C2211yescharacteristic
57C2×C4×#41C2211yescharacteristic
58C22×#117C2211yescharacteristic
59#2857C2214yescomplemented
60#2855C2214yescomplemented
61#2848C2214yes—
62#2715C2218yescomplemented
63#2713C2218yescomplemented
64#2713C2218yescomplemented
65#2707C2218yescomplemented
66#2704C2218yescomplemented
67#2700C2218yescomplemented
68#2698C2218yescomplemented
69#2695C2218yescomplemented
70#2694C2218yescomplemented
71#2690C2218yescomplemented
72#2689C2218yescomplemented
73#2687C2218yescomplemented
74#2625C2214yescomplemented
75#2621C2214yescomplemented
76#2616C2214yes—
77#2592C2214yescomplemented
78#2568C2214yescomplemented
79#2558C2218yescomplemented
80#2556C2218yescomplemented
81#2553C2218yescomplemented
82#2550C2218yescomplemented
83#2549C2218yescomplemented
84#2547C2214yescomplemented
85#2546C2214yescomplemented
86#2546C2214yescomplemented
87#2546C2214yescomplemented
88#2545C2214yescomplemented
89#2545C2214yescomplemented
90#2521C2218yescomplemented
91#2498C2218yescomplemented
92#2492C2214yescomplemented
93#2489C2214yescomplemented
94#2488C2218yescomplemented
95#2486C2218yescomplemented
96#2480C2218yes—
97#2480C2218yes—
98#2474C2218yescomplemented
99#2473C2218yes—
100#2473C2218yes—
101#2470C2218yescomplemented
102#2465C2218yescomplemented
103#2458C2218yescomplemented
104#2451C2218yescomplemented
105#2448C2214yescomplemented
106#2447C2214yescomplemented
107#2446C2214yescomplemented
108#2446C2214yescomplemented
109#2442C2218yes—
110#2442C2212yes—
111#2441C2212yescomplemented
112#2440C2212yes—
113#2439C2212yescomplemented
114#2438C2218yescomplemented
115#2438C2214yescomplemented
116#2437C2218yes—
117#2437C2214yes—
118#2435C2212yes—
119#2434C2212yes—
120#2434C2214yes—
121#2434C2212yes—
122#2434C2212yes—
123#2434C2212yescomplemented
124#2434C2214yescomplemented
125#2434C2212yescomplemented
126#2432C2212yes—
127#2432C2212yes—
128#2429C2214yescomplemented
129#2429C2214yescomplemented
130#2429C2214yescomplemented
131#2429C2214yescomplemented
132#2423C2214yescomplemented
133#2421C2214yescomplemented
134#2419C2218yescomplemented
135#2413C2218yescomplemented
136#2413C2218yescomplemented
137#2406C2214yes—
138#2405C2214yes—
139#2396C2214yescomplemented
140C2×#395C2214yescomplemented
141#2367C2214yescomplemented
142#2365C2214yescomplemented
143#2362C2214yescomplemented
144#2360C2218yes—
145#2360C2214yes—
146#2359C2218yescomplemented
147#2344C2214yescomplemented
148#2342C2218yes—
149#2342C2214yes—
150#2341C2212yes—
151Q8×C22⋊C4C2212yes—
152Q8×C22⋊C4C2214yes—
153Q8×C22⋊C4C2214yes—
154Q8×C22⋊C4C2214yescomplemented
155Q8×C22⋊C4C2214yescomplemented
156#2339C2212yes—
157#2339C2214yes—
158D4×C22⋊C4C2212yes—
159D4×C22⋊C4C2214yes—
160#2323C2214yescomplemented
161#2323C2214yescomplemented
162#2316C2211yescharacteristic, complemented
163#2311C2211yescharacteristic
164#2311C2211yescharacteristic
165#2310C2211yescharacteristic, complemented
166#2310C2211yescharacteristic, complemented
167#2310C2211yescharacteristic, complemented
168#2310C2214yescomplemented
169C4×C22⋊Q8C2214yes—
170C4×C22⋊Q8C2214yes—
171C4×C22⋊Q8C2214yescomplemented
172#2297C2212yes—
173#2297C2211yescharacteristic
174#2297C2211yescharacteristic
175#2297C2212yes—
176#2296C2211yescharacteristic, complemented
177#2296C2211yescharacteristic, complemented
178C2×#391C2211yescharacteristic, complemented
179C2×#391C2211yescharacteristic, complemented
180C2×#385C2214yes—
181#2285C2211yescharacteristic, complemented
182#2280C2212yes—
183#2280C2211yescharacteristic
184#2280C2214yes—
185#2280C2211yescharacteristic
186#2274C2211yescharacteristic, complemented
187C2×C4×C22⋊C4C2212yes—
188C2×C4×C22⋊C4C2211yescharacteristic
189C22×#41—28no—
190C22×#41—28no—
191C22×#41—44no—
192C22×#41C2311yescharacteristic
193C22×#41C2312yes—
194C22×#41C2311yescharacteristic
195C22×#41C2311yescharacteristic
196C22×#41C2312yes—
197C22×#41C2311yescharacteristic
198C23×Q8—28no—
199C23×Q8—28no—
200C23×Q8—44no—
201C23×Q8C2311yescharacteristic
202C23×Q8C2311yescharacteristic
203C23×Q8C2312yes—
204C23×Q8C2312yes—
205C23×Q8C2312yes—
206C23×Q8C2312yes—
207C23×Q8C2312yes—
208C23×Q8C2311yescharacteristic
209C23×Q8C2311yescharacteristic
210C23×D4C2312yes—
211C23×D4C2311yescharacteristic
212C24×C4C2312yes—
213C24×C4C2312yes—
214C24×C4C2311yescharacteristic
215#557—232no—
216#556—232no—
217#552—264no—
218#541—232no—
219#536—28no—
220#536—28no—
221#536—28no—
222#536—216no—
223#536—216no—
224#536—232no—
225#536—232no—
226#536—28no—
227#536—44no—
228#536D4116yes—
229#533—232no—
230#533—28no—
231C2×C4⋊Q8—28no—
232C2×C4⋊Q8—216no—
233C2×C4⋊Q8—44no—
234C2×C4⋊Q8C2312yes—
235C2×C4⋊Q8C2312yes—
236C2×C4⋊Q8C2312yes—
237C2×C4⋊Q8C2318yes—
238C2×C4⋊Q8C2312yes—
239C2×C4⋊Q8C2312yes—
240C2×C4⋊Q8C2314yes—
241C2×C4⋊Q8C2312yes—
242C2×C4⋊Q8C2312yes—
243C2×C4⋊Q8C2312yes—
244C2×C4⋊Q8C2312yes—
245C2×C4⋊Q8C2314yes—
246C2×C4⋊Q8C2312yes—
247C2×C4⋊Q8C2312yes—
248C2×#126C2318yes—
249C2×#126C2318yes—
250C2×#125C2312yes—
251C2×#125C2318yes—
252C2×#125C2318yes—
253C2×#125C2318yes—
254C2×#124—216no—
255C2×#124C2312yes—
256C2×#124C2318yes—
257C2×#124C2312yes—
258C2×#124C2312yes—
259C2×#124C2312yes—
260C2×#124C2312yes—
261C2×#124C2312yes—
262C2×#123—232no—
263C2×#123C2314yes—
264C2×#123C2314yes—
265C2×#123C2314yes—
266C2×#123C2314yes—
267C2×#123C2318yes—
268C2×#123C2318yes—
269C2×#123C2314yes—
270C2×#123C2314yes—
271C2×C22⋊Q8—28no—
272C2×C22⋊Q8—232no—
273C2×C22⋊Q8C2312yes—
274C2×C22⋊Q8C2312yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2312yes—
279C2×C22⋊Q8C2314yes—
280C2×C22⋊Q8C2314yes—
281C2×C22⋊Q8C2318yes—
282C2×C22⋊Q8C2318yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2318yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2314yes—
288#519—28no—
289#519—28no—
290#519—44no—
291C4×#41—28no—
292C4×#41—44no—
293C2×C4×Q8C2314yes—
294C2×C4×Q8C2314yes—
295C2×C4×Q8C2314yes—
296C2×C4×Q8C2314yes—
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2314yes—
299C2×C4×Q8C2318yes—
300C2×C4×Q8C2314yes—
301C2×C4×Q8C2314yes—
302C2×C4×Q8C2312yes—
303C2×C4×D4C2314yes—
304C2×C4×D4C2312yes—
305C2×C4×D4C2314yes—
306C2×C4×D4C2312yes—
307C2×#117—28no—
308C2×#117C2311yescharacteristic
309C2×#117C2311yescharacteristic
310C2×#117C2311yescharacteristic
311C2×#117C2311yescharacteristic
312C2×#117C2311yescharacteristic
313C2×#117C2314yes—
314C2×#117C2312yes—
315C2×#117C2314yes—
316C2×#117C2318yes—
317C2×#117C2312yes—
318C2×#117C2312yes—
319C2×#117C2312yes—
320C2×#117C2314yes—
321C2×#117C2312yes—
322C2×#117C2311yescharacteristic
323C22×C4⋊C4C2311yescharacteristic
324C22×C4⋊C4C2312yes—
325C22×C4⋊C4C2312yes—
326C22×C4⋊C4C2318yes—
327C22×C4⋊C4C2314yes—
328C22×C4⋊C4C2314yes—
329C22×C22⋊C4C2314yes—
330C22×C22⋊C4C2312yes—
331C22×C22⋊C4C2312yes—
332C22×C22⋊C4C2312yes—
333C22×C22⋊C4C2318yes—
334C22×C42C2312yes—
335C22×C42C2312yes—
336C22×C42C2311yescharacteristic
337C22×C42C2311yescharacteristic
338C22×C42C2312yes—
339#400C2318yes—
340#400C2318yes—
341#400C2318yes—
342#400C2314yes—
343#400C2318yes—
344#399C2314yes—
345#399C2318yes—
346#398C2318yes—
347#398C2318yes—
348#398C2318yes—
349#398C2314yes—
350#398C2314yes—
351#398C2318yes—
352#398C2318yes—
353#398C2318yes—
354#398C2318yes—
355#398C2318yes—
356#397C2318yes—
357#397C2318yes—
358#397C2318yes—
359#397C2318yes—
360#397C2318yes—
361#397C2318yes—
362#396C2314yes—
363#396C2314yes—
364#396C2318yes—
365#396C2318yes—
366#396C2318yes—
367#396C2318yes—
368#395C2318yes—
369#395C2318yes—
370#395C2318yes—
371#395C2318yes—
372#395C2318yes—
373#395C2314yes—
374#394C2318yes—
375#394C2318yes—
376#394C2318yes—
377#393C2318yes—
378#393C2314yes—
379#391C2314yes—
380#391C2314yes—
381#391C2314yes—
382#391C2314yes—
383#391C2318yes—
384#391C2318yes—
385#391C2318yes—
386#391C2314yes—
387#391C2318yes—
388#391C2314yes—
389#391C2312yes—
390#391C2312yes—
391#391C2312yes—
392#391C2314yes—
393#391C2318yes—
394#391C2312yes—
395#391C2312yes—
396#391C2314yes—
397#391C2314yes—
398#391C2312yes—
399#391C2314yes—
400#391C2312yes—
401#391C2312yes—
402#391C2314yes—
403#390C2312yes—
404#390C2312yes—
405#390C2312yes—
406#390C2314yes—
407#390C2312yes—
408#390C2314yes—
409#389C2314yes—
410#389C2314yes—
411#389C2312yes—
412#389C2318yes—
413#389C2318yes—
414#389C2312yes—
415#389C2318yes—
416#389C2318yes—
417#389C2318yes—
418#389C2318yes—
419#389C2312yes—
420#389C2318yes—
421#389C2318yes—
422#389C2312yes—
423#389C2314yes—
424#388C2318yes—
425#388C2318yes—
426#388C2318yes—
427#388C2318yes—
428#388C2318yes—
429#388C2318yes—
430#388C2318yes—
431#388C2318yes—
432#388C2318yes—
433#388C2318yes—
434#388C2318yes—
435#388C2318yes—
436#387C2318yes—
437#387C2318yes—
438#387C2318yes—
439#387C2318yes—
440#387C2318yes—
441#387C2318yes—
442#387C2318yes—
443#387C2318yes—
444#387C2314yes—
445#387C2314yes—
446#386C2314yes—
447#386C2314yes—
448#386C2314yes—
449#386C2314yes—
450#386C2314yes—
451#386C2314yes—
452#386C2314yes—
453#386C2314yes—
454#385C2318yes—
455#385C2318yes—
456#385C2318yes—
457#385C2314yes—
458#385C2318yes—
459#385C2318yes—
460#385C2318yes—
461#385C2314yes—
462#385C2318yes—
463#385C2314yes—
464#385C2318yes—
465#385C2318yes—
466#385C2318yes—
467#385C2314yes—
468#384C2312yes—
469#382C2318yes—
470#382C2312yes—
471#381C2312yes—
472#381C2312yes—
473#381C2314yes—
474#381C2314yes—
475#381C2314yes—
476#381C2314yes—
477#381C2318yes—
478#380C2314yes—
479#380C2314yes—
480#380C2314yes—
481#380C2312yes—
482#380C2312yes—
483#380C2312yes—
484#380C2314yes—
485#380C2314yes—
486#380C2318yes—
487#380C2312yes—
488#380C2318yes—
489#380C2318yes—
490#380C2318yes—
491#380C2314yes—
492#380C2314yes—
493#379C2318yes—
494#379C2312yes—
495#379C2314yes—
496#379C2312yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2318yes—
500C4×C4⋊C4C2318yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2314yes—
504C4×C22⋊C4C2314yes—
505C4×C22⋊C4C2312yes—
506C4×C22⋊C4C2312yes—
507C4×C22⋊C4C2314yes—
508C4×C22⋊C4C2318yes—
509C4×C22⋊C4C2312yes—
510C4×C22⋊C4C2312yes—
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2318yes—
514C4×C22⋊C4C2318yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2318yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2312yes—
519C4×C22⋊C4C2312yes—
520C4×C22⋊C4C2312yes—
521C4×C22⋊C4C2311yescharacteristic
522C4×C22⋊C4C2311yescharacteristic
523C4×C22⋊C4C2311yescharacteristic
524C4×C22⋊C4C2311yescharacteristic
525C2×#95C2312yes—
526C2×#95C2314yes—
527C2×#95C2314yes—
528C2×#95C2314yes—
529C25C2412yes—
530C25C2411yescharacteristic
531C2×#41—24no—
532C2×#41—28no—
533C2×#41—24no—
534C2×#41—28no—
535C2×#41—24no—
536C2×#41—24no—
537C2×#41—28no—
538C2×#41—28no—
539C2×#41—24no—
540C2×#41—24no—
541C2×#41—24no—
542C2×#41—24no—
543C2×#41—24no—
544C2×#41—44no—
545C2×#41—44no—
546C2×#41—42no—
547C2×#41—42no—
548C2×#41—464no—
549C2×#41C2×D418yes—
550C22×Q8—28no—
551C22×Q8—28no—
552C22×Q8—24no—
553C22×Q8—28no—
554C22×Q8—28no—
555C22×Q8—24no—
556C22×Q8—28no—
557C22×Q8—24no—
558C22×Q8—24no—
559C22×Q8—24no—
560C22×Q8—28no—
561C22×Q8—28no—
562C22×Q8—28no—
563C22×Q8—28no—
564C22×Q8—28no—
565C22×Q8—24no—
566C22×Q8—24no—
567C22×Q8—24no—
568C22×Q8—24no—
569C22×Q8—24no—
570C22×Q8—44no—
571C22×Q8—44no—
572C22×Q8—44no—
573C22×Q8—44no—
574C22×Q8—44no—
575C22×Q8—42no—
576C22×Q8—464no—
577C22×Q8C2×D418yes—
578C22×Q8C2412yes—
579C22×Q8C2412yes—
580C22×Q8C2412yes—
581C22×Q8C2412yes—
582C22×Q8C2411yescharacteristic
583C22×Q8C2414yes—
584C22×Q8C2414yes—
585C22×Q8C2414yes—
586C22×Q8C2412yes—
587C22×Q8C2412yes—
588C22×Q8C2412yes—
589C22×Q8C2411yescharacteristic
590C22×D4—28no—
591C22×D4—28no—
592C22×D4—24no—
593C22×D4—24no—
594C22×D4—42no—
595C22×D4—44no—
596C22×D4C2412yes—
597C22×D4C2411yescharacteristic
598C22×D4C2412yes—
599C22×D4C2412yes—
600C22×D4C2412yes—
601C22×D4C2412yes—
602C22×D4C2411yescharacteristic
603C23×C4—24no—
604C23×C4—24no—
605C23×C4—28no—
606C23×C4—28no—
607C23×C4—28no—
608C23×C4—28no—
609C23×C4—44no—
610C23×C4—44no—
611C23×C4#4118yes—
612C23×C4C2412yes—
613C23×C4C2412yes—
614C23×C4C2412yes—
615C23×C4C2414yes—
616C23×C4C2414yes—
617C23×C4C2412yes—
618C23×C4C2412yes—
619C23×C4C2414yes—
620C23×C4C2412yes—
621C23×C4C2412yes—
622C23×C4C2412yes—
623C23×C4C2414yes—
624C23×C4C2412yes—
625C23×C4C2412yes—
626C23×C4C2411yescharacteristic
627C23×C4C2411yescharacteristic
628C23×C4C2411yescharacteristic
629C23×C4C2411yescharacteristic
630C23×C4C2411yescharacteristic
631C23×C4C2412yes—
632C23×C4C2414yes—
633C23×C4C2411yescharacteristic
634C4⋊Q8—28no—
635C4⋊Q8—28no—
636C4⋊Q8—28no—
637C4⋊Q8—28no—
638C4⋊Q8—216no—
639C4⋊Q8—28no—
640C4⋊Q8—232no—
641C4⋊Q8—28no—
642C4⋊Q8—28no—
643C4⋊Q8—44no—
644C4⋊Q8—44no—
645C4⋊Q8—48no—
646C4⋊Q8—44no—
647C4⋊Q8C2×D4116yes—
648#126—232no—
649#126—232no—
650#125—28no—
651#125—232no—
652#125—232no—
653#125—232no—
654#124—28no—
655#124—28no—
656#124—28no—
657#124—232no—
658#124—28no—
659#124—44no—
660#124C2×D4116yes—
661#123—216no—
662#123—216no—
663#123—216no—
664#123—232no—
665#123—232no—
666#123—216no—
667#123—48no—
668#123C2×D4132yes—
669C22⋊Q8—216no—
670C22⋊Q8—216no—
671C22⋊Q8—216no—
672C22⋊Q8—28no—
673C22⋊Q8—28no—
674C22⋊Q8—28no—
675C22⋊Q8—28no—
676C22⋊Q8—232no—
677C22⋊Q8—216no—
678C22⋊Q8—232no—
679C22⋊Q8—216no—
680C22⋊Q8—232no—
681C22⋊Q8—216no—
682C22⋊Q8—48no—
683C22⋊Q8C2×D4132yes—
684C4×Q8—28no—
685C4×Q8—216no—
686C4×Q8—216no—
687C4×Q8—216no—
688C4×Q8—232no—
689C4×Q8—216no—
690C4×Q8—216no—
691C4×Q8—44no—
692C4×Q8—48no—
693C4×Q8—48no—
694C4×D4—216no—
695C4×D4—28no—
696C4×D4—44no—
697C4×D4—48no—
698#117—24no—
699#117—24no—
700#117—28no—
701#117—24no—
702#117—216no—
703#117—24no—
704#117—24no—
705#117—28no—
706#117—28no—
707#117—216no—
708#117—232no—
709#117—28no—
710#117—44no—
711#117—48no—
712#117C2×D418yes—
713C2×C4⋊C4—216no—
714C2×C4⋊C4—28no—
715C2×C4⋊C4—24no—
716C2×C4⋊C4—28no—
717C2×C4⋊C4—232no—
718C2×C4⋊C4—48no—
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2418yes—
722C2×C4⋊C4C2418yes—
723C2×C4⋊C4C2418yes—
724C2×C4⋊C4C2418yes—
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2418yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2418yes—
737C2×C4⋊C4C2418yes—
738C2×C4⋊C4C2418yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2418yes—
745C2×C4⋊C4C2418yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2418yes—
748C2×C4⋊C4C2418yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2418yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2418yes—
755C2×C22⋊C4—28no—
756C2×C22⋊C4—28no—
757C2×C22⋊C4—232no—
758C2×C22⋊C4—28no—
759C2×C22⋊C4—216no—
760C2×C22⋊C4C2412yes—
761C2×C22⋊C4C2414yes—
762C2×C22⋊C4C2418yes—
763C2×C22⋊C4C2418yes—
764C2×C22⋊C4C2418yes—
765C2×C22⋊C4C2414yes—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2412yes—
769C2×C22⋊C4C2412yes—
770C2×C22⋊C4C2412yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2412yes—
774C2×C22⋊C4C2412yes—
775C2×C22⋊C4C2412yes—
776C2×C22⋊C4C2412yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2418yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2418yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2418yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2418yes—
788C2×C22⋊C4C2412yes—
789C2×C22⋊C4C2418yes—
790C2×C22⋊C4C2412yes—
791C2×C42—24no—
792C2×C42—28no—
793C2×C42—24no—
794C2×C42—28no—
795C2×C42—44no—
796C2×C42C2412yes—
797C2×C42C2418yes—
798C2×C42C2418yes—
799C2×C42C2412yes—
800C2×C42C2412yes—
801C2×C42C2414yes—
802C2×C42C2411yescharacteristic
803C2×C42C2411yescharacteristic
804C2×C42C2412yes—
805C2×C42C2412yes—
806C2×C42C2414yes—
807C2×C42C2412yes—
808C2×C42C2412yes—
809C2×C42C2411yescharacteristic
810C2×C42C2411yescharacteristic
811C2×C42C2418yes—
812C2×C42C2414yes—
813C2×C42C2418yes—
814C2×C42C2412yes—
815#95C2412yes—
816#95C2414yes—
817#95C2412yes—
818#95C2412yes—
819#95C2414yes—
820#95C2412yes—
821#95C2414yes—
822#95C2418yes—
823#95C2418yes—
824#95C2418yes—
825#95C2418yes—
826#95C2414yes—
827#95C2414yes—
828#95C2418yes—
829#95C2418yes—
830#95C2418yes—
831#95C2418yes—
832#95C2414yes—
833#95C2414yes—
834#95C2418yes—
835#95C2414yes—
836#95C2418yes—
837#95C2414yes—
838#95C2418yes—
839#95C2414yes—
840#95C2418yes—
841#95C2414yes—
842#95C2418yes—
843#95C2414yes—
844#95C2414yes—
845#95C2414yes—
846#95C2418yes—
847C24—22no—
848C24—22no—
849C24—24no—
850C24—24no—
851C24—24no—
852C24—28no—
853C24—42no—
854C24—42no—
855C24—44no—
856C24C2×#4114yes—
857C24C2512yes—
858C24C2512yes—
859C24C2511yescharacteristic
860C24C2511yescharacteristic
861C24C2511yescharacteristic
862#41—232no—
863#41—432no—
864#41—432no—
865#41—416no—
866#41—416no—
867#41—416no—
868C2×Q8—232no—
869C2×Q8—28no—
870C2×Q8—24no—
871C2×Q8—24no—
872C2×Q8—28no—
873C2×Q8—24no—
874C2×Q8—28no—
875C2×Q8—24no—
876C2×Q8—24no—
877C2×Q8—22no—
878C2×Q8—24no—
879C2×Q8—24no—
880C2×Q8—22no—
881C2×Q8—24no—
882C2×Q8—24no—
883C2×Q8—28no—
884C2×Q8—28no—
885C2×Q8—24no—
886C2×Q8—24no—
887C2×Q8—24no—
888C2×Q8—22no—
889C2×Q8—24no—
890C2×Q8—24no—
891C2×Q8—22no—
892C2×Q8—24no—
893C2×Q8—24no—
894C2×Q8—24no—
895C2×Q8—24no—
896C2×Q8—22no—
897C2×Q8—28no—
898C2×Q8—44no—
899C2×Q8—44no—
900C2×Q8—42no—
901C2×Q8—44no—
902C2×Q8—432no—
903C2×Q8—432no—
904C2×Q8—432no—
905C2×Q8—432no—
906C2×Q8—432no—
907C2×Q8—416no—
908C2×Q8—416no—
909C2×Q8—416no—
910C2×Q8C22×D418yes—
911C2×Q8C22×D418yes—
912C2×Q8C22×D414yes—
913C2×D4—24no—
914C2×D4—24no—
915C2×D4—24no—
916C2×D4—24no—
917C2×D4—24no—
918C2×D4—24no—
919C2×D4—24no—
920C2×D4—24no—
921C2×D4—24no—
922C2×D4—24no—
923C2×D4—22no—
924C2×D4—22no—
925C2×D4—24no—
926C2×D4—22no—
927C2×D4—22no—
928C2×D4—22no—
929C2×D4—416no—
930C2×D4—42no—
931C2×D4—42no—
932C2×D4—42no—
933C2×D4—432no—
934C2×D4C22×D418yes—
935C2×D4C22×D414yes—
936C22×C4—22no—
937C22×C4—24no—
938C22×C4—24no—
939C22×C4—22no—
940C22×C4—232no—
941C22×C4—22no—
942C22×C4—22no—
943C22×C4—22no—
944C22×C4—22no—
945C22×C4—24no—
946C22×C4—24no—
947C22×C4—22no—
948C22×C4—22no—
949C22×C4—22no—
950C22×C4—22no—
951C22×C4—24no—
952C22×C4—28no—
953C22×C4—24no—
954C22×C4—24no—
955C22×C4—24no—
956C22×C4—24no—
957C22×C4—24no—
958C22×C4—28no—
959C22×C4—28no—
960C22×C4—24no—
961C22×C4—24no—
962C22×C4—24no—
963C22×C4—24no—
964C22×C4—28no—
965C22×C4—24no—
966C22×C4—28no—
967C22×C4—28no—
968C22×C4—24no—
969C22×C4—24no—
970C22×C4—24no—
971C22×C4—28no—
972C22×C4—24no—
973C22×C4—24no—
974C22×C4—24no—
975C22×C4—24no—
976C22×C4—24no—
977C22×C4—24no—
978C22×C4—28no—
979C22×C4—28no—
980C22×C4—42no—
981C22×C4—44no—
982C22×C4—44no—
983C22×C4—42no—
984C22×C4—42no—
985C22×C4—44no—
986C22×C4—42no—
987C22×C4—42no—
988C22×C4—44no—
989C22×C4—432no—
990C22×C4—44no—
991C22×C4—44no—
992C22×C4—44no—
993C22×C4—432no—
994C22×C4C22×D418yes—
995C22×C4C22×D418yes—
996C22×C4C22×D414yes—
997C22×C4C2×#4114yes—
998C22×C4C2×#4114yes—
999C22×C4C2×#4114yes—
1000C22×C4C2×#4114yes—
1001C22×C4C2×#4114yes—
1002C22×C4C2×#4114yes—
1003C22×C4H(5,𝔽2)14yes—
1004C22×C4C2514yes—
1005C22×C4C2514yes—
1006C22×C4C2512yes—
1007C22×C4C2514yes—
1008C22×C4C2514yes—
1009C22×C4C2512yes—
1010C22×C4C2514yes—
1011C22×C4C2514yes—
1012C22×C4C2514yes—
1013C22×C4C2512yes—
1014C22×C4C2514yes—
1015C22×C4C2514yes—
1016C22×C4C2514yes—
1017C22×C4C2512yes—
1018C22×C4C2511yescharacteristic
1019C22×C4C2511yescharacteristic
1020C22×C4C2512yes—
1021C22×C4C2512yes—
1022C22×C4C2511yescharacteristic
1023C22×C4C2511yescharacteristic
1024C4⋊C4—28no—
1025C4⋊C4—24no—
1026C4⋊C4—216no—
1027C4⋊C4—216no—
1028C4⋊C4—216no—
1029C4⋊C4—216no—
1030C4⋊C4—216no—
1031C4⋊C4—28no—
1032C4⋊C4—24no—
1033C4⋊C4—28no—
1034C4⋊C4—24no—
1035C4⋊C4—216no—
1036C4⋊C4—216no—
1037C4⋊C4—216no—
1038C4⋊C4—28no—
1039C4⋊C4—28no—
1040C4⋊C4—24no—
1041C4⋊C4—24no—
1042C4⋊C4—28no—
1043C4⋊C4—28no—
1044C4⋊C4—24no—
1045C4⋊C4—24no—
1046C4⋊C4—28no—
1047C4⋊C4—28no—
1048C4⋊C4—28no—
1049C4⋊C4—48no—
1050C4⋊C4—48no—
1051C4⋊C4—44no—
1052C4⋊C4—44no—
1053C4⋊C4—48no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—48no—
1057C4⋊C4—48no—
1058C4⋊C4C22×D418yes—
1059C4⋊C4C22×D4132yes—
1060C22⋊C4—24no—
1061C22⋊C4—216no—
1062C22⋊C4—24no—
1063C22⋊C4—24no—
1064C22⋊C4—28no—
1065C22⋊C4—216no—
1066C22⋊C4—28no—
1067C22⋊C4—28no—
1068C22⋊C4—24no—
1069C22⋊C4—24no—
1070C22⋊C4—28no—
1071C22⋊C4—24no—
1072C22⋊C4—28no—
1073C22⋊C4—28no—
1074C22⋊C4—216no—
1075C22⋊C4—216no—
1076C22⋊C4—24no—
1077C22⋊C4—28no—
1078C22⋊C4—24no—
1079C22⋊C4—28no—
1080C22⋊C4—44no—
1081C22⋊C4—44no—
1082C22⋊C4—48no—
1083C22⋊C4—48no—
1084C22⋊C4—44no—
1085C22⋊C4—44no—
1086C22⋊C4—44no—
1087C22⋊C4—48no—
1088C22⋊C4C22×D418yes—
1089C22⋊C4C22×D4132yes—
1090C22⋊C42−1+418yes—
1091C42—22no—
1092C42—24no—
1093C42—28no—
1094C42—24no—
1095C42—22no—
1096C42—28no—
1097C42—24no—
1098C42—216no—
1099C42—216no—
1100C42—24no—
1101C42—22no—
1102C42—22no—
1103C42—24no—
1104C42—24no—
1105C42—24no—
1106C42—44no—
1107C42—48no—
1108C42—48no—
1109C42C22×D418yes—
1110C23—21no—
1111C23—21no—
1112C23—22no—
1113C23—22no—
1114C23—22no—
1115C23—21no—
1116C23—22no—
1117C23—22no—
1118C23—21no—
1119C23—22no—
1120C23—24no—
1121C23—22no—
1122C23—24no—
1123C23—28no—
1124C23—28no—
1125C23—22no—
1126C23—22no—
1127C23—22no—
1128C23—24no—
1129C23—24no—
1130C23—44no—
1131C23—48no—
1132C23—48no—
1133C23—48no—
1134C23—416no—
1135C23—48no—
1136C23—84no—
1137C23—88no—
1138C23C23×D414yes—
1139C23C23×D412yes—
1140C23C22×#4112yes—
1141C23C22×#4112yes—
1142C23C22×#4112yes—
1143C23C2×H(5,𝔽2)12yes—
1144C23C2×2−1+414yes—
1145C23C2611yescharacteristic
1146Q8—216no—
1147Q8—216no—
1148Q8—28no—
1149Q8—416no—
1150Q8—416no—
1151Q8—416no—
1152Q8—48no—
1153Q8—48no—
1154Q8—48no—
1155Q8—48no—
1156Q8—48no—
1157Q8—44no—
1158D4—216no—
1159D4—28no—
1160D4—48no—
1161D4—48no—
1162D4—48no—
1163D4—48no—
1164D4—44no—
1165C2×C4—22no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—22no—
1169C2×C4—24no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—24no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—28no—
1180C2×C4—216no—
1181C2×C4—28no—
1182C2×C4—28no—
1183C2×C4—28no—
1184C2×C4—28no—
1185C2×C4—216no—
1186C2×C4—24no—
1187C2×C4—24no—
1188C2×C4—24no—
1189C2×C4—22no—
1190C2×C4—24no—
1191C2×C4—24no—
1192C2×C4—22no—
1193C2×C4—24no—
1194C2×C4—24no—
1195C2×C4—22no—
1196C2×C4—24no—
1197C2×C4—22no—
1198C2×C4—24no—
1199C2×C4—24no—
1200C2×C4—24no—
1201C2×C4—22no—
1202C2×C4—24no—
1203C2×C4—24no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—24no—
1207C2×C4—24no—
1208C2×C4—24no—
1209C2×C4—24no—
1210C2×C4—24no—
1211C2×C4—28no—
1212C2×C4—24no—
1213C2×C4—24no—
1214C2×C4—24no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—24no—
1218C2×C4—48no—
1219C2×C4—48no—
1220C2×C4—416no—
1221C2×C4—416no—
1222C2×C4—48no—
1223C2×C4—48no—
1224C2×C4—416no—
1225C2×C4—416no—
1226C2×C4—48no—
1227C2×C4—48no—
1228C2×C4—48no—
1229C2×C4—48no—
1230C2×C4—88no—
1231C2×C4—84no—
1232C2×C4#546116yes—
1233C2×C4C23×D418yes—
1234C2×C4C23×D418yes—
1235C2×C4C23×D414yes—
1236C2×C4C23×D412yes—
1237C2×C4C23×D412yes—
1238C2×C4C22×#4112yes—
1239C2×C4C22×#4112yes—
1240C2×C4C22×#4112yes—
1241C2×C4C22×#4112yes—
1242C2×C4C2×H(5,𝔽2)12yes—
1243C2×C4C2×H(5,𝔽2)12yes—
1244C2×C4C2×2−1+414yes—
1245C2×C4C2×2−1+414yes—
1246C22—24no—
1247C22—24no—
1248C22—22no—
1249C22—22no—
1250C22—22no—
1251C22—24no—
1252C22—24no—
1253C22—22no—
1254C22—28no—
1255C22—22no—
1256C22—22no—
1257C22—22no—
1258C22—24no—
1259C22—416no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—44no—
1264C22—42no—
1265C22—44no—
1266C22—42no—
1267C22—42no—
1268C22—44no—
1269C22—42no—
1270C22—816no—
1271C22C2×#54614yes—
1272C22#350914yescomplemented
1273C22C24×D411yescharacteristic
1274C22C23×#4111yescharacteristic
1275C22C22×H(5,𝔽2)11yescharacteristic
1276C22C22×2−1+412yes—
1277C222−1+612yes—
1278C4—24no—
1279C4—28no—
1280C4—24no—
1281C4—22no—
1282C4—22no—
1283C4—24no—
1284C4—28no—
1285C4—44no—
1286C4—44no—
1287C4—42no—
1288C4—44no—
1289C4—44no—
1290C4—44no—
1291C4—42no—
1292C4—44no—
1293C4—42no—
1294C4—44no—
1295C4—44no—
1296C4C2×#54614yes—
1297C4C2×#54614yes—
1298C2—24no—
1299C2—24no—
1300C2—42no—
1301C2—44no—
1302C2—82no—
1303C2C22×#54611yescharacteristic
1304C2C2×#350911yescharacteristic
1305C2#6286011yescharacteristic
1306C2#6294212yes—
1307C2D4×2−1+412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC23×#41C22
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. #59148C2semidirect
4. #59144C2semidirect
5. #59012C2semidirect
6. #45323C2semidirect
7. #45144C2semidirect
8. #44761C2semidirect
9. #39435C2semidirect
10. #37783C2semidirect
11. #37663C2semidirect
12. #36130C2semidirect
13. #35673C2semidirect
14. #35667C2semidirect
15. #35667C2semidirect
16. #35628C2semidirect
17. #35316C2semidirect
18. #35307C2semidirect
20. #34739C2semidirect
21. C2×#2434C2semidirect
22. #34268C2semidirect
23. #34203C2semidirect
24. #34173C2semidirect
29. C2×#557C22semidirect
30. C2×#556C22semidirect
31. C2×#552C22semidirect
32. C2×#541C22semidirect
44. C2×#533C22semidirect
45. C2×#533C22semidirect
47. C22×C4⋊Q8C22semidirect
48. C22×C4⋊Q8C22semidirect
53. C2×#519C22semidirect
54. C2×#519C22semidirect
55. C2×#519C22semidirect
59. #2857C22semidirect
60. #2855C22semidirect
62. #2715C22semidirect
63. #2713C22semidirect
64. #2713C22semidirect
65. #2707C22semidirect
66. #2704C22semidirect
67. #2700C22semidirect
68. #2698C22semidirect
69. #2695C22semidirect
70. #2694C22semidirect
71. #2690C22semidirect
72. #2689C22semidirect
73. #2687C22semidirect
74. #2625C22semidirect
75. #2621C22semidirect
77. #2592C22semidirect
78. #2568C22semidirect
79. #2558C22semidirect
80. #2556C22semidirect
81. #2553C22semidirect
82. #2550C22semidirect
83. #2549C22semidirect
84. #2547C22semidirect
85. #2546C22semidirect
86. #2546C22semidirect
87. #2546C22semidirect
88. #2545C22semidirect
89. #2545C22semidirect
90. #2521C22semidirect
91. #2498C22semidirect
92. #2492C22semidirect
93. #2489C22semidirect
94. #2488C22semidirect
95. #2486C22semidirect
98. #2474C22semidirect
101. #2470C22semidirect
102. #2465C22semidirect
103. #2458C22semidirect
104. #2451C22semidirect
105. #2448C22semidirect
106. #2447C22semidirect
107. #2446C22semidirect
108. #2446C22semidirect
111. #2441C22semidirect
113. #2439C22semidirect
114. #2438C22semidirect
115. #2438C22semidirect
123. #2434C22semidirect
124. #2434C22semidirect
125. #2434C22semidirect
128. #2429C22semidirect
129. #2429C22semidirect
130. #2429C22semidirect
131. #2429C22semidirect
132. #2423C22semidirect
133. #2421C22semidirect
134. #2419C22semidirect
135. #2413C22semidirect
136. #2413C22semidirect
139. #2396C22semidirect
140. C2×#395C22semidirect
141. #2367C22semidirect
142. #2365C22semidirect
143. #2362C22semidirect
146. #2359C22semidirect
147. #2344C22semidirect
154. Q8×C22⋊C4C22semidirect
155. Q8×C22⋊C4C22semidirect
160. #2323C22semidirect
161. #2323C22semidirect
162. #2316C22semidirect
165. #2310C22semidirect
166. #2310C22semidirect
167. #2310C22semidirect
168. #2310C22semidirect
171. C4×C22⋊Q8C22semidirect
176. #2296C22semidirect
177. #2296C22semidirect
178. C2×#391C22semidirect
179. C2×#391C22semidirect
181. #2285C22semidirect
186. #2274C22semidirect
1272. C22#3509semidirect

Maximal subgroups

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

subgroupindex
C2×#35092
C22×#5362
#591482
#591442
#590122
#453232
#451442
#447612
#394352
#377832
#376632
#361302
#356732
#356672
#356282
#353162
#353072
#353052
#347392
C2×#24342
#342682
#342032
#341732
C22⋊C4×#412