Finite Group Databasebeta

← #7681063

Subgroups — #7681063

Order 512.

5664 conjugacy classes of subgroups.

The subgroup lattice has 1195 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59867C214yesmaximal, complemented
2#59424C214yesmaximal, complemented
3#59268C218yesmaximal, complemented
4#45366C214yesmaximal, complemented
5#44962C214yesmaximal, complemented
6#44043C218yesmaximal, complemented
7#39563C214yesmaximal, complemented
8#37971C214yesmaximal, complemented
9#37850C214yesmaximal, complemented
10#36190C214yesmaximal, complemented
11#35673C211yesmaximal, characteristic, complemented
12#35628C211yesmaximal, characteristic, complemented
13#35557C211yesmaximal, characteristic, complemented
14#35557C211yesmaximal, characteristic, complemented
15#35307C211yesmaximal, characteristic, complemented
16#35305C211yesmaximal, characteristic
17#35280C211yesmaximal, characteristic, complemented
18C2×#2502C211yesmaximal, characteristic, complemented
19#34739C211yesmaximal, characteristic, complemented
20#34268C211yesmaximal, characteristic, complemented
21#34203C211yesmaximal, characteristic, complemented
22#34188C211yesmaximal, characteristic, complemented
23#34178C211yesmaximal, characteristic, complemented
24C22⋊C4×#41C211yesmaximal, characteristic
25C2×#2311C211yesmaximal, characteristic
26C23×#41C2211yescharacteristic
27C2×#536C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C2×#533C2211yescharacteristic, complemented
30C22×C22⋊Q8C2211yescharacteristic
31C2×#519C2211yescharacteristic, complemented
32C2×C4×#41C2211yescharacteristic
33C2×C4×#41C2211yescharacteristic
34C22×#117C2211yescharacteristic
35C23×C4⋊C4C2211yescharacteristic
36#2857C2214yescomplemented
37#2855C2214yescomplemented
38#2848C2214yes—
39#2799C2218yescomplemented
40#2786C2218yescomplemented
41#2761C2218yescomplemented
42#2755C2218yescomplemented
43#2751C2218yescomplemented
44#2750C2218yescomplemented
45#2747C2218yescomplemented
46#2744C2218yescomplemented
47#2743C2218yescomplemented
48#2740C2218yescomplemented
49#2739C2218yescomplemented
50#2722C2218yescomplemented
51#2629C2214yescomplemented
52#2625C2214yescomplemented
53#2616C2214yes—
54#2609C2218yescomplemented
55#2601C2218yescomplemented
56#2601C2218yescomplemented
57#2592C2214yescomplemented
58#2588C2218yescomplemented
59#2582C2214yescomplemented
60#2574C2218yescomplemented
61#2569C2218yes—
62#2569C2218yescomplemented
63#2568C2214yescomplemented
64#2560C2218yescomplemented
65#2538C2214yescomplemented
66#2522C2218yescomplemented
67#2520C2218yescomplemented
68#2512C2214yescomplemented
69#2512C2214yescomplemented
70#2511C2214yescomplemented
71#2511C2214yescomplemented
72#2505C2218yes—
73#2505C2218yes—
74#2502C2214yes—
75#2502C2212yes—
76#2502C2212yes—
77#2502C2214yescomplemented
78#2502C2212yescomplemented
79#2502C2212yescomplemented
80#2498C2218yescomplemented
81#2497C2214yescomplemented
82#2497C2214yescomplemented
83#2496C2214yescomplemented
84#2496C2214yescomplemented
85#2492C2214yescomplemented
86#2489C2214yescomplemented
87#2488C2218yescomplemented
88#2481C2218yescomplemented
89#2481C2218yescomplemented
90#2480C2218yes—
91#2480C2218yes—
92#2479C2218yescomplemented
93#2477C2218yescomplemented
94#2448C2214yescomplemented
95#2447C2214yescomplemented
96#2446C2214yescomplemented
97#2446C2214yescomplemented
98#2442C2212yes—
99#2441C2212yescomplemented
100#2440C2212yes—
101#2439C2212yescomplemented
102#2438C2214yescomplemented
103#2438C2218yescomplemented
104#2437C2218yes—
105#2437C2214yes—
106#2435C2212yes—
107#2434C2212yes—
108#2432C2212yes—
109#2432C2212yes—
110#2423C2214yescomplemented
111#2421C2214yescomplemented
112#2419C2218yescomplemented
113#2417C2218yescomplemented
114#2406C2214yes—
115#2405C2214yes—
116#2396C2214yescomplemented
117C2×#398C2214yescomplemented
118#2368C2218yes—
119#2367C2214yescomplemented
120#2365C2214yescomplemented
121#2362C2214yescomplemented
122#2360C2214yes—
123#2359C2218yescomplemented
124#2355C2214yescomplemented
125#2354C2214yescomplemented
126#2352C2218yescomplemented
127#2345C2214yes—
128#2345C2214yes—
129#2344C2214yescomplemented
130#2344C2214yescomplemented
131#2344C2214yescomplemented
132#2342C2218yes—
133#2342C2214yes—
134#2341C2212yes—
135Q8×C22⋊C4C2212yes—
136#2339C2214yes—
137#2339C2212yes—
138D4×C22⋊C4C2212yes—
139D4×C22⋊C4C2214yes—
140#2323C2214yescomplemented
141#2323C2214yescomplemented
142#2316C2211yescharacteristic, complemented
143#2316C2211yescharacteristic, complemented
144#2316C2211yescharacteristic, complemented
145#2314C2214yescomplemented
146#2313C2214yescomplemented
147#2311C2214yes—
148#2311C2211yescharacteristic
149#2311C2212yes—
150#2311C2214yes—
151#2311C2211yescharacteristic
152#2311C2211yescharacteristic
153#2311C2211yescharacteristic
154#2311C2212yes—
155#2311C2211yescharacteristic
156#2311C2211yescharacteristic
157#2310C2211yescharacteristic, complemented
158C4×C22⋊Q8C2214yes—
159C4×C22⋊Q8C2214yes—
160C4×C22⋊Q8C2214yescomplemented
161#2297C2211yescharacteristic
162#2297C2212yes—
163#2297C2211yescharacteristic
164#2297C2212yes—
165#2296C2211yescharacteristic, complemented
166#2296C2211yescharacteristic, complemented
167C2×#391C2212yes—
168C2×#391C2211yescharacteristic, complemented
169C2×#391C2211yescharacteristic, complemented
170C2×#390C2212yes—
171C2×#386C2214yes—
172C2×#385C2214yes—
173#2285C2214yescomplemented
174#2285C2211yescharacteristic, complemented
175C2×#384C2211yescharacteristic, complemented
176C2×#384C2211yescharacteristic, complemented
177#2280C2211yescharacteristic
178#2280C2212yes—
179#2280C2214yes—
180#2280C2211yescharacteristic
181C2×#380C2214yes—
182#2274C2211yescharacteristic, complemented
183#2274C2211yescharacteristic, complemented
184#2274C2211yescharacteristic, complemented
185C2×C4×C22⋊C4C2212yes—
186C2×C4×C22⋊C4C2211yescharacteristic
187C22×#41—28no—
188C22×#41—28no—
189C22×#41—44no—
190C22×#41C2311yescharacteristic
191C22×#41C2312yes—
192C22×#41C2311yescharacteristic
193C22×#41C2311yescharacteristic
194C22×#41C2312yes—
195C22×#41C2311yescharacteristic
196C23×Q8C2311yescharacteristic
197C23×Q8C2311yescharacteristic
198C23×D4C2312yes—
199C23×D4C2311yescharacteristic
200C24×C4C2312yes—
201C24×C4C2311yescharacteristic
202C24×C4C2312yes—
203#536—28no—
204#536—44no—
205#533—44no—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2312yes—
209C2×#126C2318yes—
210C2×#126C2318yes—
211C2×#125C2312yes—
212C2×#124C2312yes—
213C2×#124C2312yes—
214C2×#123C2314yes—
215C2×#123C2314yes—
216C2×C22⋊Q8—28no—
217C2×C22⋊Q8C2312yes—
218C2×C22⋊Q8C2314yes—
219C2×C22⋊Q8C2312yes—
220C2×C22⋊Q8C2312yes—
221C2×C22⋊Q8C2314yes—
222C2×C22⋊Q8C2312yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2318yes—
226#519—44no—
227C4×#41—28no—
228C4×#41—44no—
229C2×C4×Q8C2312yes—
230C2×C4×Q8C2314yes—
231C2×C4×Q8C2314yes—
232C2×C4×Q8C2314yes—
233C2×C4×Q8C2312yes—
234C2×C4×D4C2314yes—
235C2×C4×D4C2312yes—
236C2×C4×D4C2314yes—
237C2×C4×D4C2312yes—
238C2×#117—44no—
239C2×#117C2311yescharacteristic
240C2×#117C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C2×#117C2311yescharacteristic
244C2×#117C2312yes—
245C2×#117C2311yescharacteristic
246C2×#117C2312yes—
247C2×#117C2312yes—
248C2×#117C2312yes—
249C2×#117C2312yes—
250C2×#117C2314yes—
251C2×#117C2318yes—
252C2×#117C2318yes—
253C22×C4⋊C4—28no—
254C22×C4⋊C4C2312yes—
255C22×C4⋊C4C2311yescharacteristic
256C22×C4⋊C4C2311yescharacteristic
257C22×C4⋊C4C2312yes—
258C22×C4⋊C4C2312yes—
259C22×C4⋊C4C2311yescharacteristic
260C22×C4⋊C4C2312yes—
261C22×C4⋊C4C2312yes—
262C22×C4⋊C4C2312yes—
263C22×C4⋊C4C2312yes—
264C22×C4⋊C4C2314yes—
265C22×C4⋊C4C2314yes—
266C22×C22⋊C4C2314yes—
267C22×C22⋊C4C2312yes—
268C22×C22⋊C4C2312yes—
269C22×C22⋊C4C2312yes—
270C22×C22⋊C4C2318yes—
271C22×C42C2312yes—
272C22×C42C2311yescharacteristic
273C22×C42C2311yescharacteristic
274C22×C42C2312yes—
275C22×C42C2312yes—
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#400C2318yes—
280#400C2318yes—
281#400C2314yes—
282#400C2318yes—
283#400C2318yes—
284#400C2318yes—
285#399C2314yes—
286#399C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2314yes—
291#398C2318yes—
292#398C2318yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2314yes—
297#397C2318yes—
298#397C2318yes—
299#397C2318yes—
300#397C2318yes—
301#397C2318yes—
302#397C2318yes—
303#396C2318yes—
304#396C2314yes—
305#396C2318yes—
306#396C2318yes—
307#396C2314yes—
308#396C2318yes—
309#395C2314yes—
310#395C2318yes—
311#394C2318yes—
312#394C2318yes—
313#394C2318yes—
314#393C2318yes—
315#393C2314yes—
316#391C2314yes—
317#391C2314yes—
318#391C2314yes—
319#391C2312yes—
320#391C2312yes—
321#391C2318yes—
322#391C2312yes—
323#391C2312yes—
324#391C2312yes—
325#391C2312yes—
326#391C2312yes—
327#391C2314yes—
328#391C2318yes—
329#391C2318yes—
330#391C2312yes—
331#391C2314yes—
332#391C2312yes—
333#391C2314yes—
334#391C2312yes—
335#391C2312yes—
336#391C2314yes—
337#391C2312yes—
338#390C2318yes—
339#390C2312yes—
340#390C2312yes—
341#390C2312yes—
342#390C2312yes—
343#390C2312yes—
344#390C2312yes—
345#390C2312yes—
346#390C2314yes—
347#390C2312yes—
348#390C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2314yes—
355#389C2312yes—
356#389C2318yes—
357#389C2318yes—
358#389C2318yes—
359#389C2312yes—
360#389C2314yes—
361#389C2312yes—
362#389C2312yes—
363#388C2318yes—
364#388C2318yes—
365#388C2318yes—
366#388C2318yes—
367#388C2318yes—
368#388C2318yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#387C2318yes—
376#387C2318yes—
377#387C2318yes—
378#387C2318yes—
379#387C2318yes—
380#387C2318yes—
381#387C2318yes—
382#387C2318yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2314yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2314yes—
395#386C2314yes—
396#386C2318yes—
397#386C2314yes—
398#386C2318yes—
399#386C2314yes—
400#386C2314yes—
401#386C2314yes—
402#386C2314yes—
403#386C2314yes—
404#386C2314yes—
405#386C2314yes—
406#386C2314yes—
407#386C2314yes—
408#386C2314yes—
409#385C2318yes—
410#385C2318yes—
411#385C2318yes—
412#385C2318yes—
413#385C2318yes—
414#385C2314yes—
415#385C2318yes—
416#385C2318yes—
417#385C2318yes—
418#385C2318yes—
419#385C2314yes—
420#385C2318yes—
421#385C2314yes—
422#385C2314yes—
423#384C2312yes—
424#384C2314yes—
425#384C2312yes—
426#384C2314yes—
427#384C2312yes—
428#384C2312yes—
429#384C2312yes—
430#382C2318yes—
431#382C2312yes—
432#382C2318yes—
433#381C2314yes—
434#381C2312yes—
435#381C2312yes—
436#381C2314yes—
437#381C2318yes—
438#381C2318yes—
439#380C2318yes—
440#380C2314yes—
441#380C2318yes—
442#380C2314yes—
443#380C2314yes—
444#380C2314yes—
445#380C2314yes—
446#380C2314yes—
447#380C2314yes—
448#380C2314yes—
449#380C2314yes—
450#380C2314yes—
451#380C2318yes—
452#380C2318yes—
453#380C2318yes—
454#380C2314yes—
455#380C2312yes—
456#380C2312yes—
457#380C2312yes—
458#380C2314yes—
459#380C2312yes—
460#380C2314yes—
461#379C2318yes—
462#379C2312yes—
463#379C2314yes—
464#379C2312yes—
465C4×C4⋊C4C2318yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2318yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2318yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2314yes—
477C4×C22⋊C4C2318yes—
478C4×C22⋊C4C2314yes—
479C4×C22⋊C4C2314yes—
480C4×C22⋊C4C2318yes—
481C4×C22⋊C4C2314yes—
482C4×C22⋊C4C2314yes—
483C4×C22⋊C4C2312yes—
484C4×C22⋊C4C2312yes—
485C4×C22⋊C4C2314yes—
486C4×C22⋊C4C2318yes—
487C4×C22⋊C4C2312yes—
488C4×C22⋊C4C2312yes—
489C4×C22⋊C4C2312yes—
490C4×C22⋊C4C2312yes—
491C4×C22⋊C4C2312yes—
492C4×C22⋊C4C2312yes—
493C4×C22⋊C4C2311yescharacteristic
494C4×C22⋊C4C2311yescharacteristic
495C4×C22⋊C4C2311yescharacteristic
496C4×C22⋊C4C2311yescharacteristic
497C4×C22⋊C4C2312yes—
498C4×C22⋊C4C2312yes—
499C2×#95C2318yes—
500C2×#95C2314yes—
501C2×#95C2312yes—
502C2×#95C2314yes—
503C2×#95C2314yes—
504C25C2412yes—
505C25C2411yescharacteristic
506C2×#41—24no—
507C2×#41—28no—
508C2×#41—24no—
509C2×#41—24no—
510C2×#41—28no—
511C2×#41—28no—
512C2×#41—28no—
513C2×#41—24no—
514C2×#41—24no—
515C2×#41—24no—
516C2×#41—24no—
517C2×#41—24no—
518C2×#41—24no—
519C2×#41—44no—
520C2×#41—44no—
521C2×#41—42no—
522C2×#41—42no—
523C2×#41—464no—
524C2×#41#4118yes—
525C22×Q8—24no—
526C22×Q8—24no—
527C22×Q8—24no—
528C22×Q8—24no—
529C22×Q8—24no—
530C22×Q8—42no—
531C22×Q8C2412yes—
532C22×Q8C2412yes—
533C22×Q8C2411yescharacteristic
534C22×Q8C2412yes—
535C22×Q8C2411yescharacteristic
536C22×Q8C2414yes—
537C22×D4—28no—
538C22×D4—24no—
539C22×D4—28no—
540C22×D4—24no—
541C22×D4—42no—
542C22×D4—44no—
543C22×D4C2412yes—
544C22×D4C2411yescharacteristic
545C22×D4C2412yes—
546C22×D4C2412yes—
547C22×D4C2412yes—
548C22×D4C2412yes—
549C22×D4C2411yescharacteristic
550C23×C4—24no—
551C23×C4—24no—
552C23×C4—28no—
553C23×C4—28no—
554C23×C4—28no—
555C23×C4—44no—
556C23×C4—84no—
557C23×C4#4118yes—
558C23×C4C2412yes—
559C23×C4C2412yes—
560C23×C4C2412yes—
561C23×C4C2412yes—
562C23×C4C2414yes—
563C23×C4C2412yes—
564C23×C4C2412yes—
565C23×C4C2412yes—
566C23×C4C2411yescharacteristic
567C23×C4C2411yescharacteristic
568C23×C4C2411yescharacteristic
569C23×C4C2411yescharacteristic
570C23×C4C2411yescharacteristic
571C23×C4C2412yes—
572C23×C4C2414yes—
573C23×C4C2414yes—
574C23×C4C2412yes—
575C23×C4C2414yes—
576C23×C4C2412yes—
577C23×C4C2412yes—
578C23×C4C2414yes—
579C23×C4C2411yescharacteristic
580C4⋊Q8—28no—
581C4⋊Q8—44no—
582C4⋊Q8—44no—
583#126—88no—
584#126—88no—
585#125—44no—
586#124—28no—
587#124—44no—
588#123—216no—
589#123—48no—
590C22⋊Q8—28no—
591C22⋊Q8—28no—
592C22⋊Q8—28no—
593C22⋊Q8—28no—
594C22⋊Q8—216no—
595C22⋊Q8—216no—
596C22⋊Q8—48no—
597C22⋊Q8—48no—
598C22⋊Q8—88no—
599C4×Q8—28no—
600C4×Q8—48no—
601C4×Q8—44no—
602C4×Q8—48no—
603C4×Q8—48no—
604C4×D4—216no—
605C4×D4—28no—
606C4×D4—44no—
607C4×D4—48no—
608#117—28no—
609#117—24no—
610#117—24no—
611#117—24no—
612#117—24no—
613#117—24no—
614#117—24no—
615#117—44no—
616#117—44no—
617#117—44no—
618#117—48no—
619#117—44no—
620#117—88no—
621#117—88no—
622C2×C4⋊C4—28no—
623C2×C4⋊C4—28no—
624C2×C4⋊C4—28no—
625C2×C4⋊C4—28no—
626C2×C4⋊C4—28no—
627C2×C4⋊C4—24no—
628C2×C4⋊C4—24no—
629C2×C4⋊C4—28no—
630C2×C4⋊C4—24no—
631C2×C4⋊C4—44no—
632C2×C4⋊C4—84no—
633C2×C4⋊C4—84no—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2418yes—
669C2×C4⋊C4C2418yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C22⋊C4—28no—
673C2×C22⋊C4—28no—
674C2×C22⋊C4—216no—
675C2×C22⋊C4—44no—
676C2×C22⋊C4—88no—
677C2×C22⋊C4C2412yes—
678C2×C22⋊C4C2412yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2412yes—
683C2×C22⋊C4C2412yes—
684C2×C22⋊C4C2412yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2412yes—
688C2×C22⋊C4C2412yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2412yes—
691C2×C22⋊C4C2412yes—
692C2×C22⋊C4C2418yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2418yes—
696C2×C22⋊C4C2418yes—
697C2×C22⋊C4C2418yes—
698C2×C22⋊C4C2418yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2418yes—
703C2×C22⋊C4C2418yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2418yes—
707C2×C22⋊C4C2412yes—
708C2×C42—28no—
709C2×C42—24no—
710C2×C42—24no—
711C2×C42—44no—
712C2×C42—44no—
713C2×C42C2412yes—
714C2×C42C2412yes—
715C2×C42C2412yes—
716C2×C42C2411yescharacteristic
717C2×C42C2412yes—
718C2×C42C2411yescharacteristic
719C2×C42C2412yes—
720C2×C42C2412yes—
721C2×C42C2412yes—
722C2×C42C2412yes—
723C2×C42C2414yes—
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2418yes—
727C2×C42C2414yes—
728C2×C42C2418yes—
729C2×C42C2418yes—
730C2×C42C2418yes—
731C2×C42C2414yes—
732#95C2412yes—
733#95C2414yes—
734#95C2412yes—
735#95C2414yes—
736#95C2412yes—
737#95C2412yes—
738#95C2414yes—
739#95C2418yes—
740#95C2418yes—
741#95C2418yes—
742#95C2418yes—
743#95C2418yes—
744#95C2418yes—
745#95C2418yes—
746#95C2418yes—
747#95C2414yes—
748#95C2418yes—
749#95C2418yes—
750#95C2414yes—
751#95C2418yes—
752#95C2418yes—
753#95C2418yes—
754#95C2418yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2418yes—
760#95C2414yes—
761#95C2418yes—
762#95C2414yes—
763#95C2414yes—
764#95C2414yes—
765#95C2418yes—
766#95C2414yes—
767#95C2418yes—
768C24—22no—
769C24—22no—
770C24—24no—
771C24—24no—
772C24—24no—
773C24—28no—
774C24—42no—
775C24—44no—
776C24—42no—
777C24C2×#4114yes—
778C24C2512yes—
779C24C2511yescharacteristic
780C24C2512yes—
781C24C2511yescharacteristic
782C24C2511yescharacteristic
783#41—232no—
784#41—432no—
785#41—432no—
786#41—416no—
787#41—416no—
788#41—416no—
789C2×Q8—22no—
790C2×Q8—24no—
791C2×Q8—24no—
792C2×Q8—24no—
793C2×Q8—24no—
794C2×Q8—24no—
795C2×Q8—24no—
796C2×Q8—22no—
797C2×Q8—22no—
798C2×Q8—22no—
799C2×Q8—24no—
800C2×Q8—24no—
801C2×Q8—22no—
802C2×Q8—28no—
803C2×Q8—42no—
804C2×Q8—44no—
805C2×Q8—44no—
806C2×Q8—416no—
807C2×Q8—416no—
808C2×Q8C2×#4114yes—
809C2×D4—24no—
810C2×D4—24no—
811C2×D4—24no—
812C2×D4—24no—
813C2×D4—24no—
814C2×D4—24no—
815C2×D4—24no—
816C2×D4—24no—
817C2×D4—24no—
818C2×D4—22no—
819C2×D4—24no—
820C2×D4—24no—
821C2×D4—22no—
822C2×D4—22no—
823C2×D4—22no—
824C2×D4—22no—
825C2×D4—416no—
826C2×D4—42no—
827C2×D4—42no—
828C2×D4—42no—
829C2×D4—432no—
830C2×D4C2×#4118yes—
831C2×D4C2×#4114yes—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—232no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—24no—
840C22×C4—22no—
841C22×C4—24no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—28no—
846C22×C4—24no—
847C22×C4—24no—
848C22×C4—28no—
849C22×C4—24no—
850C22×C4—24no—
851C22×C4—24no—
852C22×C4—24no—
853C22×C4—24no—
854C22×C4—24no—
855C22×C4—24no—
856C22×C4—24no—
857C22×C4—28no—
858C22×C4—28no—
859C22×C4—24no—
860C22×C4—24no—
861C22×C4—24no—
862C22×C4—24no—
863C22×C4—24no—
864C22×C4—24no—
865C22×C4—24no—
866C22×C4—24no—
867C22×C4—28no—
868C22×C4—24no—
869C22×C4—28no—
870C22×C4—42no—
871C22×C4—42no—
872C22×C4—44no—
873C22×C4—48no—
874C22×C4—42no—
875C22×C4—42no—
876C22×C4—42no—
877C22×C4—432no—
878C22×C4—44no—
879C22×C4—44no—
880C22×C4—44no—
881C22×C4—48no—
882C22×C4—44no—
883C22×C4—44no—
884C22×C4—44no—
885C22×C4—44no—
886C22×C4—816no—
887C22×C4C2×#4118yes—
888C22×C4C2×#4114yes—
889C22×C4C2×#4114yes—
890C22×C4C2×#4114yes—
891C22×C4C2×#4114yes—
892C22×C4C2×#4114yes—
893C22×C4C2×#4114yes—
894C22×C4C2×#4114yes—
895C22×C4H(5,𝔽2)14yes—
896C22×C4C2512yes—
897C22×C4C2514yes—
898C22×C4C2512yes—
899C22×C4C2514yes—
900C22×C4C2514yes—
901C22×C4C2514yes—
902C22×C4C2514yes—
903C22×C4C2514yes—
904C22×C4C2514yes—
905C22×C4C2514yes—
906C22×C4C2514yes—
907C22×C4C2512yes—
908C22×C4C2514yes—
909C22×C4C2511yescharacteristic
910C22×C4C2512yes—
911C22×C4C2511yescharacteristic
912C22×C4C2512yes—
913C22×C4C2512yes—
914C22×C4C2511yescharacteristic
915C22×C4C2511yescharacteristic
916C4⋊C4—28no—
917C4⋊C4—28no—
918C4⋊C4—24no—
919C4⋊C4—24no—
920C4⋊C4—24no—
921C4⋊C4—24no—
922C4⋊C4—24no—
923C4⋊C4—24no—
924C4⋊C4—28no—
925C4⋊C4—28no—
926C4⋊C4—28no—
927C4⋊C4—24no—
928C4⋊C4—24no—
929C4⋊C4—216no—
930C4⋊C4—24no—
931C4⋊C4—24no—
932C4⋊C4—24no—
933C4⋊C4—24no—
934C4⋊C4—28no—
935C4⋊C4—28no—
936C4⋊C4—28no—
937C4⋊C4—44no—
938C4⋊C4—48no—
939C4⋊C4—48no—
940C4⋊C4—48no—
941C4⋊C4—48no—
942C4⋊C4—44no—
943C4⋊C4—48no—
944C4⋊C4—44no—
945C4⋊C4—48no—
946C4⋊C4—48no—
947C4⋊C4—44no—
948C4⋊C4—44no—
949C4⋊C4—44no—
950C4⋊C4—48no—
951C4⋊C4—48no—
952C4⋊C4—44no—
953C4⋊C4—44no—
954C22⋊C4—28no—
955C22⋊C4—28no—
956C22⋊C4—28no—
957C22⋊C4—24no—
958C22⋊C4—24no—
959C22⋊C4—216no—
960C22⋊C4—24no—
961C22⋊C4—24no—
962C22⋊C4—24no—
963C22⋊C4—24no—
964C22⋊C4—28no—
965C22⋊C4—24no—
966C22⋊C4—28no—
967C22⋊C4—24no—
968C22⋊C4—28no—
969C22⋊C4—24no—
970C22⋊C4—28no—
971C22⋊C4—44no—
972C22⋊C4—48no—
973C22⋊C4—48no—
974C22⋊C4—48no—
975C22⋊C4—48no—
976C22⋊C4—44no—
977C22⋊C4—44no—
978C22⋊C4—44no—
979C22⋊C4—48no—
980C22⋊C4—48no—
981C22⋊C4—44no—
982C22⋊C4—48no—
983C22⋊C4—44no—
984C22⋊C42−1+418yes—
985C42—22no—
986C42—24no—
987C42—22no—
988C42—28no—
989C42—24no—
990C42—24no—
991C42—22no—
992C42—22no—
993C42—24no—
994C42—24no—
995C42—24no—
996C42—24no—
997C42—24no—
998C42—44no—
999C42—44no—
1000C42—48no—
1001C42—48no—
1002C42—48no—
1003C42—48no—
1004C23—21no—
1005C23—21no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—21no—
1010C23—22no—
1011C23—21no—
1012C23—22no—
1013C23—22no—
1014C23—24no—
1015C23—24no—
1016C23—22no—
1017C23—28no—
1018C23—28no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—24no—
1023C23—24no—
1024C23—44no—
1025C23—48no—
1026C23—48no—
1027C23—48no—
1028C23—416no—
1029C23—48no—
1030C23—84no—
1031C23—88no—
1032C23C22×#4114yes—
1033C23C22×#4112yes—
1034C23C22×#4112yes—
1035C23C22×#4112yes—
1036C23C22×#4112yes—
1037C23C2×H(5,𝔽2)12yes—
1038C23C2×2−1+414yes—
1039C23C2611yescharacteristic
1040Q8—28no—
1041Q8—48no—
1042Q8—48no—
1043Q8—48no—
1044Q8—44no—
1045Q8—88no—
1046D4—216no—
1047D4—28no—
1048D4—48no—
1049D4—48no—
1050D4—48no—
1051D4—48no—
1052D4—44no—
1053C2×C4—22no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—21no—
1059C2×C4—22no—
1060C2×C4—21no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—28no—
1064C2×C4—28no—
1065C2×C4—28no—
1066C2×C4—28no—
1067C2×C4—28no—
1068C2×C4—216no—
1069C2×C4—24no—
1070C2×C4—22no—
1071C2×C4—24no—
1072C2×C4—24no—
1073C2×C4—24no—
1074C2×C4—24no—
1075C2×C4—24no—
1076C2×C4—24no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—24no—
1083C2×C4—24no—
1084C2×C4—24no—
1085C2×C4—22no—
1086C2×C4—24no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—24no—
1090C2×C4—24no—
1091C2×C4—24no—
1092C2×C4—24no—
1093C2×C4—24no—
1094C2×C4—24no—
1095C2×C4—24no—
1096C2×C4—24no—
1097C2×C4—24no—
1098C2×C4—24no—
1099C2×C4—28no—
1100C2×C4—28no—
1101C2×C4—24no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—28no—
1105C2×C4—48no—
1106C2×C4—48no—
1107C2×C4—416no—
1108C2×C4—48no—
1109C2×C4—48no—
1110C2×C4—48no—
1111C2×C4—416no—
1112C2×C4—48no—
1113C2×C4—48no—
1114C2×C4—88no—
1115C2×C4—84no—
1116C2×C4—88no—
1117C2×C4—84no—
1118C2×C4—84no—
1119C2×C4—88no—
1120C2×C4#551116yes—
1121C2×C4C22×#4114yes—
1122C2×C4C22×#4112yes—
1123C2×C4C22×#4112yes—
1124C2×C4C22×#4112yes—
1125C2×C4C22×#4112yes—
1126C2×C4C22×#4112yes—
1127C2×C4C22×#4112yes—
1128C2×C4C2×H(5,𝔽2)12yes—
1129C2×C4C2×H(5,𝔽2)12yes—
1130C2×C4C2×2−1+414yes—
1131C2×C4C2×2−1+414yes—
1132C22—24no—
1133C22—24no—
1134C22—22no—
1135C22—22no—
1136C22—22no—
1137C22—24no—
1138C22—24no—
1139C22—22no—
1140C22—28no—
1141C22—22no—
1142C22—22no—
1143C22—22no—
1144C22—24no—
1145C22—416no—
1146C22—42no—
1147C22—42no—
1148C22—42no—
1149C22—44no—
1150C22—42no—
1151C22—44no—
1152C22—42no—
1153C22—42no—
1154C22—44no—
1155C22—42no—
1156C22—816no—
1157C22C2×#55114yes—
1158C22#350914yes—
1159C22C23×#4111yescharacteristic
1160C22C23×#4111yescharacteristic
1161C22C22×H(5,𝔽2)11yescharacteristic
1162C22C22×2−1+412yes—
1163C22H(7,𝔽2)12yes—
1164C4—24no—
1165C4—24no—
1166C4—22no—
1167C4—22no—
1168C4—24no—
1169C4—44no—
1170C4—44no—
1171C4—42no—
1172C4—44no—
1173C4—44no—
1174C4—44no—
1175C4—42no—
1176C4—44no—
1177C4—44no—
1178C4—44no—
1179C4—44no—
1180C4—42no—
1181C4—44no—
1182C4C2×#55114yes—
1183C4C2×#55114yes—
1184C2—24no—
1185C2—24no—
1186C2—42no—
1187C2—44no—
1188C2—82no—
1189C2C22×#55111yescharacteristic
1190C2C2×#350911yescharacteristic
1191C2#6285511yescharacteristic
1192C2#6294412yes—
1193C2#6300012yes—
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. #59867C2semidirect
2. #59424C2semidirect
3. #59268C2semidirect
4. #45366C2semidirect
5. #44962C2semidirect
6. #44043C2semidirect
7. #39563C2semidirect
8. #37971C2semidirect
9. #37850C2semidirect
10. #36190C2semidirect
11. #35673C2semidirect
12. #35628C2semidirect
13. #35557C2semidirect
14. #35557C2semidirect
15. #35307C2semidirect
17. #35280C2semidirect
18. C2×#2502C2semidirect
19. #34739C2semidirect
20. #34268C2semidirect
21. #34203C2semidirect
22. #34188C2semidirect
23. #34178C2semidirect
29. C2×#533C22semidirect
31. C2×#519C22semidirect
36. #2857C22semidirect
37. #2855C22semidirect
39. #2799C22semidirect
40. #2786C22semidirect
41. #2761C22semidirect
42. #2755C22semidirect
43. #2751C22semidirect
44. #2750C22semidirect
45. #2747C22semidirect
46. #2744C22semidirect
47. #2743C22semidirect
48. #2740C22semidirect
49. #2739C22semidirect
50. #2722C22semidirect
51. #2629C22semidirect
52. #2625C22semidirect
54. #2609C22semidirect
55. #2601C22semidirect
56. #2601C22semidirect
57. #2592C22semidirect
58. #2588C22semidirect
59. #2582C22semidirect
60. #2574C22semidirect
62. #2569C22semidirect
63. #2568C22semidirect
64. #2560C22semidirect
65. #2538C22semidirect
66. #2522C22semidirect
67. #2520C22semidirect
68. #2512C22semidirect
69. #2512C22semidirect
70. #2511C22semidirect
71. #2511C22semidirect
77. #2502C22semidirect
78. #2502C22semidirect
79. #2502C22semidirect
80. #2498C22semidirect
81. #2497C22semidirect
82. #2497C22semidirect
83. #2496C22semidirect
84. #2496C22semidirect
85. #2492C22semidirect
86. #2489C22semidirect
87. #2488C22semidirect
88. #2481C22semidirect
89. #2481C22semidirect
92. #2479C22semidirect
93. #2477C22semidirect
94. #2448C22semidirect
95. #2447C22semidirect
96. #2446C22semidirect
97. #2446C22semidirect
99. #2441C22semidirect
101. #2439C22semidirect
102. #2438C22semidirect
103. #2438C22semidirect
110. #2423C22semidirect
111. #2421C22semidirect
112. #2419C22semidirect
113. #2417C22semidirect
116. #2396C22semidirect
117. C2×#398C22semidirect
119. #2367C22semidirect
120. #2365C22semidirect
121. #2362C22semidirect
123. #2359C22semidirect
124. #2355C22semidirect
125. #2354C22semidirect
126. #2352C22semidirect
129. #2344C22semidirect
130. #2344C22semidirect
131. #2344C22semidirect
140. #2323C22semidirect
141. #2323C22semidirect
142. #2316C22semidirect
143. #2316C22semidirect
144. #2316C22semidirect
145. #2314C22semidirect
146. #2313C22semidirect
157. #2310C22semidirect
160. C4×C22⋊Q8C22semidirect
165. #2296C22semidirect
166. #2296C22semidirect
168. C2×#391C22semidirect
169. C2×#391C22semidirect
173. #2285C22semidirect
174. #2285C22semidirect
175. C2×#384C22semidirect
176. C2×#384C22semidirect
182. #2274C22semidirect
183. #2274C22semidirect
184. #2274C22semidirect

Maximal subgroups

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

subgroupindex
#598672
#594242
#592682
#453662
#449622
#440432
#395632
#379712
#378502
#361902
#356732
#356282
#355572
#353072
#353052
#352802
C2×#25022
#347392
#342682
#342032
#341882
#341782
C22⋊C4×#412
C2×#23112