Finite Group Databasebeta

← #7643322

Subgroups — #7643322

Order 512.

8240 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3508C211yesmaximal, characteristic, complemented
2C2×#3444C211yesmaximal, characteristic, complemented
3#39726C214yesmaximal, complemented
4#39341C214yesmaximal, complemented
5#39137C214yesmaximal, complemented
6#38909C214yesmaximal, complemented
7#38024C218yesmaximal, complemented
8#37648C218yesmaximal, complemented
9#37276C218yesmaximal, complemented
10#36625C211yesmaximal, characteristic, complemented
11C2×#2856C211yesmaximal, characteristic, complemented
12#35563C212yesmaximal, complemented
13#35533C212yesmaximal, complemented
14#35515C212yesmaximal, complemented
15#35514C212yesmaximal, complemented
16#35292C214yesmaximal, complemented
17#35280C211yesmaximal, characteristic, complemented
18#35273C214yesmaximal, complemented
19#35272C211yesmaximal, characteristic, complemented
20#34183C211yesmaximal, characteristic, complemented
21#3508—216no—
22C2×#559C2214yescomplemented
23C2×#550C2214yescomplemented
24C2×#546C2218yes—
25C2×#540C2214yescomplemented
26C2×#537C2218yescomplemented
27C2×#535C2212yes—
28C2×#535C2212yes—
29#3444—216no—
30C2×#533C2211yescharacteristic
31C2×#533C2211yescharacteristic
32C2×#533C2212yescomplemented
33C2×#532C2211yescharacteristic
34C2×#532C2214yescomplemented
35C2×#532C2212yescomplemented
36C22×#127C2211yescharacteristic
37C2×#529C2214yes—
38C2×#529C2214yescomplemented
39C2×#529C2212yescomplemented
40C2×#529C2212yescomplemented
41C2×#525C2214yes—
42C2×#525C2211yescharacteristic
43C2×#525C2211yescharacteristic
44C22×#121C2214yes—
45C22×#121C2212yes—
46C2×#520C2212yes—
47C2×#518C2212yes—
48C2×C4×#41C2211yescharacteristic
49C2×C4×#41C2211yescharacteristic
50C2×C4×#41C2214yescomplemented
51C23×C42C2211yescharacteristic
52#2857C2212yescomplemented
53#2857C2212yescomplemented
54#2857C2214yescomplemented
55#2856C2214yes—
56#2856C2214yes—
57#2856C2214yes—
58#2856C2214yes—
59#2856C2212yescomplemented
60#2856C2212yescomplemented
61#2855C2214yes—
62#2851C2214yescomplemented
63#2848C2214yes—
64#2707C22116yescomplemented
65#2705C22116yescomplemented
66#2691C22116yescomplemented
67#2682C22116yescomplemented
68#2681C22116yescomplemented
69#2676C22116yescomplemented
70#2675C22116yescomplemented
71#2671C22116yescomplemented
72#2629C2214yescomplemented
73#2624C2218yescomplemented
74#2620C2218yescomplemented
75#2620C2218yescomplemented
76#2619C2214yescomplemented
77#2615C2218yescomplemented
78#2592C2218yescomplemented
79#2582C2214yescomplemented
80#2580C2218yescomplemented
81#2548C2214yescomplemented
82#2548C2214yescomplemented
83#2545C2214yescomplemented
84#2544C2214yescomplemented
85#2541C2214yescomplemented
86#2541C2214yescomplemented
87#2540C2218yescomplemented
88#2538C2218yescomplemented
89#2538C2218yescomplemented
90#2538C2214yescomplemented
91#2537C2218yescomplemented
92#2537C2218yescomplemented
93#2535C2218yescomplemented
94#2534C2218yes—
95#2454C2218yescomplemented
96#2452C2218yescomplemented
97#2437C22116yes—
98#2428C2218yescomplemented
99#2428C2218yescomplemented
100#2427C2218yescomplemented
101#2426C2218yescomplemented
102#2424C22116yes—
103#2417C2218yes—
104#2416C2218yescomplemented
105#2416C2218yescomplemented
106#2416C2218yescomplemented
107#2416C2218yescomplemented
108#2414C2218yescomplemented
109#2414C2218yescomplemented
110#2412C2218yes—
111#2410C2218yes—
112#2408C2218yes—
113#2408C2218yes—
114#2407C2218yescomplemented
115#2407C2218yescomplemented
116Q8×C4⋊C4C2214yescomplemented
117D4×C4⋊C4C2218yes—
118D4×C4⋊C4C2214yescomplemented
119#2324C2218yescomplemented
120#2324C2218yescomplemented
121#2317C2212yes—
122#2317C2214yescomplemented
123#2316C2212yes—
124#2311C2212yes—
125#2311C2218yescomplemented
126#2309C2212yes—
127C4×C22⋊Q8C2214yescomplemented
128C4×C22⋊Q8C2214yescomplemented
129#2296C2212yes—
130C2×#390C2214yes—
131C2×#390C2212yes—
132#2285C2211yescharacteristic
133#2285C2212yescomplemented
134C2×#384C2211yescharacteristic
135C2×#384C2212yescomplemented
136#2280C2212yes—
137C22×#41C2311yescharacteristic
138C22×#41C2314yes—
139C22×#41C2311yescharacteristic
140C22×#41C2318yes—
141C23×D4C2312yes—
142C23×D4C2314yes—
143C23×D4C2314yes—
144C24×C4C2311yescharacteristic
145C24×C4C2312yes—
146#559—232no—
147#550—232no—
148#546—264no—
149#540—232no—
150#537—432no—
151#535—216no—
152#535—48no—
153#533—216no—
154#533—28no—
155#533—28no—
156#532—28no—
157#532—216no—
158#532—232no—
159C2×C4⋊Q8C2312yes—
160C2×C4⋊Q8C2311yescharacteristic
161C2×C4⋊Q8C2312yes—
162C2×#127—28no—
163C2×#127C2312yes—
164C2×#127C2312yes—
165C2×#127C2314yes—
166C2×#127C2311yescharacteristic
167C2×#127C2314yes—
168C2×#127C2314yes—
169#529—216no—
170#529—232no—
171#529—216no—
172#529—232no—
173C2×#126C2314yes—
174C2×#126C2314yes—
175C2×#125C2312yes—
176C2×#125C2314yes—
177C2×#125C2312yes—
178C2×#124C2318yes—
179C2×#124C2314yes—
180C2×#124C2311yescharacteristic
181C2×#124C2311yescharacteristic
182C2×#124C2314yes—
183C2×#124C2314yes—
184#525—28no—
185#525—232no—
186#525—28no—
187C2×#123C2312yes—
188C2×#123C2314yes—
189C2×#123C2312yes—
190C2×#123C2314yes—
191C2×#123C23116yes—
192C2×C22⋊Q8C2314yes—
193C2×C22⋊Q8C2314yes—
194C2×C22⋊Q8C2314yes—
195C2×C22⋊Q8C2314yes—
196C2×C22⋊Q8C2312yes—
197C2×C22⋊Q8C2312yes—
198C2×C22⋊Q8C2314yes—
199C2×C22⋊Q8C2318yes—
200C2×C22⋊Q8C23116yes—
201C2×#121—48no—
202C2×#121—416no—
203C2×#121C2318yes—
204C2×#121C2318yes—
205C2×#121C2314yes—
206C2×#121C2314yes—
207C2×#121C2312yes—
208C2×#121C2312yes—
209C2×#121C2318yes—
210C2×#121C23116yes—
211C2×#121C2318yes—
212C2×#121C2318yes—
213C2×#121C2318yes—
214C2×#121C2318yes—
215C2×#121C2318yes—
216C2×#121C2318yes—
217C2×#121C2314yes—
218C2×#121C2314yes—
219C2×#121C2318yes—
220C2×#121C23116yes—
221C2×#121C23116yes—
222C2×#121C23116yes—
223C2×#120C2312yes—
224C2×#120C2318yes—
225C2×#120C2312yes—
226C2×#120C2318yes—
227#520—48no—
228#518—216no—
229C4×#41—28no—
230C4×#41—232no—
231C4×#41D4116yescomplemented
232C2×C4×Q8C2314yes—
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2314yes—
235C2×C4×Q8C2314yes—
236C2×C4×Q8C2314yes—
237C2×C4×Q8C2312yes—
238C2×C4×D4C2318yes—
239C2×C4×D4C2318yes—
240C2×C4×D4C2314yes—
241C2×C4×D4C2312yes—
242C2×C4×D4C2314yes—
243C2×C4×D4C2314yes—
244C2×C4×D4C2314yes—
245C2×C4×D4C2314yes—
246C2×C4×D4C2314yes—
247C2×C4×D4C2314yes—
248C2×C4×D4C2318yes—
249C2×C4×D4C2318yes—
250C2×C4×D4C2314yes—
251C2×C4×D4C2314yes—
252C2×C4×D4C2312yes—
253C2×#117C2311yescharacteristic
254C2×#117C2312yes—
255C2×#117C2312yes—
256C2×#117C2314yes—
257C2×#117C2314yes—
258C2×#117C2314yes—
259C2×#117C2312yes—
260C2×#117C2314yes—
261C2×#117C2311yescharacteristic
262C2×#117C2312yes—
263C22×C4⋊C4C2312yes—
264C22×C4⋊C4C2318yes—
265C22×C4⋊C4C2314yes—
266C22×C4⋊C4C2314yes—
267C22×C22⋊C4C2318yes—
268C22×C22⋊C4C2314yes—
269C22×C22⋊C4C2318yes—
270C22×C42—28no—
271C22×C42C2312yes—
272C22×C42C2312yes—
273C22×C42C2312yes—
274C22×C42C2312yes—
275C22×C42C2312yes—
276C22×C42C2312yes—
277C22×C42C2311yescharacteristic
278C22×C42C2311yescharacteristic
279C22×C42C2312yes—
280#399C23116yes—
281#398C23116yes—
282#397C23116yes—
283#396C23116yes—
284#396C23116yes—
285#396C23116yes—
286#396C23116yes—
287#396C23116yes—
288#394C23116yes—
289#394C23116yes—
290#394C23116yes—
291#394C23116yes—
292#394C23116yes—
293#394C23116yes—
294#394C23116yes—
295#393C23116yes—
296#392C23116yes—
297#392C23116yes—
298#392C23116yes—
299#392C23116yes—
300#391C2314yes—
301#391C2314yes—
302#391C2318yes—
303#391C2314yes—
304#390C2314yes—
305#390C2314yes—
306#390C2318yes—
307#390C2314yes—
308#390C2318yes—
309#390C2318yes—
310#390C2318yes—
311#390C23116yes—
312#390C23116yes—
313#390C2318yes—
314#390C2318yes—
315#390C2318yes—
316#390C2318yes—
317#390C2314yes—
318#390C2314yes—
319#389C2318yes—
320#389C2318yes—
321#389C2318yes—
322#389C23116yes—
323#389C2314yes—
324#389C2318yes—
325#389C2314yes—
326#389C2314yes—
327#389C2314yes—
328#388C23116yes—
329#388C23116yes—
330#387C2318yes—
331#387C2318yes—
332#386C2318yes—
333#386C23116yes—
334#386C23116yes—
335#386C23116yes—
336#386C23116yes—
337#385C2318yes—
338#385C23116yes—
339#385C23116yes—
340#385C23116yes—
341#385C2318yes—
342#385C2318yes—
343#385C2318yes—
344#384C2314yes—
345#384C2312yes—
346#384C2314yes—
347#384C2312yes—
348#384C2311yescharacteristic
349#384C2311yescharacteristic
350#384C2318yes—
351#382C2314yes—
352#382C2312yes—
353#381C2314yes—
354#380C2318yes—
355#380C23116yes—
356#380C23116yes—
357#380C2318yes—
358#380C2314yes—
359#380C2318yes—
360#380C2314yes—
361#380C2314yes—
362#380C2314yes—
363#380C2314yes—
364#380C2318yes—
365#379C2318yes—
366#379C2314yes—
367C4×C4⋊C4C2318yes—
368C4×C4⋊C4C2314yes—
369C4×C4⋊C4C2314yes—
370C4×C4⋊C4C2314yes—
371C4×C22⋊C4C2318yes—
372C25C2411yescharacteristic
373C25C2414yes—
374C2×#41—216no—
375C2×#41—24no—
376C2×#41—232no—
377C2×#41—24no—
378C2×#41—24no—
379C2×#41—216no—
380C2×#41—24no—
381C2×#41—24no—
382C2×#41—48no—
383C2×#41—416no—
384C2×#41—416no—
385C2×#41C2×D418yes—
386C22×Q8C2411yescharacteristic
387C22×Q8C2414yes—
388C22×Q8C2414yes—
389C22×Q8C2411yescharacteristic
390C22×D4—28no—
391C22×D4—216no—
392C22×D4—28no—
393C22×D4—28no—
394C22×D4—48no—
395C22×D4—48no—
396C22×D4—48no—
397C22×D4—416no—
398C22×D4C2412yes—
399C22×D4C2414yes—
400C22×D4C2414yes—
401C22×D4C2411yescharacteristic
402C22×D4C2418yes—
403C22×D4C2414yes—
404C22×D4C2414yes—
405C22×D4C2414yes—
406C22×D4C2412yes—
407C22×D4C2411yescharacteristic
408C22×D4C24116yes—
409C22×D4C24116yes—
410C22×D4C2418yes—
411C22×D4C2418yes—
412C22×D4C2418yes—
413C23×C4—28no—
414C23×C4—24no—
415C23×C4—28no—
416C23×C4—24no—
417C23×C4—24no—
418C23×C4—44no—
419C23×C4C2411yescharacteristic
420C23×C4C2414yes—
421C23×C4C2412yes—
422C23×C4C2412yes—
423C23×C4C2412yes—
424C23×C4C2412yes—
425C23×C4C2412yes—
426C23×C4C2412yes—
427C23×C4C2412yes—
428C23×C4C2412yes—
429C23×C4C2414yes—
430C23×C4C2412yes—
431C23×C4C2412yes—
432C23×C4C2414yes—
433C23×C4C24116yes—
434C23×C4C2418yes—
435C23×C4C2411yescharacteristic
436C4⋊Q8—24no—
437C4⋊Q8—28no—
438C4⋊Q8—28no—
439#127—24no—
440#127—216no—
441#127—28no—
442#127—28no—
443#127—216no—
444#127—48no—
445#126—216no—
446#126—216no—
447#125—216no—
448#125—28no—
449#125—28no—
450#124—24no—
451#124—216no—
452#124—24no—
453#124—216no—
454#124—232no—
455#124—48no—
456#123—28no—
457#123—216no—
458#123—264no—
459#123—216no—
460#123—28no—
461C22⋊Q8—28no—
462C22⋊Q8—216no—
463C22⋊Q8—216no—
464C22⋊Q8—216no—
465C22⋊Q8—28no—
466C22⋊Q8—216no—
467C22⋊Q8—432no—
468C22⋊Q8—48no—
469C22⋊Q8—416no—
470#121—28no—
471#121—216no—
472#121—232no—
473#121—232no—
474#121—232no—
475#121—28no—
476#121—216no—
477#121—264no—
478#121—416no—
479#121—432no—
480#121—432no—
481#121—432no—
482#121—416no—
483#121—416no—
484#121—416no—
485#121—416no—
486#121—48no—
487#121—48no—
488#121—416no—
489#121—416no—
490#120—28no—
491#120—232no—
492#120—28no—
493#120—416no—
494C4×Q8—216no—
495C4×Q8—216no—
496C4×Q8—28no—
497C4×Q8—216no—
498C4×Q8—48no—
499C4×Q8C2×D4116yescomplemented
500C4×D4—216no—
501C4×D4—216no—
502C4×D4—216no—
503C4×D4—216no—
504C4×D4—216no—
505C4×D4—232no—
506C4×D4—216no—
507C4×D4—216no—
508C4×D4—28no—
509C4×D4—232no—
510C4×D4—232no—
511C4×D4—48no—
512C4×D4—416no—
513C4×D4C2×D4132yes—
514C4×D4C2×D4116yescomplemented
515#117—24no—
516#117—216no—
517#117—28no—
518#117—28no—
519#117—216no—
520#117—216no—
521#117—28no—
522#117—48no—
523#117C2×D418yes—
524#117C2×D4116yescomplemented
525C2×C4⋊C4—28no—
526C2×C4⋊C4—48no—
527C2×C4⋊C4—48no—
528C2×C4⋊C4—416no—
529C2×C4⋊C4C2414yes—
530C2×C4⋊C4C2412yes—
531C2×C4⋊C4C2418yes—
532C2×C4⋊C4C2414yes—
533C2×C4⋊C4C2414yes—
534C2×C4⋊C4C2412yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2412yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2418yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C2418yes—
549C2×C4⋊C4C2418yes—
550C2×C4⋊C4C24116yes—
551C2×C4⋊C4C24116yes—
552C2×C4⋊C4C2418yes—
553C2×C4⋊C4C2412yes—
554C2×C4⋊C4C2414yes—
555C2×C22⋊C4—232no—
556C2×C22⋊C4—416no—
557C2×C22⋊C4—48no—
558C2×C22⋊C4C2414yes—
559C2×C22⋊C4C24116yes—
560C2×C22⋊C4C24116yes—
561C2×C22⋊C4C2414yes—
562C2×C22⋊C4C2412yes—
563C2×C22⋊C4C2414yes—
564C2×C22⋊C4C2414yes—
565C2×C22⋊C4C2414yes—
566C2×C22⋊C4C2414yes—
567C2×C22⋊C4C2414yes—
568C2×C22⋊C4C2414yes—
569C2×C22⋊C4C2414yes—
570C2×C22⋊C4C24116yes—
571C2×C22⋊C4C2418yes—
572C2×C22⋊C4C24116yes—
573C2×C22⋊C4C24116yes—
574C2×C22⋊C4C2418yes—
575C2×C22⋊C4C2418yes—
576C2×C22⋊C4C2418yes—
577C2×C22⋊C4C24116yes—
578C2×C22⋊C4C24116yes—
579C2×C22⋊C4C24116yes—
580C2×C22⋊C4C2418yes—
581C2×C22⋊C4C2412yes—
582C2×C22⋊C4C2414yes—
583C2×C42—28no—
584C2×C42—24no—
585C2×C42—28no—
586C2×C42—28no—
587C2×C42—28no—
588C2×C42—28no—
589C2×C42—28no—
590C2×C42C2×D418yes—
591C2×C42C2×D4116yescomplemented
592C2×C42C2412yes—
593C2×C42C2412yes—
594C2×C42C2414yes—
595C2×C42C2414yes—
596C2×C42C2414yes—
597C2×C42C2412yes—
598C2×C42C2412yes—
599C2×C42C2411yescharacteristic
600C2×C42C2412yes—
601C2×C42C2412yes—
602C2×C42C2411yescharacteristic
603C2×C42C2418yes—
604C2×C42C2411yescharacteristic
605C2×C42C2412yes—
606C2×C42C2414yes—
607C2×C42C2412yes—
608C2×C42C2411yescharacteristic
609#95C2418yes—
610#95C2418yes—
611#95C2418yes—
612#95C24116yes—
613#95C2418yes—
614#95C2418yes—
615#95C24116yes—
616#95C24116yes—
617C24—24no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—28no—
622C24—28no—
623C24—28no—
624C24—42no—
625C24—48no—
626C24—48no—
627C24C2518yes—
628C24C2512yes—
629C24C2512yes—
630C24C2512yes—
631C24C2511yescharacteristic
632#41—232no—
633#41—464no—
634#41—416no—
635#41—864no—
636C2×Q8—28no—
637C2×Q8—22no—
638C2×Q8—28no—
639C2×Q8—22no—
640C2×Q8—28no—
641C2×Q8—28no—
642C2×Q8—22no—
643C2×Q8—22no—
644C2×Q8—22no—
645C2×Q8—28no—
646C2×Q8—44no—
647C2×Q8C22×D414yes—
648C2×D4—24no—
649C2×D4—24no—
650C2×D4—28no—
651C2×D4—24no—
652C2×D4—28no—
653C2×D4—24no—
654C2×D4—28no—
655C2×D4—28no—
656C2×D4—24no—
657C2×D4—232no—
658C2×D4—232no—
659C2×D4—28no—
660C2×D4—22no—
661C2×D4—28no—
662C2×D4—28no—
663C2×D4—216no—
664C2×D4—216no—
665C2×D4—22no—
666C2×D4—216no—
667C2×D4—28no—
668C2×D4—28no—
669C2×D4—28no—
670C2×D4—22no—
671C2×D4—22no—
672C2×D4—28no—
673C2×D4—28no—
674C2×D4—22no—
675C2×D4—216no—
676C2×D4—44no—
677C2×D4—44no—
678C2×D4—44no—
679C2×D4—48no—
680C2×D4—416no—
681C2×D4—416no—
682C2×D4—416no—
683C2×D4—48no—
684C2×D4—416no—
685C2×D4—48no—
686C2×D4—48no—
687C2×D4—416no—
688C2×D4—416no—
689C2×D4—432no—
690C2×D4—832no—
691C2×D4—832no—
692C2×D4C22×D418yes—
693C2×D4C22×D414yes—
694C22×C4—24no—
695C22×C4—24no—
696C22×C4—24no—
697C22×C4—28no—
698C22×C4—24no—
699C22×C4—24no—
700C22×C4—24no—
701C22×C4—28no—
702C22×C4—24no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—24no—
706C22×C4—22no—
707C22×C4—28no—
708C22×C4—24no—
709C22×C4—24no—
710C22×C4—24no—
711C22×C4—24no—
712C22×C4—24no—
713C22×C4—24no—
714C22×C4—28no—
715C22×C4—24no—
716C22×C4—24no—
717C22×C4—24no—
718C22×C4—24no—
719C22×C4—24no—
720C22×C4—24no—
721C22×C4—28no—
722C22×C4—24no—
723C22×C4—24no—
724C22×C4—24no—
725C22×C4—28no—
726C22×C4—24no—
727C22×C4—232no—
728C22×C4—42no—
729C22×C4—42no—
730C22×C4—42no—
731C22×C4—432no—
732C22×C4—48no—
733C22×C4—416no—
734C22×C4—416no—
735C22×C4—48no—
736C22×C4—416no—
737C22×C4—416no—
738C22×C4C22×D418yes—
739C22×C4C22×D4116yes—
740C22×C4C22×D418yes—
741C22×C4C22×D414yes—
742C22×C4H(5,𝔽2)18yes—
743C22×C4H(5,𝔽2)14yes—
744C22×C42−1+414yes—
745C22×C4C2514yes—
746C22×C4C2512yes—
747C22×C4C2512yes—
748C22×C4C2518yes—
749C22×C4C2514yes—
750C22×C4C2518yes—
751C22×C4C2512yes—
752C22×C4C2514yes—
753C22×C4C2512yes—
754C22×C4C2514yes—
755C22×C4C2512yes—
756C22×C4C2512yes—
757C22×C4C2511yescharacteristic
758C22×C4C2511yescharacteristic
759C22×C4C2512yes—
760C4⋊C4—28no—
761C4⋊C4—28no—
762C4⋊C4—28no—
763C4⋊C4—24no—
764C4⋊C4—28no—
765C4⋊C4—28no—
766C4⋊C4—28no—
767C4⋊C4—28no—
768C4⋊C4—28no—
769C4⋊C4—28no—
770C4⋊C4—216no—
771C4⋊C4—28no—
772C4⋊C4—28no—
773C4⋊C4—24no—
774C4⋊C4—216no—
775C4⋊C4—28no—
776C4⋊C4—24no—
777C4⋊C4—216no—
778C4⋊C4—28no—
779C4⋊C4—48no—
780C4⋊C4—48no—
781C4⋊C4—416no—
782C4⋊C4—416no—
783C4⋊C4—48no—
784C4⋊C4C22×D418yes—
785C4⋊C4C22×D4116yes—
786C22⋊C4—28no—
787C22⋊C4—24no—
788C22⋊C4—28no—
789C22⋊C4—28no—
790C22⋊C4—28no—
791C22⋊C4—216no—
792C22⋊C4—232no—
793C22⋊C4—28no—
794C22⋊C4—28no—
795C22⋊C4—28no—
796C22⋊C4—28no—
797C22⋊C4—28no—
798C22⋊C4—232no—
799C22⋊C4—232no—
800C22⋊C4—416no—
801C22⋊C4—416no—
802C22⋊C4—48no—
803C22⋊C4—48no—
804C22⋊C4—48no—
805C22⋊C4—416no—
806C22⋊C4—416no—
807C22⋊C4—416no—
808C22⋊C4—48no—
809C22⋊C4C22×D418yes—
810C22⋊C4C22×D4116yes—
811C42—24no—
812C42—24no—
813C42—24no—
814C42—24no—
815C42—22no—
816C42—24no—
817C42—22no—
818C42—24no—
819C42—28no—
820C42—28no—
821C42—28no—
822C42—48no—
823C42C22×D414yes—
824C42C22×D414yes—
825C42C22×D418yes—
826C42C22×D4116yes—
827C42C22×D418yes—
828C23—22no—
829C23—22no—
830C23—28no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—24no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—22no—
840C23—24no—
841C23—22no—
842C23—28no—
843C23—216no—
844C23—24no—
845C23—28no—
846C23—22no—
847C23—22no—
848C23—28no—
849C23—216no—
850C23—24no—
851C23—48no—
852C23—48no—
853C23—44no—
854C23—44no—
855C23—416no—
856C23—816no—
857C23—88no—
858C23—816no—
859C23—88no—
860C23C23×D414yes—
861C23C23×D412yes—
862C23C2×H(5,𝔽2)14yes—
863C23C2×H(5,𝔽2)12yes—
864C23C2×2−1+412yes—
865C23C2611yescharacteristic
866Q8—28no—
867Q8—416no—
868Q8—44no—
869Q8—416no—
870D4—216no—
871D4—28no—
872D4—416no—
873D4—416no—
874D4—416no—
875D4—48no—
876D4—416no—
877D4—416no—
878D4—44no—
879D4—432no—
880D4—816no—
881D4—832no—
882D4—832no—
883D4—168no—
884D4—168no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—24no—
889C2×C4—22no—
890C2×C4—24no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—216no—
894C2×C4—216no—
895C2×C4—216no—
896C2×C4—232no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—24no—
900C2×C4—22no—
901C2×C4—28no—
902C2×C4—24no—
903C2×C4—24no—
904C2×C4—28no—
905C2×C4—28no—
906C2×C4—216no—
907C2×C4—28no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—24no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—24no—
915C2×C4—28no—
916C2×C4—28no—
917C2×C4—22no—
918C2×C4—48no—
919C2×C4—48no—
920C2×C4—48no—
921C2×C4—44no—
922C2×C4—48no—
923C2×C4—48no—
924C2×C4—48no—
925C2×C4—48no—
926C2×C4—416no—
927C2×C4—832no—
928C2×C4—88no—
929C2×C4—168no—
930C2×C4#537116yescomplemented
931C2×C4C23×D414yes—
932C2×C4C23×D414yes—
933C2×C4C23×D418yes—
934C2×C4C23×D412yes—
935C2×C4C23×D412yes—
936C2×C4C23×D414yes—
937C2×C4C2×H(5,𝔽2)14yes—
938C2×C4C2×H(5,𝔽2)12yes—
939C2×C4C2×H(5,𝔽2)12yes—
940C2×C4C2×H(5,𝔽2)14yes—
941C2×C4C2×2−1+412yes—
942C2×C4C2×2−1+412yes—
943C2×C4#58514yes—
944C22—24no—
945C22—22no—
946C22—24no—
947C22—22no—
948C22—24no—
949C22—28no—
950C22—24no—
951C22—24no—
952C22—24no—
953C22—416no—
954C22—42no—
955C22—42no—
956C22—44no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—44no—
962C22—416no—
963C22—48no—
964C22—42no—
965C22—44no—
966C22—416no—
967C22—42no—
968C22—48no—
969C22—42no—
970C22—48no—
971C22—1616no—
972C22C2×#53714yes—
973C22C24×D411yescharacteristic
974C22C22×H(5,𝔽2)12yes—
975C22C22×H(5,𝔽2)11yescharacteristic
976C22C22×2−1+411yescharacteristic
977C22C2×#58512yes—
978C4—24no—
979C4—24no—
980C4—28no—
981C4—24no—
982C4—42no—
983C4—44no—
984C4—48no—
985C4—48no—
986C4—44no—
987C4—44no—
988C4—42no—
989C4—42no—
990C4C2×#53714yes—
991C4C2×#53714yes—
992C4#348818yes—
993C2—24no—
994C2—44no—
995C2—44no—
996C2—82no—
997C2—88no—
998C2C22×#53711yescharacteristic
999C2C2×#348812yes—
1000C2#6283211yescharacteristic
1001C2#6283512yes—
1002C2#6283611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
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×#3508C2semidirect
2. C2×#3444C2semidirect
3. #39726C2semidirect
4. #39341C2semidirect
5. #39137C2semidirect
6. #38909C2semidirect
7. #38024C2semidirect
8. #37648C2semidirect
9. #37276C2semidirect
10. #36625C2semidirect
11. C2×#2856C2semidirect
12. #35563C2semidirect
13. #35533C2semidirect
14. #35515C2semidirect
15. #35514C2semidirect
16. #35292C2semidirect
17. #35280C2semidirect
18. #35273C2semidirect
19. #35272C2semidirect
20. #34183C2semidirect
22. C2×#559C22semidirect
23. C2×#550C22semidirect
25. C2×#540C22semidirect
26. C2×#537C22semidirect
32. C2×#533C22semidirect
34. C2×#532C22semidirect
35. C2×#532C22semidirect
38. C2×#529C22semidirect
39. C2×#529C22semidirect
40. C2×#529C22semidirect
50. C2×C4×#41C22semidirect
52. #2857C22semidirect
53. #2857C22semidirect
54. #2857C22semidirect
59. #2856C22semidirect
60. #2856C22semidirect
62. #2851C22semidirect
64. #2707C22semidirect
65. #2705C22semidirect
66. #2691C22semidirect
67. #2682C22semidirect
68. #2681C22semidirect
69. #2676C22semidirect
70. #2675C22semidirect
71. #2671C22semidirect
72. #2629C22semidirect
73. #2624C22semidirect
74. #2620C22semidirect
75. #2620C22semidirect
76. #2619C22semidirect
77. #2615C22semidirect
78. #2592C22semidirect
79. #2582C22semidirect
80. #2580C22semidirect
81. #2548C22semidirect
82. #2548C22semidirect
83. #2545C22semidirect
84. #2544C22semidirect
85. #2541C22semidirect
86. #2541C22semidirect
87. #2540C22semidirect
88. #2538C22semidirect
89. #2538C22semidirect
90. #2538C22semidirect
91. #2537C22semidirect
92. #2537C22semidirect
93. #2535C22semidirect
95. #2454C22semidirect
96. #2452C22semidirect
98. #2428C22semidirect
99. #2428C22semidirect
100. #2427C22semidirect
101. #2426C22semidirect
104. #2416C22semidirect
105. #2416C22semidirect
106. #2416C22semidirect
107. #2416C22semidirect
108. #2414C22semidirect
109. #2414C22semidirect
114. #2407C22semidirect
115. #2407C22semidirect
116. Q8×C4⋊C4C22semidirect
118. D4×C4⋊C4C22semidirect
119. #2324C22semidirect
120. #2324C22semidirect
122. #2317C22semidirect
125. #2311C22semidirect
127. C4×C22⋊Q8C22semidirect
128. C4×C22⋊Q8C22semidirect
133. #2285C22semidirect
135. C2×#384C22semidirect
231. C4×#41D4semidirect
499. C4×Q8C2×D4semidirect
514. C4×D4C2×D4semidirect
524. #117C2×D4semidirect
591. C2×C42C2×D4semidirect
930. C2×C4#537semidirect

Maximal subgroups

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

subgroupindex
C2×#35082
C2×#34442
#397262
#393412
#391372
#389092
#380242
#376482
#372762
#366252
C2×#28562
#355632
#355332
#355152
#355142
#352922
#352802
#352732
#352722
#341832