Finite Group Databasebeta

← #7647321

Subgroups — #7647321

Order 512.

8934 conjugacy classes of subgroups.

The subgroup lattice has 1084 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#550C211yesmaximal, characteristic, complemented
2C2×#3449C211yesmaximal, characteristic, complemented
3#42985C214yesmaximal, complemented
4#42969C214yesmaximal, complemented
5#42913C214yesmaximal, complemented
6#42909C214yesmaximal, complemented
7#39865C218yesmaximal, complemented
8#39861C218yesmaximal, complemented
9#37446C214yesmaximal, complemented
10#37232C214yesmaximal, complemented
11#37117C214yesmaximal, complemented
12#35528C212yesmaximal, complemented
13#35514C212yesmaximal, complemented
14#35262C211yesmaximal, characteristic, complemented
15#35250C211yesmaximal, characteristic, complemented
16#35182C212yesmaximal, complemented
17#35149C212yesmaximal, complemented
18#35063C214yesmaximal, complemented
19#34809C211yesmaximal, characteristic, complemented
20#34736C211yesmaximal, characteristic, complemented
21#34172C211yesmaximal, characteristic, complemented
22C23×#41C2211yescharacteristic
23C23×#41C2211yescharacteristic
24C23×#41C2211yescharacteristic, complemented
25C2×#550—216no—
26C2×#550C2214yes—
27C2×#550C2214yes—
28C2×#550C2214yescomplemented
29C2×#550C2214yescomplemented
30#3449—216no—
31C2×#537C2212yescomplemented
32C2×#537C2212yescomplemented
33C2×#536C2212yes—
34C2×#536C2212yescomplemented
35C2×#535C2212yes—
36C2×#535C2212yes—
37C2×#535C2212yescomplemented
38C2×#534C2214yes—
39C2×#532C2214yescomplemented
40C22×#127C2212yes—
41C22×#127C2211yescharacteristic, complemented
42C2×#525C2214yes—
43C2×#525C2212yes—
44C2×#525C2214yescomplemented
45C22×#121C2211yescharacteristic
46C22×#121C2212yes—
47C22×#121C2212yescomplemented
48C22×#121C2211yescharacteristic, complemented
49C2×#518C2212yescomplemented
50C22×C4×Q8C2211yescharacteristic, complemented
51C22×C4×D4C2211yescharacteristic
52C22×C4×D4C2212yescomplemented
53C22×#117C2211yescharacteristic
54#2854C2214yescomplemented
55#2853C2218yescomplemented
56#2849C2218yescomplemented
57#2847C2214yescomplemented
58#2816C2218yescomplemented
59#2815C2218yescomplemented
60#2709C22116yescomplemented
61#2708C22116yescomplemented
62#2688C22116yescomplemented
63#2673C22116yescomplemented
64#2673C22116yescomplemented
65#2671C22116yescomplemented
66#2669C22116yescomplemented
67#2668C22116yescomplemented
68#2656C2218yescomplemented
69#2639C2218yescomplemented
70#2638C2218yescomplemented
71#2635C22116yescomplemented
72#2635C2218yescomplemented
73#2624C2214yescomplemented
74#2623C2218yescomplemented
75#2615C2214yescomplemented
76#2613C2218yescomplemented
77#2600C22116yescomplemented
78#2564C2218yescomplemented
79#2544C2218yescomplemented
80#2543C22116yescomplemented
81#2543C2218yescomplemented
82#2541C2218yescomplemented
83#2537C2218yescomplemented
84#2535C2218yescomplemented
85#2504C2212yescomplemented
86#2501C2212yescomplemented
87#2500C2214yescomplemented
88#2487C2212yescomplemented
89#2486C2212yescomplemented
90#2485C2214yescomplemented
91#2484C2212yescomplemented
92#2483C2212yes—
93#2482C2212yescomplemented
94#2482C2214yescomplemented
95#2448C2218yescomplemented
96#2446C2218yescomplemented
97#2436C2212yescomplemented
98#2433C2212yescomplemented
99#2432C2218yescomplemented
100#2431C2218yescomplemented
101#2431C2214yescomplemented
102#2428C2218yescomplemented
103#2428C2218yescomplemented
104#2428C2218yescomplemented
105#2427C2218yescomplemented
106#2423C2218yescomplemented
107#2421C2218yescomplemented
108#2412C2218yescomplemented
109#2410C2218yescomplemented
110#2410C2218yescomplemented
111#2410C2218yescomplemented
112#2409C2212yescomplemented
113#2408C2212yescomplemented
114#2407C2218yescomplemented
115#2407C2218yescomplemented
116#2407C2214yescomplemented
117#2406C2212yes—
118#2405C2212yes—
119#2405C2214yes—
120#2405C2212yes—
121#2404C2212yes—
122#2404C2214yes—
123#2403C2212yes—
124#2403C2214yes—
125#2395C2214yescomplemented
126#2388C2214yescomplemented
127#2339C2214yescomplemented
128#2339C2214yescomplemented
129#2339C2214yescomplemented
130#2339C2214yescomplemented
131#2325C22116yescomplemented
132#2317C2212yescomplemented
133#2311C2212yes—
134#2310C2212yescomplemented
135#2309C2212yescomplemented
136#2308C2214yes—
137C4×#123C2214yescomplemented
138C4×#120C2214yescomplemented
139#2297C2212yes—
140#2296C2212yescomplemented
141#2280C2211yescharacteristic
142#2280C2211yescharacteristic
143#2280C2212yescomplemented
144C2×#381C2214yescomplemented
145C22×#41—28no—
146C22×#41—28no—
147C22×#41—48no—
148C22×#41—48no—
149C22×#41—48no—
150C22×#41D4116yescomplemented
151C22×#41C2312yes—
152C22×#41C2312yes—
153C22×#41C2312yes—
154C22×#41C2312yes—
155C22×#41C2314yes—
156C22×#41C2314yes—
157C22×#41C2312yes—
158C22×#41C2312yes—
159C22×#41C2312yes—
160C22×#41C2312yes—
161C23×Q8C2311yescharacteristic
162C23×Q8C2311yescharacteristic
163C23×D4C2311yescharacteristic
164C23×D4C2311yescharacteristic
165C23×D4C2312yes—
166C23×D4C2311yescharacteristic
167C23×D4C2312yes—
168C23×D4C2311yescharacteristic
169C23×D4C2312yes—
170C23×D4C2312yes—
171C23×D4C2312yes—
172C23×D4C2312yes—
173C23×D4C2312yes—
174C24×C4C2311yescharacteristic
175C24×C4C2311yescharacteristic
176C24×C4C2312yes—
177C24×C4C2312yes—
178C24×C4C2312yes—
179#550—232no—
180#550—232no—
181#550—232no—
182#550—232no—
183#537—216no—
184#537—216no—
185#536—216no—
186#536—216no—
187#535—216no—
188#535—216no—
189#535—48no—
190#534—232no—
191#532—232no—
192C2×C4⋊Q8C2314yes—
193C2×#127—216no—
194C2×#127—28no—
195C2×#127C2318yes—
196C2×#127C2318yes—
197C2×#127C2314yes—
198C2×#127C2314yes—
199C2×#127C2314yes—
200C2×#127C2314yes—
201C2×#124C2314yes—
202C2×#124C2314yes—
203C2×#124C2314yes—
204#525—232no—
205#525—232no—
206#525—48no—
207C2×#123C2318yes—
208C2×#123C2318yes—
209C2×#123C2314yes—
210C2×#123C2314yes—
211C2×#123C2318yes—
212C2×C22⋊Q8C2314yes—
213C2×C22⋊Q8C2314yes—
214C2×C22⋊Q8C2314yes—
215C2×C22⋊Q8C2314yes—
216C2×C22⋊Q8C2314yes—
217C2×#121—216no—
218C2×#121—28no—
219C2×#121—28no—
220C2×#121—216no—
221C2×#121C2318yes—
222C2×#121C2312yes—
223C2×#121C2312yes—
224C2×#121C2312yes—
225C2×#121C2312yes—
226C2×#121C2314yes—
227C2×#121C2318yes—
228C2×#121C2318yes—
229C2×#121C2318yes—
230C2×#121C2314yes—
231C2×#121C2314yes—
232C2×#121C2314yes—
233C2×#121C2314yes—
234C2×#121C2314yes—
235C2×#121C2318yes—
236C2×#121C2318yes—
237C2×#121C23116yes—
238C2×#121C2318yes—
239C2×#121C2314yes—
240C2×#121C23116yes—
241C2×#121C23116yes—
242C2×#120C2318yes—
243C2×#120C2318yes—
244C2×#120C2318yes—
245C2×#120C2314yes—
246C2×#120C2314yes—
247C2×#120C2318yes—
248#518—48no—
249C2×C4×Q8—28no—
250C2×C4×Q8C2314yes—
251C2×C4×Q8C2314yes—
252C2×C4×D4—28no—
253C2×C4×D4—216no—
254C2×C4×D4C2318yes—
255C2×C4×D4C2318yes—
256C2×C4×D4C2318yes—
257C2×C4×D4C2318yes—
258C2×C4×D4C2312yes—
259C2×C4×D4C2312yes—
260C2×C4×D4C2312yes—
261C2×C4×D4C2312yes—
262C2×C4×D4C2318yes—
263C2×C4×D4C2318yes—
264C2×C4×D4C2318yes—
265C2×#117—28no—
266C2×#117C2312yes—
267C2×#117C2312yes—
268C2×#117C2312yes—
269C2×#117C2312yes—
270C2×#117C2312yes—
271C2×#117C2312yes—
272C22×C4⋊C4C2311yescharacteristic
273C22×C4⋊C4C2312yes—
274C22×C4⋊C4C2311yescharacteristic
275C22×C4⋊C4C2311yescharacteristic
276C22×C4⋊C4C2311yescharacteristic
277C22×C22⋊C4C2312yes—
278C22×C22⋊C4C2311yescharacteristic
279C22×C22⋊C4C2311yescharacteristic
280C22×C22⋊C4C2312yes—
281C22×C22⋊C4C2312yes—
282C22×C22⋊C4C2318yes—
283C22×C42C2312yes—
284C22×C42C2312yes—
285C22×C42C2311yescharacteristic
286#400C2314yes—
287#400C23116yes—
288#399C2314yes—
289#399C2318yes—
290#399C23116yes—
291#398C23116yes—
292#398C2314yes—
293#397C23116yes—
294#397C23116yes—
295#397C2318yes—
296#397C2314yes—
297#397C2318yes—
298#395C2314yes—
299#394C23116yes—
300#394C23116yes—
301#394C23116yes—
302#394C23116yes—
303#394C23116yes—
304#394C23116yes—
305#394C23116yes—
306#394C2314yes—
307#394C2318yes—
308#394C2318yes—
309#393C2314yes—
310#393C2318yes—
311#392C23116yes—
312#392C23116yes—
313#392C23116yes—
314#392C2318yes—
315#392C23116yes—
316#392C23116yes—
317#392C23116yes—
318#392C2314yes—
319#392C2318yes—
320#391C2318yes—
321#391C2318yes—
322#391C2314yes—
323#391C2314yes—
324#390C2318yes—
325#390C2314yes—
326#390C2314yes—
327#390C2314yes—
328#390C2314yes—
329#389C2318yes—
330#389C2314yes—
331#389C2314yes—
332#388C23116yes—
333#388C23116yes—
334#388C23116yes—
335#388C2318yes—
336#387C23116yes—
337#387C2318yes—
338#387C23116yes—
339#386C23116yes—
340#386C23116yes—
341#386C23116yes—
342#386C2318yes—
343#386C23116yes—
344#386C23116yes—
345#386C23116yes—
346#386C2318yes—
347#386C23116yes—
348#386C2314yes—
349#386C2318yes—
350#386C2314yes—
351#386C2318yes—
352#386C23116yes—
353#386C23116yes—
354#386C2314yes—
355#386C2314yes—
356#385C23116yes—
357#385C2318yes—
358#385C2318yes—
359#385C23116yes—
360#385C2314yes—
361#385C2314yes—
362#385C2314yes—
363#385C2314yes—
364#384C2314yes—
365#382C2314yes—
366#381C2318yes—
367#381C2318yes—
368#381C2314yes—
369#381C2318yes—
370#381C2312yes—
371#381C2312yes—
372#381C2314yes—
373#380C23116yes—
374#380C2318yes—
375#380C2312yes—
376#380C2312yes—
377#380C2312yes—
378#380C2312yes—
379#380C2314yes—
380#380C2314yes—
381#379C2312yes—
382#379C2312yes—
383#379C2318yes—
384#379C2314yes—
385#379C2314yes—
386C4×C4⋊C4C2318yes—
387C4×C22⋊C4C2312yes—
388C4×C22⋊C4C2312yes—
389C4×C22⋊C4C2312yes—
390C4×C22⋊C4C2312yes—
391C4×C22⋊C4C2318yes—
392C4×C22⋊C4C2318yes—
393C2×#95C2318yes—
394C2×#95C2318yes—
395C25C2411yescharacteristic
396C25C2412yes—
397C25C2412yes—
398C25C2411yescharacteristic
399C25C2412yes—
400C2×#41—216no—
401C2×#41—216no—
402C2×#41—28no—
403C2×#41—28no—
404C2×#41—28no—
405C2×#41—28no—
406C2×#41—28no—
407C2×#41—28no—
408C2×#41—48no—
409C2×#41—48no—
410C2×#41—464no—
411C2×#41—48no—
412C2×#41—48no—
413C2×#41—48no—
414C2×#41—48no—
415C2×#41—44no—
416C2×#41—44no—
417C2×#41—416no—
418C2×#41—416no—
419C2×#41—464no—
420C2×#41—464no—
421C2×#41C2×D4116yes—
422C2×#41C2×D4116yes—
423C2×#41C2×D4116yes—
424C2×#41C2×D4116yes—
425C22×Q8—24no—
426C22×Q8—28no—
427C22×Q8—44no—
428C22×Q8C2×D418yes—
429C22×Q8C2412yes—
430C22×Q8C2412yes—
431C22×Q8C2412yes—
432C22×Q8C2412yes—
433C22×D4—24no—
434C22×D4—28no—
435C22×D4—28no—
436C22×D4—28no—
437C22×D4—28no—
438C22×D4—28no—
439C22×D4—28no—
440C22×D4—24no—
441C22×D4—24no—
442C22×D4—28no—
443C22×D4—28no—
444C22×D4—44no—
445C22×D4—48no—
446C22×D4—44no—
447C22×D4—48no—
448C22×D4—48no—
449C22×D4—48no—
450C22×D4—84no—
451C22×D4—84no—
452C22×D4—84no—
453C22×D4C2×D418yes—
454C22×D4C2×D4116yes—
455C22×D4C2414yes—
456C22×D4C2412yes—
457C22×D4C2412yes—
458C22×D4C2412yes—
459C22×D4C2412yes—
460C22×D4C2418yes—
461C22×D4C2412yes—
462C22×D4C2412yes—
463C22×D4C2412yes—
464C22×D4C2418yes—
465C22×D4C2418yes—
466C22×D4C2414yes—
467C22×D4C2418yes—
468C22×D4C2418yes—
469C22×D4C2414yes—
470C22×D4C2414yes—
471C22×D4C2412yes—
472C22×D4C2418yes—
473C22×D4C2418yes—
474C22×D4C24116yes—
475C22×D4C2414yes—
476C22×D4C2414yes—
477C23×C4—28no—
478C23×C4—28no—
479C23×C4—24no—
480C23×C4—28no—
481C23×C4—28no—
482C23×C4—48no—
483C23×C4—48no—
484C23×C4—48no—
485C23×C4C2×D418yes—
486C23×C4C2×D4116yes—
487C23×C4C2411yescharacteristic
488C23×C4C2411yescharacteristic
489C23×C4C2412yes—
490C23×C4C2412yes—
491C23×C4C2414yes—
492C23×C4C2411yescharacteristic
493C23×C4C2411yescharacteristic
494C23×C4C2412yes—
495C23×C4C2411yescharacteristic
496C23×C4C2411yescharacteristic
497C23×C4C2411yescharacteristic
498C23×C4C2411yescharacteristic
499C23×C4C2412yes—
500C23×C4C2412yes—
501C23×C4C2412yes—
502C23×C4C2414yes—
503C23×C4C2418yes—
504C23×C4C2412yes—
505C23×C4C24116yes—
506C23×C4C2414yes—
507C23×C4C2414yes—
508C23×C4C2411yescharacteristic
509C4⋊Q8—216no—
510#127—216no—
511#127—216no—
512#127—232no—
513#127—232no—
514#127—216no—
515#127—48no—
516#124—216no—
517#124—216no—
518#124—48no—
519#123—232no—
520#123—232no—
521#123—48no—
522#123—48no—
523#123—88no—
524C22⋊Q8—216no—
525C22⋊Q8—216no—
526C22⋊Q8—216no—
527C22⋊Q8—216no—
528C22⋊Q8—48no—
529#121—216no—
530#121—216no—
531#121—232no—
532#121—232no—
533#121—216no—
534#121—216no—
535#121—232no—
536#121—232no—
537#121—28no—
538#121—28no—
539#121—28no—
540#121—28no—
541#121—232no—
542#121—232no—
543#121—216no—
544#121—216no—
545#121—432no—
546#121—48no—
547#121—416no—
548#121—816no—
549#121—816no—
550#120—232no—
551#120—232no—
552#120—48no—
553#120—48no—
554#120—416no—
555#120—88no—
556C4×Q8—216no—
557C4×Q8—216no—
558C4×D4—28no—
559C4×D4—28no—
560C4×D4—28no—
561C4×D4—28no—
562C4×D4—232no—
563C4×D4—232no—
564C4×D4—232no—
565C4×D4—232no—
566C4×D4—416no—
567C4×D4—416no—
568C4×D4—416no—
569#117—28no—
570#117—28no—
571#117—28no—
572#117—28no—
573#117—28no—
574#117—28no—
575C2×C4⋊C4—24no—
576C2×C4⋊C4—24no—
577C2×C4⋊C4—24no—
578C2×C4⋊C4—28no—
579C2×C4⋊C4—24no—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2412yes—
583C2×C4⋊C4C2412yes—
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2412yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2418yes—
589C2×C4⋊C4C2414yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2418yes—
592C2×C4⋊C4C2418yes—
593C2×C4⋊C4C2418yes—
594C2×C4⋊C4C2418yes—
595C2×C4⋊C4C2418yes—
596C2×C4⋊C4C24116yes—
597C2×C22⋊C4—28no—
598C2×C22⋊C4—24no—
599C2×C22⋊C4—28no—
600C2×C22⋊C4—24no—
601C2×C22⋊C4—28no—
602C2×C22⋊C4—416no—
603C2×C22⋊C4C2414yes—
604C2×C22⋊C4C2414yes—
605C2×C22⋊C4C2414yes—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2412yes—
608C2×C22⋊C4C2418yes—
609C2×C22⋊C4C2412yes—
610C2×C22⋊C4C2412yes—
611C2×C22⋊C4C2414yes—
612C2×C22⋊C4C2412yes—
613C2×C22⋊C4C2414yes—
614C2×C22⋊C4C2418yes—
615C2×C22⋊C4C2418yes—
616C2×C22⋊C4C2418yes—
617C2×C22⋊C4C2418yes—
618C2×C22⋊C4C2418yes—
619C2×C22⋊C4C24116yes—
620C2×C22⋊C4C2418yes—
621C2×C22⋊C4C2418yes—
622C2×C22⋊C4C2414yes—
623C2×C22⋊C4C24116yes—
624C2×C22⋊C4C24116yes—
625C2×C22⋊C4C2414yes—
626C2×C22⋊C4C2418yes—
627C2×C22⋊C4C2418yes—
628C2×C22⋊C4C24116yes—
629C2×C22⋊C4C24116yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2418yes—
633C2×C42—28no—
634C2×C42—28no—
635C2×C42—24no—
636C2×C42C2414yes—
637C2×C42C2414yes—
638C2×C42C2414yes—
639C2×C42C2414yes—
640C2×C42C2412yes—
641C2×C42C2412yes—
642C2×C42C2418yes—
643#95C2414yes—
644#95C2414yes—
645#95C2414yes—
646#95C2414yes—
647#95C24116yes—
648#95C24116yes—
649#95C2418yes—
650#95C2418yes—
651#95C2418yes—
652#95C2418yes—
653#95C2418yes—
654#95C2418yes—
655#95C24116yes—
656#95C24116yes—
657C24—28no—
658C24—24no—
659C24—24no—
660C24—22no—
661C24—24no—
662C24—24no—
663C24—28no—
664C24—44no—
665C24—42no—
666C24—44no—
667C24—42no—
668C24—44no—
669C24—42no—
670C24—44no—
671C24—42no—
672C24—44no—
673C24—44no—
674C24—44no—
675C24C22×D414yes—
676C24C22×D418yes—
677C24C2514yes—
678C24C2512yes—
679C24C2514yes—
680C24C2511yescharacteristic
681C24C2514yes—
682C24C2511yescharacteristic
683C24C2511yescharacteristic
684#41—432no—
685#41—432no—
686#41—432no—
687#41—432no—
688#41—432no—
689#41—432no—
690#41—432no—
691#41—464no—
692#41—464no—
693#41—432no—
694C2×Q8—232no—
695C2×Q8—24no—
696C2×Q8—24no—
697C2×Q8—28no—
698C2×Q8—28no—
699C2×Q8—24no—
700C2×Q8—24no—
701C2×Q8—44no—
702C2×Q8—416no—
703C2×Q8C22×D418yes—
704C2×Q8C22×D418yes—
705C2×D4—24no—
706C2×D4—216no—
707C2×D4—24no—
708C2×D4—28no—
709C2×D4—28no—
710C2×D4—28no—
711C2×D4—28no—
712C2×D4—216no—
713C2×D4—216no—
714C2×D4—28no—
715C2×D4—216no—
716C2×D4—216no—
717C2×D4—28no—
718C2×D4—232no—
719C2×D4—24no—
720C2×D4—216no—
721C2×D4—24no—
722C2×D4—24no—
723C2×D4—24no—
724C2×D4—28no—
725C2×D4—28no—
726C2×D4—28no—
727C2×D4—24no—
728C2×D4—28no—
729C2×D4—24no—
730C2×D4—24no—
731C2×D4—216no—
732C2×D4—24no—
733C2×D4—432no—
734C2×D4—42no—
735C2×D4—42no—
736C2×D4—48no—
737C2×D4—44no—
738C2×D4—48no—
739C2×D4—48no—
740C2×D4—416no—
741C2×D4—44no—
742C2×D4—44no—
743C2×D4—416no—
744C2×D4—432no—
745C2×D4—432no—
746C2×D4—416no—
747C2×D4—48no—
748C2×D4—48no—
749C2×D4—48no—
750C2×D4—416no—
751C2×D4—48no—
752C2×D4—416no—
753C2×D4—416no—
754C2×D4—416no—
755C2×D4—48no—
756C2×D4—416no—
757C2×D4—416no—
758C2×D4—416no—
759C2×D4—432no—
760C2×D4—416no—
761C2×D4—816no—
762C2×D4—816no—
763C2×D4—816no—
764C2×D4C22×D418yes—
765C2×D4C22×D418yes—
766C2×D4C22×D4116yes—
767C2×D4C22×D4116yes—
768C22×C4—22no—
769C22×C4—24no—
770C22×C4—28no—
771C22×C4—232no—
772C22×C4—24no—
773C22×C4—24no—
774C22×C4—24no—
775C22×C4—24no—
776C22×C4—24no—
777C22×C4—24no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—24no—
781C22×C4—24no—
782C22×C4—24no—
783C22×C4—24no—
784C22×C4—28no—
785C22×C4—216no—
786C22×C4—24no—
787C22×C4—24no—
788C22×C4—28no—
789C22×C4—28no—
790C22×C4—28no—
791C22×C4—28no—
792C22×C4—28no—
793C22×C4—432no—
794C22×C4—44no—
795C22×C4—48no—
796C22×C4—44no—
797C22×C4—44no—
798C22×C4—48no—
799C22×C4—416no—
800C22×C4—44no—
801C22×C4—42no—
802C22×C4—44no—
803C22×C4—44no—
804C22×C4—416no—
805C22×C4—416no—
806C22×C4—416no—
807C22×C4—432no—
808C22×C4—432no—
809C22×C4—416no—
810C22×C4C22×D414yes—
811C22×C4C22×D418yes—
812C22×C4C22×D414yes—
813C22×C4C22×D414yes—
814C22×C4C22×D414yes—
815C22×C4C22×D414yes—
816C22×C4C22×D4116yes—
817C22×C4C22×D4116yes—
818C22×C4C22×D414yes—
819C22×C4H(5,𝔽2)18yes—
820C22×C4C2518yes—
821C22×C4C2518yes—
822C22×C4C2514yes—
823C22×C4C2512yes—
824C22×C4C2514yes—
825C22×C4C2512yes—
826C22×C4C2514yes—
827C22×C4C2514yes—
828C22×C4C2511yescharacteristic
829C22×C4C2514yes—
830C22×C4C2511yescharacteristic
831C22×C4C2512yes—
832C22×C4C2511yescharacteristic
833C22×C4C2511yescharacteristic
834C4⋊C4—24no—
835C4⋊C4—24no—
836C4⋊C4—24no—
837C4⋊C4—24no—
838C4⋊C4—24no—
839C4⋊C4—24no—
840C4⋊C4—216no—
841C4⋊C4—24no—
842C4⋊C4—24no—
843C4⋊C4—216no—
844C4⋊C4—216no—
845C4⋊C4—28no—
846C4⋊C4—28no—
847C4⋊C4—216no—
848C4⋊C4—48no—
849C4⋊C4—48no—
850C4⋊C4—416no—
851C22⋊C4—28no—
852C22⋊C4—28no—
853C22⋊C4—24no—
854C22⋊C4—216no—
855C22⋊C4—24no—
856C22⋊C4—216no—
857C22⋊C4—216no—
858C22⋊C4—28no—
859C22⋊C4—28no—
860C22⋊C4—24no—
861C22⋊C4—28no—
862C22⋊C4—24no—
863C22⋊C4—28no—
864C22⋊C4—216no—
865C22⋊C4—216no—
866C22⋊C4—216no—
867C22⋊C4—416no—
868C22⋊C4—48no—
869C22⋊C4—48no—
870C22⋊C4—44no—
871C22⋊C4—416no—
872C22⋊C4—44no—
873C22⋊C4—416no—
874C22⋊C4—416no—
875C22⋊C4—48no—
876C22⋊C4—48no—
877C22⋊C4—416no—
878C22⋊C4—48no—
879C22⋊C4—44no—
880C22⋊C4—44no—
881C42—28no—
882C42—28no—
883C42—216no—
884C42—24no—
885C42—24no—
886C42—28no—
887C42—28no—
888C23—22no—
889C23—22no—
890C23—28no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—28no—
896C23—22no—
897C23—22no—
898C23—28no—
899C23—28no—
900C23—216no—
901C23—24no—
902C23—22no—
903C23—24no—
904C23—24no—
905C23—24no—
906C23—28no—
907C23—24no—
908C23—28no—
909C23—22no—
910C23—28no—
911C23—22no—
912C23—28no—
913C23—24no—
914C23—28no—
915C23—44no—
916C23—48no—
917C23—44no—
918C23—48no—
919C23—48no—
920C23—44no—
921C23—48no—
922C23—44no—
923C23—48no—
924C23—48no—
925C23—44no—
926C23—816no—
927C23—88no—
928C23—88no—
929C23—816no—
930C23—84no—
931C23—84no—
932C23—816no—
933C23C23×D412yes—
934C23C23×D418yes—
935C23C23×D412yes—
936C23C23×D412yes—
937C23C2×H(5,𝔽2)14yes—
938C23C2611yescharacteristic
939Q8—216no—
940Q8—216no—
941Q8—48no—
942Q8—48no—
943D4—216no—
944D4—216no—
945D4—416no—
946D4—416no—
947D4—48no—
948D4—432no—
949D4—48no—
950D4—48no—
951D4—432no—
952D4—416no—
953D4—416no—
954D4—48no—
955D4—48no—
956D4—48no—
957D4—816no—
958D4—816no—
959D4—88no—
960D4—816no—
961D4—816no—
962D4—88no—
963D4—816no—
964D4—1616no—
965C2×C4—28no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—28no—
970C2×C4—22no—
971C2×C4—28no—
972C2×C4—216no—
973C2×C4—28no—
974C2×C4—28no—
975C2×C4—28no—
976C2×C4—28no—
977C2×C4—24no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—24no—
983C2×C4—28no—
984C2×C4—28no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—28no—
989C2×C4—28no—
990C2×C4—28no—
991C2×C4—28no—
992C2×C4—28no—
993C2×C4—28no—
994C2×C4—28no—
995C2×C4—24no—
996C2×C4—416no—
997C2×C4—416no—
998C2×C4—416no—
999C2×C4—432no—
1000C2×C4—48no—
1001C2×C4—48no—
1002C2×C4—44no—
1003C2×C4—44no—
1004C2×C4—48no—
1005C2×C4—48no—
1006C2×C4—416no—
1007C2×C4—84no—
1008C2×C4—84no—
1009C2×C4—1616no—
1010C2×C4#534116yes—
1011C2×C4C23×D412yes—
1012C2×C4C23×D418yes—
1013C2×C4C23×D412yes—
1014C2×C4C23×D412yes—
1015C2×C4C23×D412yes—
1016C2×C4C2×H(5,𝔽2)14yes—
1017C2×C4C2×H(5,𝔽2)14yes—
1018C2×C4#58514yes—
1019C22—22no—
1020C22—22no—
1021C22—28no—
1022C22—22no—
1023C22—28no—
1024C22—22no—
1025C22—22no—
1026C22—28no—
1027C22—22no—
1028C22—22no—
1029C22—22no—
1030C22—28no—
1031C22—416no—
1032C22—44no—
1033C22—44no—
1034C22—42no—
1035C22—44no—
1036C22—44no—
1037C22—42no—
1038C22—44no—
1039C22—44no—
1040C22—44no—
1041C22—44no—
1042C22—42no—
1043C22—44no—
1044C22—48no—
1045C22—48no—
1046C22—416no—
1047C22—44no—
1048C22—816no—
1049C22—88no—
1050C22—88no—
1051C22—816no—
1052C22—816no—
1053C22C2×#53414yes—
1054C22C24×D411yescharacteristic
1055C22C22×H(5,𝔽2)12yes—
1056C22C2×#58512yes—
1057C22H(7,𝔽2)12yes—
1058C4—24no—
1059C4—22no—
1060C4—22no—
1061C4—28no—
1062C4—44no—
1063C4—44no—
1064C4—42no—
1065C4—44no—
1066C4—42no—
1067C4—44no—
1068C4—48no—
1069C4—48no—
1070C4C2×#53414yes—
1071C4C2×#53414yes—
1072C2—24no—
1073C2—42no—
1074C2—48no—
1075C2—42no—
1076C2—82no—
1077C2—84no—
1078C2—84no—
1079C2C22×#53411yescharacteristic
1080C2#6281111yescharacteristic
1081C2#6285211yescharacteristic
1082C2#6295514yes—
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. C22×#550C2semidirect
2. C2×#3449C2semidirect
3. #42985C2semidirect
4. #42969C2semidirect
5. #42913C2semidirect
6. #42909C2semidirect
7. #39865C2semidirect
8. #39861C2semidirect
9. #37446C2semidirect
10. #37232C2semidirect
11. #37117C2semidirect
12. #35528C2semidirect
13. #35514C2semidirect
14. #35262C2semidirect
15. #35250C2semidirect
16. #35182C2semidirect
17. #35149C2semidirect
18. #35063C2semidirect
19. #34809C2semidirect
20. #34736C2semidirect
21. #34172C2semidirect
24. C23×#41C22semidirect
28. C2×#550C22semidirect
29. C2×#550C22semidirect
31. C2×#537C22semidirect
32. C2×#537C22semidirect
34. C2×#536C22semidirect
37. C2×#535C22semidirect
39. C2×#532C22semidirect
41. C22×#127C22semidirect
44. C2×#525C22semidirect
47. C22×#121C22semidirect
48. C22×#121C22semidirect
49. C2×#518C22semidirect
50. C22×C4×Q8C22semidirect
52. C22×C4×D4C22semidirect
54. #2854C22semidirect
55. #2853C22semidirect
56. #2849C22semidirect
57. #2847C22semidirect
58. #2816C22semidirect
59. #2815C22semidirect
60. #2709C22semidirect
61. #2708C22semidirect
62. #2688C22semidirect
63. #2673C22semidirect
64. #2673C22semidirect
65. #2671C22semidirect
66. #2669C22semidirect
67. #2668C22semidirect
68. #2656C22semidirect
69. #2639C22semidirect
70. #2638C22semidirect
71. #2635C22semidirect
72. #2635C22semidirect
73. #2624C22semidirect
74. #2623C22semidirect
75. #2615C22semidirect
76. #2613C22semidirect
77. #2600C22semidirect
78. #2564C22semidirect
79. #2544C22semidirect
80. #2543C22semidirect
81. #2543C22semidirect
82. #2541C22semidirect
83. #2537C22semidirect
84. #2535C22semidirect
85. #2504C22semidirect
86. #2501C22semidirect
87. #2500C22semidirect
88. #2487C22semidirect
89. #2486C22semidirect
90. #2485C22semidirect
91. #2484C22semidirect
93. #2482C22semidirect
94. #2482C22semidirect
95. #2448C22semidirect
96. #2446C22semidirect
97. #2436C22semidirect
98. #2433C22semidirect
99. #2432C22semidirect
100. #2431C22semidirect
101. #2431C22semidirect
102. #2428C22semidirect
103. #2428C22semidirect
104. #2428C22semidirect
105. #2427C22semidirect
106. #2423C22semidirect
107. #2421C22semidirect
108. #2412C22semidirect
109. #2410C22semidirect
110. #2410C22semidirect
111. #2410C22semidirect
112. #2409C22semidirect
113. #2408C22semidirect
114. #2407C22semidirect
115. #2407C22semidirect
116. #2407C22semidirect
125. #2395C22semidirect
126. #2388C22semidirect
127. #2339C22semidirect
128. #2339C22semidirect
129. #2339C22semidirect
130. #2339C22semidirect
131. #2325C22semidirect
132. #2317C22semidirect
134. #2310C22semidirect
135. #2309C22semidirect
137. C4×#123C22semidirect
138. C4×#120C22semidirect
140. #2296C22semidirect
143. #2280C22semidirect
144. C2×#381C22semidirect
150. C22×#41D4semidirect

Maximal subgroups

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

subgroupindex
C22×#5502
C2×#34492
#429852
#429692
#429132
#429092
#398652
#398612
#374462
#372322
#371172
#355282
#355142
#352622
#352502
#351822
#351492
#350632
#348092
#347362
#341722