Finite Group Databasebeta

← #6464083

Subgroups — #6464083

Order 512.

1889 conjugacy classes of subgroups.

The subgroup lattice has 922 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3137C211yesmaximal, characteristic
2C2×#2960C211yesmaximal, characteristic, complemented
3#35628C211yesmaximal, characteristic
4#35566C211yesmaximal, characteristic, complemented
5#28652C212yesmaximal, complemented
6#28652C212yesmaximal, complemented
7#28651C212yesmaximal, complemented
8#28649C212yesmaximal, complemented
9#28642C212yesmaximal, complemented
10#28641C212yesmaximal, complemented
11#28639C212yesmaximal, complemented
12#28638C212yesmaximal, complemented
13#23619C211yesmaximal, characteristic, complemented
14#23617C211yesmaximal, characteristic
15#23616C211yesmaximal, characteristic
16#23615C211yesmaximal, characteristic, complemented
17#21315C211yesmaximal, characteristic, complemented
18#21262C211yesmaximal, characteristic
19#21092C211yesmaximal, characteristic
20#21090C211yesmaximal, characteristic, complemented
21#21083C211yesmaximal, characteristic
22C2×#1933C211yesmaximal, characteristic, complemented
23#20453C211yesmaximal, characteristic, complemented
24C2×#544C2211yescharacteristic
25C2×#536C2211yescharacteristic
26C2×#533C2211yescharacteristic
27#3137—28no—
28C2×#491C2212yes—
29C2×#489C2212yes—
30C2×#488C2212yes—
31C2×#487C2212yes—
32#2960—28no—
33C2×#446C2212yes—
34C2×#446C2212yes—
35C2×C8×Q8C2212yes—
36C2×C8×Q8C2212yes—
37C2×#428C2211yescharacteristic
38C2×#428C2211yescharacteristic
39C2×#424C2211yescharacteristic
40C2×#424C2211yescharacteristic
41C2×#423C2211yescharacteristic
42C2×#417C2211yescharacteristic
43C2×#417C2211yescharacteristic
44C2×#419C2211yescharacteristic
45C2×#419C2211yescharacteristic
46C2×#416C2211yescharacteristic
47C2×#416C2211yescharacteristic
48C22×#103C2211yescharacteristic
49C22×#103C2211yescharacteristic
50C2×#405C2211yescharacteristic
51C2×#405C2211yescharacteristic
52C22×C4×C8C2211yescharacteristic
53#2592C2212yes—
54#2592C2212yes—
55#2584C2212yes—
56#2584C2212yes—
57#2568C2212yes—
58#2568C2212yes—
59#2567C2212yes—
60#2552—21no—
61#2551—21no—
62#2550—21no—
63#2550—21no—
64#2549—22no—
65#2546C2212yes—
66#2492—21no—
67#2492—21no—
68#2489—21no—
69#2489—21no—
70#2488—22no—
71#2488—22no—
72#2440—22no—
73#2317C2211yescharacteristic
74#2316C2211yescharacteristic
75#2311C2211yescharacteristic
76#2310C2211yescharacteristic
77#2297C2211yescharacteristic
78#2296C2211yescharacteristic
79C2×#391C2211yescharacteristic
80C2×#389C2211yescharacteristic
81#2274C2211yescharacteristic
82#2274C2211yescharacteristic
83#2068C2212yes—
84#2068C2212yes—
85#2068C2212yes—
86#2068C2212yes—
87#2068C2212yes—
88#2068C2212yes—
89#2067C2212yes—
90#2067C2212yes—
91#2066C2212yes—
92#2066C2212yes—
93#2066C2212yes—
94#2066C2212yes—
95#2066C2212yes—
96#2066C2212yes—
97#2065C2212yes—
98#2065C2212yes—
99#1989C2212yes—
100#1989C2212yes—
101#1988C2212yes—
102#1987C2212yes—
103#1983C2212yes—
104#1983C2212yes—
105#1981C2212yes—
106#1981C2212yes—
107#1936C2212yes—
108#1935C2212yes—
109#1935C2212yes—
110#1935C2212yes—
111#1934C2211yescharacteristic
112#1934C2211yescharacteristic
113#1934C2211yescharacteristic
114#1934C2211yescharacteristic
115#1934C2212yes—
116#1933C2212yes—
117#1933C2212yes—
118#1933C2212yes—
119#1933C2212yes—
120#1933C2211yescharacteristic
121#1933C2211yescharacteristic
122#1933C2211yescharacteristic
123#1933C2211yescharacteristic
124#1933C2212yes—
125#1933C2212yes—
126#1933C2212yes—
127#1776C2212yes—
128#1776C2212yes—
129C4×#107C2212yes—
130C4×#106C2212yes—
131#1736C2211yescharacteristic
132#1736C2211yescharacteristic
133#1735C2211yescharacteristic
134#1735C2211yescharacteristic
135C2×#340C2211yescharacteristic
136C2×#340C2211yescharacteristic
137C22×#41C2311yescharacteristic
138C23×Q8C2311yescharacteristic
139C22×M16C2311yescharacteristic
140C22×M16C2311yescharacteristic
141C23×C8C2311yescharacteristic
142C23×C8C2311yescharacteristic
143#544—24no—
144#544—24no—
145#536—24no—
146#536—24no—
147#533—24no—
148#533—24no—
149C2×C4⋊Q8—22no—
150C2×C4⋊Q8—21no—
151C2×C4⋊Q8D411yescharacteristic
152C2×C4⋊Q8D411yescharacteristic
153C2×C4⋊Q8C2312yes—
154C2×C4⋊Q8C2312yes—
155C2×#125—21no—
156C2×#125D411yescharacteristic
157C2×#125D411yescharacteristic
158C2×#125C2312yes—
159C2×#124C2312yes—
160C2×#123—22no—
161C2×C22⋊Q8—21no—
162C2×C22⋊Q8—21no—
163C2×C22⋊Q8—22no—
164C2×C22⋊Q8D412yes—
165C2×C22⋊Q8D412yes—
166C2×C4×Q8C2312yes—
167C2×C4×Q8C2312yes—
168C2×#117C2311yescharacteristic
169C2×#117C2311yescharacteristic
170C2×#117C2311yescharacteristic
171C2×#117C2311yescharacteristic
172C2×#117C2311yescharacteristic
173C22×C4⋊C4—21no—
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2311yescharacteristic
177C22×C42C2311yescharacteristic
178#491—28no—
179#489—28no—
180#488—28no—
181#487—28no—
182#446—28no—
183#446—28no—
184C8×Q8—28no—
185C8×Q8—28no—
186#428—24no—
187#428—24no—
188C2×#107C2312yes—
189C2×#107C2312yes—
190C2×#106C2312yes—
191C2×#106C2312yes—
192#424—24no—
193#424—24no—
194#423—24no—
195C2×C4⋊C8C2312yes—
196C2×C4⋊C8C2312yes—
197C2×C4⋊C8C2312yes—
198C2×C4⋊C8C2312yes—
199C2×C4⋊C8C2312yes—
200C2×C4⋊C8C2312yes—
201#419—24no—
202#419—24no—
203#417—24no—
204#417—24no—
205#416—24no—
206#416—24no—
207C2×#103—24no—
208C2×#103—24no—
209C2×#103C2312yes—
210C2×#103C2312yes—
211C2×#103C2312yes—
212C2×#103C2311yescharacteristic
213C2×#103C2312yes—
214C2×#103C2312yes—
215C2×#103C2312yes—
216C2×#103C2312yes—
217C2×#103C2311yescharacteristic
218C2×#103C2312yes—
219C2×#103C2311yescharacteristic
220C2×#103C2312yes—
221C2×#103C2312yes—
222C2×#103C2311yescharacteristic
223C2×#102C2312yes—
224C2×#102C2311yescharacteristic
225C2×#102C2312yes—
226C2×#102C2311yescharacteristic
227C2×#102C2311yescharacteristic
228C2×#102C2311yescharacteristic
229#405—24no—
230#405D418yes—
231C2×#97C2312yes—
232C2×#97C2312yes—
233C2×C4×C8—24no—
234C2×C4×C8C2311yescharacteristic
235C2×C4×C8C2311yescharacteristic
236C2×C4×C8C2311yescharacteristic
237C2×C4×C8C2311yescharacteristic
238C2×C4×C8C2312yes—
239C2×C4×C8C2312yes—
240#400—22no—
241#400—22no—
242#400—22no—
243#400—22no—
244#398—22no—
245#398—22no—
246#398—22no—
247#398—22no—
248#397—22no—
249#397—22no—
250#395—22no—
251#395—22no—
252#395—22no—
253#395—22no—
254#393—22no—
255#393—22no—
256#391—22no—
257#391—22no—
258#391—22no—
259#391—21no—
260#391—21no—
261#391—22no—
262#391—21no—
263#391—21no—
264#391C2312yes—
265#391C2312yes—
266#391C2312yes—
267#391C2311yescharacteristic
268#391C2311yescharacteristic
269#391C2312yes—
270#391C2312yes—
271#390C2312yes—
272#390C2311yescharacteristic
273#390C2311yescharacteristic
274#389—21no—
275#389—21no—
276#389—22no—
277#389—22no—
278#389—22no—
279#389—22no—
280#389—21no—
281#389—21no—
282#389C2311yescharacteristic
283#389C2312yes—
284#389C2312yes—
285#389C2312yes—
286#389C2312yes—
287#389C2312yes—
288#389C2311yescharacteristic
289#389C2311yescharacteristic
290#389C2312yes—
291#389C2311yescharacteristic
292#388—22no—
293#388—22no—
294#388—22no—
295#388—22no—
296#386—21no—
297#386—21no—
298#386—22no—
299#385—21no—
300#385—21no—
301#385—22no—
302#384—22no—
303#384—21no—
304#382—22no—
305#382—22no—
306#382—21no—
307#381—22no—
308#380—21no—
309#380—21no—
310#380—22no—
311C4×C4⋊C4—21no—
312C4×C4⋊C4—21no—
313C4×C4⋊C4—21no—
314C4×C4⋊C4—21no—
315C4×C4⋊C4—21no—
316C4×C4⋊C4—21no—
317C4×C4⋊C4C2312yes—
318C4×C4⋊C4C2312yes—
319C4×C4⋊C4C2312yes—
320C4×C4⋊C4C2312yes—
321C4×C22⋊C4—22no—
322C4×C22⋊C4—22no—
323C4×C22⋊C4—21no—
324C4×C22⋊C4—21no—
325C2×#95—21no—
326C2×#95—21no—
327C2×#95—21no—
328#340C2312yes—
329#340C2312yes—
330#340C2311yescharacteristic
331#340C2311yescharacteristic
332#340C2312yes—
333#340C2312yes—
334#340C2312yes—
335#340C2312yes—
336#340C2311yescharacteristic
337#340C2311yescharacteristic
338#340C2312yes—
339#340C2311yescharacteristic
340#340C2311yescharacteristic
341#340C2312yes—
342#340C2311yescharacteristic
343#340C2311yescharacteristic
344C2×#41—22no—
345C2×#41—22no—
346C2×#41—22no—
347C2×#41—22no—
348C2×#41—22no—
349C2×#41—22no—
350C22×Q8—21no—
351C22×Q8—22no—
352C22×Q8—22no—
353C22×Q8—22no—
354C22×Q8—22no—
355C22×Q8—22no—
356C22×Q8—22no—
357C22×Q8—22no—
358C22×Q8C2×D412yes—
359C22×Q8C2×D412yes—
360C22×Q8C2412yes—
361C22×Q8C2411yescharacteristic
362C22×D4—21no—
363C22×D4C2411yescharacteristic
364C23×C4—21no—
365C23×C4—21no—
366C23×C4—21no—
367C23×C4—21no—
368C23×C4—21no—
369C23×C4C2×D411yescharacteristic
370C23×C4C2×D411yescharacteristic
371C23×C4C2411yescharacteristic
372C2×M16—22no—
373C2×M16—22no—
374C2×M16—22no—
375C2×M16—22no—
376C2×M16—22no—
377C2×M16C2×D414yes—
378C22×C8—22no—
379C22×C8—22no—
380C22×C8—22no—
381C22×C8—22no—
382C22×C8—22no—
383C22×C8C2×D414yes—
384C22×C8C2411yescharacteristic
385C22×C8C2411yescharacteristic
386C22×C8C2412yes—
387C22×C8C2411yescharacteristic
388C22×C8C2411yescharacteristic
389C22×C8C2412yes—
390C4⋊Q8—24no—
391C4⋊Q8—24no—
392C4⋊Q8—24no—
393C4⋊Q8—24no—
394C4⋊Q8—24no—
395C4⋊Q8—24no—
396C4⋊Q8—44no—
397C4⋊Q8—84no—
398#125—24no—
399#125—24no—
400#125—24no—
401#125—24no—
402#125—44no—
403#124—24no—
404#124—24no—
405#123—48no—
406C22⋊Q8—28no—
407C22⋊Q8—28no—
408C22⋊Q8—44no—
409C22⋊Q8—44no—
410C22⋊Q8—48no—
411C4×Q8—24no—
412C4×Q8—24no—
413C4×Q8—24no—
414C4×Q8—24no—
415#117—22no—
416#117—22no—
417#117—22no—
418#117—22no—
419#117—22no—
420#117—22no—
421#117—22no—
422#117C2×D414yes—
423#117#4114yes—
424#117#4114yes—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—82no—
449C2×C4⋊C4C2×D411yescharacteristic
450C2×C4⋊C4C2×D411yescharacteristic
451C2×C4⋊C4C2×D412yes—
452C2×C4⋊C4C2×D412yes—
453C2×C4⋊C4C2×D412yes—
454C2×C4⋊C4C2×D412yes—
455C2×C4⋊C4C2×D412yes—
456C2×C4⋊C4C2×D412yes—
457C2×C4⋊C4C2×D411yescharacteristic
458C2×C4⋊C4C2×D411yescharacteristic
459C2×C4⋊C4#4114yes—
460C2×C4⋊C4C2412yes—
461C2×C4⋊C4C2412yes—
462C2×C4⋊C4C2411yescharacteristic
463C2×C4⋊C4C2411yescharacteristic
464C2×C4⋊C4C2411yescharacteristic
465C2×C4⋊C4C2411yescharacteristic
466C2×C4⋊C4C2412yes—
467C2×C4⋊C4C2411yescharacteristic
468C2×C4⋊C4C2411yescharacteristic
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4C2×D412yes—
481C2×C22⋊C4C2×D412yes—
482C2×C42—21no—
483C2×C42—22no—
484C2×C42—22no—
485C2×C42—21no—
486C2×C42—21no—
487C2×C42—22no—
488C2×C42—22no—
489C2×C42—22no—
490C2×C42—22no—
491C2×C42C2×D411yescharacteristic
492C2×C42C2×D411yescharacteristic
493C2×C42C2412yes—
494C2×C42C2411yescharacteristic
495C2×C42C2411yescharacteristic
496C2×C42C2412yes—
497#107—24no—
498#107—24no—
499#106—24no—
500#106—24no—
501C4⋊C8—24no—
502C4⋊C8—24no—
503C4⋊C8—24no—
504C4⋊C8—24no—
505C4⋊C8—24no—
506C4⋊C8—24no—
507#103—24no—
508#103—24no—
509#103—22no—
510#103—22no—
511#103—24no—
512#103—24no—
513#103—24no—
514#103—24no—
515#103—24no—
516#103—22no—
517#103—22no—
518#103—24no—
519#103—24no—
520#103—24no—
521#102—22no—
522#102—22no—
523#102—24no—
524#102—22no—
525#102—22no—
526#102—24no—
527#97—24no—
528#97C2×D418yes—
529C4×C8—22no—
530C4×C8—22no—
531C4×C8—22no—
532C4×C8—22no—
533C4×C8—24no—
534C4×C8C2×D418yes—
535#95—22no—
536#95—22no—
537#95—22no—
538#95—22no—
539#95—22no—
540#95—22no—
541#95—22no—
542#95—22no—
543#95—22no—
544#95—22no—
545#95—21no—
546#95—21no—
547#95—21no—
548#95—21no—
549#95—21no—
550#95—21no—
551#95—21no—
552#95—21no—
553#95—22no—
554#95—22no—
555#95—22no—
556#95—22no—
557#95—22no—
558#95—22no—
559#95—22no—
560#95—22no—
561#95—22no—
562#95—22no—
563C24—21no—
564C24C22×D411yescharacteristic
565#41—44no—
566#41—44no—
567#41—44no—
568#41—44no—
569C2×Q8—24no—
570C2×Q8—24no—
571C2×Q8—24no—
572C2×Q8—24no—
573C2×Q8—22no—
574C2×Q8—21no—
575C2×Q8—22no—
576C2×Q8—22no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—22no—
580C2×Q8—21no—
581C2×Q8—22no—
582C2×Q8—22no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—42no—
586C2×Q8—42no—
587C2×Q8—42no—
588C2×Q8—44no—
589C2×Q8—42no—
590C2×Q8—42no—
591C2×Q8—44no—
592C2×Q8—44no—
593C2×Q8—44no—
594C2×Q8—44no—
595C2×Q8—82no—
596C2×Q8—82no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—42no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—22no—
611C22×C4—24no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—22no—
622C22×C4—41no—
623C22×C4—41no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4—81no—
633C22×C4—81no—
634C22×C4—81no—
635C22×C4—81no—
636C22×C4—81no—
637C22×C4—81no—
638C22×C4C22×D411yescharacteristic
639C22×C4C22×D412yes—
640C22×C4C22×D411yescharacteristic
641C22×C4C22×D412yes—
642C22×C4C22×D412yes—
643C22×C4C22×D412yes—
644C22×C4C22×D411yescharacteristic
645C22×C4C22×D411yescharacteristic
646C22×C4C22×D411yescharacteristic
647C22×C4C22×D412yes—
648C22×C4C2×#4112yes—
649C22×C4C2×#4112yes—
650C22×C4C2×#4112yes—
651C22×C42−1+412yes—
652C22×C42−1+412yes—
653C22×C4C2511yescharacteristic
654M16—28no—
655M16—44no—
656C2×C8—28no—
657C2×C8—22no—
658C2×C8—22no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—22no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—22no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—22no—
672C2×C8—44no—
673C2×C8C22×D412yes—
674C2×C8C22×D412yes—
675C2×C8C22×D414yes—
676C4⋊C4—22no—
677C4⋊C4—22no—
678C4⋊C4—24no—
679C4⋊C4—24no—
680C4⋊C4—24no—
681C4⋊C4—24no—
682C4⋊C4—24no—
683C4⋊C4—24no—
684C4⋊C4—24no—
685C4⋊C4—22no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—22no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—22no—
693C4⋊C4—21no—
694C4⋊C4—22no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—22no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—42no—
701C4⋊C4—44no—
702C4⋊C4—44no—
703C4⋊C4—44no—
704C4⋊C4—44no—
705C4⋊C4—44no—
706C4⋊C4—42no—
707C4⋊C4—44no—
708C4⋊C4—42no—
709C4⋊C4—42no—
710C4⋊C4—81no—
711C4⋊C4—81no—
712C4⋊C4—82no—
713C4⋊C4—82no—
714C4⋊C4—82no—
715C4⋊C4—82no—
716C4⋊C4—82no—
717C4⋊C4#12114yes—
718C4⋊C4#12114yes—
719C4⋊C4C2×#4112yes—
720C4⋊C4C2×#4114yes—
721C4⋊C4C2×#4112yes—
722C22⋊C4—24no—
723C22⋊C4—24no—
724C22⋊C4—42no—
725C22⋊C4—42no—
726C22⋊C4—44no—
727C22⋊C4—44no—
728C22⋊C4—42no—
729C22⋊C4—42no—
730C22⋊C4—81no—
731C22⋊C4—81no—
732C22⋊C4—82no—
733C22⋊C4—82no—
734C22⋊C4#12118yes—
735C42—22no—
736C42—22no—
737C42—24no—
738C42—21no—
739C42—21no—
740C42—22no—
741C42—21no—
742C42—21no—
743C42—22no—
744C42—42no—
745C42—42no—
746C42—82no—
747C42—82no—
748C42—82no—
749C42—82no—
750C42C22×D414yes—
751C42C2×#4114yes—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23C2×#12112yes—
764C23#54812yes—
765C23#54812yes—
766C23C23×D411yescharacteristic
767Q8—48no—
768Q8—48no—
769Q8—42no—
770Q8—41no—
771Q8—42no—
772Q8—41no—
773Q8—42no—
774Q8—42no—
775Q8—41no—
776Q8—41no—
777Q8—84no—
778Q8—164no—
779D4—41no—
780D4—41no—
781D4—41no—
782D4—41no—
783D4—84no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—24no—
803C2×C4—21no—
804C2×C4—22no—
805C2×C4—21no—
806C2×C4—22no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—42no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—41no—
820C2×C4—42no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—42no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—41no—
835C2×C4—42no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—84no—
840C2×C4—84no—
841C2×C4—84no—
842C2×C4—162no—
843C2×C4—162no—
844C2×C4C2×#12114yes—
845C2×C4C2×#12114yes—
846C2×C4C2×#12112yes—
847C2×C4#53214yes—
848C2×C4#53614yes—
849C2×C4#54812yes—
850C2×C4#54812yes—
851C2×C4#55614yes—
852C2×C4#55614yes—
853C2×C4#57712yes—
854C2×C4#57812yes—
855C2×C4C23×D411yescharacteristic
856C2×C4C22×#4111yescharacteristic
857C2×C4C22×#4111yescharacteristic
858C2×C4C22×#4111yescharacteristic
859C2×C4C2×2−1+411yescharacteristic
860C2×C4C2×2−1+411yescharacteristic
861C8—24no—
862C8—22no—
863C8—22no—
864C8—41no—
865C8—41no—
866C8—42no—
867C22—22no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—22no—
873C22—81no—
874C22—81no—
875C22—81no—
876C22—81no—
877C22—81no—
878C22—81no—
879C22—81no—
880C22#254514yes—
881C22C22×#12111yescharacteristic
882C22C2×#54811yescharacteristic
883C22C2×#54811yescharacteristic
884C22C2×#57711yescharacteristic
885C22C2×#57811yescharacteristic
886C22#358411yescharacteristic
887C22#358411yescharacteristic
888C4—22no—
889C4—24no—
890C4—22no—
891C4—24no—
892C4—41no—
893C4—42no—
894C4—41no—
895C4—42no—
896C4—44no—
897C4—42no—
898C4—42no—
899C4—82no—
900C4—81no—
901C4—81no—
902C4—81no—
903C4—82no—
904C4—81no—
905C4—81no—
906C4—82no—
907C4#254514yes—
908C4C2×#53211yescharacteristic
909C4C2×#53611yescharacteristic
910C4C2×#55611yescharacteristic
911C4C2×#55611yescharacteristic
912C2—24no—
913C2—161no—
914C2C2×#254511yescharacteristic
915C2#6045711yescharacteristic
916C2#6045911yescharacteristic
917C2#6132611yescharacteristic
918C2#6132811yescharacteristic
919C2#6133011yescharacteristic
920C2#6133111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#41C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#533 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2960C2semidirect
4. #35566C2semidirect
5. #28652C2semidirect
6. #28652C2semidirect
7. #28651C2semidirect
8. #28649C2semidirect
9. #28642C2semidirect
10. #28641C2semidirect
11. #28639C2semidirect
12. #28638C2semidirect
13. #23619C2semidirect
16. #23615C2semidirect
17. #21315C2semidirect
20. #21090C2semidirect
22. C2×#1933C2semidirect
23. #20453C2semidirect

Maximal subgroups

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

subgroupindex
C2×#31372
C2×#29602
#356282
#355662
#286522
#286512
#286492
#286422
#286412
#286392
#286382
#236192
#236172
#236162
#236152
#213152
#212622
#210922
#210902
#210832
C2×#19332
#204532