Finite Group Databasebeta

← #6458603

Subgroups — #6458603

Order 512.

1773 conjugacy classes of subgroups.

The subgroup lattice has 929 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35667C211yesmaximal, characteristic
2#35543C211yesmaximal, characteristic, complemented
3#27765C212yesmaximal, complemented
4#27762C212yesmaximal, complemented
5#27762C212yesmaximal, complemented
6#27761C212yesmaximal, complemented
7#27757C212yesmaximal, complemented
8#27754C212yesmaximal, complemented
9#27752C212yesmaximal, complemented
10#27749C212yesmaximal, complemented
11#23633C211yesmaximal, characteristic, complemented
12#23627C211yesmaximal, characteristic
13#23510C211yesmaximal, characteristic
14C2×#2043C211yesmaximal, characteristic, complemented
15#21262C211yesmaximal, characteristic
16#21205C211yesmaximal, characteristic
17#21205C211yesmaximal, characteristic
18#21202C211yesmaximal, characteristic, complemented
19#21093C211yesmaximal, characteristic
20#21090C211yesmaximal, characteristic, complemented
21#20651C211yesmaximal, characteristic, complemented
22#20439C211yesmaximal, characteristic, complemented
23#20417C211yesmaximal, characteristic, complemented
24C2×#536C2211yescharacteristic
25C2×#536C2211yescharacteristic
26C22×C4⋊Q8C2211yescharacteristic
27C2×#519C2211yescharacteristic
28C2×#424C2211yescharacteristic
29C2×#417C2211yescharacteristic
30C2×#417C2211yescharacteristic
31C2×#419C2211yescharacteristic
32C2×#419C2211yescharacteristic
33C2×#419C2211yescharacteristic
34C2×#419C2211yescharacteristic
35C2×#416C2211yescharacteristic
36C2×#416C2211yescharacteristic
37C22×#103C2211yescharacteristic
38C22×#103C2211yescharacteristic
39C22×#103C2211yescharacteristic
40C22×#103C2211yescharacteristic
41C2×#405C2211yescharacteristic
42C2×#405C2211yescharacteristic
43C2×C4×M16C2211yescharacteristic
44#2571C2212yes—
45#2570C2212yes—
46#2570C2212yes—
47#2552C2212yes—
48#2546C2212yes—
49#2546C2212yes—
50#2545C2212yes—
51#2545C2212yes—
52#2509—21no—
53#2508—21no—
54#2507—21no—
55#2506—21no—
56#2505—22no—
57#2473—22no—
58#2429—21no—
59#2429—21no—
60#2429—21no—
61#2429—21no—
62#2413—22no—
63#2413—22no—
64#2317C2211yescharacteristic
65#2317C2211yescharacteristic
66#2317C2211yescharacteristic
67#2310C2211yescharacteristic
68#2297C2211yescharacteristic
69#2296C2211yescharacteristic
70C2×#389C2211yescharacteristic
71#2285C2211yescharacteristic
72#2274C2211yescharacteristic
73#2074C2211yescharacteristic
74#2074C2211yescharacteristic
75#2074C2212yes—
76#2074C2212yes—
77#2073C2211yescharacteristic
78#2073C2211yescharacteristic
79#2072C2211yescharacteristic
80#2072C2211yescharacteristic
81#2072C2212yes—
82#2072C2212yes—
83#2071C2211yescharacteristic
84#2071C2211yescharacteristic
85#2043C2212yes—
86#2043C2212yes—
87#2043C2212yes—
88#2043C2212yes—
89#2043C2212yes—
90#2043C2212yes—
91#2042C2212yes—
92#2042C2212yes—
93#1983C2212yes—
94#1983C2212yes—
95#1981C2212yes—
96#1981C2212yes—
97#1960C2212yes—
98#1960C2212yes—
99#1960C2212yes—
100#1960C2212yes—
101#1959C2212yes—
102#1959C2212yes—
103#1958C2212yes—
104#1958C2212yes—
105#1956C2212yes—
106#1956C2212yes—
107#1956C2212yes—
108#1956C2212yes—
109#1936C2212yes—
110#1935C2212yes—
111#1935C2212yes—
112#1935C2212yes—
113#1934C2212yes—
114#1933C2212yes—
115#1933C2212yes—
116#1933C2212yes—
117#1805C2212yes—
118#1805C2212yes—
119#1803C2212yes—
120#1803C2212yes—
121#1771C2212yes—
122#1771C2212yes—
123#1770C2212yes—
124C8×C4⋊C4C2212yes—
125#1763C2212yes—
126#1763C2212yes—
127C4×#103C2212yes—
128C4×#103C2212yes—
129#1736C2211yescharacteristic
130#1736C2211yescharacteristic
131#1735C2211yescharacteristic
132#1735C2211yescharacteristic
133#1729C2211yescharacteristic
134C2×#336C2211yescharacteristic
135C22×#41C2311yescharacteristic
136C23×Q8C2311yescharacteristic
137C23×Q8C2311yescharacteristic
138C22×M16C2311yescharacteristic
139C22×M16C2311yescharacteristic
140C23×C8C2311yescharacteristic
141C23×C8C2311yescharacteristic
142#536—24no—
143#536—24no—
144#536—24no—
145#536—42no—
146C2×C4⋊Q8—24no—
147C2×C4⋊Q8—21no—
148C2×C4⋊Q8—21no—
149C2×C4⋊Q8—42no—
150C2×C4⋊Q8C2312yes—
151C2×C4⋊Q8C2312yes—
152C2×C4⋊Q8C2312yes—
153C2×C4⋊Q8C2312yes—
154C2×#125—22no—
155C2×#124C2312yes—
156C2×#124C2312yes—
157C2×#123—22no—
158C2×#123—22no—
159C2×C22⋊Q8—21no—
160C2×C22⋊Q8—21no—
161C2×C22⋊Q8—21no—
162C2×C22⋊Q8—21no—
163#519—24no—
164#519—24no—
165C2×C4×Q8—21no—
166C2×C4×Q8—21no—
167C2×C4×Q8C2312yes—
168C2×C4×Q8C2312yes—
169C2×#117—22no—
170C2×#117C2311yescharacteristic
171C2×#117C2311yescharacteristic
172C2×#117C2311yescharacteristic
173C2×#117C2311yescharacteristic
174C2×#117C2311yescharacteristic
175C22×C4⋊C4—21no—
176C22×C4⋊C4—21no—
177C22×C4⋊C4—21no—
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2311yescharacteristic
180C22×C42C2311yescharacteristic
181#424—24no—
182C2×C4⋊C8C2312yes—
183C2×C4⋊C8C2312yes—
184#419—24no—
185#419—24no—
186#419—42no—
187#419—42no—
188#417—24no—
189#417—42no—
190#416—42no—
191#416—42no—
192C2×#103—24no—
193C2×#103—42no—
194C2×#103—42no—
195C2×#103—42no—
196C2×#103C2312yes—
197C2×#103C2312yes—
198C2×#103C2312yes—
199C2×#103C2312yes—
200C2×#103C2312yes—
201C2×#103C2312yes—
202C2×#103C2312yes—
203C2×#103C2312yes—
204C2×#103C2312yes—
205C2×#103C2312yes—
206C2×#103C2312yes—
207C2×#103C2312yes—
208C2×#103C2312yes—
209C2×#103C2312yes—
210C2×#103C2311yescharacteristic
211C2×#103C2311yescharacteristic
212C2×#103C2311yescharacteristic
213C2×#103C2311yescharacteristic
214C2×#103C2312yes—
215C2×#103C2312yes—
216C2×#103C2312yes—
217C2×#103C2312yes—
218C2×#102C2312yes—
219C2×#102C2311yescharacteristic
220C2×#102C2311yescharacteristic
221C2×#102C2311yescharacteristic
222C2×#102C2311yescharacteristic
223C2×#102C2312yes—
224#405—24no—
225#405—42no—
226C4×M16—42no—
227C2×#97C2312yes—
228C2×#97C2312yes—
229C2×#97C2312yes—
230C2×C4×C8C2312yes—
231C2×C4×C8C2312yes—
232C2×C4×C8C2312yes—
233#400—22no—
234#400—22no—
235#400—22no—
236#400—22no—
237#398—22no—
238#398—22no—
239#398—22no—
240#398—22no—
241#398—22no—
242#398—22no—
243#398—22no—
244#398—22no—
245#396—22no—
246#396—22no—
247#396—22no—
248#396—22no—
249#391—21no—
250#391—21no—
251#391C2312yes—
252#391C2312yes—
253#391C2311yescharacteristic
254#391C2311yescharacteristic
255#390C2311yescharacteristic
256#390C2311yescharacteristic
257#389—22no—
258#389—21no—
259#389—21no—
260#389—21no—
261#389—21no—
262#389—22no—
263#389—22no—
264#389—22no—
265#389—22no—
266#389—22no—
267#389—21no—
268#389—21no—
269#389D411yescharacteristic
270#389D411yescharacteristic
271#389D411yescharacteristic
272#389D411yescharacteristic
273#389C2312yes—
274#389C2312yes—
275#389C2312yes—
276#389C2312yes—
277#388—22no—
278#388—22no—
279#388—22no—
280#388—22no—
281#387—22no—
282#387—22no—
283#387—22no—
284#387—22no—
285#386—21no—
286#386—21no—
287#385—22no—
288#385—22no—
289#385—22no—
290#385D412yes—
291#385D412yes—
292#384—21no—
293#384C2311yescharacteristic
294#384C2312yes—
295#384C2312yes—
296#384C2311yescharacteristic
297#382—22no—
298#382—21no—
299#382C2312yes—
300#382C2311yescharacteristic
301#382C2312yes—
302#382C2311yescharacteristic
303#381—22no—
304#380—21no—
305#380—21no—
306C4×C4⋊C4—21no—
307C4×C4⋊C4—21no—
308C4×C4⋊C4—21no—
309C4×C4⋊C4—21no—
310C4×C4⋊C4C2312yes—
311C4×C4⋊C4C2312yes—
312C4×C4⋊C4C2312yes—
313C4×C4⋊C4C2312yes—
314C4×C22⋊C4—22no—
315C4×C22⋊C4—21no—
316C4×C22⋊C4—21no—
317C2×#95—21no—
318#340C2311yescharacteristic
319#340C2311yescharacteristic
320#340C2312yes—
321#340C2312yes—
322#340C2311yescharacteristic
323#340C2311yescharacteristic
324#340C2311yescharacteristic
325#340C2311yescharacteristic
326#340C2311yescharacteristic
327#340C2311yescharacteristic
328#340C2312yes—
329#340C2312yes—
330#336C2311yescharacteristic
331#336C2311yescharacteristic
332#336C2312yes—
333#336C2312yes—
334#336C2311yescharacteristic
335#336C2311yescharacteristic
336C2×#41—22no—
337C2×#41—22no—
338C2×#41—22no—
339C2×#41—22no—
340C2×#41—22no—
341C2×#41—22no—
342C22×Q8—21no—
343C22×Q8—21no—
344C22×Q8—22no—
345C22×Q8—22no—
346C22×Q8—22no—
347C22×Q8—22no—
348C22×Q8—22no—
349C22×Q8—22no—
350C22×Q8—22no—
351C22×Q8—22no—
352C22×Q8—22no—
353C22×Q8—22no—
354C22×Q8—22no—
355C22×Q8#4114yes—
356C22×Q8C2412yes—
357C22×Q8C2411yescharacteristic
358C22×Q8C2412yes—
359C22×D4—21no—
360C22×D4C2411yescharacteristic
361C23×C4—21no—
362C23×C4—21no—
363C23×C4—21no—
364C23×C4—21no—
365C23×C4—21no—
366C23×C4C2×D411yescharacteristic
367C23×C4C2×D411yescharacteristic
368C23×C4C2411yescharacteristic
369C2×M16—22no—
370C2×M16—22no—
371C2×M16—22no—
372C2×M16—22no—
373C2×M16—22no—
374C2×M16#4114yes—
375C22×C8—22no—
376C22×C8—22no—
377C22×C8—22no—
378C22×C8—22no—
379C22×C8—22no—
380C22×C8—22no—
381C22×C8C2411yescharacteristic
382C22×C8C2411yescharacteristic
383C22×C8C2411yescharacteristic
384C22×C8C2411yescharacteristic
385C22×C8C2412yes—
386C22×C8C2412yes—
387C4⋊Q8—24no—
388C4⋊Q8—24no—
389C4⋊Q8—24no—
390C4⋊Q8—24no—
391C4⋊Q8—24no—
392C4⋊Q8—42no—
393C4⋊Q8—42no—
394C4⋊Q8—42no—
395C4⋊Q8—44no—
396C4⋊Q8—44no—
397#125—84no—
398#124—24no—
399#124—24no—
400#124—24no—
401#124—42no—
402#123—48no—
403#123—48no—
404C22⋊Q8—44no—
405C22⋊Q8—44no—
406C22⋊Q8—44no—
407C22⋊Q8—44no—
408C4×Q8—24no—
409C4×Q8—24no—
410C4×Q8—24no—
411C4×Q8—24no—
412C4×Q8—44no—
413C4×Q8—44no—
414#117—22no—
415#117—22no—
416#117—22no—
417#117—22no—
418#117—22no—
419#117—22no—
420#117—22no—
421#117—22no—
422#117—48no—
423#117#4114yes—
424#117#4114yes—
425C2×C4⋊C4—22no—
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—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—44no—
454C2×C4⋊C4—44no—
455C2×C4⋊C4—82no—
456C2×C4⋊C4C2×D411yescharacteristic
457C2×C4⋊C4C2×D411yescharacteristic
458C2×C4⋊C4C2×D412yes—
459C2×C4⋊C4C2×D412yes—
460C2×C4⋊C4C2×D412yes—
461C2×C4⋊C4C2×D412yes—
462C2×C4⋊C4C2×D411yescharacteristic
463C2×C4⋊C4C2×D411yescharacteristic
464C2×C4⋊C4C2412yes—
465C2×C4⋊C4C2412yes—
466C2×C4⋊C4C2411yescharacteristic
467C2×C4⋊C4C2411yescharacteristic
468C2×C4⋊C4C2411yescharacteristic
469C2×C4⋊C4C2411yescharacteristic
470C2×C4⋊C4C2411yescharacteristic
471C2×C4⋊C4C2411yescharacteristic
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4C2×D412yes—
484C2×C22⋊C4C2×D412yes—
485C2×C42—22no—
486C2×C42—22no—
487C2×C42—22no—
488C2×C42—22no—
489C2×C42—21no—
490C2×C42—21no—
491C2×C42—21no—
492C2×C42—22no—
493C2×C42—22no—
494C2×C42C2×D411yescharacteristic
495C2×C42C2×D411yescharacteristic
496C2×C42C2412yes—
497C2×C42C2411yescharacteristic
498C2×C42C2411yescharacteristic
499C2×C42C2412yes—
500C4⋊C8—24no—
501C4⋊C8—24no—
502#103—24no—
503#103—24no—
504#103—24no—
505#103—24no—
506#103—24no—
507#103—24no—
508#103—24no—
509#103—42no—
510#103—42no—
511#103—42no—
512#103—42no—
513#103—42no—
514#103—42no—
515#103—41no—
516#103—41no—
517#103—41no—
518#103—41no—
519#103—42no—
520#103—42no—
521#103—42no—
522#103—42no—
523#103—42no—
524#102—24no—
525#102—41no—
526#102—41no—
527#102—41no—
528#102—41no—
529#102—42no—
530#97—24no—
531#97—42no—
532#97—42no—
533C4×C8—24no—
534C4×C8—42no—
535C4×C8—42no—
536#95—22no—
537#95—22no—
538#95—22no—
539#95—22no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95—21no—
544#95—21no—
545#95—21no—
546#95—21no—
547#95—21no—
548#95—22no—
549#95—22no—
550#95—22no—
551#95—22no—
552#95—22no—
553#95—22no—
554#95—22no—
555#95—22no—
556#95—22no—
557#95—22no—
558#95C2×D412yes—
559#95C2×D412yes—
560#95C2×D412yes—
561#95C2×D412yes—
562C24—21no—
563C24C22×D411yescharacteristic
564#41—44no—
565#41—44no—
566#41—44no—
567#41—44no—
568C2×Q8—24no—
569C2×Q8—22no—
570C2×Q8—28no—
571C2×Q8—28no—
572C2×Q8—22no—
573C2×Q8—22no—
574C2×Q8—22no—
575C2×Q8—22no—
576C2×Q8—21no—
577C2×Q8—22no—
578C2×Q8—22no—
579C2×Q8—22no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—22no—
584C2×Q8—22no—
585C2×Q8—21no—
586C2×Q8—22no—
587C2×Q8—21no—
588C2×Q8—42no—
589C2×Q8—42no—
590C2×Q8—44no—
591C2×Q8—42no—
592C2×Q8—42no—
593C2×Q8—42no—
594C2×Q8—44no—
595C2×Q8—44no—
596C2×Q8—44no—
597C2×Q8—44no—
598C2×Q8—44no—
599C2×Q8C2×#4114yes—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—24no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—22no—
624C22×C4—21no—
625C22×C4—41no—
626C22×C4—41no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—81no—
638C22×C4—81no—
639C22×C4—81no—
640C22×C4—81no—
641C22×C4C22×D411yescharacteristic
642C22×C4C22×D412yes—
643C22×C4C22×D411yescharacteristic
644C22×C4C22×D412yes—
645C22×C4C22×D412yes—
646C22×C4C22×D412yes—
647C22×C4C22×D411yescharacteristic
648C22×C4C22×D411yescharacteristic
649C22×C4C22×D411yescharacteristic
650C22×C4C2×#4112yes—
651C22×C4C2×#4112yes—
652C22×C4C2×#4112yes—
653C22×C4C2×#4112yes—
654C22×C4H(5,𝔽2)12yes—
655C22×C4H(5,𝔽2)12yes—
656C22×C4C2511yescharacteristic
657M16—28no—
658M16—44no—
659C2×C8—22no—
660C2×C8—22no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—22no—
668C2×C8—21no—
669C2×C8—22no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—22no—
676C2×C8—44no—
677C2×C8—44no—
678C2×C8C2×#4114yes—
679C4⋊C4—22no—
680C4⋊C4—22no—
681C4⋊C4—24no—
682C4⋊C4—24no—
683C4⋊C4—22no—
684C4⋊C4—22no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—22no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—22no—
699C4⋊C4—42no—
700C4⋊C4—42no—
701C4⋊C4—44no—
702C4⋊C4—44no—
703C4⋊C4—44no—
704C4⋊C4—44no—
705C4⋊C4—44no—
706C4⋊C4—44no—
707C4⋊C4—44no—
708C4⋊C4—44no—
709C4⋊C4—44no—
710C4⋊C4—44no—
711C4⋊C4—42no—
712C4⋊C4—42no—
713C4⋊C4—44no—
714C4⋊C4—42no—
715C4⋊C4—42no—
716C4⋊C4—82no—
717C4⋊C4—81no—
718C4⋊C4—81no—
719C4⋊C4—82no—
720C4⋊C4—82no—
721C4⋊C4—82no—
722C4⋊C4—82no—
723C4⋊C4—82no—
724C4⋊C4—82no—
725C4⋊C4#12414yes—
726C4⋊C4#12414yes—
727C22⋊C4—24no—
728C22⋊C4—44no—
729C22⋊C4—44no—
730C22⋊C4—42no—
731C22⋊C4—42no—
732C22⋊C4—42no—
733C22⋊C4—42no—
734C22⋊C4—42no—
735C22⋊C4—44no—
736C22⋊C4—44no—
737C22⋊C4—42no—
738C22⋊C4—42no—
739C22⋊C4#12418yes—
740C42—22no—
741C42—22no—
742C42—21no—
743C42—21no—
744C42—22no—
745C42—21no—
746C42—22no—
747C42—21no—
748C42—42no—
749C42—44no—
750C42—44no—
751C42—42no—
752C42—42no—
753C42—82no—
754C42—82no—
755C42C2×#4114yes—
756C42C2×#4114yes—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23C2×#12412yes—
769C23#54612yes—
770C23#55012yes—
771C23C23×D411yescharacteristic
772Q8—24no—
773Q8—24no—
774Q8—42no—
775Q8—42no—
776Q8—48no—
777Q8—42no—
778Q8—41no—
779Q8—42no—
780Q8—41no—
781Q8—42no—
782Q8—42no—
783Q8—41no—
784Q8—41no—
785Q8—84no—
786D4—41no—
787D4—41no—
788D4—41no—
789D4—41no—
790D4—84no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—24no—
808C2×C4—22no—
809C2×C4—21no—
810C2×C4—22no—
811C2×C4—21no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—48no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—42no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—42no—
828C2×C4—41no—
829C2×C4—42no—
830C2×C4—41no—
831C2×C4—42no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—42no—
837C2×C4—41no—
838C2×C4—42no—
839C2×C4—41no—
840C2×C4—42no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—42no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—84no—
848C2×C4—84no—
849C2×C4—84no—
850C2×C4—162no—
851C2×C4C2×#12414yes—
852C2×C4C2×#12414yes—
853C2×C4C2×#12412yes—
854C2×C4#52914yes—
855C2×C4#54014yes—
856C2×C4#54612yes—
857C2×C4#55012yes—
858C2×C4#55314yes—
859C2×C4#55314yes—
860C2×C4#57712yes—
861C2×C4#57812yes—
862C2×C4C22×#4111yescharacteristic
863C2×C4C22×#4111yescharacteristic
864C2×C4C22×#4111yescharacteristic
865C2×C4C22×#4111yescharacteristic
866C2×C4C2×H(5,𝔽2)11yescharacteristic
867C2×C4C2×H(5,𝔽2)11yescharacteristic
868C8—24no—
869C8—41no—
870C8—41no—
871C8—42no—
872C8—41no—
873C8—41no—
874C22—22no—
875C22—22no—
876C22—22no—
877C22—22no—
878C22—22no—
879C22—22no—
880C22—81no—
881C22—81no—
882C22—81no—
883C22—81no—
884C22—81no—
885C22—81no—
886C22—81no—
887C22#249014yes—
888C22C22×#12411yescharacteristic
889C22C2×#54611yescharacteristic
890C22C2×#55011yescharacteristic
891C22C2×#57711yescharacteristic
892C22C2×#57811yescharacteristic
893C22#358611yescharacteristic
894C22#358611yescharacteristic
895C4—22no—
896C4—22no—
897C4—24no—
898C4—24no—
899C4—42no—
900C4—41no—
901C4—42no—
902C4—41no—
903C4—44no—
904C4—82no—
905C4—81no—
906C4—81no—
907C4—81no—
908C4—82no—
909C4—81no—
910C4—81no—
911C4—82no—
912C4—81no—
913C4—81no—
914C4#249014yes—
915C4C2×#52911yescharacteristic
916C4C2×#54011yescharacteristic
917C4C2×#55311yescharacteristic
918C4C2×#55311yescharacteristic
919C2—24no—
920C2—161no—
921C2C2×#249011yescharacteristic
922C2#6062311yescharacteristic
923C2#6062711yescharacteristic
924C2#6118511yescharacteristic
925C2#6118611yescharacteristic
926C2#6142011yescharacteristic
927C2#6142211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#41C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2296 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #35543C2semidirect
3. #27765C2semidirect
4. #27762C2semidirect
5. #27762C2semidirect
6. #27761C2semidirect
7. #27757C2semidirect
8. #27754C2semidirect
9. #27752C2semidirect
10. #27749C2semidirect
11. #23633C2semidirect
14. C2×#2043C2semidirect
18. #21202C2semidirect
20. #21090C2semidirect
21. #20651C2semidirect
22. #20439C2semidirect
23. #20417C2semidirect

Maximal subgroups

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

subgroupindex
#356672
#355432
#277652
#277622
#277612
#277572
#277542
#277522
#277492
#236332
#236272
#235102
C2×#20432
#212622
#212052
#212022
#210932
#210902
#206512
#204392
#204172