Finite Group Databasebeta

← #6432506

Subgroups — #6432506

Order 512.

1838 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34267C211yesmaximal, characteristic
2#34189C211yesmaximal, characteristic, complemented
3#23772C212yesmaximal, complemented
4#23770C212yesmaximal, complemented
5#23768C212yesmaximal, complemented
6#23766C212yesmaximal, complemented
7#23765C212yesmaximal, complemented
8#23764C212yesmaximal, complemented
9#23759C212yesmaximal, complemented
10#23758C212yesmaximal, complemented
11#23747C211yesmaximal, characteristic, complemented
12#23730C211yesmaximal, characteristic, complemented
13C2×#2085C211yesmaximal, characteristic, complemented
14#23641C211yesmaximal, characteristic, complemented
15#23641C211yesmaximal, characteristic, complemented
16#23631C211yesmaximal, characteristic, complemented
17#23489C211yesmaximal, characteristic
18#23488C211yesmaximal, characteristic
19#20455C211yesmaximal, characteristic, complemented
20#20454C211yesmaximal, characteristic, complemented
21#20415C211yesmaximal, characteristic, complemented
22#20415C211yesmaximal, characteristic, complemented
23#20378C211yesmaximal, characteristic, complemented
24C2×#537C2211yescharacteristic
25C2×#520C2211yescharacteristic
26C2×C4×#41C2211yescharacteristic
27C2×#427C2211yescharacteristic
28C2×#427C2211yescharacteristic
29C22×#107C2211yescharacteristic
30C22×#106C2211yescharacteristic
31C2×#417C2211yescharacteristic
32C2×#417C2211yescharacteristic
33C2×#416C2211yescharacteristic
34C2×#416C2211yescharacteristic
35C2×#408C2211yescharacteristic
36C2×#408C2211yescharacteristic
37C2×#405C2211yescharacteristic
38C2×#405C2211yescharacteristic
39#2364—22no—
40#2363—21no—
41#2362—21no—
42#2361—22no—
43#2361—21no—
44#2360—21no—
45#2357—21no—
46#2357—21no—
47#2356—21no—
48#2356—21no—
49#2353—22no—
50#2353—22no—
51#2324C2212yes—
52#2323C2212yes—
53#2314C2212yes—
54#2314C2212yes—
55#2311C2211yescharacteristic
56#2311C2211yescharacteristic
57#2311C2211yescharacteristic
58C4×C22⋊Q8C2212yes—
59C4×#121C2212yes—
60#2297C2211yescharacteristic
61C2×#389C2211yescharacteristic
62#2285C2211yescharacteristic
63#2283C2212yes—
64#2283C2212yes—
65C2×#382C2211yescharacteristic
66#2274C2211yescharacteristic
67#2274C2211yescharacteristic
68#2274C2211yescharacteristic
69#2101C2212yes—
70#2101C2212yes—
71#2100C2212yes—
72#2099C2212yes—
73#2097C2211yescharacteristic
74#2097C2211yescharacteristic
75#2096C2211yescharacteristic
76#2095C2211yescharacteristic
77#2094C2211yescharacteristic
78#2093C2211yescharacteristic
79#2092C2211yescharacteristic
80#2092C2211yescharacteristic
81#2085C2212yes—
82#2085C2212yes—
83#2085C2212yes—
84#2085C2212yes—
85#2077C2212yes—
86#2077C2212yes—
87#2077C2212yes—
88#2077C2212yes—
89#2076C2212yes—
90#2076C2212yes—
91#2075C2212yes—
92#2075C2212yes—
93#2074C2212yes—
94#2074C2212yes—
95#2073C2212yes—
96#2073C2212yes—
97#2036C2212yes—
98#2036C2212yes—
99#2035C2212yes—
100#2035C2212yes—
101#2034C2212yes—
102#2034C2212yes—
103#2033C2212yes—
104#2033C2212yes—
105#1776C2212yes—
106#1776C2212yes—
107#1776C2212yes—
108#1776C2212yes—
109C4×#107C2212yes—
110C4×#107C2212yes—
111C4×#106C2212yes—
112C4×#106C2212yes—
113#1763C2212yes—
114#1763C2212yes—
115#1762C2212yes—
116#1762C2212yes—
117C4×#103C2212yes—
118C4×#103C2212yes—
119C4×#102C2212yes—
120C4×#102C2212yes—
121#1750C2212yes—
122#1750C2212yes—
123#1749C2212yes—
124C4×C22⋊C8C2212yes—
125#1736C2211yescharacteristic
126#1736C2211yescharacteristic
127#1736C2211yescharacteristic
128#1736C2211yescharacteristic
129#1736C2211yescharacteristic
130#1736C2211yescharacteristic
131C2×#340C2211yescharacteristic
132C2×#340C2211yescharacteristic
133#1728C2211yescharacteristic
134C2×#336C2211yescharacteristic
135C22×#41C2311yescharacteristic
136C22×#41C2311yescharacteristic
137C22×M16C2311yescharacteristic
138C22×M16C2311yescharacteristic
139C23×C8C2311yescharacteristic
140C23×C8C2311yescharacteristic
141#537—24no—
142#537—24no—
143C2×C22⋊Q8—21no—
144C2×C22⋊Q8C2312yes—
145C2×#121—21no—
146C2×#121—22no—
147C2×#121C2312yes—
148#520—24no—
149#520—24no—
150C4×#41—24no—
151C4×#41—24no—
152C2×C4×Q8D411yescharacteristic
153C2×C4×Q8D411yescharacteristic
154C2×C4×Q8C2312yes—
155C2×C4×D4—22no—
156C2×C4×D4—22no—
157C2×C4×D4D412yes—
158C2×C4×D4D412yes—
159C2×C4×D4D411yescharacteristic
160C2×C4×D4D411yescharacteristic
161C2×C4×D4C2312yes—
162C2×#117—21no—
163C2×#117C2311yescharacteristic
164C2×#117C2311yescharacteristic
165C2×#117C2311yescharacteristic
166C2×#117C2312yes—
167C2×#117C2311yescharacteristic
168C22×C4⋊C4—21no—
169C22×C4⋊C4—21no—
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2311yescharacteristic
174C22×C42C2311yescharacteristic
175C22×C42C2312yes—
176#427—24no—
177#427—24no—
178C2×#107—24no—
179C2×#107C2311yescharacteristic
180C2×#107C2311yescharacteristic
181C2×#107C2311yescharacteristic
182C2×#107C2311yescharacteristic
183C2×#107C2312yes—
184C2×#107C2312yes—
185C2×#106—24no—
186C2×#106C2311yescharacteristic
187C2×#106C2311yescharacteristic
188C2×#106C2311yescharacteristic
189C2×#106C2311yescharacteristic
190C2×#106C2312yes—
191C2×#106C2312yes—
192#417—24no—
193#417—24no—
194#416—24no—
195#416—24no—
196C2×#103C2312yes—
197C2×#103C2312yes—
198C2×#103C2311yescharacteristic
199C2×#103C2311yescharacteristic
200C2×#103C2311yescharacteristic
201C2×#103C2311yescharacteristic
202C2×#102C2312yes—
203C2×#102C2312yes—
204C2×#102C2311yescharacteristic
205C2×#102C2311yescharacteristic
206C2×#102C2311yescharacteristic
207C2×#102C2311yescharacteristic
208#408—24no—
209#408—24no—
210C2×C22⋊C8C2312yes—
211C2×C22⋊C8C2312yes—
212C2×C22⋊C8C2312yes—
213C2×C22⋊C8C2312yes—
214#405—24no—
215#405—24no—
216C2×#97C2312yes—
217C2×#97C2312yes—
218C2×C4×C8C2312yes—
219C2×C4×C8C2312yes—
220#391—21no—
221#391—21no—
222#391—21no—
223#391C2311yescharacteristic
224#391C2311yescharacteristic
225#390—21no—
226#390—21no—
227#390—21no—
228#390—22no—
229#390C2311yescharacteristic
230#390C2311yescharacteristic
231#389—22no—
232#389—21no—
233#389—21no—
234#389C2312yes—
235#389C2312yes—
236#388—22no—
237#388—22no—
238#388—22no—
239#388—22no—
240#388—22no—
241#388—22no—
242#388—22no—
243#388—22no—
244#387—22no—
245#387—22no—
246#387—22no—
247#387—22no—
248#387—22no—
249#387—22no—
250#386—22no—
251#386—22no—
252#386—22no—
253#386—21no—
254#386—22no—
255#386—21no—
256#386—22no—
257#385—22no—
258#385—22no—
259#384C2311yescharacteristic
260#384C2311yescharacteristic
261#383—22no—
262#383—22no—
263#382—21no—
264#382—21no—
265#382C2312yes—
266#382C2312yes—
267#382C2311yescharacteristic
268#382C2311yescharacteristic
269#381—22no—
270#381—22no—
271#380—21no—
272#380—21no—
273#380C2312yes—
274#380C2312yes—
275#380C2312yes—
276#380C2312yes—
277#380C2312yes—
278#380C2312yes—
279C4×C4⋊C4—21no—
280C4×C4⋊C4—21no—
281C4×C4⋊C4—21no—
282C4×C4⋊C4—21no—
283C4×C4⋊C4—21no—
284C4×C4⋊C4—21no—
285C4×C4⋊C4—21no—
286C4×C4⋊C4—21no—
287C4×C4⋊C4—22no—
288C4×C4⋊C4C2312yes—
289C4×C4⋊C4C2312yes—
290C4×C4⋊C4C2312yes—
291C4×C4⋊C4C2312yes—
292C4×C4⋊C4C2312yes—
293C4×C4⋊C4C2312yes—
294C4×C22⋊C4—22no—
295C4×C22⋊C4—22no—
296C4×C22⋊C4—22no—
297C4×C22⋊C4—22no—
298C4×C22⋊C4—22no—
299C4×C22⋊C4—22no—
300C4×C22⋊C4—21no—
301C4×C22⋊C4—22no—
302C4×C22⋊C4—21no—
303#376—22no—
304#376—22no—
305C2×#95—21no—
306C2×#95—21no—
307C2×#95—21no—
308#340C2312yes—
309#340C2312yes—
310#340C2312yes—
311#340C2312yes—
312#340C2312yes—
313#340C2312yes—
314#340C2312yes—
315#340C2312yes—
316#340C2312yes—
317#340C2312yes—
318#340C2312yes—
319#340C2312yes—
320#340C2312yes—
321#340C2312yes—
322#340C2312yes—
323#340C2312yes—
324#336C2312yes—
325#336C2312yes—
326#336C2311yescharacteristic
327#336C2311yescharacteristic
328#336C2311yescharacteristic
329#336C2311yescharacteristic
330C2×#41—22no—
331C2×#41—22no—
332C2×#41—22no—
333C2×#41—22no—
334C2×#41—22no—
335C2×#41—22no—
336C2×#41—22no—
337C2×#41—22no—
338C2×#41—22no—
339C2×#41—22no—
340C2×#41—22no—
341C2×#41#4114yes—
342C22×Q8C2×D411yescharacteristic
343C22×Q8C2411yescharacteristic
344C22×D4—21no—
345C22×D4—22no—
346C22×D4C2×D412yes—
347C22×D4C2×D411yescharacteristic
348C22×D4C2411yescharacteristic
349C23×C4—21no—
350C23×C4—21no—
351C23×C4—21no—
352C23×C4—21no—
353C23×C4—21no—
354C23×C4—22no—
355C23×C4C2×D411yescharacteristic
356C23×C4C2×D412yes—
357C23×C4C2×D411yescharacteristic
358C23×C4C2×D412yes—
359C23×C4C2412yes—
360C23×C4C2411yescharacteristic
361C2×M16—22no—
362C2×M16—22no—
363C2×M16—22no—
364C2×M16—22no—
365C2×M16—22no—
366C2×M16—22no—
367C22×C8—22no—
368C22×C8—22no—
369C22×C8—22no—
370C22×C8—22no—
371C22×C8#4114yes—
372C22×C8#4114yes—
373C22×C8C2412yes—
374C22×C8C2412yes—
375C22×C8C2411yescharacteristic
376C22×C8C2411yescharacteristic
377C22×C8C2411yescharacteristic
378C22×C8C2411yescharacteristic
379C22⋊Q8—28no—
380C22⋊Q8—24no—
381C22⋊Q8—24no—
382#121—216no—
383#121—28no—
384#121—24no—
385#121—24no—
386C4×Q8—24no—
387C4×Q8—24no—
388C4×Q8—24no—
389C4×Q8—24no—
390C4×D4—24no—
391C4×D4—24no—
392C4×D4—28no—
393C4×D4—28no—
394C4×D4—24no—
395C4×D4—24no—
396C4×D4—48no—
397C4×D4—84no—
398#117—24no—
399#117—24no—
400#117—22no—
401#117—22no—
402#117—22no—
403#117—22no—
404#117—22no—
405#117—22no—
406#117—44no—
407#117#4114yes—
408#117#4114yes—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—44no—
429C2×C4⋊C4—82no—
430C2×C4⋊C4C2×D412yes—
431C2×C4⋊C4C2×D412yes—
432C2×C4⋊C4C2×D411yescharacteristic
433C2×C4⋊C4C2×D411yescharacteristic
434C2×C4⋊C4#4114yes—
435C2×C4⋊C4C2412yes—
436C2×C4⋊C4C2412yes—
437C2×C4⋊C4C2412yes—
438C2×C4⋊C4C2411yescharacteristic
439C2×C4⋊C4C2411yescharacteristic
440C2×C4⋊C4C2411yescharacteristic
441C2×C4⋊C4C2411yescharacteristic
442C2×C4⋊C4C2411yescharacteristic
443C2×C4⋊C4C2411yescharacteristic
444C2×C4⋊C4C2412yes—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4C2×D412yes—
462C2×C22⋊C4C2×D412yes—
463C2×C22⋊C4C2×D412yes—
464C2×C42—22no—
465C2×C42—22no—
466C2×C42—24no—
467C2×C42—24no—
468C2×C42—22no—
469C2×C42—21no—
470C2×C42—21no—
471C2×C42—21no—
472C2×C42—22no—
473C2×C42—22no—
474C2×C42—22no—
475C2×C42—22no—
476C2×C42—22no—
477C2×C42—22no—
478C2×C42C2×D412yes—
479C2×C42C2×D412yes—
480C2×C42C2×D411yescharacteristic
481C2×C42C2×D411yescharacteristic
482C2×C42C2411yescharacteristic
483C2×C42C2411yescharacteristic
484C2×C42C2412yes—
485#107—22no—
486#107—22no—
487#107—22no—
488#107—22no—
489#107—24no—
490#107—24no—
491#106—22no—
492#106—22no—
493#106—22no—
494#106—22no—
495#106—24no—
496#106—24no—
497#103—24no—
498#103—24no—
499#103—22no—
500#103—22no—
501#103—22no—
502#103—22no—
503#102—24no—
504#102—24no—
505#102—22no—
506#102—22no—
507#102—22no—
508#102—22no—
509C22⋊C8—24no—
510C22⋊C8—24no—
511C22⋊C8—24no—
512C22⋊C8—24no—
513#97—24no—
514#97—24no—
515C4×C8—24no—
516C4×C8—24no—
517#95—22no—
518#95—22no—
519#95—22no—
520#95—22no—
521#95—22no—
522#95—22no—
523#95—21no—
524#95—21no—
525#95—22no—
526#95—22no—
527#95—22no—
528#95—22no—
529#95—21no—
530#95—21no—
531#95—21no—
532#95—21no—
533#95—22no—
534#95—22no—
535#95—22no—
536#95—22no—
537#95—22no—
538#95—22no—
539#95—22no—
540#95—21no—
541#95—21no—
542#95—22no—
543C24—21no—
544C24C22×D412yes—
545C24C22×D411yescharacteristic
546#41—28no—
547#41—28no—
548#41—44no—
549#41—44no—
550#41—44no—
551#41—44no—
552#41—44no—
553#41—44no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8C2×#4112yes—
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—24no—
566C2×D4—24no—
567C2×D4—28no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—82no—
579C2×D4—82no—
580C2×D4C2×#4112yes—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—24no—
594C22×C4—24no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—22no—
604C22×C4—41no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—44no—
618C22×C4—82no—
619C22×C4—82no—
620C22×C4—81no—
621C22×C4—81no—
622C22×C4—81no—
623C22×C4—81no—
624C22×C4—81no—
625C22×C4—81no—
626C22×C4—81no—
627C22×C4—81no—
628C22×C4C22×D411yescharacteristic
629C22×C4C22×D412yes—
630C22×C4C22×D411yescharacteristic
631C22×C4C22×D411yescharacteristic
632C22×C4C22×D411yescharacteristic
633C22×C4C22×D412yes—
634C22×C4C22×D412yes—
635C22×C4C22×D411yescharacteristic
636C22×C4C2×#4112yes—
637C22×C4C2×#4112yes—
638C22×C4C2×#4112yes—
639C22×C4C2×#4112yes—
640C22×C4C2×#4112yes—
641C22×C4C2×#4112yes—
642C22×C4C2511yescharacteristic
643M16—44no—
644M16—44no—
645C2×C8—28no—
646C2×C8—28no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—22no—
656C2×C8—22no—
657C2×C8—22no—
658C2×C8—22no—
659C2×C8—22no—
660C2×C8—22no—
661C2×C8C2×#4112yes—
662C2×C8C2×#4112yes—
663C2×C8C2×#4112yes—
664C2×C8C2×#4112yes—
665C4⋊C4—28no—
666C4⋊C4—24no—
667C4⋊C4—24no—
668C4⋊C4—24no—
669C4⋊C4—22no—
670C4⋊C4—22no—
671C4⋊C4—22no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—22no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—22no—
686C4⋊C4—22no—
687C4⋊C4—22no—
688C4⋊C4—44no—
689C4⋊C4—42no—
690C4⋊C4—44no—
691C4⋊C4—42no—
692C4⋊C4—42no—
693C4⋊C4—81no—
694C4⋊C4—81no—
695C4⋊C4—81no—
696C4⋊C4—81no—
697C4⋊C4—82no—
698C4⋊C4#12314yes—
699C4⋊C4#12314yes—
700C4⋊C4C2×#4114yes—
701C22⋊C4—28no—
702C22⋊C4—28no—
703C22⋊C4—24no—
704C22⋊C4—24no—
705C22⋊C4—42no—
706C22⋊C4—42no—
707C22⋊C4—42no—
708C22⋊C4—42no—
709C22⋊C4—42no—
710C22⋊C4—44no—
711C22⋊C4—81no—
712C22⋊C4—81no—
713C22⋊C4—82no—
714C22⋊C4—82no—
715C22⋊C4—82no—
716C22⋊C4—82no—
717C22⋊C4—82no—
718C22⋊C4—82no—
719C22⋊C4#12318yes—
720C42—22no—
721C42—22no—
722C42—24no—
723C42—24no—
724C42—21no—
725C42—21no—
726C42—21no—
727C42—21no—
728C42—44no—
729C42—42no—
730C42—42no—
731C42—42no—
732C42—82no—
733C42—82no—
734C42—82no—
735C42—82no—
736C42—82no—
737C42—82no—
738C42C2×#4114yes—
739C42C2×#4114yes—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23C2×#12312yes—
759C23#52512yes—
760C23#53212yes—
761C23C23×D411yescharacteristic
762Q8—22no—
763Q8—22no—
764Q8—44no—
765Q8—41no—
766Q8—41no—
767D4—22no—
768D4—22no—
769D4—48no—
770D4—48no—
771D4—44no—
772D4—41no—
773D4—41no—
774D4—88no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—22no—
792C2×C4—24no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—48no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—42no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—42no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—41no—
820C2×C4—42no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—84no—
833C2×C4—84no—
834C2×C4—82no—
835C2×C4—82no—
836C2×C4—84no—
837C2×C4—164no—
838C2×C4—162no—
839C2×C4—162no—
840C2×C4—162no—
841C2×C4C2×#12314yes—
842C2×C4C2×#12314yes—
843C2×C4C2×#12312yes—
844C2×C4#52512yes—
845C2×C4#52914yes—
846C2×C4#52914yes—
847C2×C4#52914yes—
848C2×C4#52914yes—
849C2×C4#53212yes—
850C2×C4C22×#4111yescharacteristic
851C2×C4C22×#4111yescharacteristic
852C2×C4C22×#4111yescharacteristic
853C2×C4C22×#4111yescharacteristic
854C2×C4C22×#4111yescharacteristic
855C2×C4C22×#4111yescharacteristic
856C8—22no—
857C8—22no—
858C8—22no—
859C8—22no—
860C8—42no—
861C8—42no—
862C22—22no—
863C22—22no—
864C22—22no—
865C22—22no—
866C22—22no—
867C22—22no—
868C22—42no—
869C22—42no—
870C22—42no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22—81no—
882C22#239514yes—
883C22C22×#12311yescharacteristic
884C22C2×#52511yescharacteristic
885C22C2×#53211yescharacteristic
886C22#358411yescharacteristic
887C22#358411yescharacteristic
888C22#358511yescharacteristic
889C22#358611yescharacteristic
890C4—24no—
891C4—24no—
892C4—41no—
893C4—41no—
894C4—41no—
895C4—41no—
896C4—44no—
897C4—42no—
898C4—42no—
899C4—81no—
900C4—81no—
901C4—81no—
902C4—81no—
903C4—81no—
904C4—81no—
905C4—82no—
906C4—82no—
907C4—82no—
908C4#239514yes—
909C4C2×#52911yescharacteristic
910C4C2×#52911yescharacteristic
911C4C2×#52911yescharacteristic
912C4C2×#52911yescharacteristic
913C2—24no—
914C2—82no—
915C2—82no—
916C2C2×#239511yescharacteristic
917C2#6052311yescharacteristic
918C2#6052411yescharacteristic
919C2#6059211yescharacteristic
920C2#6059511yescharacteristic
921C2#6071711yescharacteristic
922C2#6072111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#537C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×#41 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34189C2semidirect
3. #23772C2semidirect
4. #23770C2semidirect
5. #23768C2semidirect
6. #23766C2semidirect
7. #23765C2semidirect
8. #23764C2semidirect
9. #23759C2semidirect
10. #23758C2semidirect
11. #23747C2semidirect
12. #23730C2semidirect
13. C2×#2085C2semidirect
14. #23641C2semidirect
15. #23641C2semidirect
16. #23631C2semidirect
19. #20455C2semidirect
20. #20454C2semidirect
21. #20415C2semidirect
22. #20415C2semidirect
23. #20378C2semidirect

Maximal subgroups

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

subgroupindex
#342672
#341892
#237722
#237702
#237682
#237662
#237652
#237642
#237592
#237582
#237472
#237302
C2×#20852
#236412
#236312
#234892
#234882
#204552
#204542
#204152
#203782