Finite Group Databasebeta

← #6343620

Subgroups — #6343620

Order 512.

2882 conjugacy classes of subgroups.

The subgroup lattice has 885 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62815C211yesmaximal, characteristic
2#60284C211yesmaximal, characteristic, complemented
3#34195C211yesmaximal, characteristic, complemented
4#17630C214yesmaximal, complemented
5#17623C218yesmaximal, complemented
6#17616C214yesmaximal, complemented
7#17593C214yesmaximal, complemented
8#17584C211yesmaximal, characteristic, complemented
9#17583C211yesmaximal, characteristic, complemented
10#17562C211yesmaximal, characteristic, complemented
11#17561C211yesmaximal, characteristic, complemented
12#17558C214yesmaximal, complemented
13#3512—22no—
14#3511C412yescomplemented
15#3511C412yescomplemented
16#3510—22no—
17#3509C412yescomplemented
18#3508C412yescomplemented
19#3507—21no—
20#3507C2212yes—
21#3506—21no—
22#3506C2212yes—
23#3505—22no—
24#3505C2214yes—
25#3480—22no—
26#3480C414yescomplemented
27#3475—22no—
28#3475C414yescomplemented
29#3455—22no—
30#3449—21no—
31#3444C2214yes—
32C2×#533C2211yescharacteristic
33C2×#532C2211yescharacteristic
34#3428—21no—
35C2×C4×#41C2211yescharacteristic
36#2991—22no—
37#2991—22no—
38#2982C2212yescomplemented
39#2975C2214yes—
40#2975C2212yescomplemented
41#2971—22no—
42#2971—22no—
43#2920C2211yescharacteristic
44#2920C2211yescharacteristic
45#2920C2214yescomplemented
46#2356C2212yescomplemented
47#2353C2214yes—
48#2349C2212yescomplemented
49#2347—21no—
50#2343—22no—
51#2339—21no—
52#2320—21no—
53#2318—22no—
54#2283C2211yescharacteristic
55#2283C2211yescharacteristic
56#2283C2212yescomplemented
57C2×#383C2212yescomplemented
58#2275—21no—
59#1521C22116yescomplemented
60#1518C2214yescomplemented
61#1517C2214yes—
62#1515C2212yescomplemented
63#1515C2214yescomplemented
64#1515C2212yescomplemented
65#1514C2212yes—
66#1514C2214yes—
67#1514C2212yes—
68#1513C22116yescomplemented
69#1511C2214yes—
70#1510C2214yes—
71#1508C2214yes—
72#1507C2214yes—
73#1504C22116yescomplemented
74#1503C2214yescomplemented
75#1502C2214yes—
76#1500C22116yescomplemented
77C22×#41—21no—
78C22×#41D411yescharacteristic
79#559—22no—
80#559—24no—
81#559—24no—
82#559C2×C414yescomplemented
83#557—22no—
84#557C2×C414yescomplemented
85#556—22no—
86#556—24no—
87#556—24no—
88#556—22no—
89#556C2×C414yes—
90#556C2×C414yescomplemented
91#555—22no—
92#555C2×C414yes—
93#554—22no—
94#554C2×C414yescomplemented
95#553—24no—
96#553—24no—
97#553—28no—
98#553—24no—
99#553—28no—
100#553C2×C418yescomplemented
101#552—24no—
102#552—24no—
103#552—24no—
104#552C2×C418yescomplemented
105#551—28no—
106#551—28no—
107#550—22no—
108#550C2×C414yes—
109#548—24no—
110#548C2×C418yescomplemented
111#547—22no—
112#547C2×C414yes—
113#546—24no—
114#546C2×C418yescomplemented
115#542—24no—
116#542—24no—
117#541—24no—
118#540—24no—
119#539—24no—
120#539—24no—
121#538—24no—
122#538—24no—
123#537—22no—
124#537—22no—
125#536—22no—
126#536—22no—
127#535—22no—
128#535—22no—
129#534—24no—
130#533—21no—
131#533—21no—
132#533—21no—
133#533—21no—
134#533C2×C412yescomplemented
135#533C2×C412yescomplemented
136#533C2×C414yescomplemented
137#533C2×C414yescomplemented
138#533C2312yes—
139#533C2312yes—
140#532—24no—
141#532—21no—
142#532—21no—
143#532—21no—
144#532—21no—
145#532C2×C414yescomplemented
146#532C2×C412yescomplemented
147#532C2×C412yescomplemented
148#532C2×C414yescomplemented
149#532C2312yes—
150#532C2312yes—
151C2×C4⋊Q8C2×C411yescharacteristic, complemented
152C2×C4⋊Q8C2×C411yescharacteristic, complemented
153C2×C4⋊Q8C2×C411yescharacteristic, complemented
154C2×#127C2×C411yescharacteristic, complemented
155#529—28no—
156#529—28no—
157#529—24no—
158#529—24no—
159#529—24no—
160#529—24no—
161#529C2×C418yescomplemented
162#529C2318yes—
163C2×#125—21no—
164C2×#124—21no—
165#525—24no—
166#525—24no—
167#525—24no—
168#525C2318yes—
169C2×C22⋊Q8—21no—
170C2×C22⋊Q8C2312yes—
171C2×#121—21no—
172C2×#121C2312yes—
173#520—22no—
174#520—22no—
175#520—22no—
176#520—22no—
177#519—22no—
178#518—22no—
179#518—24no—
180C4×#41—24no—
181C4×#41—24no—
182C4×#41—24no—
183C4×#41C2×C412yes—
184C4×#41C2×C412yes—
185C4×#41C2×C412yes—
186C4×#41C2×C412yes—
187C4×#41C2×C418yescomplemented
188C4×#41D412yes—
189C4×#41D412yes—
190C4×#41D412yes—
191C4×#41D412yes—
192C2×C4×Q8—21no—
193C2×C4×Q8C2×C412yescomplemented
194C2×C4×Q8D411yescharacteristic
195C2×C4×Q8C2311yescharacteristic
196C2×C4×D4—22no—
197C2×C4×D4—21no—
198C2×C4×D4C2×C412yescomplemented
199C2×C4×D4D412yes—
200C2×C4×D4D411yescharacteristic
201C2×C4×D4C2311yescharacteristic
202C2×C4×D4C2312yes—
203C2×#117—21no—
204C2×#117—24no—
205C2×#117D412yes—
206C2×#117D411yescharacteristic
207C22×C42C2311yescharacteristic
208C22×C42C2312yes—
209C8×Q8—24no—
210C8×Q8—24no—
211#436—28no—
212#436—28no—
213#436—24no—
214#436—24no—
215#432—21no—
216#432—21no—
217#432—24no—
218#432C2312yes—
219#432C2312yes—
220#431—21no—
221#431—21no—
222#431—24no—
223#431C2312yes—
224#431C2312yes—
225#431C2318yes—
226#423—21no—
227#423—21no—
228#423—24no—
229#407C2312yes—
230#407C2312yes—
231#407C2318yes—
232C4×M16—21no—
233C4×M16—21no—
234C4×M16—24no—
235#391—22no—
236#389—22no—
237#388—24no—
238#387—24no—
239#387—24no—
240#386—24no—
241#385—24no—
242#383—22no—
243#383—22no—
244#383C2314yes—
245#383C2311yescharacteristic
246#383C2312yes—
247#383C2311yescharacteristic
248#382—22no—
249#382—21no—
250#382C2312yes—
251#381—21no—
252#381—22no—
253#381C2312yes—
254#380—21no—
255#380—21no—
256#380C2314yes—
257C4×C4⋊C4—22no—
258C4×C4⋊C4—21no—
259C4×C4⋊C4—22no—
260C4×C4⋊C4C2312yes—
261C4×C22⋊C4—22no—
262C4×C22⋊C4—21no—
263C4×C22⋊C4—24no—
264C4×C22⋊C4C2312yes—
265#376—21no—
266#376—21no—
267#376C2314yes—
268C2×#95—22no—
269C2×#95—22no—
270C2×#95C2314yes—
271#328C2318yes—
272#328C23116yes—
273#328C2318yes—
274#327C2318yes—
275#327C23116yes—
276#327C2318yes—
277C2×#41—22no—
278C2×#41—22no—
279C2×#41—24no—
280C2×#41—22no—
281C2×#41—22no—
282C2×#41—44no—
283C2×#41—48no—
284C2×#41C22⋊C412yes—
285C2×#41C22⋊C412yes—
286C2×#41C22⋊C412yes—
287C2×#41C22⋊C412yes—
288C2×#41C22×C418yes—
289C22×Q8—21no—
290C22×Q8—21no—
291C22×Q8C22×C412yes—
292C22×Q8C2×D411yescharacteristic
293C22×D4—22no—
294C22×D4—21no—
295C22×D4—21no—
296C22×D4C22×C412yes—
297C22×D4C2×D411yescharacteristic
298C22×D4C2×D412yes—
299C23×C4—22no—
300C23×C4—24no—
301C23×C4C2×D411yescharacteristic
302C23×C4C2×D412yes—
303C23×C4C2×D411yescharacteristic
304C23×C4C2×D412yes—
305C23×C4C2411yescharacteristic
306C23×C4C2412yes—
307C2×M16—22no—
308C2×M16—22no—
309C2×M16—28no—
310C4⋊Q8—24no—
311C4⋊Q8—21no—
312C4⋊Q8—21no—
313C4⋊Q8—21no—
314C4⋊Q8—21no—
315C4⋊Q8—21no—
316C4⋊Q8—21no—
317C4⋊Q8C22×C412yes—
318C4⋊Q8C22×C412yes—
319C4⋊Q8C22×C412yes—
320C4⋊Q8C22×C412yes—
321C4⋊Q8C22×C412yes—
322C4⋊Q8C22×C412yes—
323#127—24no—
324#127—21no—
325#127—21no—
326#127C22×C412yes—
327#127C22×C412yes—
328#126—28no—
329#126—28no—
330#126—28no—
331#126—28no—
332#126—28no—
333#126—28no—
334#125—28no—
335#125—28no—
336#125—22no—
337#125—22no—
338#125—24no—
339#125—22no—
340#125—22no—
341#125C22×C418yes—
342#124—24no—
343#124—24no—
344#124—28no—
345#124—28no—
346#124—22no—
347#124—22no—
348#124—24no—
349#124—22no—
350#124—22no—
351#124C22×C418yes—
352#123—28no—
353#123—28no—
354#123—28no—
355#123—28no—
356#123—28no—
357#123—28no—
358#123—28no—
359#123—28no—
360C22⋊Q8—24no—
361C22⋊Q8—24no—
362C22⋊Q8—22no—
363C22⋊Q8—22no—
364C22⋊Q8—24no—
365C22⋊Q8—24no—
366C22⋊Q8—24no—
367C22⋊Q8—22no—
368C22⋊Q8—22no—
369C22⋊Q8—22no—
370C22⋊Q8—22no—
371C22⋊Q8—28no—
372C22⋊Q8—28no—
373C22⋊Q8C22×C414yes—
374C22⋊Q8C22×C418yes—
375C22⋊Q8C2414yes—
376#121—24no—
377#121—24no—
378#121—28no—
379#121—28no—
380#121—22no—
381#121—22no—
382#121—24no—
383#121—24no—
384#121—24no—
385#121—22no—
386#121—22no—
387#121—22no—
388#121—22no—
389#121—28no—
390#121—28no—
391#121C22×C414yes—
392#121C22×C418yes—
393#121C2414yes—
394#120—28no—
395#120—28no—
396C4×Q8—24no—
397C4×Q8—24no—
398C4×Q8—22no—
399C4×Q8—22no—
400C4×Q8—22no—
401C4×Q8—22no—
402C4×Q8—24no—
403C4×Q8—24no—
404C4×Q8—24no—
405C4×Q8—22no—
406C4×Q8—22no—
407C4×Q8C22⋊C412yes—
408C4×Q8C22⋊C412yes—
409C4×Q8C22⋊C412yes—
410C4×Q8C22⋊C412yes—
411C4×Q8C22×C414yes—
412C4×Q8C22×C414yes—
413C4×Q8C22×C418yes—
414C4×Q8C22×C412yes—
415C4×Q8C22×C412yes—
416C4×Q8C2×D412yes—
417C4×Q8C2×D412yes—
418C4×D4—28no—
419C4×D4—28no—
420C4×D4—28no—
421C4×D4—28no—
422C4×D4—28no—
423C4×D4—28no—
424C4×D4—24no—
425C4×D4—24no—
426C4×D4—28no—
427C4×D4—28no—
428C4×D4—22no—
429C4×D4—22no—
430C4×D4—22no—
431C4×D4—22no—
432C4×D4—24no—
433C4×D4—24no—
434C4×D4—24no—
435C4×D4—22no—
436C4×D4—22no—
437C4×D4—48no—
438C4×D4C22⋊C414yes—
439C4×D4C22⋊C412yes—
440C4×D4C22⋊C414yes—
441C4×D4C22⋊C412yes—
442C4×D4C22⋊C414yes—
443C4×D4C22⋊C414yes—
444C4×D4C22⋊C412yes—
445C4×D4C22⋊C412yes—
446C4×D4C22×C414yes—
447C4×D4C22×C414yes—
448C4×D4C22×C418yes—
449C4×D4C22×C414yes—
450C4×D4C22×C412yes—
451C4×D4C22×C414yes—
452C4×D4C22×C412yes—
453C4×D4C2×D414yes—
454C4×D4C2×D414yes—
455C4×D4C2×D412yes—
456C4×D4C2×D412yes—
457#117—22no—
458#117—22no—
459#117—24no—
460#117—22no—
461#117—22no—
462#117—24no—
463#117—24no—
464#117—28no—
465#117—28no—
466#117—28no—
467#117—28no—
468#117C22⋊C412yes—
469#117C22⋊C412yes—
470#117C22⋊C412yes—
471#117C22⋊C412yes—
472#117C22⋊C414yes—
473#117C22⋊C414yes—
474#117C22⋊C414yes—
475#117C22⋊C414yes—
476#117C22×C418yes—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—24no—
484C2×C4⋊C4—24no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—24no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4C22×C412yes—
489C2×C4⋊C4C22×C412yes—
490C2×C4⋊C4C2×D411yescharacteristic
491C2×C4⋊C4C2×D412yes—
492C2×C4⋊C4C2×D411yescharacteristic
493C2×C4⋊C4C2×D412yes—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—28no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4C2×D412yes—
502C2×C22⋊C4C2×D412yes—
503C2×C22⋊C4C2×D412yes—
504C2×C42—22no—
505C2×C42—28no—
506C2×C42—22no—
507C2×C42—22no—
508C2×C42—24no—
509C2×C42C22×C411yescharacteristic
510C2×C42C22×C411yescharacteristic
511C2×C42C22×C414yes—
512C2×C42C22×C411yescharacteristic
513C2×C42C22×C411yescharacteristic
514C2×C42C22×C414yes—
515C2×C42C2×D412yes—
516C2×C42C2×D411yescharacteristic
517C2×C42C2×D412yes—
518C2×C42C2×D411yescharacteristic
519C2×C42C2×D411yescharacteristic
520C2×C42C2×D411yescharacteristic
521C2×C42C2×D414yes—
522C2×C42C2×D411yescharacteristic
523C2×C42C2×D411yescharacteristic
524C2×C42C2×D414yes—
525C2×C42C2412yes—
526C2×C42C2411yescharacteristic
527C2×C42C2411yescharacteristic
528C4⋊C8—22no—
529C4⋊C8—22no—
530C4⋊C8—28no—
531C4⋊C8—22no—
532C4⋊C8—22no—
533C22⋊C8—22no—
534C22⋊C8—22no—
535C22⋊C8—28no—
536C22⋊C8C2414yes—
537C22⋊C8C2414yes—
538#97—22no—
539#97—22no—
540C4×C8—28no—
541C4×C8—22no—
542C4×C8—22no—
543#95—21no—
544#95—21no—
545#95—22no—
546#95—22no—
547#95—24no—
548#95—24no—
549#95—24no—
550#95—21no—
551#95—22no—
552#95—22no—
553#95—24no—
554#95—21no—
555#95C2412yes—
556#95C2414yes—
557#95C2412yes—
558C24—22no—
559C24C22×D411yescharacteristic
560C24C22×D412yes—
561#41—44no—
562#41—44no—
563#41—44no—
564#41—44no—
565#41—48no—
566#41—48no—
567#41—48no—
568#41—48no—
569#41—88no—
570#41—88no—
571C2×Q8—22no—
572C2×Q8—22no—
573C2×Q8—22no—
574C2×Q8—22no—
575C2×Q8—22no—
576C2×Q8—24no—
577C2×Q8—44no—
578C2×Q8—82no—
579C2×Q8—82no—
580C2×Q8C2×C22⋊C412yes—
581C2×Q8C2×C22⋊C412yes—
582C2×Q8C23×C414yes—
583C2×D4—24no—
584C2×D4—24no—
585C2×D4—28no—
586C2×D4—28no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—24no—
593C2×D4—44no—
594C2×D4—44no—
595C2×D4—48no—
596C2×D4—82no—
597C2×D4—82no—
598C2×D4C2×C22⋊C412yes—
599C2×D4C2×C22⋊C412yes—
600C2×D4C2×C22⋊C414yes—
601C2×D4C2×C22⋊C414yes—
602C2×D4C23×C414yes—
603C22×C4—24no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—24no—
608C22×C4—24no—
609C22×C4—28no—
610C22×C4—28no—
611C22×C4—22no—
612C22×C4—24no—
613C22×C4—22no—
614C22×C4—44no—
615C22×C4—48no—
616C22×C4—48no—
617C22×C4—82no—
618C22×C4—81no—
619C22×C4—81no—
620C22×C4—82no—
621C22×C4—84no—
622C22×C4—84no—
623C22×C4C2×C22⋊C411yescharacteristic
624C22×C4C2×C22⋊C411yescharacteristic
625C22×C4C2×C22⋊C411yescharacteristic
626C22×C4C2×C22⋊C411yescharacteristic
627C22×C4C2×C22⋊C411yescharacteristic
628C22×C4C2×C22⋊C411yescharacteristic
629C22×C4C2×C22⋊C411yescharacteristic
630C22×C4C2×C22⋊C411yescharacteristic
631C22×C4C2×C22⋊C414yes—
632C22×C4C2×C22⋊C414yes—
633C22×C4C2×C22⋊C414yes—
634C22×C4C2×C22⋊C414yes—
635C22×C4C23×C411yescharacteristic
636C22×C4C23×C411yescharacteristic
637C22×C4C23×C414yes—
638C22×C4C22×D411yescharacteristic
639C22×C4C22×D412yes—
640C22×C4C22×D411yescharacteristic
641C22×C4C22×D411yescharacteristic
642C22×C4C22×D412yes—
643C22×C4C22×D412yes—
644C22×C4C22×D411yescharacteristic
645C22×C4C22×D411yescharacteristic
646C22×C4C22×D411yescharacteristic
647C22×C4C22×D414yes—
648C22×C4C22×D411yescharacteristic
649C22×C4C2511yescharacteristic
650M16—88no—
651M16—82no—
652M16—82no—
653C2×C8—24no—
654C2×C8—24no—
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—28no—
662C4⋊C4—28no—
663C4⋊C4—24no—
664C4⋊C4—22no—
665C4⋊C4—24no—
666C4⋊C4—22no—
667C4⋊C4—24no—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—28no—
671C4⋊C4—28no—
672C4⋊C4—24no—
673C4⋊C4—44no—
674C4⋊C4—82no—
675C4⋊C4—84no—
676C4⋊C4C2×C22⋊C412yes—
677C4⋊C4C2×C22⋊C412yes—
678C4⋊C4C2×C22⋊C412yes—
679C4⋊C4C2×C22⋊C412yes—
680C4⋊C4C2×C22⋊C414yes—
681C4⋊C4C2×C22⋊C414yes—
682C4⋊C4C2×C22⋊C414yes—
683C4⋊C4C2×C22⋊C414yes—
684C4⋊C4C23×C414yes—
685C4⋊C4C23×C414yes—
686C22⋊C4—24no—
687C22⋊C4—28no—
688C22⋊C4—28no—
689C22⋊C4—24no—
690C22⋊C4—28no—
691C22⋊C4—28no—
692C22⋊C4—24no—
693C22⋊C4—24no—
694C22⋊C4—24no—
695C22⋊C4—28no—
696C22⋊C4—28no—
697C22⋊C4—24no—
698C22⋊C4—48no—
699C22⋊C4—82no—
700C22⋊C4—82no—
701C22⋊C4C2×C22⋊C414yes—
702C22⋊C4C2×C22⋊C414yes—
703C22⋊C4C2×C22⋊C414yes—
704C22⋊C4C2×C22⋊C414yes—
705C22⋊C4C2×C22⋊C414yes—
706C22⋊C4C2×C22⋊C414yes—
707C42—24no—
708C42—28no—
709C42—28no—
710C42—24no—
711C42—44no—
712C42—84no—
713C42—82no—
714C42C2×C22⋊C414yes—
715C42C2×C22⋊C414yes—
716C42C2×C22⋊C411yescharacteristic
717C42C2×C22⋊C411yescharacteristic
718C42C2×C22⋊C414yes—
719C42C2×C22⋊C411yescharacteristic
720C42C2×C22⋊C411yescharacteristic
721C42C2×C22⋊C411yescharacteristic
722C42C2×C22⋊C411yescharacteristic
723C42C2×C22⋊C414yes—
724C42C2×C22⋊C411yescharacteristic
725C42C2×C22⋊C411yescharacteristic
726C42C23×C411yescharacteristic
727C42C23×C411yescharacteristic
728C42C23×C411yescharacteristic
729C42C23×C414yes—
730C42C23×C411yescharacteristic
731C42C22×D414yes—
732C42C22×D411yescharacteristic
733C42C22×D411yescharacteristic
734C42C22×D411yescharacteristic
735C42C22×D411yescharacteristic
736C23—24no—
737C23—22no—
738C23—24no—
739C23—42no—
740C23—42no—
741C23—41no—
742C23—41no—
743C23—44no—
744C23—82no—
745C23—82no—
746C23C22×C22⋊C411yescharacteristic
747C23C22×C22⋊C414yes—
748C23C22×C22⋊C411yescharacteristic
749C23C23×D411yescharacteristic
750Q8—24no—
751Q8—24no—
752Q8—44no—
753Q8—44no—
754Q8—44no—
755Q8—44no—
756Q8—82no—
757Q8—82no—
758D4—24no—
759D4—24no—
760D4—44no—
761D4—44no—
762D4—44no—
763D4—44no—
764D4—44no—
765D4—48no—
766D4—48no—
767D4—44no—
768D4—82no—
769D4—82no—
770D4—88no—
771D4—88no—
772C2×C4—22no—
773C2×C4—24no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—41no—
785C2×C4—44no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—44no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—44no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—44no—
801C2×C4—48no—
802C2×C4—44no—
803C2×C4—48no—
804C2×C4—42no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—44no—
813C2×C4—88no—
814C2×C4—88no—
815C2×C4—82no—
816C2×C4—82no—
817C2×C4—168no—
818C2×C4C22×C22⋊C411yescharacteristic
819C2×C4C22×C22⋊C414yes—
820C2×C4C22×C22⋊C414yes—
821C2×C4C22×C22⋊C411yescharacteristic
822C2×C4C22×C22⋊C411yescharacteristic
823C2×C4C22×C22⋊C411yescharacteristic
824C2×C4C22×C22⋊C411yescharacteristic
825C2×C4C22×C22⋊C411yescharacteristic
826C2×C4C22×C22⋊C411yescharacteristic
827C2×C4C22×C22⋊C414yes—
828C2×C4C22×C22⋊C411yescharacteristic
829C2×C4C22×C22⋊C411yescharacteristic
830C2×C4C22×C22⋊C411yescharacteristic
831C2×C4#57514yes—
832C2×C4C24×C411yescharacteristic
833C2×C4C23×D411yescharacteristic
834C8—44no—
835C8—44no—
836C22—21no—
837C22—21no—
838C22—21no—
839C22—24no—
840C22—21no—
841C22—21no—
842C22—21no—
843C22—24no—
844C22—21no—
845C22—24no—
846C22—21no—
847C22—48no—
848C22—44no—
849C22—44no—
850C22—44no—
851C22—82no—
852C22—164no—
853C22C23×C22⋊C411yescharacteristic
854C22C2×#57512yes—
855C4—21no—
856C4—21no—
857C4—24no—
858C4—21no—
859C4—21no—
860C4—21no—
861C4—21no—
862C4—24no—
863C4—21no—
864C4—21no—
865C4—24no—
866C4—21no—
867C4—21no—
868C4—44no—
869C4—44no—
870C4—44no—
871C4—82no—
872C4—84no—
873C4—82no—
874C4#289612yes—
875C4#289612yes—
876C2—22no—
877C2—44no—
878C2—41no—
879C2—41no—
880C2—84no—
881C2#6007011yescharacteristic
882C2C2×#289611yescharacteristic
883C2#6009311yescharacteristic
subgroupG/H
center, socleC22C23×C22⋊C4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radical#62815C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C2×C4×#41 ◁ G
LECSG ▷ C22×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60284C2semidirect
3. #34195C2semidirect
4. #17630C2semidirect
5. #17623C2semidirect
6. #17616C2semidirect
7. #17593C2semidirect
8. #17584C2semidirect
9. #17583C2semidirect
10. #17562C2semidirect
11. #17561C2semidirect
12. #17558C2semidirect
14. #3511C4semidirect
15. #3511C4semidirect
17. #3509C4semidirect
18. #3508C4semidirect
26. #3480C4semidirect
28. #3475C4semidirect
38. #2982C22semidirect
40. #2975C22semidirect
45. #2920C22semidirect
46. #2356C22semidirect
48. #2349C22semidirect
56. #2283C22semidirect
57. C2×#383C22semidirect
59. #1521C22semidirect
60. #1518C22semidirect
62. #1515C22semidirect
63. #1515C22semidirect
64. #1515C22semidirect
68. #1513C22semidirect
73. #1504C22semidirect
74. #1503C22semidirect
76. #1500C22semidirect
82. #559C2×C4semidirect
84. #557C2×C4semidirect
90. #556C2×C4semidirect
94. #554C2×C4semidirect
100. #553C2×C4semidirect
104. #552C2×C4semidirect
110. #548C2×C4semidirect
114. #546C2×C4semidirect
134. #533C2×C4semidirect
135. #533C2×C4semidirect
136. #533C2×C4semidirect
137. #533C2×C4semidirect
145. #532C2×C4semidirect
146. #532C2×C4semidirect
147. #532C2×C4semidirect
148. #532C2×C4semidirect
151. C2×C4⋊Q8C2×C4semidirect
152. C2×C4⋊Q8C2×C4semidirect
153. C2×C4⋊Q8C2×C4semidirect
154. C2×#127C2×C4semidirect
161. #529C2×C4semidirect
187. C4×#41C2×C4semidirect
193. C2×C4×Q8C2×C4semidirect
198. C2×C4×D4C2×C4semidirect

Maximal subgroups

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

subgroupindex
#628152
#602842
#341952
#176302
#176232
#176162
#175932
#175842
#175832
#175622
#175612
#175582