Finite Group Databasebeta

← #6343418

Subgroups — #6343418

Order 512.

3388 conjugacy classes of subgroups.

The subgroup lattice has 1332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3519C211yesmaximal, characteristic
2C2×#2974C211yesmaximal, characteristic, complemented
3#34194C211yesmaximal, characteristic, complemented
4#17599C214yesmaximal, complemented
5#17597C218yesmaximal, complemented
6#17595C211yesmaximal, characteristic, complemented
7#17592C212yesmaximal, complemented
8#17581C211yesmaximal, characteristic, complemented
9#17577C212yesmaximal, complemented
10#17574C211yesmaximal, characteristic, complemented
11#17572C212yesmaximal, complemented
12#17567C211yesmaximal, characteristic, complemented
13C2×#1519C212yesmaximal, complemented
14#17547C214yesmaximal, complemented
15#3519—21no—
16#3519—22no—
17#3519—21no—
18#3519—21no—
19#3519—22no—
20#3519—21no—
21#3519C412yescomplemented
22#3519C414yescomplemented
23#3519C412yescomplemented
24#3519C2212yes—
25#3519C2214yes—
26#3519C2212yes—
27C2×#555C411yescharacteristic, complemented
28C2×#554C411yescharacteristic, complemented
29C2×#553—21no—
30C2×#553C412yescomplemented
31C2×#550C411yescharacteristic, complemented
32C2×#546—22no—
33C2×#546C412yescomplemented
34C2×D42—21no—
35C2×D42C411yescharacteristic, complemented
36C2×#540—21no—
37C2×#538—22no—
38C2×#532C2211yescharacteristic
39C2×#529C2211yescharacteristic
40C2×#525C2212yes—
41C22×#121C2212yes—
42C2×#518—21no—
43C22×C4×D4C2211yescharacteristic
44#2974—21no—
45#2974—22no—
46#2974—21no—
47#2974C2212yescomplemented
48#2974C2214yescomplemented
49#2974C2212yescomplemented
50C2×#436—21no—
51C2×#435—22no—
52C2×C8×D4—21no—
53C2×#432C2211yescharacteristic, complemented
54C2×#431C2211yescharacteristic, complemented
55C2×#407C2212yescomplemented
56C22×C22⋊C8C2212yescomplemented
57#2354—21no—
58#2352—22no—
59D4×C4⋊C4—21no—
60#2345—21no—
61#2342—22no—
62D4×C22⋊C4—21no—
63#2319C2212yescomplemented
64#2318C2214yescomplemented
65#2285C2211yescharacteristic, complemented
66#2283C2211yescharacteristic, complemented
67#2280C2212yescomplemented
68C2×#380C2212yescomplemented
69#2275C2212yescomplemented
70#1521C2214yescomplemented
71#1520C2211yescharacteristic, complemented
72#1520C2211yescharacteristic, complemented
73#1520C2212yescomplemented
74#1519C2211yescharacteristic
75#1519C2212yes—
76#1519C2211yescharacteristic
77#1519C2218yescomplemented
78#1519C2212yescomplemented
79#1519C2212yescomplemented
80#1519C2212yescomplemented
81#1519C2212yescomplemented
82#1517C2214yescomplemented
83#1516C2218yescomplemented
84#1514C2214yescomplemented
85#1513C2218yescomplemented
86#1512C2214yescomplemented
87#1510C2218yescomplemented
88#1509C2214yescomplemented
89#1507C2218yescomplemented
90#1505C2214yescomplemented
91#1504C2218yescomplemented
92#1502C2214yescomplemented
93#1501C2218yescomplemented
94#1500C2214yescomplemented
95C2×#327C2218yescomplemented
96C22×#41—21no—
97C22×#41C2×C412yescomplemented
98C23×D4—22no—
99C23×D4—21no—
100C23×D4C2×C412yescomplemented
101C23×D4D411yescharacteristic
102C24×C4C2312yes—
103C22×M16—22no—
104C23×C8—22no—
105#555—21no—
106#555—21no—
107#555—22no—
108#555C2×C412yes—
109#555C2×C414yescomplemented
110#555C2×C412yescomplemented
111#554—21no—
112#554—22no—
113#554—21no—
114#554C2×C412yes—
115#554C2×C414yescomplemented
116#554C2×C412yescomplemented
117#553—22no—
118#553—22no—
119#553—22no—
120#553—22no—
121#553—22no—
122#553—22no—
123#553—24no—
124#553—22no—
125#553—24no—
126#553—22no—
127#553C2×C414yes—
128#553C2×C414yescomplemented
129#553C2×C414yescomplemented
130#553C2×C414yescomplemented
131#550—21no—
132#550—22no—
133#550—21no—
134#550C2×C412yes—
135#550C2×C412yescomplemented
136#550C2×C414yescomplemented
137#546—22no—
138#546—22no—
139#546—22no—
140#546—22no—
141#546—24no—
142#546—24no—
143#546—24no—
144#546—24no—
145#546—24no—
146#546—24no—
147#546—24no—
148#546—24no—
149#546C2×C414yes—
150#546C2×C414yescomplemented
151#546C2×C414yescomplemented
152#546C2×C414yescomplemented
153D42—22no—
154D42—24no—
155D42—22no—
156D42—22no—
157D42—24no—
158D42—22no—
159D42—22no—
160D42—21no—
161D42—21no—
162D42C2×C412yes—
163D42C2×C412yescomplemented
164D42C2×C414yescomplemented
165#540—22no—
166#540—22no—
167#540—24no—
168#540—22no—
169#540—24no—
170#540—22no—
171#538—24no—
172#538—24no—
173#538—24no—
174#538—24no—
175#538—24no—
176#538—24no—
177#538—24no—
178#538—24no—
179#532—21no—
180#532—21no—
181#532—21no—
182#532—21no—
183#532C2×C412yescomplemented
184#532C2×C412yescomplemented
185#532C2312yes—
186#532C2312yes—
187C2×C4⋊Q8C2×C411yescharacteristic, complemented
188C2×#127—21no—
189C2×#127C2×C411yescharacteristic, complemented
190#529—21no—
191#529—21no—
192#529—21no—
193#529—21no—
194#529C2×C412yescomplemented
195#529C2×C412yescomplemented
196#529C2312yes—
197#529C2312yes—
198C2×#126—22no—
199C2×#126—21no—
200C2×#125—21no—
201C2×#125C2×C411yescharacteristic, complemented
202C2×#124—22no—
203C2×#124—21no—
204C2×#124C2×C411yescharacteristic, complemented
205#525—22no—
206#525—22no—
207#525—22no—
208#525—22no—
209#525C2×C414yescomplemented
210#525C2×C414yescomplemented
211#525C2314yes—
212#525C2314yes—
213C2×#123—22no—
214C2×#123—21no—
215C2×#123—22no—
216C2×#123—22no—
217C2×C22⋊Q8—22no—
218C2×C22⋊Q8C2×C412yescomplemented
219C2×C22⋊Q8C2311yescharacteristic
220C2×#121—22no—
221C2×#121—21no—
222C2×#121—22no—
223C2×#121—22no—
224C2×#121—22no—
225C2×#121—22no—
226C2×#121—22no—
227C2×#121—22no—
228C2×#121—21no—
229C2×#121—21no—
230C2×#121—22no—
231C2×#121—22no—
232C2×#121C2×C412yescomplemented
233C2×#121C2×C412yescomplemented
234C2×#121C2×C414yescomplemented
235C2×#121C2×C414yescomplemented
236C2×#121C2×C412yescomplemented
237C2×#121C2311yescharacteristic
238C2×#121C2312yes—
239C2×#121C2314yes—
240C2×#121C2314yes—
241C2×#120—22no—
242C2×#120—22no—
243C2×#120—22no—
244#518—24no—
245#518—22no—
246#518—22no—
247#518—22no—
248#518—24no—
249#518—22no—
250C2×C4×Q8C2×C411yescharacteristic, complemented
251C2×C4×D4—21no—
252C2×C4×D4—22no—
253C2×C4×D4—22no—
254C2×C4×D4—21no—
255C2×C4×D4—22no—
256C2×C4×D4—21no—
257C2×C4×D4—22no—
258C2×C4×D4—21no—
259C2×C4×D4C2×C411yescharacteristic
260C2×C4×D4C2×C412yes—
261C2×C4×D4C2×C411yescharacteristic
262C2×C4×D4C2×C411yescharacteristic
263C2×C4×D4C2×C412yes—
264C2×C4×D4C2×C411yescharacteristic
265C2×C4×D4C2×C411yescharacteristic, complemented
266C2×C4×D4C2×C412yescomplemented
267C2×C4×D4D411yescharacteristic
268C2×C4×D4D411yescharacteristic
269C2×C4×D4D412yes—
270C2×C4×D4D411yescharacteristic
271C2×C4×D4D412yes—
272C2×C4×D4D411yescharacteristic
273C2×C4×D4D411yescharacteristic
274C2×C4×D4D412yes—
275C2×C4×D4D411yescharacteristic
276C2×C4×D4C2312yes—
277C2×C4×D4C2311yescharacteristic
278C2×C4×D4C2311yescharacteristic
279C2×#117—21no—
280C2×#117—22no—
281C2×#117—21no—
282C2×#117—21no—
283C2×#117C2×C412yescomplemented
284C22×C4⋊C4—22no—
285C22×C4⋊C4C2×C412yescomplemented
286C22×C4⋊C4D411yescharacteristic
287C22×C22⋊C4—22no—
288C22×C22⋊C4—22no—
289C22×C22⋊C4—22no—
290C22×C22⋊C4D412yes—
291C22×C42C2311yescharacteristic
292#436—22no—
293#436—24no—
294#436—22no—
295#435—24no—
296#435—24no—
297#435—24no—
298#435—24no—
299C8×D4—22no—
300C8×D4—24no—
301C8×D4—22no—
302#432—21no—
303#432—21no—
304#432C2312yescomplemented
305#432C2312yescomplemented
306#431—21no—
307#431—21no—
308#431C2312yescomplemented
309#431C2312yescomplemented
310C2×C4⋊C8—21no—
311C2×C4⋊C8—21no—
312#407—22no—
313#407—22no—
314#407C2314yescomplemented
315#407C2314yescomplemented
316C2×C22⋊C8—22no—
317C2×C22⋊C8—22no—
318C2×C22⋊C8—22no—
319C2×C22⋊C8—22no—
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2312yes—
322C2×C22⋊C8C2311yescharacteristic
323C2×C22⋊C8C2314yescomplemented
324C2×C22⋊C8C2314yescomplemented
325C2×#97—21no—
326C2×C4×C8—21no—
327#390—22no—
328#389—22no—
329#388—24no—
330#388—24no—
331#387—24no—
332#386—24no—
333#385—24no—
334#384—21no—
335#383C2312yescomplemented
336#382—21no—
337#382C2312yescomplemented
338#381—21no—
339#381C2314yescomplemented
340#380—21no—
341#380—22no—
342#380—22no—
343#380—22no—
344#380C2311yescharacteristic
345#380C2312yes—
346#380C2311yescharacteristic
347#380C2314yescomplemented
348#379—22no—
349C4×C4⋊C4—22no—
350C4×C4⋊C4—21no—
351C4×C4⋊C4—21no—
352C4×C4⋊C4C2312yescomplemented
353C4×C22⋊C4—21no—
354C4×C22⋊C4—22no—
355C4×C22⋊C4—24no—
356C4×C22⋊C4C2314yescomplemented
357#376C2312yescomplemented
358C2×#95C2314yescomplemented
359#328C2314yescomplemented
360#328C2314yescomplemented
361#328C2318yescomplemented
362#327C2314yes—
363#327C2318yes—
364#327C2314yes—
365#327C2318yescomplemented
366#327C2318yescomplemented
367#327C2318yescomplemented
368#327C2318yescomplemented
369C25—22no—
370C25C2×D412yes—
371C2×#41—22no—
372C2×#41—22no—
373C2×#41—22no—
374C2×#41—22no—
375C2×#41—22no—
376C2×#41—22no—
377C2×#41—82no—
378C2×#41—82no—
379C2×#41—84no—
380C2×#41C22×C414yes—
381C2×#41C22×C414yes—
382C22×Q8—21no—
383C22×Q8C22×C411yescharacteristic
384C22×D4—22no—
385C22×D4—22no—
386C22×D4—21no—
387C22×D4—22no—
388C22×D4—22no—
389C22×D4—22no—
390C22×D4—24no—
391C22×D4—24no—
392C22×D4—24no—
393C22×D4—24no—
394C22×D4—22no—
395C22×D4—24no—
396C22×D4—22no—
397C22×D4—21no—
398C22×D4—21no—
399C22×D4—22no—
400C22×D4—22no—
401C22×D4—22no—
402C22×D4—44no—
403C22×D4—48no—
404C22×D4—84no—
405C22×D4—84no—
406C22×D4—84no—
407C22×D4C22⋊C411yescharacteristic
408C22×D4C22⋊C411yescharacteristic
409C22×D4C22⋊C412yes—
410C22×D4C22⋊C411yescharacteristic
411C22×D4C22⋊C411yescharacteristic
412C22×D4C22⋊C412yes—
413C22×D4C22×C411yescharacteristic
414C22×D4C22×C412yes—
415C22×D4C22×C414yes—
416C22×D4C22×C414yes—
417C22×D4C2×D411yescharacteristic
418C22×D4C2×D412yes—
419C22×D4C2×D411yescharacteristic
420C23×C4—22no—
421C23×C4—21no—
422C23×C4—22no—
423C23×C4—22no—
424C23×C4—24no—
425C23×C4—84no—
426C23×C4C22×C412yes—
427C23×C4C22×C412yes—
428C23×C4C22×C412yes—
429C23×C4C22×C412yes—
430C23×C4C2×D411yescharacteristic
431C23×C4C2×D412yes—
432C23×C4C2×D411yescharacteristic
433C23×C4C2×D412yes—
434C23×C4C2×D412yes—
435C23×C4C2×D412yes—
436C23×C4C2×D412yes—
437C23×C4C2×D412yes—
438C23×C4C2×D412yes—
439C23×C4C2411yescharacteristic
440C23×C4C2412yes—
441C23×C4C2412yes—
442C2×M16—24no—
443C2×M16—24no—
444C2×M16—84no—
445C22×C8—21no—
446C22×C8—22no—
447C22×C8—21no—
448C22×C8—24no—
449C22×C8—24no—
450C22×C8—84no—
451C4⋊Q8—21no—
452C4⋊Q8—21no—
453C4⋊Q8C22×C412yes—
454C4⋊Q8C22×C412yes—
455#127—22no—
456#127—22no—
457#127—24no—
458#127—21no—
459#127—21no—
460#127C22×C412yes—
461#127C22×C412yes—
462#126—24no—
463#126—24no—
464#126—24no—
465#126—24no—
466#126—22no—
467#126—22no—
468#126—22no—
469#126—22no—
470#125—22no—
471#125—24no—
472#125—22no—
473#125—21no—
474#125—21no—
475#125C22×C412yes—
476#125C22×C412yes—
477#124—24no—
478#124—24no—
479#124—24no—
480#124—24no—
481#124—22no—
482#124—22no—
483#124—21no—
484#124—21no—
485#124—22no—
486#124—22no—
487#124C22×C412yes—
488#124C22×C412yes—
489#123—24no—
490#123—24no—
491#123—22no—
492#123—22no—
493#123—24no—
494#123—24no—
495#123—22no—
496#123—22no—
497#123—24no—
498#123—24no—
499#123—24no—
500#123—24no—
501#123—24no—
502#123—24no—
503#123—24no—
504#123—24no—
505C22⋊Q8—22no—
506C22⋊Q8—22no—
507C22⋊Q8—21no—
508C22⋊Q8—21no—
509C22⋊Q8—24no—
510C22⋊Q8—24no—
511C22⋊Q8—24no—
512C22⋊Q8—24no—
513C22⋊Q8C22×C414yes—
514C22⋊Q8C22×C414yes—
515C22⋊Q8C22×C412yes—
516C22⋊Q8C2412yes—
517#121—24no—
518#121—24no—
519#121—24no—
520#121—24no—
521#121—22no—
522#121—22no—
523#121—24no—
524#121—24no—
525#121—24no—
526#121—24no—
527#121—24no—
528#121—22no—
529#121—22no—
530#121—22no—
531#121—22no—
532#121—22no—
533#121—22no—
534#121—22no—
535#121—22no—
536#121—21no—
537#121—21no—
538#121—22no—
539#121—22no—
540#121—24no—
541#121—24no—
542#121—24no—
543#121—24no—
544#121—22no—
545#121—22no—
546#121—22no—
547#121—24no—
548#121—22no—
549#121—24no—
550#121—24no—
551#121—24no—
552#121—24no—
553#121—24no—
554#121—24no—
555#121—24no—
556#121—24no—
557#121C22×C412yes—
558#121C22×C414yes—
559#121C22×C414yes—
560#121C22×C414yes—
561#121C22×C414yes—
562#121C22×C414yes—
563#121C22×C414yes—
564#121C22×C414yes—
565#121C2412yes—
566#121C2414yes—
567#120—24no—
568#120—24no—
569#120—24no—
570#120—24no—
571#120—24no—
572#120—24no—
573#120—24no—
574#120—24no—
575#120—24no—
576#120—24no—
577#120—24no—
578#120—24no—
579C4×Q8—21no—
580C4×Q8—21no—
581C4×Q8C22×C412yes—
582C4×Q8C22×C412yes—
583C4×D4—22no—
584C4×D4—24no—
585C4×D4—22no—
586C4×D4—24no—
587C4×D4—24no—
588C4×D4—24no—
589C4×D4—24no—
590C4×D4—22no—
591C4×D4—22no—
592C4×D4—24no—
593C4×D4—24no—
594C4×D4—24no—
595C4×D4—24no—
596C4×D4—22no—
597C4×D4—22no—
598C4×D4—22no—
599C4×D4—24no—
600C4×D4—22no—
601C4×D4—24no—
602C4×D4—24no—
603C4×D4—24no—
604C4×D4—24no—
605C4×D4—22no—
606C4×D4—22no—
607C4×D4—21no—
608C4×D4—21no—
609C4×D4—22no—
610C4×D4—22no—
611C4×D4—22no—
612C4×D4—22no—
613C4×D4—48no—
614C4×D4C22⋊C412yes—
615C4×D4C22⋊C411yescharacteristic
616C4×D4C22⋊C411yescharacteristic
617C4×D4C22⋊C412yes—
618C4×D4C22⋊C412yes—
619C4×D4C22⋊C412yes—
620C4×D4C22⋊C412yes—
621C4×D4C22⋊C411yescharacteristic
622C4×D4C22⋊C411yescharacteristic
623C4×D4C22⋊C412yes—
624C4×D4C22⋊C412yes—
625C4×D4C22⋊C411yescharacteristic
626C4×D4C22⋊C411yescharacteristic
627C4×D4C22⋊C412yes—
628C4×D4C22⋊C412yes—
629C4×D4C22⋊C412yes—
630C4×D4C22⋊C412yes—
631C4×D4C22⋊C411yescharacteristic
632C4×D4C22⋊C411yescharacteristic
633C4×D4C22⋊C412yes—
634C4×D4C22×C412yes—
635C4×D4C22×C412yes—
636C4×D4C22×C414yes—
637C4×D4C22×C414yes—
638C4×D4C22×C411yescharacteristic
639C4×D4C22×C412yes—
640C4×D4C22×C411yescharacteristic
641C4×D4C22×C412yes—
642C4×D4C22×C412yes—
643C4×D4C22×C412yes—
644C4×D4C22×C412yes—
645C4×D4C22×C411yescharacteristic
646C4×D4C22×C411yescharacteristic
647C4×D4C22×C412yes—
648C4×D4C2×D411yescharacteristic
649C4×D4C2×D412yes—
650C4×D4C2×D411yescharacteristic
651C4×D4C2×D412yes—
652C4×D4C2×D412yes—
653C4×D4C2×D412yes—
654C4×D4C2×D412yes—
655C4×D4C2×D411yescharacteristic
656C4×D4C2×D412yes—
657C4×D4C2×D411yescharacteristic
658#117—22no—
659#117—22no—
660#117—22no—
661#117—24no—
662#117—22no—
663#117—22no—
664#117—22no—
665#117—22no—
666#117—22no—
667#117—82no—
668#117—84no—
669#117C22×C414yes—
670#117C22×C414yes—
671C2×C4⋊C4—22no—
672C2×C4⋊C4—22no—
673C2×C4⋊C4—22no—
674C2×C4⋊C4—21no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4—22no—
678C2×C4⋊C4—21no—
679C2×C4⋊C4—21no—
680C2×C4⋊C4—21no—
681C2×C4⋊C4—22no—
682C2×C4⋊C4—21no—
683C2×C4⋊C4—22no—
684C2×C4⋊C4—24no—
685C2×C4⋊C4—22no—
686C2×C4⋊C4—84no—
687C2×C4⋊C4C22⋊C411yescharacteristic
688C2×C4⋊C4C22⋊C411yescharacteristic
689C2×C4⋊C4C22⋊C412yes—
690C2×C4⋊C4C22⋊C411yescharacteristic
691C2×C4⋊C4C22⋊C411yescharacteristic
692C2×C4⋊C4C22⋊C412yes—
693C2×C4⋊C4C22×C411yescharacteristic
694C2×C4⋊C4C22×C412yes—
695C2×C4⋊C4C22×C414yes—
696C2×C4⋊C4C22×C414yes—
697C2×C4⋊C4C22×C411yescharacteristic
698C2×C4⋊C4C2×D411yescharacteristic
699C2×C4⋊C4C2×D412yes—
700C2×C4⋊C4C2×D411yescharacteristic
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—24no—
708C2×C22⋊C4—24no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—22no—
715C2×C22⋊C4—24no—
716C2×C22⋊C4—24no—
717C2×C22⋊C4—24no—
718C2×C22⋊C4—24no—
719C2×C22⋊C4—24no—
720C2×C22⋊C4—24no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—22no—
723C2×C22⋊C4—24no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—24no—
726C2×C22⋊C4—24no—
727C2×C22⋊C4—84no—
728C2×C22⋊C4C22⋊C412yes—
729C2×C22⋊C4C22⋊C412yes—
730C2×C22⋊C4C22⋊C412yes—
731C2×C22⋊C4C22⋊C412yes—
732C2×C22⋊C4C22⋊C412yes—
733C2×C22⋊C4C22⋊C412yes—
734C2×C22⋊C4C22⋊C412yes—
735C2×C22⋊C4C22⋊C412yes—
736C2×C22⋊C4C2×D412yes—
737C2×C22⋊C4C2×D412yes—
738C2×C22⋊C4C2×D412yes—
739C2×C22⋊C4C2×D412yes—
740C2×C42—22no—
741C2×C42—21no—
742C2×C42—22no—
743C2×C42—24no—
744C2×C42—22no—
745C2×C42C22×C411yescharacteristic
746C2×C42C22×C411yescharacteristic
747C2×C42C22×C411yescharacteristic
748C2×C42C22×C411yescharacteristic
749C2×C42C2×D411yescharacteristic
750C2×C42C2×D411yescharacteristic
751C2×C42C2×D411yescharacteristic
752C2×C42C2×D411yescharacteristic
753C2×C42C2×D411yescharacteristic
754C2×C42C2×D411yescharacteristic
755C2×C42C2411yescharacteristic
756C2×C42C2411yescharacteristic
757C4⋊C8—22no—
758C4⋊C8—22no—
759C4⋊C8—22no—
760C4⋊C8—22no—
761C22⋊C8—21no—
762C22⋊C8—22no—
763C22⋊C8—24no—
764C22⋊C8—24no—
765C22⋊C8—24no—
766C22⋊C8—24no—
767C22⋊C8—21no—
768C22⋊C8C2412yes—
769C22⋊C8C2414yes—
770C22⋊C8C2412yes—
771#97—22no—
772#97—22no—
773C4×C8—22no—
774C4×C8—22no—
775#95—24no—
776#95—22no—
777#95—24no—
778#95—22no—
779#95—22no—
780#95—22no—
781#95C2412yes—
782#95C2414yes—
783#95C2412yes—
784C24—24no—
785C24—24no—
786C24—21no—
787C24—22no—
788C24—24no—
789C24—24no—
790C24—44no—
791C24—48no—
792C24—84no—
793C24—82no—
794C24—84no—
795C24C2×C22⋊C412yes—
796C24C2×C22⋊C412yes—
797C24C2×C22⋊C412yes—
798C24C2×C22⋊C412yes—
799C24C22×D412yes—
800C24C22×D412yes—
801C24C22×D411yescharacteristic
802#41—84no—
803#41—84no—
804#41—82no—
805#41—82no—
806#41—82no—
807#41—82no—
808#41—84no—
809#41—84no—
810#41—84no—
811#41—84no—
812C2×Q8—21no—
813C2×Q8—22no—
814C2×Q8—22no—
815C2×Q8—42no—
816C2×Q8—82no—
817C2×Q8C23×C412yes—
818C2×D4—24no—
819C2×D4—24no—
820C2×D4—24no—
821C2×D4—24no—
822C2×D4—24no—
823C2×D4—24no—
824C2×D4—22no—
825C2×D4—24no—
826C2×D4—22no—
827C2×D4—24no—
828C2×D4—24no—
829C2×D4—24no—
830C2×D4—24no—
831C2×D4—24no—
832C2×D4—24no—
833C2×D4—22no—
834C2×D4—22no—
835C2×D4—21no—
836C2×D4—22no—
837C2×D4—22no—
838C2×D4—22no—
839C2×D4—24no—
840C2×D4—24no—
841C2×D4—42no—
842C2×D4—42no—
843C2×D4—42no—
844C2×D4—44no—
845C2×D4—42no—
846C2×D4—44no—
847C2×D4—44no—
848C2×D4—44no—
849C2×D4—44no—
850C2×D4—416no—
851C2×D4—48no—
852C2×D4—48no—
853C2×D4—42no—
854C2×D4—44no—
855C2×D4—42no—
856C2×D4—44no—
857C2×D4—48no—
858C2×D4—84no—
859C2×D4—84no—
860C2×D4—82no—
861C2×D4—84no—
862C2×D4—84no—
863C2×D4—84no—
864C2×D4—84no—
865C2×D4—84no—
866C2×D4—84no—
867C2×D4—88no—
868C2×D4—88no—
869C2×D4—84no—
870C2×D4—84no—
871C2×D4—84no—
872C2×D4—84no—
873C2×D4C2×C22⋊C412yes—
874C2×D4C2×C22⋊C411yescharacteristic
875C2×D4C2×C22⋊C412yes—
876C2×D4C2×C22⋊C412yes—
877C2×D4C2×C22⋊C411yescharacteristic
878C2×D4C2×C22⋊C411yescharacteristic
879C2×D4C2×C22⋊C412yes—
880C2×D4C2×C22⋊C412yes—
881C2×D4C2×C22⋊C412yes—
882C2×D4C2×C22⋊C411yescharacteristic
883C2×D4C23×C412yes—
884C2×D4C23×C414yes—
885C22×C4—22no—
886C22×C4—22no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—22no—
890C22×C4—21no—
891C22×C4—24no—
892C22×C4—24no—
893C22×C4—22no—
894C22×C4—22no—
895C22×C4—24no—
896C22×C4—24no—
897C22×C4—24no—
898C22×C4—24no—
899C22×C4—22no—
900C22×C4—22no—
901C22×C4—24no—
902C22×C4—44no—
903C22×C4—44no—
904C22×C4—44no—
905C22×C4—44no—
906C22×C4—42no—
907C22×C4—44no—
908C22×C4—44no—
909C22×C4—42no—
910C22×C4—44no—
911C22×C4—48no—
912C22×C4—84no—
913C22×C4—82no—
914C22×C4—82no—
915C22×C4—82no—
916C22×C4—82no—
917C22×C4—82no—
918C22×C4—82no—
919C22×C4—82no—
920C22×C4—84no—
921C22×C4—84no—
922C22×C4—84no—
923C22×C4—84no—
924C22×C4C2×C22⋊C411yescharacteristic
925C22×C4C2×C22⋊C411yescharacteristic
926C22×C4C2×C22⋊C411yescharacteristic
927C22×C4C2×C22⋊C411yescharacteristic
928C22×C4C2×C22⋊C411yescharacteristic
929C22×C4C2×C22⋊C411yescharacteristic
930C22×C4C2×C22⋊C412yes—
931C22×C4C2×C22⋊C412yes—
932C22×C4C2×C22⋊C412yes—
933C22×C4C2×C22⋊C412yes—
934C22×C4C2×C22⋊C412yes—
935C22×C4C2×C22⋊C411yescharacteristic
936C22×C4C2×C22⋊C411yescharacteristic
937C22×C4C2×C22⋊C412yes—
938C22×C4C2×C22⋊C412yes—
939C22×C4C2×C22⋊C412yes—
940C22×C4C2×C22⋊C412yes—
941C22×C4C2×C22⋊C412yes—
942C22×C4C2×C22⋊C412yes—
943C22×C4C2×C22⋊C412yes—
944C22×C4C23×C411yescharacteristic
945C22×C4C23×C411yescharacteristic
946C22×C4C23×C412yes—
947C22×C4C23×C412yes—
948C22×C4C23×C412yes—
949C22×C4C23×C412yes—
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C22×D412yes—
957C22×C4C22×D412yes—
958C22×C4C22×D411yescharacteristic
959C22×C4C22×D412yes—
960C22×C4C22×D412yes—
961C22×C4C22×D412yes—
962C22×C4C22×D412yes—
963C22×C4C2511yescharacteristic
964M16—84no—
965M16—84no—
966C2×C8—22no—
967C2×C8—22no—
968C2×C8—24no—
969C2×C8—42no—
970C2×C8—44no—
971C2×C8—42no—
972C2×C8—84no—
973C2×C8—84no—
974C4⋊C4—21no—
975C4⋊C4—22no—
976C4⋊C4—24no—
977C4⋊C4—24no—
978C4⋊C4—22no—
979C4⋊C4—22no—
980C4⋊C4—22no—
981C4⋊C4—22no—
982C4⋊C4—22no—
983C4⋊C4—22no—
984C4⋊C4—22no—
985C4⋊C4—24no—
986C4⋊C4—24no—
987C4⋊C4—22no—
988C4⋊C4—22no—
989C4⋊C4—21no—
990C4⋊C4—22no—
991C4⋊C4—42no—
992C4⋊C4—44no—
993C4⋊C4—42no—
994C4⋊C4—44no—
995C4⋊C4—82no—
996C4⋊C4—84no—
997C4⋊C4C2×C22⋊C412yes—
998C4⋊C4C2×C22⋊C411yescharacteristic
999C4⋊C4C2×C22⋊C411yescharacteristic
1000C4⋊C4C2×C22⋊C412yes—
1001C4⋊C4C2×C22⋊C411yescharacteristic
1002C4⋊C4C2×C22⋊C411yescharacteristic
1003C4⋊C4C2×C22⋊C412yes—
1004C4⋊C4C2×C22⋊C412yes—
1005C4⋊C4C2×C22⋊C412yes—
1006C4⋊C4C2×C22⋊C412yes—
1007C4⋊C4C23×C412yes—
1008C4⋊C4C23×C414yes—
1009C4⋊C4C23×C412yes—
1010C22⋊C4—24no—
1011C22⋊C4—24no—
1012C22⋊C4—24no—
1013C22⋊C4—24no—
1014C22⋊C4—22no—
1015C22⋊C4—22no—
1016C22⋊C4—22no—
1017C22⋊C4—22no—
1018C22⋊C4—22no—
1019C22⋊C4—24no—
1020C22⋊C4—24no—
1021C22⋊C4—24no—
1022C22⋊C4—24no—
1023C22⋊C4—24no—
1024C22⋊C4—22no—
1025C22⋊C4—22no—
1026C22⋊C4—24no—
1027C22⋊C4—24no—
1028C22⋊C4—22no—
1029C22⋊C4—22no—
1030C22⋊C4—24no—
1031C22⋊C4—24no—
1032C22⋊C4—22no—
1033C22⋊C4—24no—
1034C22⋊C4—48no—
1035C22⋊C4—42no—
1036C22⋊C4—44no—
1037C22⋊C4—42no—
1038C22⋊C4—84no—
1039C22⋊C4—84no—
1040C22⋊C4C2×C22⋊C412yes—
1041C22⋊C4C2×C22⋊C412yes—
1042C22⋊C4C2×C22⋊C412yes—
1043C22⋊C4C2×C22⋊C412yes—
1044C22⋊C4C2×C22⋊C412yes—
1045C22⋊C4C2×C22⋊C412yes—
1046C22⋊C4C2×C22⋊C412yes—
1047C22⋊C4C2×C22⋊C412yes—
1048C22⋊C4C2×C22⋊C412yes—
1049C22⋊C4C2×C22⋊C412yes—
1050C22⋊C4C2×C22⋊C412yes—
1051C22⋊C4C2×C22⋊C412yes—
1052C22⋊C4C2×C22⋊C412yes—
1053C22⋊C4C2×C22⋊C412yes—
1054C22⋊C4C2×C22⋊C412yes—
1055C22⋊C4C2×C22⋊C412yes—
1056C42—24no—
1057C42—24no—
1058C42—22no—
1059C42—22no—
1060C42—44no—
1061C42—82no—
1062C42—84no—
1063C42C2×C22⋊C411yescharacteristic
1064C42C2×C22⋊C411yescharacteristic
1065C42C2×C22⋊C411yescharacteristic
1066C42C2×C22⋊C411yescharacteristic
1067C42C2×C22⋊C411yescharacteristic
1068C42C2×C22⋊C411yescharacteristic
1069C42C2×C22⋊C411yescharacteristic
1070C42C2×C22⋊C411yescharacteristic
1071C42C23×C411yescharacteristic
1072C42C23×C411yescharacteristic
1073C42C23×C411yescharacteristic
1074C42C23×C411yescharacteristic
1075C42C22×D411yescharacteristic
1076C42C22×D411yescharacteristic
1077C42C22×D411yescharacteristic
1078C42C22×D411yescharacteristic
1079C23—24no—
1080C23—24no—
1081C23—24no—
1082C23—24no—
1083C23—24no—
1084C23—22no—
1085C23—22no—
1086C23—24no—
1087C23—24no—
1088C23—22no—
1089C23—22no—
1090C23—22no—
1091C23—24no—
1092C23—42no—
1093C23—41no—
1094C23—42no—
1095C23—42no—
1096C23—41no—
1097C23—42no—
1098C23—42no—
1099C23—42no—
1100C23—42no—
1101C23—42no—
1102C23—42no—
1103C23—42no—
1104C23—44no—
1105C23—44no—
1106C23—42no—
1107C23—48no—
1108C23—44no—
1109C23—42no—
1110C23—48no—
1111C23—84no—
1112C23—84no—
1113C23—84no—
1114C23—84no—
1115C23—88no—
1116C23—88no—
1117C23—1616no—
1118C23C22×C22⋊C412yes—
1119C23C22×C22⋊C412yes—
1120C23C22×C22⋊C412yes—
1121C23C22×C22⋊C411yescharacteristic
1122C23C22×C22⋊C411yescharacteristic
1123C23C22×C22⋊C412yes—
1124C23#57612yes—
1125C23#57712yes—
1126C23C23×D411yescharacteristic
1127Q8—42no—
1128Q8—42no—
1129Q8—82no—
1130Q8—82no—
1131D4—24no—
1132D4—24no—
1133D4—24no—
1134D4—22no—
1135D4—22no—
1136D4—22no—
1137D4—42no—
1138D4—42no—
1139D4—42no—
1140D4—42no—
1141D4—44no—
1142D4—44no—
1143D4—48no—
1144D4—44no—
1145D4—48no—
1146D4—48no—
1147D4—42no—
1148D4—44no—
1149D4—42no—
1150D4—44no—
1151D4—42no—
1152D4—44no—
1153D4—44no—
1154D4—84no—
1155D4—84no—
1156D4—82no—
1157D4—82no—
1158D4—84no—
1159D4—84no—
1160D4—84no—
1161D4—84no—
1162D4—84no—
1163D4—84no—
1164D4#42114yes—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—24no—
1179C2×C4—24no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—24no—
1186C2×C4—22no—
1187C2×C4—42no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—42no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—42no—
1201C2×C4—42no—
1202C2×C4—42no—
1203C2×C4—42no—
1204C2×C4—42no—
1205C2×C4—42no—
1206C2×C4—42no—
1207C2×C4—42no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—44no—
1212C2×C4—42no—
1213C2×C4—42no—
1214C2×C4—42no—
1215C2×C4—44no—
1216C2×C4—44no—
1217C2×C4—42no—
1218C2×C4—42no—
1219C2×C4—42no—
1220C2×C4—44no—
1221C2×C4—44no—
1222C2×C4—42no—
1223C2×C4—44no—
1224C2×C4—42no—
1225C2×C4—42no—
1226C2×C4—84no—
1227C2×C4—84no—
1228C2×C4—84no—
1229C2×C4—84no—
1230C2×C4—84no—
1231C2×C4—84no—
1232C2×C4—168no—
1233C2×C4C22×C22⋊C411yescharacteristic
1234C2×C4C22×C22⋊C412yes—
1235C2×C4C22×C22⋊C412yes—
1236C2×C4C22×C22⋊C411yescharacteristic
1237C2×C4C22×C22⋊C411yescharacteristic
1238C2×C4C22×C22⋊C411yescharacteristic
1239C2×C4C22×C22⋊C411yescharacteristic
1240C2×C4C22×C22⋊C411yescharacteristic
1241C2×C4C22×C22⋊C411yescharacteristic
1242C2×C4C22×C22⋊C411yescharacteristic
1243C2×C4C22×C22⋊C412yes—
1244C2×C4C22×C22⋊C412yes—
1245C2×C4C22×C22⋊C411yescharacteristic
1246C2×C4C22×C22⋊C411yescharacteristic
1247C2×C4C24×C411yescharacteristic
1248C2×C4C23×D411yescharacteristic
1249C8—42no—
1250C8—44no—
1251C8—42no—
1252C22—21no—
1253C22—21no—
1254C22—21no—
1255C22—22no—
1256C22—22no—
1257C22—21no—
1258C22—21no—
1259C22—21no—
1260C22—22no—
1261C22—22no—
1262C22—22no—
1263C22—22no—
1264C22—22no—
1265C22—22no—
1266C22—22no—
1267C22—22no—
1268C22—22no—
1269C22—42no—
1270C22—42no—
1271C22—44no—
1272C22—44no—
1273C22—48no—
1274C22—48no—
1275C22—44no—
1276C22—42no—
1277C22—44no—
1278C22—42no—
1279C22—42no—
1280C22—44no—
1281C22—82no—
1282C22—82no—
1283C22—84no—
1284C22—84no—
1285C22—88no—
1286C22—84no—
1287C22—168no—
1288C22—168no—
1289C22#289712yes—
1290C22#289712yes—
1291C22C2×#42114yes—
1292C22C23×C22⋊C411yescharacteristic
1293C22C2×#57611yescharacteristic
1294C22C2×#57711yescharacteristic
1295C4—21no—
1296C4—21no—
1297C4—21no—
1298C4—22no—
1299C4—22no—
1300C4—22no—
1301C4—22no—
1302C4—21no—
1303C4—21no—
1304C4—21no—
1305C4—21no—
1306C4—21no—
1307C4—21no—
1308C4—21no—
1309C4—42no—
1310C4—42no—
1311C4—44no—
1312C4—42no—
1313C4—82no—
1314C4—84no—
1315C4—82no—
1316C4#288312yes—
1317C4C2×#42112yes—
1318C2—21no—
1319C2—21no—
1320C2—22no—
1321C2—22no—
1322C2—24no—
1323C2—42no—
1324C2—42no—
1325C2—42no—
1326C2—84no—
1327C2—82no—
1328C2C2×#288311yescharacteristic
1329C2C2×#289711yescharacteristic
1330C2C22×#42111yescharacteristic
subgroupG/H
center, socleC22C23×C22⋊C4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#3519C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2974C2semidirect
3. #34194C2semidirect
4. #17599C2semidirect
5. #17597C2semidirect
6. #17595C2semidirect
7. #17592C2semidirect
8. #17581C2semidirect
9. #17577C2semidirect
10. #17574C2semidirect
11. #17572C2semidirect
12. #17567C2semidirect
13. C2×#1519C2semidirect
14. #17547C2semidirect
21. #3519C4semidirect
22. #3519C4semidirect
23. #3519C4semidirect
27. C2×#555C4semidirect
28. C2×#554C4semidirect
30. C2×#553C4semidirect
31. C2×#550C4semidirect
33. C2×#546C4semidirect
35. C2×D42C4semidirect
47. #2974C22semidirect
48. #2974C22semidirect
49. #2974C22semidirect
53. C2×#432C22semidirect
54. C2×#431C22semidirect
55. C2×#407C22semidirect
56. C22×C22⋊C8C22semidirect
63. #2319C22semidirect
64. #2318C22semidirect
65. #2285C22semidirect
66. #2283C22semidirect
67. #2280C22semidirect
68. C2×#380C22semidirect
69. #2275C22semidirect
70. #1521C22semidirect
71. #1520C22semidirect
72. #1520C22semidirect
73. #1520C22semidirect
77. #1519C22semidirect
78. #1519C22semidirect
79. #1519C22semidirect
80. #1519C22semidirect
81. #1519C22semidirect
82. #1517C22semidirect
83. #1516C22semidirect
84. #1514C22semidirect
85. #1513C22semidirect
86. #1512C22semidirect
87. #1510C22semidirect
88. #1509C22semidirect
89. #1507C22semidirect
90. #1505C22semidirect
91. #1504C22semidirect
92. #1502C22semidirect
93. #1501C22semidirect
94. #1500C22semidirect
95. C2×#327C22semidirect
97. C22×#41C2×C4semidirect
100. C23×D4C2×C4semidirect
109. #555C2×C4semidirect
110. #555C2×C4semidirect
115. #554C2×C4semidirect
116. #554C2×C4semidirect
128. #553C2×C4semidirect
129. #553C2×C4semidirect
130. #553C2×C4semidirect
135. #550C2×C4semidirect
136. #550C2×C4semidirect
150. #546C2×C4semidirect
151. #546C2×C4semidirect
152. #546C2×C4semidirect
163. D42C2×C4semidirect
164. D42C2×C4semidirect
183. #532C2×C4semidirect
184. #532C2×C4semidirect
187. C2×C4⋊Q8C2×C4semidirect
189. C2×#127C2×C4semidirect
194. #529C2×C4semidirect
195. #529C2×C4semidirect
201. C2×#125C2×C4semidirect
204. C2×#124C2×C4semidirect
209. #525C2×C4semidirect
210. #525C2×C4semidirect
218. C2×C22⋊Q8C2×C4semidirect
232. C2×#121C2×C4semidirect
233. C2×#121C2×C4semidirect
234. C2×#121C2×C4semidirect
235. C2×#121C2×C4semidirect
236. C2×#121C2×C4semidirect
250. C2×C4×Q8C2×C4semidirect
265. C2×C4×D4C2×C4semidirect
266. C2×C4×D4C2×C4semidirect
283. C2×#117C2×C4semidirect
285. C22×C4⋊C4C2×C4semidirect
304. #432C23semidirect
305. #432C23semidirect
308. #431C23semidirect
309. #431C23semidirect
314. #407C23semidirect
315. #407C23semidirect
323. C2×C22⋊C8C23semidirect
324. C2×C22⋊C8C23semidirect
335. #383C23semidirect
337. #382C23semidirect
339. #381C23semidirect
347. #380C23semidirect
352. C4×C4⋊C4C23semidirect
356. C4×C22⋊C4C23semidirect
357. #376C23semidirect
358. C2×#95C23semidirect
359. #328C23semidirect
360. #328C23semidirect
361. #328C23semidirect
365. #327C23semidirect
366. #327C23semidirect
367. #327C23semidirect
368. #327C23semidirect

Maximal subgroups

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

subgroupindex
C2×#35192
C2×#29742
#341942
#175992
#175972
#175952
#175922
#175812
#175772
#175742
#175722
#175672
C2×#15192
#175472