Finite Group Databasebeta

← #6345200

Subgroups — #6345200

Order 512.

1604 conjugacy classes of subgroups.

The subgroup lattice has 869 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60954C211yesmaximal, characteristic
2#60204C211yesmaximal, characteristic, complemented
3C2×#2966C211yesmaximal, characteristic, complemented
4#17984C212yesmaximal, complemented
5#17983C212yesmaximal, complemented
6#17965C212yesmaximal, complemented
7#17964C212yesmaximal, complemented
8#17939C212yesmaximal, complemented
9#17938C212yesmaximal, complemented
10#17937C214yesmaximal, complemented
11#17911C212yesmaximal, complemented
12#17910C212yesmaximal, complemented
13#17904C214yesmaximal, complemented
14#17821C211yesmaximal, characteristic, complemented
15#17497C211yesmaximal, characteristic, complemented
16#17494C211yesmaximal, characteristic, complemented
17#17323C211yesmaximal, characteristic, complemented
18#3444C2211yescharacteristic
19C2×#529C2211yescharacteristic
20#3256C414yes—
21#3240C412yes—
22#3236C411yescharacteristic
23#3234C411yescharacteristic
24#3219C412yes—
25#3215C411yescharacteristic
26#3213C411yescharacteristic
27#3196C412yes—
28#3194C412yes—
29#3172C2212yes—
30#3171C2212yes—
31#3108C2212yes—
32#3105C2212yes—
33#3102C2214yes—
34#2966—21no—
35#2966—21no—
36#2966—21no—
37#2966—21no—
38#2966—21no—
39#2966—21no—
40#2966C2212yes—
41#2966C2212yes—
42#2966C2212yes—
43#2966C2212yes—
44#2966C2212yes—
45#2966C2212yes—
46#2965—21no—
47#2965C2212yescomplemented
48C8×#41—21no—
49C8×#41C2212yescomplemented
50#2960C2211yescharacteristic, complemented
51#2960C2211yescharacteristic, complemented
52C2×#446C2211yescharacteristic
53C2×C8×Q8C2211yescharacteristic
54#2931C2211yescharacteristic, complemented
55#2931C2211yescharacteristic, complemented
56#2929—21no—
57#2929—21no—
58C2×#436C2211yescharacteristic
59C2×#435—21no—
60C2×C8×D4—21no—
61C2×C8×D4C2211yescharacteristic
62#2922—21no—
63#2920C2211yescharacteristic
64#2920C2211yescharacteristic
65#2920C2211yescharacteristic
66C2×#433—21no—
67C2×#432C2211yescharacteristic
68C4×#131—21no—
69C2×#405—21no—
70C22×C4×C8C2211yescharacteristic
71#1594C2214yescomplemented
72#1593C2214yescomplemented
73#1592C2214yescomplemented
74#1592C2214yescomplemented
75#1588C2214yescomplemented
76#1587C2214yescomplemented
77#1586C2214yescomplemented
78#1585C2214yescomplemented
79#1584C2214yescomplemented
80#1583C2214yescomplemented
81#1582C2214yescomplemented
82#1581C2214yescomplemented
83C8×Q16C2214yescomplemented
84C8×SD16C2214yescomplemented
85C8×SD16C2214yescomplemented
86C8×D8C2214yescomplemented
87#1573C2212yes—
88#1573C2212yes—
89#1572C2214yescomplemented
90#1569C2212yescomplemented
91#1569C2212yescomplemented
92#1497C2212yescomplemented
93#1496C2212yescomplemented
94#1495C2212yes—
95#1495C2212yes—
96#1491C2212yes—
97#1490C2212yes—
98#1488C2214yescomplemented
99#1483C2212yes—
100#1483C2212yes—
101#1482C2214yes—
102#1452C2212yescomplemented
103#1451C2212yes—
104#1451C2212yescomplemented
105#1450C2212yescomplemented
106C8×M16C2212yes—
107C8×M16C2212yescomplemented
108C2×#131—21no—
109C2×#131—21no—
110C22×M16—21no—
111C23×C8—21no—
112C23×C8D411yescharacteristic
113C23×C8D411yescharacteristic
114#533C2×C411yescharacteristic
115#533C2×C411yescharacteristic
116#533C2311yescharacteristic
117#532C2×C411yescharacteristic
118#532C2×C411yescharacteristic
119#532C2311yescharacteristic
120#529—21no—
121#529—21no—
122#529—21no—
123#529—21no—
124#529—21no—
125#529—21no—
126#529—21no—
127#529—21no—
128#529C2×C412yes—
129#529C2×C412yes—
130#529C2×C412yes—
131#529C2312yes—
132#529C2312yes—
133#529C2312yes—
134C2×#126—21no—
135C2×#125C2×C411yescharacteristic
136C2×#124C2×C411yescharacteristic
137#525—21no—
138#525—21no—
139#525C2×C412yes—
140C2×#123—21no—
141C2×C22⋊Q8C2×C411yescharacteristic
142C2×#121C2×C411yescharacteristic
143C4×#41—21no—
144C4×#41—21no—
145C4×#41C2312yes—
146C2×C4×Q8C2311yescharacteristic
147C2×C4×D4—21no—
148C2×C4×D4C2311yescharacteristic
149C2×#117—21no—
150C22×C42C2311yescharacteristic
151#501C2×C412yes—
152#501C2×C412yes—
153#497C2×C412yes—
154#496C2×C412yes—
155#491C2×C412yes—
156#490C2×C412yes—
157#489C2×C412yes—
158#489C2×C412yes—
159#485C2×C414yes—
160#484C2×C412yes—
161#483C2×C412yes—
162#482C2×C414yes—
163#481C2×C412yes—
164#480C2×C412yes—
165#479C2×C414yes—
166#479C2×C414yes—
167#478C2×C414yes—
168#478C2×C414yes—
169#470C2×C414yes—
170#469C2×C414yes—
171#468C2×C414yes—
172#468C2×C414yes—
173#464C2×C414yes—
174#464C2×C414yes—
175#463C2×C414yes—
176#463C2×C414yes—
177#452C2×C414yes—
178#451C2×C412yes—
179#450C2×C412yes—
180#449C2×C414yes—
181#448C2×C412yes—
182#447C2×C412yes—
183#446—21no—
184#446—21no—
185#446—21no—
186#446—21no—
187#446C2312yes—
188#446C2312yes—
189#446C2312yes—
190#446C2312yes—
191C8×Q8—21no—
192C8×Q8—21no—
193C8×Q8—21no—
194C8×Q8—21no—
195C8×Q8C2312yes—
196C8×Q8C2312yes—
197C8×Q8C2312yes—
198C8×Q8C2312yes—
199C4×Q16C2314yes—
200C4×SD16C2314yes—
201C4×SD16C2314yes—
202C4×D8C2314yes—
203#436—21no—
204#436—21no—
205#436—21no—
206#436—21no—
207#436C2312yes—
208#436C2312yes—
209#436C2312yes—
210#436C2312yes—
211#435—22no—
212#435—22no—
213#435—22no—
214#435—22no—
215#435—22no—
216#435—22no—
217#435—22no—
218#435—22no—
219C8×D4—22no—
220C8×D4—22no—
221C8×D4—22no—
222C8×D4—22no—
223C8×D4—22no—
224C8×D4—22no—
225C8×D4—22no—
226C8×D4—22no—
227C8×D4—21no—
228C8×D4—21no—
229C8×D4—21no—
230C8×D4—21no—
231C8×D4C2312yes—
232C8×D4C2312yes—
233C8×D4C2312yes—
234C8×D4C2312yes—
235#433—22no—
236#433—22no—
237#433—22no—
238#433—22no—
239#433—22no—
240#433—22no—
241#432—21no—
242#432—21no—
243#432—21no—
244#432—21no—
245#432—21no—
246#432C2×C411yescharacteristic
247#432C2×C411yescharacteristic
248#432C2×C412yes—
249#432C2312yes—
250#432C2312yes—
251#432C2312yes—
252#431—21no—
253#431—22no—
254#431—22no—
255#431C2312yes—
256#431C2312yes—
257#431C2312yes—
258#431C2312yes—
259#431C2312yes—
260#424—21no—
261#424—21no—
262#423—21no—
263#423C2×C412yes—
264#423C2311yescharacteristic
265#423C2311yescharacteristic
266C2×C4⋊C8—21no—
267C2×C4⋊C8—21no—
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270#408—21no—
271#408—21no—
272#407—21no—
273#407—21no—
274#407C2×C412yes—
275C2×C22⋊C8—21no—
276C2×C22⋊C8—21no—
277C2×C22⋊C8—21no—
278#405—21no—
279#405—21no—
280#405—22no—
281#405—22no—
282#405—22no—
283#405—22no—
284#405—22no—
285#405—22no—
286C4×M16—21no—
287C4×M16—22no—
288C4×M16C2312yes—
289C4×M16C2312yes—
290C2×#97—21no—
291C2×#97—21no—
292C2×C4×C8—21no—
293C2×C4×C8—22no—
294C2×C4×C8D411yescharacteristic
295C2×C4×C8D411yescharacteristic
296C2×C4×C8D411yescharacteristic
297C2×C4×C8D411yescharacteristic
298C2×C4×C8D411yescharacteristic
299C2×C4×C8D411yescharacteristic
300C2×C4×C8C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302C2×C4×C8C2311yescharacteristic
303C2×C4×C8C2311yescharacteristic
304C2×C4×C8C2311yescharacteristic
305C2×C4×C8C2311yescharacteristic
306#335C2314yes—
307#335C2314yes—
308#334C2314yes—
309#334C2314yes—
310Q8⋊C8C2314yes—
311Q8⋊C8C2314yes—
312Q8⋊C8C2314yes—
313Q8⋊C8C2314yes—
314D4⋊C8C2314yes—
315D4⋊C8C2314yes—
316D4⋊C8C2314yes—
317D4⋊C8C2314yes—
318#322C2314yes—
319#322C2314yes—
320#322C2314yes—
321C82C2314yes—
322C2×#41—21no—
323C2×#41—21no—
324C2×#41C22×C412yes—
325C22×Q8C22×C411yescharacteristic
326C22×D4—21no—
327C22×D4C22×C411yescharacteristic
328C23×C4—21no—
329C23×C4C22×C411yescharacteristic
330C23×C4C2×D411yescharacteristic
331C23×C4#4111yescharacteristic
332C2×Q16C22×C414yes—
333C2×SD16C22×C414yes—
334C2×SD16C22×C414yes—
335C2×D8C22×C414yes—
336#131—44no—
337#131—44no—
338C2×M16—21no—
339C2×M16—21no—
340C2×M16—22no—
341C2×M16—22no—
342C2×M16—22no—
343C2×M16—22no—
344C2×M16—22no—
345C2×M16—44no—
346C2×M16C22×C414yes—
347C22×C8—21no—
348C22×C8—21no—
349C22×C8—22no—
350C22×C8—22no—
351C22×C8—22no—
352C22×C8—22no—
353C22×C8—42no—
354C22×C8—42no—
355C22×C8—44no—
356C22×C8C2×D411yescharacteristic
357C22×C8C2×D411yescharacteristic
358C22×C8C2×D411yescharacteristic
359C22×C8C2×D411yescharacteristic
360C22×C8C2×D411yescharacteristic
361C22×C8C2×D411yescharacteristic
362C22×C8C2×D411yescharacteristic
363C22×C8C2×D411yescharacteristic
364C22×C8C2×D411yescharacteristic
365C22×C8C2×D411yescharacteristic
366C22×C8C2×D411yescharacteristic
367C22×C8C2×D411yescharacteristic
368C4⋊Q8C22×C411yescharacteristic
369C4⋊Q8C22×C411yescharacteristic
370C4⋊Q8C22×C411yescharacteristic
371#127C22×C411yescharacteristic
372#126—22no—
373#126—22no—
374#126—22no—
375#126—22no—
376#126—22no—
377#126—22no—
378#125—21no—
379#125—21no—
380#125—21no—
381#125—21no—
382#125C22×C412yes—
383#125C22×C412yes—
384#125C22×C412yes—
385#124—21no—
386#124—21no—
387#124—21no—
388#124—21no—
389#124C22×C412yes—
390#124C22×C412yes—
391#124C22×C412yes—
392#123—22no—
393#123—22no—
394#123—22no—
395#123—22no—
396#123—22no—
397#123—22no—
398#123—22no—
399C22⋊Q8—21no—
400C22⋊Q8—21no—
401C22⋊Q8—21no—
402C22⋊Q8—21no—
403C22⋊Q8—21no—
404C22⋊Q8—21no—
405C22⋊Q8C22×C412yes—
406C22⋊Q8C22×C412yes—
407C22⋊Q8C22×C412yes—
408C22⋊Q8C22×C412yes—
409#121—21no—
410#121—21no—
411#121—21no—
412#121—21no—
413#121—21no—
414#121—21no—
415#121C22×C412yes—
416#121C22×C412yes—
417#121C22×C412yes—
418#121C22×C412yes—
419#120—22no—
420C4×Q8—21no—
421C4×Q8—21no—
422C4×Q8—21no—
423C4×Q8—21no—
424C4×Q8—21no—
425C4×Q8—21no—
426C4×Q8C22×C412yes—
427C4×Q8C22×C412yes—
428C4×Q8C2412yes—
429C4×Q8C2412yes—
430C4×D4—22no—
431C4×D4—22no—
432C4×D4—22no—
433C4×D4—22no—
434C4×D4—22no—
435C4×D4—22no—
436C4×D4—22no—
437C4×D4—22no—
438C4×D4—22no—
439C4×D4—22no—
440C4×D4—21no—
441C4×D4—21no—
442C4×D4—21no—
443C4×D4—21no—
444C4×D4—21no—
445C4×D4—21no—
446C4×D4C22×C412yes—
447C4×D4C22×C412yes—
448C4×D4C2412yes—
449C4×D4C2412yes—
450#117—21no—
451#117—21no—
452#117—22no—
453#117—22no—
454#117—22no—
455#117—22no—
456#117—22no—
457#117—22no—
458#117—22no—
459#117C22×C412yes—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4C22×C411yescharacteristic
465C2×C4⋊C4C22×C411yescharacteristic
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C42—21no—
472C2×C42—22no—
473C2×C42C22×C411yescharacteristic
474C2×C42C22×C411yescharacteristic
475C2×C42C22×C411yescharacteristic
476C2×C42C2×D411yescharacteristic
477C2×C42C2×D411yescharacteristic
478C2×C42C2×D411yescharacteristic
479C2×C42#4111yescharacteristic
480C2×C42#4111yescharacteristic
481C2×C42#4111yescharacteristic
482C2×C42C2411yescharacteristic
483C2×C42C2411yescharacteristic
484C2×C42C2411yescharacteristic
485#107C22×C414yes—
486#107C22×C414yes—
487#106C22×C414yes—
488#106C22×C414yes—
489C4⋊C8—22no—
490C4⋊C8—22no—
491C4⋊C8—22no—
492C4⋊C8—22no—
493C4⋊C8—22no—
494C4⋊C8—22no—
495C4⋊C8—22no—
496C4⋊C8—22no—
497C4⋊C8—21no—
498C4⋊C8—21no—
499C4⋊C8—21no—
500C4⋊C8—21no—
501C4⋊C8—22no—
502C4⋊C8—22no—
503C4⋊C8C22×C412yes—
504C4⋊C8C22×C414yes—
505C4⋊C8C22×C412yes—
506C4⋊C8C2412yes—
507C4⋊C8C2412yes—
508C4⋊C8C2412yes—
509C4⋊C8C2412yes—
510#103C22×C414yes—
511#103C22×C414yes—
512#103C22×C414yes—
513#103C22×C414yes—
514#102C22×C414yes—
515#102C22×C414yes—
516#102C22×C414yes—
517#102C22×C414yes—
518C22⋊C8—22no—
519C22⋊C8—22no—
520C22⋊C8—22no—
521C22⋊C8—22no—
522C22⋊C8—22no—
523C22⋊C8—22no—
524C22⋊C8—22no—
525C22⋊C8—22no—
526C22⋊C8—22no—
527C22⋊C8—22no—
528C22⋊C8—22no—
529C22⋊C8—22no—
530C22⋊C8—22no—
531C22⋊C8—22no—
532C22⋊C8C22×C412yes—
533C22⋊C8C22×C414yes—
534C22⋊C8C22×C412yes—
535#97—22no—
536#97—22no—
537#97—22no—
538#97—22no—
539#97—22no—
540#97—22no—
541#97—22no—
542#97—22no—
543#97C22×C412yes—
544#97C22×C412yes—
545C4×C8—22no—
546C4×C8—22no—
547C4×C8—22no—
548C4×C8—22no—
549C4×C8—22no—
550C4×C8C2×D411yescharacteristic
551C4×C8C2×D411yescharacteristic
552C4×C8C2×D411yescharacteristic
553C4×C8C2×D411yescharacteristic
554C4×C8C2×D411yescharacteristic
555C4×C8C2×D411yescharacteristic
556C4×C8C2×D411yescharacteristic
557C4×C8C2×D411yescharacteristic
558C4×C8C2×D411yescharacteristic
559C4×C8C2×D411yescharacteristic
560C4×C8C2×D411yescharacteristic
561C4×C8C2×D411yescharacteristic
562C4×C8C2414yes—
563C4×C8C2414yes—
564C4×C8C2411yescharacteristic
565C4×C8C2411yescharacteristic
566C4×C8C2411yescharacteristic
567C4×C8C2411yescharacteristic
568C24—21no—
569C24C4×D411yescharacteristic
570#41—44no—
571#41—42no—
572#41—42no—
573#41—44no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—42no—
578C2×Q8C23×C412yes—
579C2×Q8C23×C412yes—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—42no—
589C2×D4—44no—
590C2×D4C23×C412yes—
591C2×D4C23×C412yes—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4C4×D411yescharacteristic
607C22×C4C4×D411yescharacteristic
608C22×C4C4×D411yescharacteristic
609C22×C4C4×D411yescharacteristic
610C22×C4C4×D411yescharacteristic
611C22×C4C4×D411yescharacteristic
612C22×C4C4×D411yescharacteristic
613C22×C4C4×D411yescharacteristic
614C22×C4C4×D411yescharacteristic
615C22×C4C23×C411yescharacteristic
616C22×C4C23×C411yescharacteristic
617C22×C4C23×C411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D411yescharacteristic
620C22×C4C22×D411yescharacteristic
621C22×C4C2×#4111yescharacteristic
622C22×C4C2×#4111yescharacteristic
623C22×C4C2×#4111yescharacteristic
624Q16—44no—
625SD16—44no—
626SD16—44no—
627D8—44no—
628M16—44no—
629M16—44no—
630M16—44no—
631M16—44no—
632M16—44no—
633M16—42no—
634M16—42no—
635M16—44no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—24no—
647C2×C8—41no—
648C2×C8—41no—
649C2×C8—41no—
650C2×C8—41no—
651C2×C8—41no—
652C2×C8—41no—
653C2×C8—44no—
654C2×C8—42no—
655C2×C8—42no—
656C2×C8—44no—
657C2×C8—44no—
658C2×C8—44no—
659C2×C8C23×C414yes—
660C2×C8C23×C414yes—
661C2×C8C22×D411yescharacteristic
662C2×C8C22×D411yescharacteristic
663C2×C8C22×D411yescharacteristic
664C2×C8C22×D411yescharacteristic
665C2×C8C22×D411yescharacteristic
666C2×C8C22×D411yescharacteristic
667C2×C8C22×D411yescharacteristic
668C2×C8C22×D411yescharacteristic
669C4⋊C4—22no—
670C4⋊C4—22no—
671C4⋊C4—22no—
672C4⋊C4—22no—
673C4⋊C4—22no—
674C4⋊C4—22no—
675C4⋊C4—22no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—22no—
683C4⋊C4—22no—
684C4⋊C4—22no—
685C4⋊C4—22no—
686C4⋊C4—22no—
687C4⋊C4—22no—
688C4⋊C4—22no—
689C4⋊C4C23×C412yes—
690C4⋊C4C23×C412yes—
691C4⋊C4C23×C412yes—
692C4⋊C4C23×C412yes—
693C22⋊C4—22no—
694C22⋊C4—22no—
695C22⋊C4—22no—
696C22⋊C4—22no—
697C22⋊C4—22no—
698C22⋊C4—22no—
699C22⋊C4—22no—
700C22⋊C4—22no—
701C22⋊C4—22no—
702C22⋊C4—22no—
703C22⋊C4—22no—
704C22⋊C4—22no—
705C22⋊C4—22no—
706C22⋊C4—22no—
707C22⋊C4—22no—
708C22⋊C4—22no—
709C22⋊C4—22no—
710C22⋊C4—22no—
711C22⋊C4—22no—
712C42—22no—
713C42—22no—
714C42—22no—
715C42—22no—
716C42—22no—
717C42C4×D411yescharacteristic
718C42C4×D411yescharacteristic
719C42C4×D411yescharacteristic
720C42C4×D411yescharacteristic
721C42C4×D411yescharacteristic
722C42C4×D411yescharacteristic
723C42C23×C411yescharacteristic
724C42C23×C411yescharacteristic
725C42C23×C411yescharacteristic
726C42C22×D411yescharacteristic
727C42C22×D411yescharacteristic
728C42C22×D411yescharacteristic
729C42C2×#4111yescharacteristic
730C42C2×#4111yescharacteristic
731C42C2×#4111yescharacteristic
732C42C2511yescharacteristic
733C23—22no—
734C23—22no—
735C23—22no—
736C23—41no—
737C23—41no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23C2×C4×D411yescharacteristic
742C23C2×C4×D411yescharacteristic
743C23C2×C4×D411yescharacteristic
744Q8—24no—
745Q8—24no—
746Q8—42no—
747Q8—42no—
748Q8—42no—
749D4—24no—
750D4—24no—
751D4—42no—
752D4—42no—
753D4—42no—
754D4—44no—
755D4—44no—
756D4—44no—
757D4—44no—
758D4—44no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4C2×C4×D411yescharacteristic
797C2×C4C2×C4×D411yescharacteristic
798C2×C4C2×C4×D411yescharacteristic
799C2×C4C2×C4×D411yescharacteristic
800C2×C4C2×C4×D411yescharacteristic
801C2×C4C2×C4×D411yescharacteristic
802C2×C4C2×C4×D411yescharacteristic
803C2×C4C2×C4×D411yescharacteristic
804C2×C4C2×C4×D411yescharacteristic
805C2×C4C24×C411yescharacteristic
806C2×C4C23×D411yescharacteristic
807C2×C4C22×#4111yescharacteristic
808C8—24no—
809C8—24no—
810C8—21no—
811C8—21no—
812C8—21no—
813C8—21no—
814C8—21no—
815C8—21no—
816C8—44no—
817C8—42no—
818C8—42no—
819C8—42no—
820C8—42no—
821C8#57512yes—
822C8#57512yes—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—21no—
829C22—21no—
830C22—21no—
831C22—44no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—84no—
839C22#295512yes—
840C22C22×C4×D411yescharacteristic
841C4—21no—
842C4—21no—
843C4—21no—
844C4—21no—
845C4—21no—
846C4—21no—
847C4—21no—
848C4—21no—
849C4—21no—
850C4—21no—
851C4—42no—
852C4—42no—
853C4—42no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4#357312yes—
858C4C2×#57511yescharacteristic
859C4C2×#57511yescharacteristic
860C2—22no—
861C2—41no—
862C2—41no—
863C2—82no—
864C2—82no—
865C2#6014011yescharacteristic
866C2C4×#57511yescharacteristic
867C2C2×#295511yescharacteristic
subgroupG/H
centerC2×C8C22×D4
commutatorC2×C4C24×C4
Frattini, cosocleC42C25
socleC22C22×C4×D4
prime radical#60954C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C8 ◁ C22×C4×C8 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60204C2semidirect
3. C2×#2966C2semidirect
4. #17984C2semidirect
5. #17983C2semidirect
6. #17965C2semidirect
7. #17964C2semidirect
8. #17939C2semidirect
9. #17938C2semidirect
10. #17937C2semidirect
11. #17911C2semidirect
12. #17910C2semidirect
13. #17904C2semidirect
14. #17821C2semidirect
15. #17497C2semidirect
16. #17494C2semidirect
17. #17323C2semidirect
47. #2965C22semidirect
49. C8×#41C22semidirect
50. #2960C22semidirect
51. #2960C22semidirect
54. #2931C22semidirect
55. #2931C22semidirect
71. #1594C22semidirect
72. #1593C22semidirect
73. #1592C22semidirect
74. #1592C22semidirect
75. #1588C22semidirect
76. #1587C22semidirect
77. #1586C22semidirect
78. #1585C22semidirect
79. #1584C22semidirect
80. #1583C22semidirect
81. #1582C22semidirect
82. #1581C22semidirect
83. C8×Q16C22semidirect
84. C8×SD16C22semidirect
85. C8×SD16C22semidirect
86. C8×D8C22semidirect
89. #1572C22semidirect
90. #1569C22semidirect
91. #1569C22semidirect
92. #1497C22semidirect
93. #1496C22semidirect
98. #1488C22semidirect
102. #1452C22semidirect
104. #1451C22semidirect
105. #1450C22semidirect
107. C8×M16C22semidirect

Maximal subgroups

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

subgroupindex
#609542
#602042
C2×#29662
#179842
#179832
#179652
#179642
#179392
#179382
#179372
#179112
#179102
#179042
#178212
#174972
#174942
#173232