Finite Group Databasebeta

← #6345210

Subgroups — #6345210

Order 512.

1525 conjugacy classes of subgroups.

The subgroup lattice has 865 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60950C211yesmaximal, characteristic
2C2×#2993C211yesmaximal, characteristic
3#60250C211yesmaximal, characteristic, complemented
4#17988C214yesmaximal, complemented
5#17969C214yesmaximal, complemented
6#17947C214yesmaximal, complemented
7#17934C211yesmaximal, characteristic, complemented
8#17933C211yesmaximal, characteristic, complemented
9#17931C211yesmaximal, characteristic, complemented
10#17930C211yesmaximal, characteristic, complemented
11#17919C214yesmaximal, complemented
12#17906C211yesmaximal, characteristic, complemented
13#17905C211yesmaximal, characteristic, complemented
14#17903C211yesmaximal, characteristic, complemented
15#17902C211yesmaximal, characteristic, complemented
16#17820C211yesmaximal, characteristic, complemented
17#17487C211yesmaximal, characteristic
18#17486C211yesmaximal, characteristic, complemented
19#17326C211yesmaximal, characteristic, complemented
20C2×#533C2211yescharacteristic
21C2×#529C2211yescharacteristic
22#3252C412yes—
23#3252C412yes—
24#3238C412yes—
25#3236C412yes—
26#3218C412yes—
27#3215C412yes—
28#3195C412yes—
29#3193C412yes—
30#3172C2214yes—
31#3108C2214yes—
32#3104C2211yescharacteristic
33#3104C2211yescharacteristic
34#3101C2211yescharacteristic
35#3101C2211yescharacteristic
36#2993—21no—
37#2993—21no—
38#2993—21no—
39#2993—21no—
40#2993C2212yes—
41#2993C2212yes—
42#2993C2212yes—
43#2993C2212yes—
44#2986—21no—
45#2986—21no—
46#2985C2212yescomplemented
47#2985C2212yescomplemented
48#2984—21no—
49#2984—21no—
50#2983C2212yescomplemented
51#2982C2212yescomplemented
52#2962—21no—
53#2962—21no—
54#2960C2211yescharacteristic
55#2960C2211yescharacteristic
56#2960C2211yescharacteristic
57#2960C2211yescharacteristic
58C2×#446C2211yescharacteristic
59C2×C8×Q8C2211yescharacteristic
60C2×#436—21no—
61C2×#436C2211yescharacteristic
62C2×#435—21no—
63C2×C8×D4C2211yescharacteristic
64#2924—21no—
65#2924—21no—
66#2920C2211yescharacteristic
67#2920C2211yescharacteristic
68C2×#433—21no—
69C2×#431C2211yescharacteristic
70C2×#431C2211yescharacteristic
71C2×#424—21no—
72C2×#423C2211yescharacteristic
73#1593C2214yescomplemented
74#1592C2214yescomplemented
75#1591C2214yescomplemented
76#1590C2214yescomplemented
77#1588C2214yescomplemented
78#1587C2214yescomplemented
79#1587C2214yescomplemented
80#1585C2214yescomplemented
81#1584C2214yescomplemented
82#1584C2214yescomplemented
83#1583C2214yescomplemented
84#1582C2214yescomplemented
85#1579C2214yescomplemented
86SD16⋊C8C2214yescomplemented
87C8×Q16C2214yescomplemented
88C8×SD16C2214yescomplemented
89#1574C2214yescomplemented
90#1571C2211yescharacteristic
91#1571C2211yescharacteristic
92#1570C2211yescharacteristic
93#1570C2211yescharacteristic
94#1569C2214yescomplemented
95#1494C2214yes—
96#1493C2214yescomplemented
97#1487C2211yescharacteristic
98#1487C2211yescharacteristic
99#1487C2214yescomplemented
100#1486C2211yescharacteristic
101#1486C2211yescharacteristic
102#1482C2214yes—
103#1481C2211yescharacteristic
104#1481C2211yescharacteristic
105#1481C2211yescharacteristic
106#1481C2211yescharacteristic
107#1454C2212yescomplemented
108#1454C2212yescomplemented
109#1452C2211yescharacteristic
110#1452C2211yescharacteristic
111#1451C2212yescomplemented
112#1450C2211yescharacteristic
113#1450C2211yescharacteristic
114C8×M16C2212yescomplemented
115C22×M16—21no—
116C22×M16—21no—
117C23×C8—21no—
118#533—21no—
119#533—21no—
120#533—21no—
121#533—21no—
122#533C2×C412yes—
123#533C2×C411yescharacteristic
124#533C2×C411yescharacteristic
125#533C2311yescharacteristic
126#533C2311yescharacteristic
127#533C2312yes—
128C2×C4⋊Q8C2×C411yescharacteristic
129C2×C4⋊Q8C2×C411yescharacteristic
130#529—21no—
131#529—21no—
132#529—21no—
133#529—21no—
134#529C2×C412yes—
135#529C2×C412yes—
136#529C2312yes—
137#529C2312yes—
138C2×#126—21no—
139C2×#125—21no—
140C2×#125C2×C411yescharacteristic
141C2×#124C2×C411yescharacteristic
142C2×#123—21no—
143C2×C22⋊Q8—21no—
144C2×C22⋊Q8C2×C411yescharacteristic
145C2×C22⋊Q8C2×C412yes—
146C2×#121C2×C411yescharacteristic
147C2×C4×Q8—21no—
148C2×C4×Q8C2311yescharacteristic
149C2×C4×Q8C2312yes—
150C2×C4×D4—21no—
151C2×C4×D4C2311yescharacteristic
152C2×#117—21no—
153C2×#117—21no—
154C22×C42C2311yescharacteristic
155#501C2×C414yes—
156#497C2×C414yes—
157#491C2×C414yes—
158#489C2×C414yes—
159#484C2×C412yes—
160#484C2×C412yes—
161#483C2×C412yes—
162#483C2×C412yes—
163#483C2×C414yes—
164#480C2×C414yes—
165#479C2×C414yes—
166#479C2×C414yes—
167#477C2×C412yes—
168#477C2×C412yes—
169#476C2×C412yes—
170#476C2×C412yes—
171#470C2×C414yes—
172#470C2×C414yes—
173#468C2×C414yes—
174#468C2×C414yes—
175#464C2×C414yes—
176#464C2×C414yes—
177#462C2×C412yes—
178#462C2×C412yes—
179#461C2×C412yes—
180#461C2×C412yes—
181#451C2×C412yes—
182#451C2×C412yes—
183#451C2×C414yes—
184#450C2×C412yes—
185#450C2×C412yes—
186#448C2×C414yes—
187#446—22no—
188#446—22no—
189#446—22no—
190#446—22no—
191#446—22no—
192#446—22no—
193#446—21no—
194#446—21no—
195#446—21no—
196#446—21no—
197#446—21no—
198#446—21no—
199#446C2312yes—
200#446C2312yes—
201#446C2312yes—
202#446C2312yes—
203#446C2312yes—
204#446C2312yes—
205C8×Q8—22no—
206C8×Q8—22no—
207C8×Q8—21no—
208C8×Q8—21no—
209C8×Q8—21no—
210C8×Q8—21no—
211C8×Q8—21no—
212C8×Q8—21no—
213C8×Q8C2312yes—
214C8×Q8C2312yes—
215C8×Q8C2312yes—
216C8×Q8C2312yes—
217C8×Q8C2312yes—
218C8×Q8C2312yes—
219C4×Q16C2314yes—
220C4×Q16C2314yes—
221C4×SD16C2314yes—
222C4×SD16C2314yes—
223#436—22no—
224#436—22no—
225#436—22no—
226#436—22no—
227#436—21no—
228#436—21no—
229#436C2312yes—
230#436C2312yes—
231#435—22no—
232#435—22no—
233#435—22no—
234#435—22no—
235C8×D4—21no—
236C8×D4—21no—
237C8×D4C2312yes—
238C8×D4C2312yes—
239#433—22no—
240#433—22no—
241#433—22no—
242#433—22no—
243#433—22no—
244#433—22no—
245#433—22no—
246#433—22no—
247#432—21no—
248#432—22no—
249#432—22no—
250#432C2×C412yes—
251#432C2×C412yes—
252#432C2312yes—
253#431—21no—
254#431—21no—
255#431—21no—
256#431—22no—
257#431—22no—
258#431D411yescharacteristic
259#431D411yescharacteristic
260#431D411yescharacteristic
261#431D411yescharacteristic
262#431C2312yes—
263#431C2311yescharacteristic
264#431C2311yescharacteristic
265#431C2312yes—
266#431C2311yescharacteristic
267#431C2311yescharacteristic
268#431C2312yes—
269#431C2311yescharacteristic
270#431C2311yescharacteristic
271#431C2311yescharacteristic
272#431C2311yescharacteristic
273#424—21no—
274#424—21no—
275#424—21no—
276#424—21no—
277#424—22no—
278#424—22no—
279#424—22no—
280#424—22no—
281#423—21no—
282#423—21no—
283#423C2×C412yes—
284#423C2312yes—
285#423C2311yescharacteristic
286#423C2311yescharacteristic
287#423C2312yes—
288C2×C4⋊C8—21no—
289C2×C4⋊C8—21no—
290C2×C4⋊C8—21no—
291C2×C4⋊C8—21no—
292C2×C4⋊C8D411yescharacteristic
293C2×C4⋊C8D411yescharacteristic
294C2×C4⋊C8C2311yescharacteristic
295C2×C4⋊C8C2311yescharacteristic
296#407—21no—
297#407C2×C412yes—
298C2×C22⋊C8—21no—
299C2×C22⋊C8—21no—
300C2×C22⋊C8—21no—
301C2×C22⋊C8D411yescharacteristic
302C2×C22⋊C8D411yescharacteristic
303#405—21no—
304#405—21no—
305#405—21no—
306#405—21no—
307C4×M16—21no—
308C4×M16C2312yes—
309C2×#97—21no—
310C2×C4×C8—21no—
311C2×C4×C8C2312yes—
312C2×C4×C8C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314#335C2314yes—
315#335C2314yes—
316#334C2314yes—
317#334C2314yes—
318Q8⋊C8C2314yes—
319Q8⋊C8C2314yes—
320Q8⋊C8C2314yes—
321Q8⋊C8C2314yes—
322Q8⋊C8C2314yes—
323Q8⋊C8C2314yes—
324D4⋊C8C2314yes—
325D4⋊C8C2314yes—
326#322C2312yes—
327#322C2312yes—
328#322C2312yes—
329#322C2312yes—
330#322C2312yes—
331#322C2312yes—
332C82C2312yes—
333C82C2312yes—
334C22×Q8—21no—
335C22×Q8C22×C411yescharacteristic
336C22×Q8C22×C412yes—
337C22×D4—21no—
338C22×D4C22×C411yescharacteristic
339C23×C4—21no—
340C23×C4C22×C411yescharacteristic
341C23×C4C2×D411yescharacteristic
342C23×C4#4111yescharacteristic
343C2×Q16C22×C414yes—
344C2×Q16C22×C414yes—
345C2×SD16C22×C414yes—
346C2×SD16C22×C414yes—
347C2×M16—21no—
348C2×M16—21no—
349C2×M16—22no—
350C2×M16—22no—
351C2×M16—22no—
352C2×M16—22no—
353C2×M16—82no—
354C2×M16—82no—
355C2×M16C22×C414yes—
356C22×C8—21no—
357C22×C8—21no—
358C22×C8—22no—
359C22×C8—22no—
360C22×C8—22no—
361C22×C8—82no—
362C22×C8C2×D411yescharacteristic
363C22×C8C2×D411yescharacteristic
364C22×C8C2×D411yescharacteristic
365C22×C8C2×D411yescharacteristic
366C4⋊Q8—21no—
367C4⋊Q8—21no—
368C4⋊Q8—21no—
369C4⋊Q8—21no—
370C4⋊Q8C22×C411yescharacteristic
371C4⋊Q8C22×C411yescharacteristic
372C4⋊Q8C22×C412yes—
373C4⋊Q8C22×C411yescharacteristic
374C4⋊Q8C22×C411yescharacteristic
375C4⋊Q8C22×C412yes—
376#126—22no—
377#126—22no—
378#126—22no—
379#126—22no—
380#125—21no—
381#125—21no—
382#125—22no—
383#125—21no—
384#125—21no—
385#125—22no—
386#125—21no—
387#125—21no—
388#125C22×C412yes—
389#125C22×C412yes—
390#124—21no—
391#124—21no—
392#124C22×C412yes—
393#124C22×C412yes—
394#123—22no—
395#123—22no—
396#123—22no—
397#123—22no—
398C22⋊Q8—22no—
399C22⋊Q8—21no—
400C22⋊Q8—21no—
401C22⋊Q8—21no—
402C22⋊Q8—21no—
403C22⋊Q8—22no—
404C22⋊Q8—22no—
405C22⋊Q8—21no—
406C22⋊Q8—21no—
407C22⋊Q8—22no—
408C22⋊Q8C22×C412yes—
409C22⋊Q8C22×C412yes—
410C22⋊Q8C22×C412yes—
411C22⋊Q8C22×C412yes—
412C22⋊Q8C22×C412yes—
413C22⋊Q8C22×C412yes—
414#121—21no—
415#121—21no—
416#121C22×C412yes—
417#121C22×C412yes—
418C4×Q8—22no—
419C4×Q8—21no—
420C4×Q8—21no—
421C4×Q8—21no—
422C4×Q8—21no—
423C4×Q8—22no—
424C4×Q8—21no—
425C4×Q8—22no—
426C4×Q8—21no—
427C4×Q8—22no—
428C4×Q8C22×C412yes—
429C4×Q8C22×C412yes—
430C4×Q8C22×C412yes—
431C4×Q8C2412yes—
432C4×Q8C2412yes—
433C4×Q8C2412yes—
434C4×D4—22no—
435C4×D4—22no—
436C4×D4—22no—
437C4×D4—22no—
438C4×D4—21no—
439C4×D4—21no—
440C4×D4C22×C412yes—
441C4×D4C2412yes—
442#117—22no—
443#117—21no—
444#117—21no—
445#117—21no—
446#117—21no—
447#117—22no—
448#117—22no—
449#117—22no—
450#117—22no—
451#117—22no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4C22×C411yescharacteristic
462C2×C4⋊C4C22×C411yescharacteristic
463C2×C4⋊C4C22×C412yes—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C42—21no—
471C2×C42—22no—
472C2×C42C22×C411yescharacteristic
473C2×C42C22×C411yescharacteristic
474C2×C42C22×C411yescharacteristic
475C2×C42C2×D411yescharacteristic
476C2×C42C2×D411yescharacteristic
477C2×C42C2×D411yescharacteristic
478C2×C42#4111yescharacteristic
479C2×C42#4111yescharacteristic
480C2×C42#4111yescharacteristic
481C2×C42C2411yescharacteristic
482C2×C42C2411yescharacteristic
483C2×C42C2411yescharacteristic
484#107C22×C414yes—
485#107C22×C414yes—
486#106C22×C414yes—
487#106C22×C414yes—
488C4⋊C8—22no—
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—22no—
498C4⋊C8—22no—
499C4⋊C8—22no—
500C4⋊C8—22no—
501C4⋊C8—22no—
502C4⋊C8—21no—
503C4⋊C8—21no—
504C4⋊C8—21no—
505C4⋊C8—21no—
506C4⋊C8—21no—
507C4⋊C8—21no—
508C4⋊C8—22no—
509C4⋊C8C22×C412yes—
510C4⋊C8C22×C412yes—
511C4⋊C8C22×C414yes—
512C4⋊C8C2×D411yescharacteristic
513C4⋊C8C2×D411yescharacteristic
514C4⋊C8C2×D411yescharacteristic
515C4⋊C8C2×D411yescharacteristic
516C4⋊C8C2×D411yescharacteristic
517C4⋊C8C2×D411yescharacteristic
518C4⋊C8C2×D411yescharacteristic
519C4⋊C8C2×D411yescharacteristic
520C4⋊C8C2412yes—
521C4⋊C8C2412yes—
522C4⋊C8C2412yes—
523C4⋊C8C2412yes—
524#103C22×C414yes—
525#103C22×C414yes—
526#103C22×C414yes—
527#103C22×C414yes—
528#103C22×C414yes—
529#103C22×C414yes—
530#102C22×C414yes—
531#102C22×C414yes—
532C22⋊C8—22no—
533C22⋊C8—22no—
534C22⋊C8—21no—
535C22⋊C8—21no—
536C22⋊C8—22no—
537C22⋊C8—22no—
538C22⋊C8—22no—
539C22⋊C8—22no—
540C22⋊C8—22no—
541C22⋊C8C22×C414yes—
542C22⋊C8C22×C412yes—
543C22⋊C8C22×C412yes—
544C22⋊C8C2×D411yescharacteristic
545C22⋊C8C2×D411yescharacteristic
546C22⋊C8C2×D411yescharacteristic
547C22⋊C8C2×D411yescharacteristic
548C22⋊C8C2×D411yescharacteristic
549C22⋊C8C2×D411yescharacteristic
550C22⋊C8C2×D411yescharacteristic
551C22⋊C8C2×D411yescharacteristic
552#97—22no—
553#97—22no—
554#97—22no—
555#97—22no—
556#97—22no—
557#97—22no—
558#97—22no—
559#97C22×C414yes—
560C4×C8—22no—
561C4×C8—22no—
562C4×C8—22no—
563C4×C8—22no—
564C4×C8—22no—
565C4×C8—22no—
566C4×C8—22no—
567C4×C8—22no—
568C4×C8C2×D411yescharacteristic
569C4×C8C2×D411yescharacteristic
570C4×C8C2×D411yescharacteristic
571C4×C8C2×D411yescharacteristic
572C4×C8C2412yes—
573C4×C8C2412yes—
574C4×C8C2412yes—
575C4×C8C2412yes—
576C4×C8C2411yescharacteristic
577C4×C8C2411yescharacteristic
578C4×C8C2411yescharacteristic
579C4×C8C2411yescharacteristic
580C24—21no—
581C24C4×D411yescharacteristic
582C2×Q8—21no—
583C2×Q8—22no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—22no—
587C2×Q8—42no—
588C2×Q8—44no—
589C2×Q8—82no—
590C2×Q8C23×C412yes—
591C2×Q8C23×C412yes—
592C2×Q8C23×C412yes—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—21no—
596C2×D4—42no—
597C2×D4—82no—
598C2×D4C23×C412yes—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—22no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—81no—
612C22×C4C4×D411yescharacteristic
613C22×C4C4×D411yescharacteristic
614C22×C4C4×D411yescharacteristic
615C22×C4C4×D411yescharacteristic
616C22×C4C4×D411yescharacteristic
617C22×C4C4×D411yescharacteristic
618C22×C4C4×D411yescharacteristic
619C22×C4C4×D411yescharacteristic
620C22×C4C4×D411yescharacteristic
621C22×C4C23×C411yescharacteristic
622C22×C4C23×C411yescharacteristic
623C22×C4C23×C411yescharacteristic
624C22×C4C22×D411yescharacteristic
625C22×C4C22×D411yescharacteristic
626C22×C4C22×D411yescharacteristic
627C22×C4C2×#4111yescharacteristic
628C22×C4C2×#4111yescharacteristic
629C22×C4C2×#4111yescharacteristic
630Q16—44no—
631Q16—44no—
632SD16—44no—
633SD16—44no—
634M16—44no—
635M16—42no—
636M16—42no—
637M16—82no—
638M16—82no—
639M16—82no—
640M16—82no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—22no—
647C2×C8—22no—
648C2×C8—22no—
649C2×C8—22no—
650C2×C8—22no—
651C2×C8—42no—
652C2×C8—42no—
653C2×C8—82no—
654C2×C8—82no—
655C2×C8—82no—
656C2×C8C23×C414yes—
657C2×C8C23×C414yes—
658C2×C8C22×D411yescharacteristic
659C2×C8C22×D411yescharacteristic
660C2×C8C22×D411yescharacteristic
661C2×C8C22×D411yescharacteristic
662C2×C8C22×D411yescharacteristic
663C2×C8C22×D411yescharacteristic
664C2×C8C22×D411yescharacteristic
665C2×C8C22×D411yescharacteristic
666C4⋊C4—22no—
667C4⋊C4—22no—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—22no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—22no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—22no—
677C4⋊C4—22no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—22no—
681C4⋊C4—22no—
682C4⋊C4—22no—
683C4⋊C4—22no—
684C4⋊C4—22no—
685C4⋊C4—22no—
686C4⋊C4—22no—
687C4⋊C4—22no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—22no—
691C4⋊C4—22no—
692C4⋊C4—22no—
693C4⋊C4—22no—
694C4⋊C4C23×C412yes—
695C4⋊C4C23×C412yes—
696C4⋊C4C23×C412yes—
697C4⋊C4C23×C412yes—
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—
717C42—22no—
718C42C4×D411yescharacteristic
719C42C4×D411yescharacteristic
720C42C4×D411yescharacteristic
721C42C4×D411yescharacteristic
722C42C4×D411yescharacteristic
723C42C4×D411yescharacteristic
724C42C23×C411yescharacteristic
725C42C23×C411yescharacteristic
726C42C23×C411yescharacteristic
727C42C22×D411yescharacteristic
728C42C22×D411yescharacteristic
729C42C22×D411yescharacteristic
730C42C2×#4111yescharacteristic
731C42C2×#4111yescharacteristic
732C42C2×#4111yescharacteristic
733C42C2511yescharacteristic
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—22no—
747Q8—22no—
748Q8—42no—
749Q8—44no—
750Q8—42no—
751Q8—42no—
752Q8—82no—
753D4—22no—
754D4—22no—
755D4—42no—
756D4—82no—
757D4—82no—
758C2×C4—22no—
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—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—41no—
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—42no—
785C2×C4—42no—
786C2×C4—44no—
787C2×C4—42no—
788C2×C4—44no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—82no—
792C2×C4C2×C4×D411yescharacteristic
793C2×C4C2×C4×D411yescharacteristic
794C2×C4C2×C4×D411yescharacteristic
795C2×C4C2×C4×D411yescharacteristic
796C2×C4C2×C4×D411yescharacteristic
797C2×C4C2×C4×D411yescharacteristic
798C2×C4C2×C4×D411yescharacteristic
799C2×C4C2×C4×D411yescharacteristic
800C2×C4C2×C4×D411yescharacteristic
801C2×C4#57712yes—
802C2×C4#57812yes—
803C2×C4C24×C411yescharacteristic
804C2×C4C23×D411yescharacteristic
805C2×C4C22×#4111yescharacteristic
806C8—24no—
807C8—24no—
808C8—21no—
809C8—21no—
810C8—21no—
811C8—21no—
812C8—21no—
813C8—21no—
814C8—21no—
815C8—21no—
816C8—42no—
817C8—42no—
818C8—42no—
819C8—42no—
820C8—42no—
821C8—42no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—21no—
829C22—21no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—82no—
834C22—84no—
835C22#294712yes—
836C22C22×C4×D411yescharacteristic
837C4—21no—
838C4—21no—
839C4—21no—
840C4—21no—
841C4—21no—
842C4—21no—
843C4—21no—
844C4—21no—
845C4—21no—
846C4—42no—
847C4—42no—
848C4—42no—
849C4—42no—
850C4—42no—
851C4—42no—
852C4—42no—
853C4#294712yes—
854C4#357312yes—
855C4C2×#57711yescharacteristic
856C4C2×#57811yescharacteristic
857C2—22no—
858C2—41no—
859C2—41no—
860C2—82no—
861C2#6014011yescharacteristic
862C2C2×#294711yescharacteristic
863C2#6018211yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC42C25
socleC22C22×C4×D4
prime radicalC2×#121C2×C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×#431 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #60250C2semidirect
4. #17988C2semidirect
5. #17969C2semidirect
6. #17947C2semidirect
7. #17934C2semidirect
8. #17933C2semidirect
9. #17931C2semidirect
10. #17930C2semidirect
11. #17919C2semidirect
12. #17906C2semidirect
13. #17905C2semidirect
14. #17903C2semidirect
15. #17902C2semidirect
16. #17820C2semidirect
18. #17486C2semidirect
19. #17326C2semidirect
46. #2985C22semidirect
47. #2985C22semidirect
50. #2983C22semidirect
51. #2982C22semidirect
73. #1593C22semidirect
74. #1592C22semidirect
75. #1591C22semidirect
76. #1590C22semidirect
77. #1588C22semidirect
78. #1587C22semidirect
79. #1587C22semidirect
80. #1585C22semidirect
81. #1584C22semidirect
82. #1584C22semidirect
83. #1583C22semidirect
84. #1582C22semidirect
85. #1579C22semidirect
86. SD16⋊C8C22semidirect
87. C8×Q16C22semidirect
88. C8×SD16C22semidirect
89. #1574C22semidirect
94. #1569C22semidirect
96. #1493C22semidirect
99. #1487C22semidirect
107. #1454C22semidirect
108. #1454C22semidirect
111. #1451C22semidirect
114. C8×M16C22semidirect

Maximal subgroups

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

subgroupindex
#609502
C2×#29932
#602502
#179882
#179692
#179472
#179342
#179332
#179312
#179302
#179192
#179062
#179052
#179032
#179022
#178202
#174872
#174862
#173262