Finite Group Databasebeta

← #6345302

Subgroups — #6345302

Order 512.

1613 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60560C211yesmaximal, characteristic
2#60268C211yesmaximal, characteristic
3C2×#2984C211yesmaximal, characteristic, complemented
4#18053C214yesmaximal, complemented
5#18051C214yesmaximal, complemented
6#18023C214yesmaximal, complemented
7#18017C214yesmaximal, complemented
8#17936C211yesmaximal, characteristic, complemented
9#17934C211yesmaximal, characteristic, complemented
10#17931C211yesmaximal, characteristic, complemented
11#17929C211yesmaximal, characteristic, complemented
12#17908C211yesmaximal, characteristic, complemented
13#17906C211yesmaximal, characteristic, complemented
14#17903C211yesmaximal, characteristic, complemented
15#17901C211yesmaximal, characteristic, complemented
16#17822C211yesmaximal, characteristic, complemented
17#17488C211yesmaximal, characteristic
18C2×#1487C211yesmaximal, characteristic, complemented
19#17325C211yesmaximal, characteristic, complemented
20#3444C2211yescharacteristic
21C22×C4×Q8C2211yescharacteristic
22#3117C412yes—
23#3117C412yes—
24#3113C412yes—
25#3112C412yes—
26#3108C2214yes—
27#3104C2211yescharacteristic
28#3104C2211yescharacteristic
29#3103C2211yescharacteristic
30#3103C2211yescharacteristic
31#3092C412yes—
32#3078C412yes—
33#3037C412yes—
34#3004C412yes—
35#2994C2212yes—
36#2994C2212yes—
37#2993—21no—
38#2993—21no—
39#2991C2212yes—
40#2990C2212yes—
41#2989—21no—
42#2988—21no—
43#2984—21no—
44#2984—21no—
45#2984—21no—
46#2984—21no—
47#2984C2212yes—
48#2984C2212yes—
49#2984C2212yes—
50#2984C2212yes—
51#2960C2211yescharacteristic
52#2960C2211yescharacteristic
53C2×#446—21no—
54C2×#446—21no—
55C2×#446C2211yescharacteristic
56C2×#446C2211yescharacteristic
57C2×C8×Q8C2211yescharacteristic
58C2×C8×Q8C2211yescharacteristic
59C4×#137C2214yes—
60#2933—21no—
61#2933—21no—
62#2931C2211yescharacteristic
63#2931C2211yescharacteristic
64#2925—21no—
65#2920C2211yescharacteristic
66C2×#432—21no—
67C2×#432C2211yescharacteristic
68C2×#431—21no—
69C2×#431C2211yescharacteristic
70C2×#431C2211yescharacteristic
71#2906—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#1573C2214yes—
90#1571C2211yescharacteristic
91#1571C2211yescharacteristic
92#1570C2211yescharacteristic
93#1570C2211yescharacteristic
94#1569C2214yes—
95#1494C2214yes—
96#1488C2214yes—
97#1487C2211yescharacteristic
98#1487C2211yescharacteristic
99#1487C2214yes—
100#1487C2211yescharacteristic
101#1487C2211yescharacteristic
102#1481C2211yescharacteristic
103#1481C2211yescharacteristic
104#1480C2211yescharacteristic
105#1480C2211yescharacteristic
106C2×Q8⋊C8C2214yes—
107#1453C2212yes—
108#1453C2212yes—
109#1452C2211yescharacteristic
110#1452C2211yescharacteristic
111#1452C2212yes—
112#1450C2211yescharacteristic
113#1450C2211yescharacteristic
114#1450C2212yes—
115C23×Q8C2×C411yescharacteristic
116C2×#137C2×C414yes—
117C2×#131—21no—
118C2×#131—21no—
119C22×M16—21no—
120#533C2×C411yescharacteristic
121#533C2×C411yescharacteristic
122#533C2311yescharacteristic
123#532C2×C411yescharacteristic
124#532C2×C411yescharacteristic
125#532C2311yescharacteristic
126#529—21no—
127#529—21no—
128#529—21no—
129#529—21no—
130#529C2×C412yes—
131#529C2312yes—
132#525—21no—
133#525—21no—
134#525C2×C412yes—
135C4×#41—21no—
136C4×#41—21no—
137C4×#41C2312yes—
138C2×C4×Q8—21no—
139C2×C4×Q8—21no—
140C2×C4×Q8—21no—
141C2×C4×Q8—21no—
142C2×C4×Q8—21no—
143C2×C4×Q8—21no—
144C2×C4×Q8C2×C412yes—
145C2×C4×Q8C2×C412yes—
146C2×C4×Q8C2×C411yescharacteristic
147C2×C4×Q8C2×C411yescharacteristic
148C2×C4×Q8C2311yescharacteristic
149C2×C4×Q8C2311yescharacteristic
150C2×C4×Q8C2312yes—
151C2×C4×Q8C2312yes—
152C22×C4⋊C4—21no—
153C22×C4⋊C4C2×C411yescharacteristic
154C22×C42—21no—
155C22×C42C2311yescharacteristic
156#484C2×C412yes—
157#484C2×C412yes—
158#483C2×C414yes—
159#481C2×C412yes—
160#481C2×C412yes—
161#480C2×C414yes—
162#479C2×C414yes—
163#479C2×C414yes—
164#477C2×C412yes—
165#477C2×C412yes—
166#475C2×C412yes—
167#475C2×C412yes—
168#464C2×C414yes—
169#464C2×C414yes—
170#462C2×C412yes—
171#462C2×C412yes—
172#460C2×C412yes—
173#460C2×C412yes—
174#451C2×C412yes—
175#451C2×C412yes—
176#451C2×C414yes—
177#448C2×C412yes—
178#448C2×C412yes—
179#448C2×C414yes—
180#446—22no—
181#446—22no—
182#446—22no—
183#446—22no—
184#446—22no—
185#446—22no—
186#446—22no—
187#446—22no—
188#446—21no—
189#446—21no—
190#446—21no—
191#446—21no—
192#446—21no—
193#446—21no—
194#446C2312yes—
195#446C2312yes—
196#446C2312yes—
197#446C2312yes—
198#446C2312yes—
199#446C2312yes—
200C8×Q8—21no—
201C8×Q8—21no—
202C8×Q8—21no—
203C8×Q8—21no—
204C8×Q8—21no—
205C8×Q8—21no—
206C8×Q8C2312yes—
207C8×Q8C2312yes—
208C8×Q8C2312yes—
209C8×Q8C2312yes—
210C8×Q8C2312yes—
211C8×Q8C2312yes—
212#441C2×C414yes—
213#441C2×C414yes—
214#440C2×C414yes—
215#440C2×C414yes—
216C4×Q16C2314yes—
217C4×Q16C2314yes—
218C4×SD16C2314yes—
219C4×SD16C2314yes—
220#436—22no—
221#436—22no—
222#436—21no—
223#436—21no—
224#436C2312yes—
225#436C2312yes—
226#435—22no—
227#435—22no—
228#435—22no—
229#435—22no—
230C8×D4—22no—
231C8×D4—22no—
232C8×D4—21no—
233C8×D4—21no—
234C8×D4C2312yes—
235C8×D4C2312yes—
236#433—22no—
237#433—22no—
238#432—21no—
239#432—21no—
240#432—22no—
241#432—22no—
242#432—22no—
243#432—22no—
244#432—22no—
245#432C2×C412yes—
246#432C2×C412yes—
247#432C2312yes—
248#432C2312yes—
249#431—21no—
250#431—21no—
251#431—22no—
252#431—22no—
253#431—22no—
254#431—22no—
255#431—22no—
256#431D411yescharacteristic
257#431D411yescharacteristic
258#431D411yescharacteristic
259#431D411yescharacteristic
260#431C2311yescharacteristic
261#431C2311yescharacteristic
262#431C2312yes—
263#431C2311yescharacteristic
264#431C2311yescharacteristic
265#431C2312yes—
266#431C2311yescharacteristic
267#431C2311yescharacteristic
268#431C2311yescharacteristic
269#431C2311yescharacteristic
270#428C2×C414yes—
271#424—21no—
272#424—21no—
273#424—22no—
274#424—22no—
275#423—21no—
276#423—21no—
277#423—22no—
278#423C2×C412yes—
279#423C2312yes—
280#423C2311yescharacteristic
281#423C2311yescharacteristic
282C2×C4⋊C8—21no—
283C2×C4⋊C8—21no—
284C2×C4⋊C8—21no—
285C2×C4⋊C8—21no—
286C2×C4⋊C8—21no—
287C2×C4⋊C8—21no—
288C2×C4⋊C8—22no—
289C2×C4⋊C8D411yescharacteristic
290C2×C4⋊C8D411yescharacteristic
291C2×C4⋊C8C2311yescharacteristic
292C2×C4⋊C8C2311yescharacteristic
293C2×C4⋊C8C2312yes—
294#419C2×C414yes—
295#417C2×C414yes—
296#408—21no—
297#408—21no—
298#407C2×C412yes—
299C2×C22⋊C8—21no—
300C2×C22⋊C8—21no—
301C2×C22⋊C8D411yescharacteristic
302C2×C22⋊C8D411yescharacteristic
303#405—21no—
304#405—21no—
305C4×M16C2312yes—
306C2×#97—21no—
307C2×#97—21no—
308C2×#97—21no—
309C2×C4×C8—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—
334C2×#41—21no—
335C2×#41—21no—
336C2×#41C22×C412yes—
337C22×Q8—21no—
338C22×Q8—21no—
339C22×Q8—21no—
340C22×Q8—44no—
341C22×Q8C22×C411yescharacteristic
342C22×Q8C22×C412yes—
343C22×Q8C22×C412yes—
344C22×Q8C22×C411yescharacteristic
345C23×C4—21no—
346C23×C4—21no—
347C23×C4C22×C411yescharacteristic
348C23×C4C2×D411yescharacteristic
349C23×C4#4111yescharacteristic
350#137—48no—
351C2×Q16C22×C414yes—
352C2×Q16C22×C414yes—
353C2×SD16C22×C414yes—
354C2×SD16C22×C414yes—
355#131—82no—
356#131—82no—
357C2×M16—21no—
358C2×M16—21no—
359C2×M16—22no—
360C2×M16—22no—
361C2×M16—22no—
362C2×M16—82no—
363C2×M16C22×C414yes—
364C22×C8—21no—
365C22×C8—21no—
366C22×C8—22no—
367C22×C8—22no—
368C22×C8—22no—
369C22×C8—22no—
370C22×C8C2×D411yescharacteristic
371C22×C8C2×D411yescharacteristic
372C22×C8C2×D411yescharacteristic
373C22×C8C2×D411yescharacteristic
374C4⋊Q8C22×C411yescharacteristic
375C4⋊Q8C22×C411yescharacteristic
376C4⋊Q8C22×C411yescharacteristic
377#127C22×C411yescharacteristic
378#126—22no—
379#126—22no—
380#125—21no—
381#125—21no—
382#125C22×C412yes—
383#124—21no—
384#124—21no—
385#124C22×C412yes—
386#123—22no—
387#123—22no—
388#123—22no—
389C22⋊Q8—21no—
390C22⋊Q8—21no—
391C22⋊Q8—21no—
392C22⋊Q8—21no—
393C22⋊Q8C22×C412yes—
394C22⋊Q8C22×C412yes—
395#121—21no—
396#121—21no—
397#121—21no—
398#121—21no—
399#121C22×C412yes—
400#121C22×C412yes—
401#120—22no—
402C4×Q8—21no—
403C4×Q8—21no—
404C4×Q8—22no—
405C4×Q8—22no—
406C4×Q8—22no—
407C4×Q8—22no—
408C4×Q8—21no—
409C4×Q8—21no—
410C4×Q8—21no—
411C4×Q8—21no—
412C4×Q8—21no—
413C4×Q8—21no—
414C4×Q8—22no—
415C4×Q8—22no—
416C4×Q8—21no—
417C4×Q8—21no—
418C4×Q8—22no—
419C4×Q8—22no—
420C4×Q8—21no—
421C4×Q8—21no—
422C4×Q8C22×C412yes—
423C4×Q8C22×C412yes—
424C4×Q8C22×C412yes—
425C4×Q8C22×C412yes—
426C4×Q8C22×C412yes—
427C4×Q8C22×C412yes—
428C4×Q8C22×C412yes—
429C4×Q8C2412yes—
430C4×Q8C2412yes—
431C4×Q8C2412yes—
432C4×D4—22no—
433C4×D4—22no—
434C4×D4—22no—
435C4×D4—22no—
436C4×D4—22no—
437C4×D4—22no—
438C4×D4—21no—
439C4×D4—21no—
440C4×D4—21no—
441C4×D4—21no—
442C4×D4C22×C412yes—
443C4×D4C2412yes—
444#117—21no—
445#117—21no—
446#117—22no—
447#117—22no—
448#117—22no—
449#117C22×C412yes—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—22no—
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×C412yes—
462C2×C4⋊C4C22×C412yes—
463C2×C4⋊C4C22×C411yescharacteristic
464C2×C4⋊C4C22×C411yescharacteristic
465C2×C42—21no—
466C2×C42—22no—
467C2×C42—22no—
468C2×C42—21no—
469C2×C42—21no—
470C2×C42—21no—
471C2×C42—22no—
472C2×C42—22no—
473C2×C42—22no—
474C2×C42C22×C411yescharacteristic
475C2×C42C22×C411yescharacteristic
476C2×C42C22×C411yescharacteristic
477C2×C42C2×D411yescharacteristic
478C2×C42C2×D411yescharacteristic
479C2×C42C2×D411yescharacteristic
480C2×C42#4111yescharacteristic
481C2×C42#4111yescharacteristic
482C2×C42#4111yescharacteristic
483C2×C42C2411yescharacteristic
484C2×C42C2411yescharacteristic
485C2×C42C2411yescharacteristic
486#107C22×C414yes—
487#107C22×C414yes—
488#106C22×C414yes—
489#106C22×C414yes—
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—22no—
503C4⋊C8—21no—
504C4⋊C8—21no—
505C4⋊C8—22no—
506C4⋊C8—21no—
507C4⋊C8—21no—
508C4⋊C8—22no—
509C4⋊C8—21no—
510C4⋊C8—21no—
511C4⋊C8C22×C412yes—
512C4⋊C8C22×C412yes—
513C4⋊C8C22×C414yes—
514C4⋊C8C2×D411yescharacteristic
515C4⋊C8C2×D411yescharacteristic
516C4⋊C8C2×D411yescharacteristic
517C4⋊C8C2×D411yescharacteristic
518C4⋊C8C2×D411yescharacteristic
519C4⋊C8C2×D411yescharacteristic
520C4⋊C8C2×D411yescharacteristic
521C4⋊C8C2×D411yescharacteristic
522C4⋊C8C2412yes—
523C4⋊C8C2412yes—
524C4⋊C8C2412yes—
525C4⋊C8C2412yes—
526#103C22×C414yes—
527#103C22×C414yes—
528#103C22×C414yes—
529#103C22×C414yes—
530#103C22×C414yes—
531#103C22×C414yes—
532#102C22×C414yes—
533#102C22×C414yes—
534C22⋊C8—22no—
535C22⋊C8—22no—
536C22⋊C8—22no—
537C22⋊C8—21no—
538C22⋊C8—21no—
539C22⋊C8—22no—
540C22⋊C8—22no—
541C22⋊C8—22no—
542C22⋊C8—22no—
543C22⋊C8C22×C414yes—
544C22⋊C8C22×C412yes—
545C22⋊C8C22×C412yes—
546C22⋊C8C2×D411yescharacteristic
547C22⋊C8C2×D411yescharacteristic
548C22⋊C8C2×D411yescharacteristic
549C22⋊C8C2×D411yescharacteristic
550C22⋊C8C2×D411yescharacteristic
551C22⋊C8C2×D411yescharacteristic
552C22⋊C8C2×D411yescharacteristic
553C22⋊C8C2×D411yescharacteristic
554#97—22no—
555#97—22no—
556#97—22no—
557#97—22no—
558#97—22no—
559#97—22no—
560#97—22no—
561#97—22no—
562#97C22×C414yes—
563C4×C8—22no—
564C4×C8—22no—
565C4×C8—22no—
566C4×C8—22no—
567C4×C8—22no—
568C4×C8—22no—
569C4×C8—22no—
570C4×C8C2×D411yescharacteristic
571C4×C8C2×D411yescharacteristic
572C4×C8C2×D411yescharacteristic
573C4×C8C2×D411yescharacteristic
574C4×C8C2412yes—
575C4×C8C2412yes—
576C4×C8C2412yes—
577C4×C8C2412yes—
578C4×C8C2411yescharacteristic
579C4×C8C2411yescharacteristic
580C4×C8C2411yescharacteristic
581C4×C8C2411yescharacteristic
582C24C4×D411yescharacteristic
583#41—44no—
584#41—44no—
585#41—42no—
586#41—42no—
587C2×Q8—24no—
588C2×Q8—21no—
589C2×Q8—22no—
590C2×Q8—22no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—24no—
595C2×Q8—24no—
596C2×Q8—42no—
597C2×Q8—42no—
598C2×Q8—42no—
599C2×Q8—44no—
600C2×Q8—44no—
601C2×Q8—44no—
602C2×Q8C23×C412yes—
603C2×Q8C23×C412yes—
604C2×Q8C23×C412yes—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4C23×C412yes—
611C22×C4—21no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—21no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—44no—
627C22×C4—44no—
628C22×C4C4×D411yescharacteristic
629C22×C4C4×D411yescharacteristic
630C22×C4C4×D411yescharacteristic
631C22×C4C4×D411yescharacteristic
632C22×C4C4×D411yescharacteristic
633C22×C4C4×D411yescharacteristic
634C22×C4C4×D411yescharacteristic
635C22×C4C4×D411yescharacteristic
636C22×C4C4×D411yescharacteristic
637C22×C4C23×C411yescharacteristic
638C22×C4C23×C411yescharacteristic
639C22×C4C23×C411yescharacteristic
640C22×C4C22×D411yescharacteristic
641C22×C4C22×D411yescharacteristic
642C22×C4C22×D411yescharacteristic
643C22×C4C2×#4111yescharacteristic
644C22×C4C2×#4111yescharacteristic
645C22×C4C2×#4111yescharacteristic
646Q16—28no—
647Q16—44no—
648SD16—28no—
649SD16—44no—
650M16—44no—
651M16—42no—
652M16—42no—
653M16—82no—
654M16—82no—
655M16—82no—
656C2×C8—22no—
657C2×C8—22no—
658C2×C8—22no—
659C2×C8—22no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—22no—
664C2×C8—22no—
665C2×C8—22no—
666C2×C8—44no—
667C2×C8—42no—
668C2×C8—42no—
669C2×C8—82no—
670C2×C8—82no—
671C2×C8—82no—
672C2×C8C23×C414yes—
673C2×C8C23×C414yes—
674C2×C8C22×D411yescharacteristic
675C2×C8C22×D411yescharacteristic
676C2×C8C22×D411yescharacteristic
677C2×C8C22×D411yescharacteristic
678C2×C8C22×D411yescharacteristic
679C2×C8C22×D411yescharacteristic
680C2×C8C22×D411yescharacteristic
681C2×C8C22×D411yescharacteristic
682C4⋊C4—22no—
683C4⋊C4—22no—
684C4⋊C4—22no—
685C4⋊C4—22no—
686C4⋊C4—22no—
687C4⋊C4—22no—
688C4⋊C4—22no—
689C4⋊C4—22no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—22no—
697C4⋊C4—22no—
698C4⋊C4—22no—
699C4⋊C4—22no—
700C4⋊C4—22no—
701C4⋊C4—22no—
702C4⋊C4—22no—
703C4⋊C4—22no—
704C4⋊C4C23×C412yes—
705C4⋊C4C23×C412yes—
706C4⋊C4C23×C412yes—
707C4⋊C4C23×C412yes—
708C22⋊C4—22no—
709C22⋊C4—22no—
710C22⋊C4—22no—
711C22⋊C4—22no—
712C22⋊C4—22no—
713C22⋊C4—22no—
714C22⋊C4—22no—
715C22⋊C4—22no—
716C22⋊C4—22no—
717C42—22no—
718C42—22no—
719C42—22no—
720C42—22no—
721C42—22no—
722C42—22no—
723C42—22no—
724C42—22no—
725C42—22no—
726C42—22no—
727C42—22no—
728C42C4×D411yescharacteristic
729C42C4×D411yescharacteristic
730C42C4×D411yescharacteristic
731C42C4×D411yescharacteristic
732C42C4×D411yescharacteristic
733C42C4×D411yescharacteristic
734C42C23×C411yescharacteristic
735C42C23×C411yescharacteristic
736C42C23×C411yescharacteristic
737C42C22×D411yescharacteristic
738C42C22×D411yescharacteristic
739C42C22×D411yescharacteristic
740C42C2×#4111yescharacteristic
741C42C2×#4111yescharacteristic
742C42C2×#4111yescharacteristic
743C42C2511yescharacteristic
744C23—22no—
745C23—22no—
746C23—22no—
747C23—41no—
748C23C2×C4×D411yescharacteristic
749C23C2×C4×D411yescharacteristic
750C23C2×C4×D411yescharacteristic
751Q8—24no—
752Q8—22no—
753Q8—22no—
754Q8—24no—
755Q8—22no—
756Q8—44no—
757Q8—44no—
758Q8—42no—
759Q8—42no—
760Q8—42no—
761Q8#56814yes—
762D4—24no—
763D4—42no—
764D4—44no—
765D4—44no—
766D4—42no—
767D4—82no—
768C2×C4—24no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—44no—
801C2×C4—42no—
802C2×C4—44no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—82no—
806C2×C4C2×C4×D411yescharacteristic
807C2×C4C2×C4×D411yescharacteristic
808C2×C4C2×C4×D411yescharacteristic
809C2×C4C2×C4×D411yescharacteristic
810C2×C4C2×C4×D411yescharacteristic
811C2×C4C2×C4×D411yescharacteristic
812C2×C4C2×C4×D411yescharacteristic
813C2×C4C2×C4×D411yescharacteristic
814C2×C4C2×C4×D411yescharacteristic
815C2×C4#57712yes—
816C2×C4#57812yes—
817C2×C4C24×C411yescharacteristic
818C2×C4C23×D411yescharacteristic
819C2×C4C22×#4111yescharacteristic
820C8—24no—
821C8—24no—
822C8—21no—
823C8—21no—
824C8—21no—
825C8—21no—
826C8—21no—
827C8—21no—
828C8—21no—
829C8—21no—
830C8—42no—
831C8—42no—
832C8—42no—
833C8—42no—
834C8—42no—
835C8—42no—
836C22—21no—
837C22—21no—
838C22—21no—
839C22—21no—
840C22—21no—
841C22—21no—
842C22—21no—
843C22—44no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22#294712yes—
848C22#295512yes—
849C22C22×C4×D411yescharacteristic
850C4—21no—
851C4—21no—
852C4—21no—
853C4—21no—
854C4—21no—
855C4—21no—
856C4—24no—
857C4—21no—
858C4—21no—
859C4—21no—
860C4—42no—
861C4—42no—
862C4—42no—
863C4—42no—
864C4—42no—
865C4—42no—
866C4#294712yes—
867C4C2×#56812yes—
868C4C2×#57711yescharacteristic
869C4C2×#57811yescharacteristic
870C2—22no—
871C2—22no—
872C2—41no—
873C2—82no—
874C2#6014111yescharacteristic
875C2C2×#294711yescharacteristic
876C2C2×#295511yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC42C25
socleC22C22×C4×D4
prime radical#3444C22
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. C2×#2984C2semidirect
4. #18053C2semidirect
5. #18051C2semidirect
6. #18023C2semidirect
7. #18017C2semidirect
8. #17936C2semidirect
9. #17934C2semidirect
10. #17931C2semidirect
11. #17929C2semidirect
12. #17908C2semidirect
13. #17906C2semidirect
14. #17903C2semidirect
15. #17901C2semidirect
16. #17822C2semidirect
18. C2×#1487C2semidirect
19. #17325C2semidirect
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

Maximal subgroups

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

subgroupindex
#605602
#602682
C2×#29842
#180532
#180512
#180232
#180172
#179362
#179342
#179312
#179292
#179082
#179062
#179032
#179012
#178222
#174882
C2×#14872
#173252