Finite Group Databasebeta

← #6345208

Subgroups — #6345208

Order 512.

1521 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60952C211yesmaximal, characteristic
2#60268C211yesmaximal, characteristic
3C2×#2985C211yesmaximal, characteristic, complemented
4#17988C214yesmaximal, complemented
5#17969C214yesmaximal, complemented
6#17949C214yesmaximal, complemented
7#17936C211yesmaximal, characteristic, complemented
8#17934C211yesmaximal, characteristic, complemented
9#17931C211yesmaximal, characteristic, complemented
10#17929C211yesmaximal, characteristic, complemented
11#17921C214yesmaximal, complemented
12#17908C211yesmaximal, characteristic, complemented
13#17906C211yesmaximal, characteristic, complemented
14#17903C211yesmaximal, characteristic, complemented
15#17901C211yesmaximal, characteristic, complemented
16#17822C211yesmaximal, characteristic, complemented
17#17488C211yesmaximal, characteristic
18#17486C211yesmaximal, characteristic, complemented
19#17326C211yesmaximal, characteristic, complemented
20#3444C2211yescharacteristic
21C2×#533C2211yescharacteristic
22#3255C412yes—
23#3254C412yes—
24#3239C412yes—
25#3237C412yes—
26#3218C412yes—
27#3216C412yes—
28#3196C412yes—
29#3196C412yes—
30#3172C2214yes—
31#3107C2214yes—
32#3104C2211yescharacteristic
33#3104C2211yescharacteristic
34#3103C2211yescharacteristic
35#3103C2211yescharacteristic
36#2994—21no—
37#2994—21no—
38#2993C2212yes—
39#2993C2212yes—
40#2991—21no—
41#2990—21no—
42#2989C2212yes—
43#2988C2212yes—
44#2985—21no—
45#2985—21no—
46#2985—21no—
47#2985—21no—
48#2985C2212yes—
49#2985C2212yes—
50#2985C2212yes—
51#2985C2212yes—
52#2960C2211yescharacteristic
53#2960C2211yescharacteristic
54C2×#446—21no—
55C2×#446—21no—
56C2×#446C2211yescharacteristic
57C2×#446C2211yescharacteristic
58C2×C8×Q8C2211yescharacteristic
59C2×C8×Q8C2211yescharacteristic
60#2933—21no—
61#2933—21no—
62#2931C2211yescharacteristic
63#2931C2211yescharacteristic
64#2925—21no—
65#2920C2211yescharacteristic
66C2×#433—21no—
67C2×#433—21no—
68C2×#432C2211yescharacteristic
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#1493C2214yes—
97#1488C2214yes—
98#1487C2211yescharacteristic
99#1487C2211yescharacteristic
100#1487C2211yescharacteristic
101#1487C2211yescharacteristic
102#1481C2214yes—
103#1481C2211yescharacteristic
104#1481C2211yescharacteristic
105#1480C2211yescharacteristic
106#1480C2211yescharacteristic
107#1454C2212yes—
108#1454C2212yes—
109#1452C2211yescharacteristic
110#1452C2211yescharacteristic
111#1451C2212yes—
112#1450C2211yescharacteristic
113#1450C2211yescharacteristic
114C8×M16C2212yes—
115C2×#131—21no—
116C2×#131—21no—
117C22×M16—21no—
118#533—21no—
119#533—21no—
120#533—21no—
121#533—21no—
122#533C2×C412yes—
123#533C2×C412yes—
124#533C2×C411yescharacteristic
125#533C2×C411yescharacteristic
126#533C2311yescharacteristic
127#533C2312yes—
128#533C2312yes—
129#532C2×C411yescharacteristic
130#532C2×C411yescharacteristic
131#532C2311yescharacteristic
132C2×C4⋊Q8C2×C411yescharacteristic
133C2×C4⋊Q8C2×C411yescharacteristic
134#529—21no—
135#529—21no—
136#529—21no—
137#529—21no—
138#529C2×C412yes—
139#529C2312yes—
140C2×#125—21no—
141#525—21no—
142#525—21no—
143#525C2×C412yes—
144C2×C22⋊Q8—21no—
145C2×C22⋊Q8C2×C411yescharacteristic
146C2×C22⋊Q8C2×C411yescharacteristic
147C4×#41—21no—
148C4×#41—21no—
149C4×#41C2312yes—
150C2×C4×Q8—21no—
151C2×C4×Q8C2311yescharacteristic
152C2×C4×Q8C2311yescharacteristic
153C2×#117—21no—
154C22×C42C2311yescharacteristic
155#501C2×C414yes—
156#497C2×C414yes—
157#491C2×C414yes—
158#489C2×C414yes—
159#485C2×C414yes—
160#485C2×C414yes—
161#484C2×C412yes—
162#484C2×C412yes—
163#481C2×C412yes—
164#481C2×C412yes—
165#477C2×C412yes—
166#477C2×C412yes—
167#475C2×C412yes—
168#475C2×C412yes—
169#475C2×C414yes—
170#474C2×C414yes—
171#470C2×C414yes—
172#470C2×C414yes—
173#468C2×C414yes—
174#468C2×C414yes—
175#462C2×C412yes—
176#462C2×C412yes—
177#462C2×C414yes—
178#461C2×C414yes—
179#460C2×C412yes—
180#460C2×C412yes—
181#452C2×C414yes—
182#452C2×C414yes—
183#451C2×C412yes—
184#451C2×C412yes—
185#448C2×C412yes—
186#448C2×C412yes—
187#446—22no—
188#446—22no—
189#446—22no—
190#446—22no—
191#446—22no—
192#446—22no—
193#446—22no—
194#446—22no—
195#446—21no—
196#446—21no—
197#446—21no—
198#446—21no—
199#446—21no—
200#446—21no—
201#446C2312yes—
202#446C2312yes—
203#446C2312yes—
204#446C2312yes—
205#446C2312yes—
206#446C2312yes—
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—21no—
226#436—21no—
227#436C2312yes—
228#436C2312yes—
229#435—22no—
230#435—22no—
231#435—22no—
232#435—22no—
233C8×D4—22no—
234C8×D4—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#433—22no—
248#433—22no—
249#432—21no—
250#432—21no—
251#432—22no—
252#432C2×C412yes—
253#432C2×C412yes—
254#432C2312yes—
255#432C2312yes—
256#431—21no—
257#431—21no—
258#431—22no—
259#431D411yescharacteristic
260#431D411yescharacteristic
261#431D411yescharacteristic
262#431D411yescharacteristic
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—22no—
276#424—22no—
277#423—21no—
278#423—21no—
279#423—22no—
280#423C2×C412yes—
281#423C2312yes—
282#423C2311yescharacteristic
283#423C2311yescharacteristic
284C2×C4⋊C8—21no—
285C2×C4⋊C8—21no—
286C2×C4⋊C8—21no—
287C2×C4⋊C8—21no—
288C2×C4⋊C8—21no—
289C2×C4⋊C8—21no—
290C2×C4⋊C8—22no—
291C2×C4⋊C8D411yescharacteristic
292C2×C4⋊C8D411yescharacteristic
293C2×C4⋊C8C2311yescharacteristic
294C2×C4⋊C8C2311yescharacteristic
295C2×C4⋊C8C2312yes—
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×Q8C22×C411yescharacteristic
339C22×Q8C22×C411yescharacteristic
340C23×C4C22×C411yescharacteristic
341C23×C4C2×D411yescharacteristic
342C23×C4#4111yescharacteristic
343C2×Q16C22×C414yes—
344C2×Q16C22×C414yes—
345C2×SD16C22×C414yes—
346C2×SD16C22×C414yes—
347#131—82no—
348#131—82no—
349C2×M16—21no—
350C2×M16—21no—
351C2×M16—22no—
352C2×M16—22no—
353C2×M16—22no—
354C2×M16—82no—
355C2×M16C22×C414yes—
356C22×C8—21no—
357C22×C8—21no—
358C22×C8—22no—
359C22×C8—22no—
360C22×C8—22no—
361C22×C8—22no—
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×C412yes—
371C4⋊Q8C22×C412yes—
372C4⋊Q8C22×C411yescharacteristic
373C4⋊Q8C22×C412yes—
374C4⋊Q8C22×C412yes—
375C4⋊Q8C22×C411yescharacteristic
376C4⋊Q8C22×C411yescharacteristic
377#127C22×C411yescharacteristic
378#126—22no—
379#126—22no—
380#125—22no—
381#125—22no—
382#125—21no—
383#125—22no—
384#125—22no—
385#125—21no—
386#125C22×C412yes—
387#124—21no—
388#124—21no—
389#124C22×C412yes—
390#123—22no—
391#123—22no—
392#123—22no—
393C22⋊Q8—22no—
394C22⋊Q8—22no—
395C22⋊Q8—21no—
396C22⋊Q8—21no—
397C22⋊Q8—21no—
398C22⋊Q8—21no—
399C22⋊Q8—21no—
400C22⋊Q8—21no—
401C22⋊Q8—21no—
402C22⋊Q8—22no—
403C22⋊Q8—22no—
404C22⋊Q8—21no—
405C22⋊Q8C22×C412yes—
406C22⋊Q8C22×C412yes—
407C22⋊Q8C22×C412yes—
408C22⋊Q8C22×C412yes—
409C22⋊Q8C22×C412yes—
410C22⋊Q8C22×C412yes—
411#121—21no—
412#121—21no—
413#121—21no—
414#121—21no—
415#121C22×C412yes—
416#121C22×C412yes—
417#120—22no—
418C4×Q8—22no—
419C4×Q8—22no—
420C4×Q8—21no—
421C4×Q8—21no—
422C4×Q8—21no—
423C4×Q8—22no—
424C4×Q8—22no—
425C4×Q8—21no—
426C4×Q8—21no—
427C4×Q8—21no—
428C4×Q8—21no—
429C4×Q8—21no—
430C4×Q8C22×C412yes—
431C4×Q8C22×C412yes—
432C4×Q8C22×C412yes—
433C4×Q8C2412yes—
434C4×Q8C2412yes—
435C4×Q8C2412yes—
436C4×D4—22no—
437C4×D4—22no—
438C4×D4—22no—
439C4×D4—22no—
440C4×D4—22no—
441C4×D4—22no—
442C4×D4—21no—
443C4×D4—21no—
444C4×D4—21no—
445C4×D4—21no—
446C4×D4C22×C412yes—
447C4×D4C2412yes—
448#117—22no—
449#117—22no—
450#117—21no—
451#117—22no—
452#117—22no—
453#117—21no—
454#117—22no—
455#117—22no—
456#117—22no—
457#117C22×C412yes—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4C22×C411yescharacteristic
466C2×C4⋊C4C22×C411yescharacteristic
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C42—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—22no—
507C4⋊C8—21no—
508C4⋊C8—21no—
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×C412yes—
542C22⋊C8C22×C412yes—
543C22⋊C8C22×C414yes—
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#97—22no—
560#97C22×C414yes—
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
580C24C4×D411yescharacteristic
581#41—44no—
582#41—42no—
583#41—42no—
584#41—82no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—22no—
590C2×Q8—22no—
591C2×Q8—42no—
592C2×Q8—42no—
593C2×Q8—82no—
594C2×Q8C23×C412yes—
595C2×Q8C23×C412yes—
596C2×Q8C23×C412yes—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4C23×C412yes—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—42no—
613C22×C4—81no—
614C22×C4C4×D411yescharacteristic
615C22×C4C4×D411yescharacteristic
616C22×C4C4×D411yescharacteristic
617C22×C4C4×D411yescharacteristic
618C22×C4C4×D411yescharacteristic
619C22×C4C4×D411yescharacteristic
620C22×C4C4×D411yescharacteristic
621C22×C4C4×D411yescharacteristic
622C22×C4C4×D411yescharacteristic
623C22×C4C23×C411yescharacteristic
624C22×C4C23×C411yescharacteristic
625C22×C4C23×C411yescharacteristic
626C22×C4C22×D411yescharacteristic
627C22×C4C22×D411yescharacteristic
628C22×C4C22×D411yescharacteristic
629C22×C4C2×#4111yescharacteristic
630C22×C4C2×#4111yescharacteristic
631C22×C4C2×#4111yescharacteristic
632Q16—44no—
633Q16—44no—
634SD16—44no—
635SD16—44no—
636M16—44no—
637M16—42no—
638M16—42no—
639M16—82no—
640M16—82no—
641M16—82no—
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—22no—
652C2×C8—42no—
653C2×C8—42no—
654C2×C8—82no—
655C2×C8—82no—
656C2×C8—82no—
657C2×C8—82no—
658C2×C8C23×C414yes—
659C2×C8C23×C414yes—
660C2×C8C22×D411yescharacteristic
661C2×C8C22×D411yescharacteristic
662C2×C8C22×D411yescharacteristic
663C2×C8C22×D411yescharacteristic
664C2×C8C22×D411yescharacteristic
665C2×C8C22×D411yescharacteristic
666C2×C8C22×D411yescharacteristic
667C2×C8C22×D411yescharacteristic
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—22no—
671C4⋊C4—22no—
672C4⋊C4—22no—
673C4⋊C4—22no—
674C4⋊C4—22no—
675C4⋊C4—22no—
676C4⋊C4—22no—
677C4⋊C4—22no—
678C4⋊C4—22no—
679C4⋊C4—22no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—22no—
687C4⋊C4—22no—
688C4⋊C4—22no—
689C4⋊C4—22no—
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—
711C42—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—
738C23C2×C4×D411yescharacteristic
739C23C2×C4×D411yescharacteristic
740C23C2×C4×D411yescharacteristic
741Q8—22no—
742Q8—22no—
743Q8—22no—
744Q8—22no—
745Q8—24no—
746Q8—42no—
747Q8—42no—
748Q8—42no—
749Q8—42no—
750Q8—82no—
751Q8—82no—
752D4—24no—
753D4—42no—
754D4—44no—
755D4—44no—
756D4—42no—
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—44no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
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#294712yes—
835C22C22×C4×D411yescharacteristic
836C4—21no—
837C4—21no—
838C4—21no—
839C4—21no—
840C4—21no—
841C4—21no—
842C4—21no—
843C4—21no—
844C4—21no—
845C4—42no—
846C4—42no—
847C4—42no—
848C4—42no—
849C4—42no—
850C4—42no—
851C4—42no—
852C4#294712yes—
853C4#357312yes—
854C4C2×#57711yescharacteristic
855C4C2×#57811yescharacteristic
856C2—22no—
857C2—41no—
858C2—41no—
859C2—82no—
860C2#6014011yescharacteristic
861C2C2×#294711yescharacteristic
862C2#6018211yescharacteristic
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×#2985C2semidirect
4. #17988C2semidirect
5. #17969C2semidirect
6. #17949C2semidirect
7. #17936C2semidirect
8. #17934C2semidirect
9. #17931C2semidirect
10. #17929C2semidirect
11. #17921C2semidirect
12. #17908C2semidirect
13. #17906C2semidirect
14. #17903C2semidirect
15. #17901C2semidirect
16. #17822C2semidirect
18. #17486C2semidirect
19. #17326C2semidirect
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
#609522
#602682
C2×#29852
#179882
#179692
#179492
#179362
#179342
#179312
#179292
#179212
#179082
#179062
#179032
#179012
#178222
#174882
#174862
#173262