Finite Group Databasebeta

← #6396754

Subgroups — #6396754

Order 512.

1606 conjugacy classes of subgroups.

The subgroup lattice has 901 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60846C211yesmaximal, characteristic
2#60268C211yesmaximal, characteristic
3#60250C211yesmaximal, characteristic, complemented
4#23082C214yesmaximal, complemented
5#22984C214yesmaximal, complemented
6#22951C214yesmaximal, complemented
7#22949C214yesmaximal, complemented
8#22256C211yesmaximal, characteristic, complemented
9#22256C211yesmaximal, characteristic, complemented
10#22234C211yesmaximal, characteristic, complemented
11#22234C211yesmaximal, characteristic, complemented
12#21993C211yesmaximal, characteristic, complemented
13#21734C211yesmaximal, characteristic, complemented
14#21732C211yesmaximal, characteristic, complemented
15#21660C211yesmaximal, characteristic, complemented
16#21658C211yesmaximal, characteristic, complemented
17#21418C211yesmaximal, characteristic
18#21329C211yesmaximal, characteristic, complemented
19#20462C211yesmaximal, characteristic, complemented
20#3444C2211yescharacteristic
21C2×#533C2211yescharacteristic
22#3233C414yescomplemented
23#3232C414yescomplemented
24#3231C411yescharacteristic, complemented
25#3231C411yescharacteristic, complemented
26#3230C411yescharacteristic, complemented
27#3229C411yescharacteristic, complemented
28#3228C411yescharacteristic, complemented
29#3228C411yescharacteristic, complemented
30#3227C411yescharacteristic, complemented
31#3226C411yescharacteristic, complemented
32#3160C2211yescharacteristic
33#3160C2211yescharacteristic
34#3131C2211yescharacteristic
35#3131C2211yescharacteristic
36#3091C2214yes—
37#3076C2214yes—
38#2994—21no—
39#2994—21no—
40#2993—21no—
41#2993—21no—
42#2991—21no—
43#2990—21no—
44#2989—21no—
45#2988—21no—
46#2986—21no—
47#2986—21no—
48#2985—21no—
49#2985—21no—
50#2984—21no—
51#2984—21no—
52#2983—21no—
53#2982—21no—
54#2962C2212yes—
55#2962C2212yes—
56#2960C2211yescharacteristic
57#2960C2211yescharacteristic
58#2960C2211yescharacteristic
59#2960C2211yescharacteristic
60#2960C2211yescharacteristic
61#2960C2211yescharacteristic
62#2933C2212yes—
63#2933C2212yes—
64#2931C2211yescharacteristic
65#2931C2211yescharacteristic
66#2925C2212yes—
67#2924C2212yes—
68#2924C2212yes—
69#2920C2211yescharacteristic
70C2×#431C2211yescharacteristic
71C2×#431C2211yescharacteristic
72#2906C2212yes—
73C2×#423C2211yescharacteristic
74C4×#117C2211yescharacteristic
75#1995C2214yes—
76#1994C2211yescharacteristic
77#1994C2211yescharacteristic
78#1994C2211yescharacteristic
79#1994C2211yescharacteristic
80#1994C2211yescharacteristic
81#1994C2211yescharacteristic
82#1962C2211yescharacteristic
83#1962C2211yescharacteristic
84#1950C2214yes—
85#1946C2214yes—
86#1945C2214yes—
87#1938C2214yes—
88#1937C2214yes—
89#1929C2214yes—
90#1929C2214yes—
91#1922C2214yes—
92#1922C2214yes—
93#1922C2214yes—
94#1922C2214yes—
95#1897C2214yes—
96#1866C2214yes—
97#1866C2214yes—
98#1855C2214yes—
99#1848C2211yescharacteristic
100#1848C2211yescharacteristic
101#1837C2211yescharacteristic
102#1837C2211yescharacteristic
103#1773C2214yes—
104#1772C2214yes—
105#1768C2212yes—
106#1768C2212yes—
107#1765C2214yes—
108#1764C2214yes—
109#1759C2214yes—
110#1750C2212yes—
111#1750C2212yes—
112#1744C2211yescharacteristic
113#1744C2211yescharacteristic
114#1733C2214yes—
115C4×#97C2211yescharacteristic
116C42×C8C2211yescharacteristic
117C2×#131C2312yes—
118C2×#131C2312yes—
119C22×M16C2312yes—
120#533—21no—
121#533—21no—
122#533—21no—
123#533—21no—
124#533C2×C411yescharacteristic
125#533C2×C411yescharacteristic
126#533C2×C411yescharacteristic
127#533C2×C411yescharacteristic
128#533C2×C412yes—
129#533C2312yes—
130#533C2311yescharacteristic
131#533C2311yescharacteristic
132#533C2311yescharacteristic
133#532C2×C411yescharacteristic
134#532C2×C411yescharacteristic
135#532C2311yescharacteristic
136C2×C4⋊Q8C2×C411yescharacteristic
137C2×C4⋊Q8C2×C411yescharacteristic
138#529—21no—
139#529—21no—
140#529—21no—
141#529—21no—
142#529C2×C412yes—
143#529C2×C412yes—
144C2×#125C2×C412yes—
145#525—21no—
146#525—21no—
147#525C2312yes—
148C2×C22⋊Q8—21no—
149C2×C22⋊Q8—21no—
150C4×#41—21no—
151C4×#41—21no—
152C4×#41C2312yes—
153C2×C4×Q8—21no—
154C2×C4×Q8—21no—
155C2×#117C2312yes—
156C2×#117C2312yes—
157C22×C42C2311yescharacteristic
158#500C2×C411yescharacteristic
159#500C2×C411yescharacteristic
160#500C2×C411yescharacteristic
161#500C2×C411yescharacteristic
162#499C2×C414yes—
163#499C2×C414yes—
164#498C2×C411yescharacteristic
165#498C2×C411yescharacteristic
166#498C2×C411yescharacteristic
167#498C2×C411yescharacteristic
168#488C2×C414yes—
169#488C2×C414yes—
170#487C2×C411yescharacteristic
171#487C2×C411yescharacteristic
172#487C2×C411yescharacteristic
173#487C2×C411yescharacteristic
174#486C2×C411yescharacteristic
175#486C2×C411yescharacteristic
176#486C2×C411yescharacteristic
177#486C2×C411yescharacteristic
178#485C2×C414yes—
179#485C2×C414yes—
180#484C2×C414yes—
181#483C2×C414yes—
182#482C2×C414yes—
183#482C2×C414yes—
184#481C2×C414yes—
185#480C2×C414yes—
186#479C2×C414yes—
187#479C2×C414yes—
188#478C2×C414yes—
189#478C2×C414yes—
190#477C2×C414yes—
191#476C2×C414yes—
192#475C2×C414yes—
193#474C2×C414yes—
194#446—22no—
195#446—22no—
196#446—22no—
197#446—22no—
198#446—22no—
199#446—22no—
200#446—21no—
201#446—21no—
202#446—21no—
203#446—21no—
204#446—21no—
205#446—21no—
206#446—21no—
207#446—21no—
208#446—21no—
209#446—21no—
210#446—21no—
211#446—21no—
212C8×Q8—22no—
213C8×Q8—22no—
214C8×Q8—21no—
215C8×Q8—21no—
216C8×Q8—21no—
217C8×Q8—21no—
218C8×Q8—21no—
219C8×Q8—21no—
220C8×Q8—21no—
221C8×Q8—21no—
222C8×Q8—21no—
223C8×Q8—21no—
224C8×Q8—21no—
225C8×Q8—21no—
226#436—22no—
227#436—22no—
228#436—21no—
229#436—21no—
230#436—21no—
231#436—21no—
232#435—22no—
233#435—22no—
234#435—22no—
235#435—22no—
236C8×D4—22no—
237C8×D4—22no—
238C8×D4—21no—
239C8×D4—21no—
240C8×D4—21no—
241C8×D4—21no—
242#433—22no—
243#433—22no—
244#433—22no—
245#433—22no—
246#433—22no—
247#433—22no—
248#432—21no—
249#432—21no—
250#432—22no—
251#432—22no—
252#432—22no—
253#431—21no—
254#431—21no—
255#431—22no—
256#431—22no—
257#431—22no—
258#431C2×C411yescharacteristic
259#431C2×C411yescharacteristic
260#431C2×C411yescharacteristic
261#431C2×C411yescharacteristic
262#431C2×C412yes—
263#431C2×C412yes—
264#431D411yescharacteristic
265#431D411yescharacteristic
266#431D411yescharacteristic
267#431D411yescharacteristic
268#431D411yescharacteristic
269#431D411yescharacteristic
270#431D411yescharacteristic
271#431D411yescharacteristic
272C2×#108C2314yes—
273C2×#108C2314yes—
274#427C2314yes—
275#427C2314yes—
276#424—22no—
277#424—22no—
278#424C2312yes—
279#424C2312yes—
280#424C2312yes—
281#424C2312yes—
282#424C2312yes—
283#424C2312yes—
284#423—21no—
285#423—21no—
286#423—22no—
287#423C2311yescharacteristic
288#423C2311yescharacteristic
289#423C2311yescharacteristic
290#423C2311yescharacteristic
291#423C2312yes—
292C2×C4⋊C8—21no—
293C2×C4⋊C8—21no—
294C2×C4⋊C8—22no—
295C2×C4⋊C8C2312yes—
296C2×C4⋊C8C2311yescharacteristic
297C2×C4⋊C8C2311yescharacteristic
298C2×#104C2314yes—
299C2×#104C2314yes—
300#416C2314yes—
301#416C2314yes—
302#408C2312yes—
303#408C2312yes—
304#407C2312yes—
305C2×C22⋊C8C2312yes—
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308#405C2312yes—
309#405C2312yes—
310#405C2312yes—
311#405C2312yes—
312#405C2312yes—
313#405C2312yes—
314C4×M16C2312yes—
315C2×#97C2312yes—
316C2×#97C2312yes—
317C2×C4×C8C2312yes—
318C2×C4×C8C2312yes—
319C2×C4×C8C2311yescharacteristic
320C2×C4×C8C2311yescharacteristic
321C2×C4×C8C2311yescharacteristic
322C2×C4×C8C2311yescharacteristic
323C4×C4⋊C4—21no—
324C4×C4⋊C4—21no—
325C4×C22⋊C4—21no—
326C4×C22⋊C4—21no—
327#376C2312yes—
328C43C2311yescharacteristic
329C43C2311yescharacteristic
330#341C2314yes—
331#341C2314yes—
332#339C2314yes—
333#339C2314yes—
334#339C2314yes—
335#339C2314yes—
336#339C2314yes—
337#339C2314yes—
338#336C2312yes—
339#336C2312yes—
340#336C2312yes—
341#336C2312yes—
342C2×#41—21no—
343C2×#41—21no—
344C2×#41C2412yes—
345C22×Q8—21no—
346C22×Q8—21no—
347C23×C4#4111yescharacteristic
348C23×C4#4111yescharacteristic
349C23×C4C2411yescharacteristic
350#131—44no—
351#131—44no—
352C2×M16—22no—
353C2×M16—22no—
354C2×M16—22no—
355C2×M16—44no—
356C2×M16C2412yes—
357C2×M16C2412yes—
358C2×M16C2412yes—
359C2×M16C2412yes—
360C22×C8—22no—
361C22×C8—22no—
362C22×C8—22no—
363C22×C8C2412yes—
364C22×C8C2412yes—
365C22×C8C2411yescharacteristic
366C22×C8C2411yescharacteristic
367C22×C8C2411yescharacteristic
368C22×C8C2411yescharacteristic
369C4⋊Q8—21no—
370C4⋊Q8—21no—
371C4⋊Q8—21no—
372C4⋊Q8—21no—
373C4⋊Q8C22×C411yescharacteristic
374C4⋊Q8C22×C412yes—
375C4⋊Q8C22×C412yes—
376C4⋊Q8C22×C411yescharacteristic
377C4⋊Q8C22×C411yescharacteristic
378C4⋊Q8C22×C411yescharacteristic
379C4⋊Q8C22×C411yescharacteristic
380C4⋊Q8C22×C411yescharacteristic
381C4⋊Q8C22×C411yescharacteristic
382#127C22×C411yescharacteristic
383#126—22no—
384#126—22no—
385#125—22no—
386#125—22no—
387#125—21no—
388#125—21no—
389#125C22×C412yes—
390#125C22×C412yes—
391#125C22×C412yes—
392#125C22×C412yes—
393#125C22×C412yes—
394#124—21no—
395#124—21no—
396#124C22×C412yes—
397#123—22no—
398#123—22no—
399#123—22no—
400C22⋊Q8—21no—
401C22⋊Q8—21no—
402C22⋊Q8—21no—
403C22⋊Q8—21no—
404C22⋊Q8—22no—
405C22⋊Q8—22no—
406C22⋊Q8—21no—
407C22⋊Q8—21no—
408C22⋊Q8—21no—
409C22⋊Q8—21no—
410C22⋊Q8—21no—
411C22⋊Q8—21no—
412C22⋊Q8—22no—
413C22⋊Q8—22no—
414C22⋊Q8—21no—
415C22⋊Q8—21no—
416C22⋊Q8C22×C412yes—
417C22⋊Q8C22×C412yes—
418#121—21no—
419#121—21no—
420#121—21no—
421#121—21no—
422#121C22×C412yes—
423#121C22×C412yes—
424#120—22no—
425C4×Q8—22no—
426C4×Q8—21no—
427C4×Q8—21no—
428C4×Q8—21no—
429C4×Q8—21no—
430C4×Q8—22no—
431C4×Q8—21no—
432C4×Q8—21no—
433C4×Q8—22no—
434C4×Q8—21no—
435C4×Q8—21no—
436C4×Q8—21no—
437C4×Q8—21no—
438C4×Q8—22no—
439C4×Q8—21no—
440C4×Q8—21no—
441C4×Q8C22×C412yes—
442C4×Q8C22×C412yes—
443C4×D4—22no—
444C4×D4—22no—
445C4×D4—22no—
446C4×D4—22no—
447C4×D4—22no—
448C4×D4—22no—
449C4×D4—21no—
450C4×D4—21no—
451C4×D4—21no—
452C4×D4—21no—
453C4×D4C22×C412yes—
454C4×D4C22×C412yes—
455#117—21no—
456#117—21no—
457#117—22no—
458#117—22no—
459#117—22no—
460#117—22no—
461#117—22no—
462#117—24no—
463#117—42no—
464#117C22×C412yes—
465#117C22×C412yes—
466#117C2412yes—
467#117C2412yes—
468#117C2412yes—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4C22×C412yes—
475C2×C4⋊C4C22×C412yes—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—22no—
478C2×C42—22no—
479C2×C42—22no—
480C2×C42—21no—
481C2×C42—21no—
482C2×C42—21no—
483C2×C42—21no—
484C2×C42C22×C411yescharacteristic
485C2×C42C22×C411yescharacteristic
486C2×C42C22×C411yescharacteristic
487C2×C42C22×C411yescharacteristic
488C2×C42C2×D411yescharacteristic
489C2×C42C2×D411yescharacteristic
490C2×C42C2×D411yescharacteristic
491C2×C42C2×D411yescharacteristic
492C2×C42#4111yescharacteristic
493C2×C42#4111yescharacteristic
494C2×C42C2412yes—
495C2×C42C2412yes—
496C2×C42C2411yescharacteristic
497C2×C42C2411yescharacteristic
498#108—44no—
499#108—44no—
500#107C22×C414yes—
501#107C22×C414yes—
502#107C22×C414yes—
503#107C22×C414yes—
504#106C22×C414yes—
505#106C22×C414yes—
506#106C22×C414yes—
507#106C22×C414yes—
508C4⋊C8—22no—
509C4⋊C8—22no—
510C4⋊C8—22no—
511C4⋊C8—22no—
512C4⋊C8—22no—
513C4⋊C8—22no—
514C4⋊C8—22no—
515C4⋊C8—22no—
516C4⋊C8—22no—
517C4⋊C8—22no—
518C4⋊C8—22no—
519C4⋊C8—22no—
520C4⋊C8—22no—
521C4⋊C8—22no—
522C4⋊C8—21no—
523C4⋊C8—21no—
524C4⋊C8—21no—
525C4⋊C8—21no—
526C4⋊C8—21no—
527C4⋊C8—21no—
528C4⋊C8—21no—
529C4⋊C8—21no—
530C4⋊C8C22×C412yes—
531C4⋊C8C22×C412yes—
532C4⋊C8C22×C412yes—
533C4⋊C8C22×C412yes—
534C4⋊C8C2×D411yescharacteristic
535C4⋊C8C2×D411yescharacteristic
536C4⋊C8C2×D411yescharacteristic
537C4⋊C8C2×D411yescharacteristic
538C4⋊C8C2×D411yescharacteristic
539C4⋊C8C2×D411yescharacteristic
540C4⋊C8C2×D411yescharacteristic
541C4⋊C8C2×D411yescharacteristic
542#104—28no—
543#104—44no—
544#103C22×C414yes—
545#103C22×C414yes—
546#103C22×C414yes—
547#103C22×C414yes—
548#102C22×C414yes—
549#102C22×C414yes—
550#102C22×C414yes—
551#102C22×C414yes—
552C22⋊C8—22no—
553C22⋊C8—22no—
554C22⋊C8—22no—
555C22⋊C8—22no—
556C22⋊C8—22no—
557C22⋊C8—22no—
558C22⋊C8C22×C412yes—
559C22⋊C8C22×C412yes—
560C22⋊C8C22×C412yes—
561C22⋊C8C22×C412yes—
562C22⋊C8C2×D411yescharacteristic
563C22⋊C8C2×D411yescharacteristic
564C22⋊C8C2×D411yescharacteristic
565C22⋊C8C2×D411yescharacteristic
566C22⋊C8C2×D411yescharacteristic
567C22⋊C8C2×D411yescharacteristic
568C22⋊C8C2×D411yescharacteristic
569C22⋊C8C2×D411yescharacteristic
570#97—22no—
571#97—22no—
572#97—22no—
573#97—22no—
574#97—22no—
575#97—22no—
576#97—22no—
577#97—24no—
578#97—42no—
579C4×C8—22no—
580C4×C8—22no—
581C4×C8—22no—
582C4×C8—22no—
583C4×C8—22no—
584C4×C8—22no—
585C4×C8—22no—
586C4×C8—24no—
587C4×C8—42no—
588C4×C8C22×C411yescharacteristic
589C4×C8C22×C411yescharacteristic
590C4×C8C22×C411yescharacteristic
591C4×C8C22×C411yescharacteristic
592C4×C8C22×C412yes—
593C4×C8C22×C412yes—
594C4×C8C2×D411yescharacteristic
595C4×C8C2×D411yescharacteristic
596C4×C8C2×D411yescharacteristic
597C4×C8C2×D411yescharacteristic
598C4×C8C2×D411yescharacteristic
599C4×C8C2×D411yescharacteristic
600C4×C8C2×D411yescharacteristic
601C4×C8C2×D411yescharacteristic
602#95—22no—
603#95—22no—
604C24C2×#4111yescharacteristic
605#41—24no—
606#41—24no—
607#41—44no—
608#41—82no—
609C2×Q8—21no—
610C2×Q8—21no—
611C2×Q8—22no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8—22no—
617C2×Q8—44no—
618C2×Q8—82no—
619C2×Q8C23×C412yes—
620C2×D4—22no—
621C2×D4—22no—
622C2×D4—22no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4C23×C412yes—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4C4×D411yescharacteristic
638C22×C4C4×D411yescharacteristic
639C22×C4C4×D411yescharacteristic
640C22×C4C4×D411yescharacteristic
641C22×C4C4×D411yescharacteristic
642C22×C4C4×D411yescharacteristic
643C22×C4C4×D411yescharacteristic
644C22×C4C4×D411yescharacteristic
645C22×C4C23×C411yescharacteristic
646C22×C4C23×C411yescharacteristic
647C22×C4C22×D411yescharacteristic
648C22×C4C22×D411yescharacteristic
649C22×C4C2×#4111yescharacteristic
650C22×C4C2×#4111yescharacteristic
651C22×C4C2×#4111yescharacteristic
652C22×C4C2×#4111yescharacteristic
653C22×C4C2×#4111yescharacteristic
654C22×C4C2511yescharacteristic
655M16—24no—
656M16—24no—
657M16—24no—
658M16—24no—
659M16—82no—
660M16—82no—
661M16—82no—
662C2×C8—22no—
663C2×C8—22no—
664C2×C8—22no—
665C2×C8—22no—
666C2×C8—22no—
667C2×C8—22no—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—22no—
671C2×C8—22no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—82no—
675C2×C8—82no—
676C2×C8—82no—
677C2×C8C23×C412yes—
678C2×C8C23×C412yes—
679C2×C8C23×C412yes—
680C2×C8C23×C412yes—
681C2×C8C22×D411yescharacteristic
682C2×C8C22×D411yescharacteristic
683C2×C8C22×D411yescharacteristic
684C2×C8C22×D411yescharacteristic
685C2×C8C22×D411yescharacteristic
686C2×C8C22×D411yescharacteristic
687C2×C8C22×D411yescharacteristic
688C2×C8C22×D411yescharacteristic
689C4⋊C4—22no—
690C4⋊C4—22no—
691C4⋊C4—22no—
692C4⋊C4—22no—
693C4⋊C4—22no—
694C4⋊C4—22no—
695C4⋊C4—22no—
696C4⋊C4—22no—
697C4⋊C4—22no—
698C4⋊C4—22no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—22no—
704C4⋊C4—22no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—22no—
710C4⋊C4—22no—
711C4⋊C4—22no—
712C4⋊C4—22no—
713C4⋊C4—22no—
714C4⋊C4—22no—
715C4⋊C4—44no—
716C4⋊C4C23×C412yes—
717C4⋊C4C23×C412yes—
718C4⋊C4C23×C412yes—
719C4⋊C4C23×C412yes—
720C4⋊C4C23×C412yes—
721C4⋊C4C23×C412yes—
722C22⋊C4—22no—
723C22⋊C4—22no—
724C22⋊C4—22no—
725C22⋊C4—22no—
726C22⋊C4—22no—
727C22⋊C4—22no—
728C22⋊C4—22no—
729C22⋊C4—22no—
730C22⋊C4—22no—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—22no—
734C22⋊C4—22no—
735C22⋊C4—44no—
736C42—22no—
737C42—22no—
738C42—22no—
739C42—22no—
740C42—22no—
741C42—22no—
742C42—22no—
743C42—22no—
744C42—22no—
745C42—22no—
746C42—42no—
747C42—42no—
748C42—42no—
749C42—42no—
750C42C4×D411yescharacteristic
751C42C4×D411yescharacteristic
752C42C4×D411yescharacteristic
753C42C4×D411yescharacteristic
754C42C4×D411yescharacteristic
755C42C4×D411yescharacteristic
756C42C4×D411yescharacteristic
757C42C4×D411yescharacteristic
758C42C23×C411yescharacteristic
759C42C23×C411yescharacteristic
760C42C23×C411yescharacteristic
761C42C23×C411yescharacteristic
762C42C22×D411yescharacteristic
763C42C22×D411yescharacteristic
764C42C22×D411yescharacteristic
765C42C22×D411yescharacteristic
766C422−1+414yes—
767C23—22no—
768C23—22no—
769C23—41no—
770C23—41no—
771C23C2×C4×D411yescharacteristic
772C23C2×C4×D411yescharacteristic
773C23C22×#4111yescharacteristic
774Q8—24no—
775Q8—44no—
776Q8—42no—
777Q8—42no—
778Q8—42no—
779Q8—42no—
780Q8—42no—
781Q8—42no—
782Q8—82no—
783D4—24no—
784D4—44no—
785D4—44no—
786D4—42no—
787D4—42no—
788D4—82no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—24no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—44no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—44no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—82no—
826C2×C4—82no—
827C2×C4C2×C4×D411yescharacteristic
828C2×C4C2×C4×D411yescharacteristic
829C2×C4C2×C4×D411yescharacteristic
830C2×C4C2×C4×D411yescharacteristic
831C2×C4C2×C4×D411yescharacteristic
832C2×C4C2×C4×D411yescharacteristic
833C2×C4C2×C4×D411yescharacteristic
834C2×C4C2×C4×D411yescharacteristic
835C2×C4C2×C4×D411yescharacteristic
836C2×C4C2×C4×D411yescharacteristic
837C2×C4C24×C411yescharacteristic
838C2×C4C23×D411yescharacteristic
839C2×C4C2×2−1+412yes—
840C2×C4#58512yes—
841C8—22no—
842C8—22no—
843C8—22no—
844C8—22no—
845C8—21no—
846C8—21no—
847C8—21no—
848C8—21no—
849C8—21no—
850C8—21no—
851C8—21no—
852C8—21no—
853C8—42no—
854C8—42no—
855C8—42no—
856C8—42no—
857C22—21no—
858C22—21no—
859C22—21no—
860C22—21no—
861C22—21no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—42no—
866C22—42no—
867C22—42no—
868C22—82no—
869C22C22×C4×D411yescharacteristic
870C22#349512yes—
871C4—21no—
872C4—21no—
873C4—21no—
874C4—21no—
875C4—21no—
876C4—21no—
877C4—21no—
878C4—21no—
879C4—44no—
880C4—42no—
881C4—42no—
882C4—42no—
883C4—42no—
884C4—42no—
885C4—42no—
886C4—42no—
887C4—82no—
888C4#295512yes—
889C4#295712yes—
890C4C4×2−1+412yes—
891C4#349911yescharacteristic
892C4#350011yescharacteristic
893C2—22no—
894C2—41no—
895C2—41no—
896C2—82no—
897C2#3427611yescharacteristic
898C2C2×#295511yescharacteristic
899C2C2×#295711yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
socleC22C22×C4×D4
prime radical#3444C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×#431 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #60250C2semidirect
4. #23082C2semidirect
5. #22984C2semidirect
6. #22951C2semidirect
7. #22949C2semidirect
8. #22256C2semidirect
9. #22256C2semidirect
10. #22234C2semidirect
11. #22234C2semidirect
12. #21993C2semidirect
13. #21734C2semidirect
14. #21732C2semidirect
15. #21660C2semidirect
16. #21658C2semidirect
18. #21329C2semidirect
19. #20462C2semidirect
22. #3233C4semidirect
23. #3232C4semidirect
24. #3231C4semidirect
25. #3231C4semidirect
26. #3230C4semidirect
27. #3229C4semidirect
28. #3228C4semidirect
29. #3228C4semidirect
30. #3227C4semidirect
31. #3226C4semidirect

Maximal subgroups

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

subgroupindex
#608462
#602682
#602502
#230822
#229842
#229512
#229492
#222562
#222342
#219932
#217342
#217322
#216602
#216582
#214182
#213292
#204622