Finite Group Databasebeta

← #6393381

Subgroups — #6393381

Order 512.

3530 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3506C211yesmaximal, characteristic
2C2×#2973C211yesmaximal, characteristic, complemented
3C2×#2352C211yesmaximal, characteristic, complemented
4#22494C214yesmaximal, complemented
5#22492C214yesmaximal, complemented
6#22422C214yesmaximal, complemented
7#22420C214yesmaximal, complemented
8#21866C211yesmaximal, characteristic, complemented
9#21865C211yesmaximal, characteristic, complemented
10#21769C212yesmaximal, complemented
11#21763C212yesmaximal, complemented
12#21395C211yesmaximal, characteristic, complemented
13#21394C211yesmaximal, characteristic, complemented
14#20909C212yesmaximal, complemented
15#20908C212yesmaximal, complemented
16#3506—28no—
17#3506C4116yescomplemented
18C2×#559—22no—
19C2×#556C2212yes—
20C2×#555C2212yes—
21C2×#553—22no—
22C2×#550C2212yes—
23C2×#547C2212yes—
24C2×#538—21no—
25C2×#538—21no—
26C2×#535—21no—
27C2×#533C2211yescharacteristic
28C2×#532C2211yescharacteristic
29C2×#525C2212yes—
30C2×#525C2212yes—
31C2×#520—21no—
32C22×C4×D4C2211yescharacteristic
33C22×#117C2211yescharacteristic
34C23×C4⋊C4C2211yescharacteristic
35#2973—28no—
36C2×#435C2214yes—
37C2×#435C2214yes—
38C2×#432C2211yescharacteristic
39C2×#432C2211yescharacteristic
40C2×#417C2214yescomplemented
41C2×#416C2214yescomplemented
42C2×#407C2212yes—
43C22×C22⋊C8C2212yes—
44#2352—22no—
45#2352—22no—
46#2352C2214yes—
47#2352C2214yes—
48C2×#388—21no—
49C2×#387—21no—
50C2×#386—21no—
51C2×#382C2211yescharacteristic
52C2×#380C2211yescharacteristic
53C2×#380C2211yescharacteristic
54C2×C4×C4⋊C4C2211yescharacteristic
55C2×C4×C22⋊C4—21no—
56#1993C2212yescomplemented
57#1993C2212yescomplemented
58#1988C2212yescomplemented
59#1987C2212yescomplemented
60#1982C2212yescomplemented
61#1981C2212yescomplemented
62#1961C2212yescomplemented
63#1960C2212yescomplemented
64#1895C2214yescomplemented
65#1894C2214yescomplemented
66#1893C2214yescomplemented
67#1892C2214yescomplemented
68#1875C2214yescomplemented
69#1874C2212yes—
70#1874C2212yes—
71#1874C2212yes—
72#1874C2212yes—
73#1874C2214yescomplemented
74#1873C2214yescomplemented
75#1872C2212yes—
76#1872C2212yes—
77#1872C2212yes—
78#1872C2212yes—
79#1872C2214yescomplemented
80#1825C2214yescomplemented
81#1825C2214yescomplemented
82#1805C2214yescomplemented
83#1804C2214yescomplemented
84#1788C2214yescomplemented
85#1788C2214yescomplemented
86#1763C2214yescomplemented
87#1762C2214yescomplemented
88#1736C2214yescomplemented
89#1735C2214yescomplemented
90C22×#41—21no—
91C22×#41C2312yes—
92C22×#41C2312yes—
93C23×D4D411yescharacteristic
94C24×C4—21no—
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C22×M16C2314yes—
98C23×C8C2314yes—
99#559—232no—
100#556—28no—
101#556C2×C4116yescomplemented
102#555—28no—
103#555C2×C4116yescomplemented
104#553—232no—
105#550—28no—
106#550C2×C4116yescomplemented
107#547—28no—
108#547C2×C4116yescomplemented
109#538—216no—
110#538—216no—
111#535—216no—
112#533—24no—
113#533C2×C418yescomplemented
114#532—24no—
115#532C2×C418yescomplemented
116C2×C4⋊Q8C2311yescharacteristic
117C2×C4⋊Q8C2311yescharacteristic
118C2×C4⋊Q8C2311yescharacteristic
119C2×#127—22no—
120C2×#127C2311yescharacteristic
121C2×#126—22no—
122C2×#126—22no—
123C2×#125—21no—
124C2×#124—22no—
125C2×#124—22no—
126C2×#124—22no—
127C2×#124—21no—
128#525—28no—
129#525—28no—
130#525C2×C4116yes—
131#525C2×C4116yescomplemented
132C2×#123—22no—
133C2×#123—22no—
134C2×#123—22no—
135C2×#123—22no—
136C2×C22⋊Q8—21no—
137C2×C22⋊Q8C2312yes—
138C2×C22⋊Q8C2312yes—
139C2×C22⋊Q8C2312yes—
140C2×#121—22no—
141C2×#121—22no—
142C2×#121—21no—
143C2×#121—22no—
144C2×#121—22no—
145C2×#121C2312yes—
146C2×#121C2312yes—
147C2×#121C2312yes—
148C2×#120—22no—
149C2×#120—22no—
150#520—216no—
151C2×C4×Q8—22no—
152C2×C4×Q8—21no—
153C2×C4×Q8C2312yes—
154C2×C4×D4—22no—
155C2×C4×D4—22no—
156C2×C4×D4—22no—
157C2×C4×D4—22no—
158C2×C4×D4—22no—
159C2×C4×D4—21no—
160C2×C4×D4C2×C418yes—
161C2×C4×D4D418yes—
162C2×C4×D4D412yes—
163C2×C4×D4D412yes—
164C2×C4×D4C2312yes—
165C2×C4×D4C2312yes—
166C2×C4×D4C2312yes—
167C2×#117—21no—
168C2×#117—22no—
169C2×#117—22no—
170C2×#117—44no—
171C2×#117C2314yes—
172C2×#117C2312yes—
173C2×#117C2312yes—
174C22×C4⋊C4—22no—
175C22×C4⋊C4—22no—
176C22×C4⋊C4—21no—
177C22×C4⋊C4—44no—
178C22×C4⋊C4D411yescharacteristic
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2314yes—
181C22×C4⋊C4C2311yescharacteristic
182C22×C4⋊C4C2311yescharacteristic
183C22×C4⋊C4C2311yescharacteristic
184C22×C22⋊C4—21no—
185C22×C22⋊C4—21no—
186C22×C22⋊C4—21no—
187C22×C22⋊C4D411yescharacteristic
188C22×C22⋊C4D411yescharacteristic
189C22×C42—21no—
190C22×C42—21no—
191C22×C42C2311yescharacteristic
192#435—216no—
193#435—216no—
194#432—24no—
195#432—24no—
196C2×C4⋊C8C2312yes—
197C2×C4⋊C8C2312yes—
198#417—48no—
199#416—48no—
200C2×#103C2314yes—
201C2×#103C2314yes—
202C2×#103C2314yes—
203C2×#103C2314yes—
204C2×#102C2314yes—
205C2×#102C2314yes—
206C2×#102C2314yes—
207C2×#102C2314yes—
208#407—28no—
209C2×C22⋊C8—28no—
210C2×C22⋊C8C2314yes—
211C2×C22⋊C8C2314yes—
212C2×C22⋊C8C2312yes—
213C2×C22⋊C8C2312yes—
214C2×#97C2312yes—
215C2×#97C2312yes—
216#388—24no—
217#388—24no—
218#387—24no—
219#387—24no—
220#386—24no—
221#386—24no—
222#382—21no—
223#382—21no—
224#382C2312yes—
225#382C2312yes—
226#380—22no—
227#380—22no—
228#380C2314yes—
229#380C2314yes—
230C4×C4⋊C4—21no—
231C4×C4⋊C4—21no—
232C4×C4⋊C4C2312yes—
233C4×C4⋊C4C2312yes—
234C4×C22⋊C4—24no—
235C4×C22⋊C4—24no—
236C2×#95—21no—
237C2×#95—21no—
238C2×#95—21no—
239C2×#95—21no—
240C2×#95—21no—
241#340C2314yes—
242#340C2314yes—
243#340C2314yes—
244#340C2314yes—
245#340C2314yes—
246#340C2314yes—
247#340C2314yes—
248#340C2314yes—
249C25C2×D411yescharacteristic
250C25C2×D411yescharacteristic
251C2×#41—28no—
252C2×#41—24no—
253C2×#41—24no—
254C2×#41—44no—
255C2×#41—44no—
256C2×#41—44no—
257C2×#41—44no—
258C2×#41—44no—
259C2×#41—44no—
260C2×#41C22×C418yes—
261C2×#41C22×C418yescomplemented
262C22×Q8—21no—
263C22×Q8—21no—
264C22×Q8C2412yes—
265C22×D4—22no—
266C22×D4—22no—
267C22×D4—22no—
268C22×D4—22no—
269C22×D4—22no—
270C22×D4—21no—
271C22×D4—21no—
272C22×D4—42no—
273C22×D4—42no—
274C22×D4C22⋊C418yes—
275C22×D4C2×D412yes—
276C22×D4C2×D412yes—
277C22×D4C2412yes—
278C23×C4—21no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—21no—
283C23×C4—21no—
284C23×C4—21no—
285C23×C4—24no—
286C23×C4—42no—
287C23×C4—42no—
288C23×C4—42no—
289C23×C4—42no—
290C23×C4—44no—
291C23×C4—44no—
292C23×C4—82no—
293C23×C4C22×C414yes—
294C23×C4C22×C414yes—
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D412yes—
300C23×C4C2×D412yes—
301C23×C4C2×D414yes—
302C23×C4C2×D414yes—
303C23×C4C2411yescharacteristic
304C23×C4C2412yes—
305C23×C4C2412yes—
306C2×M16—28no—
307C2×M16—44no—
308C2×M16—44no—
309C22×C8—28no—
310C22×C8—44no—
311C22×C8—44no—
312C22×C8C2414yes—
313C22×C8C2414yes—
314C4⋊Q8—22no—
315C4⋊Q8—22no—
316C4⋊Q8—22no—
317C4⋊Q8C22×C414yescomplemented
318C4⋊Q8C22×C414yescomplemented
319C4⋊Q8C22×C414yescomplemented
320#127—216no—
321#127—22no—
322#127C22×C414yescomplemented
323#126—216no—
324#126—216no—
325#125—28no—
326#124—216no—
327#124—216no—
328#124—216no—
329#124—28no—
330#123—216no—
331#123—216no—
332#123—216no—
333#123—216no—
334C22⋊Q8—28no—
335C22⋊Q8—24no—
336C22⋊Q8—24no—
337C22⋊Q8—24no—
338C22⋊Q8C22×C418yes—
339C22⋊Q8C22×C418yes—
340C22⋊Q8C22×C418yescomplemented
341#121—216no—
342#121—216no—
343#121—28no—
344#121—24no—
345#121—24no—
346#121—24no—
347#121—216no—
348#121—216no—
349#121C22×C418yes—
350#121C22×C418yes—
351#121C22×C418yescomplemented
352#120—216no—
353#120—216no—
354C4×Q8—216no—
355C4×Q8—28no—
356C4×Q8—24no—
357C4×Q8C22×C418yescomplemented
358C4×D4—216no—
359C4×D4—216no—
360C4×D4—216no—
361C4×D4—216no—
362C4×D4—216no—
363C4×D4—28no—
364C4×D4—24no—
365C4×D4C22⋊C4116yes—
366C4×D4C22⋊C4116yes—
367C4×D4C22×C418yes—
368C4×D4C22×C418yes—
369C4×D4C22×C418yescomplemented
370C4×D4C2×D418yes—
371C4×D4C2×D418yes—
372#117—28no—
373#117—24no—
374#117—24no—
375#117—216no—
376#117—28no—
377#117—44no—
378#117—48no—
379#117C22×C418yes—
380#117C22×C418yescomplemented
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—216no—
391C2×C4⋊C4—24no—
392C2×C4⋊C4—28no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—24no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—44no—
398C2×C4⋊C4—42no—
399C2×C4⋊C4—42no—
400C2×C4⋊C4—42no—
401C2×C4⋊C4—48no—
402C2×C4⋊C4—44no—
403C2×C4⋊C4C22⋊C418yes—
404C2×C4⋊C4C2×D412yes—
405C2×C4⋊C4C2×D412yes—
406C2×C4⋊C4C2412yes—
407C2×C4⋊C4C2412yes—
408C2×C4⋊C4C2412yes—
409C2×C4⋊C4C2412yes—
410C2×C4⋊C4C2412yes—
411C2×C4⋊C4C2412yes—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—24no—
422C2×C22⋊C4—24no—
423C2×C22⋊C4—24no—
424C2×C22⋊C4—44no—
425C2×C22⋊C4—44no—
426C2×C22⋊C4—82no—
427C2×C22⋊C4C22⋊C418yes—
428C2×C22⋊C4C22⋊C418yes—
429C2×C22⋊C4C2×D412yes—
430C2×C22⋊C4C2×D412yes—
431C2×C22⋊C4C2×D412yes—
432C2×C22⋊C4C2×D412yes—
433C2×C42—22no—
434C2×C42—22no—
435C2×C42—22no—
436C2×C42—24no—
437C2×C42—22no—
438C2×C42—22no—
439C2×C42—44no—
440C2×C42—82no—
441C2×C42C22×C414yes—
442C2×C42C2×D411yescharacteristic
443C2×C42C2×D411yescharacteristic
444C2×C42C2×D414yes—
445C2×C42C2411yescharacteristic
446C2×C42C2411yescharacteristic
447C4⋊C8—24no—
448C4⋊C8—24no—
449#103—28no—
450#103—44no—
451#103—44no—
452#103—44no—
453#102—28no—
454#102—44no—
455#102—44no—
456#102—44no—
457C22⋊C8—24no—
458C22⋊C8—24no—
459C22⋊C8—28no—
460C22⋊C8—28no—
461#97—24no—
462#97—24no—
463#95—24no—
464#95—22no—
465#95—22no—
466#95—22no—
467#95—22no—
468#95—24no—
469#95—22no—
470#95—22no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—41no—
477C24—41no—
478C24—41no—
479C24—41no—
480C24—41no—
481C24—41no—
482C24—41no—
483C24—41no—
484C24C2×C22⋊C414yes—
485C24C2×C22⋊C414yes—
486C24C22×D412yes—
487C24C22×D412yes—
488C24C22×D411yescharacteristic
489#41—432no—
490#41—416no—
491#41—416no—
492#41—88no—
493#41—88no—
494C2×Q8—24no—
495C2×Q8—24no—
496C2×Q8—22no—
497C2×Q8—24no—
498C2×Q8—24no—
499C2×Q8—42no—
500C2×Q8—42no—
501C2×Q8—81no—
502C2×Q8—81no—
503C2×Q8C23×C414yes—
504C2×D4—28no—
505C2×D4—28no—
506C2×D4—28no—
507C2×D4—28no—
508C2×D4—28no—
509C2×D4—24no—
510C2×D4—24no—
511C2×D4—22no—
512C2×D4—24no—
513C2×D4—24no—
514C2×D4—416no—
515C2×D4—42no—
516C2×D4—42no—
517C2×D4—42no—
518C2×D4—42no—
519C2×D4—42no—
520C2×D4—42no—
521C2×D4—44no—
522C2×D4—44no—
523C2×D4—81no—
524C2×D4—81no—
525C2×D4—82no—
526C2×D4—82no—
527C2×D4—82no—
528C2×D4—82no—
529C2×D4—82no—
530C2×D4—82no—
531C2×D4—82no—
532C2×D4—82no—
533C2×D4C2×C22⋊C418yes—
534C2×D4C2×C22⋊C418yes—
535C2×D4C23×C414yes—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—22no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—28no—
550C22×C4—28no—
551C22×C4—28no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—48no—
556C22×C4—48no—
557C22×C4—48no—
558C22×C4—48no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—42no—
562C22×C4—41no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4—48no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—48no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—82no—
585C22×C4—82no—
586C22×C4—82no—
587C22×C4—82no—
588C22×C4—84no—
589C22×C4—816no—
590C22×C4C2×C22⋊C414yes—
591C22×C4C2×C22⋊C414yes—
592C22×C4C2×C22⋊C414yes—
593C22×C4C2×C22⋊C414yes—
594C22×C4C2×C22⋊C418yes—
595C22×C4C2×C22⋊C418yes—
596C22×C4C23×C412yes—
597C22×C4C23×C414yes—
598C22×C4C23×C414yes—
599C22×C4C22×D411yescharacteristic
600C22×C4C22×D411yescharacteristic
601C22×C4C22×D412yes—
602C22×C4C22×D411yescharacteristic
603C22×C4C22×D411yescharacteristic
604C22×C4C22×D412yes—
605C22×C4C22×D411yescharacteristic
606C22×C4C22×D412yes—
607C22×C4C22×D414yes—
608C22×C4C22×D414yes—
609C22×C4C2511yescharacteristic
610M16—88no—
611C2×C8—24no—
612C2×C8—24no—
613C2×C8—24no—
614C2×C8—24no—
615C2×C8—24no—
616C2×C8—24no—
617C2×C8—88no—
618C4⋊C4—24no—
619C4⋊C4—24no—
620C4⋊C4—28no—
621C4⋊C4—28no—
622C4⋊C4—24no—
623C4⋊C4—28no—
624C4⋊C4—24no—
625C4⋊C4—24no—
626C4⋊C4—28no—
627C4⋊C4—22no—
628C4⋊C4—22no—
629C4⋊C4—22no—
630C4⋊C4—24no—
631C4⋊C4—24no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—48no—
635C4⋊C4—42no—
636C4⋊C4—42no—
637C4⋊C4—42no—
638C4⋊C4C2×C22⋊C418yes—
639C4⋊C4C2×C22⋊C418yes—
640C4⋊C4C23×C414yes—
641C4⋊C4C23×C414yes—
642C4⋊C4H(5,𝔽2)14yes—
643C22⋊C4—28no—
644C22⋊C4—28no—
645C22⋊C4—28no—
646C22⋊C4—28no—
647C22⋊C4—28no—
648C22⋊C4—28no—
649C22⋊C4—28no—
650C22⋊C4—28no—
651C22⋊C4—28no—
652C22⋊C4—48no—
653C22⋊C4—48no—
654C22⋊C4—84no—
655C22⋊C4C2×C22⋊C418yes—
656C22⋊C4C2×C22⋊C418yes—
657C22⋊C4C2×C22⋊C418yes—
658C22⋊C4C2×C22⋊C418yes—
659C42—28no—
660C42—28no—
661C42—28no—
662C42—48no—
663C42—82no—
664C42—82no—
665C42C2×C22⋊C414yes—
666C42C2×C22⋊C414yes—
667C42C23×C412yes—
668C42C23×C412yes—
669C42C22×D412yes—
670C42C22×D412yes—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—28no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—28no—
689C23—24no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23—44no—
696C23—44no—
697C23—44no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—82no—
705C23—82no—
706C23—82no—
707C23—82no—
708C23C22×C22⋊C414yes—
709C23C22×C22⋊C414yes—
710C23C22×C22⋊C412yes—
711C23#57512yes—
712C23#57512yes—
713C23C23×D411yescharacteristic
714Q8—28no—
715Q8—48no—
716Q8—44no—
717Q8—84no—
718D4—28no—
719D4—48no—
720D4—48no—
721D4—48no—
722D4—416no—
723D4—44no—
724D4—84no—
725D4—88no—
726D4—88no—
727D4—88no—
728D4—88no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—28no—
734C2×C4—22no—
735C2×C4—21no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—24no—
745C2×C4—28no—
746C2×C4—28no—
747C2×C4—28no—
748C2×C4—28no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—48no—
755C2×C4—48no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—416no—
760C2×C4—48no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—88no—
779C2×C4—88no—
780C2×C4—816no—
781C2×C4—84no—
782C2×C4—84no—
783C2×C4—84no—
784C2×C4C22×C22⋊C412yes—
785C2×C4C22×C22⋊C414yes—
786C2×C4C22×C22⋊C414yes—
787C2×C4C22×C22⋊C412yes—
788C2×C4C22×C22⋊C412yes—
789C2×C4C22×C22⋊C412yes—
790C2×C4C22×C22⋊C412yes—
791C2×C4C24×C411yescharacteristic
792C2×C4C23×D411yescharacteristic
793C2×C4C2×H(5,𝔽2)12yes—
794C2×C4#58512yes—
795C8—44no—
796C8—44no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—24no—
804C22—24no—
805C22—24no—
806C22—24no—
807C22—24no—
808C22—24no—
809C22—416no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—44no—
819C22—44no—
820C22—44no—
821C22—88no—
822C22—82no—
823C22—82no—
824C22—82no—
825C22—82no—
826C22#289614yes—
827C22C23×C22⋊C411yescharacteristic
828C22#348411yescharacteristic
829C22#348511yescharacteristic
830C22C2×#57511yescharacteristic
831C22C2×#57511yescharacteristic
832C22#358511yescharacteristic
833C22#358611yescharacteristic
834C4—22no—
835C4—22no—
836C4—22no—
837C4—22no—
838C4—22no—
839C4—24no—
840C4—24no—
841C4—44no—
842C4—44no—
843C4—44no—
844C4—44no—
845C4—82no—
846C4—82no—
847C4—82no—
848C4C4×H(5,𝔽2)12yes—
849C4#349612yes—
850C2—24no—
851C2—44no—
852C2—44no—
853C2—84no—
854C2#3425611yescharacteristic
855C2C2×#289611yescharacteristic
856C2#6008911yescharacteristic
857C2#6157611yescharacteristic
858C2#6157811yescharacteristic
859C2#6171111yescharacteristic
860C2#6171311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#3506C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2973C2semidirect
3. C2×#2352C2semidirect
4. #22494C2semidirect
5. #22492C2semidirect
6. #22422C2semidirect
7. #22420C2semidirect
8. #21866C2semidirect
9. #21865C2semidirect
10. #21769C2semidirect
11. #21763C2semidirect
12. #21395C2semidirect
13. #21394C2semidirect
14. #20909C2semidirect
15. #20908C2semidirect
17. #3506C4semidirect
40. C2×#417C22semidirect
41. C2×#416C22semidirect
56. #1993C22semidirect
57. #1993C22semidirect
58. #1988C22semidirect
59. #1987C22semidirect
60. #1982C22semidirect
61. #1981C22semidirect
62. #1961C22semidirect
63. #1960C22semidirect
64. #1895C22semidirect
65. #1894C22semidirect
66. #1893C22semidirect
67. #1892C22semidirect
68. #1875C22semidirect
73. #1874C22semidirect
74. #1873C22semidirect
79. #1872C22semidirect
80. #1825C22semidirect
81. #1825C22semidirect
82. #1805C22semidirect
83. #1804C22semidirect
84. #1788C22semidirect
85. #1788C22semidirect
86. #1763C22semidirect
87. #1762C22semidirect
88. #1736C22semidirect
89. #1735C22semidirect
101. #556C2×C4semidirect
103. #555C2×C4semidirect
106. #550C2×C4semidirect
108. #547C2×C4semidirect
113. #533C2×C4semidirect
115. #532C2×C4semidirect
131. #525C2×C4semidirect
261. C2×#41C22×C4semidirect
317. C4⋊Q8C22×C4semidirect
318. C4⋊Q8C22×C4semidirect
319. C4⋊Q8C22×C4semidirect
322. #127C22×C4semidirect
340. C22⋊Q8C22×C4semidirect
351. #121C22×C4semidirect
357. C4×Q8C22×C4semidirect
369. C4×D4C22×C4semidirect
380. #117C22×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#35062
C2×#29732
C2×#23522
#224942
#224922
#224222
#224202
#218662
#218652
#217692
#217632
#213952
#213942
#209092
#209082