Finite Group Databasebeta

← #6394002

Subgroups — #6394002

Order 512.

3184 conjugacy classes of subgroups.

The subgroup lattice has 819 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3515C211yesmaximal, characteristic
2C2×#2970C211yesmaximal, characteristic, complemented
3#34183C211yesmaximal, characteristic, complemented
4#22524C212yesmaximal, complemented
5#22522C212yesmaximal, complemented
6#22493C214yesmaximal, complemented
7#22491C214yesmaximal, complemented
8#22487C212yesmaximal, complemented
9#22485C212yesmaximal, complemented
10#21867C211yesmaximal, characteristic, complemented
11#21867C212yesmaximal, complemented
12#21839C211yesmaximal, characteristic, complemented
13#21838C212yesmaximal, complemented
14#21406C212yesmaximal, complemented
15#21403C211yesmaximal, characteristic, complemented
16#21322C211yesmaximal, characteristic, complemented
17C2×#1992C212yesmaximal, complemented
18#3515—28no—
19#3515C4116yescomplemented
20C2×#557C2211yescharacteristic
21C2×#554C2211yescharacteristic
22C2×#554C2211yescharacteristic
23C2×#553C2212yes—
24C2×#552—22no—
25C2×#552—21no—
26C2×#552C2212yes—
27C2×#547—21no—
28C2×#547C2211yescharacteristic
29C2×#541—21no—
30C2×#539—22no—
31C2×#533C2211yescharacteristic
32C2×#529C2211yescharacteristic
33C2×#529C2212yes—
34C22×#125C2212yes—
35C2×#520—21no—
36C2×#520—21no—
37C2×C4×#41C2211yescharacteristic
38#2970—28no—
39C2×#446C2212yes—
40C2×#435C2214yes—
41C2×C8×D4C2212yes—
42C2×#432C2212yes—
43C2×#432C2211yescharacteristic
44C2×C4×M16C2211yescharacteristic
45C22×#97C2212yes—
46Q8×C4⋊C4—21no—
47Q8×C4⋊C4C2212yes—
48D4×C4⋊C4—21no—
49D4×C4⋊C4—22no—
50D4×C4⋊C4C2212yes—
51D4×C4⋊C4C2214yes—
52#2317—22no—
53#2317—21no—
54#2285C2212yes—
55#2285C2211yescharacteristic
56C2×#384C2212yes—
57C2×#384C2211yescharacteristic
58#1992C2211yescharacteristic
59#1992C2212yes—
60#1992C2212yes—
61#1992C2212yes—
62#1992C2214yes—
63#1992C2214yes—
64#1992C2212yes—
65#1992C2211yescharacteristic
66#1992C2212yes—
67#1990C2212yes—
68#1990C2212yes—
69#1989C2214yes—
70#1989C2214yes—
71#1988C2212yes—
72#1987C2212yes—
73#1959C2211yescharacteristic
74#1959C2212yes—
75#1959C2211yescharacteristic
76#1895C2212yes—
77#1894C2212yes—
78#1893C2214yes—
79#1892C2214yes—
80#1874C2214yes—
81#1874C2212yes—
82#1872C2214yes—
83#1872C2212yes—
84#1825C2214yes—
85#1824C2214yes—
86#1823C2214yes—
87#1803C2212yes—
88#1803C2214yes—
89#1802C2212yes—
90#1802C2214yes—
91#1763C2214yes—
92#1762C2214yes—
93C4×#103C2212yes—
94C4×#102C2212yes—
95#1736C2214yes—
96C2×#340C2214yes—
97C2×#340C2214yes—
98C22×#41—21no—
99C22×#41D411yescharacteristic
100C22×M16C2312yes—
101C23×C8C2314yes—
102#557—24no—
103#557C2×C418yescomplemented
104#554—24no—
105#554—24no—
106#554C2×C418yescomplemented
107#554C2×C418yescomplemented
108#553—28no—
109#553C2×C4116yescomplemented
110#552—28no—
111#552—232no—
112#552—216no—
113#552C2×C4116yescomplemented
114#547—216no—
115#547—24no—
116#547C2×C418yescomplemented
117#541—216no—
118#539—232no—
119#533—24no—
120#533C2×C418yescomplemented
121C2×C4⋊Q8—21no—
122C2×C4⋊Q8C2311yescharacteristic
123C2×C4⋊Q8C2311yescharacteristic
124#529—28no—
125#529—24no—
126#529C2×C4116yescomplemented
127#529C2×C418yescomplemented
128C2×#126—22no—
129C2×#126—22no—
130C2×#126—22no—
131C2×#126—21no—
132C2×#125—22no—
133C2×#125—22no—
134C2×#125—21no—
135C2×#125—22no—
136C2×#125—22no—
137C2×#125—28no—
138C2×#125C2×C4116yescomplemented
139C2×#125C2311yescharacteristic
140C2×#125C2312yes—
141C2×#125C2312yes—
142C2×#125C2312yes—
143C2×#124C2311yescharacteristic
144C2×#123—22no—
145C2×#123—21no—
146C2×#123—22no—
147C2×#123—22no—
148C2×#123—22no—
149C2×C22⋊Q8—21no—
150C2×C22⋊Q8—21no—
151C2×C22⋊Q8—21no—
152C2×C22⋊Q8—22no—
153C2×C22⋊Q8—21no—
154C2×C22⋊Q8—22no—
155C2×C22⋊Q8C2312yes—
156C2×C22⋊Q8C2311yescharacteristic
157C2×#121—22no—
158C2×#121C2312yes—
159C2×#121C2311yescharacteristic
160#520—216no—
161#520—48no—
162C4×#41C2×C418yes—
163C4×#41D418yes—
164C2×C4×Q8—22no—
165C2×C4×Q8—21no—
166C2×C4×Q8—21no—
167C2×C4×Q8—21no—
168C2×C4×Q8D411yescharacteristic
169C2×C4×Q8C2312yes—
170C2×C4×Q8C2311yescharacteristic
171C2×C4×Q8C2311yescharacteristic
172C2×C4×D4—21no—
173C2×C4×D4—22no—
174C2×C4×D4—21no—
175C2×C4×D4—24no—
176C2×C4×D4—22no—
177C2×C4×D4—22no—
178C2×C4×D4D411yescharacteristic
179C2×C4×D4D412yes—
180C2×C4×D4C2311yescharacteristic
181C2×C4×D4C2312yes—
182C2×C4×D4C2311yescharacteristic
183C2×C4×D4C2312yes—
184C2×#117—22no—
185C2×#117—21no—
186C2×#117—22no—
187C2×#117—21no—
188C2×#117—22no—
189C2×#117D411yescharacteristic
190C2×#117D412yes—
191C2×#117C2312yes—
192C22×C4⋊C4—22no—
193C22×C4⋊C4—22no—
194C22×C4⋊C4—21no—
195C22×C4⋊C4—22no—
196C22×C4⋊C4—21no—
197C22×C4⋊C4—22no—
198C22×C4⋊C4—21no—
199C22×C4⋊C4C2312yes—
200C22×C4⋊C4C2312yes—
201C22×C4⋊C4C2314yes—
202C22×C4⋊C4C2312yes—
203C22×C42C2312yes—
204C22×C42C2311yescharacteristic
205#446—28no—
206#435—216no—
207C8×D4—28no—
208#432—24no—
209#432—28no—
210C2×C4⋊C8C2312yes—
211C2×C4⋊C8C2314yes—
212C2×#103C2312yes—
213C2×#103C2314yes—
214C2×#103C2312yes—
215C2×#102C2312yes—
216C2×#102C2314yes—
217C2×#102C2312yes—
218C2×C22⋊C8C2314yes—
219C2×C22⋊C8C2312yes—
220C4×M16—24no—
221C2×#97—28no—
222C2×#97C2311yescharacteristic
223C2×#97C2312yes—
224C2×#97C2314yes—
225C2×#97C2311yescharacteristic
226C2×C4×C8C2312yes—
227#389—22no—
228#389—24no—
229#389—22no—
230#389—24no—
231#385—24no—
232#385—24no—
233#385—24no—
234#384—22no—
235#384—21no—
236#384—21no—
237#384—22no—
238#384C2312yes—
239#384C2314yes—
240#384C2311yescharacteristic
241#384C2312yes—
242#384C2311yescharacteristic
243#382—22no—
244#382—21no—
245#380—22no—
246#380—21no—
247#380C2314yes—
248#380C2312yes—
249C4×C4⋊C4—21no—
250C4×C4⋊C4—22no—
251C4×C4⋊C4C2312yes—
252C4×C4⋊C4C2314yes—
253#340C2314yes—
254#340C2314yes—
255#340C2314yes—
256#340C2314yes—
257#340C2314yes—
258#340C2314yes—
259#340C2312yes—
260#340C2314yes—
261#340C2312yes—
262#340C2314yes—
263#340C2314yes—
264#340C2314yes—
265#340C2312yes—
266#340C2312yes—
267C2×#41—28no—
268C2×#41—24no—
269C2×#41—24no—
270C2×#41—44no—
271C2×#41—44no—
272C2×#41C22⋊C418yes—
273C22×Q8—21no—
274C22×Q8—21no—
275C22×Q8C2×D411yescharacteristic
276C22×Q8C2411yescharacteristic
277C22×D4—22no—
278C22×D4—21no—
279C22×D4C2×D412yes—
280C22×D4C2×D411yescharacteristic
281C22×D4C2411yescharacteristic
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—21no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—24no—
288C23×C4C2×D412yes—
289C23×C4C2×D411yescharacteristic
290C23×C4C2×D412yes—
291C23×C4C2×D411yescharacteristic
292C23×C4C2412yes—
293C23×C4C2411yescharacteristic
294C2×M16—24no—
295C2×M16—24no—
296C2×M16—42no—
297C22×C8—28no—
298C22×C8—28no—
299C22×C8—44no—
300C22×C8C2414yes—
301C22×C8C2412yes—
302C22×C8C2412yes—
303C4⋊Q8—28no—
304C4⋊Q8—22no—
305C4⋊Q8—22no—
306C4⋊Q8C22×C414yes—
307C4⋊Q8C22×C414yes—
308#126—216no—
309#126—216no—
310#126—216no—
311#126—28no—
312#125—216no—
313#125—216no—
314#125—28no—
315#125—216no—
316#125—216no—
317#125—22no—
318#125—24no—
319#125—24no—
320#125—24no—
321#125C22×C414yes—
322#125C22×C418yes—
323#125C22×C418yes—
324#125C22×C418yes—
325#124—22no—
326#124C22×C414yes—
327#123—216no—
328#123—28no—
329#123—216no—
330#123—216no—
331#123—216no—
332C22⋊Q8—28no—
333C22⋊Q8—28no—
334C22⋊Q8—28no—
335C22⋊Q8—22no—
336C22⋊Q8—24no—
337C22⋊Q8—216no—
338C22⋊Q8—28no—
339C22⋊Q8—216no—
340C22⋊Q8C22×C414yes—
341C22⋊Q8C22×C418yes—
342#121—216no—
343#121—24no—
344#121—22no—
345#121C22×C418yes—
346#121C22×C414yes—
347C4×Q8—28no—
348C4×Q8—28no—
349C4×Q8—28no—
350C4×Q8—24no—
351C4×Q8—22no—
352C4×Q8—48no—
353C4×Q8C22⋊C418yes—
354C4×Q8C22×C418yes—
355C4×Q8C22×C414yes—
356C4×Q8C22×C414yes—
357C4×Q8C2×D414yes—
358C4×D4—28no—
359C4×D4—216no—
360C4×D4—28no—
361C4×D4—216no—
362C4×D4—22no—
363C4×D4—24no—
364C4×D4—416no—
365C4×D4—48no—
366C4×D4C22⋊C418yes—
367C4×D4C22⋊C4116yes—
368C4×D4C22×C414yes—
369C4×D4C22×C418yes—
370C4×D4C22×C414yes—
371C4×D4C22×C418yes—
372C4×D4C2×D414yes—
373C4×D4C2×D418yes—
374#117—24no—
375#117—216no—
376#117—28no—
377#117—216no—
378#117—48no—
379#117—44no—
380#117C22⋊C418yes—
381#117C22⋊C4116yes—
382#117C22×C418yes—
383C2×C4⋊C4—216no—
384C2×C4⋊C4—216no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—24no—
397C2×C4⋊C4—24no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—28no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—24no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—24no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—24no—
416C2×C4⋊C4—44no—
417C2×C4⋊C4—44no—
418C2×C4⋊C4—44no—
419C2×C4⋊C4—48no—
420C2×C4⋊C4—44no—
421C2×C4⋊C4—84no—
422C2×C4⋊C4—82no—
423C2×C4⋊C4C22×C418yes—
424C2×C4⋊C4C22×C418yes—
425C2×C4⋊C4C2×D411yescharacteristic
426C2×C4⋊C4C2×D412yes—
427C2×C4⋊C4C2×D411yescharacteristic
428C2×C4⋊C4C2×D412yes—
429C2×C4⋊C4C2412yes—
430C2×C4⋊C4C2414yes—
431C2×C4⋊C4C2412yes—
432C2×C4⋊C4C2411yescharacteristic
433C2×C4⋊C4C2411yescharacteristic
434C2×C4⋊C4C2412yes—
435C2×C4⋊C4C2412yes—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—24no—
447C2×C22⋊C4C2×D412yes—
448C2×C22⋊C4C2×D412yes—
449C2×C22⋊C4C2×D412yes—
450C2×C42—22no—
451C2×C42—22no—
452C2×C42—21no—
453C2×C42—24no—
454C2×C42—22no—
455C2×C42C22×C418yes—
456C2×C42C22×C414yes—
457C2×C42C2×D412yes—
458C2×C42C2×D411yescharacteristic
459C2×C42C2×D411yescharacteristic
460C2×C42C2×D412yes—
461C2×C42C2×D418yes—
462C2×C42C2×D414yes—
463C2×C42C2412yes—
464C2×C42C2411yescharacteristic
465C2×C42C2411yescharacteristic
466C4⋊C8—24no—
467C4⋊C8—28no—
468#103—24no—
469#103—44no—
470#103—42no—
471#102—24no—
472#102—44no—
473#102—42no—
474C22⋊C8—28no—
475C22⋊C8—24no—
476#97—22no—
477#97—24no—
478#97—28no—
479#97—22no—
480C4×C8—24no—
481#95—22no—
482#95—24no—
483#95—24no—
484#95—22no—
485C24—21no—
486C24C22×D411yescharacteristic
487C24C22×D412yes—
488#41—232no—
489#41—432no—
490C2×Q8—24no—
491C2×Q8—24no—
492C2×Q8—22no—
493C2×Q8—22no—
494C2×Q8—21no—
495C2×Q8—22no—
496C2×Q8—22no—
497C2×Q8—42no—
498C2×Q8—42no—
499C2×Q8—81no—
500C2×Q8—81no—
501C2×Q8C2×C22⋊C414yes—
502C2×Q8C23×C412yes—
503C2×D4—24no—
504C2×D4—24no—
505C2×D4—28no—
506C2×D4—24no—
507C2×D4—21no—
508C2×D4—22no—
509C2×D4—22no—
510C2×D4—44no—
511C2×D4—44no—
512C2×D4—81no—
513C2×D4—81no—
514C2×D4C2×C22⋊C418yes—
515C2×D4C2×C22⋊C414yes—
516C2×D4AGL(1,ℤ/8)14yes—
517C2×D4#13714yes—
518C2×D4C23×C412yes—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—24no—
524C22×C4—22no—
525C22×C4—24no—
526C22×C4—22no—
527C22×C4—28no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—28no—
534C22×C4—24no—
535C22×C4—28no—
536C22×C4—22no—
537C22×C4—24no—
538C22×C4—22no—
539C22×C4—42no—
540C22×C4—41no—
541C22×C4—42no—
542C22×C4—41no—
543C22×C4—44no—
544C22×C4—44no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—44no—
548C22×C4—48no—
549C22×C4—82no—
550C22×C4—82no—
551C22×C4—82no—
552C22×C4—82no—
553C22×C4—84no—
554C22×C4—82no—
555C22×C4—84no—
556C22×C4—82no—
557C22×C4C2×C22⋊C418yes—
558C22×C4C2×C22⋊C414yes—
559C22×C4C2×C22⋊C418yes—
560C22×C4C2×C22⋊C414yes—
561C22×C4C23×C414yes—
562C22×C4C23×C412yes—
563C22×C4C22×D411yescharacteristic
564C22×C4C22×D412yes—
565C22×C4C22×D412yes—
566C22×C4C22×D411yescharacteristic
567C22×C4C22×D412yes—
568C22×C4C22×D411yescharacteristic
569C22×C4C22×D411yescharacteristic
570C22×C4C22×D414yes—
571C22×C4C22×D412yes—
572C22×C4C22×D411yescharacteristic
573C22×C4C2511yescharacteristic
574M16—48no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—24no—
579C2×C8—24no—
580C2×C8—22no—
581C2×C8—24no—
582C2×C8—22no—
583C2×C8—416no—
584C2×C82−1+414yes—
585C4⋊C4—28no—
586C4⋊C4—24no—
587C4⋊C4—24no—
588C4⋊C4—28no—
589C4⋊C4—24no—
590C4⋊C4—28no—
591C4⋊C4—28no—
592C4⋊C4—28no—
593C4⋊C4—28no—
594C4⋊C4—28no—
595C4⋊C4—28no—
596C4⋊C4—24no—
597C4⋊C4—28no—
598C4⋊C4—24no—
599C4⋊C4—24no—
600C4⋊C4—28no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—24no—
608C4⋊C4—22no—
609C4⋊C4—24no—
610C4⋊C4—22no—
611C4⋊C4—42no—
612C4⋊C4—44no—
613C4⋊C4—42no—
614C4⋊C4—48no—
615C4⋊C4—42no—
616C4⋊C4—44no—
617C4⋊C4—42no—
618C4⋊C4—44no—
619C4⋊C4—84no—
620C4⋊C4—82no—
621C4⋊C4—84no—
622C4⋊C4—82no—
623C4⋊C4C2×C22⋊C414yes—
624C4⋊C4C2×C22⋊C418yes—
625C4⋊C4C2×C22⋊C414yes—
626C4⋊C4C2×C22⋊C418yes—
627C4⋊C4C23×C412yes—
628C4⋊C4C23×C412yes—
629C4⋊C4C23×C414yes—
630C4⋊C4C23×C414yes—
631C22⋊C4—28no—
632C22⋊C4—28no—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—28no—
638C22⋊C4—28no—
639C22⋊C4—24no—
640C22⋊C4—44no—
641C22⋊C4—48no—
642C22⋊C4C2×C22⋊C418yes—
643C22⋊C4C2×C22⋊C418yes—
644C22⋊C4C2×C22⋊C418yes—
645C42—28no—
646C42—28no—
647C42—24no—
648C42—48no—
649C42—44no—
650C42C2×C22⋊C418yes—
651C42C2×C22⋊C414yes—
652C42C2×C22⋊C414yes—
653C42C2×C22⋊C418yes—
654C42C23×C412yes—
655C42C23×C414yes—
656C42C23×C412yes—
657C42C22×D412yes—
658C42C22×D412yes—
659C42C22×D414yes—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—22no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23C22×C22⋊C412yes—
678C23C22×C22⋊C414yes—
679C23C2×AGL(1,ℤ/8)14yes—
680C23C2×#13714yes—
681C23C23×D411yescharacteristic
682Q8—28no—
683Q8—24no—
684Q8—48no—
685Q8—42no—
686Q8—84no—
687D4—216no—
688D4—24no—
689D4—416no—
690D4—42no—
691D4—84no—
692D4#417116yes—
693C2×C4—21no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—216no—
700C2×C4—22no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—28no—
709C2×C4—28no—
710C2×C4—24no—
711C2×C4—28no—
712C2×C4—24no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—48no—
719C2×C4—44no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—416no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—42no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—48no—
732C2×C4—42no—
733C2×C4—44no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—44no—
738C2×C4—42no—
739C2×C4—44no—
740C2×C4—42no—
741C2×C4—88no—
742C2×C4—88no—
743C2×C4—168no—
744C2×C4—164no—
745C2×C4C22×C22⋊C412yes—
746C2×C4C22×C22⋊C414yes—
747C2×C4C22×C22⋊C412yes—
748C2×C4C22×C22⋊C412yes—
749C2×C4C22×C22⋊C414yes—
750C2×C4C22×C22⋊C412yes—
751C2×C4C22×C22⋊C414yes—
752C2×C4C22×C22⋊C412yes—
753C2×C4C2×AGL(1,ℤ/8)12yes—
754C2×C4C2×#13712yes—
755C2×C4C24×C411yescharacteristic
756C2×C4C23×D411yescharacteristic
757C2×C4C2×2−1+412yes—
758C2×C4#58512yes—
759C8—24no—
760C8—44no—
761C8—42no—
762C22—24no—
763C22—24no—
764C22—24no—
765C22—24no—
766C22—24no—
767C22—24no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22C2×#41718yes—
783C22C23×C22⋊C411yescharacteristic
784C22#349911yescharacteristic
785C22#350011yescharacteristic
786C22C22×AGL(1,ℤ/8)11yescharacteristic
787C22C22×#13711yescharacteristic
788C22#358511yescharacteristic
789C22#358611yescharacteristic
790C4—22no—
791C4—24no—
792C4—22no—
793C4—24no—
794C4—22no—
795C4—24no—
796C4—22no—
797C4—42no—
798C4—44no—
799C4—42no—
800C4—44no—
801C4—42no—
802C4—82no—
803C4—82no—
804C4—84no—
805C4C2×#41714yes—
806C4C4×2−1+412yes—
807C4#348912yes—
808C2—28no—
809C2—42no—
810C2—82no—
811C2#3425911yescharacteristic
812C2C22×#41711yescharacteristic
813C2#6008911yescharacteristic
814C2#6250311yescharacteristic
815C2#6250411yescharacteristic
816C2#6257611yescharacteristic
817C2#6257711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#3515C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×#41 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2970C2semidirect
3. #34183C2semidirect
4. #22524C2semidirect
5. #22522C2semidirect
6. #22493C2semidirect
7. #22491C2semidirect
8. #22487C2semidirect
9. #22485C2semidirect
10. #21867C2semidirect
11. #21867C2semidirect
12. #21839C2semidirect
13. #21838C2semidirect
14. #21406C2semidirect
15. #21403C2semidirect
16. #21322C2semidirect
17. C2×#1992C2semidirect
19. #3515C4semidirect
103. #557C2×C4semidirect
106. #554C2×C4semidirect
107. #554C2×C4semidirect
109. #553C2×C4semidirect
113. #552C2×C4semidirect
116. #547C2×C4semidirect
120. #533C2×C4semidirect
126. #529C2×C4semidirect
127. #529C2×C4semidirect
138. C2×#125C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#35152
C2×#29702
#341832
#225242
#225222
#224932
#224912
#224872
#224852
#218672
#218392
#218382
#214062
#214032
#213222
C2×#19922