Finite Group Databasebeta

← C2×#17615 #6343450

Subgroups — C2×#17615 #6343450

Order 512.

3364 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3505C211yesmaximal, characteristic
2C2×#2972C211yesmaximal, characteristic, complemented
3C2×#2353C211yesmaximal, characteristic, complemented
4#17615C2116yesmaximal, direct product factor
5C2×#1516C212yesmaximal, complemented
6C2×#1521C212yesmaximal, complemented
7C2×#1520C211yesmaximal, characteristic, complemented
8C2×#1519C211yesmaximal, characteristic, complemented
9C2×#1501C212yesmaximal, complemented
10C2×#1500C212yesmaximal, complemented
11C22×#328C211yesmaximal, characteristic, complemented
12C22×#327C211yesmaximal, characteristic, complemented
13#3505—24no—
14#3505—24no—
15#3505C418yescomplemented
16#3505C2218yes—
17C2×#553—22no—
18C2×#553C412yescomplemented
19C2×#552C412yescomplemented
20C2×#551—22no—
21C2×#548C412yescomplemented
22C2×#546C412yescomplemented
23C2×#539—21no—
24C2×#538—21no—
25C2×#534—21no—
26C2×#529C2212yes—
27C2×#525C2212yes—
28C22×C22⋊Q8C2211yescharacteristic
29C22×#121C2211yescharacteristic
30C2×#518—21no—
31C22×C4×D4C2211yescharacteristic
32#2972—24no—
33#2972C2218yescomplemented
34C2×C8×D4—22no—
35C2×C8×D4—22no—
36C2×#431C2212yescomplemented
37C22×C22⋊C8C2211yescharacteristic
38C22×C22⋊C8C2211yescharacteristic
39C22×C22⋊C8C2212yescomplemented
40#2353—24no—
41#2353C2218yescomplemented
42C2×#388—21no—
43C2×#387—21no—
44C2×#386—21no—
45C2×#383C2211yescharacteristic, complemented
46C2×#381C2211yescharacteristic, complemented
47C2×#380C2211yescharacteristic
48C2×C4×C22⋊C4—21no—
49C2×C4×C22⋊C4C2211yescharacteristic, complemented
50C2×#376C2211yescharacteristic, complemented
51C22×#95C2211yescharacteristic
52#1521C22116yescomplemented
53#1520C2218yescomplemented
54#1519C2218yescomplemented
55#1516C22116yescomplemented
56#1501C22116yescomplemented
57#1500C22116yescomplemented
58C2×#328C2212yescomplemented
59C2×#328C2212yescomplemented
60C2×#328C2218yescomplemented
61C2×#328C2212yescomplemented
62C2×#328C2212yescomplemented
63C2×#327C2212yes—
64C2×#327C2212yes—
65C2×#327C2212yes—
66C2×#327C2212yes—
67C2×#327C2218yescomplemented
68C22×#41C2×C412yescomplemented
69C23×Q8C2×C411yescharacteristic
70C23×D4—21no—
71C23×D4C2×C411yescharacteristic
72C23×D4D411yescharacteristic
73C24×C4—21no—
74C24×C4C2311yescharacteristic
75C24×C4C2311yescharacteristic
76C23×C8—21no—
77C23×C8—21no—
78C23×C8—22no—
79#553—216no—
80#553—28no—
81#553—216no—
82#553C2×C4116yescomplemented
83#552—28no—
84#552C2×C4116yescomplemented
85#551—216no—
86#551—216no—
87#548—28no—
88#548C2×C4116yescomplemented
89#546—28no—
90#546C2×C4116yescomplemented
91#539—28no—
92#539—28no—
93#538—28no—
94#538—28no—
95#534—28no—
96#534—28no—
97#529—24no—
98#529—24no—
99#529C2×C418yescomplemented
100#529C2318yes—
101C2×#126—22no—
102C2×#126—22no—
103C2×#126—22no—
104C2×#125—22no—
105C2×#125C2×C412yescomplemented
106C2×#124—22no—
107C2×#124C2×C412yescomplemented
108#525—24no—
109#525—24no—
110#525C2×C418yescomplemented
111#525C2318yes—
112C2×#123—22no—
113C2×#123—22no—
114C2×#123—22no—
115C2×#123—22no—
116C2×#123—22no—
117C2×C22⋊Q8—21no—
118C2×C22⋊Q8—21no—
119C2×C22⋊Q8—22no—
120C2×C22⋊Q8—22no—
121C2×C22⋊Q8—22no—
122C2×C22⋊Q8C2×C412yes—
123C2×C22⋊Q8C2×C414yes—
124C2×C22⋊Q8C2×C412yescomplemented
125C2×C22⋊Q8C2312yes—
126C2×C22⋊Q8C2314yes—
127C2×#121—22no—
128C2×#121—22no—
129C2×#121—21no—
130C2×#121—21no—
131C2×#121—22no—
132C2×#121—22no—
133C2×#121—22no—
134C2×#121C2×C412yes—
135C2×#121C2×C414yes—
136C2×#121C2×C412yescomplemented
137C2×#121C2312yes—
138C2×#121C2314yes—
139C2×#120—22no—
140C2×#120—22no—
141#518—28no—
142#518—28no—
143C2×C4×Q8C2×C412yescomplemented
144C2×C4×D4—22no—
145C2×C4×D4—22no—
146C2×C4×D4—22no—
147C2×C4×D4—22no—
148C2×C4×D4—22no—
149C2×C4×D4C2×C412yes—
150C2×C4×D4C2×C412yes—
151C2×C4×D4C2×C414yes—
152C2×C4×D4C2×C412yescomplemented
153C2×C4×D4D412yes—
154C2×C4×D4D412yes—
155C2×C4×D4D414yes—
156C2×C4×D4D414yes—
157C2×C4×D4C2314yes—
158C2×#117—22no—
159C2×#117—22no—
160C2×#117C2×C412yescomplemented
161C22×C4⋊C4—21no—
162C22×C4⋊C4—21no—
163C22×C4⋊C4C2×C411yescharacteristic
164C22×C4⋊C4C2×C411yescharacteristic
165C22×C4⋊C4D411yescharacteristic
166C22×C22⋊C4—21no—
167C22×C22⋊C4—21no—
168C22×C22⋊C4—22no—
169C22×C22⋊C4—21no—
170C22×C22⋊C4—21no—
171C22×C22⋊C4—21no—
172C22×C22⋊C4D411yescharacteristic
173C22×C22⋊C4D411yescharacteristic
174C22×C42—21no—
175C22×C42—21no—
176C22×C42C2311yescharacteristic
177C8×D4—216no—
178C8×D4—216no—
179#431—24no—
180#431C2318yescomplemented
181C2×C4⋊C8—22no—
182C2×C22⋊C8—21no—
183C2×C22⋊C8—21no—
184C2×C22⋊C8—22no—
185C2×C22⋊C8—22no—
186C2×C22⋊C8—22no—
187C2×C22⋊C8—24no—
188C2×C22⋊C8C2312yes—
189C2×C22⋊C8C2312yes—
190C2×C22⋊C8C2314yes—
191C2×C22⋊C8C2314yes—
192C2×C22⋊C8C2318yescomplemented
193C2×C4×C8—22no—
194#388—28no—
195#387—28no—
196#386—28no—
197#383—22no—
198#383C2314yescomplemented
199#381—22no—
200#381C2314yescomplemented
201#380—22no—
202#380C2314yes—
203C4×C22⋊C4—22no—
204C4×C22⋊C4—28no—
205C4×C22⋊C4C2314yescomplemented
206#376—22no—
207#376C2314yescomplemented
208C2×#95—22no—
209C2×#95—21no—
210C2×#95—21no—
211C2×#95—21no—
212C2×#95—21no—
213C2×#95—21no—
214C2×#95C2314yes—
215C2×#95C2311yescharacteristic
216C2×#95C2311yescharacteristic
217C2×#95C2311yescharacteristic
218C2×#95C2311yescharacteristic
219#328C2318yescomplemented
220#328C2318yescomplemented
221#328C2318yescomplemented
222#328C2318yescomplemented
223#327C2318yes—
224#327C2318yes—
225#327C2318yes—
226#327C2318yes—
227C25—21no—
228C25C2×D411yescharacteristic
229C25C2×D411yescharacteristic
230C2×#41—24no—
231C2×#41—84no—
232C2×#41C22×C418yescomplemented
233C22×Q8—21no—
234C22×Q8—22no—
235C22×Q8—82no—
236C22×Q8C22×C412yes—
237C22×Q8C22×C414yes—
238C22×D4—24no—
239C22×D4—24no—
240C22×D4—22no—
241C22×D4—24no—
242C22×D4—22no—
243C22×D4—24no—
244C22×D4—22no—
245C22×D4—22no—
246C22×D4—21no—
247C22×D4—22no—
248C22×D4—44no—
249C22×D4—44no—
250C22×D4—82no—
251C22×D4C22⋊C412yes—
252C22×D4C22⋊C412yes—
253C22×D4C22⋊C414yes—
254C22×D4C22×C412yes—
255C22×D4C22×C414yes—
256C22×D4C2×D414yes—
257C23×C4—21no—
258C23×C4—21no—
259C23×C4—21no—
260C23×C4—21no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—21no—
264C23×C4—21no—
265C23×C4—21no—
266C23×C4—24no—
267C23×C4—44no—
268C23×C4—44no—
269C23×C4—82no—
270C23×C4—82no—
271C23×C4—82no—
272C23×C4C22×C411yescharacteristic
273C23×C4C22×C411yescharacteristic
274C23×C4C22×C412yes—
275C23×C4C22×C412yes—
276C23×C4C22×C412yes—
277C23×C4C2×D411yescharacteristic
278C23×C4C2×D411yescharacteristic
279C23×C4C2×D411yescharacteristic
280C23×C4C2×D411yescharacteristic
281C23×C4C2×D411yescharacteristic
282C23×C4C2×D411yescharacteristic
283C23×C4C2×D412yes—
284C23×C4C2×D412yes—
285C23×C4C2×D412yes—
286C23×C4C2×D412yes—
287C23×C4C2×D412yes—
288C23×C4C2411yescharacteristic
289C23×C4C2412yes—
290C23×C4C2412yes—
291C22×C8—22no—
292C22×C8—22no—
293C22×C8—24no—
294C22×C8—24no—
295C22×C8—28no—
296C22×C8—82no—
297C22×C8—82no—
298C22×C8—84no—
299#126—216no—
300#126—216no—
301#126—28no—
302#126—28no—
303#125—216no—
304#125—24no—
305#125C22×C418yescomplemented
306#124—216no—
307#124—24no—
308#124C22×C418yescomplemented
309#123—216no—
310#123—28no—
311#123—28no—
312#123—28no—
313#123—28no—
314#123—216no—
315#123—216no—
316C22⋊Q8—24no—
317C22⋊Q8—24no—
318C22⋊Q8—24no—
319C22⋊Q8—24no—
320C22⋊Q8—22no—
321C22⋊Q8—22no—
322C22⋊Q8—24no—
323C22⋊Q8—24no—
324C22⋊Q8—216no—
325C22⋊Q8C22×C414yes—
326C22⋊Q8C22×C418yes—
327C22⋊Q8C22×C418yescomplemented
328C22⋊Q8C2414yes—
329#121—216no—
330#121—216no—
331#121—24no—
332#121—24no—
333#121—24no—
334#121—24no—
335#121—22no—
336#121—22no—
337#121—24no—
338#121—24no—
339#121—216no—
340#121C22×C414yes—
341#121C22×C418yes—
342#121C22×C418yescomplemented
343#121C2414yes—
344#120—28no—
345#120—28no—
346#120—216no—
347C4×Q8—24no—
348C4×Q8C22×C418yescomplemented
349C4×D4—28no—
350C4×D4—28no—
351C4×D4—28no—
352C4×D4—28no—
353C4×D4—28no—
354C4×D4—28no—
355C4×D4—216no—
356C4×D4—216no—
357C4×D4—24no—
358C4×D4C22⋊C418yes—
359C4×D4C22⋊C418yes—
360C4×D4C22⋊C418yes—
361C4×D4C22⋊C418yes—
362C4×D4C22×C418yes—
363C4×D4C22×C418yes—
364C4×D4C22×C418yescomplemented
365C4×D4C2×D418yes—
366C4×D4C2×D418yes—
367#117—24no—
368#117—216no—
369#117—28no—
370#117—28no—
371#117C22×C418yescomplemented
372C2×C4⋊C4—22no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—24no—
384C2×C4⋊C4—24no—
385C2×C4⋊C4—82no—
386C2×C4⋊C4C22⋊C412yes—
387C2×C4⋊C4C22⋊C412yes—
388C2×C4⋊C4C22⋊C414yes—
389C2×C4⋊C4C22×C412yes—
390C2×C4⋊C4C22×C412yes—
391C2×C4⋊C4C22×C414yes—
392C2×C4⋊C4C22×C414yes—
393C2×C4⋊C4C2×D414yes—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—24no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—24no—
408C2×C22⋊C4—216no—
409C2×C22⋊C4—24no—
410C2×C22⋊C4—24no—
411C2×C22⋊C4—24no—
412C2×C22⋊C4—44no—
413C2×C22⋊C4—44no—
414C2×C22⋊C4—82no—
415C2×C22⋊C4C22⋊C412yes—
416C2×C22⋊C4C22⋊C412yes—
417C2×C22⋊C4C22⋊C414yes—
418C2×C22⋊C4C22⋊C412yes—
419C2×C22⋊C4C22⋊C412yes—
420C2×C22⋊C4C22⋊C414yes—
421C2×C22⋊C4C2×D414yes—
422C2×C22⋊C4C2×D414yes—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—24no—
426C2×C42—24no—
427C2×C42—44no—
428C2×C42—82no—
429C2×C42C22×C412yes—
430C2×C42C22×C412yes—
431C2×C42C2×D412yes—
432C2×C42C2×D412yes—
433C2×C42C2×D412yes—
434C2×C42C2412yes—
435C4⋊C8—28no—
436C22⋊C8—22no—
437C22⋊C8—22no—
438C22⋊C8—24no—
439C22⋊C8—24no—
440C22⋊C8—28no—
441C22⋊C8C2414yes—
442C22⋊C8C2414yes—
443C4×C8—28no—
444#95—21no—
445#95—21no—
446#95—24no—
447#95—24no—
448#95—24no—
449#95—24no—
450#95—24no—
451#95—21no—
452#95—21no—
453#95C2412yes—
454#95C2412yes—
455#95C2412yes—
456#95C2412yes—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—24no—
461C24—42no—
462C24—42no—
463C24—42no—
464C24—42no—
465C24—44no—
466C24—82no—
467C24—82no—
468C24C2×C22⋊C412yes—
469C24C2×C22⋊C411yescharacteristic
470C24C2×C22⋊C411yescharacteristic
471C24C2×C22⋊C412yes—
472C24C2×C22⋊C412yes—
473C24#13514yes—
474C24#13514yes—
475C24C22×D411yescharacteristic
476C24C22×D412yes—
477C24C22×D412yes—
478#41—88no—
479#41—88no—
480C2×Q8—22no—
481C2×Q8—24no—
482C2×Q8—44no—
483C2×Q8—82no—
484C2×Q8—84no—
485C2×Q8—84no—
486C2×Q8C23×C414yes—
487C2×D4—28no—
488C2×D4—28no—
489C2×D4—28no—
490C2×D4—28no—
491C2×D4—216no—
492C2×D4—24no—
493C2×D4—28no—
494C2×D4—24no—
495C2×D4—28no—
496C2×D4—28no—
497C2×D4—22no—
498C2×D4—24no—
499C2×D4—44no—
500C2×D4—44no—
501C2×D4—44no—
502C2×D4—48no—
503C2×D4—48no—
504C2×D4—48no—
505C2×D4—416no—
506C2×D4—82no—
507C2×D4—84no—
508C2×D4—84no—
509C2×D4—84no—
510C2×D4—84no—
511C2×D4C2×C22⋊C418yes—
512C2×D4C2×C22⋊C418yes—
513C2×D4C23×C414yes—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—28no—
525C22×C4—28no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—44no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—44no—
539C22×C4—48no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—44no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—48no—
552C22×C4—42no—
553C22×C4—84no—
554C22×C4—84no—
555C22×C4—82no—
556C22×C4—82no—
557C22×C4—82no—
558C22×C4—82no—
559C22×C4—82no—
560C22×C4—82no—
561C22×C4—82no—
562C22×C4—82no—
563C22×C4—82no—
564C22×C4—82no—
565C22×C4—84no—
566C22×C4—816no—
567C22×C4C2×C22⋊C412yes—
568C22×C4C2×C22⋊C412yes—
569C22×C4C2×C22⋊C412yes—
570C22×C4C2×C22⋊C412yes—
571C22×C4C2×C22⋊C411yescharacteristic
572C22×C4C2×C22⋊C411yescharacteristic
573C22×C4C2×C22⋊C412yes—
574C22×C4C2×C22⋊C412yes—
575C22×C4C2×C22⋊C412yes—
576C22×C4C2×C22⋊C412yes—
577C22×C4C2×C22⋊C412yes—
578C22×C4C2×C22⋊C412yes—
579C22×C4C2×C22⋊C412yes—
580C22×C4C2×C22⋊C414yes—
581C22×C4C2×C22⋊C414yes—
582C22×C4C23×C411yescharacteristic
583C22×C4C23×C411yescharacteristic
584C22×C4C23×C412yes—
585C22×C4C23×C412yes—
586C22×C4C23×C414yes—
587C22×C4C22×D412yes—
588C22×C4C22×D411yescharacteristic
589C22×C4C22×D411yescharacteristic
590C22×C4C22×D412yes—
591C22×C4C22×D412yes—
592C22×C4C22×D412yes—
593C22×C4C22×D411yescharacteristic
594C22×C4C22×D412yes—
595C22×C4C22×D412yes—
596C22×C4C22×D414yes—
597C22×C4C2511yescharacteristic
598C2×C8—24no—
599C2×C8—24no—
600C2×C8—44no—
601C2×C8—44no—
602C2×C8—84no—
603C2×C8—84no—
604C2×C8—88no—
605C4⋊C4—24no—
606C4⋊C4—28no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4—28no—
612C4⋊C4—28no—
613C4⋊C4—28no—
614C4⋊C4—28no—
615C4⋊C4—24no—
616C4⋊C4—84no—
617C4⋊C4C2×C22⋊C418yes—
618C4⋊C4C2×C22⋊C418yes—
619C4⋊C4C23×C414yes—
620C4⋊C4C23×C414yes—
621C22⋊C4—28no—
622C22⋊C4—24no—
623C22⋊C4—28no—
624C22⋊C4—28no—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—28no—
628C22⋊C4—28no—
629C22⋊C4—28no—
630C22⋊C4—28no—
631C22⋊C4—28no—
632C22⋊C4—24no—
633C22⋊C4—48no—
634C22⋊C4—48no—
635C22⋊C4—84no—
636C22⋊C4C2×C22⋊C418yes—
637C22⋊C4C2×C22⋊C418yes—
638C22⋊C4C2×C22⋊C418yes—
639C22⋊C4C2×C22⋊C418yes—
640C42—28no—
641C42—28no—
642C42—48no—
643C42—84no—
644C42C2×C22⋊C414yes—
645C42C2×C22⋊C414yes—
646C42C23×C414yes—
647C42C22×D414yes—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—22no—
659C23—22no—
660C23—24no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—48no—
665C23—42no—
666C23—48no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—48no—
675C23—84no—
676C23—84no—
677C23—84no—
678C23—84no—
679C23—168no—
680C23#41614yes—
681C23#41614yes—
682C23#41618yes—
683C23C22×C22⋊C414yes—
684C23C22×C22⋊C412yes—
685C23C22×C22⋊C411yescharacteristic
686C23C22×C22⋊C412yes—
687C23C22×C22⋊C411yescharacteristic
688C23C2×#13512yes—
689C23C2×#13512yes—
690C23C2×#13514yes—
691C23C2×#13514yes—
692C23C23×D411yescharacteristic
693Q8—44no—
694Q8—44no—
695Q8—84no—
696D4—216no—
697D4—216no—
698D4—44no—
699D4—44no—
700D4—48no—
701D4—416no—
702D4—44no—
703D4—44no—
704D4—84no—
705D4—88no—
706D4—88no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—44no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—44no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—44no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—44no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—48no—
745C2×C4—44no—
746C2×C4—48no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—88no—
760C2×C4—88no—
761C2×C4—84no—
762C2×C4—84no—
763C2×C4—816no—
764C2×C4—84no—
765C2×C4—84no—
766C2×C4—84no—
767C2×C4C22×C22⋊C414yes—
768C2×C4C22×C22⋊C414yes—
769C2×C4C22×C22⋊C411yescharacteristic
770C2×C4C22×C22⋊C411yescharacteristic
771C2×C4C22×C22⋊C414yes—
772C2×C4C22×C22⋊C412yes—
773C2×C4C22×C22⋊C412yes—
774C2×C4C24×C411yescharacteristic
775C2×C4C23×D411yescharacteristic
776C8—44no—
777C8—44no—
778C22—21no—
779C22—21no—
780C22—22no—
781C22—22no—
782C22—21no—
783C22—21no—
784C22—22no—
785C22—22no—
786C22—24no—
787C22—24no—
788C22—28no—
789C22—28no—
790C22—24no—
791C22—24no—
792C22—24no—
793C22—44no—
794C22—44no—
795C22—48no—
796C22—48no—
797C22—44no—
798C22—44no—
799C22—44no—
800C22—82no—
801C22—82no—
802C22—84no—
803C22—88no—
804C22—168no—
805C22#288312yes—
806C22C2×#41612yes—
807C22C2×#41614yes—
808C22C2×#41614yes—
809C22C2×#41612yes—
810C22#290112yes—
811C22C23×C22⋊C411yescharacteristic
812C22C22×#13511yescharacteristic
813C22C22×#13511yescharacteristic
814C4—21no—
815C4—21no—
816C4—21no—
817C4—21no—
818C4—24no—
819C4—22no—
820C4—22no—
821C4—24no—
822C4—24no—
823C4—44no—
824C4—44no—
825C4—44no—
826C4—44no—
827C4—82no—
828C4—82no—
829C4—82no—
830C2—21no—
831C2—21no—
832C2—22no—
833C2—24no—
834C2—24no—
835C2—44no—
836C2—84no—
837C2#1761514yesdirect product factor
838C2C2×#288311yescharacteristic
839C2C22×#41611yescharacteristic
840C2C2×#290111yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#3505C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2972C2semidirect
3. C2×#2353C2semidirect
4. #17615C2direct (N × H)
5. C2×#1516C2semidirect
6. C2×#1521C2semidirect
7. C2×#1520C2semidirect
8. C2×#1519C2semidirect
9. C2×#1501C2semidirect
10. C2×#1500C2semidirect
11. C22×#328C2semidirect
12. C22×#327C2semidirect
15. #3505C4semidirect
18. C2×#553C4semidirect
19. C2×#552C4semidirect
21. C2×#548C4semidirect
22. C2×#546C4semidirect
33. #2972C22semidirect
36. C2×#431C22semidirect
39. C22×C22⋊C8C22semidirect
41. #2353C22semidirect
45. C2×#383C22semidirect
46. C2×#381C22semidirect
49. C2×C4×C22⋊C4C22semidirect
50. C2×#376C22semidirect
52. #1521C22semidirect
53. #1520C22semidirect
54. #1519C22semidirect
55. #1516C22semidirect
56. #1501C22semidirect
57. #1500C22semidirect
58. C2×#328C22semidirect
59. C2×#328C22semidirect
60. C2×#328C22semidirect
61. C2×#328C22semidirect
62. C2×#328C22semidirect
67. C2×#327C22semidirect
68. C22×#41C2×C4semidirect
82. #553C2×C4semidirect
84. #552C2×C4semidirect
88. #548C2×C4semidirect
90. #546C2×C4semidirect
99. #529C2×C4semidirect
105. C2×#125C2×C4semidirect
107. C2×#124C2×C4semidirect
110. #525C2×C4semidirect
124. C2×C22⋊Q8C2×C4semidirect
136. C2×#121C2×C4semidirect
143. C2×C4×Q8C2×C4semidirect
152. C2×C4×D4C2×C4semidirect
160. C2×#117C2×C4semidirect
180. #431C23semidirect
192. C2×C22⋊C8C23semidirect
198. #383C23semidirect
200. #381C23semidirect
205. C4×C22⋊C4C23semidirect
207. #376C23semidirect
219. #328C23semidirect
220. #328C23semidirect
221. #328C23semidirect
222. #328C23semidirect
232. C2×#41C22×C4semidirect
305. #125C22×C4semidirect
308. #124C22×C4semidirect
327. C22⋊Q8C22×C4semidirect
342. #121C22×C4semidirect
348. C4×Q8C22×C4semidirect
364. C4×D4C22×C4semidirect
371. #117C22×C4semidirect
837. C2#17615direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#35052
C2×#29722
C2×#23532
#176152
C2×#15162
C2×#15212
C2×#15202
C2×#15192
C2×#15012
C2×#15002
C22×#3282
C22×#3272