Finite Group Databasebeta

← C2×#17629 #6343473

Subgroups — C2×#17629 #6343473

Order 512.

3272 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×#3506C211yesmaximal, characteristic
2C2×#2973C211yesmaximal, characteristic, complemented
3C2×#2353C211yesmaximal, characteristic, complemented
4#17629C2116yesmaximal, direct product factor
5C2×#1516C212yesmaximal, complemented
6C2×#1515C211yesmaximal, characteristic, complemented
7C2×#1514C211yesmaximal, characteristic, complemented
8C2×#1513C212yesmaximal, complemented
9C2×#1506C211yesmaximal, characteristic, complemented
10C2×#1505C211yesmaximal, characteristic, complemented
11C2×#1504C212yesmaximal, complemented
12C2×#1501C212yesmaximal, complemented
13#3506—24no—
14#3506—24no—
15#3506C418yescomplemented
16#3506C2218yes—
17C2×#559—22no—
18C2×#556C412yescomplemented
19C2×#555C412yescomplemented
20C2×#553—22no—
21C2×#550C412yescomplemented
22C2×#547C412yescomplemented
23C2×#538—21no—
24C2×#538—21no—
25C2×#535—21no—
26C2×#533C2211yescharacteristic
27C2×#532C2211yescharacteristic
28C2×#525C2212yes—
29C2×#525C2212yes—
30C2×#520—21no—
31C22×C4×D4C2211yescharacteristic
32#2973—24no—
33#2973C2218yescomplemented
34C2×#435—22no—
35C2×#435—22no—
36C2×#432C2211yescharacteristic
37C2×#432C2211yescharacteristic
38C2×#407C2212yes—
39C22×C22⋊C8C2212yes—
40#2353—24no—
41#2353C2218yescomplemented
42C2×#388—21no—
43C2×#387—21no—
44C2×#386—21no—
45C2×#383C2211yescharacteristic
46C2×#381C2211yescharacteristic
47C2×#380C2211yescharacteristic
48C2×C4×C22⋊C4—21no—
49C2×C4×C22⋊C4C2211yescharacteristic
50C2×#376C2211yescharacteristic
51C22×#95C2211yescharacteristic
52#1516C22116yescomplemented
53#1515C2218yescomplemented
54#1514C2218yescomplemented
55#1513C22116yescomplemented
56#1506C2218yescomplemented
57#1505C2218yescomplemented
58#1504C22116yescomplemented
59#1501C22116yescomplemented
60C2×#328C2212yes—
61C2×#328C2212yes—
62C2×#328C2212yes—
63C2×#328C2212yes—
64C2×#327C2212yes—
65C2×#327C2212yes—
66C2×#327C2212yes—
67C2×#327C2212yes—
68C22×#41—21no—
69C22×#41C2×C412yes—
70C22×#41C2×C412yescomplemented
71C23×D4D411yescharacteristic
72C24×C4—21no—
73C24×C4C2311yescharacteristic
74C24×C4C2311yescharacteristic
75C22×M16—22no—
76C23×C8—22no—
77#559—216no—
78#559—216no—
79#556—28no—
80#556C2×C4116yescomplemented
81#555—28no—
82#555C2×C4116yescomplemented
83#553—216no—
84#553—216no—
85#550—28no—
86#550C2×C4116yescomplemented
87#547—28no—
88#547C2×C4116yescomplemented
89#538—28no—
90#538—28no—
91#538—28no—
92#538—28no—
93#535—28no—
94#535—28no—
95#533—22no—
96#533—22no—
97#533C2×C414yescomplemented
98#533C2314yes—
99#532—22no—
100#532—22no—
101#532C2×C414yescomplemented
102#532C2314yes—
103C2×C4⋊Q8C2×C411yescharacteristic, complemented
104C2×C4⋊Q8C2×C411yescharacteristic, complemented
105C2×C4⋊Q8C2×C411yescharacteristic, complemented
106C2×#127—22no—
107C2×#127C2×C411yescharacteristic, complemented
108C2×#126—22no—
109C2×#126—22no—
110C2×#125—21no—
111C2×#124—22no—
112C2×#124—22no—
113C2×#124—22no—
114C2×#124—21no—
115#525—24no—
116#525—24no—
117#525—24no—
118#525—24no—
119#525C2×C418yes—
120#525C2×C418yescomplemented
121#525C2318yes—
122#525C2318yes—
123C2×#123—22no—
124C2×#123—22no—
125C2×#123—22no—
126C2×#123—22no—
127C2×C22⋊Q8—21no—
128C2×C22⋊Q8C2×C412yes—
129C2×C22⋊Q8C2×C412yescomplemented
130C2×C22⋊Q8C2312yes—
131C2×#121—22no—
132C2×#121—22no—
133C2×#121—21no—
134C2×#121—22no—
135C2×#121—22no—
136C2×#121C2×C412yes—
137C2×#121C2×C412yescomplemented
138C2×#121C2312yes—
139C2×#120—22no—
140C2×#120—22no—
141#520—28no—
142#520—28no—
143C2×C4×Q8—22no—
144C2×C4×Q8—21no—
145C2×C4×Q8C2×C412yescomplemented
146C2×C4×D4—22no—
147C2×C4×D4—22no—
148C2×C4×D4—22no—
149C2×C4×D4—22no—
150C2×C4×D4—22no—
151C2×C4×D4—21no—
152C2×C4×D4C2×C412yes—
153C2×C4×D4C2×C412yes—
154C2×C4×D4C2×C414yes—
155C2×C4×D4C2×C412yescomplemented
156C2×C4×D4D412yes—
157C2×C4×D4D412yes—
158C2×C4×D4D414yes—
159C2×C4×D4D414yes—
160C2×C4×D4C2314yes—
161C2×#117—21no—
162C2×#117—22no—
163C2×#117C2×C412yes—
164C2×#117C2×C412yescomplemented
165C22×C4⋊C4—22no—
166C22×C4⋊C4—21no—
167C22×C4⋊C4D411yescharacteristic
168C22×C22⋊C4—21no—
169C22×C22⋊C4—21no—
170C22×C22⋊C4—21no—
171C22×C22⋊C4D411yescharacteristic
172C22×C22⋊C4D411yescharacteristic
173C22×C42—21no—
174C22×C42—21no—
175C22×C42C2311yescharacteristic
176#435—216no—
177#435—216no—
178#432—22no—
179#432—22no—
180#432C2314yes—
181#432C2314yes—
182C2×C4⋊C8—21no—
183C2×C4⋊C8—21no—
184#407—24no—
185#407C2318yes—
186C2×C22⋊C8—22no—
187C2×C22⋊C8—24no—
188C2×C22⋊C8—22no—
189C2×C22⋊C8C2312yes—
190C2×C22⋊C8C2312yes—
191C2×C22⋊C8C2318yes—
192C2×#97—21no—
193C2×#97—21no—
194#388—28no—
195#387—28no—
196#386—28no—
197#383—22no—
198#383C2314yes—
199#381—22no—
200#381C2314yes—
201#380—22no—
202#380C2314yes—
203C4×C22⋊C4—22no—
204C4×C22⋊C4—28no—
205C4×C22⋊C4C2314yes—
206#376—22no—
207#376C2314yes—
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#328C2318yes—
220#328C2318yes—
221#328C2318yes—
222#328C2318yes—
223#327C2318yes—
224#327C2318yes—
225#327C2318yes—
226#327C2318yes—
227C25C2×D411yescharacteristic
228C25C2×D411yescharacteristic
229C2×#41—24no—
230C2×#41—24no—
231C2×#41—24no—
232C2×#41—24no—
233C2×#41—44no—
234C2×#41—44no—
235C2×#41—84no—
236C2×#41—84no—
237C2×#41C22×C418yes—
238C2×#41C22×C418yescomplemented
239C22×Q8—21no—
240C22×Q8—21no—
241C22×Q8C22×C412yes—
242C22×D4—22no—
243C22×D4—22no—
244C22×D4—22no—
245C22×D4—22no—
246C22×D4—22no—
247C22×D4—21no—
248C22×D4—21no—
249C22×D4—42no—
250C22×D4—42no—
251C22×D4C22⋊C412yes—
252C22×D4C22⋊C412yes—
253C22×D4C22⋊C414yes—
254C22×D4C22×C412yes—
255C22×D4C2×D414yes—
256C23×C4—21no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—21no—
261C23×C4—21no—
262C23×C4—21no—
263C23×C4—24no—
264C23×C4—44no—
265C23×C4—44no—
266C23×C4—82no—
267C23×C4—82no—
268C23×C4—82no—
269C23×C4C22×C412yes—
270C23×C4C22×C412yes—
271C23×C4C22×C412yes—
272C23×C4C22×C412yes—
273C23×C4C2×D411yescharacteristic
274C23×C4C2×D411yescharacteristic
275C23×C4C2×D411yescharacteristic
276C23×C4C2×D411yescharacteristic
277C23×C4C2×D412yes—
278C23×C4C2×D412yes—
279C23×C4C2×D412yes—
280C23×C4C2×D412yes—
281C23×C4C2×D412yes—
282C23×C4C2×D412yes—
283C23×C4C2411yescharacteristic
284C23×C4C2412yes—
285C23×C4C2412yes—
286C2×M16—28no—
287C2×M16—84no—
288C22×C8—22no—
289C22×C8—22no—
290C22×C8—28no—
291C22×C8—84no—
292C4⋊Q8—22no—
293C4⋊Q8—22no—
294C4⋊Q8—22no—
295C4⋊Q8C22×C414yescomplemented
296C4⋊Q8C22×C414yescomplemented
297C4⋊Q8C22×C414yescomplemented
298#127—216no—
299#127—22no—
300#127C22×C414yescomplemented
301#126—216no—
302#126—216no—
303#125—24no—
304#125—24no—
305#124—216no—
306#124—216no—
307#124—216no—
308#124—24no—
309#124—24no—
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⋊Q8C22×C418yes—
323C22⋊Q8C22×C414yes—
324C22⋊Q8C22×C418yescomplemented
325C22⋊Q8C2414yes—
326#121—216no—
327#121—216no—
328#121—24no—
329#121—24no—
330#121—24no—
331#121—24no—
332#121—22no—
333#121—22no—
334#121—216no—
335#121—216no—
336#121C22×C418yes—
337#121C22×C414yes—
338#121C22×C418yescomplemented
339#121C2414yes—
340#120—28no—
341#120—28no—
342#120—28no—
343#120—28no—
344C4×Q8—216no—
345C4×Q8—24no—
346C4×Q8—24no—
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—28no—
356C4×D4—28no—
357C4×D4—216no—
358C4×D4—24no—
359C4×D4—24no—
360C4×D4—24no—
361C4×D4C22⋊C418yes—
362C4×D4C22⋊C418yes—
363C4×D4C22⋊C418yes—
364C4×D4C22⋊C418yes—
365C4×D4C22×C418yes—
366C4×D4C22×C418yes—
367C4×D4C22×C418yescomplemented
368C4×D4C2×D418yes—
369C4×D4C2×D418yes—
370#117—24no—
371#117—24no—
372#117—24no—
373#117—24no—
374#117—216no—
375#117C22×C418yes—
376#117C22×C418yescomplemented
377C2×C4⋊C4—21no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—216no—
386C2×C4⋊C4—24no—
387C2×C4⋊C4—82no—
388C2×C4⋊C4C22⋊C412yes—
389C2×C4⋊C4C22⋊C412yes—
390C2×C4⋊C4C22⋊C414yes—
391C2×C4⋊C4C22×C412yes—
392C2×C4⋊C4C22×C412yes—
393C2×C4⋊C4C2×D414yes—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—24no—
404C2×C22⋊C4—24no—
405C2×C22⋊C4—24no—
406C2×C22⋊C4—44no—
407C2×C22⋊C4—44no—
408C2×C22⋊C4—82no—
409C2×C22⋊C4C22⋊C412yes—
410C2×C22⋊C4C22⋊C412yes—
411C2×C22⋊C4C22⋊C412yes—
412C2×C22⋊C4C22⋊C412yes—
413C2×C22⋊C4C22⋊C414yes—
414C2×C22⋊C4C22⋊C414yes—
415C2×C22⋊C4C2×D414yes—
416C2×C22⋊C4C2×D414yes—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—24no—
421C2×C42—24no—
422C2×C42—44no—
423C2×C42—82no—
424C2×C42C22×C411yescharacteristic
425C2×C42C22×C411yescharacteristic
426C2×C42C22×C412yes—
427C2×C42C2×D412yes—
428C2×C42C2×D411yescharacteristic
429C2×C42C2×D411yescharacteristic
430C2×C42C2×D412yes—
431C2×C42C2412yes—
432C4⋊C8—24no—
433C4⋊C8—24no—
434C22⋊C8—22no—
435C22⋊C8—22no—
436C22⋊C8—28no—
437C22⋊C8—28no—
438C22⋊C8C2414yes—
439C22⋊C8C2414yes—
440#97—24no—
441#97—24no—
442#95—21no—
443#95—21no—
444#95—24no—
445#95—24no—
446#95—24no—
447#95—24no—
448#95—24no—
449#95—21no—
450#95—21no—
451#95C2412yes—
452#95C2412yes—
453#95C2412yes—
454#95C2412yes—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—42no—
461C24—42no—
462C24—42no—
463C24—42no—
464C24C2×C22⋊C412yes—
465C24C2×C22⋊C412yes—
466C24C2×C22⋊C412yes—
467C24C2×C22⋊C412yes—
468C24C22×D411yescharacteristic
469C24C22×D412yes—
470C24C22×D412yes—
471#41—416no—
472#41—48no—
473#41—48no—
474#41—88no—
475#41—88no—
476#41—88no—
477#41—88no—
478C2×Q8—24no—
479C2×Q8—22no—
480C2×Q8—24no—
481C2×Q8—44no—
482C2×Q8—44no—
483C2×Q8—82no—
484C2×Q8C23×C414yes—
485C2×D4—24no—
486C2×D4—24no—
487C2×D4—28no—
488C2×D4—28no—
489C2×D4—28no—
490C2×D4—28no—
491C2×D4—24no—
492C2×D4—22no—
493C2×D4—24no—
494C2×D4—44no—
495C2×D4—44no—
496C2×D4—48no—
497C2×D4—44no—
498C2×D4—44no—
499C2×D4—44no—
500C2×D4—44no—
501C2×D4—44no—
502C2×D4—44no—
503C2×D4—82no—
504C2×D4—84no—
505C2×D4—84no—
506C2×D4—84no—
507C2×D4—84no—
508C2×D4C2×C22⋊C418yes—
509C2×D4C2×C22⋊C418yes—
510C2×D4C23×C414yes—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—24no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—28no—
519C22×C4—28no—
520C22×C4—28no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—42no—
530C22×C4—44no—
531C22×C4—44no—
532C22×C4—48no—
533C22×C4—48no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—48no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—84no—
547C22×C4—84no—
548C22×C4—82no—
549C22×C4—82no—
550C22×C4—82no—
551C22×C4—82no—
552C22×C4—82no—
553C22×C4—82no—
554C22×C4—82no—
555C22×C4—82no—
556C22×C4—84no—
557C22×C4—816no—
558C22×C4C2×C22⋊C412yes—
559C22×C4C2×C22⋊C411yescharacteristic
560C22×C4C2×C22⋊C412yes—
561C22×C4C2×C22⋊C412yes—
562C22×C4C2×C22⋊C411yescharacteristic
563C22×C4C2×C22⋊C411yescharacteristic
564C22×C4C2×C22⋊C411yescharacteristic
565C22×C4C2×C22⋊C412yes—
566C22×C4C2×C22⋊C412yes—
567C22×C4C2×C22⋊C412yes—
568C22×C4C2×C22⋊C414yes—
569C22×C4C2×C22⋊C414yes—
570C22×C4C2×C22⋊C414yes—
571C22×C4C2×C22⋊C414yes—
572C22×C4C23×C411yescharacteristic
573C22×C4C23×C411yescharacteristic
574C22×C4C23×C414yes—
575C22×C4C23×C414yes—
576C22×C4C22×D412yes—
577C22×C4C22×D411yescharacteristic
578C22×C4C22×D411yescharacteristic
579C22×C4C22×D412yes—
580C22×C4C22×D412yes—
581C22×C4C22×D412yes—
582C22×C4C22×D411yescharacteristic
583C22×C4C22×D414yes—
584C22×C4C22×D414yes—
585C22×C4C2511yescharacteristic
586M16—88no—
587C2×C8—24no—
588C2×C8—24no—
589C2×C8—44no—
590C2×C8—44no—
591C2×C8—88no—
592C4⋊C4—24no—
593C4⋊C4—28no—
594C4⋊C4—28no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—28no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—24no—
603C4⋊C4—84no—
604C4⋊C4C2×C22⋊C418yes—
605C4⋊C4C2×C22⋊C418yes—
606C4⋊C4C23×C414yes—
607C4⋊C4C23×C414yes—
608C22⋊C4—24no—
609C22⋊C4—28no—
610C22⋊C4—28no—
611C22⋊C4—28no—
612C22⋊C4—28no—
613C22⋊C4—24no—
614C22⋊C4—28no—
615C22⋊C4—28no—
616C22⋊C4—24no—
617C22⋊C4—28no—
618C22⋊C4—24no—
619C22⋊C4—48no—
620C22⋊C4—48no—
621C22⋊C4—84no—
622C22⋊C4C2×C22⋊C418yes—
623C22⋊C4C2×C22⋊C418yes—
624C22⋊C4C2×C22⋊C418yes—
625C22⋊C4C2×C22⋊C418yes—
626C42—28no—
627C42—28no—
628C42—28no—
629C42—48no—
630C42—84no—
631C42C2×C22⋊C412yes—
632C42C2×C22⋊C412yes—
633C42C2×C22⋊C412yes—
634C42C2×C22⋊C412yes—
635C42C23×C412yes—
636C42C23×C412yes—
637C42C22×D412yes—
638C42C22×D412yes—
639C23—22no—
640C23—22no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—22no—
649C23—22no—
650C23—24no—
651C23—22no—
652C23—22no—
653C23—24no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—48no—
663C23—48no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—84no—
668C23—84no—
669C23C22×C22⋊C414yes—
670C23C22×C22⋊C414yes—
671C23C22×C22⋊C411yescharacteristic
672C23C22×C22⋊C411yescharacteristic
673C23#57512yes—
674C23#57512yes—
675C23C23×D411yescharacteristic
676Q8—44no—
677Q8—48no—
678Q8—44no—
679Q8—84no—
680D4—48no—
681D4—48no—
682D4—44no—
683D4—48no—
684D4—44no—
685D4—48no—
686D4—44no—
687D4—44no—
688D4—84no—
689D4—88no—
690D4—88no—
691D4—88no—
692D4—88no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—44no—
724C2×C4—44no—
725C2×C4—42no—
726C2×C4—416no—
727C2×C4—42no—
728C2×C4—48no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—88no—
743C2×C4—88no—
744C2×C4—816no—
745C2×C4—84no—
746C2×C4—84no—
747C2×C4—84no—
748C2×C4C22×C22⋊C412yes—
749C2×C4C22×C22⋊C414yes—
750C2×C4C22×C22⋊C414yes—
751C2×C4C22×C22⋊C411yescharacteristic
752C2×C4C22×C22⋊C411yescharacteristic
753C2×C4C22×C22⋊C412yes—
754C2×C4C22×C22⋊C412yes—
755C2×C4C22×C22⋊C412yes—
756C2×C4C24×C411yescharacteristic
757C2×C4C23×D411yescharacteristic
758C8—44no—
759C8—44no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—24no—
765C22—24no—
766C22—24no—
767C22—24no—
768C22—24no—
769C22—24no—
770C22—24no—
771C22—24no—
772C22—44no—
773C22—44no—
774C22—48no—
775C22—48no—
776C22—48no—
777C22—44no—
778C22—44no—
779C22—44no—
780C22—82no—
781C22—82no—
782C22—84no—
783C22—88no—
784C22#288312yes—
785C22#289612yes—
786C22#289612yes—
787C22#290112yes—
788C22C23×C22⋊C411yescharacteristic
789C22C2×#57511yescharacteristic
790C22C2×#57511yescharacteristic
791C4—21no—
792C4—21no—
793C4—21no—
794C4—21no—
795C4—24no—
796C4—24no—
797C4—22no—
798C4—22no—
799C4—22no—
800C4—22no—
801C4—44no—
802C4—44no—
803C4—44no—
804C4—44no—
805C4—82no—
806C4—82no—
807C4—82no—
808C2—21no—
809C2—21no—
810C2—22no—
811C2—44no—
812C2—44no—
813C2—84no—
814C2#1762914yesdirect product factor
815C2C2×#288311yescharacteristic
816C2C2×#289611yescharacteristic
817C2C2×#290111yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#3506C2
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×#2973C2semidirect
3. C2×#2353C2semidirect
4. #17629C2direct (N × H)
5. C2×#1516C2semidirect
6. C2×#1515C2semidirect
7. C2×#1514C2semidirect
8. C2×#1513C2semidirect
9. C2×#1506C2semidirect
10. C2×#1505C2semidirect
11. C2×#1504C2semidirect
12. C2×#1501C2semidirect
15. #3506C4semidirect
18. C2×#556C4semidirect
19. C2×#555C4semidirect
21. C2×#550C4semidirect
22. C2×#547C4semidirect
33. #2973C22semidirect
41. #2353C22semidirect
52. #1516C22semidirect
53. #1515C22semidirect
54. #1514C22semidirect
55. #1513C22semidirect
56. #1506C22semidirect
57. #1505C22semidirect
58. #1504C22semidirect
59. #1501C22semidirect
70. C22×#41C2×C4semidirect
80. #556C2×C4semidirect
82. #555C2×C4semidirect
86. #550C2×C4semidirect
88. #547C2×C4semidirect
97. #533C2×C4semidirect
101. #532C2×C4semidirect
103. C2×C4⋊Q8C2×C4semidirect
104. C2×C4⋊Q8C2×C4semidirect
105. C2×C4⋊Q8C2×C4semidirect
107. C2×#127C2×C4semidirect
120. #525C2×C4semidirect
129. C2×C22⋊Q8C2×C4semidirect
137. C2×#121C2×C4semidirect
145. C2×C4×Q8C2×C4semidirect
155. C2×C4×D4C2×C4semidirect
164. C2×#117C2×C4semidirect
238. C2×#41C22×C4semidirect
295. C4⋊Q8C22×C4semidirect
296. C4⋊Q8C22×C4semidirect
297. C4⋊Q8C22×C4semidirect
300. #127C22×C4semidirect
324. C22⋊Q8C22×C4semidirect
338. #121C22×C4semidirect
348. C4×Q8C22×C4semidirect
367. C4×D4C22×C4semidirect
376. #117C22×C4semidirect
814. C2#17629direct (N × H)

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×#23532
#176292
C2×#15162
C2×#15152
C2×#15142
C2×#15132
C2×#15062
C2×#15052
C2×#15042
C2×#15012