Finite Group Databasebeta

← C2×#17625 #6343468

Subgroups — C2×#17625 #6343468

Order 512.

3240 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3505C211yesmaximal, characteristic
2C2×#2973C211yesmaximal, characteristic, complemented
3C2×#2357C211yesmaximal, characteristic, complemented
4#17625C2116yesmaximal, direct product factor
5C2×#1516C212yesmaximal, complemented
6C2×#1512C212yesmaximal, complemented
7C2×#1511C211yesmaximal, characteristic, complemented
8C2×#1510C211yesmaximal, characteristic, complemented
9C2×#1509C212yesmaximal, complemented
10C2×#1508C211yesmaximal, characteristic, complemented
11C2×#1507C211yesmaximal, characteristic, complemented
12C2×#1501C212yesmaximal, 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#2973—24no—
33#2973C2218yescomplemented
34C2×#435—22no—
35C2×#435—22no—
36C2×#432C2212yescomplemented
37C2×#407C2211yescharacteristic
38C2×#407C2211yescharacteristic
39C22×C22⋊C8C2212yescomplemented
40#2357—24no—
41#2357C2218yescomplemented
42C2×#390—21no—
43C2×#388—21no—
44C2×#388—21no—
45C2×#382C2211yescharacteristic, complemented
46C2×#381C2211yescharacteristic
47C2×#381C2211yescharacteristic, complemented
48C2×C4×C4⋊C4—21no—
49C2×C4×C4⋊C4C2211yescharacteristic, complemented
50C2×C4×C22⋊C4C2211yescharacteristic
51C2×C4×C22⋊C4C2211yescharacteristic, complemented
52#1516C22116yescomplemented
53#1512C22116yescomplemented
54#1511C2218yescomplemented
55#1510C2218yescomplemented
56#1509C22116yescomplemented
57#1508C2218yescomplemented
58#1507C2218yescomplemented
59#1501C22116yescomplemented
60C2×#328C2212yescomplemented
61C2×#328C2212yescomplemented
62C2×#328C2212yescomplemented
63C2×#328C2212yescomplemented
64C2×#327C2212yes—
65C2×#327C2212yes—
66C2×#327C2212yes—
67C2×#327C2212yes—
68C22×#41C2×C412yes—
69C23×Q8C2×C411yescharacteristic
70C23×D4—21no—
71C23×D4C2×C411yescharacteristic
72C23×D4D411yescharacteristic
73C24×C4C2311yescharacteristic
74C24×C4C2311yescharacteristic
75C22×M16—21no—
76C22×M16—21no—
77C23×C8—22no—
78#553—216no—
79#553—28no—
80#553—216no—
81#553C2×C4116yescomplemented
82#552—28no—
83#552C2×C4116yescomplemented
84#551—216no—
85#551—216no—
86#548—28no—
87#548C2×C4116yescomplemented
88#546—28no—
89#546C2×C4116yescomplemented
90#539—28no—
91#539—28no—
92#538—28no—
93#538—28no—
94#534—28no—
95#534—28no—
96#529—24no—
97#529—24no—
98#529C2×C418yes—
99#529C2318yes—
100C2×#126—22no—
101C2×#126—22no—
102C2×#126—22no—
103C2×#125—22no—
104C2×#125C2×C412yes—
105C2×#124—22no—
106C2×#124C2×C412yes—
107#525—24no—
108#525—24no—
109#525C2×C418yes—
110#525C2318yes—
111C2×#123—22no—
112C2×#123—22no—
113C2×#123—22no—
114C2×#123—22no—
115C2×#123—22no—
116C2×C22⋊Q8—21no—
117C2×C22⋊Q8—21no—
118C2×C22⋊Q8—22no—
119C2×C22⋊Q8—22no—
120C2×C22⋊Q8—22no—
121C2×C22⋊Q8C2×C412yes—
122C2×C22⋊Q8C2×C414yes—
123C2×C22⋊Q8C2×C412yes—
124C2×C22⋊Q8C2312yes—
125C2×C22⋊Q8C2314yes—
126C2×#121—22no—
127C2×#121—22no—
128C2×#121—21no—
129C2×#121—21no—
130C2×#121—22no—
131C2×#121—22no—
132C2×#121—22no—
133C2×#121C2×C412yes—
134C2×#121C2×C414yes—
135C2×#121C2×C412yes—
136C2×#121C2312yes—
137C2×#121C2314yes—
138C2×#120—22no—
139C2×#120—22no—
140#518—28no—
141#518—28no—
142C2×C4×Q8C2×C412yes—
143C2×C4×D4—22no—
144C2×C4×D4—22no—
145C2×C4×D4—22no—
146C2×C4×D4—22no—
147C2×C4×D4—22no—
148C2×C4×D4C2×C412yes—
149C2×C4×D4C2×C412yes—
150C2×C4×D4C2×C412yes—
151C2×C4×D4C2×C414yes—
152C2×C4×D4D412yes—
153C2×C4×D4D412yes—
154C2×C4×D4D414yes—
155C2×C4×D4D414yes—
156C2×C4×D4C2314yes—
157C2×#117—22no—
158C2×#117—22no—
159C2×#117C2×C412yes—
160C22×C4⋊C4—21no—
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⋊C4—21no—
173C22×C22⋊C4D411yescharacteristic
174C22×C22⋊C4D411yescharacteristic
175C22×C42—21no—
176C22×C42—21no—
177C22×C42—21no—
178C22×C42C2311yescharacteristic
179#435—216no—
180#435—216no—
181#432—24no—
182#432C2318yescomplemented
183C2×C4⋊C8—22no—
184#407—22no—
185#407—22no—
186#407C2314yes—
187#407C2314yes—
188C2×C22⋊C8—22no—
189C2×C22⋊C8—24no—
190C2×C22⋊C8—21no—
191C2×C22⋊C8—21no—
192C2×C22⋊C8C2312yes—
193C2×C22⋊C8C2312yes—
194C2×C22⋊C8C2318yescomplemented
195C2×#97—22no—
196#390—28no—
197#388—28no—
198#388—28no—
199#382—22no—
200#382C2314yescomplemented
201#381—22no—
202#381—22no—
203#381C2314yes—
204#381C2314yescomplemented
205C4×C4⋊C4—28no—
206C4×C4⋊C4—22no—
207C4×C4⋊C4C2314yescomplemented
208C4×C22⋊C4—22no—
209C4×C22⋊C4—22no—
210C4×C22⋊C4C2314yes—
211C4×C22⋊C4C2314yescomplemented
212C2×#95—21no—
213C2×#95—21no—
214C2×#95—21no—
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×C418yes—
233C22×Q8—21no—
234C22×Q8—22no—
235C22×Q8—82no—
236C22×Q8C22×C412yes—
237C22×Q8C22×C414yes—
238C22×D4—22no—
239C22×D4—24no—
240C22×D4—22no—
241C22×D4—24no—
242C22×D4—22no—
243C22×D4—22no—
244C22×D4—21no—
245C22×D4—22no—
246C22×D4—42no—
247C22×D4—42no—
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—82no—
267C23×C4—82no—
268C23×C4C22×C411yescharacteristic
269C23×C4C22×C411yescharacteristic
270C23×C4C22×C412yes—
271C23×C4C22×C412yes—
272C23×C4C22×C412yes—
273C23×C4C2×D411yescharacteristic
274C23×C4C2×D411yescharacteristic
275C23×C4C2×D411yescharacteristic
276C23×C4C2×D411yescharacteristic
277C23×C4C2×D411yescharacteristic
278C23×C4C2×D411yescharacteristic
279C23×C4C2×D412yes—
280C23×C4C2×D412yes—
281C23×C4C2×D412yes—
282C23×C4C2×D412yes—
283C23×C4C2×D412yes—
284C23×C4C2411yescharacteristic
285C23×C4C2412yes—
286C23×C4C2412yes—
287C2×M16—24no—
288C2×M16—24no—
289C2×M16—82no—
290C2×M16—82no—
291C22×C8—22no—
292C22×C8—22no—
293C22×C8—28no—
294C22×C8—84no—
295#126—216no—
296#126—216no—
297#126—28no—
298#126—28no—
299#125—216no—
300#125—24no—
301#125C22×C418yes—
302#124—216no—
303#124—24no—
304#124C22×C418yes—
305#123—216no—
306#123—28no—
307#123—28no—
308#123—28no—
309#123—28no—
310#123—216no—
311#123—216no—
312C22⋊Q8—24no—
313C22⋊Q8—24no—
314C22⋊Q8—24no—
315C22⋊Q8—24no—
316C22⋊Q8—22no—
317C22⋊Q8—22no—
318C22⋊Q8—24no—
319C22⋊Q8—24no—
320C22⋊Q8—216no—
321C22⋊Q8C22×C414yes—
322C22⋊Q8C22×C418yes—
323C22⋊Q8C22×C418yes—
324C22⋊Q8C2414yes—
325#121—216no—
326#121—216no—
327#121—24no—
328#121—24no—
329#121—24no—
330#121—24no—
331#121—22no—
332#121—22no—
333#121—24no—
334#121—24no—
335#121—216no—
336#121C22×C414yes—
337#121C22×C418yes—
338#121C22×C418yes—
339#121C2414yes—
340#120—28no—
341#120—28no—
342#120—216no—
343C4×Q8—24no—
344C4×Q8C22×C418yes—
345C4×D4—28no—
346C4×D4—28no—
347C4×D4—28no—
348C4×D4—28no—
349C4×D4—28no—
350C4×D4—28no—
351C4×D4—216no—
352C4×D4—216no—
353C4×D4—24no—
354C4×D4C22⋊C418yes—
355C4×D4C22⋊C418yes—
356C4×D4C22⋊C418yes—
357C4×D4C22⋊C418yes—
358C4×D4C22×C418yes—
359C4×D4C22×C418yes—
360C4×D4C22×C418yes—
361C4×D4C2×D418yes—
362C4×D4C2×D418yes—
363#117—24no—
364#117—216no—
365#117—28no—
366#117—28no—
367#117C22×C418yes—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—24no—
380C2×C4⋊C4—24no—
381C2×C4⋊C4—24no—
382C2×C4⋊C4—44no—
383C2×C4⋊C4—44no—
384C2×C4⋊C4C22⋊C412yes—
385C2×C4⋊C4C22⋊C412yes—
386C2×C4⋊C4C22⋊C414yes—
387C2×C4⋊C4C22×C412yes—
388C2×C4⋊C4C22×C412yes—
389C2×C4⋊C4C22×C414yes—
390C2×C4⋊C4C22×C414yes—
391C2×C4⋊C4C2×D414yes—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—24no—
406C2×C22⋊C4—216no—
407C2×C22⋊C4—24no—
408C2×C22⋊C4—24no—
409C2×C22⋊C4—24no—
410C2×C22⋊C4—24no—
411C2×C22⋊C4—44no—
412C2×C22⋊C4—44no—
413C2×C22⋊C4—82no—
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—24no—
428C2×C42—44no—
429C2×C42—82no—
430C2×C42—82no—
431C2×C42C22×C412yes—
432C2×C42C22×C412yes—
433C2×C42C2×D412yes—
434C2×C42C2×D412yes—
435C2×C42C2×D412yes—
436C2×C42C2412yes—
437C4⋊C8—28no—
438C22⋊C8—22no—
439C22⋊C8—22no—
440C22⋊C8—28no—
441C22⋊C8—24no—
442C22⋊C8—24no—
443C22⋊C8C2414yes—
444C22⋊C8C2414yes—
445#97—28no—
446#95—24no—
447#95—24no—
448#95—24no—
449#95—21no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95C2412yes—
454#95C2412yes—
455#95C2412yes—
456#95C2412yes—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—24no—
463C24—42no—
464C24—42no—
465C24—42no—
466C24—42no—
467C24—44no—
468C24—82no—
469C24—82no—
470C24C2×C22⋊C411yescharacteristic
471C24C2×C22⋊C412yes—
472C24C2×C22⋊C411yescharacteristic
473C24C2×C22⋊C412yes—
474C24C2×C22⋊C412yes—
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—24no—
488C2×D4—28no—
489C2×D4—24no—
490C2×D4—28no—
491C2×D4—28no—
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—416no—
501C2×D4—48no—
502C2×D4—48no—
503C2×D4—48no—
504C2×D4—44no—
505C2×D4—44no—
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—42no—
540C22×C4—44no—
541C22×C4—42no—
542C22×C4—42no—
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—84no—
552C22×C4—84no—
553C22×C4—82no—
554C22×C4—82no—
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×C4C2×C22⋊C412yes—
564C22×C4C2×C22⋊C412yes—
565C22×C4C2×C22⋊C412yes—
566C22×C4C2×C22⋊C412yes—
567C22×C4C2×C22⋊C411yescharacteristic
568C22×C4C2×C22⋊C411yescharacteristic
569C22×C4C2×C22⋊C412yes—
570C22×C4C2×C22⋊C412yes—
571C22×C4C2×C22⋊C412yes—
572C22×C4C2×C22⋊C412yes—
573C22×C4C2×C22⋊C412yes—
574C22×C4C2×C22⋊C412yes—
575C22×C4C2×C22⋊C412yes—
576C22×C4C2×C22⋊C414yes—
577C22×C4C2×C22⋊C414yes—
578C22×C4C23×C411yescharacteristic
579C22×C4C23×C411yescharacteristic
580C22×C4C23×C412yes—
581C22×C4C23×C412yes—
582C22×C4C23×C414yes—
583C22×C4C22×D412yes—
584C22×C4C22×D411yescharacteristic
585C22×C4C22×D411yescharacteristic
586C22×C4C22×D412yes—
587C22×C4C22×D412yes—
588C22×C4C22×D412yes—
589C22×C4C22×D411yescharacteristic
590C22×C4C22×D412yes—
591C22×C4C22×D412yes—
592C22×C4C22×D414yes—
593C22×C4C2511yescharacteristic
594M16—84no—
595M16—84no—
596C2×C8—24no—
597C2×C8—24no—
598C2×C8—44no—
599C2×C8—44no—
600C2×C8—88no—
601C4⋊C4—24no—
602C4⋊C4—28no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—28no—
608C4⋊C4—28no—
609C4⋊C4—28no—
610C4⋊C4—28no—
611C4⋊C4—24no—
612C4⋊C4—48no—
613C4⋊C4—48no—
614C4⋊C4C2×C22⋊C418yes—
615C4⋊C4C2×C22⋊C418yes—
616C4⋊C4C23×C414yes—
617C4⋊C4C23×C414yes—
618C22⋊C4—28no—
619C22⋊C4—24no—
620C22⋊C4—28no—
621C22⋊C4—28no—
622C22⋊C4—24no—
623C22⋊C4—24no—
624C22⋊C4—28no—
625C22⋊C4—28no—
626C22⋊C4—28no—
627C22⋊C4—28no—
628C22⋊C4—28no—
629C22⋊C4—24no—
630C22⋊C4—48no—
631C22⋊C4—48no—
632C22⋊C4—84no—
633C22⋊C4—84no—
634C22⋊C4C2×C22⋊C418yes—
635C22⋊C4C2×C22⋊C418yes—
636C22⋊C4C2×C22⋊C418yes—
637C22⋊C4C2×C22⋊C418yes—
638C42—28no—
639C42—28no—
640C42—48no—
641C42—84no—
642C42—84no—
643C42C2×C22⋊C414yes—
644C42C2×C22⋊C414yes—
645C42C23×C414yes—
646C42C22×D414yes—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—24no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—24no—
655C23—22no—
656C23—24no—
657C23—22no—
658C23—24no—
659C23—24no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—24no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—48no—
674C23—44no—
675C23—44no—
676C23—44no—
677C23—84no—
678C23—84no—
679C23—84no—
680C23—84no—
681C23—84no—
682C23—84no—
683C23—168no—
684C23C22×C22⋊C412yes—
685C23C22×C22⋊C414yes—
686C23C22×C22⋊C412yes—
687C23C22×C22⋊C411yescharacteristic
688C23C22×C22⋊C411yescharacteristic
689C23#57512yes—
690C23#57512yes—
691C23C23×D411yescharacteristic
692Q8—44no—
693Q8—44no—
694Q8—84no—
695D4—48no—
696D4—48no—
697D4—44no—
698D4—44no—
699D4—416no—
700D4—48no—
701D4—44no—
702D4—44no—
703D4—84no—
704D4—88no—
705D4—88no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—44no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—44no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—44no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—48no—
744C2×C4—48no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—42no—
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—88no—
759C2×C4—88no—
760C2×C4—84no—
761C2×C4—84no—
762C2×C4—84no—
763C2×C4—84no—
764C2×C4—84no—
765C2×C4C22×C22⋊C414yes—
766C2×C4C22×C22⋊C414yes—
767C2×C4C22×C22⋊C411yescharacteristic
768C2×C4C22×C22⋊C411yescharacteristic
769C2×C4C22×C22⋊C414yes—
770C2×C4C22×C22⋊C412yes—
771C2×C4C22×C22⋊C412yes—
772C2×C4C24×C411yescharacteristic
773C2×C4C23×D411yescharacteristic
774C8—44no—
775C8—44no—
776C22—21no—
777C22—21no—
778C22—21no—
779C22—21no—
780C22—24no—
781C22—24no—
782C22—22no—
783C22—24no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—24no—
788C22—22no—
789C22—24no—
790C22—22no—
791C22—44no—
792C22—48no—
793C22—44no—
794C22—44no—
795C22—44no—
796C22—44no—
797C22—82no—
798C22—82no—
799C22—82no—
800C22—82no—
801C22—84no—
802C22—84no—
803C22—88no—
804C22—168no—
805C22#288312yes—
806C22#289612yes—
807C22#289612yes—
808C22#290112yes—
809C22C23×C22⋊C411yescharacteristic
810C22C2×#57511yescharacteristic
811C22C2×#57511yescharacteristic
812C4—21no—
813C4—21no—
814C4—21no—
815C4—21no—
816C4—24no—
817C4—22no—
818C4—22no—
819C4—24no—
820C4—24no—
821C4—44no—
822C4—44no—
823C4—44no—
824C4—44no—
825C4—82no—
826C4—82no—
827C4—82no—
828C2—21no—
829C2—21no—
830C2—22no—
831C2—42no—
832C2—44no—
833C2—42no—
834C2—84no—
835C2#1762514yesdirect product factor
836C2C2×#288311yescharacteristic
837C2C2×#289611yescharacteristic
838C2C2×#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×#2973C2semidirect
3. C2×#2357C2semidirect
4. #17625C2direct (N × H)
5. C2×#1516C2semidirect
6. C2×#1512C2semidirect
7. C2×#1511C2semidirect
8. C2×#1510C2semidirect
9. C2×#1509C2semidirect
10. C2×#1508C2semidirect
11. C2×#1507C2semidirect
12. C2×#1501C2semidirect
15. #3505C4semidirect
18. C2×#553C4semidirect
19. C2×#552C4semidirect
21. C2×#548C4semidirect
22. C2×#546C4semidirect
33. #2973C22semidirect
36. C2×#432C22semidirect
39. C22×C22⋊C8C22semidirect
41. #2357C22semidirect
45. C2×#382C22semidirect
47. C2×#381C22semidirect
49. C2×C4×C4⋊C4C22semidirect
51. C2×C4×C22⋊C4C22semidirect
52. #1516C22semidirect
53. #1512C22semidirect
54. #1511C22semidirect
55. #1510C22semidirect
56. #1509C22semidirect
57. #1508C22semidirect
58. #1507C22semidirect
59. #1501C22semidirect
60. C2×#328C22semidirect
61. C2×#328C22semidirect
62. C2×#328C22semidirect
63. C2×#328C22semidirect
81. #553C2×C4semidirect
83. #552C2×C4semidirect
87. #548C2×C4semidirect
89. #546C2×C4semidirect
182. #432C23semidirect
194. C2×C22⋊C8C23semidirect
200. #382C23semidirect
204. #381C23semidirect
207. C4×C4⋊C4C23semidirect
211. C4×C22⋊C4C23semidirect
219. #328C23semidirect
220. #328C23semidirect
221. #328C23semidirect
222. #328C23semidirect
835. C2#17625direct (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×#29732
C2×#23572
#176252
C2×#15162
C2×#15122
C2×#15112
C2×#15102
C2×#15092
C2×#15082
C2×#15072
C2×#15012