Finite Group Databasebeta

← #6343586

Subgroups — #6343586

Order 512.

3102 conjugacy classes of subgroups.

The subgroup lattice has 1026 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3494C211yesmaximal, characteristic
2#60124C211yesmaximal, characteristic, complemented
3#34177C211yesmaximal, characteristic, complemented
4#17604C2116yesmaximal, complemented
5#17589C212yesmaximal, complemented
6#17587C212yesmaximal, complemented
7#17580C212yesmaximal, complemented
8#17561C212yesmaximal, complemented
9#17554C212yesmaximal, complemented
10C2×#1510C212yesmaximal, complemented
11#3494—24no—
12#3494—24no—
13#3494C418yescomplemented
14#3494C2218yes—
15C2×#555—21no—
16C2×#553—21no—
17C2×#553—21no—
18C2×#551—21no—
19C2×#551—21no—
20C2×#547—21no—
21C2×#546—21no—
22C2×#546—21no—
23C2×#544C411yescharacteristic, complemented
24C2×#542C411yescharacteristic, complemented
25C2×#542C411yescharacteristic, complemented
26C2×#540C411yescharacteristic, complemented
27C2×#540C411yescharacteristic, complemented
28C2×#535C411yescharacteristic, complemented
29C2×#532C2211yescharacteristic
30C2×#532C2211yescharacteristic
31C2×#529C2211yescharacteristic
32C2×#529C2211yescharacteristic
33C2×#525C2211yescharacteristic
34C22×#121C2211yescharacteristic
35C2×#520C411yescharacteristic, complemented
36C2×#518C411yescharacteristic, complemented
37C22×#117C2211yescharacteristic
38#2924—24no—
39#2924C2218yescomplemented
40#2921—21no—
41#2921—21no—
42#2920C2212yescomplemented
43#2920C2212yescomplemented
44#2905—21no—
45C2×#407C2212yes—
46#2873—21no—
47#2343—24no—
48#2343C2218yescomplemented
49#2315—21no—
50#2313—21no—
51#2313—21no—
52#2283C2212yescomplemented
53#2283C2212yescomplemented
54C2×#381C2212yes—
55#2273—21no—
56#1521C2218yescomplemented
57#1517C2218yescomplemented
58#1516C2218yescomplemented
59#1514C2218yescomplemented
60#1512C2218yescomplemented
61#1511C2214yescomplemented
62#1510C2214yes—
63#1510C2214yes—
64#1510C2218yescomplemented
65#1510C2214yescomplemented
66#1509C2218yescomplemented
67#1505C2218yescomplemented
68#1504C2218yescomplemented
69#1502C2218yescomplemented
70#1500C2218yescomplemented
71C2×#327C2218yescomplemented
72C22×#41—21no—
73C22×#41—21no—
74C22×#41C2×C411yescharacteristic
75C23×D4—21no—
76C23×D4C2×C411yescharacteristic
77C24×C4C2311yescharacteristic
78C22×M16—22no—
79#555—28no—
80#555—28no—
81#553—28no—
82#553—28no—
83#553—28no—
84#553—28no—
85#551—28no—
86#551—28no—
87#551—28no—
88#551—28no—
89#547—28no—
90#547—28no—
91#546—28no—
92#546—28no—
93#546—28no—
94#546—28no—
95#544—24no—
96#544C2×C418yescomplemented
97#542—24no—
98#542—24no—
99#542C2×C418yescomplemented
100#542C2×C418yescomplemented
101#540—24no—
102#540—24no—
103#540C2×C418yescomplemented
104#540C2×C418yescomplemented
105#535—24no—
106#535C2×C418yescomplemented
107#532—22no—
108#532—22no—
109#532—22no—
110#532—22no—
111#532C2×C414yescomplemented
112#532C2×C414yescomplemented
113#532C2314yes—
114#532C2314yes—
115C2×C4⋊Q8—21no—
116C2×C4⋊Q8C2×C411yescharacteristic, complemented
117C2×C4⋊Q8C2×C411yescharacteristic, complemented
118C2×#127C2×C411yescharacteristic, complemented
119C2×#127C2×C411yescharacteristic, complemented
120#529—22no—
121#529—22no—
122#529—22no—
123#529—22no—
124#529C2×C414yescomplemented
125#529C2×C414yescomplemented
126#529C2314yes—
127#529C2314yes—
128C2×#126—21no—
129C2×#126—21no—
130C2×#126—21no—
131C2×#126—21no—
132C2×#125—21no—
133C2×#125C2×C411yescharacteristic, complemented
134C2×#125C2×C411yescharacteristic, complemented
135C2×#124—21no—
136C2×#124—21no—
137C2×#124—21no—
138C2×#124—21no—
139C2×#124C2×C411yescharacteristic, complemented
140C2×#124C2×C411yescharacteristic, complemented
141#525—22no—
142#525—22no—
143#525C2×C414yes—
144#525C2314yes—
145C2×#123—21no—
146C2×#123—21no—
147C2×#123—21no—
148C2×#123—21no—
149C2×#123—21no—
150C2×#123—21no—
151C2×#123—21no—
152C2×#123—21no—
153C2×#123—21no—
154C2×C22⋊Q8—21no—
155C2×C22⋊Q8—21no—
156C2×C22⋊Q8—21no—
157C2×C22⋊Q8—21no—
158C2×C22⋊Q8C2×C411yescharacteristic
159C2×C22⋊Q8C2311yescharacteristic
160C2×#121—21no—
161C2×#121—21no—
162C2×#121—22no—
163C2×#121—22no—
164C2×#121—21no—
165C2×#121—21no—
166C2×#121—21no—
167C2×#121—21no—
168C2×#121—21no—
169C2×#121—21no—
170C2×#121—21no—
171C2×#121—21no—
172C2×#121C2×C411yescharacteristic
173C2×#121C2×C411yescharacteristic
174C2×#121C2×C414yes—
175C2×#121C2×C411yescharacteristic
176C2×#121C2311yescharacteristic
177C2×#121C2311yescharacteristic
178C2×#121C2314yes—
179C2×#121C2311yescharacteristic
180C2×#120—21no—
181C2×#120—21no—
182C2×#120—21no—
183#520—24no—
184#520C2×C418yescomplemented
185#518—24no—
186#518C2×C418yescomplemented
187C2×C4×Q8C2×C411yescharacteristic, complemented
188C2×C4×Q8C2×C411yescharacteristic, complemented
189C2×C4×D4—21no—
190C2×C4×D4—21no—
191C2×C4×D4—21no—
192C2×C4×D4—21no—
193C2×C4×D4—21no—
194C2×C4×D4—21no—
195C2×C4×D4—21no—
196C2×C4×D4—21no—
197C2×C4×D4—21no—
198C2×C4×D4—21no—
199C2×C4×D4C2×C411yescharacteristic, complemented
200C2×C4×D4C2×C411yescharacteristic, complemented
201C2×C4×D4C2×C411yescharacteristic, complemented
202C2×C4×D4C2×C411yescharacteristic, complemented
203C2×C4×D4C2×C411yescharacteristic, complemented
204C2×C4×D4C2×C411yescharacteristic, complemented
205C2×#117—21no—
206C2×#117—21no—
207C2×#117—21no—
208C2×#117C2×C411yescharacteristic
209C2×#117C2×C411yescharacteristic
210C2×#117C2×C411yescharacteristic
211C2×#117C2×C411yescharacteristic
212C2×#117C2×C411yescharacteristic
213C2×#117C2×C414yes—
214C2×#117D411yescharacteristic
215C2×#117D411yescharacteristic
216C2×#117D411yescharacteristic
217C2×#117D411yescharacteristic
218C2×#117D414yes—
219C2×#117D414yes—
220C2×#117C2314yes—
221C22×C4⋊C4—21no—
222C22×C4⋊C4C2×C411yescharacteristic
223C22×C4⋊C4D411yescharacteristic
224C22×C4⋊C4D411yescharacteristic
225C22×C22⋊C4—21no—
226C22×C22⋊C4—21no—
227C22×C22⋊C4—21no—
228C22×C22⋊C4—22no—
229C22×C22⋊C4D411yescharacteristic
230C22×C22⋊C4D411yescharacteristic
231C22×C42C2311yescharacteristic
232C22×C42C2311yescharacteristic
233#433—28no—
234#433—28no—
235#432—22no—
236#432—22no—
237#432C2314yescomplemented
238#432C2314yescomplemented
239#431—22no—
240#431—22no—
241#431C2314yescomplemented
242#431C2314yescomplemented
243#424—28no—
244#423—22no—
245#423—22no—
246#407—22no—
247#407—22no—
248#407C2314yes—
249#407C2314yes—
250C2×C22⋊C8—22no—
251C2×C22⋊C8C2314yes—
252#405—28no—
253C4×M16—22no—
254C4×M16—22no—
255#387—28no—
256#387—28no—
257#385—28no—
258#383—22no—
259#383C2314yescomplemented
260#382—22no—
261#382C2314yescomplemented
262#381—22no—
263#381—22no—
264#381C2314yes—
265#381C2314yes—
266#380—22no—
267#380—22no—
268C4×C4⋊C4—22no—
269C4×C4⋊C4C2314yescomplemented
270C4×C22⋊C4—22no—
271C4×C22⋊C4—22no—
272C4×C22⋊C4—28no—
273#376—22no—
274#376C2314yescomplemented
275C2×#95—22no—
276C2×#95C2314yes—
277#328C23116yescomplemented
278#327C23116yes—
279#327C23116yes—
280#327C23116yescomplemented
281C25—21no—
282C25C2×D411yescharacteristic
283C2×#41—22no—
284C2×#41—24no—
285C2×#41—24no—
286C2×#41—24no—
287C2×#41—24no—
288C2×#41—44no—
289C2×#41—84no—
290C2×#41—84no—
291C2×#41C22×C414yes—
292C22×Q8—21no—
293C22×Q8—21no—
294C22×Q8C22×C411yescharacteristic
295C22×D4—21no—
296C22×D4—21no—
297C22×D4—21no—
298C22×D4—21no—
299C22×D4—21no—
300C22×D4—21no—
301C22×D4—21no—
302C22×D4—24no—
303C22×D4—24no—
304C22×D4—21no—
305C22×D4—22no—
306C22×D4—21no—
307C22×D4—21no—
308C22×D4—21no—
309C22×D4—21no—
310C22×D4—44no—
311C22×D4—84no—
312C22×D4C22×C411yescharacteristic
313C22×D4C22×C411yescharacteristic
314C22×D4C22×C411yescharacteristic
315C22×D4C22×C414yes—
316C23×C4—21no—
317C23×C4—21no—
318C23×C4—21no—
319C23×C4—21no—
320C23×C4—21no—
321C23×C4—21no—
322C23×C4—21no—
323C23×C4—21no—
324C23×C4—24no—
325C23×C4—44no—
326C23×C4C22×C411yescharacteristic
327C23×C4C22×C411yescharacteristic
328C23×C4C22×C412yes—
329C23×C4C2×D411yescharacteristic
330C23×C4C2×D411yescharacteristic
331C23×C4C2×D411yescharacteristic
332C23×C4C2×D411yescharacteristic
333C23×C4C2×D412yes—
334C23×C4C2×D411yescharacteristic
335C23×C4C2×D412yes—
336C23×C4C2×D411yescharacteristic
337C23×C4C2×D411yescharacteristic
338C23×C4C2412yes—
339C23×C4C2411yescharacteristic
340C2×M16—24no—
341C2×M16—24no—
342C2×M16—48no—
343C22×C8—24no—
344C4⋊Q8—28no—
345C4⋊Q8—22no—
346C4⋊Q8—22no—
347C4⋊Q8C22×C414yes—
348C4⋊Q8C22×C414yes—
349#127—22no—
350#127—22no—
351#127C22×C414yes—
352#127C22×C414yes—
353#126—28no—
354#126—28no—
355#126—24no—
356#126—24no—
357#126—24no—
358#126—24no—
359#125—28no—
360#125—22no—
361#125—22no—
362#125C22×C414yes—
363#125C22×C414yes—
364#124—28no—
365#124—28no—
366#124—24no—
367#124—24no—
368#124—22no—
369#124—22no—
370#124—24no—
371#124—24no—
372#124C22×C414yes—
373#124C22×C414yes—
374#123—24no—
375#123—24no—
376#123—24no—
377#123—24no—
378#123—24no—
379#123—24no—
380#123—28no—
381#123—28no—
382#123—28no—
383#123—28no—
384#123—28no—
385#123—28no—
386C22⋊Q8—22no—
387C22⋊Q8—21no—
388C22⋊Q8—21no—
389C22⋊Q8—28no—
390C22⋊Q8—28no—
391C22⋊Q8—28no—
392C22⋊Q8—28no—
393C22⋊Q8C22×C414yes—
394C22⋊Q8C22×C412yes—
395C22⋊Q8C2412yes—
396#121—22no—
397#121—22no—
398#121—24no—
399#121—24no—
400#121—24no—
401#121—24no—
402#121—22no—
403#121—21no—
404#121—21no—
405#121—21no—
406#121—21no—
407#121—24no—
408#121—24no—
409#121—24no—
410#121—24no—
411#121—21no—
412#121—21no—
413#121—28no—
414#121—28no—
415#121—28no—
416#121—28no—
417#121—28no—
418#121—28no—
419#121C22×C412yes—
420#121C22×C412yes—
421#121C22×C414yes—
422#121C22×C414yes—
423#121C22×C414yes—
424#121C22×C412yes—
425#121C2412yes—
426#121C2412yes—
427#121C2412yes—
428#120—24no—
429#120—24no—
430#120—28no—
431#120—28no—
432C4×Q8—22no—
433C4×Q8—22no—
434C4×Q8C22×C414yes—
435C4×Q8C22×C414yes—
436C4×D4—24no—
437C4×D4—24no—
438C4×D4—24no—
439C4×D4—24no—
440C4×D4—24no—
441C4×D4—24no—
442C4×D4—24no—
443C4×D4—24no—
444C4×D4—28no—
445C4×D4—28no—
446C4×D4—28no—
447C4×D4—28no—
448C4×D4—24no—
449C4×D4—24no—
450C4×D4—22no—
451C4×D4—22no—
452C4×D4—22no—
453C4×D4—22no—
454C4×D4—22no—
455C4×D4—22no—
456C4×D4—24no—
457C4×D4—24no—
458C4×D4C22×C414yes—
459C4×D4C22×C414yes—
460C4×D4C22×C414yes—
461C4×D4C22×C414yes—
462C4×D4C22×C414yes—
463C4×D4C22×C414yes—
464#117—22no—
465#117—28no—
466#117—24no—
467#117—24no—
468#117—24no—
469#117—24no—
470#117C22⋊C414yes—
471#117C22⋊C414yes—
472#117C22⋊C414yes—
473#117C22⋊C414yes—
474#117C22⋊C414yes—
475#117C22⋊C414yes—
476#117C22⋊C414yes—
477#117C22⋊C414yes—
478#117C22×C414yes—
479#117C22×C414yes—
480#117C22×C414yes—
481#117C22×C414yes—
482#117C22×C414yes—
483#117C2×D414yes—
484#117C2×D414yes—
485#117C2×D414yes—
486#117C2×D414yes—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—22no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—28no—
500C2×C4⋊C4—24no—
501C2×C4⋊C4—24no—
502C2×C4⋊C4C22⋊C411yescharacteristic
503C2×C4⋊C4C22⋊C411yescharacteristic
504C2×C4⋊C4C22⋊C411yescharacteristic
505C2×C4⋊C4C22⋊C411yescharacteristic
506C2×C4⋊C4C22⋊C411yescharacteristic
507C2×C4⋊C4C22⋊C411yescharacteristic
508C2×C4⋊C4C22⋊C411yescharacteristic
509C2×C4⋊C4C22⋊C411yescharacteristic
510C2×C4⋊C4C22⋊C414yes—
511C2×C4⋊C4C22⋊C414yes—
512C2×C4⋊C4C22×C411yescharacteristic
513C2×C4⋊C4C22×C411yescharacteristic
514C2×C4⋊C4C22×C414yes—
515C2×C4⋊C4C22×C411yescharacteristic
516C2×C4⋊C4C22×C411yescharacteristic
517C2×C4⋊C4C2×D414yes—
518C2×C4⋊C4C2×D414yes—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—24no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—28no—
541C2×C22⋊C4—28no—
542C2×C22⋊C4—24no—
543C2×C22⋊C4—24no—
544C2×C22⋊C4—48no—
545C2×C22⋊C4C22⋊C411yescharacteristic
546C2×C22⋊C4C22⋊C411yescharacteristic
547C2×C22⋊C4C22⋊C411yescharacteristic
548C2×C22⋊C4C22⋊C411yescharacteristic
549C2×C22⋊C4C22⋊C411yescharacteristic
550C2×C22⋊C4C22⋊C411yescharacteristic
551C2×C22⋊C4C22⋊C411yescharacteristic
552C2×C22⋊C4C22⋊C411yescharacteristic
553C2×C22⋊C4C22⋊C414yes—
554C2×C22⋊C4C22⋊C414yes—
555C2×C22⋊C4C2×D414yes—
556C2×C22⋊C4C2×D414yes—
557C2×C42—21no—
558C2×C42—21no—
559C2×C42—21no—
560C2×C42—24no—
561C2×C42—24no—
562C2×C42C22×C411yescharacteristic
563C2×C42C22×C411yescharacteristic
564C2×C42C22×C411yescharacteristic
565C2×C42C22×C411yescharacteristic
566C2×C42C22×C412yes—
567C2×C42C22×C412yes—
568C2×C42C2×D412yes—
569C2×C42C2×D412yes—
570C2×C42C2×D411yescharacteristic
571C2×C42C2×D411yescharacteristic
572C2×C42C2×D411yescharacteristic
573C2×C42C2×D411yescharacteristic
574C2×C42C2×D412yes—
575C2×C42C2×D412yes—
576C2×C42C2412yes—
577C2×C42C2412yes—
578C4⋊C8—24no—
579C4⋊C8—24no—
580C4⋊C8—24no—
581C4⋊C8—24no—
582C22⋊C8—24no—
583C22⋊C8—24no—
584C22⋊C8—24no—
585C22⋊C8C2418yes—
586#97—24no—
587#97—24no—
588C4×C8—24no—
589C4×C8—24no—
590#95—24no—
591#95—24no—
592#95—24no—
593#95—24no—
594#95—24no—
595#95—24no—
596#95—24no—
597#95C2418yes—
598C24—24no—
599C24—21no—
600C24—21no—
601C24—21no—
602C24—24no—
603C24—42no—
604C24—44no—
605C24—81no—
606C24—82no—
607C24—82no—
608C24C2×C22⋊C411yescharacteristic
609C24C2×C22⋊C412yes—
610C24C2×C22⋊C411yescharacteristic
611C24C22×D411yescharacteristic
612C24C22×D412yes—
613#41—48no—
614#41—48no—
615#41—88no—
616#41—88no—
617#41—88no—
618#41—88no—
619C2×Q8—21no—
620C2×Q8—24no—
621C2×Q8—24no—
622C2×Q8—42no—
623C2×Q8—82no—
624C2×Q8—82no—
625C2×Q8C23×C412yes—
626C2×D4—24no—
627C2×D4—22no—
628C2×D4—22no—
629C2×D4—22no—
630C2×D4—22no—
631C2×D4—22no—
632C2×D4—22no—
633C2×D4—24no—
634C2×D4—24no—
635C2×D4—24no—
636C2×D4—24no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—24no—
641C2×D4—24no—
642C2×D4—24no—
643C2×D4—24no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—48no—
647C2×D4—42no—
648C2×D4—44no—
649C2×D4—48no—
650C2×D4—44no—
651C2×D4—44no—
652C2×D4—44no—
653C2×D4—44no—
654C2×D4—82no—
655C2×D4—82no—
656C2×D4—82no—
657C2×D4—82no—
658C2×D4—82no—
659C2×D4—82no—
660C2×D4—82no—
661C2×D4—88no—
662C2×D4—88no—
663C2×D4C23×C412yes—
664C2×D4C23×C412yes—
665C2×D4C23×C412yes—
666C22×C4—24no—
667C22×C4—24no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—24no—
674C22×C4—24no—
675C22×C4—24no—
676C22×C4—24no—
677C22×C4—24no—
678C22×C4—24no—
679C22×C4—24no—
680C22×C4—24no—
681C22×C4—28no—
682C22×C4—42no—
683C22×C4—44no—
684C22×C4—44no—
685C22×C4—42no—
686C22×C4—42no—
687C22×C4—44no—
688C22×C4—44no—
689C22×C4—42no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—44no—
693C22×C4—48no—
694C22×C4—81no—
695C22×C4—81no—
696C22×C4—82no—
697C22×C4—82no—
698C22×C4—82no—
699C22×C4—82no—
700C22×C4—82no—
701C22×C4—82no—
702C22×C4—82no—
703C22×C4—84no—
704C22×C4—84no—
705C22×C4C2×C22⋊C411yescharacteristic
706C22×C4C2×C22⋊C411yescharacteristic
707C22×C4C2×C22⋊C412yes—
708C22×C4C2×C22⋊C412yes—
709C22×C4C2×C22⋊C411yescharacteristic
710C22×C4C2×C22⋊C411yescharacteristic
711C22×C4C2×C22⋊C411yescharacteristic
712C22×C4C2×C22⋊C411yescharacteristic
713C22×C4C2×C22⋊C411yescharacteristic
714C22×C4C2×C22⋊C411yescharacteristic
715C22×C4C2×C22⋊C411yescharacteristic
716C22×C4C2×C22⋊C411yescharacteristic
717C22×C4C2×C22⋊C412yes—
718C22×C4C2×C22⋊C412yes—
719C22×C4C2×C22⋊C412yes—
720C22×C4C2×C22⋊C412yes—
721C22×C4C2×C22⋊C412yes—
722C22×C4C2×C22⋊C412yes—
723C22×C4C2×C22⋊C412yes—
724C22×C4C23×C411yescharacteristic
725C22×C4C23×C412yes—
726C22×C4C23×C411yescharacteristic
727C22×C4C23×C412yes—
728C22×C4C22×D412yes—
729C22×C4C22×D412yes—
730C22×C4C22×D411yescharacteristic
731C22×C4C22×D412yes—
732C22×C4C22×D411yescharacteristic
733C22×C4C22×D412yes—
734C22×C4C22×D412yes—
735C22×C4C22×D412yes—
736C22×C4C22×D411yescharacteristic
737C22×C4C22×D412yes—
738C22×C4C2511yescharacteristic
739M16—48no—
740M16—48no—
741C2×C8—28no—
742C2×C8—48no—
743C4⋊C4—24no—
744C4⋊C4—24no—
745C4⋊C4—24no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—22no—
749C4⋊C4—24no—
750C4⋊C4—24no—
751C4⋊C4—24no—
752C4⋊C4—24no—
753C4⋊C4—24no—
754C4⋊C4—24no—
755C4⋊C4—24no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—22no—
759C4⋊C4—84no—
760C4⋊C4—84no—
761C4⋊C4C2×C22⋊C414yes—
762C4⋊C4C2×C22⋊C414yes—
763C4⋊C4C2×C22⋊C414yes—
764C4⋊C4C2×C22⋊C414yes—
765C4⋊C4C2×C22⋊C414yes—
766C4⋊C4C2×C22⋊C414yes—
767C4⋊C4C2×C22⋊C414yes—
768C4⋊C4C2×C22⋊C414yes—
769C4⋊C4C23×C412yes—
770C4⋊C4C23×C412yes—
771C4⋊C4C23×C412yes—
772C4⋊C4C23×C412yes—
773C22⋊C4—24no—
774C22⋊C4—22no—
775C22⋊C4—24no—
776C22⋊C4—22no—
777C22⋊C4—22no—
778C22⋊C4—22no—
779C22⋊C4—24no—
780C22⋊C4—24no—
781C22⋊C4—24no—
782C22⋊C4—24no—
783C22⋊C4—24no—
784C22⋊C4—24no—
785C22⋊C4—24no—
786C22⋊C4—24no—
787C22⋊C4—24no—
788C22⋊C4—24no—
789C22⋊C4—22no—
790C22⋊C4—24no—
791C22⋊C4—24no—
792C22⋊C4—24no—
793C22⋊C4—22no—
794C22⋊C4—22no—
795C22⋊C4—22no—
796C22⋊C4—48no—
797C22⋊C4—48no—
798C22⋊C4C2×C22⋊C414yes—
799C22⋊C4C2×C22⋊C414yes—
800C22⋊C4C2×C22⋊C414yes—
801C22⋊C4C2×C22⋊C414yes—
802C22⋊C4C2×C22⋊C414yes—
803C22⋊C4C2×C22⋊C414yes—
804C22⋊C4C2×C22⋊C414yes—
805C22⋊C4C2×C22⋊C414yes—
806C42—24no—
807C42—24no—
808C42—24no—
809C42—84no—
810C42—84no—
811C42C2×C22⋊C412yes—
812C42C2×C22⋊C412yes—
813C42C2×C22⋊C412yes—
814C42C2×C22⋊C412yes—
815C42C2×C22⋊C412yes—
816C42C2×C22⋊C412yes—
817C42C2×C22⋊C412yes—
818C42C2×C22⋊C412yes—
819C42C23×C412yes—
820C42C23×C412yes—
821C42C23×C412yes—
822C42C23×C412yes—
823C42C22×D412yes—
824C42C22×D412yes—
825C42C22×D412yes—
826C42C22×D412yes—
827C23—22no—
828C23—24no—
829C23—22no—
830C23—24no—
831C23—22no—
832C23—24no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—41no—
837C23—41no—
838C23—42no—
839C23—41no—
840C23—41no—
841C23—42no—
842C23—41no—
843C23—42no—
844C23—42no—
845C23—42no—
846C23—42no—
847C23—42no—
848C23—42no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—42no—
853C23—48no—
854C23—84no—
855C23—84no—
856C23—88no—
857C23—168no—
858C23#41014yes—
859C23C22×C22⋊C412yes—
860C23C22×C22⋊C411yescharacteristic
861C23C22×C22⋊C412yes—
862C23C22×C22⋊C411yescharacteristic
863C23C23×D411yescharacteristic
864Q8—42no—
865Q8—42no—
866Q8—84no—
867Q8—84no—
868D4—42no—
869D4—42no—
870D4—42no—
871D4—48no—
872D4—42no—
873D4—42no—
874D4—42no—
875D4—44no—
876D4—44no—
877D4—44no—
878D4—44no—
879D4—44no—
880D4—44no—
881D4—48no—
882D4—84no—
883D4—84no—
884D4—84no—
885D4—84no—
886D4—84no—
887D4—84no—
888D4—84no—
889C2×C4—24no—
890C2×C4—24no—
891C2×C4—24no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—24no—
896C2×C4—24no—
897C2×C4—22no—
898C2×C4—24no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—42no—
905C2×C4—42no—
906C2×C4—42no—
907C2×C4—42no—
908C2×C4—42no—
909C2×C4—41no—
910C2×C4—42no—
911C2×C4—42no—
912C2×C4—41no—
913C2×C4—42no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—42no—
921C2×C4—42no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—42no—
925C2×C4—42no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—48no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—42no—
933C2×C4—42no—
934C2×C4—48no—
935C2×C4—48no—
936C2×C4—48no—
937C2×C4—84no—
938C2×C4—84no—
939C2×C4—84no—
940C2×C4—84no—
941C2×C4—84no—
942C2×C4—84no—
943C2×C4—84no—
944C2×C4—168no—
945C2×C4C22×C22⋊C412yes—
946C2×C4C22×C22⋊C412yes—
947C2×C4C22×C22⋊C412yes—
948C2×C4C22×C22⋊C411yescharacteristic
949C2×C4C22×C22⋊C411yescharacteristic
950C2×C4C22×C22⋊C412yes—
951C2×C4C22×C22⋊C412yes—
952C2×C4C22×C22⋊C412yes—
953C2×C4C22×C22⋊C412yes—
954C2×C4C22×C22⋊C412yes—
955C2×C4C22×C22⋊C412yes—
956C2×C4C22×C22⋊C412yes—
957C2×C4C24×C411yescharacteristic
958C2×C4C23×D411yescharacteristic
959C8—48no—
960C22—21no—
961C22—21no—
962C22—22no—
963C22—21no—
964C22—21no—
965C22—22no—
966C22—21no—
967C22—22no—
968C22—21no—
969C22—22no—
970C22—21no—
971C22—22no—
972C22—44no—
973C22—48no—
974C22—44no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—42no—
979C22—42no—
980C22—42no—
981C22—42no—
982C22—42no—
983C22—42no—
984C22—82no—
985C22—84no—
986C22—84no—
987C22—84no—
988C22—84no—
989C22—168no—
990C22C2×#41012yes—
991C22C2×#41014yes—
992C22C23×C22⋊C411yescharacteristic
993C22#358512yes—
994C4—21no—
995C4—22no—
996C4—22no—
997C4—21no—
998C4—21no—
999C4—21no—
1000C4—22no—
1001C4—22no—
1002C4—22no—
1003C4—22no—
1004C4—22no—
1005C4—22no—
1006C4—22no—
1007C4—22no—
1008C4—42no—
1009C4—42no—
1010C4—42no—
1011C4—42no—
1012C4—42no—
1013C4—88no—
1014C2—22no—
1015C2—22no—
1016C2—24no—
1017C2—41no—
1018C2—42no—
1019C2—82no—
1020C2—82no—
1021C2—82no—
1022C2C22×#41011yescharacteristic
1023C2#6008711yescharacteristic
1024C2#6009311yescharacteristic
subgroupG/H
center, socleC22C23×C22⋊C4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#3494C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C22×#117 ◁ G
LECSG ▷ C22×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60124C2semidirect
3. #34177C2semidirect
4. #17604C2semidirect
5. #17589C2semidirect
6. #17587C2semidirect
7. #17580C2semidirect
8. #17561C2semidirect
9. #17554C2semidirect
10. C2×#1510C2semidirect
13. #3494C4semidirect
23. C2×#544C4semidirect
24. C2×#542C4semidirect
25. C2×#542C4semidirect
26. C2×#540C4semidirect
27. C2×#540C4semidirect
28. C2×#535C4semidirect
35. C2×#520C4semidirect
36. C2×#518C4semidirect
39. #2924C22semidirect
42. #2920C22semidirect
43. #2920C22semidirect
48. #2343C22semidirect
52. #2283C22semidirect
53. #2283C22semidirect
56. #1521C22semidirect
57. #1517C22semidirect
58. #1516C22semidirect
59. #1514C22semidirect
60. #1512C22semidirect
61. #1511C22semidirect
64. #1510C22semidirect
65. #1510C22semidirect
66. #1509C22semidirect
67. #1505C22semidirect
68. #1504C22semidirect
69. #1502C22semidirect
70. #1500C22semidirect
71. C2×#327C22semidirect
96. #544C2×C4semidirect
99. #542C2×C4semidirect
100. #542C2×C4semidirect
103. #540C2×C4semidirect
104. #540C2×C4semidirect
106. #535C2×C4semidirect
111. #532C2×C4semidirect
112. #532C2×C4semidirect
116. C2×C4⋊Q8C2×C4semidirect
117. C2×C4⋊Q8C2×C4semidirect
118. C2×#127C2×C4semidirect
119. C2×#127C2×C4semidirect
124. #529C2×C4semidirect
125. #529C2×C4semidirect
133. C2×#125C2×C4semidirect
134. C2×#125C2×C4semidirect
139. C2×#124C2×C4semidirect
140. C2×#124C2×C4semidirect
184. #520C2×C4semidirect
186. #518C2×C4semidirect
187. C2×C4×Q8C2×C4semidirect
188. C2×C4×Q8C2×C4semidirect
199. C2×C4×D4C2×C4semidirect
200. C2×C4×D4C2×C4semidirect
201. C2×C4×D4C2×C4semidirect
202. C2×C4×D4C2×C4semidirect
203. C2×C4×D4C2×C4semidirect
204. C2×C4×D4C2×C4semidirect
237. #432C23semidirect
238. #432C23semidirect
241. #431C23semidirect
242. #431C23semidirect
259. #383C23semidirect
261. #382C23semidirect
269. C4×C4⋊C4C23semidirect
274. #376C23semidirect
277. #328C23semidirect
280. #327C23semidirect

Maximal subgroups

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

subgroupindex
C2×#34942
#601242
#341772
#176042
#175892
#175872
#175802
#175612
#175542
C2×#15102