Finite Group Databasebeta

← #182684

Subgroups — #182684

Order 512.

1358 conjugacy classes of subgroups.

The subgroup lattice has 927 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34223C211yesmaximal, characteristic
2#20524C211yesmaximal, characteristic, complemented
3C2×#1513C211yesmaximal, characteristic
4C2×#1504C211yesmaximal, characteristic
5#13802C211yesmaximal, characteristic, complemented
6#8221C211yesmaximal, characteristic, complemented
7#8220C211yesmaximal, characteristic, complemented
8#8219C211yesmaximal, characteristic, complemented
9#8218C211yesmaximal, characteristic, complemented
10#8217C211yesmaximal, characteristic, complemented
11#8216C211yesmaximal, characteristic, complemented
12C4×#328C211yesmaximal, characteristic, complemented
13C4×#327C211yesmaximal, characteristic, complemented
14#8020C211yesmaximal, characteristic, complemented
15#8016C211yesmaximal, characteristic, complemented
16C2×#525C2211yescharacteristic
17C2×#407C2211yescharacteristic
18C2×#407C2211yescharacteristic
19#2374—21no—
20#2374—21no—
21#2363C411yescharacteristic, complemented
22#2363C411yescharacteristic, complemented
23#2362C411yescharacteristic, complemented
24#2362C411yescharacteristic, complemented
25#2357—21no—
26#2353—21no—
27#2347C411yescharacteristic, complemented
28#2346C411yescharacteristic, complemented
29#2341C411yescharacteristic, complemented
30#2339C411yescharacteristic, complemented
31#2321—21no—
32#2321—21no—
33#2318—21no—
34C4×C22⋊Q8C2211yescharacteristic
35C4×C22⋊Q8C2211yescharacteristic
36C4×#121C2211yescharacteristic
37C4×#121C2211yescharacteristic
38#2280C2211yescharacteristic
39C2×#380C2211yescharacteristic
40#2275—21no—
41C2×C4×C22⋊C4—21no—
42C2×C4×C22⋊C4C2211yescharacteristic
43C22×#95C2211yescharacteristic
44#1753—21no—
45#1753—21no—
46#1753—21no—
47#1753—21no—
48#1749C2211yescharacteristic
49#1749C2211yescharacteristic
50C4×C22⋊C8C2211yescharacteristic
51C4×C22⋊C8C2211yescharacteristic
52#1513C418yescomplemented
53#1504C418yescomplemented
54C2×#328C2211yescharacteristic
55C2×#328C2211yescharacteristic
56C2×#328C2211yescharacteristic
57C2×#328C2211yescharacteristic
58C2×#327C2211yescharacteristic
59C2×#327C2211yescharacteristic
60C2×#327C2211yescharacteristic
61C2×#327C2211yescharacteristic
62#1436—21no—
63#1436—21no—
64#1434C2211yescharacteristic
65#1434C2211yescharacteristic
66C22⋊#95—21no—
67C4×#95C2211yescharacteristic
68C4×#95C2211yescharacteristic
69#1294C2211yescharacteristic
70#1294C2211yescharacteristic
71#1294C2211yescharacteristic
72#1294C2211yescharacteristic
73#1294C2211yescharacteristic
74#1294C2211yescharacteristic
75#1294C2211yescharacteristic
76#1294C2211yescharacteristic
77C22×#41C2×C411yescharacteristic
78C24×C4—21no—
79C24×C4C2311yescharacteristic
80C22×M16—21no—
81C22×M16—21no—
82#525—22no—
83#525—22no—
84#525C2×C414yes—
85#525C2×C414yes—
86C2×#123—21no—
87C2×C22⋊Q8C2×C411yescharacteristic
88C2×C22⋊Q8C2311yescharacteristic
89C2×#121C2×C411yescharacteristic
90C2×#121C2311yescharacteristic
91C2×#120—21no—
92C2×C4×Q8C2×C411yescharacteristic, complemented
93C2×C4×Q8C2×C411yescharacteristic, complemented
94C2×C4×D4—21no—
95C2×C4×D4—21no—
96C2×C4×D4—21no—
97C2×C4×D4—21no—
98C2×C4×D4C2×C411yescharacteristic, complemented
99C2×C4×D4C2×C411yescharacteristic, complemented
100C2×#117C2×C411yescharacteristic
101C2×#117C2×C411yescharacteristic
102C2×#117C2×C411yescharacteristic
103C22×C4⋊C4—21no—
104C22×C22⋊C4—21no—
105C22×C22⋊C4D411yescharacteristic
106C22×C22⋊C4D411yescharacteristic
107C22×C42—21no—
108C22×C42—21no—
109C22×C42C2311yescharacteristic
110C22×C42C2311yescharacteristic
111#407—22no—
112#407—22no—
113#407C2×C414yescomplemented
114#407C2×C414yescomplemented
115C2×C22⋊C8—21no—
116C2×C22⋊C8—21no—
117C2×C22⋊C8C2311yescharacteristic
118C2×C22⋊C8C2311yescharacteristic
119C2×C22⋊C8C2311yescharacteristic
120C2×C22⋊C8C2311yescharacteristic
121C2×#97—21no—
122C2×#97—21no—
123C2×C4×C8—21no—
124C2×C4×C8—21no—
125#391C2×C411yescharacteristic, complemented
126#391C2×C411yescharacteristic, complemented
127#390—21no—
128#390—21no—
129#390—21no—
130#390—21no—
131#390C2×C411yescharacteristic, complemented
132#390C2×C411yescharacteristic, complemented
133#389C2×C411yescharacteristic, complemented
134#389C2×C411yescharacteristic, complemented
135#389C2×C411yescharacteristic, complemented
136#389C2×C411yescharacteristic, complemented
137#388—21no—
138#388—21no—
139#388—21no—
140#388—21no—
141#388—21no—
142#388—21no—
143#388—21no—
144#388—21no—
145#388—21no—
146#388—21no—
147#388—21no—
148#388—21no—
149#387—21no—
150#387—21no—
151#387—21no—
152#387—21no—
153#386—21no—
154#386—21no—
155#386—21no—
156#386—21no—
157#386—21no—
158#386—21no—
159#385—21no—
160#385—21no—
161#383—21no—
162#382—21no—
163#381—21no—
164#381—21no—
165#380—22no—
166#380—21no—
167#380C2×C411yescharacteristic
168#380C2×C411yescharacteristic
169#380C2×C414yescomplemented
170#380C2311yescharacteristic
171#380C2311yescharacteristic
172#379—21no—
173C4×C4⋊C4—21no—
174C4×C4⋊C4—21no—
175C4×C4⋊C4—21no—
176C4×C4⋊C4—21no—
177C4×C4⋊C4—21no—
178C4×C4⋊C4C2×C411yescharacteristic, complemented
179C4×C4⋊C4C2×C411yescharacteristic, complemented
180C4×C4⋊C4C2×C411yescharacteristic, complemented
181C4×C4⋊C4C2×C411yescharacteristic, complemented
182C4×C22⋊C4—21no—
183C4×C22⋊C4—21no—
184C4×C22⋊C4—21no—
185C4×C22⋊C4—21no—
186C4×C22⋊C4—21no—
187C4×C22⋊C4—21no—
188C4×C22⋊C4—21no—
189C4×C22⋊C4—21no—
190C4×C22⋊C4—21no—
191C4×C22⋊C4—44no—
192C4×C22⋊C4C2×C411yescharacteristic
193C4×C22⋊C4C2×C411yescharacteristic
194C4×C22⋊C4C2×C411yescharacteristic
195C4×C22⋊C4C2×C411yescharacteristic
196C4×C22⋊C4D411yescharacteristic
197C4×C22⋊C4D411yescharacteristic
198C4×C22⋊C4D411yescharacteristic
199C4×C22⋊C4D411yescharacteristic
200#376—21no—
201C2×#95—21no—
202C2×#95—22no—
203C2×#95—21no—
204C2×#95—21no—
205C2×#95—21no—
206C2×#95—21no—
207C2×#95—21no—
208C2×#95—21no—
209C2×#95—21no—
210C2×#95C2×C414yescomplemented
211C2×#95D411yescharacteristic
212C2×#95D411yescharacteristic
213C2×#95C2311yescharacteristic
214C2×#95C2311yescharacteristic
215C2×#95C2311yescharacteristic
216C2×#95C2311yescharacteristic
217#336—21no—
218#336—21no—
219#336—21no—
220#336—21no—
221#328C2×C414yescomplemented
222#328C2×C414yescomplemented
223#328C2×C414yescomplemented
224#328C2×C414yescomplemented
225#327C2×C414yes—
226#327C2×C414yes—
227#327C2×C414yescomplemented
228#327C2×C414yescomplemented
229C25C2×D411yescharacteristic
230C2×#41—22no—
231C2×#41—81no—
232C2×#41—81no—
233C2×#41C4214yescomplemented
234C22×Q8C22×C411yescharacteristic
235C22×D4—21no—
236C22×D4—21no—
237C22×D4—21no—
238C22×D4C22×C411yescharacteristic
239C23×C4—21no—
240C23×C4—21no—
241C23×C4—21no—
242C23×C4—21no—
243C23×C4—21no—
244C23×C4—24no—
245C23×C4—21no—
246C23×C4—21no—
247C23×C4—42no—
248C23×C4—42no—
249C23×C4—42no—
250C23×C4—42no—
251C23×C4—81no—
252C23×C4—81no—
253C23×C4—81no—
254C23×C4—81no—
255C23×C4C22×C411yescharacteristic
256C23×C4C22×C411yescharacteristic
257C23×C4C22×C412yes—
258C23×C4C22×C412yes—
259C23×C4C2×D411yescharacteristic
260C23×C4C2×D411yescharacteristic
261C23×C4C2×D411yescharacteristic
262C23×C4C2×D411yescharacteristic
263C23×C4C2×D411yescharacteristic
264C23×C4C2×D411yescharacteristic
265C23×C4C2×D411yescharacteristic
266C23×C4#4112yes—
267C23×C4#4112yes—
268C23×C4C2411yescharacteristic
269C2×M16—24no—
270C2×M16—24no—
271C2×M16—81no—
272C2×M16—81no—
273C2×M16—81no—
274C2×M16—81no—
275C22×C8—21no—
276C22×C8—21no—
277C22×C8—21no—
278C22×C8—21no—
279#123—24no—
280#123—24no—
281C22⋊Q8—22no—
282C22⋊Q8—21no—
283C22⋊Q8—21no—
284C22⋊Q8C4214yescomplemented
285C22⋊Q8C22×C412yes—
286C22⋊Q8C22×C412yes—
287#121—22no—
288#121—21no—
289#121—21no—
290#121C4214yescomplemented
291#121C22×C412yes—
292#121C22×C412yes—
293#120—24no—
294#120—24no—
295C4×Q8—81no—
296C4×Q8—81no—
297C4×D4—24no—
298C4×D4—24no—
299C4×D4—24no—
300C4×D4—24no—
301C4×D4—42no—
302C4×D4—42no—
303C4×D4—42no—
304C4×D4—42no—
305C4×D4—81no—
306C4×D4—81no—
307#117—22no—
308#117—81no—
309#117—81no—
310#117C4214yescomplemented
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—81no—
321C2×C4⋊C4—81no—
322C2×C4⋊C4C22×C411yescharacteristic
323C2×C4⋊C4C22×C411yescharacteristic
324C2×C4⋊C4C22×C411yescharacteristic
325C2×C4⋊C4C22×C411yescharacteristic
326C2×C4⋊C4C22×C411yescharacteristic
327C2×C4⋊C4C22×C411yescharacteristic
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—21no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—41no—
349C2×C22⋊C4—41no—
350C2×C22⋊C4—42no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4C22⋊C411yescharacteristic
353C2×C22⋊C4C22⋊C411yescharacteristic
354C2×C22⋊C4C22⋊C411yescharacteristic
355C2×C22⋊C4C22⋊C411yescharacteristic
356C2×C22⋊C4C22⋊C411yescharacteristic
357C2×C22⋊C4C22⋊C411yescharacteristic
358C2×C22⋊C4C22⋊C411yescharacteristic
359C2×C22⋊C4C22⋊C411yescharacteristic
360C2×C42—21no—
361C2×C42—21no—
362C2×C42—21no—
363C2×C42—21no—
364C2×C42—21no—
365C2×C42—21no—
366C2×C42—21no—
367C2×C42—21no—
368C2×C42—21no—
369C2×C42—42no—
370C2×C42—42no—
371C2×C42—42no—
372C2×C42—42no—
373C2×C42—81no—
374C2×C42—81no—
375C2×C42—81no—
376C2×C42—81no—
377C2×C42C22×C411yescharacteristic
378C2×C42C22×C411yescharacteristic
379C2×C42C22×C411yescharacteristic
380C2×C42C22×C411yescharacteristic
381C2×C42C2×D411yescharacteristic
382C2×C42C2×D411yescharacteristic
383C2×C42C2×D411yescharacteristic
384C2×C42C2×D411yescharacteristic
385C22⋊C8—24no—
386C22⋊C8—24no—
387C22⋊C8—21no—
388C22⋊C8—21no—
389C22⋊C8—21no—
390C22⋊C8—21no—
391C22⋊C8C22×C412yes—
392C22⋊C8C22×C412yes—
393C22⋊C8C22×C412yes—
394C22⋊C8C22×C412yes—
395#97—81no—
396#97—81no—
397C4×C8—81no—
398C4×C8—81no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—24no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—42no—
421#95—42no—
422#95—42no—
423#95—42no—
424#95—81no—
425#95—81no—
426#95C22⋊C411yescharacteristic
427#95C22⋊C411yescharacteristic
428#95C22⋊C411yescharacteristic
429#95C22⋊C411yescharacteristic
430#95C22⋊C411yescharacteristic
431#95C22⋊C411yescharacteristic
432#95C22⋊C411yescharacteristic
433#95C22⋊C411yescharacteristic
434#95C22×C412yes—
435#95C22×C412yes—
436#95C22×C412yes—
437#95C22×C412yes—
438C24—21no—
439C24—21no—
440C24—21no—
441C24—21no—
442C24—21no—
443C24—41no—
444C24—41no—
445C24—41no—
446C24—41no—
447C24C2×C22⋊C411yescharacteristic
448C24C2×C22⋊C411yescharacteristic
449C24C4×D412yes—
450C24C4×D412yes—
451C24C22×D411yescharacteristic
452#41—84no—
453#41—84no—
454C2×Q8—21no—
455C2×Q8—41no—
456C2×Q8—41no—
457C2×Q8C2×C4212yes—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—24no—
461C2×D4—24no—
462C2×D4—21no—
463C2×D4—41no—
464C2×D4—41no—
465C2×D4—41no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4—41no—
469C2×D4—81no—
470C2×D4—81no—
471C2×D4—81no—
472C2×D4—81no—
473C2×D4C2×C4212yes—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—24no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—48no—
515C22×C4—42no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—48no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—42no—
540C22×C4—81no—
541C22×C4—81no—
542C22×C4—81no—
543C22×C4—81no—
544C22×C4—81no—
545C22×C4—81no—
546C22×C4—82no—
547C22×C4—82no—
548C22×C4—82no—
549C22×C4—82no—
550C22×C4—84no—
551C22×C4—84no—
552C22×C4—84no—
553C22×C4—84no—
554C22×C4—84no—
555C22×C4C2×C4212yes—
556C22×C4C2×C4212yes—
557C22×C4C2×C22⋊C411yescharacteristic
558C22×C4C2×C22⋊C411yescharacteristic
559C22×C4C2×C22⋊C411yescharacteristic
560C22×C4C2×C22⋊C411yescharacteristic
561C22×C4C2×C22⋊C411yescharacteristic
562C22×C4C2×C22⋊C411yescharacteristic
563C22×C4C2×C22⋊C411yescharacteristic
564C22×C4C2×C22⋊C411yescharacteristic
565C22×C4C2×C22⋊C411yescharacteristic
566C22×C4C2×C22⋊C411yescharacteristic
567C22×C4#11712yes—
568C22×C4#11712yes—
569C22×C4C4×D412yes—
570C22×C4C4×D412yes—
571C22×C4C4×D412yes—
572C22×C4C4×D412yes—
573C22×C4C4×D412yes—
574C22×C4C4×D412yes—
575C22×C4AGL(1,ℤ/8)12yes—
576C22×C4#13712yes—
577C22×C4C23×C411yescharacteristic
578C22×C4C23×C411yescharacteristic
579C22×C4C23×C411yescharacteristic
580C22×C4C22×D411yescharacteristic
581C22×C4C2×#4111yescharacteristic
582C22×C4C2×#4111yescharacteristic
583M16—84no—
584M16—84no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—41no—
590C2×C8—41no—
591C2×C8—41no—
592C2×C8—41no—
593C2×C8—41no—
594C2×C8—41no—
595C2×C8—41no—
596C2×C8—41no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—24no—
602C4⋊C4—41no—
603C4⋊C4—41no—
604C4⋊C4—41no—
605C4⋊C4—41no—
606C4⋊C4—42no—
607C4⋊C4—42no—
608C4⋊C4—81no—
609C4⋊C4—81no—
610C4⋊C4—81no—
611C4⋊C4—81no—
612C4⋊C4—84no—
613C4⋊C4C2×C4212yes—
614C4⋊C4C2×C4212yes—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—24no—
618C22⋊C4—24no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—24no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—41no—
627C22⋊C4—41no—
628C22⋊C4—41no—
629C22⋊C4—41no—
630C22⋊C4—42no—
631C22⋊C4—48no—
632C22⋊C4—41no—
633C22⋊C4—41no—
634C22⋊C4—41no—
635C22⋊C4—41no—
636C22⋊C4—42no—
637C22⋊C4—81no—
638C22⋊C4—81no—
639C22⋊C4—81no—
640C22⋊C4—81no—
641C22⋊C4—81no—
642C22⋊C4—81no—
643C22⋊C4—81no—
644C22⋊C4—81no—
645C42—24no—
646C42—41no—
647C42—41no—
648C42—41no—
649C42—41no—
650C42—41no—
651C42—41no—
652C42—41no—
653C42—41no—
654C42—42no—
655C42—42no—
656C42—81no—
657C42—81no—
658C42—81no—
659C42—81no—
660C42—81no—
661C42—81no—
662C42—84no—
663C42—84no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23C4×C22⋊C412yes—
704C23C4×C22⋊C412yes—
705C23C22×C22⋊C411yescharacteristic
706C23C2×C4×D411yescharacteristic
707C23C2×C4×D411yescharacteristic
708C23C2×AGL(1,ℤ/8)11yescharacteristic
709C23C2×#13711yescharacteristic
710C23#57511yescharacteristic
711C23#57511yescharacteristic
712Q8—42no—
713Q8—42no—
714D4—42no—
715D4—42no—
716D4—42no—
717D4—42no—
718D4—42no—
719D4—42no—
720D4—84no—
721D4—84no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—24no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—84no—
808C2×C4—81no—
809C2×C4—81no—
810C2×C4—81no—
811C2×C4—81no—
812C2×C4—816no—
813C2×C4—81no—
814C2×C4—81no—
815C2×C4—81no—
816C2×C4—81no—
817C2×C4—81no—
818C2×C4—81no—
819C2×C4—81no—
820C2×C4—81no—
821C2×C4—81no—
822C2×C4—81no—
823C2×C4—81no—
824C2×C4—81no—
825C2×C4—162no—
826C2×C4—162no—
827C2×C4C4×C22⋊C412yes—
828C2×C4C4×C22⋊C412yes—
829C2×C4#41712yes—
830C2×C4#41712yes—
831C2×C4C22×C4211yescharacteristic
832C2×C4C2×#11711yescharacteristic
833C2×C4C2×C4×D411yescharacteristic
834C2×C4C2×C4×D411yescharacteristic
835C8—42no—
836C8—42no—
837C8—42no—
838C8—42no—
839C22—21no—
840C22—21no—
841C22—21no—
842C22—21no—
843C22—21no—
844C22—21no—
845C22—21no—
846C22—21no—
847C22—21no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—22no—
852C22—22no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—44no—
858C22—44no—
859C22—44no—
860C22—44no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—42no—
870C22—42no—
871C22—42no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22—81no—
876C22C2×C4×C22⋊C411yescharacteristic
877C22#288311yescharacteristic
878C22#288311yescharacteristic
879C22C2×#41711yescharacteristic
880C22#289611yescharacteristic
881C22#290111yescharacteristic
882C22#290111yescharacteristic
883C22C4×AGL(1,ℤ/8)11yescharacteristic
884C22C4×AGL(1,ℤ/8)11yescharacteristic
885C22C4×#13711yescharacteristic
886C22C4×#13711yescharacteristic
887C4—21no—
888C4—21no—
889C4—22no—
890C4—21no—
891C4—22no—
892C4—21no—
893C4—22no—
894C4—22no—
895C4—44no—
896C4—42no—
897C4—42no—
898C4—42no—
899C4—41no—
900C4—41no—
901C4—41no—
902C4—41no—
903C4—41no—
904C4—41no—
905C4—82no—
906C4—82no—
907C4—82no—
908C4—81no—
909C4—81no—
910C4—81no—
911C4—81no—
912C2—21no—
913C2—21no—
914C2—21no—
915C2—21no—
916C2—42no—
917C2—42no—
918C2—82no—
919C2#1762211yescharacteristic
920C2#1762311yescharacteristic
921C2#1762911yescharacteristic
922C2#1763011yescharacteristic
923C2#2039211yescharacteristic
924C2#2040511yescharacteristic
925C2C4×#41711yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC2×C4C22×C42
Frattini, cosocleC23×C4C24
prime radicalC2×#525C22
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #20524C2semidirect
5. #13802C2semidirect
6. #8221C2semidirect
7. #8220C2semidirect
8. #8219C2semidirect
9. #8218C2semidirect
10. #8217C2semidirect
11. #8216C2semidirect
12. C4×#328C2semidirect
13. C4×#327C2semidirect
14. #8020C2semidirect
15. #8016C2semidirect
21. #2363C4semidirect
22. #2363C4semidirect
23. #2362C4semidirect
24. #2362C4semidirect
27. #2347C4semidirect
28. #2346C4semidirect
29. #2341C4semidirect
30. #2339C4semidirect
52. #1513C4semidirect
53. #1504C4semidirect
92. C2×C4×Q8C2×C4semidirect
93. C2×C4×Q8C2×C4semidirect
98. C2×C4×D4C2×C4semidirect
99. C2×C4×D4C2×C4semidirect
113. #407C2×C4semidirect
114. #407C2×C4semidirect
125. #391C2×C4semidirect
126. #391C2×C4semidirect
131. #390C2×C4semidirect
132. #390C2×C4semidirect
133. #389C2×C4semidirect
134. #389C2×C4semidirect
135. #389C2×C4semidirect
136. #389C2×C4semidirect
169. #380C2×C4semidirect
178. C4×C4⋊C4C2×C4semidirect
179. C4×C4⋊C4C2×C4semidirect
180. C4×C4⋊C4C2×C4semidirect
181. C4×C4⋊C4C2×C4semidirect
210. C2×#95C2×C4semidirect
221. #328C2×C4semidirect
222. #328C2×C4semidirect
223. #328C2×C4semidirect
224. #328C2×C4semidirect
227. #327C2×C4semidirect
228. #327C2×C4semidirect
233. C2×#41C42semidirect
284. C22⋊Q8C42semidirect
290. #121C42semidirect
310. #117C42semidirect

Maximal subgroups

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

subgroupindex
#342232
#205242
C2×#15132
C2×#15042
#138022
#82212
#82202
#82192
#82182
#82172
#82162
C4×#3282
C4×#3272
#80202
#80162