Finite Group Databasebeta

← #221522

Subgroups — #221522

Order 512.

1268 conjugacy classes of subgroups.

The subgroup lattice has 871 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D4×Q8C211yesmaximal, characteristic
2#22648C211yesmaximal, characteristic
3#21101C211yesmaximal, characteristic
4C2×#1487C211yesmaximal, characteristic, complemented
5C22×Q8⋊C8C211yesmaximal, characteristic, complemented
6#9677C211yesmaximal, characteristic, complemented
7#9643C211yesmaximal, characteristic, complemented
8#9075C211yesmaximal, characteristic, complemented
9#9071C211yesmaximal, characteristic, complemented
10#8942C211yesmaximal, characteristic, complemented
11#8937C211yesmaximal, characteristic, complemented
12#8564C211yesmaximal, characteristic, complemented
13#8311C211yesmaximal, characteristic, complemented
14#8311C211yesmaximal, characteristic, complemented
15#8175C211yesmaximal, characteristic, complemented
16C2×D4×Q8C411yescharacteristic
17C22×C4×Q8C2211yescharacteristic
18C22×C4×Q8C2211yescharacteristic
19C2×#435—21no—
20C2×#431C2211yescharacteristic
21C2×#423C2211yescharacteristic
22C22×C4⋊C8C2211yescharacteristic
23C22×C4×C8C2211yescharacteristic
24#2365—21no—
25#2365C411yescharacteristic
26#2360—21no—
27#2360—21no—
28#2360C411yescharacteristic
29#2360C411yescharacteristic
30Q8×C4⋊C4C411yescharacteristic
31D4×C4⋊C4—21no—
32D4×C4⋊C4C411yescharacteristic
33Q8×C22⋊C4C411yescharacteristic
34Q8×C22⋊C4C411yescharacteristic
35C4×C4⋊Q8—21no—
36C4×C4⋊Q8C2211yescharacteristic
37C4×C22⋊Q8—21no—
38C4×C22⋊Q8—21no—
39C4×C22⋊Q8C2211yescharacteristic
40C4×C22⋊Q8C2211yescharacteristic
41C42×Q8C2211yescharacteristic
42C42×D4—21no—
43C42×D4C2211yescharacteristic
44#1940—21no—
45#1923—21no—
46#1916—21no—
47#1869—21no—
48#1851—21no—
49#1850—21no—
50#1850—21no—
51#1842C2211yescharacteristic
52#1797C2211yescharacteristic
53#1797C2211yescharacteristic
54#1767C2211yescharacteristic
55C4×C4⋊C8C2211yescharacteristic
56C4×C22⋊C8C2211yescharacteristic
57C4×C22⋊C8C2211yescharacteristic
58#1744C2211yescharacteristic
59#1487—24no—
60C2×Q8⋊C8—24no—
61C2×Q8⋊C8C2211yescharacteristic
62C2×Q8⋊C8C2211yescharacteristic
63C2×Q8⋊C8C2211yescharacteristic
64C2×Q8⋊C8C2211yescharacteristic
65C2×Q8⋊C8C2211yescharacteristic
66C2×Q8⋊C8C2211yescharacteristic
67C2×Q8⋊C8C2211yescharacteristic
68C2×Q8⋊C8C2211yescharacteristic
69C2×Q8⋊C8C2211yescharacteristic
70C2×Q8⋊C8C2211yescharacteristic
71C2×Q8⋊C8C2211yescharacteristic
72C2×Q8⋊C8C2211yescharacteristic
73#1279C2211yescharacteristic
74#1279C2211yescharacteristic
75#1279C2211yescharacteristic
76#1279C2211yescharacteristic
77C23×Q8C2×C411yescharacteristic
78C23×Q8C2×C411yescharacteristic
79C22×M16—21no—
80C23×C8—21no—
81C23×C8—21no—
82D4×Q8—24no—
83D4×Q8—24no—
84C2×C4⋊Q8—21no—
85C2×C4⋊Q8C2×C411yescharacteristic
86C2×C22⋊Q8—21no—
87C2×C22⋊Q8—21no—
88C2×C22⋊Q8C2×C411yescharacteristic
89C2×C22⋊Q8C2×C411yescharacteristic
90C2×C4×Q8—21no—
91C2×C4×Q8—21no—
92C2×C4×Q8—21no—
93C2×C4×Q8—21no—
94C2×C4×Q8—22no—
95C2×C4×Q8—22no—
96C2×C4×Q8—22no—
97C2×C4×Q8—22no—
98C2×C4×Q8—41no—
99C2×C4×Q8—41no—
100C2×C4×Q8—41no—
101C2×C4×Q8—41no—
102C2×C4×Q8C2×C411yescharacteristic
103C2×C4×Q8C2×C411yescharacteristic
104C2×C4×Q8C2×C411yescharacteristic
105C2×C4×Q8C2×C411yescharacteristic
106C2×C4×Q8C2×C411yescharacteristic
107C2×C4×Q8C2×C411yescharacteristic
108C2×C4×Q8C2311yescharacteristic
109C2×C4×Q8C2311yescharacteristic
110C2×C4×Q8C2311yescharacteristic
111C2×C4×D4—21no—
112C2×C4×D4—21no—
113C2×C4×D4C2×C411yescharacteristic
114C2×C4×D4D411yescharacteristic
115C2×C4×D4D411yescharacteristic
116C22×C4⋊C4—21no—
117C22×C4⋊C4—21no—
118C22×C4⋊C4C2×C411yescharacteristic
119C22×C4⋊C4C2×C411yescharacteristic
120C22×C42—21no—
121C22×C42—21no—
122C22×C42C2311yescharacteristic
123C22×C42C2311yescharacteristic
124#435—44no—
125#431—22no—
126#431—41no—
127#423—22no—
128#423—41no—
129C2×C4⋊C8—22no—
130C2×C4⋊C8—21no—
131C2×C4⋊C8—21no—
132C2×C4⋊C8—21no—
133C2×C4⋊C8—21no—
134C2×C4⋊C8—21no—
135C2×C4⋊C8—21no—
136C2×C4⋊C8—41no—
137C2×C4⋊C8C2311yescharacteristic
138C2×C4⋊C8C2311yescharacteristic
139C2×C4⋊C8C2311yescharacteristic
140C2×C4⋊C8C2311yescharacteristic
141C2×C22⋊C8—21no—
142C2×C22⋊C8—21no—
143C2×C22⋊C8—21no—
144C2×C22⋊C8—21no—
145C2×C22⋊C8—21no—
146C2×#97—21no—
147C2×C4×C8—22no—
148C2×C4×C8—21no—
149C2×C4×C8—41no—
150C2×C4×C8C2311yescharacteristic
151C2×C4×C8C2311yescharacteristic
152C2×C4×C8C2311yescharacteristic
153C2×C4×C8C2311yescharacteristic
154#391—21no—
155#391—21no—
156#391—21no—
157#391—21no—
158#391C2×C411yescharacteristic
159#391C2×C411yescharacteristic
160#391C2×C411yescharacteristic
161#391C2×C411yescharacteristic
162#389—21no—
163#389—21no—
164#389—21no—
165#389—21no—
166#389—21no—
167#389—21no—
168#389—21no—
169#389—21no—
170#389C2×C411yescharacteristic
171#389C2×C411yescharacteristic
172#387—21no—
173#387—21no—
174#387—21no—
175#387—21no—
176#387—21no—
177#387—21no—
178#385—21no—
179#385—21no—
180#385—21no—
181#385—21no—
182#385—21no—
183#385—21no—
184#384—21no—
185#384C2×C411yescharacteristic
186#380—21no—
187#380—21no—
188#380C2×C411yescharacteristic
189#380C2×C411yescharacteristic
190C4×C4⋊C4—21no—
191C4×C4⋊C4—21no—
192C4×C4⋊C4—21no—
193C4×C4⋊C4—21no—
194C4×C4⋊C4—21no—
195C4×C4⋊C4—21no—
196C4×C4⋊C4—21no—
197C4×C4⋊C4—21no—
198C4×C4⋊C4—21no—
199C4×C4⋊C4C2×C411yescharacteristic
200C4×C4⋊C4C2×C411yescharacteristic
201C4×C4⋊C4C2×C411yescharacteristic
202C4×C4⋊C4D411yescharacteristic
203C4×C4⋊C4D411yescharacteristic
204C4×C4⋊C4C2311yescharacteristic
205C4×C22⋊C4—21no—
206C4×C22⋊C4—21no—
207C4×C22⋊C4—21no—
208C4×C22⋊C4—21no—
209C4×C22⋊C4—21no—
210C4×C22⋊C4—21no—
211C4×C22⋊C4C2×C411yescharacteristic
212C4×C22⋊C4C2×C411yescharacteristic
213C4×C22⋊C4D411yescharacteristic
214C4×C22⋊C4D411yescharacteristic
215C4×C22⋊C4D411yescharacteristic
216C4×C22⋊C4D411yescharacteristic
217C43—21no—
218C43C2311yescharacteristic
219#336—21no—
220#336—21no—
221#336—21no—
222#336—21no—
223#336—21no—
224#336—21no—
225#336—21no—
226#336—21no—
227Q8⋊C8—22no—
228Q8⋊C8—22no—
229Q8⋊C8—22no—
230Q8⋊C8—22no—
231Q8⋊C8—22no—
232Q8⋊C8—22no—
233Q8⋊C8—22no—
234Q8⋊C8—41no—
235Q8⋊C8—41no—
236Q8⋊C8—41no—
237Q8⋊C8—41no—
238Q8⋊C8D414yescomplemented
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—21no—
242C22×Q8—21no—
243C22×Q8—22no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—41no—
249C22×Q8—41no—
250C22×Q8—41no—
251C22×Q8—41no—
252C22×Q8M1614yescomplemented
253C22×Q8C22×C411yescharacteristic
254C22×Q8C22×C411yescharacteristic
255C22×Q8C22×C411yescharacteristic
256C22×D4C22⋊C411yescharacteristic
257C23×C4—21no—
258C23×C4—21no—
259C23×C4—21no—
260C23×C4—21no—
261C23×C4C22×C411yescharacteristic
262C23×C4C22×C411yescharacteristic
263C23×C4C2×D411yescharacteristic
264C23×C4C2×D411yescharacteristic
265C23×C4C2×D411yescharacteristic
266C23×C4C2×D411yescharacteristic
267C2×M16—42no—
268C2×M16—42no—
269C2×M16—81no—
270C22×C8—21no—
271C22×C8—21no—
272C22×C8—21no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8—21no—
276C22×C8—21no—
277C22×C8—21no—
278C22×C8—42no—
279C22×C8—42no—
280C22×C8—42no—
281C22×C8—42no—
282C22×C8—42no—
283C22×C8—81no—
284C4⋊Q8—28no—
285C4⋊Q8—22no—
286C4⋊Q8—22no—
287C22⋊Q8—28no—
288C22⋊Q8—28no—
289C22⋊Q8—22no—
290C22⋊Q8—22no—
291C22⋊Q8—22no—
292C22⋊Q8M1614yescomplemented
293C4×Q8—22no—
294C4×Q8—22no—
295C4×Q8—21no—
296C4×Q8—21no—
297C4×Q8—22no—
298C4×Q8—22no—
299C4×Q8—22no—
300C4×Q8—22no—
301C4×Q8—22no—
302C4×Q8—21no—
303C4×Q8—21no—
304C4×Q8—21no—
305C4×Q8—21no—
306C4×Q8—21no—
307C4×Q8—21no—
308C4×Q8—21no—
309C4×Q8—21no—
310C4×Q8—42no—
311C4×Q8—42no—
312C4×Q8—42no—
313C4×Q8—42no—
314C4×Q8—41no—
315C4×Q8—41no—
316C4×Q8—41no—
317C4×Q8—41no—
318C4×Q8—41no—
319C4×Q8—42no—
320C4×Q8—42no—
321C4×Q8—42no—
322C4×Q8—42no—
323C4×Q8C2×D412yes—
324C4×Q8#4112yes—
325C4×D4—28no—
326C4×D4—22no—
327C4×D4—22no—
328C4×D4—42no—
329C4×D4—44no—
330C4×D4SD1614yes—
331C4×D4Q1614yes—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—41no—
354C2×C4⋊C4—41no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4C22⋊C411yescharacteristic
360C2×C4⋊C4C22⋊C411yescharacteristic
361C2×C4⋊C4C22⋊C411yescharacteristic
362C2×C4⋊C4C22×C411yescharacteristic
363C2×C4⋊C4C22×C411yescharacteristic
364C2×C4⋊C4C22×C411yescharacteristic
365C2×C4⋊C4C22×C411yescharacteristic
366C2×C4⋊C4C22×C411yescharacteristic
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4C22⋊C411yescharacteristic
372C2×C22⋊C4C22⋊C411yescharacteristic
373C2×C22⋊C4C22⋊C411yescharacteristic
374C2×C22⋊C4C22⋊C411yescharacteristic
375C2×C22⋊C4C22⋊C411yescharacteristic
376C2×C22⋊C4C22⋊C411yescharacteristic
377C2×C42—21no—
378C2×C42—21no—
379C2×C42—21no—
380C2×C42—21no—
381C2×C42—21no—
382C2×C42—21no—
383C2×C42—21no—
384C2×C42—21no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—42no—
398C2×C42—42no—
399C2×C42—42no—
400C2×C42—42no—
401C2×C42C22×C411yescharacteristic
402C2×C42C22×C411yescharacteristic
403C2×C42C22×C411yescharacteristic
404C2×C42C22×C411yescharacteristic
405C2×C42C2×D411yescharacteristic
406C2×C42C2×D411yescharacteristic
407C2×C42C2×D411yescharacteristic
408C2×C42C2×D411yescharacteristic
409C2×C42C2×D411yescharacteristic
410C2×C42C2×D411yescharacteristic
411C2×C42C2×D411yescharacteristic
412C2×C42C2×D411yescharacteristic
413C2×C42C2411yescharacteristic
414C4⋊C8—21no—
415C4⋊C8—21no—
416C4⋊C8—21no—
417C4⋊C8—21no—
418C4⋊C8—21no—
419C4⋊C8—21no—
420C4⋊C8—21no—
421C4⋊C8—42no—
422C4⋊C8—42no—
423C4⋊C8—42no—
424C4⋊C8—42no—
425C4⋊C8—42no—
426C4⋊C8—81no—
427C4⋊C8C2×D412yes—
428C22⋊C8—42no—
429C22⋊C8—42no—
430C22⋊C8—42no—
431C22⋊C8—42no—
432C22⋊C8—42no—
433#97—42no—
434C4×C8—21no—
435C4×C8—21no—
436C4×C8—21no—
437C4×C8—21no—
438C4×C8—21no—
439C4×C8—21no—
440C4×C8—21no—
441C4×C8—42no—
442C4×C8C2×D412yes—
443#95—21no—
444#95—21no—
445#95—21no—
446#95—21no—
447#95—21no—
448#95—21no—
449#95—21no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95—21no—
454#95—21no—
455#95—21no—
456#95—21no—
457#95—21no—
458#95C22⋊C411yescharacteristic
459#95C22⋊C411yescharacteristic
460#95C22⋊C411yescharacteristic
461#95C22⋊C411yescharacteristic
462#95C22⋊C411yescharacteristic
463#95C22⋊C411yescharacteristic
464C24C2×C22⋊C411yescharacteristic
465C24C2×C22⋊C411yescharacteristic
466C2×Q8—24no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—24no—
473C2×Q8—28no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—42no—
483C2×Q8—42no—
484C2×Q8—42no—
485C2×Q8—42no—
486C2×Q8—44no—
487C2×Q8—44no—
488C2×Q8—44no—
489C2×Q8—44no—
490C2×Q8—44no—
491C2×Q8—44no—
492C2×Q8—44no—
493C2×Q8C4×D412yes—
494C2×Q8C2×M1612yes—
495C2×Q8C2×M1612yes—
496C2×Q8C2×M1612yes—
497C2×Q8#13112yes—
498C2×D4—22no—
499C2×D4—22no—
500C2×D4#10314yes—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—24no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—24no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—81no—
546C22×C4—81no—
547C22×C4C2×C22⋊C411yescharacteristic
548C22×C4C2×C22⋊C411yescharacteristic
549C22×C4C2×C22⋊C411yescharacteristic
550C22×C4C2×C22⋊C411yescharacteristic
551C22×C4C2×C22⋊C411yescharacteristic
552C22×C4C2×C22⋊C411yescharacteristic
553C22×C4C2×C22⋊C411yescharacteristic
554C22×C4C2×C22⋊C411yescharacteristic
555C22×C4C2×C22⋊C411yescharacteristic
556C22×C4C2×C22⋊C411yescharacteristic
557C22×C4C2×M1612yes—
558C22×C4C2×M1612yes—
559C22×C4C2×SD1612yes—
560C22×C4C2×SD1612yes—
561C22×C4C2×Q1612yes—
562C22×C4C2×Q1612yes—
563C22×C4C23×C411yescharacteristic
564C22×C4C22×D411yescharacteristic
565C22×C4C22×D411yescharacteristic
566M16—84no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—41no—
571C2×C8—41no—
572C2×C8—41no—
573C2×C8—48no—
574C2×C8—41no—
575C2×C8—41no—
576C2×C8—41no—
577C2×C8—41no—
578C2×C8—41no—
579C2×C8—41no—
580C2×C8—41no—
581C2×C8—41no—
582C2×C8—41no—
583C2×C8—41no—
584C2×C8—41no—
585C2×C8—41no—
586C2×C8—41no—
587C2×C8—41no—
588C2×C8—41no—
589C2×C8—41no—
590C2×C8—41no—
591C2×C8—41no—
592C2×C8—84no—
593C4⋊C4—24no—
594C4⋊C4—24no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—21no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—21no—
601C4⋊C4—24no—
602C4⋊C4—22no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—41no—
610C4⋊C4—42no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4—42no—
618C4⋊C4—41no—
619C4⋊C4—41no—
620C4⋊C4—41no—
621C4⋊C4—41no—
622C4⋊C4—81no—
623C4⋊C4—81no—
624C4⋊C4—81no—
625C4⋊C4#10314yes—
626C4⋊C4C4×D412yes—
627C4⋊C4C2×M1612yes—
628C22⋊C4—24no—
629C22⋊C4—24no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—41no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4#10314yes—
637C22⋊C4#10314yes—
638C42—24no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—21no—
646C42—21no—
647C42—22no—
648C42—21no—
649C42—21no—
650C42—21no—
651C42—21no—
652C42—22no—
653C42—21no—
654C42—21no—
655C42—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C42—41no—
660C42—41no—
661C42—42no—
662C42—42no—
663C42—42no—
664C42—42no—
665C42—42no—
666C42—42no—
667C42—41no—
668C42—41no—
669C42—41no—
670C42—41no—
671C42—41no—
672C42—41no—
673C42—81no—
674C42C2×SD1612yes—
675C42C2×Q1612yes—
676C42C22×D411yescharacteristic
677C42C2×#4111yescharacteristic
678C42H(5,𝔽2)11yescharacteristic
679C42H(5,𝔽2)11yescharacteristic
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23#40712yes—
691C23C2×#10312yes—
692C23C2×#10312yes—
693C23#42112yes—
694C23C22×C22⋊C411yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—22no—
698Q8—22no—
699Q8—22no—
700Q8—22no—
701Q8—22no—
702Q8—48no—
703Q8—48no—
704Q8—41no—
705Q8—41no—
706Q8—41no—
707Q8—41no—
708Q8#43514yescomplemented
709D4—28no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—22no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—22no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—22no—
741C2×C4—21no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
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—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—48no—
759C2×C4—48no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—81no—
782C2×C4—81no—
783C2×C4—84no—
784C2×C4—84no—
785C2×C4#40712yes—
786C2×C4C2×#10312yes—
787C2×C4C2×#10312yes—
788C2×C4C2×#10312yes—
789C2×C4C2×#10312yes—
790C2×C4C2×C4×D411yescharacteristic
791C2×C4#51811yescharacteristic
792C2×C4D4211yescharacteristic
793C2×C4D4211yescharacteristic
794C2×C4#54611yescharacteristic
795C2×C4#54611yescharacteristic
796C2×C4C22×M1611yescharacteristic
797C2×C4C22×M1611yescharacteristic
798C2×C4C2×#13111yescharacteristic
799C2×C4#56811yescharacteristic
800C2×C4C22×SD1611yescharacteristic
801C2×C4C22×Q1611yescharacteristic
802C2×C4#57711yescharacteristic
803C2×C4#57811yescharacteristic
804C8—42no—
805C8—42no—
806C8—42no—
807C8—81no—
808C8—81no—
809C8—81no—
810C8—81no—
811C8—81no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22#148714yescomplemented
826C22D4×C22⋊C411yescharacteristic
827C22C2×#40711yescharacteristic
828C22#288011yescharacteristic
829C22C22×#10311yescharacteristic
830C22#289811yescharacteristic
831C22C2×#42111yescharacteristic
832C22#290111yescharacteristic
833C4—22no—
834C4—22no—
835C4—22no—
836C4—24no—
837C4—22no—
838C4—22no—
839C4—21no—
840C4—21no—
841C4—41no—
842C4—42no—
843C4—41no—
844C4—41no—
845C4—42no—
846C4—42no—
847C4—41no—
848C4—41no—
849C4—42no—
850C4—81no—
851C4—81no—
852C4—81no—
853C4C2×#43511yescharacteristic
854C4D4×M1611yescharacteristic
855C4#297311yescharacteristic
856C4#297411yescharacteristic
857C4D4×SD1611yescharacteristic
858C4D4×Q1611yescharacteristic
859C4#329811yescharacteristic
860C4#329911yescharacteristic
861C2—24no—
862C2—42no—
863C2C2×#148711yescharacteristic
864C2#1745411yescharacteristic
865C2#1750911yescharacteristic
866C2#1752411yescharacteristic
867C2#2239911yescharacteristic
868C2D4×#10311yescharacteristic
869C2#2243411yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
socleC23C22×C22⋊C4
prime radicalC22×D4C22⋊C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C42×D4 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C2×#1487C2semidirect
5. C22×Q8⋊C8C2semidirect
6. #9677C2semidirect
7. #9643C2semidirect
8. #9075C2semidirect
9. #9071C2semidirect
10. #8942C2semidirect
11. #8937C2semidirect
12. #8564C2semidirect
13. #8311C2semidirect
14. #8311C2semidirect
15. #8175C2semidirect
238. Q8⋊C8D4semidirect
252. C22×Q8M16semidirect
292. C22⋊Q8M16semidirect
708. Q8#435semidirect
825. C22#1487semidirect

Maximal subgroups

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

subgroupindex
C4×D4×Q82
#226482
#211012
C2×#14872
C22×Q8⋊C82
#96772
#96432
#90752
#90712
#89422
#89372
#85642
#83112
#81752