Finite Group Databasebeta

← #221530

Subgroups — #221530

Order 512.

1262 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#548C211yesmaximal, characteristic
2#22648C211yesmaximal, characteristic, complemented
3#21265C211yesmaximal, characteristic, complemented
4C2×#1487C211yesmaximal, characteristic, complemented
5C2×#1477C211yesmaximal, characteristic, complemented
6#9676C211yesmaximal, characteristic, complemented
7#9646C211yesmaximal, characteristic, complemented
8#9076C211yesmaximal, characteristic, complemented
9#9073C211yesmaximal, characteristic, complemented
10#8944C211yesmaximal, characteristic, complemented
11#8937C211yesmaximal, characteristic, complemented
12#8564C211yesmaximal, characteristic, complemented
13#8312C211yesmaximal, characteristic, complemented
14#8311C211yesmaximal, characteristic, complemented
15#8173C211yesmaximal, characteristic, complemented
16C2×#548C411yescharacteristic
17C2×C4×#41C2211yescharacteristic
18C22×C4×Q8C2211yescharacteristic
19C2×#435—21no—
20C2×#431C2211yescharacteristic
21C2×#431C2211yescharacteristic
22C2×#423C2211yescharacteristic
23C22×C4⋊C8C2211yescharacteristic
24#2367—21no—
25#2367C411yescharacteristic
26#2362—21no—
27#2362C411yescharacteristic
28#2361—21no—
29#2361C411yescharacteristic
30#2352—21no—
31#2352C411yescharacteristic
32#2351C411yescharacteristic
33#2341C411yescharacteristic
34Q8×C22⋊C4C411yescharacteristic
35C4×#124—21no—
36C4×#124C2211yescharacteristic
37C4×C22⋊Q8—21no—
38C4×C22⋊Q8C2211yescharacteristic
39C4×#121—21no—
40C4×#121C2211yescharacteristic
41C42×Q8C2211yescharacteristic
42C42×D4—21no—
43C42×D4C2211yescharacteristic
44#1955—21no—
45#1940—21no—
46#1940—21no—
47#1924—21no—
48#1924—21no—
49#1851—21no—
50#1850—21no—
51#1842C2211yescharacteristic
52#1797C2211yescharacteristic
53#1797C2211yescharacteristic
54#1767C2211yescharacteristic
55C4×C4⋊C8C2211yescharacteristic
56C4×C22⋊C8C2211yescharacteristic
57C4×C22⋊C8C2211yescharacteristic
58C4×#97C2211yescharacteristic
59#1487—24no—
60#1477—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×D4⋊C8C2211yescharacteristic
70C2×D4⋊C8C2211yescharacteristic
71C2×D4⋊C8C2211yescharacteristic
72C2×D4⋊C8C2211yescharacteristic
73#1279C2211yescharacteristic
74#1279C2211yescharacteristic
75#1279C2211yescharacteristic
76#1279C2211yescharacteristic
77C22×#41C2×C411yescharacteristic
78C23×Q8C2×C411yescharacteristic
79C22×M16—21no—
80C23×C8—21no—
81#548—24no—
82#548—24no—
83C2×#124—21no—
84C2×#124C2×C411yescharacteristic
85C2×C22⋊Q8—21no—
86C2×C22⋊Q8C2×C411yescharacteristic
87C2×#121—21no—
88C2×#121C2×C411yescharacteristic
89C4×#41—22no—
90C4×#41—22no—
91C4×#41—41no—
92C4×#41—41no—
93C2×C4×Q8—21no—
94C2×C4×Q8—21no—
95C2×C4×Q8—22no—
96C2×C4×Q8—22no—
97C2×C4×Q8—41no—
98C2×C4×Q8—41no—
99C2×C4×Q8C2×C411yescharacteristic
100C2×C4×Q8C2×C411yescharacteristic
101C2×C4×Q8C2×C411yescharacteristic
102C2×C4×Q8C2×C411yescharacteristic
103C2×C4×Q8C2×C411yescharacteristic
104C2×C4×Q8C2311yescharacteristic
105C2×C4×Q8C2311yescharacteristic
106C2×C4×D4—21no—
107C2×C4×D4—21no—
108C2×C4×D4—21no—
109C2×C4×D4—21no—
110C2×C4×D4—21no—
111C2×C4×D4C2×C411yescharacteristic
112C2×C4×D4C2×C411yescharacteristic
113C2×C4×D4D411yescharacteristic
114C2×C4×D4D411yescharacteristic
115C2×C4×D4C2311yescharacteristic
116C2×#117—21no—
117C2×#117C2×C411yescharacteristic
118C22×C4⋊C4—21no—
119C22×C4⋊C4C2×C411yescharacteristic
120C22×C42—21no—
121C22×C42—21no—
122C22×C42C2311yescharacteristic
123C22×C42C2311yescharacteristic
124#435—44no—
125#431—22no—
126#431—22no—
127#431—41no—
128#431—41no—
129#423—22no—
130#423—41no—
131C2×C4⋊C8—22no—
132C2×C4⋊C8—21no—
133C2×C4⋊C8—21no—
134C2×C4⋊C8—21no—
135C2×C4⋊C8—21no—
136C2×C4⋊C8—21no—
137C2×C4⋊C8—21no—
138C2×C4⋊C8—21no—
139C2×C4⋊C8—41no—
140C2×C4⋊C8C2311yescharacteristic
141C2×C4⋊C8C2311yescharacteristic
142C2×C4⋊C8C2311yescharacteristic
143C2×C4⋊C8C2311yescharacteristic
144C2×C22⋊C8—21no—
145C2×C22⋊C8—21no—
146C2×C22⋊C8—21no—
147C2×C22⋊C8—21no—
148C2×C22⋊C8—21no—
149C2×C22⋊C8—21no—
150C2×#97—21no—
151C2×#97—21no—
152C2×#97—21no—
153C2×C4×C8C2311yescharacteristic
154C2×C4×C8C2311yescharacteristic
155C2×C4×C8C2311yescharacteristic
156C2×C4×C8C2311yescharacteristic
157#391—21no—
158#391—21no—
159#391C2×C411yescharacteristic
160#391C2×C411yescharacteristic
161#390—21no—
162#390—21no—
163#390C2×C411yescharacteristic
164#390C2×C411yescharacteristic
165#389—21no—
166#389—21no—
167#389C2×C411yescharacteristic
168#389C2×C411yescharacteristic
169#388—21no—
170#388—21no—
171#388—21no—
172#388—21no—
173#388—21no—
174#388—21no—
175#388—21no—
176#388—21no—
177#388—21no—
178#387—21no—
179#387—21no—
180#387—21no—
181#386—21no—
182#386—21no—
183#386—21no—
184#385—21no—
185#385—21no—
186#385—21no—
187#382—21no—
188#382C2×C411yescharacteristic
189#380—21no—
190#380—21no—
191#380C2×C411yescharacteristic
192#380C2×C411yescharacteristic
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⋊C4—21no—
212C4×C22⋊C4—21no—
213C4×C22⋊C4C2×C411yescharacteristic
214C4×C22⋊C4C2×C411yescharacteristic
215C4×C22⋊C4D411yescharacteristic
216C4×C22⋊C4D411yescharacteristic
217C4×C22⋊C4D411yescharacteristic
218C4×C22⋊C4D411yescharacteristic
219C43—21no—
220C43C2311yescharacteristic
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—41no—
233Q8⋊C8—41no—
234Q8⋊C8D414yescomplemented
235D4⋊C8—22no—
236D4⋊C8—22no—
237D4⋊C8—41no—
238D4⋊C8—41no—
239C2×#41—22no—
240C2×#41—22no—
241C2×#41—22no—
242C2×#41—41no—
243C2×#41—41no—
244C2×#41M1614yescomplemented
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—21no—
248C22×Q8—22no—
249C22×Q8—22no—
250C22×Q8—41no—
251C22×Q8—41no—
252C22×Q8C22×C411yescharacteristic
253C22×Q8C22×C411yescharacteristic
254C22×D4—21no—
255C22×D4—21no—
256C22×D4C22⋊C411yescharacteristic
257C22×D4C22×C411yescharacteristic
258C23×C4—21no—
259C23×C4—21no—
260C23×C4—21no—
261C23×C4—21no—
262C23×C4—21no—
263C23×C4C22×C411yescharacteristic
264C23×C4C22×C411yescharacteristic
265C23×C4C2×D411yescharacteristic
266C23×C4C2×D411yescharacteristic
267C23×C4C2×D411yescharacteristic
268C23×C4C2×D411yescharacteristic
269C2×M16—42no—
270C2×M16—42no—
271C2×M16—81no—
272C22×C8—21no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8—21no—
276C22×C8—21no—
277C22×C8—21no—
278C22×C8—21no—
279C22×C8—21no—
280C22×C8—42no—
281C22×C8—42no—
282C22×C8—81no—
283#124—28no—
284#124—22no—
285#124—22no—
286C22⋊Q8—28no—
287C22⋊Q8—22no—
288C22⋊Q8M1614yescomplemented
289#121—28no—
290#121—22no—
291#121—22no—
292C4×Q8—22no—
293C4×Q8—22no—
294C4×Q8—21no—
295C4×Q8—21no—
296C4×Q8—22no—
297C4×Q8—22no—
298C4×Q8—22no—
299C4×Q8—22no—
300C4×Q8—21no—
301C4×Q8—21no—
302C4×Q8—21no—
303C4×Q8—21no—
304C4×Q8—42no—
305C4×Q8—42no—
306C4×Q8—41no—
307C4×Q8—41no—
308C4×Q8—41no—
309C4×Q8—41no—
310C4×Q8—42no—
311C4×Q8—42no—
312C4×Q8C2×D412yes—
313C4×Q8#4112yes—
314C4×D4—28no—
315C4×D4—22no—
316C4×D4—22no—
317C4×D4—22no—
318C4×D4—22no—
319C4×D4—22no—
320C4×D4—21no—
321C4×D4—21no—
322C4×D4—21no—
323C4×D4—21no—
324C4×D4—42no—
325C4×D4—41no—
326C4×D4—42no—
327C4×D4—42no—
328C4×D4—44no—
329C4×D4—42no—
330C4×D4—42no—
331C4×D4—42no—
332C4×D4—42no—
333#117—22no—
334#117—42no—
335#117—42no—
336#117—41no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—22no—
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—41no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4C22⋊C411yescharacteristic
353C2×C4⋊C4C22⋊C411yescharacteristic
354C2×C4⋊C4C22⋊C411yescharacteristic
355C2×C4⋊C4C22×C411yescharacteristic
356C2×C4⋊C4C22×C411yescharacteristic
357C2×C4⋊C4C22×C411yescharacteristic
358C2×C4⋊C4C22×C411yescharacteristic
359C2×C4⋊C4C22×C411yescharacteristic
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4C22⋊C411yescharacteristic
374C2×C22⋊C4C22⋊C411yescharacteristic
375C2×C22⋊C4C22⋊C411yescharacteristic
376C2×C22⋊C4C22⋊C411yescharacteristic
377C2×C22⋊C4C22⋊C411yescharacteristic
378C2×C22⋊C4C22⋊C411yescharacteristic
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—21no—
398C2×C42—42no—
399C2×C42—42no—
400C2×C42—42no—
401C2×C42—42no—
402C2×C42C22×C411yescharacteristic
403C2×C42C22×C411yescharacteristic
404C2×C42C22×C411yescharacteristic
405C2×C42C22×C411yescharacteristic
406C2×C42C2×D411yescharacteristic
407C2×C42C2×D411yescharacteristic
408C2×C42C2×D411yescharacteristic
409C2×C42C2×D411yescharacteristic
410C2×C42C2×D411yescharacteristic
411C2×C42C2×D411yescharacteristic
412C2×C42C2×D411yescharacteristic
413C2×C42C2×D411yescharacteristic
414C2×C42C2411yescharacteristic
415C4⋊C8—21no—
416C4⋊C8—21no—
417C4⋊C8—21no—
418C4⋊C8—21no—
419C4⋊C8—21no—
420C4⋊C8—21no—
421C4⋊C8—21no—
422C4⋊C8—42no—
423C4⋊C8—42no—
424C4⋊C8—42no—
425C4⋊C8—42no—
426C4⋊C8—42no—
427C4⋊C8—42no—
428C4⋊C8—81no—
429C4⋊C8C2×D412yes—
430C22⋊C8—42no—
431C22⋊C8—42no—
432C22⋊C8—42no—
433C22⋊C8—42no—
434C22⋊C8—42no—
435C22⋊C8—42no—
436#97—42no—
437#97—42no—
438#97—42no—
439C4×C8—21no—
440C4×C8—21no—
441C4×C8—21no—
442C4×C8—21no—
443C4×C8—21no—
444C4×C8—21no—
445C4×C8—21no—
446C4×C8C2×D412yes—
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#95—21no—
459#95—21no—
460#95C22⋊C411yescharacteristic
461#95C22⋊C411yescharacteristic
462#95C22⋊C411yescharacteristic
463#95C22⋊C411yescharacteristic
464#95C22⋊C411yescharacteristic
465#95C22⋊C411yescharacteristic
466C24—21no—
467C24C2×C22⋊C411yescharacteristic
468C24C2×C22⋊C411yescharacteristic
469#41—28no—
470#41—44no—
471#41—44no—
472#41—44no—
473C2×Q8—24no—
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—44no—
485C2×Q8—44no—
486C2×Q8—44no—
487C2×Q8—44no—
488C2×Q8C4×D412yes—
489C2×Q8C2×M1612yes—
490C2×Q8C2×M1612yes—
491C2×Q8#13112yes—
492C2×D4—24no—
493C2×D4—22no—
494C2×D4—24no—
495C2×D4—22no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—41no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4C2×M1612yes—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—24no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
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—24no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—81no—
559C22×C4—81no—
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×C4C2×C22⋊C411yescharacteristic
568C22×C4C2×C22⋊C411yescharacteristic
569C22×C4C2×C22⋊C411yescharacteristic
570C22×C4C2×M1612yes—
571C22×C4C2×M1612yes—
572C22×C4AGL(1,ℤ/8)12yes—
573C22×C4#13712yes—
574C22×C4C23×C411yescharacteristic
575C22×C4C22×D411yescharacteristic
576C22×C4C22×D411yescharacteristic
577M16—84no—
578C2×C8—22no—
579C2×C8—22no—
580C2×C8—22no—
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—41no—
593C2×C8—41no—
594C2×C8—41no—
595C2×C8—41no—
596C2×C8—41no—
597C2×C8—41no—
598C2×C8—41no—
599C2×C8—41no—
600C2×C8—41no—
601C2×C8—41no—
602C2×C8—84no—
603C4⋊C4—24no—
604C4⋊C4—21no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—21no—
608C4⋊C4—24no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—41no—
618C4⋊C4—42no—
619C4⋊C4—42no—
620C4⋊C4—42no—
621C4⋊C4—42no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C4⋊C4—41no—
625C4⋊C4—41no—
626C4⋊C4—42no—
627C4⋊C4C4×D412yes—
628C4⋊C4C2×M1612yes—
629C22⋊C4—24no—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—22no—
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—22no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—41no—
643C22⋊C4—41no—
644C22⋊C4—42no—
645C22⋊C4—42no—
646C22⋊C4—81no—
647C22⋊C4—81no—
648C22⋊C4—81no—
649C42—24no—
650C42—21no—
651C42—21no—
652C42—21no—
653C42—21no—
654C42—21no—
655C42—21no—
656C42—21no—
657C42—21no—
658C42—22no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—22no—
664C42—21no—
665C42—21no—
666C42—21no—
667C42—21no—
668C42—21no—
669C42—21no—
670C42—21no—
671C42—21no—
672C42—22no—
673C42—41no—
674C42—42no—
675C42—42no—
676C42—42no—
677C42—42no—
678C42—42no—
679C42—41no—
680C42—41no—
681C42—41no—
682C42—41no—
683C42—42no—
684C42—81no—
685C42C22×D411yescharacteristic
686C42C2×#4111yescharacteristic
687C42H(5,𝔽2)11yescharacteristic
688C42H(5,𝔽2)11yescharacteristic
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—22no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23#40712yes—
709C23#41712yes—
710C23C22×C22⋊C411yescharacteristic
711Q8—22no—
712Q8—22no—
713Q8—22no—
714Q8—22no—
715Q8—22no—
716Q8—48no—
717Q8—41no—
718Q8—41no—
719Q8#43514yescomplemented
720D4—22no—
721D4—22no—
722D4—48no—
723D4—44no—
724D4—48no—
725D4—41no—
726D4—41no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—21no—
732C2×C4—22no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—22no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—48no—
771C2×C4—48no—
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—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—81no—
796C2×C4—81no—
797C2×C4—81no—
798C2×C4—81no—
799C2×C4—84no—
800C2×C4—84no—
801C2×C4—81no—
802C2×C4—81no—
803C2×C4—81no—
804C2×C4—81no—
805C2×C4#40712yes—
806C2×C4#41712yes—
807C2×C4#42112yes—
808C2×C4C2×C4×D411yescharacteristic
809C2×C4#51811yescharacteristic
810C2×C4D4211yescharacteristic
811C2×C4D4211yescharacteristic
812C2×C4#54611yescharacteristic
813C2×C4#54611yescharacteristic
814C2×C4C22×M1611yescharacteristic
815C2×C4C22×M1611yescharacteristic
816C2×C4C2×#13111yescharacteristic
817C2×C4#56811yescharacteristic
818C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
819C2×C4C2×#13711yescharacteristic
820C2×C4#57711yescharacteristic
821C2×C4#57811yescharacteristic
822C8—42no—
823C8—42no—
824C8—42no—
825C8—81no—
826C8—81no—
827C8—81no—
828C8—81no—
829C8—81no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—81no—
848C22—81no—
849C22—81no—
850C22—81no—
851C22D4×C22⋊C411yescharacteristic
852C22C2×#40711yescharacteristic
853C22#288011yescharacteristic
854C22C2×#41711yescharacteristic
855C22#289811yescharacteristic
856C22C2×#42111yescharacteristic
857C22#290111yescharacteristic
858C4—22no—
859C4—22no—
860C4—24no—
861C4—22no—
862C4—21no—
863C4—21no—
864C4—41no—
865C4—42no—
866C4—41no—
867C4—41no—
868C4—41no—
869C4—42no—
870C4—41no—
871C4—41no—
872C4—41no—
873C4—42no—
874C4—81no—
875C4—81no—
876C4—81no—
877C4C2×#43511yescharacteristic
878C4D4×M1611yescharacteristic
879C4#297311yescharacteristic
880C4#297411yescharacteristic
881C4#326511yescharacteristic
882C4#327011yescharacteristic
883C4#330811yescharacteristic
884C4#331611yescharacteristic
885C2—42no—
886C2—42no—
887C2—82no—
888C2#1745111yescharacteristic
889C2#1745411yescharacteristic
890C2#1751511yescharacteristic
891C2#1752411yescharacteristic
892C2#2239911yescharacteristic
893C2#2242111yescharacteristic
894C2#2243511yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
socleC23C22×C22⋊C4
prime radicalC2×#548C4
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
2. #22648C2semidirect
3. #21265C2semidirect
4. C2×#1487C2semidirect
5. C2×#1477C2semidirect
6. #9676C2semidirect
7. #9646C2semidirect
8. #9076C2semidirect
9. #9073C2semidirect
10. #8944C2semidirect
11. #8937C2semidirect
12. #8564C2semidirect
13. #8312C2semidirect
14. #8311C2semidirect
15. #8173C2semidirect
234. Q8⋊C8D4semidirect
244. C2×#41M16semidirect
288. C22⋊Q8M16semidirect
719. Q8#435semidirect

Maximal subgroups

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

subgroupindex
C4×#5482
#226482
#212652
C2×#14872
C2×#14772
#96762
#96462
#90762
#90732
#89442
#89372
#85642
#83122
#83112
#81732