Finite Group Databasebeta

← #219802

Subgroups — #219802

Order 512.

1396 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#546C211yesmaximal, characteristic
2#22748C211yesmaximal, characteristic, complemented
3#21264C211yesmaximal, characteristic, complemented
4C2×#1477C211yesmaximal, characteristic, complemented
5C2×#1478C211yesmaximal, characteristic, complemented
6#9675C211yesmaximal, characteristic, complemented
7#9639C211yesmaximal, characteristic, complemented
8#9074C211yesmaximal, characteristic, complemented
9#9073C211yesmaximal, characteristic, complemented
10#8939C211yesmaximal, characteristic, complemented
11#8938C211yesmaximal, characteristic, complemented
12#8565C211yesmaximal, characteristic, complemented
13#8312C211yesmaximal, characteristic, complemented
14#8310C211yesmaximal, characteristic, complemented
15C4×D4⋊C8C211yesmaximal, characteristic, complemented
16C2×#546C411yescharacteristic
17C2×C4×#41C2211yescharacteristic
18C22×C4×D4C2211yescharacteristic
19C2×#431C2211yescharacteristic
20C2×#431C2211yescharacteristic
21C2×#431C2211yescharacteristic, complemented
22C22×C4⋊C8C2211yescharacteristic, complemented
23#2367C411yescharacteristic
24#2364—21no—
25#2363C411yescharacteristic
26#2360C411yescharacteristic
27#2359—21no—
28#2358—21no—
29#2352C411yescharacteristic
30#2349C411yescharacteristic
31#2342—21no—
32#2339C411yescharacteristic
33D4×C22⋊C4C411yescharacteristic
34C4×#124C2211yescharacteristic
35C4×C22⋊Q8C2211yescharacteristic
36C4×#123—21no—
37C4×#121—21no—
38C4×#121C2211yescharacteristic
39C4×#120—21no—
40C42×D4C2211yescharacteristic
41C42×D4C2211yescharacteristic
42C2×C4×C22⋊C4—21no—
43#1954—21no—
44#1939—21no—
45#1923—21no—
46#1923—21no—
47#1923—21no—
48#1916—21no—
49#1869—21no—
50#1831C2211yescharacteristic, complemented
51#1797C2211yescharacteristic
52#1797C2211yescharacteristic, complemented
53C4×C4⋊C8C2211yescharacteristic, complemented
54C4×C4⋊C8C2211yescharacteristic, complemented
55C8×C22⋊C4—21no—
56C4×C22⋊C8C2211yescharacteristic
57C4×C22⋊C8C2211yescharacteristic, complemented
58C42×C8C2211yescharacteristic, complemented
59#1478—24no—
60#1477—24no—
61C2×Q8⋊C8C2211yescharacteristic, complemented
62C2×Q8⋊C8C2211yescharacteristic, complemented
63C2×Q8⋊C8C2211yescharacteristic, complemented
64C2×Q8⋊C8C2211yescharacteristic, complemented
65C2×D4⋊C8C2211yescharacteristic
66C2×D4⋊C8C2211yescharacteristic
67C2×D4⋊C8C2211yescharacteristic
68C2×D4⋊C8C2211yescharacteristic
69C2×D4⋊C8C2211yescharacteristic
70C2×D4⋊C8C2211yescharacteristic
71C2×D4⋊C8C2211yescharacteristic
72C2×D4⋊C8C2211yescharacteristic
73#1279C2211yescharacteristic, complemented
74#1279C2211yescharacteristic, complemented
75#1279C2211yescharacteristic, complemented
76#1279C2211yescharacteristic, complemented
77C22×#41C2×C411yescharacteristic
78C23×D4C2×C411yescharacteristic
79C24×C4—21no—
80C23×C8—21no—
81#546—24no—
82#546C818yescomplemented
83C2×#124C2×C411yescharacteristic
84C2×#123—21no—
85C2×C22⋊Q8C2×C411yescharacteristic
86C2×#121—21no—
87C2×#121C2×C411yescharacteristic
88C2×#120—21no—
89C4×#41—22no—
90C4×#41—22no—
91C4×#41—41no—
92C4×#41—41no—
93C2×C4×Q8C2×C411yescharacteristic
94C2×C4×Q8C2311yescharacteristic
95C2×C4×D4—21no—
96C2×C4×D4—21no—
97C2×C4×D4—21no—
98C2×C4×D4—22no—
99C2×C4×D4—22no—
100C2×C4×D4—21no—
101C2×C4×D4—21no—
102C2×C4×D4—41no—
103C2×C4×D4—41no—
104C2×C4×D4C2×C411yescharacteristic
105C2×C4×D4C2×C411yescharacteristic
106C2×C4×D4C2×C411yescharacteristic
107C2×C4×D4C2×C411yescharacteristic
108C2×C4×D4C2×C411yescharacteristic
109C2×C4×D4C2×C411yescharacteristic
110C2×C4×D4D411yescharacteristic
111C2×C4×D4D411yescharacteristic
112C2×C4×D4C2311yescharacteristic
113C2×C4×D4C2311yescharacteristic
114C2×#117—21no—
115C2×#117C2×C411yescharacteristic
116C22×C4⋊C4C2×C411yescharacteristic
117C22×C22⋊C4—21no—
118C22×C22⋊C4—21no—
119C22×C22⋊C4—21no—
120C22×C42—21no—
121C22×C42—21no—
122C22×C42C2311yescharacteristic
123C22×C42C2311yescharacteristic
124#431—22no—
125#431—22no—
126#431—22no—
127#431—41no—
128#431—41no—
129#431—41no—
130C2×C4⋊C8—22no—
131C2×C4⋊C8—21no—
132C2×C4⋊C8—21no—
133C2×C4⋊C8—21no—
134C2×C4⋊C8—21no—
135C2×C4⋊C8—41no—
136C2×C4⋊C8C2311yescharacteristic
137C2×C4⋊C8C2311yescharacteristic
138C2×C4⋊C8C2311yescharacteristic
139C2×C4⋊C8C2311yescharacteristic
140C2×C22⋊C8—21no—
141C2×C22⋊C8—21no—
142C2×C22⋊C8—21no—
143C2×C22⋊C8—21no—
144C2×C22⋊C8—21no—
145C2×C22⋊C8—21no—
146C2×C22⋊C8—21no—
147C2×C4×C8—21no—
148C2×C4×C8—21no—
149C2×C4×C8—21no—
150C2×C4×C8—21no—
151C2×C4×C8C2311yescharacteristic
152C2×C4×C8C2311yescharacteristic
153C2×C4×C8C2311yescharacteristic
154C2×C4×C8C2311yescharacteristic
155#391C2×C411yescharacteristic
156#391C2×C411yescharacteristic
157#390—21no—
158#390C2×C411yescharacteristic
159#390C2×C411yescharacteristic
160#389—21no—
161#389C2×C411yescharacteristic
162#389C2×C411yescharacteristic
163#388—21no—
164#388—21no—
165#388—21no—
166#388—21no—
167#388—21no—
168#388—21no—
169#388—21no—
170#387—21no—
171#387—21no—
172#387—21no—
173#386—21no—
174#386—21no—
175#386—21no—
176#386—21no—
177#386—21no—
178#386—21no—
179#386—21no—
180#385—21no—
181#385—21no—
182#385—21no—
183#385—21no—
184#385—21no—
185#382C2×C411yescharacteristic
186#381—21no—
187#380—21no—
188#380C2×C411yescharacteristic
189#380C2×C411yescharacteristic
190#379—21no—
191C4×C4⋊C4—21no—
192C4×C4⋊C4C2×C411yescharacteristic
193C4×C4⋊C4C2×C411yescharacteristic
194C4×C4⋊C4C2×C411yescharacteristic
195C4×C4⋊C4D411yescharacteristic
196C4×C4⋊C4D411yescharacteristic
197C4×C4⋊C4C2311yescharacteristic
198C4×C22⋊C4—21no—
199C4×C22⋊C4—21no—
200C4×C22⋊C4—21no—
201C4×C22⋊C4—21no—
202C4×C22⋊C4—21no—
203C4×C22⋊C4—21no—
204C4×C22⋊C4—21no—
205C4×C22⋊C4—21no—
206C4×C22⋊C4—21no—
207C4×C22⋊C4—21no—
208C4×C22⋊C4—21no—
209C4×C22⋊C4C2×C411yescharacteristic
210C4×C22⋊C4C2×C411yescharacteristic
211C4×C22⋊C4D411yescharacteristic
212C4×C22⋊C4D411yescharacteristic
213C4×C22⋊C4D411yescharacteristic
214C4×C22⋊C4D411yescharacteristic
215C2×#95—21no—
216C2×#95—21no—
217C43C2311yescharacteristic
218#336—21no—
219#336—21no—
220#336—21no—
221#336—21no—
222#336—21no—
223#336—21no—
224#336—21no—
225#336—21no—
226Q8⋊C8—22no—
227Q8⋊C8—22no—
228Q8⋊C8—41no—
229Q8⋊C8—41no—
230D4⋊C8—22no—
231D4⋊C8—22no—
232D4⋊C8—22no—
233D4⋊C8—22no—
234D4⋊C8—22no—
235D4⋊C8—41no—
236D4⋊C8—41no—
237D4⋊C8D414yescomplemented
238C25—21no—
239C2×#41—22no—
240C2×#41—22no—
241C2×#41—22no—
242C2×#41—41no—
243C2×#41—41no—
244C2×#41C2×C814yes—
245C22×Q8C22×C411yescharacteristic
246C22×D4—22no—
247C22×D4—22no—
248C22×D4—21no—
249C22×D4—21no—
250C22×D4—21no—
251C22×D4—22no—
252C22×D4—41no—
253C22×D4—41no—
254C22×D4C22⋊C411yescharacteristic
255C22×D4C2×C814yescomplemented
256C22×D4C22×C411yescharacteristic
257C22×D4C22×C411yescharacteristic
258C23×C4—21no—
259C23×C4—21no—
260C23×C4—21no—
261C23×C4—21no—
262C23×C4—21no—
263C23×C4—21no—
264C23×C4—21no—
265C23×C4—21no—
266C23×C4—21no—
267C23×C4—42no—
268C23×C4—42no—
269C23×C4—42no—
270C23×C4—42no—
271C23×C4—81no—
272C23×C4—81no—
273C23×C4C22×C411yescharacteristic
274C23×C4C22×C411yescharacteristic
275C23×C4C2×D411yescharacteristic
276C23×C4C2×D411yescharacteristic
277C23×C4C2×D411yescharacteristic
278C23×C4C2×D411yescharacteristic
279C22×C8—21no—
280C22×C8—21no—
281C22×C8—21no—
282C22×C8—21no—
283C22×C8—21no—
284C22×C8—21no—
285C22×C8—21no—
286C22×C8—21no—
287C22×C8—42no—
288C22×C8—42no—
289C22×C8—81no—
290#124—22no—
291#124C2×C814yescomplemented
292#123—28no—
293C22⋊Q8—22no—
294C22⋊Q8C2×C814yescomplemented
295#121—22no—
296#121—28no—
297#121C2×C814yes—
298#120—28no—
299C4×Q8—22no—
300C4×Q8—21no—
301C4×Q8—21no—
302C4×Q8—21no—
303C4×Q8—21no—
304C4×Q8—41no—
305C4×D4—22no—
306C4×D4—22no—
307C4×D4—22no—
308C4×D4—22no—
309C4×D4—22no—
310C4×D4—21no—
311C4×D4—21no—
312C4×D4—21no—
313C4×D4—21no—
314C4×D4—21no—
315C4×D4—21no—
316C4×D4—42no—
317C4×D4—42no—
318C4×D4—42no—
319C4×D4—41no—
320C4×D4—41no—
321C4×D4—41no—
322C4×D4—41no—
323C4×D4—41no—
324C4×D4—41no—
325C4×D4—42no—
326C4×D4—42no—
327C4×D4—42no—
328C4×D4—42no—
329C4×D4—42no—
330C4×D4—42no—
331C4×D4—81no—
332C4×D4—81no—
333C4×D4C2×C814yes—
334C4×D4C2×C814yescomplemented
335C4×D4M1614yes—
336C4×D4C2×D412yes—
337C4×D4#4112yes—
338#117—22no—
339#117—42no—
340#117—42no—
341#117—41no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—22no—
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⋊C4C22⋊C411yescharacteristic
351C2×C4⋊C4C22⋊C411yescharacteristic
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×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—28no—
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⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4C22⋊C411yescharacteristic
381C2×C22⋊C4C22⋊C411yescharacteristic
382C2×C22⋊C4C22⋊C411yescharacteristic
383C2×C22⋊C4C22⋊C411yescharacteristic
384C2×C22⋊C4C22⋊C411yescharacteristic
385C2×C22⋊C4C22⋊C411yescharacteristic
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—21no—
399C2×C42—21no—
400C2×C42—42no—
401C2×C42—42no—
402C2×C42—81no—
403C2×C42—81no—
404C2×C42C22×C411yescharacteristic
405C2×C42C22×C411yescharacteristic
406C2×C42C22×C411yescharacteristic
407C2×C42C22×C411yescharacteristic
408C2×C42C2×D411yescharacteristic
409C2×C42C2×D411yescharacteristic
410C2×C42C2×D411yescharacteristic
411C2×C42C2×D411yescharacteristic
412C2×C42C2×D411yescharacteristic
413C2×C42C2×D411yescharacteristic
414C2×C42C2×D411yescharacteristic
415C2×C42C2×D411yescharacteristic
416C2×C42C2411yescharacteristic
417C4⋊C8—21no—
418C4⋊C8—21no—
419C4⋊C8—21no—
420C4⋊C8—21no—
421C4⋊C8—21no—
422C4⋊C8—21no—
423C4⋊C8—21no—
424C4⋊C8—42no—
425C4⋊C8—42no—
426C4⋊C8—42no—
427C4⋊C8—42no—
428C4⋊C8C2×D412yes—
429C22⋊C8—42no—
430C22⋊C8—42no—
431C22⋊C8—42no—
432C22⋊C8—42no—
433C22⋊C8—42no—
434C22⋊C8—42no—
435C22⋊C8—81no—
436C4×C8—21no—
437C4×C8—21no—
438C4×C8—21no—
439C4×C8—21no—
440C4×C8—21no—
441C4×C8—21no—
442C4×C8—21no—
443C4×C8—42no—
444C4×C8—42no—
445C4×C8—42no—
446C4×C8—81no—
447C4×C8C2×D412yes—
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#95—21no—
461#95C22⋊C411yescharacteristic
462#95C22⋊C411yescharacteristic
463#95C22⋊C411yescharacteristic
464#95C22⋊C411yescharacteristic
465#95C22⋊C411yescharacteristic
466#95C22⋊C411yescharacteristic
467C24—21no—
468C24—21no—
469C24—24no—
470C24—42no—
471C24—42no—
472C24—42no—
473C24—42no—
474C24—81no—
475C24—81no—
476C24C2×C22⋊C411yescharacteristic
477C24C2×C22⋊C411yescharacteristic
478#41—28no—
479#41—44no—
480#41—44no—
481#41—44no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8C22×C812yes—
488C2×D4—28no—
489C2×D4—24no—
490C2×D4—24no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—24no—
500C2×D4—44no—
501C2×D4—44no—
502C2×D4—44no—
503C2×D4—41no—
504C2×D4—41no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4—42no—
508C2×D4—42no—
509C2×D4—81no—
510C2×D4—81no—
511C2×D4C22⋊C814yes—
512C2×D4C4×D412yes—
513C2×D4C22×C812yes—
514C2×D4C22×C812yes—
515C2×D4#13112yes—
516C22×C4—21no—
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—22no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—24no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—24no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—42no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—42no—
576C22×C4—81no—
577C22×C4—81no—
578C22×C4—81no—
579C22×C4—81no—
580C22×C4—81no—
581C22×C4—81no—
582C22×C4—81no—
583C22×C4—84no—
584C22×C4—84no—
585C22×C4—84no—
586C22×C4—84no—
587C22×C4C2×C22⋊C411yescharacteristic
588C22×C4C2×C22⋊C411yescharacteristic
589C22×C4C2×C22⋊C411yescharacteristic
590C22×C4C2×C22⋊C411yescharacteristic
591C22×C4C2×C22⋊C411yescharacteristic
592C22×C4C2×C22⋊C411yescharacteristic
593C22×C4C2×C22⋊C411yescharacteristic
594C22×C4C2×C22⋊C411yescharacteristic
595C22×C4C2×C22⋊C411yescharacteristic
596C22×C4C2×C22⋊C411yescharacteristic
597C22×C4C22×C812yes—
598C22×C4C22×C812yes—
599C22×C4C2×M1612yes—
600C22×C4C2×M1612yes—
601C22×C4C23×C411yescharacteristic
602C22×C4C22×D411yescharacteristic
603C22×C4C22×D411yescharacteristic
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—41no—
608C2×C8—41no—
609C2×C8—41no—
610C2×C8—41no—
611C2×C8—41no—
612C2×C8—41no—
613C2×C8—41no—
614C2×C8—41no—
615C2×C8—41no—
616C2×C8—41no—
617C2×C8—41no—
618C2×C8—41no—
619C2×C8—41no—
620C2×C8—41no—
621C2×C8—41no—
622C2×C8—41no—
623C2×C8—41no—
624C2×C8—41no—
625C2×C8—41no—
626C2×C8—41no—
627C2×C8—41no—
628C2×C8—84no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—24no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—41no—
639C4⋊C4—41no—
640C4⋊C4—42no—
641C4⋊C4—42no—
642C4⋊C4—41no—
643C4⋊C4—41no—
644C4⋊C4—81no—
645C4⋊C4—81no—
646C4⋊C4C22⋊C814yes—
647C4⋊C4C4×D412yes—
648C4⋊C4C22×C812yes—
649C22⋊C4—24no—
650C22⋊C4—22no—
651C22⋊C4—22no—
652C22⋊C4—24no—
653C22⋊C4—24no—
654C22⋊C4—24no—
655C22⋊C4—24no—
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—41no—
659C22⋊C4—41no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—41no—
668C22⋊C4—41no—
669C22⋊C4—42no—
670C22⋊C4—81no—
671C22⋊C4—81no—
672C22⋊C4—81no—
673C22⋊C4C22⋊C814yes—
674C22⋊C4C22⋊C814yes—
675C42—21no—
676C42—21no—
677C42—21no—
678C42—21no—
679C42—21no—
680C42—21no—
681C42—21no—
682C42—21no—
683C42—21no—
684C42—21no—
685C42—21no—
686C42—21no—
687C42—21no—
688C42—21no—
689C42—21no—
690C42—21no—
691C42—21no—
692C42—21no—
693C42—22no—
694C42—41no—
695C42—42no—
696C42—42no—
697C42—41no—
698C42—41no—
699C42—41no—
700C42—41no—
701C42—81no—
702C42—81no—
703C42C22×C812yes—
704C42C2×M1612yes—
705C42C22×D411yescharacteristic
706C42C2×#4111yescharacteristic
707C42H(5,𝔽2)11yescharacteristic
708C42H(5,𝔽2)11yescharacteristic
709C23—22no—
710C23—21no—
711C23—21no—
712C23—22no—
713C23—22no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—22no—
725C23—48no—
726C23—48no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—84no—
738C23—84no—
739C23—84no—
740C23—84no—
741C23—84no—
742C23C2×C22⋊C812yes—
743C23C2×C22⋊C812yes—
744C23C22×C22⋊C411yescharacteristic
745Q8—22no—
746Q8—22no—
747Q8—41no—
748Q8—41no—
749D4—22no—
750D4—22no—
751D4—22no—
752D4—22no—
753D4—22no—
754D4—44no—
755D4—48no—
756D4—48no—
757D4—41no—
758D4—41no—
759D4—84no—
760D4C8×D414yes—
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—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—48no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—42no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—42no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—42no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—42no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—81no—
828C2×C4—81no—
829C2×C4—81no—
830C2×C4—81no—
831C2×C4—84no—
832C2×C4—84no—
833C2×C4—84no—
834C2×C4—84no—
835C2×C4—84no—
836C2×C4—84no—
837C2×C4—81no—
838C2×C4—81no—
839C2×C4—81no—
840C2×C4—81no—
841C2×C4C2×C22⋊C812yes—
842C2×C4C2×C22⋊C812yes—
843C2×C4C2×C22⋊C812yes—
844C2×C4C2×C22⋊C812yes—
845C2×C4#42112yes—
846C2×C4C2×C4×D411yescharacteristic
847C2×C4#51811yescharacteristic
848C2×C4D4211yescharacteristic
849C2×C4D4211yescharacteristic
850C2×C4#54611yescharacteristic
851C2×C4#54611yescharacteristic
852C2×C4C23×C811yescharacteristic
853C2×C4C22×M1611yescharacteristic
854C2×C4C2×#13111yescharacteristic
855C2×C4#56811yescharacteristic
856C2×C4#57511yescharacteristic
857C2×C4#57511yescharacteristic
858C2×C4#57611yescharacteristic
859C2×C4#57711yescharacteristic
860C8—42no—
861C8—42no—
862C8—42no—
863C8—81no—
864C8—81no—
865C8—81no—
866C8—81no—
867C8—81no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—22no—
873C22—22no—
874C22—24no—
875C22—42no—
876C22—42no—
877C22—41no—
878C22—41no—
879C22—42no—
880C22—42no—
881C22—41no—
882C22—41no—
883C22—41no—
884C22—42no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—816no—
893C22—81no—
894C22—81no—
895C22—81no—
896C22—81no—
897C22D4×C22⋊C411yescharacteristic
898C22C22×C22⋊C811yescharacteristic
899C22#288011yescharacteristic
900C22#289611yescharacteristic
901C22#289711yescharacteristic
902C22C2×#42111yescharacteristic
903C22#290111yescharacteristic
904C4—22no—
905C4—22no—
906C4—22no—
907C4—22no—
908C4—22no—
909C4—21no—
910C4—21no—
911C4—42no—
912C4—41no—
913C4—42no—
914C4—41no—
915C4—41no—
916C4—42no—
917C4—41no—
918C4—41no—
919C4—81no—
920C4—81no—
921C4—81no—
922C4C2×C8×D411yescharacteristic
923C4D4×M1611yescharacteristic
924C4#297211yescharacteristic
925C4#297411yescharacteristic
926C4#327311yescharacteristic
927C4#327511yescharacteristic
928C4#332211yescharacteristic
929C4#332311yescharacteristic
930C2—42no—
931C2—42no—
932C2—44no—
933C2—82no—
934C2#1743711yescharacteristic
935C2#1743811yescharacteristic
936C2#1751311yescharacteristic
937C2#1752111yescharacteristic
938C2D4×C22⋊C811yescharacteristic
939C2#2242711yescharacteristic
940C2#2243511yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC2×C4C23×C8
Frattini, cosocleC2×C42C24
socleC23C22×C22⋊C4
prime radicalC2×#546C4
LCSG ▷ C2×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. #22748C2semidirect
3. #21264C2semidirect
4. C2×#1477C2semidirect
5. C2×#1478C2semidirect
6. #9675C2semidirect
7. #9639C2semidirect
8. #9074C2semidirect
9. #9073C2semidirect
10. #8939C2semidirect
11. #8938C2semidirect
12. #8565C2semidirect
13. #8312C2semidirect
14. #8310C2semidirect
15. C4×D4⋊C8C2semidirect
21. C2×#431C22semidirect
22. C22×C4⋊C8C22semidirect
50. #1831C22semidirect
52. #1797C22semidirect
53. C4×C4⋊C8C22semidirect
54. C4×C4⋊C8C22semidirect
57. C4×C22⋊C8C22semidirect
58. C42×C8C22semidirect
61. C2×Q8⋊C8C22semidirect
62. C2×Q8⋊C8C22semidirect
63. C2×Q8⋊C8C22semidirect
64. C2×Q8⋊C8C22semidirect
73. #1279C22semidirect
74. #1279C22semidirect
75. #1279C22semidirect
76. #1279C22semidirect
82. #546C8semidirect
237. D4⋊C8D4semidirect
255. C22×D4C2×C8semidirect
291. #124C2×C8semidirect
294. C22⋊Q8C2×C8semidirect
334. C4×D4C2×C8semidirect

Maximal subgroups

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

subgroupindex
C4×#5462
#227482
#212642
C2×#14772
C2×#14782
#96752
#96392
#90742
#90732
#89392
#89382
#85652
#83122
#83102
C4×D4⋊C82