Finite Group Databasebeta

← #223381

Subgroups — #223381

Order 512.

1010 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#552C211yesmaximal, characteristic
2#22795C211yesmaximal, characteristic
3#21101C211yesmaximal, characteristic
4#9872C211yesmaximal, characteristic, complemented
5#9866C211yesmaximal, characteristic, complemented
6#9073C211yesmaximal, characteristic, complemented
7#9071C211yesmaximal, characteristic, complemented
8#8938C211yesmaximal, characteristic, complemented
9#8938C211yesmaximal, characteristic, complemented
10#8708C211yesmaximal, characteristic, complemented
11#8707C211yesmaximal, characteristic, complemented
12#8564C211yesmaximal, characteristic, complemented
13#8171C211yesmaximal, characteristic, complemented
14#7892C211yesmaximal, characteristic, complemented
15#7890C211yesmaximal, characteristic, complemented
16C2×#552C411yescharacteristic
17C2×#431C2211yescharacteristic
18C2×#431C2211yescharacteristic
19C2×#431C2211yescharacteristic
20C22×C4×C8C2211yescharacteristic
21#2373—21no—
22#2371—21no—
23#2370C411yescharacteristic
24#2362C411yescharacteristic
25#2360C411yescharacteristic
26#2359—21no—
27#2356C411yescharacteristic
28#2352C411yescharacteristic
29#2346C411yescharacteristic
30#2344C411yescharacteristic
31#2343—21no—
32C4×#125—21no—
33C4×#125C2211yescharacteristic
34C4×#126—21no—
35C4×C22⋊Q8C2211yescharacteristic
36C4×C22⋊Q8C2211yescharacteristic
37C4×#123—21no—
38C42×Q8C2211yescharacteristic
39C42×D4C2211yescharacteristic
40C4×#117—21no—
41C4×#117C2211yescharacteristic
42C2×C4×C4⋊C4C2211yescharacteristic
43#1954—21no—
44#1923—21no—
45#1923—21no—
46#1923—21no—
47#1916—21no—
48#1869—21no—
49#1850—21no—
50#1842C2211yescharacteristic
51#1797C2211yescharacteristic
52#1797C2211yescharacteristic
53C8×C4⋊C4—21no—
54C4×C4⋊C8C2211yescharacteristic
55C4×C4⋊C8C2211yescharacteristic
56C4×C22⋊C8C2211yescharacteristic
57C4×C22⋊C8C2211yescharacteristic
58#1744C2211yescharacteristic
59C2×Q8⋊C8C2211yescharacteristic
60C2×Q8⋊C8C2211yescharacteristic
61C2×Q8⋊C8C2211yescharacteristic
62C2×Q8⋊C8C2211yescharacteristic
63#1279C2211yescharacteristic
64#1279C2211yescharacteristic
65#1279C2211yescharacteristic
66#1279C2211yescharacteristic
67#1279C2211yescharacteristic
68#1279C2211yescharacteristic
69#1279C2211yescharacteristic
70#1279C2211yescharacteristic
71#1279C2211yescharacteristic
72#1279C2211yescharacteristic
73#1279C2211yescharacteristic
74#1279C2211yescharacteristic
75C23×C8—21no—
76#552—24no—
77#552C818yescomplemented
78C2×#126—21no—
79C2×#125—21no—
80C2×#125C2×C411yescharacteristic
81C2×#123—21no—
82C2×C22⋊Q8C2×C411yescharacteristic
83C2×C22⋊Q8C2×C411yescharacteristic
84C2×C4×Q8C2×C411yescharacteristic
85C2×C4×Q8C2×C411yescharacteristic
86C2×C4×Q8C2311yescharacteristic
87C2×C4×D4C2×C411yescharacteristic
88C2×C4×D4D411yescharacteristic
89C2×C4×D4D411yescharacteristic
90C2×#117—21no—
91C2×#117—21no—
92C2×#117C2×C411yescharacteristic
93C2×#117C2×C411yescharacteristic
94C22×C4⋊C4C2×C411yescharacteristic
95C22×C4⋊C4C2×C411yescharacteristic
96C22×C42—21no—
97C22×C42C2311yescharacteristic
98C22×C42C2311yescharacteristic
99#431—22no—
100#431—22no—
101#431—22no—
102#431—41no—
103#431—41no—
104#431—41no—
105C2×C4⋊C8—21no—
106C2×C4⋊C8—21no—
107C2×C4⋊C8—21no—
108C2×C4⋊C8—21no—
109C2×C4⋊C8C2311yescharacteristic
110C2×C4⋊C8C2311yescharacteristic
111C2×C4⋊C8C2311yescharacteristic
112C2×C4⋊C8C2311yescharacteristic
113C2×C22⋊C8—21no—
114C2×C22⋊C8—21no—
115C2×C22⋊C8—21no—
116C2×C22⋊C8—21no—
117C2×C22⋊C8—21no—
118C2×C22⋊C8—21no—
119C2×C22⋊C8—21no—
120C2×C4×C8—22no—
121C2×C4×C8—21no—
122C2×C4×C8—21no—
123C2×C4×C8—21no—
124C2×C4×C8—21no—
125C2×C4×C8—41no—
126C2×C4×C8C2311yescharacteristic
127C2×C4×C8C2311yescharacteristic
128C2×C4×C8C2311yescharacteristic
129C2×C4×C8C2311yescharacteristic
130#391C2×C411yescharacteristic
131#391C2×C411yescharacteristic
132#389—21no—
133#389—21no—
134#389C2×C411yescharacteristic
135#389C2×C411yescharacteristic
136#389C2×C411yescharacteristic
137#389C2×C411yescharacteristic
138#388—21no—
139#388—21no—
140#388—21no—
141#388—21no—
142#388—21no—
143#387—21no—
144#387—21no—
145#387—21no—
146#387—21no—
147#387—21no—
148#387—21no—
149#387—21no—
150#387—21no—
151#387—21no—
152#387—21no—
153#387—21no—
154#387—21no—
155#387—21no—
156#386—21no—
157#385—21no—
158#385—21no—
159#385—21no—
160#383—21no—
161#382—21no—
162#382C2×C411yescharacteristic
163#381—21no—
164#380C2×C411yescharacteristic
165#380C2×C411yescharacteristic
166C4×C4⋊C4—21no—
167C4×C4⋊C4—21no—
168C4×C4⋊C4—21no—
169C4×C4⋊C4—21no—
170C4×C4⋊C4—21no—
171C4×C4⋊C4—21no—
172C4×C4⋊C4—21no—
173C4×C4⋊C4—21no—
174C4×C4⋊C4—21no—
175C4×C4⋊C4—21no—
176C4×C4⋊C4—21no—
177C4×C4⋊C4C2×C411yescharacteristic
178C4×C4⋊C4C2×C411yescharacteristic
179C4×C4⋊C4C2×C411yescharacteristic
180C4×C4⋊C4C2×C411yescharacteristic
181C4×C4⋊C4C2×C411yescharacteristic
182C4×C4⋊C4C2×C411yescharacteristic
183C4×C4⋊C4C2×C411yescharacteristic
184C4×C4⋊C4D411yescharacteristic
185C4×C4⋊C4D411yescharacteristic
186C4×C4⋊C4C2311yescharacteristic
187C4×C4⋊C4C2311yescharacteristic
188C4×C4⋊C4C2311yescharacteristic
189C4×C22⋊C4—21no—
190C4×C22⋊C4—21no—
191C4×C22⋊C4—21no—
192C4×C22⋊C4—21no—
193C4×C22⋊C4—21no—
194C4×C22⋊C4—21no—
195C4×C22⋊C4C2×C411yescharacteristic
196C4×C22⋊C4C2×C411yescharacteristic
197C4×C22⋊C4D411yescharacteristic
198C4×C22⋊C4D411yescharacteristic
199C4×C22⋊C4D411yescharacteristic
200C4×C22⋊C4D411yescharacteristic
201#376—21no—
202#376—21no—
203#376—21no—
204C2×#95—21no—
205C43—21no—
206C43—21no—
207C43C2311yescharacteristic
208#336—21no—
209#336—21no—
210#336—21no—
211#336—21no—
212#336—21no—
213#336—21no—
214#336—21no—
215#336—21no—
216Q8⋊C8—22no—
217Q8⋊C8—22no—
218Q8⋊C8—41no—
219Q8⋊C8—41no—
220C22×Q8C22×C411yescharacteristic
221C22×D4C22⋊C411yescharacteristic
222C23×C4—21no—
223C23×C4—21no—
224C23×C4C22×C411yescharacteristic
225C23×C4C22×C411yescharacteristic
226C23×C4C2×D411yescharacteristic
227C23×C4C2×D411yescharacteristic
228C23×C4C2×D411yescharacteristic
229C23×C4C2×D411yescharacteristic
230C22×C8—21no—
231C22×C8—21no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—42no—
239C22×C8—42no—
240C22×C8—42no—
241#126—28no—
242#125—28no—
243#125—22no—
244#125C2×C814yescomplemented
245#123—28no—
246C22⋊Q8—22no—
247C22⋊Q8—22no—
248C22⋊Q8C2×C814yes—
249C22⋊Q8C2×C814yescomplemented
250C4×Q8—22no—
251C4×Q8—22no—
252C4×Q8—21no—
253C4×Q8—21no—
254C4×Q8—21no—
255C4×Q8—21no—
256C4×Q8—41no—
257C4×Q8C2×C814yescomplemented
258C4×D4—41no—
259C4×D4—41no—
260C4×D4—42no—
261C4×D4C2×C814yes—
262C4×D4M1614yes—
263#117—22no—
264#117—28no—
265#117—22no—
266#117—44no—
267#117—41no—
268#117C2×C814yes—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—41no—
285C2×C4⋊C4C22⋊C411yescharacteristic
286C2×C4⋊C4C22⋊C411yescharacteristic
287C2×C4⋊C4C22⋊C411yescharacteristic
288C2×C4⋊C4C2×C814yescomplemented
289C2×C4⋊C4C22×C411yescharacteristic
290C2×C4⋊C4C22×C411yescharacteristic
291C2×C4⋊C4C22×C411yescharacteristic
292C2×C4⋊C4C22×C411yescharacteristic
293C2×C4⋊C4C22×C411yescharacteristic
294C2×C4⋊C4C22×C411yescharacteristic
295C2×C4⋊C4C22×C411yescharacteristic
296C2×C22⋊C4—21no—
297C2×C22⋊C4—21no—
298C2×C22⋊C4—21no—
299C2×C22⋊C4—21no—
300C2×C22⋊C4—21no—
301C2×C22⋊C4—21no—
302C2×C22⋊C4C22⋊C411yescharacteristic
303C2×C22⋊C4C22⋊C411yescharacteristic
304C2×C22⋊C4C22⋊C411yescharacteristic
305C2×C22⋊C4C22⋊C411yescharacteristic
306C2×C22⋊C4C22⋊C411yescharacteristic
307C2×C22⋊C4C22⋊C411yescharacteristic
308C2×C42—21no—
309C2×C42—21no—
310C2×C42—21no—
311C2×C42—21no—
312C2×C42—21no—
313C2×C42—21no—
314C2×C42—21no—
315C2×C42—21no—
316C2×C42—21no—
317C2×C42—21no—
318C2×C42—21no—
319C2×C42—21no—
320C2×C42—21no—
321C2×C42—21no—
322C2×C42—21no—
323C2×C42—21no—
324C2×C42—21no—
325C2×C42—21no—
326C2×C42—21no—
327C2×C42—21no—
328C2×C42—21no—
329C2×C42—21no—
330C2×C42—42no—
331C2×C42—42no—
332C2×C42C22×C411yescharacteristic
333C2×C42C22×C411yescharacteristic
334C2×C42C22×C411yescharacteristic
335C2×C42C22×C411yescharacteristic
336C2×C42C2×D411yescharacteristic
337C2×C42C2×D411yescharacteristic
338C2×C42C2×D411yescharacteristic
339C2×C42C2×D411yescharacteristic
340C2×C42C2×D411yescharacteristic
341C2×C42C2×D411yescharacteristic
342C2×C42C2×D411yescharacteristic
343C2×C42C2×D411yescharacteristic
344C2×C42C2411yescharacteristic
345C4⋊C8—21no—
346C4⋊C8—21no—
347C4⋊C8—21no—
348C4⋊C8—21no—
349C4⋊C8—21no—
350C4⋊C8—21no—
351C4⋊C8—21no—
352C4⋊C8—42no—
353C4⋊C8—42no—
354C4⋊C8—42no—
355C4⋊C8—81no—
356C4⋊C8#4112yes—
357C22⋊C8—42no—
358C22⋊C8—42no—
359C22⋊C8—42no—
360C22⋊C8—42no—
361C22⋊C8—42no—
362C22⋊C8—81no—
363C22⋊C8—81no—
364C4×C8—21no—
365C4×C8—21no—
366C4×C8—21no—
367C4×C8—21no—
368C4×C8—21no—
369C4×C8—21no—
370C4×C8—21no—
371C4×C8—42no—
372C4×C8—42no—
373C4×C8—42no—
374C4×C8—42no—
375C4×C8#4112yes—
376#95—21no—
377#95—21no—
378#95—21no—
379#95—21no—
380#95—21no—
381#95—21no—
382#95—21no—
383#95—21no—
384#95—21no—
385#95—21no—
386#95—21no—
387#95—21no—
388#95—21no—
389#95—21no—
390#95—21no—
391#95—21no—
392#95—21no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95C22⋊C411yescharacteristic
398#95C22⋊C411yescharacteristic
399#95C22⋊C411yescharacteristic
400#95C22⋊C411yescharacteristic
401#95C22⋊C411yescharacteristic
402#95C22⋊C411yescharacteristic
403C24C2×C22⋊C411yescharacteristic
404C24C2×C22⋊C411yescharacteristic
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8—21no—
409C2×Q8—21no—
410C2×Q8C22×C812yes—
411C2×D4—41no—
412C2×D4—41no—
413C2×D4C22⋊C814yes—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—24no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—81no—
456C22×C4C2×C22⋊C411yescharacteristic
457C22×C4C2×C22⋊C411yescharacteristic
458C22×C4C2×C22⋊C411yescharacteristic
459C22×C4C2×C22⋊C411yescharacteristic
460C22×C4C2×C22⋊C411yescharacteristic
461C22×C4C2×C22⋊C411yescharacteristic
462C22×C4C2×C22⋊C411yescharacteristic
463C22×C4C2×C22⋊C411yescharacteristic
464C22×C4C2×C22⋊C411yescharacteristic
465C22×C4C2×C22⋊C411yescharacteristic
466C22×C4C22×C812yes—
467C22×C4C22×C812yes—
468C22×C4C2×M1612yes—
469C22×C4C2×M1612yes—
470C22×C4C23×C411yescharacteristic
471C22×C4C22×D411yescharacteristic
472C22×C4C22×D411yescharacteristic
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—41no—
477C2×C8—41no—
478C2×C8—41no—
479C2×C8—48no—
480C2×C8—41no—
481C2×C8—41no—
482C2×C8—41no—
483C2×C8—41no—
484C2×C8—41no—
485C2×C8—41no—
486C2×C8—41no—
487C2×C8—41no—
488C2×C8—41no—
489C2×C8—41no—
490C2×C8—41no—
491C2×C8—41no—
492C2×C8—41no—
493C2×C8—41no—
494C2×C8—41no—
495C2×C8—41no—
496C2×C8—41no—
497C2×C8—41no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—24no—
503C4⋊C4—24no—
504C4⋊C4—24no—
505C4⋊C4—24no—
506C4⋊C4—24no—
507C4⋊C4—24no—
508C4⋊C4—22no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—41no—
516C4⋊C4—42no—
517C4⋊C4—42no—
518C4⋊C4—42no—
519C4⋊C4—41no—
520C4⋊C4—41no—
521C4⋊C4—42no—
522C4⋊C4—81no—
523C4⋊C4—81no—
524C4⋊C4C22⋊C814yes—
525C4⋊C4C22×C812yes—
526C4⋊C4C22×C812yes—
527C4⋊C4C22×C812yes—
528C4⋊C4#13112yes—
529C22⋊C4—24no—
530C22⋊C4—24no—
531C22⋊C4—24no—
532C22⋊C4—22no—
533C22⋊C4—41no—
534C22⋊C4—41no—
535C22⋊C4—41no—
536C22⋊C4—42no—
537C22⋊C4—42no—
538C22⋊C4—81no—
539C22⋊C4C22⋊C814yes—
540C22⋊C4C22⋊C814yes—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—21no—
549C42—21no—
550C42—21no—
551C42—21no—
552C42—21no—
553C42—21no—
554C42—21no—
555C42—21no—
556C42—21no—
557C42—21no—
558C42—21no—
559C42—24no—
560C42—24no—
561C42—41no—
562C42—41no—
563C42—42no—
564C42—42no—
565C42—42no—
566C42—42no—
567C42—42no—
568C42—41no—
569C42—41no—
570C42—41no—
571C42—41no—
572C42—41no—
573C42—41no—
574C42—41no—
575C42—41no—
576C42—42no—
577C42—81no—
578C42—81no—
579C42C22×C812yes—
580C42C2×M1612yes—
581C42C2×#4111yescharacteristic
582C42C2×#4111yescharacteristic
583C42H(5,𝔽2)11yescharacteristic
584C422−1+411yescharacteristic
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23C2×C22⋊C812yes—
598C23C2×C22⋊C812yes—
599C23C22×C22⋊C411yescharacteristic
600Q8—22no—
601Q8—22no—
602Q8—41no—
603Q8—41no—
604D4—44no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—22no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—48no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—81no—
676C2×C4—81no—
677C2×C4—84no—
678C2×C4C2×C22⋊C812yes—
679C2×C4C2×C22⋊C812yes—
680C2×C4C2×C22⋊C812yes—
681C2×C4C2×C22⋊C812yes—
682C2×C4#42112yes—
683C2×C4C4×#4111yescharacteristic
684C2×C4#52011yescharacteristic
685C2×C4#54611yescharacteristic
686C2×C4#54611yescharacteristic
687C2×C4#54711yescharacteristic
688C2×C4#54711yescharacteristic
689C2×C4C23×C811yescharacteristic
690C2×C4C22×M1611yescharacteristic
691C2×C4C2×#13111yescharacteristic
692C2×C4#56811yescharacteristic
693C2×C4#57511yescharacteristic
694C2×C4#57511yescharacteristic
695C2×C4#57711yescharacteristic
696C2×C4#57811yescharacteristic
697C8—42no—
698C8—42no—
699C8—42no—
700C8—81no—
701C8—81no—
702C8—81no—
703C8—81no—
704C8—81no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22#233911yescharacteristic
720C22C22×C22⋊C811yescharacteristic
721C22#288011yescharacteristic
722C22#289611yescharacteristic
723C22#289811yescharacteristic
724C22C2×#42111yescharacteristic
725C22#290111yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—21no—
731C4—21no—
732C4—22no—
733C4—42no—
734C4—42no—
735C4—42no—
736C4—41no—
737C4—42no—
738C4—41no—
739C4—42no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4—81no—
744C4—81no—
745C4—81no—
746C4C8×#4111yescharacteristic
747C4#297011yescharacteristic
748C4#298811yescharacteristic
749C4#299011yescharacteristic
750C4#331511yescharacteristic
751C4#331711yescharacteristic
752C4#334811yescharacteristic
753C4#334911yescharacteristic
754C2—42no—
755C2—42no—
756C2#1743711yescharacteristic
757C2#1743911yescharacteristic
758C2#1751311yescharacteristic
759C2#1752511yescharacteristic
760C2#2246911yescharacteristic
761C2#2249611yescharacteristic
762C2#2250611yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC2×C4C23×C8
Frattini, cosocleC2×C42C24
socleC23C22×C22⋊C4
prime radicalC22×D4C22⋊C4
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
4. #9872C2semidirect
5. #9866C2semidirect
6. #9073C2semidirect
7. #9071C2semidirect
8. #8938C2semidirect
9. #8938C2semidirect
10. #8708C2semidirect
11. #8707C2semidirect
12. #8564C2semidirect
13. #8171C2semidirect
14. #7892C2semidirect
15. #7890C2semidirect
77. #552C8semidirect
244. #125C2×C8semidirect
249. C22⋊Q8C2×C8semidirect
257. C4×Q8C2×C8semidirect
288. C2×C4⋊C4C2×C8semidirect

Maximal subgroups

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

subgroupindex
C4×#5522
#227952
#211012
#98722
#98662
#90732
#90712
#89382
#87082
#87072
#85642
#81712
#78922
#78902