Finite Group Databasebeta

← C2×#17399 #6342632

Subgroups — C2×#17399 #6342632

Order 512.

3252 conjugacy classes of subgroups.

The subgroup lattice has 777 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#529C211yesmaximal, characteristic
2C2×#2920C211yesmaximal, characteristic, complemented
3C22×#432C211yesmaximal, characteristic, complemented
4#17399C2116yesmaximal, direct product factor
5C2×#1473C214yesmaximal, complemented
6C2×#1472C212yesmaximal, complemented
7C2×#1471C212yesmaximal
8C2×#1464C214yesmaximal, complemented
9C2×#529—21no—
10C2×#529—21no—
11C2×#529—21no—
12C2×#529—21no—
13C2×#529—21no—
14C2×#529—21no—
15C2×#529—21no—
16C2×#529—21no—
17C2×#529—24no—
18C2×#529—24no—
19C2×#529C418yes—
20C2×#529C2218yes—
21C22×#126C2212yes—
22C22×#125C411yescharacteristic
23C22×#124C411yescharacteristic
24C22×#123C412yes—
25C22×C22⋊Q8C2211yescharacteristic
26C22×#121C2211yescharacteristic
27C22×C4×Q8C411yescharacteristic
28C22×C4×D4C412yes—
29C22×C4×D4C411yescharacteristic
30C22×#117C2212yes—
31C23×C42C2211yescharacteristic
32#2920—24no—
33#2920C2218yescomplemented
34C2×#432—21no—
35C2×#432—21no—
36C2×#432—24no—
37C2×#432—21no—
38C2×#432C2212yes—
39C2×#432C2212yes—
40C2×#432C2212yes—
41C2×#432C2218yescomplemented
42C2×#431—21no—
43C2×#431C2212yes—
44C2×#423—21no—
45C22×C4⋊C8—21no—
46C2×#407C2212yes—
47C22×C22⋊C8C2212yes—
48C2×C4×M16—21no—
49C22×#97—21no—
50#1473C22132yescomplemented
51#1472C22116yescomplemented
52#1471C22116yes—
53#1464C22132yescomplemented
54C2×#324C2218yes—
55C2×#323C2218yes—
56C23×Q8C2×C411yescharacteristic
57C23×D4C2×C412yes—
58C23×D4C2×C411yescharacteristic
59C24×C4C2×C412yes—
60C24×C4C2×C411yescharacteristic
61C24×C4C2×C411yescharacteristic
62C24×C4C2311yescharacteristic
63C22×M16—22no—
64C23×C8—22no—
65#529—28no—
66#529—28no—
67#529—28no—
68#529—28no—
69#529—28no—
70#529—28no—
71#529—28no—
72#529—28no—
73#529—28no—
74#529—28no—
75#529—28no—
76#529—28no—
77#529—28no—
78#529—28no—
79#529—28no—
80#529—28no—
81C2×#126—22no—
82C2×#126—22no—
83C2×#126—22no—
84C2×#126—22no—
85C2×#126—24no—
86C2×#126—24no—
87C2×#126C2×C418yes—
88C2×#126C2318yes—
89C2×#125—24no—
90C2×#125—21no—
91C2×#125—21no—
92C2×#125—21no—
93C2×#125—21no—
94C2×#125C2×C418yes—
95C2×#124—24no—
96C2×#124—21no—
97C2×#124—21no—
98C2×#124—21no—
99C2×#124—21no—
100C2×#124C2×C418yes—
101C2×#123—22no—
102C2×#123—22no—
103C2×#123—28no—
104C2×#123—22no—
105C2×#123—22no—
106C2×#123C2×C4116yes—
107C2×C22⋊Q8—21no—
108C2×C22⋊Q8—21no—
109C2×C22⋊Q8—22no—
110C2×C22⋊Q8—21no—
111C2×C22⋊Q8—21no—
112C2×C22⋊Q8—22no—
113C2×C22⋊Q8C2×C414yes—
114C2×C22⋊Q8C2314yes—
115C2×#121—21no—
116C2×#121—21no—
117C2×#121—22no—
118C2×#121—21no—
119C2×#121—21no—
120C2×#121—22no—
121C2×#121C2×C414yes—
122C2×#121C2314yes—
123C2×C4×Q8—24no—
124C2×C4×Q8—21no—
125C2×C4×Q8—21no—
126C2×C4×Q8—21no—
127C2×C4×Q8—21no—
128C2×C4×Q8C2×C418yes—
129C2×C4×D4—28no—
130C2×C4×D4—22no—
131C2×C4×D4—22no—
132C2×C4×D4—22no—
133C2×C4×D4—22no—
134C2×C4×D4—24no—
135C2×C4×D4—21no—
136C2×C4×D4—21no—
137C2×C4×D4—21no—
138C2×C4×D4—21no—
139C2×C4×D4C2×C4116yes—
140C2×C4×D4C2×C418yes—
141C2×#117—22no—
142C2×#117—22no—
143C2×#117—22no—
144C2×#117—22no—
145C2×#117—24no—
146C2×#117—24no—
147C2×#117C2×C418yes—
148C2×#117C2318yes—
149C22×C4⋊C4C2×C412yes—
150C22×C4⋊C4C2×C411yescharacteristic
151C22×C4⋊C4C2×C412yes—
152C22×C4⋊C4C2×C411yescharacteristic
153C22×C4⋊C4C2×C412yes—
154C22×C4⋊C4C2312yes—
155C22×C22⋊C4C2×C412yes—
156C22×C22⋊C4C2×C412yes—
157C22×C22⋊C4C2×C412yes—
158C22×C22⋊C4C2×C412yes—
159C22×C22⋊C4C2312yes—
160C22×C42C2×C412yes—
161C22×C42C2×C411yescharacteristic
162C22×C42C2×C411yescharacteristic
163C22×C42C2×C414yes—
164C22×C42D411yescharacteristic
165C22×C42D411yescharacteristic
166C22×C42D411yescharacteristic
167C22×C42D411yescharacteristic
168C22×C42D411yescharacteristic
169C22×C42D411yescharacteristic
170C22×C42D411yescharacteristic
171C22×C42D411yescharacteristic
172C22×C42D414yes—
173C22×C42D414yes—
174C22×C42C2311yescharacteristic
175C22×C42C2311yescharacteristic
176C22×C42C2314yes—
177#432—24no—
178#432—24no—
179#432—28no—
180#432—28no—
181#432—28no—
182#432—24no—
183#432C2318yes—
184#432C2318yes—
185#432C2318yes—
186#431—28no—
187#431—24no—
188#431C2318yes—
189#423—28no—
190C2×C4⋊C8—22no—
191C2×C4⋊C8—22no—
192C2×C4⋊C8—28no—
193C2×C4⋊C8—22no—
194C2×C4⋊C8—22no—
195#407—24no—
196#407C2318yes—
197C2×C22⋊C8—24no—
198C2×C22⋊C8—22no—
199C2×C22⋊C8—22no—
200C2×C22⋊C8C2314yes—
201C2×C22⋊C8C2318yes—
202C2×C22⋊C8C2314yes—
203C4×M16—28no—
204C2×#97—22no—
205C2×#97—22no—
206C2×#97—28no—
207C2×#97—22no—
208C2×C4×C8—22no—
209#324C23132yes—
210#323C23132yes—
211C25C22×C411yescharacteristic
212C25C22×C412yes—
213C22×Q8—22no—
214C22×Q8—21no—
215C22×Q8—21no—
216C22×Q8—44no—
217C22×Q8C22×C414yes—
218C22×D4—24no—
219C22×D4—22no—
220C22×D4—22no—
221C22×D4—22no—
222C22×D4—21no—
223C22×D4—21no—
224C22×D4—44no—
225C22×D4—48no—
226C22×D4C22×C418yes—
227C22×D4C22×C414yes—
228C23×C4—24no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—44no—
232C23×C4—44no—
233C23×C4—48no—
234C23×C4—44no—
235C23×C4C22⋊C411yescharacteristic
236C23×C4C22⋊C411yescharacteristic
237C23×C4C22⋊C414yes—
238C23×C4C22⋊C411yescharacteristic
239C23×C4C22⋊C411yescharacteristic
240C23×C4C22⋊C411yescharacteristic
241C23×C4C22⋊C411yescharacteristic
242C23×C4C22⋊C414yes—
243C23×C4C22⋊C411yescharacteristic
244C23×C4C22⋊C411yescharacteristic
245C23×C4C22×C412yes—
246C23×C4C22×C411yescharacteristic
247C23×C4C22×C411yescharacteristic
248C23×C4C22×C411yescharacteristic
249C23×C4C22×C412yes—
250C23×C4C22×C412yes—
251C23×C4C22×C418yes—
252C23×C4C22×C411yescharacteristic
253C23×C4C22×C411yescharacteristic
254C23×C4C22×C414yes—
255C23×C4C22×C412yes—
256C23×C4C22×C414yes—
257C23×C4C2×D411yescharacteristic
258C23×C4C2×D411yescharacteristic
259C23×C4C2×D412yes—
260C23×C4C2×D411yescharacteristic
261C23×C4C2×D411yescharacteristic
262C23×C4C2×D412yes—
263C23×C4C2411yescharacteristic
264C23×C4C2412yes—
265C2×M16—28no—
266C2×M16—48no—
267C22×C8—28no—
268C22×C8—24no—
269C22×C8—24no—
270C22×C8—48no—
271#126—28no—
272#126—28no—
273#126—28no—
274#126—28no—
275#126—28no—
276#126—28no—
277#126—28no—
278#126—28no—
279#125—28no—
280#125—28no—
281#125—28no—
282#125—28no—
283#124—28no—
284#124—28no—
285#124—28no—
286#124—28no—
287#123—216no—
288#123—216no—
289#123—216no—
290#123—216no—
291C22⋊Q8—24no—
292C22⋊Q8—24no—
293C22⋊Q8—24no—
294C22⋊Q8—24no—
295C22⋊Q8—24no—
296C22⋊Q8—24no—
297C22⋊Q8—24no—
298C22⋊Q8—24no—
299#121—24no—
300#121—24no—
301#121—24no—
302#121—24no—
303#121—24no—
304#121—24no—
305#121—24no—
306#121—24no—
307C4×Q8—28no—
308C4×Q8—28no—
309C4×Q8—28no—
310C4×Q8—28no—
311C4×D4—216no—
312C4×D4—216no—
313C4×D4—216no—
314C4×D4—216no—
315C4×D4—28no—
316C4×D4—28no—
317C4×D4—28no—
318C4×D4—28no—
319#117—28no—
320#117—28no—
321#117—28no—
322#117—28no—
323#117—28no—
324#117—28no—
325#117—28no—
326#117—28no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4C22×C418yes—
347C2×C4⋊C4C22×C414yes—
348C2×C4⋊C4C22×C418yes—
349C2×C4⋊C4C22×C414yes—
350C2×C4⋊C4C22×C418yes—
351C2×C4⋊C4C22×C414yes—
352C2×C4⋊C4C2414yes—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4C22×C418yes—
370C2×C22⋊C4C22×C418yes—
371C2×C22⋊C4C22×C418yes—
372C2×C22⋊C4C22×C418yes—
373C2×C22⋊C4C22×C414yes—
374C2×C22⋊C4C2414yes—
375C2×C42—24no—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42C22⋊C414yes—
379C2×C42C22⋊C411yescharacteristic
380C2×C42C22⋊C411yescharacteristic
381C2×C42C22⋊C411yescharacteristic
382C2×C42C22⋊C411yescharacteristic
383C2×C42C22⋊C414yes—
384C2×C42C22⋊C411yescharacteristic
385C2×C42C22⋊C411yescharacteristic
386C2×C42C22⋊C411yescharacteristic
387C2×C42C22⋊C411yescharacteristic
388C2×C42C22⋊C414yes—
389C2×C42C22⋊C414yes—
390C2×C42C22⋊C414yes—
391C2×C42C22⋊C414yes—
392C2×C42C22⋊C414yes—
393C2×C42C22⋊C414yes—
394C2×C42C22⋊C414yes—
395C2×C42C22⋊C414yes—
396C2×C42C22×C418yes—
397C2×C42C22×C412yes—
398C2×C42C22×C414yes—
399C2×C42C22×C414yes—
400C2×C42C22×C412yes—
401C2×C42C2×D411yescharacteristic
402C2×C42C2×D411yescharacteristic
403C2×C42C2×D411yescharacteristic
404C2×C42C2×D411yescharacteristic
405C2×C42C2×D412yes—
406C2×C42C2×D412yes—
407C2×C42C2×D411yescharacteristic
408C2×C42C2×D411yescharacteristic
409C2×C42C2×D411yescharacteristic
410C2×C42C2×D411yescharacteristic
411C2×C42C2×D412yes—
412C2×C42C2×D412yes—
413C2×C42C2×D414yes—
414C2×C42C2×D414yes—
415C2×C42C2×D414yes—
416C2×C42C2×D414yes—
417C2×C42C2×D414yes—
418C2×C42C2×D414yes—
419C2×C42C2×D414yes—
420C2×C42C2×D414yes—
421C2×C42C2412yes—
422C2×C42C2412yes—
423C4⋊C8—28no—
424C4⋊C8—28no—
425C4⋊C8—28no—
426C4⋊C8—28no—
427C22⋊C8—24no—
428C22⋊C8—28no—
429C22⋊C8—28no—
430C22⋊C8—24no—
431C22⋊C8C2418yes—
432C22⋊C8C2418yes—
433#97—28no—
434#97—28no—
435#97—28no—
436C4×C8—28no—
437C24—24no—
438C24—24no—
439C24—22no—
440C24—22no—
441C24—28no—
442C24—42no—
443C24—44no—
444C24—44no—
445C24C2×C22⋊C411yescharacteristic
446C24C2×C22⋊C412yes—
447C24C2×C22⋊C411yescharacteristic
448C24C23×C412yes—
449C24C23×C411yescharacteristic
450C24C23×C414yes—
451C2×Q8—24no—
452C2×Q8—24no—
453C2×Q8—48no—
454C2×Q8—44no—
455C2×Q8—48no—
456C2×Q8—44no—
457C2×D4—28no—
458C2×D4—28no—
459C2×D4—24no—
460C2×D4—24no—
461C2×D4—44no—
462C2×D4—48no—
463C2×D4—48no—
464C2×D4—416no—
465C2×D4—48no—
466C2×D4—48no—
467C2×D4—416no—
468C2×D4—44no—
469C22×C4—24no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—28no—
483C22×C4—28no—
484C22×C4—28no—
485C22×C4—44no—
486C22×C4—44no—
487C22×C4—44no—
488C22×C4—44no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—48no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—48no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—48no—
500C22×C4—48no—
501C22×C4—416no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—416no—
506C22×C4—48no—
507C22×C4—48no—
508C22×C4—44no—
509C22×C4—44no—
510C22×C4C2×C22⋊C412yes—
511C22×C4C2×C22⋊C412yes—
512C22×C4C2×C22⋊C412yes—
513C22×C4C2×C22⋊C412yes—
514C22×C4C2×C22⋊C412yes—
515C22×C4C2×C22⋊C414yes—
516C22×C4C2×C22⋊C414yes—
517C22×C4C2×C22⋊C411yescharacteristic
518C22×C4C2×C22⋊C411yescharacteristic
519C22×C4C2×C22⋊C411yescharacteristic
520C22×C4C2×C22⋊C411yescharacteristic
521C22×C4C2×C22⋊C411yescharacteristic
522C22×C4C2×C22⋊C411yescharacteristic
523C22×C4C2×C22⋊C411yescharacteristic
524C22×C4C2×C22⋊C411yescharacteristic
525C22×C4C2×C22⋊C411yescharacteristic
526C22×C4C2×C22⋊C412yes—
527C22×C4C2×C22⋊C412yes—
528C22×C4C2×C22⋊C412yes—
529C22×C4C2×C22⋊C412yes—
530C22×C4C2×C22⋊C414yes—
531C22×C4C2×C22⋊C414yes—
532C22×C4C2×C22⋊C414yes—
533C22×C4C2×C22⋊C414yes—
534C22×C4C2×C22⋊C414yes—
535C22×C4C2×C22⋊C414yes—
536C22×C4C2×C22⋊C411yescharacteristic
537C22×C4C23×C414yes—
538C22×C4C23×C412yes—
539C22×C4C23×C412yes—
540C22×C4C23×C412yes—
541C22×C4C23×C414yes—
542C22×C4C23×C414yes—
543C22×C4C23×C411yescharacteristic
544C22×C4C23×C412yes—
545C22×C4C23×C412yes—
546C22×C4C22×D412yes—
547C22×C4C22×D412yes—
548C22×C4C22×D411yescharacteristic
549C22×C4C22×D411yescharacteristic
550C22×C4C22×D411yescharacteristic
551C22×C4C22×D411yescharacteristic
552C22×C4C22×D412yes—
553C22×C4C22×D412yes—
554C22×C4C2511yescharacteristic
555M16—416no—
556C2×C8—28no—
557C2×C8—28no—
558C2×C8—48no—
559C2×C8—416no—
560C2×C8—48no—
561C4⋊C4—24no—
562C4⋊C4—24no—
563C4⋊C4—28no—
564C4⋊C4—28no—
565C4⋊C4—24no—
566C4⋊C4—24no—
567C4⋊C4—28no—
568C4⋊C4—28no—
569C4⋊C4—24no—
570C4⋊C4—24no—
571C4⋊C4—28no—
572C4⋊C4—28no—
573C4⋊C4—24no—
574C4⋊C4—24no—
575C22⋊C4—28no—
576C22⋊C4—28no—
577C22⋊C4—24no—
578C22⋊C4—24no—
579C22⋊C4—28no—
580C22⋊C4—28no—
581C22⋊C4—28no—
582C22⋊C4—28no—
583C22⋊C4—28no—
584C22⋊C4—28no—
585C22⋊C4—24no—
586C22⋊C4—24no—
587C42—28no—
588C42—28no—
589C42C2×C22⋊C412yes—
590C42C2×C22⋊C412yes—
591C42C2×C22⋊C412yes—
592C42C2×C22⋊C412yes—
593C42C2×C22⋊C414yes—
594C42C2×C22⋊C414yes—
595C42C2×C22⋊C414yes—
596C42C2×C22⋊C414yes—
597C42C2×C22⋊C414yes—
598C42C2×C22⋊C414yes—
599C42C2×C22⋊C414yes—
600C42C2×C22⋊C414yes—
601C42C2×C22⋊C412yes—
602C42C2×C22⋊C412yes—
603C42C2×C22⋊C412yes—
604C42C2×C22⋊C412yes—
605C42C22×D412yes—
606C42C22×D412yes—
607C42C22×D412yes—
608C42C22×D412yes—
609C42C22×D412yes—
610C42C22×D412yes—
611C42C22×D412yes—
612C42C22×D412yes—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—24no—
618C23—22no—
619C23—22no—
620C23—24no—
621C23—22no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—28no—
626C23—42no—
627C23—42no—
628C23—416no—
629C23—44no—
630C23—44no—
631C23—44no—
632C23—44no—
633C23—44no—
634C23—44no—
635C23—44no—
636C23—44no—
637C23—816no—
638C23#41314yes—
639C23C22×C22⋊C412yes—
640C23C22×C22⋊C411yescharacteristic
641C23C22×C22⋊C412yes—
642C23C22×C22⋊C411yescharacteristic
643C23#56814yes—
644C23C24×C411yescharacteristic
645Q8—48no—
646Q8—48no—
647D4—48no—
648D4—416no—
649D4—416no—
650D4—48no—
651C2×C4—24no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—28no—
661C2×C4—28no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—28no—
678C2×C4—44no—
679C2×C4—44no—
680C2×C4—44no—
681C2×C4—44no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—41no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—41no—
696C2×C4—416no—
697C2×C4—416no—
698C2×C4—44no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—44no—
702C2×C4—44no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4#41014yes—
707C2×C4C22×C22⋊C412yes—
708C2×C4C22×C22⋊C412yes—
709C2×C4C22×C22⋊C411yescharacteristic
710C2×C4C22×C22⋊C411yescharacteristic
711C2×C4C22×C22⋊C412yes—
712C2×C4C22×C22⋊C412yes—
713C2×C4C22×C22⋊C412yes—
714C2×C4C22×C22⋊C412yes—
715C2×C4C22×C22⋊C412yes—
716C2×C4C22×C22⋊C412yes—
717C2×C4C22×C22⋊C412yes—
718C2×C4C22×C22⋊C412yes—
719C2×C4C23×D411yescharacteristic
720C2×C4C23×D411yescharacteristic
721C8—48no—
722C8—48no—
723C22—22no—
724C22—21no—
725C22—21no—
726C22—22no—
727C22—21no—
728C22—21no—
729C22—28no—
730C22—28no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—48no—
735C22—48no—
736C22—44no—
737C22—44no—
738C22—44no—
739C22—44no—
740C22—88no—
741C22—88no—
742C22—88no—
743C22#287912yes—
744C22#287912yes—
745C22C2×#41012yes—
746C22C2×#41314yes—
747C22C2×#41312yes—
748C22C23×C22⋊C411yescharacteristic
749C22C2×#56812yes—
750C4—22no—
751C4—22no—
752C4—22no—
753C4—22no—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—21no—
758C4—22no—
759C4—22no—
760C4—22no—
761C4—22no—
762C4—22no—
763C4—44no—
764C4—44no—
765C4—44no—
766C4C2×#41014yes—
767C2—22no—
768C2—22no—
769C2—24no—
770C2—42no—
771C2—84no—
772C2#1739914yesdirect product factor
773C2C2×#287911yescharacteristic
774C2C22×#41011yescharacteristic
775C2C22×#41311yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC23C24×C4
Frattini, cosocleC22×C4C25
prime radicalC22×#121C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C42 ◁ G
LECSG ▷ C22×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2920C2semidirect
3. C22×#432C2semidirect
4. #17399C2direct (N × H)
5. C2×#1473C2semidirect
6. C2×#1472C2semidirect
8. C2×#1464C2semidirect
33. #2920C22semidirect
41. C2×#432C22semidirect
50. #1473C22semidirect
51. #1472C22semidirect
53. #1464C22semidirect
772. C2#17399direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#5292
C2×#29202
C22×#4322
#173992
C2×#14732
C2×#14722
C2×#14712
C2×#14642