Finite Group Databasebeta

← C2×#17548 #6343304

Subgroups — C2×#17548 #6343304

Order 512.

3592 conjugacy classes of subgroups.

The subgroup lattice has 815 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3520C211yesmaximal, characteristic
2C2×#2974C211yesmaximal, characteristic, complemented
3C2×#2275C211yesmaximal, characteristic, complemented
4#17548C2116yesmaximal, direct product factor
5C2×#1506C211yesmaximal, characteristic, complemented
6C2×#1504C212yesmaximal, complemented
7C2×#1509C211yesmaximal, characteristic, complemented
8C2×#1508C212yesmaximal, complemented
9C2×#1503C211yesmaximal, characteristic, complemented
10C2×#1501C212yesmaximal, complemented
11C2×#1500C211yesmaximal, characteristic, complemented
12C22×#328C212yesmaximal, complemented
13#3520—24no—
14#3520—24no—
15#3520C418yescomplemented
16#3520C2218yes—
17C2×#556C411yescharacteristic, complemented
18C2×#554—21no—
19C2×#552C412yescomplemented
20C2×#551—22no—
21C2×D4×Q8C411yescharacteristic, complemented
22C2×#548C412yescomplemented
23C2×#547C411yescharacteristic, complemented
24C2×#547C411yescharacteristic, complemented
25C2×#546—21no—
26C2×#542—21no—
27C2×#539—22no—
28C2×#533C2211yescharacteristic
29C2×#529C2211yescharacteristic
30C2×#525C2212yes—
31C22×C22⋊Q8C2212yes—
32C2×#520—21no—
33C22×C4×D4—21no—
34C22×C4×D4C2211yescharacteristic
35#2974—24no—
36#2974C2218yescomplemented
37C2×#436—21no—
38C2×#435—22no—
39C2×C8×D4—21no—
40C2×#432C2211yescharacteristic
41C2×#431C2211yescharacteristic
42C2×#407C2212yes—
43C22×C22⋊C8C2212yes—
44#2275—24no—
45#2275C2218yescomplemented
46C2×C4×C4⋊C4—21no—
47C2×C4×C4⋊C4C2211yescharacteristic
48C2×C4×C22⋊C4—22no—
49C2×C4×C22⋊C4C2212yes—
50C2×#376C2211yescharacteristic
51C22×#95C2212yes—
52#1509C2218yescomplemented
53#1508C22116yescomplemented
54#1506C2218yescomplemented
55#1504C22116yescomplemented
56#1503C2218yescomplemented
57#1501C22116yescomplemented
58#1500C2218yescomplemented
59C2×#328C2211yescharacteristic
60C2×#328C2212yes—
61C2×#328C2212yes—
62C2×#328C2212yes—
63C2×#328C2211yescharacteristic
64C2×#328C2212yes—
65C2×#328C2212yes—
66C2×#328C22116yescomplemented
67C2×#327C2211yescharacteristic
68C2×#327C2211yescharacteristic
69C2×#327C2212yes—
70C22×#41—21no—
71C22×#41C2×C412yescomplemented
72C23×Q8C2×C412yescomplemented
73C23×D4D411yescharacteristic
74C24×C4—22no—
75C24×C4C2312yes—
76C22×M16—22no—
77C23×C8—22no—
78#556—24no—
79#556C2×C418yescomplemented
80#554—28no—
81#554—28no—
82#552—28no—
83#552C2×C4116yescomplemented
84#551—216no—
85#551—216no—
86D4×Q8—24no—
87D4×Q8C2×C418yescomplemented
88#548—28no—
89#548C2×C4116yescomplemented
90#547—24no—
91#547—24no—
92#547C2×C418yescomplemented
93#547C2×C418yescomplemented
94#546—28no—
95#546—28no—
96#542—28no—
97#542—28no—
98#539—216no—
99#539—216no—
100#533—22no—
101#533—22no—
102#533C2×C414yescomplemented
103#533C2314yes—
104C2×C4⋊Q8—21no—
105C2×C4⋊Q8C2×C411yescharacteristic, complemented
106C2×C4⋊Q8C2×C411yescharacteristic, complemented
107#529—22no—
108#529—22no—
109#529C2×C414yescomplemented
110#529C2314yes—
111C2×#126—22no—
112C2×#126—22no—
113C2×#126—21no—
114C2×#125—22no—
115C2×#125—21no—
116C2×#125C2×C411yescharacteristic, complemented
117C2×#124—21no—
118C2×#124—22no—
119C2×#124C2×C411yescharacteristic, complemented
120#525—24no—
121#525—24no—
122#525C2×C418yescomplemented
123#525C2318yes—
124C2×#123—22no—
125C2×#123—22no—
126C2×#123—21no—
127C2×#123—22no—
128C2×#123—22no—
129C2×C22⋊Q8—22no—
130C2×C22⋊Q8—22no—
131C2×C22⋊Q8—24no—
132C2×C22⋊Q8—24no—
133C2×C22⋊Q8—21no—
134C2×C22⋊Q8—22no—
135C2×C22⋊Q8—21no—
136C2×C22⋊Q8—22no—
137C2×C22⋊Q8C2×C412yescomplemented
138C2×C22⋊Q8C2×C412yescomplemented
139C2×C22⋊Q8C2×C412yescomplemented
140C2×C22⋊Q8C2×C418yescomplemented
141C2×C22⋊Q8C2311yescharacteristic
142C2×C22⋊Q8C2312yes—
143C2×C22⋊Q8C2318yes—
144C2×#121—22no—
145C2×#121—21no—
146C2×#121C2×C412yescomplemented
147C2×#121C2311yescharacteristic
148C2×#120—22no—
149#520—28no—
150#520—28no—
151C2×C4×Q8—21no—
152C2×C4×Q8—21no—
153C2×C4×Q8C2×C411yescharacteristic, complemented
154C2×C4×Q8C2×C412yescomplemented
155C2×C4×D4—216no—
156C2×C4×D4—21no—
157C2×C4×D4—28no—
158C2×C4×D4—22no—
159C2×C4×D4—22no—
160C2×C4×D4—21no—
161C2×C4×D4—22no—
162C2×C4×D4C2×C411yescharacteristic
163C2×C4×D4C2×C411yescharacteristic
164C2×C4×D4C2×C412yes—
165C2×C4×D4C2×C414yes—
166C2×C4×D4C2×C411yescharacteristic, complemented
167C2×C4×D4D411yescharacteristic
168C2×C4×D4D412yes—
169C2×C4×D4D411yescharacteristic
170C2×C4×D4D414yes—
171C2×C4×D4D414yes—
172C2×C4×D4C2314yes—
173C2×#117—21no—
174C2×#117—22no—
175C2×#117—21no—
176C2×#117C2×C412yescomplemented
177C22×C4⋊C4—21no—
178C22×C4⋊C4—22no—
179C22×C4⋊C4—21no—
180C22×C4⋊C4C2×C412yescomplemented
181C22×C4⋊C4D411yescharacteristic
182C22×C22⋊C4—22no—
183C22×C22⋊C4—22no—
184C22×C22⋊C4D412yes—
185C22×C42—21no—
186C22×C42—21no—
187C22×C42—22no—
188C22×C42C2311yescharacteristic
189#436—28no—
190#435—216no—
191C8×D4—28no—
192#432—22no—
193#432C2314yes—
194#431—22no—
195#431C2314yes—
196C2×C4⋊C8—21no—
197C2×C4⋊C8—21no—
198#407—24no—
199#407C2318yes—
200C2×C22⋊C8—22no—
201C2×C22⋊C8—24no—
202C2×C22⋊C8—22no—
203C2×C22⋊C8C2311yescharacteristic
204C2×C22⋊C8C2312yes—
205C2×C22⋊C8C2318yes—
206C2×C22⋊C8C2311yescharacteristic
207C2×#97—21no—
208C2×C4×C8—21no—
209C4×C4⋊C4—28no—
210C4×C4⋊C4—22no—
211C4×C4⋊C4C2314yes—
212C4×C22⋊C4—24no—
213C4×C22⋊C4—216no—
214C4×C22⋊C4C2318yes—
215#376—22no—
216#376C2314yes—
217C2×#95—22no—
218C2×#95—24no—
219C2×#95—21no—
220C2×#95C2311yescharacteristic
221C2×#95C2312yes—
222C2×#95C2311yescharacteristic
223C2×#95C2318yes—
224#328C2314yes—
225#328C2318yes—
226#328C2318yes—
227#328C2318yes—
228#328C2314yes—
229#328C2318yes—
230#328C2318yes—
231#327C2314yes—
232#327C2314yes—
233#327C2318yes—
234C25C2×D412yes—
235C2×#41—28no—
236C2×#41—24no—
237C2×#41—48no—
238C2×#41—84no—
239C2×#41C22×C418yescomplemented
240C22×Q8—21no—
241C22×Q8—22no—
242C22×Q8—24no—
243C22×Q8—84no—
244C22×Q8C22×C411yescharacteristic
245C22×Q8C22×C412yes—
246C22×Q8C22×C418yescomplemented
247C22×D4—28no—
248C22×D4—22no—
249C22×D4—21no—
250C22×D4—22no—
251C22×D4C22⋊C412yes—
252C22×D4C22⋊C411yescharacteristic
253C22×D4C22⋊C414yes—
254C22×D4C22⋊C411yescharacteristic
255C22×D4C22×C411yescharacteristic
256C22×D4C2×D414yes—
257C23×C4—22no—
258C23×C4—21no—
259C23×C4—22no—
260C23×C4—21no—
261C23×C4—216no—
262C23×C4—22no—
263C23×C4—28no—
264C23×C4—21no—
265C23×C4—22no—
266C23×C4—84no—
267C23×C4—84no—
268C23×C4—84no—
269C23×C4C22×C412yes—
270C23×C4C22×C412yes—
271C23×C4C22×C414yes—
272C23×C4C2×D411yescharacteristic
273C23×C4C2×D411yescharacteristic
274C23×C4C2×D412yes—
275C23×C4C2×D412yes—
276C23×C4C2×D412yes—
277C23×C4C2×D414yes—
278C23×C4C2×D414yes—
279C23×C4C2411yescharacteristic
280C23×C4C2414yes—
281C2×M16—28no—
282C2×M16—84no—
283C22×C8—21no—
284C22×C8—22no—
285C22×C8—21no—
286C22×C8—28no—
287C22×C8—84no—
288C4⋊Q8—28no—
289C4⋊Q8—22no—
290C4⋊Q8—22no—
291C4⋊Q8C22×C414yescomplemented
292C4⋊Q8C22×C414yescomplemented
293#126—216no—
294#126—216no—
295#126—24no—
296#126—24no—
297#125—216no—
298#125—24no—
299#125—22no—
300#125—24no—
301#125C22×C414yescomplemented
302#124—28no—
303#124—216no—
304#124—22no—
305#124C22×C414yescomplemented
306#123—216no—
307#123—28no—
308#123—24no—
309#123—28no—
310#123—24no—
311#123—216no—
312#123—216no—
313C22⋊Q8—28no—
314C22⋊Q8—24no—
315C22⋊Q8—24no—
316C22⋊Q8—28no—
317C22⋊Q8—24no—
318C22⋊Q8—24no—
319C22⋊Q8—21no—
320C22⋊Q8—21no—
321C22⋊Q8—22no—
322C22⋊Q8—22no—
323C22⋊Q8—28no—
324C22⋊Q8—28no—
325C22⋊Q8—24no—
326C22⋊Q8—216no—
327C22⋊Q8—28no—
328C22⋊Q8—216no—
329C22⋊Q8C22×C412yes—
330C22⋊Q8C22×C414yes—
331C22⋊Q8C22×C418yescomplemented
332C22⋊Q8C22×C418yescomplemented
333C22⋊Q8C22×C418yescomplemented
334C22⋊Q8C2412yes—
335C22⋊Q8C2414yes—
336#121—216no—
337#121—28no—
338#121—24no—
339#121—21no—
340#121—21no—
341#121C22×C412yes—
342#121C22×C418yescomplemented
343#121C2412yes—
344#120—28no—
345#120—28no—
346C4×Q8—28no—
347C4×Q8—24no—
348C4×Q8—22no—
349C4×Q8—24no—
350C4×Q8—24no—
351C4×Q8C22×C414yescomplemented
352C4×Q8C22×C418yescomplemented
353C4×D4—264no—
354C4×D4—28no—
355C4×D4—28no—
356C4×D4—28no—
357C4×D4—24no—
358C4×D4—28no—
359C4×D4—28no—
360C4×D4—24no—
361C4×D4—216no—
362C4×D4—22no—
363C4×D4C22⋊C414yes—
364C4×D4C22⋊C418yes—
365C4×D4C22⋊C414yes—
366C4×D4C22⋊C414yes—
367C4×D4C22⋊C414yes—
368C4×D4C22⋊C418yes—
369C4×D4C22×C414yes—
370C4×D4C22×C414yes—
371C4×D4C22×C418yes—
372C4×D4C22×C414yescomplemented
373C4×D4C2×D414yes—
374C4×D4C2×D418yes—
375C4×D4C2×D414yes—
376#117—24no—
377#117—24no—
378#117—24no—
379#117—216no—
380#117—24no—
381#117—24no—
382#117C22×C418yescomplemented
383C2×C4⋊C4—28no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—28no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—24no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—28no—
401C2×C4⋊C4—28no—
402C2×C4⋊C4C22⋊C411yescharacteristic
403C2×C4⋊C4C22⋊C412yes—
404C2×C4⋊C4C22⋊C411yescharacteristic
405C2×C4⋊C4C22⋊C414yes—
406C2×C4⋊C4C22×C411yescharacteristic
407C2×C4⋊C4C22×C412yes—
408C2×C4⋊C4C22×C411yescharacteristic
409C2×C4⋊C4C22×C418yescomplemented
410C2×C4⋊C4C2×D414yes—
411C2×C22⋊C4—216no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—28no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—28no—
420C2×C22⋊C4—28no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4C22⋊C412yes—
427C2×C22⋊C4C22⋊C412yes—
428C2×C22⋊C4C22⋊C412yes—
429C2×C22⋊C4C22⋊C412yes—
430C2×C22⋊C4C22⋊C418yes—
431C2×C22⋊C4C2×D418yes—
432C2×C42—28no—
433C2×C42—22no—
434C2×C42—22no—
435C2×C42—21no—
436C2×C42—24no—
437C2×C42—24no—
438C2×C42—28no—
439C2×C42—82no—
440C2×C42—84no—
441C2×C42C22×C411yescharacteristic
442C2×C42C22×C411yescharacteristic
443C2×C42C22×C412yes—
444C2×C42C2×D412yes—
445C2×C42C2×D411yescharacteristic
446C2×C42C2×D411yescharacteristic
447C2×C42C2×D412yes—
448C2×C42C2412yes—
449C4⋊C8—24no—
450C4⋊C8—24no—
451C22⋊C8—21no—
452C22⋊C8—22no—
453C22⋊C8—28no—
454C22⋊C8—28no—
455C22⋊C8—21no—
456C22⋊C8C2412yes—
457C22⋊C8C2414yes—
458C22⋊C8C2412yes—
459#97—24no—
460C4×C8—24no—
461#95—21no—
462#95—28no—
463#95—22no—
464#95—24no—
465#95—21no—
466#95C2412yes—
467#95C2414yes—
468#95C2412yes—
469C24—24no—
470C24—24no—
471C24—28no—
472C24—21no—
473C24—44no—
474C24C2×C22⋊C412yes—
475C24C2×C22⋊C414yes—
476C24C2×C22⋊C412yes—
477C24C22×D414yes—
478C24C22×D411yescharacteristic
479#41—432no—
480#41—88no—
481#41—88no—
482C2×Q8—24no—
483C2×Q8—21no—
484C2×Q8—22no—
485C2×Q8—28no—
486C2×Q8—42no—
487C2×Q8—44no—
488C2×Q8—44no—
489C2×Q8—84no—
490C2×Q8—88no—
491C2×Q8—88no—
492C2×Q8C23×C412yes—
493C2×Q8C23×C414yes—
494C2×D4—28no—
495C2×D4—216no—
496C2×D4—216no—
497C2×D4—22no—
498C2×D4—28no—
499C2×D4—22no—
500C2×D4—28no—
501C2×D4—21no—
502C2×D4—24no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4—48no—
507C2×D4—84no—
508C2×D4#10418yes—
509C2×D4C2×C22⋊C418yes—
510C2×D4C2×C22⋊C414yes—
511C2×D4C2×C22⋊C414yes—
512C2×D4C23×C412yes—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—28no—
519C22×C4—28no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—24no—
528C22×C4—232no—
529C22×C4—28no—
530C22×C4—24no—
531C22×C4—28no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—42no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4—42no—
539C22×C4—44no—
540C22×C4—42no—
541C22×C4—44no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—48no—
545C22×C4—44no—
546C22×C4—84no—
547C22×C4—84no—
548C22×C4—84no—
549C22×C4—84no—
550C22×C4—84no—
551C22×C4—88no—
552C22×C4—84no—
553C22×C4—88no—
554C22×C4—832no—
555C22×C4C2×C22⋊C412yes—
556C22×C4C2×C22⋊C412yes—
557C22×C4C2×C22⋊C411yescharacteristic
558C22×C4C2×C22⋊C412yes—
559C22×C4C2×C22⋊C411yescharacteristic
560C22×C4C2×C22⋊C411yescharacteristic
561C22×C4C2×C22⋊C412yes—
562C22×C4C2×C22⋊C414yes—
563C22×C4C2×C22⋊C414yes—
564C22×C4C2×C22⋊C414yes—
565C22×C4C2×C22⋊C414yes—
566C22×C4C2×C22⋊C414yes—
567C22×C4C2×C22⋊C411yescharacteristic
568C22×C4C23×C411yescharacteristic
569C22×C4C23×C411yescharacteristic
570C22×C4C23×C414yes—
571C22×C4C23×C414yes—
572C22×C4C22×D412yes—
573C22×C4C22×D412yes—
574C22×C4C22×D411yescharacteristic
575C22×C4C22×D411yescharacteristic
576C22×C4C22×D414yes—
577C22×C4C22×D411yescharacteristic
578C22×C4C22×D414yes—
579C22×C4C22×D414yes—
580C22×C4C2511yescharacteristic
581M16—88no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—24no—
585C2×C8—42no—
586C2×C8—44no—
587C2×C8—42no—
588C2×C8—88no—
589C4⋊C4—216no—
590C4⋊C4—22no—
591C4⋊C4—28no—
592C4⋊C4—21no—
593C4⋊C4—24no—
594C4⋊C4—28no—
595C4⋊C4—24no—
596C4⋊C4—22no—
597C4⋊C4—28no—
598C4⋊C4—24no—
599C4⋊C4—24no—
600C4⋊C4—24no—
601C4⋊C4—28no—
602C4⋊C4—24no—
603C4⋊C4—28no—
604C4⋊C4—24no—
605C4⋊C4—21no—
606C4⋊C4—22no—
607C4⋊C4—24no—
608C4⋊C4C2×C22⋊C414yes—
609C4⋊C4C2×C22⋊C418yes—
610C4⋊C4C2×C22⋊C414yes—
611C4⋊C4C23×C412yes—
612C4⋊C4C23×C414yes—
613C4⋊C4C23×C412yes—
614C22⋊C4—232no—
615C22⋊C4—22no—
616C22⋊C4—24no—
617C22⋊C4—28no—
618C22⋊C4—28no—
619C22⋊C4—28no—
620C22⋊C4—28no—
621C22⋊C4—22no—
622C22⋊C4—24no—
623C22⋊C4—22no—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—28no—
627C22⋊C4—24no—
628C22⋊C4—22no—
629C22⋊C4C2×C22⋊C418yes—
630C22⋊C4C2×C22⋊C418yes—
631C22⋊C4C2×C22⋊C418yes—
632C22⋊C4C2×C22⋊C418yes—
633C42—216no—
634C42—28no—
635C42—28no—
636C42—24no—
637C42—84no—
638C42—88no—
639C42C2×C22⋊C412yes—
640C42C2×C22⋊C412yes—
641C42C2×C22⋊C412yes—
642C42C2×C22⋊C412yes—
643C42C23×C412yes—
644C42C23×C412yes—
645C42C22×D412yes—
646C42C22×D412yes—
647C23—22no—
648C23—24no—
649C23—24no—
650C23—22no—
651C23—24no—
652C23—28no—
653C23—24no—
654C23—28no—
655C23—28no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—22no—
660C23—44no—
661C23—44no—
662C23—416no—
663C23—416no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23C2×#10418yes—
668C23C22×C22⋊C414yes—
669C23C22×C22⋊C411yescharacteristic
670C23C22×C22⋊C414yes—
671C23C22×C22⋊C411yescharacteristic
672C23#57712yes—
673C23#57812yes—
674C23C23×D411yescharacteristic
675Q8—42no—
676Q8—44no—
677Q8—42no—
678Q8—44no—
679Q8—48no—
680Q8—88no—
681D4—216no—
682D4—28no—
683D4—42no—
684D4—42no—
685D4—44no—
686D4—416no—
687D4—42no—
688D4—42no—
689D4—88no—
690D4C2×#104116yes—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—28no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—22no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—44no—
724C2×C4—44no—
725C2×C4—42no—
726C2×C4—44no—
727C2×C4—48no—
728C2×C4—416no—
729C2×C4—48no—
730C2×C4—42no—
731C2×C4—44no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—44no—
736C2×C4—416no—
737C2×C4—44no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—48no—
741C2×C4—88no—
742C2×C4—88no—
743C2×C4—832no—
744C2×C4C2×#10414yes—
745C2×C4C22×C22⋊C412yes—
746C2×C4C22×C22⋊C414yes—
747C2×C4C22×C22⋊C411yescharacteristic
748C2×C4C22×C22⋊C411yescharacteristic
749C2×C4C22×C22⋊C412yes—
750C2×C4C22×C22⋊C412yes—
751C2×C4C22×C22⋊C414yes—
752C2×C4C22×C22⋊C412yes—
753C2×C4C24×C411yescharacteristic
754C2×C4C23×D411yescharacteristic
755C8—42no—
756C8—44no—
757C8—42no—
758C22—24no—
759C22—24no—
760C22—216no—
761C22—21no—
762C22—21no—
763C22—24no—
764C22—24no—
765C22—21no—
766C22—21no—
767C22—24no—
768C22—24no—
769C22—24no—
770C22—48no—
771C22—48no—
772C22—416no—
773C22—48no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—84no—
778C22#288312yes—
779C22#289812yes—
780C22#289812yes—
781C22C22×#10418yes—
782C22C22×#10412yes—
783C22C23×C22⋊C411yescharacteristic
784C22C2×#57711yescharacteristic
785C22C2×#57811yescharacteristic
786C4—21no—
787C4—21no—
788C4—21no—
789C4—21no—
790C4—24no—
791C4—24no—
792C4—22no—
793C4—22no—
794C4—22no—
795C4—44no—
796C4—48no—
797C4—44no—
798C4—44no—
799C4—42no—
800C4—42no—
801C4—42no—
802C4—44no—
803C4C22×#10414yes—
804C2—21no—
805C2—21no—
806C2—22no—
807C2—28no—
808C2—44no—
809C2—82no—
810C2#1754814yesdirect product factor
811C2C2×#288311yescharacteristic
812C2C2×#289811yescharacteristic
813C2C23×#10411yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#3520C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2974C2semidirect
3. C2×#2275C2semidirect
4. #17548C2direct (N × H)
5. C2×#1506C2semidirect
6. C2×#1504C2semidirect
7. C2×#1509C2semidirect
8. C2×#1508C2semidirect
9. C2×#1503C2semidirect
10. C2×#1501C2semidirect
11. C2×#1500C2semidirect
12. C22×#328C2semidirect
15. #3520C4semidirect
17. C2×#556C4semidirect
19. C2×#552C4semidirect
21. C2×D4×Q8C4semidirect
22. C2×#548C4semidirect
23. C2×#547C4semidirect
24. C2×#547C4semidirect
36. #2974C22semidirect
45. #2275C22semidirect
52. #1509C22semidirect
53. #1508C22semidirect
54. #1506C22semidirect
55. #1504C22semidirect
56. #1503C22semidirect
57. #1501C22semidirect
58. #1500C22semidirect
66. C2×#328C22semidirect
71. C22×#41C2×C4semidirect
72. C23×Q8C2×C4semidirect
79. #556C2×C4semidirect
83. #552C2×C4semidirect
87. D4×Q8C2×C4semidirect
89. #548C2×C4semidirect
92. #547C2×C4semidirect
93. #547C2×C4semidirect
102. #533C2×C4semidirect
105. C2×C4⋊Q8C2×C4semidirect
106. C2×C4⋊Q8C2×C4semidirect
109. #529C2×C4semidirect
116. C2×#125C2×C4semidirect
119. C2×#124C2×C4semidirect
122. #525C2×C4semidirect
137. C2×C22⋊Q8C2×C4semidirect
138. C2×C22⋊Q8C2×C4semidirect
139. C2×C22⋊Q8C2×C4semidirect
140. C2×C22⋊Q8C2×C4semidirect
146. C2×#121C2×C4semidirect
153. C2×C4×Q8C2×C4semidirect
154. C2×C4×Q8C2×C4semidirect
166. C2×C4×D4C2×C4semidirect
176. C2×#117C2×C4semidirect
180. C22×C4⋊C4C2×C4semidirect
239. C2×#41C22×C4semidirect
246. C22×Q8C22×C4semidirect
291. C4⋊Q8C22×C4semidirect
292. C4⋊Q8C22×C4semidirect
301. #125C22×C4semidirect
305. #124C22×C4semidirect
331. C22⋊Q8C22×C4semidirect
332. C22⋊Q8C22×C4semidirect
333. C22⋊Q8C22×C4semidirect
342. #121C22×C4semidirect
351. C4×Q8C22×C4semidirect
352. C4×Q8C22×C4semidirect
372. C4×D4C22×C4semidirect
382. #117C22×C4semidirect
409. C2×C4⋊C4C22×C4semidirect
810. C2#17548direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#35202
C2×#29742
C2×#22752
#175482
C2×#15062
C2×#15042
C2×#15092
C2×#15082
C2×#15032
C2×#15012
C2×#15002
C22×#3282