Finite Group Databasebeta

← C2×#39620 #7637151

Subgroups — C2×#39620 #7637151

Order 512.

5566 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2806C212yesmaximal, complemented
2C2×#2792C212yesmaximal, complemented
3C2×#2792C212yesmaximal, complemented
4C2×#2734C212yesmaximal, complemented
5#39620C2132yesmaximal, direct product factor
6C2×#2857C211yesmaximal, characteristic
7C2×#2586C212yesmaximal, complemented
8C2×#2586C212yesmaximal, complemented
9C2×#2549C212yesmaximal
10C2×#2549C212yesmaximal
11C2×#2507C212yesmaximal, complemented
12C2×#2451C212yesmaximal, complemented
13C2×#2440C212yesmaximal
14C2×#2659C211yesmaximal, characteristic
15C2×#2659C211yesmaximal, characteristic
16C2×#2345C212yesmaximal
17C2×#2329C211yesmaximal, characteristic
18C2×#2329C211yesmaximal, characteristic
19C2×C4×C22⋊Q8C211yesmaximal, characteristic
20C22×#387C211yesmaximal, characteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×C4⋊Q8C2212yes—
23C22×C22⋊Q8C2212yes—
24C22×C22⋊Q8C2212yes—
25C22×C22⋊Q8C2212yes—
26C22×C22⋊Q8C2211yescharacteristic
27C22×C4×Q8C2211yescharacteristic
28C23×C4⋊C4C2211yescharacteristic
29C23×C4⋊C4C2211yescharacteristic
30C23×C42C2211yescharacteristic
31#2857C22116yes—
32#2806C22132yescomplemented
33#2792C22132yescomplemented
34#2792C22132yescomplemented
35#2734C22132yescomplemented
36#2659C22116yes—
37#2659C22116yes—
38#2586C22132yescomplemented
39#2586C22132yescomplemented
40#2549C22132yes—
41#2549C22132yes—
42#2507C22132yescomplemented
43#2451C22132yescomplemented
44#2440C22132yes—
45C2×#398C2212yes—
46C2×#398C2212yes—
47C2×#398C2212yes—
48C2×#398C2212yes—
49C2×#398C2212yes—
50C2×#398C2212yes—
51C2×#398C2212yes—
52C2×#398C2212yes—
53C2×#398C2212yes—
54C2×#398C2212yes—
55C2×#395C2212yes—
56C2×#395C2212yes—
57C2×#395C2212yes—
58C2×#395C2212yes—
59C2×#395C2212yes—
60C2×#395C2212yes—
61C2×#395C2212yes—
62C2×#395C2212yes—
63C2×#395C2212yes—
64C2×#395C2212yes—
65#2345C22132yes—
66#2329C22116yes—
67#2329C22116yes—
68C4×C22⋊Q8C22116yes—
69C2×#391C2212yes—
70C2×#391C2212yes—
71C2×#391C2212yes—
72C2×#391C2212yes—
73C2×#391C2212yes—
74C2×#391C2212yes—
75C2×#391C2212yes—
76C2×#391C2211yescharacteristic
77C2×#389C2212yes—
78C2×#389C2212yes—
79C2×#389C2212yes—
80C2×#389C2212yes—
81C2×#389C2211yescharacteristic
82C2×#389C2212yes—
83C2×#389C2212yes—
84C2×#389C2212yes—
85C2×#389C2212yes—
86C2×#389C2212yes—
87C2×#389C2211yescharacteristic
88C2×#389C2211yescharacteristic
89C2×#389C2212yes—
90C2×#389C2212yes—
91C2×#387C2212yes—
92C2×#387C2212yes—
93C2×#387C2212yes—
94C2×#387C2212yes—
95C2×#387C2212yes—
96C2×#387C2212yes—
97C2×#387C2212yes—
98C2×#387C2212yes—
99C2×#387C2212yes—
100C2×#387C2212yes—
101C2×#387C2212yes—
102C2×#387C2212yes—
103C2×#387C2212yes—
104C2×#387C22116yes—
105C2×#385C2212yes—
106C2×#385C2212yes—
107C2×#385C2212yes—
108C2×#384C2211yescharacteristic
109C2×#384C2212yes—
110C2×#380C2212yes—
111C2×#380C2212yes—
112C2×#380C2211yescharacteristic
113C2×#380C2211yescharacteristic
114C2×#380C2211yescharacteristic
115C2×#380C2212yes—
116C2×C4×C4⋊C4C2211yescharacteristic
117C2×C4×C4⋊C4C2212yes—
118C2×C4×C4⋊C4C2212yes—
119C2×C4×C4⋊C4C2212yes—
120C2×C4×C22⋊C4C2212yes—
121C2×C4×C22⋊C4C2212yes—
122C2×C4×C22⋊C4C2212yes—
123C22×#95C2211yescharacteristic
124C22×#95C2211yescharacteristic
125C22×#95C2211yescharacteristic
126C22×#95C2211yescharacteristic
127C23×Q8C2312yes—
128C23×Q8C2312yes—
129C23×Q8C2312yes—
130C23×Q8C2311yescharacteristic
131C24×C4C2311yescharacteristic
132C24×C4C2311yescharacteristic
133C24×C4C2311yescharacteristic
134C24×C4C2311yescharacteristic
135C24×C4C2311yescharacteristic
136C24×C4C2311yescharacteristic
137C24×C4C2311yescharacteristic
138C2×C4⋊Q8—44no—
139C2×C4⋊Q8—48no—
140C2×C4⋊Q8C2318yes—
141C2×C4⋊Q8C23116yes—
142C2×C22⋊Q8—48no—
143C2×C22⋊Q8—48no—
144C2×C22⋊Q8—48no—
145C2×C22⋊Q8Q8116yescomplemented
146C2×C22⋊Q8C23116yes—
147C2×C22⋊Q8C23116yes—
148C2×C22⋊Q8C23116yes—
149C2×C22⋊Q8C2318yes—
150C2×C4×Q8—44no—
151C2×C4×Q8C2318yes—
152C22×C4⋊C4—44no—
153C22×C4⋊C4Q8116yescomplemented
154C22×C4⋊C4C2312yes—
155C22×C4⋊C4C2312yes—
156C22×C4⋊C4C2312yes—
157C22×C4⋊C4C2311yescharacteristic
158C22×C4⋊C4C2312yes—
159C22×C4⋊C4C2312yes—
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2311yescharacteristic
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C2312yes—
165C22×C4⋊C4C2312yes—
166C22×C4⋊C4C2312yes—
167C22×C4⋊C4C2312yes—
168C22×C4⋊C4C2312yes—
169C22×C4⋊C4C2312yes—
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2312yes—
176C22×C4⋊C4C2312yes—
177C22×C4⋊C4C2312yes—
178C22×C4⋊C4C2312yes—
179C22×C4⋊C4C2312yes—
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2312yes—
182C22×C4⋊C4C2311yescharacteristic
183C22×C4⋊C4C2318yes—
184C22×C4⋊C4C2312yes—
185C22×C4⋊C4C2312yes—
186C22×C4⋊C4C2311yescharacteristic
187C22×C4⋊C4C2312yes—
188C22×C4⋊C4C2318yes—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C42—44no—
194C22×C42C2311yescharacteristic
195C22×C42C2311yescharacteristic
196C22×C42C2318yes—
197C22×C42C2311yescharacteristic
198C22×C42C2311yescharacteristic
199C22×C42C2312yes—
200C22×C42C2312yes—
201C22×C42C2312yes—
202C22×C42C2312yes—
203C22×C42C2312yes—
204C22×C42C2312yes—
205#398C23116yes—
206#398C23116yes—
207#398C23116yes—
208#398C23116yes—
209#398C23116yes—
210#398C23116yes—
211#398C23116yes—
212#398C23116yes—
213#398C23116yes—
214#398C23116yes—
215#395C23116yes—
216#395C23116yes—
217#395C23116yes—
218#395C23116yes—
219#395C23116yes—
220#395C23116yes—
221#395C23116yes—
222#395C23116yes—
223#395C23116yes—
224#395C23116yes—
225#391C23116yes—
226#391C23116yes—
227#391C23116yes—
228#391C23116yes—
229#391C23116yes—
230#391C23116yes—
231#391C23116yes—
232#391C2318yes—
233#389C23116yes—
234#389C23116yes—
235#389C2318yes—
236#389C23116yes—
237#389C23116yes—
238#389C23116yes—
239#389C23116yes—
240#389C23116yes—
241#389C2318yes—
242#389C23116yes—
243#389C23116yes—
244#389C23116yes—
245#389C23116yes—
246#389C2318yes—
247#387C23116yes—
248#387C23116yes—
249#387C23116yes—
250#387C23116yes—
251#387C23116yes—
252#387C23116yes—
253#387C23116yes—
254#387C23116yes—
255#387C23116yes—
256#387C23116yes—
257#387C23116yes—
258#387C23116yes—
259#387C23116yes—
260#385C23116yes—
261#385C23116yes—
262#385C23116yes—
263#384C2318yes—
264#384C23116yes—
265#380C2318yes—
266#380C2318yes—
267#380C23116yes—
268#380C23116yes—
269#380C23116yes—
270#380C2318yes—
271C4×C4⋊C4C2318yes—
272C4×C4⋊C4C23116yes—
273C4×C4⋊C4C23116yes—
274C4×C4⋊C4C23116yes—
275C4×C22⋊C4C23116yes—
276C4×C22⋊C4C23116yes—
277C4×C22⋊C4C23116yes—
278C2×#95C2318yes—
279C2×#95C2318yes—
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2312yes—
305C2×#95C2312yes—
306C2×#95C2312yes—
307C2×#95C2318yes—
308C2×#95C2318yes—
309C2×#95C2312yes—
310C2×#95C2312yes—
311C25C2411yescharacteristic
312C22×Q8—28no—
313C22×Q8—42no—
314C22×Q8—42no—
315C22×Q8—44no—
316C22×Q8—44no—
317C22×Q8—44no—
318C22×Q8—44no—
319C22×Q8—44no—
320C22×Q8—44no—
321C22×Q8—44no—
322C22×Q8—44no—
323C22×Q8C2×Q818yes—
324C22×Q8C2418yes—
325C22×Q8C2418yes—
326C22×Q8C2418yes—
327C22×Q8C2414yes—
328C23×C4—24no—
329C23×C4—24no—
330C23×C4—24no—
331C23×C4—24no—
332C23×C4—42no—
333C23×C4—42no—
334C23×C4—42no—
335C23×C4—42no—
336C23×C4—42no—
337C23×C4—42no—
338C23×C4—42no—
339C23×C4—42no—
340C23×C4—42no—
341C23×C4—42no—
342C23×C4—42no—
343C23×C4—42no—
344C23×C4—42no—
345C23×C4C2×Q818yes—
346C23×C4C2×Q818yes—
347C23×C4C2×Q818yes—
348C23×C4C2×Q818yes—
349C23×C4C2412yes—
350C23×C4C2412yes—
351C23×C4C2412yes—
352C23×C4C2412yes—
353C23×C4C2412yes—
354C23×C4C2412yes—
355C23×C4C2411yescharacteristic
356C23×C4C2412yes—
357C23×C4C2412yes—
358C23×C4C2414yes—
359C23×C4C2412yes—
360C23×C4C2412yes—
361C23×C4C2411yescharacteristic
362C23×C4C2411yescharacteristic
363C23×C4C2412yes—
364C23×C4C2412yes—
365C23×C4C2411yescharacteristic
366C23×C4C2411yescharacteristic
367C23×C4C2411yescharacteristic
368C23×C4C2414yes—
369C23×C4C2414yes—
370C23×C4C2414yes—
371C23×C4C2414yes—
372C23×C4C2414yes—
373C23×C4C2414yes—
374C4⋊Q8—416no—
375C4⋊Q8—432no—
376C22⋊Q8—432no—
377C22⋊Q8—432no—
378C22⋊Q8—432no—
379C22⋊Q8C2×Q8164yescomplemented
380C4×Q8—416no—
381C2×C4⋊C4—28no—
382C2×C4⋊C4—28no—
383C2×C4⋊C4—416no—
384C2×C4⋊C4—44no—
385C2×C4⋊C4—44no—
386C2×C4⋊C4—44no—
387C2×C4⋊C4—44no—
388C2×C4⋊C4—44no—
389C2×C4⋊C4—44no—
390C2×C4⋊C4—44no—
391C2×C4⋊C4—44no—
392C2×C4⋊C4—44no—
393C2×C4⋊C4—42no—
394C2×C4⋊C4—42no—
395C2×C4⋊C4—42no—
396C2×C4⋊C4—42no—
397C2×C4⋊C4—44no—
398C2×C4⋊C4—44no—
399C2×C4⋊C4—44no—
400C2×C4⋊C4—44no—
401C2×C4⋊C4—44no—
402C2×C4⋊C4—44no—
403C2×C4⋊C4—44no—
404C2×C4⋊C4—44no—
405C2×C4⋊C4—44no—
406C2×C4⋊C4—42no—
407C2×C4⋊C4—44no—
408C2×C4⋊C4—42no—
409C2×C4⋊C4—44no—
410C2×C4⋊C4—44no—
411C2×C4⋊C4C2×Q8116yes—
412C2×C4⋊C4C2×Q8116yes—
413C2×C4⋊C4C2×Q818yes—
414C2×C4⋊C4C2×Q8116yes—
415C2×C4⋊C4C2×Q8164yescomplemented
416C2×C4⋊C4C2418yes—
417C2×C4⋊C4C2418yes—
418C2×C4⋊C4C2418yes—
419C2×C4⋊C4C2414yes—
420C2×C4⋊C4C2418yes—
421C2×C4⋊C4C2418yes—
422C2×C4⋊C4C2418yes—
423C2×C4⋊C4C2418yes—
424C2×C4⋊C4C2418yes—
425C2×C4⋊C4C2418yes—
426C2×C4⋊C4C2418yes—
427C2×C4⋊C4C2418yes—
428C2×C4⋊C4C2418yes—
429C2×C4⋊C4C2418yes—
430C2×C4⋊C4C2414yes—
431C2×C4⋊C4C2418yes—
432C2×C4⋊C4C2414yes—
433C2×C4⋊C4C2418yes—
434C2×C4⋊C4C2418yes—
435C2×C4⋊C4C2418yes—
436C2×C4⋊C4C2414yes—
437C2×C4⋊C4C2418yes—
438C2×C4⋊C4C2414yes—
439C2×C4⋊C4C2418yes—
440C2×C4⋊C4C2414yes—
441C2×C4⋊C4C2418yes—
442C2×C4⋊C4C2418yes—
443C2×C4⋊C4C2418yes—
444C2×C4⋊C4C2418yes—
445C2×C4⋊C4C2418yes—
446C2×C4⋊C4C2418yes—
447C2×C4⋊C4C2414yes—
448C2×C4⋊C4C2418yes—
449C2×C22⋊C4—28no—
450C2×C22⋊C4—28no—
451C2×C22⋊C4—28no—
452C2×C22⋊C4C2×Q8116yes—
453C2×C22⋊C4C2418yes—
454C2×C22⋊C4C2418yes—
455C2×C22⋊C4C2418yes—
456C2×C22⋊C4C2418yes—
457C2×C42—24no—
458C2×C42—24no—
459C2×C42—416no—
460C2×C42—44no—
461C2×C42—44no—
462C2×C42—42no—
463C2×C42—42no—
464C2×C42—44no—
465C2×C42—44no—
466C2×C42—44no—
467C2×C42—44no—
468C2×C42C2414yes—
469C2×C42C2414yes—
470C2×C42C2418yes—
471C2×C42C2418yes—
472C2×C42C2418yes—
473C2×C42C2418yes—
474C2×C42C2418yes—
475C2×C42C2418yes—
476C2×C42C2414yes—
477C2×C42C2414yes—
478#95C2418yes—
479#95C2418yes—
480#95C2418yes—
481#95C2418yes—
482#95C2418yes—
483#95C2418yes—
484#95C2418yes—
485#95C2418yes—
486#95C2418yes—
487#95C2418yes—
488#95C2418yes—
489#95C2418yes—
490#95C2418yes—
491#95C2418yes—
492#95C2418yes—
493#95C2418yes—
494#95C2418yes—
495#95C2418yes—
496#95C2418yes—
497#95C2418yes—
498#95C2418yes—
499#95C2418yes—
500#95C2418yes—
501#95C2418yes—
502#95C2418yes—
503#95C2418yes—
504#95C2418yes—
505#95C2418yes—
506#95C2418yes—
507C24—22no—
508C24—22no—
509C24—22no—
510C24—22no—
511C24C22×Q814yes—
512C24C22×Q814yes—
513C24H(5,𝔽2)14yes—
514C24C2512yes—
515C24C2511yescharacteristic
516C2×Q8—216no—
517C2×Q8—44no—
518C2×Q8—416no—
519C2×Q8—44no—
520C2×Q8—48no—
521C2×Q8—48no—
522C2×Q8—48no—
523C2×Q8—48no—
524C2×Q8—48no—
525C2×Q8—48no—
526C2×Q8—48no—
527C2×Q8—48no—
528C2×Q8—816no—
529C2×Q8—816no—
530C2×Q8—816no—
531C2×Q8C22×Q8116yes—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—22no—
539C22×C4—24no—
540C22×C4—22no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—22no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—28no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—22no—
571C22×C4—24no—
572C22×C4—24no—
573C22×C4—24no—
574C22×C4—24no—
575C22×C4—24no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—28no—
579C22×C4—28no—
580C22×C4—28no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—416no—
585C22×C4—416no—
586C22×C4—416no—
587C22×C4—416no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—416no—
599C22×C4—88no—
600C22×C4—88no—
601C22×C4C22×Q818yes—
602C22×C4C22×Q818yes—
603C22×C4C22×Q818yes—
604C22×C4C22×Q814yes—
605C22×C4C22×Q818yes—
606C22×C4C22×Q814yes—
607C22×C4C22×Q814yes—
608C22×C4C22×Q814yes—
609C22×C4C22×Q8116yes—
610C22×C4C22×Q8116yes—
611C22×C4C22×Q8116yes—
612C22×C4C22×Q8116yes—
613C22×C4H(5,𝔽2)14yes—
614C22×C4C2514yes—
615C22×C4C2514yes—
616C22×C4C2514yes—
617C22×C4C2514yes—
618C22×C4C2514yes—
619C22×C4C2512yes—
620C22×C4C2514yes—
621C22×C4C2514yes—
622C22×C4C2514yes—
623C22×C4C2514yes—
624C22×C4C2512yes—
625C22×C4C2512yes—
626C22×C4C2514yes—
627C22×C4C2514yes—
628C22×C4C2512yes—
629C22×C4C2512yes—
630C22×C4C2514yes—
631C22×C4C2512yes—
632C4⋊C4—216no—
633C4⋊C4—216no—
634C4⋊C4—48no—
635C4⋊C4—48no—
636C4⋊C4—48no—
637C4⋊C4—48no—
638C4⋊C4—48no—
639C4⋊C4—48no—
640C4⋊C4—48no—
641C4⋊C4—48no—
642C4⋊C4—48no—
643C4⋊C4—44no—
644C4⋊C4—44no—
645C4⋊C4—44no—
646C4⋊C4—44no—
647C4⋊C4—48no—
648C4⋊C4—48no—
649C4⋊C4—48no—
650C4⋊C4—48no—
651C4⋊C4—48no—
652C4⋊C4—48no—
653C4⋊C4—48no—
654C4⋊C4—48no—
655C4⋊C4—48no—
656C4⋊C4—44no—
657C4⋊C4—48no—
658C4⋊C4—44no—
659C4⋊C4—48no—
660C4⋊C4—48no—
661C4⋊C4C22×Q8132yes—
662C4⋊C4C22×Q8132yes—
663C4⋊C4C22×Q8116yes—
664C4⋊C4C22×Q8132yes—
665C22⋊C4—216no—
666C22⋊C4—216no—
667C22⋊C4—216no—
668C22⋊C4C22×Q8132yes—
669C42—28no—
670C42—28no—
671C42—44no—
672C42—44no—
673C42—48no—
674C42—48no—
675C42—48no—
676C42—48no—
677C42—48no—
678C42—48no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—28no—
684C23—28no—
685C23—28no—
686C23—28no—
687C23—28no—
688C23—28no—
689C23Q82116yes—
690C23C23×Q814yes—
691C23C23×Q814yes—
692C23C23×Q812yes—
693C23C23×Q812yes—
694C23C2×H(5,𝔽2)14yes—
695C23C2×H(5,𝔽2)12yes—
696C23C2×H(5,𝔽2)12yes—
697C23#58512yes—
698C23#58512yes—
699C23#58512yes—
700C23C2611yescharacteristic
701Q8—416no—
702Q8—816no—
703Q8—816no—
704Q8—816no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—216no—
724C2×C4—28no—
725C2×C4—28no—
726C2×C4—28no—
727C2×C4—216no—
728C2×C4—28no—
729C2×C4—216no—
730C2×C4—216no—
731C2×C4—28no—
732C2×C4—22no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—22no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—416no—
760C2×C4—416no—
761C2×C4—416no—
762C2×C4—416no—
763C2×C4—416no—
764C2×C4—44no—
765C2×C4—48no—
766C2×C4—48no—
767C2×C4—48no—
768C2×C4—48no—
769C2×C4—48no—
770C2×C4—48no—
771C2×C4—48no—
772C2×C4—48no—
773C2×C4—88no—
774C2×C4—88no—
775C2×C4C23×Q818yes—
776C2×C4C23×Q818yes—
777C2×C4C23×Q814yes—
778C2×C4C23×Q814yes—
779C2×C4C23×Q814yes—
780C2×C4C23×Q818yes—
781C2×C4C23×Q818yes—
782C2×C4C23×Q814yes—
783C2×C4C2×H(5,𝔽2)14yes—
784C22—24no—
785C22—24no—
786C22—24no—
787C22—24no—
788C22—24no—
789C22—232no—
790C22—24no—
791C22#345814yes—
792C22C2×Q8218yes—
793C22C2×Q8214yes—
794C22#350114yes—
795C22#350114yes—
796C22#350414yes—
797C22#353414yes—
798C22#356014yes—
799C22C24×Q811yescharacteristic
800C22C24×Q811yescharacteristic
801C22C22×H(5,𝔽2)11yescharacteristic
802C22C22×H(5,𝔽2)11yescharacteristic
803C22C2×#58511yescharacteristic
804C22C2×#58511yescharacteristic
805C22C2×#58511yescharacteristic
806C4—24no—
807C4—24no—
808C4—24no—
809C4—24no—
810C4—28no—
811C4—24no—
812C4—28no—
813C4—28no—
814C4—28no—
815C4—42no—
816C4—44no—
817C4—44no—
818C4—44no—
819C4—44no—
820C4—44no—
821C4—44no—
822C4—44no—
823C4—44no—
824C2—28no—
825C2#3962018yesdirect product factor
826C2C2×#345811yescharacteristic
827C2C22×Q8211yescharacteristic
828C2C2×#353411yescharacteristic
829C2C2×#356011yescharacteristic
830C2C2×#350111yescharacteristic
831C2C2×#350111yescharacteristic
832C2C2×#350411yescharacteristic
subgroupG/H
center, socleC24C25
commutator, Frattini, cosocleC23C26
prime radicalC25C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2806C2semidirect
2. C2×#2792C2semidirect
3. C2×#2792C2semidirect
4. C2×#2734C2semidirect
5. #39620C2direct (N × H)
7. C2×#2586C2semidirect
8. C2×#2586C2semidirect
11. C2×#2507C2semidirect
12. C2×#2451C2semidirect
32. #2806C22semidirect
33. #2792C22semidirect
34. #2792C22semidirect
35. #2734C22semidirect
38. #2586C22semidirect
39. #2586C22semidirect
42. #2507C22semidirect
43. #2451C22semidirect
145. C2×C22⋊Q8Q8semidirect
153. C22×C4⋊C4Q8semidirect
379. C22⋊Q8C2×Q8semidirect
415. C2×C4⋊C4C2×Q8semidirect
825. C2#39620direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#28062
C2×#27922
C2×#27342
#396202
C2×#28572
C2×#25862
C2×#25492
C2×#25072
C2×#24512
C2×#24402
C2×#26592
C2×#23452
C2×#23292
C2×C4×C22⋊Q82
C22×#3872