Finite Group Databasebeta

← C2×#46847 #7700780

Subgroups — C2×#46847 #7700780

Order 512.

5598 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2807C211yesmaximal, characteristic, complemented
2C2×#2791C212yesmaximal, complemented
3C2×#2742C212yesmaximal, complemented
4C2×#2734C212yesmaximal, complemented
5C2×#2692C212yesmaximal
6C2×#2677C211yesmaximal, characteristic, complemented
7C2×#2677C212yesmaximal, complemented
8#46847C2132yesmaximal, direct product factor
9C2×#2841C211yesmaximal, characteristic, complemented
10C2×#2567C212yesmaximal, complemented
11C2×#2542C211yesmaximal, characteristic
12C2×#2607C211yesmaximal, characteristic, complemented
13C2×#2588C212yesmaximal, complemented
14C2×#2564C211yesmaximal, characteristic
15C2×#2549C212yesmaximal, complemented
16C2×#2423C212yesmaximal, complemented
17C2×#2465C212yesmaximal, complemented
18C2×#2440C212yesmaximal, complemented
19C2×#2335C212yesmaximal
20C2×#2322C211yesmaximal, characteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×C4⋊Q8C2212yes—
23C22×C4⋊Q8C2212yes—
24C22×#123C2211yescharacteristic
25C22×C22⋊Q8C2212yes—
26C22×C22⋊Q8C2212yes—
27C22×C22⋊Q8C2211yescharacteristic
28C22×C22⋊Q8C2212yes—
29C22×C22⋊Q8C2212yes—
30C22×C4×Q8C2212yes—
31C22×C4×D4C2211yescharacteristic
32C23×C4⋊C4C2211yescharacteristic
33#2841C22116yescomplemented
34#2807C22116yescomplemented
35#2791C22132yescomplemented
36#2742C22132yescomplemented
37#2734C22132yescomplemented
38#2692C22132yes—
39#2677C22132yescomplemented
40#2677C22116yescomplemented
41#2607C22116yescomplemented
42#2588C22132yescomplemented
43#2567C22132yescomplemented
44#2564C22116yes—
45#2549C22132yescomplemented
46#2542C22116yes—
47#2465C22132yescomplemented
48#2440C22132yescomplemented
49#2423C22132yescomplemented
50C2×#400C2211yescharacteristic
51C2×#400C2212yes—
52C2×#400C2212yes—
53C2×#399C2211yescharacteristic
54C2×#399C2211yescharacteristic
55C2×#399C2211yescharacteristic
56C2×#399C2211yescharacteristic
57C2×#399C2211yescharacteristic
58C2×#399C2212yes—
59C2×#398C2212yes—
60C2×#398C2212yes—
61C2×#398C2212yes—
62C2×#398C2212yes—
63C2×#398C2212yes—
64C2×#398C2212yes—
65C2×#398C2212yes—
66C2×#396C2212yes—
67C2×#395C2212yes—
68C2×#395C2212yes—
69C2×#395C2211yescharacteristic
70C2×#395C2212yes—
71C2×#395C2212yes—
72C2×#395C2212yes—
73C2×#395C2212yes—
74C2×#395C2212yes—
75C2×#393C2211yescharacteristic
76C2×#393C2212yes—
77C2×#393C2212yes—
78#2335C22132yes—
79#2322C22116yes—
80C2×#391C2212yes—
81C2×#391C2212yes—
82C2×#391C2212yes—
83C2×#391C2212yes—
84C2×#390C2212yes—
85C2×#389C2212yes—
86C2×#389C2212yes—
87C2×#389C2212yes—
88C2×#389C2212yes—
89C2×#389C2212yes—
90C2×#389C2212yes—
91C2×#389C2212yes—
92C2×#388C2212yes—
93C2×#388C2212yes—
94C2×#388C2212yes—
95C2×#388C2212yes—
96C2×#388C2212yes—
97C2×#387C2212yes—
98C2×#387C2212yes—
99C2×#387C2212yes—
100C2×#387C2212yes—
101C2×#387C2212yes—
102C2×#387C2212yes—
103C2×#387C2212yes—
104C2×#387C2212yes—
105C2×#387C2212yes—
106C2×#387C2212yes—
107C2×#387C2212yes—
108C2×#386C2211yescharacteristic
109C2×#386C2212yes—
110C2×#385C2212yes—
111C2×#385C2212yes—
112C2×#385C2211yescharacteristic
113C2×#385C2212yes—
114C2×#385C2212yes—
115C2×#384C2212yes—
116C2×#384C2212yes—
117C2×#381C2211yescharacteristic
118C2×#380C2212yes—
119C2×#380C2212yes—
120C2×#380C2212yes—
121C2×C4×C4⋊C4C2211yescharacteristic
122C2×C4×C4⋊C4C2212yes—
123C2×C4×C22⋊C4C2212yes—
124C2×C4×C22⋊C4C2211yescharacteristic
125C2×C4×C22⋊C4C2212yes—
126C22×#95C2211yescharacteristic
127C23×Q8C2312yes—
128C23×Q8C2312yes—
129C23×Q8C2311yescharacteristic
130C23×Q8C2312yes—
131C23×D4C2311yescharacteristic
132C24×C4C2311yescharacteristic
133C24×C4C2311yescharacteristic
134C24×C4C2312yes—
135C24×C4C2311yescharacteristic
136C24×C4C2311yescharacteristic
137C2×C4⋊Q8—48no—
138C2×C4⋊Q8—44no—
139C2×C4⋊Q8—48no—
140C2×C4⋊Q8C23116yes—
141C2×C4⋊Q8C23116yes—
142C2×C4⋊Q8C2318yes—
143C2×#123Q8116yescomplemented
144C2×#123C2318yes—
145C2×C22⋊Q8—48no—
146C2×C22⋊Q8—48no—
147C2×C22⋊Q8—48no—
148C2×C22⋊Q8—48no—
149C2×C22⋊Q8—44no—
150C2×C22⋊Q8C2318yes—
151C2×C22⋊Q8C23116yes—
152C2×C22⋊Q8C23116yes—
153C2×C22⋊Q8C23116yes—
154C2×C22⋊Q8C23116yes—
155C2×C4×Q8—48no—
156C2×C4×Q8C23116yes—
157C2×C4×D4—44no—
158C2×C4×D4C2318yes—
159C22×C4⋊C4—44no—
160C22×C4⋊C4C2312yes—
161C22×C4⋊C4C2312yes—
162C22×C4⋊C4C2312yes—
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C2312yes—
165C22×C4⋊C4C2312yes—
166C22×C4⋊C4C2312yes—
167C22×C4⋊C4C2312yes—
168C22×C4⋊C4C2312yes—
169C22×C4⋊C4C2318yes—
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2312yes—
176C22×C4⋊C4C2312yes—
177C22×C4⋊C4C2312yes—
178C22×C4⋊C4C2312yes—
179C22×C4⋊C4C2312yes—
180C22×C4⋊C4C2312yes—
181C22×C4⋊C4C2312yes—
182C22×C4⋊C4C2311yescharacteristic
183C22×C4⋊C4C2312yes—
184C22×C4⋊C4C2312yes—
185C22×C4⋊C4C2311yescharacteristic
186C22×C4⋊C4C2311yescharacteristic
187C22×C4⋊C4C2312yes—
188C22×C4⋊C4C2312yes—
189C22×C4⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2311yescharacteristic
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2311yescharacteristic
203C22×C42C2311yescharacteristic
204C22×C42C2312yes—
205C22×C42C2312yes—
206C22×C42C2312yes—
207C22×C42C2312yes—
208C22×C42C2312yes—
209C22×C42C2312yes—
210#400C2318yes—
211#400C23116yes—
212#400C23116yes—
213#399C2318yes—
214#399C2318yes—
215#399C2318yes—
216#399C23116yes—
217#399C2318yes—
218#399C2318yes—
219#398C23116yes—
220#398C23116yes—
221#398C23116yes—
222#398C23116yes—
223#398C23116yes—
224#398C23116yes—
225#398C23116yes—
226#396C23116yes—
227#395C2318yes—
228#395C23116yes—
229#395C23116yes—
230#395C23116yes—
231#395C23116yes—
232#395C23116yes—
233#395C23116yes—
234#395C23116yes—
235#393C2318yes—
236#393C23116yes—
237#393C23116yes—
238#391C23116yes—
239#391C23116yes—
240#391C23116yes—
241#391C23116yes—
242#390C23116yes—
243#389C23116yes—
244#389C23116yes—
245#389C23116yes—
246#389C23116yes—
247#389C23116yes—
248#389C23116yes—
249#389C23116yes—
250#388C23116yes—
251#388C23116yes—
252#388C23116yes—
253#388C23116yes—
254#388C23116yes—
255#387C23116yes—
256#387C23116yes—
257#387C23116yes—
258#387C23116yes—
259#387C23116yes—
260#387C23116yes—
261#387C23116yes—
262#387C23116yes—
263#387C23116yes—
264#387C23116yes—
265#387C23116yes—
266#386C23116yes—
267#386C2318yes—
268#385C23116yes—
269#385C23116yes—
270#385C2318yes—
271#385C23116yes—
272#385C23116yes—
273#384C23116yes—
274#384C23116yes—
275#381C2318yes—
276#380C23116yes—
277#380C23116yes—
278#380C23116yes—
279C4×C4⋊C4C23116yes—
280C4×C4⋊C4C2318yes—
281C4×C22⋊C4C2318yes—
282C4×C22⋊C4C23116yes—
283C4×C22⋊C4C23116yes—
284C2×#95C2318yes—
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2311yescharacteristic
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×#95C2311yescharacteristic
304C2×#95C2312yes—
305C2×#95C2312yes—
306C2×#95C2312yes—
307C2×#95C2312yes—
308C2×#95C2312yes—
309C2×#95C2312yes—
310C2×#95C2312yes—
311C2×#95C2311yescharacteristic
312C2×#95C2311yescharacteristic
313C25C2411yescharacteristic
314C25C2411yescharacteristic
315C22×Q8—28no—
316C22×Q8—28no—
317C22×Q8—28no—
318C22×Q8—44no—
319C22×Q8—44no—
320C22×Q8—44no—
321C22×Q8—44no—
322C22×Q8—42no—
323C22×Q8—44no—
324C22×Q8—44no—
325C22×Q8—44no—
326C22×Q8C2418yes—
327C22×Q8C2418yes—
328C22×Q8C2414yes—
329C22×Q8C2418yes—
330C22×D4—42no—
331C22×D4—42no—
332C22×D4C2×Q818yes—
333C22×D4C2414yes—
334C23×C4—24no—
335C23×C4—24no—
336C23×C4—28no—
337C23×C4—42no—
338C23×C4—42no—
339C23×C4—42no—
340C23×C4—44no—
341C23×C4—44no—
342C23×C4—44no—
343C23×C4—44no—
344C23×C4—44no—
345C23×C4C2×Q818yes—
346C23×C4C2412yes—
347C23×C4C2412yes—
348C23×C4C2412yes—
349C23×C4C2412yes—
350C23×C4C2411yescharacteristic
351C23×C4C2412yes—
352C23×C4C2412yes—
353C23×C4C2411yescharacteristic
354C23×C4C2412yes—
355C23×C4C2411yescharacteristic
356C23×C4C2412yes—
357C23×C4C2412yes—
358C23×C4C2412yes—
359C23×C4C2411yescharacteristic
360C23×C4C2412yes—
361C23×C4C2411yescharacteristic
362C23×C4C2412yes—
363C23×C4C2414yes—
364C23×C4C2414yes—
365C23×C4C2418yes—
366C23×C4C2414yes—
367C23×C4C2414yes—
368C4⋊Q8—432no—
369C4⋊Q8—416no—
370C4⋊Q8—432no—
371#123C2×Q8164yescomplemented
372C22⋊Q8—432no—
373C22⋊Q8—432no—
374C22⋊Q8—432no—
375C22⋊Q8—432no—
376C22⋊Q8—416no—
377C4×Q8—432no—
378C4×D4—416no—
379C2×C4⋊C4—28no—
380C2×C4⋊C4—28no—
381C2×C4⋊C4—28no—
382C2×C4⋊C4—28no—
383C2×C4⋊C4—28no—
384C2×C4⋊C4—28no—
385C2×C4⋊C4—28no—
386C2×C4⋊C4—28no—
387C2×C4⋊C4—28no—
388C2×C4⋊C4—416no—
389C2×C4⋊C4—44no—
390C2×C4⋊C4—44no—
391C2×C4⋊C4—44no—
392C2×C4⋊C4—42no—
393C2×C4⋊C4—44no—
394C2×C4⋊C4—44no—
395C2×C4⋊C4—44no—
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—42no—
406C2×C4⋊C4—42no—
407C2×C4⋊C4—44no—
408C2×C4⋊C4C2×Q8116yes—
409C2×C4⋊C4C2418yes—
410C2×C4⋊C4C2418yes—
411C2×C4⋊C4C2418yes—
412C2×C4⋊C4C2418yes—
413C2×C4⋊C4C2418yes—
414C2×C4⋊C4C2418yes—
415C2×C4⋊C4C2418yes—
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⋊C4C2414yes—
427C2×C4⋊C4C2418yes—
428C2×C4⋊C4C2418yes—
429C2×C4⋊C4C2418yes—
430C2×C4⋊C4C2418yes—
431C2×C4⋊C4C2418yes—
432C2×C4⋊C4C2414yes—
433C2×C4⋊C4C2418yes—
434C2×C4⋊C4C2414yes—
435C2×C4⋊C4C2418yes—
436C2×C4⋊C4C2418yes—
437C2×C4⋊C4C2418yes—
438C2×C22⋊C4—28no—
439C2×C22⋊C4—28no—
440C2×C22⋊C4—28no—
441C2×C22⋊C4—42no—
442C2×C22⋊C4—42no—
443C2×C22⋊C4—42no—
444C2×C22⋊C4—44no—
445C2×C22⋊C4—44no—
446C2×C22⋊C4—44no—
447C2×C22⋊C4—44no—
448C2×C22⋊C4—44no—
449C2×C22⋊C4C2×Q818yes—
450C2×C22⋊C4C2×Q8116yes—
451C2×C22⋊C4C2418yes—
452C2×C22⋊C4C2418yes—
453C2×C22⋊C4C2418yes—
454C2×C22⋊C4C2414yes—
455C2×C22⋊C4C2414yes—
456C2×C22⋊C4C2418yes—
457C2×C22⋊C4C2418yes—
458C2×C22⋊C4C2418yes—
459C2×C22⋊C4C2418yes—
460C2×C22⋊C4C2418yes—
461C2×C22⋊C4C2414yes—
462C2×C22⋊C4C2418yes—
463C2×C22⋊C4C2414yes—
464C2×C42—24no—
465C2×C42—28no—
466C2×C42—44no—
467C2×C42—44no—
468C2×C42—44no—
469C2×C42—44no—
470C2×C42—44no—
471C2×C42C2414yes—
472C2×C42C2418yes—
473C2×C42C2418yes—
474C2×C42C2418yes—
475C2×C42C2418yes—
476C2×C42C2418yes—
477C2×C42C2418yes—
478#95C2418yes—
479#95C2414yes—
480#95C2414yes—
481#95C2418yes—
482#95C2418yes—
483#95C2418yes—
484#95C2418yes—
485#95C2418yes—
486#95C2418yes—
487#95C2418yes—
488#95C2414yes—
489#95C2414yes—
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—
506C24—24no—
507C24—24no—
508C24—22no—
509C24—22no—
510C24—24no—
511C24—24no—
512C24—22no—
513C24—22no—
514C24C22×Q814yes—
515C24C22×Q814yes—
516C24C2512yes—
517C24C2512yes—
518C24C2511yescharacteristic
519C2×Q8—216no—
520C2×Q8—216no—
521C2×Q8—216no—
522C2×Q8—48no—
523C2×Q8—48no—
524C2×Q8—48no—
525C2×Q8—48no—
526C2×Q8—44no—
527C2×Q8—48no—
528C2×Q8—48no—
529C2×Q8—48no—
530C2×Q8—432no—
531C2×Q8—816no—
532C2×Q8—816no—
533C2×Q8—88no—
534C2×D4—44no—
535C2×D4—416no—
536C2×D4—44no—
537C2×D4C22×Q8116yes—
538C22×C4—24no—
539C22×C4—22no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—22no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—22no—
550C22×C4—24no—
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—24no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—24no—
573C22×C4—24no—
574C22×C4—24no—
575C22×C4—24no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—28no—
580C22×C4—28no—
581C22×C4—216no—
582C22×C4—44no—
583C22×C4—416no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—48no—
591C22×C4—816no—
592C22×C4—88no—
593C22×C4—88no—
594C22×C4—88no—
595C22×C4C22×Q818yes—
596C22×C4C22×Q818yes—
597C22×C4C22×Q814yes—
598C22×C4C22×Q8116yes—
599C22×C4H(5,𝔽2)18yes—
600C22×C4H(5,𝔽2)14yes—
601C22×C42−1+418yes—
602C22×C4C2512yes—
603C22×C4C2514yes—
604C22×C4C2514yes—
605C22×C4C2514yes—
606C22×C4C2514yes—
607C22×C4C2514yes—
608C22×C4C2514yes—
609C22×C4C2514yes—
610C22×C4C2512yes—
611C22×C4C2512yes—
612C22×C4C2514yes—
613C22×C4C2514yes—
614C22×C4C2512yes—
615C22×C4C2514yes—
616C22×C4C2514yes—
617C22×C4C2512yes—
618C22×C4C2514yes—
619C4⋊C4—216no—
620C4⋊C4—216no—
621C4⋊C4—216no—
622C4⋊C4—216no—
623C4⋊C4—216no—
624C4⋊C4—216no—
625C4⋊C4—216no—
626C4⋊C4—216no—
627C4⋊C4—216no—
628C4⋊C4—48no—
629C4⋊C4—48no—
630C4⋊C4—48no—
631C4⋊C4—44no—
632C4⋊C4—48no—
633C4⋊C4—48no—
634C4⋊C4—48no—
635C4⋊C4—44no—
636C4⋊C4—48no—
637C4⋊C4—48no—
638C4⋊C4—48no—
639C4⋊C4—48no—
640C4⋊C4—48no—
641C4⋊C4—48no—
642C4⋊C4—48no—
643C4⋊C4—48no—
644C4⋊C4—44no—
645C4⋊C4—44no—
646C4⋊C4—48no—
647C4⋊C4C22×Q8132yes—
648C22⋊C4—216no—
649C22⋊C4—216no—
650C22⋊C4—216no—
651C22⋊C4—44no—
652C22⋊C4—44no—
653C22⋊C4—44no—
654C22⋊C4—48no—
655C22⋊C4—48no—
656C22⋊C4—48no—
657C22⋊C4—48no—
658C22⋊C4—48no—
659C22⋊C4C22×Q8116yes—
660C22⋊C4C22×Q8132yes—
661C42—28no—
662C42—216no—
663C42—48no—
664C42—48no—
665C42—48no—
666C42—48no—
667C42—48no—
668C23—24no—
669C23—24no—
670C23—22no—
671C23—22no—
672C23—24no—
673C23—24no—
674C23—22no—
675C23—22no—
676C23—28no—
677C23—28no—
678C23—216no—
679C23—216no—
680C23—48no—
681C23—48no—
682C23—44no—
683C23—44no—
684C23—44no—
685C23—44no—
686C23C23×Q814yes—
687C23C23×Q814yes—
688C23C23×Q812yes—
689C23C2×H(5,𝔽2)12yes—
690C23C2×H(5,𝔽2)14yes—
691C23C2×2−1+414yes—
692C23#58512yes—
693C23C2611yescharacteristic
694Q8—432no—
695Q8—816no—
696Q8—816no—
697Q8—88no—
698D4—416no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—216no—
711C2×C4—28no—
712C2×C4—216no—
713C2×C4—216no—
714C2×C4—216no—
715C2×C4—28no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—22no—
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—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—416no—
747C2×C4—48no—
748C2×C4—48no—
749C2×C4—48no—
750C2×C4—44no—
751C2×C4—48no—
752C2×C4—44no—
753C2×C4—48no—
754C2×C4—48no—
755C2×C4—48no—
756C2×C4—44no—
757C2×C4—48no—
758C2×C4—816no—
759C2×C4—88no—
760C2×C4—88no—
761C2×C4—88no—
762C2×C4C23×Q818yes—
763C2×C4C23×Q818yes—
764C2×C4C23×Q814yes—
765C2×C4C2×H(5,𝔽2)18yes—
766C2×C4C2×H(5,𝔽2)14yes—
767C2×C4C2×2−1+418yes—
768C22—24no—
769C22—24no—
770C22—28no—
771C22—28no—
772C22—44no—
773C22—44no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—416no—
779C22—416no—
780C22#350114yes—
781C22#350318yes—
782C22#353518yes—
783C22#354314yes—
784C22#355014yes—
785C22C24×Q811yescharacteristic
786C22C22×H(5,𝔽2)12yes—
787C22C22×H(5,𝔽2)11yescharacteristic
788C22C22×2−1+412yes—
789C22C2×#58511yescharacteristic
790C4—28no—
791C4—28no—
792C4—24no—
793C4—28no—
794C4—24no—
795C4—28no—
796C4—44no—
797C4—44no—
798C4—44no—
799C4—42no—
800C4—44no—
801C4—42no—
802C4—44no—
803C4—44no—
804C4—44no—
805C4—42no—
806C4—44no—
807C2—44no—
808C2—44no—
809C2#4684718yesdirect product factor
810C2C2×#353512yes—
811C2C2×#354311yescharacteristic
812C2C2×#355011yescharacteristic
813C2C2×#350111yescharacteristic
814C2C2×#350312yes—
subgroupG/H
center, socleC24C25
commutator, Frattini, cosocleC23C26
prime radicalC23×D4C23
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×#2807C2semidirect
2. C2×#2791C2semidirect
3. C2×#2742C2semidirect
4. C2×#2734C2semidirect
6. C2×#2677C2semidirect
7. C2×#2677C2semidirect
8. #46847C2direct (N × H)
9. C2×#2841C2semidirect
10. C2×#2567C2semidirect
12. C2×#2607C2semidirect
13. C2×#2588C2semidirect
15. C2×#2549C2semidirect
16. C2×#2423C2semidirect
17. C2×#2465C2semidirect
18. C2×#2440C2semidirect
33. #2841C22semidirect
34. #2807C22semidirect
35. #2791C22semidirect
36. #2742C22semidirect
37. #2734C22semidirect
39. #2677C22semidirect
40. #2677C22semidirect
41. #2607C22semidirect
42. #2588C22semidirect
43. #2567C22semidirect
45. #2549C22semidirect
47. #2465C22semidirect
48. #2440C22semidirect
49. #2423C22semidirect
143. C2×#123Q8semidirect
371. #123C2×Q8semidirect
809. C2#46847direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#28072
C2×#27912
C2×#27422
C2×#27342
C2×#26922
C2×#26772
#468472
C2×#28412
C2×#25672
C2×#25422
C2×#26072
C2×#25882
C2×#25642
C2×#25492
C2×#24232
C2×#24652
C2×#24402
C2×#23352
C2×#23222