Finite Group Databasebeta

← C2×#34596 #7627751

Subgroups — C2×#34596 #7627751

Order 512.

5928 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34596C2132yesmaximal, direct product factor
2C2×#2650C212yesmaximal, complemented
3C2×#2655C212yesmaximal, complemented
4C2×#2665C212yesmaximal, complemented
5C2×#2663C212yesmaximal, complemented
6C2×#2653C212yesmaximal, complemented
7C2×#2652C212yesmaximal, complemented
8C2×#2638C212yesmaximal, complemented
9C2×#2630C212yesmaximal
10C2×#2401C212yesmaximal, complemented
11C2×#2399C211yesmaximal, characteristic, complemented
12C2×#2398C212yesmaximal, complemented
13C2×#2398C211yesmaximal, characteristic, complemented
14C2×#2396C211yesmaximal, characteristic, complemented
15C2×#2392C211yesmaximal, characteristic
16C2×C4×C22⋊Q8C212yesmaximal, complemented
17C2×C4×#123C212yesmaximal, complemented
18C2×#2298C211yesmaximal, characteristic, complemented
19C2×#2295C211yesmaximal, characteristic, complemented
20C2×C42×D4C211yesmaximal, characteristic, complemented
21C22×#123C2212yes—
22C22×C22⋊Q8C2212yes—
23C22×C4×Q8C2211yescharacteristic
24C22×C4×Q8C2212yes—
25C22×C4×D4C2212yes—
26C22×C4×D4C2211yescharacteristic
27C22×C4×D4C2212yes—
28C22×#117C2211yescharacteristic
29C23×C42C2212yes—
30#2665C22132yescomplemented
31#2663C22132yescomplemented
32#2655C22132yescomplemented
33#2653C22132yescomplemented
34#2652C22132yescomplemented
35#2650C22132yescomplemented
36#2638C22132yescomplemented
37#2630C22132yes—
38#2401C22132yescomplemented
39C2×#401C2212yes—
40#2399C22116yescomplemented
41#2398C22116yescomplemented
42#2398C22132yescomplemented
43#2396C22116yescomplemented
44C2×#400C2211yescharacteristic
45C2×#400C2212yes—
46C2×#400C2212yes—
47C2×#400C2212yes—
48C2×#400C2212yes—
49C2×#400C2212yes—
50C2×#400C2212yes—
51C2×#399C2211yescharacteristic
52#2392C22116yes—
53C2×#398C2212yes—
54C2×#398C2212yes—
55C2×#398C2211yescharacteristic
56C2×#398C2212yes—
57C2×#397C2212yes—
58C2×#397C2212yes—
59C2×#397C2212yes—
60C2×#397C2212yes—
61C2×#397C2212yes—
62C2×#397C2212yes—
63C2×#397C2211yescharacteristic
64C2×#396C2212yes—
65C2×#396C2212yes—
66C2×#396C2212yes—
67C2×#395C2212yes—
68C2×#395C2212yes—
69C2×#395C2211yescharacteristic
70C2×#394C2211yescharacteristic
71C2×#394C2212yes—
72C2×#394C2212yes—
73C2×#394C2212yes—
74C2×#394C2212yes—
75C2×#393C2212yes—
76C2×#393C2211yescharacteristic
77C2×#393C2212yes—
78C2×#393C2212yes—
79C2×#392C2211yescharacteristic
80C4×C22⋊Q8C22132yescomplemented
81C4×#123C22132yescomplemented
82#2298C22116yescomplemented
83#2295C22116yescomplemented
84C2×#391C2212yes—
85C2×#391C2212yes—
86C2×#389C2212yes—
87C2×#389C2212yes—
88C2×#388C2212yes—
89C2×#388C2212yes—
90C2×#388C2212yes—
91C2×#388C2212yes—
92C2×#387C2212yes—
93C2×#387C2212yes—
94C2×#387C2212yes—
95C2×#387C2212yes—
96C2×#387C2212yes—
97C2×#387C2212yes—
98C2×#387C2212yes—
99C2×#387C2212yes—
100C2×#386C2212yes—
101C2×#385C2212yes—
102C2×#385C2212yes—
103C2×#385C2212yes—
104C2×#381C2212yes—
105C2×#380C2212yes—
106C42×D4C22116yescomplemented
107C2×C4×C4⋊C4C2212yes—
108C2×C4×C4⋊C4C2211yescharacteristic
109C2×C4×C4⋊C4C2211yescharacteristic
110C2×C4×C4⋊C4C2212yes—
111C2×C4×C4⋊C4C2211yescharacteristic
112C2×C4×C4⋊C4C2211yescharacteristic
113C2×C4×C4⋊C4C2212yes—
114C2×C4×C4⋊C4C2212yes—
115C2×C4×C22⋊C4C2212yes—
116C2×C4×C22⋊C4C2212yes—
117C2×C4×C22⋊C4C2212yes—
118C2×C4×C22⋊C4C2211yescharacteristic
119C2×C4×C22⋊C4C2211yescharacteristic
120C2×C4×C22⋊C4C2212yes—
121C2×C4×C22⋊C4C2212yes—
122C2×C4×C22⋊C4C2212yes—
123C2×C4×C22⋊C4C2212yes—
124C2×#376C2212yes—
125C2×#376C2211yescharacteristic
126C2×C43C2211yescharacteristic
127C23×Q8C2311yescharacteristic
128C23×Q8C2312yes—
129C23×D4C2311yescharacteristic
130C23×D4C2312yes—
131C24×C4C2312yes—
132C24×C4C2311yescharacteristic
133C24×C4C2312yes—
134C24×C4C2312yes—
135C2×#123—216no—
136C2×#123C23116yes—
137C2×C22⋊Q8—216no—
138C2×C22⋊Q8C23116yes—
139C2×C4×Q8—28no—
140C2×C4×Q8—48no—
141C2×C4×Q8C2318yes—
142C2×C4×Q8C23116yes—
143C2×C4×D4—216no—
144C2×C4×D4—28no—
145C2×C4×D4—48no—
146C2×C4×D4C23116yes—
147C2×C4×D4C2318yes—
148C2×C4×D4C23116yes—
149C2×#117—28no—
150C2×#117C2318yes—
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2311yescharacteristic
153C22×C4⋊C4C2311yescharacteristic
154C22×C4⋊C4C2312yes—
155C22×C4⋊C4C2312yes—
156C22×C4⋊C4C2311yescharacteristic
157C22×C4⋊C4C2312yes—
158C22×C4⋊C4C2311yescharacteristic
159C22×C4⋊C4C2312yes—
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⋊C4C2312yes—
170C22×C22⋊C4C2311yescharacteristic
171C22×C22⋊C4C2311yescharacteristic
172C22×C22⋊C4C2312yes—
173C22×C22⋊C4C2312yes—
174C22×C22⋊C4C2312yes—
175C22×C22⋊C4C2312yes—
176C22×C22⋊C4C2312yes—
177C22×C22⋊C4C2312yes—
178C22×C22⋊C4C2312yes—
179C22×C22⋊C4C2312yes—
180C22×C22⋊C4C2312yes—
181C22×C22⋊C4C2312yes—
182C22×C22⋊C4C2312yes—
183C22×C22⋊C4C2312yes—
184C22×C22⋊C4C2312yes—
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2312yes—
187C22×C42—48no—
188C22×C42C2312yes—
189C22×C42C2311yescharacteristic
190C22×C42C2312yes—
191C22×C42C2311yescharacteristic
192C22×C42C2312yes—
193C22×C42C2311yescharacteristic
194C22×C42C2312yes—
195C22×C42C2311yescharacteristic
196C22×C42C2311yescharacteristic
197C22×C42C2312yes—
198C22×C42C2312yes—
199C22×C42C23116yes—
200C22×C42C2312yes—
201C22×C42C2311yescharacteristic
202#401C23116yes—
203#400C23116yes—
204#400C23116yes—
205#400C23116yes—
206#400C2318yes—
207#400C23116yes—
208#400C23116yes—
209#400C23116yes—
210#399C2318yes—
211#398C23116yes—
212#398C23116yes—
213#398C2318yes—
214#398C23116yes—
215#397C23116yes—
216#397C23116yes—
217#397C23116yes—
218#397C23116yes—
219#397C2318yes—
220#397C23116yes—
221#397C23116yes—
222#396C23116yes—
223#396C23116yes—
224#396C23116yes—
225#395C23116yes—
226#395C2318yes—
227#395C23116yes—
228#394C23116yes—
229#394C23116yes—
230#394C23116yes—
231#394C2318yes—
232#394C23116yes—
233#393C23116yes—
234#393C23116yes—
235#393C2318yes—
236#393C23116yes—
237#392C2318yes—
238#391C23116yes—
239#391C23116yes—
240#389C23116yes—
241#389C23116yes—
242#388C23116yes—
243#388C23116yes—
244#388C23116yes—
245#388C23116yes—
246#387C23116yes—
247#387C23116yes—
248#387C23116yes—
249#387C23116yes—
250#387C23116yes—
251#387C23116yes—
252#387C23116yes—
253#387C23116yes—
254#386C23116yes—
255#385C23116yes—
256#385C23116yes—
257#385C23116yes—
258#381C23116yes—
259#380C23116yes—
260C4×C4⋊C4C2318yes—
261C4×C4⋊C4C23116yes—
262C4×C4⋊C4C2318yes—
263C4×C4⋊C4C23116yes—
264C4×C4⋊C4C23116yes—
265C4×C4⋊C4C2318yes—
266C4×C4⋊C4C23116yes—
267C4×C4⋊C4C2318yes—
268C4×C22⋊C4C23116yes—
269C4×C22⋊C4C23116yes—
270C4×C22⋊C4C23116yes—
271C4×C22⋊C4C2318yes—
272C4×C22⋊C4C23116yes—
273C4×C22⋊C4C23116yes—
274C4×C22⋊C4C23116yes—
275C4×C22⋊C4C23116yes—
276C4×C22⋊C4C2318yes—
277#376C2318yes—
278#376C23116yes—
279C2×#95C2311yescharacteristic
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2311yescharacteristic
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2311yescharacteristic
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2311yescharacteristic
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2312yes—
305C2×#95C2312yes—
306C2×#95C2312yes—
307C2×#95C2312yes—
308C2×#95C2312yes—
309C43C2318yes—
310C25C2411yescharacteristic
311C25C2412yes—
312C22×Q8—24no—
313C22×Q8—28no—
314C22×Q8—44no—
315C22×Q8—44no—
316C22×Q8—44no—
317C22×Q8C2418yes—
318C22×Q8C2414yes—
319C22×D4—28no—
320C22×D4—28no—
321C22×D4—24no—
322C22×D4—44no—
323C22×D4—44no—
324C22×D4C2414yes—
325C22×D4C2418yes—
326C23×C4—24no—
327C23×C4—28no—
328C23×C4—28no—
329C23×C4—24no—
330C23×C4—28no—
331C23×C4—28no—
332C23×C4—24no—
333C23×C4—44no—
334C23×C4—44no—
335C23×C4—44no—
336C23×C4—44no—
337C23×C4#41116yes—
338C23×C4C2411yescharacteristic
339C23×C4C2411yescharacteristic
340C23×C4C2412yes—
341C23×C4C2412yes—
342C23×C4C2412yes—
343C23×C4C2412yes—
344C23×C4C2412yes—
345C23×C4C2412yes—
346C23×C4C2411yescharacteristic
347C23×C4C2412yes—
348C23×C4C2412yes—
349C23×C4C2412yes—
350C23×C4C2414yes—
351C23×C4C2418yes—
352C23×C4C2411yescharacteristic
353C23×C4C2412yes—
354C23×C4C2411yescharacteristic
355C23×C4C2412yes—
356C23×C4C2418yes—
357C23×C4C2418yes—
358C23×C4C2411yescharacteristic
359#123—264no—
360C22⋊Q8—264no—
361C4×Q8—232no—
362C4×Q8—432no—
363C4×D4—264no—
364C4×D4—232no—
365C4×D4—432no—
366#117—232no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—28no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—28no—
373C2×C4⋊C4—28no—
374C2×C4⋊C4—28no—
375C2×C4⋊C4—28no—
376C2×C4⋊C4—28no—
377C2×C4⋊C4—28no—
378C2×C4⋊C4—44no—
379C2×C4⋊C4—44no—
380C2×C4⋊C4—44no—
381C2×C4⋊C4—44no—
382C2×C4⋊C4—44no—
383C2×C4⋊C4—44no—
384C2×C4⋊C4—44no—
385C2×C4⋊C4—44no—
386C2×C4⋊C4C2414yes—
387C2×C4⋊C4C2414yes—
388C2×C4⋊C4C2418yes—
389C2×C4⋊C4C2414yes—
390C2×C4⋊C4C2418yes—
391C2×C4⋊C4C2414yes—
392C2×C4⋊C4C2418yes—
393C2×C4⋊C4C2418yes—
394C2×C4⋊C4C2418yes—
395C2×C4⋊C4C2418yes—
396C2×C4⋊C4C2418yes—
397C2×C4⋊C4C2418yes—
398C2×C4⋊C4C2418yes—
399C2×C4⋊C4C2418yes—
400C2×C4⋊C4C2418yes—
401C2×C4⋊C4C2418yes—
402C2×C4⋊C4C2418yes—
403C2×C4⋊C4C2418yes—
404C2×C4⋊C4C2418yes—
405C2×C22⋊C4—28no—
406C2×C22⋊C4—28no—
407C2×C22⋊C4—28no—
408C2×C22⋊C4—28no—
409C2×C22⋊C4—24no—
410C2×C22⋊C4—24no—
411C2×C22⋊C4—28no—
412C2×C22⋊C4—28no—
413C2×C22⋊C4—28no—
414C2×C22⋊C4—28no—
415C2×C22⋊C4—44no—
416C2×C22⋊C4—44no—
417C2×C22⋊C4—44no—
418C2×C22⋊C4—44no—
419C2×C22⋊C4—44no—
420C2×C22⋊C4—44no—
421C2×C22⋊C4—44no—
422C2×C22⋊C4C2414yes—
423C2×C22⋊C4C2414yes—
424C2×C22⋊C4C2418yes—
425C2×C22⋊C4C2418yes—
426C2×C22⋊C4C2418yes—
427C2×C22⋊C4C2418yes—
428C2×C22⋊C4C2418yes—
429C2×C22⋊C4C2418yes—
430C2×C22⋊C4C2418yes—
431C2×C22⋊C4C2418yes—
432C2×C22⋊C4C2418yes—
433C2×C22⋊C4C2418yes—
434C2×C22⋊C4C2418yes—
435C2×C22⋊C4C2418yes—
436C2×C22⋊C4C2418yes—
437C2×C22⋊C4C2418yes—
438C2×C22⋊C4C2418yes—
439C2×C42—24no—
440C2×C42—28no—
441C2×C42—28no—
442C2×C42—28no—
443C2×C42—24no—
444C2×C42—28no—
445C2×C42—24no—
446C2×C42—24no—
447C2×C42—24no—
448C2×C42—432no—
449C2×C42—44no—
450C2×C42—44no—
451C2×C42—44no—
452C2×C42#4118yes—
453C2×C42C2414yes—
454C2×C42C2418yes—
455C2×C42C2418yes—
456C2×C42C2414yes—
457C2×C42C2418yes—
458C2×C42C2418yes—
459C2×C42C2414yes—
460C2×C42C2414yes—
461C2×C42C2414yes—
462C2×C42C2418yes—
463C2×C42C2418yes—
464C2×C42C2418yes—
465C2×C42C2414yes—
466#95C2418yes—
467#95C2418yes—
468#95C2418yes—
469#95C2418yes—
470#95C2418yes—
471#95C2418yes—
472#95C2414yes—
473#95C2418yes—
474#95C2414yes—
475#95C2418yes—
476#95C2418yes—
477#95C2418yes—
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#95C2414yes—
494#95C2414yes—
495#95C2418yes—
496C24—24no—
497C24—24no—
498C24—24no—
499C24—24no—
500C24—24no—
501C24—24no—
502C24—22no—
503C24—24no—
504C24—22no—
505C24—22no—
506C24—24no—
507C24C2×#4118yes—
508C24C2512yes—
509C24C2514yes—
510C24C2511yescharacteristic
511C2×Q8—28no—
512C2×Q8—216no—
513C2×Q8—48no—
514C2×Q8—48no—
515C2×Q8—48no—
516C2×Q8—416no—
517C2×Q8—432no—
518C2×D4—232no—
519C2×D4—216no—
520C2×D4—216no—
521C2×D4—28no—
522C2×D4—48no—
523C2×D4—48no—
524C2×D4—432no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—22no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—22no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—22no—
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—24no—
565C22×C4—28no—
566C22×C4—216no—
567C22×C4—216no—
568C22×C4—216no—
569C22×C4—28no—
570C22×C4—216no—
571C22×C4—28no—
572C22×C4—48no—
573C22×C4—48no—
574C22×C4—432no—
575C22×C4—48no—
576C22×C4—48no—
577C22×C4—432no—
578C22×C4—432no—
579C22×C4—416no—
580C22×C4C2×#4118yes—
581C22×C4C2×#4114yes—
582C22×C4C2×#4114yes—
583C22×C4C2×#4118yes—
584C22×C4C2×#41132yes—
585C22×C4C2×#4114yes—
586C22×C4H(5,𝔽2)14yes—
587C22×C42−1+414yes—
588C22×C4C2514yes—
589C22×C4C2514yes—
590C22×C4C2514yes—
591C22×C4C2514yes—
592C22×C4C2512yes—
593C22×C4C2514yes—
594C22×C4C2512yes—
595C22×C4C2512yes—
596C22×C4C2514yes—
597C22×C4C2514yes—
598C22×C4C2514yes—
599C22×C4C2514yes—
600C22×C4C2514yes—
601C22×C4C2512yes—
602C22×C4C2512yes—
603C22×C4C2514yes—
604C22×C4C2512yes—
605C4⋊C4—28no—
606C4⋊C4—28no—
607C4⋊C4—216no—
608C4⋊C4—28no—
609C4⋊C4—28no—
610C4⋊C4—216no—
611C4⋊C4—216no—
612C4⋊C4—216no—
613C4⋊C4—216no—
614C4⋊C4—216no—
615C4⋊C4—216no—
616C4⋊C4—48no—
617C4⋊C4—48no—
618C4⋊C4—48no—
619C4⋊C4—48no—
620C4⋊C4—48no—
621C4⋊C4—48no—
622C4⋊C4—48no—
623C4⋊C4—48no—
624C22⋊C4—216no—
625C22⋊C4—216no—
626C22⋊C4—216no—
627C22⋊C4—216no—
628C22⋊C4—28no—
629C22⋊C4—28no—
630C22⋊C4—216no—
631C22⋊C4—216no—
632C22⋊C4—216no—
633C22⋊C4—216no—
634C22⋊C4—48no—
635C22⋊C4—48no—
636C22⋊C4—48no—
637C22⋊C4—48no—
638C22⋊C4—48no—
639C22⋊C4—48no—
640C22⋊C4—48no—
641C42—28no—
642C42—216no—
643C42—216no—
644C42—28no—
645C42—216no—
646C42—216no—
647C42—28no—
648C42—28no—
649C42—28no—
650C42—48no—
651C42—48no—
652C42—48no—
653C42C2×#41116yes—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—216no—
661C23—216no—
662C23—216no—
663C23—22no—
664C23—24no—
665C23—22no—
666C23—22no—
667C23—24no—
668C23—48no—
669C23—48no—
670C23—48no—
671C23—48no—
672C23—44no—
673C23—44no—
674C23—44no—
675C23—48no—
676C23—48no—
677C23C22×#4118yes—
678C23C22×#4112yes—
679C23C22×#4114yes—
680C23C2×H(5,𝔽2)12yes—
681C23C2×2−1+412yes—
682C23#58514yes—
683C23C2611yescharacteristic
684Q8—432no—
685Q8—416no—
686D4—232no—
687D4—432no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—28no—
695C2×C4—28no—
696C2×C4—216no—
697C2×C4—216no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—22no—
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—24no—
732C2×C4—432no—
733C2×C4—432no—
734C2×C4—44no—
735C2×C4—48no—
736C2×C4—48no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—48no—
740C2×C4—48no—
741C2×C4—48no—
742C2×C4—48no—
743C2×C4—48no—
744C2×C4—48no—
745C2×C4—48no—
746C2×C4—432no—
747C2×C4—416no—
748C2×C4#542116yes—
749C2×C4C22×#4118yes—
750C2×C4C22×#4114yes—
751C2×C4C22×#4114yes—
752C2×C4C22×#4118yes—
753C2×C4C22×#4114yes—
754C2×C4C2×H(5,𝔽2)14yes—
755C2×C4C2×2−1+414yes—
756C22—28no—
757C22—28no—
758C22—28no—
759C22—432no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—44no—
764C22—42no—
765C22—44no—
766C22—42no—
767C22—44no—
768C22—42no—
769C22—88no—
770C22#344414yes—
771C22C2×#54214yes—
772C22#345514yes—
773C22#345918yes—
774C22#346118yes—
775C22C23×#4112yes—
776C22C23×#4111yescharacteristic
777C22C22×H(5,𝔽2)11yescharacteristic
778C22C22×2−1+411yescharacteristic
779C22C2×#58512yes—
780C4—24no—
781C4—28no—
782C4—28no—
783C4—24no—
784C4—42no—
785C4—44no—
786C4—44no—
787C4—44no—
788C4—44no—
789C4—44no—
790C4—44no—
791C4—42no—
792C4—44no—
793C4—44no—
794C4—42no—
795C4—44no—
796C4C2×#54218yes—
797C2—48no—
798C2—82no—
799C2#3459618yesdirect product factor
800C2C2×#344411yescharacteristic
801C2C2×#345912yes—
802C2C22×#54211yescharacteristic
803C2C2×#346112yes—
804C2C2×#345511yescharacteristic
subgroupG/H
centerC23×C4C24
commutator, Frattini, cosocleC23C26
socleC24C25
prime radicalC2×#392C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C4 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #34596C2direct (N × H)
2. C2×#2650C2semidirect
3. C2×#2655C2semidirect
4. C2×#2665C2semidirect
5. C2×#2663C2semidirect
6. C2×#2653C2semidirect
7. C2×#2652C2semidirect
8. C2×#2638C2semidirect
10. C2×#2401C2semidirect
11. C2×#2399C2semidirect
12. C2×#2398C2semidirect
13. C2×#2398C2semidirect
14. C2×#2396C2semidirect
16. C2×C4×C22⋊Q8C2semidirect
17. C2×C4×#123C2semidirect
18. C2×#2298C2semidirect
19. C2×#2295C2semidirect
20. C2×C42×D4C2semidirect
30. #2665C22semidirect
31. #2663C22semidirect
32. #2655C22semidirect
33. #2653C22semidirect
34. #2652C22semidirect
35. #2650C22semidirect
36. #2638C22semidirect
38. #2401C22semidirect
40. #2399C22semidirect
41. #2398C22semidirect
42. #2398C22semidirect
43. #2396C22semidirect
80. C4×C22⋊Q8C22semidirect
81. C4×#123C22semidirect
82. #2298C22semidirect
83. #2295C22semidirect
106. C42×D4C22semidirect
799. C2#34596direct (N × H)

Maximal subgroups

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

subgroupindex
#345962
C2×#26502
C2×#26552
C2×#26652
C2×#26632
C2×#26532
C2×#26522
C2×#26382
C2×#26302
C2×#24012
C2×#23992
C2×#23982
C2×#23962
C2×#23922
C2×C4×C22⋊Q82
C2×C4×#1232
C2×#22982
C2×#22952
C2×C42×D42