Finite Group Databasebeta

← C2×#49594 #7705234

Subgroups — C2×#49594 #7705234

Order 512.

5946 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2800C212yesmaximal, complemented
2C2×#2727C212yesmaximal, complemented
3C2×#2722C212yesmaximal, complemented
4C2×#2707C212yesmaximal, complemented
5C2×#2704C212yesmaximal, complemented
6C2×#2694C212yesmaximal, complemented
7#49594C2132yesmaximal, direct product factor
8C2×#2584C212yesmaximal, complemented
9C2×#2601C212yesmaximal, complemented
10C2×#2583C211yesmaximal, characteristic, complemented
11C2×#2556C212yesmaximal, complemented
12C2×#2522C212yesmaximal, complemented
13C2×#2406C211yesmaximal, characteristic
14C2×#2479C212yesmaximal, complemented
15C2×#2462C212yesmaximal, complemented
16C2×#2616C211yesmaximal, characteristic
17C2×#2667C211yesmaximal, characteristic, complemented
18C2×#2378C211yesmaximal, characteristic, complemented
19C2×#2341C211yesmaximal, characteristic
20C2×#2316C211yesmaximal, characteristic, complemented
21C23×#41C2211yescharacteristic
22C22×#126C2212yes—
23C22×#126C2212yes—
24C22×#125C2212yes—
25C22×#125C2212yes—
26C22×#123C2212yes—
27C22×C22⋊Q8C2211yescharacteristic
28C22×C22⋊Q8C2212yes—
29C22×C4×Q8C2212yes—
30C22×#117C2211yescharacteristic
31C22×#117C2211yescharacteristic
32C23×C4⋊C4C2211yescharacteristic
33#2800C22132yescomplemented
34#2727C22132yescomplemented
35#2722C22132yescomplemented
36#2707C22132yescomplemented
37#2704C22132yescomplemented
38#2694C22132yescomplemented
39#2667C22116yescomplemented
40#2616C22116yes—
41#2601C22132yescomplemented
42#2584C22132yescomplemented
43#2583C22116yescomplemented
44#2556C22132yescomplemented
45#2522C22132yescomplemented
46#2479C22132yescomplemented
47#2462C22132yescomplemented
48#2406C22116yes—
49C2×#399C2212yes—
50C2×#399C2212yes—
51C2×#399C2212yes—
52C2×#398C2212yes—
53C2×#398C2211yescharacteristic
54C2×#398C2211yescharacteristic
55C2×#398C2212yes—
56C2×#398C2212yes—
57C2×#398C2212yes—
58C2×#398C2212yes—
59C2×#398C2212yes—
60C2×#397C2212yes—
61C2×#397C2212yes—
62C2×#396C2212yes—
63C2×#396C2212yes—
64C2×#396C2212yes—
65C2×#396C2212yes—
66C2×#396C2212yes—
67C2×#395C2211yescharacteristic
68C2×#395C2211yescharacteristic
69C2×#395C2212yes—
70C2×#395C2211yescharacteristic
71C2×#395C2211yescharacteristic
72C2×#394C2211yescharacteristic
73C2×#394C2212yes—
74C2×#394C2212yes—
75C2×#394C2212yes—
76C2×#394C2211yescharacteristic
77#2378C22116yescomplemented
78#2341C22116yes—
79#2316C22116yescomplemented
80C2×#391C2212yes—
81C2×#390C2212yes—
82C2×#390C2212yes—
83C2×#390C2212yes—
84C2×#389C2212yes—
85C2×#389C2212yes—
86C2×#389C2212yes—
87C2×#389C2212yes—
88C2×#389C2212yes—
89C2×#389C2212yes—
90C2×#389C2212yes—
91C2×#389C2212yes—
92C2×#389C2212yes—
93C2×#389C2212yes—
94C2×#389C2212yes—
95C2×#389C2212yes—
96C2×#388C2212yes—
97C2×#388C2212yes—
98C2×#388C2212yes—
99C2×#388C2212yes—
100C2×#388C2212yes—
101C2×#388C2212yes—
102C2×#388C2212yes—
103C2×#388C2212yes—
104C2×#387C2212yes—
105C2×#387C2212yes—
106C2×#387C2212yes—
107C2×#387C2212yes—
108C2×#387C2212yes—
109C2×#387C2212yes—
110C2×#387C2212yes—
111C2×#386C2212yes—
112C2×#385C2212yes—
113C2×#385C2212yes—
114C2×#385C2212yes—
115C2×#385C2212yes—
116C2×#381C2211yescharacteristic
117C2×#380C2211yescharacteristic
118C2×#380C2211yescharacteristic
119C2×#380C2211yescharacteristic
120C2×#380C2211yescharacteristic
121C2×#380C2212yes—
122C2×#380C2212yes—
123C2×C4×C4⋊C4C2212yes—
124C2×C4×C4⋊C4C2212yes—
125C2×C4×C22⋊C4C2212yes—
126C2×C4×C22⋊C4C2211yescharacteristic
127C22×#41—28no—
128C22×#41—48no—
129C22×#41C2318yes—
130C23×Q8C2311yescharacteristic
131C23×Q8C2311yescharacteristic
132C23×D4C2312yes—
133C23×D4C2311yescharacteristic
134C24×C4C2311yescharacteristic
135C24×C4C2312yes—
136C24×C4C2311yescharacteristic
137C24×C4C2311yescharacteristic
138C2×#126—48no—
139C2×#126—48no—
140C2×#126C23116yes—
141C2×#126C23116yes—
142C2×#125—48no—
143C2×#125—48no—
144C2×#125C23116yes—
145C2×#125C23116yes—
146C2×#123—48no—
147C2×#123C23116yes—
148C2×C22⋊Q8—28no—
149C2×C22⋊Q8—48no—
150C2×C22⋊Q8C2318yes—
151C2×C22⋊Q8C23116yes—
152C2×C4×Q8—48no—
153C2×C4×Q8C23116yes—
154C2×#117—44no—
155C2×#117—44no—
156C2×#117C2318yes—
157C2×#117C2318yes—
158C22×C4⋊C4—28no—
159C22×C4⋊C4C2318yes—
160C22×C4⋊C4C2312yes—
161C22×C4⋊C4C2311yescharacteristic
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C2312yes—
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2312yes—
168C22×C4⋊C4C2312yes—
169C22×C4⋊C4C2312yes—
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⋊C4C2312yes—
183C22×C4⋊C4C2312yes—
184C22×C4⋊C4C2312yes—
185C22×C4⋊C4C2312yes—
186C22×C4⋊C4C2312yes—
187C22×C4⋊C4C2312yes—
188C22×C4⋊C4C2312yes—
189C22×C4⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2311yescharacteristic
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2311yescharacteristic
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2311yescharacteristic
208C22×C22⋊C4C2311yescharacteristic
209C22×C42C2312yes—
210C22×C42C2312yes—
211C22×C42C2312yes—
212C22×C42C2312yes—
213C22×C42C2312yes—
214C22×C42C2312yes—
215C22×C42C2312yes—
216#399C23116yes—
217#399C23116yes—
218#399C23116yes—
219#398C2318yes—
220#398C2318yes—
221#398C23116yes—
222#398C23116yes—
223#398C23116yes—
224#398C23116yes—
225#398C23116yes—
226#398C23116yes—
227#397C23116yes—
228#397C23116yes—
229#396C23116yes—
230#396C23116yes—
231#396C23116yes—
232#396C23116yes—
233#396C23116yes—
234#395C2318yes—
235#395C2318yes—
236#395C2318yes—
237#395C23116yes—
238#395C2318yes—
239#394C23116yes—
240#394C23116yes—
241#394C23116yes—
242#394C2318yes—
243#394C2318yes—
244#391C23116yes—
245#390C23116yes—
246#390C23116yes—
247#390C23116yes—
248#389C23116yes—
249#389C23116yes—
250#389C23116yes—
251#389C23116yes—
252#389C23116yes—
253#389C23116yes—
254#389C23116yes—
255#389C23116yes—
256#389C23116yes—
257#389C23116yes—
258#389C23116yes—
259#389C23116yes—
260#388C23116yes—
261#388C23116yes—
262#388C23116yes—
263#388C23116yes—
264#388C23116yes—
265#388C23116yes—
266#388C23116yes—
267#388C23116yes—
268#387C23116yes—
269#387C23116yes—
270#387C23116yes—
271#387C23116yes—
272#387C23116yes—
273#387C23116yes—
274#387C23116yes—
275#386C23116yes—
276#385C23116yes—
277#385C23116yes—
278#385C23116yes—
279#385C23116yes—
280#381C2318yes—
281#380C2318yes—
282#380C2318yes—
283#380C2318yes—
284#380C2318yes—
285#380C23116yes—
286#380C23116yes—
287C4×C4⋊C4C23116yes—
288C4×C4⋊C4C23116yes—
289C4×C22⋊C4C2318yes—
290C4×C22⋊C4C23116yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2311yescharacteristic
295C2×#95C2311yescharacteristic
296C2×#95C2311yescharacteristic
297C2×#95C2311yescharacteristic
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2312yes—
305C2×#95C2312yes—
306C2×#95C2312yes—
307C2×#95C2312yes—
308C2×#95C2312yes—
309C2×#95C2312yes—
310C2×#95C2312yes—
311C2×#95C2312yes—
312C2×#95C2312yes—
313C2×#95C2312yes—
314C25C2412yes—
315C25C2411yescharacteristic
316C2×#41—232no—
317C2×#41—432no—
318C2×#41—464no—
319C22×Q8—24no—
320C22×Q8—24no—
321C22×Q8—28no—
322C22×Q8—44no—
323C22×Q8C2414yes—
324C22×Q8C2414yes—
325C22×D4—28no—
326C22×D4—24no—
327C22×D4—28no—
328C22×D4—44no—
329C22×D4—44no—
330C22×D4C2418yes—
331C22×D4C2414yes—
332C23×C4—24no—
333C23×C4—24no—
334C23×C4—24no—
335C23×C4—24no—
336C23×C4—28no—
337C23×C4—28no—
338C23×C4—44no—
339C23×C4—44no—
340C23×C4—44no—
341C23×C4#4118yes—
342C23×C4C2414yes—
343C23×C4C2412yes—
344C23×C4C2412yes—
345C23×C4C2412yes—
346C23×C4C2412yes—
347C23×C4C2412yes—
348C23×C4C2412yes—
349C23×C4C2412yes—
350C23×C4C2412yes—
351C23×C4C2412yes—
352C23×C4C2411yescharacteristic
353C23×C4C2411yescharacteristic
354C23×C4C2418yes—
355C23×C4C2411yescharacteristic
356C23×C4C2411yescharacteristic
357C23×C4C2411yescharacteristic
358C23×C4C2412yes—
359C23×C4C2412yes—
360C23×C4C2411yescharacteristic
361C23×C4C2414yes—
362C23×C4C2414yes—
363#126—432no—
364#126—432no—
365#125—432no—
366#125—432no—
367#123—432no—
368C22⋊Q8—232no—
369C22⋊Q8—432no—
370C4×Q8—432no—
371#117—416no—
372#117—416no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—24no—
377C2×C4⋊C4—232no—
378C2×C4⋊C4—24no—
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—28no—
389C2×C4⋊C4—28no—
390C2×C4⋊C4—44no—
391C2×C4⋊C4—44no—
392C2×C4⋊C4—44no—
393C2×C4⋊C4—44no—
394C2×C4⋊C4—44no—
395C2×C4⋊C4—44no—
396C2×C4⋊C4—44no—
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⋊C4C2414yes—
405C2×C4⋊C4C2414yes—
406C2×C4⋊C4C2414yes—
407C2×C4⋊C4C2414yes—
408C2×C4⋊C4C2418yes—
409C2×C4⋊C4C2418yes—
410C2×C4⋊C4C2418yes—
411C2×C4⋊C4C2418yes—
412C2×C4⋊C4C2414yes—
413C2×C4⋊C4C2418yes—
414C2×C4⋊C4C2418yes—
415C2×C4⋊C4C2418yes—
416C2×C4⋊C4C2418yes—
417C2×C4⋊C4C2418yes—
418C2×C4⋊C4C2418yes—
419C2×C4⋊C4C2418yes—
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⋊C4C2418yes—
431C2×C4⋊C4C2418yes—
432C2×C4⋊C4C2418yes—
433C2×C4⋊C4C2418yes—
434C2×C22⋊C4—28no—
435C2×C22⋊C4—28no—
436C2×C22⋊C4—28no—
437C2×C22⋊C4—28no—
438C2×C22⋊C4—28no—
439C2×C22⋊C4—28no—
440C2×C22⋊C4—42no—
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⋊C4—44no—
450C2×C22⋊C4—44no—
451C2×C22⋊C4—44no—
452C2×C22⋊C4—44no—
453C2×C22⋊C4C2418yes—
454C2×C22⋊C4C2418yes—
455C2×C22⋊C4C2418yes—
456C2×C22⋊C4C2418yes—
457C2×C22⋊C4C2418yes—
458C2×C22⋊C4C2418yes—
459C2×C22⋊C4C2414yes—
460C2×C22⋊C4C2414yes—
461C2×C22⋊C4C2414yes—
462C2×C22⋊C4C2414yes—
463C2×C22⋊C4C2418yes—
464C2×C22⋊C4C2418yes—
465C2×C22⋊C4C2418yes—
466C2×C22⋊C4C2418yes—
467C2×C22⋊C4C2418yes—
468C2×C22⋊C4C2418yes—
469C2×C22⋊C4C2418yes—
470C2×C22⋊C4C2418yes—
471C2×C22⋊C4C2418yes—
472C2×C42—28no—
473C2×C42—28no—
474C2×C42—44no—
475C2×C42—44no—
476C2×C42—44no—
477C2×C42—44no—
478C2×C42—44no—
479C2×C42C2418yes—
480C2×C42C2418yes—
481C2×C42C2418yes—
482C2×C42C2418yes—
483C2×C42C2418yes—
484C2×C42C2418yes—
485C2×C42C2418yes—
486#95C2414yes—
487#95C2418yes—
488#95C2414yes—
489#95C2418yes—
490#95C2418yes—
491#95C2418yes—
492#95C2418yes—
493#95C2418yes—
494#95C2418yes—
495#95C2418yes—
496#95C2418yes—
497#95C2418yes—
498#95C2414yes—
499#95C2414yes—
500#95C2418yes—
501#95C2418yes—
502#95C2418yes—
503#95C2418yes—
504#95C2418yes—
505#95C2418yes—
506#95C2418yes—
507#95C2418yes—
508#95C2418yes—
509C24—22no—
510C24—24no—
511C24—24no—
512C24—22no—
513C24—24no—
514C24—24no—
515C24—24no—
516C24—24no—
517C24—24no—
518C24—24no—
519C24—24no—
520C24C2×#4114yes—
521C24C2514yes—
522C24C2512yes—
523C24C2511yescharacteristic
524#41—4128no—
525C2×Q8—232no—
526C2×Q8—28no—
527C2×Q8—28no—
528C2×Q8—216no—
529C2×Q8—48no—
530C2×Q8—88no—
531C2×D4—216no—
532C2×D4—28no—
533C2×D4—216no—
534C2×D4—48no—
535C2×D4—48no—
536C2×D4—432no—
537C2×D4—416no—
538C22×C4—232no—
539C22×C4—28no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—22no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—22no—
550C22×C4—28no—
551C22×C4—28no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—22no—
555C22×C4—22no—
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—24no—
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—24no—
580C22×C4—24no—
581C22×C4—24no—
582C22×C4—24no—
583C22×C4—28no—
584C22×C4—216no—
585C22×C4—216no—
586C22×C4—416no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4—432no—
590C22×C4—48no—
591C22×C4—88no—
592C22×C4C2×#4114yes—
593C22×C4C2×#4114yes—
594C22×C4C2×#41116yes—
595C22×C4H(5,𝔽2)14yes—
596C22×C4H(5,𝔽2)18yes—
597C22×C42−1+418yes—
598C22×C42−1+414yes—
599C22×C4C2514yes—
600C22×C4C2514yes—
601C22×C4C2514yes—
602C22×C4C2514yes—
603C22×C4C2514yes—
604C22×C4C2514yes—
605C22×C4C2514yes—
606C22×C4C2514yes—
607C22×C4C2514yes—
608C22×C4C2512yes—
609C22×C4C2512yes—
610C22×C4C2512yes—
611C22×C4C2512yes—
612C22×C4C2512yes—
613C22×C4C2514yes—
614C22×C4C2514yes—
615C22×C4C2512yes—
616C4⋊C4—28no—
617C4⋊C4—28no—
618C4⋊C4—28no—
619C4⋊C4—28no—
620C4⋊C4—28no—
621C4⋊C4—216no—
622C4⋊C4—216no—
623C4⋊C4—216no—
624C4⋊C4—216no—
625C4⋊C4—216no—
626C4⋊C4—216no—
627C4⋊C4—216no—
628C4⋊C4—216no—
629C4⋊C4—216no—
630C4⋊C4—216no—
631C4⋊C4—216no—
632C4⋊C4—48no—
633C4⋊C4—48no—
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—48no—
644C4⋊C4—48no—
645C4⋊C4—48no—
646C22⋊C4—216no—
647C22⋊C4—216no—
648C22⋊C4—216no—
649C22⋊C4—216no—
650C22⋊C4—216no—
651C22⋊C4—216no—
652C22⋊C4—44no—
653C22⋊C4—44no—
654C22⋊C4—44no—
655C22⋊C4—44no—
656C22⋊C4—48no—
657C22⋊C4—48no—
658C22⋊C4—48no—
659C22⋊C4—48no—
660C22⋊C4—48no—
661C22⋊C4—48no—
662C22⋊C4—48no—
663C22⋊C4—48no—
664C22⋊C4—48no—
665C42—216no—
666C42—216no—
667C42—48no—
668C42—48no—
669C42—48no—
670C42—48no—
671C42—48no—
672C23—22no—
673C23—24no—
674C23—24no—
675C23—22no—
676C23—28no—
677C23—28no—
678C23—28no—
679C23—24no—
680C23—24no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—24no—
685C23—24no—
686C23—48no—
687C23—48no—
688C23—48no—
689C23—48no—
690C23—48no—
691C23—48no—
692C23—48no—
693C23—48no—
694C23—48no—
695C23C22×#4114yes—
696C23C22×#4112yes—
697C23C2×H(5,𝔽2)14yes—
698C23C2×H(5,𝔽2)12yes—
699C23C2×2−1+412yes—
700C23C2×2−1+414yes—
701C23C2611yescharacteristic
702Q8—232no—
703Q8—88no—
704D4—432no—
705D4—416no—
706C2×C4—232no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—28no—
718C2×C4—28no—
719C2×C4—216no—
720C2×C4—28no—
721C2×C4—28no—
722C2×C4—216no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
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—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—416no—
755C2×C4—432no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—48no—
759C2×C4—48no—
760C2×C4—48no—
761C2×C4—48no—
762C2×C4—48no—
763C2×C4—48no—
764C2×C4—48no—
765C2×C4—48no—
766C2×C4—48no—
767C2×C4—88no—
768C2×C4C22×#4114yes—
769C2×C4C22×#4114yes—
770C2×C4C2×H(5,𝔽2)14yes—
771C2×C4C2×H(5,𝔽2)18yes—
772C2×C4C2×2−1+418yes—
773C2×C4C2×2−1+414yes—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—44no—
778C22—44no—
779C22—416no—
780C22—44no—
781C22—44no—
782C22—44no—
783C22—44no—
784C22—44no—
785C22—44no—
786C22—44no—
787C22—816no—
788C22#349014yes—
789C22#349214yes—
790C22#350914yes—
791C22#354818yes—
792C22#355218yes—
793C22C23×#4111yescharacteristic
794C22C22×H(5,𝔽2)12yes—
795C22C22×H(5,𝔽2)11yescharacteristic
796C22C22×2−1+411yescharacteristic
797C22C22×2−1+412yes—
798C4—28no—
799C4—24no—
800C4—24no—
801C4—28no—
802C4—24no—
803C4—24no—
804C4—44no—
805C4—44no—
806C4—44no—
807C4—44no—
808C4—44no—
809C4—44no—
810C4—44no—
811C4—42no—
812C4—42no—
813C4—44no—
814C4—44no—
815C2—44no—
816C2—84no—
817C2#4959418yesdirect product factor
818C2C2×#355212yes—
819C2C2×#354812yes—
820C2C2×#349011yescharacteristic
821C2C2×#349211yescharacteristic
822C2C2×#350911yescharacteristic
subgroupG/H
center, socleC24C25
commutator, Frattini, cosocleC23C26
prime radicalC23×#41C22
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×#2800C2semidirect
2. C2×#2727C2semidirect
3. C2×#2722C2semidirect
4. C2×#2707C2semidirect
5. C2×#2704C2semidirect
6. C2×#2694C2semidirect
7. #49594C2direct (N × H)
8. C2×#2584C2semidirect
9. C2×#2601C2semidirect
10. C2×#2583C2semidirect
11. C2×#2556C2semidirect
12. C2×#2522C2semidirect
14. C2×#2479C2semidirect
15. C2×#2462C2semidirect
17. C2×#2667C2semidirect
18. C2×#2378C2semidirect
20. C2×#2316C2semidirect
33. #2800C22semidirect
34. #2727C22semidirect
35. #2722C22semidirect
36. #2707C22semidirect
37. #2704C22semidirect
38. #2694C22semidirect
39. #2667C22semidirect
41. #2601C22semidirect
42. #2584C22semidirect
43. #2583C22semidirect
44. #2556C22semidirect
45. #2522C22semidirect
46. #2479C22semidirect
47. #2462C22semidirect
77. #2378C22semidirect
79. #2316C22semidirect
817. C2#49594direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#28002
C2×#27272
C2×#27222
C2×#27072
C2×#27042
C2×#26942
#495942
C2×#25842
C2×#26012
C2×#25832
C2×#25562
C2×#25222
C2×#24062
C2×#24792
C2×#24622
C2×#26162
C2×#26672
C2×#23782
C2×#23412
C2×#23162