Finite Group Databasebeta

← C2×#46247 #7702925

Subgroups — C2×#46247 #7702925

Order 512.

5174 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2800C212yesmaximal, complemented
2C2×#2797C212yesmaximal, complemented
3C2×#2797C212yesmaximal, complemented
4C2×#2775C212yesmaximal, complemented
5C2×#2757C212yesmaximal, complemented
6C2×#2754C212yesmaximal, complemented
7#46247C2132yesmaximal, direct product factor
8C2×#2820C211yesmaximal, characteristic, complemented
9C2×#2819C211yesmaximal, characteristic
10C2×#2864C211yesmaximal, characteristic, complemented
11C2×#2861C211yesmaximal, characteristic, complemented
12C2×#2602C212yesmaximal, complemented
13C2×#2599C212yesmaximal, complemented
14C2×#2523C212yesmaximal, complemented
15C2×#2518C212yesmaximal, complemented
16C2×#2471C212yesmaximal, complemented
17C2×#2470C212yesmaximal, complemented
18C2×#2382C211yesmaximal, characteristic, complemented
19C2×#2379C211yesmaximal, characteristic, complemented
20C2×C4×#124C211yesmaximal, characteristic, complemented
21C22×#125C2211yescharacteristic
22C22×#124C2211yescharacteristic
23C22×#124C2211yescharacteristic
24C22×#123C2212yes—
25C22×C4×Q8C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27C22×#117C2212yes—
28#2864C22116yescomplemented
29#2861C22116yescomplemented
30#2820C22116yescomplemented
31#2819C22116yes—
32#2800C22132yescomplemented
33#2797C22132yescomplemented
34#2797C22132yescomplemented
35#2775C22132yescomplemented
36#2757C22132yescomplemented
37#2754C22132yescomplemented
38#2602C22132yescomplemented
39#2599C22132yescomplemented
40#2523C22132yescomplemented
41#2518C22132yescomplemented
42#2471C22132yescomplemented
43#2470C22132yescomplemented
44C2×#400C2212yes—
45C2×#399C2212yes—
46C2×#398C2212yes—
47C2×#397C2212yes—
48C2×#397C2212yes—
49C2×#397C2212yes—
50C2×#397C2212yes—
51C2×#397C2212yes—
52C2×#397C2212yes—
53C2×#397C2212yes—
54C2×#397C2212yes—
55C2×#396C2212yes—
56C2×#396C2212yes—
57C2×#396C2212yes—
58C2×#395C2212yes—
59C2×#394C2212yes—
60C2×#394C2212yes—
61C2×#394C2212yes—
62C2×#394C2212yes—
63C2×#394C2212yes—
64C2×#393C2212yes—
65C2×#393C2212yes—
66C2×#392C2212yes—
67C2×#392C2212yes—
68#2382C22116yescomplemented
69#2379C22116yescomplemented
70C4×#124C22116yescomplemented
71C2×#391C2211yescharacteristic
72C2×#391C2211yescharacteristic
73C2×#391C2212yes—
74C2×#391C2211yescharacteristic
75C2×#390C2211yescharacteristic
76C2×#390C2211yescharacteristic
77C2×#390C2211yescharacteristic
78C2×#390C2212yes—
79C2×#390C2212yes—
80C2×#389C2211yescharacteristic
81C2×#389C2211yescharacteristic
82C2×#389C2211yescharacteristic
83C2×#389C2211yescharacteristic
84C2×#389C2212yes—
85C2×#389C2212yes—
86C2×#388C2212yes—
87C2×#388C2212yes—
88C2×#388C2212yes—
89C2×#388C2212yes—
90C2×#388C2212yes—
91C2×#388C2212yes—
92C2×#388C2212yes—
93C2×#388C2212yes—
94C2×#388C2212yes—
95C2×#388C2212yes—
96C2×#388C2212yes—
97C2×#388C2212yes—
98C2×#387C2212yes—
99C2×#387C2212yes—
100C2×#387C2212yes—
101C2×#387C2212yes—
102C2×#387C2212yes—
103C2×#387C2212yes—
104C2×#387C2212yes—
105C2×#387C2212yes—
106C2×#387C2212yes—
107C2×#387C2212yes—
108C2×#387C2212yes—
109C2×#386C2212yes—
110C2×#386C2212yes—
111C2×#386C2212yes—
112C2×#386C2212yes—
113C2×#385C2212yes—
114C2×#385C2212yes—
115C2×#385C2212yes—
116C2×#385C2212yes—
117C2×#383C2212yes—
118C2×#383C2212yes—
119C2×#382C2211yescharacteristic
120C2×#382C2211yescharacteristic
121C2×#382C2211yescharacteristic
122C2×#382C2212yes—
123C2×C4×C22⋊C4C2212yes—
124C2×C4×C22⋊C4C2212yes—
125C2×C4×C22⋊C4C2212yes—
126C2×C43C2211yescharacteristic
127C23×Q8C2311yescharacteristic
128C23×Q8C2311yescharacteristic
129C23×D4C2311yescharacteristic
130C23×D4C2311yescharacteristic
131C23×D4C2312yes—
132C23×D4C2312yes—
133C24×C4C2312yes—
134C24×C4C2312yes—
135C2×#125—28no—
136C2×#125C2318yes—
137C2×#124—28no—
138C2×#124—28no—
139C2×#124C2318yes—
140C2×#124C2318yes—
141C2×#123—48no—
142C2×#123C23116yes—
143C2×C4×Q8—44no—
144C2×C4×Q8C2318yes—
145C2×C4×D4—44no—
146C2×C4×D4C2318yes—
147C2×#117—48no—
148C2×#117C23116yes—
149C22×C4⋊C4C2312yes—
150C22×C4⋊C4C2312yes—
151C22×C4⋊C4C2311yescharacteristic
152C22×C4⋊C4C2311yescharacteristic
153C22×C4⋊C4C2312yes—
154C22×C4⋊C4C2311yescharacteristic
155C22×C4⋊C4C2311yescharacteristic
156C22×C4⋊C4C2312yes—
157C22×C4⋊C4C2312yes—
158C22×C4⋊C4C2312yes—
159C22×C4⋊C4C2312yes—
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2311yescharacteristic
162C22×C4⋊C4C2312yes—
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C2312yes—
165C22×C4⋊C4C2312yes—
166C22×C4⋊C4C2312yes—
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C22⋊C4C2312yes—
170C22×C22⋊C4C2312yes—
171C22×C22⋊C4C2312yes—
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×C22⋊C4C2312yes—
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C42C2312yes—
192C22×C42C2311yescharacteristic
193C22×C42C2312yes—
194C22×C42C2311yescharacteristic
195C22×C42C2311yescharacteristic
196C22×C42C2311yescharacteristic
197C22×C42C2311yescharacteristic
198C22×C42C2311yescharacteristic
199C22×C42C2312yes—
200C22×C42C2312yes—
201C22×C42C2311yescharacteristic
202#400C23116yes—
203#399C23116yes—
204#398C23116yes—
205#397C23116yes—
206#397C23116yes—
207#397C23116yes—
208#397C23116yes—
209#397C23116yes—
210#397C23116yes—
211#397C23116yes—
212#397C23116yes—
213#396C23116yes—
214#396C23116yes—
215#396C23116yes—
216#395C23116yes—
217#394C23116yes—
218#394C23116yes—
219#394C23116yes—
220#394C23116yes—
221#394C23116yes—
222#393C23116yes—
223#393C23116yes—
224#392C23116yes—
225#392C23116yes—
226#391C2318yes—
227#391C2318yes—
228#391C23116yes—
229#391C2318yes—
230#390C23116yes—
231#390C2318yes—
232#390C2318yes—
233#390C23116yes—
234#390C2318yes—
235#389C23116yes—
236#389C2318yes—
237#389C2318yes—
238#389C2318yes—
239#389C2318yes—
240#389C23116yes—
241#388C23116yes—
242#388C23116yes—
243#388C23116yes—
244#388C23116yes—
245#388C23116yes—
246#388C23116yes—
247#388C23116yes—
248#388C23116yes—
249#388C23116yes—
250#388C23116yes—
251#388C23116yes—
252#388C23116yes—
253#387C23116yes—
254#387C23116yes—
255#387C23116yes—
256#387C23116yes—
257#387C23116yes—
258#387C23116yes—
259#387C23116yes—
260#387C23116yes—
261#387C23116yes—
262#387C23116yes—
263#387C23116yes—
264#386C23116yes—
265#386C23116yes—
266#386C23116yes—
267#386C23116yes—
268#385C23116yes—
269#385C23116yes—
270#385C23116yes—
271#385C23116yes—
272#383C23116yes—
273#383C23116yes—
274#382C2318yes—
275#382C2318yes—
276#382C2318yes—
277#382C23116yes—
278C4×C22⋊C4C23116yes—
279C4×C22⋊C4C23116yes—
280C4×C22⋊C4C23116yes—
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—
307C43C2318yes—
308C25C2412yes—
309C25C2412yes—
310C22×Q8—24no—
311C22×Q8—24no—
312C22×Q8—42no—
313C22×Q8—42no—
314C22×Q8—42no—
315C22×Q8—42no—
316C22×Q8C2414yes—
317C22×Q8C2414yes—
318C22×D4—24no—
319C22×D4—24no—
320C22×D4—42no—
321C22×D4—42no—
322C22×D4—44no—
323C22×D4—42no—
324C22×D4—42no—
325C22×D4—44no—
326C22×D4—44no—
327C22×D4—44no—
328C22×D4—44no—
329C22×D4—44no—
330C22×D4C2414yes—
331C22×D4C2414yes—
332C22×D4C2418yes—
333C22×D4C2418yes—
334C23×C4—28no—
335C23×C4—44no—
336C23×C4—44no—
337C23×C4—44no—
338C23×C4—44no—
339C23×C4—44no—
340C23×C4C2412yes—
341C23×C4C2412yes—
342C23×C4C2412yes—
343C23×C4C2411yescharacteristic
344C23×C4C2412yes—
345C23×C4C2411yescharacteristic
346C23×C4C2411yescharacteristic
347C23×C4C2412yes—
348C23×C4C2412yes—
349C23×C4C2412yes—
350C23×C4C2412yes—
351C23×C4C2412yes—
352C23×C4C2412yes—
353C23×C4C2411yescharacteristic
354C23×C4C2411yescharacteristic
355C23×C4C2411yescharacteristic
356C23×C4C2411yescharacteristic
357C23×C4C2418yes—
358C23×C4C2418yes—
359#125—232no—
360#124—232no—
361#124—232no—
362#123—432no—
363C4×Q8—416no—
364C4×D4—416no—
365#117—432no—
366C2×C4⋊C4—28no—
367C2×C4⋊C4—28no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—28no—
371C2×C4⋊C4—42no—
372C2×C4⋊C4—42no—
373C2×C4⋊C4—42no—
374C2×C4⋊C4—42no—
375C2×C4⋊C4—44no—
376C2×C4⋊C4—44no—
377C2×C4⋊C4—44no—
378C2×C4⋊C4—44no—
379C2×C4⋊C4—44no—
380C2×C4⋊C4—44no—
381C2×C4⋊C4—44no—
382C2×C4⋊C4—42no—
383C2×C4⋊C4—42no—
384C2×C4⋊C4—44no—
385C2×C4⋊C4—44no—
386C2×C4⋊C4C2418yes—
387C2×C4⋊C4C2414yes—
388C2×C4⋊C4C2414yes—
389C2×C4⋊C4C2418yes—
390C2×C4⋊C4C2418yes—
391C2×C4⋊C4C2418yes—
392C2×C4⋊C4C2414yes—
393C2×C4⋊C4C2414yes—
394C2×C4⋊C4C2418yes—
395C2×C4⋊C4C2418yes—
396C2×C4⋊C4C2414yes—
397C2×C4⋊C4C2418yes—
398C2×C4⋊C4C2414yes—
399C2×C4⋊C4C2418yes—
400C2×C4⋊C4C2414yes—
401C2×C4⋊C4C2414yes—
402C2×C4⋊C4C2418yes—
403C2×C4⋊C4C2418yes—
404C2×C4⋊C4C2418yes—
405C2×C4⋊C4C2418yes—
406C2×C22⋊C4—28no—
407C2×C22⋊C4—28no—
408C2×C22⋊C4—28no—
409C2×C22⋊C4—28no—
410C2×C22⋊C4—28no—
411C2×C22⋊C4—44no—
412C2×C22⋊C4—44no—
413C2×C22⋊C4—44no—
414C2×C22⋊C4—44no—
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⋊C4—44no—
423C2×C22⋊C4—44no—
424C2×C22⋊C4—44no—
425C2×C22⋊C4—44no—
426C2×C22⋊C4—44no—
427C2×C22⋊C4—44no—
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×C22⋊C4C2418yes—
440C2×C22⋊C4C2418yes—
441C2×C22⋊C4C2418yes—
442C2×C22⋊C4C2418yes—
443C2×C22⋊C4C2418yes—
444C2×C22⋊C4C2418yes—
445C2×C22⋊C4C2418yes—
446C2×C22⋊C4C2418yes—
447C2×C22⋊C4C2418yes—
448C2×C22⋊C4C2418yes—
449C2×C22⋊C4C2418yes—
450C2×C42—28no—
451C2×C42—24no—
452C2×C42—44no—
453C2×C42—42no—
454C2×C42—42no—
455C2×C42—42no—
456C2×C42—42no—
457C2×C42—42no—
458C2×C42—44no—
459C2×C42—44no—
460C2×C42#4118yes—
461C2×C42C2418yes—
462C2×C42C2414yes—
463C2×C42C2418yes—
464C2×C42C2414yes—
465C2×C42C2414yes—
466C2×C42C2414yes—
467C2×C42C2414yes—
468C2×C42C2414yes—
469C2×C42C2418yes—
470C2×C42C2418yes—
471C2×C42C2414yes—
472#95C2418yes—
473#95C2418yes—
474#95C2418yes—
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#95C2418yes—
494#95C2418yes—
495#95C2418yes—
496#95C2418yes—
497#95C2418yes—
498C24—24no—
499C24—24no—
500C24—24no—
501C24—24no—
502C24—24no—
503C24—24no—
504C24—24no—
505C24—24no—
506C24—24no—
507C24—24no—
508C24—24no—
509C24—24no—
510C24—24no—
511C24—24no—
512C24C2514yes—
513C24C2514yes—
514C24C2511yescharacteristic
515C2×Q8—28no—
516C2×Q8—28no—
517C2×Q8—44no—
518C2×Q8—44no—
519C2×Q8—44no—
520C2×Q8—44no—
521C2×Q8—416no—
522C2×Q8—88no—
523C2×D4—28no—
524C2×D4—28no—
525C2×D4—44no—
526C2×D4—44no—
527C2×D4—416no—
528C2×D4—48no—
529C2×D4—44no—
530C2×D4—44no—
531C2×D4—48no—
532C2×D4—48no—
533C2×D4—48no—
534C2×D4—48no—
535C2×D4—48no—
536C2×D4—88no—
537C2×D4—816no—
538C2×D4—816no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—22no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
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—24no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—216no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—48no—
591C22×C4—48no—
592C22×C4—432no—
593C22×C4—816no—
594C22×C4C2×#4114yes—
595C22×C4C2×#4114yes—
596C22×C4C2×#4114yes—
597C22×C4H(5,𝔽2)14yes—
598C22×C4C2514yes—
599C22×C4C2514yes—
600C22×C4C2512yes—
601C22×C4C2512yes—
602C22×C4C2514yes—
603C22×C4C2514yes—
604C22×C4C2514yes—
605C22×C4C2514yes—
606C22×C4C2514yes—
607C22×C4C2514yes—
608C22×C4C2514yes—
609C22×C4C2512yes—
610C22×C4C2514yes—
611C22×C4C2512yes—
612C22×C4C2512yes—
613C22×C4C2512yes—
614C22×C4C2512yes—
615C4⋊C4—216no—
616C4⋊C4—28no—
617C4⋊C4—28no—
618C4⋊C4—216no—
619C4⋊C4—216no—
620C4⋊C4—44no—
621C4⋊C4—44no—
622C4⋊C4—44no—
623C4⋊C4—44no—
624C4⋊C4—48no—
625C4⋊C4—48no—
626C4⋊C4—48no—
627C4⋊C4—48no—
628C4⋊C4—48no—
629C4⋊C4—48no—
630C4⋊C4—48no—
631C4⋊C4—44no—
632C4⋊C4—44no—
633C4⋊C4—48no—
634C4⋊C4—48no—
635C22⋊C4—216no—
636C22⋊C4—216no—
637C22⋊C4—216no—
638C22⋊C4—216no—
639C22⋊C4—216no—
640C22⋊C4—48no—
641C22⋊C4—48no—
642C22⋊C4—48no—
643C22⋊C4—48no—
644C22⋊C4—48no—
645C22⋊C4—48no—
646C22⋊C4—48no—
647C22⋊C4—48no—
648C22⋊C4—48no—
649C22⋊C4—48no—
650C22⋊C4—48no—
651C22⋊C4—48no—
652C22⋊C4—48no—
653C22⋊C4—48no—
654C22⋊C4—48no—
655C22⋊C4—48no—
656C22⋊C4—48no—
657C42—216no—
658C42—28no—
659C42—44no—
660C42—44no—
661C42—44no—
662C42—44no—
663C42—44no—
664C42—48no—
665C42—48no—
666C42—48no—
667C42C2×#41116yes—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—24no—
682C23—48no—
683C23—48no—
684C23—48no—
685C23—48no—
686C23—48no—
687C23—48no—
688C23—48no—
689C23—48no—
690C23—48no—
691C23—48no—
692C23—48no—
693C23—48no—
694C23—48no—
695C23—48no—
696C23C22×#4112yes—
697C23C2×H(5,𝔽2)12yes—
698C23#58512yes—
699C23#58512yes—
700C23#58512yes—
701C23#58512yes—
702C23#58512yes—
703C23C2611yescharacteristic
704Q8—416no—
705Q8—88no—
706D4—416no—
707D4—88no—
708D4—816no—
709D4—816no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—28no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
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—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—432no—
762C2×C4—48no—
763C2×C4—48no—
764C2×C4—48no—
765C2×C4—48no—
766C2×C4—44no—
767C2×C4—48no—
768C2×C4—48no—
769C2×C4—48no—
770C2×C4—48no—
771C2×C4—44no—
772C2×C4—48no—
773C2×C4—44no—
774C2×C4—48no—
775C2×C4—816no—
776C2×C4C22×#4114yes—
777C2×C4C22×#4114yes—
778C2×C4C22×#4114yes—
779C2×C4C2×H(5,𝔽2)14yes—
780C22—44no—
781C22—44no—
782C22—44no—
783C22—44no—
784C22—44no—
785C22—44no—
786C22—44no—
787C22—44no—
788C22—44no—
789C22—44no—
790C22—44no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—816no—
795C22—816no—
796C22#350614yes—
797C22#351014yes—
798C22#351214yes—
799C22#352914yes—
800C22#354514yes—
801C22#356714yes—
802C22#356814yes—
803C22C23×#4111yescharacteristic
804C22C22×H(5,𝔽2)11yescharacteristic
805C22C2×#58511yescharacteristic
806C22C2×#58511yescharacteristic
807C22C2×#58511yescharacteristic
808C22C2×#58511yescharacteristic
809C22C2×#58511yescharacteristic
810C4—24no—
811C4—24no—
812C4—24no—
813C4—24no—
814C4—42no—
815C4—44no—
816C4—42no—
817C4—44no—
818C4—44no—
819C4—44no—
820C4—44no—
821C4—44no—
822C4—44no—
823C4—44no—
824C4—42no—
825C4—44no—
826C4—44no—
827C2—84no—
828C2—84no—
829C2#4624718yesdirect product factor
830C2C2×#352911yescharacteristic
831C2C2×#356811yescharacteristic
832C2C2×#356711yescharacteristic
833C2C2×#354511yescharacteristic
834C2C2×#350611yescharacteristic
835C2C2×#351011yescharacteristic
836C2C2×#351211yescharacteristic
subgroupG/H
center, socleC24C25
commutator, Frattini, cosocleC23C26
prime radicalC2×#2819C2
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×#2797C2semidirect
3. C2×#2797C2semidirect
4. C2×#2775C2semidirect
5. C2×#2757C2semidirect
6. C2×#2754C2semidirect
7. #46247C2direct (N × H)
8. C2×#2820C2semidirect
10. C2×#2864C2semidirect
11. C2×#2861C2semidirect
12. C2×#2602C2semidirect
13. C2×#2599C2semidirect
14. C2×#2523C2semidirect
15. C2×#2518C2semidirect
16. C2×#2471C2semidirect
17. C2×#2470C2semidirect
18. C2×#2382C2semidirect
19. C2×#2379C2semidirect
20. C2×C4×#124C2semidirect
28. #2864C22semidirect
29. #2861C22semidirect
30. #2820C22semidirect
32. #2800C22semidirect
33. #2797C22semidirect
34. #2797C22semidirect
35. #2775C22semidirect
36. #2757C22semidirect
37. #2754C22semidirect
38. #2602C22semidirect
39. #2599C22semidirect
40. #2523C22semidirect
41. #2518C22semidirect
42. #2471C22semidirect
43. #2470C22semidirect
68. #2382C22semidirect
69. #2379C22semidirect
70. C4×#124C22semidirect
829. C2#46247direct (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×#27972
C2×#27752
C2×#27572
C2×#27542
#462472
C2×#28202
C2×#28192
C2×#28642
C2×#28612
C2×#26022
C2×#25992
C2×#25232
C2×#25182
C2×#24712
C2×#24702
C2×#23822
C2×#23792
C2×C4×#1242