Finite Group Databasebeta

← C2×#52887 #8092499

Subgroups — C2×#52887 #8092499

Order 512.

5146 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52887C2132yesmaximal, direct product factor
2C2×#2809C211yesmaximal, characteristic, complemented
3C2×#2784C211yesmaximal, characteristic, complemented
4C2×#2716C212yesmaximal, complemented
5C2×#2710C212yesmaximal, complemented
6C2×#2705C212yesmaximal, complemented
7C2×#2830C212yesmaximal, complemented
8C2×#2828C211yesmaximal, characteristic
9C2×#2832C211yesmaximal, characteristic, complemented
10C2×#2836C212yesmaximal, complemented
11C2×#2827C212yesmaximal, complemented
12C2×#2545C211yesmaximal, characteristic, complemented
13C2×#2581C211yesmaximal, characteristic, complemented
14C2×#2557C212yesmaximal, complemented
15C2×#2553C212yesmaximal, complemented
16C2×#2530C212yesmaximal, complemented
17C2×#2522C212yesmaximal, complemented
18C2×#2458C212yesmaximal, complemented
19C2×#2630C212yesmaximal, complemented
20C2×#2398C211yesmaximal, characteristic, complemented
21C22×C4⋊Q8C2211yescharacteristic
22C22×#126C2212yes—
23C22×#124C2211yescharacteristic
24C22×#124C2211yescharacteristic
25C22×#123C2212yes—
26C22×#123C2212yes—
27C22×C4×Q8C2211yescharacteristic
28C22×C4×Q8C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30#2836C22132yescomplemented
31#2832C22116yescomplemented
32#2830C22132yescomplemented
33#2828C22116yes—
34#2827C22132yescomplemented
35#2809C22116yescomplemented
36#2784C22116yescomplemented
37#2716C22132yescomplemented
38#2710C22132yescomplemented
39#2705C22132yescomplemented
40#2630C22132yescomplemented
41#2581C22116yescomplemented
42#2557C22132yescomplemented
43#2553C22132yescomplemented
44#2545C22116yescomplemented
45#2530C22132yescomplemented
46#2522C22132yescomplemented
47#2458C22132yescomplemented
48#2398C22116yescomplemented
49C2×#400C2211yescharacteristic
50C2×#400C2211yescharacteristic
51C2×#400C2211yescharacteristic
52C2×#400C2212yes—
53C2×#400C2211yescharacteristic
54C2×#400C2212yes—
55C2×#399C2212yes—
56C2×#399C2212yes—
57C2×#398C2212yes—
58C2×#398C2212yes—
59C2×#398C2212yes—
60C2×#398C2212yes—
61C2×#398C2212yes—
62C2×#397C2212yes—
63C2×#397C2212yes—
64C2×#397C2212yes—
65C2×#397C2212yes—
66C2×#397C2212yes—
67C2×#397C2212yes—
68C2×#397C2212yes—
69C2×#396C2212yes—
70C2×#396C2212yes—
71C2×#396C2212yes—
72C2×#396C2212yes—
73C2×#396C2212yes—
74C2×#395C2211yescharacteristic
75C2×#395C2211yescharacteristic
76C2×#394C2212yes—
77C2×#394C2212yes—
78C2×#394C2212yes—
79C2×#394C2211yescharacteristic
80C2×#394C2212yes—
81C2×#394C2212yes—
82C2×#394C2211yescharacteristic
83C2×#393C2212yes—
84C2×#393C2212yes—
85C2×#393C2212yes—
86C2×#393C2212yes—
87C2×#392C2212yes—
88C2×#392C2212yes—
89C2×#391C2212yes—
90C2×#391C2211yescharacteristic
91C2×#391C2212yes—
92C2×#390C2211yescharacteristic
93C2×#390C2212yes—
94C2×#390C2212yes—
95C2×#389C2212yes—
96C2×#389C2212yes—
97C2×#389C2212yes—
98C2×#388C2212yes—
99C2×#388C2212yes—
100C2×#388C2212yes—
101C2×#388C2212yes—
102C2×#388C2212yes—
103C2×#388C2212yes—
104C2×#388C2212yes—
105C2×#387C2212yes—
106C2×#387C2212yes—
107C2×#387C2212yes—
108C2×#387C2212yes—
109C2×#387C2212yes—
110C2×#387C2212yes—
111C2×#387C2212yes—
112C2×#387C2212yes—
113C2×#386C2212yes—
114C2×#386C2212yes—
115C2×#386C2212yes—
116C2×#385C2212yes—
117C2×#385C2212yes—
118C2×#385C2212yes—
119C2×#382C2211yescharacteristic
120C2×#380C2212yes—
121C2×#380C2212yes—
122C2×C4×C4⋊C4C2211yescharacteristic
123C2×C4×C22⋊C4C2212yes—
124C2×C4×C22⋊C4C2212yes—
125C2×C4×C22⋊C4C2212yes—
126C2×#376C2211yescharacteristic
127C23×Q8C2311yescharacteristic
128C23×Q8C2311yescharacteristic
129C23×Q8C2311yescharacteristic
130C23×D4C2311yescharacteristic
131C23×D4C2311yescharacteristic
132C23×D4C2312yes—
133C23×D4C2312yes—
134C24×C4C2312yes—
135C24×C4C2312yes—
136C2×C4⋊Q8—44no—
137C2×C4⋊Q8C2318yes—
138C2×#126—48no—
139C2×#126C23116yes—
140C2×#124—44no—
141C2×#124—44no—
142C2×#124C2318yes—
143C2×#124C2318yes—
144C2×#123—48no—
145C2×#123—48no—
146C2×#123C23116yes—
147C2×#123C23116yes—
148C2×C4×Q8—44no—
149C2×C4×Q8—44no—
150C2×C4×Q8C2318yes—
151C2×C4×Q8C2318yes—
152C2×C4×D4—44no—
153C2×C4×D4C2318yes—
154C22×C4⋊C4C2312yes—
155C22×C4⋊C4C2312yes—
156C22×C4⋊C4C2312yes—
157C22×C4⋊C4C2311yescharacteristic
158C22×C4⋊C4C2312yes—
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2312yes—
162C22×C4⋊C4C2312yes—
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2312yes—
166C22×C4⋊C4C2312yes—
167C22×C4⋊C4C2312yes—
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2312yes—
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2312yes—
174C22×C4⋊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×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C42C2311yescharacteristic
198C22×C42C2311yescharacteristic
199C22×C42C2311yescharacteristic
200C22×C42C2312yes—
201C22×C42C2311yescharacteristic
202C22×C42C2312yes—
203C22×C42C2311yescharacteristic
204C22×C42C2312yes—
205#400C2318yes—
206#400C23116yes—
207#400C2318yes—
208#400C23116yes—
209#400C2318yes—
210#400C2318yes—
211#399C23116yes—
212#399C23116yes—
213#398C23116yes—
214#398C23116yes—
215#398C23116yes—
216#398C23116yes—
217#398C23116yes—
218#397C23116yes—
219#397C23116yes—
220#397C23116yes—
221#397C23116yes—
222#397C23116yes—
223#397C23116yes—
224#397C23116yes—
225#396C23116yes—
226#396C23116yes—
227#396C23116yes—
228#396C23116yes—
229#396C23116yes—
230#395C2318yes—
231#395C2318yes—
232#394C23116yes—
233#394C23116yes—
234#394C23116yes—
235#394C2318yes—
236#394C23116yes—
237#394C23116yes—
238#394C2318yes—
239#393C23116yes—
240#393C23116yes—
241#393C23116yes—
242#393C23116yes—
243#392C23116yes—
244#392C23116yes—
245#391C2318yes—
246#391C23116yes—
247#391C23116yes—
248#390C2318yes—
249#390C23116yes—
250#390C23116yes—
251#389C23116yes—
252#389C23116yes—
253#389C23116yes—
254#388C23116yes—
255#388C23116yes—
256#388C23116yes—
257#388C23116yes—
258#388C23116yes—
259#388C23116yes—
260#388C23116yes—
261#387C23116yes—
262#387C23116yes—
263#387C23116yes—
264#387C23116yes—
265#387C23116yes—
266#387C23116yes—
267#387C23116yes—
268#387C23116yes—
269#386C23116yes—
270#386C23116yes—
271#386C23116yes—
272#385C23116yes—
273#385C23116yes—
274#385C23116yes—
275#382C2318yes—
276#380C23116yes—
277#380C23116yes—
278C4×C4⋊C4C2318yes—
279C4×C22⋊C4C23116yes—
280C4×C22⋊C4C23116yes—
281C4×C22⋊C4C23116yes—
282#376C2318yes—
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×#95C2311yescharacteristic
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2311yescharacteristic
301C2×#95C2312yes—
302C2×#95C2311yescharacteristic
303C2×#95C2311yescharacteristic
304C2×#95C2312yes—
305C2×#95C2312yes—
306C2×#95C2312yes—
307C2×#95C2312yes—
308C2×#95C2312yes—
309C2×#95C2312yes—
310C25C2412yes—
311C25C2412yes—
312C22×Q8—24no—
313C22×Q8—24no—
314C22×Q8—24no—
315C22×Q8—42no—
316C22×Q8—42no—
317C22×Q8—44no—
318C22×Q8—42no—
319C22×Q8—42no—
320C22×Q8C2414yes—
321C22×Q8C2414yes—
322C22×Q8C2414yes—
323C22×D4—24no—
324C22×D4—42no—
325C22×D4—44no—
326C22×D4—44no—
327C22×D4—44no—
328C22×D4—42no—
329C22×D4—42no—
330C22×D4—44no—
331C22×D4—44no—
332C22×D4—44no—
333C22×D4—44no—
334C22×D4C2414yes—
335C22×D4C2414yes—
336C22×D4C2418yes—
337C22×D4C2418yes—
338C23×C4—28no—
339C23×C4—44no—
340C23×C4—44no—
341C23×C4—44no—
342C23×C4—44no—
343C23×C4—44no—
344C23×C4C2411yescharacteristic
345C23×C4C2412yes—
346C23×C4C2412yes—
347C23×C4C2411yescharacteristic
348C23×C4C2411yescharacteristic
349C23×C4C2412yes—
350C23×C4C2412yes—
351C23×C4C2412yes—
352C23×C4C2412yes—
353C23×C4C2412yes—
354C23×C4C2412yes—
355C23×C4C2411yescharacteristic
356C23×C4C2412yes—
357C23×C4C2412yes—
358C23×C4C2411yescharacteristic
359C23×C4C2411yescharacteristic
360C23×C4C2411yescharacteristic
361C23×C4C2418yes—
362C23×C4C2418yes—
363C4⋊Q8—416no—
364#126—432no—
365#124—416no—
366#124—416no—
367#123—432no—
368#123—432no—
369C4×Q8—416no—
370C4×Q8—416no—
371C4×D4—416no—
372C2×C4⋊C4—28no—
373C2×C4⋊C4—28no—
374C2×C4⋊C4—28no—
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—44no—
383C2×C4⋊C4—44no—
384C2×C4⋊C4—42no—
385C2×C4⋊C4—42no—
386C2×C4⋊C4—42no—
387C2×C4⋊C4—42no—
388C2×C4⋊C4—42no—
389C2×C4⋊C4—44no—
390C2×C4⋊C4—44no—
391C2×C4⋊C4—44no—
392C2×C4⋊C4—44no—
393C2×C4⋊C4C2418yes—
394C2×C4⋊C4C2418yes—
395C2×C4⋊C4C2418yes—
396C2×C4⋊C4C2414yes—
397C2×C4⋊C4C2414yes—
398C2×C4⋊C4C2414yes—
399C2×C4⋊C4C2414yes—
400C2×C4⋊C4C2414yes—
401C2×C4⋊C4C2418yes—
402C2×C4⋊C4C2418yes—
403C2×C4⋊C4C2418yes—
404C2×C4⋊C4C2418yes—
405C2×C4⋊C4C2418yes—
406C2×C4⋊C4C2418yes—
407C2×C4⋊C4C2418yes—
408C2×C4⋊C4C2418yes—
409C2×C4⋊C4C2418yes—
410C2×C4⋊C4C2418yes—
411C2×C4⋊C4C2418yes—
412C2×C4⋊C4C2418yes—
413C2×C4⋊C4C2418yes—
414C2×C22⋊C4—28no—
415C2×C22⋊C4—28no—
416C2×C22⋊C4—28no—
417C2×C22⋊C4—28no—
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⋊C4—44no—
429C2×C22⋊C4—44no—
430C2×C22⋊C4—44no—
431C2×C22⋊C4—44no—
432C2×C22⋊C4—44no—
433C2×C22⋊C4—44no—
434C2×C22⋊C4—44no—
435C2×C22⋊C4—44no—
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×C22⋊C4C2418yes—
451C2×C22⋊C4C2418yes—
452C2×C22⋊C4C2418yes—
453C2×C22⋊C4C2418yes—
454C2×C22⋊C4C2418yes—
455C2×C22⋊C4C2418yes—
456C2×C22⋊C4C2418yes—
457C2×C22⋊C4C2418yes—
458C2×C42—24no—
459C2×C42—24no—
460C2×C42—24no—
461C2×C42—44no—
462C2×C42—42no—
463C2×C42—44no—
464C2×C42—42no—
465C2×C42—44no—
466C2×C42C2414yes—
467C2×C42C2414yes—
468C2×C42C2414yes—
469C2×C42C2418yes—
470C2×C42C2414yes—
471C2×C42C2418yes—
472C2×C42C2414yes—
473C2×C42C2418yes—
474#95C2414yes—
475#95C2418yes—
476#95C2414yes—
477#95C2418yes—
478#95C2418yes—
479#95C2418yes—
480#95C2418yes—
481#95C2418yes—
482#95C2418yes—
483#95C2418yes—
484#95C2418yes—
485#95C2414yes—
486#95C2414yes—
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—
501C24—24no—
502C24—24no—
503C24—24no—
504C24—24no—
505C24—24no—
506C24—24no—
507C24—24no—
508C24—24no—
509C24—24no—
510C24—24no—
511C24—24no—
512C24—24no—
513C24—24no—
514C24—24no—
515C24C2514yes—
516C24C2514yes—
517C24C2511yescharacteristic
518C2×Q8—28no—
519C2×Q8—28no—
520C2×Q8—28no—
521C2×Q8—44no—
522C2×Q8—44no—
523C2×Q8—48no—
524C2×Q8—44no—
525C2×Q8—44no—
526C2×Q8—416no—
527C2×Q8—416no—
528C2×Q8—88no—
529C2×D4—28no—
530C2×D4—44no—
531C2×D4—48no—
532C2×D4—48no—
533C2×D4—48no—
534C2×D4—44no—
535C2×D4—44no—
536C2×D4—48no—
537C2×D4—48no—
538C2×D4—48no—
539C2×D4—48no—
540C2×D4—416no—
541C2×D4—88no—
542C2×D4—816no—
543C2×D4—816no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—24no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
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—22no—
564C22×C4—24no—
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—24no—
580C22×C4—24no—
581C22×C4—24no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—216no—
589C22×C4—48no—
590C22×C4—48no—
591C22×C4—48no—
592C22×C4—48no—
593C22×C4—48no—
594C22×C4—816no—
595C22×C4—816no—
596C22×C4H(5,𝔽2)14yes—
597C22×C4H(5,𝔽2)14yes—
598C22×C42−1+414yes—
599C22×C4C2514yes—
600C22×C4C2514yes—
601C22×C4C2512yes—
602C22×C4C2512yes—
603C22×C4C2514yes—
604C22×C4C2514yes—
605C22×C4C2512yes—
606C22×C4C2514yes—
607C22×C4C2514yes—
608C22×C4C2514yes—
609C22×C4C2514yes—
610C22×C4C2512yes—
611C22×C4C2514yes—
612C22×C4C2514yes—
613C22×C4C2512yes—
614C22×C4C2512yes—
615C22×C4C2512yes—
616C4⋊C4—216no—
617C4⋊C4—216no—
618C4⋊C4—216no—
619C4⋊C4—48no—
620C4⋊C4—48no—
621C4⋊C4—48no—
622C4⋊C4—48no—
623C4⋊C4—48no—
624C4⋊C4—48no—
625C4⋊C4—48no—
626C4⋊C4—48no—
627C4⋊C4—48no—
628C4⋊C4—44no—
629C4⋊C4—44no—
630C4⋊C4—44no—
631C4⋊C4—44no—
632C4⋊C4—44no—
633C4⋊C4—48no—
634C4⋊C4—48no—
635C4⋊C4—48no—
636C4⋊C4—48no—
637C22⋊C4—216no—
638C22⋊C4—216no—
639C22⋊C4—216no—
640C22⋊C4—216no—
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—
657C22⋊C4—48no—
658C22⋊C4—48no—
659C42—28no—
660C42—28no—
661C42—28no—
662C42—48no—
663C42—48no—
664C42—44no—
665C42—48no—
666C42—44no—
667C23—24no—
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—48no—
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—
695C23C2×H(5,𝔽2)12yes—
696C23C2×H(5,𝔽2)12yes—
697C23C2×2−1+412yes—
698C23#58514yes—
699C23#58514yes—
700C23C2611yescharacteristic
701Q8—416no—
702Q8—416no—
703Q8—88no—
704D4—416no—
705D4—88no—
706D4—816no—
707D4—816no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—28no—
714C2×C4—28no—
715C2×C4—28no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
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—22no—
731C2×C4—24no—
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—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—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—48no—
759C2×C4—44no—
760C2×C4—48no—
761C2×C4—48no—
762C2×C4—48no—
763C2×C4—48no—
764C2×C4—48no—
765C2×C4—48no—
766C2×C4—48no—
767C2×C4—48no—
768C2×C4—48no—
769C2×C4—816no—
770C2×C4—816no—
771C2×C4C2×H(5,𝔽2)14yes—
772C2×C4C2×H(5,𝔽2)14yes—
773C2×C4C2×2−1+414yes—
774C22—44no—
775C22—44no—
776C22—44no—
777C22—44no—
778C22—44no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—44no—
783C22—44no—
784C22—44no—
785C22—44no—
786C22—44no—
787C22—44no—
788C22—816no—
789C22—816no—
790C22#352914yes—
791C22#353614yes—
792C22#354514yes—
793C22#355718yes—
794C22#356218yes—
795C22C22×H(5,𝔽2)11yescharacteristic
796C22C22×H(5,𝔽2)11yescharacteristic
797C22C22×2−1+411yescharacteristic
798C22C2×#58512yes—
799C22C2×#58512yes—
800C4—24no—
801C4—24no—
802C4—24no—
803C4—42no—
804C4—44no—
805C4—44no—
806C4—44no—
807C4—44no—
808C4—44no—
809C4—44no—
810C4—44no—
811C4—44no—
812C4—44no—
813C4—42no—
814C4—42no—
815C4—42no—
816C4—44no—
817C2—84no—
818C2—84no—
819C2#5288718yesdirect product factor
820C2C2×#352911yescharacteristic
821C2C2×#353611yescharacteristic
822C2C2×#355712yes—
823C2C2×#356212yes—
824C2C2×#354511yescharacteristic
subgroupG/H
center, socleC24C25
commutator, Frattini, cosocleC23C26
prime radicalC2×#2828C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #52887C2direct (N × H)
2. C2×#2809C2semidirect
3. C2×#2784C2semidirect
4. C2×#2716C2semidirect
5. C2×#2710C2semidirect
6. C2×#2705C2semidirect
7. C2×#2830C2semidirect
9. C2×#2832C2semidirect
10. C2×#2836C2semidirect
11. C2×#2827C2semidirect
12. C2×#2545C2semidirect
13. C2×#2581C2semidirect
14. C2×#2557C2semidirect
15. C2×#2553C2semidirect
16. C2×#2530C2semidirect
17. C2×#2522C2semidirect
18. C2×#2458C2semidirect
19. C2×#2630C2semidirect
20. C2×#2398C2semidirect
30. #2836C22semidirect
31. #2832C22semidirect
32. #2830C22semidirect
34. #2827C22semidirect
35. #2809C22semidirect
36. #2784C22semidirect
37. #2716C22semidirect
38. #2710C22semidirect
39. #2705C22semidirect
40. #2630C22semidirect
41. #2581C22semidirect
42. #2557C22semidirect
43. #2553C22semidirect
44. #2545C22semidirect
45. #2530C22semidirect
46. #2522C22semidirect
47. #2458C22semidirect
48. #2398C22semidirect
819. C2#52887direct (N × H)

Maximal subgroups

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

subgroupindex
#528872
C2×#28092
C2×#27842
C2×#27162
C2×#27102
C2×#27052
C2×#28302
C2×#28282
C2×#28322
C2×#28362
C2×#28272
C2×#25452
C2×#25812
C2×#25572
C2×#25532
C2×#25302
C2×#25222
C2×#24582
C2×#26302
C2×#23982