Finite Group Databasebeta

← C2×#51473 #7707321

Subgroups — C2×#51473 #7707321

Order 512.

5884 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×#2763C212yesmaximal, complemented
2C2×#2754C212yesmaximal, complemented
3C2×#2751C212yesmaximal, complemented
4C2×#2749C212yesmaximal, complemented
5C2×#2712C212yesmaximal, complemented
6C2×#2700C212yesmaximal, complemented
7#51473C2132yesmaximal, direct product factor
8C2×#2610C212yesmaximal, complemented
9C2×#2609C212yesmaximal, complemented
10C2×#2605C212yesmaximal, complemented
11C2×#2532C212yesmaximal, complemented
12C2×#2477C212yesmaximal, complemented
13C2×#2474C212yesmaximal, complemented
14C2×#2436C211yesmaximal, characteristic, complemented
15C2×#2409C211yesmaximal, characteristic, complemented
16C2×#2665C211yesmaximal, characteristic, complemented
17C2×#2635C211yesmaximal, characteristic
18C2×#2377C211yesmaximal, characteristic, complemented
19C2×#2357C211yesmaximal, characteristic, complemented
20C2×#2310C211yesmaximal, characteristic, complemented
21C24×Q8C2211yescharacteristic
22C22×#124C2212yes—
23C22×#124C2212yes—
24C22×C22⋊Q8C2212yes—
25C22×#121C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27C22×#117C2212yes—
28C22×#117C2212yes—
29#2763C22132yescomplemented
30#2754C22132yescomplemented
31#2751C22132yescomplemented
32#2749C22132yescomplemented
33#2712C22132yescomplemented
34#2700C22132yescomplemented
35#2665C22116yescomplemented
36#2635C22116yes—
37#2610C22132yescomplemented
38#2609C22132yescomplemented
39#2605C22132yescomplemented
40#2532C22132yescomplemented
41#2477C22132yescomplemented
42#2474C22132yescomplemented
43#2436C22116yescomplemented
44#2409C22116yescomplemented
45C2×#400C2211yescharacteristic
46C2×#400C2212yes—
47C2×#400C2212yes—
48C2×#400C2212yes—
49C2×#399C2211yescharacteristic
50C2×#398C2212yes—
51C2×#397C2212yes—
52C2×#397C2212yes—
53C2×#397C2212yes—
54C2×#397C2212yes—
55C2×#396C2212yes—
56C2×#396C2212yes—
57C2×#395C2212yes—
58C2×#395C2212yes—
59C2×#395C2212yes—
60C2×#394C2212yes—
61C2×#394C2211yescharacteristic
62C2×#394C2212yes—
63C2×#394C2212yes—
64C2×#393C2212yes—
65C2×#393C2212yes—
66C2×#393C2212yes—
67C2×#393C2212yes—
68C2×#393C2212yes—
69C2×#392C2212yes—
70C2×#392C2211yescharacteristic
71#2377C22116yescomplemented
72#2357C22116yescomplemented
73#2310C22116yescomplemented
74C2×#391C2212yes—
75C2×#391C2212yes—
76C2×#391C2212yes—
77C2×#391C2212yes—
78C2×#391C2212yes—
79C2×#391C2212yes—
80C2×#391C2212yes—
81C2×#391C2212yes—
82C2×#390C2212yes—
83C2×#390C2212yes—
84C2×#388C2212yes—
85C2×#388C2212yes—
86C2×#388C2212yes—
87C2×#388C2212yes—
88C2×#388C2212yes—
89C2×#388C2212yes—
90C2×#388C2212yes—
91C2×#388C2212yes—
92C2×#388C2212yes—
93C2×#388C2212yes—
94C2×#388C2212yes—
95C2×#387C2212yes—
96C2×#387C2212yes—
97C2×#387C2212yes—
98C2×#387C2212yes—
99C2×#387C2212yes—
100C2×#387C2212yes—
101C2×#386C2212yes—
102C2×#386C2212yes—
103C2×#386C2212yes—
104C2×#386C2212yes—
105C2×#386C2211yescharacteristic
106C2×#386C2211yescharacteristic
107C2×#386C2212yes—
108C2×#386C2212yes—
109C2×#385C2212yes—
110C2×#385C2211yescharacteristic
111C2×#385C2212yes—
112C2×#385C2211yescharacteristic
113C2×#385C2212yes—
114C2×#383C2212yes—
115C2×#382C2212yes—
116C2×#382C2211yescharacteristic
117C2×#381C2211yescharacteristic
118C2×#381C2211yescharacteristic
119C2×#381C2211yescharacteristic
120C2×#381C2212yes—
121C2×#380C2211yescharacteristic
122C2×C4×C4⋊C4C2212yes—
123C2×C4×C4⋊C4C2211yescharacteristic
124C2×C4×C22⋊C4C2211yescharacteristic
125C2×C4×C22⋊C4C2211yescharacteristic
126C2×#376C2212yes—
127C23×Q8—28no—
128C23×Q8—48no—
129C23×Q8C2312yes—
130C23×Q8C2312yes—
131C23×Q8C2318yes—
132C23×Q8C2312yes—
133C23×D4C2311yescharacteristic
134C23×D4C2311yescharacteristic
135C23×D4C2312yes—
136C23×D4C2312yes—
137C24×C4C2311yescharacteristic
138C24×C4C2311yescharacteristic
139C24×C4C2311yescharacteristic
140C24×C4C2312yes—
141C24×C4C2311yescharacteristic
142C2×#124—48no—
143C2×#124—48no—
144C2×#124C23116yes—
145C2×#124C23116yes—
146C2×C22⋊Q8—48no—
147C2×C22⋊Q8C23116yes—
148C2×#121—28no—
149C2×#121C2318yes—
150C2×C4×D4—28no—
151C2×C4×D4C2318yes—
152C2×#117—48no—
153C2×#117—48no—
154C2×#117C23116yes—
155C2×#117C23116yes—
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⋊C4C2312yes—
172C22×C22⋊C4C2312yes—
173C22×C22⋊C4C2312yes—
174C22×C22⋊C4C2312yes—
175C22×C22⋊C4C2312yes—
176C22×C22⋊C4C2311yescharacteristic
177C22×C22⋊C4C2312yes—
178C22×C22⋊C4C2312yes—
179C22×C22⋊C4C2312yes—
180C22×C22⋊C4C2312yes—
181C22×C22⋊C4C2311yescharacteristic
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⋊C4C2311yescharacteristic
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C42C2312yes—
194C22×C42C2312yes—
195C22×C42C2311yescharacteristic
196C22×C42C2312yes—
197C22×C42C2312yes—
198C22×C42C2312yes—
199C22×C42C2312yes—
200#400C2318yes—
201#400C23116yes—
202#400C23116yes—
203#400C23116yes—
204#399C2318yes—
205#398C23116yes—
206#397C23116yes—
207#397C23116yes—
208#397C23116yes—
209#397C23116yes—
210#396C23116yes—
211#396C23116yes—
212#395C23116yes—
213#395C23116yes—
214#395C23116yes—
215#394C23116yes—
216#394C23116yes—
217#394C2318yes—
218#394C23116yes—
219#393C23116yes—
220#393C23116yes—
221#393C23116yes—
222#393C23116yes—
223#393C23116yes—
224#392C23116yes—
225#392C2318yes—
226#391C23116yes—
227#391C23116yes—
228#391C23116yes—
229#391C23116yes—
230#391C23116yes—
231#391C23116yes—
232#391C23116yes—
233#391C23116yes—
234#390C23116yes—
235#390C23116yes—
236#388C23116yes—
237#388C23116yes—
238#388C23116yes—
239#388C23116yes—
240#388C23116yes—
241#388C23116yes—
242#388C23116yes—
243#388C23116yes—
244#388C23116yes—
245#388C23116yes—
246#388C23116yes—
247#387C23116yes—
248#387C23116yes—
249#387C23116yes—
250#387C23116yes—
251#387C23116yes—
252#387C23116yes—
253#386C23116yes—
254#386C23116yes—
255#386C2318yes—
256#386C23116yes—
257#386C23116yes—
258#386C2318yes—
259#386C23116yes—
260#386C23116yes—
261#385C2318yes—
262#385C23116yes—
263#385C23116yes—
264#385C2318yes—
265#385C23116yes—
266#383C23116yes—
267#382C23116yes—
268#382C2318yes—
269#381C2318yes—
270#381C2318yes—
271#381C23116yes—
272#381C2318yes—
273#380C2318yes—
274C4×C4⋊C4C23116yes—
275C4×C4⋊C4C2318yes—
276C4×C22⋊C4C2318yes—
277C4×C22⋊C4C2318yes—
278#376C23116yes—
279C2×#95C2312yes—
280C2×#95C2311yescharacteristic
281C2×#95C2311yescharacteristic
282C2×#95C2312yes—
283C2×#95C2311yescharacteristic
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×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2312yes—
305C2×#95C2312yes—
306C2×#95C2312yes—
307C2×#95C2311yescharacteristic
308C2×#95C2311yescharacteristic
309C2×#95C2312yes—
310C25C2411yescharacteristic
311C25C2412yes—
312C25C2411yescharacteristic
313C22×Q8—28no—
314C22×Q8—28no—
315C22×Q8—232no—
316C22×Q8—28no—
317C22×Q8—28no—
318C22×Q8—44no—
319C22×Q8—44no—
320C22×Q8—44no—
321C22×Q8—44no—
322C22×Q8—44no—
323C22×Q8—432no—
324C22×Q8—464no—
325C22×Q8C2418yes—
326C22×Q8C2418yes—
327C22×Q8C2418yes—
328C22×D4—24no—
329C22×D4—28no—
330C22×D4—24no—
331C22×D4—24no—
332C22×D4—42no—
333C22×D4—44no—
334C22×D4—44no—
335C22×D4—44no—
336C22×D4—44no—
337C22×D4—44no—
338C22×D4—44no—
339C22×D4C2414yes—
340C22×D4C2414yes—
341C22×D4C2418yes—
342C22×D4C2418yes—
343C23×C4—24no—
344C23×C4—28no—
345C23×C4—24no—
346C23×C4—24no—
347C23×C4—44no—
348C23×C4—44no—
349C23×C4—44no—
350C23×C4—44no—
351C23×C4—44no—
352C23×C4—44no—
353C23×C4#4118yes—
354C23×C4C2414yes—
355C23×C4C2411yescharacteristic
356C23×C4C2412yes—
357C23×C4C2412yes—
358C23×C4C2412yes—
359C23×C4C2412yes—
360C23×C4C2412yes—
361C23×C4C2412yes—
362C23×C4C2411yescharacteristic
363C23×C4C2412yes—
364C23×C4C2412yes—
365C23×C4C2412yes—
366C23×C4C2412yes—
367C23×C4C2411yescharacteristic
368C23×C4C2411yescharacteristic
369C23×C4C2412yes—
370C23×C4C2411yescharacteristic
371C23×C4C2414yes—
372C23×C4C2414yes—
373C23×C4C2418yes—
374C23×C4C2414yes—
375#124—432no—
376#124—432no—
377C22⋊Q8—432no—
378#121—232no—
379C4×D4—232no—
380#117—432no—
381#117—432no—
382C2×C4⋊C4—24no—
383C2×C4⋊C4—24no—
384C2×C4⋊C4—28no—
385C2×C4⋊C4—44no—
386C2×C4⋊C4—44no—
387C2×C4⋊C4—44no—
388C2×C4⋊C4—44no—
389C2×C4⋊C4—44no—
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⋊C4C2418yes—
397C2×C4⋊C4C2414yes—
398C2×C4⋊C4C2414yes—
399C2×C4⋊C4C2418yes—
400C2×C4⋊C4C2418yes—
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×C22⋊C4—24no—
411C2×C22⋊C4—24no—
412C2×C22⋊C4—28no—
413C2×C22⋊C4—28no—
414C2×C22⋊C4—28no—
415C2×C22⋊C4—28no—
416C2×C22⋊C4—28no—
417C2×C22⋊C4—44no—
418C2×C22⋊C4—44no—
419C2×C22⋊C4—44no—
420C2×C22⋊C4—44no—
421C2×C22⋊C4—42no—
422C2×C22⋊C4—44no—
423C2×C22⋊C4—44no—
424C2×C22⋊C4—42no—
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⋊C4C2418yes—
434C2×C22⋊C4C2414yes—
435C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
451C2×C22⋊C4C2414yes—
452C2×C22⋊C4C2418yes—
453C2×C22⋊C4C2418yes—
454C2×C22⋊C4C2418yes—
455C2×C22⋊C4C2418yes—
456C2×C42—24no—
457C2×C42—28no—
458C2×C42—28no—
459C2×C42—28no—
460C2×C42—44no—
461C2×C42—44no—
462C2×C42—44no—
463C2×C42C2418yes—
464C2×C42C2418yes—
465C2×C42C2414yes—
466C2×C42C2418yes—
467C2×C42C2418yes—
468C2×C42C2418yes—
469C2×C42C2418yes—
470#95C2418yes—
471#95C2418yes—
472#95C2418yes—
473#95C2418yes—
474#95C2414yes—
475#95C2414yes—
476#95C2414yes—
477#95C2414yes—
478#95C2418yes—
479#95C2418yes—
480#95C2418yes—
481#95C2418yes—
482#95C2418yes—
483#95C2418yes—
484#95C2418yes—
485#95C2414yes—
486#95C2418yes—
487#95C2414yes—
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—22no—
503C24—22no—
504C24—24no—
505C24—22no—
506C24—24no—
507C24—24no—
508C24—24no—
509C24—24no—
510C24—24no—
511C24—22no—
512C24—24no—
513C24—24no—
514C24—24no—
515C24—24no—
516C24—22no—
517C24C2×#4114yes—
518C24C2512yes—
519C24C2514yes—
520C24C2512yes—
521C24C2511yescharacteristic
522C2×Q8—216no—
523C2×Q8—216no—
524C2×Q8—216no—
525C2×Q8—216no—
526C2×Q8—48no—
527C2×Q8—48no—
528C2×Q8—48no—
529C2×Q8—48no—
530C2×Q8—48no—
531C2×Q8—432no—
532C2×Q8—432no—
533C2×Q8—4128no—
534C2×Q8—816no—
535C2×D4—28no—
536C2×D4—216no—
537C2×D4—28no—
538C2×D4—28no—
539C2×D4—44no—
540C2×D4—416no—
541C2×D4—48no—
542C2×D4—48no—
543C2×D4—48no—
544C2×D4—48no—
545C2×D4—48no—
546C2×D4—48no—
547C2×D4—88no—
548C2×D4—816no—
549C2×D4—816no—
550C22×C4—232no—
551C22×C4—22no—
552C22×C4—28no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—22no—
558C22×C4—216no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—24no—
562C22×C4—28no—
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—24no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—24no—
590C22×C4—24no—
591C22×C4—24no—
592C22×C4—24no—
593C22×C4—24no—
594C22×C4—28no—
595C22×C4—48no—
596C22×C4—416no—
597C22×C4—48no—
598C22×C4—48no—
599C22×C4—48no—
600C22×C4—48no—
601C22×C4—48no—
602C22×C4—416no—
603C22×C4—432no—
604C22×C4—88no—
605C22×C4C2×#4114yes—
606C22×C4C2×#4114yes—
607C22×C4C2×#41116yes—
608C22×C4H(5,𝔽2)18yes—
609C22×C42−1+414yes—
610C22×C4C2514yes—
611C22×C4C2514yes—
612C22×C4C2514yes—
613C22×C4C2514yes—
614C22×C4C2514yes—
615C22×C4C2514yes—
616C22×C4C2512yes—
617C22×C4C2514yes—
618C22×C4C2514yes—
619C22×C4C2514yes—
620C22×C4C2514yes—
621C22×C4C2512yes—
622C22×C4C2512yes—
623C22×C4C2512yes—
624C22×C4C2514yes—
625C22×C4C2512yes—
626C4⋊C4—28no—
627C4⋊C4—28no—
628C4⋊C4—216no—
629C4⋊C4—48no—
630C4⋊C4—48no—
631C4⋊C4—48no—
632C4⋊C4—48no—
633C4⋊C4—48no—
634C4⋊C4—48no—
635C4⋊C4—48no—
636C4⋊C4—48no—
637C4⋊C4—48no—
638C4⋊C4—48no—
639C4⋊C4—48no—
640C22⋊C4—28no—
641C22⋊C4—28no—
642C22⋊C4—216no—
643C22⋊C4—216no—
644C22⋊C4—216no—
645C22⋊C4—216no—
646C22⋊C4—216no—
647C22⋊C4—48no—
648C22⋊C4—48no—
649C22⋊C4—48no—
650C22⋊C4—48no—
651C22⋊C4—44no—
652C22⋊C4—48no—
653C22⋊C4—48no—
654C22⋊C4—44no—
655C22⋊C4—48no—
656C22⋊C4—48no—
657C22⋊C4—48no—
658C22⋊C4—48no—
659C22⋊C4—48no—
660C22⋊C4—48no—
661C22⋊C4—48no—
662C22⋊C4—48no—
663C42—28no—
664C42—216no—
665C42—216no—
666C42—216no—
667C42—48no—
668C42—48no—
669C42—48no—
670C23—24no—
671C23—22no—
672C23—22no—
673C23—24no—
674C23—28no—
675C23—28no—
676C23—28no—
677C23—22no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—24no—
682C23—24no—
683C23—22no—
684C23—24no—
685C23—24no—
686C23—24no—
687C23—24no—
688C23—22no—
689C23—48no—
690C23—48no—
691C23—44no—
692C23—48no—
693C23—44no—
694C23—48no—
695C23—48no—
696C23—44no—
697C23—48no—
698C23—48no—
699C23—48no—
700C23—48no—
701C23—48no—
702C23—48no—
703C23C22×#4114yes—
704C23C22×#4112yes—
705C23C2×H(5,𝔽2)14yes—
706C23C2×2−1+412yes—
707C23#58512yes—
708C23#58514yes—
709C23C2611yescharacteristic
710Q8—432no—
711Q8—432no—
712Q8—816no—
713D4—416no—
714D4—88no—
715D4—816no—
716D4—816no—
717C2×C4—232no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—216no—
725C2×C4—28no—
726C2×C4—28no—
727C2×C4—28no—
728C2×C4—22no—
729C2×C4—22no—
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—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—416no—
763C2×C4—416no—
764C2×C4—432no—
765C2×C4—48no—
766C2×C4—44no—
767C2×C4—44no—
768C2×C4—48no—
769C2×C4—48no—
770C2×C4—48no—
771C2×C4—48no—
772C2×C4—48no—
773C2×C4—48no—
774C2×C4—48no—
775C2×C4—48no—
776C2×C4—48no—
777C2×C4—88no—
778C2×C4C22×#4114yes—
779C2×C4C22×#4114yes—
780C2×C4C2×H(5,𝔽2)18yes—
781C2×C4C2×2−1+414yes—
782C22—24no—
783C22—24no—
784C22—24no—
785C22—44no—
786C22—416no—
787C22—44no—
788C22—44no—
789C22—44no—
790C22—44no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—42no—
795C22—44no—
796C22—42no—
797C22—44no—
798C22—44no—
799C22—42no—
800C22—88no—
801C22—816no—
802C22#349014yes—
803C22#349514yes—
804C22#351014yes—
805C22#354018yes—
806C22#354718yes—
807C22C23×#4111yescharacteristic
808C22C22×H(5,𝔽2)12yes—
809C22C22×2−1+411yescharacteristic
810C22C2×#58511yescharacteristic
811C22C2×#58512yes—
812C4—28no—
813C4—24no—
814C4—24no—
815C4—24no—
816C4—44no—
817C4—44no—
818C4—44no—
819C4—44no—
820C4—44no—
821C4—44no—
822C4—44no—
823C4—44no—
824C4—44no—
825C4—42no—
826C4—42no—
827C4—44no—
828C2—44no—
829C2—84no—
830C2—82no—
831C2#5147318yesdirect product factor
832C2C2×#354012yes—
833C2C2×#354712yes—
834C2C2×#349011yescharacteristic
835C2C2×#349511yescharacteristic
836C2C2×#351011yescharacteristic
subgroupG/H
center, socleC24C25
commutator, Frattini, cosocleC23C26
prime radicalC2×#2635C2
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×#2763C2semidirect
2. C2×#2754C2semidirect
3. C2×#2751C2semidirect
4. C2×#2749C2semidirect
5. C2×#2712C2semidirect
6. C2×#2700C2semidirect
7. #51473C2direct (N × H)
8. C2×#2610C2semidirect
9. C2×#2609C2semidirect
10. C2×#2605C2semidirect
11. C2×#2532C2semidirect
12. C2×#2477C2semidirect
13. C2×#2474C2semidirect
14. C2×#2436C2semidirect
15. C2×#2409C2semidirect
16. C2×#2665C2semidirect
18. C2×#2377C2semidirect
19. C2×#2357C2semidirect
20. C2×#2310C2semidirect
29. #2763C22semidirect
30. #2754C22semidirect
31. #2751C22semidirect
32. #2749C22semidirect
33. #2712C22semidirect
34. #2700C22semidirect
35. #2665C22semidirect
37. #2610C22semidirect
38. #2609C22semidirect
39. #2605C22semidirect
40. #2532C22semidirect
41. #2477C22semidirect
42. #2474C22semidirect
43. #2436C22semidirect
44. #2409C22semidirect
71. #2377C22semidirect
72. #2357C22semidirect
73. #2310C22semidirect
831. C2#51473direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#27632
C2×#27542
C2×#27512
C2×#27492
C2×#27122
C2×#27002
#514732
C2×#26102
C2×#26092
C2×#26052
C2×#25322
C2×#24772
C2×#24742
C2×#24362
C2×#24092
C2×#26652
C2×#26352
C2×#23772
C2×#23572
C2×#23102