Finite Group Databasebeta

← C2×#41977 #7640479

Subgroups — C2×#41977 #7640479

Order 512.

5532 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2797C212yesmaximal, complemented
2C2×#2754C212yesmaximal, complemented
3C2×#2730C212yesmaximal, complemented
4C2×#2721C212yesmaximal, complemented
5#41977C2132yesmaximal, direct product factor
6C2×#2836C212yesmaximal, complemented
7C2×#2566C211yesmaximal, characteristic, complemented
8C2×#2605C211yesmaximal, characteristic, complemented
9C2×#2556C212yesmaximal, complemented
10C2×#2447C212yesmaximal, complemented
11C2×#2468C212yesmaximal, complemented
12C2×#2450C212yesmaximal, complemented
13C2×#2460C212yesmaximal, complemented
14C2×#2633C211yesmaximal, characteristic, complemented
15C2×#2662C212yesmaximal, complemented
16C2×#2648C212yesmaximal, complemented
17C2×#2397C211yesmaximal, characteristic
18C2×#2371C211yesmaximal, characteristic, complemented
19C2×#2353C211yesmaximal, characteristic, complemented
20C2×#2319C211yesmaximal, characteristic, complemented
21C22×#126C2212yes—
22C22×#125C2211yescharacteristic
23C22×#125C2212yes—
24C22×#124C2212yes—
25C22×C22⋊Q8C2212yes—
26C22×C4×D4C2211yescharacteristic
27C22×C4×D4C2211yescharacteristic
28C22×C4×D4C2212yes—
29C22×C4×D4C2212yes—
30#2836C22132yescomplemented
31#2797C22132yescomplemented
32#2754C22132yescomplemented
33#2730C22132yescomplemented
34#2721C22132yescomplemented
35#2662C22132yescomplemented
36#2648C22132yescomplemented
37#2633C22116yescomplemented
38#2605C22116yescomplemented
39#2566C22116yescomplemented
40#2556C22132yescomplemented
41#2468C22132yescomplemented
42#2460C22132yescomplemented
43#2450C22132yescomplemented
44#2447C22132yescomplemented
45#2397C22116yes—
46C2×#400C2212yes—
47C2×#400C2212yes—
48C2×#399C2211yescharacteristic
49C2×#399C2212yes—
50C2×#399C2211yescharacteristic
51C2×#399C2212yes—
52C2×#398C2212yes—
53C2×#398C2212yes—
54C2×#398C2212yes—
55C2×#398C2212yes—
56C2×#397C2212yes—
57C2×#397C2212yes—
58C2×#397C2212yes—
59C2×#397C2212yes—
60C2×#397C2212yes—
61C2×#397C2212yes—
62C2×#396C2212yes—
63C2×#396C2212yes—
64C2×#396C2212yes—
65C2×#396C2212yes—
66C2×#395C2212yes—
67C2×#394C2212yes—
68C2×#394C2212yes—
69C2×#394C2212yes—
70C2×#394C2212yes—
71C2×#394C2212yes—
72C2×#393C2212yes—
73C2×#392C2211yescharacteristic
74C2×#392C2211yescharacteristic
75C2×#392C2212yes—
76#2371C22116yescomplemented
77#2353C22116yescomplemented
78#2319C22116yescomplemented
79C2×#391C2212yes—
80C2×#391C2212yes—
81C2×#391C2212yes—
82C2×#390C2212yes—
83C2×#390C2212yes—
84C2×#390C2211yescharacteristic
85C2×#390C2211yescharacteristic
86C2×#389C2212yes—
87C2×#389C2212yes—
88C2×#388C2212yes—
89C2×#388C2212yes—
90C2×#388C2212yes—
91C2×#388C2212yes—
92C2×#388C2212yes—
93C2×#388C2212yes—
94C2×#388C2212yes—
95C2×#388C2212yes—
96C2×#387C2212yes—
97C2×#387C2212yes—
98C2×#387C2212yes—
99C2×#387C2212yes—
100C2×#387C2212yes—
101C2×#387C2212yes—
102C2×#387C2212yes—
103C2×#387C2212yes—
104C2×#386C2212yes—
105C2×#386C2212yes—
106C2×#386C2212yes—
107C2×#385C2212yes—
108C2×#385C2212yes—
109C2×#385C2212yes—
110C2×#385C2212yes—
111C2×#385C2212yes—
112C2×#384C2211yescharacteristic
113C2×#383C2211yescharacteristic
114C2×#382C2211yescharacteristic
115C2×#381C2212yes—
116C2×#381C2211yescharacteristic
117C2×#380C2212yes—
118C2×#380C2211yescharacteristic
119C2×C4×C4⋊C4C2211yescharacteristic
120C2×C4×C4⋊C4C2212yes—
121C2×C4×C4⋊C4C2212yes—
122C2×C4×C22⋊C4C2212yes—
123C2×C4×C22⋊C4C2211yescharacteristic
124C2×#376C2211yescharacteristic
125C2×#376C2211yescharacteristic
126C22×#95C2211yescharacteristic
127C23×Q8C2312yes—
128C23×D4C2311yescharacteristic
129C23×D4C2312yes—
130C23×D4C2312yes—
131C23×D4C2311yescharacteristic
132C24×C4C2311yescharacteristic
133C24×C4C2311yescharacteristic
134C24×C4C2312yes—
135C24×C4C2312yes—
136C2×#126—48no—
137C2×#126C23116yes—
138C2×#125—28no—
139C2×#125—48no—
140C2×#125C2318yes—
141C2×#125C23116yes—
142C2×#124—48no—
143C2×#124C23116yes—
144C2×C22⋊Q8—48no—
145C2×C22⋊Q8C23116yes—
146C2×C4×D4—28no—
147C2×C4×D4—28no—
148C2×C4×D4—48no—
149C2×C4×D4—48no—
150C2×C4×D4C2318yes—
151C2×C4×D4C2318yes—
152C2×C4×D4C23116yes—
153C2×C4×D4C23116yes—
154C22×C4⋊C4C2312yes—
155C22×C4⋊C4C2312yes—
156C22×C4⋊C4C2312yes—
157C22×C4⋊C4C2311yescharacteristic
158C22×C4⋊C4C2311yescharacteristic
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⋊C4C2312yes—
168C22×C4⋊C4C2312yes—
169C22×C4⋊C4C2312yes—
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2312yes—
175C22×C22⋊C4C2312yes—
176C22×C22⋊C4C2311yescharacteristic
177C22×C22⋊C4C2311yescharacteristic
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×C42C2312yes—
198C22×C42C2312yes—
199C22×C42C2312yes—
200C22×C42C2312yes—
201C22×C42C2312yes—
202C22×C42C2311yescharacteristic
203C22×C42C2311yescharacteristic
204C22×C42C2311yescharacteristic
205#400C23116yes—
206#400C23116yes—
207#399C2318yes—
208#399C23116yes—
209#399C23116yes—
210#399C2318yes—
211#398C23116yes—
212#398C23116yes—
213#398C23116yes—
214#398C23116yes—
215#397C23116yes—
216#397C23116yes—
217#397C23116yes—
218#397C23116yes—
219#397C23116yes—
220#397C23116yes—
221#396C23116yes—
222#396C23116yes—
223#396C23116yes—
224#396C23116yes—
225#395C23116yes—
226#394C23116yes—
227#394C23116yes—
228#394C23116yes—
229#394C23116yes—
230#394C23116yes—
231#393C23116yes—
232#392C2318yes—
233#392C2318yes—
234#392C23116yes—
235#391C23116yes—
236#391C23116yes—
237#391C23116yes—
238#390C2318yes—
239#390C2318yes—
240#390C23116yes—
241#390C23116yes—
242#389C23116yes—
243#389C23116yes—
244#388C23116yes—
245#388C23116yes—
246#388C23116yes—
247#388C23116yes—
248#388C23116yes—
249#388C23116yes—
250#388C23116yes—
251#388C23116yes—
252#387C23116yes—
253#387C23116yes—
254#387C23116yes—
255#387C23116yes—
256#387C23116yes—
257#387C23116yes—
258#387C23116yes—
259#387C23116yes—
260#386C23116yes—
261#386C23116yes—
262#386C23116yes—
263#385C23116yes—
264#385C23116yes—
265#385C23116yes—
266#385C23116yes—
267#385C23116yes—
268#384C2318yes—
269#383C2318yes—
270#382C2318yes—
271#381C23116yes—
272#381C2318yes—
273#380C23116yes—
274#380C2318yes—
275C4×C4⋊C4C2318yes—
276C4×C4⋊C4C23116yes—
277C4×C4⋊C4C23116yes—
278C4×C22⋊C4C23116yes—
279C4×C22⋊C4C2318yes—
280#376C2318yes—
281#376C2318yes—
282C2×#95C2318yes—
283C2×#95C2311yescharacteristic
284C2×#95C2311yescharacteristic
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×#95C2311yescharacteristic
305C2×#95C2311yescharacteristic
306C2×#95C2311yescharacteristic
307C2×#95C2312yes—
308C2×#95C2311yescharacteristic
309C2×#95C2312yes—
310C25C2412yes—
311C25C2411yescharacteristic
312C25C2411yescharacteristic
313C22×Q8—28no—
314C22×Q8—44no—
315C22×Q8—44no—
316C22×Q8C2418yes—
317C22×D4—24no—
318C22×D4—28no—
319C22×D4—24no—
320C22×D4—24no—
321C22×D4—28no—
322C22×D4—44no—
323C22×D4—42no—
324C22×D4—44no—
325C22×D4—44no—
326C22×D4—44no—
327C22×D4—44no—
328C22×D4C2414yes—
329C22×D4C2418yes—
330C22×D4C2418yes—
331C22×D4C2414yes—
332C23×C4—24no—
333C23×C4—24no—
334C23×C4—28no—
335C23×C4—44no—
336C23×C4—44no—
337C23×C4—44no—
338C23×C4—44no—
339C23×C4—44no—
340C23×C4—44no—
341C23×C4—44no—
342C23×C4C2412yes—
343C23×C4C2412yes—
344C23×C4C2412yes—
345C23×C4C2412yes—
346C23×C4C2412yes—
347C23×C4C2412yes—
348C23×C4C2411yescharacteristic
349C23×C4C2412yes—
350C23×C4C2411yescharacteristic
351C23×C4C2412yes—
352C23×C4C2412yes—
353C23×C4C2412yes—
354C23×C4C2411yescharacteristic
355C23×C4C2411yescharacteristic
356C23×C4C2411yescharacteristic
357C23×C4C2412yes—
358C23×C4C2414yes—
359C23×C4C2414yes—
360C23×C4C2418yes—
361C23×C4C2418yes—
362#126—432no—
363#125—232no—
364#125—432no—
365#124—432no—
366C22⋊Q8—432no—
367C4×D4—232no—
368C4×D4—232no—
369C4×D4—432no—
370C4×D4—432no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—24no—
373C2×C4⋊C4—28no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—28no—
377C2×C4⋊C4—28no—
378C2×C4⋊C4—28no—
379C2×C4⋊C4—28no—
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⋊C4—44no—
387C2×C4⋊C4—44no—
388C2×C4⋊C4—44no—
389C2×C4⋊C4—44no—
390C2×C4⋊C4—44no—
391C2×C4⋊C4—44no—
392C2×C4⋊C4C2418yes—
393C2×C4⋊C4C2414yes—
394C2×C4⋊C4C2414yes—
395C2×C4⋊C4C2418yes—
396C2×C4⋊C4C2418yes—
397C2×C4⋊C4C2418yes—
398C2×C4⋊C4C2418yes—
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×C22⋊C4—28no—
414C2×C22⋊C4—24no—
415C2×C22⋊C4—24no—
416C2×C22⋊C4—28no—
417C2×C22⋊C4—28no—
418C2×C22⋊C4—28no—
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⋊C4C2418yes—
436C2×C22⋊C4C2418yes—
437C2×C22⋊C4C2414yes—
438C2×C22⋊C4C2414yes—
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×C42—28no—
458C2×C42—28no—
459C2×C42—44no—
460C2×C42—42no—
461C2×C42—42no—
462C2×C42—44no—
463C2×C42—44no—
464C2×C42#4118yes—
465C2×C42C2418yes—
466C2×C42C2418yes—
467C2×C42C2418yes—
468C2×C42C2418yes—
469C2×C42C2418yes—
470C2×C42C2414yes—
471C2×C42C2414yes—
472C2×C42C2414yes—
473#95C2414yes—
474#95C2414yes—
475#95C2418yes—
476#95C2414yes—
477#95C2414yes—
478#95C2418yes—
479#95C2418yes—
480#95C2414yes—
481#95C2414yes—
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—
498#95C2418yes—
499#95C2418yes—
500C24—22no—
501C24—24no—
502C24—24no—
503C24—22no—
504C24—24no—
505C24—22no—
506C24—24no—
507C24—24no—
508C24—24no—
509C24—22no—
510C24—24no—
511C24—24no—
512C24—24no—
513C24—24no—
514C24—24no—
515C24—22no—
516C242−1+414yes—
517C24C2514yes—
518C24C2512yes—
519C24C2512yes—
520C24C2511yescharacteristic
521C2×Q8—216no—
522C2×Q8—48no—
523C2×Q8—48no—
524C2×Q8—816no—
525C2×D4—28no—
526C2×D4—216no—
527C2×D4—28no—
528C2×D4—28no—
529C2×D4—216no—
530C2×D4—48no—
531C2×D4—44no—
532C2×D4—48no—
533C2×D4—48no—
534C2×D4—48no—
535C2×D4—48no—
536C2×D4—416no—
537C2×D4—416no—
538C2×D4—432no—
539C2×D4—432no—
540C22×C4—24no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—22no—
547C22×C4—24no—
548C22×C4—22no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
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—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—28no—
581C22×C4—28no—
582C22×C4—216no—
583C22×C4—48no—
584C22×C4—48no—
585C22×C4—48no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—88no—
591C22×C4—88no—
592C22×C4—816no—
593C22×C4—816no—
594C22×C4C2×#4114yes—
595C22×C4C2×#4114yes—
596C22×C4C2×#4114yes—
597C22×C4H(5,𝔽2)18yes—
598C22×C4C2514yes—
599C22×C4C2514yes—
600C22×C4C2514yes—
601C22×C4C2514yes—
602C22×C4C2514yes—
603C22×C4C2514yes—
604C22×C4C2514yes—
605C22×C4C2512yes—
606C22×C4C2514yes—
607C22×C4C2512yes—
608C22×C4C2514yes—
609C22×C4C2514yes—
610C22×C4C2512yes—
611C22×C4C2512yes—
612C22×C4C2512yes—
613C22×C4C2514yes—
614C4⋊C4—28no—
615C4⋊C4—28no—
616C4⋊C4—216no—
617C4⋊C4—28no—
618C4⋊C4—28no—
619C4⋊C4—216no—
620C4⋊C4—216no—
621C4⋊C4—216no—
622C4⋊C4—216no—
623C4⋊C4—48no—
624C4⋊C4—48no—
625C4⋊C4—48no—
626C4⋊C4—48no—
627C4⋊C4—48no—
628C4⋊C4—48no—
629C4⋊C4—48no—
630C4⋊C4—48no—
631C4⋊C4—48no—
632C4⋊C4—48no—
633C4⋊C4—48no—
634C4⋊C4—48no—
635C22⋊C4—216no—
636C22⋊C4—28no—
637C22⋊C4—28no—
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—
657C42—216no—
658C42—216no—
659C42—44no—
660C42—44no—
661C42—48no—
662C42—48no—
663C42—48no—
664C42C2×#41116yes—
665C23—22no—
666C23—24no—
667C23—24no—
668C23—22no—
669C23—28no—
670C23—216no—
671C23—22no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—22no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—24no—
682C23—22no—
683C23—44no—
684C23—44no—
685C23—48no—
686C23—48no—
687C23—44no—
688C23—44no—
689C23—48no—
690C23—48no—
691C23—44no—
692C23—48no—
693C23—48no—
694C23—48no—
695C23—48no—
696C23—48no—
697C23—48no—
698C23C22×#4112yes—
699C23C2×H(5,𝔽2)14yes—
700C23C2×2−1+414yes—
701C23C2×2−1+412yes—
702C23#58514yes—
703C23#58512yes—
704C23C2611yescharacteristic
705Q8—816no—
706D4—416no—
707D4—432no—
708D4—416no—
709D4—432no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—28no—
717C2×C4—28no—
718C2×C4—28no—
719C2×C4—216no—
720C2×C4—22no—
721C2×C4—22no—
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—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—48no—
755C2×C4—48no—
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—88no—
767C2×C4—88no—
768C2×C4—816no—
769C2×C4—816no—
770C2×C4C22×#4114yes—
771C2×C4C22×#4114yes—
772C2×C4C22×#4114yes—
773C2×C4C2×H(5,𝔽2)18yes—
774C22—28no—
775C22—24no—
776C22—44no—
777C22—42no—
778C22—42no—
779C22—416no—
780C22—44no—
781C22—44no—
782C22—44no—
783C22—44no—
784C22—44no—
785C22—44no—
786C22—44no—
787C22—42no—
788C22—42no—
789C22—44no—
790C22—44no—
791C22—42no—
792C22—816no—
793C22—88no—
794C22#345514yes—
795C22#349514yes—
796C22#350814yes—
797C22#353318yes—
798C22#354118yes—
799C22C23×#4111yescharacteristic
800C22C22×H(5,𝔽2)12yes—
801C22C22×2−1+411yescharacteristic
802C22C2×#58512yes—
803C22C2×#58511yescharacteristic
804C4—28no—
805C4—24no—
806C4—24no—
807C4—24no—
808C4—44no—
809C4—44no—
810C4—44no—
811C4—44no—
812C4—44no—
813C4—44no—
814C4—44no—
815C4—44no—
816C4—42no—
817C4—42no—
818C4—44no—
819C4—44no—
820C2—44no—
821C2—84no—
822C2—82no—
823C2#4197718yesdirect product factor
824C2C2×#345511yescharacteristic
825C2C2×#354112yes—
826C2C2×#353312yes—
827C2C2×#350811yescharacteristic
828C2C2×#349511yescharacteristic
subgroupG/H
center, socleC24C25
commutator, Frattini, cosocleC23C26
prime radicalC2×#2397C2
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×#2797C2semidirect
2. C2×#2754C2semidirect
3. C2×#2730C2semidirect
4. C2×#2721C2semidirect
5. #41977C2direct (N × H)
6. C2×#2836C2semidirect
7. C2×#2566C2semidirect
8. C2×#2605C2semidirect
9. C2×#2556C2semidirect
10. C2×#2447C2semidirect
11. C2×#2468C2semidirect
12. C2×#2450C2semidirect
13. C2×#2460C2semidirect
14. C2×#2633C2semidirect
15. C2×#2662C2semidirect
16. C2×#2648C2semidirect
18. C2×#2371C2semidirect
19. C2×#2353C2semidirect
20. C2×#2319C2semidirect
30. #2836C22semidirect
31. #2797C22semidirect
32. #2754C22semidirect
33. #2730C22semidirect
34. #2721C22semidirect
35. #2662C22semidirect
36. #2648C22semidirect
37. #2633C22semidirect
38. #2605C22semidirect
39. #2566C22semidirect
40. #2556C22semidirect
41. #2468C22semidirect
42. #2460C22semidirect
43. #2450C22semidirect
44. #2447C22semidirect
76. #2371C22semidirect
77. #2353C22semidirect
78. #2319C22semidirect
823. C2#41977direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#27972
C2×#27542
C2×#27302
C2×#27212
#419772
C2×#28362
C2×#25662
C2×#26052
C2×#25562
C2×#24472
C2×#24682
C2×#24502
C2×#24602
C2×#26332
C2×#26622
C2×#26482
C2×#23972
C2×#23712
C2×#23532
C2×#23192