Finite Group Databasebeta

← C2×#55190 #8102034

Subgroups — C2×#55190 #8102034

Order 512.

5428 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#55190C2132yesmaximal, direct product factor
2C2×#2809C211yesmaximal, characteristic, complemented
3C2×#2782C211yesmaximal, characteristic, complemented
4C2×#2769C212yesmaximal, complemented
5C2×#2763C212yesmaximal, complemented
6C2×#2744C212yesmaximal, complemented
7C2×#2723C212yesmaximal, complemented
8C2×#2696C212yesmaximal
9C2×#2692C212yesmaximal, complemented
10C2×#2677C212yesmaximal, complemented
11C2×#2844C211yesmaximal, characteristic, complemented
12C2×#2821C212yesmaximal, complemented
13C2×#2598C211yesmaximal, characteristic
14C2×#2572C211yesmaximal, characteristic, complemented
15C2×#2553C212yesmaximal, complemented
16C2×#2499C211yesmaximal, characteristic, complemented
17C2×#2440C212yesmaximal, complemented
18C2×#2449C212yesmaximal, complemented
19C2×#2628C211yesmaximal, characteristic, complemented
20C2×#2623C212yesmaximal, complemented
21C22×C4⋊Q8C2211yescharacteristic
22C22×C4⋊Q8C2212yes—
23C22×#126C2212yes—
24C22×#123C2212yes—
25C22×C22⋊Q8C2212yes—
26C22×C22⋊Q8C2212yes—
27C22×C22⋊Q8C2212yes—
28C22×C22⋊Q8C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30C22×#117C2211yescharacteristic
31C23×C4⋊C4C2212yes—
32#2844C22116yescomplemented
33#2821C22132yescomplemented
34#2809C22116yescomplemented
35#2782C22116yescomplemented
36#2769C22132yescomplemented
37#2763C22132yescomplemented
38#2744C22132yescomplemented
39#2723C22132yescomplemented
40#2696C22132yes—
41#2692C22132yescomplemented
42#2677C22132yescomplemented
43#2628C22116yescomplemented
44#2623C22132yescomplemented
45#2598C22116yes—
46#2572C22116yescomplemented
47#2553C22132yescomplemented
48#2499C22116yescomplemented
49#2449C22132yescomplemented
50#2440C22132yescomplemented
51C2×#400C2212yes—
52C2×#400C2212yes—
53C2×#400C2211yescharacteristic
54C2×#400C2211yescharacteristic
55C2×#400C2211yescharacteristic
56C2×#400C2212yes—
57C2×#400C2212yes—
58C2×#400C2212yes—
59C2×#399C2212yes—
60C2×#399C2211yescharacteristic
61C2×#399C2212yes—
62C2×#399C2211yescharacteristic
63C2×#399C2211yescharacteristic
64C2×#398C2212yes—
65C2×#398C2212yes—
66C2×#398C2212yes—
67C2×#398C2212yes—
68C2×#398C2212yes—
69C2×#398C2212yes—
70C2×#397C2212yes—
71C2×#397C2212yes—
72C2×#397C2212yes—
73C2×#397C2212yes—
74C2×#396C2212yes—
75C2×#395C2212yes—
76C2×#395C2212yes—
77C2×#395C2212yes—
78C2×#395C2212yes—
79C2×#395C2212yes—
80C2×#394C2212yes—
81C2×#394C2211yescharacteristic
82C2×#393C2212yes—
83C2×#393C2212yes—
84C2×#393C2212yes—
85C2×#393C2212yes—
86C2×#392C2211yescharacteristic
87C2×#391C2211yescharacteristic
88C2×#391C2212yes—
89C2×#391C2211yescharacteristic
90C2×#390C2212yes—
91C2×#389C2212yes—
92C2×#389C2212yes—
93C2×#389C2212yes—
94C2×#388C2212yes—
95C2×#388C2212yes—
96C2×#388C2212yes—
97C2×#388C2212yes—
98C2×#387C2212yes—
99C2×#387C2212yes—
100C2×#387C2212yes—
101C2×#387C2212yes—
102C2×#387C2212yes—
103C2×#387C2212yes—
104C2×#386C2212yes—
105C2×#386C2212yes—
106C2×#386C2212yes—
107C2×#386C2212yes—
108C2×#386C2212yes—
109C2×#385C2212yes—
110C2×#385C2212yes—
111C2×#385C2212yes—
112C2×#385C2212yes—
113C2×#385C2212yes—
114C2×#385C2212yes—
115C2×#384C2211yescharacteristic
116C2×#383C2212yes—
117C2×#383C2211yescharacteristic
118C2×#382C2212yes—
119C2×#382C2211yescharacteristic
120C2×#382C2211yescharacteristic
121C2×#382C2212yes—
122C2×#381C2212yes—
123C2×#380C2212yes—
124C2×#380C2212yes—
125C2×C4×C22⋊C4C2211yescharacteristic
126C2×C4×C22⋊C4C2212yes—
127C23×Q8C2311yescharacteristic
128C23×Q8C2312yes—
129C23×Q8C2312yes—
130C23×D4C2311yescharacteristic
131C23×D4C2312yes—
132C24×C4C2312yes—
133C24×C4C2311yescharacteristic
134C24×C4C2312yes—
135C24×C4C2312yes—
136C2×C4⋊Q8—44no—
137C2×C4⋊Q8—48no—
138C2×C4⋊Q8C23116yes—
139C2×C4⋊Q8C2318yes—
140C2×#126—48no—
141C2×#126C23116yes—
142C2×#123—48no—
143C2×#123C23116yes—
144C2×C22⋊Q8—48no—
145C2×C22⋊Q8—48no—
146C2×C22⋊Q8—48no—
147C2×C22⋊Q8—44no—
148C2×C22⋊Q8C23116yes—
149C2×C22⋊Q8C23116yes—
150C2×C22⋊Q8C2318yes—
151C2×C22⋊Q8C23116yes—
152C2×C4×D4—44no—
153C2×C4×D4C2318yes—
154C2×#117—44no—
155C2×#117C2318yes—
156C22×C4⋊C4—48no—
157C22×C4⋊C4C2312yes—
158C22×C4⋊C4C2312yes—
159C22×C4⋊C4C2312yes—
160C22×C4⋊C4C2312yes—
161C22×C4⋊C4C2312yes—
162C22×C4⋊C4C2312yes—
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C23116yes—
165C22×C4⋊C4C2312yes—
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2312yes—
168C22×C4⋊C4C2312yes—
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2311yescharacteristic
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2312yes—
176C22×C4⋊C4C2312yes—
177C22×C4⋊C4C2312yes—
178C22×C4⋊C4C2312yes—
179C22×C4⋊C4C2312yes—
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2312yes—
182C22×C4⋊C4C2312yes—
183C22×C22⋊C4C2312yes—
184C22×C22⋊C4C2312yes—
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2311yescharacteristic
200C22×C42C2311yescharacteristic
201C22×C42C2311yescharacteristic
202C22×C42C2312yes—
203C22×C42C2311yescharacteristic
204C22×C42C2311yescharacteristic
205C22×C42C2312yes—
206#400C23116yes—
207#400C23116yes—
208#400C2318yes—
209#400C2318yes—
210#400C23116yes—
211#400C23116yes—
212#400C23116yes—
213#400C2318yes—
214#399C2318yes—
215#399C23116yes—
216#399C2318yes—
217#399C2318yes—
218#399C23116yes—
219#398C23116yes—
220#398C23116yes—
221#398C23116yes—
222#398C23116yes—
223#398C23116yes—
224#398C23116yes—
225#397C23116yes—
226#397C23116yes—
227#397C23116yes—
228#397C23116yes—
229#396C23116yes—
230#395C23116yes—
231#395C23116yes—
232#395C23116yes—
233#395C23116yes—
234#395C23116yes—
235#394C2318yes—
236#394C23116yes—
237#393C23116yes—
238#393C23116yes—
239#393C23116yes—
240#393C23116yes—
241#392C2318yes—
242#391C2318yes—
243#391C23116yes—
244#391C2318yes—
245#390C23116yes—
246#389C23116yes—
247#389C23116yes—
248#389C23116yes—
249#388C23116yes—
250#388C23116yes—
251#388C23116yes—
252#388C23116yes—
253#387C23116yes—
254#387C23116yes—
255#387C23116yes—
256#387C23116yes—
257#387C23116yes—
258#387C23116yes—
259#386C23116yes—
260#386C23116yes—
261#386C23116yes—
262#386C23116yes—
263#386C23116yes—
264#385C23116yes—
265#385C23116yes—
266#385C23116yes—
267#385C23116yes—
268#385C23116yes—
269#385C23116yes—
270#384C2318yes—
271#383C23116yes—
272#383C2318yes—
273#382C2318yes—
274#382C23116yes—
275#382C2318yes—
276#382C23116yes—
277#381C23116yes—
278#380C23116yes—
279#380C23116yes—
280C4×C22⋊C4C23116yes—
281C4×C22⋊C4C2318yes—
282C2×#95C2311yescharacteristic
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2311yescharacteristic
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2311yescharacteristic
304C2×#95C2312yes—
305C2×#95C2312yes—
306C2×#95C2312yes—
307C2×#95C2312yes—
308C2×#95C2312yes—
309C2×#95C2312yes—
310C2×#95C2312yes—
311C2×#95C2311yescharacteristic
312C25C2411yescharacteristic
313C25C2412yes—
314C22×Q8—24no—
315C22×Q8—42no—
316C22×Q8—44no—
317C22×Q8—44no—
318C22×Q8—44no—
319C22×Q8—44no—
320C22×Q8—44no—
321C22×Q8—44no—
322C22×Q8—42no—
323C22×Q8C2414yes—
324C22×Q8C2418yes—
325C22×Q8C2418yes—
326C22×D4—28no—
327C22×D4—28no—
328C22×D4—42no—
329C22×D4—44no—
330C22×D4—44no—
331C22×D4C2414yes—
332C22×D4C2418yes—
333C23×C4—28no—
334C23×C4—28no—
335C23×C4—24no—
336C23×C4—24no—
337C23×C4—44no—
338C23×C4—42no—
339C23×C4—44no—
340C23×C4—44no—
341C23×C4—44no—
342C23×C4—44no—
343C23×C4—44no—
344C23×C4—44no—
345C23×C4C2412yes—
346C23×C4C2411yescharacteristic
347C23×C4C2412yes—
348C23×C4C2412yes—
349C23×C4C2411yescharacteristic
350C23×C4C2412yes—
351C23×C4C2412yes—
352C23×C4C2412yes—
353C23×C4C2412yes—
354C23×C4C2412yes—
355C23×C4C2412yes—
356C23×C4C2411yescharacteristic
357C23×C4C2412yes—
358C23×C4C2411yescharacteristic
359C23×C4C2418yes—
360C23×C4C2414yes—
361C23×C4C2412yes—
362C23×C4C2411yescharacteristic
363C23×C4C2411yescharacteristic
364C23×C4C2418yes—
365C23×C4C2418yes—
366C4⋊Q8—416no—
367C4⋊Q8—432no—
368#126—432no—
369#123—432no—
370C22⋊Q8—432no—
371C22⋊Q8—432no—
372C22⋊Q8—432no—
373C22⋊Q8—416no—
374C4×D4—416no—
375#117—416no—
376C2×C4⋊C4—28no—
377C2×C4⋊C4—28no—
378C2×C4⋊C4—28no—
379C2×C4⋊C4—28no—
380C2×C4⋊C4—28no—
381C2×C4⋊C4—28no—
382C2×C4⋊C4—28no—
383C2×C4⋊C4—432no—
384C2×C4⋊C4—44no—
385C2×C4⋊C4—44no—
386C2×C4⋊C4—44no—
387C2×C4⋊C4—44no—
388C2×C4⋊C4—42no—
389C2×C4⋊C4—42no—
390C2×C4⋊C4—42no—
391C2×C4⋊C4—42no—
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—42no—
399C2×C4⋊C4—44no—
400C2×C4⋊C4—42no—
401C2×C4⋊C4—44no—
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⋊C4C2414yes—
412C2×C4⋊C4C2414yes—
413C2×C4⋊C4C2414yes—
414C2×C4⋊C4C2414yes—
415C2×C4⋊C4C2418yes—
416C2×C4⋊C4C2418yes—
417C2×C4⋊C4C2418yes—
418C2×C4⋊C4C2418yes—
419C2×C4⋊C4C2418yes—
420C2×C4⋊C4C2418yes—
421C2×C4⋊C4C2418yes—
422C2×C4⋊C4C2414yes—
423C2×C4⋊C4C2418yes—
424C2×C4⋊C4C2414yes—
425C2×C4⋊C4C2418yes—
426C2×C4⋊C4C2418yes—
427C2×C22⋊C4—28no—
428C2×C22⋊C4—28no—
429C2×C22⋊C4—28no—
430C2×C22⋊C4—28no—
431C2×C22⋊C4—28no—
432C2×C22⋊C4—28no—
433C2×C22⋊C4—44no—
434C2×C22⋊C4—42no—
435C2×C22⋊C4—42no—
436C2×C22⋊C4—44no—
437C2×C22⋊C4—44no—
438C2×C22⋊C4—44no—
439C2×C22⋊C4—44no—
440C2×C22⋊C4—44no—
441C2×C22⋊C4—44no—
442C2×C22⋊C4—44no—
443C2×C22⋊C4—44no—
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×C22⋊C4C2418yes—
457C2×C22⋊C4C2418yes—
458C2×C22⋊C4C2418yes—
459C2×C22⋊C4C2418yes—
460C2×C22⋊C4C2418yes—
461C2×C42—24no—
462C2×C42—24no—
463C2×C42—28no—
464C2×C42—24no—
465C2×C42—42no—
466C2×C42—44no—
467C2×C42C2414yes—
468C2×C42C2414yes—
469C2×C42C2418yes—
470C2×C42C2414yes—
471C2×C42C2414yes—
472C2×C42C2418yes—
473#95C2418yes—
474#95C2418yes—
475#95C2418yes—
476#95C2418yes—
477#95C2418yes—
478#95C2418yes—
479#95C2414yes—
480#95C2418yes—
481#95C2418yes—
482#95C2418yes—
483#95C2418yes—
484#95C2418yes—
485#95C2418yes—
486#95C2418yes—
487#95C2418yes—
488#95C2418yes—
489#95C2418yes—
490#95C2414yes—
491#95C2414yes—
492#95C2418yes—
493#95C2418yes—
494#95C2418yes—
495#95C2414yes—
496#95C2418yes—
497#95C2418yes—
498#95C2418yes—
499#95C2418yes—
500#95C2418yes—
501#95C2418yes—
502#95C2418yes—
503C24—24no—
504C24—24no—
505C24—24no—
506C24—24no—
507C24—24no—
508C24—24no—
509C24—24no—
510C24—22no—
511C24—22no—
512C24—24no—
513C24—22no—
514C242−1+418yes—
515C24C2512yes—
516C24C2514yes—
517C24C2511yescharacteristic
518C2×Q8—28no—
519C2×Q8—44no—
520C2×Q8—48no—
521C2×Q8—48no—
522C2×Q8—48no—
523C2×Q8—48no—
524C2×Q8—48no—
525C2×Q8—48no—
526C2×Q8—44no—
527C2×Q8—88no—
528C2×Q8—816no—
529C2×Q8—816no—
530C2×D4—216no—
531C2×D4—216no—
532C2×D4—44no—
533C2×D4—48no—
534C2×D4—48no—
535C2×D4—416no—
536C2×D4—816no—
537C22×C4—22no—
538C22×C4—24no—
539C22×C4—22no—
540C22×C4—24no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—24no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—24no—
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—216no—
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—216no—
583C22×C4—28no—
584C22×C4—28no—
585C22×C4—48no—
586C22×C4—44no—
587C22×C4—416no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—48no—
591C22×C4—48no—
592C22×C4—48no—
593C22×C4—48no—
594C22×C4—432no—
595C22×C4—816no—
596C22×C4—816no—
597C22×C4H(5,𝔽2)14yes—
598C22×C4H(5,𝔽2)18yes—
599C22×C42−1+414yes—
600C22×C4C2512yes—
601C22×C4C2514yes—
602C22×C4C2512yes—
603C22×C4C2514yes—
604C22×C4C2514yes—
605C22×C4C2514yes—
606C22×C4C2514yes—
607C22×C4C2514yes—
608C22×C4C2514yes—
609C22×C4C2512yes—
610C22×C4C2512yes—
611C22×C4C2514yes—
612C22×C4C2514yes—
613C22×C4C2514yes—
614C22×C4C2514yes—
615C22×C4C2512yes—
616C22×C4C2512yes—
617C4⋊C4—216no—
618C4⋊C4—216no—
619C4⋊C4—216no—
620C4⋊C4—216no—
621C4⋊C4—216no—
622C4⋊C4—216no—
623C4⋊C4—216no—
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—48no—
633C4⋊C4—48no—
634C4⋊C4—48no—
635C4⋊C4—48no—
636C4⋊C4—48no—
637C4⋊C4—48no—
638C4⋊C4—44no—
639C4⋊C4—48no—
640C4⋊C4—44no—
641C4⋊C4—48no—
642C22⋊C4—216no—
643C22⋊C4—216no—
644C22⋊C4—216no—
645C22⋊C4—216no—
646C22⋊C4—216no—
647C22⋊C4—216no—
648C22⋊C4—48no—
649C22⋊C4—44no—
650C22⋊C4—44no—
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—216no—
662C42—28no—
663C42—44no—
664C42—48no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—216no—
672C23—216no—
673C23—216no—
674C23—24no—
675C23—22no—
676C23—22no—
677C23—24no—
678C23—22no—
679C23—48no—
680C23—48no—
681C23—48no—
682C23—48no—
683C23—44no—
684C23—48no—
685C23—44no—
686C23—44no—
687C23—48no—
688C23C2×H(5,𝔽2)12yes—
689C23C2×H(5,𝔽2)14yes—
690C23C2×2−1+418yes—
691C23C2×2−1+414yes—
692C23C2×2−1+412yes—
693C23#58512yes—
694C23C2611yescharacteristic
695Q8—88no—
696Q8—816no—
697Q8—816no—
698D4—416no—
699D4—816no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—28no—
707C2×C4—216no—
708C2×C4—28no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
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—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—416no—
748C2×C4—432no—
749C2×C4—48no—
750C2×C4—48no—
751C2×C4—48no—
752C2×C4—48no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—48no—
757C2×C4—48no—
758C2×C4—48no—
759C2×C4—48no—
760C2×C4—44no—
761C2×C4—48no—
762C2×C4—48no—
763C2×C4—816no—
764C2×C4—816no—
765C2×C4C2×H(5,𝔽2)14yes—
766C2×C4C2×H(5,𝔽2)18yes—
767C2×C4C2×2−1+414yes—
768C22—28no—
769C22—28no—
770C22—28no—
771C22—44no—
772C22—44no—
773C22—44no—
774C22—44no—
775C22—432no—
776C22—42no—
777C22—44no—
778C22—42no—
779C22—44no—
780C22—42no—
781C22—88no—
782C22#353514yes—
783C22#353518yes—
784C22#353814yes—
785C22#354914yes—
786C22#355218yes—
787C22C22×H(5,𝔽2)11yescharacteristic
788C22C22×H(5,𝔽2)12yes—
789C22C22×2−1+412yes—
790C22C22×2−1+411yescharacteristic
791C22C2×#58511yescharacteristic
792C4—24no—
793C4—28no—
794C4—24no—
795C4—44no—
796C4—44no—
797C4—44no—
798C4—44no—
799C4—42no—
800C4—42no—
801C4—44no—
802C4—44no—
803C4—42no—
804C4—44no—
805C4—44no—
806C4—44no—
807C4—44no—
808C4—42no—
809C2—48no—
810C2—82no—
811C2#5519018yesdirect product factor
812C2C2×#353511yescharacteristic
813C2C2×#353512yes—
814C2C2×#353811yescharacteristic
815C2C2×#355212yes—
816C2C2×#354911yescharacteristic
subgroupG/H
center, socleC24C25
commutator, Frattini, cosocleC23C26
prime radicalC2×#392C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #55190C2direct (N × H)
2. C2×#2809C2semidirect
3. C2×#2782C2semidirect
4. C2×#2769C2semidirect
5. C2×#2763C2semidirect
6. C2×#2744C2semidirect
7. C2×#2723C2semidirect
9. C2×#2692C2semidirect
10. C2×#2677C2semidirect
11. C2×#2844C2semidirect
12. C2×#2821C2semidirect
14. C2×#2572C2semidirect
15. C2×#2553C2semidirect
16. C2×#2499C2semidirect
17. C2×#2440C2semidirect
18. C2×#2449C2semidirect
19. C2×#2628C2semidirect
20. C2×#2623C2semidirect
32. #2844C22semidirect
33. #2821C22semidirect
34. #2809C22semidirect
35. #2782C22semidirect
36. #2769C22semidirect
37. #2763C22semidirect
38. #2744C22semidirect
39. #2723C22semidirect
41. #2692C22semidirect
42. #2677C22semidirect
43. #2628C22semidirect
44. #2623C22semidirect
46. #2572C22semidirect
47. #2553C22semidirect
48. #2499C22semidirect
49. #2449C22semidirect
50. #2440C22semidirect
811. C2#55190direct (N × H)

Maximal subgroups

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

subgroupindex
#551902
C2×#28092
C2×#27822
C2×#27692
C2×#27632
C2×#27442
C2×#27232
C2×#26962
C2×#26922
C2×#26772
C2×#28442
C2×#28212
C2×#25982
C2×#25722
C2×#25532
C2×#24992
C2×#24402
C2×#24492
C2×#26282
C2×#26232