Finite Group Databasebeta

← C2×#52414 #8092234

Subgroups — C2×#52414 #8092234

Order 512.

5802 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#52414C2132yesmaximal, direct product factor
2C2×#2789C211yesmaximal, characteristic, complemented
3C2×#2774C212yesmaximal, complemented
4C2×#2723C212yesmaximal, complemented
5C2×#2689C212yesmaximal, complemented
6C2×#2683C211yesmaximal, characteristic, complemented
7C2×#2844C211yesmaximal, characteristic, complemented
8C2×#2830C211yesmaximal, characteristic, complemented
9C2×#2831C212yesmaximal, complemented
10C2×#2838C212yesmaximal, complemented
11C2×#2817C212yesmaximal, complemented
12C2×#2583C211yesmaximal, characteristic, complemented
13C2×#2504C211yesmaximal, characteristic
14C2×#2505C212yesmaximal, complemented
15C2×#2409C212yesmaximal, complemented
16C2×#2444C212yesmaximal
17C2×#2481C212yesmaximal, complemented
18C2×#2449C212yesmaximal, complemented
19C2×#2643C212yesmaximal, complemented
20C22×#395C211yesmaximal, characteristic, complemented
21C24×Q8C2211yescharacteristic
22C22×#126C2212yes—
23C22×C22⋊Q8C2211yescharacteristic
24C22×C22⋊Q8C2212yes—
25C22×C22⋊Q8C2212yes—
26C22×C22⋊Q8C2212yes—
27C22×#121C2211yescharacteristic
28C22×C4×D4C2212yes—
29C23×C4⋊C4C2211yescharacteristic
30C23×C4⋊C4C2212yes—
31#2844C22116yescomplemented
32#2838C22132yescomplemented
33#2831C22132yescomplemented
34#2830C22116yescomplemented
35#2817C22132yescomplemented
36#2789C22116yescomplemented
37#2774C22132yescomplemented
38#2723C22132yescomplemented
39#2689C22132yescomplemented
40#2683C22116yescomplemented
41#2643C22132yescomplemented
42#2583C22116yescomplemented
43#2505C22132yescomplemented
44#2504C22116yes—
45#2481C22132yescomplemented
46#2449C22132yescomplemented
47#2444C22132yes—
48#2409C22132yescomplemented
49C2×#401C2212yes—
50C2×#400C2212yes—
51C2×#400C2212yes—
52C2×#400C2212yes—
53C2×#400C2212yes—
54C2×#400C2212yes—
55C2×#400C2212yes—
56C2×#400C2212yes—
57C2×#400C2212yes—
58C2×#400C2212yes—
59C2×#399C2212yes—
60C2×#398C2211yescharacteristic
61C2×#398C2211yescharacteristic
62C2×#398C2212yes—
63C2×#398C2212yes—
64C2×#397C2212yes—
65C2×#397C2212yes—
66C2×#397C2212yes—
67C2×#397C2212yes—
68C2×#397C2212yes—
69C2×#397C2212yes—
70C2×#397C2212yes—
71C2×#397C2212yes—
72C2×#396C2212yes—
73C2×#396C2212yes—
74C2×#396C2212yes—
75C2×#395C2211yescharacteristic
76C2×#395C2211yescharacteristic
77C2×#395C2211yescharacteristic
78C2×#395C2212yes—
79C2×#395C2212yes—
80C2×#395C2212yes—
81C2×#395C2211yescharacteristic
82C2×#395C2212yes—
83C2×#395C2211yescharacteristic
84C2×#395C2211yescharacteristic
85C2×#395C2212yes—
86C2×#395C22116yescomplemented
87C2×#394C2212yes—
88C2×#393C2212yes—
89C2×#393C2212yes—
90C2×#391C2212yes—
91C2×#391C2212yes—
92C2×#390C2211yescharacteristic
93C2×#390C2211yescharacteristic
94C2×#389C2212yes—
95C2×#389C2212yes—
96C2×#389C2212yes—
97C2×#389C2212yes—
98C2×#388C2212yes—
99C2×#388C2212yes—
100C2×#387C2212yes—
101C2×#387C2212yes—
102C2×#387C2212yes—
103C2×#387C2212yes—
104C2×#387C2212yes—
105C2×#387C2212yes—
106C2×#386C2212yes—
107C2×#386C2212yes—
108C2×#386C2212yes—
109C2×#386C2212yes—
110C2×#386C2212yes—
111C2×#386C2212yes—
112C2×#385C2212yes—
113C2×#385C2212yes—
114C2×#385C2212yes—
115C2×#385C2212yes—
116C2×#385C2212yes—
117C2×#385C2212yes—
118C2×#382C2211yescharacteristic
119C2×#382C2212yes—
120C2×#382C2211yescharacteristic
121C2×#381C2212yes—
122C2×#380C2212yes—
123C2×C4×C22⋊C4C2211yescharacteristic
124C2×C4×C22⋊C4C2211yescharacteristic
125C22×#95C2211yescharacteristic
126C22×#95C2212yes—
127C23×Q8—44no—
128C23×Q8—48no—
129C23×Q8C2311yescharacteristic
130C23×Q8C2312yes—
131C23×Q8C2311yescharacteristic
132C23×Q8C2318yes—
133C23×Q8C2311yescharacteristic
134C23×D4C2312yes—
135C23×D4C2311yescharacteristic
136C24×C4C2312yes—
137C24×C4C2311yescharacteristic
138C24×C4C2311yescharacteristic
139C24×C4C2311yescharacteristic
140C24×C4C2312yes—
141C24×C4C2312yes—
142C2×#126—48no—
143C2×#126C23116yes—
144C2×C22⋊Q8—44no—
145C2×C22⋊Q8—48no—
146C2×C22⋊Q8—48no—
147C2×C22⋊Q8—48no—
148C2×C22⋊Q8C23116yes—
149C2×C22⋊Q8C23116yes—
150C2×C22⋊Q8C2318yes—
151C2×C22⋊Q8C23116yes—
152C2×#121—44no—
153C2×#121C2318yes—
154C2×C4×D4—48no—
155C2×C4×D4C23116yes—
156C22×C4⋊C4—48no—
157C22×C4⋊C4—44no—
158C22×C4⋊C4C2312yes—
159C22×C4⋊C4C2312yes—
160C22×C4⋊C4C2312yes—
161C22×C4⋊C4C2312yes—
162C22×C4⋊C4C2312yes—
163C22×C4⋊C4C2318yes—
164C22×C4⋊C4C2312yes—
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2312yes—
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2312yes—
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2311yescharacteristic
174C22×C4⋊C4C23116yes—
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2312yes—
177C22×C4⋊C4C2312yes—
178C22×C4⋊C4C2312yes—
179C22×C4⋊C4C2312yes—
180C22×C4⋊C4C2312yes—
181C22×C4⋊C4C2312yes—
182C22×C4⋊C4C2312yes—
183C22×C4⋊C4C2311yescharacteristic
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×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C42C2311yescharacteristic
200C22×C42C2312yes—
201C22×C42C2312yes—
202C22×C42C2311yescharacteristic
203#401C23116yes—
204#400C23116yes—
205#400C23116yes—
206#400C23116yes—
207#400C23116yes—
208#400C23116yes—
209#400C23116yes—
210#400C23116yes—
211#400C23116yes—
212#400C23116yes—
213#399C23116yes—
214#398C2318yes—
215#398C2318yes—
216#398C23116yes—
217#398C23116yes—
218#397C23116yes—
219#397C23116yes—
220#397C23116yes—
221#397C23116yes—
222#397C23116yes—
223#397C23116yes—
224#397C23116yes—
225#397C23116yes—
226#396C23116yes—
227#396C23116yes—
228#396C23116yes—
229#395C2318yes—
230#395C23116yes—
231#395C23116yes—
232#395C23116yes—
233#395C2318yes—
234#395C2318yes—
235#395C23116yes—
236#395C2318yes—
237#395C2318yes—
238#395C2318yes—
239#395C23116yes—
240#394C23116yes—
241#393C23116yes—
242#393C23116yes—
243#391C23116yes—
244#391C23116yes—
245#390C2318yes—
246#390C2318yes—
247#389C23116yes—
248#389C23116yes—
249#389C23116yes—
250#389C23116yes—
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#386C23116yes—
265#385C23116yes—
266#385C23116yes—
267#385C23116yes—
268#385C23116yes—
269#385C23116yes—
270#385C23116yes—
271#382C23116yes—
272#382C2318yes—
273#382C2318yes—
274#381C23116yes—
275#380C23116yes—
276C4×C22⋊C4C2318yes—
277C4×C22⋊C4C2318yes—
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2311yescharacteristic
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2311yescharacteristic
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2311yescharacteristic
292C2×#95C2311yescharacteristic
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2318yes—
303C2×#95C23116yes—
304C2×#95C2312yes—
305C2×#95C2312yes—
306C2×#95C2312yes—
307C2×#95C2312yes—
308C2×#95C2312yes—
309C2×#95C2312yes—
310C2×#95C2312yes—
311C2×#95C2312yes—
312C25C2412yes—
313C25C2411yescharacteristic
314C22×Q8—28no—
315C22×Q8—28no—
316C22×Q8—42no—
317C22×Q8—44no—
318C22×Q8—44no—
319C22×Q8—42no—
320C22×Q8—44no—
321C22×Q8—416no—
322C22×Q8—42no—
323C22×Q8—44no—
324C22×Q8—432no—
325C22×Q8—464no—
326C22×Q8C2414yes—
327C22×Q8C2418yes—
328C22×Q8C2414yes—
329C22×Q8C2414yes—
330C22×D4—28no—
331C22×D4—28no—
332C22×D4—28no—
333C22×D4—24no—
334C22×D4—42no—
335C22×D4—42no—
336C22×D4C2418yes—
337C22×D4C2414yes—
338C23×C4—24no—
339C23×C4—24no—
340C23×C4—28no—
341C23×C4—28no—
342C23×C4—24no—
343C23×C4—28no—
344C23×C4—24no—
345C23×C4—28no—
346C23×C4—44no—
347C23×C4—42no—
348C23×C4—44no—
349C23×C4—44no—
350C23×C4—44no—
351C23×C4—44no—
352C23×C4—44no—
353C23×C4—44no—
354C23×C4C2412yes—
355C23×C4C2412yes—
356C23×C4C2412yes—
357C23×C4C2412yes—
358C23×C4C2412yes—
359C23×C4C2411yescharacteristic
360C23×C4C2412yes—
361C23×C4C2411yescharacteristic
362C23×C4C2412yes—
363C23×C4C2411yescharacteristic
364C23×C4C2411yescharacteristic
365C23×C4C2411yescharacteristic
366C23×C4C2412yes—
367C23×C4C2412yes—
368C23×C4C2412yes—
369C23×C4C2418yes—
370C23×C4C2414yes—
371C23×C4C2412yes—
372C23×C4C2411yescharacteristic
373C23×C4C2414yes—
374C23×C4C2414yes—
375C23×C4C2418yes—
376C23×C4C2418yes—
377#126—432no—
378C22⋊Q8—416no—
379C22⋊Q8—432no—
380C22⋊Q8—432no—
381C22⋊Q8—432no—
382#121—416no—
383C4×D4—432no—
384C2×C4⋊C4—28no—
385C2×C4⋊C4—28no—
386C2×C4⋊C4—28no—
387C2×C4⋊C4—28no—
388C2×C4⋊C4—28no—
389C2×C4⋊C4—432no—
390C2×C4⋊C4—42no—
391C2×C4⋊C4—42no—
392C2×C4⋊C4—44no—
393C2×C4⋊C4—42no—
394C2×C4⋊C4—42no—
395C2×C4⋊C4—44no—
396C2×C4⋊C4—416no—
397C2×C4⋊C4—44no—
398C2×C4⋊C4—44no—
399C2×C4⋊C4—44no—
400C2×C4⋊C4—44no—
401C2×C4⋊C4—42no—
402C2×C4⋊C4—44no—
403C2×C4⋊C4—42no—
404C2×C4⋊C4—44no—
405C2×C4⋊C4—44no—
406C2×C4⋊C4—44no—
407C2×C4⋊C4—44no—
408C2×C4⋊C4—44no—
409C2×C4⋊C4—44no—
410C2×C4⋊C4C2418yes—
411C2×C4⋊C4C2418yes—
412C2×C4⋊C4C2418yes—
413C2×C4⋊C4C2418yes—
414C2×C4⋊C4C2418yes—
415C2×C4⋊C4C2414yes—
416C2×C4⋊C4C2414yes—
417C2×C4⋊C4C2418yes—
418C2×C4⋊C4C2414yes—
419C2×C4⋊C4C2418yes—
420C2×C4⋊C4C2414yes—
421C2×C4⋊C4C2418yes—
422C2×C4⋊C4C2414yes—
423C2×C4⋊C4C2418yes—
424C2×C4⋊C4C2418yes—
425C2×C4⋊C4C2418yes—
426C2×C4⋊C4C2418yes—
427C2×C4⋊C4C2418yes—
428C2×C4⋊C4C2418yes—
429C2×C4⋊C4C2414yes—
430C2×C4⋊C4C2418yes—
431C2×C4⋊C4C2418yes—
432C2×C4⋊C4C2418yes—
433C2×C4⋊C4C2418yes—
434C2×C22⋊C4—28no—
435C2×C22⋊C4—28no—
436C2×C22⋊C4—28no—
437C2×C22⋊C4—28no—
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⋊C4—44no—
445C2×C22⋊C4—44no—
446C2×C22⋊C4—44no—
447C2×C22⋊C4—44no—
448C2×C22⋊C4—44no—
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×C22⋊C4C2418yes—
459C2×C22⋊C4C2418yes—
460C2×C22⋊C4C2418yes—
461C2×C22⋊C4C2418yes—
462C2×C22⋊C4C2418yes—
463C2×C22⋊C4C2418yes—
464C2×C42—24no—
465C2×C42—44no—
466C2×C42—44no—
467C2×C42—42no—
468C2×C42C2414yes—
469C2×C42C2418yes—
470C2×C42C2418yes—
471C2×C42C2414yes—
472#95C2418yes—
473#95C2418yes—
474#95C2418yes—
475#95C2414yes—
476#95C2418yes—
477#95C2414yes—
478#95C2418yes—
479#95C2414yes—
480#95C2414yes—
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—
498#95C2418yes—
499#95C2418yes—
500#95C2418yes—
501#95C2418yes—
502#95C2418yes—
503#95C2418yes—
504C24—24no—
505C24—22no—
506C24—22no—
507C24—24no—
508C24—24no—
509C24—24no—
510C24—24no—
511C24—24no—
512C24—24no—
513C24—24no—
514C24H(5,𝔽2)14yes—
515C242−1+418yes—
516C24C2514yes—
517C24C2512yes—
518C24C2511yescharacteristic
519C2×Q8—216no—
520C2×Q8—216no—
521C2×Q8—44no—
522C2×Q8—48no—
523C2×Q8—48no—
524C2×Q8—44no—
525C2×Q8—48no—
526C2×Q8—44no—
527C2×Q8—48no—
528C2×Q8—416no—
529C2×Q8—432no—
530C2×Q8—4128no—
531C2×Q8—416no—
532C2×Q8—88no—
533C2×D4—216no—
534C2×D4—216no—
535C2×D4—216no—
536C2×D4—28no—
537C2×D4—44no—
538C2×D4—44no—
539C2×D4—432no—
540C2×D4—88no—
541C22×C4—24no—
542C22×C4—22no—
543C22×C4—24no—
544C22×C4—22no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—22no—
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—22no—
563C22×C4—22no—
564C22×C4—24no—
565C22×C4—28no—
566C22×C4—28no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—24no—
570C22×C4—216no—
571C22×C4—24no—
572C22×C4—24no—
573C22×C4—24no—
574C22×C4—24no—
575C22×C4—24no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—216no—
579C22×C4—22no—
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—22no—
590C22×C4—28no—
591C22×C4—216no—
592C22×C4—28no—
593C22×C4—216no—
594C22×C4—48no—
595C22×C4—44no—
596C22×C4—48no—
597C22×C4—48no—
598C22×C4—48no—
599C22×C4—48no—
600C22×C4—48no—
601C22×C4—48no—
602C22×C4—416no—
603C22×C4—432no—
604C22×C4—432no—
605C22×C4—416no—
606C22×C4—816no—
607C22×C4—88no—
608C22×C4H(5,𝔽2)18yes—
609C22×C42−1+414yes—
610C22×C4C2514yes—
611C22×C4C2514yes—
612C22×C4C2514yes—
613C22×C4C2512yes—
614C22×C4C2514yes—
615C22×C4C2514yes—
616C22×C4C2514yes—
617C22×C4C2514yes—
618C22×C4C2514yes—
619C22×C4C2514yes—
620C22×C4C2512yes—
621C22×C4C2512yes—
622C22×C4C2514yes—
623C22×C4C2512yes—
624C22×C4C2512yes—
625C22×C4C2514yes—
626C22×C4C2512yes—
627C4⋊C4—216no—
628C4⋊C4—216no—
629C4⋊C4—216no—
630C4⋊C4—216no—
631C4⋊C4—216no—
632C4⋊C4—44no—
633C4⋊C4—44no—
634C4⋊C4—48no—
635C4⋊C4—44no—
636C4⋊C4—44no—
637C4⋊C4—48no—
638C4⋊C4—48no—
639C4⋊C4—48no—
640C4⋊C4—48no—
641C4⋊C4—48no—
642C4⋊C4—44no—
643C4⋊C4—48no—
644C4⋊C4—44no—
645C4⋊C4—48no—
646C4⋊C4—48no—
647C4⋊C4—48no—
648C4⋊C4—48no—
649C4⋊C4—48no—
650C4⋊C4—48no—
651C22⋊C4—216no—
652C22⋊C4—216no—
653C22⋊C4—216no—
654C22⋊C4—216no—
655C22⋊C4—48no—
656C22⋊C4—48no—
657C22⋊C4—48no—
658C22⋊C4—48no—
659C22⋊C4—48no—
660C22⋊C4—48no—
661C22⋊C4—48no—
662C22⋊C4—48no—
663C22⋊C4—48no—
664C22⋊C4—48no—
665C22⋊C4—48no—
666C42—28no—
667C42—44no—
668C42—48no—
669C42—48no—
670C23—24no—
671C23—22no—
672C23—22no—
673C23—28no—
674C23—28no—
675C23—216no—
676C23—216no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—48no—
685C23—48no—
686C23—48no—
687C23—48no—
688C23—48no—
689C23—48no—
690C23—48no—
691C23#563116yes—
692C23C2×H(5,𝔽2)14yes—
693C23C2×H(5,𝔽2)12yes—
694C23C2×H(5,𝔽2)14yes—
695C23C2×2−1+418yes—
696C23C2×2−1+414yes—
697C23C2×2−1+412yes—
698C23#58512yes—
699C23C2611yescharacteristic
700Q8—416no—
701Q8—432no—
702Q8—416no—
703Q8—88no—
704D4—432no—
705D4—88no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—216no—
711C2×C4—28no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—22no—
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—22no—
730C2×C4—24no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—22no—
734C2×C4—22no—
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—22no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—22no—
753C2×C4—416no—
754C2×C4—432no—
755C2×C4—432no—
756C2×C4—416no—
757C2×C4—48no—
758C2×C4—48no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—48no—
763C2×C4—44no—
764C2×C4—48no—
765C2×C4—44no—
766C2×C4—48no—
767C2×C4—48no—
768C2×C4—48no—
769C2×C4—48no—
770C2×C4—48no—
771C2×C4—48no—
772C2×C4—816no—
773C2×C4—88no—
774C2×C4C2×H(5,𝔽2)18yes—
775C2×C4C2×2−1+414yes—
776C22—28no—
777C22—24no—
778C22—28no—
779C22—232no—
780C22—24no—
781C22—44no—
782C22—44no—
783C22—44no—
784C22—44no—
785C22—44no—
786C22—44no—
787C22—44no—
788C22—816no—
789C22C2×#56318yes—
790C22C2×#56314yes—
791C22#353214yes—
792C22#353514yes—
793C22#354118yes—
794C22#355218yes—
795C22C22×H(5,𝔽2)12yes—
796C22C22×H(5,𝔽2)11yescharacteristic
797C22C22×2−1+412yes—
798C22C22×2−1+411yescharacteristic
799C22C2×#58511yescharacteristic
800C4—24no—
801C4—28no—
802C4—44no—
803C4—44no—
804C4—44no—
805C4—44no—
806C4—44no—
807C4—42no—
808C4—44no—
809C4—44no—
810C4—44no—
811C4—44no—
812C4—42no—
813C4—42no—
814C4—42no—
815C4—44no—
816C4—42no—
817C2—28no—
818C2—84no—
819C2#5241418yesdirect product factor
820C2C22×#56311yescharacteristic
821C2C2×#353211yescharacteristic
822C2C2×#354112yes—
823C2C2×#353511yescharacteristic
824C2C2×#355212yes—
subgroupG/H
center, socleC24C25
commutator, Frattini, cosocleC23C26
prime radicalC22×#121C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #52414C2direct (N × H)
2. C2×#2789C2semidirect
3. C2×#2774C2semidirect
4. C2×#2723C2semidirect
5. C2×#2689C2semidirect
6. C2×#2683C2semidirect
7. C2×#2844C2semidirect
8. C2×#2830C2semidirect
9. C2×#2831C2semidirect
10. C2×#2838C2semidirect
11. C2×#2817C2semidirect
12. C2×#2583C2semidirect
14. C2×#2505C2semidirect
15. C2×#2409C2semidirect
17. C2×#2481C2semidirect
18. C2×#2449C2semidirect
19. C2×#2643C2semidirect
20. C22×#395C2semidirect
31. #2844C22semidirect
32. #2838C22semidirect
33. #2831C22semidirect
34. #2830C22semidirect
35. #2817C22semidirect
36. #2789C22semidirect
37. #2774C22semidirect
38. #2723C22semidirect
39. #2689C22semidirect
40. #2683C22semidirect
41. #2643C22semidirect
42. #2583C22semidirect
43. #2505C22semidirect
45. #2481C22semidirect
46. #2449C22semidirect
48. #2409C22semidirect
86. C2×#395C22semidirect
819. C2#52414direct (N × H)

Maximal subgroups

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

subgroupindex
#524142
C2×#27892
C2×#27742
C2×#27232
C2×#26892
C2×#26832
C2×#28442
C2×#28302
C2×#28312
C2×#28382
C2×#28172
C2×#25832
C2×#25042
C2×#25052
C2×#24092
C2×#24442
C2×#24812
C2×#24492
C2×#26432
C22×#3952