Finite Group Databasebeta

← C2×#37862 #7635221

Subgroups — C2×#37862 #7635221

Order 512.

8186 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#553C211yesmaximal, characteristic
2C22×#554C211yesmaximal, characteristic, complemented
3C2×#2721C214yesmaximal, complemented
4C2×#2680C214yesmaximal, complemented
5#37862C2132yesmaximal, direct product factor
6C2×#2850C211yesmaximal, characteristic, complemented
7C2×#2542C211yesmaximal, characteristic, complemented
8C2×#2565C211yesmaximal, characteristic, complemented
9C2×#2499C211yesmaximal, characteristic, complemented
10C2×#2504C211yesmaximal, characteristic, complemented
11C2×#2502C211yesmaximal, characteristic, complemented
12C2×#2501C211yesmaximal, characteristic, complemented
13C2×#2449C214yesmaximal, complemented
14C2×#2443C214yesmaximal, complemented
15C2×#2660C211yesmaximal, characteristic, complemented
16C2×#2620C211yesmaximal, characteristic, complemented
17C2×#2326C211yesmaximal, characteristic, complemented
18C2×#2317C211yesmaximal, characteristic, complemented
19C2×#2290C211yesmaximal, characteristic, complemented
20C22×#384C211yesmaximal, characteristic, complemented
21C2×#554—216no—
22C2×#554C22116yescomplemented
23C2×#553—216no—
24C2×#553C22116yes—
25C22×C4⋊Q8C2211yescharacteristic
26C22×#126C2212yes—
27C22×#125C2211yescharacteristic
28C22×#125C2212yes—
29C22×#124C2211yescharacteristic
30C22×#123C2212yes—
31C22×#123C2214yes—
32C22×C22⋊Q8C2211yescharacteristic
33C22×C22⋊Q8C2211yescharacteristic
34C22×C22⋊Q8C2212yes—
35C22×C22⋊Q8C2212yes—
36C22×C22⋊Q8C2214yes—
37C22×#121C2211yescharacteristic
38C22×#121C2211yescharacteristic
39C22×#121C2212yes—
40C22×C4×Q8C2211yescharacteristic
41C22×C4×D4C2211yescharacteristic
42C22×C4×D4C2212yes—
43C22×C4×D4C2212yes—
44C22×C4×D4C2211yescharacteristic
45C22×#117C2211yescharacteristic
46C22×#117C2211yescharacteristic
47C23×C4⋊C4C2211yescharacteristic
48C23×C4⋊C4C2211yescharacteristic
49C23×C4⋊C4C2211yescharacteristic
50C23×C4⋊C4C2214yes—
51C23×C42C2211yescharacteristic
52#2850C22116yescomplemented
53#2721C22164yescomplemented
54#2680C22164yescomplemented
55#2660C22116yescomplemented
56#2620C22116yescomplemented
57#2565C22116yescomplemented
58#2542C22116yescomplemented
59#2504C22116yescomplemented
60#2502C22116yescomplemented
61#2501C22116yescomplemented
62#2499C22116yescomplemented
63#2449C22164yescomplemented
64#2443C22164yescomplemented
65C2×#399C2214yes—
66C2×#399C2214yes—
67C2×#398C2214yes—
68C2×#398C2214yes—
69C2×#398C2214yes—
70C2×#397C2214yes—
71C2×#397C2214yes—
72C2×#396C2214yes—
73C2×#395C2214yes—
74C2×#394C2214yes—
75#2326C22116yescomplemented
76#2317C22116yescomplemented
77C2×#391C2211yescharacteristic
78C2×#391C2211yescharacteristic
79C2×#391C2211yescharacteristic
80C2×#390C2211yescharacteristic
81C2×#390C2211yescharacteristic
82C2×#390C2211yescharacteristic
83C2×#389C2214yes—
84#2290C22116yescomplemented
85C2×#388C2214yes—
86C2×#388C2214yes—
87C2×#388C2212yes—
88C2×#387C2214yes—
89C2×#387C2214yes—
90C2×#387C2212yes—
91C2×#386C2214yes—
92C2×#386C2212yes—
93C2×#386C2214yes—
94C2×#385C2214yes—
95C2×#385C2214yes—
96C2×#385C2214yes—
97C2×#385C2212yes—
98C2×#384C2211yescharacteristic
99C2×#384C2211yescharacteristic
100C2×#384C2211yescharacteristic
101C2×#384C2211yescharacteristic
102C2×#384C2211yescharacteristic
103C2×#384C2211yescharacteristic
104C2×#384C2214yes—
105C2×#384C22116yescomplemented
106C2×#382C2211yescharacteristic
107C2×#382C2211yescharacteristic
108C2×#382C2211yescharacteristic
109C2×C4×C4⋊C4C2211yescharacteristic
110C2×C4×C22⋊C4C2211yescharacteristic
111C2×C4×C22⋊C4C2211yescharacteristic
112C2×#376C2211yescharacteristic
113C23×Q8C2311yescharacteristic
114C23×Q8C2312yes—
115C23×D4C2311yescharacteristic
116C23×D4C2312yes—
117C23×D4C2311yescharacteristic
118C23×D4C2312yes—
119C24×C4C2312yes—
120C24×C4C2311yescharacteristic
121C24×C4C2311yescharacteristic
122C24×C4C2312yes—
123C24×C4C2312yes—
124C24×C4C2312yes—
125C24×C4C2312yes—
126#554—2128no—
127#553—2128no—
128C2×C4⋊Q8—28no—
129C2×C4⋊Q8C2318yes—
130C2×#126—216no—
131C2×#126C23116yes—
132C2×#125—216no—
133C2×#125—28no—
134C2×#125C2318yes—
135C2×#125C23116yes—
136C2×#124—28no—
137C2×#124C2318yes—
138C2×#123—216no—
139C2×#123—416no—
140C2×#123C23116yes—
141C2×#123C23132yes—
142C2×C22⋊Q8—28no—
143C2×C22⋊Q8—28no—
144C2×C22⋊Q8—216no—
145C2×C22⋊Q8—216no—
146C2×C22⋊Q8—416no—
147C2×C22⋊Q8C2318yes—
148C2×C22⋊Q8C2318yes—
149C2×C22⋊Q8C23116yes—
150C2×C22⋊Q8C23116yes—
151C2×C22⋊Q8C23132yes—
152C2×#121—216no—
153C2×#121—28no—
154C2×#121—28no—
155C2×#121C2318yes—
156C2×#121C2318yes—
157C2×#121C23116yes—
158C2×C4×Q8—28no—
159C2×C4×Q8C2318yes—
160C2×C4×D4—216no—
161C2×C4×D4—216no—
162C2×C4×D4—28no—
163C2×C4×D4D4116yes—
164C2×C4×D4C2318yes—
165C2×C4×D4C23116yes—
166C2×C4×D4C23116yes—
167C2×C4×D4C2318yes—
168C2×#117—28no—
169C2×#117—28no—
170C2×#117C2318yes—
171C2×#117C2318yes—
172C22×C4⋊C4—28no—
173C22×C4⋊C4—28no—
174C22×C4⋊C4—28no—
175C22×C4⋊C4—416no—
176C22×C4⋊C4C2318yes—
177C22×C4⋊C4C2312yes—
178C22×C4⋊C4C2312yes—
179C22×C4⋊C4C2312yes—
180C22×C4⋊C4C2312yes—
181C22×C4⋊C4C2314yes—
182C22×C4⋊C4C2312yes—
183C22×C4⋊C4C2312yes—
184C22×C4⋊C4C2312yes—
185C22×C4⋊C4C2312yes—
186C22×C4⋊C4C2312yes—
187C22×C4⋊C4C2312yes—
188C22×C4⋊C4C2314yes—
189C22×C4⋊C4C2312yes—
190C22×C4⋊C4C2311yescharacteristic
191C22×C4⋊C4C2311yescharacteristic
192C22×C4⋊C4C2311yescharacteristic
193C22×C4⋊C4C2311yescharacteristic
194C22×C4⋊C4C2311yescharacteristic
195C22×C4⋊C4C2318yes—
196C22×C4⋊C4C2318yes—
197C22×C4⋊C4C2311yescharacteristic
198C22×C4⋊C4C2314yes—
199C22×C4⋊C4C2314yes—
200C22×C4⋊C4C2314yes—
201C22×C4⋊C4C23132yes—
202C22×C4⋊C4C2314yes—
203C22×C4⋊C4C2311yescharacteristic
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2314yes—
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2314yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2314yes—
216C22×C22⋊C4C2314yes—
217C22×C22⋊C4C2311yescharacteristic
218C22×C22⋊C4C2311yescharacteristic
219C22×C42—28no—
220C22×C42C2318yes—
221C22×C42C2311yescharacteristic
222C22×C42C2312yes—
223C22×C42C2312yes—
224C22×C42C2311yescharacteristic
225C22×C42C2312yes—
226C22×C42C2311yescharacteristic
227C22×C42C2311yescharacteristic
228C22×C42C2311yescharacteristic
229#399C23132yes—
230#399C23132yes—
231#398C23132yes—
232#398C23132yes—
233#398C23132yes—
234#397C23132yes—
235#397C23132yes—
236#396C23132yes—
237#395C23132yes—
238#394C23132yes—
239#391C2318yes—
240#391C2318yes—
241#391C2318yes—
242#390C2318yes—
243#390C2318yes—
244#390C2318yes—
245#389C23132yes—
246#388C23132yes—
247#388C23132yes—
248#388C23116yes—
249#387C23132yes—
250#387C23132yes—
251#387C23116yes—
252#386C23132yes—
253#386C23116yes—
254#386C23132yes—
255#385C23132yes—
256#385C23132yes—
257#385C23132yes—
258#385C23116yes—
259#384C2318yes—
260#384C2318yes—
261#384C2318yes—
262#384C2318yes—
263#384C2318yes—
264#384C23132yes—
265#384C2318yes—
266#382C2318yes—
267#382C2318yes—
268#382C2318yes—
269C4×C4⋊C4C2318yes—
270C4×C22⋊C4C2318yes—
271C4×C22⋊C4C2318yes—
272#376C2318yes—
273C2×#95C2314yes—
274C2×#95C2312yes—
275C2×#95C2314yes—
276C2×#95C2314yes—
277C2×#95C2312yes—
278C2×#95C2314yes—
279C2×#95C2314yes—
280C2×#95C2314yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2312yes—
284C25C2412yes—
285C25C2411yescharacteristic
286C25C2411yescharacteristic
287C22×Q8—24no—
288C22×Q8—28no—
289C22×Q8—24no—
290C22×Q8—24no—
291C22×Q8—48no—
292C22×Q8C2414yes—
293C22×Q8C2418yes—
294C22×D4—28no—
295C22×D4—28no—
296C22×D4—216no—
297C22×D4—28no—
298C22×D4—24no—
299C22×D4—24no—
300C22×D4—24no—
301C22×D4—48no—
302C22×D4C2×D418yes—
303C22×D4C2414yes—
304C22×D4C2418yes—
305C22×D4C2414yes—
306C22×D4C2418yes—
307C23×C4—28no—
308C23×C4—24no—
309C23×C4—28no—
310C23×C4—24no—
311C23×C4—28no—
312C23×C4—24no—
313C23×C4—24no—
314C23×C4—28no—
315C23×C4—28no—
316C23×C4—28no—
317C23×C4—28no—
318C23×C4—48no—
319C23×C4—48no—
320C23×C4—48no—
321C23×C4—48no—
322C23×C4C2×D418yes—
323C23×C4C2×D418yes—
324C23×C4C2418yes—
325C23×C4C2412yes—
326C23×C4C2412yes—
327C23×C4C2412yes—
328C23×C4C2412yes—
329C23×C4C2412yes—
330C23×C4C2412yes—
331C23×C4C2412yes—
332C23×C4C2412yes—
333C23×C4C2412yes—
334C23×C4C2414yes—
335C23×C4C2414yes—
336C23×C4C2411yescharacteristic
337C23×C4C2411yescharacteristic
338C23×C4C2411yescharacteristic
339C23×C4C2411yescharacteristic
340C23×C4C2412yes—
341C23×C4C2412yes—
342C23×C4C2418yes—
343C23×C4C2418yes—
344C23×C4C2418yes—
345C23×C4C2418yes—
346C23×C4C2411yescharacteristic
347C4⋊Q8—232no—
348#126—264no—
349#125—264no—
350#125—232no—
351#124—232no—
352#123—264no—
353#123—464no—
354C22⋊Q8—232no—
355C22⋊Q8—232no—
356C22⋊Q8—264no—
357C22⋊Q8—264no—
358C22⋊Q8—464no—
359#121—264no—
360#121—232no—
361#121—232no—
362C4×Q8—232no—
363C4×D4—264no—
364C4×D4—264no—
365C4×D4—232no—
366C4×D4C2×D4164yes—
367#117—232no—
368#117—232no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—28no—
373C2×C4⋊C4—28no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—28no—
377C2×C4⋊C4—232no—
378C2×C4⋊C4—232no—
379C2×C4⋊C4—232no—
380C2×C4⋊C4—24no—
381C2×C4⋊C4—28no—
382C2×C4⋊C4—28no—
383C2×C4⋊C4—28no—
384C2×C4⋊C4—28no—
385C2×C4⋊C4—28no—
386C2×C4⋊C4—28no—
387C2×C4⋊C4—28no—
388C2×C4⋊C4—216no—
389C2×C4⋊C4—216no—
390C2×C4⋊C4—28no—
391C2×C4⋊C4—464no—
392C2×C4⋊C4—48no—
393C2×C4⋊C4—48no—
394C2×C4⋊C4—48no—
395C2×C4⋊C4—48no—
396C2×C4⋊C4C2×D418yes—
397C2×C4⋊C4C2414yes—
398C2×C4⋊C4C2414yes—
399C2×C4⋊C4C2414yes—
400C2×C4⋊C4C2418yes—
401C2×C4⋊C4C2418yes—
402C2×C4⋊C4C2414yes—
403C2×C4⋊C4C2414yes—
404C2×C4⋊C4C24116yes—
405C2×C4⋊C4C2418yes—
406C2×C4⋊C4C24116yes—
407C2×C4⋊C4C2414yes—
408C2×C4⋊C4C2418yes—
409C2×C4⋊C4C2418yes—
410C2×C4⋊C4C2418yes—
411C2×C4⋊C4C2418yes—
412C2×C4⋊C4C2418yes—
413C2×C4⋊C4C2418yes—
414C2×C4⋊C4C2418yes—
415C2×C4⋊C4C2418yes—
416C2×C4⋊C4C24116yes—
417C2×C4⋊C4C24116yes—
418C2×C4⋊C4C24116yes—
419C2×C4⋊C4C24116yes—
420C2×C4⋊C4C2414yes—
421C2×C22⋊C4—28no—
422C2×C22⋊C4—28no—
423C2×C22⋊C4—28no—
424C2×C22⋊C4—28no—
425C2×C22⋊C4—28no—
426C2×C22⋊C4—28no—
427C2×C22⋊C4—28no—
428C2×C22⋊C4—28no—
429C2×C22⋊C4—216no—
430C2×C22⋊C4—216no—
431C2×C22⋊C4—28no—
432C2×C22⋊C4—48no—
433C2×C22⋊C4—48no—
434C2×C22⋊C4C2×D418yes—
435C2×C22⋊C4C2×D418yes—
436C2×C22⋊C4C2418yes—
437C2×C22⋊C4C2418yes—
438C2×C22⋊C4C2418yes—
439C2×C22⋊C4C2418yes—
440C2×C22⋊C4C2418yes—
441C2×C22⋊C4C2418yes—
442C2×C22⋊C4C2418yes—
443C2×C22⋊C4C24116yes—
444C2×C22⋊C4C2418yes—
445C2×C22⋊C4C24116yes—
446C2×C22⋊C4C2418yes—
447C2×C22⋊C4C24116yes—
448C2×C22⋊C4C24116yes—
449C2×C22⋊C4C2414yes—
450C2×C22⋊C4C2414yes—
451C2×C42—28no—
452C2×C42—28no—
453C2×C42—24no—
454C2×C42—28no—
455C2×C42—24no—
456C2×C42—24no—
457C2×C42—232no—
458C2×C42C2×D418yes—
459C2×C42#4118yes—
460C2×C42C2418yes—
461C2×C42C2414yes—
462C2×C42C2418yes—
463C2×C42C2414yes—
464C2×C42C2414yes—
465C2×C42C2418yes—
466C2×C42C2414yes—
467C2×C42C2414yes—
468#95C2418yes—
469#95C2418yes—
470#95C2418yes—
471#95C2418yes—
472#95C2418yes—
473#95C24116yes—
474#95C24116yes—
475#95C24116yes—
476#95C24116yes—
477#95C24116yes—
478#95C24116yes—
479C24—22no—
480C24—24no—
481C24—22no—
482C24—22no—
483C24—24no—
484C24—22no—
485C24—24no—
486C24—24no—
487C24—24no—
488C24—28no—
489C24—28no—
490C24—24no—
491C24C22×D414yes—
492C24C22×D414yes—
493C242−1+418yes—
494C24C2514yes—
495C24C2512yes—
496C24C2512yes—
497C24C2511yescharacteristic
498C2×Q8—28no—
499C2×Q8—216no—
500C2×Q8—28no—
501C2×Q8—28no—
502C2×Q8—416no—
503C2×Q8—416no—
504C2×Q8—816no—
505C2×D4—232no—
506C2×D4—216no—
507C2×D4—216no—
508C2×D4—232no—
509C2×D4—216no—
510C2×D4—28no—
511C2×D4—28no—
512C2×D4—28no—
513C2×D4—416no—
514C2×D4—432no—
515C2×D4—416no—
516C2×D4—816no—
517C2×D4C22×D4116yes—
518C22×C4—264no—
519C22×C4—22no—
520C22×C4—24no—
521C22×C4—22no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—216no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—232no—
531C22×C4—232no—
532C22×C4—216no—
533C22×C4—28no—
534C22×C4—28no—
535C22×C4—216no—
536C22×C4—28no—
537C22×C4—28no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—28no—
549C22×C4—24no—
550C22×C4—28no—
551C22×C4—28no—
552C22×C4—28no—
553C22×C4—28no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—28no—
558C22×C4—24no—
559C22×C4—216no—
560C22×C4—216no—
561C22×C4—216no—
562C22×C4—216no—
563C22×C4—416no—
564C22×C4—416no—
565C22×C4—416no—
566C22×C4—416no—
567C22×C4—816no—
568C22×C4—816no—
569C22×C4—816no—
570C22×C4—816no—
571C22×C4C22×D414yes—
572C22×C4C22×D414yes—
573C22×C4C22×D414yes—
574C22×C4C22×D414yes—
575C22×C4C22×D4116yes—
576C22×C4C22×D4116yes—
577C22×C4C22×D414yes—
578C22×C4C2×#4118yes—
579C22×C4C2×#4114yes—
580C22×C4H(5,𝔽2)18yes—
581C22×C42−1+414yes—
582C22×C4C2514yes—
583C22×C4C2514yes—
584C22×C4C2514yes—
585C22×C4C2514yes—
586C22×C4C2514yes—
587C22×C4C2514yes—
588C22×C4C2514yes—
589C22×C4C2514yes—
590C22×C4C2514yes—
591C22×C4C2512yes—
592C22×C4C2512yes—
593C22×C4C2512yes—
594C22×C4C2512yes—
595C22×C4C2514yes—
596C22×C4C2514yes—
597C22×C4C2512yes—
598C4⋊C4—28no—
599C4⋊C4—28no—
600C4⋊C4—28no—
601C4⋊C4—216no—
602C4⋊C4—216no—
603C4⋊C4—28no—
604C4⋊C4—28no—
605C4⋊C4—216no—
606C4⋊C4—28no—
607C4⋊C4—216no—
608C4⋊C4—216no—
609C4⋊C4—216no—
610C4⋊C4—216no—
611C4⋊C4—216no—
612C4⋊C4—216no—
613C4⋊C4—216no—
614C4⋊C4—232no—
615C4⋊C4—232no—
616C4⋊C4—216no—
617C4⋊C4—416no—
618C4⋊C4—416no—
619C4⋊C4—416no—
620C4⋊C4—416no—
621C4⋊C4C22×D4116yes—
622C22⋊C4—216no—
623C22⋊C4—216no—
624C22⋊C4—216no—
625C22⋊C4—216no—
626C22⋊C4—216no—
627C22⋊C4—216no—
628C22⋊C4—216no—
629C22⋊C4—216no—
630C22⋊C4—232no—
631C22⋊C4—232no—
632C22⋊C4—216no—
633C22⋊C4—416no—
634C22⋊C4—416no—
635C22⋊C4C22×D4116yes—
636C22⋊C4C22×D4116yes—
637C42—216no—
638C42—216no—
639C42—216no—
640C42—28no—
641C42—28no—
642C42—28no—
643C42C22×D4116yes—
644C42C2×#41116yes—
645C23—22no—
646C23—24no—
647C23—22no—
648C23—28no—
649C23—216no—
650C23—28no—
651C23—216no—
652C23—22no—
653C23—24no—
654C23—22no—
655C23—24no—
656C23—28no—
657C23—28no—
658C23—28no—
659C23—24no—
660C23—24no—
661C23—28no—
662C23—24no—
663C23—28no—
664C23—48no—
665C23—48no—
666C23—48no—
667C23—48no—
668C23—416no—
669C23—48no—
670C23—416no—
671C23#536116yes—
672C23C23×D414yes—
673C23C23×D414yes—
674C23C23×D412yes—
675C23C22×#4112yes—
676C23C2×H(5,𝔽2)14yes—
677C23C2×2−1+418yes—
678C23C2×2−1+414yes—
679C23C2×2−1+412yes—
680C23C2611yescharacteristic
681Q8—416no—
682Q8—816no—
683D4—232no—
684D4—432no—
685D4—416no—
686D4—816no—
687C2×C4—264no—
688C2×C4—24no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—28no—
699C2×C4—28no—
700C2×C4—28no—
701C2×C4—216no—
702C2×C4—216no—
703C2×C4—28no—
704C2×C4—232no—
705C2×C4—232no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—28no—
717C2×C4—24no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—28no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—28no—
726C2×C4—24no—
727C2×C4—48no—
728C2×C4—48no—
729C2×C4—48no—
730C2×C4—48no—
731C2×C4—48no—
732C2×C4—48no—
733C2×C4—48no—
734C2×C4—48no—
735C2×C4—48no—
736C2×C4—816no—
737C2×C4—816no—
738C2×C4—816no—
739C2×C4—816no—
740C2×C4#547116yes—
741C2×C4C23×D414yes—
742C2×C4C23×D414yes—
743C2×C4C23×D414yes—
744C2×C4C23×D414yes—
745C2×C4C23×D414yes—
746C2×C4C22×#4118yes—
747C2×C4C22×#4114yes—
748C2×C4C2×H(5,𝔽2)18yes—
749C2×C4C2×2−1+414yes—
750C22—28no—
751C22—28no—
752C22—24no—
753C22—232no—
754C22—24no—
755C22—24no—
756C22—24no—
757C22—24no—
758C22—44no—
759C22—44no—
760C22—416no—
761C22—48no—
762C22—48no—
763C22—44no—
764C22—44no—
765C22—44no—
766C22—816no—
767C22C2×#53618yes—
768C22C2×#53614yes—
769C22C2×#54714yes—
770C22#349218yes—
771C22#349814yes—
772C22#355218yes—
773C22C24×D411yescharacteristic
774C22C23×#4111yescharacteristic
775C22C22×H(5,𝔽2)12yes—
776C22C22×2−1+411yescharacteristic
777C22C22×2−1+412yes—
778C4—28no—
779C4—28no—
780C4—24no—
781C4—24no—
782C4—24no—
783C4—24no—
784C4—44no—
785C4—44no—
786C4—44no—
787C4—44no—
788C4—44no—
789C4—44no—
790C4—44no—
791C4—44no—
792C4—44no—
793C4C2×#54718yes—
794C2—28no—
795C2—44no—
796C2—84no—
797C2#3786218yesdirect product factor
798C2C22×#53611yescharacteristic
799C2C22×#54711yescharacteristic
800C2C2×#355212yes—
801C2C2×#349212yes—
802C2C2×#349811yescharacteristic
subgroupG/H
center, socleC24C25
commutator, Frattini, cosocleC23C26
prime radicalC22×#553C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×#554C2semidirect
3. C2×#2721C2semidirect
4. C2×#2680C2semidirect
5. #37862C2direct (N × H)
6. C2×#2850C2semidirect
7. C2×#2542C2semidirect
8. C2×#2565C2semidirect
9. C2×#2499C2semidirect
10. C2×#2504C2semidirect
11. C2×#2502C2semidirect
12. C2×#2501C2semidirect
13. C2×#2449C2semidirect
14. C2×#2443C2semidirect
15. C2×#2660C2semidirect
16. C2×#2620C2semidirect
17. C2×#2326C2semidirect
18. C2×#2317C2semidirect
19. C2×#2290C2semidirect
20. C22×#384C2semidirect
22. C2×#554C22semidirect
52. #2850C22semidirect
53. #2721C22semidirect
54. #2680C22semidirect
55. #2660C22semidirect
56. #2620C22semidirect
57. #2565C22semidirect
58. #2542C22semidirect
59. #2504C22semidirect
60. #2502C22semidirect
61. #2501C22semidirect
62. #2499C22semidirect
63. #2449C22semidirect
64. #2443C22semidirect
75. #2326C22semidirect
76. #2317C22semidirect
84. #2290C22semidirect
105. C2×#384C22semidirect
797. C2#37862direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#5532
C22×#5542
C2×#27212
C2×#26802
#378622
C2×#28502
C2×#25422
C2×#25652
C2×#24992
C2×#25042
C2×#25022
C2×#25012
C2×#24492
C2×#24432
C2×#26602
C2×#26202
C2×#23262
C2×#23172
C2×#22902
C22×#3842