Finite Group Databasebeta

← C2×#24921380 #36312905

Subgroups — C2×#24921380 #36312905

Order 21248.

7238 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24921380C2132yesmaximal, direct product factor
2C2×#19128400C214yesmaximal, complemented
3C2×#19128399C212yesmaximal, complemented
4C2×#19128397C214yesmaximal, complemented
5C2×#19128395C212yesmaximal, complemented
6C2×#19128390C212yesmaximal, complemented
7C2×#19128386C212yesmaximal, complemented
8C2×#19128309C212yesmaximal, complemented
9C2×#19128302C212yesmaximal, complemented
10C2×#19128282C211yesmaximal, characteristic, complemented
11C2×#19128279C211yesmaximal, characteristic, complemented
12C2×#19128247C211yesmaximal, characteristic, complemented
13C2×#19128238C212yesmaximal, complemented
14C2×#19128233C212yesmaximal, complemented
15C22×#14581783C211yesmaximal, characteristic, complemented
16C2×#19128181C211yesmaximal, characteristic, complemented
17C2×#19128169C211yesmaximal, characteristic, complemented
18C2×#520×C83C211yesmaximal, characteristic, complemented
19C22×#13050590C2211yescharacteristic
20C22×#13050590C2211yescharacteristic
21#19128400C22164yescomplemented
22#19128399C22132yescomplemented
23#19128397C22164yescomplemented
24#19128395C22132yescomplemented
25#19128390C22132yescomplemented
26#19128386C22132yescomplemented
27#19128309C22132yescomplemented
28#19128302C22132yescomplemented
29#19128282C22116yescomplemented
30#19128279C22116yescomplemented
31#19128247C22116yescomplemented
32C2×#14581790C2211yescharacteristic
33C2×#14581788C2211yescharacteristic
34#19128238C22132yescomplemented
35#19128233C22132yescomplemented
36C2×#14581787C2214yes—
37C2×#14581787C2214yes—
38C2×#14581786C2214yes—
39C2×#14581785C2214yes—
40C2×#14581784C2214yes—
41C2×#14581783C2212yes—
42C2×#14581783C2212yes—
43C2×#14581783C2212yes—
44C2×#14581783C2212yes—
45C2×#14581783C22116yescomplemented
46C2×#14581782C2214yes—
47C2×#14581781C2211yescharacteristic
48C2×#14581779C2211yescharacteristic
49C2×#14581777C2214yes—
50C2×#14581775C2214yes—
51C2×#14581774C2214yes—
52C2×#14581774C2214yes—
53C2×#14581772C2212yes—
54C2×#14581772C2212yes—
55C2×#14581771C2212yes—
56C2×#14581768C2212yes—
57C2×#14581767C2212yes—
58C2×#14581767C2212yes—
59C2×#14581766C2212yes—
60C2×#14581766C2214yes—
61C2×#14581766C2214yes—
62C2×#14581765C2214yes—
63C2×#14581764C2212yes—
64C2×#14581764C2214yes—
65C2×#14581764C2212yes—
66C2×#14581763C2212yes—
67#19128181C22116yescomplemented
68#19128169C22116yescomplemented
69C2×C4×Dic166C2212yes—
70C2×#14581757C2211yescharacteristic
71C2×#14581757C2211yescharacteristic
72C2×C4×D332C2212yes—
73C2×C4×D332C2214yes—
74C2×#14581754C2211yescharacteristic
75C2×#14581754C2211yescharacteristic
76C2×C4×C22⋊D83C2212yes—
77C2×C4×C22⋊D83C2212yes—
78C2×C4×C22⋊D83C2214yes—
79C2×(C22⋊D83)⋊C4C2212yes—
80C2×(C22⋊D83)⋊C4C2212yes—
81C2×(C22⋊D83)⋊C4C2214yes—
82C2×#14581751C2214yes—
83C2×#14581750C2212yes—
84C2×#14581749C2212yes—
85C2×#14581749C2214yes—
86C22×C4⋊Dic83C2211yescharacteristic
87C22×C4⋊Dic83C2212yes—
88C22×Dic83⋊C4C2212yes—
89C2×C4⋊C4×D83C2212yes—
90C22×C4×Dic83C2211yescharacteristic
91C2×C42×D83C2212yes—
92C22×#41×C83C2211yescharacteristic
93#520×C83C22116yescomplemented
94C2×C4×Q8×C83C2212yes—
95C2×C4×D4×C83C2214yes—
96C2×C4×D4×C83C2212yes—
97C2×#117×C83C2211yescharacteristic
98C2×#117×C83C2212yes—
99C22×C4⋊C4×C83C2212yes—
100C22×C4⋊C4×C83C2211yescharacteristic
101C2×#13050590—28no—
102C2×#13050590—28no—
103C2×#13050590C2318yes—
104C2×#13050590C2318yes—
105C22×Dic166C2311yescharacteristic
106C22×Dic166C2311yescharacteristic
107C22×D332C2311yescharacteristic
108C22×D332C2311yescharacteristic
109C22×D332C2314yes—
110C22×C22⋊D83C2312yes—
111C22×C22⋊D83C2312yes—
112C22×C22⋊D83C2314yes—
113C22×C22⋊D83C2312yes—
114C22×C22⋊D83C2312yes—
115C23×Dic83C2311yescharacteristic
116C23×Dic83C2311yescharacteristic
117C23×Dic83C2312yes—
118C22×C4×D83C2312yes—
119C22×C4×D83C2312yes—
120C22×C4×D83C2312yes—
121C22×C4×D83C2312yes—
122C22×C4×D83C2314yes—
123#14581790C2318yes—
124#14581788C2318yes—
125#14581787C23132yes—
126#14581787C23132yes—
127#14581786C23132yes—
128#14581785C23132yes—
129#14581784C23132yes—
130#14581783C23116yes—
131#14581783C23116yes—
132#14581783C23116yes—
133#14581783C23116yes—
134#14581782C23132yes—
135#14581781C2318yes—
136#14581779C2318yes—
137#14581777C23132yes—
138#14581775C23132yes—
139#14581774C23132yes—
140#14581774C23132yes—
141#14581772C23116yes—
142#14581772C23116yes—
143#14581771C23116yes—
144#14581768C23116yes—
145#14581767C23116yes—
146#14581767C23116yes—
147#14581766C23116yes—
148#14581766C23132yes—
149#14581766C23132yes—
150#14581765C23132yes—
151#14581764C23116yes—
152#14581764C23132yes—
153#14581764C23116yes—
154#14581763C23116yes—
155C4×Dic166C23116yes—
156#14581757C2318yes—
157#14581757C2318yes—
158C4×D332C23132yes—
159C4×D332C23116yes—
160#14581754C2318yes—
161#14581754C2318yes—
162C4×C22⋊D83C23116yes—
163C4×C22⋊D83C23116yes—
164C4×C22⋊D83C23132yes—
165(C22⋊D83)⋊C4C23116yes—
166(C22⋊D83)⋊C4C23132yes—
167(C22⋊D83)⋊C4C23116yes—
168#14581751C23132yes—
169#14581750C23116yes—
170#14581749C23132yes—
171#14581749C23116yes—
172C2×C4⋊Dic83C23116yes—
173C2×C4⋊Dic83C2312yes—
174C2×C4⋊Dic83C2314yes—
175C2×C4⋊Dic83C2312yes—
176C2×C4⋊Dic83C2318yes—
177C2×C4⋊Dic83C2314yes—
178C2×C4⋊Dic83C2314yes—
179C2×Dic83⋊C4C23116yes—
180C2×Dic83⋊C4C2314yes—
181C2×Dic83⋊C4C2314yes—
182C2×Dic83⋊C4C2314yes—
183C2×Dic83⋊C4C2312yes—
184C2×Dic83⋊C4C2312yes—
185C2×Dic83⋊C4C2314yes—
186C2×Dic83⋊C4C2312yes—
187C2×Dic83⋊C4C2312yes—
188C4⋊C4×D83C23116yes—
189C2×C22⋊Dic83C2312yes—
190C2×C22⋊Dic83C2314yes—
191C2×C22⋊Dic83C2312yes—
192C2×(C2×D83)⋊C4C2312yes—
193C2×(C2×D83)⋊C4C2312yes—
194C2×(C2×D83)⋊C4C2312yes—
195C2×(C2×D83)⋊C4C2314yes—
196C2×(C2×D83)⋊C4C2314yes—
197C2×(C2×D83)⋊C4C2312yes—
198C2×(C2×D83)⋊C4C2314yes—
199C2×(C2×D83)⋊C4C2314yes—
200C2×C4×Dic83C2311yescharacteristic
201C2×C4×Dic83C2312yes—
202C2×C4×Dic83C2312yes—
203C2×C4×Dic83C2311yescharacteristic
204C2×C4×Dic83C2311yescharacteristic
205C2×C4×Dic83C2311yescharacteristic
206C2×C4×Dic83C2318yes—
207C2×C4×Dic83C2314yes—
208C42×D83C23116yes—
209C2×#41×C83—28no—
210C2×#41×C83C2318yes—
211C22×Q8×C83C2311yescharacteristic
212C22×D4×C83C2311yescharacteristic
213C22×D4×C83C2312yes—
214C23×C4×C83C2312yes—
215C23×C4×C83C2312yes—
216C23×C4×C83C2314yes—
217C23×C4×C83C2311yescharacteristic
218C4×Q8×C83C23116yes—
219C4×D4×C83C23132yes—
220C4×D4×C83C23116yes—
221#117×C83C23116yes—
222#117×C83C2318yes—
223C2×C4⋊C4×C83C2311yescharacteristic
224C2×C4⋊C4×C83C2312yes—
225C2×C4⋊C4×C83C2312yes—
226C2×C4⋊C4×C83C2314yes—
227C2×C4⋊C4×C83C23116yes—
228C2×C4⋊C4×C83C2318yes—
229C2×C4⋊C4×C83C2311yescharacteristic
230C2×C22⋊C4×C83C2312yes—
231C2×C22⋊C4×C83C2314yes—
232C2×C42×C83C2312yes—
233C2×C42×C83C2314yes—
234C23×D83C2412yes—
235C23×D83C2412yes—
236#13050590—232no—
237#13050590—232no—
238C2×Dic166—24no—
239C2×Dic166—24no—
240C2×Dic166C2414yes—
241C2×Dic166C2414yes—
242C2×D332—24no—
243C2×D332—24no—
244C2×D332—48no—
245C2×D332C2414yes—
246C2×D332C2414yes—
247C2×D332C24116yes—
248C2×C22⋊D83—28no—
249C2×C22⋊D83—28no—
250C2×C22⋊D83—48no—
251C2×C22⋊D83—44no—
252C2×C22⋊D83—44no—
253C2×C22⋊D83C2418yes—
254C2×C22⋊D83C2418yes—
255C2×C22⋊D83C24116yes—
256C2×C22⋊D83C2418yes—
257C2×C22⋊D83C2418yes—
258C22×Dic83—42no—
259C22×Dic83—42no—
260C22×Dic83—44no—
261C22×Dic83C2411yescharacteristic
262C22×Dic83C2411yescharacteristic
263C22×Dic83C2414yes—
264C22×Dic83C2412yes—
265C22×Dic83C2412yes—
266C22×Dic83C2411yescharacteristic
267C22×Dic83C2411yescharacteristic
268C22×Dic83C2414yes—
269C22×Dic83C2414yes—
270C22×Dic83C2418yes—
271C2×C4×D83—28no—
272C2×C4×D83—28no—
273C2×C4×D83—44no—
274C2×C4×D83—44no—
275C2×C4×D83—48no—
276C2×C4×D83C2418yes—
277C2×C4×D83C2418yes—
278C2×C4×D83C24116yes—
279C2×C4×D83C2418yes—
280C2×C4×D83C2418yes—
281C4⋊Dic83C2418yes—
282C4⋊Dic83C2418yes—
283C4⋊Dic83C24116yes—
284C4⋊Dic83C24116yes—
285C4⋊Dic83C24116yes—
286Dic83⋊C4C24116yes—
287Dic83⋊C4C2418yes—
288Dic83⋊C4C2418yes—
289Dic83⋊C4C24116yes—
290Dic83⋊C4C2418yes—
291Dic83⋊C4C24116yes—
292Dic83⋊C4C2418yes—
293Dic83⋊C4C24116yes—
294C22⋊Dic83C24116yes—
295C22⋊Dic83C2418yes—
296C22⋊Dic83C2418yes—
297(C2×D83)⋊C4C24116yes—
298(C2×D83)⋊C4C2418yes—
299(C2×D83)⋊C4C2418yes—
300(C2×D83)⋊C4C2418yes—
301(C2×D83)⋊C4C2418yes—
302(C2×D83)⋊C4C24116yes—
303(C2×D83)⋊C4C24116yes—
304(C2×D83)⋊C4C24116yes—
305C4×Dic83C2414yes—
306C4×Dic83C24116yes—
307C4×Dic83C2414yes—
308C4×Dic83C2414yes—
309C4×Dic83C2414yes—
310C4×Dic83C2418yes—
311C4×Dic83C2418yes—
312C24×C83C2412yes—
313C24×C83C2411yescharacteristic
314#41×C83—232no—
315C2×Q8×C83—24no—
316C2×Q8×C83C2414yes—
317C2×D4×C83—28no—
318C2×D4×C83—24no—
319C2×D4×C83C2414yes—
320C2×D4×C83C2418yes—
321C22×C4×C83—28no—
322C22×C4×C83—48no—
323C22×C4×C83—44no—
324C22×C4×C83#4118yes—
325C22×C4×C83C2418yes—
326C22×C4×C83C2412yes—
327C22×C4×C83C2412yes—
328C22×C4×C83C2414yes—
329C22×C4×C83C2412yes—
330C22×C4×C83C2418yes—
331C22×C4×C83C24116yes—
332C22×C4×C83C2411yescharacteristic
333C22×C4×C83C2411yescharacteristic
334C22×C4×C83C2414yes—
335C4⋊C4×C83C2418yes—
336C4⋊C4×C83C2418yes—
337C4⋊C4×C83C24116yes—
338C4⋊C4×C83C2414yes—
339C4⋊C4×C83C2414yes—
340C22⋊C4×C83C24116yes—
341C22⋊C4×C83C2418yes—
342C42×C83C24116yes—
343C42×C83C2418yes—
344C23×C83—22no—
345C23×C83—22no—
346C23×C83—24no—
347C23×C83—24no—
348C23×C83—24no—
349C23×C83C2×#4114yes—
350C23×C83C2514yes—
351C23×C83C2512yes—
352C23×C83C2511yescharacteristic
353C22×D83—24no—
354C22×D83—24no—
355C22×D83—24no—
356C22×D83—24no—
357C22×D83—24no—
358C22×D83—24no—
359C22×D83C2514yes—
360C22×D83C2514yes—
361Q8×C83—28no—
362D4×C83—216no—
363D4×C83—28no—
364C2×C4×C83—24no—
365C2×C4×C83—24no—
366C2×C4×C83—28no—
367C2×C4×C83—24no—
368C2×C4×C83—216no—
369C2×C4×C83—416no—
370C2×C4×C83—48no—
371C2×C4×C83C2×#4114yes—
372C2×C4×C83C2×#4114yes—
373C2×C4×C83C2×#41116yes—
374C2×C4×C83C2514yes—
375C2×C4×C83C2514yes—
376C2×C4×C83C2514yes—
377C2×C4×C83C2518yes—
378C2×C4×C83C2512yes—
379C2×C4×C83C2512yes—
380C22⋊D83—216no—
381C22⋊D83—216no—
382C22⋊D83—416no—
383C22⋊D83—48no—
384C22⋊D83—48no—
385C2×Dic83—24no—
386C2×Dic83—24no—
387C2×Dic83—22no—
388C2×Dic83—22no—
389C2×Dic83—28no—
390C2×Dic83—22no—
391C2×Dic83—22no—
392C2×Dic83—44no—
393C2×Dic83—44no—
394C2×Dic83—48no—
395C2×Dic83C2512yes—
396C2×Dic83C2512yes—
397C2×Dic83C2514yes—
398C2×Dic83C2514yes—
399C2×Dic83C2512yes—
400C2×Dic83C2512yes—
401C2×Dic83C2518yes—
402D332—28no—
403D332—28no—
404D332—416no—
405C4×D83—216no—
406C4×D83—216no—
407C4×D83—48no—
408C4×D83—48no—
409C4×D83—416no—
410Dic166—28no—
411Dic166—28no—
412C22×C83—22no—
413C22×C83—22no—
414C22×C83—28no—
415C22×C83—24no—
416C22×C83—24no—
417C22×C83—24no—
418C22×C83—48no—
419C22×C83C22×#4114yes—
420C22×C83C22×#4112yes—
421C22×C83#58512yes—
422C22×C83#58512yes—
423C22×C83C2611yescharacteristic
424C2×D83—24no—
425C2×D83—24no—
426C2×D83—24no—
427C2×D83—24no—
428C2×D83—24no—
429C2×D83—24no—
430C2×D83—48no—
431C2×D83—48no—
432C4×C83—24no—
433C4×C83—24no—
434C4×C83—24no—
435C4×C83—28no—
436C4×C83C22×#4114yes—
437C4×C83C22×#4114yes—
438Dic83—24no—
439Dic83—24no—
440Dic83—22no—
441Dic83—22no—
442Dic83—28no—
443Dic83—22no—
444Dic83—22no—
445C2×#3512—831nomaximal, Sylow
446C2×C83—24no—
447C2×C83—44no—
448C2×C83#351214yescomplemented
449C2×C83C23×#4111yescharacteristic
450C2×C83C2×#58511yescharacteristic
451C2×C83C2×#58511yescharacteristic
452D83—44no—
453D83—44no—
454#3512—8332no—
455C2×#553—834no—
456C2×#553—834no—
457C2×#553—832no—
458C2×#553—832no—
459C2×#552—832no—
460C2×#552—832no—
461C2×#541—832no—
462C2×#540—832no—
463C2×#537—831no—
464C2×#537—831no—
465C2×#532—831no—
466C2×#529—832no—
467C2×#529—832no—
468C22×#125—831no—
469C2×#520—831no—
470C2×#520D8311yescharacteristic, complemented
471C2×C4×#41—831no—
472C83C2×#351211yescharacteristic, complemented, Sylow
473C22×#41—831no—
474C22×#41—831no—
475C22×#41C2×D8311yescharacteristic
476#553—8364no—
477#553—8364no—
478#553—8332no—
479#553—8332no—
480#552—8332no—
481#552—8332no—
482#541—8332no—
483#540—8332no—
484#537—8316no—
485#537—8316no—
486#532—8316no—
487C2×C4⋊Q8—831no—
488C2×#127—831no—
489#529—8332no—
490#529—8332no—
491C2×#126—834no—
492C2×#126—834no—
493C2×#126—834no—
494C2×#126—834no—
495C2×#125—832no—
496C2×#125—832no—
497C2×#125—832no—
498C2×#125—832no—
499C2×#125—8316no—
500C2×#125—834no—
501C2×#125—834no—
502C2×#124—831no—
503C2×#124—831no—
504C2×#123—834no—
505C2×#123—834no—
506C2×#123—834no—
507C2×#123—834no—
508C2×C22⋊Q8—832no—
509C2×C22⋊Q8—832no—
510C2×C22⋊Q8—832no—
511C2×C22⋊Q8—832no—
512C2×#121—832no—
513C2×#121—832no—
514C2×#121—832no—
515C2×#121—834no—
516C2×#121—834no—
517C2×#121—832no—
518C2×#121—834no—
519C2×#121—832no—
520C2×#121—832no—
521C2×#121—834no—
522#520—8316no—
523#520C2×D83116yescomplemented
524C4×#41—8316no—
525C2×C4×Q8—831no—
526C2×C4×Q8—831no—
527C2×C4×Q8—832no—
528C2×C4×Q8C2×D8312yes—
529C2×C4×D4—834no—
530C2×C4×D4—832no—
531C2×C4×D4—832no—
532C2×C4×D4—831no—
533C2×C4×D4—831no—
534C2×C4×D4—832no—
535C2×C4×D4—832no—
536C2×C4×D4—834no—
537C2×C4×D4—832no—
538C2×C4×D4—834no—
539C2×C4×D4C2×D8312yes—
540C2×C4×D4C2×D8314yes—
541C2×#117—834no—
542C2×#117—832no—
543C2×#117—832no—
544C2×#117—834no—
545C2×#117C2×D8311yescharacteristic
546C2×#117C2×D8312yes—
547C22×C4⋊C4—832no—
548C22×C4⋊C4—831no—
549C22×C4⋊C4—832no—
550C22×C4⋊C4—832no—
551C22×C4⋊C4C2×D8311yescharacteristic
552C22×C4⋊C4C2×D8312yes—
553C22×C42—831no—
554C22×C42—832no—
555C2×#41—28no—
556C2×#41—838no—
557C2×#41—838no—
558C2×#41—1668no—
559C2×#41—1668no—
560C2×#41C22×D8318yes—
561C22×Q8—831no—
562C22×Q8—831no—
563C22×Q8C22×D8311yescharacteristic
564C22×D4—834no—
565C22×D4—832no—
566C22×D4—832no—
567C22×D4—832no—
568C22×D4—832no—
569C22×D4—834no—
570C22×D4—831no—
571C22×D4—831no—
572C22×D4C22×D8312yes—
573C22×D4C22×D8311yescharacteristic
574C23×C4—832no—
575C23×C4—831no—
576C23×C4—831no—
577C23×C4—834no—
578C23×C4—832no—
579C23×C4—832no—
580C23×C4—832no—
581C23×C4—832no—
582C23×C4C22×D8312yes—
583C23×C4C22×D8312yes—
584C23×C4C22×D8314yes—
585C23×C4C22×D8311yescharacteristic
586C4⋊Q8—838no—
587#127—838no—
588#126—8332no—
589#126—8332no—
590#126—8332no—
591#126—8332no—
592#125—8316no—
593#125—8316no—
594#125—8316no—
595#125—8316no—
596#125—8332no—
597#125—8332no—
598#124—838no—
599#124—838no—
600#123—8332no—
601#123—8332no—
602#123—8332no—
603#123—8332no—
604C22⋊Q8—8316no—
605C22⋊Q8—8316no—
606C22⋊Q8—8316no—
607C22⋊Q8—8316no—
608#121—8316no—
609#121—8316no—
610#121—8316no—
611#121—8332no—
612#121—8332no—
613#121—8316no—
614#121—8332no—
615#121—8316no—
616#121—8316no—
617#121—8332no—
618C4×Q8—838no—
619C4×Q8—838no—
620C4×Q8—8316no—
621C4×Q8C22×D83116yes—
622C4×D4—8332no—
623C4×D4—8316no—
624C4×D4—8316no—
625C4×D4—838no—
626C4×D4—838no—
627C4×D4—8316no—
628C4×D4—8316no—
629C4×D4—8332no—
630C4×D4—8316no—
631C4×D4—8332no—
632C4×D4C22×D83116yes—
633C4×D4C22×D83132yes—
634#117—8332no—
635#117—8316no—
636#117—8316no—
637#117—8332no—
638#117C22×D8318yes—
639#117C22×D83116yes—
640C2×C4⋊C4—832no—
641C2×C4⋊C4—834no—
642C2×C4⋊C4—834no—
643C2×C4⋊C4—832no—
644C2×C4⋊C4—834no—
645C2×C4⋊C4—838no—
646C2×C4⋊C4—834no—
647C2×C4⋊C4—834no—
648C2×C4⋊C4—8316no—
649C2×C4⋊C4—8316no—
650C2×C4⋊C4—832no—
651C2×C4⋊C4—832no—
652C2×C4⋊C4—834no—
653C2×C4⋊C4—834no—
654C2×C4⋊C4—832no—
655C2×C4⋊C4—832no—
656C2×C4⋊C4—8316no—
657C2×C4⋊C4C22×D8311yescharacteristic
658C2×C4⋊C4C22×D8311yescharacteristic
659C2×C4⋊C4C22×D8312yes—
660C2×C4⋊C4C22×D8312yes—
661C2×C4⋊C4C22×D8314yes—
662C2×C4⋊C4C22×D8318yes—
663C2×C4⋊C4C22×D83116yes—
664C2×C22⋊C4—832no—
665C2×C22⋊C4—834no—
666C2×C22⋊C4—832no—
667C2×C22⋊C4—832no—
668C2×C22⋊C4—832no—
669C2×C22⋊C4—832no—
670C2×C22⋊C4—834no—
671C2×C22⋊C4—834no—
672C2×C22⋊C4—832no—
673C2×C22⋊C4—834no—
674C2×C22⋊C4—834no—
675C2×C22⋊C4C22×D8312yes—
676C2×C22⋊C4C22×D8314yes—
677C2×C42—834no—
678C2×C42—832no—
679C2×C42—832no—
680C2×C42—831no—
681C2×C42—831no—
682C2×C42—831no—
683C2×C42—838no—
684C2×C42—831no—
685C2×C42—8316no—
686C2×C42C22×D8312yes—
687C2×C42C22×D8314yes—
688C24—832no—
689C24—832no—
690C24C23×D8312yes—
691C24C23×D8311yescharacteristic
692#41—232no—
693#41—16632no—
694#41—16632no—
695C2×Q8—24no—
696C2×Q8—834no—
697C2×Q8—834no—
698C2×Q8—1664no—
699C2×Q8—1664no—
700C2×Q8C23×D8314yes—
701C2×D4—28no—
702C2×D4—24no—
703C2×D4—3328no—
704C2×D4—3324no—
705C2×D4—3328no—
706C2×D4—3324no—
707C2×D4—8316no—
708C2×D4—838no—
709C2×D4—838no—
710C2×D4—838no—
711C2×D4—838no—
712C2×D4—8316no—
713C2×D4—834no—
714C2×D4—834no—
715C2×D4—1668no—
716C2×D4—1668no—
717C2×D4—1664no—
718C2×D4—1664no—
719C2×D4C23×D8318yes—
720C2×D4C23×D8314yes—
721C22×C4—28no—
722C22×C4—48no—
723C22×C4—44no—
724C22×C4—3324no—
725C22×C4—3324no—
726C22×C4—3328no—
727C22×C4—3322no—
728C22×C4—3322no—
729C22×C4—3324no—
730C22×C4—834no—
731C22×C4—834no—
732C22×C4—838no—
733C22×C4—838no—
734C22×C4—838no—
735C22×C4—8316no—
736C22×C4—831no—
737C22×C4—831no—
738C22×C4—832no—
739C22×C4—832no—
740C22×C4—831no—
741C22×C4—831no—
742C22×C4—834no—
743C22×C4—838no—
744C22×C4—838no—
745C22×C4—1668no—
746C22×C4—1668no—
747C22×C4#1305059018yes—
748C22×C4C23×D8318yes—
749C22×C4C23×D8312yes—
750C22×C4C23×D8312yes—
751C22×C4C23×D8312yes—
752C22×C4C23×D8314yes—
753C22×C4C23×D8318yes—
754C22×C4C23×D83116yes—
755C22×C4C23×D8314yes—
756C22×C4C23×D8311yescharacteristic
757C22×C4C23×D8311yescharacteristic
758C4⋊C4—838no—
759C4⋊C4—8316no—
760C4⋊C4—8316no—
761C4⋊C4—838no—
762C4⋊C4—8316no—
763C4⋊C4—8316no—
764C4⋊C4—8316no—
765C4⋊C4—838no—
766C4⋊C4—838no—
767C4⋊C4—8316no—
768C4⋊C4—8316no—
769C4⋊C4—838no—
770C4⋊C4—838no—
771C4⋊C4C23×D8314yes—
772C4⋊C4C23×D8314yes—
773C4⋊C4C23×D8318yes—
774C4⋊C4C23×D8318yes—
775C4⋊C4C23×D83116yes—
776C22⋊C4—838no—
777C22⋊C4—8316no—
778C22⋊C4—838no—
779C22⋊C4—838no—
780C22⋊C4—838no—
781C22⋊C4—838no—
782C22⋊C4—8316no—
783C22⋊C4—8316no—
784C22⋊C4—838no—
785C22⋊C4—8316no—
786C22⋊C4—8316no—
787C22⋊C4C23×D8318yes—
788C22⋊C4C23×D83116yes—
789C42—834no—
790C42—838no—
791C42—838no—
792C42—834no—
793C42—834no—
794C42—834no—
795C42—8316no—
796C42C23×D8318yes—
797C42C23×D83116yes—
798C23—22no—
799C23—22no—
800C23—24no—
801C23—24no—
802C23—24no—
803C23—834no—
804C23—834no—
805C23—1664no—
806C23—1664no—
807C23—1664no—
808C23—1664no—
809C23—1664no—
810C23—1664no—
811C23C2×#1305059014yes—
812C23C24×D8314yes—
813C23C24×D8312yes—
814C23C24×D8311yescharacteristic
815Q8—28no—
816Q8—1668no—
817Q8—1668no—
818D4—216no—
819D4—28no—
820D4—33216no—
821D4—3328no—
822D4—33216no—
823D4—3328no—
824D4—16616no—
825D4—16616no—
826D4—1668no—
827D4—1668no—
828C2×C4—24no—
829C2×C4—24no—
830C2×C4—28no—
831C2×C4—24no—
832C2×C4—216no—
833C2×C4—416no—
834C2×C4—48no—
835C2×C4—3328no—
836C2×C4—3328no—
837C2×C4—33216no—
838C2×C4—3324no—
839C2×C4—3324no—
840C2×C4—3328no—
841C2×C4—832no—
842C2×C4—832no—
843C2×C4—834no—
844C2×C4—834no—
845C2×C4—832no—
846C2×C4—832no—
847C2×C4—838no—
848C2×C4—1664no—
849C2×C4—1664no—
850C2×C4—1662no—
851C2×C4—1662no—
852C2×C4—1662no—
853C2×C4—1668no—
854C2×C4—1662no—
855C2×C4—16616no—
856C2×C4—16616no—
857C2×C4C2×#1305059014yes—
858C2×C4C2×#1305059014yes—
859C2×C4C2×#13050590116yes—
860C2×C4C24×D8314yes—
861C2×C4C24×D8314yes—
862C2×C4C24×D8314yes—
863C2×C4C24×D8318yes—
864C2×C4C24×D8312yes—
865C2×C4C24×D8312yes—
866C22—28no—
867C22—22no—
868C22—22no—
869C22—24no—
870C22—24no—
871C22—24no—
872C22—48no—
873C22—3328no—
874C22—3328no—
875C22—1664no—
876C22—1664no—
877C22—1664no—
878C22—1664no—
879C22—1664no—
880C22—1664no—
881C22C22×#1305059014yes—
882C22C22×#1305059012yes—
883C22#1912853612yes—
884C22#1912853812yes—
885C22C25×D8311yescharacteristic
886C4—24no—
887C4—24no—
888C4—28no—
889C4—24no—
890C4—1664no—
891C4—1664no—
892C4—1662no—
893C4—1662no—
894C4—1662no—
895C4—1668no—
896C4—1662no—
897C4C22×#1305059014yes—
898C4C22×#1305059014yes—
899C2—24no—
900C2—44no—
901C2—3324no—
902C2—3324no—
903C2#2492138014yesdirect product factor
904C2C23×#1305059011yescharacteristic
905C2C2×#1912853611yescharacteristic
906C2C2×#1912853811yescharacteristic
subgroupG/H
centerC23C24×D83
commutator, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC2×#520×C83C2
socleC23×C83C25
hypercenterC2×#520D83
hypocenterC83C2×#3512
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #24921380C2direct (N × H)
2. C2×#19128400C2semidirect
3. C2×#19128399C2semidirect
4. C2×#19128397C2semidirect
5. C2×#19128395C2semidirect
6. C2×#19128390C2semidirect
7. C2×#19128386C2semidirect
8. C2×#19128309C2semidirect
9. C2×#19128302C2semidirect
10. C2×#19128282C2semidirect
11. C2×#19128279C2semidirect
12. C2×#19128247C2semidirect
13. C2×#19128238C2semidirect
14. C2×#19128233C2semidirect
15. C22×#14581783C2semidirect
16. C2×#19128181C2semidirect
17. C2×#19128169C2semidirect
18. C2×#520×C83C2semidirect
21. #19128400C22semidirect
22. #19128399C22semidirect
23. #19128397C22semidirect
24. #19128395C22semidirect
25. #19128390C22semidirect
26. #19128386C22semidirect
27. #19128309C22semidirect
28. #19128302C22semidirect
29. #19128282C22semidirect
30. #19128279C22semidirect
31. #19128247C22semidirect
34. #19128238C22semidirect
35. #19128233C22semidirect
45. C2×#14581783C22semidirect
67. #19128181C22semidirect
68. #19128169C22semidirect
93. #520×C83C22semidirect
448. C2×C83#3512semidirect
470. C2×#520D83semidirect
472. C83C2×#3512semidirect
523. #520C2×D83semidirect
903. C2#24921380direct (N × H)

Maximal subgroups

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

subgroupindex
#249213802
C2×#191284002
C2×#191283992
C2×#191283972
C2×#191283952
C2×#191283902
C2×#191283862
C2×#191283092
C2×#191283022
C2×#191282822
C2×#191282792
C2×#191282472
C2×#191282382
C2×#191282332
C22×#145817832
C2×#191281812
C2×#191281692
C2×#520×C832
C2×#351283