Finite Group Databasebeta

← C2×#24921382 #36312908

Subgroups — C2×#24921382 #36312908

Order 21248.

7238 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24921382C2132yesmaximal, direct product factor
2C2×#19128398C214yesmaximal, complemented
3C2×#19128396C214yesmaximal, complemented
4C2×#19128394C214yesmaximal, complemented
5C2×#19128388C214yesmaximal, complemented
6C2×#19128314C211yesmaximal, characteristic, complemented
7C2×#19128313C211yesmaximal, characteristic, complemented
8C2×#19128305C211yesmaximal, characteristic, complemented
9C2×#19128280C212yesmaximal, complemented
10C2×#19128249C211yesmaximal, characteristic, complemented
11C2×#19128233C212yesmaximal, complemented
12C2×#19128232C212yesmaximal, complemented
13C2×#125×D83C211yesmaximal, characteristic, complemented
14C2×#19128180C212yesmaximal, complemented
15C2×#19128169C211yesmaximal, characteristic, complemented
16C2×#540×C83C211yesmaximal, characteristic, complemented
17C22×#13050590C2211yescharacteristic
18C22×#13050589C2212yes—
19#19128398C22164yescomplemented
20#19128396C22164yescomplemented
21#19128394C22164yescomplemented
22#19128388C22164yescomplemented
23#19128314C22116yescomplemented
24#19128313C22116yescomplemented
25#19128305C22116yescomplemented
26#19128280C22132yescomplemented
27#19128249C22116yescomplemented
28C2×#14581792C2211yescharacteristic
29#19128233C22132yescomplemented
30#19128232C22132yescomplemented
31C2×#14581787C2214yes—
32C2×#14581785C2214yes—
33C2×#14581785C2214yes—
34C2×#14581785C2214yes—
35C2×#14581784C2211yescharacteristic
36C2×#14581783C2214yes—
37C2×#14581783C2212yes—
38C2×#14581782C2214yes—
39C2×#14581782C2214yes—
40#125×D83C22116yescomplemented
41C2×#14581779C2212yes—
42C2×#14581774C2214yes—
43C2×#14581773C2214yes—
44C2×#14581773C2214yes—
45C2×#14581772C2212yes—
46C2×#14581771C2212yes—
47C2×#14581769C2214yes—
48C2×#14581765C2214yes—
49C2×#14581764C2214yes—
50C2×#14581764C2214yes—
51C2×#14581763C2214yes—
52C2×#14581763C2212yes—
53C2×#14581763C2214yes—
54#19128180C22132yescomplemented
55#19128169C22116yescomplemented
56C2×C4×Dic166C2212yes—
57C2×#14581757C2212yes—
58C2×#14581757C2212yes—
59C2×D4×Dic83C2212yes—
60C2×D4×Dic83C2214yes—
61C2×D4×Dic83C2214yes—
62C2×#14581754C2212yes—
63C2×C4×C22⋊D83C2214yes—
64C2×C4×C22⋊D83C2214yes—
65C2×(C22⋊D83)⋊C4C2212yes—
66C2×(C22⋊D83)⋊C4C2212yes—
67C2×(C22⋊D83)⋊C4C2214yes—
68C2×#14581751C2214yes—
69C2×#14581749C2211yescharacteristic
70C2×#14581749C2211yescharacteristic
71C2×#14581748C2214yes—
72C2×#14581748C2214yes—
73C22×Dic83⋊C4C2214yes—
74C2×C4⋊C4×D83C2212yes—
75C2×C4⋊C4×D83C2214yes—
76C22×C4×Dic83C2211yescharacteristic
77C2×C42×D83C2211yescharacteristic
78C2×C42×D83C2211yescharacteristic
79#540×C83C22116yescomplemented
80C2×#127×C83C2211yescharacteristic
81C2×#125×C83C2211yescharacteristic
82C2×#123×C83C2214yes—
83C2×#121×C83C2214yes—
84C2×#121×C83C2212yes—
85C2×C4×D4×C83C2212yes—
86C2×#117×C83C2211yescharacteristic
87C2×#13050590—28no—
88C2×#13050590C2318yes—
89C2×#13050589—216no—
90C2×#13050589C23116yes—
91C22×Dic166C2311yescharacteristic
92C22×Dic166C2312yes—
93C22×D332C2311yescharacteristic
94C22×C22⋊D83C2311yescharacteristic
95C22×C22⋊D83C2311yescharacteristic
96C22×C22⋊D83C2314yes—
97C22×C22⋊D83C2314yes—
98C23×Dic83C2314yes—
99C23×Dic83C2312yes—
100C23×Dic83C2314yes—
101C22×C4×D83C2311yescharacteristic
102C22×C4×D83C2312yes—
103C22×C4×D83C2312yes—
104C22×C4×D83C2314yes—
105C22×C4×D83C2311yescharacteristic
106#14581792C2318yes—
107#14581787C23132yes—
108#14581785C23132yes—
109#14581785C23132yes—
110#14581785C23132yes—
111#14581784C2318yes—
112#14581783C23132yes—
113#14581783C23116yes—
114#14581782C23132yes—
115#14581782C23132yes—
116#14581779C23116yes—
117#14581774C23132yes—
118#14581773C23132yes—
119#14581773C23132yes—
120#14581772C23116yes—
121#14581771C23116yes—
122#14581769C23132yes—
123#14581765C23132yes—
124#14581764C23132yes—
125#14581764C23132yes—
126#14581763C23132yes—
127#14581763C23132yes—
128#14581763C23116yes—
129C4×Dic166C23116yes—
130#14581757C23116yes—
131#14581757C23116yes—
132D4×Dic83C23132yes—
133D4×Dic83C23132yes—
134D4×Dic83C23116yes—
135#14581754C23116yes—
136C4×C22⋊D83C23132yes—
137C4×C22⋊D83C23132yes—
138(C22⋊D83)⋊C4C23116yes—
139(C22⋊D83)⋊C4C23132yes—
140(C22⋊D83)⋊C4C23116yes—
141#14581751C23132yes—
142#14581749C2318yes—
143#14581749C2318yes—
144#14581748C23132yes—
145#14581748C23132yes—
146C2×C4⋊Dic83C2314yes—
147C2×C4⋊Dic83C2312yes—
148C2×C4⋊Dic83C2314yes—
149C2×C4⋊Dic83C2314yes—
150C2×Dic83⋊C4C23132yes—
151C2×Dic83⋊C4C2314yes—
152C2×Dic83⋊C4C2314yes—
153C2×Dic83⋊C4C2314yes—
154C2×Dic83⋊C4C2312yes—
155C2×Dic83⋊C4C2314yes—
156C2×Dic83⋊C4C2314yes—
157C2×Dic83⋊C4C2314yes—
158C2×Dic83⋊C4C2312yes—
159C4⋊C4×D83C23132yes—
160C4⋊C4×D83C23116yes—
161C2×C22⋊Dic83C2314yes—
162C2×C22⋊Dic83C2314yes—
163C2×C22⋊Dic83C2314yes—
164C2×C22⋊Dic83C2314yes—
165C2×C22⋊Dic83C2314yes—
166C2×(C2×D83)⋊C4C2312yes—
167C2×(C2×D83)⋊C4C2312yes—
168C2×(C2×D83)⋊C4C2314yes—
169C2×C4×Dic83C2311yescharacteristic
170C2×C4×Dic83C2312yes—
171C2×C4×Dic83C2312yes—
172C2×C4×Dic83C2312yes—
173C2×C4×Dic83C2311yescharacteristic
174C2×C4×Dic83C2318yes—
175C2×C4×Dic83C2314yes—
176C2×C4×Dic83C2314yes—
177C42×D83C2318yes—
178C42×D83C2318yes—
179C22×D4×C83C2312yes—
180C22×D4×C83C2314yes—
181C22×D4×C83C2314yes—
182C23×C4×C83C2311yescharacteristic
183C23×C4×C83C2314yes—
184#127×C83C2318yes—
185#125×C83C2318yes—
186#123×C83C23132yes—
187#121×C83C23132yes—
188#121×C83C23116yes—
189C4×D4×C83C23116yes—
190#117×C83C2318yes—
191C2×C4⋊C4×C83C2312yes—
192C2×C4⋊C4×C83C2312yes—
193C2×C4⋊C4×C83C2314yes—
194C2×C22⋊C4×C83C2312yes—
195C2×C22⋊C4×C83C2314yes—
196C2×C22⋊C4×C83C2314yes—
197C2×C42×C83C2311yescharacteristic
198C2×C42×C83C2311yescharacteristic
199C23×D83C2411yescharacteristic
200C23×D83C2411yescharacteristic
201#13050590—232no—
202#13050589—264no—
203C2×Dic166—28no—
204C2×Dic166—24no—
205C2×Dic166C2414yes—
206C2×Dic166C2418yes—
207C2×D332—24no—
208C2×D332C2414yes—
209C2×C22⋊D83—216no—
210C2×C22⋊D83—24no—
211C2×C22⋊D83—24no—
212C2×C22⋊D83—48no—
213C2×C22⋊D83C2414yes—
214C2×C22⋊D83C24116yes—
215C2×C22⋊D83C2414yes—
216C2×C22⋊D83C24116yes—
217C22×Dic83—216no—
218C22×Dic83—44no—
219C22×Dic83—48no—
220C22×Dic83C24116yes—
221C22×Dic83C2412yes—
222C22×Dic83C2414yes—
223C22×Dic83C2411yescharacteristic
224C22×Dic83C2412yes—
225C22×Dic83C2414yes—
226C22×Dic83C24116yes—
227C22×Dic83C2418yes—
228C22×Dic83C2411yescharacteristic
229C2×C4×D83—24no—
230C2×C4×D83—44no—
231C2×C4×D83—44no—
232C2×C4×D83—48no—
233C2×C4×D83#4118yes—
234C2×C4×D83C2414yes—
235C2×C4×D83C2418yes—
236C2×C4×D83C24116yes—
237C2×C4×D83C2418yes—
238C2×C4×D83C2414yes—
239C4⋊Dic83C24116yes—
240C4⋊Dic83C2418yes—
241C4⋊Dic83C24116yes—
242C4⋊Dic83C24116yes—
243Dic83⋊C4C24116yes—
244Dic83⋊C4C24116yes—
245Dic83⋊C4C24116yes—
246Dic83⋊C4C2418yes—
247Dic83⋊C4C24116yes—
248Dic83⋊C4C24116yes—
249Dic83⋊C4C24116yes—
250Dic83⋊C4C2418yes—
251C22⋊Dic83C24116yes—
252C22⋊Dic83C24116yes—
253C22⋊Dic83C24116yes—
254C22⋊Dic83C24116yes—
255C22⋊Dic83C24116yes—
256(C2×D83)⋊C4C2418yes—
257(C2×D83)⋊C4C24116yes—
258(C2×D83)⋊C4C2418yes—
259C4×Dic83C2414yes—
260C4×Dic83C2418yes—
261C4×Dic83C24116yes—
262C4×Dic83C24116yes—
263C4×Dic83C2418yes—
264C4×Dic83C2418yes—
265C4×Dic83C2414yes—
266C24×C83C2411yescharacteristic
267C24×C83C2414yes—
268C2×D4×C83—28no—
269C2×D4×C83—48no—
270C2×D4×C83—48no—
271C2×D4×C83C2418yes—
272C2×D4×C83C24116yes—
273C2×D4×C83C24116yes—
274C22×C4×C83—24no—
275C22×C4×C83—48no—
276C22×C4×C83C2414yes—
277C22×C4×C83C2412yes—
278C22×C4×C83C2412yes—
279C22×C4×C83C2414yes—
280C22×C4×C83C2411yescharacteristic
281C22×C4×C83C24116yes—
282C22×C4×C83C2411yescharacteristic
283C4⋊C4×C83C2418yes—
284C4⋊C4×C83C2418yes—
285C4⋊C4×C83C24116yes—
286C22⋊C4×C83C24116yes—
287C22⋊C4×C83C24116yes—
288C22⋊C4×C83C2418yes—
289C42×C83C2414yes—
290C42×C83C2414yes—
291C23×C83—22no—
292C23×C83—28no—
293C23×C83—28no—
294C23×C83—24no—
295C23×C83—28no—
296C23×C83C2518yes—
297C23×C83C2512yes—
298C23×C83C2511yescharacteristic
299C22×D83—24no—
300C22×D83—22no—
301C22×D83—24no—
302C22×D83C2×#4114yes—
303C22×D83C2512yes—
304C22×D83C2512yes—
305D4×C83—216no—
306D4×C83—416no—
307D4×C83—416no—
308C2×C4×C83—22no—
309C2×C4×C83—24no—
310C2×C4×C83—28no—
311C2×C4×C83—24no—
312C2×C4×C83—28no—
313C2×C4×C83—416no—
314C2×C4×C83C2×#4114yes—
315C2×C4×C83C2514yes—
316C2×C4×C83C2514yes—
317C2×C4×C83C2512yes—
318C2×C4×C83C2518yes—
319C2×C4×C83C2512yes—
320C22⋊D83—232no—
321C22⋊D83—28no—
322C22⋊D83—28no—
323C22⋊D83—416no—
324C2×Dic83—22no—
325C2×Dic83—28no—
326C2×Dic83—24no—
327C2×Dic83—28no—
328C2×Dic83—24no—
329C2×Dic83—232no—
330C2×Dic83—48no—
331C2×Dic83—416no—
332C2×Dic83C2×#4114yes—
333C2×Dic83C2514yes—
334C2×Dic83C2514yes—
335C2×Dic83C2518yes—
336C2×Dic83C2512yes—
337C2×Dic83C2518yes—
338C2×Dic83C2512yes—
339D332—28no—
340C4×D83—28no—
341C4×D83—48no—
342C4×D83—48no—
343C4×D83—416no—
344C4×D83C2×#41116yes—
345Dic166—216no—
346Dic166—28no—
347C22×C83—28no—
348C22×C83—22no—
349C22×C83—28no—
350C22×C83—24no—
351C22×C83—28no—
352C22×C83—44no—
353C22×C83—416no—
354C22×C83C22×#4112yes—
355C22×C83#58514yes—
356C22×C83C2611yescharacteristic
357C2×D83—24no—
358C2×D83—28no—
359C2×D83—22no—
360C2×D83—24no—
361C2×D83—44no—
362C2×D83C22×#4114yes—
363C4×C83—22no—
364C4×C83—24no—
365C4×C83—28no—
366C4×C83—24no—
367C4×C83C22×#4114yes—
368Dic83—22no—
369Dic83—28no—
370Dic83—24no—
371Dic83—28no—
372Dic83—24no—
373Dic83C22×#4114yes—
374C2×#3512—831nomaximal, Sylow
375C2×C83—48no—
376C2×C83—42no—
377C2×C83#351214yescomplemented
378C2×C83C23×#4111yescharacteristic
379C2×C83C2×#58512yes—
380D83—24no—
381D83—42no—
382#3512—8332no—
383C2×#553—834no—
384C2×#553—834no—
385C2×#553—834no—
386C2×#552—834no—
387C2×#541—831no—
388C2×#541—831no—
389C2×#540—831no—
390C2×#540D8311yescharacteristic, complemented
391C2×#537—832no—
392C2×#532—831no—
393C2×#529—832no—
394C2×#529—832no—
395C22×#125—831no—
396C2×#520—832no—
397C2×C4×#41—831no—
398C83C2×#351211yescharacteristic, complemented, Sylow
399C22×#41—832no—
400C22×#41—831no—
401#553—8364no—
402#553—8364no—
403#553—8364no—
404#552—8364no—
405#541—8316no—
406#541—8316no—
407#540—8316no—
408#540C2×D83116yescomplemented
409#537—8332no—
410#532—8316no—
411C2×C4⋊Q8—831no—
412C2×#127C2×D8311yescharacteristic
413#529—8332no—
414#529—8332no—
415C2×#126—834no—
416C2×#126—834no—
417C2×#126—834no—
418C2×#126—834no—
419C2×#125—8316no—
420C2×#125—832no—
421C2×#125—834no—
422C2×#125—834no—
423C2×#125—834no—
424C2×#125—831no—
425C2×#125C2×D8311yescharacteristic
426C2×#124—832no—
427C2×#123—834no—
428C2×#123—834no—
429C2×#123—834no—
430C2×#123C2×D8314yes—
431C2×C22⋊Q8—832no—
432C2×C22⋊Q8—832no—
433C2×C22⋊Q8—834no—
434C2×#121—832no—
435C2×#121—834no—
436C2×#121—834no—
437C2×#121—834no—
438C2×#121—834no—
439C2×#121—834no—
440C2×#121C2×D8312yes—
441C2×#121C2×D8314yes—
442#520—8332no—
443C4×#41—8316no—
444C2×C4×Q8—832no—
445C2×C4×Q8—832no—
446C2×C4×Q8—832no—
447C2×C4×D4—832no—
448C2×C4×D4—834no—
449C2×C4×D4—834no—
450C2×C4×D4—834no—
451C2×C4×D4—834no—
452C2×C4×D4—832no—
453C2×C4×D4—832no—
454C2×C4×D4—832no—
455C2×C4×D4—834no—
456C2×C4×D4C2×D8312yes—
457C2×#117—834no—
458C2×#117—834no—
459C2×#117—834no—
460C2×#117—831no—
461C2×#117—831no—
462C2×#117C2×D8311yescharacteristic
463C22×C4⋊C4—834no—
464C22×C4⋊C4—832no—
465C22×C4⋊C4—834no—
466C22×C42—831no—
467C22×C42—831no—
468C22×C42—831no—
469C2×#41—8316no—
470C2×#41—838no—
471C2×#41—1668no—
472C2×#41—16616no—
473C22×Q8—831no—
474C22×Q8—832no—
475C22×D4—834no—
476C22×D4—831no—
477C22×D4—834no—
478C22×D4—831no—
479C22×D4—831no—
480C22×D4C22×D8312yes—
481C22×D4C22×D8314yes—
482C22×D4C22×D8314yes—
483C23×C4—834no—
484C23×C4—832no—
485C23×C4—834no—
486C23×C4—832no—
487C23×C4—832no—
488C23×C4—831no—
489C23×C4—834no—
490C23×C4—831no—
491C23×C4C22×D8311yescharacteristic
492C23×C4C22×D8314yes—
493C4⋊Q8—838no—
494#127C22×D8318yes—
495#126—8332no—
496#126—8332no—
497#126—8332no—
498#126—8332no—
499#125—8316no—
500#125—8332no—
501#125—8332no—
502#125—8332no—
503#125—838no—
504#125C22×D8318yes—
505#124—8316no—
506#123—8332no—
507#123—8332no—
508#123—8332no—
509#123C22×D83132yes—
510C22⋊Q8—8316no—
511C22⋊Q8—8316no—
512C22⋊Q8—8332no—
513#121—8316no—
514#121—8332no—
515#121—8332no—
516#121—8332no—
517#121—8332no—
518#121—8332no—
519#121C22×D83116yes—
520#121C22×D83132yes—
521C4×Q8—8316no—
522C4×Q8—8316no—
523C4×Q8—8316no—
524C4×D4—8316no—
525C4×D4—8332no—
526C4×D4—8332no—
527C4×D4—8332no—
528C4×D4—8332no—
529C4×D4—8316no—
530C4×D4—8316no—
531C4×D4—8316no—
532C4×D4—8332no—
533C4×D4C22×D83116yes—
534#117—8332no—
535#117—8332no—
536#117—8332no—
537#117—838no—
538#117—838no—
539#117C22×D8318yes—
540C2×C4⋊C4—832no—
541C2×C4⋊C4—834no—
542C2×C4⋊C4—834no—
543C2×C4⋊C4—834no—
544C2×C4⋊C4—832no—
545C2×C4⋊C4—834no—
546C2×C4⋊C4—834no—
547C2×C4⋊C4—8332no—
548C2×C4⋊C4—834no—
549C2×C4⋊C4—832no—
550C2×C4⋊C4—834no—
551C2×C4⋊C4—834no—
552C2×C4⋊C4—834no—
553C2×C4⋊C4—8316no—
554C2×C4⋊C4—8332no—
555C2×C4⋊C4C22×D8312yes—
556C2×C4⋊C4C22×D8314yes—
557C2×C4⋊C4C22×D8312yes—
558C2×C22⋊C4—834no—
559C2×C22⋊C4—834no—
560C2×C22⋊C4—834no—
561C2×C22⋊C4—834no—
562C2×C22⋊C4—834no—
563C2×C22⋊C4—832no—
564C2×C22⋊C4—832no—
565C2×C22⋊C4—834no—
566C2×C22⋊C4C22×D8314yes—
567C2×C22⋊C4C22×D8314yes—
568C2×C22⋊C4C22×D8312yes—
569C2×C42—831no—
570C2×C42—834no—
571C2×C42—834no—
572C2×C42—832no—
573C2×C42—832no—
574C2×C42—832no—
575C2×C42—838no—
576C2×C42—831no—
577C2×C42—838no—
578C2×C42—838no—
579C2×C42C22×D8311yescharacteristic
580C2×C42C22×D8311yescharacteristic
581C24—831no—
582C24—831no—
583C24C23×D8311yescharacteristic
584C24C23×D8314yes—
585#41—16632no—
586#41—16664no—
587C2×Q8—834no—
588C2×Q8—838no—
589C2×Q8—1664no—
590C2×Q8—1668no—
591C2×D4—28no—
592C2×D4—48no—
593C2×D4—48no—
594C2×D4—3328no—
595C2×D4—8316no—
596C2×D4—834no—
597C2×D4—8316no—
598C2×D4—834no—
599C2×D4—834no—
600C2×D4—1664no—
601C2×D4—1664no—
602C2×D4—1664no—
603C2×D4—16616no—
604C2×D4C23×D8318yes—
605C2×D4C23×D83116yes—
606C2×D4C23×D83116yes—
607C22×C4—24no—
608C22×C4—48no—
609C22×C4—3324no—
610C22×C4—3328no—
611C22×C4—3324no—
612C22×C4—3324no—
613C22×C4—3328no—
614C22×C4—838no—
615C22×C4—8316no—
616C22×C4—838no—
617C22×C4—838no—
618C22×C4—8316no—
619C22×C4—831no—
620C22×C4—838no—
621C22×C4—834no—
622C22×C4—8316no—
623C22×C4—832no—
624C22×C4—832no—
625C22×C4—834no—
626C22×C4—831no—
627C22×C4—834no—
628C22×C4—834no—
629C22×C4—16616no—
630C22×C4—1664no—
631C22×C4C23×D8314yes—
632C22×C4C23×D8312yes—
633C22×C4C23×D8311yescharacteristic
634C22×C4C23×D8312yes—
635C22×C4C23×D8314yes—
636C22×C4C23×D83116yes—
637C22×C4C23×D8311yescharacteristic
638C4⋊C4—838no—
639C4⋊C4—8316no—
640C4⋊C4—8316no—
641C4⋊C4—8316no—
642C4⋊C4—838no—
643C4⋊C4—8316no—
644C4⋊C4—8316no—
645C4⋊C4—8316no—
646C4⋊C4—838no—
647C4⋊C4—8316no—
648C4⋊C4—8316no—
649C4⋊C4—8316no—
650C4⋊C4C23×D8318yes—
651C4⋊C4C23×D83116yes—
652C4⋊C4C23×D8318yes—
653C22⋊C4—8316no—
654C22⋊C4—8316no—
655C22⋊C4—8316no—
656C22⋊C4—8316no—
657C22⋊C4—8316no—
658C22⋊C4—838no—
659C22⋊C4—838no—
660C22⋊C4—8316no—
661C22⋊C4C23×D83116yes—
662C22⋊C4C23×D83116yes—
663C22⋊C4C23×D8318yes—
664C42—834no—
665C42—834no—
666C42—838no—
667C42—838no—
668C42—838no—
669C42—8316no—
670C42—8316no—
671C42C23×D8314yes—
672C42C23×D8314yes—
673C23—22no—
674C23—28no—
675C23—28no—
676C23—24no—
677C23—28no—
678C23—834no—
679C23—832no—
680C23—832no—
681C23—1662no—
682C23—1664no—
683C23—1664no—
684C23C24×D8312yes—
685C23C24×D8318yes—
686C23C24×D8311yescharacteristic
687Q8—1668no—
688Q8—16616no—
689D4—216no—
690D4—416no—
691D4—416no—
692D4—33216no—
693D4—1668no—
694D4—1668no—
695D4—1668no—
696D4—16632no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—28no—
700C2×C4—24no—
701C2×C4—28no—
702C2×C4—416no—
703C2×C4—3328no—
704C2×C4—33216no—
705C2×C4—3328no—
706C2×C4—3328no—
707C2×C4—33216no—
708C2×C4—834no—
709C2×C4—832no—
710C2×C4—8316no—
711C2×C4—834no—
712C2×C4—834no—
713C2×C4—832no—
714C2×C4—838no—
715C2×C4—838no—
716C2×C4—16632no—
717C2×C4—1668no—
718C2×C4—1662no—
719C2×C4—1664no—
720C2×C4—1664no—
721C2×C4—1668no—
722C2×C4—1668no—
723C2×C4#41×D8314yes—
724C2×C4C24×D8314yes—
725C2×C4C24×D8312yes—
726C2×C4C24×D8314yes—
727C2×C4C24×D8318yes—
728C2×C4C24×D8312yes—
729C22—22no—
730C22—28no—
731C22—28no—
732C22—24no—
733C22—28no—
734C22—44no—
735C22—416no—
736C22—3324no—
737C22—834no—
738C22—1662no—
739C22—1664no—
740C22—1668no—
741C22—1664no—
742C22C2×#41×D8312yes—
743C22#1912853614yes—
744C22C25×D8311yescharacteristic
745C4—22no—
746C4—24no—
747C4—28no—
748C4—24no—
749C4—834no—
750C4—1668no—
751C4—1662no—
752C4—1664no—
753C4—1664no—
754C4—1668no—
755C4C2×#41×D8314yes—
756C2—42no—
757C2—48no—
758C2—3322no—
759C2—1664no—
760C2#2492138214yesdirect product factor
761C2C22×#41×D8311yescharacteristic
762C2C2×#1912853612yes—
subgroupG/H
centerC23C24×D83
commutator, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC2×#540×C83C2
socleC23×C83C25
hypercenterC2×#540D83
hypocenterC83C2×#3512
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. #24921382C2direct (N × H)
2. C2×#19128398C2semidirect
3. C2×#19128396C2semidirect
4. C2×#19128394C2semidirect
5. C2×#19128388C2semidirect
6. C2×#19128314C2semidirect
7. C2×#19128313C2semidirect
8. C2×#19128305C2semidirect
9. C2×#19128280C2semidirect
10. C2×#19128249C2semidirect
11. C2×#19128233C2semidirect
12. C2×#19128232C2semidirect
13. C2×#125×D83C2semidirect
14. C2×#19128180C2semidirect
15. C2×#19128169C2semidirect
16. C2×#540×C83C2semidirect
19. #19128398C22semidirect
20. #19128396C22semidirect
21. #19128394C22semidirect
22. #19128388C22semidirect
23. #19128314C22semidirect
24. #19128313C22semidirect
25. #19128305C22semidirect
26. #19128280C22semidirect
27. #19128249C22semidirect
29. #19128233C22semidirect
30. #19128232C22semidirect
40. #125×D83C22semidirect
54. #19128180C22semidirect
55. #19128169C22semidirect
79. #540×C83C22semidirect
377. C2×C83#3512semidirect
390. C2×#540D83semidirect
398. C83C2×#3512semidirect
408. #540C2×D83semidirect
760. C2#24921382direct (N × H)

Maximal subgroups

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

subgroupindex
#249213822
C2×#191283982
C2×#191283962
C2×#191283942
C2×#191283882
C2×#191283142
C2×#191283132
C2×#191283052
C2×#191282802
C2×#191282492
C2×#191282332
C2×#191282322
C2×#125×D832
C2×#191281802
C2×#191281692
C2×#540×C832
C2×#351283