Finite Group Databasebeta

← C2×#24921857 #36312194

Subgroups — C2×#24921857 #36312194

Order 21248.

7810 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24921857C2132yesmaximal, direct product factor
2C2×#19128448C214yesmaximal, complemented
3C2×#19128410C212yesmaximal, complemented
4C2×#19128407C212yesmaximal, complemented
5C2×#19128372C212yesmaximal, complemented
6C2×#19128371C212yesmaximal, complemented
7C2×#19128349C214yesmaximal, complemented
8C2×#19128306C211yesmaximal, characteristic, complemented
9C2×#19128304C212yesmaximal, complemented
10C2×#19128280C214yesmaximal, complemented
11C2×#19128278C214yesmaximal, complemented
12C2×#19128254C211yesmaximal, characteristic, complemented
13C2×#19128246C212yesmaximal, complemented
14C2×#540×C83C211yesmaximal, characteristic, complemented
15C22×#13050590C2214yes—
16C22×#13050589C2214yes—
17C22×#13050589C2214yes—
18#19128448C22164yescomplemented
19#19128410C22132yescomplemented
20#19128407C22132yescomplemented
21#19128372C22132yescomplemented
22#19128371C22132yescomplemented
23#19128349C22164yescomplemented
24#19128306C22116yescomplemented
25#19128304C22132yescomplemented
26#19128280C22164yescomplemented
27#19128278C22164yescomplemented
28#19128254C22116yescomplemented
29#19128246C22132yescomplemented
30C2×#14581791C2212yes—
31C2×#14581791C2212yes—
32C2×#14581789C2211yescharacteristic
33C2×#14581788C2212yes—
34C2×#14581788C2212yes—
35C2×#14581784C2211yescharacteristic
36C2×#14581783C2212yes—
37C2×#14581783C2212yes—
38C2×#14581778C2214yes—
39C2×#14581777C2214yes—
40C2×#14581776C2214yes—
41C2×#14581774C2214yes—
42C2×#14581772C2214yes—
43C2×#14581771C2214yes—
44C2×#14581770C2214yes—
45C2×#14581770C2214yes—
46C2×#14581769C2214yes—
47C2×#14581769C2214yes—
48C2×#14581769C2212yes—
49C2×#14581769C2212yes—
50C2×#14581766C2214yes—
51C2×#14581766C2212yes—
52C2×#14581765C2214yes—
53C2×#14581765C2214yes—
54C2×#14581765C2214yes—
55C2×#14581764C2214yes—
56C2×#14581764C2214yes—
57C2×#14581764C2214yes—
58C2×#14581764C2214yes—
59C2×#14581763C2214yes—
60C2×#14581763C2214yes—
61C2×C4×Dic166C2212yes—
62C2×C4×Dic166C2212yes—
63C2×C4×D332C2212yes—
64C2×D4×Dic83C2212yes—
65C2×D4×Dic83C2212yes—
66C2×#14581754C2212yes—
67C2×#14581754C2212yes—
68C2×(C22⋊D83)⋊C4C2214yes—
69C2×#14581751C2211yescharacteristic
70C22×Dic83⋊C4C2214yes—
71C2×C4⋊C4×D83C2214yes—
72C22×C4×Dic83C2211yescharacteristic
73#540×C83C22116yescomplemented
74C2×#127×C83C2211yescharacteristic
75C2×#125×C83C2211yescharacteristic
76C2×#123×C83C2214yes—
77C2×#121×C83C2212yes—
78C2×#121×C83C2214yes—
79C2×C4×D4×C83C2212yes—
80C2×#117×C83C2211yescharacteristic
81C2×#13050590—416no—
82C2×#13050590C23132yes—
83C2×#13050589—416no—
84C2×#13050589—416no—
85C2×#13050589C23132yes—
86C2×#13050589C23132yes—
87C22×Dic166C2312yes—
88C22×Dic166C2312yes—
89C22×Dic166C2314yes—
90C22×D332C2312yes—
91C22×D332C2314yes—
92C22×C22⋊D83C2314yes—
93C22×C22⋊D83C2314yes—
94C22×C22⋊D83C2314yes—
95C22×C22⋊D83C2314yes—
96C22×C22⋊D83C2314yes—
97C23×Dic83C2312yes—
98C23×Dic83C2314yes—
99C23×Dic83C2314yes—
100C22×C4×D83C2314yes—
101C22×C4×D83C2314yes—
102C22×C4×D83C2314yes—
103#14581791C23116yes—
104#14581791C23116yes—
105#14581789C2318yes—
106#14581788C23116yes—
107#14581788C23116yes—
108#14581784C2318yes—
109#14581783C23116yes—
110#14581783C23116yes—
111#14581778C23132yes—
112#14581777C23132yes—
113#14581776C23132yes—
114#14581774C23132yes—
115#14581772C23132yes—
116#14581771C23132yes—
117#14581770C23132yes—
118#14581770C23132yes—
119#14581769C23132yes—
120#14581769C23132yes—
121#14581769C23116yes—
122#14581769C23116yes—
123#14581766C23132yes—
124#14581766C23116yes—
125#14581765C23132yes—
126#14581765C23132yes—
127#14581765C23132yes—
128#14581764C23132yes—
129#14581764C23132yes—
130#14581764C23132yes—
131#14581764C23132yes—
132#14581763C23132yes—
133#14581763C23132yes—
134C4×Dic166C23116yes—
135C4×Dic166C23116yes—
136C4×D332C23116yes—
137D4×Dic83C23116yes—
138D4×Dic83C23116yes—
139#14581754C23116yes—
140#14581754C23116yes—
141(C22⋊D83)⋊C4C23132yes—
142#14581751C2318yes—
143C2×C4⋊Dic83C2314yes—
144C2×C4⋊Dic83C2312yes—
145C2×C4⋊Dic83C2312yes—
146C2×C4⋊Dic83C2312yes—
147C2×C4⋊Dic83C2312yes—
148C2×Dic83⋊C4C23132yes—
149C2×Dic83⋊C4C2312yes—
150C2×Dic83⋊C4C2314yes—
151C2×Dic83⋊C4C2312yes—
152C2×Dic83⋊C4C2314yes—
153C2×Dic83⋊C4C2314yes—
154C2×Dic83⋊C4C2312yes—
155C2×Dic83⋊C4C2312yes—
156C4⋊C4×D83C23132yes—
157C2×C22⋊Dic83C2311yescharacteristic
158C2×C22⋊Dic83C2311yescharacteristic
159C2×C22⋊Dic83C2314yes—
160C2×C22⋊Dic83C2314yes—
161C2×(C2×D83)⋊C4C2314yes—
162C2×(C2×D83)⋊C4C2314yes—
163C2×(C2×D83)⋊C4C2314yes—
164C2×(C2×D83)⋊C4C2314yes—
165C2×C4×Dic83C2311yescharacteristic
166C2×C4×Dic83C2312yes—
167C2×C4×Dic83C2311yescharacteristic
168C2×C4×Dic83C2318yes—
169C2×C4×Dic83C2312yes—
170C22×D4×C83C2312yes—
171C22×D4×C83C2314yes—
172C22×D4×C83C2314yes—
173C23×C4×C83C2311yescharacteristic
174C23×C4×C83C2314yes—
175#127×C83C2318yes—
176#125×C83C2318yes—
177#123×C83C23132yes—
178#121×C83C23116yes—
179#121×C83C23132yes—
180C4×D4×C83C23116yes—
181#117×C83C2318yes—
182C2×C4⋊C4×C83C2312yes—
183C2×C4⋊C4×C83C2312yes—
184C2×C4⋊C4×C83C2314yes—
185C2×C22⋊C4×C83C2312yes—
186C2×C22⋊C4×C83C2314yes—
187C2×C22⋊C4×C83C2314yes—
188C2×C42×C83C2311yescharacteristic
189C2×C42×C83C2311yescharacteristic
190C23×D83C2414yes—
191#13050590—464no—
192#13050589—464no—
193#13050589—464no—
194C2×Dic166—28no—
195C2×Dic166—28no—
196C2×Dic166—48no—
197C2×Dic166C2418yes—
198C2×Dic166C2418yes—
199C2×Dic166C24116yes—
200C2×D332—28no—
201C2×D332—48no—
202C2×D332C2418yes—
203C2×D332C24116yes—
204C2×C22⋊D83—216no—
205C2×C22⋊D83—48no—
206C2×C22⋊D83—48no—
207C2×C22⋊D83—48no—
208C2×C22⋊D83—48no—
209C2×C22⋊D83C24116yes—
210C2×C22⋊D83C24116yes—
211C2×C22⋊D83C24116yes—
212C2×C22⋊D83C24116yes—
213C2×C22⋊D83C24116yes—
214C22×Dic83—216no—
215C22×Dic83—28no—
216C22×Dic83—48no—
217C22×Dic83C2418yes—
218C22×Dic83C24116yes—
219C22×Dic83C2412yes—
220C22×Dic83C2414yes—
221C22×Dic83C2412yes—
222C22×Dic83C2412yes—
223C22×Dic83C24116yes—
224C22×Dic83C2412yes—
225C2×C4×D83—216no—
226C2×C4×D83—48no—
227C2×C4×D83—48no—
228C2×C4×D83C24116yes—
229C2×C4×D83C24116yes—
230C2×C4×D83C24116yes—
231C4⋊Dic83C2418yes—
232C4⋊Dic83C24116yes—
233C4⋊Dic83C2418yes—
234C4⋊Dic83C2418yes—
235C4⋊Dic83C2418yes—
236Dic83⋊C4C2418yes—
237Dic83⋊C4C2418yes—
238Dic83⋊C4C24116yes—
239Dic83⋊C4C24116yes—
240Dic83⋊C4C2418yes—
241Dic83⋊C4C2418yes—
242Dic83⋊C4C24116yes—
243C22⋊Dic83C2414yes—
244C22⋊Dic83C24116yes—
245C22⋊Dic83C24116yes—
246C22⋊Dic83C2414yes—
247(C2×D83)⋊C4C24116yes—
248(C2×D83)⋊C4C24116yes—
249(C2×D83)⋊C4C24116yes—
250(C2×D83)⋊C4C24116yes—
251C4×Dic83C2414yes—
252C4×Dic83C2418yes—
253C4×Dic83C2418yes—
254C4×Dic83C2414yes—
255C24×C83C2414yes—
256C24×C83C2411yescharacteristic
257C2×D4×C83—28no—
258C2×D4×C83—48no—
259C2×D4×C83—48no—
260C2×D4×C83C2418yes—
261C2×D4×C83C24116yes—
262C2×D4×C83C24116yes—
263C22×C4×C83—24no—
264C22×C4×C83—48no—
265C22×C4×C83C2414yes—
266C22×C4×C83C2412yes—
267C22×C4×C83C2414yes—
268C22×C4×C83C2412yes—
269C22×C4×C83C2411yescharacteristic
270C22×C4×C83C24116yes—
271C22×C4×C83C2411yescharacteristic
272C4⋊C4×C83C24116yes—
273C4⋊C4×C83C2418yes—
274C4⋊C4×C83C2418yes—
275C22⋊C4×C83C2418yes—
276C22⋊C4×C83C24116yes—
277C22⋊C4×C83C24116yes—
278C42×C83C2414yes—
279C42×C83C2414yes—
280C23×C83—28no—
281C23×C83—28no—
282C23×C83—24no—
283C23×C83—22no—
284C23×C83—28no—
285C23×C83C2512yes—
286C23×C83C2518yes—
287C23×C83C2511yescharacteristic
288C22×D83—28no—
289C22×D83—28no—
290C22×D83—28no—
291C22×D83C2518yes—
292D4×C83—216no—
293D4×C83—416no—
294D4×C83—416no—
295C2×C4×C83—24no—
296C2×C4×C83—28no—
297C2×C4×C83—24no—
298C2×C4×C83—22no—
299C2×C4×C83—28no—
300C2×C4×C83—416no—
301C2×C4×C832−1+414yes—
302C2×C4×C83C2514yes—
303C2×C4×C83C2514yes—
304C2×C4×C83C2512yes—
305C2×C4×C83C2518yes—
306C2×C4×C83C2512yes—
307C22⋊D83—232no—
308C22⋊D83—416no—
309C22⋊D83—416no—
310C22⋊D83—416no—
311C22⋊D83—416no—
312C2×Dic83—24no—
313C2×Dic83—28no—
314C2×Dic83—24no—
315C2×Dic83—24no—
316C2×Dic83—216no—
317C2×Dic83—232no—
318C2×Dic83—416no—
319C2×Dic83H(5,𝔽2)18yes—
320C2×Dic83C2514yes—
321C2×Dic83C2514yes—
322C2×Dic83C2514yes—
323C2×Dic83C2518yes—
324C2×Dic83C2514yes—
325D332—216no—
326D332—416no—
327C4×D83—232no—
328C4×D83—416no—
329C4×D83—416no—
330Dic166—216no—
331Dic166—216no—
332Dic166—416no—
333C22×C83—24no—
334C22×C83—28no—
335C22×C83—28no—
336C22×C83—22no—
337C22×C83—28no—
338C22×C83—416no—
339C22×C83—44no—
340C22×C83C2×H(5,𝔽2)14yes—
341C22×C83C2×2−1+412yes—
342C22×C83C2611yescharacteristic
343C2×D83—28no—
344C2×D83—28no—
345C2×D83—28no—
346C2×D83—416no—
347C4×C83—24no—
348C4×C83—24no—
349C4×C83—28no—
350C4×C83—22no—
351C4×C83C2×2−1+414yes—
352Dic83—24no—
353Dic83—24no—
354Dic83—24no—
355Dic83—28no—
356Dic83C2×H(5,𝔽2)18yes—
357C2×#3548—831nomaximal, Sylow
358C2×C83—42no—
359C2×C83—48no—
360C2×C83#354814yescomplemented
361C2×C83C22×H(5,𝔽2)12yes—
362C2×C83C22×2−1+411yescharacteristic
363D83—48no—
364#3548—8332no—
365C2×#562—834no—
366C2×#554—832no—
367C2×#554—832no—
368C2×#550—832no—
369C2×#550—832no—
370C2×#547—834no—
371C2×#540—832no—
372C2×#540—831no—
373C2×#540D8311yescharacteristic, complemented
374C2×#537—834no—
375C2×#537—834no—
376C2×#533—831no—
377C2×#532—832no—
378C83C2×#354811yescharacteristic, complemented, Sylow
379C22×#41—834no—
380C22×#41—834no—
381C22×#41—834no—
382#562—8364no—
383#554—8332no—
384#554—8332no—
385#550—8332no—
386#550—8332no—
387#547—8364no—
388#540—8332no—
389#540—8316no—
390#540C2×D83116yescomplemented
391#537—8364no—
392#537—8364no—
393#533—8316no—
394#532—8332no—
395C2×C4⋊Q8—832no—
396C2×C4⋊Q8—832no—
397C2×#127—832no—
398C2×#127—832no—
399C2×#127—831no—
400C2×#127C2×D8311yescharacteristic
401C2×#125—832no—
402C2×#125—832no—
403C2×#125—831no—
404C2×#125C2×D8311yescharacteristic
405C2×#124—834no—
406C2×#123—834no—
407C2×#123—834no—
408C2×#123—834no—
409C2×#123C2×D8314yes—
410C2×C22⋊Q8—834no—
411C2×C22⋊Q8—834no—
412C2×C22⋊Q8—834no—
413C2×C22⋊Q8—834no—
414C2×C22⋊Q8—832no—
415C2×C22⋊Q8—832no—
416C2×C22⋊Q8—834no—
417C2×C22⋊Q8—834no—
418C2×#121—834no—
419C2×#121—834no—
420C2×#121—834no—
421C2×#121—834no—
422C2×#121—834no—
423C2×#121—834no—
424C2×#121—832no—
425C2×#121—834no—
426C2×#121—834no—
427C2×#121—834no—
428C2×#121—834no—
429C2×#121C2×D8312yes—
430C2×#121C2×D8314yes—
431C2×C4×Q8—832no—
432C2×C4×Q8—832no—
433C2×C4×D4—832no—
434C2×C4×D4—832no—
435C2×C4×D4—832no—
436C2×C4×D4—832no—
437C2×C4×D4—834no—
438C2×C4×D4—832no—
439C2×C4×D4C2×D8312yes—
440C2×#117—831no—
441C2×#117C2×D8311yescharacteristic
442C22×C4⋊C4—834no—
443C22×C4⋊C4—834no—
444C22×C42—831no—
445C2×#41—33216no—
446C2×#41—33216no—
447C2×#41—33216no—
448C2×#41—8332no—
449C2×#41—8332no—
450C2×#41—8332no—
451C22×Q8—834no—
452C22×Q8—832no—
453C22×Q8—832no—
454C22×D4—834no—
455C22×D4—834no—
456C22×D4—834no—
457C22×D4—834no—
458C22×D4—834no—
459C22×D4—834no—
460C22×D4—832no—
461C22×D4C22×D8312yes—
462C22×D4C22×D8314yes—
463C22×D4C22×D8314yes—
464C23×C4—834no—
465C23×C4—834no—
466C23×C4—834no—
467C23×C4—834no—
468C23×C4—832no—
469C23×C4—834no—
470C23×C4C22×D8311yescharacteristic
471C23×C4C22×D8314yes—
472C4⋊Q8—8316no—
473C4⋊Q8—8316no—
474#127—8316no—
475#127—8316no—
476#127—838no—
477#127C22×D8318yes—
478#125—8316no—
479#125—8316no—
480#125—838no—
481#125C22×D8318yes—
482#124—8332no—
483#123—8332no—
484#123—8332no—
485#123—8332no—
486#123C22×D83132yes—
487C22⋊Q8—8332no—
488C22⋊Q8—8332no—
489C22⋊Q8—8332no—
490C22⋊Q8—8332no—
491C22⋊Q8—8316no—
492C22⋊Q8—8316no—
493C22⋊Q8—8332no—
494C22⋊Q8—8332no—
495#121—8332no—
496#121—8332no—
497#121—8332no—
498#121—8332no—
499#121—8332no—
500#121—8332no—
501#121—8316no—
502#121—8332no—
503#121—8332no—
504#121—8332no—
505#121—8332no—
506#121C22×D83116yes—
507#121C22×D83132yes—
508C4×Q8—8316no—
509C4×Q8—8316no—
510C4×D4—8316no—
511C4×D4—8316no—
512C4×D4—8316no—
513C4×D4—8316no—
514C4×D4—8332no—
515C4×D4—8316no—
516C4×D4C22×D83116yes—
517#117—838no—
518#117C22×D8318yes—
519C2×C4⋊C4—834no—
520C2×C4⋊C4—832no—
521C2×C4⋊C4—832no—
522C2×C4⋊C4—834no—
523C2×C4⋊C4—834no—
524C2×C4⋊C4—834no—
525C2×C4⋊C4—8332no—
526C2×C4⋊C4—832no—
527C2×C4⋊C4—832no—
528C2×C4⋊C4—832no—
529C2×C4⋊C4—832no—
530C2×C4⋊C4—832no—
531C2×C4⋊C4—832no—
532C2×C4⋊C4—8332no—
533C2×C4⋊C4C22×D8314yes—
534C2×C4⋊C4C22×D8312yes—
535C2×C4⋊C4C22×D8312yes—
536C2×C22⋊C4—831no—
537C2×C22⋊C4—831no—
538C2×C22⋊C4—834no—
539C2×C22⋊C4—834no—
540C2×C22⋊C4—834no—
541C2×C22⋊C4—834no—
542C2×C22⋊C4—834no—
543C2×C22⋊C4—834no—
544C2×C22⋊C4C22×D8312yes—
545C2×C22⋊C4C22×D8314yes—
546C2×C22⋊C4C22×D8314yes—
547C2×C42—832no—
548C2×C42—831no—
549C2×C42—832no—
550C2×C42—831no—
551C2×C42—838no—
552C2×C42C22×D8311yescharacteristic
553C2×C42C22×D8311yescharacteristic
554C24—834no—
555C24C23×D8314yes—
556C24C23×D8311yescharacteristic
557#41—33264no—
558#41—33264no—
559#41—33264no—
560C2×Q8—3328no—
561C2×Q8—8316no—
562C2×Q8—838no—
563C2×Q8—838no—
564C2×Q8—1668no—
565C2×Q8—1668no—
566C2×D4—28no—
567C2×D4—48no—
568C2×D4—48no—
569C2×D4—3328no—
570C2×D4—3328no—
571C2×D4—3328no—
572C2×D4—3328no—
573C2×D4—3328no—
574C2×D4—8316no—
575C2×D4—8316no—
576C2×D4—8316no—
577C2×D4—8316no—
578C2×D4—8316no—
579C2×D4—8316no—
580C2×D4—838no—
581C2×D4—16616no—
582C2×D4—1668no—
583C2×D4C23×D8318yes—
584C2×D4C23×D83116yes—
585C2×D4C23×D83116yes—
586C22×C4—24no—
587C22×C4—48no—
588C22×C4—3328no—
589C22×C4—3328no—
590C22×C4—3328no—
591C22×C4—8316no—
592C22×C4—8316no—
593C22×C4—8316no—
594C22×C4—832no—
595C22×C4—838no—
596C22×C4—8316no—
597C22×C4—832no—
598C22×C4—832no—
599C22×C4—832no—
600C22×C4—834no—
601C22×C4—8316no—
602C22×C4—16616no—
603C22×C4—16616no—
604C22×C4—1668no—
605C22×C4C23×D8314yes—
606C22×C4C23×D8311yescharacteristic
607C22×C4C23×D8312yes—
608C22×C4C23×D8312yes—
609C22×C4C23×D8314yes—
610C22×C4C23×D83116yes—
611C22×C4C23×D8311yescharacteristic
612C4⋊C4—8316no—
613C4⋊C4—838no—
614C4⋊C4—838no—
615C4⋊C4—8316no—
616C4⋊C4—8316no—
617C4⋊C4—8316no—
618C4⋊C4—838no—
619C4⋊C4—838no—
620C4⋊C4—838no—
621C4⋊C4—838no—
622C4⋊C4—838no—
623C4⋊C4—838no—
624C4⋊C4C23×D83116yes—
625C4⋊C4C23×D8318yes—
626C4⋊C4C23×D8318yes—
627C22⋊C4—834no—
628C22⋊C4—834no—
629C22⋊C4—8316no—
630C22⋊C4—8316no—
631C22⋊C4—8316no—
632C22⋊C4—8316no—
633C22⋊C4—8316no—
634C22⋊C4—8316no—
635C22⋊C4C23×D8318yes—
636C22⋊C4C23×D83116yes—
637C22⋊C4C23×D83116yes—
638C42—834no—
639C42—838no—
640C42—834no—
641C42—838no—
642C42C23×D8314yes—
643C42C23×D8314yes—
644C23—28no—
645C23—28no—
646C23—24no—
647C23—22no—
648C23—28no—
649C23—838no—
650C23—1668no—
651C23—1668no—
652C23—1668no—
653C23C24×D8318yes—
654C23C24×D8312yes—
655C23C24×D8311yescharacteristic
656Q8—33216no—
657Q8—16616no—
658Q8—16616no—
659D4—216no—
660D4—416no—
661D4—416no—
662D4—33216no—
663D4—33216no—
664D4—33216no—
665D4—33216no—
666D4—33216no—
667D4—16632no—
668D4—16616no—
669C2×C4—24no—
670C2×C4—28no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—28no—
674C2×C4—416no—
675C2×C4—33216no—
676C2×C4—33216no—
677C2×C4—33216no—
678C2×C4—838no—
679C2×C4—834no—
680C2×C4—834no—
681C2×C4—834no—
682C2×C4—834no—
683C2×C4—838no—
684C2×C4—16632no—
685C2×C4—16632no—
686C2×C4—16616no—
687C2×C4—1668no—
688C2×C4—1664no—
689C2×C4—1664no—
690C2×C4—1664no—
691C2×C4#1458183914yes—
692C2×C4C24×D8312yes—
693C2×C4C24×D8314yes—
694C2×C4C24×D8314yes—
695C2×C4C24×D8318yes—
696C2×C4C24×D8312yes—
697C22—28no—
698C22—28no—
699C22—24no—
700C22—22no—
701C22—28no—
702C22—416no—
703C22—44no—
704C22—33216no—
705C22—1668no—
706C22—1668no—
707C22—1668no—
708C22H(5,𝔽2)×D8314yes—
709C22C2×#1458183912yes—
710C22C25×D8311yescharacteristic
711C4—24no—
712C4—28no—
713C4—24no—
714C4—22no—
715C4—838no—
716C4—1668no—
717C4—1664no—
718C4—1664no—
719C4—1664no—
720C4C2×#1458183914yes—
721C2—48no—
722C2—42no—
723C2—3328no—
724C2#2492185714yesdirect product factor
725C2C2×H(5,𝔽2)×D8312yes—
726C2C22×#1458183911yescharacteristic
subgroupG/H
centerC23C24×D83
commutator, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC2×#540×C83C2
socleC23×C83C25
hypercenterC2×#540D83
hypocenterC83C2×#3548
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. #24921857C2direct (N × H)
2. C2×#19128448C2semidirect
3. C2×#19128410C2semidirect
4. C2×#19128407C2semidirect
5. C2×#19128372C2semidirect
6. C2×#19128371C2semidirect
7. C2×#19128349C2semidirect
8. C2×#19128306C2semidirect
9. C2×#19128304C2semidirect
10. C2×#19128280C2semidirect
11. C2×#19128278C2semidirect
12. C2×#19128254C2semidirect
13. C2×#19128246C2semidirect
14. C2×#540×C83C2semidirect
18. #19128448C22semidirect
19. #19128410C22semidirect
20. #19128407C22semidirect
21. #19128372C22semidirect
22. #19128371C22semidirect
23. #19128349C22semidirect
24. #19128306C22semidirect
25. #19128304C22semidirect
26. #19128280C22semidirect
27. #19128278C22semidirect
28. #19128254C22semidirect
29. #19128246C22semidirect
73. #540×C83C22semidirect
360. C2×C83#3548semidirect
373. C2×#540D83semidirect
378. C83C2×#3548semidirect
390. #540C2×D83semidirect
724. C2#24921857direct (N × H)

Maximal subgroups

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

subgroupindex
#249218572
C2×#191284482
C2×#191284102
C2×#191284072
C2×#191283722
C2×#191283712
C2×#191283492
C2×#191283062
C2×#191283042
C2×#191282802
C2×#191282782
C2×#191282542
C2×#191282462
C2×#540×C832
C2×#354883