Finite Group Databasebeta

← C2×#19148410 #26004927

Subgroups — C2×#19148410 #26004927

Order 11008.

7478 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148410C2132yesmaximal, direct product factor
2C2×#14583629C212yesmaximal, complemented
3C2×#14583626C212yesmaximal, complemented
4C2×#14583605C212yesmaximal, complemented
5C2×#14583603C214yesmaximal, complemented
6C2×#14583564C212yesmaximal, complemented
7C2×#14583562C214yesmaximal, complemented
8C2×#14583529C212yesmaximal, complemented
9C2×#14583527C211yesmaximal, characteristic, complemented
10C2×#14583526C212yesmaximal, complemented
11C2×#14583455C212yesmaximal, complemented
12C2×#14583452C211yesmaximal, characteristic, complemented
13C22×#13063324C211yesmaximal, characteristic, complemented
14C2×C4⋊Q8×D43C212yesmaximal, complemented
15C2×#14583380C211yesmaximal, characteristic
16C2×#14583379C211yesmaximal, characteristic
17C2×#14583367C211yesmaximal, characteristic
18C2×C43×#544C211yesmaximal, characteristic, complemented
19C22×#10621898C2211yescharacteristic
20C23×Dic86C2212yes—
21C22×Q8×D43C2214yes—
22#14583629C22132yescomplemented
23#14583626C22132yescomplemented
24#14583605C22132yescomplemented
25#14583603C22164yescomplemented
26#14583564C22132yescomplemented
27#14583562C22164yescomplemented
28#14583529C22132yescomplemented
29#14583527C22116yescomplemented
30#14583526C22132yescomplemented
31#14583455C22132yescomplemented
32#14583452C22116yescomplemented
33C2×#13063325C2212yes—
34C2×#13063324C2214yes—
35C2×#13063324C2214yes—
36C2×#13063324C2212yes—
37C2×#13063324C2212yes—
38C2×#13063324C2211yescharacteristic
39C2×#13063324C2212yes—
40C2×#13063324C2212yes—
41C2×#13063324C2212yes—
42C2×#13063324C2211yescharacteristic
43C2×#13063324C22116yescomplemented
44C2×#13063323C2214yes—
45C2×#13063323C2214yes—
46C4⋊Q8×D43C22132yescomplemented
47C2×#13063317C2212yes—
48C2×#13063316C2212yes—
49C2×#13063316C2211yescharacteristic
50C2×#13063316C2211yescharacteristic
51C2×#13063315C2214yes—
52C2×#13063315C2214yes—
53C2×#13063305C2214yes—
54C2×#13063303C2214yes—
55C2×#13063303C2214yes—
56C2×#13063303C2214yes—
57C2×#13063303C2214yes—
58C2×#13063302C2212yes—
59C2×#13063302C2214yes—
60C2×#13063302C2212yes—
61C2×#13063301C2214yes—
62#14583380C22116yes—
63#14583379C22116yes—
64#14583367C22116yes—
65C2×C4×Dic86C2212yes—
66C2×C4×Dic86C2212yes—
67C2×C4×Dic86C2212yes—
68C2×#13063290C2212yes—
69C2×#13063290C2214yes—
70C2×#13063290C2214yes—
71C2×#13063290C2211yescharacteristic
72C2×#13063290C2211yescharacteristic
73C2×C4×D172C2212yes—
74C2×#13063287C2212yes—
75C2×#13063287C2211yescharacteristic
76C2×#13063287C2211yescharacteristic
77C2×C4×C22⋊D43C2214yes—
78C2×(C22⋊D43)⋊C4C2214yes—
79C2×(C22⋊D43)⋊C4C2212yes—
80C2×(C22⋊D43)⋊C4C2212yes—
81C2×#13063284C2211yescharacteristic
82C2×#13063283C2212yes—
83C2×#13063283C2212yes—
84C2×#13063282C2212yes—
85C22×C4⋊Dic43C2211yescharacteristic
86C22×Dic43⋊C4C2212yes—
87C2×C4⋊C4×D43C2212yes—
88C2×C4⋊C4×D43C2212yes—
89C2×C4⋊C4×D43C2214yes—
90C22×C4×Dic43C2211yescharacteristic
91C2×C42×D43C2212yes—
92C43×#544C22116yescomplemented
93C2×C4⋊Q8×C43C2212yes—
94C2×C4⋊Q8×C43C2212yes—
95C2×#125×C43C2212yes—
96C2×#125×C43C2212yes—
97C2×C22⋊Q8×C43C2214yes—
98C2×#117×C43C2211yescharacteristic
99C2×#117×C43C2211yescharacteristic
100C22×C4⋊C4×C43C2211yescharacteristic
101C2×#10621898Q8116yescomplemented
102C2×#10621898C2318yes—
103C22×Dic86—48no—
104C22×Dic86C2312yes—
105C22×Dic86C2314yes—
106C22×Dic86C2312yes—
107C22×Dic86C23116yes—
108C22×Dic86C2314yes—
109C22×Dic86C2314yes—
110C22×Dic86C2311yescharacteristic
111C2×Q8×D43—416no—
112C2×Q8×D43C23132yes—
113C22×D172C2311yescharacteristic
114C22×C22⋊D43C2312yes—
115C23×Dic43C2311yescharacteristic
116C23×Dic43C2311yescharacteristic
117C23×Dic43C2312yes—
118C22×C4×D43C2312yes—
119C22×C4×D43C2312yes—
120C22×C4×D43C2314yes—
121C22×C4×D43C2314yes—
122C22×C4×D43C2312yes—
123#13063325C23116yes—
124#13063324C23132yes—
125#13063324C23132yes—
126#13063324C23116yes—
127#13063324C23116yes—
128#13063324C23116yes—
129#13063324C2318yes—
130#13063324C23116yes—
131#13063324C23116yes—
132#13063324C2318yes—
133#13063323C23132yes—
134#13063323C23132yes—
135#13063317C23116yes—
136#13063316C23116yes—
137#13063316C2318yes—
138#13063316C2318yes—
139#13063315C23132yes—
140#13063315C23132yes—
141#13063305C23132yes—
142#13063303C23132yes—
143#13063303C23132yes—
144#13063303C23132yes—
145#13063303C23132yes—
146#13063302C23116yes—
147#13063302C23132yes—
148#13063302C23116yes—
149#13063301C23132yes—
150C4×Dic86C23116yes—
151C4×Dic86C23116yes—
152C4×Dic86C23116yes—
153#13063290C23132yes—
154#13063290C23132yes—
155#13063290C2318yes—
156#13063290C2318yes—
157#13063290C23116yes—
158C4×D172C23116yes—
159#13063287C2318yes—
160#13063287C23116yes—
161#13063287C2318yes—
162C4×C22⋊D43C23132yes—
163(C22⋊D43)⋊C4C23116yes—
164(C22⋊D43)⋊C4C23132yes—
165(C22⋊D43)⋊C4C23116yes—
166#13063284C2318yes—
167#13063283C23116yes—
168#13063283C23116yes—
169#13063282C23116yes—
170C2×C4⋊Dic43C2311yescharacteristic
171C2×C4⋊Dic43C2312yes—
172C2×C4⋊Dic43C2314yes—
173C2×C4⋊Dic43C2312yes—
174C2×C4⋊Dic43C2318yes—
175C2×C4⋊Dic43C2311yescharacteristic
176C2×C4⋊Dic43C2312yes—
177C2×C4⋊Dic43C2312yes—
178C2×Dic43⋊C4C23116yes—
179C2×Dic43⋊C4C2312yes—
180C2×Dic43⋊C4C2314yes—
181C2×Dic43⋊C4C2314yes—
182C2×Dic43⋊C4C2314yes—
183C2×Dic43⋊C4C2314yes—
184C2×Dic43⋊C4C2312yes—
185C2×Dic43⋊C4C2312yes—
186C2×Dic43⋊C4C2312yes—
187C2×Dic43⋊C4C2314yes—
188C2×Dic43⋊C4C2314yes—
189C2×Dic43⋊C4C2312yes—
190C2×Dic43⋊C4C2312yes—
191C4⋊C4×D43C23132yes—
192C4⋊C4×D43C23116yes—
193C4⋊C4×D43C23116yes—
194C2×C22⋊Dic43C2312yes—
195C2×(C2×D43)⋊C4C2312yes—
196C2×(C2×D43)⋊C4C2312yes—
197C2×(C2×D43)⋊C4C2314yes—
198C2×(C2×D43)⋊C4C2314yes—
199C2×C4×Dic43C2311yescharacteristic
200C2×C4×Dic43C2312yes—
201C2×C4×Dic43C2312yes—
202C2×C4×Dic43C2311yescharacteristic
203C2×C4×Dic43C2311yescharacteristic
204C2×C4×Dic43C2311yescharacteristic
205C2×C4×Dic43C2318yes—
206C2×C4×Dic43C2314yes—
207C2×C4×Dic43C2314yes—
208C2×C4×Dic43C2312yes—
209C42×D43C23116yes—
210C22×Q8×C43C2314yes—
211C23×C4×C43C2312yes—
212C23×C4×C43C2311yescharacteristic
213C4⋊Q8×C43C23116yes—
214C4⋊Q8×C43C23116yes—
215#125×C43C23116yes—
216#125×C43C23116yes—
217C22⋊Q8×C43C23132yes—
218#117×C43C2318yes—
219#117×C43C2318yes—
220C2×C4⋊C4×C43C2312yes—
221C2×C4⋊C4×C43C2312yes—
222C2×C4⋊C4×C43C2318yes—
223C2×C4⋊C4×C43C2311yescharacteristic
224C2×C4⋊C4×C43C2311yescharacteristic
225C2×C4⋊C4×C43C2311yescharacteristic
226C2×C4⋊C4×C43C2311yescharacteristic
227C2×C4⋊C4×C43C2314yes—
228C2×C4⋊C4×C43C2314yes—
229C2×C4⋊C4×C43C2314yes—
230C2×C22⋊C4×C43C2312yes—
231C2×C22⋊C4×C43C2312yes—
232C2×C42×C43C2312yes—
233C2×C42×C43C2312yes—
234C24×C43C2411yescharacteristic
235C23×D43C2412yes—
236C2×Q8×C43—48no—
237C2×Q8×C43C24116yes—
238C22×C4×C43—44no—
239C22×C4×C43C2×Q818yescomplemented
240C22×C4×C43C2412yes—
241C22×C4×C43C2412yes—
242C22×C4×C43C2412yes—
243C22×C4×C43C2412yes—
244C22×C4×C43C2414yes—
245C22×C4×C43C2418yes—
246C22×C4×C43C2411yescharacteristic
247C22×C4×C43C2411yescharacteristic
248C22×C4×C43C2414yes—
249C2×C22⋊D43C2×Q8116yescomplemented
250C2×C22⋊D43C2418yes—
251C22×Dic43—24no—
252C22×Dic43—24no—
253C22×Dic43—44no—
254C22×Dic43C2412yes—
255C22×Dic43C2411yescharacteristic
256C22×Dic43C2411yescharacteristic
257C22×Dic43C2414yes—
258C22×Dic43C2414yes—
259C22×Dic43C2414yes—
260C22×Dic43C2412yes—
261C22×Dic43C2418yes—
262C22×Dic43C2412yes—
263C22×Dic43C2411yescharacteristic
264C22×Dic43C2411yescharacteristic
265Q8×D43—464no—
266#10621898C2×Q8164yescomplemented
267C2×D172C2×Q818yescomplemented
268C2×D172C2414yes—
269C2×C4×D43—28no—
270C2×C4×D43—28no—
271C2×C4×D43—48no—
272C2×C4×D43—48no—
273C2×C4×D43C2×Q8116yescomplemented
274C2×C4×D43C2418yes—
275C2×C4×D43C2418yes—
276C2×C4×D43C24116yes—
277C2×C4×D43C24116yes—
278C2×C4×D43C2418yes—
279C2×Dic86—28no—
280C2×Dic86—216no—
281C2×Dic86—28no—
282C2×Dic86—432no—
283C2×Dic86—48no—
284C2×Dic86—48no—
285C2×Dic86C2×Q818yescomplemented
286C2×Dic86C2418yes—
287C2×Dic86C24116yes—
288C2×Dic86C2418yes—
289C2×Dic86C24116yes—
290C2×Dic86C24116yes—
291C2×Dic86C2414yes—
292C4⋊C4×C43C2418yes—
293C4⋊C4×C43C2418yes—
294C4⋊C4×C43C2414yes—
295C4⋊C4×C43C2414yes—
296C4⋊C4×C43C2414yes—
297C4⋊C4×C43C2414yes—
298C4⋊C4×C43C24116yes—
299C4⋊C4×C43C24116yes—
300C4⋊C4×C43C24116yes—
301C22⋊C4×C43C2418yes—
302C22⋊C4×C43C2418yes—
303C42×C43C2418yes—
304C42×C43C2418yes—
305C22⋊Dic43C2418yes—
306(C2×D43)⋊C4C2418yes—
307(C2×D43)⋊C4C2418yes—
308(C2×D43)⋊C4C24116yes—
309(C2×D43)⋊C4C24116yes—
310C4⋊Dic43C2414yes—
311C4⋊Dic43C2418yes—
312C4⋊Dic43C24116yes—
313C4⋊Dic43C2418yes—
314C4⋊Dic43C2414yes—
315C4⋊Dic43C2418yes—
316C4⋊Dic43C2418yes—
317Dic43⋊C4C2418yes—
318Dic43⋊C4C24116yes—
319Dic43⋊C4C24116yes—
320Dic43⋊C4C24116yes—
321Dic43⋊C4C24116yes—
322Dic43⋊C4C2418yes—
323Dic43⋊C4C2418yes—
324Dic43⋊C4C2418yes—
325Dic43⋊C4C24116yes—
326Dic43⋊C4C24116yes—
327Dic43⋊C4C2418yes—
328Dic43⋊C4C2418yes—
329C4×Dic43C2414yes—
330C4×Dic43C2418yes—
331C4×Dic43C2418yes—
332C4×Dic43C2414yes—
333C4×Dic43C2414yes—
334C4×Dic43C2414yes—
335C4×Dic43C24116yes—
336C4×Dic43C24116yes—
337C4×Dic43C2418yes—
338C23×C43—22no—
339C23×C43—22no—
340C23×C43C22×Q814yes—
341C23×C43C2512yes—
342C23×C43C2511yescharacteristic
343C22×D43—24no—
344C22×D43—24no—
345C22×D43C22×Q818yes—
346C22×D43C2514yes—
347Q8×C43—416no—
348C2×C4×C43—28no—
349C2×C4×C43—24no—
350C2×C4×C43—24no—
351C2×C4×C43—24no—
352C2×C4×C43—24no—
353C2×C4×C43—48no—
354C2×C4×C43C22×Q814yes—
355C2×C4×C43C22×Q814yes—
356C2×C4×C43C22×Q8116yescomplemented
357C2×C4×C43C2514yes—
358C2×C4×C43C2514yes—
359C2×C4×C43C2514yes—
360C2×C4×C43C2518yes—
361C2×C4×C43C2514yes—
362C2×C4×C43C2512yes—
363C2×C4×C43C2512yes—
364C22⋊D43C22×Q8132yescomplemented
365C2×Dic43—24no—
366C2×Dic43—28no—
367C2×Dic43—22no—
368C2×Dic43—24no—
369C2×Dic43—22no—
370C2×Dic43—28no—
371C2×Dic43—28no—
372C2×Dic43—48no—
373C2×Dic43C22×Q818yes—
374C2×Dic43H(5,𝔽2)14yes—
375C2×Dic432−1+414yes—
376C2×Dic43C2514yes—
377C2×Dic43C2512yes—
378C2×Dic43C2512yes—
379C2×Dic43C2518yes—
380C2×Dic43C2514yes—
381C2×Dic43C2514yes—
382C2×Dic43C2512yes—
383C2×Dic43C2512yes—
384D172C22×Q8116yescomplemented
385C4×D43—216no—
386C4×D43—216no—
387C4×D43—416no—
388C4×D43—416no—
389C4×D43C22×Q8132yescomplemented
390Dic86—232no—
391Dic86—216no—
392Dic86—216no—
393Dic86—416no—
394Dic86—416no—
395Dic86C22×Q8116yescomplemented
396C2×#3503—431nomaximal, Sylow
397C22×C43—22no—
398C22×C43—22no—
399C22×C43—28no—
400C22×C43C23×Q814yes—
401C22×C43C23×Q812yes—
402C22×C43C2×H(5,𝔽2)12yes—
403C22×C43C2×2−1+412yes—
404C22×C43C2611yescharacteristic
405C2×D43—24no—
406C2×D43—24no—
407C2×D43—216no—
408C2×D43C23×Q818yes—
409C4×C43—28no—
410C4×C43—24no—
411C4×C43—24no—
412C4×C43—24no—
413C4×C43—24no—
414C4×C43C23×Q814yes—
415C4×C43C23×Q814yes—
416Dic43—24no—
417Dic43—28no—
418Dic43—22no—
419Dic43—24no—
420Dic43—22no—
421Dic43C23×Q818yes—
422Dic43C2×H(5,𝔽2)14yes—
423Dic43C2×2−1+414yes—
424#3503—4332no—
425C2×Q82—432no—
426C2×#557—432no—
427C2×#554—432no—
428C2×#554—434no—
429C2×D4×Q8—432no—
430C2×D4×Q8—434no—
431C2×#544—432no—
432C2×#544—432no—
433C2×#544—431no—
434C2×#544D4311yescharacteristic, complemented
435C2×#533—432no—
436C2×#533—431no—
437C22×C4⋊Q8—432no—
438C22×C4⋊Q8—431no—
439C2×#520—431no—
440C2×#520—431no—
441C2×C4×#41—431no—
442C2×C43—24no—
443C2×C43#350314yescomplemented
444C2×C43C24×Q811yescharacteristic
445C2×C43C22×H(5,𝔽2)11yescharacteristic
446C2×C43C22×2−1+411yescharacteristic
447D43—28no—
448C22×#41—431no—
449C23×Q8—434no—
450C23×Q8—432no—
451Q82—4332no—
452#557—4332no—
453#554—4332no—
454#554—4364no—
455D4×Q8—4332no—
456D4×Q8—4364no—
457#544—4332no—
458#544—4332no—
459#544—4316no—
460#544C2×D43116yescomplemented
461#533—4332no—
462#533—4316no—
463C2×C4⋊Q8—434no—
464C2×C4⋊Q8—434no—
465C2×C4⋊Q8—4332no—
466C2×C4⋊Q8—431no—
467C2×C4⋊Q8—432no—
468C2×C4⋊Q8—432no—
469C2×C4⋊Q8—434no—
470C2×C4⋊Q8—432no—
471C2×C4⋊Q8—432no—
472C2×C4⋊Q8—4316no—
473C2×C4⋊Q8—431no—
474C2×C4⋊Q8—434no—
475C2×C4⋊Q8—432no—
476C2×C4⋊Q8—432no—
477C2×C4⋊Q8C2×D4312yes—
478C2×C4⋊Q8C2×D4312yes—
479C2×#125—431no—
480C2×#125—431no—
481C2×#125—434no—
482C2×#125—434no—
483C2×#125—432no—
484C2×#125—432no—
485C2×#125C2×D4312yes—
486C2×#125C2×D4312yes—
487C2×C22⋊Q8—434no—
488C2×C22⋊Q8—434no—
489C2×C22⋊Q8—434no—
490C2×C22⋊Q8—434no—
491C2×C22⋊Q8—434no—
492C2×C22⋊Q8—434no—
493C2×C22⋊Q8—432no—
494C2×C22⋊Q8—432no—
495C2×C22⋊Q8—434no—
496C2×C22⋊Q8C2×D4314yes—
497#520—4316no—
498#520—4316no—
499C4×#41—4316no—
500C2×C4×Q8—431no—
501C2×C4×Q8—431no—
502C2×C4×Q8—432no—
503C2×C4×Q8—434no—
504C2×C4×Q8—434no—
505C2×C4×Q8—432no—
506C2×C4×Q8—432no—
507C2×C4×Q8—432no—
508C2×C4×D4—434no—
509C2×C4×D4—431no—
510C2×C4×D4—431no—
511C2×C4×D4—432no—
512C2×C4×D4—432no—
513C2×C4×D4—432no—
514C2×C4×D4—434no—
515C2×C4×D4—432no—
516C2×#117—431no—
517C2×#117—432no—
518C2×#117—432no—
519C2×#117—432no—
520C2×#117C2×D4311yescharacteristic
521C2×#117C2×D4311yescharacteristic
522C22×C4⋊C4—432no—
523C22×C4⋊C4—431no—
524C22×C4⋊C4—432no—
525C22×C4⋊C4—432no—
526C22×C4⋊C4—434no—
527C22×C4⋊C4C2×D4311yescharacteristic
528C22×C42—431no—
529C22×C42—432no—
530C43C2×#350311yescharacteristic, complemented, Sylow
531C2×#41—4316no—
532C2×#41—438no—
533C22×Q8—4332no—
534C22×Q8—431no—
535C22×Q8—432no—
536C22×Q8—434no—
537C22×Q8—432no—
538C22×Q8—434no—
539C22×Q8—434no—
540C22×Q8—4316no—
541C22×Q8—1728no—
542C22×Q8—17216no—
543C22×Q8C22×D4314yes—
544C22×D4—432no—
545C22×D4—431no—
546C23×C4—432no—
547C23×C4—431no—
548C23×C4—431no—
549C23×C4—432no—
550C23×C4—432no—
551C23×C4—432no—
552C23×C4—434no—
553C23×C4—434no—
554C23×C4C22×D4312yes—
555C23×C4C22×D4311yescharacteristic
556C4⋊Q8—4332no—
557C4⋊Q8—4332no—
558C4⋊Q8—438no—
559C4⋊Q8—4316no—
560C4⋊Q8—4316no—
561C4⋊Q8—4332no—
562C4⋊Q8—4316no—
563C4⋊Q8—4316no—
564C4⋊Q8—438no—
565C4⋊Q8—4332no—
566C4⋊Q8—4316no—
567C4⋊Q8—4316no—
568C4⋊Q8C22×D43116yes—
569C4⋊Q8C22×D43116yes—
570#125—438no—
571#125—438no—
572#125—4332no—
573#125—4332no—
574#125—4316no—
575#125—4316no—
576#125C22×D43116yes—
577#125C22×D43116yes—
578C22⋊Q8—4332no—
579C22⋊Q8—4332no—
580C22⋊Q8—4332no—
581C22⋊Q8—4332no—
582C22⋊Q8—4332no—
583C22⋊Q8—4332no—
584C22⋊Q8—4316no—
585C22⋊Q8—4316no—
586C22⋊Q8—4332no—
587C22⋊Q8C22×D43132yes—
588C4×Q8—438no—
589C4×Q8—438no—
590C4×Q8—4316no—
591C4×Q8—4332no—
592C4×Q8—4332no—
593C4×Q8—4316no—
594C4×Q8—4316no—
595C4×Q8—4316no—
596C4×D4—4332no—
597C4×D4—438no—
598C4×D4—438no—
599C4×D4—4316no—
600C4×D4—4316no—
601C4×D4—4316no—
602C4×D4—4332no—
603C4×D4—4316no—
604#117—438no—
605#117—4316no—
606#117—4316no—
607#117—4316no—
608#117C22×D4318yes—
609#117C22×D4318yes—
610C2×C4⋊C4—432no—
611C2×C4⋊C4—431no—
612C2×C4⋊C4—434no—
613C2×C4⋊C4—432no—
614C2×C4⋊C4—434no—
615C2×C4⋊C4—434no—
616C2×C4⋊C4—432no—
617C2×C4⋊C4—438no—
618C2×C4⋊C4—434no—
619C2×C4⋊C4—434no—
620C2×C4⋊C4—4316no—
621C2×C4⋊C4—431no—
622C2×C4⋊C4—432no—
623C2×C4⋊C4—432no—
624C2×C4⋊C4—432no—
625C2×C4⋊C4—434no—
626C2×C4⋊C4—432no—
627C2×C4⋊C4—432no—
628C2×C4⋊C4—432no—
629C2×C4⋊C4—434no—
630C2×C4⋊C4—432no—
631C2×C4⋊C4—4316no—
632C2×C4⋊C4—4316no—
633C2×C4⋊C4—4332no—
634C2×C4⋊C4C22×D4311yescharacteristic
635C2×C4⋊C4C22×D4312yes—
636C2×C4⋊C4C22×D4314yes—
637C2×C4⋊C4C22×D4312yes—
638C2×C4⋊C4C22×D4318yes—
639C2×C4⋊C4C22×D4311yescharacteristic
640C2×C4⋊C4C22×D4311yescharacteristic
641C2×C4⋊C4C22×D4311yescharacteristic
642C2×C4⋊C4C22×D4314yes—
643C2×C4⋊C4C22×D4314yes—
644C2×C22⋊C4—432no—
645C2×C22⋊C4—434no—
646C2×C22⋊C4—432no—
647C2×C22⋊C4—432no—
648C2×C22⋊C4—434no—
649C2×C22⋊C4C22×D4312yes—
650C2×C22⋊C4C22×D4312yes—
651C2×C42—431no—
652C2×C42—434no—
653C2×C42—434no—
654C2×C42—432no—
655C2×C42—432no—
656C2×C42—432no—
657C2×C42—431no—
658C2×C42—431no—
659C2×C42—438no—
660C2×C42—431no—
661C2×C42—4316no—
662C2×C42C22×D4312yes—
663C2×C42C22×D4312yes—
664C24—432no—
665C24C23×D4311yescharacteristic
666#41—4364no—
667C2×Q8—48no—
668C2×Q8—438no—
669C2×Q8—434no—
670C2×Q8—438no—
671C2×Q8—4316no—
672C2×Q8—438no—
673C2×Q8—4316no—
674C2×Q8—4316no—
675C2×Q8—8616no—
676C2×Q8—868no—
677C2×Q8—868no—
678C2×Q8—1728no—
679C2×Q8—1728no—
680C2×Q8—17232no—
681C2×Q8—17264no—
682C2×Q8C23×D43116yes—
683C2×D4—4316no—
684C2×D4—438no—
685C2×D4—438no—
686C2×D4—434no—
687C22×C4—44no—
688C22×C4—432no—
689C22×C4—431no—
690C22×C4—431no—
691C22×C4—4316no—
692C22×C4—438no—
693C22×C4—434no—
694C22×C4—434no—
695C22×C4—432no—
696C22×C4—431no—
697C22×C4—431no—
698C22×C4—432no—
699C22×C4—434no—
700C22×C4—438no—
701C22×C4—438no—
702C22×C4—438no—
703C22×C4—4316no—
704C22×C4—4316no—
705C22×C4—868no—
706C22×C4—868no—
707C22×C4—864no—
708C22×C4—864no—
709C22×C4—1728no—
710C22×C4—1728no—
711C22×C4—1724no—
712C22×C4Q8×D4318yescomplemented
713C22×C4C23×D4312yes—
714C22×C4C23×D4312yes—
715C22×C4C23×D4312yes—
716C22×C4C23×D4314yes—
717C22×C4C23×D4312yes—
718C22×C4C23×D4318yes—
719C22×C4C23×D4311yescharacteristic
720C22×C4C23×D4311yescharacteristic
721C22×C4C23×D4314yes—
722C4⋊C4—438no—
723C4⋊C4—434no—
724C4⋊C4—4316no—
725C4⋊C4—438no—
726C4⋊C4—4316no—
727C4⋊C4—4316no—
728C4⋊C4—438no—
729C4⋊C4—4316no—
730C4⋊C4—4316no—
731C4⋊C4—434no—
732C4⋊C4—438no—
733C4⋊C4—438no—
734C4⋊C4—438no—
735C4⋊C4—4316no—
736C4⋊C4—438no—
737C4⋊C4—438no—
738C4⋊C4—438no—
739C4⋊C4—4316no—
740C4⋊C4—438no—
741C4⋊C4C23×D4314yes—
742C4⋊C4C23×D4318yes—
743C4⋊C4C23×D43116yes—
744C4⋊C4C23×D4318yes—
745C4⋊C4C23×D4314yes—
746C4⋊C4C23×D4314yes—
747C4⋊C4C23×D4314yes—
748C4⋊C4C23×D43116yes—
749C4⋊C4C23×D43116yes—
750C22⋊C4—438no—
751C22⋊C4—4316no—
752C22⋊C4—438no—
753C22⋊C4—438no—
754C22⋊C4—4316no—
755C22⋊C4C23×D4318yes—
756C22⋊C4C23×D4318yes—
757C42—434no—
758C42—434no—
759C42—438no—
760C42—438no—
761C42—434no—
762C42—434no—
763C42—4316no—
764C42—4316no—
765C42—438no—
766C42C23×D4318yes—
767C42C23×D4318yes—
768C23—22no—
769C23—22no—
770C23—438no—
771C23—434no—
772C23—864no—
773C23—864no—
774C23C2×Q8×D4314yes—
775C23C24×D4312yes—
776C23C24×D4311yescharacteristic
777Q8—416no—
778Q8—4316no—
779Q8—8632no—
780Q8—8616no—
781Q8—8616no—
782Q8—17216no—
783Q8—17216no—
784D4—4332no—
785D4—4316no—
786C2×C4—28no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—48no—
792C2×C4—438no—
793C2×C4—434no—
794C2×C4—434no—
795C2×C4—434no—
796C2×C4—432no—
797C2×C4—432no—
798C2×C4—4332no—
799C2×C4—434no—
800C2×C4—432no—
801C2×C4—432no—
802C2×C4—434no—
803C2×C4—438no—
804C2×C4—8616no—
805C2×C4—8616no—
806C2×C4—868no—
807C2×C4—868no—
808C2×C4—862no—
809C2×C4—864no—
810C2×C4—868no—
811C2×C4—862no—
812C2×C4—864no—
813C2×C4—17216no—
814C2×C4—17216no—
815C2×C4—1728no—
816C2×C4C2×Q8×D4314yes—
817C2×C4C2×Q8×D4314yes—
818C2×C4C2×Q8×D43116yescomplemented
819C2×C4C24×D4314yes—
820C2×C4C24×D4314yes—
821C2×C4C24×D4314yes—
822C2×C4C24×D4318yes—
823C2×C4C24×D4314yes—
824C2×C4C24×D4312yes—
825C2×C4C24×D4312yes—
826C22—22no—
827C22—22no—
828C22—28no—
829C22—438no—
830C22—864no—
831C22—864no—
832C22—8616no—
833C22C22×Q8×D4314yes—
834C22C22×Q8×D4312yes—
835C22H(5,𝔽2)×D4312yes—
836C222−1+4×D4312yes—
837C22C25×D4311yescharacteristic
838C4—28no—
839C4—24no—
840C4—24no—
841C4—24no—
842C4—24no—
843C4—438no—
844C4—434no—
845C4—434no—
846C4—862no—
847C4—864no—
848C4—868no—
849C4—862no—
850C4—864no—
851C4C22×Q8×D4314yes—
852C4C22×Q8×D4314yes—
853C2—24no—
854C2—868no—
855C2#1914841014yesdirect product factor
856C2C23×Q8×D4311yescharacteristic
857C2C2×H(5,𝔽2)×D4311yescharacteristic
858C2C2×2−1+4×D4311yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#544C2
socleC23×C43C25
prime radicalC22×#10621898C22
hypercenterC2×#544D43
hypocenterC43C2×#3503
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
1. #19148410C2direct (N × H)
2. C2×#14583629C2semidirect
3. C2×#14583626C2semidirect
4. C2×#14583605C2semidirect
5. C2×#14583603C2semidirect
6. C2×#14583564C2semidirect
7. C2×#14583562C2semidirect
8. C2×#14583529C2semidirect
9. C2×#14583527C2semidirect
10. C2×#14583526C2semidirect
11. C2×#14583455C2semidirect
12. C2×#14583452C2semidirect
13. C22×#13063324C2semidirect
14. C2×C4⋊Q8×D43C2semidirect
18. C2×C43×#544C2semidirect
22. #14583629C22semidirect
23. #14583626C22semidirect
24. #14583605C22semidirect
25. #14583603C22semidirect
26. #14583564C22semidirect
27. #14583562C22semidirect
28. #14583529C22semidirect
29. #14583527C22semidirect
30. #14583526C22semidirect
31. #14583455C22semidirect
32. #14583452C22semidirect
43. C2×#13063324C22semidirect
46. C4⋊Q8×D43C22semidirect
92. C43×#544C22semidirect
101. C2×#10621898Q8semidirect
239. C22×C4×C43C2×Q8semidirect
249. C2×C22⋊D43C2×Q8semidirect
266. #10621898C2×Q8semidirect
267. C2×D172C2×Q8semidirect
273. C2×C4×D43C2×Q8semidirect
285. C2×Dic86C2×Q8semidirect
356. C2×C4×C43C22×Q8semidirect
364. C22⋊D43C22×Q8semidirect
384. D172C22×Q8semidirect
389. C4×D43C22×Q8semidirect
395. Dic86C22×Q8semidirect
434. C2×#544D43semidirect
443. C2×C43#3503semidirect
460. #544C2×D43semidirect
530. C43C2×#3503semidirect
712. C22×C4Q8×D43semidirect
818. C2×C4C2×Q8×D43semidirect
855. C2#19148410direct (N × H)

Maximal subgroups

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

subgroupindex
#191484102
C2×#145836292
C2×#145836262
C2×#145836052
C2×#145836032
C2×#145835642
C2×#145835622
C2×#145835292
C2×#145835272
C2×#145835262
C2×#145834552
C2×#145834522
C22×#130633242
C2×C4⋊Q8×D432
C2×#145833802
C2×#145833792
C2×#145833672
C2×C43×#5442
C2×#350343