Finite Group Databasebeta

← C2×#19147986 #26003452

Subgroups — C2×#19147986 #26003452

Order 11008.

7302 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147986C2132yesmaximal, direct product factor
2C2×#14583522C212yesmaximal, complemented
3C2×#14583521C212yesmaximal, complemented
4C2×#14583510C211yesmaximal, characteristic, complemented
5C2×#14583505C211yesmaximal, characteristic, complemented
6C2×#14583504C211yesmaximal, characteristic, complemented
7C2×#14583497C214yesmaximal, complemented
8C2×#14583488C214yesmaximal, complemented
9C2×#14583455C211yesmaximal, characteristic, complemented
10C2×#14583450C211yesmaximal, characteristic, complemented
11C2×#14583434C214yesmaximal, complemented
12C2×#14583432C214yesmaximal, complemented
13C2×#14583412C212yesmaximal, complemented
14C2×C4×#10621902C212yesmaximal, complemented
15C2×#117×D43C211yesmaximal, characteristic, complemented
16C2×C43×#541C211yesmaximal, characteristic, complemented
17C22×#10621902C2212yes—
18C23×C4×D43C2211yescharacteristic
19#14583522C22132yescomplemented
20#14583521C22132yescomplemented
21#14583510C22116yescomplemented
22#14583505C22116yescomplemented
23#14583504C22116yescomplemented
24#14583497C22164yescomplemented
25#14583488C22164yescomplemented
26#14583455C22116yescomplemented
27#14583450C22116yescomplemented
28C2×#13063324C2212yescomplemented
29C2×#13063322C2211yescharacteristic, complemented
30#14583434C22164yescomplemented
31#14583432C22164yescomplemented
32C2×#13063320C2214yes—
33C2×#13063320C2214yescomplemented
34C2×#13063319C2214yescomplemented
35C2×#13063317C2211yescharacteristic, complemented
36C2×#13063315C2214yescomplemented
37C2×#13063314C2212yescomplemented
38C2×#13063313C2214yes—
39C2×#13063311C2214yes—
40#14583412C22132yescomplemented
41C2×#13063310C2214yes—
42C2×#13063310C2214yes—
43C2×#13063310C2214yescomplemented
44C2×#13063310C2214yescomplemented
45C2×#13063307C2214yes—
46C2×#13063305C2214yescomplemented
47C2×#13063303C2214yes—
48C2×#13063303C2214yescomplemented
49C2×#13063301C2212yes—
50C2×#13063300C2212yes—
51C2×#13063300C2214yes—
52C2×#13063300C2214yes—
53C2×#13063299C2212yes—
54C2×#13063298C2214yes—
55C2×#13063295C2214yes—
56C4×#10621902C22132yescomplemented
57C2×Q8×Dic43C2212yescomplemented
58C2×#13063290C2214yescomplemented
59C2×C4×D172C2214yes—
60C2×C4×D172C2212yescomplemented
61C2×#13063287C2214yes—
62C2×#13063287C2214yes—
63C2×#13063287C2212yescomplemented
64C2×#13063287C2214yescomplemented
65C2×(C22⋊D43)⋊C4C2214yes—
66C2×#13063284C2211yescharacteristic
67C2×#13063283C2212yes—
68C2×#13063283C2212yes—
69C2×#13063283C2214yescomplemented
70C2×#13063282C2211yescharacteristic
71C2×#13063282C2211yescharacteristic
72C2×#13063281C2212yes—
73#117×D43C22116yescomplemented
74C2×C4⋊C4×D43C2212yes—
75C2×C22⋊C4×D43C2212yes—
76C2×C42×D43C2211yescharacteristic
77C2×C42×D43C2211yescharacteristic
78C2×C42×D43C2214yescomplemented
79C43×#541C22116yescomplemented
80C2×C4⋊Q8×C43C2211yescharacteristic, complemented
81C2×#126×C43C2214yes—
82C2×#125×C43C2214yescomplemented
83C2×#125×C43C2211yescharacteristic, complemented
84C2×C22⋊Q8×C43C2212yes—
85C2×C4×Q8×C43C2212yescomplemented
86C2×#117×C43C2211yescharacteristic
87C24×D43C2311yescharacteristic
88C2×#10621902—216no—
89C2×#10621902C23116yes—
90C22×Dic86C2314yes—
91C22×D172C2314yes—
92C22×D172C2312yes—
93C22×D172C2314yes—
94C22×D172C2314yes—
95C22×C22⋊D43C2314yes—
96C23×Dic43C2311yescharacteristic
97C22×C4×D43—28no—
98C22×C4×D43C2314yes—
99C22×C4×D43C2311yescharacteristic
100C22×C4×D43C2318yes—
101C22×C4×D43C2311yescharacteristic
102C22×C4×D43C2311yescharacteristic
103C22×C4×D43C2312yes—
104C22×C4×D43C2312yes—
105C22×C4×D43C2314yes—
106C22×C4×D43C2314yes—
107C22×C4×D43C2311yescharacteristic
108#13063324C23116yescomplemented
109#13063322C2318yescomplemented
110#13063320C23132yes—
111#13063320C23132yescomplemented
112#13063319C23132yescomplemented
113#13063317C2318yescomplemented
114#13063315C23132yescomplemented
115#13063314C23116yescomplemented
116#13063313C23132yes—
117#13063311C23132yes—
118#13063310C23132yes—
119#13063310C23132yes—
120#13063310C23132yescomplemented
121#13063310C23132yescomplemented
122#13063307C23132yes—
123#13063305C23132yescomplemented
124#13063303C23132yes—
125#13063303C23132yescomplemented
126#13063301C23116yes—
127#13063300C23116yes—
128#13063300C23132yes—
129#13063300C23132yes—
130#13063299C23116yes—
131#13063298C23132yes—
132#13063295C23132yes—
133Q8×Dic43C23116yescomplemented
134#13063290C23132yescomplemented
135C4×D172C23132yes—
136C4×D172C23116yescomplemented
137#13063287C23132yes—
138#13063287C23132yes—
139#13063287C23116yescomplemented
140#13063287C23132yescomplemented
141(C22⋊D43)⋊C4C23132yes—
142#13063284C2318yes—
143#13063283C23116yes—
144#13063283C23116yes—
145#13063283C23132yescomplemented
146#13063282C2318yes—
147#13063282C2318yes—
148#13063281C23116yes—
149C2×C4⋊Dic43C2312yes—
150C2×C4⋊Dic43C2312yes—
151C2×C4⋊Dic43C2314yes—
152C2×Dic43⋊C4C2312yes—
153C2×Dic43⋊C4C2312yes—
154C2×Dic43⋊C4C2314yes—
155C2×Dic43⋊C4C2314yes—
156C2×Dic43⋊C4C2314yes—
157C4⋊C4×D43C23116yes—
158C2×C22⋊Dic43C2312yes—
159C2×(C2×D43)⋊C4C2312yes—
160C2×(C2×D43)⋊C4C2312yes—
161C2×(C2×D43)⋊C4C2314yes—
162C2×(C2×D43)⋊C4C2314yes—
163C2×(C2×D43)⋊C4C2314yes—
164C2×(C2×D43)⋊C4C2314yes—
165C2×(C2×D43)⋊C4C2314yes—
166C2×(C2×D43)⋊C4C2314yes—
167C2×(C2×D43)⋊C4C2314yes—
168C2×(C2×D43)⋊C4C2314yes—
169C22⋊C4×D43C23116yes—
170C2×C4×Dic43C2312yes—
171C2×C4×Dic43C2312yes—
172C2×C4×Dic43C2311yescharacteristic
173C2×C4×Dic43C2311yescharacteristic
174C2×C4×Dic43C2314yes—
175C2×C4×Dic43C2314yes—
176C42×D43C2318yes—
177C42×D43C2318yes—
178C42×D43C23132yescomplemented
179C22×Q8×C43C2312yes—
180C23×C4×C43C2311yescharacteristic
181C4⋊Q8×C43C2318yescomplemented
182#126×C43C23132yes—
183#125×C43C23132yescomplemented
184#125×C43C2318yescomplemented
185C22⋊Q8×C43C23116yes—
186C4×Q8×C43C23116yescomplemented
187#117×C43C2318yes—
188C2×C4⋊C4×C43C2312yes—
189C2×C4⋊C4×C43C2312yes—
190C2×C4⋊C4×C43C2314yes—
191C2×C4⋊C4×C43C2314yes—
192C2×C4⋊C4×C43C2314yes—
193C2×C4⋊C4×C43C2314yes—
194C2×C22⋊C4×C43C2312yes—
195C2×C22⋊C4×C43C2314yes—
196C2×C42×C43C2311yescharacteristic
197C2×C42×C43C2311yescharacteristic
198C2×C42×C43C2314yes—
199C24×C43C2411yescharacteristic
200C23×D43—24no—
201C23×D43—44no—
202C23×D43C2411yescharacteristic
203C23×D43C2414yes—
204C23×D43C2411yescharacteristic
205C23×D43C2414yes—
206C2×Q8×C43—28no—
207C2×Q8×C43C2418yes—
208C22×C4×C43—24no—
209C22×C4×C43C2412yes—
210C22×C4×C43C2414yes—
211C22×C4×C43C2412yes—
212C22×C4×C43C2414yes—
213C22×C4×C43C2411yescharacteristic
214C22×C4×C43C2414yes—
215C22×C4×C43C2411yescharacteristic
216C2×C22⋊D43—48no—
217C2×C22⋊D43C24116yes—
218C22×Dic43—24no—
219C22×Dic43C2412yes—
220C22×Dic43C2412yes—
221C22×Dic43C2414yes—
222C22×Dic43C2411yescharacteristic
223C22×Dic43C2414yes—
224C22×Dic43C2411yescharacteristic
225#10621902—264no—
226C2×D172—28no—
227C2×D172—216no—
228C2×D172—48no—
229C2×D172—48no—
230C2×D172C24116yes—
231C2×D172C2418yes—
232C2×D172C24116yes—
233C2×D172C24116yes—
234C2×C4×D43—24no—
235C2×C4×D43—24no—
236C2×C4×D43—216no—
237C2×C4×D43—232no—
238C2×C4×D43—24no—
239C2×C4×D43—44no—
240C2×C4×D43—44no—
241C2×C4×D43—48no—
242C2×C4×D43—48no—
243C2×C4×D43#4118yes—
244C2×C4×D43C24116yes—
245C2×C4×D43C2414yes—
246C2×C4×D43C2414yes—
247C2×C4×D43C2414yes—
248C2×C4×D43C2418yes—
249C2×C4×D43C2418yes—
250C2×C4×D43C24116yes—
251C2×C4×D43C24116yes—
252C2×C4×D43C2414yes—
253C2×Dic86—48no—
254C2×Dic86C24116yes—
255C4⋊C4×C43C2418yes—
256C4⋊C4×C43C2418yes—
257C4⋊C4×C43C24116yes—
258C4⋊C4×C43C24116yes—
259C4⋊C4×C43C24116yes—
260C4⋊C4×C43C24116yes—
261C22⋊C4×C43C2418yes—
262C22⋊C4×C43C24116yes—
263C42×C43C2414yes—
264C42×C43C2414yes—
265C42×C43C24116yes—
266C22⋊Dic43C2418yes—
267(C2×D43)⋊C4C2418yes—
268(C2×D43)⋊C4C2418yes—
269(C2×D43)⋊C4C24116yes—
270(C2×D43)⋊C4C24116yes—
271(C2×D43)⋊C4C24116yes—
272(C2×D43)⋊C4C24116yes—
273(C2×D43)⋊C4C24116yes—
274(C2×D43)⋊C4C24116yes—
275(C2×D43)⋊C4C24116yes—
276(C2×D43)⋊C4C24116yes—
277C4⋊Dic43C2418yes—
278C4⋊Dic43C2418yes—
279C4⋊Dic43C24116yes—
280Dic43⋊C4C2418yes—
281Dic43⋊C4C2418yes—
282Dic43⋊C4C24116yes—
283Dic43⋊C4C24116yes—
284Dic43⋊C4C24116yes—
285C4×Dic43C2418yes—
286C4×Dic43C2418yes—
287C4×Dic43C2414yes—
288C4×Dic43C2414yes—
289C4×Dic43C24116yes—
290C4×Dic43C24116yes—
291C23×C43—22no—
292C23×C43—24no—
293C23×C43C2512yes—
294C23×C43C2511yescharacteristic
295C22×D43—24no—
296C22×D43—22no—
297C22×D43—28no—
298C22×D43—28no—
299C22×D43—28no—
300C22×D43—24no—
301C22×D43—28no—
302C22×D43—48no—
303C22×D43—416no—
304C22×D43C2×#4114yes—
305C22×D43C2512yes—
306C22×D43C2518yes—
307C22×D43C2512yes—
308Q8×C43—216no—
309C2×C4×C43—22no—
310C2×C4×C43—28no—
311C2×C4×C43—28no—
312C2×C4×C43—24no—
313C2×C4×C43—24no—
314C2×C4×C43—28no—
315C2×C4×C43C2×#4114yes—
316C2×C4×C43C2514yes—
317C2×C4×C43C2518yes—
318C2×C4×C43C2514yes—
319C2×C4×C43C2518yes—
320C2×C4×C43C2512yes—
321C2×C4×C43C2512yes—
322C22⋊D43—416no—
323C2×Dic43—22no—
324C2×Dic43—24no—
325C2×Dic43—28no—
326C2×Dic43—24no—
327C2×Dic43—28no—
328C2×Dic43C2×#4114yes—
329C2×Dic43C2514yes—
330C2×Dic43C2518yes—
331C2×Dic43C2514yes—
332C2×Dic43C2512yes—
333C2×Dic43C2512yes—
334D172—232no—
335D172—216no—
336D172—416no—
337D172—416no—
338C4×D43—28no—
339C4×D43—28no—
340C4×D43—28no—
341C4×D43—232no—
342C4×D43—48no—
343C4×D43—416no—
344C4×D43—416no—
345C4×D43—48no—
346C4×D43C2×#41116yes—
347Dic86—416no—
348C2×#3455—431nomaximal, Sylow
349C22×C43—22no—
350C22×C43—24no—
351C22×C43—44no—
352C22×C43C22×#4112yes—
353C22×C43#58514yes—
354C22×C43C2611yescharacteristic
355C2×D43—24no—
356C2×D43—28no—
357C2×D43—22no—
358C2×D43—28no—
359C2×D43—24no—
360C2×D43—28no—
361C2×D43—28no—
362C2×D43—416no—
363C2×D43—416no—
364C2×D43—44no—
365C2×D43C22×#4114yes—
366C4×C43—22no—
367C4×C43—28no—
368C4×C43—28no—
369C4×C43—24no—
370C4×C43—24no—
371C4×C43C22×#4114yes—
372Dic43—22no—
373Dic43—24no—
374Dic43—28no—
375Dic43—24no—
376Dic43C22×#4114yes—
377#3455—4332no—
378C2×#542—432no—
379C2×#542—432no—
380C2×#541—431no—
381C2×#541D4311yescharacteristic, complemented
382C2×#540—431no—
383C2×#540—431no—
384C2×#539—434no—
385C2×#538—434no—
386C2×#533—431no—
387C2×#532—431no—
388C2×#529—434no—
389C2×#529—434no—
390C2×#525—432no—
391C2×C4×#41—432no—
392C22×#117—431no—
393C2×C43—42no—
394C2×C43#345514yescomplemented
395C2×C43C23×#4111yescharacteristic
396C2×C43C2×#58512yes—
397D43—24no—
398D43—48no—
399D43—42no—
400C22×#41—432no—
401C24×C4—431no—
402#542—4332no—
403#542—4332no—
404#541—4316no—
405#541C2×D43116yescomplemented
406#540—4316no—
407#540—4316no—
408#539—4364no—
409#538—4364no—
410#533—4316no—
411#532—4316no—
412C2×C4⋊Q8—432no—
413C2×C4⋊Q8C2×D4311yescharacteristic, complemented
414C2×#127—431no—
415#529—4364no—
416#529—4364no—
417C2×#126—434no—
418C2×#126—434no—
419C2×#126—434no—
420C2×#126C2×D4314yes—
421C2×#125—434no—
422C2×#125—431no—
423C2×#125C2×D4314yescomplemented
424C2×#125C2×D4311yescharacteristic, complemented
425C2×#124—432no—
426C2×#124—434no—
427C2×#124—434no—
428#525—4332no—
429C2×#123—434no—
430C2×#123—434no—
431C2×#123—434no—
432C2×#123—434no—
433C2×#123—434no—
434C2×C22⋊Q8—432no—
435C2×C22⋊Q8—434no—
436C2×C22⋊Q8—434no—
437C2×C22⋊Q8—434no—
438C2×C22⋊Q8C2×D4312yes—
439C2×#121—432no—
440C2×#121—432no—
441C2×#121—434no—
442C2×#121—434no—
443C2×#121—434no—
444C2×#120—434no—
445C4×#41—4332no—
446C2×C4×Q8—432no—
447C2×C4×Q8—434no—
448C2×C4×Q8C2×D4312yescomplemented
449C2×C4×D4—434no—
450C2×C4×D4—434no—
451C2×C4×D4—432no—
452C2×C4×D4—434no—
453C2×C4×D4—434no—
454C2×C4×D4—434no—
455C2×C4×D4—432no—
456C2×#117—431no—
457C2×#117—4316no—
458C2×#117—432no—
459C2×#117—432no—
460C2×#117—434no—
461C2×#117—432no—
462C2×#117—431no—
463C2×#117—431no—
464C2×#117C2×D4311yescharacteristic
465C22×C4⋊C4—432no—
466C22×C22⋊C4—432no—
467C22×C42—431no—
468C22×C42—431no—
469C22×C42—434no—
470C43C2×#345511yescharacteristic, complemented, Sylow
471C25—431no—
472C2×#41—4316no—
473C2×#41—8616no—
474C22×Q8—434no—
475C22×Q8C22×D4312yes—
476C22×D4—434no—
477C22×D4—434no—
478C22×D4—432no—
479C22×D4—434no—
480C22×D4—434no—
481C23×C4—431no—
482C23×C4—431no—
483C23×C4—431no—
484C23×C4—431no—
485C23×C4—431no—
486C23×C4—438no—
487C23×C4—434no—
488C23×C4—432no—
489C23×C4—432no—
490C23×C4—434no—
491C23×C4—434no—
492C23×C4—868no—
493C23×C4C22×D4311yescharacteristic
494C4⋊Q8—4316no—
495C4⋊Q8C22×D4318yescomplemented
496#127—438no—
497#126—4332no—
498#126—4332no—
499#126—4332no—
500#126C22×D43132yes—
501#125—4332no—
502#125—438no—
503#125C22×D43132yescomplemented
504#125C22×D4318yescomplemented
505#124—4316no—
506#124—4332no—
507#124—4332no—
508#123—4332no—
509#123—4332no—
510#123—4332no—
511#123—4332no—
512#123—4332no—
513C22⋊Q8—4316no—
514C22⋊Q8—4332no—
515C22⋊Q8—4332no—
516C22⋊Q8—4332no—
517C22⋊Q8C22×D43116yes—
518#121—4316no—
519#121—4316no—
520#121—4332no—
521#121—4332no—
522#121—4332no—
523#120—4332no—
524C4×Q8—4316no—
525C4×Q8—4332no—
526C4×Q8C22×D43116yescomplemented
527C4×D4—4332no—
528C4×D4—4316no—
529C4×D4—4332no—
530C4×D4—4332no—
531C4×D4—4332no—
532C4×D4—4332no—
533C4×D4—4316no—
534#117—438no—
535#117—4316no—
536#117—4316no—
537#117—4332no—
538#117—4316no—
539#117—438no—
540#117—438no—
541#117C22×D4318yes—
542C2×C4⋊C4—432no—
543C2×C4⋊C4—432no—
544C2×C4⋊C4—432no—
545C2×C4⋊C4—432no—
546C2×C4⋊C4—434no—
547C2×C4⋊C4—434no—
548C2×C4⋊C4—434no—
549C2×C4⋊C4—434no—
550C2×C4⋊C4—4316no—
551C2×C4⋊C4C22×D4312yes—
552C2×C4⋊C4C22×D4312yes—
553C2×C4⋊C4C22×D4314yes—
554C2×C4⋊C4C22×D4314yes—
555C2×C4⋊C4C22×D4314yes—
556C2×C4⋊C4C22×D4314yes—
557C2×C22⋊C4—432no—
558C2×C22⋊C4—432no—
559C2×C22⋊C4—432no—
560C2×C22⋊C4—434no—
561C2×C22⋊C4—434no—
562C2×C22⋊C4—434no—
563C2×C22⋊C4—434no—
564C2×C22⋊C4—434no—
565C2×C22⋊C4—434no—
566C2×C22⋊C4—434no—
567C2×C22⋊C4—434no—
568C2×C22⋊C4—4316no—
569C2×C22⋊C4C22×D4312yes—
570C2×C22⋊C4C22×D4314yes—
571C2×C42—432no—
572C2×C42—432no—
573C2×C42—434no—
574C2×C42—431no—
575C2×C42—431no—
576C2×C42—434no—
577C2×C42—438no—
578C2×C42—438no—
579C2×C42—4332no—
580C2×C42C22×D4311yescharacteristic
581C2×C42C22×D4311yescharacteristic
582C2×C42C22×D4314yes—
583C24—431no—
584C24—431no—
585C24—434no—
586C24—434no—
587C24—864no—
588C24—1724no—
589C24C23×D4311yescharacteristic
590#41—8664no—
591C2×Q8—28no—
592C2×Q8—4316no—
593C2×Q8—1728no—
594C2×Q8C23×D4318yes—
595C2×D4—4316no—
596C2×D4—4316no—
597C2×D4—438no—
598C2×D4—4316no—
599C2×D4—4316no—
600C2×D4—8616no—
601C2×D4—868no—
602C2×D4—1728no—
603C2×D4—1728no—
604C2×D4—1728no—
605C22×C4—24no—
606C22×C4—431no—
607C22×C4—438no—
608C22×C4—434no—
609C22×C4—434no—
610C22×C4—432no—
611C22×C4—432no—
612C22×C4—434no—
613C22×C4—431no—
614C22×C4—4316no—
615C22×C4—434no—
616C22×C4—434no—
617C22×C4—434no—
618C22×C4—438no—
619C22×C4—438no—
620C22×C4—4316no—
621C22×C4—4316no—
622C22×C4—864no—
623C22×C4—8632no—
624C22×C4—8616no—
625C22×C4—864no—
626C22×C4—864no—
627C22×C4—864no—
628C22×C4—1724no—
629C22×C4—1728no—
630C22×C4—1724no—
631C22×C4—1728no—
632C22×C4C23×D4314yes—
633C22×C4C23×D4312yes—
634C22×C4C23×D4314yes—
635C22×C4C23×D4314yes—
636C22×C4C23×D4312yes—
637C22×C4C23×D4311yescharacteristic
638C22×C4C23×D4311yescharacteristic
639C4⋊C4—438no—
640C4⋊C4—438no—
641C4⋊C4—438no—
642C4⋊C4—438no—
643C4⋊C4—4316no—
644C4⋊C4—4316no—
645C4⋊C4—4316no—
646C4⋊C4—4316no—
647C4⋊C4C23×D4318yes—
648C4⋊C4C23×D4318yes—
649C4⋊C4C23×D43116yes—
650C4⋊C4C23×D43116yes—
651C4⋊C4C23×D43116yes—
652C4⋊C4C23×D43116yes—
653C22⋊C4—438no—
654C22⋊C4—438no—
655C22⋊C4—438no—
656C22⋊C4—4316no—
657C22⋊C4—4316no—
658C22⋊C4—4316no—
659C22⋊C4—4316no—
660C22⋊C4—4316no—
661C22⋊C4—4316no—
662C22⋊C4—4316no—
663C22⋊C4—4316no—
664C22⋊C4C23×D4318yes—
665C22⋊C4C23×D43116yes—
666C42—438no—
667C42—438no—
668C42—4316no—
669C42—434no—
670C42—434no—
671C42—4316no—
672C42C23×D4314yes—
673C42C23×D4314yes—
674C42C23×D43116yes—
675C23—22no—
676C23—24no—
677C23—434no—
678C23—432no—
679C23—432no—
680C23—438no—
681C23—868no—
682C23—864no—
683C23—862no—
684C23—868no—
685C23—868no—
686C23—868no—
687C23—864no—
688C23—1728no—
689C23—17216no—
690C23C24×D4312yes—
691C23C24×D4311yescharacteristic
692Q8—216no—
693Q8—17216no—
694D4—8632no—
695D4—8616no—
696D4—17216no—
697D4—17216no—
698D4—17216no—
699C2×C4—22no—
700C2×C4—28no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—28no—
704C2×C4—28no—
705C2×C4—434no—
706C2×C4—432no—
707C2×C4—4316no—
708C2×C4—434no—
709C2×C4—434no—
710C2×C4—438no—
711C2×C4—432no—
712C2×C4—868no—
713C2×C4—8632no—
714C2×C4—868no—
715C2×C4—868no—
716C2×C4—862no—
717C2×C4—864no—
718C2×C4—868no—
719C2×C4—864no—
720C2×C4—868no—
721C2×C4—1728no—
722C2×C4—17216no—
723C2×C4—1728no—
724C2×C4—17216no—
725C2×C4#41×D4314yes—
726C2×C4C24×D4314yes—
727C2×C4C24×D4318yes—
728C2×C4C24×D4318yes—
729C2×C4C24×D4314yes—
730C2×C4C24×D4312yes—
731C2×C4C24×D4312yes—
732C22—22no—
733C22—24no—
734C22—44no—
735C22—434no—
736C22—864no—
737C22—868no—
738C22—862no—
739C22—868no—
740C22—868no—
741C22—868no—
742C22—864no—
743C22—17216no—
744C22—1724no—
745C22—17216no—
746C22C2×#41×D4312yes—
747C22#1458373614yes—
748C22C25×D4311yescharacteristic
749C4—22no—
750C4—28no—
751C4—24no—
752C4—24no—
753C4—28no—
754C4—434no—
755C4—862no—
756C4—864no—
757C4—868no—
758C4—864no—
759C4C2×#41×D4314yes—
760C2—42no—
761C2—864no—
762C2—1722no—
763C2—1728no—
764C2#1914798614yesdirect product factor
765C2C22×#41×D4311yescharacteristic
766C2C2×#1458373612yes—
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#541C2
socleC23×C43C25
hypercenterC2×#541D43
hypocenterC43C2×#3455
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
1. #19147986C2direct (N × H)
2. C2×#14583522C2semidirect
3. C2×#14583521C2semidirect
4. C2×#14583510C2semidirect
5. C2×#14583505C2semidirect
6. C2×#14583504C2semidirect
7. C2×#14583497C2semidirect
8. C2×#14583488C2semidirect
9. C2×#14583455C2semidirect
10. C2×#14583450C2semidirect
11. C2×#14583434C2semidirect
12. C2×#14583432C2semidirect
13. C2×#14583412C2semidirect
14. C2×C4×#10621902C2semidirect
15. C2×#117×D43C2semidirect
16. C2×C43×#541C2semidirect
19. #14583522C22semidirect
20. #14583521C22semidirect
21. #14583510C22semidirect
22. #14583505C22semidirect
23. #14583504C22semidirect
24. #14583497C22semidirect
25. #14583488C22semidirect
26. #14583455C22semidirect
27. #14583450C22semidirect
28. C2×#13063324C22semidirect
29. C2×#13063322C22semidirect
30. #14583434C22semidirect
31. #14583432C22semidirect
33. C2×#13063320C22semidirect
34. C2×#13063319C22semidirect
35. C2×#13063317C22semidirect
36. C2×#13063315C22semidirect
37. C2×#13063314C22semidirect
40. #14583412C22semidirect
43. C2×#13063310C22semidirect
44. C2×#13063310C22semidirect
46. C2×#13063305C22semidirect
48. C2×#13063303C22semidirect
56. C4×#10621902C22semidirect
57. C2×Q8×Dic43C22semidirect
58. C2×#13063290C22semidirect
60. C2×C4×D172C22semidirect
63. C2×#13063287C22semidirect
64. C2×#13063287C22semidirect
69. C2×#13063283C22semidirect
73. #117×D43C22semidirect
78. C2×C42×D43C22semidirect
79. C43×#541C22semidirect
80. C2×C4⋊Q8×C43C22semidirect
82. C2×#125×C43C22semidirect
83. C2×#125×C43C22semidirect
85. C2×C4×Q8×C43C22semidirect
108. #13063324C23semidirect
109. #13063322C23semidirect
111. #13063320C23semidirect
112. #13063319C23semidirect
113. #13063317C23semidirect
114. #13063315C23semidirect
115. #13063314C23semidirect
120. #13063310C23semidirect
121. #13063310C23semidirect
123. #13063305C23semidirect
125. #13063303C23semidirect
133. Q8×Dic43C23semidirect
134. #13063290C23semidirect
136. C4×D172C23semidirect
139. #13063287C23semidirect
140. #13063287C23semidirect
145. #13063283C23semidirect
178. C42×D43C23semidirect
181. C4⋊Q8×C43C23semidirect
183. #125×C43C23semidirect
184. #125×C43C23semidirect
186. C4×Q8×C43C23semidirect
381. C2×#541D43semidirect
394. C2×C43#3455semidirect
405. #541C2×D43semidirect
413. C2×C4⋊Q8C2×D43semidirect
423. C2×#125C2×D43semidirect
424. C2×#125C2×D43semidirect
448. C2×C4×Q8C2×D43semidirect
470. C43C2×#3455semidirect
495. C4⋊Q8C22×D43semidirect
503. #125C22×D43semidirect
504. #125C22×D43semidirect
526. C4×Q8C22×D43semidirect
764. C2#19147986direct (N × H)

Maximal subgroups

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

subgroupindex
#191479862
C2×#145835222
C2×#145835212
C2×#145835102
C2×#145835052
C2×#145835042
C2×#145834972
C2×#145834882
C2×#145834552
C2×#145834502
C2×#145834342
C2×#145834322
C2×#145834122
C2×C4×#106219022
C2×#117×D432
C2×C43×#5412
C2×#345543