Finite Group Databasebeta

← C2×#13082843 #15660994

Subgroups — C2×#13082843 #15660994

Order 2816.

7962 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082843C2132yesmaximal, direct product factor
2C2×#10623198C214yesmaximal, complemented
3C2×#10623074C212yesmaximal, complemented
4C2×#10623083C212yesmaximal, complemented
5C2×#10623086C212yesmaximal, complemented
6C2×#10623081C212yesmaximal, complemented
7C2×#10623122C214yesmaximal, complemented
8C2×#10623165C212yesmaximal, complemented
9C2×#10623065C212yesmaximal, complemented
10C2×#10623176C212yesmaximal, complemented
11C2×#10623148C212yesmaximal, complemented
12C2×#10623364C212yesmaximal, complemented
13C2×#10623128C212yesmaximal, complemented
14C22×#66977C211yesmaximal, characteristic, complemented
15C22×#66983C211yesmaximal, characteristic, complemented
16C2×C11×#525C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic, complemented
18C24×C4×C11C2211yescharacteristic
19C23×C22⋊D11C2212yes—
20C22×#4341C2214yescomplemented
21C22×#4339C2212yescomplemented
22C23×D44C2211yescharacteristic
23C23×Dic22C2211yescharacteristic, complemented
24C11×#525C22116yescomplemented
25C2×C11×#123C2212yescomplemented
26C2×C11×C22⋊Q8C2211yescharacteristic
27C2×C11×C22⋊Q8C2211yescharacteristic, complemented
28C2×C11×#121C2211yescharacteristic
29C2×C11×#121C2211yescharacteristic, complemented
30C2×C11×#120C2212yes—
31C2×C4×D4×C11C2212yes—
32C2×C4×D4×C11C2212yescomplemented
33C2×C11×#117C2211yescharacteristic, complemented
34C22×C22⋊Dic11C2212yes—
35#10623364C22132yescomplemented
36C2×#66999C2214yescomplemented
37C2×#66992C2214yescomplemented
38C2×#66992C2214yescomplemented
39C2×#66992C2214yescomplemented
40C2×#66991C2214yescomplemented
41C2×#66990C2214yes—
42C2×D4×Dic11C2214yes—
43C2×#66983C2212yes—
44C2×#66983C2212yes—
45C2×#66983C2212yes—
46C2×#66983C2212yes—
47C2×#66983C22116yescomplemented
48C2×#66983C2212yescomplemented
49C22×(C2×D11)⋊C4C2212yes—
50C22×C4⋊Dic11C2211yescharacteristic
51C22×C4⋊Dic11C2212yescomplemented
52C22×C4⋊Dic11C2211yescharacteristic, complemented
53C2×#66977C2212yes—
54C2×#66977C2212yes—
55C2×#66977C2212yescomplemented
56C2×#66977C2212yescomplemented
57C2×#66977C2212yescomplemented
58C2×#66977C22116yescomplemented
59C22×Dic11⋊C4C2212yescomplemented
60#10623198C22164yescomplemented
61#10623176C22132yescomplemented
62#10623165C22132yescomplemented
63#10623148C22132yescomplemented
64#10623128C22132yescomplemented
65#10623122C22164yescomplemented
66#10623086C22132yescomplemented
67#10623083C22132yescomplemented
68#10623081C22132yescomplemented
69#10623074C22132yescomplemented
70#10623065C22132yescomplemented
71C2×#66951C2214yescomplemented
72C2×#66950C2214yescomplemented
73C2×#66949C2214yescomplemented
74C2×#66949C2214yescomplemented
75C2×#66947C2214yescomplemented
76C2×#66943C2214yescomplemented
77C2×#66939C2214yescomplemented
78C2×#66939C2214yescomplemented
79C2×#66938C2214yescomplemented
80C2×#66938C2214yescomplemented
81C2×#66937C2214yescomplemented
82C2×#66936C2214yescomplemented
83C2×(C22⋊D11)⋊C4C2214yescomplemented
84C2×C22⋊C4×D11C2214yes—
85C2×#66931C2214yes—
86C2×#66931C2214yescomplemented
87C2×#66928C2212yescomplemented
88C2×C4×D44C2212yescomplemented
89C2×#66922C2212yescomplemented
90C2×C4×Dic22C2212yescomplemented
91C25×C11C2311yescharacteristic
92C24×D11C2312yes—
93C2×C11×#41—44no—
94C2×C11×#41C2318yescomplemented
95C22×Q8×C11C2311yescharacteristic
96C22×D4×C11C2312yes—
97C22×D4×C11C2312yes—
98C22×D4×C11C2312yes—
99C22×D4×C11C2311yescharacteristic
100C23×C4×C11—44no—
101C23×C4×C11C2311yescharacteristic
102C23×C4×C11C2311yescharacteristic
103C23×C4×C11C2312yes—
104C23×C4×C11C2311yescharacteristic
105C23×C4×C11C2311yescharacteristic
106C23×C4×C11C2311yescharacteristic
107C23×C4×C11C2311yescharacteristic
108C23×C4×C11C2318yes—
109C22×C22⋊D11—48no—
110C22×C22⋊D11C2314yes—
111C22×C22⋊D11C2314yes—
112C22×C22⋊D11C2314yes—
113C22×C22⋊D11C2314yes—
114C22×C22⋊D11C23116yes—
115C23×Dic11C2312yes—
116C23×Dic11C2312yes—
117C23×Dic11C2314yes—
118C23×Dic11C2312yes—
119C2×#4341—416no—
120C2×#4341C23132yescomplemented
121C2×#4339—48no—
122C2×#4339C23116yescomplemented
123C22×D44—44no—
124C22×D44C2312yes—
125C22×D44C2312yes—
126C22×D44C2318yes—
127C22×C4×D11C2314yes—
128C22×C4×D11C2314yes—
129C22×Dic22—44no—
130C22×Dic22C2312yes—
131C22×Dic22C2314yes—
132C22×Dic22C2312yes—
133C22×Dic22C2318yescomplemented
134C11×#123C23116yescomplemented
135C11×C22⋊Q8C2318yes—
136C11×C22⋊Q8C2318yescomplemented
137C11×#121C2318yes—
138C11×#121C2318yescomplemented
139C11×#120C23116yes—
140C4×D4×C11C23116yes—
141C4×D4×C11C23116yescomplemented
142C11×#117C2318yescomplemented
143C2×C11×C4⋊C4C2312yes—
144C2×C11×C4⋊C4C2311yescharacteristic
145C2×C11×C4⋊C4C2312yes—
146C2×C11×C4⋊C4C2311yescharacteristic
147C2×C11×C22⋊C4C2312yes—
148C2×C11×C22⋊C4C2312yes—
149C2×C11×C22⋊C4C2312yes—
150C2×C11×C22⋊C4C2312yes—
151C2×C11×C22⋊C4C2312yes—
152C2×C42×C11C2312yes—
153C2×C22⋊Dic11C2314yes—
154C2×C22⋊Dic11C2314yes—
155C2×C22⋊Dic11C2314yes—
156C2×C22⋊Dic11C23116yes—
157#66999C23132yescomplemented
158#66992C23132yescomplemented
159#66992C23132yescomplemented
160#66992C23132yescomplemented
161#66991C23132yescomplemented
162#66990C23132yes—
163D4×Dic11C23132yes—
164#66983C23116yes—
165#66983C23116yes—
166#66983C23116yes—
167#66983C23116yes—
168#66983C23116yescomplemented
169C2×(C2×D11)⋊C4C2314yes—
170C2×(C2×D11)⋊C4C2314yes—
171C2×(C2×D11)⋊C4C2314yes—
172C2×(C2×D11)⋊C4C2314yes—
173C2×(C2×D11)⋊C4C2314yes—
174C2×(C2×D11)⋊C4C2314yes—
175C2×(C2×D11)⋊C4C23116yes—
176C2×C4⋊Dic11C2312yes—
177C2×C4⋊Dic11C2312yes—
178C2×C4⋊Dic11C2314yes—
179C2×C4⋊Dic11C2314yes—
180C2×C4⋊Dic11C2312yes—
181C2×C4⋊Dic11C2312yes—
182C2×C4⋊Dic11C2318yes—
183C2×C4⋊Dic11C2318yescomplemented
184C2×C4⋊Dic11C23116yescomplemented
185#66977C23116yes—
186#66977C23116yes—
187#66977C23116yescomplemented
188#66977C23116yescomplemented
189#66977C23116yescomplemented
190C2×Dic11⋊C4C2314yes—
191C2×Dic11⋊C4C2314yes—
192C2×Dic11⋊C4C2314yes—
193C2×Dic11⋊C4C2314yes—
194C2×Dic11⋊C4C23116yescomplemented
195C2×C4×Dic11C2314yes—
196#66951C23132yescomplemented
197#66950C23132yescomplemented
198#66949C23132yescomplemented
199#66949C23132yescomplemented
200#66947C23132yescomplemented
201#66943C23132yescomplemented
202#66939C23132yescomplemented
203#66939C23132yescomplemented
204#66938C23132yescomplemented
205#66938C23132yescomplemented
206#66937C23132yescomplemented
207#66936C23132yescomplemented
208(C22⋊D11)⋊C4C23132yescomplemented
209C22⋊C4×D11C23132yes—
210#66931C23132yes—
211#66931C23132yescomplemented
212#66928C23116yescomplemented
213C4×D44C23116yescomplemented
214#66922C23116yescomplemented
215C4×Dic22C23116yescomplemented
216C2×#3536—111nomaximal, Sylow
217C24×C11—24no—
218C24×C11—24no—
219C24×C11—42no—
220C24×C11C2411yescharacteristic
221C24×C11C2412yes—
222C24×C11C2414yes—
223C24×C11C2411yescharacteristic
224C24×C11C2411yescharacteristic
225C23×D11—28no—
226C23×D11—44no—
227C23×D11—44no—
228C23×D11C2414yes—
229C23×D11C2418yes—
230C11×#41—416no—
231C2×Q8×C11—42no—
232C2×Q8×C11C2414yes—
233C2×D4×C11—28no—
234C2×D4×C11—28no—
235C2×D4×C11—44no—
236C2×D4×C11—42no—
237C2×D4×C11C2418yes—
238C2×D4×C11C2418yes—
239C2×D4×C11C2418yes—
240C2×D4×C11C2414yes—
241C22×C4×C11—24no—
242C22×C4×C11—24no—
243C22×C4×C11—28no—
244C22×C4×C11—24no—
245C22×C4×C11—416no—
246C22×C4×C11—42no—
247C22×C4×C11—42no—
248C22×C4×C11—42no—
249C22×C4×C11C2412yes—
250C22×C4×C11C2411yescharacteristic
251C22×C4×C11C2411yescharacteristic
252C22×C4×C11C2412yes—
253C22×C4×C11C2412yes—
254C22×C4×C11C2414yes—
255C22×C4×C11C2414yes—
256C22×C4×C11C2418yes—
257C22×C4×C11C2411yescharacteristic
258C22×C4×C11C2414yes—
259C22×C4×C11C2414yes—
260C22×C4×C11C2414yes—
261C22×C4×C11C2414yes—
262C22×C4×C11C2411yescharacteristic
263C2×C22⋊D11—216no—
264C2×C22⋊D11—48no—
265C2×C22⋊D11—48no—
266C2×C22⋊D11—48no—
267C2×C22⋊D11—432no—
268C2×C22⋊D11C24116yes—
269C2×C22⋊D11C24116yes—
270C2×C22⋊D11C24116yes—
271C2×C22⋊D11C24116yes—
272C22×Dic11—28no—
273C22×Dic11—44no—
274C22×Dic11—48no—
275C22×Dic11—44no—
276C22×Dic11C2418yes—
277C22×Dic11C2414yes—
278C22×Dic11C2414yes—
279C22×Dic11C2414yes—
280C22×Dic11C2418yes—
281C22×Dic11C24116yes—
282C22×Dic11C2418yes—
283#4341—464no—
284#4339—432no—
285C2×D44—28no—
286C2×D44—44no—
287C2×D44—416no—
288C2×D44C2418yes—
289C2×D44C2418yes—
290C2×C4×D11—48no—
291C2×C4×D11—48no—
292C2×C4×D11C24116yes—
293C2×C4×D11C24116yes—
294C2×Dic22—28no—
295C2×Dic22—416no—
296C2×Dic22—44no—
297C2×Dic22—48no—
298C2×Dic22C2418yes—
299C2×Dic22C24116yes—
300C2×Dic22C2418yes—
301C11×C4⋊C4C2418yes—
302C11×C4⋊C4C2414yes—
303C11×C4⋊C4C2418yes—
304C11×C4⋊C4C2414yes—
305C11×C22⋊C4C2418yes—
306C11×C22⋊C4C2418yes—
307C11×C22⋊C4C2418yes—
308C11×C22⋊C4C2418yes—
309C11×C22⋊C4C2418yes—
310C42×C11C2418yes—
311C22⋊Dic11C24116yes—
312C22⋊Dic11C24116yes—
313C22⋊Dic11C24116yes—
314(C2×D11)⋊C4C24116yes—
315(C2×D11)⋊C4C24116yes—
316(C2×D11)⋊C4C24116yes—
317(C2×D11)⋊C4C24116yes—
318(C2×D11)⋊C4C24116yes—
319(C2×D11)⋊C4C24116yes—
320C4⋊Dic11C2418yes—
321C4⋊Dic11C2418yes—
322C4⋊Dic11C24116yes—
323C4⋊Dic11C24116yes—
324C4⋊Dic11C2418yes—
325C4⋊Dic11C2418yes—
326Dic11⋊C4C24116yes—
327Dic11⋊C4C24116yes—
328Dic11⋊C4C24116yes—
329Dic11⋊C4C24116yes—
330C4×Dic11C24116yes—
331#3536—1132no—
332C2×#562—114no—
333C2×#554—112no—
334C2×#548—112no—
335C2×#547—112no—
336C2×#546—114no—
337C2×#546—112no—
338C2×#543—112no—
339C2×#542—112no—
340C2×#539—112no—
341C2×#538—112no—
342C2×#537—112no—
343C2×#537—112no—
344C2×#525D1111yescharacteristic, complemented
345C22×C22⋊Q8—111no—
346C22×#121—111no—
347C23×C11—22no—
348C23×C11—22no—
349C23×C11—22no—
350C23×C11—22no—
351C23×C11—24no—
352C23×C11—28no—
353C23×C11—22no—
354C23×C11—24no—
355C23×C11—22no—
356C23×C11—24no—
357C23×C11—28no—
358C23×C11—22no—
359C23×C11—44no—
360C23×C11—416no—
361C23×C11H(5,𝔽2)14yes—
362C23×C112−1+414yes—
363C23×C11C2512yes—
364C23×C11C2514yes—
365C23×C11C2512yes—
366C23×C11C2512yes—
367C23×C11C2511yescharacteristic
368C22×D11—28no—
369C22×D11—28no—
370C22×D11—28no—
371C22×D11—216no—
372C22×D11—48no—
373C22×D11—48no—
374C22×D11—816no—
375C22×D11C2518yes—
376Q8×C11—44no—
377D4×C11—216no—
378D4×C11—216no—
379D4×C11—44no—
380D4×C11—48no—
381C2×C4×C11—24no—
382C2×C4×C11—22no—
383C2×C4×C11—24no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—24no—
387C2×C4×C11—28no—
388C2×C4×C11—28no—
389C2×C4×C11—216no—
390C2×C4×C11—28no—
391C2×C4×C11—44no—
392C2×C4×C11—44no—
393C2×C4×C11—44no—
394C2×C4×C11H(5,𝔽2)14yes—
395C2×C4×C11C2514yes—
396C2×C4×C11C2512yes—
397C2×C4×C11C2512yes—
398C2×C4×C11C2514yes—
399C2×C4×C11C2514yes—
400C2×C4×C11C2512yes—
401C2×C4×C11C2512yes—
402C22⋊D11—232no—
403C22⋊D11—416no—
404C22⋊D11—416no—
405C22⋊D11—416no—
406C2×Dic11—28no—
407C2×Dic11—28no—
408C2×Dic11—28no—
409C2×Dic11—216no—
410C2×Dic11—48no—
411C2×Dic11—416no—
412C2×Dic11—48no—
413C2×Dic11C2518yes—
414C2×Dic11C2518yes—
415C2×Dic11C2518yes—
416D44—216no—
417D44—48no—
418C4×D11—416no—
419C4×D11—416no—
420Dic22—216no—
421Dic22—48no—
422Dic22—416no—
423C22×#41—114no—
424C22×#41—112no—
425C22×#41C2×D1111yescharacteristic, complemented
426C23×Q8—111no—
427C23×D4—112no—
428C23×D4—111no—
429C24×C4C2×D1111yescharacteristic
430#562—1164no—
431#554—1132no—
432#548—1132no—
433#547—1132no—
434#546—1164no—
435#546—1132no—
436#543—1132no—
437#542—1132no—
438#539—1132no—
439#538—1132no—
440#537—1132no—
441#537—1132no—
442C2×C4⋊Q8—112no—
443C2×#126—114no—
444C2×#125—114no—
445C2×#124—114no—
446C2×#124—114no—
447C2×#124—112no—
448#525C2×D11116yescomplemented
449C2×#123—114no—
450C2×#123—114no—
451C2×#123—114no—
452C2×#123—114no—
453C2×#123C2×D1112yescomplemented
454C2×C22⋊Q8—114no—
455C2×C22⋊Q8—112no—
456C2×C22⋊Q8—112no—
457C2×C22⋊Q8—112no—
458C2×C22⋊Q8—112no—
459C2×C22⋊Q8—1116no—
460C2×C22⋊Q8—112no—
461C2×C22⋊Q8—114no—
462C2×C22⋊Q8—114no—
463C2×C22⋊Q8—114no—
464C2×C22⋊Q8—114no—
465C2×C22⋊Q8—114no—
466C2×C22⋊Q8C2×D1111yescharacteristic
467C2×C22⋊Q8C2×D1111yescharacteristic, complemented
468C2×#121—114no—
469C2×#121—114no—
470C2×#121—114no—
471C2×#121—114no—
472C2×#121—112no—
473C2×#121—112no—
474C2×#121—112no—
475C2×#121—112no—
476C2×#121—1116no—
477C2×#121—112no—
478C2×#121—114no—
479C2×#121C2×D1111yescharacteristic
480C2×#121C2×D1111yescharacteristic, complemented
481C2×#120—114no—
482C2×#120C2×D1112yes—
483C2×C4×Q8—112no—
484C2×C4×D4—114no—
485C2×C4×D4—114no—
486C2×C4×D4—112no—
487C2×C4×D4C2×D1112yes—
488C2×C4×D4C2×D1112yescomplemented
489C2×#117C2×D1111yescharacteristic, complemented
490C22×C4⋊C4—112no—
491C22×C4⋊C4—111no—
492C22×C4⋊C4—111no—
493C22×C4⋊C4—112no—
494C22×C22⋊C4—112no—
495C22×C22⋊C4—112no—
496C22×C22⋊C4—114no—
497C22×C11—22no—
498C22×C11—22no—
499C22×C11—22no—
500C22×C11—22no—
501C22×C11—28no—
502C22×C11—28no—
503C22×C11—22no—
504C22×C11—24no—
505C22×C11—24no—
506C22×C11—22no—
507C22×C11—24no—
508C22×C11—22no—
509C22×C11—416no—
510C22×C11—48no—
511C22×C11—44no—
512C22×C11C2×H(5,𝔽2)12yes—
513C22×C11C2×H(5,𝔽2)14yes—
514C22×C11C2×H(5,𝔽2)12yes—
515C22×C11C2×2−1+414yes—
516C22×C11C2×2−1+412yes—
517C22×C11C2611yescharacteristic
518C2×D11—28no—
519C2×D11—28no—
520C2×D11—28no—
521C2×D11—416no—
522C2×D11—816no—
523C4×C11—22no—
524C4×C11—22no—
525C4×C11—22no—
526C4×C11—24no—
527C4×C11—24no—
528C4×C11—24no—
529C4×C11C2×H(5,𝔽2)14yes—
530Dic11—28no—
531Dic11—28no—
532Dic11—28no—
533C25—112no—
534C25C22×D1111yescharacteristic
535C2×#41—44no—
536C2×#41—1132no—
537C2×#41—1116no—
538C2×#41—448no—
539C2×#41—4416no—
540C2×#41C22×D1118yescomplemented
541C22×Q8—112no—
542C22×Q8—112no—
543C22×Q8—114no—
544C22×Q8—118no—
545C22×Q8—444no—
546C22×Q8C22×D1111yescharacteristic
547C22×D4—114no—
548C22×D4—114no—
549C22×D4—114no—
550C22×D4—114no—
551C22×D4—1116no—
552C22×D4—112no—
553C22×D4—112no—
554C22×D4—118no—
555C22×D4—444no—
556C22×D4—448no—
557C22×D4C22×D1112yes—
558C22×D4C22×D1112yes—
559C22×D4C22×D1112yes—
560C22×D4C22×D1111yescharacteristic
561C23×C4—44no—
562C23×C4—112no—
563C23×C4—112no—
564C23×C4—112no—
565C23×C4—114no—
566C23×C4—114no—
567C23×C4—114no—
568C23×C4C22×D1111yescharacteristic
569C23×C4C22×D1112yes—
570C23×C4C22×D1111yescharacteristic
571C23×C4C22×D1111yescharacteristic
572C23×C4C22×D1111yescharacteristic
573C23×C4C22×D1111yescharacteristic
574C23×C4C22×D1111yescharacteristic
575C23×C4C22×D1118yes—
576C4⋊Q8—1116no—
577#126—1132no—
578#125—1132no—
579#124—1132no—
580#124—1132no—
581#124—1116no—
582#123—1132no—
583#123—1132no—
584#123—1132no—
585#123—1132no—
586#123C22×D11116yescomplemented
587C22⋊Q8—1132no—
588C22⋊Q8—1116no—
589C22⋊Q8—1116no—
590C22⋊Q8—1116no—
591C22⋊Q8—1116no—
592C22⋊Q8—1116no—
593C22⋊Q8—1132no—
594C22⋊Q8—1132no—
595C22⋊Q8—1132no—
596C22⋊Q8—1132no—
597C22⋊Q8—1132no—
598C22⋊Q8C22×D1118yes—
599C22⋊Q8C22×D1118yescomplemented
600#121—1132no—
601#121—1132no—
602#121—1132no—
603#121—1132no—
604#121—1116no—
605#121—1116no—
606#121—1116no—
607#121—1116no—
608#121—1116no—
609#121—1132no—
610#121C22×D1118yes—
611#121C22×D1118yescomplemented
612#120—1132no—
613#120C22×D11116yes—
614C4×Q8—1116no—
615C4×D4—1132no—
616C4×D4—1132no—
617C4×D4—1116no—
618C4×D4C22×D11116yes—
619C4×D4C22×D11116yescomplemented
620#117C22×D1118yescomplemented
621C2×C4⋊C4—112no—
622C2×C4⋊C4—112no—
623C2×C4⋊C4—112no—
624C2×C4⋊C4—118no—
625C2×C4⋊C4—114no—
626C2×C4⋊C4—114no—
627C2×C4⋊C4—114no—
628C2×C4⋊C4—112no—
629C2×C4⋊C4—1116no—
630C2×C4⋊C4—118no—
631C2×C4⋊C4—1116no—
632C2×C4⋊C4—114no—
633C2×C4⋊C4—114no—
634C2×C4⋊C4—114no—
635C2×C4⋊C4C22×D1111yescharacteristic
636C2×C4⋊C4C22×D1111yescharacteristic
637C2×C4⋊C4C22×D1112yes—
638C2×C4⋊C4C22×D1112yes—
639C2×C22⋊C4—114no—
640C2×C22⋊C4—114no—
641C2×C22⋊C4—1116no—
642C2×C22⋊C4—114no—
643C2×C22⋊C4—114no—
644C2×C22⋊C4—114no—
645C2×C22⋊C4—114no—
646C2×C22⋊C4—114no—
647C2×C22⋊C4—1116no—
648C2×C22⋊C4—114no—
649C2×C22⋊C4—114no—
650C2×C22⋊C4—1132no—
651C2×C22⋊C4C22×D1112yes—
652C2×C22⋊C4C22×D1112yes—
653C2×C22⋊C4C22×D1112yes—
654C2×C22⋊C4C22×D1112yes—
655C2×C22⋊C4C22×D1112yes—
656C2×C42—114no—
657C2×C42C22×D1112yes—
658C2×C11—24no—
659C2×C11—24no—
660C2×C11—44no—
661C2×C11—42no—
662C2×C11#353614yescomplemented
663C2×C11C22×H(5,𝔽2)11yescharacteristic
664C2×C11C22×H(5,𝔽2)11yescharacteristic
665C2×C11C22×2−1+411yescharacteristic
666D11—48no—
667C24—24no—
668C24—24no—
669C24—42no—
670C24—114no—
671C24—118no—
672C24—228no—
673C24—444no—
674C24—444no—
675C24C23×D1111yescharacteristic
676C24C23×D1112yes—
677C24C23×D1114yes—
678C24C23×D1111yescharacteristic
679C24C23×D1111yescharacteristic
680#41—416no—
681#41—4432no—
682#41—4464no—
683C2×Q8—42no—
684C2×Q8—118no—
685C2×Q8—118no—
686C2×Q8—1116no—
687C2×Q8—228no—
688C2×Q8—444no—
689C2×Q8—448no—
690C2×Q8—4416no—
691C2×Q8C23×D1114yes—
692C2×D4—28no—
693C2×D4—28no—
694C2×D4—42no—
695C2×D4—44no—
696C2×D4—1116no—
697C2×D4—1116no—
698C2×D4—1116no—
699C2×D4—1116no—
700C2×D4—118no—
701C2×D4—118no—
702C2×D4—2216no—
703C2×D4—228no—
704C2×D4—4416no—
705C2×D4—444no—
706C2×D4—448no—
707C2×D4—448no—
708C2×D4—448no—
709C2×D4—4432no—
710C2×D4C23×D1118yes—
711C2×D4C23×D1118yes—
712C2×D4C23×D1118yes—
713C2×D4C23×D1114yes—
714C22×C4—24no—
715C22×C4—24no—
716C22×C4—24no—
717C22×C4—28no—
718C22×C4—416no—
719C22×C4—42no—
720C22×C4—42no—
721C22×C4—42no—
722C22×C4—118no—
723C22×C4—114no—
724C22×C4—114no—
725C22×C4—114no—
726C22×C4—118no—
727C22×C4—118no—
728C22×C4—1116no—
729C22×C4—1116no—
730C22×C4—1116no—
731C22×C4—228no—
732C22×C4—448no—
733C22×C4—448no—
734C22×C4—444no—
735C22×C4—444no—
736C22×C4—448no—
737C22×C4C23×D1114yes—
738C22×C4C23×D1118yes—
739C22×C4C23×D1114yes—
740C22×C4C23×D1114yes—
741C22×C4C23×D1112yes—
742C22×C4C23×D1112yes—
743C22×C4C23×D1111yescharacteristic
744C22×C4C23×D1111yescharacteristic
745C22×C4C23×D1112yes—
746C22×C4C23×D1111yescharacteristic
747C22×C4C23×D1114yes—
748C22×C4C23×D1114yes—
749C22×C4C23×D1114yes—
750C22×C4C23×D1111yescharacteristic
751C4⋊C4—118no—
752C4⋊C4—118no—
753C4⋊C4—118no—
754C4⋊C4—1116no—
755C4⋊C4—1116no—
756C4⋊C4—1116no—
757C4⋊C4—118no—
758C4⋊C4—1116no—
759C4⋊C4—1116no—
760C4⋊C4—1116no—
761C4⋊C4C23×D1114yes—
762C4⋊C4C23×D1114yes—
763C4⋊C4C23×D1118yes—
764C4⋊C4C23×D1118yes—
765C22⋊C4—1116no—
766C22⋊C4—1116no—
767C22⋊C4—1116no—
768C22⋊C4—1116no—
769C22⋊C4—1116no—
770C22⋊C4—1116no—
771C22⋊C4—1116no—
772C22⋊C4—1116no—
773C22⋊C4—1116no—
774C22⋊C4C23×D1118yes—
775C22⋊C4C23×D1118yes—
776C22⋊C4C23×D1118yes—
777C22⋊C4C23×D1118yes—
778C22⋊C4C23×D1118yes—
779C42—1116no—
780C42C23×D1118yes—
781C11C2×#353611yescharacteristic, complemented, Sylow
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—24no—
788C23—24no—
789C23—28no—
790C23—22no—
791C23—24no—
792C23—28no—
793C23—22no—
794C23—44no—
795C23—416no—
796C23—118no—
797C23—228no—
798C23—228no—
799C23—228no—
800C23—2216no—
801C23—448no—
802C23—448no—
803C23—8816no—
804C23#6704214yes—
805C23#6704314yes—
806C23C24×D1112yes—
807C23C24×D1114yes—
808C23C24×D1112yes—
809C23C24×D1112yes—
810C23C24×D1111yescharacteristic
811Q8—44no—
812Q8—2216no—
813Q8—448no—
814Q8—4416no—
815D4—216no—
816D4—216no—
817D4—44no—
818D4—48no—
819D4—2232no—
820D4—2216no—
821D4—448no—
822D4—4416no—
823D4—4416no—
824D4—4416no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—24no—
829C2×C4—24no—
830C2×C4—24no—
831C2×C4—28no—
832C2×C4—28no—
833C2×C4—28no—
834C2×C4—216no—
835C2×C4—44no—
836C2×C4—44no—
837C2×C4—44no—
838C2×C4—118no—
839C2×C4—118no—
840C2×C4—118no—
841C2×C4—228no—
842C2×C4—228no—
843C2×C4—2216no—
844C2×C4—228no—
845C2×C4—4416no—
846C2×C4—4416no—
847C2×C4—448no—
848C2×C4—448no—
849C2×C4—4416no—
850C2×C4#6703714yes—
851C2×C4C24×D1114yes—
852C2×C4C24×D1114yes—
853C2×C4C24×D1112yes—
854C2×C4C24×D1112yes—
855C2×C4C24×D1114yes—
856C2×C4C24×D1112yes—
857C2×C4C24×D1112yes—
858C22—22no—
859C22—22no—
860C22—22no—
861C22—22no—
862C22—28no—
863C22—28no—
864C22—22no—
865C22—24no—
866C22—24no—
867C22—22no—
868C22—24no—
869C22—22no—
870C22—416no—
871C22—44no—
872C22—48no—
873C22—228no—
874C22—228no—
875C22—228no—
876C22—4416no—
877C22—8816no—
878C22C2×#6703712yes—
879C22C2×#6704214yes—
880C22C2×#6704212yes—
881C22C2×#6704314yes—
882C22C2×#6704312yes—
883C22C25×D1111yescharacteristic
884C4—22no—
885C4—22no—
886C4—22no—
887C4—24no—
888C4—24no—
889C4—24no—
890C4—228no—
891C4—228no—
892C4—228no—
893C4C2×#6703714yes—
894C2—24no—
895C2—24no—
896C2—42no—
897C2—44no—
898C2—448no—
899C2#1308284314yesdirect product factor
900C2C22×#6703711yescharacteristic
901C2C22×#6704211yescharacteristic
902C2C22×#6704311yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#525C2
socleC23×C11C25
hypercenterC2×#525D11
hypocenterC11C2×#3536
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. #13082843C2direct (N × H)
2. C2×#10623198C2semidirect
3. C2×#10623074C2semidirect
4. C2×#10623083C2semidirect
5. C2×#10623086C2semidirect
6. C2×#10623081C2semidirect
7. C2×#10623122C2semidirect
8. C2×#10623165C2semidirect
9. C2×#10623065C2semidirect
10. C2×#10623176C2semidirect
11. C2×#10623148C2semidirect
12. C2×#10623364C2semidirect
13. C2×#10623128C2semidirect
14. C22×#66977C2semidirect
15. C22×#66983C2semidirect
16. C2×C11×#525C2semidirect
17. C22×C11×#41C22semidirect
20. C22×#4341C22semidirect
21. C22×#4339C22semidirect
23. C23×Dic22C22semidirect
24. C11×#525C22semidirect
25. C2×C11×#123C22semidirect
27. C2×C11×C22⋊Q8C22semidirect
29. C2×C11×#121C22semidirect
32. C2×C4×D4×C11C22semidirect
33. C2×C11×#117C22semidirect
35. #10623364C22semidirect
36. C2×#66999C22semidirect
37. C2×#66992C22semidirect
38. C2×#66992C22semidirect
39. C2×#66992C22semidirect
40. C2×#66991C22semidirect
47. C2×#66983C22semidirect
48. C2×#66983C22semidirect
51. C22×C4⋊Dic11C22semidirect
52. C22×C4⋊Dic11C22semidirect
55. C2×#66977C22semidirect
56. C2×#66977C22semidirect
57. C2×#66977C22semidirect
58. C2×#66977C22semidirect
59. C22×Dic11⋊C4C22semidirect
60. #10623198C22semidirect
61. #10623176C22semidirect
62. #10623165C22semidirect
63. #10623148C22semidirect
64. #10623128C22semidirect
65. #10623122C22semidirect
66. #10623086C22semidirect
67. #10623083C22semidirect
68. #10623081C22semidirect
69. #10623074C22semidirect
70. #10623065C22semidirect
71. C2×#66951C22semidirect
72. C2×#66950C22semidirect
73. C2×#66949C22semidirect
74. C2×#66949C22semidirect
75. C2×#66947C22semidirect
76. C2×#66943C22semidirect
77. C2×#66939C22semidirect
78. C2×#66939C22semidirect
79. C2×#66938C22semidirect
80. C2×#66938C22semidirect
81. C2×#66937C22semidirect
82. C2×#66936C22semidirect
83. C2×(C22⋊D11)⋊C4C22semidirect
86. C2×#66931C22semidirect
87. C2×#66928C22semidirect
88. C2×C4×D44C22semidirect
89. C2×#66922C22semidirect
90. C2×C4×Dic22C22semidirect
94. C2×C11×#41C23semidirect
120. C2×#4341C23semidirect
122. C2×#4339C23semidirect
133. C22×Dic22C23semidirect
134. C11×#123C23semidirect
136. C11×C22⋊Q8C23semidirect
138. C11×#121C23semidirect
141. C4×D4×C11C23semidirect
142. C11×#117C23semidirect
157. #66999C23semidirect
158. #66992C23semidirect
159. #66992C23semidirect
160. #66992C23semidirect
161. #66991C23semidirect
168. #66983C23semidirect
183. C2×C4⋊Dic11C23semidirect
184. C2×C4⋊Dic11C23semidirect
187. #66977C23semidirect
188. #66977C23semidirect
189. #66977C23semidirect
194. C2×Dic11⋊C4C23semidirect
196. #66951C23semidirect
197. #66950C23semidirect
198. #66949C23semidirect
199. #66949C23semidirect
200. #66947C23semidirect
201. #66943C23semidirect
202. #66939C23semidirect
203. #66939C23semidirect
204. #66938C23semidirect
205. #66938C23semidirect
206. #66937C23semidirect
207. #66936C23semidirect
208. (C22⋊D11)⋊C4C23semidirect
211. #66931C23semidirect
212. #66928C23semidirect
213. C4×D44C23semidirect
214. #66922C23semidirect
215. C4×Dic22C23semidirect
344. C2×#525D11semidirect
425. C22×#41C2×D11semidirect
448. #525C2×D11semidirect
453. C2×#123C2×D11semidirect
467. C2×C22⋊Q8C2×D11semidirect
480. C2×#121C2×D11semidirect
488. C2×C4×D4C2×D11semidirect
489. C2×#117C2×D11semidirect
540. C2×#41C22×D11semidirect
586. #123C22×D11semidirect
599. C22⋊Q8C22×D11semidirect
611. #121C22×D11semidirect
619. C4×D4C22×D11semidirect
620. #117C22×D11semidirect
662. C2×C11#3536semidirect
781. C11C2×#3536semidirect
899. C2#13082843direct (N × H)

Maximal subgroups

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

subgroupindex
#130828432
C2×#106231982
C2×#106230742
C2×#106230832
C2×#106230862
C2×#106230812
C2×#106231222
C2×#106231652
C2×#106230652
C2×#106231762
C2×#106231482
C2×#106233642
C2×#106231282
C22×#669772
C22×#669832
C2×C11×#5252
C2×#353611