Finite Group Databasebeta

← C2×#13082845 #15661001

Subgroups — C2×#13082845 #15661001

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#13082845C2132yesmaximal, direct product factor
2C2×#10623178C214yesmaximal, complemented
3C2×#10623166C212yesmaximal, complemented
4C2×#10623348C212yesmaximal, complemented
5C2×#10623038C212yesmaximal, complemented
6C2×#10623161C212yesmaximal, complemented
7C2×#10623021C214yesmaximal, complemented
8C2×#10623165C212yesmaximal, complemented
9C2×#10623174C212yesmaximal, complemented
10C2×#10623046C212yesmaximal, complemented
11C2×#10623175C212yesmaximal, complemented
12C2×#10623041C212yesmaximal, complemented
13C2×#10623160C212yesmaximal, complemented
14C2×#10623322C211yesmaximal, characteristic, complemented
15C22×#66983C211yesmaximal, characteristic, complemented
16C22×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
17C23×Q8×C11C2211yescharacteristic, complemented
18C24×C4×C11C2211yescharacteristic
19C23×C22⋊D11C2212yes—
20C22×#4343C2212yescomplemented
21C22×#4339C2211yescharacteristic, complemented
22C22×#4339C2214yescomplemented
23C23×D44C2211yescharacteristic
24C2×C11×C22⋊Q8C2212yes—
25C2×C11×C22⋊Q8C2212yes—
26C2×C11×C22⋊Q8C2212yescomplemented
27C2×C11×C22⋊Q8C2212yescomplemented
28C2×C11×C22⋊Q8C22116yescomplemented
29C22×C11×C4⋊C4C2212yescomplemented
30C22×C11×C4⋊C4C2211yescharacteristic, complemented
31C22×C11×C22⋊C4C2212yes—
32C2×#67006C2212yes—
33#10623348C22132yescomplemented
34C2×#67000C2214yescomplemented
35C2×#67000C2212yescomplemented
36C2×#66999C2212yescomplemented
37C2×#66999C2214yescomplemented
38C2×Q8×Dic11C2212yescomplemented
39#10623322C22116yescomplemented
40C2×#66983C2211yescharacteristic
41C2×#66983C2212yes—
42C2×#66983C2212yes—
43C2×#66983C2212yes—
44C2×#66983C2212yes—
45C2×#66983C22116yescomplemented
46C2×#66983C2211yescharacteristic, complemented
47C2×#66983C2214yescomplemented
48C2×#66982C2212yescomplemented
49C2×#66982C2214yescomplemented
50C2×C4×C22⋊D11C2212yes—
51C2×C4×C22⋊D11C2212yescomplemented
52C2×C4×C22⋊D11C2214yescomplemented
53C22×(C2×D11)⋊C4C2212yes—
54C2×#66979C2211yescharacteristic, complemented
55C22×C4⋊Dic11C2211yescharacteristic
56C2×#66977C2211yescharacteristic
57C2×#66977C2211yescharacteristic, complemented
58#10623178C22164yescomplemented
59#10623175C22132yescomplemented
60#10623174C22132yescomplemented
61#10623166C22132yescomplemented
62#10623165C22132yescomplemented
63#10623161C22132yescomplemented
64#10623160C22132yescomplemented
65#10623046C22132yescomplemented
66C2×#66951C2214yescomplemented
67#10623041C22132yescomplemented
68C2×#66950C2214yescomplemented
69C2×#66950C2214yescomplemented
70C2×#66949C2214yescomplemented
71C2×#66949C2214yescomplemented
72#10623038C22132yescomplemented
73C2×#66948C2214yescomplemented
74C2×#66948C2212yescomplemented
75C2×#66948C2214yescomplemented
76C2×#66947C2214yescomplemented
77C2×#66947C2214yescomplemented
78C2×#66946C2212yescomplemented
79C2×C4⋊C4×D11C2212yescomplemented
80C2×#66942C2214yescomplemented
81C2×#66941C2212yescomplemented
82C2×#66938C2214yescomplemented
83#10623021C22164yescomplemented
84C2×#66937C2214yescomplemented
85C2×#66937C2214yescomplemented
86C2×#66936C2214yescomplemented
87C2×#66935C2214yes—
88C2×(C22⋊D11)⋊C4C2214yes—
89C2×C22⋊C4×D11C2214yes—
90C2×#66931C2214yes—
91C25×C11C2311yescharacteristic
92C24×D11C2312yes—
93C22×Q8×C11—44no—
94C22×Q8×C11C2312yes—
95C22×Q8×C11C2312yes—
96C22×Q8×C11C2318yescomplemented
97C23×C4×C11—44no—
98C23×C4×C11C2311yescharacteristic
99C23×C4×C11C2311yescharacteristic
100C23×C4×C11C2311yescharacteristic
101C23×C4×C11C2312yes—
102C23×C4×C11C2311yescharacteristic
103C23×C4×C11C2311yescharacteristic
104C23×C4×C11C2312yes—
105C23×C4×C11C2311yescharacteristic
106C23×C4×C11C2318yes—
107C22×C22⋊D11—48no—
108C22×C22⋊D11C2312yes—
109C22×C22⋊D11C2314yes—
110C22×C22⋊D11C2312yes—
111C22×C22⋊D11C2314yes—
112C22×C22⋊D11C2312yes—
113C22×C22⋊D11C23116yes—
114C23×Dic11C2312yes—
115C2×#4343—48no—
116C2×#4343C23116yescomplemented
117C2×#4339—44no—
118C2×#4339—416no—
119C2×#4339C23132yescomplemented
120C2×#4339C2318yescomplemented
121C22×D44—44no—
122C22×D44C2312yes—
123C22×D44C2314yes—
124C22×D44C2314yes—
125C22×D44C2312yes—
126C22×D44C2311yescharacteristic
127C22×D44C2318yes—
128C22×C4×D11C2312yes—
129C22×C4×D11C2314yes—
130C22×C4×D11C2314yes—
131C22×C4×D11C2314yes—
132C22×Dic22C2314yes—
133C22×Dic22C2311yescharacteristic
134C11×C22⋊Q8C23116yes—
135C11×C22⋊Q8C23116yes—
136C11×C22⋊Q8C23116yescomplemented
137C11×C22⋊Q8C23116yescomplemented
138C2×C11×C4⋊C4C2312yes—
139C2×C11×C4⋊C4C2314yes—
140C2×C11×C4⋊C4C2312yes—
141C2×C11×C4⋊C4C2314yes—
142C2×C11×C4⋊C4C2318yescomplemented
143C2×C11×C4⋊C4C23116yescomplemented
144C2×C11×C22⋊C4C2314yes—
145C2×C11×C22⋊C4C2314yes—
146C2×C11×C22⋊C4C23116yes—
147#67006C23116yes—
148C2×C22⋊Dic11C2312yes—
149C2×C22⋊Dic11C2312yes—
150C2×C22⋊Dic11C2312yes—
151#67000C23116yescomplemented
152#67000C23132yescomplemented
153#66999C23116yescomplemented
154#66999C23132yescomplemented
155Q8×Dic11C23116yescomplemented
156#66983C23116yes—
157#66983C23116yes—
158#66983C23116yes—
159#66983C23116yes—
160#66983C2318yes—
161#66983C23132yescomplemented
162#66983C2318yescomplemented
163#66982C23132yescomplemented
164#66982C23116yescomplemented
165C4×C22⋊D11C23116yes—
166C4×C22⋊D11C23132yescomplemented
167C4×C22⋊D11C23116yescomplemented
168C2×(C2×D11)⋊C4C2314yes—
169C2×(C2×D11)⋊C4C2314yes—
170C2×(C2×D11)⋊C4C2314yes—
171C2×(C2×D11)⋊C4C2314yes—
172C2×(C2×D11)⋊C4C2314yes—
173C2×(C2×D11)⋊C4C2312yes—
174C2×(C2×D11)⋊C4C2314yes—
175C2×(C2×D11)⋊C4C2312yes—
176C2×(C2×D11)⋊C4C2314yes—
177C2×(C2×D11)⋊C4C23116yes—
178#66979C2318yescomplemented
179C2×C4⋊Dic11C2314yes—
180C2×C4⋊Dic11C2312yes—
181C2×C4⋊Dic11C2312yes—
182C2×C4⋊Dic11C2311yescharacteristic
183C2×C4⋊Dic11C2311yescharacteristic
184C2×C4⋊Dic11C2318yes—
185#66977C2318yes—
186#66977C2318yescomplemented
187C2×Dic11⋊C4C2314yes—
188C2×Dic11⋊C4C2314yes—
189C2×Dic11⋊C4C2314yes—
190C2×Dic11⋊C4C2312yes—
191C2×Dic11⋊C4C2312yes—
192C2×C4×Dic11C2314yes—
193C2×C4×Dic11C2312yes—
194#66951C23132yescomplemented
195#66950C23132yescomplemented
196#66950C23132yescomplemented
197#66949C23132yescomplemented
198#66949C23132yescomplemented
199#66948C23116yescomplemented
200#66948C23132yescomplemented
201#66948C23132yescomplemented
202#66947C23132yescomplemented
203#66947C23132yescomplemented
204#66946C23116yescomplemented
205C4⋊C4×D11C23116yescomplemented
206#66942C23132yescomplemented
207#66941C23116yescomplemented
208#66938C23132yescomplemented
209#66937C23132yescomplemented
210#66937C23132yescomplemented
211#66936C23132yescomplemented
212#66935C23132yes—
213(C22⋊D11)⋊C4C23132yes—
214C22⋊C4×D11C23132yes—
215#66931C23132yes—
216C2×#3536—111nomaximal, Sylow
217C24×C11—24no—
218C24×C11—24no—
219C24×C11—42no—
220C24×C11C2411yescharacteristic
221C24×C11C2414yes—
222C24×C11C2411yescharacteristic
223C24×C11C2411yescharacteristic
224C23×D11—28no—
225C23×D11—44no—
226C23×D11—44no—
227C23×D11C2414yes—
228C23×D11C2412yes—
229C23×D11C2418yes—
230C2×Q8×C11—28no—
231C2×Q8×C11—44no—
232C2×Q8×C11—416no—
233C2×Q8×C11C2418yes—
234C2×Q8×C11C2418yes—
235C22×C4×C11—28no—
236C22×C4×C11—24no—
237C22×C4×C11—24no—
238C22×C4×C11—24no—
239C22×C4×C11—416no—
240C22×C4×C11—42no—
241C22×C4×C11—42no—
242C22×C4×C11—42no—
243C22×C4×C11—44no—
244C22×C4×C11C2414yes—
245C22×C4×C11C2411yescharacteristic
246C22×C4×C11C2411yescharacteristic
247C22×C4×C11C2414yes—
248C22×C4×C11C2411yescharacteristic
249C22×C4×C11C2414yes—
250C22×C4×C11C2414yes—
251C22×C4×C11C2414yes—
252C22×C4×C11C2418yes—
253C22×C4×C11C2414yes—
254C22×C4×C11C2414yes—
255C22×C4×C11C2418yes—
256C22×C4×C11C2414yes—
257C22×C4×C11C2411yescharacteristic
258C2×C22⋊D11—28no—
259C2×C22⋊D11—216no—
260C2×C22⋊D11—28no—
261C2×C22⋊D11—44no—
262C2×C22⋊D11—48no—
263C2×C22⋊D11—432no—
264C2×C22⋊D11C2418yes—
265C2×C22⋊D11C24116yes—
266C2×C22⋊D11C2418yes—
267C2×C22⋊D11C24116yes—
268C2×C22⋊D11C2418yes—
269C22×Dic11—44no—
270C22×Dic11C2412yes—
271C22×Dic11C2414yes—
272C22×Dic11C2412yes—
273C22×Dic11C2412yes—
274C22×Dic11C2418yes—
275#4343—432no—
276#4339—416no—
277#4339—464no—
278C2×D44—28no—
279C2×D44—44no—
280C2×D44—48no—
281C2×D44—42no—
282C2×D44—48no—
283C2×D44—416no—
284C2×D44C2418yes—
285C2×D44C24116yes—
286C2×D44C24116yes—
287C2×D44C2418yes—
288C2×D44C2414yes—
289C2×C4×D11—28no—
290C2×C4×D11—48no—
291C2×C4×D11—48no—
292C2×C4×D11—48no—
293C2×C4×D11C2418yes—
294C2×C4×D11C24116yes—
295C2×C4×D11C24116yes—
296C2×C4×D11C24116yes—
297C2×Dic22—48no—
298C2×Dic22—42no—
299C2×Dic22C24116yes—
300C2×Dic22C2414yes—
301C11×C4⋊C4C2418yes—
302C11×C4⋊C4C24116yes—
303C11×C4⋊C4C2418yes—
304C11×C4⋊C4C24116yes—
305C11×C22⋊C4C24116yes—
306C11×C22⋊C4C24116yes—
307C22⋊Dic11C2418yes—
308C22⋊Dic11C2418yes—
309C22⋊Dic11C2418yes—
310(C2×D11)⋊C4C24116yes—
311(C2×D11)⋊C4C24116yes—
312(C2×D11)⋊C4C24116yes—
313(C2×D11)⋊C4C24116yes—
314(C2×D11)⋊C4C24116yes—
315(C2×D11)⋊C4C2418yes—
316(C2×D11)⋊C4C24116yes—
317(C2×D11)⋊C4C2418yes—
318(C2×D11)⋊C4C24116yes—
319C4⋊Dic11C24116yes—
320C4⋊Dic11C2418yes—
321C4⋊Dic11C2418yes—
322C4⋊Dic11C2414yes—
323C4⋊Dic11C2414yes—
324Dic11⋊C4C24116yes—
325Dic11⋊C4C24116yes—
326Dic11⋊C4C24116yes—
327Dic11⋊C4C2418yes—
328Dic11⋊C4C2418yes—
329C4×Dic11C24116yes—
330C4×Dic11C2418yes—
331#3536—1132no—
332C2×#562—114no—
333C2×#554—112no—
334C2×#548—112no—
335C2×#547—112no—
336C2×#546—112no—
337C2×#546—114no—
338C2×#543—112no—
339C2×#542—112no—
340C2×#539—112no—
341C2×#538—112no—
342C2×#537—112no—
343C2×#537—112no—
344C2×#525—111no—
345C22×C22⋊Q8D1111yescharacteristic, complemented
346C22×#121—111no—
347C23×C11—22no—
348C23×C11—22no—
349C23×C11—22no—
350C23×C11—22no—
351C23×C11—28no—
352C23×C11—22no—
353C23×C11—22no—
354C23×C11—28no—
355C23×C11—22no—
356C23×C11—44no—
357C23×C11—416no—
358C23×C11H(5,𝔽2)14yes—
359C23×C112−1+414yes—
360C23×C11C2512yes—
361C23×C11C2512yes—
362C23×C11C2512yes—
363C23×C11C2511yescharacteristic
364C22×D11—24no—
365C22×D11—24no—
366C22×D11—28no—
367C22×D11—28no—
368C22×D11—24no—
369C22×D11—28no—
370C22×D11—216no—
371C22×D11—48no—
372C22×D11—48no—
373C22×D11—816no—
374C22×D11C2518yes—
375C22×D11C2514yes—
376Q8×C11—216no—
377Q8×C11—48no—
378C2×C4×C11—28no—
379C2×C4×C11—22no—
380C2×C4×C11—28no—
381C2×C4×C11—22no—
382C2×C4×C11—216no—
383C2×C4×C11—22no—
384C2×C4×C11—28no—
385C2×C4×C11—28no—
386C2×C4×C11—28no—
387C2×C4×C11—44no—
388C2×C4×C11—44no—
389C2×C4×C11—44no—
390C2×C4×C11—48no—
391C2×C4×C11H(5,𝔽2)14yes—
392C2×C4×C11C2518yes—
393C2×C4×C11C2512yes—
394C2×C4×C11C2512yes—
395C2×C4×C11C2518yes—
396C2×C4×C11C2512yes—
397C2×C4×C11C2512yes—
398C22⋊D11—216no—
399C22⋊D11—232no—
400C22⋊D11—216no—
401C22⋊D11—48no—
402C22⋊D11—416no—
403C2×Dic11—24no—
404C2×Dic11—24no—
405C2×Dic11—28no—
406C2×Dic11—24no—
407C2×Dic11—48no—
408C2×Dic11C2514yes—
409C2×Dic11C2518yes—
410C2×Dic11C2514yes—
411C2×Dic11C2514yes—
412D44—216no—
413D44—48no—
414D44—44no—
415D44—416no—
416D44—416no—
417C4×D11—216no—
418C4×D11—416no—
419C4×D11—416no—
420C4×D11—416no—
421Dic22—416no—
422Dic22—44no—
423C22×#41—112no—
424C22×#41—111no—
425C22×#41—114no—
426C23×Q8C2×D1111yescharacteristic, complemented
427C23×D4—112no—
428C23×D4—111no—
429C24×C4C2×D1111yescharacteristic
430#562—1164no—
431#554—1132no—
432#548—1132no—
433#547—1132no—
434#546—1132no—
435#546—1164no—
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—112no—
447C2×#124—114no—
448#525—1116no—
449C2×#123—112no—
450C2×#123—114no—
451C2×#123—114no—
452C2×#123—114no—
453C2×#123—114no—
454C2×C22⋊Q8—112no—
455C2×C22⋊Q8—114no—
456C2×C22⋊Q8—111no—
457C2×C22⋊Q8—111no—
458C2×C22⋊Q8—114no—
459C2×C22⋊Q8—114no—
460C2×C22⋊Q8—114no—
461C2×C22⋊Q8—114no—
462C2×C22⋊Q8—114no—
463C2×C22⋊Q8C2×D1112yes—
464C2×C22⋊Q8C2×D1112yes—
465C2×C22⋊Q8C2×D1112yescomplemented
466C2×C22⋊Q8C2×D1112yescomplemented
467C2×C22⋊Q8C2×D11116yescomplemented
468C2×#121—112no—
469C2×#121—112no—
470C2×#121—112no—
471C2×#121—112no—
472C2×#121—111no—
473C2×#121—1116no—
474C2×#121—111no—
475C2×#121—114no—
476C2×#121—114no—
477C2×#121—112no—
478C2×#121—114no—
479C2×#121—114no—
480C2×#121—114no—
481C2×#120—112no—
482C2×#120—114no—
483C2×C4×Q8—112no—
484C2×C4×D4—112no—
485C2×C4×D4—112no—
486C2×C4×D4—114no—
487C2×C4×D4—112no—
488C2×C4×D4—114no—
489C2×#117—111no—
490C22×C4⋊C4—111no—
491C22×C4⋊C4—112no—
492C22×C4⋊C4C2×D1112yescomplemented
493C22×C4⋊C4C2×D1111yescharacteristic, complemented
494C22×C22⋊C4—112no—
495C22×C22⋊C4—114no—
496C22×C22⋊C4C2×D1112yes—
497C22×C11—22no—
498C22×C11—22no—
499C22×C11—22no—
500C22×C11—22no—
501C22×C11—28no—
502C22×C11—28no—
503C22×C11—22no—
504C22×C11—22no—
505C22×C11—22no—
506C22×C11—416no—
507C22×C11—44no—
508C22×C11C2×H(5,𝔽2)12yes—
509C22×C11C2×H(5,𝔽2)14yes—
510C22×C11C2×H(5,𝔽2)12yes—
511C22×C11C2×2−1+414yes—
512C22×C11C2×2−1+412yes—
513C22×C11C2611yescharacteristic
514C2×D11—28no—
515C2×D11—28no—
516C2×D11—24no—
517C2×D11—24no—
518C2×D11—28no—
519C2×D11—24no—
520C2×D11—48no—
521C2×D11—416no—
522C2×D11—816no—
523C4×C11—22no—
524C4×C11—22no—
525C4×C11—22no—
526C4×C11—28no—
527C4×C11—28no—
528C4×C11C2×H(5,𝔽2)14yes—
529Dic11—24no—
530Dic11—24no—
531Dic11—28no—
532Dic11—24no—
533C25—112no—
534C25C22×D1111yescharacteristic
535C2×#41—1116no—
536C2×#41—118no—
537C2×#41—1132no—
538C2×#41—444no—
539C2×#41—4416no—
540C2×#41—448no—
541C22×Q8—44no—
542C22×Q8—111no—
543C22×Q8—114no—
544C22×Q8C22×D1112yes—
545C22×Q8C22×D1112yes—
546C22×Q8C22×D1118yescomplemented
547C22×D4—112no—
548C22×D4—112no—
549C22×D4—114no—
550C22×D4—112no—
551C22×D4—114no—
552C22×D4—1116no—
553C22×D4—112no—
554C22×D4—114no—
555C22×D4—114no—
556C22×D4—111no—
557C22×D4—112no—
558C22×D4—118no—
559C22×D4—444no—
560C22×D4—448no—
561C23×C4—44no—
562C23×C4—112no—
563C23×C4—112no—
564C23×C4—114no—
565C23×C4—114no—
566C23×C4—114no—
567C23×C4C22×D1112yes—
568C23×C4C22×D1111yescharacteristic
569C23×C4C22×D1111yescharacteristic
570C23×C4C22×D1111yescharacteristic
571C23×C4C22×D1111yescharacteristic
572C23×C4C22×D1112yes—
573C23×C4C22×D1111yescharacteristic
574C23×C4C22×D1111yescharacteristic
575C23×C4C22×D1118yes—
576C4⋊Q8—1116no—
577#126—1132no—
578#125—1132no—
579#124—1132no—
580#124—1116no—
581#124—1132no—
582#123—1116no—
583#123—1132no—
584#123—1132no—
585#123—1132no—
586#123—1132no—
587C22⋊Q8—1116no—
588C22⋊Q8—1132no—
589C22⋊Q8—118no—
590C22⋊Q8—118no—
591C22⋊Q8—1132no—
592C22⋊Q8—1132no—
593C22⋊Q8—1132no—
594C22⋊Q8—1132no—
595C22⋊Q8—1132no—
596C22⋊Q8C22×D11116yes—
597C22⋊Q8C22×D11116yes—
598C22⋊Q8C22×D11116yescomplemented
599C22⋊Q8C22×D11116yescomplemented
600#121—1116no—
601#121—1116no—
602#121—1116no—
603#121—1116no—
604#121—118no—
605#121—118no—
606#121—1132no—
607#121—1132no—
608#121—1116no—
609#121—1132no—
610#121—1132no—
611#121—1132no—
612#120—1116no—
613#120—1132no—
614C4×Q8—1116no—
615C4×D4—1116no—
616C4×D4—1116no—
617C4×D4—1132no—
618C4×D4—1116no—
619C4×D4—1132no—
620#117—118no—
621C2×C4⋊C4—112no—
622C2×C4⋊C4—112no—
623C2×C4⋊C4—118no—
624C2×C4⋊C4—114no—
625C2×C4⋊C4—111no—
626C2×C4⋊C4—111no—
627C2×C4⋊C4—114no—
628C2×C4⋊C4—112no—
629C2×C4⋊C4—112no—
630C2×C4⋊C4—114no—
631C2×C4⋊C4—114no—
632C2×C4⋊C4—1116no—
633C2×C4⋊C4C22×D1112yes—
634C2×C4⋊C4C22×D1114yes—
635C2×C4⋊C4C22×D1114yes—
636C2×C4⋊C4C22×D1112yes—
637C2×C4⋊C4C22×D11116yescomplemented
638C2×C4⋊C4C22×D1118yescomplemented
639C2×C22⋊C4—112no—
640C2×C22⋊C4—112no—
641C2×C22⋊C4—112no—
642C2×C22⋊C4—114no—
643C2×C22⋊C4—114no—
644C2×C22⋊C4—114no—
645C2×C22⋊C4—114no—
646C2×C22⋊C4—1116no—
647C2×C22⋊C4—114no—
648C2×C22⋊C4—114no—
649C2×C22⋊C4—112no—
650C2×C22⋊C4—114no—
651C2×C22⋊C4—112no—
652C2×C22⋊C4—1132no—
653C2×C22⋊C4C22×D1114yes—
654C2×C22⋊C4C22×D1114yes—
655C2×C22⋊C4C22×D11116yes—
656C2×C42—112no—
657C2×C42—114no—
658C2×C11—24no—
659C2×C11—24no—
660C2×C11—42no—
661C2×C11#353614yescomplemented
662C2×C11C22×H(5,𝔽2)11yescharacteristic
663C2×C11C22×H(5,𝔽2)11yescharacteristic
664C2×C11C22×2−1+411yescharacteristic
665D11—44no—
666D11—48no—
667C24—24no—
668C24—24no—
669C24—42no—
670C24—114no—
671C24—112no—
672C24—118no—
673C24—228no—
674C24—444no—
675C24—444no—
676C24C23×D1111yescharacteristic
677C24C23×D1114yes—
678C24C23×D1111yescharacteristic
679C24C23×D1111yescharacteristic
680#41—4416no—
681#41—4464no—
682#41—4432no—
683C2×Q8—28no—
684C2×Q8—44no—
685C2×Q8—416no—
686C2×Q8—114no—
687C2×Q8—1116no—
688C2×Q8—442no—
689C2×Q8—448no—
690C2×Q8C23×D1118yes—
691C2×Q8C23×D1118yes—
692C2×D4—118no—
693C2×D4—118no—
694C2×D4—1116no—
695C2×D4—118no—
696C2×D4—1116no—
697C2×D4—118no—
698C2×D4—1116no—
699C2×D4—1116no—
700C2×D4—114no—
701C2×D4—118no—
702C2×D4—228no—
703C2×D4—2216no—
704C2×D4—228no—
705C2×D4—228no—
706C2×D4—4416no—
707C2×D4—444no—
708C2×D4—442no—
709C2×D4—448no—
710C2×D4—448no—
711C2×D4—448no—
712C2×D4—444no—
713C2×D4—4432no—
714C22×C4—28no—
715C22×C4—24no—
716C22×C4—24no—
717C22×C4—24no—
718C22×C4—416no—
719C22×C4—42no—
720C22×C4—42no—
721C22×C4—42no—
722C22×C4—44no—
723C22×C4—112no—
724C22×C4—112no—
725C22×C4—114no—
726C22×C4—112no—
727C22×C4—118no—
728C22×C4—118no—
729C22×C4—1116no—
730C22×C4—1116no—
731C22×C4—1116no—
732C22×C4—228no—
733C22×C4—448no—
734C22×C4—448no—
735C22×C4—448no—
736C22×C4—444no—
737C22×C4C23×D1118yes—
738C22×C4C23×D1114yes—
739C22×C4C23×D1114yes—
740C22×C4C23×D1114yes—
741C22×C4C23×D1114yes—
742C22×C4C23×D1111yescharacteristic
743C22×C4C23×D1111yescharacteristic
744C22×C4C23×D1114yes—
745C22×C4C23×D1111yescharacteristic
746C22×C4C23×D1114yes—
747C22×C4C23×D1118yes—
748C22×C4C23×D1114yes—
749C22×C4C23×D1114yes—
750C22×C4C23×D1111yescharacteristic
751C4⋊C4—118no—
752C4⋊C4—118no—
753C4⋊C4—1116no—
754C4⋊C4—114no—
755C4⋊C4—114no—
756C4⋊C4—1116no—
757C4⋊C4—118no—
758C4⋊C4—118no—
759C4⋊C4—1116no—
760C4⋊C4—1116no—
761C4⋊C4C23×D1118yes—
762C4⋊C4C23×D11116yes—
763C4⋊C4C23×D11116yes—
764C4⋊C4C23×D1118yes—
765C22⋊C4—118no—
766C22⋊C4—118no—
767C22⋊C4—118no—
768C22⋊C4—1116no—
769C22⋊C4—1116no—
770C22⋊C4—1116no—
771C22⋊C4—1116no—
772C22⋊C4—1116no—
773C22⋊C4—1116no—
774C22⋊C4—118no—
775C22⋊C4—1116no—
776C22⋊C4—118no—
777C22⋊C4C23×D11116yes—
778C22⋊C4C23×D11116yes—
779C42—118no—
780C42—1116no—
781C11C2×#353611yescharacteristic, complemented, Sylow
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—28no—
788C23—22no—
789C23—28no—
790C23—22no—
791C23—44no—
792C23—416no—
793C23—118no—
794C23—114no—
795C23—224no—
796C23—228no—
797C23—224no—
798C23—228no—
799C23—224no—
800C23—228no—
801C23—2216no—
802C23—448no—
803C23—448no—
804C23—8816no—
805C23#6704014yes—
806C23#6704214yes—
807C23C24×D1112yes—
808C23C24×D1112yes—
809C23C24×D1112yes—
810C23C24×D1111yescharacteristic
811Q8—216no—
812Q8—48no—
813Q8—444no—
814Q8—4416no—
815D4—2216no—
816D4—2232no—
817D4—2216no—
818D4—2216no—
819D4—448no—
820D4—444no—
821D4—4416no—
822D4—4416no—
823D4—4416no—
824D4—448no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—28no—
829C2×C4—28no—
830C2×C4—216no—
831C2×C4—28no—
832C2×C4—28no—
833C2×C4—28no—
834C2×C4—44no—
835C2×C4—44no—
836C2×C4—44no—
837C2×C4—48no—
838C2×C4—114no—
839C2×C4—114no—
840C2×C4—118no—
841C2×C4—114no—
842C2×C4—224no—
843C2×C4—224no—
844C2×C4—228no—
845C2×C4—224no—
846C2×C4—2216no—
847C2×C4—4416no—
848C2×C4—4416no—
849C2×C4—4416no—
850C2×C4—448no—
851C2×C4#6703714yes—
852C2×C4C24×D1118yes—
853C2×C4C24×D1112yes—
854C2×C4C24×D1112yes—
855C2×C4C24×D1118yes—
856C2×C4C24×D1112yes—
857C2×C4C24×D1112yes—
858C22—22no—
859C22—22no—
860C22—22no—
861C22—22no—
862C22—28no—
863C22—28no—
864C22—22no—
865C22—22no—
866C22—22no—
867C22—416no—
868C22—44no—
869C22—224no—
870C22—228no—
871C22—224no—
872C22—228no—
873C22—224no—
874C22—228no—
875C22—4416no—
876C22—448no—
877C22—8816no—
878C22C2×#6703712yes—
879C22C2×#6704014yes—
880C22C2×#6704012yes—
881C22C2×#6704214yes—
882C22C2×#6704212yes—
883C22C25×D1111yescharacteristic
884C4—22no—
885C4—22no—
886C4—22no—
887C4—28no—
888C4—28no—
889C4—224no—
890C4—228no—
891C4—224no—
892C4—224no—
893C4C2×#6703714yes—
894C2—24no—
895C2—24no—
896C2—42no—
897C2—448no—
898C2—444no—
899C2#1308284514yesdirect product factor
900C2C22×#6703711yescharacteristic
901C2C22×#6704211yescharacteristic
902C2C22×#6704011yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC22×C11×C22⋊Q8C2
socleC23×C11C25
hypercenterC22×C22⋊Q8D11
hypocenterC11C2×#3536
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #13082845C2direct (N × H)
2. C2×#10623178C2semidirect
3. C2×#10623166C2semidirect
4. C2×#10623348C2semidirect
5. C2×#10623038C2semidirect
6. C2×#10623161C2semidirect
7. C2×#10623021C2semidirect
8. C2×#10623165C2semidirect
9. C2×#10623174C2semidirect
10. C2×#10623046C2semidirect
11. C2×#10623175C2semidirect
12. C2×#10623041C2semidirect
13. C2×#10623160C2semidirect
14. C2×#10623322C2semidirect
15. C22×#66983C2semidirect
16. C22×C11×C22⋊Q8C2semidirect
17. C23×Q8×C11C22semidirect
20. C22×#4343C22semidirect
21. C22×#4339C22semidirect
22. C22×#4339C22semidirect
26. C2×C11×C22⋊Q8C22semidirect
27. C2×C11×C22⋊Q8C22semidirect
28. C2×C11×C22⋊Q8C22semidirect
29. C22×C11×C4⋊C4C22semidirect
30. C22×C11×C4⋊C4C22semidirect
33. #10623348C22semidirect
34. C2×#67000C22semidirect
35. C2×#67000C22semidirect
36. C2×#66999C22semidirect
37. C2×#66999C22semidirect
38. C2×Q8×Dic11C22semidirect
39. #10623322C22semidirect
45. C2×#66983C22semidirect
46. C2×#66983C22semidirect
47. C2×#66983C22semidirect
48. C2×#66982C22semidirect
49. C2×#66982C22semidirect
51. C2×C4×C22⋊D11C22semidirect
52. C2×C4×C22⋊D11C22semidirect
54. C2×#66979C22semidirect
57. C2×#66977C22semidirect
58. #10623178C22semidirect
59. #10623175C22semidirect
60. #10623174C22semidirect
61. #10623166C22semidirect
62. #10623165C22semidirect
63. #10623161C22semidirect
64. #10623160C22semidirect
65. #10623046C22semidirect
66. C2×#66951C22semidirect
67. #10623041C22semidirect
68. C2×#66950C22semidirect
69. C2×#66950C22semidirect
70. C2×#66949C22semidirect
71. C2×#66949C22semidirect
72. #10623038C22semidirect
73. C2×#66948C22semidirect
74. C2×#66948C22semidirect
75. C2×#66948C22semidirect
76. C2×#66947C22semidirect
77. C2×#66947C22semidirect
78. C2×#66946C22semidirect
79. C2×C4⋊C4×D11C22semidirect
80. C2×#66942C22semidirect
81. C2×#66941C22semidirect
82. C2×#66938C22semidirect
83. #10623021C22semidirect
84. C2×#66937C22semidirect
85. C2×#66937C22semidirect
86. C2×#66936C22semidirect
96. C22×Q8×C11C23semidirect
116. C2×#4343C23semidirect
119. C2×#4339C23semidirect
120. C2×#4339C23semidirect
136. C11×C22⋊Q8C23semidirect
137. C11×C22⋊Q8C23semidirect
142. C2×C11×C4⋊C4C23semidirect
143. C2×C11×C4⋊C4C23semidirect
151. #67000C23semidirect
152. #67000C23semidirect
153. #66999C23semidirect
154. #66999C23semidirect
155. Q8×Dic11C23semidirect
161. #66983C23semidirect
162. #66983C23semidirect
163. #66982C23semidirect
164. #66982C23semidirect
166. C4×C22⋊D11C23semidirect
167. C4×C22⋊D11C23semidirect
178. #66979C23semidirect
186. #66977C23semidirect
194. #66951C23semidirect
195. #66950C23semidirect
196. #66950C23semidirect
197. #66949C23semidirect
198. #66949C23semidirect
199. #66948C23semidirect
200. #66948C23semidirect
201. #66948C23semidirect
202. #66947C23semidirect
203. #66947C23semidirect
204. #66946C23semidirect
205. C4⋊C4×D11C23semidirect
206. #66942C23semidirect
207. #66941C23semidirect
208. #66938C23semidirect
209. #66937C23semidirect
210. #66937C23semidirect
211. #66936C23semidirect
345. C22×C22⋊Q8D11semidirect
426. C23×Q8C2×D11semidirect
465. C2×C22⋊Q8C2×D11semidirect
466. C2×C22⋊Q8C2×D11semidirect
467. C2×C22⋊Q8C2×D11semidirect
492. C22×C4⋊C4C2×D11semidirect
493. C22×C4⋊C4C2×D11semidirect
546. C22×Q8C22×D11semidirect
598. C22⋊Q8C22×D11semidirect
599. C22⋊Q8C22×D11semidirect
637. C2×C4⋊C4C22×D11semidirect
638. C2×C4⋊C4C22×D11semidirect
661. C2×C11#3536semidirect
781. C11C2×#3536semidirect
899. C2#13082845direct (N × H)

Maximal subgroups

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

subgroupindex
#130828452
C2×#106231782
C2×#106231662
C2×#106233482
C2×#106230382
C2×#106231612
C2×#106230212
C2×#106231652
C2×#106231742
C2×#106230462
C2×#106231752
C2×#106230412
C2×#106231602
C2×#106233222
C22×#669832
C22×C11×C22⋊Q82
C2×#353611