Finite Group Databasebeta

← C2×#13082280 #15662083

Subgroups — C2×#13082280 #15662083

Order 2816.

12366 conjugacy classes of subgroups.

The subgroup lattice has 1140 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67042C211yesmaximal, characteristic, complemented
2C22×#41×D11C211yesmaximal, characteristic, complemented
3#13082280C2132yesmaximal, direct product factor
4C2×#10623130C212yesmaximal, complemented
5C2×#10623164C212yesmaximal, complemented
6C2×#10623161C212yesmaximal, complemented
7C2×#10623141C214yesmaximal, complemented
8C2×#10623140C212yesmaximal, complemented
9C2×#10623140C214yesmaximal, complemented
10C2×#10623160C212yesmaximal, complemented
11C2×#10623138C212yesmaximal, complemented
12C2×#10623361C211yesmaximal, characteristic, complemented
13C2×#10623158C212yesmaximal, complemented
14C2×#10623359C211yesmaximal, characteristic, complemented
15C22×#66948C211yesmaximal, characteristic, complemented
16C2×D11×#121C212yesmaximal, complemented
17C2×#10623035C211yesmaximal, characteristic, complemented
18C2×C11×#537C211yesmaximal, characteristic, complemented
19C22×C11×#41C2211yescharacteristic, complemented
20C22×C11×#41C2211yescharacteristic, complemented
21C2×#67042—216no—
22C2×#67042C22116yescomplemented
23C2×#41×D11—216no—
24C2×#41×D11C22116yescomplemented
25C22×#4343C2212yescomplemented
26C22×#4343C2211yescharacteristic, complemented
27C22×Q8×D11C2211yescharacteristic, complemented
28C22×#4341C2212yescomplemented
29C22×#4341C2211yescharacteristic, complemented
30C22×D4×D11C2212yescomplemented
31C22×D4×D11C2211yescharacteristic, complemented
32C22×D4×D11C2212yescomplemented
33C22×D4×D11C2214yescomplemented
34C22×D4×D11C2214yescomplemented
35C22×#4339C2211yescharacteristic
36C22×#4339C2212yescomplemented
37C22×#4339C2212yescomplemented
38C23×D44C2211yescharacteristic, complemented
39C23×D44C2212yescomplemented
40C23×D44C2212yescomplemented
41C23×C4×D11C2212yescomplemented
42C23×C4×D11C2211yescharacteristic, complemented
43C11×#537C22116yescomplemented
44C2×C11×C22⋊Q8C2212yescomplemented
45C2×C11×C22⋊Q8C2212yescomplemented
46C2×C11×#121C2212yescomplemented
47C2×C11×#121C2214yescomplemented
48C2×C11×#121C2212yescomplemented
49C22×C11×C4⋊C4C2211yescharacteristic, complemented
50#10623361C22116yescomplemented
51#10623359C22116yescomplemented
52C2×#67000C2212yescomplemented
53C2×#66999C2211yescharacteristic, complemented
54C2×#66999C2211yescharacteristic, complemented
55C2×#66993C2212yescomplemented
56C2×#66993C2214yescomplemented
57C2×#66992C2214yescomplemented
58C2×#66991C2211yescharacteristic, complemented
59C2×#66991C2211yescharacteristic, complemented
60C2×#66990C2214yescomplemented
61C2×#66990C2214yescomplemented
62C2×#66990C2212yescomplemented
63C2×#66988C2212yescomplemented
64C2×#66983C2212yescomplemented
65C2×#66983C2212yescomplemented
66C2×C4×C22⋊D11C2214yescomplemented
67C2×C4×C22⋊D11C2212yescomplemented
68C2×C4×C22⋊D11C2212yescomplemented
69C22×(C2×D11)⋊C4C2212yescomplemented
70C2×#66979C2211yescharacteristic, complemented
71#10623164C22132yescomplemented
72#10623161C22132yescomplemented
73#10623160C22132yescomplemented
74#10623158C22132yescomplemented
75#10623141C22164yescomplemented
76#10623140C22164yescomplemented
77#10623140C22132yescomplemented
78#10623138C22132yescomplemented
79D11×#121C22132yescomplemented
80#10623130C22132yescomplemented
81C2×#66949C2214yescomplemented
82C2×#66948C2212yescomplemented
83C2×#66948C2212yescomplemented
84C2×#66948C2214yescomplemented
85C2×#66948C2212yescomplemented
86C2×#66948C2212yescomplemented
87C2×#66948C22116yescomplemented
88C2×#66947C2214yescomplemented
89#10623035C22116yescomplemented
90C2×#66946C2214yescomplemented
91C2×#66946C2212yescomplemented
92C2×#66945C2212yescomplemented
93C2×C4⋊C4×D11C2212yescomplemented
94C2×#66940C2212yescomplemented
95C2×#66938C2214yescomplemented
96C2×#66937C2214yescomplemented
97C2×#66937C2214yescomplemented
98C2×#66937C2214yescomplemented
99C2×#66935C2214yescomplemented
100C2×#66935C2214yescomplemented
101C2×(C22⋊D11)⋊C4C2214yescomplemented
102C2×C22⋊C4×D11C2214yescomplemented
103C24×D11C2312yes—
104C24×D11C2311yescharacteristic
105C24×D11C2314yes—
106C24×D11C2312yes—
107C2×C11×#41—28no—
108C2×C11×#41—28no—
109C2×C11×#41C2318yescomplemented
110C2×C11×#41C2318yescomplemented
111C22×Q8×C11C2311yescharacteristic
112C22×Q8×C11C2311yescharacteristic
113C22×D4×C11C2312yes—
114C22×D4×C11C2312yes—
115C22×D4×C11C2311yescharacteristic
116C22×D4×C11C2311yescharacteristic
117C22×D4×C11C2314yes—
118C23×C4×C11C2312yes—
119C23×C4×C11C2312yes—
120C23×C4×C11C2312yes—
121C23×C4×C11C2311yescharacteristic
122C22×C22⋊D11C2312yes—
123C22×C22⋊D11C2312yes—
124C22×C22⋊D11C2312yes—
125C22×C22⋊D11C2314yes—
126C22×C22⋊D11C2314yes—
127C22×C22⋊D11C2312yes—
128C22×C22⋊D11C2314yes—
129C22×C22⋊D11C2312yes—
130C23×Dic11C2312yes—
131C23×Dic11C2311yescharacteristic
132#67042—2128no—
133#41×D11—2128no—
134C2×#4343—28no—
135C2×#4343—216no—
136C2×#4343C23116yescomplemented
137C2×#4343C2318yescomplemented
138C2×Q8×D11—28no—
139C2×Q8×D11C2318yescomplemented
140C2×#4341—216no—
141C2×#4341—28no—
142C2×#4341C2318yescomplemented
143C2×#4341C23116yescomplemented
144C2×D4×D11—216no—
145C2×D4×D11—232no—
146C2×D4×D11—28no—
147C2×D4×D11—216no—
148C2×D4×D11—416no—
149C2×D4×D11C23116yescomplemented
150C2×D4×D11C23116yescomplemented
151C2×D4×D11C2318yescomplemented
152C2×D4×D11C23132yescomplemented
153C2×D4×D11C23132yescomplemented
154C2×#4339—216no—
155C2×#4339—216no—
156C2×#4339D4116yescomplemented
157C2×#4339C2318yes—
158C2×#4339C23116yescomplemented
159C2×#4339C23116yescomplemented
160C22×D44—28no—
161C22×D44—216no—
162C22×D44—48no—
163C22×D44C2312yes—
164C22×D44C2314yes—
165C22×D44C2314yes—
166C22×D44C2312yes—
167C22×D44C2312yes—
168C22×D44C2314yes—
169C22×D44C2311yescharacteristic
170C22×D44C2318yescomplemented
171C22×D44C23116yescomplemented
172C22×D44C23116yescomplemented
173C22×C4×D11—28no—
174C22×C4×D11—216no—
175C22×C4×D11C2312yes—
176C22×C4×D11C2314yes—
177C22×C4×D11C2312yes—
178C22×C4×D11C2311yescharacteristic
179C22×C4×D11C2311yescharacteristic
180C22×C4×D11C2311yescharacteristic
181C22×C4×D11C2311yescharacteristic
182C22×C4×D11C2314yes—
183C22×C4×D11C2312yes—
184C22×C4×D11C2318yescomplemented
185C22×C4×D11C23116yescomplemented
186C22×Dic22C2312yes—
187C22×Dic22C2311yescharacteristic
188C11×C22⋊Q8C23116yescomplemented
189C11×C22⋊Q8C23116yescomplemented
190C11×#121C23116yescomplemented
191C11×#121C23116yescomplemented
192C11×#121C23132yescomplemented
193C2×C11×C4⋊C4C2312yes—
194C2×C11×C4⋊C4C2312yes—
195C2×C11×C4⋊C4C2314yes—
196C2×C11×C4⋊C4C2318yescomplemented
197C2×C11×C22⋊C4C2314yes—
198C2×C11×C22⋊C4C2314yes—
199C2×C22⋊Dic11C2312yes—
200C2×C22⋊Dic11C2312yes—
201C2×C22⋊Dic11C2312yes—
202#67000C23116yescomplemented
203#66999C2318yescomplemented
204#66999C2318yescomplemented
205#66993C23116yescomplemented
206#66993C23132yescomplemented
207#66992C23132yescomplemented
208#66991C2318yescomplemented
209#66991C2318yescomplemented
210#66990C23116yescomplemented
211#66990C23132yescomplemented
212#66990C23132yescomplemented
213#66988C23116yescomplemented
214#66983C23116yescomplemented
215#66983C23116yescomplemented
216C4×C22⋊D11C23132yescomplemented
217C4×C22⋊D11C23116yescomplemented
218C4×C22⋊D11C23116yescomplemented
219C2×(C2×D11)⋊C4C2314yes—
220C2×(C2×D11)⋊C4C2314yes—
221C2×(C2×D11)⋊C4C2314yes—
222C2×(C2×D11)⋊C4C2312yes—
223C2×(C2×D11)⋊C4C2314yes—
224C2×(C2×D11)⋊C4C2312yes—
225C2×(C2×D11)⋊C4C2314yes—
226C2×(C2×D11)⋊C4C23116yescomplemented
227#66979C2318yescomplemented
228C2×C4⋊Dic11C2311yescharacteristic
229C2×C4⋊Dic11C2311yescharacteristic
230C2×Dic11⋊C4C2312yes—
231C2×Dic11⋊C4C2314yes—
232C2×Dic11⋊C4C2312yes—
233C2×C4×Dic11C2314yes—
234C2×C4×Dic11C2312yes—
235#66949C23132yescomplemented
236#66948C23116yescomplemented
237#66948C23116yescomplemented
238#66948C23116yescomplemented
239#66948C23116yescomplemented
240#66948C23132yescomplemented
241#66947C23132yescomplemented
242#66946C23116yescomplemented
243#66946C23132yescomplemented
244#66945C23116yescomplemented
245C4⋊C4×D11C23116yescomplemented
246#66940C23116yescomplemented
247#66938C23132yescomplemented
248#66937C23132yescomplemented
249#66937C23132yescomplemented
250#66937C23132yescomplemented
251#66935C23132yescomplemented
252#66935C23132yescomplemented
253(C22⋊D11)⋊C4C23132yescomplemented
254C22⋊C4×D11C23132yescomplemented
255C2×#3488—111nomaximal, Sylow
256C24×C11C2412yes—
257C24×C11C2412yes—
258C24×C11C2411yescharacteristic
259C23×D11—24no—
260C23×D11—28no—
261C23×D11—28no—
262C23×D11—24no—
263C23×D11—28no—
264C23×D11—216no—
265C23×D11—44no—
266C23×D11—42no—
267C23×D11—44no—
268C23×D11—48no—
269C23×D11—48no—
270C23×D11—44no—
271C23×D11C2414yes—
272C23×D11C2411yescharacteristic
273C23×D11C2418yes—
274C23×D11C2414yes—
275C23×D11C2412yes—
276C23×D11C2411yescharacteristic
277C23×D11C24116yes—
278C23×D11C2418yes—
279C11×#41—232no—
280C11×#41—232no—
281C2×Q8×C11—24no—
282C2×Q8×C11—24no—
283C2×Q8×C11C2414yes—
284C2×Q8×C11C2414yes—
285C2×D4×C11—28no—
286C2×D4×C11—28no—
287C2×D4×C11—24no—
288C2×D4×C11—24no—
289C2×D4×C11—48no—
290C2×D4×C11C2418yes—
291C2×D4×C11C2418yes—
292C2×D4×C11C2414yes—
293C2×D4×C11C2414yes—
294C2×D4×C11C24116yes—
295C22×C4×C11—28no—
296C22×C4×C11—28no—
297C22×C4×C11—44no—
298C22×C4×C11C2×D418yescomplemented
299C22×C4×C11C2414yes—
300C22×C4×C11C2412yes—
301C22×C4×C11C2412yes—
302C22×C4×C11C2418yes—
303C22×C4×C11C2418yes—
304C22×C4×C11C2418yes—
305C22×C4×C11C2411yescharacteristic
306C22×C4×C11C2411yescharacteristic
307C22×C4×C11C2414yes—
308C2×C22⋊D11—216no—
309C2×C22⋊D11—28no—
310C2×C22⋊D11—28no—
311C2×C22⋊D11—28no—
312C2×C22⋊D11—48no—
313C2×C22⋊D11—44no—
314C2×C22⋊D11—48no—
315C2×C22⋊D11C2×D4116yescomplemented
316C2×C22⋊D11C2418yes—
317C2×C22⋊D11C2418yes—
318C2×C22⋊D11C2418yes—
319C2×C22⋊D11C24116yes—
320C2×C22⋊D11C24116yes—
321C2×C22⋊D11C2418yes—
322C2×C22⋊D11C24116yes—
323C2×C22⋊D11C2418yes—
324C22×Dic11—28no—
325C22×Dic11—24no—
326C22×Dic11C2418yes—
327C22×Dic11C2412yes—
328C22×Dic11C2412yes—
329C22×Dic11C2411yescharacteristic
330C22×Dic11C2411yescharacteristic
331C22×Dic11C2414yes—
332C22×Dic11C2412yes—
333#4343—232no—
334#4343—264no—
335Q8×D11—232no—
336#4341—264no—
337#4341—232no—
338D4×D11—264no—
339D4×D11—2128no—
340D4×D11—232no—
341D4×D11—264no—
342D4×D11—464no—
343#4339—264no—
344#4339—264no—
345#4339C2×D4164yescomplemented
346C2×D44—264no—
347C2×D44—216no—
348C2×D44—28no—
349C2×D44—216no—
350C2×D44—28no—
351C2×D44—28no—
352C2×D44—232no—
353C2×D44—48no—
354C2×D44—432no—
355C2×D44C2×D418yescomplemented
356C2×D44C2418yes—
357C2×D44C24116yes—
358C2×D44C24116yes—
359C2×D44C2418yes—
360C2×D44C2418yes—
361C2×D44C24116yes—
362C2×D44C2414yes—
363C2×C4×D11—28no—
364C2×C4×D11—216no—
365C2×C4×D11—264no—
366C2×C4×D11—28no—
367C2×C4×D11—24no—
368C2×C4×D11—24no—
369C2×C4×D11—24no—
370C2×C4×D11—24no—
371C2×C4×D11—232no—
372C2×C4×D11—48no—
373C2×C4×D11C2×D4116yescomplemented
374C2×C4×D11C2418yes—
375C2×C4×D11C24116yes—
376C2×C4×D11C2418yes—
377C2×C4×D11C2414yes—
378C2×C4×D11C2414yes—
379C2×C4×D11C2414yes—
380C2×C4×D11C2414yes—
381C2×C4×D11C24116yes—
382C2×C4×D11C2418yes—
383C2×Dic22—28no—
384C2×Dic22C2×D418yescomplemented
385C2×Dic22C2418yes—
386C2×Dic22C2414yes—
387C11×C4⋊C4C2418yes—
388C11×C4⋊C4C2418yes—
389C11×C4⋊C4C24116yes—
390C11×C22⋊C4C24116yes—
391C11×C22⋊C4C24116yes—
392C22⋊Dic11C2418yes—
393C22⋊Dic11C2418yes—
394C22⋊Dic11C2418yes—
395(C2×D11)⋊C4C24116yes—
396(C2×D11)⋊C4C24116yes—
397(C2×D11)⋊C4C24116yes—
398(C2×D11)⋊C4C2418yes—
399(C2×D11)⋊C4C24116yes—
400(C2×D11)⋊C4C2418yes—
401(C2×D11)⋊C4C24116yes—
402C4⋊Dic11C2414yes—
403C4⋊Dic11C2414yes—
404Dic11⋊C4C2418yes—
405Dic11⋊C4C24116yes—
406Dic11⋊C4C2418yes—
407C4×Dic11C24116yes—
408C4×Dic11C2418yes—
409C22×H(5,𝔽2)—111no—
410C23×#41—111no—
411#3488—1132no—
412C2×#550—112no—
413C2×#548—112no—
414C2×#546—112no—
415C2×#546—114no—
416C2×D42—114no—
417C2×D42—112no—
418C2×#537—112no—
419C2×#537D1111yescharacteristic, complemented
420C2×#535—111no—
421C2×#535—112no—
422C2×#525—111no—
423C2×#525—112no—
424C22×#121—112no—
425C22×#121—111no—
426C2×#520—111no—
427C23×C11—22no—
428C23×C11—22no—
429C23×C11—24no—
430C23×C11—24no—
431C23×C11—24no—
432C23×C11—24no—
433C23×C11—24no—
434C23×C11—24no—
435C23×C11C22×D414yes—
436C23×C11C2514yes—
437C23×C11C2514yes—
438C23×C11C2512yes—
439C23×C11C2511yescharacteristic
440C22×D11—22no—
441C22×D11—24no—
442C22×D11—22no—
443C22×D11—24no—
444C22×D11—22no—
445C22×D11—28no—
446C22×D11—28no—
447C22×D11—28no—
448C22×D11—22no—
449C22×D11—22no—
450C22×D11—28no—
451C22×D11—216no—
452C22×D11—216no—
453C22×D11—28no—
454C22×D11—216no—
455C22×D11—232no—
456C22×D11—48no—
457C22×D11—44no—
458C22×D11—432no—
459C22×D11—48no—
460C22×D11—416no—
461C22×D11—416no—
462C22×D11—48no—
463C22×D11—416no—
464C22×D11—832no—
465C22×D11—816no—
466C22×D11C22×D418yes—
467C22×D11H(5,𝔽2)14yescomplemented
468C22×D11C2518yes—
469C22×D11C2512yes—
470C22×D11C2514yes—
471C22×D11C2512yes—
472Q8×C11—28no—
473Q8×C11—28no—
474D4×C11—216no—
475D4×C11—216no—
476D4×C11—28no—
477D4×C11—28no—
478D4×C11—416no—
479C2×C4×C11—24no—
480C2×C4×C11—24no—
481C2×C4×C11—28no—
482C2×C4×C11—216no—
483C2×C4×C11—216no—
484C2×C4×C11—48no—
485C2×C4×C11C22×D414yes—
486C2×C4×C11C22×D414yes—
487C2×C4×C11C22×D4116yescomplemented
488C2×C4×C11C2518yes—
489C2×C4×C11C2514yes—
490C2×C4×C11C2514yes—
491C2×C4×C11C2512yes—
492C2×C4×C11C2512yes—
493C22⋊D11—216no—
494C22⋊D11—216no—
495C22⋊D11—232no—
496C22⋊D11—216no—
497C22⋊D11—416no—
498C22⋊D11—416no—
499C22⋊D11—48no—
500C22⋊D11C22×D4132yescomplemented
501C2×Dic11—22no—
502C2×Dic11—22no—
503C2×Dic11—28no—
504C2×Dic11—24no—
505C2×Dic11—24no—
506C2×Dic11—216no—
507C2×Dic11C22×D418yes—
508C2×Dic11C2514yes—
509C2×Dic11C2514yes—
510C2×Dic11C2512yes—
511C2×Dic11C2512yes—
512C2×Dic11C2514yes—
513D44—232no—
514D44—216no—
515D44—232no—
516D44—216no—
517D44—216no—
518D44—416no—
519D44C22×D4116yescomplemented
520C4×D11—216no—
521C4×D11—28no—
522C4×D11—28no—
523C4×D11—28no—
524C4×D11—28no—
525C4×D11—216no—
526C4×D11—232no—
527C4×D11—416no—
528C4×D11C22×D4132yescomplemented
529Dic22—216no—
530Dic22C22×D4116yescomplemented
531C2×H(5,𝔽2)—1116no—
532C2×H(5,𝔽2)—2216no—
533C22×#41—1116no—
534C22×#41—111no—
535C22×#41—112no—
536C22×#41—112no—
537C22×#41—111no—
538C22×#41—111no—
539C22×#41—112no—
540C22×#41—112no—
541C22×#41—2216no—
542C22×#41C2×D1111yescharacteristic, complemented
543C22×#41C2×D1111yescharacteristic, complemented
544C23×Q8—111no—
545C23×D4—112no—
546C23×D4—111no—
547C23×D4—112no—
548C23×D4—114no—
549C23×D4—114no—
550C23×D4—111no—
551C23×D4—112no—
552C23×D4—112no—
553C24×C4—112no—
554C24×C4—111no—
555#550—1132no—
556#548—1132no—
557#546—1132no—
558#546—1164no—
559D42—1164no—
560D42—1132no—
561#537—1132no—
562#537C2×D11116yescomplemented
563#535—1116no—
564#535—1132no—
565C2×#127—114no—
566C2×#127—112no—
567C2×#124—112no—
568C2×#124—114no—
569#525—1116no—
570#525—1132no—
571C2×#123—112no—
572C2×#123—114no—
573C2×C22⋊Q8—111no—
574C2×C22⋊Q8—111no—
575C2×C22⋊Q8—114no—
576C2×C22⋊Q8C2×D1112yescomplemented
577C2×C22⋊Q8C2×D1112yescomplemented
578C2×#121—111no—
579C2×#121—111no—
580C2×#121—114no—
581C2×#121—112no—
582C2×#121—112no—
583C2×#121—1132no—
584C2×#121—112no—
585C2×#121—112no—
586C2×#121—112no—
587C2×#121—112no—
588C2×#121—114no—
589C2×#121—1116no—
590C2×#121—114no—
591C2×#121—114no—
592C2×#121—114no—
593C2×#121C2×D1112yescomplemented
594C2×#121C2×D1114yescomplemented
595C2×#121C2×D1112yescomplemented
596C2×#120—112no—
597C2×#120—114no—
598C2×#120—114no—
599C2×#120—114no—
600C2×#120—114no—
601#520—1116no—
602C2×C4×Q8—112no—
603C2×C4×D4—114no—
604C2×C4×D4—112no—
605C2×C4×D4—112no—
606C2×C4×D4—112no—
607C2×C4×D4—114no—
608C2×C4×D4—114no—
609C2×#117—111no—
610C2×#117—112no—
611C22×C4⋊C4—112no—
612C22×C4⋊C4C2×D1111yescharacteristic, complemented
613C22×C22⋊C4—112no—
614C22×C22⋊C4—114no—
615C22×C11—22no—
616C22×C11—22no—
617C22×C11—28no—
618C22×C11—24no—
619C22×C11—24no—
620C22×C11—24no—
621C22×C11—24no—
622C22×C11—24no—
623C22×C11—24no—
624C22×C11—48no—
625C22×C11—48no—
626C22×C11C23×D414yes—
627C22×C11C23×D412yes—
628C22×C11C2×H(5,𝔽2)12yes—
629C22×C11#58512yes—
630C22×C11C2611yescharacteristic
631C2×D11—22no—
632C2×D11—24no—
633C2×D11—22no—
634C2×D11—24no—
635C2×D11—28no—
636C2×D11—216no—
637C2×D11—28no—
638C2×D11—22no—
639C2×D11—22no—
640C2×D11—28no—
641C2×D11—28no—
642C2×D11—22no—
643C2×D11—432no—
644C2×D11—416no—
645C2×D11—44no—
646C2×D11—416no—
647C2×D11—832no—
648C2×D11—816no—
649C2×D11C23×D418yes—
650C2×D11C2×H(5,𝔽2)14yescomplemented
651C4×C11—24no—
652C4×C11—24no—
653C4×C11—28no—
654C4×C11C23×D414yes—
655C4×C11C23×D414yes—
656Dic11—22no—
657Dic11—22no—
658Dic11—24no—
659Dic11—24no—
660Dic11C23×D418yes—
661C25—112no—
662C25—111no—
663C25—114no—
664C25—112no—
665H(5,𝔽2)—22128no—
666C2×#41—28no—
667C2×#41—28no—
668C2×#41—1116no—
669C2×#41—118no—
670C2×#41—1116no—
671C2×#41—118no—
672C2×#41—1116no—
673C2×#41—118no—
674C2×#41—1116no—
675C2×#41—1116no—
676C2×#41—2216no—
677C2×#41—2216no—
678C2×#41—2216no—
679C2×#41—2216no—
680C2×#41—228no—
681C2×#41—228no—
682C2×#41—22128no—
683C2×#41C22×D1118yescomplemented
684C2×#41C22×D1118yescomplemented
685C22×Q8—118no—
686C22×Q8—111no—
687C22×Q8—112no—
688C22×Q8—228no—
689C22×Q8C22×D1111yescharacteristic
690C22×Q8C22×D1111yescharacteristic
691C22×D4—112no—
692C22×D4—112no—
693C22×D4—112no—
694C22×D4—114no—
695C22×D4—112no—
696C22×D4—114no—
697C22×D4—112no—
698C22×D4—114no—
699C22×D4—1116no—
700C22×D4—1116no—
701C22×D4—118no—
702C22×D4—1132no—
703C22×D4—1132no—
704C22×D4—111no—
705C22×D4—114no—
706C22×D4—112no—
707C22×D4—114no—
708C22×D4—112no—
709C22×D4—112no—
710C22×D4—118no—
711C22×D4—1116no—
712C22×D4—114no—
713C22×D4—1116no—
714C22×D4—2216no—
715C22×D4—2216no—
716C22×D4—2216no—
717C22×D4—228no—
718C22×D4—2232no—
719C22×D4—228no—
720C22×D4—448no—
721C22×D4—4416no—
722C22×D4C22×D1112yes—
723C22×D4C22×D1112yes—
724C22×D4C22×D1111yescharacteristic
725C22×D4C22×D1111yescharacteristic
726C22×D4C22×D1114yes—
727C23×C4—112no—
728C23×C4—111no—
729C23×C4—112no—
730C23×C4—112no—
731C23×C4—112no—
732C23×C4—111no—
733C23×C4—111no—
734C23×C4—114no—
735C23×C4—111no—
736C23×C4—111no—
737C23×C4—1116no—
738C23×C4—118no—
739C23×C4—114no—
740C23×C4—2216no—
741C23×C4—228no—
742C23×C4C22×D1112yes—
743C23×C4C22×D1112yes—
744C23×C4C22×D1112yes—
745C23×C4C22×D1111yescharacteristic
746#127—1132no—
747#127—1116no—
748#124—1116no—
749#124—1132no—
750#123—1116no—
751#123—1132no—
752C22⋊Q8—118no—
753C22⋊Q8—118no—
754C22⋊Q8—1132no—
755C22⋊Q8C22×D11116yescomplemented
756C22⋊Q8C22×D11116yescomplemented
757#121—118no—
758#121—1132no—
759#121—118no—
760#121—1116no—
761#121—1116no—
762#121—1116no—
763#121—1116no—
764#121—1116no—
765#121—1116no—
766#121—1132no—
767#121—1132no—
768#121—1132no—
769#121—1132no—
770#121C22×D11116yescomplemented
771#121C22×D11132yescomplemented
772#121C22×D11116yescomplemented
773#120—1116no—
774#120—1132no—
775#120—1132no—
776#120—1132no—
777#120—1132no—
778C4×Q8—1116no—
779C4×D4—1132no—
780C4×D4—1116no—
781C4×D4—1116no—
782C4×D4—1116no—
783C4×D4—1132no—
784C4×D4—1132no—
785#117—118no—
786#117—1116no—
787C2×C4⋊C4—111no—
788C2×C4⋊C4—114no—
789C2×C4⋊C4—111no—
790C2×C4⋊C4—112no—
791C2×C4⋊C4—112no—
792C2×C4⋊C4—1116no—
793C2×C4⋊C4C22×D1112yes—
794C2×C4⋊C4C22×D1112yes—
795C2×C4⋊C4C22×D1114yes—
796C2×C4⋊C4C22×D1118yescomplemented
797C2×C22⋊C4—112no—
798C2×C22⋊C4—112no—
799C2×C22⋊C4—112no—
800C2×C22⋊C4—114no—
801C2×C22⋊C4—114no—
802C2×C22⋊C4—114no—
803C2×C22⋊C4—1116no—
804C2×C22⋊C4—114no—
805C2×C22⋊C4—112no—
806C2×C22⋊C4—114no—
807C2×C22⋊C4—112no—
808C2×C22⋊C4—1132no—
809C2×C22⋊C4C22×D1114yes—
810C2×C22⋊C4C22×D1114yes—
811C2×C42—114no—
812C2×C42—112no—
813C2×C11—24no—
814C2×C11—44no—
815C2×C11—44no—
816C2×C11#348814yescomplemented
817C2×C11C24×D411yescharacteristic
818C2×C11C22×H(5,𝔽2)11yescharacteristic
819C2×C11C2×#58511yescharacteristic
820D11—24no—
821D11—28no—
822D11—42no—
823D11—48no—
824C24—112no—
825C24—111no—
826C24—114no—
827C24—111no—
828C24—118no—
829C24—114no—
830C24—1116no—
831C24—118no—
832C24—228no—
833C24—224no—
834C24—228no—
835C24—2216no—
836C24—224no—
837C24—228no—
838C24—442no—
839C24—444no—
840C24—444no—
841C24—448no—
842C24—444no—
843C24—448no—
844C24C23×D1112yes—
845C24C23×D1112yes—
846C24C23×D1111yescharacteristic
847#41—232no—
848#41—232no—
849#41—1164no—
850#41—2264no—
851#41—2264no—
852#41—2264no—
853#41—2264no—
854#41—2232no—
855#41—2232no—
856C2×Q8—24no—
857C2×Q8—24no—
858C2×Q8—118no—
859C2×Q8—114no—
860C2×Q8—118no—
861C2×Q8—228no—
862C2×Q8—2232no—
863C2×Q8C23×D1114yes—
864C2×Q8C23×D1114yes—
865C2×D4—28no—
866C2×D4—28no—
867C2×D4—24no—
868C2×D4—24no—
869C2×D4—48no—
870C2×D4—1116no—
871C2×D4—118no—
872C2×D4—118no—
873C2×D4—118no—
874C2×D4—1116no—
875C2×D4—118no—
876C2×D4—1116no—
877C2×D4—118no—
878C2×D4—1116no—
879C2×D4—118no—
880C2×D4—114no—
881C2×D4—1116no—
882C2×D4—118no—
883C2×D4—1116no—
884C2×D4—118no—
885C2×D4—118no—
886C2×D4—1116no—
887C2×D4—2264no—
888C2×D4—2216no—
889C2×D4—228no—
890C2×D4—2216no—
891C2×D4—2264no—
892C2×D4—2216no—
893C2×D4—228no—
894C2×D4—2264no—
895C2×D4—2232no—
896C2×D4—22128no—
897C2×D4—228no—
898C2×D4—228no—
899C2×D4—228no—
900C2×D4—228no—
901C2×D4—2232no—
902C2×D4—448no—
903C2×D4—4432no—
904C2×D4—448no—
905C2×D4—448no—
906C2×D4—444no—
907C2×D4—4464no—
908C2×D4C23×D1118yes—
909C2×D4C23×D1118yes—
910C2×D4C23×D1114yes—
911C2×D4C23×D1114yes—
912C2×D4C23×D11116yes—
913C22×C4—28no—
914C22×C4—28no—
915C22×C4—44no—
916C22×C4—112no—
917C22×C4—1116no—
918C22×C4—118no—
919C22×C4—114no—
920C22×C4—118no—
921C22×C4—112no—
922C22×C4—112no—
923C22×C4—111no—
924C22×C4—111no—
925C22×C4—118no—
926C22×C4—118no—
927C22×C4—114no—
928C22×C4—114no—
929C22×C4—1116no—
930C22×C4—114no—
931C22×C4—114no—
932C22×C4—1116no—
933C22×C4—228no—
934C22×C4—2264no—
935C22×C4—2216no—
936C22×C4—228no—
937C22×C4—228no—
938C22×C4—224no—
939C22×C4—224no—
940C22×C4—224no—
941C22×C4—224no—
942C22×C4—224no—
943C22×C4—2232no—
944C22×C4—448no—
945C22×C4D4×D1118yescomplemented
946C22×C4C23×D1118yes—
947C22×C4C23×D1118yes—
948C22×C4C23×D1114yes—
949C22×C4C23×D1112yes—
950C22×C4C23×D1112yes—
951C22×C4C23×D1118yes—
952C22×C4C23×D1111yescharacteristic
953C22×C4C23×D1111yescharacteristic
954C22×C4C23×D1114yes—
955C4⋊C4—114no—
956C4⋊C4—1116no—
957C4⋊C4—114no—
958C4⋊C4—118no—
959C4⋊C4—118no—
960C4⋊C4C23×D1118yes—
961C4⋊C4C23×D1118yes—
962C4⋊C4C23×D11116yes—
963C22⋊C4—118no—
964C22⋊C4—118no—
965C22⋊C4—118no—
966C22⋊C4—1116no—
967C22⋊C4—1116no—
968C22⋊C4—1116no—
969C22⋊C4—1116no—
970C22⋊C4—118no—
971C22⋊C4—1116no—
972C22⋊C4—118no—
973C22⋊C4C23×D11116yes—
974C22⋊C4C23×D11116yes—
975C42—1116no—
976C42—118no—
977C11C2×#348811yescharacteristic, complemented, Sylow
978C23—22no—
979C23—22no—
980C23—24no—
981C23—24no—
982C23—24no—
983C23—24no—
984C23—24no—
985C23—24no—
986C23—118no—
987C23—114no—
988C23—114no—
989C23—112no—
990C23—118no—
991C23—112no—
992C23—2216no—
993C23—228no—
994C23—2216no—
995C23—2232no—
996C23—222no—
997C23—224no—
998C23—222no—
999C23—224no—
1000C23—228no—
1001C23—222no—
1002C23—228no—
1003C23—228no—
1004C23—222no—
1005C23—222no—
1006C23—228no—
1007C23—2216no—
1008C23—444no—
1009C23—448no—
1010C23—448no—
1011C23—4416no—
1012C23—448no—
1013C23—4416no—
1014C23—4416no—
1015C23—4432no—
1016C23—8816no—
1017C23—8832no—
1018C23C2×D4×D1114yes—
1019C23C24×D1114yes—
1020C23C24×D1114yes—
1021C23C24×D1112yes—
1022C23C24×D1111yescharacteristic
1023Q8—28no—
1024Q8—28no—
1025Q8—1116no—
1026Q8—2216no—
1027D4—216no—
1028D4—216no—
1029D4—28no—
1030D4—28no—
1031D4—416no—
1032D4—1132no—
1033D4—1116no—
1034D4—2232no—
1035D4—2216no—
1036D4—2232no—
1037D4—2232no—
1038D4—2216no—
1039D4—2216no—
1040D4—2216no—
1041D4—2216no—
1042D4—2216no—
1043D4—4416no—
1044D4—4416no—
1045D4—4416no—
1046D4—448no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—28no—
1050C2×C4—216no—
1051C2×C4—216no—
1052C2×C4—48no—
1053C2×C4—118no—
1054C2×C4—114no—
1055C2×C4—1132no—
1056C2×C4—114no—
1057C2×C4—114no—
1058C2×C4—112no—
1059C2×C4—112no—
1060C2×C4—2216no—
1061C2×C4—2232no—
1062C2×C4—2216no—
1063C2×C4—2216no—
1064C2×C4—222no—
1065C2×C4—222no—
1066C2×C4—228no—
1067C2×C4—224no—
1068C2×C4—224no—
1069C2×C4—228no—
1070C2×C4—228no—
1071C2×C4—228no—
1072C2×C4—228no—
1073C2×C4—4416no—
1074C2×C4C2×D4×D1114yes—
1075C2×C4C2×D4×D1114yes—
1076C2×C4C2×D4×D11116yescomplemented
1077C2×C4C24×D1118yes—
1078C2×C4C24×D1114yes—
1079C2×C4C24×D1114yes—
1080C2×C4C24×D1112yes—
1081C2×C4C24×D1112yes—
1082C22—22no—
1083C22—22no—
1084C22—28no—
1085C22—24no—
1086C22—24no—
1087C22—24no—
1088C22—24no—
1089C22—24no—
1090C22—24no—
1091C22—48no—
1092C22—48no—
1093C22—118no—
1094C22—114no—
1095C22—222no—
1096C22—224no—
1097C22—222no—
1098C22—224no—
1099C22—228no—
1100C22—2216no—
1101C22—222no—
1102C22—228no—
1103C22—228no—
1104C22—222no—
1105C22—222no—
1106C22—228no—
1107C22—4416no—
1108C22—4432no—
1109C22—444no—
1110C22—4416no—
1111C22—8816no—
1112C22—8832no—
1113C22C22×D4×D1114yes—
1114C22C22×D4×D1112yes—
1115C22D11×H(5,𝔽2)12yes—
1116C22#1062345712yes—
1117C22C25×D1111yescharacteristic
1118C4—24no—
1119C4—24no—
1120C4—28no—
1121C4—118no—
1122C4—222no—
1123C4—222no—
1124C4—224no—
1125C4—224no—
1126C4C22×D4×D1114yes—
1127C4C22×D4×D1114yes—
1128C2—24no—
1129C2—44no—
1130C2—44no—
1131C2—224no—
1132C2—228no—
1133C2—442no—
1134C2—448no—
1135C2#1308228014yesdirect product factor
1136C2C23×D4×D1111yescharacteristic
1137C2C2×D11×H(5,𝔽2)11yescharacteristic
1138C2C2×#1062345711yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#537C2
socleC23×C11C25
hypercenterC2×#537D11
hypocenterC11C2×#3488
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. C22×#67042C2semidirect
2. C22×#41×D11C2semidirect
3. #13082280C2direct (N × H)
4. C2×#10623130C2semidirect
5. C2×#10623164C2semidirect
6. C2×#10623161C2semidirect
7. C2×#10623141C2semidirect
8. C2×#10623140C2semidirect
9. C2×#10623140C2semidirect
10. C2×#10623160C2semidirect
11. C2×#10623138C2semidirect
12. C2×#10623361C2semidirect
13. C2×#10623158C2semidirect
14. C2×#10623359C2semidirect
15. C22×#66948C2semidirect
16. C2×D11×#121C2semidirect
17. C2×#10623035C2semidirect
18. C2×C11×#537C2semidirect
19. C22×C11×#41C22semidirect
20. C22×C11×#41C22semidirect
22. C2×#67042C22semidirect
24. C2×#41×D11C22semidirect
25. C22×#4343C22semidirect
26. C22×#4343C22semidirect
27. C22×Q8×D11C22semidirect
28. C22×#4341C22semidirect
29. C22×#4341C22semidirect
30. C22×D4×D11C22semidirect
31. C22×D4×D11C22semidirect
32. C22×D4×D11C22semidirect
33. C22×D4×D11C22semidirect
34. C22×D4×D11C22semidirect
36. C22×#4339C22semidirect
37. C22×#4339C22semidirect
38. C23×D44C22semidirect
39. C23×D44C22semidirect
40. C23×D44C22semidirect
41. C23×C4×D11C22semidirect
42. C23×C4×D11C22semidirect
43. C11×#537C22semidirect
44. C2×C11×C22⋊Q8C22semidirect
45. C2×C11×C22⋊Q8C22semidirect
46. C2×C11×#121C22semidirect
47. C2×C11×#121C22semidirect
48. C2×C11×#121C22semidirect
49. C22×C11×C4⋊C4C22semidirect
50. #10623361C22semidirect
51. #10623359C22semidirect
52. C2×#67000C22semidirect
53. C2×#66999C22semidirect
54. C2×#66999C22semidirect
55. C2×#66993C22semidirect
56. C2×#66993C22semidirect
57. C2×#66992C22semidirect
58. C2×#66991C22semidirect
59. C2×#66991C22semidirect
60. C2×#66990C22semidirect
61. C2×#66990C22semidirect
62. C2×#66990C22semidirect
63. C2×#66988C22semidirect
64. C2×#66983C22semidirect
65. C2×#66983C22semidirect
66. C2×C4×C22⋊D11C22semidirect
67. C2×C4×C22⋊D11C22semidirect
68. C2×C4×C22⋊D11C22semidirect
69. C22×(C2×D11)⋊C4C22semidirect
70. C2×#66979C22semidirect
71. #10623164C22semidirect
72. #10623161C22semidirect
73. #10623160C22semidirect
74. #10623158C22semidirect
75. #10623141C22semidirect
76. #10623140C22semidirect
77. #10623140C22semidirect
78. #10623138C22semidirect
79. D11×#121C22semidirect
80. #10623130C22semidirect
81. C2×#66949C22semidirect
82. C2×#66948C22semidirect
83. C2×#66948C22semidirect
84. C2×#66948C22semidirect
85. C2×#66948C22semidirect
86. C2×#66948C22semidirect
87. C2×#66948C22semidirect
88. C2×#66947C22semidirect
89. #10623035C22semidirect
90. C2×#66946C22semidirect
91. C2×#66946C22semidirect
92. C2×#66945C22semidirect
93. C2×C4⋊C4×D11C22semidirect
94. C2×#66940C22semidirect
95. C2×#66938C22semidirect
96. C2×#66937C22semidirect
97. C2×#66937C22semidirect
98. C2×#66937C22semidirect
99. C2×#66935C22semidirect
100. C2×#66935C22semidirect
101. C2×(C22⋊D11)⋊C4C22semidirect
102. C2×C22⋊C4×D11C22semidirect
109. C2×C11×#41C23semidirect
110. C2×C11×#41C23semidirect
136. C2×#4343C23semidirect
137. C2×#4343C23semidirect
139. C2×Q8×D11C23semidirect
142. C2×#4341C23semidirect
143. C2×#4341C23semidirect
149. C2×D4×D11C23semidirect
150. C2×D4×D11C23semidirect
151. C2×D4×D11C23semidirect
152. C2×D4×D11C23semidirect
153. C2×D4×D11C23semidirect
156. C2×#4339D4semidirect
158. C2×#4339C23semidirect
159. C2×#4339C23semidirect
170. C22×D44C23semidirect
171. C22×D44C23semidirect
172. C22×D44C23semidirect
184. C22×C4×D11C23semidirect
185. C22×C4×D11C23semidirect
188. C11×C22⋊Q8C23semidirect
189. C11×C22⋊Q8C23semidirect
190. C11×#121C23semidirect
191. C11×#121C23semidirect
192. C11×#121C23semidirect
196. C2×C11×C4⋊C4C23semidirect
202. #67000C23semidirect
203. #66999C23semidirect
204. #66999C23semidirect
205. #66993C23semidirect
206. #66993C23semidirect
207. #66992C23semidirect
208. #66991C23semidirect
209. #66991C23semidirect
210. #66990C23semidirect
211. #66990C23semidirect
212. #66990C23semidirect
213. #66988C23semidirect
214. #66983C23semidirect
215. #66983C23semidirect
216. C4×C22⋊D11C23semidirect
217. C4×C22⋊D11C23semidirect
218. C4×C22⋊D11C23semidirect
226. C2×(C2×D11)⋊C4C23semidirect
227. #66979C23semidirect
235. #66949C23semidirect
236. #66948C23semidirect
237. #66948C23semidirect
238. #66948C23semidirect
239. #66948C23semidirect
240. #66948C23semidirect
241. #66947C23semidirect
242. #66946C23semidirect
243. #66946C23semidirect
244. #66945C23semidirect
245. C4⋊C4×D11C23semidirect
246. #66940C23semidirect
247. #66938C23semidirect
248. #66937C23semidirect
249. #66937C23semidirect
250. #66937C23semidirect
251. #66935C23semidirect
252. #66935C23semidirect
253. (C22⋊D11)⋊C4C23semidirect
254. C22⋊C4×D11C23semidirect
298. C22×C4×C11C2×D4semidirect
315. C2×C22⋊D11C2×D4semidirect
345. #4339C2×D4semidirect
355. C2×D44C2×D4semidirect
373. C2×C4×D11C2×D4semidirect
384. C2×Dic22C2×D4semidirect
419. C2×#537D11semidirect
467. C22×D11H(5,𝔽2)semidirect
487. C2×C4×C11C22×D4semidirect
500. C22⋊D11C22×D4semidirect
519. D44C22×D4semidirect
528. C4×D11C22×D4semidirect
530. Dic22C22×D4semidirect
542. C22×#41C2×D11semidirect
543. C22×#41C2×D11semidirect
562. #537C2×D11semidirect
576. C2×C22⋊Q8C2×D11semidirect
577. C2×C22⋊Q8C2×D11semidirect
593. C2×#121C2×D11semidirect
594. C2×#121C2×D11semidirect
595. C2×#121C2×D11semidirect
612. C22×C4⋊C4C2×D11semidirect
650. C2×D11C2×H(5,𝔽2)semidirect
683. C2×#41C22×D11semidirect
684. C2×#41C22×D11semidirect
755. C22⋊Q8C22×D11semidirect
756. C22⋊Q8C22×D11semidirect
770. #121C22×D11semidirect
771. #121C22×D11semidirect
772. #121C22×D11semidirect
796. C2×C4⋊C4C22×D11semidirect
816. C2×C11#3488semidirect
945. C22×C4D4×D11semidirect
977. C11C2×#3488semidirect
1076. C2×C4C2×D4×D11semidirect
1135. C2#13082280direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670422
C22×#41×D112
#130822802
C2×#106231302
C2×#106231642
C2×#106231612
C2×#106231412
C2×#106231402
C2×#106231602
C2×#106231382
C2×#106233612
C2×#106231582
C2×#106233592
C22×#669482
C2×D11×#1212
C2×#106230352
C2×C11×#5372
C2×#348811