Finite Group Databasebeta

← C2×#13082283 #15662084

Subgroups — C2×#13082283 #15662084

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×#67037C211yesmaximal, characteristic, complemented
2C22×#41×D11C211yesmaximal, characteristic, complemented
3#13082283C2132yesmaximal, direct product factor
4C2×#10623249C212yesmaximal, complemented
5C2×#10623208C212yesmaximal, complemented
6C2×#10623207C212yesmaximal, complemented
7C2×#10623122C214yesmaximal, complemented
8C2×#10623248C212yesmaximal, complemented
9C2×#10623121C214yesmaximal, complemented
10C2×#10623139C212yesmaximal, complemented
11C2×#10623364C211yesmaximal, characteristic, complemented
12C2×#10623138C212yesmaximal, complemented
13C2×#10623055C211yesmaximal, characteristic, complemented
14C2×#10623137C212yesmaximal, complemented
15C22×#66991C211yesmaximal, characteristic, complemented
16C2×D11×#121C212yesmaximal, complemented
17C2×#10623054C211yesmaximal, characteristic, complemented
18C2×C11×#535C211yesmaximal, characteristic, complemented
19C22×C11×#41C2211yescharacteristic, complemented
20C23×D4×C11C2211yescharacteristic, complemented
21C23×C22⋊D11C2214yescomplemented
22C23×C22⋊D11C2212yescomplemented
23C2×#41×D11—216no—
24C2×#41×D11C22116yescomplemented
25C22×#4343C2211yescharacteristic, complemented
26C22×Q8×D11C2211yescharacteristic, complemented
27C2×#67037—216no—
28C2×#67037C22116yescomplemented
29C22×#4341C2212yescomplemented
30C22×#4341C2212yescomplemented
31C22×#4341C2211yescharacteristic, complemented
32C22×#4341C2212yescomplemented
33C22×D4×D11C2212yescomplemented
34C22×D4×D11C2211yescharacteristic, complemented
35C22×D4×D11C2212yescomplemented
36C22×D4×D11C2212yescomplemented
37C22×D4×D11C2214yescomplemented
38C22×#4339C2211yescharacteristic
39C22×#4339C2211yescharacteristic, complemented
40C22×#4339C2212yescomplemented
41C23×C4×D11C2212yescomplemented
42C23×C4×D11C2211yescharacteristic, complemented
43C11×#535C22116yescomplemented
44C2×C11×#127C2212yescomplemented
45C2×C11×#124C2212yescomplemented
46C2×C11×#121C2212yescomplemented
47C2×C11×#121C2212yescomplemented
48C2×C11×#120C2214yescomplemented
49C2×C11×#117C2211yescharacteristic, complemented
50C22×C22⋊Dic11C2212yescomplemented
51#10623364C22116yescomplemented
52C2×#66999C2212yescomplemented
53C2×#66993C2214yescomplemented
54C2×#66992C2214yescomplemented
55C2×#66992C2214yescomplemented
56C2×#66992C2214yescomplemented
57C2×#66991C2212yescomplemented
58C2×#66991C2212yescomplemented
59C2×#66991C2212yescomplemented
60C2×#66991C2214yescomplemented
61C2×#66991C2212yescomplemented
62C2×#66991C2212yescomplemented
63C2×#66991C22116yescomplemented
64C2×#66990C2214yescomplemented
65C2×#66990C2214yescomplemented
66C2×D4×Dic11C2214yescomplemented
67C2×#66983C2212yescomplemented
68C22×C4⋊Dic11C2211yescharacteristic, complemented
69C2×#66977C2212yescomplemented
70#10623249C22132yescomplemented
71#10623248C22132yescomplemented
72#10623208C22132yescomplemented
73#10623207C22132yescomplemented
74#10623139C22132yescomplemented
75#10623138C22132yescomplemented
76#10623137C22132yescomplemented
77D11×#121C22132yescomplemented
78#10623122C22164yescomplemented
79#10623121C22164yescomplemented
80#10623055C22116yescomplemented
81#10623054C22116yescomplemented
82C2×#66950C2211yescharacteristic, complemented
83C2×#66950C2211yescharacteristic, complemented
84C2×#66948C2211yescharacteristic, complemented
85C2×#66948C2211yescharacteristic, complemented
86C2×#66945C2212yescomplemented
87C2×C4⋊C4×D11C2212yescomplemented
88C2×#66939C2212yescomplemented
89C2×#66938C2214yescomplemented
90C2×#66937C2214yescomplemented
91C2×#66937C2214yescomplemented
92C2×#66936C2214yescomplemented
93C2×#66935C2212yescomplemented
94C2×#66935C2214yescomplemented
95C2×(C22⋊D11)⋊C4C2214yescomplemented
96C2×(C22⋊D11)⋊C4C2214yescomplemented
97C2×C22⋊C4×D11C2214yescomplemented
98C2×#66931C2214yescomplemented
99C2×C4×D44C2212yescomplemented
100C2×C4×D44C2212yescomplemented
101C2×C4×D44C2212yescomplemented
102C2×C4×Dic22C2212yescomplemented
103C25×C11C2312yes—
104C24×D11C2311yescharacteristic
105C24×D11C2312yes—
106C24×D11C2314yes—
107C2×C11×#41—28no—
108C2×C11×#41C2318yescomplemented
109C22×Q8×C11C2311yescharacteristic
110C22×D4×C11—28no—
111C22×D4×C11C2312yes—
112C22×D4×C11C2312yes—
113C22×D4×C11C2311yescharacteristic
114C22×D4×C11C2312yes—
115C22×D4×C11C2314yes—
116C22×D4×C11C2314yes—
117C22×D4×C11C2318yescomplemented
118C23×C4×C11C2312yes—
119C23×C4×C11C2311yescharacteristic
120C22×C22⋊D11—232no—
121C22×C22⋊D11—48no—
122C22×C22⋊D11C2314yes—
123C22×C22⋊D11C2312yes—
124C22×C22⋊D11C2314yes—
125C22×C22⋊D11C2314yes—
126C22×C22⋊D11C2312yes—
127C22×C22⋊D11C2312yes—
128C22×C22⋊D11C2314yes—
129C22×C22⋊D11C2314yes—
130C22×C22⋊D11C2312yes—
131C22×C22⋊D11C23132yescomplemented
132C22×C22⋊D11C23116yescomplemented
133C23×Dic11C2314yes—
134C23×Dic11C2311yescharacteristic
135C23×Dic11C2312yes—
136C23×Dic11C2312yes—
137#41×D11—2128no—
138C2×#4343—28no—
139C2×#4343C2318yescomplemented
140C2×Q8×D11—28no—
141C2×Q8×D11C2318yescomplemented
142#67037—2128no—
143C2×#4341—216no—
144C2×#4341—216no—
145C2×#4341—216no—
146C2×#4341—28no—
147C2×#4341C2318yescomplemented
148C2×#4341C23116yescomplemented
149C2×#4341C23116yescomplemented
150C2×#4341C23116yescomplemented
151C2×D4×D11—216no—
152C2×D4×D11—216no—
153C2×D4×D11—28no—
154C2×D4×D11—216no—
155C2×D4×D11—416no—
156C2×D4×D11C2318yescomplemented
157C2×D4×D11C23116yescomplemented
158C2×D4×D11C23116yescomplemented
159C2×D4×D11C23116yescomplemented
160C2×D4×D11C23132yescomplemented
161C2×#4339—28no—
162C2×#4339—216no—
163C2×#4339D4116yescomplemented
164C2×#4339C2318yes—
165C2×#4339C2318yescomplemented
166C2×#4339C23116yescomplemented
167C22×D44C2312yes—
168C22×D44C2312yes—
169C22×D44C2311yescharacteristic
170C22×D44C2312yes—
171C22×D44C2311yescharacteristic
172C22×C4×D11—28no—
173C22×C4×D11—216no—
174C22×C4×D11C2311yescharacteristic
175C22×C4×D11C2311yescharacteristic
176C22×C4×D11C2312yes—
177C22×C4×D11C2312yes—
178C22×C4×D11C2312yes—
179C22×C4×D11C2311yescharacteristic
180C22×C4×D11C2311yescharacteristic
181C22×C4×D11C2314yes—
182C22×C4×D11C2312yes—
183C22×C4×D11C2318yescomplemented
184C22×C4×D11C23116yescomplemented
185C22×Dic22C2312yes—
186C22×Dic22C2311yescharacteristic
187C22×Dic22C2311yescharacteristic
188C11×#127C23116yescomplemented
189C11×#124C23116yescomplemented
190C11×#121C23116yescomplemented
191C11×#121C23116yescomplemented
192C11×#120C23132yescomplemented
193C11×#117C2318yescomplemented
194C2×C11×C4⋊C4C2311yescharacteristic
195C2×C11×C4⋊C4C2311yescharacteristic
196C2×C11×C22⋊C4C2314yes—
197C2×C11×C22⋊C4C2312yes—
198C2×C11×C22⋊C4C2314yes—
199C2×C42×C11C2312yes—
200C2×C22⋊Dic11C2314yes—
201C2×C22⋊Dic11C2314yes—
202C2×C22⋊Dic11C2314yes—
203C2×C22⋊Dic11C23116yescomplemented
204#66999C23116yescomplemented
205#66993C23132yescomplemented
206#66992C23132yescomplemented
207#66992C23132yescomplemented
208#66992C23132yescomplemented
209#66991C23116yescomplemented
210#66991C23116yescomplemented
211#66991C23132yescomplemented
212#66991C23116yescomplemented
213#66991C23116yescomplemented
214#66991C23116yescomplemented
215#66990C23132yescomplemented
216#66990C23132yescomplemented
217D4×Dic11C23132yescomplemented
218#66983C23116yescomplemented
219C2×(C2×D11)⋊C4C2312yes—
220C2×(C2×D11)⋊C4C2312yes—
221C2×(C2×D11)⋊C4C2314yes—
222C2×(C2×D11)⋊C4C2312yes—
223C2×(C2×D11)⋊C4C2312yes—
224C2×(C2×D11)⋊C4C2314yes—
225C2×C4⋊Dic11C2312yes—
226C2×C4⋊Dic11C2312yes—
227C2×C4⋊Dic11C2312yes—
228C2×C4⋊Dic11C2312yes—
229C2×C4⋊Dic11C2318yescomplemented
230#66977C23116yescomplemented
231C2×Dic11⋊C4C2314yes—
232C2×Dic11⋊C4C2314yes—
233C2×C4×Dic11C2314yes—
234#66950C2318yescomplemented
235#66950C2318yescomplemented
236#66948C2318yescomplemented
237#66948C2318yescomplemented
238#66945C23116yescomplemented
239C4⋊C4×D11C23116yescomplemented
240#66939C23116yescomplemented
241#66938C23132yescomplemented
242#66937C23132yescomplemented
243#66937C23132yescomplemented
244#66936C23132yescomplemented
245#66935C23116yescomplemented
246#66935C23132yescomplemented
247(C22⋊D11)⋊C4C23132yescomplemented
248(C22⋊D11)⋊C4C23132yescomplemented
249C22⋊C4×D11C23132yescomplemented
250#66931C23132yescomplemented
251C4×D44C23116yescomplemented
252C4×D44C23116yescomplemented
253C4×D44C23116yescomplemented
254C4×Dic22C23116yescomplemented
255C2×#3488—111nomaximal, Sylow
256C24×C11—28no—
257C24×C11—44no—
258C24×C11—44no—
259C24×C11C2414yes—
260C24×C11C2412yes—
261C24×C11C2411yescharacteristic
262C24×C11C2418yes—
263C23×D11—24no—
264C23×D11—28no—
265C23×D11—28no—
266C23×D11—24no—
267C23×D11—216no—
268C23×D11—44no—
269C23×D11—42no—
270C23×D11—48no—
271C23×D11—48no—
272C23×D11C2412yes—
273C23×D11C2411yescharacteristic
274C23×D11C2414yes—
275C23×D11C2418yes—
276C23×D11C2412yes—
277C23×D11C2411yescharacteristic
278C23×D11C24116yes—
279C11×#41—232no—
280C2×Q8×C11—24no—
281C2×Q8×C11C2414yes—
282C2×D4×C11—28no—
283C2×D4×C11—28no—
284C2×D4×C11—28no—
285C2×D4×C11—24no—
286C2×D4×C11—232no—
287C2×D4×C11—48no—
288C2×D4×C11—48no—
289C2×D4×C11C2418yes—
290C2×D4×C11C2418yes—
291C2×D4×C11C2414yes—
292C2×D4×C11C2418yes—
293C2×D4×C11C24116yes—
294C2×D4×C11C24116yes—
295C22×C4×C11—28no—
296C22×C4×C11C2×D418yescomplemented
297C22×C4×C11C2412yes—
298C22×C4×C11C2412yes—
299C22×C4×C11C2412yes—
300C22×C4×C11C2418yes—
301C22×C4×C11C2411yescharacteristic
302C22×C4×C11C2411yescharacteristic
303C22×C4×C11C2414yes—
304C2×C22⋊D11—2128no—
305C2×C22⋊D11—28no—
306C2×C22⋊D11—216no—
307C2×C22⋊D11—28no—
308C2×C22⋊D11—28no—
309C2×C22⋊D11—216no—
310C2×C22⋊D11—216no—
311C2×C22⋊D11—48no—
312C2×C22⋊D11—48no—
313C2×C22⋊D11—432no—
314C2×C22⋊D11C2×D4116yescomplemented
315C2×C22⋊D11C24116yes—
316C2×C22⋊D11C2418yes—
317C2×C22⋊D11C24116yes—
318C2×C22⋊D11C24116yes—
319C2×C22⋊D11C2418yes—
320C2×C22⋊D11C2418yes—
321C2×C22⋊D11C24116yes—
322C2×C22⋊D11C24116yes—
323C2×C22⋊D11C2418yes—
324C22×Dic11—28no—
325C22×Dic11—216no—
326C22×Dic11—24no—
327C22×Dic11—44no—
328C22×Dic11C24116yes—
329C22×Dic11C2414yes—
330C22×Dic11C2414yes—
331C22×Dic11C2412yes—
332C22×Dic11C2411yescharacteristic
333C22×Dic11C2411yescharacteristic
334C22×Dic11C2418yes—
335C22×Dic11C2418yes—
336C22×Dic11C2412yes—
337#4343—232no—
338Q8×D11—232no—
339#4341—264no—
340#4341—264no—
341#4341—264no—
342#4341—232no—
343D4×D11—264no—
344D4×D11—264no—
345D4×D11—232no—
346D4×D11—264no—
347D4×D11—464no—
348#4339—264no—
349#4339—232no—
350#4339C2×D4164yescomplemented
351C2×D44—28no—
352C2×D44—28no—
353C2×D44—24no—
354C2×D44—44no—
355C2×D44C2×D418yescomplemented
356C2×D44C2418yes—
357C2×D44C2418yes—
358C2×D44C2414yes—
359C2×D44C2418yes—
360C2×D44C2414yes—
361C2×C4×D11—28no—
362C2×C4×D11—264no—
363C2×C4×D11—28no—
364C2×C4×D11—24no—
365C2×C4×D11—24no—
366C2×C4×D11—24no—
367C2×C4×D11—24no—
368C2×C4×D11—28no—
369C2×C4×D11—232no—
370C2×C4×D11—48no—
371C2×C4×D11C2×D4116yescomplemented
372C2×C4×D11C2414yes—
373C2×C4×D11C2414yes—
374C2×C4×D11C2418yes—
375C2×C4×D11C2418yes—
376C2×C4×D11C2418yes—
377C2×C4×D11C2414yes—
378C2×C4×D11C2414yes—
379C2×C4×D11C24116yes—
380C2×C4×D11C2418yes—
381C2×Dic22—28no—
382C2×Dic22—24no—
383C2×Dic22C2×D418yescomplemented
384C2×Dic22C2418yes—
385C2×Dic22C2414yes—
386C2×Dic22C2414yes—
387C11×C4⋊C4C2414yes—
388C11×C4⋊C4C2414yes—
389C11×C22⋊C4C24116yes—
390C11×C22⋊C4C2418yes—
391C11×C22⋊C4C24116yes—
392C42×C11C2418yes—
393C22⋊Dic11C24116yes—
394C22⋊Dic11C24116yes—
395C22⋊Dic11C24116yes—
396(C2×D11)⋊C4C2418yes—
397(C2×D11)⋊C4C2418yes—
398(C2×D11)⋊C4C24116yes—
399(C2×D11)⋊C4C2418yes—
400(C2×D11)⋊C4C2418yes—
401(C2×D11)⋊C4C24116yes—
402C4⋊Dic11C2418yes—
403C4⋊Dic11C2418yes—
404C4⋊Dic11C2418yes—
405C4⋊Dic11C2418yes—
406Dic11⋊C4C24116yes—
407Dic11⋊C4C24116yes—
408C4×Dic11C24116yes—
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—112no—
417C2×D42—114no—
418C2×#537—111no—
419C2×#537—112no—
420C2×#535—112no—
421C2×#535D1111yescharacteristic, complemented
422C2×#525—112no—
423C2×#525—111no—
424C22×#121—111no—
425C22×#121—112no—
426C2×#520—111no—
427C23×C11—22no—
428C23×C11—22no—
429C23×C11—24no—
430C23×C11—28no—
431C23×C11—28no—
432C23×C11—24no—
433C23×C11—24no—
434C23×C11—28no—
435C23×C11—216no—
436C23×C11—48no—
437C23×C11—48no—
438C23×C11—816no—
439C23×C11C22×D414yes—
440C23×C11C2518yes—
441C23×C11C2514yes—
442C23×C11C2512yes—
443C23×C11C2511yescharacteristic
444C22×D11—22no—
445C22×D11—24no—
446C22×D11—22no—
447C22×D11—24no—
448C22×D11—22no—
449C22×D11—28no—
450C22×D11—24no—
451C22×D11—24no—
452C22×D11—22no—
453C22×D11—22no—
454C22×D11—24no—
455C22×D11—216no—
456C22×D11—216no—
457C22×D11—28no—
458C22×D11—232no—
459C22×D11—48no—
460C22×D11—44no—
461C22×D11—432no—
462C22×D11—416no—
463C22×D11—416no—
464C22×D11—416no—
465C22×D11—832no—
466C22×D11C22×D418yes—
467C22×D11H(5,𝔽2)14yescomplemented
468C22×D11C2514yes—
469C22×D11C2512yes—
470C22×D11C2514yes—
471C22×D11C2512yes—
472Q8×C11—28no—
473D4×C11—216no—
474D4×C11—216no—
475D4×C11—216no—
476D4×C11—28no—
477D4×C11—416no—
478D4×C11—416no—
479C2×C4×C11—24no—
480C2×C4×C11—24no—
481C2×C4×C11—24no—
482C2×C4×C11—216no—
483C2×C4×C11C22×D414yes—
484C2×C4×C11C22×D414yes—
485C2×C4×C11C22×D4116yescomplemented
486C2×C4×C11C2514yes—
487C2×C4×C11C2514yes—
488C2×C4×C11C2514yes—
489C2×C4×C11C2512yes—
490C2×C4×C11C2512yes—
491C22⋊D11—216no—
492C22⋊D11—216no—
493C22⋊D11—232no—
494C22⋊D11—232no—
495C22⋊D11—216no—
496C22⋊D11—232no—
497C22⋊D11—416no—
498C22⋊D11—416no—
499C22⋊D11C22×D4132yescomplemented
500C2×Dic11—22no—
501C2×Dic11—24no—
502C2×Dic11—22no—
503C2×Dic11—28no—
504C2×Dic11—28no—
505C2×Dic11—216no—
506C2×Dic11—232no—
507C2×Dic11—48no—
508C2×Dic11C22×D418yes—
509C2×Dic11C2518yes—
510C2×Dic11C2514yes—
511C2×Dic11C2512yes—
512C2×Dic11C2512yes—
513C2×Dic11C2514yes—
514D44—216no—
515D44—216no—
516D44—28no—
517D44—48no—
518D44C22×D4116yescomplemented
519C4×D11—216no—
520C4×D11—28no—
521C4×D11—28no—
522C4×D11—28no—
523C4×D11—28no—
524C4×D11—216no—
525C4×D11—216no—
526C4×D11—416no—
527C4×D11C22×D4132yescomplemented
528Dic22—28no—
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—111no—
537C22×#41—112no—
538C22×#41—112no—
539C22×#41—111no—
540C22×#41—112no—
541C22×#41—111no—
542C22×#41—2216no—
543C22×#41C2×D1111yescharacteristic, complemented
544C23×Q8—111no—
545C23×D4—114no—
546C23×D4—112no—
547C23×D4—112no—
548C23×D4—111no—
549C23×D4—112no—
550C23×D4—112no—
551C23×D4—114no—
552C23×D4C2×D1111yescharacteristic, complemented
553C24×C4—112no—
554C24×C4—111no—
555#550—1132no—
556#548—1132no—
557#546—1132no—
558#546—1164no—
559D42—1132no—
560D42—1164no—
561#537—1116no—
562#537—1132no—
563#535—1132no—
564#535C2×D11116yescomplemented
565C2×#127—114no—
566C2×#127C2×D1112yescomplemented
567C2×#124—114no—
568C2×#124C2×D1112yescomplemented
569#525—1132no—
570#525—1116no—
571C2×#123—114no—
572C2×#123—112no—
573C2×C22⋊Q8—112no—
574C2×C22⋊Q8—112no—
575C2×C22⋊Q8—111no—
576C2×C22⋊Q8—111no—
577C2×C22⋊Q8—114no—
578C2×#121—112no—
579C2×#121—112no—
580C2×#121—112no—
581C2×#121—112no—
582C2×#121—114no—
583C2×#121—112no—
584C2×#121—114no—
585C2×#121—114no—
586C2×#121—114no—
587C2×#121—1116no—
588C2×#121—112no—
589C2×#121—1132no—
590C2×#121—111no—
591C2×#121—111no—
592C2×#121—114no—
593C2×#121—114no—
594C2×#121C2×D1112yescomplemented
595C2×#121C2×D1112yescomplemented
596C2×#120—114no—
597C2×#120—114no—
598C2×#120—112no—
599C2×#120—114no—
600C2×#120C2×D1114yescomplemented
601#520—1116no—
602C2×C4×Q8—112no—
603C2×C4×D4—114no—
604C2×C4×D4—114no—
605C2×C4×D4—114no—
606C2×C4×D4—112no—
607C2×C4×D4—112no—
608C2×C4×D4—112no—
609C2×#117—112no—
610C2×#117C2×D1111yescharacteristic, complemented
611C22×C4⋊C4—111no—
612C22×C4⋊C4—112no—
613C22×C22⋊C4—112no—
614C22×C22⋊C4—114no—
615C22×C11—22no—
616C22×C11—22no—
617C22×C11—28no—
618C22×C11—24no—
619C22×C11—28no—
620C22×C11—24no—
621C22×C11—28no—
622C22×C11—24no—
623C22×C11—28no—
624C22×C11—48no—
625C22×C11—416no—
626C22×C11—816no—
627C22×C11C23×D414yes—
628C22×C11C23×D412yes—
629C22×C11C2×H(5,𝔽2)12yes—
630C22×C11#58512yes—
631C22×C11C2611yescharacteristic
632C2×D11—22no—
633C2×D11—24no—
634C2×D11—22no—
635C2×D11—24no—
636C2×D11—28no—
637C2×D11—216no—
638C2×D11—24no—
639C2×D11—22no—
640C2×D11—22no—
641C2×D11—24no—
642C2×D11—24no—
643C2×D11—22no—
644C2×D11—432no—
645C2×D11—416no—
646C2×D11—44no—
647C2×D11—48no—
648C2×D11—832no—
649C2×D11C23×D418yes—
650C2×D11C2×H(5,𝔽2)14yescomplemented
651C4×C11—24no—
652C4×C11—24no—
653C4×C11—24no—
654C4×C11C23×D414yes—
655C4×C11C23×D414yes—
656Dic11—22no—
657Dic11—24no—
658Dic11—22no—
659Dic11—28no—
660Dic11C23×D418yes—
661C25—112no—
662C25—111no—
663C25—114no—
664C25C22×D1112yes—
665H(5,𝔽2)—22128no—
666C2×#41—28no—
667C2×#41—118no—
668C2×#41—1116no—
669C2×#41—1116no—
670C2×#41—1116no—
671C2×#41—118no—
672C2×#41—1116no—
673C2×#41—118no—
674C2×#41—118no—
675C2×#41—1116no—
676C2×#41—2216no—
677C2×#41—2216no—
678C2×#41—2216no—
679C2×#41—228no—
680C2×#41—2216no—
681C2×#41—228no—
682C2×#41—22128no—
683C2×#41—228no—
684C2×#41C22×D1118yescomplemented
685C22×Q8—118no—
686C22×Q8—111no—
687C22×Q8—111no—
688C22×Q8—112no—
689C22×Q8—228no—
690C22×Q8C22×D1111yescharacteristic
691C22×D4—28no—
692C22×D4—112no—
693C22×D4—114no—
694C22×D4—112no—
695C22×D4—114no—
696C22×D4—112no—
697C22×D4—114no—
698C22×D4—112no—
699C22×D4—1132no—
700C22×D4—114no—
701C22×D4—114no—
702C22×D4—1116no—
703C22×D4—1116no—
704C22×D4—1116no—
705C22×D4—118no—
706C22×D4—1116no—
707C22×D4—1132no—
708C22×D4—111no—
709C22×D4—112no—
710C22×D4—112no—
711C22×D4—111no—
712C22×D4—112no—
713C22×D4—2216no—
714C22×D4—2216no—
715C22×D4—228no—
716C22×D4—2216no—
717C22×D4—2232no—
718C22×D4—4416no—
719C22×D4—448no—
720C22×D4C22×D1112yes—
721C22×D4C22×D1112yes—
722C22×D4C22×D1112yes—
723C22×D4C22×D1111yescharacteristic
724C22×D4C22×D1114yes—
725C22×D4C22×D1114yes—
726C22×D4C22×D1118yescomplemented
727C23×C4—112no—
728C23×C4—111no—
729C23×C4—112no—
730C23×C4—114no—
731C23×C4—112no—
732C23×C4—112no—
733C23×C4—112no—
734C23×C4—111no—
735C23×C4—111no—
736C23×C4—112no—
737C23×C4—111no—
738C23×C4—111no—
739C23×C4—1116no—
740C23×C4—118no—
741C23×C4—114no—
742C23×C4—2216no—
743C23×C4—228no—
744C23×C4C22×D1112yes—
745C23×C4C22×D1111yescharacteristic
746#127—1132no—
747#127C22×D11116yescomplemented
748#124—1132no—
749#124C22×D11116yescomplemented
750#123—1132no—
751#123—1116no—
752C22⋊Q8—1116no—
753C22⋊Q8—1116no—
754C22⋊Q8—118no—
755C22⋊Q8—118no—
756C22⋊Q8—1132no—
757#121—1116no—
758#121—1116no—
759#121—1116no—
760#121—1116no—
761#121—1132no—
762#121—1132no—
763#121—1132no—
764#121—1116no—
765#121—1132no—
766#121—1116no—
767#121—118no—
768#121—118no—
769#121—1132no—
770#121—1132no—
771#121C22×D11116yescomplemented
772#121C22×D11116yescomplemented
773#120—1132no—
774#120—1132no—
775#120—1116no—
776#120—1132no—
777#120C22×D11132yescomplemented
778C4×Q8—1116no—
779C4×D4—1132no—
780C4×D4—1132no—
781C4×D4—1132no—
782C4×D4—1116no—
783C4×D4—1116no—
784C4×D4—1116no—
785#117—1116no—
786#117C22×D1118yescomplemented
787C2×C4⋊C4—112no—
788C2×C4⋊C4—114no—
789C2×C4⋊C4—112no—
790C2×C4⋊C4—118no—
791C2×C4⋊C4—112no—
792C2×C4⋊C4—114no—
793C2×C4⋊C4—112no—
794C2×C4⋊C4—1116no—
795C2×C4⋊C4C22×D1111yescharacteristic
796C2×C4⋊C4C22×D1111yescharacteristic
797C2×C22⋊C4—114no—
798C2×C22⋊C4—114no—
799C2×C22⋊C4—1116no—
800C2×C22⋊C4—114no—
801C2×C22⋊C4—112no—
802C2×C22⋊C4—114no—
803C2×C22⋊C4—114no—
804C2×C22⋊C4—112no—
805C2×C22⋊C4—112no—
806C2×C22⋊C4—112no—
807C2×C22⋊C4—1132no—
808C2×C22⋊C4C22×D1114yes—
809C2×C22⋊C4C22×D1112yes—
810C2×C22⋊C4C22×D1114yes—
811C2×C42—114no—
812C2×C42C22×D1112yes—
813C2×C11—24no—
814C2×C11—44no—
815C2×C11—48no—
816C2×C11#348814yescomplemented
817C2×C11C24×D411yescharacteristic
818C2×C11C22×H(5,𝔽2)11yescharacteristic
819C2×C11C2×#58511yescharacteristic
820D11—24no—
821D11—28no—
822D11—42no—
823D11—44no—
824C24—28no—
825C24—44no—
826C24—44no—
827C24—112no—
828C24—111no—
829C24—112no—
830C24—111no—
831C24—118no—
832C24—114no—
833C24—1116no—
834C24—228no—
835C24—224no—
836C24—228no—
837C24—2216no—
838C24—224no—
839C24—442no—
840C24—444no—
841C24—448no—
842C24—448no—
843C24C23×D1114yes—
844C24C23×D1112yes—
845C24C23×D1111yescharacteristic
846C24C23×D1118yes—
847#41—232no—
848#41—1164no—
849#41—2264no—
850#41—2264no—
851#41—2264no—
852#41—2232no—
853#41—2264no—
854#41—2232no—
855#41—2232no—
856C2×Q8—24no—
857C2×Q8—118no—
858C2×Q8—114no—
859C2×Q8—114no—
860C2×Q8—118no—
861C2×Q8—228no—
862C2×Q8—2232no—
863C2×Q8—224no—
864C2×Q8C23×D1114yes—
865C2×D4—28no—
866C2×D4—28no—
867C2×D4—28no—
868C2×D4—24no—
869C2×D4—232no—
870C2×D4—48no—
871C2×D4—48no—
872C2×D4—1116no—
873C2×D4—118no—
874C2×D4—1116no—
875C2×D4—118no—
876C2×D4—1116no—
877C2×D4—118no—
878C2×D4—1116no—
879C2×D4—118no—
880C2×D4—1116no—
881C2×D4—1116no—
882C2×D4—118no—
883C2×D4—114no—
884C2×D4—118no—
885C2×D4—118no—
886C2×D4—114no—
887C2×D4—118no—
888C2×D4—228no—
889C2×D4—228no—
890C2×D4—2264no—
891C2×D4—2216no—
892C2×D4—228no—
893C2×D4—2264no—
894C2×D4—2232no—
895C2×D4—2264no—
896C2×D4—22128no—
897C2×D4—2216no—
898C2×D4—228no—
899C2×D4—2216no—
900C2×D4—228no—
901C2×D4—224no—
902C2×D4—444no—
903C2×D4—448no—
904C2×D4—448no—
905C2×D4—4464no—
906C2×D4—4432no—
907C2×D4C23×D1118yes—
908C2×D4C23×D1118yes—
909C2×D4C23×D1118yes—
910C2×D4C23×D1114yes—
911C2×D4C23×D11116yes—
912C2×D4C23×D11116yes—
913C22×C4—28no—
914C22×C4—112no—
915C22×C4—1116no—
916C22×C4—118no—
917C22×C4—114no—
918C22×C4—118no—
919C22×C4—1116no—
920C22×C4—114no—
921C22×C4—111no—
922C22×C4—111no—
923C22×C4—112no—
924C22×C4—118no—
925C22×C4—118no—
926C22×C4—118no—
927C22×C4—114no—
928C22×C4—114no—
929C22×C4—118no—
930C22×C4—114no—
931C22×C4—114no—
932C22×C4—1116no—
933C22×C4—228no—
934C22×C4—2264no—
935C22×C4—228no—
936C22×C4—228no—
937C22×C4—2216no—
938C22×C4—224no—
939C22×C4—224no—
940C22×C4—224no—
941C22×C4—224no—
942C22×C4—224no—
943C22×C4—228no—
944C22×C4—2232no—
945C22×C4—448no—
946C22×C4—444no—
947C22×C4D4×D1118yescomplemented
948C22×C4C23×D1118yes—
949C22×C4C23×D1112yes—
950C22×C4C23×D1112yes—
951C22×C4C23×D1112yes—
952C22×C4C23×D1111yescharacteristic
953C22×C4C23×D1111yescharacteristic
954C22×C4C23×D1114yes—
955C4⋊C4—118no—
956C4⋊C4—1116no—
957C4⋊C4—118no—
958C4⋊C4—118no—
959C4⋊C4—1116no—
960C4⋊C4—118no—
961C4⋊C4C23×D1114yes—
962C4⋊C4C23×D1114yes—
963C22⋊C4—1116no—
964C22⋊C4—1116no—
965C22⋊C4—1116no—
966C22⋊C4—118no—
967C22⋊C4—1116no—
968C22⋊C4—1116no—
969C22⋊C4—118no—
970C22⋊C4—118no—
971C22⋊C4—118no—
972C22⋊C4C23×D11116yes—
973C22⋊C4C23×D1118yes—
974C22⋊C4C23×D11116yes—
975C42—1116no—
976C42C23×D1118yes—
977C11C2×#348811yescharacteristic, complemented, Sylow
978C23—22no—
979C23—22no—
980C23—24no—
981C23—28no—
982C23—24no—
983C23—28no—
984C23—24no—
985C23—28no—
986C23—216no—
987C23—48no—
988C23—48no—
989C23—816no—
990C23—118no—
991C23—114no—
992C23—114no—
993C23—112no—
994C23—114no—
995C23—112no—
996C23—2216no—
997C23—228no—
998C23—2216no—
999C23—2232no—
1000C23—222no—
1001C23—224no—
1002C23—222no—
1003C23—224no—
1004C23—228no—
1005C23—222no—
1006C23—224no—
1007C23—224no—
1008C23—222no—
1009C23—222no—
1010C23—224no—
1011C23—444no—
1012C23—448no—
1013C23—4416no—
1014C23—4416no—
1015C23—4416no—
1016C23—4432no—
1017C23—8832no—
1018C23C2×D4×D1114yes—
1019C23C24×D1118yes—
1020C23C24×D1114yes—
1021C23C24×D1112yes—
1022C23C24×D1111yescharacteristic
1023Q8—28no—
1024Q8—1116no—
1025Q8—2216no—
1026Q8—228no—
1027D4—216no—
1028D4—216no—
1029D4—216no—
1030D4—28no—
1031D4—416no—
1032D4—416no—
1033D4—1132no—
1034D4—1116no—
1035D4—2216no—
1036D4—2216no—
1037D4—2232no—
1038D4—2216no—
1039D4—2232no—
1040D4—2216no—
1041D4—2232no—
1042D4—2216no—
1043D4—228no—
1044D4—448no—
1045D4—4416no—
1046D4—4416no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—216no—
1051C2×C4—118no—
1052C2×C4—114no—
1053C2×C4—1132no—
1054C2×C4—118no—
1055C2×C4—112no—
1056C2×C4—112no—
1057C2×C4—114no—
1058C2×C4—2216no—
1059C2×C4—2216no—
1060C2×C4—2216no—
1061C2×C4—2232no—
1062C2×C4—222no—
1063C2×C4—224no—
1064C2×C4—222no—
1065C2×C4—228no—
1066C2×C4—228no—
1067C2×C4—228no—
1068C2×C4—228no—
1069C2×C4—228no—
1070C2×C4—228no—
1071C2×C4—2216no—
1072C2×C4—4416no—
1073C2×C4—448no—
1074C2×C4C2×D4×D1114yes—
1075C2×C4C2×D4×D1114yes—
1076C2×C4C2×D4×D11116yescomplemented
1077C2×C4C24×D1114yes—
1078C2×C4C24×D1114yes—
1079C2×C4C24×D1114yes—
1080C2×C4C24×D1112yes—
1081C2×C4C24×D1112yes—
1082C22—22no—
1083C22—22no—
1084C22—28no—
1085C22—24no—
1086C22—28no—
1087C22—24no—
1088C22—28no—
1089C22—24no—
1090C22—28no—
1091C22—416no—
1092C22—48no—
1093C22—816no—
1094C22—118no—
1095C22—114no—
1096C22—222no—
1097C22—224no—
1098C22—222no—
1099C22—224no—
1100C22—228no—
1101C22—2216no—
1102C22—222no—
1103C22—224no—
1104C22—224no—
1105C22—222no—
1106C22—222no—
1107C22—224no—
1108C22—4416no—
1109C22—4432no—
1110C22—444no—
1111C22—448no—
1112C22—8832no—
1113C22C22×D4×D1114yes—
1114C22C22×D4×D1112yes—
1115C22D11×H(5,𝔽2)12yes—
1116C22#1062345512yes—
1117C22C25×D1111yescharacteristic
1118C4—24no—
1119C4—24no—
1120C4—24no—
1121C4—118no—
1122C4—222no—
1123C4—224no—
1124C4—222no—
1125C4—228no—
1126C4C22×D4×D1114yes—
1127C4C22×D4×D1114yes—
1128C2—24no—
1129C2—48no—
1130C2—44no—
1131C2—224no—
1132C2—228no—
1133C2—442no—
1134C2—444no—
1135C2#1308228314yesdirect product factor
1136C2C23×D4×D1111yescharacteristic
1137C2C2×D11×H(5,𝔽2)11yescharacteristic
1138C2C2×#1062345511yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#535C2
socleC23×C11C25
hypercenterC2×#535D11
hypocenterC11C2×#3488
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#535

Complements

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

NH ≅ G/Ntype
1. C22×#67037C2semidirect
2. C22×#41×D11C2semidirect
3. #13082283C2direct (N × H)
4. C2×#10623249C2semidirect
5. C2×#10623208C2semidirect
6. C2×#10623207C2semidirect
7. C2×#10623122C2semidirect
8. C2×#10623248C2semidirect
9. C2×#10623121C2semidirect
10. C2×#10623139C2semidirect
11. C2×#10623364C2semidirect
12. C2×#10623138C2semidirect
13. C2×#10623055C2semidirect
14. C2×#10623137C2semidirect
15. C22×#66991C2semidirect
16. C2×D11×#121C2semidirect
17. C2×#10623054C2semidirect
18. C2×C11×#535C2semidirect
19. C22×C11×#41C22semidirect
20. C23×D4×C11C22semidirect
21. C23×C22⋊D11C22semidirect
22. C23×C22⋊D11C22semidirect
24. C2×#41×D11C22semidirect
25. C22×#4343C22semidirect
26. C22×Q8×D11C22semidirect
28. C2×#67037C22semidirect
29. C22×#4341C22semidirect
30. C22×#4341C22semidirect
31. C22×#4341C22semidirect
32. C22×#4341C22semidirect
33. C22×D4×D11C22semidirect
34. C22×D4×D11C22semidirect
35. C22×D4×D11C22semidirect
36. C22×D4×D11C22semidirect
37. C22×D4×D11C22semidirect
39. C22×#4339C22semidirect
40. C22×#4339C22semidirect
41. C23×C4×D11C22semidirect
42. C23×C4×D11C22semidirect
43. C11×#535C22semidirect
44. C2×C11×#127C22semidirect
45. C2×C11×#124C22semidirect
46. C2×C11×#121C22semidirect
47. C2×C11×#121C22semidirect
48. C2×C11×#120C22semidirect
49. C2×C11×#117C22semidirect
50. C22×C22⋊Dic11C22semidirect
51. #10623364C22semidirect
52. C2×#66999C22semidirect
53. C2×#66993C22semidirect
54. C2×#66992C22semidirect
55. C2×#66992C22semidirect
56. C2×#66992C22semidirect
57. C2×#66991C22semidirect
58. C2×#66991C22semidirect
59. C2×#66991C22semidirect
60. C2×#66991C22semidirect
61. C2×#66991C22semidirect
62. C2×#66991C22semidirect
63. C2×#66991C22semidirect
64. C2×#66990C22semidirect
65. C2×#66990C22semidirect
66. C2×D4×Dic11C22semidirect
67. C2×#66983C22semidirect
68. C22×C4⋊Dic11C22semidirect
69. C2×#66977C22semidirect
70. #10623249C22semidirect
71. #10623248C22semidirect
72. #10623208C22semidirect
73. #10623207C22semidirect
74. #10623139C22semidirect
75. #10623138C22semidirect
76. #10623137C22semidirect
77. D11×#121C22semidirect
78. #10623122C22semidirect
79. #10623121C22semidirect
80. #10623055C22semidirect
81. #10623054C22semidirect
82. C2×#66950C22semidirect
83. C2×#66950C22semidirect
84. C2×#66948C22semidirect
85. C2×#66948C22semidirect
86. C2×#66945C22semidirect
87. C2×C4⋊C4×D11C22semidirect
88. C2×#66939C22semidirect
89. C2×#66938C22semidirect
90. C2×#66937C22semidirect
91. C2×#66937C22semidirect
92. C2×#66936C22semidirect
93. C2×#66935C22semidirect
94. C2×#66935C22semidirect
95. C2×(C22⋊D11)⋊C4C22semidirect
96. C2×(C22⋊D11)⋊C4C22semidirect
97. C2×C22⋊C4×D11C22semidirect
98. C2×#66931C22semidirect
99. C2×C4×D44C22semidirect
100. C2×C4×D44C22semidirect
101. C2×C4×D44C22semidirect
102. C2×C4×Dic22C22semidirect
108. C2×C11×#41C23semidirect
117. C22×D4×C11C23semidirect
131. C22×C22⋊D11C23semidirect
132. C22×C22⋊D11C23semidirect
139. C2×#4343C23semidirect
141. C2×Q8×D11C23semidirect
147. C2×#4341C23semidirect
148. C2×#4341C23semidirect
149. C2×#4341C23semidirect
150. C2×#4341C23semidirect
156. C2×D4×D11C23semidirect
157. C2×D4×D11C23semidirect
158. C2×D4×D11C23semidirect
159. C2×D4×D11C23semidirect
160. C2×D4×D11C23semidirect
163. C2×#4339D4semidirect
165. C2×#4339C23semidirect
166. C2×#4339C23semidirect
183. C22×C4×D11C23semidirect
184. C22×C4×D11C23semidirect
188. C11×#127C23semidirect
189. C11×#124C23semidirect
190. C11×#121C23semidirect
191. C11×#121C23semidirect
192. C11×#120C23semidirect
193. C11×#117C23semidirect
203. C2×C22⋊Dic11C23semidirect
204. #66999C23semidirect
205. #66993C23semidirect
206. #66992C23semidirect
207. #66992C23semidirect
208. #66992C23semidirect
209. #66991C23semidirect
210. #66991C23semidirect
211. #66991C23semidirect
212. #66991C23semidirect
213. #66991C23semidirect
214. #66991C23semidirect
215. #66990C23semidirect
216. #66990C23semidirect
217. D4×Dic11C23semidirect
218. #66983C23semidirect
229. C2×C4⋊Dic11C23semidirect
230. #66977C23semidirect
234. #66950C23semidirect
235. #66950C23semidirect
236. #66948C23semidirect
237. #66948C23semidirect
238. #66945C23semidirect
239. C4⋊C4×D11C23semidirect
240. #66939C23semidirect
241. #66938C23semidirect
242. #66937C23semidirect
243. #66937C23semidirect
244. #66936C23semidirect
245. #66935C23semidirect
246. #66935C23semidirect
247. (C22⋊D11)⋊C4C23semidirect
248. (C22⋊D11)⋊C4C23semidirect
249. C22⋊C4×D11C23semidirect
250. #66931C23semidirect
251. C4×D44C23semidirect
252. C4×D44C23semidirect
253. C4×D44C23semidirect
254. C4×Dic22C23semidirect
296. C22×C4×C11C2×D4semidirect
314. C2×C22⋊D11C2×D4semidirect
350. #4339C2×D4semidirect
355. C2×D44C2×D4semidirect
371. C2×C4×D11C2×D4semidirect
383. C2×Dic22C2×D4semidirect
421. C2×#535D11semidirect
467. C22×D11H(5,𝔽2)semidirect
485. C2×C4×C11C22×D4semidirect
499. C22⋊D11C22×D4semidirect
518. D44C22×D4semidirect
527. C4×D11C22×D4semidirect
530. Dic22C22×D4semidirect
543. C22×#41C2×D11semidirect
552. C23×D4C2×D11semidirect
564. #535C2×D11semidirect
566. C2×#127C2×D11semidirect
568. C2×#124C2×D11semidirect
594. C2×#121C2×D11semidirect
595. C2×#121C2×D11semidirect
600. C2×#120C2×D11semidirect
610. C2×#117C2×D11semidirect
650. C2×D11C2×H(5,𝔽2)semidirect
684. C2×#41C22×D11semidirect
726. C22×D4C22×D11semidirect
747. #127C22×D11semidirect
749. #124C22×D11semidirect
771. #121C22×D11semidirect
772. #121C22×D11semidirect
777. #120C22×D11semidirect
786. #117C22×D11semidirect
816. C2×C11#3488semidirect
947. C22×C4D4×D11semidirect
977. C11C2×#3488semidirect
1076. C2×C4C2×D4×D11semidirect
1135. C2#13082283direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670372
C22×#41×D112
#130822832
C2×#106232492
C2×#106232082
C2×#106232072
C2×#106231222
C2×#106232482
C2×#106231212
C2×#106231392
C2×#106233642
C2×#106231382
C2×#106230552
C2×#106231372
C22×#669912
C2×D11×#1212
C2×#106230542
C2×C11×#5352
C2×#348811