Finite Group Databasebeta

← C2×#13082103 #15660732

Subgroups — C2×#13082103 #15660732

Order 2816.

12314 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#41×D11C212yesmaximal, complemented
2#13082103C2132yesmaximal, direct product factor
3C2×#10623084C211yesmaximal, characteristic, complemented
4C2×#10623258C211yesmaximal, characteristic, complemented
5C2×#10623164C212yesmaximal, complemented
6C2×#10623038C212yesmaximal, complemented
7C2×#10623185C214yesmaximal, complemented
8C2×#10623360C212yesmaximal, complemented
9C2×D4×D44C211yesmaximal, characteristic, complemented
10C2×#10623140C212yesmaximal, complemented
11C2×#10623256C211yesmaximal, characteristic, complemented
12C2×#10623127C212yesmaximal, complemented
13C2×#10623158C212yesmaximal, complemented
14C2×#10623187C214yesmaximal, complemented
15C2×C4×#4341C211yesmaximal, characteristic, complemented
16C22×#66946C212yesmaximal, complemented
17C2×C4×D4×D11C211yesmaximal, characteristic, complemented
18C2×C11×#547C211yesmaximal, characteristic, complemented
19C22×C11×#41C2212yescomplemented
20C2×#41×D11—232no—
21C2×#41×D11C22132yescomplemented
22C22×#4343C2212yescomplemented
23C22×Q8×D11C2212yescomplemented
24C22×#4341C2211yescharacteristic
25C22×#4341C2214yescomplemented
26C22×D4×D11C2211yescharacteristic
27C22×D4×D11C2214yescomplemented
28C22×D4×D11C2212yescomplemented
29C22×#4339C2214yescomplemented
30C22×#4339C2212yescomplemented
31C23×D44C2212yes—
32C23×C4×D11C2212yescomplemented
33C23×C4×D11C2214yescomplemented
34C11×#547C22116yescomplemented
35C2×C11×C4⋊Q8C2211yescharacteristic, complemented
36C2×C11×#123C2214yescomplemented
37C2×C11×C22⋊Q8C2212yescomplemented
38C2×C11×#121C2212yescomplemented
39C2×C4×D4×C11C2211yescharacteristic, complemented
40C2×C4×D4×C11C2211yescharacteristic, complemented
41C22×C11×C4⋊C4C2212yescomplemented
42#10623360C22132yescomplemented
43C2×#67000C2212yescomplemented
44C2×#66999C2212yescomplemented
45C2×#66993C2212yescomplemented
46C2×#66992C2214yescomplemented
47C2×#66990C2214yescomplemented
48C2×D4×Dic11C2211yescharacteristic, complemented
49C2×D4×Dic11C2211yescharacteristic, complemented
50C2×#66983C2212yescomplemented
51C2×#66983C2212yescomplemented
52C2×#66982C2214yescomplemented
53C2×C4×C22⋊D11C2212yescomplemented
54C2×C4×C22⋊D11C2212yescomplemented
55C22×(C2×D11)⋊C4C2214yescomplemented
56C22×C4×Dic11C2212yescomplemented
57#10623258C22116yescomplemented
58#10623256C22116yescomplemented
59#10623187C22164yescomplemented
60#10623185C22164yescomplemented
61#10623164C22132yescomplemented
62#10623158C22132yescomplemented
63#10623140C22132yescomplemented
64#10623127C22132yescomplemented
65#10623084C22116yescomplemented
66D4×D44C22116yescomplemented
67C4×D4×D11C22116yescomplemented
68C4×#4341C22116yescomplemented
69C2×#66949C2214yescomplemented
70C2×#66949C2214yescomplemented
71#10623038C22132yescomplemented
72C2×#66948C2212yescomplemented
73C2×#66948C2212yescomplemented
74C2×#66948C2212yescomplemented
75C2×#66947C2214yescomplemented
76C2×#66946C2211yescharacteristic
77C2×#66946C2212yes—
78C2×#66946C22132yescomplemented
79C2×#66946C2214yescomplemented
80C2×#66946C2212yescomplemented
81C2×#66946C2212yescomplemented
82C2×#66946C2214yescomplemented
83C2×#66946C2212yescomplemented
84C2×#66945C2211yescharacteristic, complemented
85C2×C4⋊C4×D11C2211yescharacteristic, complemented
86C2×#66941C2212yescomplemented
87C2×#66940C2211yescharacteristic, complemented
88C2×#66938C2214yescomplemented
89C2×#66937C2214yescomplemented
90C2×#66937C2214yescomplemented
91C2×#66935C2214yescomplemented
92C2×#66935C2214yescomplemented
93C2×(C22⋊D11)⋊C4C2214yescomplemented
94C2×(C22⋊D11)⋊C4C2212yescomplemented
95C2×(C22⋊D11)⋊C4C2212yescomplemented
96C2×C22⋊C4×D11C2212yescomplemented
97C2×#66930C2212yescomplemented
98C2×#66927C2211yescharacteristic, complemented
99C2×C4×D44C2211yescharacteristic
100C2×C42×D11C2211yescharacteristic, complemented
101C2×C4×Dic22C2211yescharacteristic, complemented
102C24×D11C2312yes—
103C24×D11C2314yes—
104C2×C11×#41—216no—
105C2×C11×#41C23116yescomplemented
106C22×Q8×C11C2312yes—
107C22×D4×C11C2311yescharacteristic
108C22×D4×C11C2314yes—
109C22×D4×C11C2311yescharacteristic
110C23×C4×C11C2312yes—
111C23×C4×C11C2314yes—
112C23×C4×C11C2312yes—
113C22×C22⋊D11C2312yes—
114C22×C22⋊D11C2314yes—
115C22×C22⋊D11C2314yes—
116C22×C22⋊D11C2314yes—
117C22×C22⋊D11C2312yes—
118C23×Dic11C2312yes—
119C23×Dic11C2312yes—
120C23×Dic11C2312yes—
121#41×D11—2256no—
122C2×#4343—216no—
123C2×#4343C23116yescomplemented
124C2×Q8×D11—216no—
125C2×Q8×D11C23116yescomplemented
126C2×#4341—232no—
127C2×#4341D4116yescomplemented
128C2×#4341C2318yes—
129C2×#4341C23132yescomplemented
130C2×D4×D11—216no—
131C2×D4×D11—232no—
132C2×D4×D11—28no—
133C2×D4×D11C2318yes—
134C2×D4×D11C23116yescomplemented
135C2×D4×D11C23132yescomplemented
136C2×#4339—232no—
137C2×#4339—216no—
138C2×#4339C23132yescomplemented
139C2×#4339C23116yescomplemented
140C22×D44—216no—
141C22×D44C2312yes—
142C22×D44C2312yes—
143C22×D44C2314yes—
144C22×D44C2314yes—
145C22×D44C23116yes—
146C22×D44C2312yes—
147C22×D44C2311yescharacteristic
148C22×C4×D11—232no—
149C22×C4×D11—216no—
150C22×C4×D11C2311yescharacteristic
151C22×C4×D11C2312yes—
152C22×C4×D11C2312yes—
153C22×C4×D11C2312yes—
154C22×C4×D11C2314yes—
155C22×C4×D11C2314yes—
156C22×C4×D11C2314yes—
157C22×C4×D11C2311yescharacteristic
158C22×C4×D11C2311yescharacteristic
159C22×C4×D11C23132yescomplemented
160C22×C4×D11C23116yescomplemented
161C22×Dic22C2314yes—
162C22×Dic22C2311yescharacteristic
163C11×C4⋊Q8C2318yescomplemented
164C11×#123C23132yescomplemented
165C11×C22⋊Q8C23116yescomplemented
166C11×#121C23116yescomplemented
167C4×D4×C11C2318yescomplemented
168C4×D4×C11C2318yescomplemented
169C2×C11×C4⋊C4C2311yescharacteristic
170C2×C11×C4⋊C4C2312yes—
171C2×C11×C4⋊C4C2311yescharacteristic
172C2×C11×C4⋊C4C2314yes—
173C2×C11×C4⋊C4C2312yes—
174C2×C11×C4⋊C4C23116yescomplemented
175C2×C11×C22⋊C4C2312yes—
176C2×C11×C22⋊C4C2312yes—
177C2×C11×C22⋊C4C2314yes—
178C2×C42×C11C2311yescharacteristic
179C2×C22⋊Dic11C2312yes—
180C2×C22⋊Dic11C2312yes—
181#67000C23116yescomplemented
182#66999C23116yescomplemented
183#66993C23116yescomplemented
184#66992C23132yescomplemented
185#66990C23132yescomplemented
186D4×Dic11C2318yescomplemented
187D4×Dic11C2318yescomplemented
188#66983C23116yescomplemented
189#66983C23116yescomplemented
190#66982C23132yescomplemented
191C4×C22⋊D11C23116yescomplemented
192C4×C22⋊D11C23116yescomplemented
193C2×(C2×D11)⋊C4C2312yes—
194C2×(C2×D11)⋊C4C2312yes—
195C2×(C2×D11)⋊C4C2312yes—
196C2×(C2×D11)⋊C4C2314yes—
197C2×(C2×D11)⋊C4C2314yes—
198C2×(C2×D11)⋊C4C2314yes—
199C2×(C2×D11)⋊C4C2314yes—
200C2×(C2×D11)⋊C4C2314yes—
201C2×(C2×D11)⋊C4C23132yescomplemented
202C2×C4⋊Dic11C2311yescharacteristic
203C2×C4⋊Dic11C2311yescharacteristic
204C2×Dic11⋊C4C2312yes—
205C2×Dic11⋊C4C2312yes—
206C2×Dic11⋊C4C2314yes—
207C2×Dic11⋊C4C2312yes—
208C2×C4×Dic11C2312yes—
209C2×C4×Dic11C2311yescharacteristic
210C2×C4×Dic11C2311yescharacteristic
211C2×C4×Dic11C2311yescharacteristic
212C2×C4×Dic11C2312yes—
213C2×C4×Dic11C2312yes—
214C2×C4×Dic11C23116yescomplemented
215#66949C23132yescomplemented
216#66949C23132yescomplemented
217#66948C23116yescomplemented
218#66948C23116yescomplemented
219#66948C23116yescomplemented
220#66947C23132yescomplemented
221#66946C23116yes—
222#66946C2318yes—
223#66946C23116yescomplemented
224#66946C23116yescomplemented
225#66946C23116yescomplemented
226#66946C23132yescomplemented
227#66946C23132yescomplemented
228#66945C2318yescomplemented
229C4⋊C4×D11C2318yescomplemented
230#66941C23116yescomplemented
231#66940C2318yescomplemented
232#66938C23132yescomplemented
233#66937C23132yescomplemented
234#66937C23132yescomplemented
235#66935C23132yescomplemented
236#66935C23132yescomplemented
237(C22⋊D11)⋊C4C23116yescomplemented
238(C22⋊D11)⋊C4C23116yescomplemented
239(C22⋊D11)⋊C4C23132yescomplemented
240C22⋊C4×D11C23116yescomplemented
241#66930C23116yescomplemented
242#66927C2318yescomplemented
243C4×D44C2318yes—
244C42×D11C2318yescomplemented
245C4×Dic22C2318yescomplemented
246C2×D4×#41—111nomaximal, Sylow
247C24×C11C2412yes—
248C24×C11C2412yes—
249C23×D11—216no—
250C23×D11—28no—
251C23×D11—216no—
252C23×D11—28no—
253C23×D11—44no—
254C23×D11—48no—
255C23×D11C2414yes—
256C23×D11C2418yes—
257C23×D11C24116yes—
258C23×D11C2411yescharacteristic
259C23×D11C2412yes—
260C11×#41—264no—
261C2×Q8×C11—28no—
262C2×Q8×C11C2418yes—
263C2×D4×C11—216no—
264C2×D4×C11—24no—
265C2×D4×C11C2×D418yescomplemented
266C2×D4×C11C2414yes—
267C2×D4×C11C24116yes—
268C2×D4×C11C2414yes—
269C22×C4×C11—216no—
270C22×C4×C11—28no—
271C22×C4×C11—28no—
272C22×C4×C11C2412yes—
273C22×C4×C11C2411yescharacteristic
274C22×C4×C11C2418yes—
275C22×C4×C11C2414yes—
276C22×C4×C11C2412yes—
277C22×C4×C11C24116yes—
278C22×C4×C11C2418yes—
279C22×C4×C11C2411yescharacteristic
280C22×C4×C11C2411yescharacteristic
281C2×C22⋊D11—216no—
282C2×C22⋊D11—216no—
283C2×C22⋊D11—28no—
284C2×C22⋊D11—48no—
285C2×C22⋊D11C2×D4116yescomplemented
286C2×C22⋊D11C2418yes—
287C2×C22⋊D11C24116yes—
288C2×C22⋊D11C24116yes—
289C2×C22⋊D11C24116yes—
290C2×C22⋊D11C2418yes—
291C22×Dic11—28no—
292C22×Dic11—44no—
293C22×Dic11C2×D4116yescomplemented
294C22×Dic11C2418yes—
295C22×Dic11C2411yescharacteristic
296C22×Dic11C2411yescharacteristic
297C22×Dic11C2412yes—
298C22×Dic11C2412yes—
299C22×Dic11C2418yes—
300C22×Dic11C2411yescharacteristic
301C22×Dic11C2412yes—
302C22×Dic11C2418yes—
303#4343—264no—
304Q8×D11—264no—
305#4341—2128no—
306#4341C2×D4164yescomplemented
307D4×D11—2128no—
308D4×D11—232no—
309D4×D11—264no—
310#4339—2128no—
311#4339—264no—
312C2×D44—264no—
313C2×D44—216no—
314C2×D44—216no—
315C2×D44—28no—
316C2×D44—28no—
317C2×D44—44no—
318C2×D44#4118yescomplemented
319C2×D44C2418yes—
320C2×D44C2418yes—
321C2×D44C24116yes—
322C2×D44C24116yes—
323C2×D44C2418yes—
324C2×D44C2414yes—
325C2×C4×D11—28no—
326C2×C4×D11—216no—
327C2×C4×D11—216no—
328C2×C4×D11—216no—
329C2×C4×D11—2128no—
330C2×C4×D11—264no—
331C2×C4×D11—28no—
332C2×C4×D11—28no—
333C2×C4×D11—24no—
334C2×C4×D11—42no—
335C2×C4×D11C2×D418yescomplemented
336C2×C4×D11C2414yes—
337C2×C4×D11C2418yes—
338C2×C4×D11C2418yes—
339C2×C4×D11C2418yes—
340C2×C4×D11C24116yes—
341C2×C4×D11C24116yes—
342C2×C4×D11C24116yes—
343C2×C4×D11C2414yes—
344C2×C4×D11C2414yes—
345C2×Dic22—216no—
346C2×Dic22C2×D418yescomplemented
347C2×Dic22C24116yes—
348C2×Dic22C2414yes—
349C11×C4⋊C4C2414yes—
350C11×C4⋊C4C2418yes—
351C11×C4⋊C4C2414yes—
352C11×C4⋊C4C24116yes—
353C11×C4⋊C4C2418yes—
354C11×C22⋊C4C2418yes—
355C11×C22⋊C4C2418yes—
356C11×C22⋊C4C24116yes—
357C42×C11C2414yes—
358C22⋊Dic11C2418yes—
359C22⋊Dic11C2418yes—
360(C2×D11)⋊C4C2418yes—
361(C2×D11)⋊C4C2418yes—
362(C2×D11)⋊C4C2418yes—
363(C2×D11)⋊C4C24116yes—
364(C2×D11)⋊C4C24116yes—
365(C2×D11)⋊C4C24116yes—
366(C2×D11)⋊C4C24116yes—
367(C2×D11)⋊C4C24116yes—
368C4⋊Dic11C2414yes—
369C4⋊Dic11C2414yes—
370Dic11⋊C4C2418yes—
371Dic11⋊C4C2418yes—
372Dic11⋊C4C24116yes—
373Dic11⋊C4C2418yes—
374C4×Dic11C2418yes—
375C4×Dic11C2414yes—
376C4×Dic11C2414yes—
377C4×Dic11C2414yes—
378C4×Dic11C2418yes—
379C4×Dic11C2418yes—
380C23×#41—112no—
381D4×#41—1132no—
382C2×#550—111no—
383C2×D4×Q8—111no—
384C2×#548—112no—
385C2×#547—112no—
386C2×#547D1111yescharacteristic, complemented
387C2×#546—112no—
388C2×#546—114no—
389C2×D42—112no—
390C2×D42—111no—
391C2×#532—111no—
392C2×#532—112no—
393C2×#525—114no—
394C2×#525—112no—
395C2×C4×#41—111no—
396C22×C4×D4—111no—
397C22×C4×D4—112no—
398C23×C11—24no—
399C23×C11—24no—
400C23×C11—24no—
401C23×C11—24no—
402C23×C11—24no—
403C23×C11C22×D418yes—
404C23×C11C2514yes—
405C23×C11C2514yes—
406C23×C11C2511yescharacteristic
407C22×D11—24no—
408C22×D11—22no—
409C22×D11—22no—
410C22×D11—24no—
411C22×D11—28no—
412C22×D11—232no—
413C22×D11—28no—
414C22×D11—28no—
415C22×D11—216no—
416C22×D11—232no—
417C22×D11—216no—
418C22×D11—48no—
419C22×D11—416no—
420C22×D11—432no—
421C22×D11—464no—
422C22×D11C22×D414yes—
423C22×D11C2×#4118yescomplemented
424C22×D11C2518yes—
425C22×D11C2512yes—
426C22×D11C2514yes—
427Q8×C11—216no—
428D4×C11—232no—
429D4×C11—28no—
430D4×C11C22×D4116yescomplemented
431C2×C4×C11—28no—
432C2×C4×C11—24no—
433C2×C4×C11—232no—
434C2×C4×C11—24no—
435C2×C4×C11—22no—
436C2×C4×C11—216no—
437C2×C4×C11—216no—
438C2×C4×C11C22×D414yes—
439C2×C4×C11C2×#4114yescomplemented
440C2×C4×C11C2514yes—
441C2×C4×C11C2512yes—
442C2×C4×C11C2518yes—
443C2×C4×C11C2514yes—
444C2×C4×C11C2512yes—
445C2×C4×C11C2512yes—
446C22⋊D11—232no—
447C22⋊D11—216no—
448C22⋊D11—232no—
449C22⋊D11—416no—
450C22⋊D11C22×D4132yescomplemented
451C2×Dic11—24no—
452C2×Dic11—22no—
453C2×Dic11—22no—
454C2×Dic11—24no—
455C2×Dic11—216no—
456C2×Dic11—48no—
457C2×Dic11C22×D418yes—
458C2×Dic11C22×D414yes—
459C2×Dic11C22×D4132yescomplemented
460C2×Dic11C2512yes—
461C2×Dic11C2512yes—
462C2×Dic11C2514yes—
463C2×Dic11C2514yes—
464C2×Dic11C2512yes—
465C2×Dic11C2514yes—
466D44—232no—
467D44—232no—
468D44—216no—
469D44—216no—
470D44—48no—
471D44C2×#41116yescomplemented
472C4×D11—216no—
473C4×D11—216no—
474C4×D11—28no—
475C4×D11—216no—
476C4×D11—232no—
477C4×D11—232no—
478C4×D11—232no—
479C4×D11—44no—
480C4×D11C22×D4116yescomplemented
481Dic22—232no—
482Dic22C22×D4116yescomplemented
483C22×#41—1132no—
484C22×#41—112no—
485C22×#41—111no—
486C22×#41—114no—
487C22×#41—114no—
488C22×#41—112no—
489C22×#41—2232no—
490C22×#41C2×D1112yescomplemented
491C23×Q8—112no—
492C23×D4—114no—
493C23×D4—112no—
494C23×D4—111no—
495C23×D4—112no—
496C24×C4—114no—
497C24×C4—112no—
498#550—1116no—
499D4×Q8—1116no—
500#548—1132no—
501#547—1132no—
502#547C2×D11116yescomplemented
503#546—1132no—
504#546—1164no—
505D42—1132no—
506D42—1116no—
507#532—1116no—
508#532—1132no—
509C2×C4⋊Q8—112no—
510C2×C4⋊Q8C2×D1111yescharacteristic, complemented
511C2×#127—112no—
512C2×#127—111no—
513C2×#124—112no—
514C2×#124—114no—
515#525—1164no—
516#525—1132no—
517C2×#123—114no—
518C2×#123—114no—
519C2×#123C2×D1114yescomplemented
520C2×C22⋊Q8—112no—
521C2×C22⋊Q8—114no—
522C2×C22⋊Q8—114no—
523C2×C22⋊Q8C2×D1112yescomplemented
524C2×#121—114no—
525C2×#121—112no—
526C2×#121—112no—
527C2×#121—112no—
528C2×#121—112no—
529C2×#121—112no—
530C2×#121—114no—
531C2×#121—114no—
532C2×#121C2×D1112yescomplemented
533C2×#120—114no—
534C2×#120—114no—
535C2×#120—114no—
536C4×#41—1116no—
537C2×C4×Q8—111no—
538C2×C4×Q8—111no—
539C2×C4×D4—111no—
540C2×C4×D4—111no—
541C2×C4×D4—112no—
542C2×C4×D4—112no—
543C2×C4×D4—1116no—
544C2×C4×D4—111no—
545C2×C4×D4—112no—
546C2×C4×D4—114no—
547C2×C4×D4—112no—
548C2×C4×D4—114no—
549C2×C4×D4—112no—
550C2×C4×D4—112no—
551C2×C4×D4—1132no—
552C2×C4×D4—112no—
553C2×C4×D4—112no—
554C2×C4×D4—114no—
555C2×C4×D4—111no—
556C2×C4×D4C2×D1111yescharacteristic, complemented
557C2×C4×D4C2×D1111yescharacteristic, complemented
558C2×#117—111no—
559C2×#117—112no—
560C22×C4⋊C4—111no—
561C22×C4⋊C4C2×D1112yescomplemented
562C22×C22⋊C4—114no—
563C22×C22⋊C4—112no—
564C22×C42—112no—
565C22×C42—111no—
566C22×C11—24no—
567C22×C11—24no—
568C22×C11—216no—
569C22×C11—24no—
570C22×C11—24no—
571C22×C11—24no—
572C22×C11—48no—
573C22×C11C23×D418yes—
574C22×C11C23×D412yes—
575C22×C11C22×#4112yes—
576C22×C11#58512yes—
577C22×C11C2611yescharacteristic
578C2×D11—24no—
579C2×D11—22no—
580C2×D11—24no—
581C2×D11—22no—
582C2×D11—216no—
583C2×D11—28no—
584C2×D11—28no—
585C2×D11—28no—
586C2×D11—28no—
587C2×D11—432no—
588C2×D11—464no—
589C2×D11—416no—
590C2×D11C23×D414yes—
591C2×D11C22×#4118yescomplemented
592C4×C11—24no—
593C4×C11—28no—
594C4×C11—24no—
595C4×C11—22no—
596C4×C11C23×D414yes—
597C4×C11C22×#4114yescomplemented
598Dic11—24no—
599Dic11—22no—
600Dic11—22no—
601Dic11—24no—
602Dic11C23×D418yes—
603Dic11C23×D414yes—
604C25—112no—
605C25—114no—
606C2×#41—216no—
607C2×#41—1116no—
608C2×#41—1116no—
609C2×#41—118no—
610C2×#41—1132no—
611C2×#41—1132no—
612C2×#41—1116no—
613C2×#41—2232no—
614C2×#41—2216no—
615C2×#41—2232no—
616C2×#41—2216no—
617C2×#41—22256no—
618C2×#41C22×D11116yescomplemented
619C22×Q8—1116no—
620C22×Q8—111no—
621C22×Q8—114no—
622C22×Q8—2216no—
623C22×Q8C22×D1112yes—
624C22×D4—112no—
625C22×D4—112no—
626C22×D4—114no—
627C22×D4—114no—
628C22×D4—114no—
629C22×D4—118no—
630C22×D4—1132no—
631C22×D4—1116no—
632C22×D4—111no—
633C22×D4—114no—
634C22×D4—112no—
635C22×D4—1116no—
636C22×D4—114no—
637C22×D4—112no—
638C22×D4—112no—
639C22×D4—2216no—
640C22×D4—2232no—
641C22×D4—228no—
642C22×D4—2216no—
643C22×D4C22×D1111yescharacteristic
644C22×D4C22×D1114yes—
645C22×D4C22×D1111yescharacteristic
646C23×C4—112no—
647C23×C4—111no—
648C23×C4—112no—
649C23×C4—112no—
650C23×C4—112no—
651C23×C4—111no—
652C23×C4—112no—
653C23×C4—114no—
654C23×C4—114no—
655C23×C4—112no—
656C23×C4—114no—
657C23×C4—1132no—
658C23×C4—1116no—
659C23×C4—111no—
660C23×C4—2232no—
661C23×C4—2216no—
662C23×C4C22×D1114yes—
663C23×C4C22×D1112yes—
664C23×C4C22×D1112yes—
665C4⋊Q8—1116no—
666C4⋊Q8C22×D1118yescomplemented
667#127—1116no—
668#127—118no—
669#124—1116no—
670#124—1132no—
671#123—1132no—
672#123—1132no—
673#123C22×D11132yescomplemented
674C22⋊Q8—1116no—
675C22⋊Q8—1132no—
676C22⋊Q8—1132no—
677C22⋊Q8C22×D11116yescomplemented
678#121—1132no—
679#121—1116no—
680#121—1116no—
681#121—1116no—
682#121—1116no—
683#121—1116no—
684#121—1132no—
685#121—1132no—
686#121C22×D11116yescomplemented
687#120—1132no—
688#120—1132no—
689#120—1132no—
690C4×Q8—118no—
691C4×Q8—118no—
692C4×D4—118no—
693C4×D4—118no—
694C4×D4—1116no—
695C4×D4—1116no—
696C4×D4—118no—
697C4×D4—1132no—
698C4×D4—1116no—
699C4×D4—1116no—
700C4×D4—1132no—
701C4×D4—1116no—
702C4×D4—1116no—
703C4×D4—1116no—
704C4×D4—1116no—
705C4×D4—1132no—
706C4×D4—118no—
707C4×D4C22×D1118yescomplemented
708C4×D4C22×D1118yescomplemented
709#117—118no—
710#117—1116no—
711C2×C4⋊C4—111no—
712C2×C4⋊C4—112no—
713C2×C4⋊C4—112no—
714C2×C4⋊C4—112no—
715C2×C4⋊C4—111no—
716C2×C4⋊C4—114no—
717C2×C4⋊C4—118no—
718C2×C4⋊C4C22×D1111yescharacteristic
719C2×C4⋊C4C22×D1112yes—
720C2×C4⋊C4C22×D1114yes—
721C2×C4⋊C4C22×D1111yescharacteristic
722C2×C4⋊C4C22×D1112yes—
723C2×C4⋊C4C22×D11116yescomplemented
724C2×C22⋊C4—112no—
725C2×C22⋊C4—112no—
726C2×C22⋊C4—112no—
727C2×C22⋊C4—114no—
728C2×C22⋊C4—112no—
729C2×C22⋊C4—114no—
730C2×C22⋊C4—114no—
731C2×C22⋊C4—1132no—
732C2×C22⋊C4—112no—
733C2×C22⋊C4—114no—
734C2×C22⋊C4—114no—
735C2×C22⋊C4—1116no—
736C2×C22⋊C4C22×D1112yes—
737C2×C22⋊C4C22×D1112yes—
738C2×C22⋊C4C22×D1114yes—
739C2×C42—112no—
740C2×C42—111no—
741C2×C42—111no—
742C2×C42—112no—
743C2×C42—111no—
744C2×C42—112no—
745C2×C42—1116no—
746C2×C42—118no—
747C2×C42C22×D1111yescharacteristic
748C2×C11—28no—
749C2×C11—44no—
750C2×C11D4×#4114yescomplemented
751C2×C11C24×D411yescharacteristic
752C2×C11C23×#4111yescharacteristic
753C2×C11C2×#58511yescharacteristic
754D11—28no—
755D11—24no—
756D11—48no—
757C24—112no—
758C24—111no—
759C24—114no—
760C24—118no—
761C24—1116no—
762C24—228no—
763C24—2216no—
764C24—228no—
765C24—2216no—
766C24—448no—
767C24—444no—
768C24C23×D1112yes—
769C24C23×D1112yes—
770#41—264no—
771#41—1164no—
772#41—22128no—
773#41—2264no—
774#41—22128no—
775#41—2264no—
776C2×Q8—28no—
777C2×Q8—118no—
778C2×Q8—114no—
779C2×Q8—1116no—
780C2×Q8—2216no—
781C2×Q8—2264no—
782C2×Q8C23×D1118yes—
783C2×D4—216no—
784C2×D4—24no—
785C2×D4—1116no—
786C2×D4—118no—
787C2×D4—118no—
788C2×D4—1116no—
789C2×D4—1116no—
790C2×D4—1116no—
791C2×D4—118no—
792C2×D4—114no—
793C2×D4—1116no—
794C2×D4—118no—
795C2×D4—1116no—
796C2×D4—118no—
797C2×D4—118no—
798C2×D4—2264no—
799C2×D4—2216no—
800C2×D4—2216no—
801C2×D4—2216no—
802C2×D4—22128no—
803C2×D4—2232no—
804C2×D4—228no—
805C2×D4—2216no—
806C2×D4—2264no—
807C2×D4—228no—
808C2×D4—228no—
809C2×D4—444no—
810C2×D4—448no—
811C2×D4D4×D1118yescomplemented
812C2×D4C23×D1114yes—
813C2×D4C23×D11116yes—
814C2×D4C23×D1114yes—
815C22×C4—216no—
816C22×C4—28no—
817C22×C4—28no—
818C22×C4—1116no—
819C22×C4—118no—
820C22×C4—111no—
821C22×C4—112no—
822C22×C4—118no—
823C22×C4—114no—
824C22×C4—118no—
825C22×C4—111no—
826C22×C4—111no—
827C22×C4—112no—
828C22×C4—112no—
829C22×C4—118no—
830C22×C4—114no—
831C22×C4—118no—
832C22×C4—118no—
833C22×C4—1116no—
834C22×C4—1116no—
835C22×C4—118no—
836C22×C4—1116no—
837C22×C4—114no—
838C22×C4—228no—
839C22×C4—2216no—
840C22×C4—2216no—
841C22×C4—2216no—
842C22×C4—22128no—
843C22×C4—2264no—
844C22×C4—228no—
845C22×C4—228no—
846C22×C4—228no—
847C22×C4—224no—
848C22×C4—442no—
849C22×C4—444no—
850C22×C4C23×D1118yes—
851C22×C4C23×D11116yes—
852C22×C4C23×D1118yes—
853C22×C4C23×D1112yes—
854C22×C4C23×D1111yescharacteristic
855C22×C4C23×D1112yes—
856C22×C4C23×D1114yes—
857C22×C4C23×D1111yescharacteristic
858C22×C4C23×D1111yescharacteristic
859C4⋊C4—114no—
860C4⋊C4—118no—
861C4⋊C4—118no—
862C4⋊C4—118no—
863C4⋊C4—114no—
864C4⋊C4—1116no—
865C4⋊C4C23×D1114yes—
866C4⋊C4C23×D1118yes—
867C4⋊C4C23×D11116yes—
868C4⋊C4C23×D1114yes—
869C4⋊C4C23×D1118yes—
870C22⋊C4—118no—
871C22⋊C4—118no—
872C22⋊C4—118no—
873C22⋊C4—1116no—
874C22⋊C4—118no—
875C22⋊C4—1116no—
876C22⋊C4—1116no—
877C22⋊C4—118no—
878C22⋊C4—1116no—
879C22⋊C4—1116no—
880C22⋊C4C23×D1118yes—
881C22⋊C4C23×D1118yes—
882C22⋊C4C23×D11116yes—
883C42—114no—
884C42—118no—
885C42—114no—
886C42—118no—
887C42—114no—
888C42—118no—
889C42C23×D1114yes—
890C11C2×D4×#4111yescharacteristic, complemented, Sylow
891C23—24no—
892C23—24no—
893C23—24no—
894C23—24no—
895C23—24no—
896C23—114no—
897C23—118no—
898C23—114no—
899C23—112no—
900C23—118no—
901C23—2216no—
902C23—2232no—
903C23—2216no—
904C23—224no—
905C23—222no—
906C23—222no—
907C23—224no—
908C23—2232no—
909C23—228no—
910C23—228no—
911C23—228no—
912C23—4416no—
913C23—448no—
914C23—4464no—
915C23—4432no—
916C23C2×D4×D1118yes—
917C23C24×D1114yes—
918C23C24×D1114yes—
919C23C24×D1111yescharacteristic
920Q8—216no—
921Q8—1116no—
922Q8—2232no—
923D4—232no—
924D4—28no—
925D4—1132no—
926D4—1116no—
927D4—2232no—
928D4—2232no—
929D4—2232no—
930D4—2216no—
931D4—2232no—
932D4—2216no—
933D4—2216no—
934D4—448no—
935D4—4416no—
936D4C2×D4×D11116yescomplemented
937C2×C4—24no—
938C2×C4—28no—
939C2×C4—232no—
940C2×C4—24no—
941C2×C4—22no—
942C2×C4—216no—
943C2×C4—216no—
944C2×C4—114no—
945C2×C4—118no—
946C2×C4—1132no—
947C2×C4—112no—
948C2×C4—114no—
949C2×C4—1116no—
950C2×C4—112no—
951C2×C4—112no—
952C2×C4—114no—
953C2×C4—114no—
954C2×C4—2216no—
955C2×C4—2232no—
956C2×C4—2232no—
957C2×C4—2232no—
958C2×C4—2216no—
959C2×C4—2216no—
960C2×C4—224no—
961C2×C4—222no—
962C2×C4—222no—
963C2×C4—224no—
964C2×C4—2216no—
965C2×C4—228no—
966C2×C4—444no—
967C2×C4—448no—
968C2×C4C2×D4×D1114yes—
969C2×C4#41×D1114yescomplemented
970C2×C4C24×D1114yes—
971C2×C4C24×D1112yes—
972C2×C4C24×D1114yes—
973C2×C4C24×D1118yes—
974C2×C4C24×D1112yes—
975C2×C4C24×D1112yes—
976C22—24no—
977C22—24no—
978C22—216no—
979C22—24no—
980C22—24no—
981C22—24no—
982C22—48no—
983C22—114no—
984C22—118no—
985C22—224no—
986C22—222no—
987C22—222no—
988C22—224no—
989C22—2216no—
990C22—228no—
991C22—228no—
992C22—228no—
993C22—228no—
994C22—4464no—
995C22—4432no—
996C22—4416no—
997C22C22×D4×D1118yes—
998C22C22×D4×D1112yes—
999C22C2×#41×D1112yes—
1000C22#1062345712yes—
1001C22C25×D1111yescharacteristic
1002C4—24no—
1003C4—28no—
1004C4—24no—
1005C4—22no—
1006C4—114no—
1007C4—118no—
1008C4—224no—
1009C4—222no—
1010C4—222no—
1011C4—224no—
1012C4C22×D4×D1114yes—
1013C4C2×#41×D1114yescomplemented
1014C2—28no—
1015C2—44no—
1016C2—228no—
1017C2—224no—
1018C2—448no—
1019C2#1308210314yesdirect product factor
1020C2C23×D4×D1111yescharacteristic
1021C2C22×#41×D1111yescharacteristic
1022C2C2×#1062345711yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#547C2
socleC23×C11C25
hypercenterC2×#547D11
hypocenterC11C2×D4×#41
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C22×#41×D11C2semidirect
2. #13082103C2direct (N × H)
3. C2×#10623084C2semidirect
4. C2×#10623258C2semidirect
5. C2×#10623164C2semidirect
6. C2×#10623038C2semidirect
7. C2×#10623185C2semidirect
8. C2×#10623360C2semidirect
9. C2×D4×D44C2semidirect
10. C2×#10623140C2semidirect
11. C2×#10623256C2semidirect
12. C2×#10623127C2semidirect
13. C2×#10623158C2semidirect
14. C2×#10623187C2semidirect
15. C2×C4×#4341C2semidirect
16. C22×#66946C2semidirect
17. C2×C4×D4×D11C2semidirect
18. C2×C11×#547C2semidirect
19. C22×C11×#41C22semidirect
21. C2×#41×D11C22semidirect
22. C22×#4343C22semidirect
23. C22×Q8×D11C22semidirect
25. C22×#4341C22semidirect
27. C22×D4×D11C22semidirect
28. C22×D4×D11C22semidirect
29. C22×#4339C22semidirect
30. C22×#4339C22semidirect
32. C23×C4×D11C22semidirect
33. C23×C4×D11C22semidirect
34. C11×#547C22semidirect
35. C2×C11×C4⋊Q8C22semidirect
36. C2×C11×#123C22semidirect
37. C2×C11×C22⋊Q8C22semidirect
38. C2×C11×#121C22semidirect
39. C2×C4×D4×C11C22semidirect
40. C2×C4×D4×C11C22semidirect
41. C22×C11×C4⋊C4C22semidirect
42. #10623360C22semidirect
43. C2×#67000C22semidirect
44. C2×#66999C22semidirect
45. C2×#66993C22semidirect
46. C2×#66992C22semidirect
47. C2×#66990C22semidirect
48. C2×D4×Dic11C22semidirect
49. C2×D4×Dic11C22semidirect
50. C2×#66983C22semidirect
51. C2×#66983C22semidirect
52. C2×#66982C22semidirect
53. C2×C4×C22⋊D11C22semidirect
54. C2×C4×C22⋊D11C22semidirect
55. C22×(C2×D11)⋊C4C22semidirect
56. C22×C4×Dic11C22semidirect
57. #10623258C22semidirect
58. #10623256C22semidirect
59. #10623187C22semidirect
60. #10623185C22semidirect
61. #10623164C22semidirect
62. #10623158C22semidirect
63. #10623140C22semidirect
64. #10623127C22semidirect
65. #10623084C22semidirect
66. D4×D44C22semidirect
67. C4×D4×D11C22semidirect
68. C4×#4341C22semidirect
69. C2×#66949C22semidirect
70. C2×#66949C22semidirect
71. #10623038C22semidirect
72. C2×#66948C22semidirect
73. C2×#66948C22semidirect
74. C2×#66948C22semidirect
75. C2×#66947C22semidirect
78. C2×#66946C22semidirect
79. C2×#66946C22semidirect
80. C2×#66946C22semidirect
81. C2×#66946C22semidirect
82. C2×#66946C22semidirect
83. C2×#66946C22semidirect
84. C2×#66945C22semidirect
85. C2×C4⋊C4×D11C22semidirect
86. C2×#66941C22semidirect
87. C2×#66940C22semidirect
88. C2×#66938C22semidirect
89. C2×#66937C22semidirect
90. C2×#66937C22semidirect
91. C2×#66935C22semidirect
92. C2×#66935C22semidirect
93. C2×(C22⋊D11)⋊C4C22semidirect
94. C2×(C22⋊D11)⋊C4C22semidirect
95. C2×(C22⋊D11)⋊C4C22semidirect
96. C2×C22⋊C4×D11C22semidirect
97. C2×#66930C22semidirect
98. C2×#66927C22semidirect
100. C2×C42×D11C22semidirect
101. C2×C4×Dic22C22semidirect
105. C2×C11×#41C23semidirect
123. C2×#4343C23semidirect
125. C2×Q8×D11C23semidirect
127. C2×#4341D4semidirect
129. C2×#4341C23semidirect
134. C2×D4×D11C23semidirect
135. C2×D4×D11C23semidirect
138. C2×#4339C23semidirect
139. C2×#4339C23semidirect
159. C22×C4×D11C23semidirect
160. C22×C4×D11C23semidirect
163. C11×C4⋊Q8C23semidirect
164. C11×#123C23semidirect
165. C11×C22⋊Q8C23semidirect
166. C11×#121C23semidirect
167. C4×D4×C11C23semidirect
168. C4×D4×C11C23semidirect
174. C2×C11×C4⋊C4C23semidirect
181. #67000C23semidirect
182. #66999C23semidirect
183. #66993C23semidirect
184. #66992C23semidirect
185. #66990C23semidirect
186. D4×Dic11C23semidirect
187. D4×Dic11C23semidirect
188. #66983C23semidirect
189. #66983C23semidirect
190. #66982C23semidirect
191. C4×C22⋊D11C23semidirect
192. C4×C22⋊D11C23semidirect
201. C2×(C2×D11)⋊C4C23semidirect
214. C2×C4×Dic11C23semidirect
215. #66949C23semidirect
216. #66949C23semidirect
217. #66948C23semidirect
218. #66948C23semidirect
219. #66948C23semidirect
220. #66947C23semidirect
223. #66946C23semidirect
224. #66946C23semidirect
225. #66946C23semidirect
226. #66946C23semidirect
227. #66946C23semidirect
228. #66945C23semidirect
229. C4⋊C4×D11C23semidirect
230. #66941C23semidirect
231. #66940C23semidirect
232. #66938C23semidirect
233. #66937C23semidirect
234. #66937C23semidirect
235. #66935C23semidirect
236. #66935C23semidirect
237. (C22⋊D11)⋊C4C23semidirect
238. (C22⋊D11)⋊C4C23semidirect
239. (C22⋊D11)⋊C4C23semidirect
240. C22⋊C4×D11C23semidirect
241. #66930C23semidirect
242. #66927C23semidirect
244. C42×D11C23semidirect
245. C4×Dic22C23semidirect
265. C2×D4×C11C2×D4semidirect
285. C2×C22⋊D11C2×D4semidirect
293. C22×Dic11C2×D4semidirect
306. #4341C2×D4semidirect
318. C2×D44#41semidirect
335. C2×C4×D11C2×D4semidirect
346. C2×Dic22C2×D4semidirect
386. C2×#547D11semidirect
423. C22×D11C2×#41semidirect
430. D4×C11C22×D4semidirect
439. C2×C4×C11C2×#41semidirect
450. C22⋊D11C22×D4semidirect
459. C2×Dic11C22×D4semidirect
471. D44C2×#41semidirect
480. C4×D11C22×D4semidirect
482. Dic22C22×D4semidirect
490. C22×#41C2×D11semidirect
502. #547C2×D11semidirect
510. C2×C4⋊Q8C2×D11semidirect
519. C2×#123C2×D11semidirect
523. C2×C22⋊Q8C2×D11semidirect
532. C2×#121C2×D11semidirect
556. C2×C4×D4C2×D11semidirect
557. C2×C4×D4C2×D11semidirect
561. C22×C4⋊C4C2×D11semidirect
591. C2×D11C22×#41semidirect
597. C4×C11C22×#41semidirect
618. C2×#41C22×D11semidirect
666. C4⋊Q8C22×D11semidirect
673. #123C22×D11semidirect
677. C22⋊Q8C22×D11semidirect
686. #121C22×D11semidirect
707. C4×D4C22×D11semidirect
708. C4×D4C22×D11semidirect
723. C2×C4⋊C4C22×D11semidirect
750. C2×C11D4×#41semidirect
811. C2×D4D4×D11semidirect
890. C11C2×D4×#41semidirect
936. D4C2×D4×D11semidirect
969. C2×C4#41×D11semidirect
1013. C4C2×#41×D11semidirect
1019. C2#13082103direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#41×D112
#130821032
C2×#106230842
C2×#106232582
C2×#106231642
C2×#106230382
C2×#106231852
C2×#106233602
C2×D4×D442
C2×#106231402
C2×#106232562
C2×#106231272
C2×#106231582
C2×#106231872
C2×C4×#43412
C22×#669462
C2×C4×D4×D112
C2×C11×#5472
C2×D4×#4111