Finite Group Databasebeta

← #14912349

Subgroups — #14912349

Order 2816.

5406 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66979C212yesmaximal, complemented
2#13071208C218yesmaximal, complemented
3#13071202C212yesmaximal, complemented
4#13071198C212yesmaximal, complemented
5#13071194C214yesmaximal, complemented
6#13071107C218yesmaximal, complemented
7#13070999C214yesmaximal, complemented
8C23×C11×#41C211yesmaximal, characteristic
9C22×C11×#41—216no—
10C22×C11×#41C4116yescomplemented
11C22×C11×#41C2214yes—
12C22×C11×#41C2214yes—
13C23×Q8×C11C2211yescharacteristic
14C23×D4×C11C2212yes—
15C23×D4×C11C2211yescharacteristic
16C24×C4×C11C2212yes—
17C24×C4×C11C2211yescharacteristic
18C22×C22⋊Dic11C2214yes—
19C2×#66979—216no—
20C2×#66979C2214yes—
21C2×#66979C2214yes—
22C2×#66979C2214yescomplemented
23C2×#66979C2214yescomplemented
24C22×C4⋊Dic11C2214yescomplemented
25C22×C4×Dic11C2214yescomplemented
26#10622860C2218yes—
27#10622843C22116yescomplemented
28#10622834C22116yescomplemented
29#10622833C22132yescomplemented
30#10622825C22116yescomplemented
31#10622824C2218yes—
32C4×C22⋊Dic11C22116yescomplemented
33C25×C11C2312yes—
34C25×C11C2311yescharacteristic
35C2×C11×#41—2128no—
36C2×C11×#41—216no—
37C2×C11×#41—216no—
38C2×C11×#41—216no—
39C2×C11×#41—216no—
40C2×C11×#41C2×C4132yescomplemented
41C2×C11×#41C2×C4132yescomplemented
42C22×Q8×C11—28no—
43C22×Q8×C11C2×C418yescomplemented
44C22×Q8×C11C2314yes—
45C22×D4×C11—216no—
46C22×D4×C11—28no—
47C22×D4×C11C2×C4116yes—
48C22×D4×C11C2×C418yescomplemented
49C22×D4×C11C2318yes—
50C22×D4×C11C2314yes—
51C23×C4×C11—216no—
52C23×C4×C11C2×C418yes—
53C23×C4×C11C2×C4116yescomplemented
54C23×C4×C11D4116yes—
55C23×C4×C11C2314yes—
56C23×C4×C11C2312yes—
57C23×C4×C11C2314yes—
58C23×C4×C11C2312yes—
59C23×C4×C11C2312yes—
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×Dic11C2318yes—
63C2×C22⋊Dic11—216no—
64C2×C22⋊Dic11C2318yes—
65C2×C22⋊Dic11C2318yes—
66C2×C22⋊Dic11C23132yes—
67#66979—216no—
68#66979—216no—
69#66979—216no—
70#66979—216no—
71C2×C4⋊Dic11—216no—
72C2×C4⋊Dic11C2318yes—
73C2×C4⋊Dic11C2318yes—
74C2×C4×Dic11—216no—
75C2×C4×Dic11C2318yes—
76C2×C4×Dic11C2318yes—
77C11⋊#95C23132yes—
78#34044—111nomaximal, Sylow
79C24×C11—28no—
80C24×C11—44no—
81C24×C11—48no—
82C24×C11C22×C418yes—
83C24×C11C22×C414yes—
84C24×C11C2×D418yes—
85C24×C11C2414yes—
86C24×C11C2411yescharacteristic
87C24×C11C2412yes—
88C11×#41—2128no—
89C11×#41—2128no—
90C2×Q8×C11—232no—
91C2×Q8×C11—28no—
92C2×Q8×C11—28no—
93C2×Q8×C11C22×C4116yes—
94C2×D4×C11—264no—
95C2×D4×C11—216no—
96C2×D4×C11—216no—
97C2×D4×C11—232no—
98C2×D4×C11—28no—
99C2×D4×C11—28no—
100C2×D4×C11C22×C4132yes—
101C2×D4×C11C22×C4116yes—
102C22×C4×C11—28no—
103C22×C4×C11—264no—
104C22×C4×C11—216no—
105C22×C4×C11—216no—
106C22×C4×C11C22⋊C4164yescomplemented
107C22×C4×C11C22×C418yes—
108C22×C4×C11C22×C4116yes—
109C22×C4×C11C22×C4116yes—
110C22×C4×C11C22×C414yes—
111C22×C4×C11C22×C414yes—
112C22×C4×C11C22×C418yes—
113C22×C4×C11C22×C418yes—
114C22×C4×C11C2×D418yes—
115C22×C4×C11C2×D418yes—
116C22×C4×C11C2×D418yes—
117C22×C4×C11C2×D418yes—
118C22×C4×C11C2×D418yes—
119C22×C4×C11C2×D418yes—
120C22×C4×C11C2414yes—
121C22×C4×C11C2412yes—
122C22×C4×C11C2411yescharacteristic
123C22×C4×C11C2411yescharacteristic
124C22×Dic11—216no—
125C22×Dic11—416no—
126C22×Dic11C24116yes—
127C22⋊Dic11—216no—
128C22⋊Dic11—216no—
129C22⋊Dic11—432no—
130C4⋊Dic11—216no—
131C4⋊Dic11—216no—
132C4×Dic11—216no—
133C4×Dic11—216no—
134C23×#41D1111yescharacteristic
135C22×#117—112no—
136#2311—118no—
137#2310—112no—
138#2309—112no—
139#2308—114no—
140#2297—118no—
141#2280—114no—
142C23×C11—28no—
143C23×C11—24no—
144C23×C11—216no—
145C23×C11—28no—
146C23×C11—216no—
147C23×C11—48no—
148C23×C11—416no—
149C23×C11—416no—
150C23×C11—432no—
151C23×C11C2×C22⋊C4116yes—
152C23×C11C23×C418yes—
153C23×C11C23×C412yes—
154C23×C11C23×C414yes—
155C23×C11C22×D414yes—
156C23×C11C22×D414yes—
157C23×C11C22×D414yes—
158C23×C11C2511yescharacteristic
159Q8×C11—232no—
160D4×C11—264no—
161D4×C11—232no—
162C2×C4×C11—216no—
163C2×C4×C11—28no—
164C2×C4×C11—232no—
165C2×C4×C11—232no—
166C2×C4×C11C2×C22⋊C4116yes—
167C2×C4×C11C2×C22⋊C4116yes—
168C2×C4×C11C2×C22⋊C4132yes—
169C2×C4×C11C2×C22⋊C4132yes—
170C2×C4×C11C23×C418yes—
171C2×C4×C11C23×C412yes—
172C2×C4×C11C23×C412yes—
173C2×C4×C11C23×C414yes—
174C2×C4×C11C22×D414yes—
175C2×C4×C11C22×D414yes—
176C2×C4×C11C22×D414yes—
177C2×C4×C11C22×D414yes—
178C2×Dic11—216no—
179C2×Dic11—232no—
180C2×Dic11—432no—
181C22×#41—216no—
182C22×#41Dic11116yescomplemented
183C22×#41C2×D1114yes—
184C22×#41C2×D1114yes—
185C23×Q8C2×D1111yescharacteristic
186C23×D4C2×D1112yes—
187C23×D4C2×D1111yescharacteristic
188C24×C4C2×D1112yes—
189C24×C4C2×D1111yescharacteristic
190C2×#117—114no—
191C2×#117—114no—
192C2×#117—114no—
193C2×#117—114no—
194C2×#117—2216no—
195C22×C4⋊C4—114no—
196C22×C22⋊C4—114no—
197C22×C42—114no—
198#391—1116no—
199#390—1116no—
200#386—1132no—
201#381—118no—
202#380—1116no—
203#379—118no—
204C4×C22⋊C4—1116no—
205C22×C11—24no—
206C22×C11—28no—
207C22×C11—28no—
208C22×C11—28no—
209C22×C11—28no—
210C22×C11—28no—
211C22×C11—216no—
212C22×C11—416no—
213C22×C11—432no—
214C22×C11—416no—
215C22×C11C22×C22⋊C414yes—
216C22×C11C22×C22⋊C418yes—
217C22×C11C24×C411yescharacteristic
218C22×C11C23×D412yes—
219C22×C11#58514yes—
220C4×C11—28no—
221C4×C11C22×C22⋊C414yes—
222C4×C11C22×C22⋊C414yes—
223C4×C11C22×C22⋊C418yes—
224Dic11—416no—
225C25C22×D1112yes—
226C25C22×D1111yescharacteristic
227C2×#41—2128no—
228C2×#41—216no—
229C2×#41—216no—
230C2×#41—216no—
231C2×#41—216no—
232C2×#41C2×Dic11132yescomplemented
233C2×#41C2×Dic11132yescomplemented
234C22×Q8—28no—
235C22×Q8C2×Dic1118yescomplemented
236C22×Q8C22×D1114yes—
237C22×D4—216no—
238C22×D4—28no—
239C22×D4C2×Dic11116yes—
240C22×D4C2×Dic1118yescomplemented
241C22×D4C22×D1118yes—
242C22×D4C22×D1114yes—
243C23×C4—216no—
244C23×C4—118no—
245C23×C4C2×Dic1118yes—
246C23×C4C2×Dic11116yescomplemented
247C23×C4C22⋊D11116yes—
248C23×C4C22×D1112yes—
249C23×C4C22×D1114yes—
250C23×C4C22×D1114yes—
251C23×C4C22×D1112yes—
252C23×C4C22×D1111yescharacteristic
253C23×C4C22×D1111yescharacteristic
254C23×C4C22×D1112yes—
255#117—2216no—
256#117—2216no—
257#117—2216no—
258#117—2216no—
259C2×C4⋊C4—118no—
260C2×C4⋊C4—118no—
261C2×C4⋊C4—2216no—
262C2×C22⋊C4—118no—
263C2×C22⋊C4—118no—
264C2×C22⋊C4—1132no—
265C2×C22⋊C4—2216no—
266C2×C42—118no—
267C2×C42—118no—
268C2×C42—2216no—
269#95—1132no—
270C2×C11—24no—
271C2×C11—28no—
272C2×C11—48no—
273C2×C11C23×C22⋊C411yescharacteristic
274C2×C11#342812yes—
275C2×C11#344914yes—
276C24—28no—
277C24—44no—
278C24—48no—
279C24C22×Dic1118yes—
280C24C22×Dic1114yes—
281C24C2×C22⋊D1118yes—
282C24C23×D1114yes—
283C24C23×D1111yescharacteristic
284C24C23×D1112yes—
285#41—2128no—
286#41—2128no—
287C2×Q8—232no—
288C2×Q8—28no—
289C2×Q8—28no—
290C2×Q8C22×Dic11116yes—
291C2×D4—264no—
292C2×D4—216no—
293C2×D4—216no—
294C2×D4—232no—
295C2×D4—28no—
296C2×D4—28no—
297C2×D4C22×Dic11132yes—
298C2×D4C22×Dic11116yes—
299C22×C4—28no—
300C22×C4—264no—
301C22×C4—216no—
302C22×C4—216no—
303C22×C4—1116no—
304C22×C4—2216no—
305C22×C4—4416no—
306C22×C4C22⋊Dic11164yescomplemented
307C22×C4C22×Dic1118yes—
308C22×C4C22×Dic11116yes—
309C22×C4C22×Dic11116yes—
310C22×C4C22×Dic1114yes—
311C22×C4C22×Dic1114yes—
312C22×C4C22×Dic1118yes—
313C22×C4C22×Dic1118yes—
314C22×C4C2×C22⋊D1118yes—
315C22×C4C2×C22⋊D1118yes—
316C22×C4C2×C22⋊D1118yes—
317C22×C4C2×C22⋊D1118yes—
318C22×C4C2×C22⋊D1118yes—
319C22×C4C2×C22⋊D1118yes—
320C22×C4C23×D1114yes—
321C22×C4C23×D1112yes—
322C22×C4C23×D1111yescharacteristic
323C22×C4C23×D1111yescharacteristic
324C4⋊C4—2216no—
325C4⋊C4—2216no—
326C22⋊C4—2216no—
327C22⋊C4—2216no—
328C22⋊C4—4432no—
329C42—2216no—
330C42—2216no—
331C11#3404411yescharacteristic, complemented, Sylow
332C23—28no—
333C23—24no—
334C23—216no—
335C23—216no—
336C23—28no—
337C23—48no—
338C23—416no—
339C23—416no—
340C23—432no—
341C23C2×C22⋊Dic11116yes—
342C23C23×Dic1118yes—
343C23C23×Dic1112yes—
344C23C23×Dic1114yes—
345C23C22×C22⋊D1114yes—
346C23C22×C22⋊D1114yes—
347C23C22×C22⋊D1114yes—
348C23C24×D1111yescharacteristic
349Q8—232no—
350D4—264no—
351D4—232no—
352C2×C4—216no—
353C2×C4—28no—
354C2×C4—232no—
355C2×C4—232no—
356C2×C4—2232no—
357C2×C4—2216no—
358C2×C4—4432no—
359C2×C4C2×C22⋊Dic11116yes—
360C2×C4C2×C22⋊Dic11116yes—
361C2×C4C2×C22⋊Dic11132yes—
362C2×C4C2×C22⋊Dic11132yes—
363C2×C4C23×Dic1118yes—
364C2×C4C23×Dic1112yes—
365C2×C4C23×Dic1112yes—
366C2×C4C23×Dic1114yes—
367C2×C4C22×C22⋊D1114yes—
368C2×C4C22×C22⋊D1114yes—
369C2×C4C22×C22⋊D1114yes—
370C2×C4C22×C22⋊D1114yes—
371C22—28no—
372C22—28no—
373C22—28no—
374C22—24no—
375C22—28no—
376C22—28no—
377C22—216no—
378C22—416no—
379C22—432no—
380C22—416no—
381C22C22×C22⋊Dic1114yes—
382C22C22×C22⋊Dic1118yes—
383C22#1062345314yes—
384C22C24×Dic1111yescharacteristic
385C22C23×C22⋊D1112yes—
386C4—28no—
387C4—4416no—
388C4C22×C22⋊Dic1114yes—
389C4C22×C22⋊Dic1114yes—
390C4C22×C22⋊Dic1118yes—
391C2—24no—
392C2—28no—
393C2—48no—
394C2C23×C22⋊Dic1111yescharacteristic
395C2#1308181912yes—
396C2#1308194514yes—
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
Fitting, prime radicalC23×C11×#41C2
socle, cosocleC23×C11C25
hypercenterC23×#41D11
hypocenterC11#34044
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C23×#41

Complements

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

NH ≅ G/Ntype
1. C22×#66979C2semidirect
2. #13071208C2semidirect
3. #13071202C2semidirect
4. #13071198C2semidirect
5. #13071194C2semidirect
6. #13071107C2semidirect
7. #13070999C2semidirect
10. C22×C11×#41C4semidirect
22. C2×#66979C22semidirect
23. C2×#66979C22semidirect
24. C22×C4⋊Dic11C22semidirect
25. C22×C4×Dic11C22semidirect
27. #10622843C22semidirect
28. #10622834C22semidirect
29. #10622833C22semidirect
30. #10622825C22semidirect
32. C4×C22⋊Dic11C22semidirect
40. C2×C11×#41C2×C4semidirect
41. C2×C11×#41C2×C4semidirect
43. C22×Q8×C11C2×C4semidirect
48. C22×D4×C11C2×C4semidirect
53. C23×C4×C11C2×C4semidirect
106. C22×C4×C11C22⋊C4semidirect
182. C22×#41Dic11semidirect
232. C2×#41C2×Dic11semidirect
233. C2×#41C2×Dic11semidirect
235. C22×Q8C2×Dic11semidirect
240. C22×D4C2×Dic11semidirect
246. C23×C4C2×Dic11semidirect
306. C22×C4C22⋊Dic11semidirect
331. C11#34044semidirect

Maximal subgroups

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

subgroupindex
C22×#669792
#130712082
#130712022
#130711982
#130711942
#130711072
#130709992
C23×C11×#412
#3404411