Finite Group Databasebeta

← #14913869

Subgroups — #14913869

Order 2816.

2858 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623047C212yesmaximal
2C22×#66940C211yesmaximal, characteristic
3#13071535C218yesmaximal, complemented
4#13071530C218yesmaximal, complemented
5#13071234C211yesmaximal, characteristic
6#13071233C214yesmaximal
7#13071019C212yesmaximal
8#13071018C214yesmaximal
9C11×#2316C211yesmaximal, characteristic
10C23×Dic22C2211yescharacteristic
11C2×C11×#117C2212yes—
12C22×C11×C4⋊C4C2211yescharacteristic
13C2×#66979C2212yes—
14C22×Dic11⋊C4C2212yes—
15C22×C4×Dic11C2212yes—
16C22×C4×Dic11C2211yescharacteristic
17#10623047—216no—
18C2×#66940C4116yescomplemented
19C2×#66940C2218yes—
20C2×#66940C2214yes—
21C2×#66940C2214yes—
22C2×#66930C2218yes—
23C2×C4×Dic22C2218yes—
24C11×#389C2218yes—
25C11×#380C2214yes—
26#10622825C2214yes—
27#10622598C2218yes—
28#10622590C2214yes—
29#10622589C2218yes—
30#10622589C2214yes—
31C4⋊C4×Dic11C2218yes—
32#10622585C22116yes—
33#10622555C2214yes—
34#10622555C2214yes—
35C4×Dic11⋊C4C2214yes—
36C4×Dic11⋊C4C2214yes—
37#10622263C2218yes—
38#10622262C2218yes—
39#10622260C22116yes—
40C23×C4×C11C2312yes—
41C23×C4×C11C2311yescharacteristic
42C23×Dic11C2311yescharacteristic
43C23×Dic11C2311yescharacteristic
44C23×Dic11C2312yes—
45C22×Dic22C2×C418yes—
46C22×Dic22D418yes—
47C22×Dic22Q818yes—
48C22×Dic22C2314yes—
49C11×#117—28no—
50C2×C11×C4⋊C4C2×C418yes—
51C2×C11×C4⋊C4C2314yes—
52C2×C11×C4⋊C4C2318yes—
53C2×C11×C4⋊C4C2314yes—
54C2×C11×C22⋊C4C2314yes—
55C2×C42×C11C2314yes—
56C2×C22⋊Dic11C2314yes—
57#66979—28no—
58C2×C4⋊Dic11C2314yes—
59C2×C4⋊Dic11C2318yes—
60C2×Dic11⋊C4C2×C4116yes—
61C2×Dic11⋊C4C23116yes—
62C2×Dic11⋊C4C2318yes—
63C2×Dic11⋊C4C2318yes—
64C2×Dic11⋊C4C2318yes—
65C2×C4×Dic11C2×C418yes—
66C2×C4×Dic11C2×C4116yes—
67C2×C4×Dic11C23116yes—
68C2×C4×Dic11C2314yes—
69C2×C4×Dic11C2314yes—
70C2×C4×Dic11C2314yes—
71C2×C4×Dic11C2312yes—
72C2×C4×Dic11C2312yes—
73#66940—232no—
74#66940C2×C4132yes—
75#66940C2×C4132yes—
76#66930—232no—
77C4×Dic22—232no—
78C11×#95C2318yes—
79C11⋊#95C2318yes—
80C11⋊#95C2318yes—
81C11⋊#95C2318yes—
82#34182—111nomaximal, Sylow
83C24×C11C2411yescharacteristic
84C22×C4×C11—44no—
85C22×C4×C11C22×C418yes—
86C22×C4×C11C22×C414yes—
87C22×C4×C11C2×D414yes—
88C22×C4×C11C2×Q814yes—
89C22×C4×C11C2418yes—
90C22×C4×C11C2414yes—
91C22×C4×C11C2412yes—
92C22×Dic11—24no—
93C22×Dic11—42no—
94C22×Dic11C22×C414yes—
95C22×Dic11C22×C414yes—
96C22×Dic11C22×C418yes—
97C22×Dic11C2×D418yes—
98C22×Dic11C2×Q818yes—
99C22×Dic11C2418yes—
100C22×Dic11C2411yescharacteristic
101C22×Dic11C2412yes—
102C22×Dic11C2414yes—
103C22×Dic11C2411yescharacteristic
104C2×Dic22C4⋊C4164yescomplemented
105C2×Dic22C22×C4116yes—
106C2×Dic22C2×D4116yes—
107C2×Dic22C2×Q8116yes—
108C11×C4⋊C4—28no—
109C11×C4⋊C4—48no—
110C11×C4⋊C4C22×C4116yes—
111C11×C22⋊C4—28no—
112C42×C11—28no—
113C22⋊Dic11—28no—
114C4⋊Dic11—28no—
115C4⋊Dic11—48no—
116Dic11⋊C4—232no—
117Dic11⋊C4—216no—
118Dic11⋊C4—48no—
119Dic11⋊C4C22×C4132yes—
120C4×Dic11—232no—
121C4×Dic11—28no—
122C4×Dic11C22×C4116yes—
123C4×Dic11C22×C4116yes—
124C4×Dic11C22×C418yes—
125C4×Dic11C22×C418yes—
126C2×#519—112no—
127C22×C4×Q8—111no—
128#2351—118no—
129Q8×C4⋊C4—118no—
130#2316—114no—
131#2316—111no—
132#2316D1111yescharacteristic
133#2285—114no—
134#2285—112no—
135C23×C11—22no—
136C23×C11—22no—
137C23×C11C23×C412yes—
138C23×C11C22×D412yes—
139C23×C11C22×Q812yes—
140C23×C11C2511yescharacteristic
141C2×C4×C11—28no—
142C2×C4×C11—28no—
143C2×C4×C11—28no—
144C2×C4×C11—28no—
145C2×C4×C11—48no—
146C2×C4×C11C2×C4⋊C4116yes—
147C2×C4×C11C23×C418yes—
148C2×C4×C11C23×C414yes—
149C2×C4×C11C22×D414yes—
150C2×C4×C11C22×Q814yes—
151C2×Dic11—22no—
152C2×Dic11—24no—
153C2×Dic11—28no—
154C2×Dic11—28no—
155C2×Dic11—28no—
156C2×Dic11—28no—
157C2×Dic11—44no—
158C2×Dic11C2×C4⋊C4132yes—
159C2×Dic11C23×C412yes—
160C2×Dic11C23×C414yes—
161C2×Dic11C23×C418yes—
162C2×Dic11C23×C412yes—
163C2×Dic11C22×D418yes—
164C2×Dic11C22×Q818yes—
165C2×Dic112−1+414yes—
166Dic22C2×C4⋊C4164yes—
167C23×Q8—111no—
168#519—2216no—
169C2×C4×Q8—114no—
170C2×C4×Q8—114no—
171C2×C4×Q8—118no—
172C2×C4×Q8—1116no—
173C2×C4×Q8—118no—
174C2×#117—112no—
175C2×#117—118no—
176C2×#117C2×D1112yes—
177C22×C4⋊C4—112no—
178C22×C4⋊C4C2×D1111yescharacteristic
179C22×C42—112no—
180C22×C42—111no—
181#389—1116no—
182#389—118no—
183#389—1116no—
184#389C2×D1118yes—
185#384—118no—
186#384—114no—
187#382—114no—
188#382—118no—
189#380—114no—
190#380—114no—
191#380—114no—
192#380C2×D1114yes—
193C4×C4⋊C4—118no—
194C4×C4⋊C4—114no—
195C4×C4⋊C4—114no—
196C4×C4⋊C4—118no—
197C22×C11—22no—
198C22×C11—22no—
199C22×C11—24no—
200C22×C11—24no—
201C22×C11C22×C4⋊C414yes—
202C22×C11C24×C411yescharacteristic
203C22×C11C23×D411yescharacteristic
204C22×C11C23×Q811yescharacteristic
205C22×C11C2×2−1+412yes—
206C22×C11#58512yes—
207C4×C11—28no—
208C4×C11—48no—
209C4×C11C22×C4⋊C418yes—
210Dic11—22no—
211Dic11—24no—
212Dic11—48no—
213Dic11C22×C4⋊C4116yes—
214Dic11#51914yescomplemented
215C22×Q8—118no—
216C22×Q8—118no—
217C22×Q8—118no—
218C22×Q8—114no—
219C23×C4—112no—
220C23×C4—111no—
221C23×C4—111no—
222C23×C4C22×D1112yes—
223C23×C4C22×D1111yescharacteristic
224C4×Q8—1132no—
225C4×Q8—1132no—
226C4×Q8—2232no—
227C4×Q8—2232no—
228#117—28no—
229#117—2232no—
230#117—228no—
231C2×C4⋊C4—1116no—
232C2×C4⋊C4—118no—
233C2×C4⋊C4—1116no—
234C2×C4⋊C4—114no—
235C2×C4⋊C4—118no—
236C2×C4⋊C4—118no—
237C2×C4⋊C4—118no—
238C2×C4⋊C4C4×D1118yes—
239C2×C4⋊C4C22×D1114yes—
240C2×C4⋊C4C22×D1118yes—
241C2×C4⋊C4C22×D1114yes—
242C2×C22⋊C4—114no—
243C2×C22⋊C4C22×D1114yes—
244C2×C42—1116no—
245C2×C42—118no—
246C2×C42—114no—
247C2×C42—112no—
248C2×C42—114no—
249C2×C42—112no—
250C2×C42—1116no—
251C2×C42—114no—
252C2×C42C22×D1114yes—
253#95—118no—
254#95—118no—
255#95—118no—
256#95C22×D1118yes—
257C2×C11—24no—
258C2×C11C23×C4⋊C411yescharacteristic
259C2×C11C2×#51911yescharacteristic
260C2×C11#342811yescharacteristic
261C2×C11#349712yes—
262C2×C11#350212yes—
263C24C23×D1111yescharacteristic
264C2×Q8—1164no—
265C2×Q8—1116no—
266C2×Q8—1116no—
267C2×Q8—1116no—
268C22×C4—44no—
269C22×C4—118no—
270C22×C4—118no—
271C22×C4—118no—
272C22×C4—111no—
273C22×C4—114no—
274C22×C4—114no—
275C22×C4—111no—
276C22×C4—112no—
277C22×C4—114no—
278C22×C4—118no—
279C22×C4—224no—
280C22×C4—442no—
281C22×C4C2×C4×D1118yes—
282C22×C4C2×C4×D1114yes—
283C22×C4D4×D1114yes—
284C22×C4Q8×D1114yes—
285C22×C4C23×D1118yes—
286C22×C4C23×D1114yes—
287C22×C4C23×D1112yes—
288C4⋊C4—28no—
289C4⋊C4—48no—
290C4⋊C4—1132no—
291C4⋊C4—2232no—
292C4⋊C4—2216no—
293C4⋊C4—228no—
294C4⋊C4—448no—
295C4⋊C4—448no—
296C4⋊C4C2×C4×D11116yes—
297C22⋊C4—28no—
298C22⋊C4—228no—
299C42—28no—
300C42—1116no—
301C42—118no—
302C42—1116no—
303C42—118no—
304C42—2232no—
305C42—228no—
306C11#3418211yescharacteristic, complemented, Sylow
307C23—22no—
308C23—22no—
309C23C22×C4×D1112yes—
310C23C2×D4×D1112yes—
311C23C2×Q8×D1112yes—
312C23C24×D1111yescharacteristic
313Q8—1164no—
314C2×C4—28no—
315C2×C4—28no—
316C2×C4—28no—
317C2×C4—28no—
318C2×C4—48no—
319C2×C4—1132no—
320C2×C4—112no—
321C2×C4—118no—
322C2×C4—118no—
323C2×C4—118no—
324C2×C4—114no—
325C2×C4—112no—
326C2×C4—114no—
327C2×C4—228no—
328C2×C4—224no—
329C2×C4—222no—
330C2×C4—228no—
331C2×C4—228no—
332C2×C4—228no—
333C2×C4—444no—
334C2×C4C4⋊C4×D11116yes—
335C2×C4C22×C4×D1118yes—
336C2×C4C22×C4×D1114yes—
337C2×C4C2×D4×D1114yes—
338C2×C4C2×Q8×D1114yes—
339C22—24no—
340C22—24no—
341C22—22no—
342C22—22no—
343C22C2×C4⋊C4×D1114yes—
344C22C23×C4×D1111yescharacteristic
345C22C22×D4×D1111yescharacteristic
346C22C22×Q8×D1111yescharacteristic
347C22#1062345512yes—
348C22D11×2−1+412yes—
349C4—28no—
350C4—48no—
351C4—1116no—
352C4—114no—
353C4—222no—
354C4—224no—
355C4—448no—
356C4C2×C4⋊C4×D1118yes—
357C2—24no—
358C2C22×C4⋊C4×D1111yescharacteristic
359C2D11×#51911yescharacteristic
360C2#1308181411yescharacteristic
361C2#1308238512yes—
362C2#1308242412yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2316C2
socle, cosocleC23×C11C25
prime radicalC24×C11C24
hypercenter#2316D11
hypocenterC11#34182
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2316

Complements

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

NH ≅ G/Ntype
3. #13071535C2semidirect
4. #13071530C2semidirect
18. C2×#66940C4semidirect
104. C2×Dic22C4⋊C4semidirect
214. Dic11#519semidirect
306. C11#34182semidirect

Maximal subgroups

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

subgroupindex
C2×#106230472
C22×#669402
#130715352
#130715302
#130712342
#130712332
#130710192
#130710182
C11×#23162
#3418211