Finite Group Databasebeta

← #14912465

Subgroups — #14912465

Order 2816.

2250 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66940C211yesmaximal, characteristic
2#13071263C218yesmaximal, complemented
3#13071234C211yesmaximal, characteristic
4#13071218C214yesmaximal
5#13071200C212yesmaximal
6#13071087C218yesmaximal, complemented
7#13071011C214yesmaximal
8#117×Dic11C212yesmaximal
9C11×#2316C211yesmaximal, characteristic
10C23×Dic22C2211yescharacteristic
11C2×C11×#117C2212yes—
12C22×C11×C4⋊C4C2211yescharacteristic
13C2×#66979C2212yes—
14C22×Dic11⋊C4C2212yes—
15C22×C4×Dic11C2211yescharacteristic
16C22×C4×Dic11C2212yes—
17C2×#66940C4116yescomplemented
18C2×#66940C2214yes—
19C2×#66940C2214yes—
20C11×#389C2218yes—
21C11×#380C2214yes—
22#10622825C2214yes—
23#10622598C2218yes—
24#10622591C22116yes—
25#10622590C2218yes—
26C4⋊C4×Dic11C2214yes—
27C4⋊C4×Dic11C2214yes—
28C4⋊C4×Dic11C2218yes—
29#10622587C2218yes—
30#10622556C2218yes—
31C22⋊C4×Dic11C2214yes—
32C22⋊C4×Dic11C2214yes—
33#10622545C2214yes—
34C42×Dic11C2214yes—
35#10622542C2218yes—
36#10622268C22116yes—
37#10622264C2218yes—
38#10622261C2218yes—
39C23×C4×C11C2312yes—
40C23×C4×C11C2311yescharacteristic
41C23×Dic11C2311yescharacteristic
42C23×Dic11C2312yes—
43C23×Dic11C2311yescharacteristic
44C22×Dic22—24no—
45C22×Dic22—24no—
46C22×Dic22C2×C418yes—
47C22×Dic22C2314yes—
48C11×#117—28no—
49C2×C11×C4⋊C4C2×C418yes—
50C2×C11×C4⋊C4C2314yes—
51C2×C11×C4⋊C4C2318yes—
52C2×C11×C4⋊C4C2314yes—
53C2×C11×C22⋊C4C2314yes—
54C2×C42×C11C2314yes—
55C2×C22⋊Dic11C2314yes—
56#66979—28no—
57C2×C4⋊Dic11C2314yes—
58C2×C4⋊Dic11C2318yes—
59C2×Dic11⋊C4C2×C4116yes—
60C2×Dic11⋊C4C2318yes—
61C2×C4×Dic11C2×C4116yes—
62C2×C4×Dic11C2×C418yes—
63C2×C4×Dic11C2318yes—
64C2×C4×Dic11C2314yes—
65C2×C4×Dic11C2318yes—
66C2×C4×Dic11C2314yes—
67C2×C4×Dic11C2314yes—
68C2×C4×Dic11C2312yes—
69C2×C4×Dic11C2312yes—
70#66940C2×C4132yes—
71#66940C2×C4132yes—
72C11×#95C2318yes—
73C11⋊#95C2318yes—
74C11⋊#95C23116yes—
75C11⋊#95C2318yes—
76C11⋊#95C23116yes—
77C11⋊#95C2318yes—
78#34059—111nomaximal, Sylow
79C24×C11C2411yescharacteristic
80C22×C4×C11—44no—
81C22×C4×C11C22×C418yes—
82C22×C4×C11C22×C414yes—
83C22×C4×C11#4114yes—
84C22×C4×C11#4114yes—
85C22×C4×C11C2418yes—
86C22×C4×C11C2414yes—
87C22×C4×C11C2412yes—
88C22×Dic11—24no—
89C22×Dic11—24no—
90C22×Dic11—24no—
91C22×Dic11—42no—
92C22×Dic11C22×C414yes—
93C22×Dic11C22×C418yes—
94C22×Dic11C22×C414yes—
95C22×Dic11C2418yes—
96C22×Dic11C2411yescharacteristic
97C22×Dic11C2414yes—
98C22×Dic11C2412yes—
99C22×Dic11C2411yescharacteristic
100C2×Dic22—232no—
101C2×Dic22—28no—
102C2×Dic22—28no—
103C2×Dic22C22×C4116yes—
104C11×C4⋊C4—28no—
105C11×C4⋊C4—48no—
106C11×C4⋊C4C22×C4116yes—
107C11×C22⋊C4—28no—
108C42×C11—28no—
109C22⋊Dic11—28no—
110C4⋊Dic11—28no—
111C4⋊Dic11—48no—
112Dic11⋊C4C22×C4132yes—
113C4×Dic11—216no—
114C4×Dic11—28no—
115C4×Dic11—48no—
116C4×Dic11C22×C4116yes—
117C4×Dic11C22×C4116yes—
118C4×Dic11C22×C418yes—
119C4×Dic11C22×C418yes—
120C22×C4×Q8—111no—
121#2320—118no—
122#2316—111no—
123#2316D1111yescharacteristic
124#2313—114no—
125#2310—112no—
126#2295—118no—
127#2283—114no—
128C4×#117—112no—
129C23×C11—22no—
130C23×C11—22no—
131C23×C11C23×C412yes—
132C23×C11C2×#4112yes—
133C23×C11C2×#4112yes—
134C23×C11C2511yescharacteristic
135C2×C4×C11—28no—
136C2×C4×C11—28no—
137C2×C4×C11—28no—
138C2×C4×C11—28no—
139C2×C4×C11—48no—
140C2×C4×C11#117116yes—
141C2×C4×C11C23×C418yes—
142C2×C4×C11C23×C414yes—
143C2×C4×C11C2×#4114yes—
144C2×C4×C11C2×#4114yes—
145C2×Dic11—216no—
146C2×Dic11—24no—
147C2×Dic11—24no—
148C2×Dic11—22no—
149C2×Dic11—24no—
150C2×Dic11—28no—
151C2×Dic11—28no—
152C2×Dic11—28no—
153C2×Dic11—28no—
154C2×Dic11—44no—
155C2×Dic11C23×C412yes—
156C2×Dic11C23×C414yes—
157C2×Dic11C23×C418yes—
158C2×Dic11C23×C412yes—
159C2×Dic112−1+414yes—
160Dic22—232no—
161C23×Q8—111no—
162C2×C4×Q8—114no—
163C2×C4×Q8—114no—
164C2×C4×Q8—1116no—
165C2×#117—112no—
166C2×#117C2×D1112yes—
167C22×C4⋊C4—112no—
168C22×C4⋊C4C2×D1111yescharacteristic
169C22×C42—111no—
170C22×C42—112no—
171#391—118no—
172#391—118no—
173#389—118no—
174#389C2×D1118yes—
175#387—1116no—
176#387—1116no—
177#383—118no—
178#382—118no—
179#381—118no—
180#380—114no—
181#380C2×D1114yes—
182C4×C4⋊C4—114no—
183C4×C4⋊C4—114no—
184C4×C4⋊C4—118no—
185C4×C22⋊C4—114no—
186C4×C22⋊C4—114no—
187#376—114no—
188#376—118no—
189C43—114no—
190C22×C11—22no—
191C22×C11—22no—
192C22×C11—24no—
193C22×C11—24no—
194C22×C11C2×#11714yes—
195C22×C11C24×C411yescharacteristic
196C22×C11C22×#4111yescharacteristic
197C22×C11C22×#4111yescharacteristic
198C22×C11C2×2−1+412yes—
199C22×C11#58512yes—
200C4×C11—28no—
201C4×C11—48no—
202C4×C11C2×#11718yes—
203Dic11—28no—
204Dic11—22no—
205Dic11—24no—
206Dic11—48no—
207Dic11#51914yes—
208C22×Q8—118no—
209C22×Q8—114no—
210C22×Q8—224no—
211C22×Q8—224no—
212C23×C4—112no—
213C23×C4—111no—
214C23×C4—111no—
215C23×C4C22×D1112yes—
216C23×C4C22×D1111yescharacteristic
217C4×Q8—1132no—
218C4×Q8—1132no—
219#117—28no—
220#117—228no—
221C2×C4⋊C4—1116no—
222C2×C4⋊C4—118no—
223C2×C4⋊C4—114no—
224C2×C4⋊C4—118no—
225C2×C4⋊C4C4×D1118yes—
226C2×C4⋊C4C22×D1114yes—
227C2×C4⋊C4C22×D1118yes—
228C2×C4⋊C4C22×D1114yes—
229C2×C22⋊C4—114no—
230C2×C22⋊C4C22×D1114yes—
231C2×C42—1116no—
232C2×C42—118no—
233C2×C42—112no—
234C2×C42—114no—
235C2×C42—112no—
236C2×C42—114no—
237C2×C42—114no—
238C2×C42—118no—
239C2×C42—118no—
240C2×C42C22×D1114yes—
241#95—118no—
242#95—118no—
243#95—118no—
244#95—1116no—
245#95—1116no—
246#95C22×D1118yes—
247C2×C11—24no—
248C2×C11C22×#11711yescharacteristic
249C2×C11C2×#51911yescharacteristic
250C2×C11#342811yescharacteristic
251C2×C11#346112yes—
252C2×C11#346112yes—
253C24C23×D1111yescharacteristic
254C2×Q8—1116no—
255C2×Q8—2232no—
256C2×Q8—228no—
257C2×Q8—228no—
258C22×C4—44no—
259C22×C4—111no—
260C22×C4—114no—
261C22×C4—118no—
262C22×C4—111no—
263C22×C4—114no—
264C22×C4—112no—
265C22×C4—114no—
266C22×C4—118no—
267C22×C4—224no—
268C22×C4—224no—
269C22×C4—224no—
270C22×C4—442no—
271C22×C4C2×C4×D1118yes—
272C22×C4C2×C4×D1114yes—
273C22×C4#434114yes—
274C22×C4#434314yes—
275C22×C4C23×D1118yes—
276C22×C4C23×D1114yes—
277C22×C4C23×D1112yes—
278C4⋊C4—28no—
279C4⋊C4—48no—
280C4⋊C4—1132no—
281C4⋊C4—228no—
282C4⋊C4—448no—
283C4⋊C4C2×C4×D11116yes—
284C22⋊C4—28no—
285C22⋊C4—228no—
286C42—28no—
287C42—118no—
288C42—1116no—
289C42—118no—
290C42—1116no—
291C42—2216no—
292C42—228no—
293C42—448no—
294C11#3405911yescharacteristic, complemented, Sylow
295C23—22no—
296C23—22no—
297C23C22×C4×D1112yes—
298C23C2×#434112yes—
299C23C2×#434312yes—
300C23C24×D1111yescharacteristic
301Q8—2232no—
302C2×C4—28no—
303C2×C4—28no—
304C2×C4—28no—
305C2×C4—28no—
306C2×C4—48no—
307C2×C4—112no—
308C2×C4—114no—
309C2×C4—112no—
310C2×C4—114no—
311C2×C4—118no—
312C2×C4—228no—
313C2×C4—2216no—
314C2×C4—224no—
315C2×C4—224no—
316C2×C4—224no—
317C2×C4—222no—
318C2×C4—228no—
319C2×C4—228no—
320C2×C4—228no—
321C2×C4—444no—
322C2×C4#66945116yes—
323C2×C4C22×C4×D1118yes—
324C2×C4C22×C4×D1114yes—
325C2×C4C2×#434114yes—
326C2×C4C2×#434314yes—
327C22—24no—
328C22—24no—
329C22—22no—
330C22—22no—
331C22C2×#6694514yes—
332C22C23×C4×D1111yescharacteristic
333C22C22×#434111yescharacteristic
334C22C22×#434311yescharacteristic
335C22#1062345512yes—
336C22D11×2−1+412yes—
337C4—28no—
338C4—48no—
339C4—114no—
340C4—228no—
341C4—222no—
342C4—224no—
343C4—448no—
344C4C2×#6694518yes—
345C2—24no—
346C2C22×#6694511yescharacteristic
347C2D11×#51911yescharacteristic
348C2#1308181411yescharacteristic
349C2#1308204412yes—
350C2#1308205012yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2316C2
socle, cosocleC23×C11C25
prime radicalC24×C11C24
hypercenter#2316D11
hypocenterC11#34059
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2316

Complements

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

NH ≅ G/Ntype
2. #13071263C2semidirect
6. #13071087C2semidirect
17. C2×#66940C4semidirect
294. C11#34059semidirect

Maximal subgroups

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

subgroupindex
C22×#669402
#130712632
#130712342
#130712182
#130712002
#130710872
#130710112
#117×Dic112
C11×#23162
#3405911