Finite Group Databasebeta

← #14758369

Subgroups — #14758369

Order 2816.

1382 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4318C211yesmaximal, characteristic
2#13071023C211yesmaximal, characteristic
3#13069590C214yesmaximal, complemented
4#13069578C214yesmaximal, complemented
5#13068335C214yesmaximal
6C22×C11×C4⋊Q8C211yesmaximal, characteristic
7C23×Q8×C11—21no—
8C2×C11×C4⋊Q8—21no—
9C2×C11×C4⋊Q8—21no—
10C2×C11×C4⋊Q8—24no—
11C2×C11×C4⋊Q8C418yescomplemented
12C2×C11×C4⋊Q8C2212yes—
13C2×C11×C4⋊Q8C2212yes—
14C22×C11×C4⋊C4—21no—
15C22×C11×C4⋊C4C2212yes—
16C22×C42×C11C2211yescharacteristic
17C2×#66979C2212yes—
18C22×#4318C2212yes—
19#10622825—21no—
20#10622825—21no—
21#10622549C2212yes—
22#10622548C2212yes—
23C4×C4⋊Dic11—21no—
24C4×C4⋊Dic11—21no—
25C4×#4318—24no—
26C2×#66867C2212yes—
27C2×C4×C11⋊C8C2212yes—
28#10622167C22116yes—
29C22×Q8×C11—28no—
30C22×Q8×C11—22no—
31C22×Q8×C11—22no—
32C22×Q8×C11—48no—
33C23×C4×C11—22no—
34C23×C4×C11D411yescharacteristic
35C23×C4×C11D411yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C11×C4⋊Q8—28no—
38C11×C4⋊Q8—28no—
39C11×C4⋊Q8—24no—
40C11×C4⋊Q8—24no—
41C11×C4⋊Q8C2×C418yes—
42C11×C4⋊Q8C2×C418yes—
43C2×C11×C4⋊C4—28no—
44C2×C11×C4⋊C4—22no—
45C2×C11×C4⋊C4—22no—
46C2×C11×C4⋊C4—22no—
47C2×C11×C4⋊C4—24no—
48C2×C11×C4⋊C4C2×C418yes—
49C2×C11×C4⋊C4C2314yes—
50C2×C42×C11C2×C414yes—
51C2×C42×C11D411yescharacteristic
52C2×C42×C11D411yescharacteristic
53C2×C42×C11D414yes—
54C2×C42×C11C2311yescharacteristic
55C2×C42×C11C2311yescharacteristic
56C2×C22⋊Dic11—22no—
57#66979—28no—
58C2×C4⋊Dic11—22no—
59C2×C4⋊Dic11—22no—
60C2×C4⋊Dic11C2314yes—
61C2×C4×Dic11—22no—
62C2×#4318—24no—
63C2×#4318—24no—
64C2×#4318Q818yescomplemented
65C22×C11⋊C8C2314yes—
66C11⋊#95—22no—
67C11⋊#95—22no—
68#66867—24no—
69C4×C11⋊C8—24no—
70#21324—111nomaximal, Sylow
71C24×C11C2×D411yescharacteristic
72C2×Q8×C11—28no—
73C2×Q8×C11—28no—
74C2×Q8×C11—48no—
75C2×Q8×C11—432no—
76C2×Q8×C11—48no—
77C22×C4×C11—24no—
78C22×C4×C11—24no—
79C22×C4×C11—28no—
80C22×C4×C11—24no—
81C22×C4×C11—48no—
82C22×C4×C11C22⋊C414yes—
83C22×C4×C11C22⋊C414yes—
84C22×C4×C11C22×C412yes—
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D412yes—
91C22×C4×C11C2×Q814yes—
92C22×C4×C11#4114yes—
93C22×C4×C11C2411yescharacteristic
94C22×Dic11—24no—
95C11×C4⋊C4—28no—
96C11×C4⋊C4—28no—
97C11×C4⋊C4—28no—
98C11×C4⋊C4—24no—
99C11×C4⋊C4C22×C418yes—
100C42×C11C22⋊C414yes—
101C42×C11C22⋊C414yes—
102C42×C11C22×C412yes—
103C42×C11C22×C412yes—
104C42×C11C2×D412yes—
105C42×C11C2×D412yes—
106C22⋊Dic11—44no—
107C4⋊Dic11—28no—
108C4⋊Dic11—44no—
109C4⋊Dic11—44no—
110C4×Dic11—44no—
111#4318—216no—
112C2×C11⋊C8—24no—
113C2×C11⋊C8—24no—
114C2×C11⋊C8C2×Q818yescomplemented
115C22×C4⋊Q8D1111yescharacteristic
116C2×C4×M16—111no—
117#2285—111no—
118#1993—114no—
119#1990—114no—
120#1736—114no—
121C23×C11—22no—
122C23×C11—22no—
123C23×C11C2×C22⋊C412yes—
124C23×C11#12412yes—
125C23×C11C4⋊Q812yes—
126C23×C11C22×D411yescharacteristic
127Q8×C11—416no—
128Q8×C11—416no—
129C2×C4×C11—22no—
130C2×C4×C11—22no—
131C2×C4×C11—28no—
132C2×C4×C11—28no—
133C2×C4×C11—28no—
134C2×C4×C11—416no—
135C2×C4×C11—48no—
136C2×C4×C11C2×C22⋊C412yes—
137C2×C4×C11C2×C22⋊C412yes—
138C2×C4×C11C2×C22⋊C412yes—
139C2×C4×C11C2×C22⋊C412yes—
140C2×C4×C11C2×C22⋊C412yes—
141C2×C4×C11C4×Q818yes—
142C2×C4×C11C22⋊Q818yes—
143C2×C4×C11#12412yes—
144C2×C4×C11C4⋊Q812yes—
145C2×C4×C11AGL(1,ℤ/8)14yes—
146C2×C4×C11#13714yes—
147C2×C4×C11C23×C411yescharacteristic
148C2×C4×C11C22×D411yescharacteristic
149C2×C4×C11C22×Q812yes—
150C2×C4×C11C2×#4112yes—
151C2×Dic11—44no—
152C2×Dic11—44no—
153C2×Dic11—44no—
154C11⋊C8—28no—
155C23×Q8—21no—
156C22×M16—112no—
157C2×C4⋊Q8—21no—
158C2×C4⋊Q8—21no—
159C2×C4⋊Q8—24no—
160C2×C4⋊Q8Dic1118yescomplemented
161C2×C4⋊Q8C2×D1112yes—
162C2×C4⋊Q8C2×D1112yes—
163C2×#117—112no—
164C22×C4⋊C4—21no—
165C22×C4⋊C4C2×D1112yes—
166C22×C42C2×D1111yescharacteristic
167C4×M16—224no—
168C2×#97—112no—
169C2×C4×C8—112no—
170#384—112no—
171#382—112no—
172#380—221no—
173#380—221no—
174C4×C4⋊C4—221no—
175C4×C4⋊C4—221no—
176#340—1116no—
177C22×C11—24no—
178C22×C11—22no—
179C22×C11—22no—
180C22×C11—24no—
181C22×C11#39114yes—
182C22×C11C22×C22⋊C411yescharacteristic
183C22×C11C2×#12411yescharacteristic
184C22×C11C2×C4⋊Q811yescharacteristic
185C22×C11C2×AGL(1,ℤ/8)12yes—
186C22×C11C2×#13712yes—
187C4×C11—22no—
188C4×C11—22no—
189C4×C11—48no—
190C4×C11#39114yes—
191C4×C11#41814yes—
192C4×C11#41914yes—
193C4×C11C2×C4×Q812yes—
194C4×C11C2×C22⋊Q812yes—
195Dic11—84no—
196C22×Q8—28no—
197C22×Q8—22no—
198C22×Q8—22no—
199C22×Q8—48no—
200C23×C4—22no—
201C23×C4C22⋊D1111yescharacteristic
202C23×C4C22⋊D1111yescharacteristic
203C23×C4C22×D1111yescharacteristic
204C2×M16—118no—
205C2×M16—224no—
206C2×M16—224no—
207C22×C8—114no—
208C4⋊Q8—28no—
209C4⋊Q8—28no—
210C4⋊Q8—24no—
211C4⋊Q8—24no—
212C4⋊Q8C2×Dic1118yes—
213C4⋊Q8C2×Dic1118yes—
214#117—228no—
215C2×C4⋊C4—28no—
216C2×C4⋊C4—22no—
217C2×C4⋊C4—22no—
218C2×C4⋊C4—22no—
219C2×C4⋊C4—24no—
220C2×C4⋊C4—114no—
221C2×C4⋊C4—222no—
222C2×C4⋊C4—222no—
223C2×C4⋊C4C2×Dic1118yes—
224C2×C4⋊C4C22×D1114yes—
225C2×C22⋊C4—222no—
226C2×C42—222no—
227C2×C42C2×Dic1114yes—
228C2×C42C22⋊D1111yescharacteristic
229C2×C42C22⋊D1111yescharacteristic
230C2×C42C22⋊D1114yes—
231C2×C42C22×D1111yescharacteristic
232C2×C42C22×D1111yescharacteristic
233#97—224no—
234C4×C8—224no—
235#95—222no—
236#95—222no—
237C2×C11—24no—
238C2×C11C2×#39111yescharacteristic
239C2×C11C2×#41811yescharacteristic
240C2×C11C2×#41911yescharacteristic
241C2×C11#314112yes—
242C2×C11#316512yes—
243C24C2×C22⋊D1111yescharacteristic
244C2×Q8—28no—
245C2×Q8—28no—
246C2×Q8—48no—
247C2×Q8—432no—
248C2×Q8—48no—
249C22×C4—24no—
250C22×C4—24no—
251C22×C4—28no—
252C22×C4—24no—
253C22×C4—48no—
254C22×C4—224no—
255C22×C4C22⋊Dic1114yes—
256C22×C4C22⋊Dic1114yes—
257C22×C4Q8×D1114yes—
258C22×C4#434314yes—
259C22×C4C22×Dic1112yes—
260C22×C4C2×C22⋊D1111yescharacteristic
261C22×C4C2×C22⋊D1111yescharacteristic
262C22×C4C2×C22⋊D1111yescharacteristic
263C22×C4C2×C22⋊D1111yescharacteristic
264C22×C4C2×C22⋊D1111yescharacteristic
265C22×C4C2×C22⋊D1112yes—
266C22×C4C23×D1111yescharacteristic
267M16—2216no—
268C2×C8—118no—
269C2×C8—224no—
270C2×C8—224no—
271C4⋊C4—28no—
272C4⋊C4—28no—
273C4⋊C4—28no—
274C4⋊C4—24no—
275C4⋊C4—228no—
276C4⋊C4—444no—
277C4⋊C4—444no—
278C4⋊C4C22×Dic1118yes—
279C22⋊C4—444no—
280C42—444no—
281C42C22⋊Dic1114yes—
282C42C22⋊Dic1114yes—
283C42C22×Dic1112yes—
284C42C22×Dic1112yes—
285C42C2×C22⋊D1112yes—
286C42C2×C22⋊D1112yes—
287C11#2132411yescharacteristic, complemented, Sylow
288C23—22no—
289C23—22no—
290C23#6699712yes—
291C23#6700012yes—
292C23C2×C22⋊Dic1112yes—
293C23C22×C22⋊D1111yescharacteristic
294Q8—416no—
295Q8—416no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—28no—
299C2×C4—28no—
300C2×C4—28no—
301C2×C4—416no—
302C2×C4—48no—
303C2×C4—444no—
304C2×C4—444no—
305C2×C4—444no—
306C2×C4#6698514yes—
307C2×C4#6699514yes—
308C2×C4#6699712yes—
309C2×C4Q8×Dic1118yes—
310C2×C4#6699918yes—
311C2×C4#6700012yes—
312C2×C4C2×C22⋊Dic1112yes—
313C2×C4C2×C22⋊Dic1112yes—
314C2×C4C2×C22⋊Dic1112yes—
315C2×C4C2×C22⋊Dic1112yes—
316C2×C4C2×C22⋊Dic1112yes—
317C2×C4C2×Q8×D1112yes—
318C2×C4C2×#434312yes—
319C2×C4C23×Dic1111yescharacteristic
320C2×C4C22×C22⋊D1111yescharacteristic
321C8—228no—
322C22—24no—
323C22—22no—
324C22—22no—
325C22—24no—
326C22#1062284314yes—
327C22C2×#6698512yes—
328C22C2×#6699512yes—
329C22C2×#6699711yescharacteristic
330C22C2×#6700011yescharacteristic
331C22C22×C22⋊Dic1111yescharacteristic
332C4—22no—
333C4—22no—
334C4—48no—
335C4—884no—
336C4#1062282814yes—
337C4#1062283814yes—
338C4#1062284314yes—
339C4C2×Q8×Dic1112yes—
340C4C2×#6699912yes—
341C2—24no—
342C2C2×#1062284311yescharacteristic
343C2C2×#1062282811yescharacteristic
344C2C2×#1062283811yescharacteristic
345C2#1307901212yes—
346C2#1307915812yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×C4⋊Q8C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC22×C4⋊Q8D11
hypocenterC11#21324
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. #13069590C2semidirect
4. #13069578C2semidirect
11. C2×C11×C4⋊Q8C4semidirect
64. C2×#4318Q8semidirect
114. C2×C11⋊C8C2×Q8semidirect
160. C2×C4⋊Q8Dic11semidirect
287. C11#21324semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43182
#130710232
#130695902
#130695782
#130683352
C22×C11×C4⋊Q82
#2132411