Finite Group Databasebeta

← #14643202

Subgroups — #14643202

Order 2816.

552 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
1C2×#10622539C211yesmaximal, characteristic
2C2×#10622538C211yesmaximal, characteristic
3#13066446C214yesmaximal, complemented
4C11×#2920C211yesmaximal, characteristic
5C22×C42×C11C2211yescharacteristic
6C11×#432—21no—
7C11×#432—21no—
8C11×#431C412yes—
9C11×#431C2212yes—
10C11×#423—21no—
11C11×#407—21no—
12C4×C11×M16C412yes—
13C2×C22⋊(C11⋊C8)—21no—
14C2×C22⋊(C11⋊C8)C412yes—
15#10622539—21no—
16#10622539—21no—
17#10622539—21no—
18#10622539—21no—
19#10622538—21no—
20#10622538—21no—
21#10622538C412yes—
22#10622538C2212yes—
23C2×C4⋊(C11⋊C8)—21no—
24C2×C4⋊(C11⋊C8)C412yes—
25C2×#66867C2212yes—
26C2×C4×C11⋊C8C412yes—
27C23×C4×C11C2×C411yescharacteristic
28C23×C4×C11D411yescharacteristic
29C23×C4×C11Q811yescharacteristic
30C2×C11×M16—22no—
31C2×C42×C11C2×C411yescharacteristic
32C2×C42×C11C2×C411yescharacteristic
33C2×C42×C11C2×C411yescharacteristic
34C2×C42×C11C2×C411yescharacteristic
35C2×C42×C11C2×C411yescharacteristic
36C2×C42×C11D411yescharacteristic
37C2×C42×C11D411yescharacteristic
38C2×C42×C11D411yescharacteristic
39C2×C42×C11D411yescharacteristic
40C2×C42×C11D411yescharacteristic
41C2×C42×C11Q811yescharacteristic
42C2×C42×C11C2311yescharacteristic
43C22×C11⋊C8—22no—
44C22×C11⋊C8C2×C414yes—
45C11×C4⋊C8—22no—
46C11×C4⋊C8—22no—
47C11×C22⋊C8—22no—
48C11×C22⋊C8—22no—
49C11×#97—22no—
50C4×C8×C11C2×C414yes—
51C22⋊(C11⋊C8)—22no—
52C22⋊(C11⋊C8)—22no—
53C22⋊(C11⋊C8)—22no—
54C22⋊(C11⋊C8)—22no—
55C4⋊(C11⋊C8)—22no—
56C4⋊(C11⋊C8)—22no—
57C4⋊(C11⋊C8)—22no—
58C4⋊(C11⋊C8)—22no—
59#66867—22no—
60#66867—22no—
61C4×C11⋊C8—22no—
62C4×C11⋊C8C2×C414yes—
63#7863—111nomaximal, Sylow
64C24×C11C4⋊C411yescharacteristic
65C22×C4×C11—24no—
66C22×C4×C11—42no—
67C22×C4×C11—42no—
68C22×C4×C11C4211yescharacteristic
69C22×C4×C11C4211yescharacteristic
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11C22⋊C411yescharacteristic
75C22×C4×C11C22⋊C411yescharacteristic
76C22×C4×C11C4⋊C411yescharacteristic
77C22×C4×C11C4⋊C411yescharacteristic
78C22×C4×C11C4⋊C411yescharacteristic
79C22×C4×C11C4⋊C411yescharacteristic
80C22×C4×C11C4⋊C411yescharacteristic
81C22×C4×C11C4⋊C411yescharacteristic
82C22×C4×C11C4⋊C411yescharacteristic
83C22×C4×C11C22×C411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×Q811yescharacteristic
86C11×M16—44no—
87C2×C8×C11—24no—
88C42×C11C4211yescharacteristic
89C42×C11C4211yescharacteristic
90C42×C11C22⋊C411yescharacteristic
91C42×C11C22⋊C411yescharacteristic
92C42×C11C22⋊C411yescharacteristic
93C42×C11C22⋊C411yescharacteristic
94C42×C11C22⋊C411yescharacteristic
95C42×C11C22⋊C411yescharacteristic
96C42×C11C4⋊C411yescharacteristic
97C42×C11C4⋊C411yescharacteristic
98C42×C11C4⋊C411yescharacteristic
99C42×C11C4⋊C411yescharacteristic
100C42×C11C22×C411yescharacteristic
101C42×C11C22×C411yescharacteristic
102C42×C11C2×D411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C2×C11⋊C8—24no—
105C2×C11⋊C8—24no—
106C2×C11⋊C8—28no—
107C2×C11⋊C8—44no—
108#2920D1111yescharacteristic
109C2×#432—111no—
110C2×#431—111no—
111#1275—114no—
112C23×C11—22no—
113C23×C11—22no—
114C23×C11—41no—
115C23×C11#9511yescharacteristic
116C23×C11#9511yescharacteristic
117C23×C11C2×C4⋊C411yescharacteristic
118C2×C4×C11—22no—
119C2×C4×C11—22no—
120C2×C4×C11—22no—
121C2×C4×C11—22no—
122C2×C4×C11—22no—
123C2×C4×C11—22no—
124C2×C4×C11—22no—
125C2×C4×C11—22no—
126C2×C4×C11—22no—
127C2×C4×C11—22no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11#9511yescharacteristic
136C2×C4×C11#9511yescharacteristic
137C2×C4×C11#9511yescharacteristic
138C2×C4×C11#9511yescharacteristic
139C2×C4×C11#9511yescharacteristic
140C2×C4×C11#9511yescharacteristic
141C2×C4×C11C2×C4211yescharacteristic
142C2×C4×C11C2×C22⋊C411yescharacteristic
143C2×C4×C11C2×C22⋊C411yescharacteristic
144C2×C4×C11C2×C22⋊C411yescharacteristic
145C2×C4×C11C2×C4⋊C411yescharacteristic
146C2×C4×C11C2×C4⋊C411yescharacteristic
147C2×C4×C11#13114yes—
148C8×C11—44no—
149C11⋊C8—44no—
150C11⋊C8—44no—
151C22×C42C2×D1111yescharacteristic
152#432—21no—
153#432—21no—
154#432—221no—
155#432—221no—
156#432—221no—
157#432—221no—
158#431—112no—
159#431—112no—
160#431—221no—
161#431—221no—
162#431Dic1112yes—
163#431C2×D1112yes—
164#423—21no—
165C2×C4⋊C8—112no—
166C2×C4⋊C8—221no—
167#407—21no—
168C2×C22⋊C8—112no—
169C2×C22⋊C8—221no—
170C4×M16Dic1112yes—
171C2×#97—112no—
172C2×C4×C8—112no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11—44no—
181C22×C11H(3,ℤ/4)12yes—
182C22×C11C2×#9511yescharacteristic
183C22×C11#42412yes—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11#33812yes—
194C4×C11#40512yes—
195C4×C11#40812yes—
196C23×C4Dic2211yescharacteristic
197C23×C4C4×D1111yescharacteristic
198C23×C4C22⋊D1111yescharacteristic
199C2×M16—22no—
200C22×C8—114no—
201C22×C8—222no—
202C2×C42Dic2211yescharacteristic
203C2×C42C4×D1111yescharacteristic
204C2×C42C4×D1111yescharacteristic
205C2×C42C4×D1111yescharacteristic
206C2×C42D4411yescharacteristic
207C2×C42D4411yescharacteristic
208C2×C42C2×Dic1111yescharacteristic
209C2×C42C2×Dic1111yescharacteristic
210C2×C42C22⋊D1111yescharacteristic
211C2×C42C22⋊D1111yescharacteristic
212C2×C42C22⋊D1111yescharacteristic
213C2×C42C22×D1111yescharacteristic
214C4⋊C8—22no—
215C4⋊C8—22no—
216C4⋊C8—222no—
217C4⋊C8—222no—
218C4⋊C8—222no—
219C4⋊C8—222no—
220C22⋊C8—22no—
221C22⋊C8—22no—
222C22⋊C8—222no—
223C22⋊C8—222no—
224C22⋊C8—222no—
225C22⋊C8—222no—
226#97—22no—
227#97—222no—
228#97—222no—
229C4×C8—114no—
230C4×C8—222no—
231C4×C8C2×Dic1114yes—
232C2×C11—22no—
233C2×C11—22no—
234C2×C11—41no—
235C2×C11#172911yescharacteristic
236C2×C11C2×H(3,ℤ/4)11yescharacteristic
237C2×C11C2×#33811yescharacteristic
238C24Dic11⋊C411yescharacteristic
239C22×C4—24no—
240C22×C4—42no—
241C22×C4—42no—
242C22×C4C4×Dic1111yescharacteristic
243C22×C4C4×Dic1111yescharacteristic
244C22×C4Dic11⋊C411yescharacteristic
245C22×C4Dic11⋊C411yescharacteristic
246C22×C4Dic11⋊C411yescharacteristic
247C22×C4Dic11⋊C411yescharacteristic
248C22×C4Dic11⋊C411yescharacteristic
249C22×C4C4⋊Dic1111yescharacteristic
250C22×C4C4⋊Dic1111yescharacteristic
251C22×C4(C2×D11)⋊C411yescharacteristic
252C22×C4(C2×D11)⋊C411yescharacteristic
253C22×C4(C2×D11)⋊C411yescharacteristic
254C22×C4(C2×D11)⋊C411yescharacteristic
255C22×C4C22⋊Dic1111yescharacteristic
256C22×C4C22⋊Dic1111yescharacteristic
257C22×C4C2×Dic2211yescharacteristic
258C22×C4C2×C4×D1111yescharacteristic
259C22×C4C2×C22⋊D1111yescharacteristic
260M16—44no—
261C2×C8—24no—
262C2×C8—228no—
263C2×C8—224no—
264C2×C8—224no—
265C2×C8—444no—
266C42C4×Dic1111yescharacteristic
267C42C4×Dic1111yescharacteristic
268C42Dic11⋊C411yescharacteristic
269C42Dic11⋊C411yescharacteristic
270C42C4⋊Dic1111yescharacteristic
271C42C4⋊Dic1111yescharacteristic
272C42(C2×D11)⋊C411yescharacteristic
273C42(C2×D11)⋊C411yescharacteristic
274C42(C2×D11)⋊C411yescharacteristic
275C42(C2×D11)⋊C411yescharacteristic
276C42C22⋊Dic1111yescharacteristic
277C42C22⋊Dic1111yescharacteristic
278C42C2×C4×D1111yescharacteristic
279C42C2×D4411yescharacteristic
280C42C22×Dic1111yescharacteristic
281C42C2×C22⋊D1111yescharacteristic
282C11#786311yescharacteristic, complemented, Sylow
283C23—22no—
284C23—22no—
285C23—41no—
286C23C11⋊#9511yescharacteristic
287C23C11⋊#9511yescharacteristic
288C23C2×Dic11⋊C411yescharacteristic
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4C11⋊#9511yescharacteristic
307C2×C4C11⋊#9511yescharacteristic
308C2×C4C11⋊#9511yescharacteristic
309C2×C4C11⋊#9511yescharacteristic
310C2×C4C11⋊#9511yescharacteristic
311C2×C4C11⋊#9511yescharacteristic
312C2×C4#6696014yes—
313C2×C4C2×C4×Dic1111yescharacteristic
314C2×C4C2×Dic11⋊C411yescharacteristic
315C2×C4C2×C4⋊Dic1111yescharacteristic
316C2×C4C2×(C2×D11)⋊C411yescharacteristic
317C2×C4C2×(C2×D11)⋊C411yescharacteristic
318C2×C4C2×C22⋊Dic1111yescharacteristic
319C8—44no—
320C8—444no—
321C8—444no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—44no—
330C22#1062216912yes—
331C22#1062273212yes—
332C22C2×C11⋊#9511yescharacteristic
333C4—21no—
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4C11⋊#33812yes—
343C4#1062273512yes—
344C4#1062274212yes—
345C2—22no—
346C2—22no—
347C2—41no—
348C2#1306831411yescharacteristic
349C2C2×#1062216911yescharacteristic
350C2C2×C11⋊#33811yescharacteristic
subgroupG/H
centerC2×C4C2×C4×Dic11
commutatorC2×C4×C11C2×C42
FrattiniC2×C42C22×D11
FittingC11×#2920C2
socleC22×C11C2×#95
prime radicalC24×C11C4⋊C4
cosocleC2×C42×C11C23
hypercenter#2920D11
hypocenterC11#7863
LCSG ▷ C2×C4×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #2920

Complements

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

NH ≅ G/Ntype
3. #13066446C2semidirect
282. C11#7863semidirect

Maximal subgroups

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

subgroupindex
C2×#106225392
C2×#106225382
#130664462
C11×#29202
#786311