Finite Group Databasebeta

← #14647190

Subgroups — #14647190

Order 2816.

630 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622548C211yesmaximal, characteristic
2#13068596C211yesmaximal, characteristic
3#13066500C214yesmaximal, complemented
4C11×#1797C211yesmaximal, characteristic
5C22×C42×C11C2211yescharacteristic
6C22×C4⋊Dic11—21no—
7C22×C4⋊Dic11—21no—
8C22×C4⋊Dic11C412yes—
9C2×C11×C4⋊C8C2212yes—
10C2×C11×C22⋊C8—21no—
11C2×C22⋊(C11⋊C8)—21no—
12#10622548—21no—
13#10622548—21no—
14#10622548C412yes—
15#10622548C2212yes—
16C2×C4⋊(C11⋊C8)C2212yes—
17C11×#336—21no—
18#10622162—21no—
19C23×C4×C11C2×C411yescharacteristic
20C23×C4×C11D411yescharacteristic
21C23×C4×C11D411yescharacteristic
22C23×Dic11—22no—
23C22×C8×C11—22no—
24C2×C42×C11—24no—
25C2×C42×C11C2×C411yescharacteristic
26C2×C42×C11D411yescharacteristic
27C2×C42×C11D411yescharacteristic
28C2×C42×C11C2311yescharacteristic
29C2×C4⋊Dic11—22no—
30C2×C4⋊Dic11—22no—
31C2×C4⋊Dic11—22no—
32C2×C4⋊Dic11—22no—
33C2×C4⋊Dic11—22no—
34C2×C4⋊Dic11—44no—
35C2×C4⋊Dic11—42no—
36C2×C4⋊Dic11—42no—
37C2×C4⋊Dic11—44no—
38C2×C4⋊Dic11C2×C414yes—
39C22×C11⋊C8—22no—
40C11×C4⋊C8—24no—
41C11×C22⋊C8—42no—
42C22⋊(C11⋊C8)—42no—
43C4⋊(C11⋊C8)—24no—
44#8724—111nomaximal, Sylow
45C24×C11C22⋊C411yescharacteristic
46C22×C4×C11—22no—
47C22×C4×C11—22no—
48C22×C4×C11—22no—
49C22×C4×C11—22no—
50C22×C4×C11—22no—
51C22×C4×C11—22no—
52C22×C4×C11—22no—
53C22×C4×C11C22⋊C411yescharacteristic
54C22×C4×C11C22⋊C411yescharacteristic
55C22×C4×C11C22⋊C411yescharacteristic
56C22×C4×C11D812yes—
57C22×C4×C11SD1612yes—
58C22×C4×C11SD1612yes—
59C22×C4×C11Q1612yes—
60C22×C4×C11C22×C411yescharacteristic
61C22×C4×C11C2×D411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C22×Dic11—24no—
64C22×Dic11—44no—
65C22×Dic11—44no—
66C22×Dic11—44no—
67C2×C8×C11—42no—
68C2×C8×C11—42no—
69C2×C8×C11—42no—
70C42×C11—22no—
71C42×C11—22no—
72C42×C11—22no—
73C42×C11#4114yes—
74C4⋊Dic11—44no—
75C4⋊Dic11—44no—
76C4⋊Dic11—44no—
77C4⋊Dic11—44no—
78C4⋊Dic11—42no—
79C4⋊Dic11—42no—
80C4⋊Dic11—44no—
81C2×C11⋊C8—42no—
82C2×C11⋊C8—42no—
83C2×C11⋊C8—42no—
84C2×#384—111no—
85#1797—111no—
86#1797D1111yescharacteristic
87#1296—114no—
88C23×C11—21no—
89C23×C11—21no—
90C23×C11—21no—
91C23×C11—21no—
92C23×C11#10112yes—
93C23×C11#10212yes—
94C23×C11#10312yes—
95C23×C11C2×C22⋊C411yescharacteristic
96C2×C4×C11—28no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—24no—
106C2×C4×C11—24no—
107C2×C4×C11—24no—
108C2×C4×C11—24no—
109C2×C4×C11#10012yes—
110C2×C4×C11#10212yes—
111C2×C4×C11#10312yes—
112C2×C4×C11#11712yes—
113C2×C4×C11#12312yes—
114C2×C4×C11#12312yes—
115C2×C4×C11C2×D811yescharacteristic
116C2×C4×C11C2×SD1611yescharacteristic
117C2×C4×C11C2×SD1611yescharacteristic
118C2×C4×C11C2×Q1611yescharacteristic
119C2×C4×C11AGL(1,ℤ/8)12yes—
120C2×C4×C11#13712yes—
121C2×Dic11—44no—
122C2×Dic11—44no—
123C2×Dic11—44no—
124C2×Dic11—88no—
125C8×C11—82no—
126C11⋊C8—82no—
127C22×C4⋊C4—112no—
128C22×C4⋊C4—221no—
129C22×C4⋊C4—221no—
130C22×C42C2×D1111yescharacteristic
131C2×C4⋊C8—112no—
132C2×C4⋊C8C2×D1112yes—
133C2×C22⋊C8—21no—
134C2×C22⋊C8—221no—
135#384—112no—
136#384—112no—
137#384—221no—
138#384—221no—
139#336—21no—
140#336—221no—
141C22×C11—22no—
142C22×C11—22no—
143C22×C11—22no—
144C22×C11—22no—
145C22×C11—22no—
146C22×C11—22no—
147C22×C11#33214yes—
148C22×C11#38111yescharacteristic
149C22×C11C2×#10011yescharacteristic
150C22×C11C2×#10111yescharacteristic
151C22×C11C2×#10211yescharacteristic
152C22×C11C2×#10311yescharacteristic
153C22×C11#41811yescharacteristic
154C22×C11#41911yescharacteristic
155C4×C11—22no—
156C4×C11—22no—
157C4×C11—22no—
158C4×C11—22no—
159C4×C11#48012yes—
160C4×C11#48112yes—
161C4×C11#48312yes—
162C4×C11#48412yes—
163Dic11—84no—
164C23×C4—222no—
165C23×C4C4×D1111yescharacteristic
166C23×C4D4411yescharacteristic
167C23×C4C22⋊D1111yescharacteristic
168C22×C8—22no—
169C22×C8—222no—
170C2×C4⋊C4—114no—
171C2×C4⋊C4—222no—
172C2×C4⋊C4—222no—
173C2×C4⋊C4—222no—
174C2×C4⋊C4—222no—
175C2×C4⋊C4—222no—
176C2×C4⋊C4—444no—
177C2×C4⋊C4—442no—
178C2×C4⋊C4—442no—
179C2×C4⋊C4—444no—
180C2×C42—24no—
181C2×C42C4×D1111yescharacteristic
182C2×C42D4411yescharacteristic
183C2×C42C22⋊D1111yescharacteristic
184C2×C42C22×D1111yescharacteristic
185C4⋊C8—24no—
186C4⋊C8—224no—
187C22⋊C8—42no—
188C22⋊C8—442no—
189C2×C11—24no—
190C2×C11C2×#33211yescharacteristic
191C2×C11#154511yescharacteristic
192C2×C11#154811yescharacteristic
193C2×C11#155611yescharacteristic
194C2×C11#182111yescharacteristic
195C2×C11#182311yescharacteristic
196C2×C11#182411yescharacteristic
197C24(C2×D11)⋊C411yescharacteristic
198C22×C4—22no—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—224no—
206C22×C4—444no—
207C22×C4—444no—
208C22×C4—444no—
209C22×C4#431412yes—
210C22×C4D8812yes—
211C22×C4(C2×D11)⋊C411yescharacteristic
212C22×C4(C2×D11)⋊C411yescharacteristic
213C22×C4(C2×D11)⋊C411yescharacteristic
214C22×C4#432412yes—
215C22×C4#432612yes—
216C22×C4C2×C4×D1111yescharacteristic
217C22×C4C2×D4411yescharacteristic
218C22×C4C2×C22⋊D1111yescharacteristic
219C2×C8—42no—
220C2×C8—42no—
221C2×C8—42no—
222C2×C8—442no—
223C2×C8—442no—
224C2×C8—442no—
225C4⋊C4—444no—
226C4⋊C4—444no—
227C4⋊C4—444no—
228C4⋊C4—444no—
229C4⋊C4—442no—
230C4⋊C4—442no—
231C4⋊C4—444no—
232C42—22no—
233C42—22no—
234C42—22no—
235C42#434114yes—
236C11#872411yescharacteristic, complemented, Sylow
237C23—21no—
238C23—21no—
239C23—21no—
240C23—21no—
241C23#6687412yes—
242C23#6688512yes—
243C23#6688812yes—
244C23C2×(C2×D11)⋊C411yescharacteristic
245C2×C4—28no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—24no—
255C2×C4—24no—
256C2×C4—24no—
257C2×C4—24no—
258C2×C4—444no—
259C2×C4—444no—
260C2×C4—444no—
261C2×C4—888no—
262C2×C4#6687412yes—
263C2×C4#6688512yes—
264C2×C4#6688712yes—
265C2×C4#6693012yes—
266C2×C4#6693912yes—
267C2×C4C2×#431411yescharacteristic
268C2×C4C2×D8811yescharacteristic
269C2×C4#6696212yes—
270C2×C4C2×#432411yescharacteristic
271C2×C4#6698812yes—
272C2×C4C2×#432611yescharacteristic
273C2×C4#6700212yes—
274C8—82no—
275C8—882no—
276C22—22no—
277C22—22no—
278C22—22no—
279C22—22no—
280C22—22no—
281C22—22no—
282C22#1062212414yes—
283C22#1062255611yescharacteristic
284C22C2×#6687411yescharacteristic
285C22#1062261411yescharacteristic
286C22C2×#6688511yescharacteristic
287C22#1062273311yescharacteristic
288C22C2×#6688711yescharacteristic
289C22C2×#6688811yescharacteristic
290C4—22no—
291C4—22no—
292C4—22no—
293C4—22no—
294C4—884no—
295C4#1062233412yes—
296C4#1062234912yes—
297C4#1062264712yes—
298C4#1062265712yes—
299C2—24no—
300C2C2×#1062212411yescharacteristic
301C2#1306728311yescharacteristic
302C2#1306729811yescharacteristic
303C2#1306733411yescharacteristic
304C2#1306869411yescharacteristic
305C2#1306870311yescharacteristic
306C2#1306870411yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1797C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1797D11
hypocenterC11#8724
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
3. #13066500C2semidirect
236. C11#8724semidirect

Maximal subgroups

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

subgroupindex
C2×#106225482
#130685962
#130665002
C11×#17972
#872411