Finite Group Databasebeta

← #14658846

Subgroups — #14658846

Order 2816.

478 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13069422C211yesmaximal, characteristic
2#13069421C211yesmaximal, characteristic
3#13069421C211yesmaximal, characteristic
4#13068743C211yesmaximal, characteristic, complemented
5#13068743C211yesmaximal, characteristic, complemented
6C11⋊#1273C211yesmaximal, characteristic, complemented
7C11×#1834C211yesmaximal, characteristic, complemented
8C2×#66927C2211yescharacteristic
9C2×C4×C8×C11C2211yescharacteristic
10C11×#384C2211yescharacteristic
11C11×#384C2211yescharacteristic
12C2×#66885—22no—
13C2×#66873—22no—
14C2×#66873—22no—
15#10622548C2211yescharacteristic
16C2×C4×C11⋊C8C2211yescharacteristic
17C2×C4×C11⋊C8C2211yescharacteristic
18C11×#340—22no—
19#10622167—22no—
20#10622167—22no—
21C22×D44—21no—
22C22×D44—21no—
23C22×D44—21no—
24C22×C8×C11D412yes—
25C2×C11×C4⋊C4—21no—
26C2×C11×C4⋊C4—21no—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C42×C11C2311yescharacteristic
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35C22×C11⋊C8D412yes—
36C22×C11⋊C8D412yes—
37#66927—21no—
38#66927—21no—
39#66927—21no—
40#66927Q812yes—
41C4×C8×C11—21no—
42C4×C8×C11—21no—
43#66885—44no—
44#66873—44no—
45#66873—44no—
46C4×C11⋊C8—21no—
47C4×C11⋊C8—21no—
48C4×C11⋊C8—21no—
49C4×C11⋊C8—21no—
50#10678—111nomaximal, Sylow
51C23×D11—41no—
52C22×C4×C11—41no—
53C22×C4×C11—41no—
54C22×C4×C11C2×D411yescharacteristic
55C22×C4×C11C2×D411yescharacteristic
56C22×C4×C11C2×D411yescharacteristic
57C22×Dic11—41no—
58C2×D44—22no—
59C2×D44—22no—
60C2×D44—22no—
61C2×D44—41no—
62C2×D44—41no—
63C2×D44—41no—
64C2×D44—42no—
65C2×D44—42no—
66C2×D44—42no—
67C2×D44—42no—
68C2×D44—42no—
69C2×D44—42no—
70C2×C8×C11—22no—
71C2×C8×C11—22no—
72C2×C8×C11—22no—
73C11×C4⋊C4—42no—
74C11×C4⋊C4—42no—
75C11×C4⋊C4—42no—
76C11×C4⋊C4—42no—
77C11×C4⋊C4—42no—
78C11×C4⋊C4—42no—
79C42×C11C2×Q811yescharacteristic
80C42×C11#4111yescharacteristic
81C42×C11#4111yescharacteristic
82C42×C11#4111yescharacteristic
83C4⋊Dic11—42no—
84C4⋊Dic11—42no—
85C4⋊Dic11—42no—
86C2×C11⋊C8—22no—
87C2×C11⋊C8—22no—
88C2×C11⋊C8—22no—
89C2×C11⋊C8—22no—
90C2×C11⋊C8—22no—
91C2×C11⋊C8—22no—
92#1957—111no—
93#1957—111no—
94#1957—111no—
95#1834—111no—
96#1834—111no—
97#1834D1111yescharacteristic, complemented
98#1273—111no—
99C23×C11#12711yescharacteristic
100C22×D11—42no—
101C22×D11—81no—
102C22×D11—81no—
103C22×D11—81no—
104C22×D11—81no—
105C22×D11—81no—
106C22×D11—81no—
107C2×C4×C11—81no—
108C2×C4×C11—81no—
109C2×C4×C11—81no—
110C2×C4×C11—81no—
111C2×C4×C11—81no—
112C2×C4×C11—81no—
113C2×C4×C11C22⋊Q811yescharacteristic
114C2×C4×C11C22⋊Q811yescharacteristic
115C2×C4×C11C22⋊Q811yescharacteristic
116C2×C4×C11#12311yescharacteristic
117C2×C4×C11#12311yescharacteristic
118C2×C4×C11#12311yescharacteristic
119C2×C4×C11#13512yes—
120C2×C4×C11#13512yes—
121C2×C4×C11#13512yes—
122C2×C4×C11AGL(1,ℤ/8)12yes—
123C2×C4×C11AGL(1,ℤ/8)12yes—
124C2×C4×C11AGL(1,ℤ/8)12yes—
125C2×Dic11—81no—
126C2×Dic11—81no—
127C2×Dic11—81no—
128D44—44no—
129D44—44no—
130D44—44no—
131D44—82no—
132D44—82no—
133D44—82no—
134C8×C11—42no—
135C11⋊C8—42no—
136C11⋊C8—42no—
137C2×#127—111no—
138C2×#102—222no—
139C2×#102—222no—
140C2×#102—222no—
141C2×C4×C8—111no—
142C2×C4×C8—111no—
143C2×C4×C8C2×D1111yescharacteristic
144#384—111no—
145#384C2×D1111yescharacteristic
146#384C2×D1111yescharacteristic
147#340—22no—
148#340—222no—
149#340—222no—
150C22×C11#39911yescharacteristic
151C22×C11#49511yescharacteristic
152C22×C11#49511yescharacteristic
153C22×C11#49511yescharacteristic
154C22×C11#49611yescharacteristic
155C22×C11#49611yescharacteristic
156C22×C11#49611yescharacteristic
157C2×D11—82no—
158C2×D11—82no—
159C2×D11—82no—
160C2×D11—161no—
161C2×D11—161no—
162C2×D11—161no—
163C2×D11—161no—
164C4×C11—161no—
165C4×C11—161no—
166C4×C11#47812yes—
167C4×C11#47812yes—
168C4×C11#47812yes—
169C4×C11#48212yes—
170C4×C11#48212yes—
171C4×C11#48212yes—
172Dic11—161no—
173C22×D4—221no—
174C22×D4—221no—
175C22×D4—221no—
176C22×C8—112no—
177C22×C8—112no—
178C22×C8C22⋊D1112yes—
179#127—112no—
180#127—221no—
181#127—221no—
182#127—221no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—221no—
190C2×C4⋊C4—221no—
191C2×C4⋊C4—221no—
192C2×C42C22×D1111yescharacteristic
193#102—444no—
194#102—444no—
195#102—444no—
196C4×C8—21no—
197C4×C8—21no—
198C4×C8—221no—
199C4×C8—221no—
200C4×C8—221no—
201C4×C8—221no—
202C2×C11#171111yescharacteristic
203C2×C11#171711yescharacteristic
204C2×C11#171711yescharacteristic
205C2×C11#171711yescharacteristic
206C2×C11#209211yescharacteristic
207C2×C11#209211yescharacteristic
208C2×C11#209211yescharacteristic
209D11—162no—
210C24—441no—
211C2×D4—222no—
212C2×D4—222no—
213C2×D4—222no—
214C2×D4—441no—
215C2×D4—441no—
216C2×D4—442no—
217C2×D4—442no—
218C2×D4—442no—
219C2×D4—442no—
220C2×D4—441no—
221C2×D4—442no—
222C2×D4—442no—
223C22×C4—41no—
224C22×C4—41no—
225C22×C4—441no—
226C22×C4D4×D1111yescharacteristic
227C22×C4D4×D1111yescharacteristic
228C22×C4C2×C22⋊D1111yescharacteristic
229C2×C8—22no—
230C2×C8—22no—
231C2×C8—22no—
232C2×C8—222no—
233C2×C8—222no—
234C2×C8—222no—
235C2×C8—222no—
236C2×C8—222no—
237C2×C8—222no—
238C4⋊C4—42no—
239C4⋊C4—42no—
240C4⋊C4—42no—
241C4⋊C4—42no—
242C4⋊C4—42no—
243C4⋊C4—42no—
244C4⋊C4—442no—
245C4⋊C4—442no—
246C4⋊C4—442no—
247C42#433911yescharacteristic
248C42#433911yescharacteristic
249C42Q8×D1111yescharacteristic
250C42#434311yescharacteristic
251C11#1067811yescharacteristic, complemented, Sylow
252C23—442no—
253C23—881no—
254C23—881no—
255C23—881no—
256C23—881no—
257C23—881no—
258C23—881no—
259C23#6699311yescharacteristic
260D4—444no—
261D4—444no—
262D4—444no—
263D4—882no—
264D4—882no—
265D4—882no—
266C2×C4—81no—
267C2×C4—81no—
268C2×C4—81no—
269C2×C4—81no—
270C2×C4—81no—
271C2×C4—81no—
272C2×C4—881no—
273C2×C4—881no—
274C2×C4—881no—
275C2×C4#6694711yescharacteristic
276C2×C4#6694711yescharacteristic
277C2×C4#6694911yescharacteristic
278C2×C4#6694911yescharacteristic
279C2×C4#6696412yes—
280C2×C4#6696712yes—
281C2×C4#6696912yes—
282C2×C4#6697212yes—
283C2×C4#6698211yescharacteristic
284C2×C4#6699911yescharacteristic
285C2×C4#6700212yes—
286C2×C4#6700312yes—
287C8—42no—
288C8—442no—
289C8—442no—
290C22—882no—
291C22—882no—
292C22—882no—
293C22—1761no—
294C22—1761no—
295C22—1761no—
296C22—1761no—
297C22#1062260511yescharacteristic
298C22#1062267111yescharacteristic
299C22#1062267211yescharacteristic
300C22#1062276711yescharacteristic
301C22#1062278111yescharacteristic
302C22#1062278911yescharacteristic
303C22#1062280411yescharacteristic
304C4—161no—
305C4—161no—
306C4—1761no—
307C4#1062247912yes—
308C4#1062248412yes—
309C4#1062249812yes—
310C4#1062250412yes—
311C4#1062261612yes—
312C4#1062267912yes—
313C2—1762no—
314C2#1306822911yescharacteristic
315C2#1306825611yescharacteristic
316C2#1306825711yescharacteristic
317C2#1306825811yescharacteristic
318C2#1307013411yescharacteristic
319C2#1307013811yescharacteristic
320C2#1307014011yescharacteristic
subgroupG/H
centerC23#66993
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1834C2
socleC23×C11#127
prime radicalC2×#66927C22
hypercenter#1834D11
hypocenterC11#10678
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1834

Complements

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

NH ≅ G/Ntype
4. #13068743C2semidirect
5. #13068743C2semidirect
6. C11⋊#1273C2semidirect
7. C11×#1834C2semidirect
97. #1834D11semidirect
251. C11#10678semidirect

Maximal subgroups

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

subgroupindex
#130694222
#130694212
#130687432
C11⋊#12732
C11×#18342
#1067811