Finite Group Databasebeta

← #14674113

Subgroups — #14674113

Order 2816.

398 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079074C211yesmaximal, characteristic
2#13070300C212yesmaximal
3#13066785C211yesmaximal, characteristic, complemented
4#13066784C212yesmaximal, complemented
5C11×#1411C211yesmaximal, characteristic, complemented
6C2×#66971—22no—
7#10623256C2211yescharacteristic
8D11×C4⋊Q8C411yescharacteristic
9C11×#494C2211yescharacteristic
10#10622803—22no—
11#10622705C2211yescharacteristic
12#10622698C411yescharacteristic
13#10622364—22no—
14#10622306C411yescharacteristic
15C4×#4313C411yescharacteristic
16C11×#356C2212yes—
17#10622186C2212yes—
18#10622115—22no—
19C2×#4343D412yes—
20C2×Q8×D11—21no—
21C2×C11×Q16—22no—
22C11×C4⋊Q8C2×C411yescharacteristic
23C11×C4⋊Q8C2311yescharacteristic
24#67000D412yes—
25#66997—21no—
26C2×#4326—22no—
27C2×#4325—22no—
28#66971—44no—
29#66971—44no—
30M16×D11—42no—
31C2×#4314—22no—
32C2×#4313—21no—
33#66948—41no—
34#66946—41no—
35C4⋊C4×D11—41no—
36#66941—41no—
37#66927C2×C411yescharacteristic
38C42×D11C2×C411yescharacteristic
39#66922C2×C411yescharacteristic
40C11×#101—22no—
41C4×C8×C11C2×C411yescharacteristic
42#66900—22no—
43#66887—42no—
44#66879—21no—
45C4×C11⋊C8C2×C411yescharacteristic
46#13592—111nomaximal, Sylow
47C2×Q8×C11—21no—
48C2×Q8×C11C2×D412yes—
49#4343—42no—
50#4343—42no—
51Q8×D11—42no—
52Q8×D11—42no—
53C2×D44—22no—
54C2×D44—41no—
55C2×D44C22⋊C412yes—
56C2×C4×D11—22no—
57C2×C4×D11—21no—
58C2×C4×D11—41no—
59C2×C4×D11C22⋊C411yescharacteristic
60C2×Dic22—21no—
61C2×Dic22—41no—
62C11×Q16—44no—
63C11×M16—42no—
64C2×C8×C11—21no—
65C11×C4⋊C4—41no—
66C11×C4⋊C4—41no—
67C42×C11C22×C411yescharacteristic
68#4326—44no—
69#4325—44no—
70(C2×D11)⋊C4—42no—
71C4⋊Dic11—41no—
72Dic11⋊C4—42no—
73C4×Dic11—21no—
74C4×Dic11C22⋊C411yescharacteristic
75#4318—42no—
76C2×C11⋊C8—21no—
77#4314—44no—
78#4313—24no—
79#4313—82no—
80C8×D11—82no—
81#3152—111no—
82#2132—112no—
83#1411—111no—
84#1411—112no—
85#1411D1111yescharacteristic, complemented
86C22×D11—22no—
87C22×D11#9911yescharacteristic
88Q8×C11—42no—
89Q8×C11—42no—
90C2×C4×C11—21no—
91C2×C4×C11—22no—
92C2×C4×C11—41no—
93C2×C4×C11C2×C22⋊C411yescharacteristic
94C2×Dic11—21no—
95C2×Dic11—41no—
96C2×Dic11#9911yescharacteristic
97D44—42no—
98D44—82no—
99D44—82no—
100C4×D11—22no—
101C4×D11—42no—
102C4×D11—42no—
103C4×D11—42no—
104C4×D11—81no—
105C4×D11—81no—
106Dic22—42no—
107Dic22—82no—
108C8×C11—22no—
109C8×C11—82no—
110C11⋊C8—22no—
111C11⋊C8—82no—
112C2×#137—222no—
113#532—111no—
114C2×C4⋊Q8—111no—
115#497—222no—
116#494—111no—
117#494C2×D1111yescharacteristic
118#492—111no—
119#492—111no—
120#413—222no—
121C4×M16—111no—
122#356—112no—
123#356C2×D1112yes—
124#355—222no—
125C22×C11C2×#9911yescharacteristic
126C2×D11—21no—
127C2×D11—41no—
128C2×D11—42no—
129C2×D11—82no—
130C4×C11—22no—
131C4×C11—21no—
132C4×C11—42no—
133C4×C11—81no—
134Dic11—41no—
135Dic11—81no—
136Dic11#35312yes—
137C2×#41—112no—
138C22×Q8—221no—
139#137—444no—
140#137—444no—
141C2×Q16—22no—
142C2×Q16—222no—
143C2×SD16—222no—
144C2×SD16—222no—
145C2×M16—221no—
146C2×M16—442no—
147C4⋊Q8—111no—
148C4⋊Q8—221no—
149C4⋊Q8—441no—
150C4⋊Q8C4×D1111yescharacteristic
151C4⋊Q8C22×D1111yescharacteristic
152#127—111no—
153#124—112no—
154#121—441no—
155C4×D4—441no—
156C2×C4⋊C4—441no—
157C2×C42—111no—
158#101—22no—
159#101—222no—
160#100—442no—
161#97—221no—
162C4×C8—111no—
163C4×C8C4×D1111yescharacteristic
164C2×C11—21no—
165C2×C11C2×#35311yescharacteristic
166D11—41no—
167D11—82no—
168#41—442no—
169#41—442no—
170C2×Q8—21no—
171C2×Q8—221no—
172C2×Q8—441no—
173C2×Q8—442no—
174C2×Q8—442no—
175C2×Q8D4×D1112yes—
176C2×D4—112no—
177C2×D4—222no—
178C2×D4—441no—
179C22×C4—111no—
180C22×C4—222no—
181C22×C4—221no—
182C22×C4—441no—
183Q16—44no—
184Q16—444no—
185SD16—444no—
186SD16—444no—
187M16—42no—
188M16—224no—
189M16—442no—
190M16—882no—
191C2×C8—21no—
192C2×C8—221no—
193C2×C8—882no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—441no—
197C4⋊C4—442no—
198C22⋊C4—442no—
199C42—111no—
200C42—221no—
201C42C2×C4×D1111yescharacteristic
202C11#1359211yescharacteristic, complemented, Sylow
203C23—111no—
204C23—222no—
205Q8—42no—
206Q8—42no—
207Q8—442no—
208Q8—882no—
209D4—442no—
210D4—882no—
211D4—882no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—41no—
215C2×C4—111no—
216C2×C4—222no—
217C2×C4—221no—
218C2×C4—442no—
219C2×C4—442no—
220C2×C4—442no—
221C2×C4—441no—
222C2×C4—881no—
223C2×C4—881no—
224C2×C4C22⋊C4×D1111yescharacteristic
225C8—22no—
226C8—82no—
227C8—222no—
228C8—882no—
229C22—221no—
230C22—441no—
231C22—442no—
232C22—882no—
233C22D11×#9911yescharacteristic
234C4—22no—
235C4—21no—
236C4—42no—
237C4—81no—
238C4—112no—
239C4—441no—
240C4—881no—
241C2—21no—
242C2—441no—
243C2—882no—
244C2D11×#35311yescharacteristic
subgroupG/H
centerC2D11×#353
commutatorC42×C11C22×C4
FrattiniC4⋊Q8C22×D11
FittingC11×#1411C2
socleC2×C11C2×#353
prime radical#10623256C22
cosocleC11×C4⋊Q8C23
hypercenter#1411D11
hypocenterC11#13592
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C4⋊Q8 ◁ #1411

Complements

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

NH ≅ G/Ntype
3. #13066785C2semidirect
4. #13066784C2semidirect
5. C11×#1411C2semidirect
85. #1411D11semidirect
202. C11#13592semidirect

Maximal subgroups

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

subgroupindex
#130790742
#130703002
#130667852
#130667842
C11×#14112
#1359211