Finite Group Databasebeta

← #14667384

Subgroups — #14667384

Order 2816.

318 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 67 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#13081039C211yesmaximal, characteristic, complemented
2#13070839C211yesmaximal, characteristic, complemented
3#13070648C211yesmaximal, characteristic, complemented
4#13066675C211yesmaximal, characteristic, complemented
5#13066576C211yesmaximal, characteristic, complemented
6D4⋊(C11⋊C16)C211yesmaximal, characteristic, complemented
7C11×#1667C211yesmaximal, characteristic, complemented
8#10623094—21no—
9C11×#493C2211yescharacteristic
10C11×#459—21no—
11C8×D4×C11C2211yescharacteristic
12C2×#66890—21no—
13#10622728—21no—
14#10622719—21no—
15#10622455—21no—
16#10622350—22no—
17C4×D88C2211yescharacteristic
18#10622295C2211yescharacteristic
19C11×#335C2211yescharacteristic
20C11×#331—21no—
21#10622200—21no—
22#10622200—22no—
23C4⋊(C11⋊C16)C2211yescharacteristic
24C4×C11⋊C16C2211yescharacteristic
25C2×C11×D8—21no—
26C2×C11×D8—21no—
27C2×C11×D8—41no—
28C22×C8×C11—21no—
29C11×#127—21no—
30C4×D4×C11D411yescharacteristic
31#66991—41no—
32#66983—22no—
33#66979—22no—
34C2×D88D411yescharacteristic
35#66945—41no—
36#66938—42no—
37C4×D44—21no—
38#66922—21no—
39C11×C4⋊C8—21no—
40C11×C4⋊C8D411yescharacteristic
41C11×#102—41no—
42C11×C22⋊C8—21no—
43C4×C8×C11C2311yescharacteristic
44#66890—42no—
45#66885—22no—
46#66885—21no—
47#66882—21no—
48#66882D412yes—
49#66882D411yescharacteristic
50#66881—22no—
51C2×C11⋊C16—21no—
52C2×C11⋊C16—21no—
53#12343—111nomaximal, Sylow
54C2×D4×C11—41no—
55C2×D4×C11—41no—
56C2×D4×C11—41no—
57C2×D4×C11D811yescharacteristic
58C22×C4×C11—21no—
59C2×C22⋊D11—42no—
60C2×D44—21no—
61C2×C4×D11—41no—
62C2×Dic22—41no—
63C11×D8—42no—
64C11×D8—41no—
65C11×D8—41no—
66C11×D8—82no—
67C2×C8×C11—21no—
68C2×C8×C11—41no—
69C2×C8×C11—41no—
70C2×C8×C11—41no—
71C2×C8×C11C2×D411yescharacteristic
72C2×C8×C11C2×D411yescharacteristic
73C11×C4⋊C4D811yescharacteristic
74C11×C22⋊C4—21no—
75C42×C11C2×D411yescharacteristic
76C22⋊Dic11—42no—
77(C2×D11)⋊C4—42no—
78(C2×D11)⋊C4—41no—
79C4⋊Dic11—21no—
80C4⋊Dic11—22no—
81C4⋊Dic11—41no—
82C4×Dic11—42no—
83D88—21no—
84D88—21no—
85C11⋊C16—41no—
86C11⋊C16—41no—
87#3341—111no—
88#2240—111no—
89#2206—111no—
90#1667D1111yescharacteristic, complemented
91#1365—111no—
92#1331—111no—
93D4⋊C16—111no—
94C23×C11—21no—
95C23×C11—81no—
96C22×D11—41no—
97D4×C11—21no—
98D4×C11—21no—
99D4×C11—81no—
100D4×C11—81no—
101D4×C11—81no—
102D4×C11—81no—
103D4×C11—161no—
104C2×C4×C11—21no—
105C2×C4×C11—41no—
106C2×C4×C11—41no—
107C2×C4×C11#12011yescharacteristic
108C2×C4×C11C2×D811yescharacteristic
109C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
110C22⋊D11—162no—
111C2×Dic11—41no—
112C2×Dic11—42no—
113D44—41no—
114D44—41no—
115C4×D11—81no—
116C4×D11—81no—
117Dic22—161no—
118C8×C11—21no—
119C8×C11—41no—
120C8×C11—81no—
121C8×C11#13511yescharacteristic
122C8×C11AGL(1,ℤ/8)11yescharacteristic
123#555—221no—
124C2×D16—221no—
125#500—111no—
126#493C2×D1111yescharacteristic
127#482—222no—
128#476—221no—
129#466—221no—
130#459—21no—
131C4×D8—111no—
132C8×D4C2×D1111yescharacteristic
133#427—221no—
134C4⋊C16—111no—
135#357—221no—
136#357—222no—
137C4×C16—111no—
138#335C2×D1111yescharacteristic
139#331—21no—
140C22×C11—41no—
141C22×C11—41no—
142C22×C11—41no—
143C22×C11—161no—
144C22×C11—161no—
145C22×C11—161no—
146C22×C11#44711yescharacteristic
147C2×D11—81no—
148C2×D11—81no—
149C2×D11—81no—
150C4×C11—21no—
151C4×C11—41no—
152C4×C11#44911yescharacteristic
153C4×C11#45411yescharacteristic
154C4×C11#50811yescharacteristic
155C4×C11#50911yescharacteristic
156Dic11—81no—
157Dic11—82no—
158C2×D8—21no—
159C2×D8—21no—
160C2×D8—41no—
161C2×D8—111no—
162C22×C8—21no—
163C4⋊Q8—221no—
164#127—21no—
165#124—442no—
166#121—222no—
167#121—441no—
168C4×D4—221no—
169C4×D4C22⋊D1111yescharacteristic
170#117—222no—
171#117—441no—
172D16—442no—
173C2×C16—221no—
174C2×C16—221no—
175#107—111no—
176#107—112no—
177#107—221no—
178#106—222no—
179C4⋊C8—21no—
180C4⋊C8C22⋊D1111yescharacteristic
181#102—41no—
182#102—222no—
183#102—221no—
184C22⋊C8—21no—
185C4×C8C22×D1111yescharacteristic
186C2×C11—81no—
187C2×C11—321no—
188C2×C11#162511yescharacteristic
189C2×C11#218611yescharacteristic
190C2×C11#219211yescharacteristic
191D11—161no—
192C2×Q8—441no—
193C2×D4—41no—
194C2×D4—41no—
195C2×D4—41no—
196C2×D4—221no—
197C2×D4—442no—
198C2×D4#432311yescharacteristic
199C22×C4—21no—
200C22×C4—441no—
201D8—42no—
202D8—41no—
203D8—41no—
204D8—82no—
205D8—221no—
206D8—221no—
207C2×C8—21no—
208C2×C8—41no—
209C2×C8—41no—
210C2×C8—41no—
211C2×C8D4×D1111yescharacteristic
212C2×C8D4×D1111yescharacteristic
213C4⋊C4—221no—
214C4⋊C4—222no—
215C4⋊C4—441no—
216C4⋊C4#432311yescharacteristic
217C22⋊C4—21no—
218C22⋊C4—442no—
219C22⋊C4—442no—
220C22⋊C4—441no—
221C42—442no—
222C42C2×C22⋊D1111yescharacteristic
223C16—441no—
224C16—441no—
225C11#1234311yescharacteristic, complemented, Sylow
226C23—21no—
227C23—81no—
228C23—441no—
229Q8—1761no—
230D4—21no—
231D4—21no—
232D4—81no—
233D4—81no—
234D4—81no—
235D4—81no—
236D4—161no—
237D4—441no—
238D4—441no—
239D4—1762no—
240C2×C4—21no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—441no—
244C2×C4—442no—
245C2×C4—881no—
246C2×C4—881no—
247C2×C4C2×#432311yescharacteristic
248C2×C4#6699011yescharacteristic
249C2×C4#6700211yescharacteristic
250C8—21no—
251C8—41no—
252C8—81no—
253C8#6696411yescharacteristic
254C8#6696511yescharacteristic
255C22—41no—
256C22—41no—
257C22—41no—
258C22—161no—
259C22—161no—
260C22—161no—
261C22—881no—
262C22—881no—
263C22—881no—
264C22#1062264911yescharacteristic
265C4—21no—
266C4—41no—
267C4—881no—
268C4—882no—
269C4#1062276011yescharacteristic
270C4#1062277111yescharacteristic
271C4#1062280711yescharacteristic
272C4#1062281411yescharacteristic
273C2—81no—
274C2—321no—
275C2—1761no—
276C2#1306770311yescharacteristic
277C2#1307053711yescharacteristic
278C2#1307057111yescharacteristic
subgroupG/H
centerC22#10622649
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1667C2
socleC22×C11#447
hypercenter#1667D11
hypocenterC11#12343
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C8×D4 ◁ #1667

Complements

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

NH ≅ G/Ntype
1. #13081039C2semidirect
2. #13070839C2semidirect
3. #13070648C2semidirect
4. #13066675C2semidirect
5. #13066576C2semidirect
6. D4⋊(C11⋊C16)C2semidirect
7. C11×#1667C2semidirect
90. #1667D11semidirect
225. C11#12343semidirect

Maximal subgroups

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

subgroupindex
#130810392
#130708392
#130706482
#130666752
#130665762
D4⋊(C11⋊C16)2
C11×#16672
#1234311