Finite Group Databasebeta

← #14672649

Subgroups — #14672649

Order 2816.

546 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 103 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
1C2×#10622808C212yesmaximal
2C2×#10622312C211yesmaximal, characteristic, complemented
3C2×#10622134C212yesmaximal, complemented
4#13066698C211yesmaximal, characteristic, complemented
5C11×#1974C211yesmaximal, characteristic
6C2×C11×#135C2211yescharacteristic
7C22×Dic44—21no—
8C22×Dic44C2212yes—
9C2×#66922—21no—
10C2×C11×#108C2211yescharacteristic
11C2×C11×#104—21no—
12C11×#408—21no—
13C2×C4×C8×C11C2211yescharacteristic
14#10622808—24no—
15#10622808—24no—
16C2×#66893—22no—
17C2×#66891—22no—
18C2×#66876C2212yes—
19#10622312—24no—
20#10622134—24no—
21C2×C11×#41—21no—
22C22×Dic22—22no—
23C11×#135—22no—
24C11×#135—22no—
25C2×C11×Q16D411yescharacteristic
26C2×C11×SD16—21no—
27C2×C11×D8D411yescharacteristic
28C2×C11×M16—21no—
29C22×C8×C11D411yescharacteristic
30C22×C8×C11C2311yescharacteristic
31C2×C42×C11D411yescharacteristic
32C2×C4⋊Dic11—42no—
33C2×Dic44—22no—
34C2×Dic44—22no—
35C2×Dic44—22no—
36C2×Dic44—22no—
37C2×Dic44—24no—
38C2×Dic44—22no—
39C2×Dic44—42no—
40C2×Dic44—42no—
41C2×Dic44D414yes—
42#66922—24no—
43#66922—42no—
44C11×#108—22no—
45C11×#104—42no—
46C11×C22⋊C8—42no—
47C4×C8×C11—22no—
48#66893—28no—
49#66891—28no—
50#66876—22no—
51#66876D414yes—
52C2×C11⋊C16—22no—
53#13333—111nomaximal, Sylow
54C11×#41—41no—
55C11×#41—41no—
56C11×#41—41no—
57C11×#41—41no—
58C2×Q8×C11—21no—
59C2×D4×C11—21no—
60C2×D4×C11—41no—
61C22×C4×C11—21no—
62C22×C4×C11—41no—
63C22×C4×C11C2×D411yescharacteristic
64C22×Dic11—42no—
65C2×Dic22—24no—
66C2×Dic22—42no—
67C2×Dic22—42no—
68C2×Dic22—42no—
69C2×Dic22—42no—
70C2×Dic22—42no—
71C11×Q16—22no—
72C11×SD16—42no—
73C11×D8—22no—
74C11×M16—41no—
75C11×M16—41no—
76C2×C8×C11—21no—
77C2×C8×C11—21no—
78C2×C8×C11—41no—
79C2×C8×C11D812yes—
80C2×C8×C11C2×D412yes—
81C2×C8×C11C2×D411yescharacteristic
82C2×C8×C11C2×D412yes—
83C2×C8×C11#4111yescharacteristic
84C42×C11—21no—
85C42×C11D812yes—
86C4⋊Dic11—48no—
87Dic44—24no—
88Dic44—24no—
89Dic44—48no—
90Dic44—42no—
91Dic44—42no—
92C11⋊C16—24no—
93C2×#510—112no—
94C2×#494—111no—
95C2×#362—112no—
96#1974D1111yescharacteristic
97#1376—111no—
98C23×C11—41no—
99C23×C11AGL(1,ℤ/8)11yescharacteristic
100Q8×C11—41no—
101Q8×C11—41no—
102D4×C11—41no—
103D4×C11—41no—
104D4×C11—81no—
105D4×C11—81no—
106C2×C4×C11—24no—
107C2×C4×C11—22no—
108C2×C4×C11—41no—
109C2×C4×C11—81no—
110C2×C4×C11—81no—
111C2×C4×C11#12011yescharacteristic
112C2×C4×C11#12111yescharacteristic
113C2×C4×C11#12711yescharacteristic
114C2×C4×C11C2×D811yescharacteristic
115C2×C4×C11C2×D811yescharacteristic
116C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
117C2×Dic11—44no—
118C2×Dic11—82no—
119C2×Dic11—82no—
120Dic22—44no—
121Dic22—44no—
122Dic22—82no—
123Dic22—82no—
124C8×C11—22no—
125C8×C11—81no—
126C8×C11#12012yes—
127C8×C11#12112yes—
128C2×#135C2×D1111yescharacteristic
129C22×Q16—112no—
130C22×Q16—221no—
131C2×C4⋊Q8—221no—
132#510—224no—
133#510—224no—
134C2×Q32—222no—
135C2×SD32—222no—
136C2×M32—112no—
137#494—224no—
138C2×#108C2×D1111yescharacteristic
139C2×#104—21no—
140#408—21no—
141C2×C4×C8C2×D1111yescharacteristic
142#362—224no—
143C22×C11—22no—
144C22×C11—82no—
145C22×C11—81no—
146C22×C11#44711yescharacteristic
147C22×C11#45911yescharacteristic
148C22×C11#49611yescharacteristic
149C4×C11—24no—
150C4×C11—81no—
151C4×C11#39211yescharacteristic
152C4×C11#44711yescharacteristic
153C4×C11#45911yescharacteristic
154C4×C11#49311yescharacteristic
155Dic11—84no—
156C2×#41—21no—
157C22×Q8—222no—
158#135—22no—
159#135—22no—
160C2×Q16—114no—
161C2×Q16—224no—
162C2×Q16—222no—
163C2×Q16—222no—
164C2×Q16—222no—
165C2×Q16—222no—
166C2×Q16—222no—
167C2×Q16—442no—
168C2×Q16—442no—
169C2×Q16D4411yescharacteristic
170C2×SD16—21no—
171C2×D8D4411yescharacteristic
172C2×M16—21no—
173C22×C8C22⋊D1111yescharacteristic
174C22×C8C22×D1111yescharacteristic
175C4⋊Q8—224no—
176C4⋊Q8—442no—
177C2×C4⋊C4—442no—
178C2×C42C22⋊D1111yescharacteristic
179Q32—228no—
180SD32—228no—
181M32—114no—
182M32—222no—
183C2×C16—222no—
184#108—22no—
185#104—42no—
186C22⋊C8—42no—
187C4×C8—22no—
188C2×C11—21no—
189C2×C11—21no—
190C2×C11—161no—
191C2×C11#201111yescharacteristic
192C2×C11#221412yes—
193#41—41no—
194#41—41no—
195#41—41no—
196#41—41no—
197C2×Q8—21no—
198C2×Q8—224no—
199C2×Q8—442no—
200C2×Q8—442no—
201C2×Q8—442no—
202C2×Q8—442no—
203C2×Q8—442no—
204C2×D4—21no—
205C2×D4—41no—
206C22×C4—21no—
207C22×C4—41no—
208C22×C4—442no—
209C22×C4C2×C22⋊D1111yescharacteristic
210Q16—22no—
211Q16—224no—
212Q16—224no—
213Q16—448no—
214Q16—442no—
215Q16—442no—
216SD16—42no—
217D8—22no—
218M16—41no—
219M16—41no—
220C2×C8—21no—
221C2×C8—21no—
222C2×C8—41no—
223C2×C8#432312yes—
224C2×C8C2×D4411yescharacteristic
225C2×C8#433911yescharacteristic
226C2×C8D4×D1112yes—
227C2×C8D4×D1112yes—
228C4⋊C4—448no—
229C42—21no—
230C42#432312yes—
231C16—224no—
232C11#1333311yescharacteristic, complemented, Sylow
233C23—41no—
234C23#6700211yescharacteristic
235Q8—41no—
236Q8—41no—
237Q8—444no—
238Q8—444no—
239Q8—882no—
240Q8—882no—
241D4—41no—
242D4—41no—
243D4—81no—
244D4—81no—
245C2×C4—24no—
246C2×C4—22no—
247C2×C4—41no—
248C2×C4—81no—
249C2×C4—81no—
250C2×C4—444no—
251C2×C4—882no—
252C2×C4—882no—
253C2×C4#6698311yescharacteristic
254C2×C4C2×#432311yescharacteristic
255C2×C4C2×#432311yescharacteristic
256C2×C4#6699011yescharacteristic
257C2×C4#6699311yescharacteristic
258C2×C4#6700211yescharacteristic
259C8—22no—
260C8—81no—
261C8#6693512yes—
262C8#6693712yes—
263C22—22no—
264C22—82no—
265C22—81no—
266C22#1062262811yescharacteristic
267C22#1062264911yescharacteristic
268C22#1062267111yescharacteristic
269C4—24no—
270C4—81no—
271C4—884no—
272C4#1062257311yescharacteristic
273C4#1062262811yescharacteristic
274C4#1062264911yescharacteristic
275C4#1062268611yescharacteristic
276C2—21no—
277C2—21no—
278C2—161no—
279C2#1306968611yescharacteristic
280C2#1307069712yes—
subgroupG/H
centerC22#10622628
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#1974C2
socleC22×C11#459
prime radicalC2×C11×#135C22
hypercenter#1974D11
hypocenterC11#13333
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8 ◁ #1974

Complements

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

NH ≅ G/Ntype
2. C2×#10622312C2semidirect
3. C2×#10622134C2semidirect
4. #13066698C2semidirect
232. C11#13333semidirect

Maximal subgroups

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

subgroupindex
C2×#106228082
C2×#106223122
C2×#106221342
#130666982
C11×#19742
#1333311