Finite Group Databasebeta

← #14673243

Subgroups — #14673243

Order 2816.

444 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 77 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×#10622186C212yesmaximal
2#13069010C212yesmaximal
3#13068830C211yesmaximal, characteristic
4#13066743C211yesmaximal, characteristic
5C11×#2734C211yesmaximal, characteristic
6C2×C11×C4⋊Q8C2212yes—
7#10623343C2211yescharacteristic
8C11×#398—21no—
9C11×#395—22no—
10C11×#391C2211yescharacteristic
11C11×#389—21no—
12C11×#387—22no—
13C2×#66900C2212yes—
14C2×#66900C2211yescharacteristic
15#10622838—22no—
16#10622577—21no—
17#10622186—24no—
18#10622161—21no—
19#10622161—22no—
20C22×Q8×C11D412yes—
21C22×Q8×C11C2311yescharacteristic
22C11×C4⋊Q8—22no—
23C11×C4⋊Q8—22no—
24C11×C4⋊Q8—22no—
25C11×C4⋊Q8—22no—
26C2×C11×C4⋊C4—21no—
27C2×C11×C4⋊C4—22no—
28C2×C11×C4⋊C4—22no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4D411yescharacteristic
32C2×C42×C11D412yes—
33C2×C42×C11D411yescharacteristic
34Q8×Dic11—41no—
35Q8×Dic11—41no—
36#66979—21no—
37#66979—22no—
38C2×#4318—21no—
39C2×#4318—22no—
40C11×#95—21no—
41C11×#95—22no—
42C11×#95—22no—
43C11×#95—22no—
44#66900—21no—
45#66900—22no—
46#66900—22no—
47#66900D412yes—
48#66899—42no—
49#66899—42no—
50#66872—41no—
51#66871—41no—
52#13428—111nomaximal, Sylow
53C2×Q8×C11—22no—
54C2×Q8×C11—22no—
55C2×Q8×C11—41no—
56C2×Q8×C11—41no—
57C2×Q8×C11—42no—
58C2×Q8×C11—42no—
59C2×Q8×C11C2×D411yescharacteristic
60C2×Q8×C11#4111yescharacteristic
61C2×Q8×C11#4112yes—
62C22×C4×C11—21no—
63C22×C4×C11—22no—
64C22×C4×C11—21no—
65C22×C4×C11—22no—
66C22×C4×C11C2×D412yes—
67C22×C4×C11C2×D411yescharacteristic
68C11×C4⋊C4—24no—
69C11×C4⋊C4—41no—
70C11×C4⋊C4—42no—
71C11×C4⋊C4—42no—
72C11×C4⋊C4—42no—
73C11×C4⋊C4—42no—
74C11×C4⋊C4—81no—
75C11×C4⋊C4—81no—
76C42×C11—22no—
77C42×C11—22no—
78C42×C11—41no—
79C22⋊Dic11—41no—
80C4⋊Dic11—21no—
81C4⋊Dic11—21no—
82C4⋊Dic11—22no—
83C4⋊Dic11—22no—
84C4×Dic11—41no—
85C4×Dic11—42no—
86#4318—22no—
87#4318—41no—
88#4318—42no—
89#4318—42no—
90C2×C11⋊C8—41no—
91C2×C11⋊C8—42no—
92#2734D1111yescharacteristic
93C2×#356—112no—
94#1886—112no—
95#1857—111no—
96#1394—111no—
97C23×C11#12011yescharacteristic
98Q8×C11—41no—
99Q8×C11—42no—
100Q8×C11—41no—
101Q8×C11—44no—
102Q8×C11—82no—
103C2×C4×C11—21no—
104C2×C4×C11—22no—
105C2×C4×C11—21no—
106C2×C4×C11—22no—
107C2×C4×C11—22no—
108C2×C4×C11—24no—
109C2×C4×C11—41no—
110C2×C4×C11—42no—
111C2×C4×C11—42no—
112C2×C4×C11—41no—
113C2×C4×C11—42no—
114C2×C4×C11—42no—
115C2×C4×C11—41no—
116C2×C4×C11—42no—
117C2×C4×C11—42no—
118C2×C4×C11#12111yescharacteristic
119C2×C4×C11#12112yes—
120C2×C4×C11#12312yes—
121C2×C4×C11#12411yescharacteristic
122C2×Dic11—41no—
123C2×Dic11—41no—
124C11⋊C8—42no—
125C11⋊C8—82no—
126C2×C4⋊Q8C2×D1112yes—
127#519—111no—
128#428—221no—
129#419—222no—
130C2×#101—111no—
131C2×#101—112no—
132#398—21no—
133#395—22no—
134#391C2×D1111yescharacteristic
135#389—21no—
136#387—22no—
137#356—224no—
138#339—221no—
139#339—222no—
140C22×C11—21no—
141C22×C11—21no—
142C22×C11#39411yescharacteristic
143C22×C11B(4,𝔽2)11yescharacteristic
144C22×C11#45811yescharacteristic
145C4×C11—22no—
146C4×C11—21no—
147C4×C11—22no—
148C4×C11—21no—
149C4×C11—44no—
150C4×C11—42no—
151C4×C11—81no—
152C4×C11—82no—
153Dic11—81no—
154Dic11—81no—
155C22×Q8C22⋊D1112yes—
156C22×Q8C22×D1111yescharacteristic
157C2×M16—221no—
158C2×M16—222no—
159C4⋊Q8—22no—
160C4⋊Q8—22no—
161C4⋊Q8—22no—
162C4⋊Q8—22no—
163C4×Q8—441no—
164C4×Q8—441no—
165#117—222no—
166#117—221no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4C22⋊D1111yescharacteristic
173C2×C42C22⋊D1112yes—
174C2×C42C22⋊D1111yescharacteristic
175#107—441no—
176#106—441no—
177#103—442no—
178#103—442no—
179#101—112no—
180#101—221no—
181#101—222no—
182#101—222no—
183#95—21no—
184#95—22no—
185#95—22no—
186#95—22no—
187C2×C11—21no—
188C2×C11—21no—
189C2×C11#204411yescharacteristic
190C2×C11#220311yescharacteristic
191C2×C11#220511yescharacteristic
192C2×Q8—22no—
193C2×Q8—22no—
194C2×Q8—41no—
195C2×Q8—41no—
196C2×Q8—42no—
197C2×Q8—42no—
198C2×Q8D4×D1111yescharacteristic
199C2×Q8#434111yescharacteristic
200C2×Q8#434112yes—
201C22×C4—21no—
202C22×C4—22no—
203C22×C4—21no—
204C22×C4—22no—
205C22×C4C2×C22⋊D1112yes—
206C22×C4C2×C22⋊D1111yescharacteristic
207M16—222no—
208M16—441no—
209M16—442no—
210M16—442no—
211C2×C8—441no—
212C2×C8—442no—
213C4⋊C4—24no—
214C4⋊C4—41no—
215C4⋊C4—42no—
216C4⋊C4—42no—
217C4⋊C4—42no—
218C4⋊C4—42no—
219C4⋊C4—81no—
220C4⋊C4—81no—
221C4⋊C4—222no—
222C4⋊C4—222no—
223C4⋊C4—221no—
224C4⋊C4—221no—
225C22⋊C4—441no—
226C42—22no—
227C42—22no—
228C42—41no—
229C42—441no—
230C42—442no—
231C11#1342811yescharacteristic, complemented, Sylow
232C23#6700611yescharacteristic
233Q8—41no—
234Q8—41no—
235Q8—42no—
236Q8—44no—
237Q8—82no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—24no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—41no—
252C2×C4—42no—
253C2×C4—441no—
254C2×C4—441no—
255C2×C4#6698812yes—
256C2×C4#6698911yescharacteristic
257C2×C4#6699111yescharacteristic
258C2×C4#6699212yes—
259C8—442no—
260C8—882no—
261C22—21no—
262C22—21no—
263C22#1062283511yescharacteristic
264C22#1062285611yescharacteristic
265C22#1062285711yescharacteristic
266C4—21no—
267C4—22no—
268C4—22no—
269C4—21no—
270C4—44no—
271C4—42no—
272C4—82no—
273C4—81no—
274C4—881no—
275C4—881no—
276C2—21no—
277C2—21no—
278C2#1306986411yescharacteristic
279C2#1307063711yescharacteristic
280C2#1307064611yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC22×Q8×C11C23
FrattiniC22×Q8C22×D11
FittingC11×#2734C2
socleC22×C11B(4,𝔽2)
prime radicalC23×C11#120
hypercenter#2734D11
hypocenterC11#13428
LCSG ▷ C22×Q8×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #2734

Complements

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

NH ≅ G/Ntype
231. C11#13428semidirect

Maximal subgroups

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

subgroupindex
C2×#106221862
#130690102
#130688302
#130667432
C11×#27342
#1342811