Finite Group Databasebeta

← #14673456

Subgroups — #14673456

Order 2816.

484 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 81 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#13076562C211yesmaximal, characteristic
2#13068899C212yesmaximal
3#13068825C211yesmaximal, characteristic
4#13066733C212yesmaximal
5C11×#1393C211yesmaximal, characteristic
6#10623329C2211yescharacteristic
7C2×C11×#99C2212yes—
8C11×#390C2211yescharacteristic
9#10622833C2212yes—
10C2×#66897C2211yescharacteristic
11#10622599—21no—
12#10622577—21no—
13#10622563—22no—
14#10622563—22no—
15#10622560—22no—
16#10622542—21no—
17#10622165—22no—
18#10622161—21no—
19C22×D4×C11C2311yescharacteristic
20C23×Dic11D412yes—
21C22×Dic22—21no—
22C2×C11×C4⋊C4D411yescharacteristic
23C2×C11×C22⋊C4—22no—
24C2×C11×C22⋊C4—22no—
25C2×C42×C11D411yescharacteristic
26C2×C22⋊Dic11—22no—
27C2×C22⋊Dic11—22no—
28C2×C22⋊Dic11D412yes—
29D4×Dic11—41no—
30D4×Dic11—41no—
31#66979—21no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—42no—
35C2×#4318—21no—
36C11×#99—22no—
37C11×#99Q814yescomplemented
38#66897—21no—
39#66897Q812yescomplemented
40C11⋊#95—22no—
41C11⋊#95—21no—
42C11⋊#95—22no—
43C11⋊#95—22no—
44C11⋊#95—42no—
45#66872—41no—
46#66871—41no—
47#13463—111nomaximal, Sylow
48C24×C11C2×D412yes—
49C2×D4×C11—41no—
50C2×D4×C11—41no—
51C2×D4×C11C2×Q811yescharacteristic
52C2×D4×C11C2×Q812yes—
53C2×D4×C11#4111yescharacteristic
54C22×C4×C11—21no—
55C22×C4×C11—21no—
56C22×C4×C11—42no—
57C22×C4×C11C2×D411yescharacteristic
58C22×Dic11—22no—
59C22×Dic11—22no—
60C22×Dic11—22no—
61C22×Dic11—22no—
62C22×Dic11—42no—
63C22×Dic11—82no—
64C2×Dic22—42no—
65C2×Dic22—81no—
66C2×Dic22—81no—
67C11×C4⋊C4—41no—
68C11×C22⋊C4—24no—
69C11×C22⋊C4—44no—
70C11×C22⋊C4—42no—
71C42×C11—41no—
72C22⋊Dic11—42no—
73C22⋊Dic11—42no—
74C22⋊Dic11—41no—
75C22⋊Dic11—82no—
76C4⋊Dic11—21no—
77C4⋊Dic11—21no—
78C4⋊Dic11—81no—
79C4⋊Dic11—81no—
80C4⋊Dic11—84no—
81C4×Dic11—41no—
82#4318—22no—
83#4318—41no—
84C2×C11⋊C8—41no—
85#2804—111no—
86#1867—112no—
87#1856—111no—
88#1393D1111yescharacteristic
89#1390—112no—
90C23×C11—22no—
91C23×C11—22no—
92C23×C11—42no—
93C23×C11—42no—
94C23×C11#12011yescharacteristic
95C23×C11C22⋊Q812yes—
96C23×C11C4⋊Q812yes—
97D4×C11—42no—
98D4×C11—41no—
99D4×C11—41no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—22no—
103C2×C4×C11—41no—
104C2×C4×C11—41no—
105C2×C4×C11—44no—
106C2×C4×C11—42no—
107C2×C4×C11—41no—
108C2×C4×C11—82no—
109C2×C4×C11—82no—
110C2×C4×C11C22⋊Q811yescharacteristic
111C2×C4×C11C4⋊Q811yescharacteristic
112C2×Dic11—42no—
113C2×Dic11—42no—
114C2×Dic11—42no—
115C2×Dic11—42no—
116C2×Dic11—44no—
117C2×Dic11—41no—
118C2×Dic11—41no—
119C2×Dic11—42no—
120C2×Dic11—42no—
121C2×Dic11—82no—
122C2×Dic11—82no—
123C2×Dic11—82no—
124Dic22—84no—
125C11⋊C8—42no—
126#518—111no—
127#428—221no—
128C2×#100—111no—
129C2×#99C2×D1112yes—
130#400—221no—
131#393—222no—
132#391—221no—
133#390C2×D1111yescharacteristic
134#386—112no—
135#385—222no—
136#385—222no—
137#342—222no—
138#339—221no—
139C22×C11—21no—
140C22×C11—21no—
141C22×C11—22no—
142C22×C11—22no—
143C22×C11—42no—
144C22×C11—42no—
145C22×C11—42no—
146C22×C11—42no—
147C22×C11—82no—
148C22×C11#39511yescharacteristic
149C22×C11B(4,𝔽2)11yescharacteristic
150C22×C11#45811yescharacteristic
151C4×C11—21no—
152C4×C11—21no—
153C4×C11—42no—
154C4×C11—84no—
155C4×C11—81no—
156Dic11—82no—
157Dic11—81no—
158Dic11—82no—
159Dic11—81no—
160C22×Q8—221no—
161C22×D4C22×D1111yescharacteristic
162C23×C4—112no—
163C2×M16—221no—
164C4×D4—441no—
165C4×D4—441no—
166#117—221no—
167C2×C4⋊C4—221no—
168C2×C4⋊C4—221no—
169C2×C4⋊C4—442no—
170C2×C4⋊C4D4411yescharacteristic
171C2×C22⋊C4—22no—
172C2×C22⋊C4—22no—
173C2×C22⋊C4—112no—
174C2×C22⋊C4—222no—
175C2×C22⋊C4—222no—
176C2×C42D4411yescharacteristic
177#107—441no—
178#106—441no—
179#100—112no—
180#100—221no—
181#99—22no—
182#99Dic2214yescomplemented
183#95—222no—
184#95—222no—
185#95—221no—
186#95—222no—
187#95—442no—
188C2×C11—21no—
189C2×C11—21no—
190C2×C11—42no—
191C2×C11—42no—
192C2×C11#206211yescharacteristic
193C2×C11#219811yescharacteristic
194C2×C11#219911yescharacteristic
195C24D4×D1112yes—
196C2×Q8—442no—
197C2×Q8—881no—
198C2×Q8—881no—
199C2×D4—41no—
200C2×D4—41no—
201C2×D4C2×Dic2212yes—
202C2×D4#434111yescharacteristic
203C2×D4Q8×D1111yescharacteristic
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—42no—
207C22×C4—222no—
208C22×C4—222no—
209C22×C4—222no—
210C22×C4—222no—
211C22×C4—442no—
212C22×C4—882no—
213C22×C4C2×D4411yescharacteristic
214M16—222no—
215M16—441no—
216C2×C8—441no—
217C4⋊C4—41no—
218C4⋊C4—221no—
219C4⋊C4—221no—
220C4⋊C4—881no—
221C4⋊C4—881no—
222C4⋊C4—884no—
223C22⋊C4—24no—
224C22⋊C4—44no—
225C22⋊C4—42no—
226C22⋊C4—442no—
227C22⋊C4—441no—
228C22⋊C4—442no—
229C22⋊C4—882no—
230C42—41no—
231C42—441no—
232C11#1346311yescharacteristic, complemented, Sylow
233C23—22no—
234C23—22no—
235C23—42no—
236C23—42no—
237C23#6693112yes—
238C23#6693511yescharacteristic
239C23#6694112yes—
240Q8—884no—
241D4—42no—
242D4—41no—
243D4—41no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—44no—
250C2×C4—42no—
251C2×C4—41no—
252C2×C4—82no—
253C2×C4—82no—
254C2×C4—442no—
255C2×C4—442no—
256C2×C4—442no—
257C2×C4—442no—
258C2×C4—444no—
259C2×C4—441no—
260C2×C4—441no—
261C2×C4—442no—
262C2×C4—442no—
263C2×C4—882no—
264C2×C4—882no—
265C2×C4—882no—
266C2×C4#6692211yescharacteristic
267C2×C4#6695011yescharacteristic
268C8—442no—
269C22—21no—
270C22—21no—
271C22—22no—
272C22—22no—
273C22—42no—
274C22—42no—
275C22—42no—
276C22—42no—
277C22—82no—
278C22#1062226911yescharacteristic
279C22#1062235411yescharacteristic
280C22#1062235511yescharacteristic
281C4—21no—
282C4—21no—
283C4—42no—
284C4—84no—
285C4—81no—
286C4—882no—
287C4—881no—
288C4—882no—
289C4—881no—
290C2—21no—
291C2—21no—
292C2—42no—
293C2—42no—
294C2#1306997011yescharacteristic
295C2#1307061411yescharacteristic
296C2#1307061911yescharacteristic
subgroupG/H
centerC22#10622354
commutator, prime radical, cosocleC22×D4×C11C23
FrattiniC22×D4C22×D11
FittingC11×#1393C2
socleC22×C11B(4,𝔽2)
hypercenter#1393D11
hypocenterC11#13463
LCSG ▷ C22×D4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #1393

Complements

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

NH ≅ G/Ntype
37. C11×#99Q8semidirect
39. #66897Q8semidirect
182. #99Dic22semidirect
232. C11#13463semidirect

Maximal subgroups

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

subgroupindex
#130765622
#130688992
#130688252
#130667332
C11×#13932
#1346311