Finite Group Databasebeta

← #14673198

Subgroups — #14673198

Order 2816.

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

normal subgroups only

This group has 496 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×#10622177C212yesmaximal
2#13069030C212yesmaximal
3#13068825C211yesmaximal, characteristic
4#13066741C211yesmaximal, characteristic
5C11×#2724C211yesmaximal, characteristic
6C2×C11×#123C2212yes—
7#10623329C2211yescharacteristic
8C11×#398—21no—
9C11×#397—22no—
10C11×#390C2211yescharacteristic
11C11×#389—21no—
12C11×#385—22no—
13C2×#66898C2212yes—
14C2×#66897C2211yescharacteristic
15#10622824—22no—
16#10622577—21no—
17#10622177—24no—
18#10622165—22no—
19#10622161—21no—
20C22×D4×C11C2311yescharacteristic
21C23×C4×C11D412yes—
22C11×#123—22no—
23C11×#123—22no—
24C11×#123—22no—
25C11×#123—22no—
26C2×C11×C4⋊C4—21no—
27C2×C11×C4⋊C4—22no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4D411yescharacteristic
31C2×C11×C22⋊C4—22no—
32C2×C11×C22⋊C4—22no—
33C2×C11×C22⋊C4D412yes—
34C2×C42×C11D411yescharacteristic
35C2×C22⋊Dic11—22no—
36C2×C22⋊Dic11—22no—
37D4×Dic11—41no—
38D4×Dic11—41no—
39#66979—21no—
40C2×#4318—21no—
41C11×#95—22no—
42C11×#95—22no—
43C11×#95—21no—
44#66898—22no—
45#66898—22no—
46#66897—21no—
47#66897D412yes—
48C11⋊#95—42no—
49C11⋊#95—42no—
50#66872—41no—
51#66871—41no—
52#13421—111nomaximal, Sylow
53C24×C11C2×D412yes—
54C2×D4×C11—41no—
55C2×D4×C11—41no—
56C2×D4×C11C2×D411yescharacteristic
57C2×D4×C11#4111yescharacteristic
58C2×D4×C11#4112yes—
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—22no—
62C22×C4×C11—22no—
63C22×C4×C11—22no—
64C22×C4×C11—22no—
65C22×C4×C11—42no—
66C22×C4×C11—42no—
67C22×C4×C11C2×D411yescharacteristic
68C22×Dic11—22no—
69C22×Dic11—22no—
70C22×Dic11—42no—
71C11×C4⋊C4—42no—
72C11×C4⋊C4—41no—
73C11×C4⋊C4—42no—
74C11×C4⋊C4—42no—
75C11×C4⋊C4—81no—
76C11×C4⋊C4—81no—
77C11×C22⋊C4—22no—
78C11×C22⋊C4—22no—
79C11×C22⋊C4—44no—
80C11×C22⋊C4—42no—
81C11×C22⋊C4—42no—
82C42×C11—41no—
83C22⋊Dic11—42no—
84C22⋊Dic11—42no—
85C22⋊Dic11—41no—
86C22⋊Dic11—42no—
87C4⋊Dic11—21no—
88C4⋊Dic11—21no—
89C4×Dic11—41no—
90#4318—22no—
91#4318—41no—
92C2×C11⋊C8—41no—
93#2724D1111yescharacteristic
94C2×#352—112no—
95#1890—112no—
96#1856—111no—
97#1393—111no—
98C23×C11—22no—
99C23×C11—22no—
100C23×C11—42no—
101C23×C11—42no—
102C23×C11#12011yescharacteristic
103C23×C11#12112yes—
104C23×C11#12312yes—
105D4×C11—41no—
106D4×C11—41no—
107D4×C11—42no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—22no—
111C2×C4×C11—41no—
112C2×C4×C11—41no—
113C2×C4×C11—42no—
114C2×C4×C11—42no—
115C2×C4×C11—42no—
116C2×C4×C11—44no—
117C2×C4×C11—42no—
118C2×C4×C11—42no—
119C2×C4×C11—41no—
120C2×C4×C11—42no—
121C2×C4×C11—42no—
122C2×C4×C11—82no—
123C2×C4×C11#12111yescharacteristic
124C2×C4×C11#12411yescharacteristic
125C2×Dic11—41no—
126C2×Dic11—41no—
127C2×Dic11—82no—
128C2×Dic11—82no—
129C2×Dic11—82no—
130C2×Dic11—82no—
131C2×Dic11—82no—
132C11⋊C8—42no—
133C2×#123C2×D1112yes—
134#518—111no—
135#428—221no—
136C2×#100—111no—
137C2×#99—112no—
138#398—21no—
139#397—22no—
140#390C2×D1111yescharacteristic
141#389—21no—
142#385—22no—
143#381—222no—
144#352—224no—
145#342—222no—
146#339—221no—
147C22×C11—21no—
148C22×C11—21no—
149C22×C11—22no—
150C22×C11—22no—
151C22×C11—42no—
152C22×C11—42no—
153C22×C11—42no—
154C22×C11—42no—
155C22×C11—82no—
156C22×C11#39411yescharacteristic
157C22×C11B(4,𝔽2)11yescharacteristic
158C22×C11#45811yescharacteristic
159C4×C11—21no—
160C4×C11—21no—
161C4×C11—42no—
162C4×C11—82no—
163C4×C11—81no—
164C4×C11—82no—
165Dic11—81no—
166Dic11—81no—
167Dic11—162no—
168C22×D4C22×D1111yescharacteristic
169C23×C4C22⋊D1112yes—
170C2×M16—221no—
171#123—22no—
172#123—22no—
173#123—22no—
174#123—22no—
175C4×D4—441no—
176C4×D4—441no—
177#117—221no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4C22⋊D1111yescharacteristic
183C2×C22⋊C4—22no—
184C2×C22⋊C4—22no—
185C2×C22⋊C4—222no—
186C2×C22⋊C4—222no—
187C2×C22⋊C4C22⋊D1112yes—
188C2×C42C22⋊D1111yescharacteristic
189#107—441no—
190#106—441no—
191#100—112no—
192#100—221no—
193#99—222no—
194#99—222no—
195#95—22no—
196#95—22no—
197#95—21no—
198#95—442no—
199#95—442no—
200C2×C11—21no—
201C2×C11—21no—
202C2×C11—42no—
203C2×C11—42no—
204C2×C11#204411yescharacteristic
205C2×C11#219811yescharacteristic
206C2×C11#220111yescharacteristic
207C24C2×C22⋊D1112yes—
208C2×D4—41no—
209C2×D4—41no—
210C2×D4D4×D1111yescharacteristic
211C2×D4#434112yes—
212C2×D4#434111yescharacteristic
213C22×C4—21no—
214C22×C4—22no—
215C22×C4—21no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—42no—
220C22×C4—42no—
221C22×C4—222no—
222C22×C4—222no—
223C22×C4—442no—
224C22×C4C2×C22⋊D1111yescharacteristic
225M16—222no—
226M16—441no—
227C2×C8—441no—
228C4⋊C4—41no—
229C4⋊C4—42no—
230C4⋊C4—42no—
231C4⋊C4—42no—
232C4⋊C4—81no—
233C4⋊C4—81no—
234C4⋊C4—221no—
235C4⋊C4—221no—
236C22⋊C4—22no—
237C22⋊C4—22no—
238C22⋊C4—44no—
239C22⋊C4—42no—
240C22⋊C4—42no—
241C22⋊C4—442no—
242C22⋊C4—441no—
243C22⋊C4—442no—
244C22⋊C4—442no—
245C42—41no—
246C42—441no—
247C11#1342111yescharacteristic, complemented, Sylow
248C23—22no—
249C23—22no—
250C23—42no—
251C23—42no—
252C23#6698812yes—
253C23#6699212yes—
254C23#6700611yescharacteristic
255D4—41no—
256D4—41no—
257D4—42no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—44no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—41no—
271C2×C4—42no—
272C2×C4—82no—
273C2×C4—441no—
274C2×C4—441no—
275C2×C4—882no—
276C2×C4—882no—
277C2×C4—882no—
278C2×C4—882no—
279C2×C4—882no—
280C2×C4#6698911yescharacteristic
281C2×C4#6699111yescharacteristic
282C8—442no—
283C22—21no—
284C22—21no—
285C22—22no—
286C22—22no—
287C22—42no—
288C22—42no—
289C22—42no—
290C22—42no—
291C22—82no—
292C22#1062283511yescharacteristic
293C22#1062285611yescharacteristic
294C22#1062285711yescharacteristic
295C4—21no—
296C4—21no—
297C4—42no—
298C4—82no—
299C4—81no—
300C4—82no—
301C4—881no—
302C4—881no—
303C4—1762no—
304C2—21no—
305C2—21no—
306C2—42no—
307C2—42no—
308C2#1306986411yescharacteristic
309C2#1307061211yescharacteristic
310C2#1307062911yescharacteristic
subgroupG/H
centerC22#10622857
commutator, prime radical, cosocleC22×D4×C11C23
FrattiniC22×D4C22×D11
FittingC11×#2724C2
socleC22×C11B(4,𝔽2)
hypercenter#2724D11
hypocenterC11#13421
LCSG ▷ C22×D4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #2724

Complements

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

NH ≅ G/Ntype
247. C11#13421semidirect

Maximal subgroups

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

subgroupindex
C2×#106221772
#130690302
#130688252
#130667412
C11×#27242
#1342111