Finite Group Databasebeta

← #14654383

Subgroups — #14654383

Order 2816.

716 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 716 conjugacy classes of subgroups — too many to draw. Only its 85 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#13077874C212yesmaximal
2#13068527C211yesmaximal, characteristic
3#13066980C212yesmaximal, complemented
4#13066493C211yesmaximal, characteristic, complemented
5C11×#3189C211yesmaximal, characteristic, complemented
6C22×#4339C2211yescharacteristic
7C2×C11×C22⋊Q8C2212yes—
8C2×#66995—22no—
9C11×#484—22no—
10C11×#467—22no—
11C11×#451—22no—
12C2×C11×C22⋊C8C2211yescharacteristic
13#10622820C2212yes—
14C2×C22⋊(C11⋊C8)C2211yescharacteristic
15C2×(C2×D11)⋊C8—22no—
16#10622663—22no—
17#10622660—24no—
18#10622659—22no—
19#10622579—22no—
20#10622166—24no—
21C22×Q8×C11D412yes—
22C23×C4×C11C2311yescharacteristic
23C22×C22⋊D11—21no—
24C2×#4339—22no—
25C2×#4339—22no—
26C2×#4339—44no—
27C22×D44D411yescharacteristic
28C22×C4×D11—21no—
29C22×Dic22D411yescharacteristic
30C2×C11×Q16—22no—
31C22×C8×C11D412yes—
32C11×C22⋊Q8—22no—
33C11×C22⋊Q8—22no—
34C11×C22⋊Q8—22no—
35C11×C22⋊Q8—22no—
36C2×C11×C4⋊C4—22no—
37C2×C11×C4⋊C4D412yes—
38C2×C11×C22⋊C4—22no—
39C2×#4326—24no—
40#66995—48no—
41C2×#4325—24no—
42C2×#4318—22no—
43C22×C11⋊C8—21no—
44C11×#107—22no—
45C11×#103—24no—
46C11×C22⋊C8—22no—
47C22⋊(C11⋊C8)—22no—
48C22⋊(C11⋊C8)—22no—
49C22⋊(C11⋊C8)D414yes—
50(C2×D11)⋊C8—44no—
51#66874—24no—
52#66873—24no—
53#9976—111nomaximal, Sylow
54C24×C11#4111yescharacteristic
55C23×D11—21no—
56C2×Q8×C11—22no—
57C2×Q8×C11—22no—
58C2×Q8×C11—44no—
59C22×C4×C11—22no—
60C22×C4×C11—22no—
61C22×C4×C11—42no—
62C22×C4×C11C2×D412yes—
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D412yes—
66C2×C22⋊D11—42no—
67C2×C22⋊D11—42no—
68C2×C22⋊D11—42no—
69C22×Dic11—21no—
70#4339—28no—
71#4339—44no—
72#4339—44no—
73#4339—44no—
74C2×D44—22no—
75C2×D44—42no—
76C2×C4×D11—24no—
77C2×C4×D11—42no—
78C2×C4×D11—41no—
79C2×C4×D11—41no—
80C2×Dic22—22no—
81C2×Dic22—42no—
82C11×Q16—82no—
83C2×C8×C11—22no—
84C2×C8×C11—42no—
85C11×C4⋊C4—22no—
86C11×C4⋊C4—22no—
87C11×C4⋊C4—42no—
88C11×C4⋊C4—42no—
89C11×C22⋊C4—42no—
90C11×C22⋊C4—42no—
91#4326—48no—
92#4325—48no—
93#4318—44no—
94C2×C11⋊C8—24no—
95C2×C11⋊C8—42no—
96C2×C11⋊C8—41no—
97#3189D1111yescharacteristic, complemented
98#3007—112no—
99#1780—111no—
100#1472—112no—
101#1293—111no—
102C23×C11—22no—
103C23×C11—41no—
104C23×C11—41no—
105C23×C11#12111yescharacteristic
106C23×C11#12112yes—
107C22×D11—22no—
108C22×D11—41no—
109C22×D11—42no—
110C22×D11—41no—
111C22×D11—42no—
112Q8×C11—44no—
113Q8×C11—44no—
114C2×C4×C11—22no—
115C2×C4×C11—24no—
116C2×C4×C11—41no—
117C2×C4×C11—42no—
118C2×C4×C11—44no—
119C2×C4×C11—42no—
120C2×C4×C11—42no—
121C2×C4×C11—82no—
122C2×C4×C11#12012yes—
123C2×C4×C11#12011yescharacteristic
124C2×C4×C11#12711yescharacteristic
125C22⋊D11—48no—
126C2×Dic11—22no—
127C2×Dic11—41no—
128C2×Dic11—41no—
129D44—24no—
130D44—42no—
131C4×D11—44no—
132C4×D11—44no—
133Dic22—24no—
134Dic22—42no—
135C8×C11—42no—
136C11⋊C8—44no—
137C11⋊C8—81no—
138C22×#41—111no—
139C2×#137—222no—
140C2×C22⋊Q8C2×D1112yes—
141#484—22no—
142#467—22no—
143#452—224no—
144#451—22no—
145#451—222no—
146#450—222no—
147#417—222no—
148#407—112no—
149C2×C22⋊C8—111no—
150C2×C22⋊C8—222no—
151C2×C22⋊C8C2×D1111yescharacteristic
152#324—224no—
153C22×C11—21no—
154C22×C11—21no—
155C22×C11—22no—
156C22×C11—22no—
157C22×C11—22no—
158C22×C11—82no—
159C22×C11#39211yescharacteristic
160C22×C11#47312yes—
161C2×D11—44no—
162C2×D11—42no—
163C2×D11—82no—
164C2×D11—81no—
165C2×D11—81no—
166C4×C11—22no—
167C4×C11—21no—
168C4×C11—82no—
169C4×C11—82no—
170C4×C11B(4,𝔽2)12yes—
171Dic11—42no—
172C2×#41—222no—
173C2×#41—222no—
174C2×#41—444no—
175C22×Q8—111no—
176C22×Q8C22⋊D1112yes—
177C22×D4—111no—
178C22×D4—221no—
179C23×C4—221no—
180C23×C4C22×D1111yescharacteristic
181#137—448no—
182C2×Q16—22no—
183C2×Q16—224no—
184C2×SD16—224no—
185C2×M16—222no—
186C22×C8—221no—
187C22×C8C22⋊D1112yes—
188C22⋊Q8—22no—
189C22⋊Q8—22no—
190C22⋊Q8—22no—
191C22⋊Q8—22no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4C22⋊D1112yes—
194C2×C22⋊C4—22no—
195#107—22no—
196#103—24no—
197#103—224no—
198#102—224no—
199C22⋊C8—22no—
200C22⋊C8—114no—
201C22⋊C8—222no—
202C22⋊C8—222no—
203C22⋊C8—444no—
204C2×C11—22no—
205C2×C11—42no—
206C2×C11#201711yescharacteristic
207C2×C11#202011yescharacteristic
208C2×C11#202111yescharacteristic
209D11—82no—
210C24—221no—
211C24#434111yescharacteristic
212#41—228no—
213#41—444no—
214#41—444no—
215#41—444no—
216C2×Q8—22no—
217C2×Q8—22no—
218C2×Q8—44no—
219C2×Q8—222no—
220C2×Q8—442no—
221C2×D4—222no—
222C2×D4—442no—
223C2×D4—442no—
224C2×D4—442no—
225C2×D4—442no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—42no—
229C22×C4—224no—
230C22×C4—221no—
231C22×C4—442no—
232C22×C4—441no—
233C22×C4—441no—
234C22×C4D4×D1111yescharacteristic
235C22×C4D4×D1112yes—
236C22×C4C2×C22⋊D1112yes—
237C22×C4C2×C22⋊D1111yescharacteristic
238Q16—82no—
239Q16—448no—
240SD16—448no—
241M16—444no—
242C2×C8—22no—
243C2×C8—42no—
244C2×C8—224no—
245C2×C8—442no—
246C2×C8—441no—
247C4⋊C4—22no—
248C4⋊C4—22no—
249C4⋊C4—42no—
250C4⋊C4—42no—
251C22⋊C4—42no—
252C22⋊C4—42no—
253C11#997611yescharacteristic, complemented, Sylow
254C23—22no—
255C23—41no—
256C23—41no—
257C23—222no—
258C23—441no—
259C23—442no—
260C23—442no—
261C23—441no—
262C23#6699111yescharacteristic
263C23#6699212yes—
264Q8—44no—
265Q8—44no—
266Q8—224no—
267Q8—442no—
268D4—224no—
269D4—442no—
270D4—448no—
271C2×C4—22no—
272C2×C4—24no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—44no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—82no—
279C2×C4—222no—
280C2×C4—444no—
281C2×C4—441no—
282C2×C4—441no—
283C2×C4—444no—
284C2×C4#6699012yes—
285C2×C4#6699311yescharacteristic
286C2×C4#6700611yescharacteristic
287C8—42no—
288C8—444no—
289C8—881no—
290C22—21no—
291C22—21no—
292C22—22no—
293C22—22no—
294C22—22no—
295C22—82no—
296C22—444no—
297C22—442no—
298C22—882no—
299C22—881no—
300C22—881no—
301C22#1062280512yes—
302C22#1062283611yescharacteristic
303C4—22no—
304C4—21no—
305C4—82no—
306C4—82no—
307C4—442no—
308C4#1062285712yes—
309C2—22no—
310C2—42no—
311C2—882no—
312C2#1306971911yescharacteristic
313C2#1306973511yescharacteristic
314C2#1306974011yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#3189C2
socleC22×C11#392
prime radicalC22×#4339C22
hypercenter#3189D11
hypocenterC11#9976
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3189

Complements

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

NH ≅ G/Ntype
3. #13066980C2semidirect
4. #13066493C2semidirect
5. C11×#3189C2semidirect
97. #3189D11semidirect
253. C11#9976semidirect

Maximal subgroups

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

subgroupindex
#130778742
#130685272
#130669802
#130664932
C11×#31892
#997611