Finite Group Databasebeta

← #14663984

Subgroups — #14663984

Order 2816.

552 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 115 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#13068355C211yesmaximal, characteristic, complemented
2#13066930C211yesmaximal, characteristic, complemented
3#13066619C214yesmaximal, complemented
4C11×#2619C211yesmaximal, characteristic
5C2×C11×#127C411yescharacteristic
6C2×C11×#121—21no—
7C2×C11×#117C2211yescharacteristic
8C22×#4318—21no—
9C11×#394—21no—
10C11×#394C2212yes—
11C11×#392—21no—
12C11×#392C412yes—
13C11×#390—21no—
14C11×#382C411yescharacteristic
15#10622538—21no—
16#10622168—21no—
17#10622168C2212yes—
18#10622166C2212yes—
19#10622163—21no—
20C22×D4×C11—22no—
21C22×D4×C11—21no—
22C22×D4×C11—21no—
23C22×D4×C11C2×C412yes—
24C23×C4×C11D411yescharacteristic
25C11×#127—41no—
26C11×#127—41no—
27C11×#121—42no—
28C11×#121—42no—
29C11×#117—41no—
30C11×#117—41no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C4⋊C4C2311yescharacteristic
34C2×C11×C22⋊C4—22no—
35C2×C11×C22⋊C4—22no—
36C2×C11×C22⋊C4—22no—
37C2×C11×C22⋊C4C2×C411yescharacteristic
38C2×C11×C22⋊C4D411yescharacteristic
39C2×C42×C11C2×C411yescharacteristic
40C2×C42×C11D411yescharacteristic
41C2×#4318—24no—
42C2×#4318—22no—
43C2×#4318—41no—
44C2×#4318—42no—
45C22×C11⋊C8—41no—
46C11×#95—21no—
47C11×#95C2×C412yes—
48C22⋊(C11⋊C8)—22no—
49C4⋊(C11⋊C8)—41no—
50C4×C11⋊C8—41no—
51#11699—111nomaximal, Sylow
52C24×C11—22no—
53C24×C11C22⋊C411yescharacteristic
54C2×D4×C11—42no—
55C2×D4×C11—42no—
56C2×D4×C11—44no—
57C2×D4×C11—41no—
58C2×D4×C11—41no—
59C2×D4×C11—42no—
60C2×D4×C11—42no—
61C2×D4×C11—82no—
62C2×D4×C11—82no—
63C2×D4×C11—82no—
64C2×D4×C11—82no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—22no—
68C22×C4×C11—22no—
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11D812yes—
73C22×C4×C11SD1612yes—
74C22×C4×C11C22×C411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C11×C4⋊C4—41no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—42no—
80C11×C22⋊C4—41no—
81C11×C22⋊C4—41no—
82C11×C22⋊C4—42no—
83C11×C22⋊C4—42no—
84C11×C22⋊C4—82no—
85C11×C22⋊C4—82no—
86C42×C11—21no—
87C42×C11—21no—
88C42×C11—21no—
89C42×C11—21no—
90#4318—24no—
91#4318—44no—
92#4318—42no—
93C2×C11⋊C8—42no—
94C2×C11⋊C8—44no—
95C2×C11⋊C8—42no—
96#2619D1111yescharacteristic
97#1742—111no—
98#1458—111no—
99#1345—114no—
100C23×C11—21no—
101C23×C11—21no—
102C23×C11—41no—
103C23×C11—41no—
104C23×C11—42no—
105C23×C11—42no—
106C23×C11—42no—
107C23×C11—42no—
108C23×C11—42no—
109C23×C11—42no—
110C23×C11—42no—
111C23×C11#10212yes—
112C23×C11C2×C22⋊C411yescharacteristic
113D4×C11—84no—
114D4×C11—84no—
115D4×C11—88no—
116D4×C11—82no—
117D4×C11—82no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—22no—
121C2×C4×C11—22no—
122C2×C4×C11—22no—
123C2×C4×C11—22no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—42no—
133C2×C4×C11—42no—
134C2×C4×C11—42no—
135C2×C4×C11#9911yescharacteristic
136C2×C4×C11#9911yescharacteristic
137C2×C4×C11#10212yes—
138C2×C4×C11#10412yes—
139C2×C4×C11C2×D811yescharacteristic
140C2×C4×C11C2×SD1611yescharacteristic
141C11⋊C8—44no—
142C11⋊C8—82no—
143C22×M16—221no—
144C2×#127Dic1111yescharacteristic
145C2×#121—21no—
146C2×#117C2×D1111yescharacteristic
147#431—221no—
148#394—21no—
149#394C2×D1112yes—
150#392—21no—
151#392Dic1112yes—
152#390—21no—
153#382Dic1111yescharacteristic
154#343—112no—
155#343—221no—
156#324—112no—
157#323—221no—
158C22×C11—21no—
159C22×C11—21no—
160C22×C11—22no—
161C22×C11—42no—
162C22×C11—41no—
163C22×C11—41no—
164C22×C11—81no—
165C22×C11—82no—
166C22×C11—82no—
167C22×C11—82no—
168C22×C11—82no—
169C22×C11—82no—
170C22×C11—82no—
171C22×C11—82no—
172C22×C11C2×#9911yescharacteristic
173C22×C11C2×#10211yescharacteristic
174C22×C11C2×#10411yescharacteristic
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—41no—
178C4×C11—41no—
179C4×C11—41no—
180C4×C11—41no—
181C4×C11—82no—
182C4×C11#32712yes—
183C4×C11#32712yes—
184C22×D4—22no—
185C22×D4—21no—
186C22×D4—21no—
187C22×D4C2×Dic1112yes—
188C23×C4C22⋊D1111yescharacteristic
189C2×M16—224no—
190C2×M16—222no—
191C2×M16—441no—
192C2×M16—442no—
193C22×C8—441no—
194#127—41no—
195#127—41no—
196#121—42no—
197#121—42no—
198#117—41no—
199#117—41no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4C22⋊D1111yescharacteristic
202C2×C4⋊C4C22×D1111yescharacteristic
203C2×C22⋊C4—22no—
204C2×C22⋊C4—22no—
205C2×C22⋊C4—22no—
206C2×C22⋊C4C2×Dic1111yescharacteristic
207C2×C22⋊C4C22⋊D1111yescharacteristic
208C2×C42C2×Dic1111yescharacteristic
209C2×C42C22⋊D1111yescharacteristic
210C4⋊C8—441no—
211C22⋊C8—222no—
212C4×C8—441no—
213#95—21no—
214#95C2×Dic1112yes—
215C2×C11—21no—
216C2×C11—21no—
217C2×C11—42no—
218C2×C11—162no—
219C2×C11C2×#32711yescharacteristic
220C2×C11#212211yescharacteristic
221C2×C11#213411yescharacteristic
222C24—22no—
223C24C22⋊Dic1111yescharacteristic
224C2×D4—42no—
225C2×D4—42no—
226C2×D4—44no—
227C2×D4—42no—
228C2×D4—41no—
229C2×D4—41no—
230C2×D4—42no—
231C2×D4—82no—
232C2×D4—82no—
233C2×D4—82no—
234C2×D4—82no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4#432312yes—
240C22×C4#432412yes—
241C22×C4C22⋊Dic1111yescharacteristic
242C22×C4C22⋊Dic1111yescharacteristic
243C22×C4C22⋊Dic1111yescharacteristic
244C22×C4C22×Dic1111yescharacteristic
245C22×C4C2×C22⋊D1111yescharacteristic
246C22×C4C2×C22⋊D1111yescharacteristic
247M16—224no—
248M16—444no—
249M16—442no—
250C2×C8—442no—
251C2×C8—444no—
252C2×C8—442no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—42no—
256C22⋊C4—41no—
257C22⋊C4—41no—
258C22⋊C4—42no—
259C22⋊C4—42no—
260C22⋊C4—82no—
261C22⋊C4—82no—
262C42—21no—
263C42—21no—
264C42—21no—
265C42—21no—
266C11#1169911yescharacteristic, complemented, Sylow
267C23—21no—
268C23—21no—
269C23—41no—
270C23—41no—
271C23—42no—
272C23—42no—
273C23—42no—
274C23—42no—
275C23—42no—
276C23—42no—
277C23—42no—
278C23#6689612yes—
279C23C2×C22⋊Dic1111yescharacteristic
280D4—84no—
281D4—84no—
282D4—88no—
283D4—82no—
284D4—82no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4#6689612yes—
303C2×C4#6689811yescharacteristic
304C2×C4#6689811yescharacteristic
305C2×C4#6690112yes—
306C2×C4C2×#432311yescharacteristic
307C2×C4C2×#432411yescharacteristic
308C8—444no—
309C8—882no—
310C22—21no—
311C22—21no—
312C22—22no—
313C22—42no—
314C22—41no—
315C22—41no—
316C22—81no—
317C22—82no—
318C22—82no—
319C22—82no—
320C22—82no—
321C22—82no—
322C22—82no—
323C22—82no—
324C22C2×#6689611yescharacteristic
325C22C2×#6689811yescharacteristic
326C22C2×#6690111yescharacteristic
327C4—21no—
328C4—21no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—82no—
334C4#1062217512yes—
335C4#1062217512yes—
336C2—21no—
337C2—21no—
338C2—42no—
339C2—162no—
340C2C2×#1062217511yescharacteristic
341C2#1307026611yescharacteristic
342C2#1307030811yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
Fitting, prime radicalC11×#2619C2
socleC22×C11C2×#99
cosocleC2×C11×C4⋊C4C23
hypercenter#2619D11
hypocenterC11#11699
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2619

Complements

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

NH ≅ G/Ntype
1. #13068355C2semidirect
2. #13066930C2semidirect
3. #13066619C2semidirect
266. C11#11699semidirect

Maximal subgroups

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

subgroupindex
#130683552
#130669302
#130666192
C11×#26192
#1169911