Finite Group Databasebeta

← #14672096

Subgroups — #14672096

Order 2816.

540 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 111 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×#10622180C214yesmaximal, complemented
2#13068612C211yesmaximal, characteristic, complemented
3C4×#66900C211yesmaximal, characteristic, complemented
4C11×#2548C211yesmaximal, characteristic
5C2×C11×#127C411yescharacteristic
6C2×C11×#124C2212yes—
7C2×C4×Q8×C11C2211yescharacteristic
8C11×#394—21no—
9C11×#394—21no—
10C11×#390—21no—
11C11×#390—21no—
12C11×#390C412yes—
13C4×C11×C4⋊C4C411yescharacteristic
14C2×#66900C2212yes—
15C2×#66900C2212yes—
16#10622537—21no—
17C4×#4318—21no—
18#10622180—28no—
19#10622168—21no—
20#10622168—21no—
21C22×Q8×C11C2311yescharacteristic
22C22×D4×C11—21no—
23C22×D4×C11—21no—
24C22×D4×C11C2×C412yes—
25C11×#127—41no—
26C11×#127—41no—
27C11×#124—24no—
28C11×#124—24no—
29C4×Q8×C11—41no—
30C4×Q8×C11—41no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4C2×C411yescharacteristic
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C11×C22⋊C4—22no—
36C2×C11×C22⋊C4—22no—
37C2×C11×C22⋊C4—22no—
38C2×C11×C22⋊C4—22no—
39C2×C42×C11C2×C412yes—
40C2×C42×C11C2×C411yescharacteristic
41C2×C42×C11D411yescharacteristic
42C2×C42×C11D411yescharacteristic
43C2×#4318—22no—
44C2×#4318—22no—
45C11×#95—21no—
46#66900—22no—
47#66900—24no—
48#66900D414yescomplemented
49C4⋊(C11⋊C8)—41no—
50C4⋊(C11⋊C8)—41no—
51#66867—41no—
52C4×C11⋊C8—41no—
53#13226—111nomaximal, Sylow
54C24×C11—22no—
55C2×Q8×C11—41no—
56C2×Q8×C11—41no—
57C2×Q8×C11C2×D412yes—
58C2×Q8×C11#4112yes—
59C2×D4×C11—24no—
60C2×D4×C11—42no—
61C2×D4×C11—42no—
62C2×D4×C11—42no—
63C2×D4×C11—42no—
64C2×D4×C11—42no—
65C2×D4×C11—41no—
66C2×D4×C11—41no—
67C2×D4×C11—82no—
68C22×C4×C11—22no—
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22×C411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—42no—
80C11×C22⋊C4—44no—
81C11×C22⋊C4—42no—
82C11×C22⋊C4—42no—
83C11×C22⋊C4—82no—
84C11×C22⋊C4—82no—
85C42×C11—21no—
86C42×C11—21no—
87C42×C11—21no—
88C42×C11—21no—
89C42×C11—21no—
90C42×C11—21no—
91C42×C11—24no—
92#4318—24no—
93#4318—42no—
94#4318—42no—
95#4318—42no—
96C2×C11⋊C8—42no—
97C2×C11⋊C8—42no—
98#2548D1111yescharacteristic
99C2×#355—114no—
100#1801—111no—
101C4×#101—111no—
102C23×C11—42no—
103C23×C11—42no—
104C23×C11—42no—
105C23×C11—42no—
106C23×C11—42no—
107C23×C11—42no—
108C23×C11—42no—
109C23×C11C2×C22⋊C411yescharacteristic
110Q8×C11—42no—
111Q8×C11—42no—
112D4×C11—84no—
113D4×C11—82no—
114D4×C11—84no—
115D4×C11—82no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—22no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—42no—
130C2×C4×C11—42no—
131C2×C4×C11—42no—
132C2×C4×C11#9911yescharacteristic
133C2×C4×C11#9911yescharacteristic
134C2×C4×C11C4×D412yes—
135C2×C4×C11#12112yes—
136C2×C4×C11#12411yescharacteristic
137C2×C4×C11#12711yescharacteristic
138C11⋊C8—44no—
139C11⋊C8—82no—
140C2×#127Dic1111yescharacteristic
141C2×#124C2×D1112yes—
142C2×C4×Q8C2×D1111yescharacteristic
143#423—221no—
144C2×#101—112no—
145C2×#101—112no—
146C4×M16—221no—
147#394—21no—
148#394—21no—
149#390—21no—
150#390—21no—
151#390Dic1112yes—
152C4×C4⋊C4Dic1111yescharacteristic
153#355—228no—
154#343—221no—
155#343—221no—
156C22×C11—21no—
157C22×C11—21no—
158C22×C11—82no—
159C22×C11—82no—
160C22×C11—82no—
161C22×C11—82no—
162C22×C11—82no—
163C22×C11—82no—
164C22×C11—82no—
165C22×C11#39011yescharacteristic
166C22×C11C2×#9911yescharacteristic
167C22×C11#41011yescharacteristic
168C4×C11—21no—
169C4×C11—22no—
170C4×C11—22no—
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—41no—
174C4×C11—41no—
175C4×C11—41no—
176C4×C11—82no—
177C4×C11#35512yescomplemented
178C22×Q8C22×D1111yescharacteristic
179C22×D4—21no—
180C22×D4—21no—
181C22×D4C2×Dic1112yes—
182C2×M16—222no—
183C2×M16—222no—
184#127—41no—
185#127—41no—
186#124—24no—
187#124—24no—
188C4×Q8—41no—
189C4×Q8—41no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4C2×Dic1111yescharacteristic
192C2×C4⋊C4C22⋊D1111yescharacteristic
193C2×C4⋊C4C22⋊D1111yescharacteristic
194C2×C22⋊C4—22no—
195C2×C22⋊C4—22no—
196C2×C22⋊C4—22no—
197C2×C22⋊C4—22no—
198C2×C42C2×Dic1112yes—
199C2×C42C2×Dic1111yescharacteristic
200C2×C42C22⋊D1111yescharacteristic
201C2×C42C22⋊D1111yescharacteristic
202C4⋊C8—441no—
203C4⋊C8—441no—
204#101—114no—
205#101—222no—
206#101—224no—
207#97—441no—
208C4×C8—441no—
209#95—21no—
210C2×C11—21no—
211C2×C11—21no—
212C2×C11—162no—
213C2×C11#196411yescharacteristic
214C2×C11C2×#35511yescharacteristic
215C2×C11#213411yescharacteristic
216C24—22no—
217C2×Q8—41no—
218C2×Q8—41no—
219C2×Q8D4×D1112yes—
220C2×Q8#434112yes—
221C2×D4—24no—
222C2×D4—42no—
223C2×D4—42no—
224C2×D4—42no—
225C2×D4—42no—
226C2×D4—42no—
227C2×D4—41no—
228C2×D4—41no—
229C2×D4—82no—
230C22×C4—22no—
231C22×C4C22⋊Dic1111yescharacteristic
232C22×C4C22⋊Dic1111yescharacteristic
233C22×C4C22⋊Dic1111yescharacteristic
234C22×C4C22⋊Dic1111yescharacteristic
235C22×C4C22×Dic1111yescharacteristic
236C22×C4C2×C22⋊D1111yescharacteristic
237C22×C4C2×C22⋊D1111yescharacteristic
238M16—224no—
239M16—442no—
240M16—442no—
241M16—442no—
242C2×C8—442no—
243C2×C8—442no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—42no—
248C22⋊C4—42no—
249C22⋊C4—44no—
250C22⋊C4—42no—
251C22⋊C4—82no—
252C22⋊C4—82no—
253C42—21no—
254C42—21no—
255C42—21no—
256C42—21no—
257C42—21no—
258C42—21no—
259C42—24no—
260C11#1322611yescharacteristic, complemented, Sylow
261C23—42no—
262C23—42no—
263C23—42no—
264C23—42no—
265C23—42no—
266C23—42no—
267C23—42no—
268C23C2×C22⋊Dic1111yescharacteristic
269Q8—42no—
270Q8—42no—
271D4—84no—
272D4—82no—
273D4—84no—
274D4—82no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—22no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4#6689811yescharacteristic
292C2×C4#6689811yescharacteristic
293C2×C4D4×Dic1112yes—
294C2×C4#6698911yescharacteristic
295C2×C4#6699112yes—
296C2×C4#6699311yescharacteristic
297C8—444no—
298C8—882no—
299C22—21no—
300C22—21no—
301C22—82no—
302C22—82no—
303C22—82no—
304C22—82no—
305C22—82no—
306C22—82no—
307C22—82no—
308C22C2×#6689811yescharacteristic
309C22#1062283411yescharacteristic
310C22#1062285311yescharacteristic
311C4—22no—
312C4—21no—
313C4—22no—
314C4—21no—
315C4—21no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—82no—
320C4#1062218012yescomplemented
321C2—21no—
322C2—21no—
323C2—162no—
324C2#1306945311yescharacteristic
325C2C2×#1062218011yescharacteristic
326C2#1307030811yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC22×Q8C22×D11
FittingC11×#2548C2
socleC22×C11C2×#99
prime radicalC2×C11×#127C4
cosocleC22×Q8×C11C23
hypercenter#2548D11
hypocenterC11#13226
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2548

Complements

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

NH ≅ G/Ntype
1. C2×#10622180C2semidirect
2. #13068612C2semidirect
3. C4×#66900C2semidirect
48. #66900D4semidirect
177. C4×C11#355semidirect
260. C11#13226semidirect
320. C4#10622180semidirect

Maximal subgroups

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

subgroupindex
C2×#106221802
#130686122
C4×#669002
C11×#25482
#1322611