Finite Group Databasebeta

← #14672094

Subgroups — #14672094

Order 2816.

540 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 103 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#13073615C211yesmaximal, characteristic
2C2×#10622115C214yesmaximal, complemented
3C4×#66900C211yesmaximal, characteristic, complemented
4C11×#1801C211yesmaximal, characteristic, complemented
5C2×C4×Q8×C11C2211yescharacteristic
6C2×#67000C2212yes—
7C2×#66927C411yescharacteristic
8C11×#423—21no—
9C2×C11×#101C2212yes—
10C2×#66900C2212yes—
11#10622604—21no—
12#10622604—21no—
13#10622601C412yes—
14#10622552—21no—
15#10622552—21no—
16C4×C4⋊Dic11C411yescharacteristic
17C4×#4318—21no—
18C11×#343—21no—
19#10622168—21no—
20#10622115—28no—
21C22×Q8×C11C2311yescharacteristic
22C22×D44—21no—
23C22×D44—21no—
24C22×D44C2×C412yes—
25C2×C11×M16—22no—
26C4×Q8×C11—41no—
27C4×Q8×C11—41no—
28C2×C11×C4⋊C4C2×C411yescharacteristic
29C2×C11×C4⋊C4D411yescharacteristic
30C2×C11×C4⋊C4D411yescharacteristic
31C2×C42×C11C2×C411yescharacteristic
32C2×C42×C11D411yescharacteristic
33C2×C42×C11D411yescharacteristic
34#67000—24no—
35#67000—24no—
36C2×(C2×D11)⋊C4—22no—
37C2×(C2×D11)⋊C4—22no—
38C2×(C2×D11)⋊C4—22no—
39C2×(C2×D11)⋊C4—22no—
40C2×C4⋊Dic11—21no—
41C2×C4×Dic11C2×C412yes—
42C2×#4318—22no—
43#66927—41no—
44#66927—41no—
45C11×C4⋊C8—41no—
46C11×C4⋊C8—41no—
47C11×#101—24no—
48#66900—22no—
49#66900D414yescomplemented
50C11⋊#95—21no—
51#66867—41no—
52C4×C11⋊C8—41no—
53#13226—111nomaximal, Sylow
54C23×D11—22no—
55C2×Q8×C11—41no—
56C2×Q8×C11—41no—
57C2×Q8×C11C2×D412yes—
58C2×Q8×C11#4112yes—
59C22×C4×C11C22⋊C411yescharacteristic
60C22×C4×C11C22⋊C411yescharacteristic
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11C22⋊C411yescharacteristic
63C22×C4×C11C22×C411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×Dic11—22no—
67C2×D44—24no—
68C2×D44—42no—
69C2×D44—42no—
70C2×D44—42no—
71C2×D44—42no—
72C2×D44—42no—
73C2×D44—41no—
74C2×D44—41no—
75C2×D44—82no—
76C11×M16—42no—
77C11×M16—42no—
78C2×C8×C11—42no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C42×C11—21no—
83C42×C11—21no—
84C42×C11—21no—
85C42×C11—21no—
86C42×C11—21no—
87C42×C11—21no—
88(C2×D11)⋊C4—44no—
89(C2×D11)⋊C4—42no—
90(C2×D11)⋊C4—42no—
91(C2×D11)⋊C4—82no—
92(C2×D11)⋊C4—82no—
93C4⋊Dic11—42no—
94C4×Dic11—24no—
95#4318—24no—
96#4318—42no—
97C2×C11⋊C8—42no—
98#2548—111no—
99C2×#355—114no—
100#1801D1111yescharacteristic, complemented
101C4×#101—111no—
102C23×C11C2×C22⋊C411yescharacteristic
103C22×D11—42no—
104C22×D11—42no—
105C22×D11—42no—
106C22×D11—42no—
107C22×D11—42no—
108C22×D11—42no—
109C22×D11—42no—
110Q8×C11—42no—
111Q8×C11—42no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—22no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11#9911yescharacteristic
126C2×C4×C11#9911yescharacteristic
127C2×C4×C11C4×D412yes—
128C2×C4×C11#12112yes—
129C2×C4×C11#12411yescharacteristic
130C2×C4×C11#12711yescharacteristic
131C2×Dic11—42no—
132C2×Dic11—42no—
133C2×Dic11—42no—
134D44—84no—
135D44—82no—
136D44—84no—
137D44—82no—
138C8×C11—82no—
139C11⋊C8—44no—
140C2×#127—111no—
141C2×#124—112no—
142C2×C4×Q8C2×D1111yescharacteristic
143#423—21no—
144C2×#101—112no—
145C2×#101C2×D1112yes—
146C4×M16—221no—
147#394—221no—
148#394—221no—
149#390—112no—
150#390—221no—
151#390—221no—
152C4×C4⋊C4—111no—
153#355—228no—
154#343—21no—
155#343—221no—
156C22×C11—21no—
157C22×C11—21no—
158C22×C11#39011yescharacteristic
159C22×C11C2×#9911yescharacteristic
160C22×C11#41011yescharacteristic
161C2×D11—82no—
162C2×D11—82no—
163C2×D11—82no—
164C2×D11—82no—
165C2×D11—82no—
166C2×D11—82no—
167C2×D11—82no—
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#35512yescomplemented
177Dic11—82no—
178C22×Q8C22×D1111yescharacteristic
179C22×D4—112no—
180C22×D4—221no—
181C22×D4—221no—
182C2×M16—22no—
183C2×M16—222no—
184#127—441no—
185#127—441no—
186#124—224no—
187#124—224no—
188C4×Q8—41no—
189C4×Q8—41no—
190C2×C4⋊C4—221no—
191C2×C4⋊C4C4×D1111yescharacteristic
192C2×C4⋊C4D4411yescharacteristic
193C2×C4⋊C4C22⋊D1111yescharacteristic
194C2×C22⋊C4—222no—
195C2×C22⋊C4—222no—
196C2×C22⋊C4—222no—
197C2×C22⋊C4—222no—
198C2×C42—112no—
199C2×C42C4×D1111yescharacteristic
200C2×C42D4411yescharacteristic
201C2×C42C22⋊D1111yescharacteristic
202C4⋊C8—41no—
203C4⋊C8—41no—
204#101—24no—
205#101—114no—
206#101—222no—
207#97—441no—
208C4×C8—441no—
209#95—221no—
210C2×C11—21no—
211C2×C11—21no—
212C2×C11#196411yescharacteristic
213C2×C11C2×#35511yescharacteristic
214C2×C11#213411yescharacteristic
215D11—162no—
216C24—222no—
217C2×Q8—41no—
218C2×Q8—41no—
219C2×Q8D4×D1112yes—
220C2×Q8#434312yes—
221C2×D4—224no—
222C2×D4—442no—
223C2×D4—442no—
224C2×D4—442no—
225C2×D4—442no—
226C2×D4—442no—
227C2×D4—441no—
228C2×D4—441no—
229C2×D4—882no—
230C22×C4—222no—
231C22×C4(C2×D11)⋊C411yescharacteristic
232C22×C4(C2×D11)⋊C411yescharacteristic
233C22×C4(C2×D11)⋊C411yescharacteristic
234C22×C4(C2×D11)⋊C411yescharacteristic
235C22×C4C2×C4×D1111yescharacteristic
236C22×C4C2×D4411yescharacteristic
237C22×C4C2×C22⋊D1111yescharacteristic
238M16—42no—
239M16—42no—
240M16—224no—
241M16—442no—
242C2×C8—42no—
243C2×C8—442no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—442no—
248C22⋊C4—444no—
249C22⋊C4—442no—
250C22⋊C4—442no—
251C22⋊C4—882no—
252C22⋊C4—882no—
253C42—21no—
254C42—21no—
255C42—21no—
256C42—21no—
257C42—21no—
258C42—21no—
259C42—224no—
260C11#1322611yescharacteristic, complemented, Sylow
261C23—442no—
262C23—442no—
263C23—442no—
264C23—442no—
265C23—442no—
266C23—442no—
267C23—442no—
268C23C2×(C2×D11)⋊C411yescharacteristic
269Q8—42no—
270Q8—42no—
271D4—884no—
272D4—882no—
273D4—884no—
274D4—882no—
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—442no—
289C2×C4—442no—
290C2×C4—442no—
291C2×C4#6687011yescharacteristic
292C2×C4#6687011yescharacteristic
293C2×C4#6694612yes—
294C2×C4#6694812yes—
295C2×C4#6699311yescharacteristic
296C2×C4#6700011yescharacteristic
297C8—82no—
298C8—444no—
299C22—21no—
300C22—21no—
301C22—882no—
302C22—882no—
303C22—882no—
304C22—882no—
305C22—882no—
306C22—882no—
307C22—882no—
308C22C2×#6687011yescharacteristic
309C22#1062260111yescharacteristic
310C22#1062261911yescharacteristic
311C4—21no—
312C4—22no—
313C4—22no—
314C4—21no—
315C4—21no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—882no—
320C4#1062211512yescomplemented
321C2—21no—
322C2—21no—
323C2—1762no—
324C2#1306945111yescharacteristic
325C2C2×#1062211511yescharacteristic
326C2#1307030711yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC22×Q8C22×D11
FittingC11×#1801C2
socleC22×C11C2×#99
prime radicalC2×#66927C4
cosocleC22×Q8×C11C23
hypercenter#1801D11
hypocenterC11#13226
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1801

Complements

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

NH ≅ G/Ntype
2. C2×#10622115C2semidirect
3. C4×#66900C2semidirect
4. C11×#1801C2semidirect
49. #66900D4semidirect
100. #1801D11semidirect
176. C4×C11#355semidirect
260. C11#13226semidirect
320. C4#10622115semidirect

Maximal subgroups

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

subgroupindex
#130736152
C2×#106221152
C4×#669002
C11×#18012
#1322611