Finite Group Databasebeta

← #14908114

Subgroups — #14908114

Order 2816.

680 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 680 conjugacy classes of subgroups — too many to draw. Only its 163 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×#10622522C211yesmaximal, characteristic
2C22×#66893C211yesmaximal, characteristic, complemented
3#13079105C211yesmaximal, characteristic
4#13077483C211yesmaximal, characteristic, complemented
5#13070681C214yesmaximal, complemented
6#13070665C214yesmaximal, complemented
7#13070376C211yesmaximal, characteristic, complemented
8#13070321C211yesmaximal, characteristic
9C11×#2141C211yesmaximal, characteristic, complemented
10C22×C11×Q16C2211yescharacteristic
11#10623347—21no—
12C2×#66995—21no—
13C22×Dic44C2211yescharacteristic
14C2×#66957C2211yescharacteristic
15#10623047—21no—
16C2×C11×M32C2211yescharacteristic
17C11×#427C2211yescharacteristic
18#10622804C2212yes—
19#10622803—22no—
20#10622794C2212yes—
21C2×#66893—24no—
22C2×#66893C2214yes—
23#10622714C2211yescharacteristic
24C22×C11⋊C16C2211yescharacteristic
25#10622617—21no—
26#10622522—24no—
27C2×Dic88C2212yes—
28C2×#66864C2212yes—
29#10622486C2214yes—
30#10622466—22no—
31C11×#358C2214yes—
32Dic11⋊C16C2214yes—
33#10622130C2212yes—
34#10622129C2212yes—
35C22×Q8×C11—21no—
36C2×#4339—21no—
37C22×Dic22—21no—
38C2×C11×Q16—22no—
39C2×C11×Q16—21no—
40C2×C11×Q16—22no—
41C2×C11×Q16C2312yes—
42C22×C8×C11C2311yescharacteristic
43C11×#117—21no—
44#67000—22no—
45#66999—42no—
46#66997—22no—
47C2×#4326—22no—
48#66995—44no—
49C2×#4325—22no—
50#66982—42no—
51#66979D411yescharacteristic
52C2×#4318D411yescharacteristic
53C2×Dic44—21no—
54C2×Dic44—22no—
55C2×Dic44D414yes—
56C2×Dic44C2311yescharacteristic
57C2×Dic44C2312yes—
58#66957—22no—
59#66957—22no—
60C2×D88C2311yescharacteristic
61C2×#4314—21no—
62#66940—24no—
63#66930—42no—
64C4×Dic22—42no—
65C11×M32—22no—
66C2×C11×C16C2312yes—
67C11×#107C2312yes—
68C11×#106—21no—
69#66893—28no—
70#66879D412yes—
71C8×Dic11C2312yes—
72C2×C11⋊C16—22no—
73C2×C11⋊C16C2312yes—
74#66874—24no—
75Dic88—24no—
76#66864—24no—
77#33588—111nomaximal, Sylow
78C2×Q8×C11—22no—
79C2×Q8×C11—41no—
80C2×Q8×C11—42no—
81C2×Q8×C11—42no—
82C22×C4×C11—41no—
83C22×C4×C11C2×D411yescharacteristic
84C2×C22⋊D11—41no—
85C22×Dic11—41no—
86#4339—42no—
87#4339—42no—
88C2×D44—21no—
89C2×C4×D11—41no—
90C2×Dic22—24no—
91C2×Dic22—22no—
92C2×Dic22—21no—
93C2×Dic22—41no—
94C2×Dic22—42no—
95C11×Q16—22no—
96C11×Q16—22no—
97C11×Q16—42no—
98C2×C8×C11C2×D412yes—
99C2×C8×C11C2×D411yescharacteristic
100C2×C8×C11#4112yes—
101C2×C8×C11C2411yescharacteristic
102C11×C4⋊C4—22no—
103C11×C22⋊C4—41no—
104C42×C11—41no—
105C22⋊Dic11D812yes—
106#4326—44no—
107#4325—44no—
108(C2×D11)⋊C4—44no—
109C4⋊Dic11D812yes—
110Dic11⋊C4—44no—
111Dic11⋊C4—44no—
112C4×Dic11—44no—
113C4×Dic11C2×D412yes—
114#4318—22no—
115C2×C11⋊C8C2×D412yes—
116Dic44—24no—
117Dic44—21no—
118Dic44—22no—
119Dic44—21no—
120Dic44C2×D414yes—
121D88—21no—
122D88—21no—
123#4314—42no—
124C11×C16—22no—
125C11⋊C16—22no—
126C2×#510—111no—
127C22×Q32—111no—
128#3156—111no—
129#2950—111no—
130#2211—114no—
131#2209—114no—
132#2151—111no—
133#2141D1111yescharacteristic, complemented
134#2138—111no—
135C23×C11C2×D811yescharacteristic
136C22×D11—41no—
137Q8×C11—42no—
138Q8×C11—42no—
139Q8×C11—82no—
140C2×C4×C11—42no—
141C2×C4×C11—42no—
142C2×C4×C11—82no—
143C2×C4×C11#12112yes—
144C2×C4×C11C2×D811yescharacteristic
145C2×C4×C11AGL(1,ℤ/8)12yes—
146C2×C4×C11C22×D411yescharacteristic
147C22⋊D11—82no—
148C2×Dic11—42no—
149C2×Dic11—44no—
150C2×Dic11—41no—
151C2×Dic11C2×D814yes—
152D44—41no—
153D44—41no—
154C4×D11—82no—
155Dic22—24no—
156Dic22—42no—
157Dic22—44no—
158Dic22—41no—
159Dic22—41no—
160C8×C11#12112yes—
161C8×C11C22×D411yescharacteristic
162C8×C11C2×#4111yescharacteristic
163C11⋊C8—22no—
164C2×#137—221no—
165C2×#135—111no—
166C22×Q16—111no—
167C22×Q16C2×D1111yescharacteristic
168#536—221no—
169#519—221no—
170#510—224no—
171C2×Q32—114no—
172C2×Q32—112no—
173C2×Q32—224no—
174C2×SD32—112no—
175C2×M32C2×D1111yescharacteristic
176C22×C16—111no—
177#497—222no—
178#495—112no—
179#494—112no—
180#441—222no—
181C4×Q16—114no—
182#427C2×D1111yescharacteristic
183#419—221no—
184#405—111no—
185C4⋊C16—114no—
186#358—112no—
187#358C2×D1114yes—
188#357—112no—
189C22×C11—22no—
190C22×C11#45912yes—
191C22×C11C22×D811yescharacteristic
192C2×D11—82no—
193C2×D11—81no—
194C4×C11—82no—
195C4×C11—82no—
196C4×C11#45912yes—
197C4×C11C2×#12111yescharacteristic
198C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
199Dic11—24no—
200Dic11—44no—
201Dic11—81no—
202C2×#41—221no—
203C22×Q8—21no—
204C22×Q8—221no—
205#137—444no—
206#135—222no—
207#135—222no—
208C2×Q16—22no—
209C2×Q16—22no—
210C2×Q16—21no—
211C2×Q16—114no—
212C2×Q16—112no—
213C2×Q16—111no—
214C2×Q16—222no—
215C2×Q16—222no—
216C2×Q16—221no—
217C2×Q16C22×D1112yes—
218C2×SD16—222no—
219C2×SD16—221no—
220C2×D8—111no—
221C2×M16—111no—
222C22×C8C22×D1111yescharacteristic
223C4⋊Q8—222no—
224#124—222no—
225#123—442no—
226C22⋊Q8—442no—
227C4×Q8—224no—
228C4×Q8—442no—
229#117—21no—
230#117—111no—
231#117—442no—
232Q32—224no—
233Q32—228no—
234SD32—224no—
235M32—22no—
236C2×C16—112no—
237C2×C16—222no—
238C2×C16C22×D1112yes—
239#107C22×D1112yes—
240#106—21no—
241#103—224no—
242#97—112no—
243C4×C8—112no—
244C2×C11—22no—
245C2×C11C2×#45911yescharacteristic
246C2×C11#341712yes—
247D11—161no—
248#41—442no—
249#41—442no—
250C2×Q8—22no—
251C2×Q8—41no—
252C2×Q8—42no—
253C2×Q8—42no—
254C2×Q8—224no—
255C2×Q8—222no—
256C2×Q8—221no—
257C2×Q8—441no—
258C2×Q8—442no—
259C2×D4—221no—
260C2×D4—441no—
261C22×C4—41no—
262C22×C4—441no—
263C22×C4—441no—
264C22×C4D4×D1111yescharacteristic
265Q16—22no—
266Q16—22no—
267Q16—42no—
268Q16—114no—
269Q16—224no—
270Q16—222no—
271Q16—221no—
272Q16—221no—
273Q16—444no—
274SD16—444no—
275SD16—442no—
276D8—221no—
277D8—221no—
278M16—222no—
279C2×C8—112no—
280C2×C8#433912yes—
281C2×C8D4×D1111yescharacteristic
282C2×C8D4×D1112yes—
283C2×C8C23×D1111yescharacteristic
284C4⋊C4—22no—
285C4⋊C4—112no—
286C4⋊C4—444no—
287C4⋊C4—444no—
288C22⋊C4—41no—
289C22⋊C4—112no—
290C22⋊C4—444no—
291C42—41no—
292C42—112no—
293C42—444no—
294C16—22no—
295C16—222no—
296C11#3358811yescharacteristic, complemented, Sylow
297C23—441no—
298C23D8×D1111yescharacteristic
299Q8—42no—
300Q8—42no—
301Q8—82no—
302Q8—224no—
303Q8—442no—
304Q8—444no—
305Q8—441no—
306Q8—441no—
307D4—441no—
308D4—441no—
309D4—882no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—82no—
313C2×C4—114no—
314C2×C4—442no—
315C2×C4—444no—
316C2×C4—441no—
317C2×C4—882no—
318C2×C4#6693712yes—
319C2×C4D8×D1111yescharacteristic
320C2×C4#6696712yes—
321C2×C4C2×D4×D1111yescharacteristic
322C8—222no—
323C8#6693712yes—
324C8C2×#433911yescharacteristic
325C8C2×D4×D1111yescharacteristic
326C22—22no—
327C22—881no—
328C22—882no—
329C22#1062239912yes—
330C22C2×D8×D1111yescharacteristic
331C4—82no—
332C4—82no—
333C4—224no—
334C4—444no—
335C4—881no—
336C4#1062239912yes—
337C4C2×#6693711yescharacteristic
338C4C2×#6696711yescharacteristic
339C2—22no—
340C2—1761no—
341C2C2×#1062239911yescharacteristic
342C2#1308176812yes—
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2141C2
socleC22×C11C22×D8
prime radicalC2×#66957C22
hypercenter#2141D11
hypocenterC11#33588
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2141

Complements

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

NH ≅ G/Ntype
2. C22×#66893C2semidirect
4. #13077483C2semidirect
5. #13070681C2semidirect
6. #13070665C2semidirect
7. #13070376C2semidirect
9. C11×#2141C2semidirect
133. #2141D11semidirect
296. C11#33588semidirect

Maximal subgroups

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

subgroupindex
C2×#106225222
C22×#668932
#130791052
#130774832
#130706812
#130706652
#130703762
#130703212
C11×#21412
#3358811