Finite Group Databasebeta

← #14908112

Subgroups — #14908112

Order 2816.

680 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 680 conjugacy classes of subgroups — too many to draw. Only its 171 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×#10622792C211yesmaximal, characteristic
2#13079105C211yesmaximal, characteristic
3#13077484C211yesmaximal, characteristic, complemented
4#13070680C214yesmaximal, complemented
5#13070664C214yesmaximal, complemented
6#13070374C211yesmaximal, characteristic, complemented
7#13070336C211yesmaximal, characteristic, complemented
8#13070324C211yesmaximal, characteristic
9C22×C11×Q32C211yesmaximal, characteristic, complemented
10C22×C11×Q16C2211yescharacteristic
11C22×C11×Q16C2211yescharacteristic
12#10623347—21no—
13#10623343—21no—
14C2×#66995—21no—
15C2×#66957C2211yescharacteristic
16C2×C11×Q32—24no—
17C2×C11×Q32C2214yes—
18C22×C11×C16C2211yescharacteristic
19#10622838—21no—
20#10622804C2212yes—
21#10622803—22no—
22#10622797—22no—
23Q16×Dic11C2214yes—
24#10622794C2212yes—
25C2×#66893C2212yes—
26#10622792—24no—
27C2×#66892C2212yes—
28#10622719C2211yescharacteristic
29#10622714C2211yescharacteristic
30C2×#66876C2211yescharacteristic
31#10622202C2214yes—
32#10622147C2212yes—
33#10622141C2212yes—
34Dic11⋊C16C2214yes—
35C22×Q8×C11—21no—
36C22×Q8×C11—21no—
37C2×#4339—21no—
38C2×C11×Q16—21no—
39C2×C11×Q16—22no—
40C2×C11×Q16—21no—
41C2×C11×Q16—22no—
42C2×C11×Q16—22no—
43C2×C11×Q16D414yes—
44C2×C11×Q16C2312yes—
45C2×C11×Q16C2312yes—
46C22×C8×C11C2311yescharacteristic
47#67000—22no—
48#66999—42no—
49Q8×Dic11—24no—
50Q8×Dic11—42no—
51#66997—22no—
52C2×#4326—22no—
53#66995—44no—
54C2×#4325—22no—
55#66982—42no—
56#66979—21no—
57#66979—42no—
58#66979D411yescharacteristic
59C2×#4318D411yescharacteristic
60C2×Dic44C2311yescharacteristic
61#66957—22no—
62#66957—22no—
63C2×D88C2311yescharacteristic
64C2×#4314—21no—
65C11×Q32—28no—
66C2×C11×C16—22no—
67C2×C11×C16C2312yes—
68#66899—24no—
69#66893—24no—
70#66892—24no—
71#66882C2312yes—
72#66881—21no—
73#66879D412yes—
74C8×Dic11C2312yes—
75#66876—22no—
76C2×C11⋊C16C2312yes—
77#33588—111nomaximal, Sylow
78C2×Q8×C11—24no—
79C2×Q8×C11—22no—
80C2×Q8×C11—22no—
81C2×Q8×C11—41no—
82C2×Q8×C11—41no—
83C2×Q8×C11—42no—
84C2×Q8×C11—42no—
85C2×Q8×C11—42no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11C2×D411yescharacteristic
89C2×C22⋊D11—41no—
90#4339—42no—
91#4339—42no—
92C2×D44—21no—
93C2×C4×D11—41no—
94C2×Dic22—21no—
95C11×Q16—24no—
96C11×Q16—22no—
97C11×Q16—22no—
98C11×Q16—22no—
99C11×Q16—42no—
100C11×Q16C2×D414yes—
101C2×C8×C11C2×D412yes—
102C2×C8×C11C2×D411yescharacteristic
103C2×C8×C11#4112yes—
104C2×C8×C11C2411yescharacteristic
105C22⋊Dic11—41no—
106C22⋊Dic11D812yes—
107#4326—44no—
108#4325—44no—
109(C2×D11)⋊C4—44no—
110C4⋊Dic11—22no—
111C4⋊Dic11—44no—
112C4⋊Dic11D812yes—
113Dic11⋊C4—44no—
114C4×Dic11—44no—
115C4×Dic11—41no—
116C4×Dic11C2×D412yes—
117#4318—22no—
118C2×C11⋊C8C2×D412yes—
119Dic44—21no—
120Dic44—21no—
121D88—21no—
122D88—21no—
123#4314—42no—
124C11×C16—22no—
125C11⋊C16—22no—
126C2×#510—111no—
127C22×Q32D1111yescharacteristic, complemented
128#3156—111no—
129#2950—111no—
130#2211—114no—
131#2209—114no—
132#2151—111no—
133#2141—111no—
134#2138—111no—
135C23×C11C2×D811yescharacteristic
136C22×D11—41no—
137Q8×C11—24no—
138Q8×C11—42no—
139Q8×C11—44no—
140Q8×C11—42no—
141Q8×C11—42no—
142Q8×C11—82no—
143C2×C4×C11—42no—
144C2×C4×C11—44no—
145C2×C4×C11—42no—
146C2×C4×C11—82no—
147C2×C4×C11#12112yes—
148C2×C4×C11C2×D811yescharacteristic
149C2×C4×C11AGL(1,ℤ/8)12yes—
150C2×C4×C11C22×D411yescharacteristic
151C22⋊D11—82no—
152C2×Dic11—42no—
153C2×Dic11—41no—
154C2×Dic11C2×D814yes—
155D44—41no—
156D44—41no—
157C4×D11—82no—
158Dic22—41no—
159Dic22—41no—
160C8×C11#12112yes—
161C8×C11C22×D411yescharacteristic
162C8×C11C2×#4111yescharacteristic
163C11⋊C8—22no—
164C2×#137—221no—
165C2×#135—111no—
166C22×Q16C2×D1111yescharacteristic
167C22×Q16C2×D1111yescharacteristic
168#536—221no—
169#519—221no—
170#510—224no—
171C2×Q32—24no—
172C2×Q32—112no—
173C2×Q32C2×D1114yes—
174C2×SD32—112no—
175C2×M32—111no—
176C22×C16C2×D1111yescharacteristic
177#497—222no—
178#495—112no—
179#494—112no—
180#441—222no—
181C4×Q16—114no—
182#427—111no—
183#419—221no—
184#405—111no—
185C4⋊C16—114no—
186#358—114no—
187#358—112no—
188#357—112no—
189C22×C11—22no—
190C22×C11#45912yes—
191C22×C11C22×D811yescharacteristic
192C2×D11—82no—
193C2×D11—81no—
194C4×C11—44no—
195C4×C11—82no—
196C4×C11#45912yes—
197C4×C11C2×#12111yescharacteristic
198C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
199Dic11—24no—
200Dic11—82no—
201Dic11—81no—
202C2×#41—221no—
203C22×Q8—21no—
204C22×Q8—21no—
205#137—444no—
206#135—222no—
207#135—222no—
208C2×Q16—21no—
209C2×Q16—21no—
210C2×Q16—22no—
211C2×Q16—22no—
212C2×Q16—22no—
213C2×Q16—111no—
214C2×Q16—222no—
215C2×Q16C22⋊D1114yes—
216C2×Q16C22×D1112yes—
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—111no—
230#117—221no—
231#117—442no—
232Q32—28no—
233Q32—224no—
234SD32—224no—
235M32—222no—
236C2×C16—22no—
237C2×C16—112no—
238C2×C16C22×D1112yes—
239#107—112no—
240#106—221no—
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—24no—
251C2×Q8—22no—
252C2×Q8—22no—
253C2×Q8—41no—
254C2×Q8—41no—
255C2×Q8—42no—
256C2×Q8—42no—
257C2×Q8—42no—
258C2×Q8—221no—
259C2×D4—221no—
260C2×D4—441no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—441no—
264C22×C4D4×D1111yescharacteristic
265Q16—24no—
266Q16—22no—
267Q16—22no—
268Q16—22no—
269Q16—42no—
270Q16—221no—
271Q16—221no—
272Q16—444no—
273Q16C2×C22⋊D1114yes—
274SD16—444no—
275SD16—442no—
276D8—221no—
277D8—221no—
278M16—222no—
279C2×C8—112no—
280C2×C8D4×D1111yescharacteristic
281C2×C8#434112yes—
282C2×C8C2×C22⋊D1112yes—
283C2×C8C23×D1111yescharacteristic
284C4⋊C4—112no—
285C4⋊C4—222no—
286C4⋊C4—444no—
287C4⋊C4—444no—
288C22⋊C4—112no—
289C22⋊C4—444no—
290C22⋊C4—441no—
291C42—112no—
292C42—444no—
293C42—441no—
294C16—22no—
295C16—222no—
296C11#3358811yescharacteristic, complemented, Sylow
297C23—441no—
298C23D8×D1111yescharacteristic
299Q8—24no—
300Q8—44no—
301Q8—42no—
302Q8—42no—
303Q8—42no—
304Q8—82no—
305Q8—441no—
306Q8—441no—
307D4—441no—
308D4—441no—
309D4—882no—
310C2×C4—44no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—82no—
314C2×C4—114no—
315C2×C4—442no—
316C2×C4—441no—
317C2×C4—882no—
318C2×C4D8×D1111yescharacteristic
319C2×C4#6696412yes—
320C2×C4#6699212yes—
321C2×C4C2×D4×D1111yescharacteristic
322C8—222no—
323C8#6699212yes—
324C8C2×#434111yescharacteristic
325C8C22×C22⋊D1111yescharacteristic
326C22—22no—
327C22—881no—
328C22—882no—
329C22#1062276312yes—
330C22C2×D8×D1111yescharacteristic
331C4—44no—
332C4—82no—
333C4—224no—
334C4—881no—
335C4—882no—
336C4#1062276312yes—
337C4C2×#6696411yescharacteristic
338C4C2×#6699211yescharacteristic
339C2—22no—
340C2—1761no—
341C2C2×#1062276311yescharacteristic
342C2#1308176512yes—
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC22×C11×Q32C2
socleC22×C11C22×D8
prime radicalC2×#66957C22
hypercenterC22×Q32D11
hypocenterC11#33588
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×Q32

Complements

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

NH ≅ G/Ntype
3. #13077484C2semidirect
4. #13070680C2semidirect
5. #13070664C2semidirect
6. #13070374C2semidirect
7. #13070336C2semidirect
9. C22×C11×Q32C2semidirect
127. C22×Q32D11semidirect
296. C11#33588semidirect

Maximal subgroups

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

subgroupindex
C2×#106227922
#130791052
#130774842
#130706802
#130706642
#130703742
#130703362
#130703242
C22×C11×Q322
#3358811