Finite Group Databasebeta

← #14911523

Subgroups — #14911523

Order 2816.

474 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081605C211yesmaximal, characteristic
2#13070855C212yesmaximal
3#13070845C211yesmaximal, characteristic, complemented
4#13070760C211yesmaximal, characteristic
5#13070755C212yesmaximal, complemented
6#13070678C212yesmaximal
7#13070666C211yesmaximal, characteristic, complemented
8#13070525C211yesmaximal, characteristic, complemented
9#13070485C212yesmaximal, complemented
10C4×#66892C211yesmaximal, characteristic
11Q8×C11×Q16C211yesmaximal, characteristic, complemented
12Q82×C11—21no—
13#10623115—21no—
14C11×#500C2212yes—
15C11×#500C2211yescharacteristic
16C11×#477—21no—
17C11×#477—22no—
18C8×Q8×C11C2211yescharacteristic
19C4×C11×Q16C2211yescharacteristic
20C4×C11×Q16C2212yes—
21C2×#66893C2212yes—
22C2×#66892C2211yescharacteristic
23#10622458—22no—
24#10622454—21no—
25#10622312C2211yescharacteristic
26C4×Dic44C2212yes—
27#10622309C2212yes—
28C4×D88C2211yescharacteristic
29#10622202C2211yescharacteristic
30#10622130C2212yes—
31#10622130C2212yes—
32#10622130C2212yes—
33#10622129C2211yescharacteristic
34#10622129C2212yes—
35#10622128C2211yescharacteristic
36#10622128C2212yes—
37C4⋊(C11⋊C16)C2211yescharacteristic
38C4⋊(C11⋊C16)C2212yes—
39#10622099C2212yes—
40C4×C11⋊C16C2211yescharacteristic
41C2×C11×Q16C2311yescharacteristic
42C11×C4⋊Q8—22no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8—41no—
45C11×C4⋊Q8—42no—
46C4×Q8×C11—22no—
47C4×Q8×C11—21no—
48C4×Q8×C11—41no—
49C4×Q8×C11D411yescharacteristic
50#66999—41no—
51C2×Dic44—21no—
52C2×Dic44C2312yes—
53C2×D88C2311yescharacteristic
54C2×#4314—22no—
55#66951—42no—
56#66945—41no—
57#66928—22no—
58C4×D44—21no—
59#66922—21no—
60C4×Dic22—22no—
61C11×#107—22no—
62C11×#107—21no—
63C11×#107C2311yescharacteristic
64C11×#107C2312yes—
65C11×C4⋊C8D411yescharacteristic
66C11×C4⋊C8D412yes—
67C11×#103—22no—
68C11×#103—21no—
69C4×C8×C11C2311yescharacteristic
70C4×C8×C11C2312yes—
71#66893—24no—
72#66892—22no—
73#66885—21no—
74#66882C2311yescharacteristic
75#66880—22no—
76C2×C11⋊C16C2311yescharacteristic
77C2×C11⋊C16C2312yes—
78C2×C11⋊C16C2311yescharacteristic
79#33936—111nomaximal, Sylow
80C2×Q8×C11—21no—
81C2×Q8×C11—42no—
82C2×Q8×C11—41no—
83C2×Q8×C11D811yescharacteristic
84C2×D44—21no—
85C2×C4×D11—41no—
86C2×Dic22—22no—
87C11×Q16—21no—
88C11×Q16#4112yes—
89C2×C8×C11C2×D412yes—
90C2×C8×C11C2×D411yescharacteristic
91C2×C8×C11C2411yescharacteristic
92C11×C4⋊C4—22no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—42no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—42no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4D811yescharacteristic
99C11×C4⋊C4D812yes—
100C42×C11—42no—
101C42×C11—41no—
102C42×C11C2×D412yes—
103C42×C11C2×D411yescharacteristic
104(C2×D11)⋊C4—41no—
105(C2×D11)⋊C4—42no—
106(C2×D11)⋊C4—42no—
107C4⋊Dic11—21no—
108C4⋊Dic11—41no—
109C4⋊Dic11—41no—
110Dic11⋊C4—42no—
111C4×Dic11—42no—
112Dic44—22no—
113Dic44—22no—
114Dic44—81no—
115D88—21no—
116D88—21no—
117#4314—82no—
118C11⋊C16—21no—
119C11⋊C16—22no—
120C11⋊C16—21no—
121#3393—111no—
122Q8×Q16D1111yescharacteristic, complemented
123#2243—112no—
124#2241—111no—
125#2226—111no—
126#2225—112no—
127#2211—112no—
128#2209—111no—
129#2183—111no—
130#2176—112no—
131C4×SD32—111no—
132C22×D11—41no—
133Q8×C11—22no—
134Q8×C11—22no—
135Q8×C11—41no—
136Q8×C11—162no—
137Q8×C11—161no—
138C2×C4×C11—41no—
139C2×C4×C11—42no—
140C2×C4×C11—41no—
141C2×C4×C11C2×D812yes—
142C2×C4×C11C2×D812yes—
143C2×C4×C11C2×D811yescharacteristic
144C2×C4×C11C2×D811yescharacteristic
145C2×C4×C11C22×D411yescharacteristic
146C2×Dic11—41no—
147C2×Dic11—42no—
148D44—41no—
149D44—41no—
150C4×D11—82no—
151Dic22—42no—
152Dic22—42no—
153C8×C11—22no—
154C8×C11—21no—
155C8×C11C2×#4111yescharacteristic
156C8×C112−1+411yescharacteristic
157Q82—21no—
158#556—221no—
159C2×Q32—112no—
160C2×SD32—111no—
161#500C2×D1112yes—
162#500C2×D1111yescharacteristic
163#495—112no—
164#494—111no—
165#477—21no—
166#477—22no—
167#464—222no—
168#461—221no—
169C8×Q8C2×D1111yescharacteristic
170C4×Q16—112no—
171C4×Q16C2×D1111yescharacteristic
172C4×Q16C2×D1112yes—
173C4×D8—111no—
174#367—111no—
175#367—112no—
176C4⋊C16—111no—
177C4⋊C16—112no—
178#358—111no—
179#358—112no—
180#358—112no—
181#358—112no—
182#357—111no—
183#357—112no—
184#346—112no—
185C4×C16—111no—
186C22×C11C22×D811yescharacteristic
187C2×D11—81no—
188C2×D11—81no—
189C2×D11—81no—
190C4×C11—22no—
191C4×C11—22no—
192C4×C11—21no—
193C4×C11—42no—
194C4×C11—82no—
195C4×C11—81no—
196C4×C11#51012yes—
197C4×C11#54811yescharacteristic
198C4×C11#57711yescharacteristic
199Dic11—82no—
200Dic11—81no—
201C2×Q16—112no—
202C2×Q16—221no—
203C2×Q16C22×D1111yescharacteristic
204C2×SD16—222no—
205C2×D8—111no—
206C4⋊Q8—21no—
207C4⋊Q8—22no—
208C4⋊Q8—41no—
209C4⋊Q8—42no—
210C4⋊Q8—221no—
211#126—442no—
212#124—222no—
213C22⋊Q8—441no—
214C4×Q8—21no—
215C4×Q8—22no—
216C4×Q8—41no—
217C4×Q8—222no—
218C4×Q8C22⋊D1111yescharacteristic
219C4×D4—221no—
220#117—441no—
221Q32—224no—
222SD32—222no—
223C2×C16—111no—
224C2×C16—111no—
225C2×C16—112no—
226#107—21no—
227#107—22no—
228#107—111no—
229#107C22×D1111yescharacteristic
230#107C22×D1112yes—
231C4⋊C8C22⋊D1111yescharacteristic
232C4⋊C8C22⋊D1112yes—
233#103—21no—
234#103—22no—
235#103—222no—
236#102—221no—
237C4×C8C22×D1111yescharacteristic
238C4×C8C22×D1112yes—
239C2×C11#335811yescharacteristic
240C2×C11C2×#51011yescharacteristic
241C2×C11#341611yescharacteristic
242D11—161no—
243C2×Q8—21no—
244C2×Q8—42no—
245C2×Q8—41no—
246C2×Q8—222no—
247C2×Q8#432311yescharacteristic
248C2×D4—221no—
249C22×C4—441no—
250Q16—21no—
251Q16—222no—
252Q16—222no—
253Q16—881no—
254Q16#434312yes—
255SD16—882no—
256D8—221no—
257D8—221no—
258C2×C8C2×C22⋊D1111yescharacteristic
259C2×C8C2×C22⋊D1112yes—
260C2×C8C23×D1111yescharacteristic
261C4⋊C4—21no—
262C4⋊C4—22no—
263C4⋊C4—42no—
264C4⋊C4—41no—
265C4⋊C4—42no—
266C4⋊C4—41no—
267C4⋊C4—221no—
268C4⋊C4—441no—
269C4⋊C4—442no—
270C4⋊C4—441no—
271C4⋊C4#432311yescharacteristic
272C4⋊C4#432312yes—
273C22⋊C4—442no—
274C22⋊C4—441no—
275C22⋊C4—442no—
276C42—42no—
277C42—41no—
278C42—442no—
279C42C2×C22⋊D1111yescharacteristic
280C42C2×C22⋊D1112yes—
281C16—221no—
282C16—222no—
283C16—221no—
284C11#3393611yescharacteristic, complemented, Sylow
285C23—441no—
286Q8—22no—
287Q8—22no—
288Q8—41no—
289Q8—162no—
290Q8—161no—
291Q8—442no—
292Q8—442no—
293D4—441no—
294D4—441no—
295C2×C4—41no—
296C2×C4—42no—
297C2×C4—41no—
298C2×C4—441no—
299C2×C4—442no—
300C2×C4—882no—
301C2×C4C2×#432312yes—
302C2×C4C2×#432312yes—
303C2×C4C2×#432311yescharacteristic
304C2×C4C2×#432311yescharacteristic
305C2×C4C22×C22⋊D1111yescharacteristic
306C8—22no—
307C8—21no—
308C8C2×#434311yescharacteristic
309C8#6704011yescharacteristic
310C22—881no—
311C22—881no—
312C22—881no—
313C22C22×#432311yescharacteristic
314C4—22no—
315C4—22no—
316C4—21no—
317C4—42no—
318C4—82no—
319C4—81no—
320C4—881no—
321C4—882no—
322C4#1062279212yes—
323C4#1062334811yescharacteristic
324C4#1062336811yescharacteristic
325C2—1761no—
326C2#1308125111yescharacteristic
327C2C2×#1062279211yescharacteristic
328C2#1308176311yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingQ8×C11×Q16C2
socleC22×C11C22×D8
prime radicalC2×D88C23
hypercenterQ8×Q16D11
hypocenterC11#33936
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8 ◁ Q8×Q16

Complements

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

NH ≅ G/Ntype
3. #13070845C2semidirect
5. #13070755C2semidirect
7. #13070666C2semidirect
8. #13070525C2semidirect
9. #13070485C2semidirect
11. Q8×C11×Q16C2semidirect
122. Q8×Q16D11semidirect
284. C11#33936semidirect

Maximal subgroups

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

subgroupindex
#130816052
#130708552
#130708452
#130707602
#130707552
#130706782
#130706662
#130705252
#130704852
C4×#668922
Q8×C11×Q162
#3393611