Finite Group Databasebeta

← #14911477

Subgroups — #14911477

Order 2816.

484 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081626C211yesmaximal, characteristic
2#13081505C211yesmaximal, characteristic, complemented
3#13070849C212yesmaximal, complemented
4#13070840C211yesmaximal, characteristic
5#13070776C212yesmaximal, complemented
6#13070758C211yesmaximal, characteristic, complemented
7#13070680C212yesmaximal, complemented
8#13070656C211yesmaximal, characteristic
9C16×Dic22C211yesmaximal, characteristic, complemented
10#13070465C212yesmaximal, complemented
11C4×C11×Q32C211yesmaximal, characteristic, complemented
12#10623116—21no—
13#10623101—21no—
14C2×C11×Q32C2211yescharacteristic
15C4×C11×Q16C2211yescharacteristic
16C4×C11×Q16C2211yescharacteristic
17#10622804C2212yes—
18Q16×Dic11C2212yes—
19C2×#66892C2212yes—
20#10622640—21no—
21#10622633—21no—
22#10622491C2212yes—
23#10622485C2212yes—
24#10622432—22no—
25#10622409—22no—
26#10622308C2211yescharacteristic
27#10622295C2211yescharacteristic
28C8×Dic22C2211yescharacteristic
29C11×#366C2211yescharacteristic
30C11×#358C2211yescharacteristic
31C11×#358C2211yescharacteristic
32C4×C11×C16C2211yescharacteristic
33#10622202C2212yes—
34#10622147C2212yes—
35#10622147C2212yes—
36Dic11⋊C16C2212yes—
37C16×Dic11C2212yes—
38#10622129C2212yes—
39#10622128C2212yes—
40C4⋊(C11⋊C16)C2211yescharacteristic
41C2×C11×Q16C2311yescharacteristic
42C2×C11×Q16C2311yescharacteristic
43C4×Q8×C11—21no—
44C4×Q8×C11—21no—
45#67000—22no—
46Q8×Dic11—22no—
47C2×#4325—22no—
48C2×D88—21no—
49C2×D88C2312yes—
50#66947—42no—
51#66946—22no—
52#66943—22no—
53#66943—42no—
54#66928—41no—
55#66927—21no—
56C4×D44—41no—
57#66922—21no—
58#66922—41no—
59C4×Dic22—41no—
60C4×Dic22D411yescharacteristic
61C11×Q32—22no—
62C2×C11×C16C2311yescharacteristic
63C2×C11×C16C2311yescharacteristic
64C11×#107C2311yescharacteristic
65C11×#107C2311yescharacteristic
66C11×#103—21no—
67C11×#103—21no—
68C4×C8×C11C2311yescharacteristic
69#66899—22no—
70#66892—24no—
71#66882—21no—
72#66882C2312yes—
73Dic11⋊C8D412yes—
74C8×Dic11C2312yes—
75C2×C11⋊C16C2312yes—
76#66873—22no—
77#66872—22no—
78C4⋊(C11⋊C8)D411yescharacteristic
79#33932—111nomaximal, Sylow
80C2×Q8×C11—21no—
81C2×Q8×C11—21no—
82C2×D44—22no—
83C2×D44—41no—
84C2×D44—41no—
85C2×C4×D11—42no—
86C2×Dic22—41no—
87C2×Dic22D811yescharacteristic
88C11×Q16—21no—
89C11×Q16—21no—
90C11×Q16—21no—
91C11×Q16#4112yes—
92C2×C8×C11C2×D411yescharacteristic
93C2×C8×C11C2411yescharacteristic
94C11×C4⋊C4—21no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C42×C11—41no—
99C42×C11—41no—
100C42×C11C2×D411yescharacteristic
101#4325—82no—
102(C2×D11)⋊C4—42no—
103(C2×D11)⋊C4—42no—
104(C2×D11)⋊C4—42no—
105C4⋊Dic11—22no—
106C4⋊Dic11—42no—
107C4⋊Dic11—42no—
108C4⋊Dic11—41no—
109C4⋊Dic11D811yescharacteristic
110Dic11⋊C4—42no—
111Dic11⋊C4D812yes—
112C4×Dic11—42no—
113C4×Dic11C2×D412yes—
114C2×C11⋊C8C2×D412yes—
115D88—22no—
116D88—22no—
117D88—81no—
118C11×C16—21no—
119C11×C16—21no—
120C11⋊C16—22no—
121#3396—111no—
122#3383—111no—
123#2242—112no—
124#2240—111no—
125#2228—112no—
126#2225—111no—
127#2211—112no—
128#2207—111no—
129Q8×C16—111no—
130C4×Q32D1111yescharacteristic, complemented
131C4×SD32—112no—
132C22×D11—42no—
133Q8×C11—22no—
134Q8×C11—41no—
135Q8×C11—41no—
136Q8×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11C2×D811yescharacteristic
142C2×C4×C11C2×D811yescharacteristic
143C2×C4×C11C22×D411yescharacteristic
144C2×Dic11—42no—
145C2×Dic11C2×D812yes—
146C2×Dic11C2×D812yes—
147D44—42no—
148D44—42no—
149D44—82no—
150D44—161no—
151C4×D11—162no—
152Dic22—22no—
153Dic22—82no—
154C8×C11—21no—
155C8×C11C2×#4111yescharacteristic
156C8×C112−1+411yescharacteristic
157C11⋊C8—22no—
158#559—221no—
159#557—221no—
160C2×Q32C2×D1111yescharacteristic
161C2×SD32—112no—
162#500—111no—
163#499—112no—
164#495—112no—
165#493—111no—
166#479—222no—
167#475—221no—
168#463—222no—
169#460—221no—
170C8×Q8—111no—
171C4×Q16—112no—
172C4×Q16C2×D1111yescharacteristic
173C4×Q16C2×D1111yescharacteristic
174C4×D8—112no—
175#367—112no—
176#366C2×D1111yescharacteristic
177C4⋊C16—112no—
178C4⋊C16—111no—
179#358—112no—
180#358C2×D1111yescharacteristic
181#358C2×D1111yescharacteristic
182#357—112no—
183#357—112no—
184#357—112no—
185C4×C16—112no—
186C4×C16C2×D1111yescharacteristic
187C22×C11C22×D811yescharacteristic
188C2×D11—82no—
189C2×D11—82no—
190C2×D11—82no—
191C4×C11—21no—
192C4×C11—42no—
193C4×C11—81no—
194C4×C11—81no—
195C4×C11—81no—
196C4×C11#50812yes—
197C4×C11#54811yescharacteristic
198C4×C11#57711yescharacteristic
199Dic11—22no—
200Dic11—22no—
201Dic11—82no—
202C2×Q16C22×D1111yescharacteristic
203C2×Q16C22×D1111yescharacteristic
204C2×SD16—222no—
205C2×D8—112no—
206C2×D8—221no—
207C4⋊Q8—221no—
208C4⋊Q8—441no—
209#127—221no—
210#125—222no—
211#125—442no—
212#124—222no—
213#124—441no—
214#123—442no—
215C4×Q8—21no—
216C4×Q8—21no—
217C4×Q8—111no—
218C4×Q8—222no—
219C4×Q8—441no—
220C4×D4—222no—
221C4×D4—441no—
222Q32—22no—
223SD32—224no—
224C2×C16—112no—
225C2×C16C22×D1111yescharacteristic
226C2×C16C22×D1111yescharacteristic
227#107—112no—
228#107—221no—
229#107C22×D1111yescharacteristic
230#107C22×D1111yescharacteristic
231#106—222no—
232C4⋊C8—112no—
233C4⋊C8—111no—
234#103—21no—
235#103—21no—
236#103—222no—
237#102—222no—
238C4×C8—112no—
239C4×C8C22×D1111yescharacteristic
240C2×C11#335811yescharacteristic
241C2×C11C2×#50811yescharacteristic
242C2×C11#341611yescharacteristic
243D11—162no—
244C2×Q8—21no—
245C2×Q8—21no—
246C2×Q8—111no—
247C2×Q8—441no—
248C2×D4—222no—
249C2×D4—441no—
250C2×D4—441no—
251C22×C4—442no—
252Q16—21no—
253Q16—21no—
254Q16—21no—
255Q16#433912yes—
256SD16—882no—
257D8—222no—
258D8—222no—
259D8—881no—
260C2×C8—112no—
261C2×C8D4×D1111yescharacteristic
262C2×C8C23×D1111yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—111no—
268C4⋊C4—112no—
269C4⋊C4—222no—
270C4⋊C4—442no—
271C4⋊C4—442no—
272C4⋊C4—442no—
273C4⋊C4—441no—
274C22⋊C4—442no—
275C22⋊C4—442no—
276C22⋊C4—442no—
277C42—41no—
278C42—41no—
279C42—112no—
280C42—442no—
281C42D4×D1111yescharacteristic
282C16—21no—
283C16—21no—
284C16—222no—
285C11#3393211yescharacteristic, complemented, Sylow
286C23—442no—
287Q8—22no—
288Q8—41no—
289Q8—41no—
290Q8—41no—
291Q8—222no—
292Q8—882no—
293D4—442no—
294D4—442no—
295D4—882no—
296D4—1761no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—112no—
302C2×C4—112no—
303C2×C4—442no—
304C2×C4—1762no—
305C2×C4D8×D1111yescharacteristic
306C2×C4D8×D1111yescharacteristic
307C2×C4C2×D4×D1111yescharacteristic
308C8—21no—
309C8—222no—
310C8C2×#433911yescharacteristic
311C8#6704311yescharacteristic
312C22—882no—
313C22—882no—
314C22—882no—
315C22C2×D8×D1111yescharacteristic
316C4—21no—
317C4—42no—
318C4—81no—
319C4—81no—
320C4—81no—
321C4—222no—
322C4—222no—
323C4—882no—
324C4#1062253212yes—
325C4#1062308311yescharacteristic
326C4#1062330111yescharacteristic
327C2—1762no—
328C2#1308124911yescharacteristic
329C2C2×#1062253211yescharacteristic
330C2#1308175911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC4×C11×Q32C2
socleC22×C11C22×D8
prime radical#10622308C22
hypercenterC4×Q32D11
hypocenterC11#33932
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×Q32

Complements

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

NH ≅ G/Ntype
2. #13081505C2semidirect
3. #13070849C2semidirect
5. #13070776C2semidirect
6. #13070758C2semidirect
7. #13070680C2semidirect
9. C16×Dic22C2semidirect
10. #13070465C2semidirect
11. C4×C11×Q32C2semidirect
130. C4×Q32D11semidirect
285. C11#33932semidirect

Maximal subgroups

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

subgroupindex
#130816262
#130815052
#130708492
#130708402
#130707762
#130707582
#130706802
#130706562
C16×Dic222
#130704652
C4×C11×Q322
#3393211