Finite Group Databasebeta

← #14911430

Subgroups — #14911430

Order 2816.

486 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081602C211yesmaximal, characteristic, complemented
2#13081481C211yesmaximal, characteristic, complemented
3#13070846C212yesmaximal, complemented
4#13070844C211yesmaximal, characteristic, complemented
5#13070779C212yesmaximal, complemented
6#13070763C211yesmaximal, characteristic, complemented
7#13070669C212yesmaximal
8#13070661C211yesmaximal, characteristic, complemented
9C16×Dic22C211yesmaximal, characteristic, complemented
10#13070471C212yesmaximal, complemented
11C4×C11×D16C211yesmaximal, characteristic
12#10623074—21no—
13#10623073—21no—
14C2×C11×D16C2211yescharacteristic
15C4×C11×D8C2211yescharacteristic
16C4×C11×D8C2211yescharacteristic
17#10622768C2212yes—
18D8×Dic11C2212yes—
19C2×#66891C2212yes—
20#10622632—21no—
21#10622621—21no—
22#10622491C2212yes—
23#10622486C2212yes—
24#10622380—22no—
25#10622379—22no—
26#10622312C2211yescharacteristic
27#10622295C2211yescharacteristic
28C8×Dic22C2211yescharacteristic
29C11×#366C2211yescharacteristic
30C11×#357C2211yescharacteristic
31C11×#357C2211yescharacteristic
32C4×C11×C16C2211yescharacteristic
33#10622200C2212yes—
34#10622141C2212yes—
35#10622141C2212yes—
36Dic11⋊C16C2212yes—
37C16×Dic11C2212yes—
38#10622130C2212yes—
39#10622128C2212yes—
40C4⋊(C11⋊C16)C2211yescharacteristic
41C2×C11×D8C2311yescharacteristic
42C2×C11×D8C2311yescharacteristic
43C4×D4×C11—21no—
44C4×D4×C11—21no—
45#66989—22no—
46D4×Dic11—22no—
47C2×#4324—22no—
48#66979—41no—
49C2×C4⋊Dic11—41no—
50#66977—41no—
51#66977—41no—
52C2×Dic44—21no—
53C2×Dic44C2312yes—
54#66943—22no—
55#66940—22no—
56#66932—42no—
57#66931—42no—
58#66922—21no—
59#66922—21no—
60C4×Dic22D411yescharacteristic
61C11×D16—22no—
62C2×C11×C16C2311yescharacteristic
63C2×C11×C16C2311yescharacteristic
64C11×#107C2311yescharacteristic
65C11×#107C2311yescharacteristic
66C11×#102—21no—
67C11×#102—21no—
68C4×C8×C11C2311yescharacteristic
69#66896—22no—
70#66891—24no—
71#66882—21no—
72#66882C2312yes—
73Dic11⋊C8D412yes—
74C8×Dic11C2312yes—
75C2×C11⋊C16C2312yes—
76#66874—22no—
77#66872—22no—
78C4⋊(C11⋊C8)D411yescharacteristic
79#33927—111nomaximal, Sylow
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C22×C4×C11—41no—
83C22×C4×C11—41no—
84C22×Dic11—42no—
85C2×Dic22—22no—
86C2×Dic22—41no—
87C2×Dic22D811yescharacteristic
88C11×D8—21no—
89C11×D8—21no—
90C11×D8—21no—
91C11×D8#4112yes—
92C2×C8×C11C2×D411yescharacteristic
93C2×C8×C11C2411yescharacteristic
94C11×C4⋊C4—21no—
95C11×C4⋊C4—21no—
96C11×C22⋊C4—41no—
97C11×C22⋊C4—41no—
98C42×C11C2×D411yescharacteristic
99C22⋊Dic11—42no—
100C22⋊Dic11—42no—
101C22⋊Dic11—42no—
102#4324—82no—
103C4⋊Dic11—22no—
104C4⋊Dic11—42no—
105C4⋊Dic11—41no—
106C4⋊Dic11—41no—
107C4⋊Dic11—41no—
108C4⋊Dic11D811yescharacteristic
109Dic11⋊C4—42no—
110Dic11⋊C4—42no—
111Dic11⋊C4D812yes—
112C4×Dic11—42no—
113C4×Dic11C2×D412yes—
114C2×C11⋊C8C2×D412yes—
115Dic44—22no—
116Dic44—22no—
117Dic44—81no—
118C11×C16—21no—
119C11×C16—21no—
120C11⋊C16—22no—
121#3393—111no—
122#3380—111no—
123#2242—112no—
124#2241—111no—
125#2229—112no—
126#2226—111no—
127#2210—112no—
128#2208—111no—
129Q8×C16—111no—
130C4×SD32—112no—
131C4×D16D1111yescharacteristic
132C23×C11—41no—
133C23×C11—41no—
134D4×C11—22no—
135D4×C11—41no—
136D4×C11—41no—
137D4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—82no—
141C2×C4×C11—82no—
142C2×C4×C11C2×D811yescharacteristic
143C2×C4×C11C2×D811yescharacteristic
144C2×C4×C11C22×D411yescharacteristic
145C2×Dic11—42no—
146C2×Dic11—42no—
147C2×Dic11—162no—
148C2×Dic11C2×D812yes—
149C2×Dic11C2×D812yes—
150Dic22—22no—
151Dic22—42no—
152Dic22—42no—
153Dic22—161no—
154C8×C11—21no—
155C8×C11C2×#4111yescharacteristic
156C8×C112−1+411yescharacteristic
157C11⋊C8—22no—
158#556—221no—
159#554—221no—
160C2×SD32—112no—
161C2×D16C2×D1111yescharacteristic
162#500—111no—
163#499—112no—
164#495—112no—
165#494—111no—
166#478—222no—
167#476—221no—
168#464—222no—
169#461—221no—
170C8×Q8—111no—
171C4×Q16—112no—
172C4×D8—112no—
173C4×D8C2×D1111yescharacteristic
174C4×D8C2×D1111yescharacteristic
175#367—112no—
176#366C2×D1111yescharacteristic
177C4⋊C16—112no—
178C4⋊C16—111no—
179#358—112no—
180#358—112no—
181#358—112no—
182#357—112no—
183#357C2×D1111yescharacteristic
184#357C2×D1111yescharacteristic
185C4×C16—112no—
186C4×C16C2×D1111yescharacteristic
187C22×C11—42no—
188C22×C11—81no—
189C22×C11—81no—
190C22×C11—81no—
191C22×C11—81no—
192C22×C11—81no—
193C22×C11C22×D811yescharacteristic
194C4×C11—21no—
195C4×C11—81no—
196C4×C11—81no—
197C4×C11#50812yes—
198C4×C11#54811yescharacteristic
199C4×C11#57711yescharacteristic
200Dic11—22no—
201Dic11—22no—
202Dic11—82no—
203Dic11—82no—
204C2×Q16—112no—
205C2×Q16—221no—
206C2×SD16—222no—
207C2×D8C22×D1111yescharacteristic
208C2×D8C22×D1111yescharacteristic
209C4⋊Q8—221no—
210C4⋊Q8—221no—
211#126—442no—
212#125—222no—
213#124—222no—
214C22⋊Q8—442no—
215C22⋊Q8—441no—
216C22⋊Q8—441no—
217C4×Q8—111no—
218C4×Q8—222no—
219C4×D4—21no—
220C4×D4—21no—
221C4×D4—222no—
222#117—441no—
223C2×C4⋊C4—441no—
224SD32—224no—
225D16—22no—
226C2×C16—112no—
227C2×C16C22×D1111yescharacteristic
228C2×C16C22×D1111yescharacteristic
229#107—112no—
230#107—221no—
231#107C22×D1111yescharacteristic
232#107C22×D1111yescharacteristic
233#106—222no—
234C4⋊C8—112no—
235C4⋊C8—111no—
236#103—222no—
237#102—21no—
238#102—21no—
239#102—222no—
240C4×C8—112no—
241C4×C8C22×D1111yescharacteristic
242C2×C11—82no—
243C2×C11—161no—
244C2×C11#335811yescharacteristic
245C2×C11C2×#50811yescharacteristic
246C2×C11#341611yescharacteristic
247C2×Q8—111no—
248C2×Q8—222no—
249C2×Q8—441no—
250C2×D4—21no—
251C2×D4—21no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—442no—
255Q16—222no—
256Q16—222no—
257Q16—881no—
258SD16—882no—
259D8—21no—
260D8—21no—
261D8—21no—
262D8#433912yes—
263C2×C8—112no—
264C2×C8D4×D1111yescharacteristic
265C2×C8C23×D1111yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—111no—
269C4⋊C4—112no—
270C4⋊C4—222no—
271C4⋊C4—442no—
272C4⋊C4—442no—
273C4⋊C4—442no—
274C4⋊C4—441no—
275C4⋊C4—441no—
276C4⋊C4—441no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4—442no—
280C22⋊C4—442no—
281C22⋊C4—442no—
282C42—112no—
283C42—442no—
284C42D4×D1111yescharacteristic
285C16—21no—
286C16—21no—
287C16—222no—
288C11#3392711yescharacteristic, complemented, Sylow
289C23—41no—
290C23—41no—
291Q8—222no—
292Q8—442no—
293Q8—442no—
294Q8—1761no—
295D4—22no—
296D4—41no—
297D4—41no—
298D4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—82no—
302C2×C4—82no—
303C2×C4—112no—
304C2×C4—112no—
305C2×C4—442no—
306C2×C4—442no—
307C2×C4—1762no—
308C2×C4D8×D1111yescharacteristic
309C2×C4D8×D1111yescharacteristic
310C2×C4C2×D4×D1111yescharacteristic
311C8—21no—
312C8—222no—
313C8C2×#433911yescharacteristic
314C8#6704311yescharacteristic
315C22—42no—
316C22—81no—
317C22—81no—
318C22—81no—
319C22—81no—
320C22—81no—
321C22C2×D8×D1111yescharacteristic
322C4—21no—
323C4—81no—
324C4—81no—
325C4—222no—
326C4—222no—
327C4—882no—
328C4—882no—
329C4#1062252512yes—
330C4#1062308311yescharacteristic
331C4#1062330111yescharacteristic
332C2—82no—
333C2—161no—
334C2#1308124911yescharacteristic
335C2C2×#1062252511yescharacteristic
336C2#1308175911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC4×C11×D16C2
socleC22×C11C22×D8
prime radicalC2×C11×D16C22
hypercenterC4×D16D11
hypocenterC11#33927
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×D16

Complements

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

NH ≅ G/Ntype
1. #13081602C2semidirect
2. #13081481C2semidirect
3. #13070846C2semidirect
4. #13070844C2semidirect
5. #13070779C2semidirect
6. #13070763C2semidirect
8. #13070661C2semidirect
9. C16×Dic22C2semidirect
10. #13070471C2semidirect
288. C11#33927semidirect

Maximal subgroups

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

subgroupindex
#130816022
#130814812
#130708462
#130708442
#130707792
#130707632
#130706692
#130706612
C16×Dic222
#130704712
C4×C11×D162
#3392711