Finite Group Databasebeta

← #14911500

Subgroups — #14911500

Order 2816.

508 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081602C211yesmaximal, characteristic, complemented
2#13081468C211yesmaximal, characteristic, complemented
3#13070851C212yesmaximal, complemented
4#13070845C211yesmaximal, characteristic, complemented
5#13070767C212yesmaximal, complemented
6#13070670C212yesmaximal
7#13070662C211yesmaximal, characteristic, complemented
8#13070521C211yesmaximal, characteristic, complemented
9#13070479C212yesmaximal, complemented
10C4×#66890C211yesmaximal, characteristic
11C11×#2224C211yesmaximal, characteristic, complemented
12#10623258—21no—
13#10623073—21no—
14C11×#500C2211yescharacteristic
15C4×C11×D8C2211yescharacteristic
16#10622768C2212yes—
17C2×#66890C2211yescharacteristic
18#10622700—21no—
19#10622632—21no—
20C2×#66864C2212yes—
21#10622503—22no—
22#10622487C2212yes—
23#10622486C2212yes—
24#10622485C2212yes—
25#10622380—22no—
26#10622312C2211yescharacteristic
27C4×D88C2211yescharacteristic
28C8×Dic22C2211yescharacteristic
29C11×#366C2212yes—
30C11×C4⋊C16C2211yescharacteristic
31C11×#357C2212yes—
32#10622200C2211yescharacteristic
33#10622141C2212yes—
34#10622140C2212yes—
35Dic11⋊C16C2212yes—
36#10622130C2212yes—
37#10622130C2212yes—
38#10622129C2211yescharacteristic
39#10622127C2211yescharacteristic
40C4×C11⋊C16C2211yescharacteristic
41C2×Q8×D11—41no—
42C2×C11×D8C2311yescharacteristic
43C11×C4⋊Q8—21no—
44C4×D4×C11—21no—
45#66999—41no—
46#66989—22no—
47C2×#4324—22no—
48#66979—41no—
49#66977—41no—
50C2×Dic44—21no—
51C2×Dic44C2312yes—
52C2×D88C2311yescharacteristic
53#66949—42no—
54#66946—22no—
55#66941—22no—
56#66940—22no—
57#66932—42no—
58C4×D44—21no—
59#66922—21no—
60C4×Dic22D411yescharacteristic
61C2×C11×C16C2312yes—
62C11×#107—21no—
63C11×#107C2312yes—
64C11×#107C2311yescharacteristic
65C11×#102—21no—
66C4×C8×C11C2311yescharacteristic
67#66890—22no—
68#66885—21no—
69#66882C2311yescharacteristic
70Dic11⋊C8D412yes—
71C8×Dic11C2312yes—
72C2×C11⋊C16C2311yescharacteristic
73C2×C11⋊C16C2311yescharacteristic
74#66874—22no—
75#66873—22no—
76#66871—22no—
77C4⋊(C11⋊C8)D411yescharacteristic
78#66864—24no—
79#33934—111nomaximal, Sylow
80C2×Q8×C11—41no—
81C2×D4×C11—21no—
82C22×C4×C11—41no—
83Q8×D11—84no—
84C2×D44—21no—
85C2×C4×D11—42no—
86C2×C4×D11—41no—
87C2×Dic22—22no—
88C2×Dic22—42no—
89C2×Dic22D811yescharacteristic
90C11×D8—21no—
91C11×D8—21no—
92C2×C8×C11C2×D411yescharacteristic
93C2×C8×C11C2411yescharacteristic
94C11×C4⋊C4—22no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—41no—
97C11×C22⋊C4—41no—
98C42×C11C2×D411yescharacteristic
99C22⋊Dic11—42no—
100C22⋊Dic11—42no—
101#4324—82no—
102(C2×D11)⋊C4—42no—
103(C2×D11)⋊C4—41no—
104C4⋊Dic11—21no—
105C4⋊Dic11—41no—
106C4⋊Dic11—41no—
107C4⋊Dic11D811yescharacteristic
108Dic11⋊C4—42no—
109Dic11⋊C4—42no—
110Dic11⋊C4D812yes—
111C4×Dic11—42no—
112C4×Dic11C2×D412yes—
113C2×C11⋊C8C2×D412yes—
114Dic44—22no—
115Dic44—22no—
116Dic44—81no—
117D88—21no—
118D88#4112yes—
119C11×C16—22no—
120C11⋊C16—21no—
121C11⋊C16—21no—
122#3393—111no—
123Q8×D8—111no—
124#2243—112no—
125#2241—111no—
126#2227—112no—
127#2224D1111yescharacteristic, complemented
128#2210—112no—
129#2208—111no—
130#2183—111no—
131#2175—112no—
132C4×D16—111no—
133C23×C11—41no—
134C22×D11—41no—
135Q8×C11—82no—
136D4×C11—41no—
137D4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—42no—
140C2×C4×C11—82no—
141C2×C4×C11C2×D811yescharacteristic
142C2×C4×C11C2×D811yescharacteristic
143C2×C4×C11C22×D411yescharacteristic
144C2×Dic11—42no—
145C2×Dic11—41no—
146C2×Dic11C2×D812yes—
147C2×Dic11C2×D812yes—
148D44—22no—
149D44—41no—
150C4×D11—84no—
151C4×D11—82no—
152Dic22—22no—
153Dic22—42no—
154Dic22—42no—
155Dic22—84no—
156C8×C11—21no—
157C8×C11C2×#4111yescharacteristic
158C8×C112−1+411yescharacteristic
159C11⋊C8—22no—
160#556—221no—
161D4×Q8—221no—
162C2×SD32—112no—
163C2×D16—111no—
164#500—112no—
165#500C2×D1111yescharacteristic
166#495—112no—
167#494—111no—
168#474—222no—
169#474—221no—
170#464—222no—
171#461—221no—
172C8×Q8—111no—
173C4×Q16—112no—
174C4×D8—112no—
175C4×D8—111no—
176C4×D8C2×D1111yescharacteristic
177#366—111no—
178#366C2×D1112yes—
179C4⋊C16—112no—
180C4⋊C16C2×D1111yescharacteristic
181#358—112no—
182#358—112no—
183#358—112no—
184#357—111no—
185#357—111no—
186#357C2×D1112yes—
187#346—112no—
188C4×C16—111no—
189C22×C11—81no—
190C22×C11—81no—
191C22×C11—81no—
192C22×C11C22×D811yescharacteristic
193C2×D11—42no—
194C2×D11—81no—
195C2×D11—81no—
196C4×C11—21no—
197C4×C11—81no—
198C4×C11—82no—
199C4×C11#50912yes—
200C4×C11#54811yescharacteristic
201C4×C11#57711yescharacteristic
202Dic11—22no—
203Dic11—22no—
204Dic11—82no—
205Dic11—81no—
206C22×Q8—441no—
207C2×Q16—112no—
208C2×Q16—221no—
209C2×SD16—222no—
210C2×D8—111no—
211C2×D8C22×D1111yescharacteristic
212C4⋊Q8—21no—
213C4⋊Q8—222no—
214C4⋊Q8—221no—
215#126—442no—
216#124—222no—
217C22⋊Q8—442no—
218C22⋊Q8—441no—
219C22⋊Q8—441no—
220C4×Q8—111no—
221C4×Q8—222no—
222C4×D4—21no—
223C4×D4—222no—
224C4×D4—221no—
225#117—441no—
226SD32—224no—
227D16—222no—
228C2×C16—111no—
229C2×C16—111no—
230C2×C16C22×D1112yes—
231#107—21no—
232#107—111no—
233#107—222no—
234#107C22×D1111yescharacteristic
235#107C22×D1112yes—
236C4⋊C8—112no—
237C4⋊C8—111no—
238#103—222no—
239#102—21no—
240#102—222no—
241#102—221no—
242C4×C8—112no—
243C4×C8C22×D1111yescharacteristic
244C2×C11—161no—
245C2×C11#335811yescharacteristic
246C2×C11C2×#50911yescharacteristic
247C2×C11#341711yescharacteristic
248D11—82no—
249C2×Q8—41no—
250C2×Q8—111no—
251C2×Q8—222no—
252C2×Q8—442no—
253C2×Q8—884no—
254C2×D4—21no—
255C2×D4—221no—
256C22×C4—41no—
257C22×C4—442no—
258C22×C4—441no—
259Q16—222no—
260Q16—222no—
261Q16—881no—
262SD16—882no—
263D8—21no—
264D8—21no—
265D8—112no—
266D8—221no—
267C2×C8—112no—
268C2×C8D4×D1111yescharacteristic
269C2×C8C23×D1111yescharacteristic
270C4⋊C4—21no—
271C4⋊C4—22no—
272C4⋊C4—41no—
273C4⋊C4—111no—
274C4⋊C4—112no—
275C4⋊C4—221no—
276C4⋊C4—442no—
277C4⋊C4—442no—
278C4⋊C4—441no—
279C4⋊C4—441no—
280C22⋊C4—41no—
281C22⋊C4—442no—
282C22⋊C4—442no—
283C22⋊C4—442no—
284C22⋊C4—441no—
285C42—112no—
286C42—442no—
287C42D4×D1111yescharacteristic
288C16—22no—
289C16—221no—
290C16—221no—
291C11#3393411yescharacteristic, complemented, Sylow
292C23—41no—
293C23—441no—
294Q8—82no—
295Q8—222no—
296Q8—442no—
297Q8—442no—
298Q8—884no—
299D4—41no—
300D4—41no—
301D4—222no—
302D4—441no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—82no—
306C2×C4—112no—
307C2×C4—112no—
308C2×C4—442no—
309C2×C4—441no—
310C2×C4—884no—
311C2×C4—882no—
312C2×C4D8×D1111yescharacteristic
313C2×C4D8×D1111yescharacteristic
314C2×C4C2×D4×D1111yescharacteristic
315C8—21no—
316C8—222no—
317C8#6704011yescharacteristic
318C8#41×D1111yescharacteristic
319C22—81no—
320C22—81no—
321C22—81no—
322C22—442no—
323C22—881no—
324C22—881no—
325C22C2×D8×D1111yescharacteristic
326C4—21no—
327C4—81no—
328C4—82no—
329C4—222no—
330C4—222no—
331C4—881no—
332C4—882no—
333C4#1062252412yes—
334C4#1062316411yescharacteristic
335C4#1062330911yescharacteristic
336C2—161no—
337C2—882no—
338C2#1308125011yescharacteristic
339C2C2×#1062252411yescharacteristic
340C2#1308176811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2224C2
socleC22×C11C22×D8
prime radicalC2×#66890C22
hypercenter#2224D11
hypocenterC11#33934
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2224

Complements

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

NH ≅ G/Ntype
1. #13081602C2semidirect
2. #13081468C2semidirect
3. #13070851C2semidirect
4. #13070845C2semidirect
5. #13070767C2semidirect
7. #13070662C2semidirect
8. #13070521C2semidirect
9. #13070479C2semidirect
11. C11×#2224C2semidirect
127. #2224D11semidirect
291. C11#33934semidirect

Maximal subgroups

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

subgroupindex
#130816022
#130814682
#130708512
#130708452
#130707672
#130706702
#130706622
#130705212
#130704792
C4×#668902
C11×#22242
#3393411