Finite Group Databasebeta

← #14911506

Subgroups — #14911506

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#13081606C211yesmaximal, characteristic, complemented
2#13081468C211yesmaximal, characteristic, complemented
3#13070854C212yesmaximal, complemented
4#13070766C212yesmaximal, complemented
5#13070750C211yesmaximal, characteristic, complemented
6#13070674C212yesmaximal
7#13070658C211yesmaximal, characteristic, complemented
8#13070524C211yesmaximal, characteristic, complemented
9#13070483C212yesmaximal, complemented
10C4×D176C211yesmaximal, characteristic
11C11×#2241C211yesmaximal, characteristic, complemented
12#10623263—21no—
13#10623258—21no—
14C11×#500C2211yescharacteristic
15C11×#494C2211yescharacteristic
16#10622804C2212yes—
17#10622798—22no—
18Q16×Dic11C2212yes—
19C2×#66892C2212yes—
20#10622700—21no—
21#10622696—21no—
22C2×D176C2211yescharacteristic
23#10622503—22no—
24#10622487C2212yes—
25#10622485C2212yes—
26C4×D88C2211yescharacteristic
27C4×D88C2211yescharacteristic
28C8×Dic22C2211yescharacteristic
29C11×#358C2212yes—
30C11×#358C2212yes—
31C4×C11×C16C2211yescharacteristic
32#10622202C2212yes—
33#10622147C2211yescharacteristic
34#10622147C2211yescharacteristic
35#10622142C2211yescharacteristic
36#10622140C2212yes—
37Dic11⋊C16C2212yes—
38#10622129C2212yes—
39#10622127C2212yes—
40C4⋊(C11⋊C16)C2211yescharacteristic
41C2×Q8×D11—41no—
42C2×C11×Q16—21no—
43C2×C11×Q16C2312yes—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8—21no—
46#67000—22no—
47#66999—41no—
48Q8×Dic11—22no—
49C2×#4325—22no—
50C2×D88C2311yescharacteristic
51C2×D88C2311yescharacteristic
52#66951—42no—
53#66950—41no—
54#66949—42no—
55#66946—22no—
56#66945—41no—
57#66941—22no—
58C4×D44—21no—
59C4×D44—21no—
60C4×Dic22D411yescharacteristic
61C2×C11×C16C2311yescharacteristic
62C2×C11×C16C2311yescharacteristic
63C11×#107—21no—
64C11×#107C2312yes—
65C4×C8×C11C2311yescharacteristic
66#66899—22no—
67#66892—24no—
68#66885—21no—
69#66885—21no—
70#66882C2311yescharacteristic
71#66882C2311yescharacteristic
72Dic11⋊C8D412yes—
73C8×Dic11C2312yes—
74C2×C11⋊C16C2312yes—
75#66873—22no—
76#66871—22no—
77C4⋊(C11⋊C8)D411yescharacteristic
78D176—22no—
79#33934—111nomaximal, Sylow
80C2×Q8×C11—22no—
81C2×Q8×C11—41no—
82Q8×D11—84no—
83C2×D44—21no—
84C2×D44—21no—
85C2×C4×D11—42no—
86C2×C4×D11—41no—
87C2×C4×D11—41no—
88C2×Dic22—42no—
89C2×Dic22D811yescharacteristic
90C11×Q16—22no—
91C11×Q16—22no—
92C11×Q16—81no—
93C2×C8×C11C2×D411yescharacteristic
94C2×C8×C11C2411yescharacteristic
95C11×C4⋊C4—22no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C42×C11C2×D411yescharacteristic
100#4325—82no—
101(C2×D11)⋊C4—42no—
102(C2×D11)⋊C4—42no—
103(C2×D11)⋊C4—42no—
104(C2×D11)⋊C4—41no—
105(C2×D11)⋊C4—41no—
106C4⋊Dic11—21no—
107C4⋊Dic11—21no—
108C4⋊Dic11—42no—
109C4⋊Dic11D811yescharacteristic
110Dic11⋊C4—42no—
111Dic11⋊C4D812yes—
112C4×Dic11—42no—
113C4×Dic11C2×D412yes—
114C2×C11⋊C8C2×D412yes—
115D88—21no—
116D88—21no—
117D88—21no—
118D88#4112yes—
119C11×C16—21no—
120C11×C16—21no—
121C11⋊C16—22no—
122#3393—111no—
123Q8×D8—111no—
124#2243—112no—
125#2241D1111yescharacteristic, complemented
126#2227—112no—
127#2224—111no—
128#2210—112no—
129#2208—111no—
130#2183—111no—
131#2175—112no—
132C4×D16—111no—
133C22×D11—41no—
134C22×D11—41no—
135Q8×C11—42no—
136Q8×C11—42no—
137Q8×C11—82no—
138C2×C4×C11—42no—
139C2×C4×C11—42no—
140C2×C4×C11C2×D811yescharacteristic
141C2×C4×C11C2×D811yescharacteristic
142C2×C4×C11C22×D411yescharacteristic
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11C2×D812yes—
146C2×Dic11C2×D812yes—
147D44—22no—
148D44—41no—
149D44—41no—
150D44—41no—
151C4×D11—84no—
152C4×D11—82no—
153C4×D11—82no—
154Dic22—22no—
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#494C2×D1111yescharacteristic
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×D8—111no—
177#366—111no—
178#366—112no—
179C4⋊C16—112no—
180C4⋊C16—111no—
181#358—112no—
182#358C2×D1112yes—
183#358C2×D1112yes—
184#357—111no—
185#357—111no—
186#357—112no—
187#346—112no—
188C4×C16C2×D1111yescharacteristic
189C22×C11C22×D811yescharacteristic
190C2×D11—42no—
191C2×D11—81no—
192C2×D11—81no—
193C2×D11—81no—
194C2×D11—81no—
195C2×D11—81no—
196C4×C11—21no—
197C4×C11—82no—
198C4×C11—82no—
199C4×C11#50912yes—
200C4×C11#54811yescharacteristic
201C4×C11#57711yescharacteristic
202Dic11—22no—
203Dic11—22no—
204Dic11—81no—
205Dic11—81no—
206C22×Q8—441no—
207C2×Q16—21no—
208C2×Q16C22×D1112yes—
209C2×SD16—222no—
210C2×D8—111no—
211C2×D8—111no—
212C4⋊Q8—21no—
213C4⋊Q8—21no—
214C4⋊Q8—222no—
215#126—442no—
216#124—222no—
217C22⋊Q8—442no—
218C22⋊Q8—441no—
219C22⋊Q8—441no—
220C4×Q8—111no—
221C4×Q8—222no—
222C4×D4—222no—
223C4×D4—221no—
224C4×D4—221no—
225#117—441no—
226SD32—224no—
227D16—222no—
228C2×C16—112no—
229C2×C16C22×D1111yescharacteristic
230C2×C16C22×D1111yescharacteristic
231#107—21no—
232#107—111no—
233#107—111no—
234#107—222no—
235#107C22×D1112yes—
236C4⋊C8—112no—
237C4⋊C8—111no—
238#103—222no—
239#102—222no—
240#102—221no—
241#102—221no—
242C4×C8—112no—
243C4×C8C22×D1111yescharacteristic
244C2×C11#335811yescharacteristic
245C2×C11C2×#50911yescharacteristic
246C2×C11#341711yescharacteristic
247D11—82no—
248D11—161no—
249C2×Q8—22no—
250C2×Q8—41no—
251C2×Q8—111no—
252C2×Q8—442no—
253C2×Q8—884no—
254C2×D4—221no—
255C2×D4—221no—
256C22×C4—442no—
257C22×C4—441no—
258C22×C4—441no—
259Q16—22no—
260Q16—22no—
261Q16—81no—
262SD16—882no—
263D8—112no—
264D8—221no—
265D8—221no—
266D8—221no—
267C2×C8—112no—
268C2×C8D4×D1111yescharacteristic
269C2×C8C23×D1111yescharacteristic
270C4⋊C4—22no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—111no—
275C4⋊C4—112no—
276C4⋊C4—221no—
277C4⋊C4—221no—
278C4⋊C4—442no—
279C4⋊C4—442no—
280C22⋊C4—442no—
281C22⋊C4—442no—
282C22⋊C4—442no—
283C22⋊C4—441no—
284C22⋊C4—441no—
285C42—112no—
286C42—442no—
287C42D4×D1111yescharacteristic
288C16—21no—
289C16—21no—
290C16—222no—
291C11#3393411yescharacteristic, complemented, Sylow
292C23—441no—
293C23—441no—
294Q8—42no—
295Q8—42no—
296Q8—82no—
297Q8—222no—
298Q8—884no—
299D4—222no—
300D4—441no—
301D4—441no—
302D4—441no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—112no—
306C2×C4—112no—
307C2×C4—441no—
308C2×C4—441no—
309C2×C4—884no—
310C2×C4—882no—
311C2×C4—882no—
312C2×C4D8×D1111yescharacteristic
313C2×C4D8×D1111yescharacteristic
314C2×C4C2×D4×D1111yescharacteristic
315C8—21no—
316C8—222no—
317C8#41×D1111yescharacteristic
318C8#6704311yescharacteristic
319C22—442no—
320C22—881no—
321C22—881no—
322C22—881no—
323C22—881no—
324C22—881no—
325C22C2×D8×D1111yescharacteristic
326C4—21no—
327C4—82no—
328C4—82no—
329C4—222no—
330C4—222no—
331C4—881no—
332C4—881no—
333C4#1062252712yes—
334C4#1062320811yescharacteristic
335C4#1062329311yescharacteristic
336C2—882no—
337C2—1761no—
338C2#1308124811yescharacteristic
339C2C2×#1062252711yescharacteristic
340C2#1308176511yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2241C2
socleC22×C11C22×D8
prime radicalC2×D176C22
hypercenter#2241D11
hypocenterC11#33934
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2241

Complements

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

NH ≅ G/Ntype
1. #13081606C2semidirect
2. #13081468C2semidirect
3. #13070854C2semidirect
4. #13070766C2semidirect
5. #13070750C2semidirect
7. #13070658C2semidirect
8. #13070524C2semidirect
9. #13070483C2semidirect
11. C11×#2241C2semidirect
125. #2241D11semidirect
291. C11#33934semidirect

Maximal subgroups

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

subgroupindex
#130816062
#130814682
#130708542
#130707662
#130707502
#130706742
#130706582
#130705242
#130704832
C4×D1762
C11×#22412
#3393411