Finite Group Databasebeta

← #14911442

Subgroups — #14911442

Order 2816.

498 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#13081626C211yesmaximal, characteristic, complemented
2#13081485C211yesmaximal, characteristic, complemented
3#13070849C212yesmaximal, complemented
4#13070841C211yesmaximal, characteristic, complemented
5#13070776C212yesmaximal, complemented
6#13070674C212yesmaximal, complemented
7#13070652C211yesmaximal, characteristic
8#13070518C211yesmaximal, characteristic, complemented
9C4×#66892C211yesmaximal, characteristic, complemented
10#13070462C212yesmaximal, complemented
11C11×#2227C211yesmaximal, characteristic, complemented
12#10623261—21no—
13#10623116—21no—
14C11×#500C2211yescharacteristic
15C4×C11×Q16C2211yescharacteristic
16#10622804C2212yes—
17C2×#66892C2211yescharacteristic
18#10622697—21no—
19#10622640—21no—
20C2×D176C2212yes—
21#10622504—22no—
22#10622491C2212yes—
23#10622485C2212yes—
24#10622485C2212yes—
25#10622432—22no—
26#10622308C2211yescharacteristic
27C4×D88C2211yescharacteristic
28C8×Dic22C2211yescharacteristic
29C11×#366C2212yes—
30C11×C4⋊C16C2211yescharacteristic
31C11×#358C2212yes—
32#10622202C2211yescharacteristic
33#10622147C2212yes—
34Dic11⋊C16C2212yes—
35C16×Dic11C2212yes—
36#10622129C2212yes—
37#10622129C2212yes—
38#10622129C2211yescharacteristic
39#10622128C2211yescharacteristic
40C4×C11⋊C16C2211yescharacteristic
41C2×C11×Q16C2311yescharacteristic
42C11×C4⋊Q8—21no—
43C4×Q8×C11—21no—
44#67000—22no—
45#66999—42no—
46C2×#4325—22no—
47C2×D88—21no—
48C2×D88C2312yes—
49C2×D88C2311yescharacteristic
50#66950—41no—
51#66947—42no—
52#66946—22no—
53#66946—22no—
54C4⋊C4×D11—41no—
55#66943—22no—
56#66928—41no—
57#66927—21no—
58C4×D44—21no—
59C4×D44—41no—
60C4×Dic22D411yescharacteristic
61C2×C11×C16C2312yes—
62C11×#107—21no—
63C11×#107C2312yes—
64C11×#107C2311yescharacteristic
65C11×#103—21no—
66C4×C8×C11C2311yescharacteristic
67#66892—22no—
68#66885—21no—
69#66882C2311yescharacteristic
70Dic11⋊C8D412yes—
71C8×Dic11C2312yes—
72C2×C11⋊C16C2311yescharacteristic
73C2×C11⋊C16C2311yescharacteristic
74#66873—22no—
75#66873—22no—
76#66872—22no—
77C4⋊(C11⋊C8)D411yescharacteristic
78D176—24no—
79#33928—111nomaximal, Sylow
80C2×Q8×C11—21no—
81C2×Q8×C11—41no—
82C2×D44—21no—
83C2×D44—22no—
84C2×D44—41no—
85C2×D44—41no—
86C2×C4×D11—42no—
87C2×C4×D11—42no—
88C2×C4×D11—41no—
89C2×Dic22D811yescharacteristic
90C11×Q16—21no—
91C11×Q16—21no—
92C2×C8×C11C2×D411yescharacteristic
93C2×C8×C11C2411yescharacteristic
94C11×C4⋊C4—22no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C42×C11—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—42no—
105(C2×D11)⋊C4—41no—
106C4⋊Dic11—21no—
107C4⋊Dic11—42no—
108C4⋊Dic11D811yescharacteristic
109Dic11⋊C4—42no—
110Dic11⋊C4D812yes—
111C4×Dic11C2×D412yes—
112C2×C11⋊C8C2×D412yes—
113D88—22no—
114D88—21no—
115D88—22no—
116D88—81no—
117D88#4112yes—
118C11×C16—22no—
119C11⋊C16—21no—
120C11⋊C16—21no—
121#3396—111no—
122#3380—111no—
123#2242—112no—
124#2240—111no—
125#2228—112no—
126#2227D1111yescharacteristic, complemented
127#2210—112no—
128#2206—111no—
129Q8×C16—111no—
130C4×SD32—111no—
131C4×D16—112no—
132C22×D11—41no—
133C22×D11—42no—
134Q8×C11—41no—
135Q8×C11—41no—
136Q8×C11—161no—
137C2×C4×C11—42no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11C2×D811yescharacteristic
141C2×C4×C11C2×D811yescharacteristic
142C2×C4×C11C22×D411yescharacteristic
143C2×Dic11—41no—
144C2×Dic11C2×D812yes—
145C2×Dic11C2×D812yes—
146D44—22no—
147D44—42no—
148D44—41no—
149D44—42no—
150D44—82no—
151D44—161no—
152C4×D11—82no—
153C4×D11—162no—
154C4×D11—162no—
155Dic22—22no—
156C8×C11—21no—
157C8×C11C2×#4111yescharacteristic
158C8×C112−1+411yescharacteristic
159C11⋊C8—22no—
160#559—221no—
161#554—221no—
162C2×SD32—111no—
163C2×D16—112no—
164#500C2×D1111yescharacteristic
165#499—112no—
166#495—112no—
167#493—111no—
168#478—222no—
169#476—221no—
170#463—222no—
171#460—221no—
172C8×Q8—111no—
173C4×Q16C2×D1111yescharacteristic
174C4×D8—112no—
175C4×D8—112no—
176C4×D8—111no—
177#367—111no—
178#366C2×D1112yes—
179C4⋊C16—112no—
180C4⋊C16C2×D1111yescharacteristic
181#358—111no—
182#358C2×D1112yes—
183#357—112no—
184#357—111no—
185#357—112no—
186#357—112no—
187C4×C16—112no—
188C4×C16—111no—
189C22×C11C22×D811yescharacteristic
190C2×D11—42no—
191C2×D11—81no—
192C2×D11—81no—
193C2×D11—82no—
194C2×D11—82no—
195C2×D11—82no—
196C4×C11—21no—
197C4×C11—81no—
198C4×C11—82no—
199C4×C11—81no—
200C4×C11#50812yes—
201C4×C11#54811yescharacteristic
202C4×C11#57711yescharacteristic
203Dic11—22no—
204Dic11—22no—
205Dic11—81no—
206C2×Q16C22×D1111yescharacteristic
207C2×SD16—222no—
208C2×D8—111no—
209C2×D8—112no—
210C2×D8—221no—
211C4⋊Q8—21no—
212#127—221no—
213#125—222no—
214#124—222no—
215#124—441no—
216#123—442no—
217C22⋊Q8—441no—
218C22⋊Q8—442no—
219C4×Q8—21no—
220C4×Q8—111no—
221C4×D4—222no—
222C4×D4—222no—
223C4×D4—221no—
224C4×D4—441no—
225C2×C4⋊C4—441no—
226SD32—222no—
227D16—224no—
228C2×C16—111no—
229C2×C16—111no—
230C2×C16C22×D1112yes—
231#107—21no—
232#107—111no—
233#107C22×D1112yes—
234#107C22×D1111yescharacteristic
235#106—222no—
236C4⋊C8—112no—
237C4⋊C8—111no—
238#103—21no—
239#102—222no—
240#102—222no—
241#102—221no—
242C4×C8—112no—
243C4×C8C22×D1111yescharacteristic
244C2×C11#335811yescharacteristic
245C2×C11C2×#50811yescharacteristic
246C2×C11#341511yescharacteristic
247D11—82no—
248D11—162no—
249C2×Q8—21no—
250C2×Q8—41no—
251C2×Q8—111no—
252C2×D4—221no—
253C2×D4—222no—
254C2×D4—441no—
255C2×D4—441no—
256C22×C4—442no—
257C22×C4—442no—
258C22×C4—441no—
259Q16—21no—
260Q16—21no—
261SD16—882no—
262D8—112no—
263D8—221no—
264D8—222no—
265D8—222no—
266D8—881no—
267C2×C8—112no—
268C2×C8D4×D1111yescharacteristic
269C2×C8C23×D1111yescharacteristic
270C4⋊C4—21no—
271C4⋊C4—22no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—111no—
275C4⋊C4—112no—
276C4⋊C4—221no—
277C4⋊C4—442no—
278C4⋊C4—442no—
279C22⋊C4—442no—
280C22⋊C4—442no—
281C22⋊C4—442no—
282C22⋊C4—442no—
283C22⋊C4—441no—
284C42—41no—
285C42—112no—
286C42D4×D1111yescharacteristic
287C16—22no—
288C16—221no—
289C16—221no—
290C11#3392811yescharacteristic, complemented, Sylow
291C23—441no—
292C23—442no—
293Q8—41no—
294Q8—41no—
295Q8—161no—
296Q8—222no—
297D4—222no—
298D4—441no—
299D4—442no—
300D4—442no—
301D4—882no—
302D4—1761no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—112no—
307C2×C4—112no—
308C2×C4—441no—
309C2×C4—882no—
310C2×C4—1762no—
311C2×C4—1762no—
312C2×C4D8×D1111yescharacteristic
313C2×C4D8×D1111yescharacteristic
314C2×C4C2×D4×D1111yescharacteristic
315C8—21no—
316C8—222no—
317C8#6704011yescharacteristic
318C8#41×D1111yescharacteristic
319C22—442no—
320C22—881no—
321C22—881no—
322C22—882no—
323C22—882no—
324C22—882no—
325C22C2×D8×D1111yescharacteristic
326C4—21no—
327C4—81no—
328C4—82no—
329C4—81no—
330C4—222no—
331C4—222no—
332C4—881no—
333C4#1062253212yes—
334C4#1062316411yescharacteristic
335C4#1062330911yescharacteristic
336C2—882no—
337C2—1762no—
338C2#1308125011yescharacteristic
339C2C2×#1062253211yescharacteristic
340C2#1308175611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2227C2
socleC22×C11C22×D8
prime radical#13070652C2
hypercenter#2227D11
hypocenterC11#33928
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2227

Complements

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

NH ≅ G/Ntype
1. #13081626C2semidirect
2. #13081485C2semidirect
3. #13070849C2semidirect
4. #13070841C2semidirect
5. #13070776C2semidirect
6. #13070674C2semidirect
8. #13070518C2semidirect
9. C4×#66892C2semidirect
10. #13070462C2semidirect
11. C11×#2227C2semidirect
126. #2227D11semidirect
290. C11#33928semidirect

Maximal subgroups

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

subgroupindex
#130816262
#130814852
#130708492
#130708412
#130707762
#130706742
#130706522
#130705182
C4×#668922
#130704622
C11×#22272
#3392811