Finite Group Databasebeta

← #14911574

Subgroups — #14911574

Order 2816.

520 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081626C211yesmaximal, characteristic, complemented
2#13081468C211yesmaximal, characteristic, complemented
3#13070854C212yesmaximal, complemented
4#13070841C211yesmaximal, characteristic, complemented
5#13070762C212yesmaximal, complemented
6#13070674C212yesmaximal, complemented
7#13070652C211yesmaximal, characteristic
8#13070521C211yesmaximal, characteristic, complemented
9#13070491C212yesmaximal, complemented
10C4×#66892C211yesmaximal, characteristic, complemented
11C11×#2225C211yesmaximal, characteristic, complemented
12#10623258—21no—
13#10623116—21no—
14C11×#500C2211yescharacteristic
15C4×C11×Q16C2211yescharacteristic
16#10622804C2212yes—
17C2×#66892C2211yescharacteristic
18#10622700—21no—
19#10622640—21no—
20C2×D176C2212yes—
21#10622503—22no—
22#10622487C2212yes—
23#10622485C2212yes—
24#10622485C2212yes—
25#10622432—22no—
26#10622308C2211yescharacteristic
27C4×D88C2211yescharacteristic
28C8×Dic22C2211yescharacteristic
29C11×#367C2212yes—
30C11×C4⋊C16C2211yescharacteristic
31C11×#358C2212yes—
32#10622202C2211yescharacteristic
33#10622147C2212yes—
34#10622140C2212yes—
35Dic11⋊C16C2212yes—
36#10622129C2212yes—
37#10622129C2212yes—
38#10622129C2211yescharacteristic
39#10622128C2211yescharacteristic
40C4×C11⋊C16C2211yescharacteristic
41C2×Q8×D11—41no—
42C2×C11×Q16C2311yescharacteristic
43C11×C4⋊Q8—21no—
44C4×Q8×C11—21no—
45#67000—22no—
46#66999—41no—
47C2×#4325—22no—
48C2×D88—21no—
49C2×D88C2312yes—
50C2×D88C2311yescharacteristic
51#66949—42no—
52#66947—42no—
53#66946—22no—
54#66946—22no—
55#66941—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#66871—22no—
77C4⋊(C11⋊C8)D411yescharacteristic
78D176—24no—
79#33940—111nomaximal, Sylow
80C2×Q8×C11—21no—
81C2×Q8×C11—41no—
82Q8×D11—84no—
83C2×D44—21no—
84C2×D44—22no—
85C2×D44—41no—
86C2×D44—41no—
87C2×C4×D11—42no—
88C2×C4×D11—42no—
89C2×C4×D11—41no—
90C2×Dic22—42no—
91C2×Dic22D811yescharacteristic
92C11×Q16—21no—
93C11×Q16—21no—
94C2×C8×C11C2×D411yescharacteristic
95C2×C8×C11C2411yescharacteristic
96C11×C4⋊C4—22no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C42×C11—41no—
101C42×C11C2×D411yescharacteristic
102#4325—82no—
103(C2×D11)⋊C4—42no—
104(C2×D11)⋊C4—42no—
105(C2×D11)⋊C4—42no—
106(C2×D11)⋊C4—42no—
107(C2×D11)⋊C4—41no—
108C4⋊Dic11—21no—
109C4⋊Dic11D811yescharacteristic
110Dic11⋊C4—42no—
111Dic11⋊C4D812yes—
112C4×Dic11C2×D412yes—
113C2×C11⋊C8C2×D412yes—
114D88—22no—
115D88—21no—
116D88—22no—
117D88—81no—
118D88#4112yes—
119C11×C16—22no—
120C11⋊C16—21no—
121C11⋊C16—21no—
122#3396—111no—
123Q8×D8—111no—
124#2243—112no—
125#2240—111no—
126#2226—112no—
127#2225D1111yescharacteristic, complemented
128#2210—112no—
129#2206—111no—
130#2183—111no—
131#2177—112no—
132C4×SD32—111no—
133C22×D11—41no—
134C22×D11—42no—
135Q8×C11—41no—
136Q8×C11—41no—
137Q8×C11—82no—
138C2×C4×C11—42no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11C2×D811yescharacteristic
142C2×C4×C11C2×D811yescharacteristic
143C2×C4×C11C22×D411yescharacteristic
144C2×Dic11—41no—
145C2×Dic11C2×D812yes—
146C2×Dic11C2×D812yes—
147D44—22no—
148D44—42no—
149D44—41no—
150D44—42no—
151D44—82no—
152D44—161no—
153C4×D11—84no—
154C4×D11—82no—
155C4×D11—162no—
156Dic22—22no—
157Dic22—84no—
158C8×C11—21no—
159C8×C11C2×#4111yescharacteristic
160C8×C112−1+411yescharacteristic
161C11⋊C8—22no—
162#559—221no—
163D4×Q8—221no—
164C2×SD32—111no—
165C2×D16—112no—
166#500—112no—
167#500C2×D1111yescharacteristic
168#495—112no—
169#493—111no—
170#474—222no—
171#474—221no—
172#463—222no—
173#460—221no—
174C8×Q8—111no—
175C4×Q16C2×D1111yescharacteristic
176C4×D8—112no—
177C4×D8—112no—
178C4×D8—111no—
179#367—111no—
180#367C2×D1112yes—
181C4⋊C16—112no—
182C4⋊C16C2×D1111yescharacteristic
183#358—111no—
184#358C2×D1112yes—
185#357—112no—
186#357—111no—
187#357—112no—
188#357—112no—
189#346—112no—
190C4×C16—111no—
191C22×C11C22×D811yescharacteristic
192C2×D11—42no—
193C2×D11—81no—
194C2×D11—81no—
195C2×D11—82no—
196C2×D11—82no—
197C2×D11—82no—
198C4×C11—21no—
199C4×C11—81no—
200C4×C11—82no—
201C4×C11—81no—
202C4×C11#50912yes—
203C4×C11#54811yescharacteristic
204C4×C11#57711yescharacteristic
205Dic11—22no—
206Dic11—22no—
207Dic11—81no—
208C22×Q8—441no—
209C2×Q16C22×D1111yescharacteristic
210C2×SD16—222no—
211C2×D8—111no—
212C2×D8—112no—
213C2×D8—221no—
214C4⋊Q8—21no—
215C4⋊Q8—222no—
216#127—221no—
217#124—222no—
218#124—441no—
219#123—442no—
220C22⋊Q8—442no—
221C22⋊Q8—441no—
222C4×Q8—21no—
223C4×Q8—111no—
224C4×D4—222no—
225C4×D4—222no—
226C4×D4—221no—
227C4×D4—441no—
228SD32—222no—
229D16—224no—
230C2×C16—111no—
231C2×C16—111no—
232C2×C16C22×D1112yes—
233#107—21no—
234#107—111no—
235#107—222no—
236#107C22×D1112yes—
237#107C22×D1111yescharacteristic
238C4⋊C8—112no—
239C4⋊C8—111no—
240#103—21no—
241#102—222no—
242#102—222no—
243#102—221no—
244C4×C8—112no—
245C4×C8C22×D1111yescharacteristic
246C2×C11#335811yescharacteristic
247C2×C11C2×#50911yescharacteristic
248C2×C11#341611yescharacteristic
249D11—82no—
250D11—162no—
251C2×Q8—21no—
252C2×Q8—41no—
253C2×Q8—111no—
254C2×Q8—442no—
255C2×Q8—884no—
256C2×D4—221no—
257C2×D4—222no—
258C2×D4—441no—
259C2×D4—441no—
260C22×C4—442no—
261C22×C4—442no—
262C22×C4—441no—
263Q16—21no—
264Q16—21no—
265SD16—882no—
266D8—112no—
267D8—221no—
268D8—222no—
269D8—222no—
270D8—881no—
271C2×C8—112no—
272C2×C8D4×D1111yescharacteristic
273C2×C8C23×D1111yescharacteristic
274C4⋊C4—21no—
275C4⋊C4—22no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—111no—
279C4⋊C4—112no—
280C4⋊C4—221no—
281C4⋊C4—442no—
282C22⋊C4—442no—
283C22⋊C4—442no—
284C22⋊C4—442no—
285C22⋊C4—442no—
286C22⋊C4—441no—
287C42—41no—
288C42—112no—
289C42D4×D1111yescharacteristic
290C16—22no—
291C16—221no—
292C16—221no—
293C11#3394011yescharacteristic, complemented, Sylow
294C23—441no—
295C23—442no—
296Q8—41no—
297Q8—41no—
298Q8—82no—
299Q8—222no—
300Q8—884no—
301D4—222no—
302D4—441no—
303D4—442no—
304D4—442no—
305D4—882no—
306D4—1761no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—42no—
310C2×C4—112no—
311C2×C4—112no—
312C2×C4—441no—
313C2×C4—884no—
314C2×C4—882no—
315C2×C4—1762no—
316C2×C4D8×D1111yescharacteristic
317C2×C4D8×D1111yescharacteristic
318C2×C4C2×D4×D1111yescharacteristic
319C8—21no—
320C8—222no—
321C8#6704011yescharacteristic
322C8#41×D1111yescharacteristic
323C22—442no—
324C22—881no—
325C22—881no—
326C22—882no—
327C22—882no—
328C22—882no—
329C22C2×D8×D1111yescharacteristic
330C4—21no—
331C4—82no—
332C4—81no—
333C4—81no—
334C4—222no—
335C4—222no—
336C4—881no—
337C4#1062252712yes—
338C4#1062316411yescharacteristic
339C4#1062330911yescharacteristic
340C2—882no—
341C2—1762no—
342C2#1308125011yescharacteristic
343C2C2×#1062252711yescharacteristic
344C2#1308176111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2225C2
socleC22×C11C22×D8
prime radical#13070652C2
hypercenter#2225D11
hypocenterC11#33940
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2225

Complements

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

NH ≅ G/Ntype
1. #13081626C2semidirect
2. #13081468C2semidirect
3. #13070854C2semidirect
4. #13070841C2semidirect
5. #13070762C2semidirect
6. #13070674C2semidirect
8. #13070521C2semidirect
9. #13070491C2semidirect
10. C4×#66892C2semidirect
11. C11×#2225C2semidirect
127. #2225D11semidirect
293. C11#33940semidirect

Maximal subgroups

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

subgroupindex
#130816262
#130814682
#130708542
#130708412
#130707622
#130706742
#130706522
#130705212
#130704912
C4×#668922
C11×#22252
#3394011