Finite Group Databasebeta

← #14911204

Subgroups — #14911204

Order 2816.

492 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081040C211yesmaximal, characteristic, complemented
2#13081038C211yesmaximal, characteristic, complemented
3#13070889C211yesmaximal, characteristic, complemented
4#13070809C212yesmaximal, complemented
5#13070806C212yesmaximal, complemented
6#13070764C211yesmaximal, characteristic, complemented
7#13070701C212yesmaximal, complemented
8C4×#66890C211yesmaximal, characteristic, complemented
9#13070435C211yesmaximal, characteristic, complemented
10#13070399C212yesmaximal, complemented
11C11×#2226C211yesmaximal, characteristic, complemented
12#10623265—21no—
13#10623094—21no—
14C11×#500C2211yescharacteristic
15C4×C11×D8C2211yescharacteristic
16#10622770C2212yes—
17C2×#66890C2211yescharacteristic
18#10622697—21no—
19#10622621—21no—
20C2×C16×D11C2212yes—
21#10622498—22no—
22#10622496C2212yes—
23#10622493C2212yes—
24#10622493C2212yes—
25#10622397—22no—
26C4×D88C2211yescharacteristic
27C8×D44C2211yescharacteristic
28#10622295C2211yescharacteristic
29C11×#367C2212yes—
30C11×C4⋊C16C2211yescharacteristic
31C11×#357C2212yes—
32#10622200C2211yescharacteristic
33#10622147C2212yes—
34(C2×D11)⋊C16C2212yes—
35#10622143C2212yes—
36#10622129C2211yescharacteristic
37#10622127C2212yes—
38#10622127C2212yes—
39#10622127C2211yescharacteristic
40C4×C11⋊C16C2211yescharacteristic
41C2×C11×D8C2311yescharacteristic
42C11×C4⋊Q8—21no—
43C4×D4×C11—21no—
44#67000—42no—
45#66991—22no—
46#66983—41no—
47#66979—41no—
48C2×D88C2311yescharacteristic
49C2×C8×D11C2312yes—
50#66948—22no—
51#66948—41no—
52#66945—22no—
53#66945—22no—
54#66945—41no—
55#66938—42no—
56C4×D44—21no—
57C4×D44D411yescharacteristic
58#66922—21no—
59C2×C11×C16C2312yes—
60C11×#107—21no—
61C11×#107C2312yes—
62C11×#107C2311yescharacteristic
63C11×#102—21no—
64C4×C8×C11C2311yescharacteristic
65#66896—22no—
66#66890—22no—
67#66885—21no—
68(C2×D11)⋊C8D412yes—
69#66882—21no—
70#66882C2311yescharacteristic
71#66882C2312yes—
72C2×C11⋊C16C2311yescharacteristic
73C2×C11⋊C16C2311yescharacteristic
74#66873—22no—
75#66872—22no—
76#66872—22no—
77C4⋊(C11⋊C8)D411yescharacteristic
78C16×D11—24no—
79#33908—111nomaximal, Sylow
80C2×Q8×C11—41no—
81C2×D4×C11—21no—
82C22×C4×C11—41no—
83C2×C22⋊D11—42no—
84C2×D44—21no—
85C2×D44—42no—
86C2×D44D811yescharacteristic
87C2×C4×D11—41no—
88C2×C4×D11C2×D412yes—
89C2×Dic22—41no—
90C11×D8—21no—
91C11×D8—21no—
92C2×C8×C11C2×D411yescharacteristic
93C2×C8×C11C2411yescharacteristic
94C11×C4⋊C4—21no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—41no—
97C11×C22⋊C4—41no—
98C42×C11C2×D411yescharacteristic
99C22⋊Dic11—42no—
100(C2×D11)⋊C4—42no—
101(C2×D11)⋊C4—42no—
102(C2×D11)⋊C4—42no—
103(C2×D11)⋊C4—41no—
104(C2×D11)⋊C4D812yes—
105C4⋊Dic11—21no—
106C4⋊Dic11—22no—
107C4⋊Dic11—41no—
108C4⋊Dic11D811yescharacteristic
109C4×Dic11—42no—
110C4×Dic11—42no—
111C2×C11⋊C8C2×D412yes—
112D88—21no—
113D88—21no—
114C8×D11—22no—
115C8×D11—22no—
116C11×C16—22no—
117C11⋊C16—21no—
118C11⋊C16#4112yes—
119#3341—111no—
120#3341—111no—
121#2252—111no—
122#2234—112no—
123#2234—112no—
124#2226—111no—
125#2226D1111yescharacteristic, complemented
126#2215—112no—
127C4×D16—111no—
128D4×C16—111no—
129#2158—112no—
130C23×C11—41no—
131C22×D11—41no—
132C22×D11C2×D812yes—
133Q8×C11—161no—
134D4×C11—41no—
135D4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—42no—
138C2×C4×C11—82no—
139C2×C4×C11C2×D811yescharacteristic
140C2×C4×C11C2×D811yescharacteristic
141C2×C4×C11C22×D411yescharacteristic
142C22⋊D11—162no—
143C2×Dic11—41no—
144C2×Dic11—42no—
145C2×Dic11C2×D812yes—
146D44—22no—
147D44—41no—
148D44—41no—
149D44—162no—
150C4×D11—22no—
151C4×D11—22no—
152C4×D11—82no—
153Dic22—161no—
154C8×C11—21no—
155C8×C11C2×#4111yescharacteristic
156C8×C112−1+411yescharacteristic
157C11⋊C8—22no—
158#555—221no—
159#555—221no—
160C2×D16—111no—
161C22×C16—112no—
162#500—111no—
163#500C2×D1111yescharacteristic
164#482—222no—
165#482—222no—
166#476—221no—
167#476—221no—
168#466—112no—
169#466—112no—
170C4×D8—111no—
171C4×D8C2×D1111yescharacteristic
172C8×D4—111no—
173#427—112no—
174#427—112no—
175#367—112no—
176#367C2×D1112yes—
177#366—111no—
178#366—112no—
179#366—112no—
180C4⋊C16C2×D1111yescharacteristic
181#357—111no—
182#357—112no—
183#357—111no—
184#357C2×D1112yes—
185C22⋊C16—112no—
186C4×C16—111no—
187C22×C11—81no—
188C22×C11—81no—
189C22×C11—81no—
190C22×C11C22×D811yescharacteristic
191C2×D11—22no—
192C2×D11—22no—
193C2×D11—22no—
194C2×D11—81no—
195C2×D11—81no—
196C2×D11—81no—
197C4×C11—21no—
198C4×C11—81no—
199C4×C11—82no—
200C4×C11#50812yes—
201C4×C11#54711yescharacteristic
202C4×C11#57811yescharacteristic
203Dic11—22no—
204Dic11—81no—
205Dic11—82no—
206C2×D8—111no—
207C2×D8C22×D1111yescharacteristic
208C22×C8—112no—
209C4⋊Q8—21no—
210C4⋊Q8—221no—
211#124—442no—
212#124—442no—
213#121—222no—
214#121—222no—
215#121—441no—
216#121—441no—
217C4×D4—21no—
218C4×D4—111no—
219C4×D4—221no—
220#117—222no—
221#117—222no—
222#117—441no—
223#117—441no—
224D16—222no—
225C2×C16—111no—
226C2×C16—111no—
227C2×C16—224no—
228C2×C16C22×D1112yes—
229#107—21no—
230#107—112no—
231#107—111no—
232#107—221no—
233#107C22×D1111yescharacteristic
234#107C22×D1112yes—
235#106—222no—
236#106—222no—
237C4⋊C8—111no—
238#102—21no—
239#102—222no—
240#102—222no—
241#102—221no—
242C22⋊C8—112no—
243C4×C8C22×D1111yescharacteristic
244C2×C11—161no—
245C2×C11#333411yescharacteristic
246C2×C11C2×#50811yescharacteristic
247C2×C11#341511yescharacteristic
248D11—42no—
249D11—161no—
250C2×Q8—41no—
251C2×Q8—441no—
252C2×D4—21no—
253C2×D4—111no—
254C2×D4—221no—
255C2×D4—442no—
256C2×D4—442no—
257C22×C4—41no—
258C22×C4—112no—
259C22×C4—441no—
260D8—21no—
261D8—21no—
262D8—221no—
263D8—221no—
264C2×C8—112no—
265C2×C8—222no—
266C2×C8—222no—
267C2×C8D4×D1111yescharacteristic
268C2×C8C23×D1111yescharacteristic
269C4⋊C4—21no—
270C4⋊C4—22no—
271C4⋊C4—41no—
272C4⋊C4—111no—
273C4⋊C4—221no—
274C4⋊C4—222no—
275C4⋊C4—441no—
276C22⋊C4—41no—
277C22⋊C4—112no—
278C22⋊C4—442no—
279C22⋊C4—442no—
280C22⋊C4—442no—
281C22⋊C4—442no—
282C22⋊C4—441no—
283C42—442no—
284C42—442no—
285C42D4×D1111yescharacteristic
286C16—22no—
287C16—112no—
288C16—221no—
289C11#3390811yescharacteristic, complemented, Sylow
290C23—41no—
291C23—112no—
292C23—441no—
293Q8—161no—
294Q8—1761no—
295D4—41no—
296D4—41no—
297D4—222no—
298D4—441no—
299D4—441no—
300D4—1762no—
301D4—1762no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—82no—
305C2×C4—112no—
306C2×C4—222no—
307C2×C4—222no—
308C2×C4—441no—
309C2×C4—442no—
310C2×C4—882no—
311C2×C4D8×D1111yescharacteristic
312C2×C4D8×D1111yescharacteristic
313C2×C4C2×D4×D1111yescharacteristic
314C8—21no—
315C8—222no—
316C8#6704011yescharacteristic
317C8#41×D1111yescharacteristic
318C22—81no—
319C22—81no—
320C22—81no—
321C22—222no—
322C22—222no—
323C22—222no—
324C22—881no—
325C22—881no—
326C22—881no—
327C22C2×D8×D1111yescharacteristic
328C4—21no—
329C4—81no—
330C4—82no—
331C4—222no—
332C4—881no—
333C4—882no—
334C4#1062252912yes—
335C4#1062316211yescharacteristic
336C4#1062331011yescharacteristic
337C2—161no—
338C2—442no—
339C2—1761no—
340C2#1308096211yescharacteristic
341C2C2×#1062252911yescharacteristic
342C2#1308175611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2226C2
socleC22×C11C22×D8
hypercenter#2226D11
hypocenterC11#33908
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2226

Complements

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

NH ≅ G/Ntype
1. #13081040C2semidirect
2. #13081038C2semidirect
3. #13070889C2semidirect
4. #13070809C2semidirect
5. #13070806C2semidirect
6. #13070764C2semidirect
7. #13070701C2semidirect
8. C4×#66890C2semidirect
9. #13070435C2semidirect
10. #13070399C2semidirect
11. C11×#2226C2semidirect
125. #2226D11semidirect
289. C11#33908semidirect

Maximal subgroups

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

subgroupindex
#130810402
#130810382
#130708892
#130708092
#130708062
#130707642
#130707012
C4×#668902
#130704352
#130703992
C11×#22262
#3390811