Finite Group Databasebeta

← #14911473

Subgroups — #14911473

Order 2816.

472 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081606C211yesmaximal, characteristic
2#13081509C211yesmaximal, characteristic, complemented
3#13070849C212yesmaximal
4#13070778C212yesmaximal, complemented
5#13070750C211yesmaximal, characteristic
6#13070681C212yesmaximal
7#13070663C211yesmaximal, characteristic, complemented
8C16×Dic22C211yesmaximal, characteristic, complemented
9#13070472C212yesmaximal, complemented
10C4×#66864C211yesmaximal, characteristic
11C11×#2241C211yesmaximal, characteristic, complemented
12#10623263—21no—
13#10623252—21no—
14C11×#500C2211yescharacteristic
15C11×#494C2211yescharacteristic
16#10622804C2212yes—
17#10622798—22no—
18Q16×Dic11C2212yes—
19C2×#66893C2212yes—
20#10622707—21no—
21#10622696—21no—
22C2×#66864C2211yescharacteristic
23#10622491C2212yes—
24#10622490—22no—
25#10622486C2212yes—
26C4×Dic44C2211yescharacteristic
27C4×D88C2211yescharacteristic
28C8×Dic22C2211yescharacteristic
29C11×#358C2212yes—
30C11×#358C2212yes—
31C4×C11×C16C2211yescharacteristic
32#10622202C2212yes—
33#10622147C2211yescharacteristic
34#10622143C2211yescharacteristic
35#10622141C2211yescharacteristic
36Dic11⋊C16C2212yes—
37C16×Dic11C2212yes—
38#10622129C2212yes—
39#10622127C2212yes—
40C4⋊(C11⋊C16)C2211yescharacteristic
41C2×C11×Q16—21no—
42C2×C11×Q16C2312yes—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8—21no—
45#67000—22no—
46Q8×Dic11—22no—
47Q8×Dic11—41no—
48#66997—41no—
49C2×#4325—22no—
50C2×Dic44C2311yescharacteristic
51C2×D88C2311yescharacteristic
52#66951—42no—
53#66950—41no—
54#66945—41no—
55#66943—22no—
56#66942—42no—
57#66940—22no—
58C4×D44—21no—
59C4×Dic22—21no—
60C4×Dic22D411yescharacteristic
61C2×C11×C16C2311yescharacteristic
62C2×C11×C16C2311yescharacteristic
63C11×#107—21no—
64C11×#107C2312yes—
65C4×C8×C11C2311yescharacteristic
66#66899—22no—
67#66893—24no—
68#66885—21no—
69#66882C2311yescharacteristic
70#66882C2311yescharacteristic
71#66880—21no—
72Dic11⋊C8D412yes—
73C8×Dic11C2312yes—
74C2×C11⋊C16C2312yes—
75#66874—22no—
76#66872—22no—
77C4⋊(C11⋊C8)D411yescharacteristic
78#66864—22no—
79#33931—111nomaximal, Sylow
80C2×Q8×C11—22no—
81C2×Q8×C11—41no—
82C2×D44—21no—
83C2×C4×D11—41no—
84C2×Dic22—21no—
85C2×Dic22D811yescharacteristic
86C11×Q16—22no—
87C11×Q16—22no—
88C11×Q16—81no—
89C2×C8×C11C2×D411yescharacteristic
90C2×C8×C11C2411yescharacteristic
91C11×C4⋊C4—22no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—41no—
95C42×C11C2×D411yescharacteristic
96#4325—82no—
97(C2×D11)⋊C4—42no—
98(C2×D11)⋊C4—42no—
99(C2×D11)⋊C4—41no—
100C4⋊Dic11—21no—
101C4⋊Dic11—21no—
102C4⋊Dic11—42no—
103C4⋊Dic11—42no—
104C4⋊Dic11D811yescharacteristic
105Dic11⋊C4—42no—
106Dic11⋊C4—42no—
107Dic11⋊C4—41no—
108Dic11⋊C4D812yes—
109C4×Dic11—42no—
110C4×Dic11—42no—
111C4×Dic11—41no—
112C4×Dic11C2×D412yes—
113C2×C11⋊C8C2×D412yes—
114Dic44—21no—
115Dic44#4112yes—
116D88—21no—
117D88—21no—
118C11×C16—21no—
119C11×C16—21no—
120C11⋊C16—22no—
121#3393—111no—
122#3383—111no—
123#2242—112no—
124#2241D1111yescharacteristic, complemented
125#2229—112no—
126#2224—111no—
127#2211—112no—
128#2209—111no—
129Q8×C16—111no—
130C4×Q32—112no—
131C4×SD32—111no—
132C22×D11—41no—
133Q8×C11—42no—
134Q8×C11—42no—
135Q8×C11—82no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11C2×D811yescharacteristic
139C2×C4×C11C2×D811yescharacteristic
140C2×C4×C11C22×D411yescharacteristic
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11C2×D812yes—
145C2×Dic11C2×D812yes—
146D44—41no—
147D44—41no—
148C4×D11—82no—
149Dic22—22no—
150Dic22—22no—
151Dic22—41no—
152C8×C11—21no—
153C8×C11C2×#4111yescharacteristic
154C8×C112−1+411yescharacteristic
155C11⋊C8—22no—
156#557—221no—
157#556—221no—
158C2×Q32—112no—
159C2×SD32—111no—
160#500C2×D1111yescharacteristic
161#499—112no—
162#495—112no—
163#494C2×D1111yescharacteristic
164#479—222no—
165#475—221no—
166#464—222no—
167#461—221no—
168C8×Q8—111no—
169C4×Q16—112no—
170C4×Q16—112no—
171C4×Q16—111no—
172C4×D8—111no—
173#367—111no—
174#366—112no—
175C4⋊C16—112no—
176C4⋊C16—111no—
177#358—112no—
178#358—111no—
179#358C2×D1112yes—
180#358C2×D1112yes—
181#357—111no—
182#357—112no—
183C4×C16—112no—
184C4×C16C2×D1111yescharacteristic
185C22×C11C22×D811yescharacteristic
186C2×D11—81no—
187C2×D11—81no—
188C2×D11—81no—
189C4×C11—21no—
190C4×C11—82no—
191C4×C11—82no—
192C4×C11#50812yes—
193C4×C11#54811yescharacteristic
194C4×C11#57711yescharacteristic
195Dic11—22no—
196Dic11—22no—
197Dic11—42no—
198Dic11—81no—
199Dic11—81no—
200C2×Q16—21no—
201C2×Q16—111no—
202C2×Q16C22×D1112yes—
203C2×SD16—222no—
204C2×D8—111no—
205C4⋊Q8—21no—
206C4⋊Q8—21no—
207C4⋊Q8—441no—
208#126—442no—
209#125—222no—
210#125—442no—
211#124—222no—
212C22⋊Q8—441no—
213C4×Q8—111no—
214C4×Q8—222no—
215C4×Q8—222no—
216C4×Q8—221no—
217C4×Q8—441no—
218C4×D4—221no—
219#117—441no—
220Q32—224no—
221SD32—222no—
222C2×C16—112no—
223C2×C16C22×D1111yescharacteristic
224C2×C16C22×D1111yescharacteristic
225#107—21no—
226#107—111no—
227#107—111no—
228#107C22×D1112yes—
229#106—222no—
230C4⋊C8—112no—
231C4⋊C8—111no—
232#103—222no—
233#103—222no—
234#103—221no—
235#102—221no—
236C4×C8—112no—
237C4×C8C22×D1111yescharacteristic
238C2×C11#335811yescharacteristic
239C2×C11C2×#50811yescharacteristic
240C2×C11#341711yescharacteristic
241D11—161no—
242C2×Q8—22no—
243C2×Q8—41no—
244C2×Q8—111no—
245C2×Q8—221no—
246C2×D4—221no—
247C22×C4—441no—
248Q16—22no—
249Q16—22no—
250Q16—81no—
251Q16—112no—
252Q16—221no—
253SD16—882no—
254D8—221no—
255D8—221no—
256C2×C8—112no—
257C2×C8D4×D1111yescharacteristic
258C2×C8C23×D1111yescharacteristic
259C4⋊C4—22no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—111no—
264C4⋊C4—112no—
265C4⋊C4—221no—
266C4⋊C4—221no—
267C4⋊C4—442no—
268C4⋊C4—442no—
269C4⋊C4—442no—
270C4⋊C4—442no—
271C4⋊C4—441no—
272C22⋊C4—442no—
273C22⋊C4—442no—
274C22⋊C4—441no—
275C42—112no—
276C42—442no—
277C42—442no—
278C42—441no—
279C42D4×D1111yescharacteristic
280C16—21no—
281C16—21no—
282C16—222no—
283C11#3393111yescharacteristic, complemented, Sylow
284C23—441no—
285Q8—42no—
286Q8—42no—
287Q8—82no—
288Q8—222no—
289Q8—222no—
290Q8—441no—
291D4—441no—
292D4—441no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—112no—
296C2×C4—112no—
297C2×C4—441no—
298C2×C4—441no—
299C2×C4—441no—
300C2×C4—882no—
301C2×C4D8×D1111yescharacteristic
302C2×C4D8×D1111yescharacteristic
303C2×C4C2×D4×D1111yescharacteristic
304C8—21no—
305C8—222no—
306C8#41×D1111yescharacteristic
307C8#6704311yescharacteristic
308C22—881no—
309C22—881no—
310C22—881no—
311C22C2×D8×D1111yescharacteristic
312C4—21no—
313C4—82no—
314C4—82no—
315C4—222no—
316C4—222no—
317C4—442no—
318C4—881no—
319C4—881no—
320C4#1062252912yes—
321C4#1062320811yescharacteristic
322C4#1062329311yescharacteristic
323C2—1761no—
324C2#1308124811yescharacteristic
325C2C2×#1062252911yescharacteristic
326C2#1308176511yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2241C2
socleC22×C11C22×D8
prime radicalC2×D88C23
hypercenter#2241D11
hypocenterC11#33931
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
2. #13081509C2semidirect
4. #13070778C2semidirect
7. #13070663C2semidirect
8. C16×Dic22C2semidirect
9. #13070472C2semidirect
11. C11×#2241C2semidirect
124. #2241D11semidirect
283. C11#33931semidirect

Maximal subgroups

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

subgroupindex
#130816062
#130815092
#130708492
#130707782
#130707502
#130706812
#130706632
C16×Dic222
#130704722
C4×#668642
C11×#22412
#3393111