Finite Group Databasebeta

← #14911437

Subgroups — #14911437

Order 2816.

486 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081606C211yesmaximal, characteristic, complemented
2#13081485C211yesmaximal, characteristic, complemented
3#13070849C212yesmaximal, complemented
4#13070782C212yesmaximal, complemented
5#13070760C211yesmaximal, characteristic, complemented
6#13070674C212yesmaximal
7#13070658C211yesmaximal, characteristic, complemented
8C16×Dic22C211yesmaximal, characteristic, complemented
9#13070465C212yesmaximal, complemented
10C4×D176C211yesmaximal, characteristic
11C11×#2241C211yesmaximal, characteristic, complemented
12#10623263—21no—
13#10623261—21no—
14C11×#500C2211yescharacteristic
15C11×#494C2211yescharacteristic
16#10622804C2212yes—
17#10622798—22no—
18Q16×Dic11C2212yes—
19C2×#66892C2212yes—
20#10622697—21no—
21#10622696—21no—
22C2×D176C2211yescharacteristic
23#10622504—22no—
24#10622491C2212yes—
25#10622485C2212yes—
26C4×D88C2211yescharacteristic
27C4×D88C2211yescharacteristic
28C8×Dic22C2211yescharacteristic
29C11×#358C2212yes—
30C11×#358C2212yes—
31C4×C11×C16C2211yescharacteristic
32#10622202C2212yes—
33#10622147C2211yescharacteristic
34#10622147C2211yescharacteristic
35#10622142C2211yescharacteristic
36Dic11⋊C16C2212yes—
37C16×Dic11C2212yes—
38#10622129C2212yes—
39#10622128C2212yes—
40C4⋊(C11⋊C16)C2211yescharacteristic
41C2×C11×Q16—21no—
42C2×C11×Q16C2312yes—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8—21no—
45#67000—22no—
46#66999—42no—
47Q8×Dic11—22no—
48C2×#4325—22no—
49C2×D88C2311yescharacteristic
50C2×D88C2311yescharacteristic
51#66951—42no—
52#66950—41no—
53#66950—41no—
54#66946—22no—
55#66945—41no—
56C4⋊C4×D11—41no—
57#66943—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#66872—22no—
77C4⋊(C11⋊C8)D411yescharacteristic
78D176—22no—
79#33927—111nomaximal, Sylow
80C2×Q8×C11—22no—
81C2×Q8×C11—41no—
82C2×D44—21no—
83C2×D44—21no—
84C2×C4×D11—42no—
85C2×C4×D11—41no—
86C2×C4×D11—41no—
87C2×Dic22D811yescharacteristic
88C11×Q16—22no—
89C11×Q16—22no—
90C11×Q16—81no—
91C2×C8×C11C2×D411yescharacteristic
92C2×C8×C11C2411yescharacteristic
93C11×C4⋊C4—22no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—41no—
97C42×C11C2×D411yescharacteristic
98#4325—82no—
99(C2×D11)⋊C4—42no—
100(C2×D11)⋊C4—42no—
101(C2×D11)⋊C4—42no—
102(C2×D11)⋊C4—41no—
103(C2×D11)⋊C4—41no—
104C4⋊Dic11—21no—
105C4⋊Dic11—21no—
106C4⋊Dic11—42no—
107C4⋊Dic11—42no—
108C4⋊Dic11D811yescharacteristic
109Dic11⋊C4—42no—
110Dic11⋊C4D812yes—
111C4×Dic11—42no—
112C4×Dic11C2×D412yes—
113C2×C11⋊C8C2×D412yes—
114D88—21no—
115D88—21no—
116D88—21no—
117D88#4112yes—
118C11×C16—21no—
119C11×C16—21no—
120C11⋊C16—22no—
121#3393—111no—
122#3380—111no—
123#2242—112no—
124#2241D1111yescharacteristic, complemented
125#2229—112no—
126#2226—111no—
127#2210—112no—
128#2208—111no—
129Q8×C16—111no—
130C4×SD32—112no—
131C4×D16—111no—
132C22×D11—41no—
133C22×D11—41no—
134Q8×C11—42no—
135Q8×C11—42no—
136Q8×C11—161no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11C2×D811yescharacteristic
140C2×C4×C11C2×D811yescharacteristic
141C2×C4×C11C22×D411yescharacteristic
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11C2×D812yes—
145C2×Dic11C2×D812yes—
146D44—22no—
147D44—41no—
148D44—41no—
149D44—41no—
150C4×D11—82no—
151C4×D11—82no—
152C4×D11—162no—
153Dic22—22no—
154C8×C11—21no—
155C8×C11C2×#4111yescharacteristic
156C8×C112−1+411yescharacteristic
157C11⋊C8—22no—
158#556—221no—
159#554—221no—
160C2×SD32—112no—
161C2×D16—111no—
162#500C2×D1111yescharacteristic
163#499—112no—
164#495—112no—
165#494C2×D1111yescharacteristic
166#478—222no—
167#476—221no—
168#464—222no—
169#461—221no—
170C8×Q8—111no—
171C4×Q16—112no—
172C4×D8—112no—
173C4×D8—111no—
174C4×D8—111no—
175#367—112no—
176#366—111no—
177C4⋊C16—112no—
178C4⋊C16—111no—
179#358—112no—
180#358C2×D1112yes—
181#358C2×D1112yes—
182#357—111no—
183#357—111no—
184#357—112no—
185C4×C16—112no—
186C4×C16C2×D1111yescharacteristic
187C22×C11C22×D811yescharacteristic
188C2×D11—42no—
189C2×D11—81no—
190C2×D11—81no—
191C2×D11—81no—
192C2×D11—81no—
193C2×D11—81no—
194C4×C11—21no—
195C4×C11—82no—
196C4×C11—82no—
197C4×C11#50812yes—
198C4×C11#54811yescharacteristic
199C4×C11#57711yescharacteristic
200Dic11—22no—
201Dic11—22no—
202Dic11—81no—
203Dic11—81no—
204C2×Q16—21no—
205C2×Q16C22×D1112yes—
206C2×SD16—222no—
207C2×D8—111no—
208C2×D8—111no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211#126—442no—
212#125—222no—
213#124—222no—
214C22⋊Q8—441no—
215C22⋊Q8—441no—
216C22⋊Q8—442no—
217C4×Q8—111no—
218C4×Q8—222no—
219C4×D4—222no—
220C4×D4—221no—
221C4×D4—221no—
222#117—441no—
223C2×C4⋊C4—441no—
224SD32—224no—
225D16—222no—
226C2×C16—112no—
227C2×C16C22×D1111yescharacteristic
228C2×C16C22×D1111yescharacteristic
229#107—21no—
230#107—111no—
231#107—111no—
232#107C22×D1112yes—
233#106—222no—
234C4⋊C8—112no—
235C4⋊C8—111no—
236#103—222no—
237#102—222no—
238#102—221no—
239#102—221no—
240C4×C8—112no—
241C4×C8C22×D1111yescharacteristic
242C2×C11#335811yescharacteristic
243C2×C11C2×#50811yescharacteristic
244C2×C11#341611yescharacteristic
245D11—82no—
246D11—161no—
247C2×Q8—22no—
248C2×Q8—41no—
249C2×Q8—111no—
250C2×D4—221no—
251C2×D4—221no—
252C22×C4—442no—
253C22×C4—441no—
254C22×C4—441no—
255Q16—22no—
256Q16—22no—
257Q16—81no—
258SD16—882no—
259D8—112no—
260D8—221no—
261D8—221no—
262D8—221no—
263C2×C8—112no—
264C2×C8D4×D1111yescharacteristic
265C2×C8C23×D1111yescharacteristic
266C4⋊C4—22no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—111no—
271C4⋊C4—112no—
272C4⋊C4—221no—
273C4⋊C4—221no—
274C4⋊C4—442no—
275C4⋊C4—442no—
276C4⋊C4—442no—
277C22⋊C4—442no—
278C22⋊C4—442no—
279C22⋊C4—442no—
280C22⋊C4—441no—
281C22⋊C4—441no—
282C42—112no—
283C42—442no—
284C42D4×D1111yescharacteristic
285C16—21no—
286C16—21no—
287C16—222no—
288C11#3392711yescharacteristic, complemented, Sylow
289C23—441no—
290C23—441no—
291Q8—42no—
292Q8—42no—
293Q8—161no—
294Q8—222no—
295D4—222no—
296D4—441no—
297D4—441no—
298D4—441no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—112no—
302C2×C4—112no—
303C2×C4—441no—
304C2×C4—441no—
305C2×C4—882no—
306C2×C4—882no—
307C2×C4—1762no—
308C2×C4D8×D1111yescharacteristic
309C2×C4D8×D1111yescharacteristic
310C2×C4C2×D4×D1111yescharacteristic
311C8—21no—
312C8—222no—
313C8#41×D1111yescharacteristic
314C8#6704311yescharacteristic
315C22—442no—
316C22—881no—
317C22—881no—
318C22—881no—
319C22—881no—
320C22—881no—
321C22C2×D8×D1111yescharacteristic
322C4—21no—
323C4—82no—
324C4—82no—
325C4—222no—
326C4—222no—
327C4—881no—
328C4—881no—
329C4#1062253212yes—
330C4#1062320811yescharacteristic
331C4#1062329311yescharacteristic
332C2—882no—
333C2—1761no—
334C2#1308124811yescharacteristic
335C2C2×#1062253211yescharacteristic
336C2#1308175811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2241C2
socleC22×C11C22×D8
prime radicalC2×D176C22
hypercenter#2241D11
hypocenterC11#33927
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. #13081485C2semidirect
3. #13070849C2semidirect
4. #13070782C2semidirect
5. #13070760C2semidirect
7. #13070658C2semidirect
8. C16×Dic22C2semidirect
9. #13070465C2semidirect
11. C11×#2241C2semidirect
124. #2241D11semidirect
288. C11#33927semidirect

Maximal subgroups

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

subgroupindex
#130816062
#130814852
#130708492
#130707822
#130707602
#130706742
#130706582
C16×Dic222
#130704652
C4×D1762
C11×#22412
#3392711