Finite Group Databasebeta

← #14911436

Subgroups — #14911436

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#13081481C211yesmaximal, characteristic, complemented
3#13070849C212yesmaximal, complemented
4#13070843C211yesmaximal, characteristic, complemented
5#13070778C212yesmaximal, complemented
6#13070764C211yesmaximal, characteristic, complemented
7#13070673C212yesmaximal
8#13070518C211yesmaximal, characteristic, complemented
9SD32×Dic11C212yesmaximal, complemented
10C4×#66890C211yesmaximal, characteristic
11C11×#2208C211yesmaximal, characteristic, complemented
12#10623263—21no—
13#10623074—21no—
14C2×C11×SD32C2212yes—
15C11×#494C2211yescharacteristic
16C4×C11×D8C2211yescharacteristic
17#10622804C2212yes—
18#10622798—22no—
19Q16×Dic11C2212yes—
20D8×Dic11C2212yes—
21C2×#66890C2211yescharacteristic
22#10622696—21no—
23#10622621—21no—
24#10622491C2212yes—
25#10622379—22no—
26C4×D88C2211yescharacteristic
27#10622295C2211yescharacteristic
28C8×Dic22C2211yescharacteristic
29C11×C4⋊C16C2211yescharacteristic
30C11×#358C2212yes—
31#10622202C2212yes—
32#10622202C2212yes—
33#10622200C2211yescharacteristic
34#10622147C2212yes—
35#10622143C2212yes—
36Dic11⋊C16C2212yes—
37C16×Dic11C2212yes—
38#10622129C2211yescharacteristic
39#10622127C2211yescharacteristic
40C4×C11⋊C16C2211yescharacteristic
41C2×C11×Q16—21no—
42C2×C11×Q16C2312yes—
43C2×C11×D8C2311yescharacteristic
44C11×C4⋊Q8—21no—
45C4×D4×C11—21no—
46#67000—22no—
47Q8×Dic11—22no—
48C2×#4325—22no—
49D4×Dic11—22no—
50C2×C4⋊Dic11—41no—
51#66977—41no—
52C2×D88C2311yescharacteristic
53#66951—42no—
54#66950—41no—
55#66945—41no—
56#66943—22no—
57#66931—42no—
58C4×D44—21no—
59#66922—21no—
60C4×Dic22D411yescharacteristic
61C11×SD32—24no—
62C2×C11×C16C2312yes—
63C11×#107C2311yescharacteristic
64C11×#102—21no—
65C4×C8×C11C2311yescharacteristic
66#66899—22no—
67#66896—22no—
68#66890—22no—
69#66885—21no—
70#66882—21no—
71#66882C2312yes—
72#66882C2311yescharacteristic
73Dic11⋊C8D412yes—
74C8×Dic11C2312yes—
75C2×C11⋊C16C2311yescharacteristic
76C2×C11⋊C16C2311yescharacteristic
77#66872—22no—
78C4⋊(C11⋊C8)D411yescharacteristic
79#33927—111nomaximal, Sylow
80C2×Q8×C11—22no—
81C2×D4×C11—21no—
82C22×C4×C11—41no—
83C22×Dic11—42no—
84C2×D44—21no—
85C2×C4×D11—41no—
86C2×Dic22—41no—
87C2×Dic22D811yescharacteristic
88C11×Q16—22no—
89C11×Q16—22no—
90C11×Q16—81no—
91C11×D8—21no—
92C11×D8#4112yes—
93C2×C8×C11C2×D411yescharacteristic
94C2×C8×C11C2411yescharacteristic
95C11×C4⋊C4—21no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C11×C22⋊C4—41no—
99C42×C11C2×D411yescharacteristic
100C22⋊Dic11—42no—
101#4325—82no—
102(C2×D11)⋊C4—42no—
103(C2×D11)⋊C4—42no—
104(C2×D11)⋊C4—41no—
105C4⋊Dic11—22no—
106C4⋊Dic11—21no—
107C4⋊Dic11—42no—
108C4⋊Dic11—42no—
109C4⋊Dic11—41no—
110C4⋊Dic11D811yescharacteristic
111Dic11⋊C4—42no—
112Dic11⋊C4D812yes—
113C4×Dic11—42no—
114C4×Dic11C2×D412yes—
115C2×C11⋊C8C2×D412yes—
116D88—21no—
117D88—21no—
118C11×C16—22no—
119C11⋊C16—21no—
120C11⋊C16—21no—
121#3393—111no—
122#3380—111no—
123#2242—112no—
124#2241—111no—
125#2229—112no—
126#2226—111no—
127#2210—112no—
128#2208D1111yescharacteristic, complemented
129Q8×C16—111no—
130C4×SD32—112no—
131C4×D16—111no—
132C23×C11—41no—
133C22×D11—41no—
134Q8×C11—42no—
135Q8×C11—42no—
136D4×C11—22no—
137D4×C11—41no—
138C2×C4×C11—42no—
139C2×C4×C11—41no—
140C2×C4×C11—82no—
141C2×C4×C11C2×D811yescharacteristic
142C2×C4×C11C2×D811yescharacteristic
143C2×C4×C11C22×D411yescharacteristic
144C2×Dic11—41no—
145C2×Dic11—42no—
146C2×Dic11—162no—
147C2×Dic11C2×D812yes—
148C2×Dic11C2×D812yes—
149D44—41no—
150D44—41no—
151C4×D11—82no—
152Dic22—22no—
153Dic22—161no—
154C8×C11—21no—
155C8×C11C2×#4111yescharacteristic
156C8×C112−1+411yescharacteristic
157C11⋊C8—22no—
158#556—221no—
159#554—221no—
160C2×SD32C2×D1112yes—
161C2×D16—111no—
162#500—111no—
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×D8C2×D1111yescharacteristic
175#367—112no—
176#366—111no—
177C4⋊C16—112no—
178C4⋊C16C2×D1111yescharacteristic
179#358—112no—
180#358—112no—
181#358C2×D1112yes—
182#357—111no—
183#357—112no—
184#357—111no—
185C4×C16—112no—
186C4×C16—111no—
187C22×C11—42no—
188C22×C11—81no—
189C22×C11—81no—
190C22×C11C22×D811yescharacteristic
191C2×D11—81no—
192C2×D11—81no—
193C2×D11—81no—
194C4×C11—21no—
195C4×C11—82no—
196C4×C11—81no—
197C4×C11#50812yes—
198C4×C11#54811yescharacteristic
199C4×C11#57711yescharacteristic
200Dic11—22no—
201Dic11—22no—
202Dic11—81no—
203Dic11—82no—
204C2×Q16—21no—
205C2×Q16C22×D1112yes—
206C2×SD16—222no—
207C2×D8—111no—
208C2×D8C22×D1111yescharacteristic
209C4⋊Q8—21no—
210C4⋊Q8—221no—
211#126—442no—
212#125—222no—
213#124—222no—
214C22⋊Q8—442no—
215C22⋊Q8—441no—
216C22⋊Q8—441no—
217C4×Q8—111no—
218C4×Q8—222no—
219C4×D4—21no—
220C4×D4—222no—
221C4×D4—221no—
222#117—441no—
223C2×C4⋊C4—441no—
224SD32—24no—
225D16—222no—
226C2×C16—111no—
227C2×C16—111no—
228C2×C16C22×D1112yes—
229#107—112no—
230#107—111no—
231#107—221no—
232#107C22×D1111yescharacteristic
233#106—222no—
234C4⋊C8—112no—
235C4⋊C8—111no—
236#103—222no—
237#102—21no—
238#102—222no—
239#102—221no—
240C4×C8—112no—
241C4×C8C22×D1111yescharacteristic
242C2×C11—82no—
243C2×C11#335811yescharacteristic
244C2×C11C2×#50811yescharacteristic
245C2×C11#341611yescharacteristic
246D11—161no—
247C2×Q8—22no—
248C2×Q8—111no—
249C2×Q8—441no—
250C2×D4—21no—
251C2×D4—221no—
252C22×C4—41no—
253C22×C4—442no—
254C22×C4—441no—
255Q16—22no—
256Q16—22no—
257Q16—81no—
258SD16—882no—
259D8—21no—
260D8—221no—
261D8—221no—
262D8#434112yes—
263C2×C8—112no—
264C2×C8D4×D1111yescharacteristic
265C2×C8C23×D1111yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—111no—
270C4⋊C4—112no—
271C4⋊C4—221no—
272C4⋊C4—222no—
273C4⋊C4—442no—
274C4⋊C4—442no—
275C4⋊C4—442no—
276C4⋊C4—441no—
277C22⋊C4—41no—
278C22⋊C4—442no—
279C22⋊C4—442no—
280C22⋊C4—442no—
281C22⋊C4—441no—
282C42—112no—
283C42—442no—
284C42D4×D1111yescharacteristic
285C16—22no—
286C16—221no—
287C16—221no—
288C11#3392711yescharacteristic, complemented, Sylow
289C23—41no—
290C23—441no—
291Q8—42no—
292Q8—42no—
293Q8—222no—
294Q8—1761no—
295D4—22no—
296D4—41no—
297D4—441no—
298D4—441no—
299C2×C4—42no—
300C2×C4—41no—
301C2×C4—82no—
302C2×C4—112no—
303C2×C4—112no—
304C2×C4—441no—
305C2×C4—442no—
306C2×C4—882no—
307C2×C4—1762no—
308C2×C4D8×D1111yescharacteristic
309C2×C4D8×D1111yescharacteristic
310C2×C4C2×D4×D1111yescharacteristic
311C8—21no—
312C8—222no—
313C8C2×#434111yescharacteristic
314C8#6704311yescharacteristic
315C22—42no—
316C22—81no—
317C22—81no—
318C22—881no—
319C22—881no—
320C22—881no—
321C22C2×D8×D1111yescharacteristic
322C4—21no—
323C4—81no—
324C4—82no—
325C4—222no—
326C4—222no—
327C4—881no—
328C4—882no—
329C4#1062252912yes—
330C4#1062312911yescharacteristic
331C4#1062330611yescharacteristic
332C2—82no—
333C2—1761no—
334C2#1308124611yescharacteristic
335C2C2×#1062252911yescharacteristic
336C2#1308176111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2208C2
socleC22×C11C22×D8
prime radicalC2×#66890C22
hypercenter#2208D11
hypocenterC11#33927
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2208

Complements

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

NH ≅ G/Ntype
1. #13081606C2semidirect
2. #13081481C2semidirect
3. #13070849C2semidirect
4. #13070843C2semidirect
5. #13070778C2semidirect
6. #13070764C2semidirect
8. #13070518C2semidirect
9. SD32×Dic11C2semidirect
11. C11×#2208C2semidirect
128. #2208D11semidirect
288. C11#33927semidirect

Maximal subgroups

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

subgroupindex
#130816062
#130814812
#130708492
#130708432
#130707782
#130707642
#130706732
#130705182
SD32×Dic112
C4×#668902
C11×#22082
#3392711