Finite Group Databasebeta

← #14911479

Subgroups — #14911479

Order 2816.

484 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081629C211yesmaximal, characteristic
2#13070850C212yesmaximal, complemented
3#13070841C211yesmaximal, characteristic
4#13070770C212yesmaximal, complemented
5#13070755C211yesmaximal, characteristic, complemented
6#13070678C212yesmaximal, complemented
7#13070656C211yesmaximal, characteristic
8Q8×C11⋊C16C211yesmaximal, characteristic, complemented
9C4×#66893C211yesmaximal, characteristic, complemented
10C4×#66892C212yesmaximal, complemented
11C11×#3383C211yesmaximal, characteristic, complemented
12C11×#557—21no—
13#10623116—21no—
14C11×#500C2211yescharacteristic
15C11×#499C2212yes—
16C11×#479—22no—
17C11×#475—21no—
18C8×Q8×C11C2211yescharacteristic
19C4×C11×Q16C2211yescharacteristic
20C4×C11×Q16C2212yes—
21C2×#66893C2211yescharacteristic
22C2×#66892C2212yes—
23#10622461—21no—
24#10622457—22no—
25C4×Dic44C2211yescharacteristic
26#10622309C2212yes—
27#10622308C2211yescharacteristic
28C4×D88C2212yes—
29#10622202C2211yescharacteristic
30#10622130C2211yescharacteristic
31#10622130C2212yes—
32#10622129C2212yes—
33#10622129C2212yes—
34#10622129C2212yes—
35#10622128C2212yes—
36#10622127C2211yescharacteristic
37C4⋊(C11⋊C16)C2211yescharacteristic
38C4⋊(C11⋊C16)C2212yes—
39C4×C11⋊C16C2212yes—
40C4×C11⋊C16C2211yescharacteristic
41C2×C11×Q16C2311yescharacteristic
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—41no—
44C11×#125—22no—
45C11×#125—42no—
46C4×Q8×C11—21no—
47C4×Q8×C11—22no—
48C4×Q8×C11—41no—
49C4×Q8×C11D411yescharacteristic
50#67000—41no—
51C2×Dic44C2311yescharacteristic
52C2×D88—21no—
53C2×D88C2312yes—
54C2×#4314—22no—
55#66947—42no—
56#66946—41no—
57#66928—22no—
58#66927—21no—
59C4×D44—22no—
60C4×Dic22—21no—
61C11×#107—21no—
62C11×#107C2311yescharacteristic
63C11×#107C2312yes—
64C11×#106—22no—
65C11×C4⋊C8D411yescharacteristic
66C11×C4⋊C8D412yes—
67C11×#103—22no—
68C11×#103—21no—
69C4×C8×C11C2312yes—
70C4×C8×C11C2311yescharacteristic
71#66893—22no—
72#66892—24no—
73#66885—22no—
74#66882C2311yescharacteristic
75#66880—21no—
76C2×C11⋊C16C2312yes—
77C2×C11⋊C16C2311yescharacteristic
78C2×C11⋊C16C2311yescharacteristic
79#33932—111nomaximal, Sylow
80C2×Q8×C11—21no—
81C2×Q8×C11—41no—
82C2×Q8×C11D811yescharacteristic
83C2×D44—22no—
84C2×D44—41no—
85C2×D44—41no—
86C2×C4×D11—42no—
87C2×Dic22—21no—
88C11×Q16—21no—
89C11×Q16#4112yes—
90C2×C8×C11C2×D411yescharacteristic
91C2×C8×C11C2×D412yes—
92C2×C8×C11C2411yescharacteristic
93C11×C4⋊C4—21no—
94C11×C4⋊C4—22no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—42no—
97C11×C4⋊C4—42no—
98C11×C4⋊C4—42no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4D811yescharacteristic
101C11×C4⋊C4D812yes—
102C42×C11—42no—
103C42×C11—41no—
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D412yes—
106(C2×D11)⋊C4—42no—
107(C2×D11)⋊C4—42no—
108(C2×D11)⋊C4—42no—
109C4⋊Dic11—21no—
110Dic11⋊C4—41no—
111C4×Dic11—41no—
112Dic44—21no—
113Dic44—21no—
114D88—22no—
115D88—22no—
116D88—81no—
117#4314—82no—
118C11⋊C16—22no—
119C11⋊C16—21no—
120C11⋊C16—21no—
121#3396—111no—
122#3383D1111yescharacteristic, complemented
123#2242—112no—
124#2240—111no—
125#2228—112no—
126#2225—111no—
127#2211—112no—
128#2207—111no—
129Q8×C16—111no—
130C4×Q32—111no—
131C4×SD32—112no—
132C22×D11—42no—
133Q8×C11—22no—
134Q8×C11—22no—
135Q8×C11—41no—
136Q8×C11—82no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—42no—
140C2×C4×C11C2×D811yescharacteristic
141C2×C4×C11C2×D812yes—
142C2×C4×C11C2×D812yes—
143C2×C4×C11C2×D811yescharacteristic
144C2×C4×C11C22×D411yescharacteristic
145C2×Dic11—41no—
146C2×Dic11—41no—
147D44—42no—
148D44—42no—
149D44—82no—
150D44—161no—
151C4×D11—162no—
152Dic22—41no—
153Dic22—41no—
154C8×C11—22no—
155C8×C11—21no—
156C8×C11C2×#4111yescharacteristic
157C8×C112−1+411yescharacteristic
158#559—221no—
159#557—21no—
160C2×Q32—111no—
161C2×SD32—112no—
162#500C2×D1111yescharacteristic
163#499C2×D1112yes—
164#495—112no—
165#493—111no—
166#479—22no—
167#475—21no—
168#463—222no—
169#460—221no—
170C8×Q8C2×D1111yescharacteristic
171C4×Q16—111no—
172C4×Q16C2×D1112yes—
173C4×Q16C2×D1111yescharacteristic
174C4×D8—112no—
175#367—112no—
176#366—111no—
177C4⋊C16—111no—
178C4⋊C16—112no—
179#358—111no—
180#358—111no—
181#358—112no—
182#357—112no—
183#357—112no—
184#357—112no—
185C4×C16—112no—
186C4×C16—111no—
187C22×C11C22×D811yescharacteristic
188C2×D11—82no—
189C2×D11—82no—
190C2×D11—82no—
191C4×C11—22no—
192C4×C11—22no—
193C4×C11—21no—
194C4×C11—42no—
195C4×C11—82no—
196C4×C11—81no—
197C4×C11#50812yes—
198C4×C11#54811yescharacteristic
199C4×C11#57711yescharacteristic
200Dic11—81no—
201Dic11—81no—
202C2×Q16—111no—
203C2×Q16C22×D1111yescharacteristic
204C2×SD16—222no—
205C2×D8—112no—
206C2×D8—221no—
207C4⋊Q8—21no—
208C4⋊Q8—41no—
209#127—221no—
210#125—22no—
211#125—42no—
212#124—222no—
213#124—441no—
214#123—442no—
215C4×Q8—21no—
216C4×Q8—22no—
217C4×Q8—41no—
218C4×Q8—221no—
219C4×Q8C22⋊D1111yescharacteristic
220C4×D4—222no—
221C4×D4—441no—
222Q32—222no—
223SD32—224no—
224C2×C16—111no—
225C2×C16—111no—
226C2×C16—112no—
227#107—21no—
228#107—111no—
229#107C22×D1111yescharacteristic
230#107C22×D1112yes—
231#106—22no—
232C4⋊C8C22⋊D1111yescharacteristic
233C4⋊C8C22⋊D1112yes—
234#103—22no—
235#103—21no—
236#103—221no—
237#102—222no—
238C4×C8C22×D1112yes—
239C4×C8C22×D1111yescharacteristic
240C2×C11#335811yescharacteristic
241C2×C11C2×#50811yescharacteristic
242C2×C11#341611yescharacteristic
243D11—162no—
244C2×Q8—21no—
245C2×Q8—41no—
246C2×Q8—221no—
247C2×Q8#432311yescharacteristic
248C2×D4—222no—
249C2×D4—441no—
250C2×D4—441no—
251C22×C4—442no—
252Q16—21no—
253Q16—221no—
254Q16—221no—
255Q16#434312yes—
256SD16—882no—
257D8—222no—
258D8—222no—
259D8—881no—
260C2×C8C2×C22⋊D1112yes—
261C2×C8C2×C22⋊D1111yescharacteristic
262C2×C8C23×D1111yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—22no—
265C4⋊C4—41no—
266C4⋊C4—42no—
267C4⋊C4—42no—
268C4⋊C4—42no—
269C4⋊C4—41no—
270C4⋊C4—221no—
271C4⋊C4—441no—
272C4⋊C4#432311yescharacteristic
273C4⋊C4#432312yes—
274C22⋊C4—442no—
275C22⋊C4—442no—
276C22⋊C4—442no—
277C42—42no—
278C42—41no—
279C42—441no—
280C42C2×C22⋊D1112yes—
281C42C2×C22⋊D1111yescharacteristic
282C16—222no—
283C16—221no—
284C16—221no—
285C11#3393211yescharacteristic, complemented, Sylow
286C23—442no—
287Q8—22no—
288Q8—22no—
289Q8—41no—
290Q8—82no—
291Q8—441no—
292Q8—441no—
293D4—442no—
294D4—442no—
295D4—882no—
296D4—1761no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—441no—
301C2×C4—441no—
302C2×C4—1762no—
303C2×C4C2×#432312yes—
304C2×C4C2×#432312yes—
305C2×C4C2×#432311yescharacteristic
306C2×C4C2×#432311yescharacteristic
307C2×C4C22×C22⋊D1111yescharacteristic
308C8—21no—
309C8—22no—
310C8C2×#434311yescharacteristic
311C8#6704011yescharacteristic
312C22—882no—
313C22—882no—
314C22—882no—
315C22C22×#432311yescharacteristic
316C4—22no—
317C4—22no—
318C4—21no—
319C4—42no—
320C4—82no—
321C4—81no—
322C4—881no—
323C4—881no—
324C4#1062280712yes—
325C4#1062334811yescharacteristic
326C4#1062336811yescharacteristic
327C2—1762no—
328C2#1308125111yescharacteristic
329C2C2×#1062280711yescharacteristic
330C2#1308176011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3383C2
socleC22×C11C22×D8
prime radical#10622308C22
hypercenter#3383D11
hypocenterC11#33932
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8 ◁ #3383

Complements

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

NH ≅ G/Ntype
2. #13070850C2semidirect
4. #13070770C2semidirect
5. #13070755C2semidirect
6. #13070678C2semidirect
8. Q8×C11⋊C16C2semidirect
9. C4×#66893C2semidirect
10. C4×#66892C2semidirect
11. C11×#3383C2semidirect
122. #3383D11semidirect
285. C11#33932semidirect

Maximal subgroups

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

subgroupindex
#130816292
#130708502
#130708412
#130707702
#130707552
#130706782
#130706562
Q8×C11⋊C162
C4×#668932
C4×#668922
C11×#33832
#3393211