Finite Group Databasebeta

← #14911367

Subgroups — #14911367

Order 2816.

502 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#13081047C211yesmaximal, characteristic, complemented
2#13070889C211yesmaximal, characteristic, complemented
3#13070818C212yesmaximal, complemented
4#13070804C212yesmaximal, complemented
5#13070755C211yesmaximal, characteristic, complemented
6#13070753C211yesmaximal, characteristic, complemented
7#13070727C212yesmaximal, complemented
8C4×#66891C211yesmaximal, characteristic, complemented
9#13070448C211yesmaximal, characteristic, complemented
10#13070402C212yesmaximal, complemented
11C11×#3334C211yesmaximal, characteristic
12C11×#547—21no—
13#10623073—21no—
14C11×#500C2211yescharacteristic
15C11×#480—22no—
16C11×#474—21no—
17C11×#466C2212yes—
18C4×C11×D8C2211yescharacteristic
19C8×D4×C11C2211yescharacteristic
20C2×C11×#107C2212yes—
21C2×#66891C2211yescharacteristic
22#10622729C2212yes—
23#10622719C2212yes—
24C2×#66876C2212yes—
25#10622464—21no—
26#10622336—22no—
27C4×Dic44C2211yescharacteristic
28#10622295C2211yescharacteristic
29#10622200C2211yescharacteristic
30#10622200C2212yes—
31C22⋊(C11⋊C16)C2212yes—
32#10622130C2211yescharacteristic
33#10622130C2212yes—
34#10622128C2211yescharacteristic
35#10622128C2212yes—
36#10622127C2212yes—
37#10622127C2212yes—
38#10622127C2212yes—
39C4⋊(C11⋊C16)C2211yescharacteristic
40C4×C11⋊C16C2211yescharacteristic
41C2×C11×#41—41no—
42C2×C11×D8C2311yescharacteristic
43C22×C8×C11C2312yes—
44C11×C4⋊Q8—21no—
45C11×#123—42no—
46C11×C22⋊Q8—41no—
47C11×#121—22no—
48C4×D4×C11—21no—
49C4×D4×C11D411yescharacteristic
50C2×C11×C4⋊C4—22no—
51#66989—41no—
52#66979—22no—
53#66977—22no—
54C2×Dic44C2311yescharacteristic
55#66940—41no—
56#66932—42no—
57#66922—21no—
58C4×Dic22—21no—
59C11×#107—21no—
60C11×#107—22no—
61C11×#107C2312yes—
62C11×#107C2311yescharacteristic
63C11×C4⋊C8D411yescharacteristic
64C11×#102—21no—
65C11×#102—22no—
66C11×C22⋊C8D412yes—
67C4×C8×C11C2311yescharacteristic
68#66891—22no—
69#66882—21no—
70#66882C2312yes—
71#66882C2311yescharacteristic
72#66881—22no—
73#66880—22no—
74#66880—21no—
75#66876—24no—
76C2×C11⋊C16C2311yescharacteristic
77C2×C11⋊C16C2312yes—
78C2×C11⋊C16C2311yescharacteristic
79#33920—111nomaximal, Sylow
80C11×#41—84no—
81C2×Q8×C11—41no—
82C2×D4×C11—21no—
83C2×D4×C11—42no—
84C2×D4×C11D811yescharacteristic
85C22×C4×C11—42no—
86C22×C4×C11—41no—
87C22×C4×C11C2×D412yes—
88C2×Dic22—21no—
89C2×Dic22—41no—
90C11×D8—21no—
91C11×D8—21no—
92C2×C8×C11—22no—
93C2×C8×C11—22no—
94C2×C8×C11C2×D412yes—
95C2×C8×C11C2×D411yescharacteristic
96C2×C8×C11C2411yescharacteristic
97C11×C4⋊C4—21no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—42no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4D811yescharacteristic
102C11×C22⋊C4—41no—
103C11×C22⋊C4—42no—
104C11×C22⋊C4D812yes—
105C42×C11C2×D411yescharacteristic
106C22⋊Dic11—42no—
107C22⋊Dic11—42no—
108C4⋊Dic11—21no—
109C4⋊Dic11—22no—
110C4⋊Dic11—41no—
111Dic11⋊C4—41no—
112Dic11⋊C4—42no—
113C4×Dic11—41no—
114C4×Dic11—42no—
115Dic44—21no—
116Dic44—21no—
117C11⋊C16—22no—
118C11⋊C16—21no—
119C11⋊C16#4112yescomplemented
120#3342—111no—
121#3334D1111yescharacteristic
122#2252—111no—
123#2236—112no—
124#2234—112no—
125#2225—111no—
126#2224—111no—
127#2220—112no—
128C4×SD32—111no—
129#2169—111no—
130#2159—112no—
131C23×C11—41no—
132C23×C11C2×D812yes—
133Q8×C11—82no—
134D4×C11—22no—
135D4×C11—41no—
136D4×C11—41no—
137D4×C11—84no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11—41no—
141C2×C4×C11—42no—
142C2×C4×C11—84no—
143C2×C4×C11—82no—
144C2×C4×C11C2×D812yes—
145C2×C4×C11C2×D811yescharacteristic
146C2×C4×C11C2×D811yescharacteristic
147C2×C4×C11C22×D411yescharacteristic
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—42no—
151Dic22—41no—
152Dic22—41no—
153Dic22—82no—
154C8×C11—22no—
155C8×C11—21no—
156C8×C11C2×#4111yescharacteristic
157C8×C112−1+411yescharacteristic
158#556—221no—
159#547—21no—
160C2×SD32—111no—
161C2×M32—112no—
162#500—111no—
163#500C2×D1111yescharacteristic
164#485—222no—
165#480—22no—
166#475—221no—
167#474—21no—
168#467—112no—
169#466C2×D1112yes—
170C4×Q16—111no—
171C4×D8C2×D1111yescharacteristic
172C8×D4C2×D1111yescharacteristic
173#427—112no—
174C2×#107C2×D1112yes—
175#367—111no—
176#367—112no—
177#366—112no—
178#366—112no—
179#366—112no—
180C4⋊C16—111no—
181#358—111no—
182#358—112no—
183#357—111no—
184#357—112no—
185C22⋊C16—112no—
186C4×C16—111no—
187C22×C11—22no—
188C22×C11—22no—
189C22×C11—22no—
190C22×C11—81no—
191C22×C11—81no—
192C22×C11—81no—
193C22×C11C22×D811yescharacteristic
194C4×C11—22no—
195C4×C11—21no—
196C4×C11—81no—
197C4×C11—82no—
198C4×C11#50912yes—
199C4×C11#54711yescharacteristic
200C4×C11#57811yescharacteristic
201Dic11—81no—
202Dic11—82no—
203Dic11—81no—
204C2×#41—41no—
205C2×Q16—111no—
206C2×D8C22×D1111yescharacteristic
207C22×C8C22×D1112yes—
208C4⋊Q8—21no—
209C4⋊Q8—221no—
210#126—442no—
211#124—441no—
212#123—42no—
213C22⋊Q8—41no—
214C22⋊Q8—222no—
215#121—22no—
216C4×Q8—221no—
217C4×Q8—441no—
218C4×D4—21no—
219C4×D4C22⋊D1111yescharacteristic
220#117—222no—
221C2×C4⋊C4—22no—
222SD32—222no—
223M32—224no—
224C2×C16—111no—
225C2×C16—111no—
226C2×C16—112no—
227#107—22no—
228#107—21no—
229#107—112no—
230#107—111no—
231#107—221no—
232#107C22×D1111yescharacteristic
233#107C22×D1112yes—
234#106—222no—
235C4⋊C8C22⋊D1111yescharacteristic
236#103—221no—
237#103—222no—
238#102—21no—
239#102—22no—
240C22⋊C8C22⋊D1112yes—
241C4×C8C22×D1111yescharacteristic
242C2×C11—42no—
243C2×C11—161no—
244C2×C11#333411yescharacteristic
245C2×C11C2×#50911yescharacteristic
246C2×C11#341711yescharacteristic
247#41—84no—
248C2×Q8—41no—
249C2×Q8—221no—
250C2×Q8—441no—
251C2×D4—21no—
252C2×D4—42no—
253C2×D4#432311yescharacteristic
254C22×C4—42no—
255C22×C4—41no—
256C22×C4C2×C22⋊D1112yes—
257Q16—221no—
258Q16—221no—
259D8—21no—
260D8—21no—
261C2×C8—22no—
262C2×C8—22no—
263C2×C8C2×C22⋊D1111yescharacteristic
264C2×C8C2×C22⋊D1112yes—
265C2×C8C23×D1111yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—22no—
268C4⋊C4—42no—
269C4⋊C4—41no—
270C4⋊C4—221no—
271C4⋊C4—222no—
272C4⋊C4—441no—
273C4⋊C4—442no—
274C4⋊C4—441no—
275C4⋊C4#432311yescharacteristic
276C22⋊C4—41no—
277C22⋊C4—42no—
278C22⋊C4—442no—
279C22⋊C4—442no—
280C22⋊C4#432312yes—
281C42—442no—
282C42—441no—
283C42C2×C22⋊D1111yescharacteristic
284C16—112no—
285C16—222no—
286C16—221no—
287C11#3392011yescharacteristic, complemented, Sylow
288C23—41no—
289C23C2×#432312yes—
290Q8—82no—
291Q8—441no—
292Q8—441no—
293Q8—882no—
294D4—22no—
295D4—41no—
296D4—41no—
297D4—84no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—84no—
303C2×C4—82no—
304C2×C4—441no—
305C2×C4—442no—
306C2×C4—441no—
307C2×C4C2×#432312yes—
308C2×C4C2×#432311yescharacteristic
309C2×C4C2×#432311yescharacteristic
310C2×C4C22×C22⋊D1111yescharacteristic
311C8—22no—
312C8—21no—
313C8#41×D1111yescharacteristic
314C8#6704311yescharacteristic
315C22—22no—
316C22—22no—
317C22—22no—
318C22—81no—
319C22—81no—
320C22—81no—
321C22C22×#432311yescharacteristic
322C4—22no—
323C4—21no—
324C4—81no—
325C4—82no—
326C4—881no—
327C4—882no—
328C4—881no—
329C4#1062276012yes—
330C4#1062335511yescharacteristic
331C4#1062336911yescharacteristic
332C2—42no—
333C2—161no—
334C2#1308095911yescharacteristic
335C2C2×#1062276011yescharacteristic
336C2#1308176711yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
Fitting, prime radicalC11×#3334C2
socleC22×C11C22×D8
hypercenter#3334D11
hypocenterC11#33920
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3334

Complements

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

NH ≅ G/Ntype
1. #13081047C2semidirect
2. #13070889C2semidirect
3. #13070818C2semidirect
4. #13070804C2semidirect
5. #13070755C2semidirect
6. #13070753C2semidirect
7. #13070727C2semidirect
8. C4×#66891C2semidirect
9. #13070448C2semidirect
10. #13070402C2semidirect
119. C11⋊C16#41semidirect
287. C11#33920semidirect

Maximal subgroups

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

subgroupindex
#130810472
#130708892
#130708182
#130708042
#130707552
#130707532
#130707272
C4×#668912
#130704482
#130704022
C11×#33342
#3392011