Finite Group Databasebeta

← #14911439

Subgroups — #14911439

Order 2816.

498 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081484C211yesmaximal, characteristic, complemented
2#13070847C212yesmaximal, complemented
3#13070839C211yesmaximal, characteristic, complemented
4#13070773C212yesmaximal, complemented
5#13070768C211yesmaximal, characteristic, complemented
6#13070668C212yesmaximal, complemented
7#13070648C211yesmaximal, characteristic
8Q8×C11⋊C16C211yesmaximal, characteristic, complemented
9C4×#66892C211yesmaximal, characteristic, complemented
10C4×#66890C212yesmaximal, complemented
11C11×#3396C211yesmaximal, characteristic, complemented
12C11×#559—21no—
13#10623110—21no—
14C11×#495C2212yes—
15C11×#493C2211yescharacteristic
16C11×#463—22no—
17C11×#460—21no—
18C8×Q8×C11C2211yescharacteristic
19C4×C11×Q16C2211yescharacteristic
20C4×C11×D8C2212yes—
21C2×#66892C2211yescharacteristic
22C2×#66890C2212yes—
23#10622460—22no—
24#10622455—21no—
25C4×D88C2211yescharacteristic
26C4×D88C2212yes—
27#10622296C2212yes—
28#10622295C2211yescharacteristic
29#10622202C2212yes—
30#10622202C2211yescharacteristic
31#10622200C2212yes—
32#10622200C2212yes—
33#10622200C2212yes—
34#10622129C2211yescharacteristic
35#10622128C2211yescharacteristic
36#10622127C2212yes—
37C4⋊(C11⋊C16)C2211yescharacteristic
38C4⋊(C11⋊C16)C2212yes—
39C4×C11⋊C16C2212yes—
40C4×C11⋊C16C2211yescharacteristic
41C2×C11×Q16C2311yescharacteristic
42C2×C11×SD16—22no—
43C2×C11×D8—21no—
44C2×C11×D8C2312yes—
45C11×#127—21no—
46C11×#124—22no—
47C11×#124—41no—
48C11×#123—42no—
49C4×Q8×C11—21no—
50C4×Q8×C11D411yescharacteristic
51C4×D4×C11—22no—
52C4×D4×C11—41no—
53#66999—41no—
54C2×D88C2311yescharacteristic
55#66949—42no—
56C4⋊C4×D11—41no—
57C4×D44—21no—
58C4×D44—22no—
59#66923—22no—
60#66922—21no—
61C11×#107C2311yescharacteristic
62C11×C4⋊C8D411yescharacteristic
63C11×C4⋊C8D412yes—
64C11×#103—21no—
65C11×#102—22no—
66C4×C8×C11C2311yescharacteristic
67C4×C8×C11C2312yes—
68#66892—22no—
69#66890—24no—
70#66885—22no—
71#66885—21no—
72#66882—21no—
73#66882C2312yes—
74#66882C2311yescharacteristic
75#66881—22no—
76C2×C11⋊C16C2312yes—
77C2×C11⋊C16C2311yescharacteristic
78C2×C11⋊C16C2311yescharacteristic
79#33928—111nomaximal, Sylow
80C2×Q8×C11—21no—
81C2×Q8×C11D811yescharacteristic
82C2×D4×C11—22no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C22×C4×C11—42no—
86C2×D44—21no—
87C2×C4×D11—41no—
88C2×C4×D11—42no—
89C2×Dic22—41no—
90C11×Q16—21no—
91C11×Q16—21no—
92C11×SD16—82no—
93C11×D8—22no—
94C11×D8—22no—
95C11×D8—81no—
96C2×C8×C11C2×D412yes—
97C2×C8×C11C2×D411yescharacteristic
98C2×C8×C11C2411yescharacteristic
99C11×C4⋊C4—21no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4D811yescharacteristic
102C11×C4⋊C4D812yes—
103C11×C22⋊C4—42no—
104C11×C22⋊C4—42no—
105C11×C22⋊C4—42no—
106C42×C11—41no—
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D412yes—
109(C2×D11)⋊C4—41no—
110(C2×D11)⋊C4—42no—
111C4⋊Dic11—21no—
112C4⋊Dic11—22no—
113C4⋊Dic11—41no—
114Dic11⋊C4—42no—
115Dic11⋊C4—42no—
116D88—21no—
117D88#4112yes—
118C11⋊C16—22no—
119C11⋊C16—21no—
120C11⋊C16—21no—
121#3396D1111yescharacteristic, complemented
122#3380—111no—
123#2242—112no—
124#2240—111no—
125#2228—112no—
126#2227—111no—
127#2210—112no—
128#2206—111no—
129Q8×C16—111no—
130C4×SD32—111no—
131C4×D16—112no—
132C23×C11—42no—
133C22×D11—41no—
134Q8×C11—22no—
135Q8×C11—41no—
136Q8×C11—41no—
137D4×C11—42no—
138D4×C11—42no—
139D4×C11—82no—
140D4×C11—161no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—162no—
144C2×C4×C11C2×D812yes—
145C2×C4×C11C2×D812yes—
146C2×C4×C11C2×D811yescharacteristic
147C2×C4×C11C2×D811yescharacteristic
148C2×C4×C11C22×D411yescharacteristic
149C2×Dic11—41no—
150C2×Dic11—42no—
151D44—22no—
152D44—41no—
153C4×D11—82no—
154C4×D11—162no—
155Dic22—161no—
156C8×C11—21no—
157C8×C11—22no—
158C8×C11C2×#4111yescharacteristic
159C8×C112−1+411yescharacteristic
160#559—21no—
161#554—221no—
162C2×SD32—111no—
163C2×D16—112no—
164#500—111no—
165#499—112no—
166#495C2×D1112yes—
167#493C2×D1111yescharacteristic
168#478—222no—
169#476—221no—
170#463—22no—
171#460—21no—
172C8×Q8C2×D1111yescharacteristic
173C4×Q16C2×D1111yescharacteristic
174C4×D8—112no—
175C4×D8—111no—
176C4×D8C2×D1112yes—
177#367—111no—
178#366—112no—
179C4⋊C16—111no—
180C4⋊C16—112no—
181#358—111no—
182#358—112no—
183#357—112no—
184#357—112no—
185#357—112no—
186#357—111no—
187C4×C16—112no—
188C4×C16—111no—
189C22×C11—82no—
190C22×C11—82no—
191C22×C11—82no—
192C22×C11C22×D811yescharacteristic
193C2×D11—42no—
194C2×D11—81no—
195C2×D11—81no—
196C4×C11—22no—
197C4×C11—22no—
198C4×C11—21no—
199C4×C11—81no—
200C4×C11—81no—
201C4×C11#50812yes—
202C4×C11#54811yescharacteristic
203C4×C11#57711yescharacteristic
204Dic11—81no—
205Dic11—82no—
206C2×Q16C22×D1111yescharacteristic
207C2×SD16—22no—
208C2×D8—21no—
209C2×D8—111no—
210C2×D8C22×D1112yes—
211C4⋊Q8—221no—
212#127—21no—
213#125—222no—
214#124—22no—
215#124—41no—
216#123—42no—
217C22⋊Q8—441no—
218C22⋊Q8—442no—
219C4×Q8—21no—
220C4×Q8C22⋊D1111yescharacteristic
221C4×D4—22no—
222C4×D4—41no—
223C4×D4—221no—
224C4×D4—222no—
225C2×C4⋊C4—441no—
226SD32—222no—
227D16—224no—
228C2×C16—111no—
229C2×C16—111no—
230C2×C16—112no—
231#107—112no—
232#107—111no—
233#107—221no—
234#107C22×D1111yescharacteristic
235#106—222no—
236C4⋊C8C22⋊D1111yescharacteristic
237C4⋊C8C22⋊D1112yes—
238#103—21no—
239#102—22no—
240#102—222no—
241#102—221no—
242C4×C8C22×D1112yes—
243C4×C8C22×D1111yescharacteristic
244C2×C11—162no—
245C2×C11#335811yescharacteristic
246C2×C11C2×#50811yescharacteristic
247C2×C11#341511yescharacteristic
248D11—82no—
249C2×Q8—21no—
250C2×Q8—441no—
251C2×Q8#432311yescharacteristic
252C2×D4—22no—
253C2×D4—41no—
254C2×D4—41no—
255C2×D4—221no—
256C22×C4—42no—
257C22×C4—441no—
258C22×C4—442no—
259Q16—21no—
260Q16—21no—
261SD16—82no—
262D8—22no—
263D8—22no—
264D8—81no—
265D8—112no—
266D8—221no—
267C2×C8C2×C22⋊D1112yes—
268C2×C8C2×C22⋊D1111yescharacteristic
269C2×C8C23×D1111yescharacteristic
270C4⋊C4—21no—
271C4⋊C4—41no—
272C4⋊C4—221no—
273C4⋊C4—222no—
274C4⋊C4—442no—
275C4⋊C4—441no—
276C4⋊C4—442no—
277C4⋊C4#432311yescharacteristic
278C4⋊C4#432312yes—
279C22⋊C4—42no—
280C22⋊C4—42no—
281C22⋊C4—42no—
282C22⋊C4—441no—
283C22⋊C4—442no—
284C42—41no—
285C42C2×C22⋊D1112yes—
286C42C2×C22⋊D1111yescharacteristic
287C16—222no—
288C16—221no—
289C16—221no—
290C11#3392811yescharacteristic, complemented, Sylow
291C23—42no—
292C23—441no—
293Q8—22no—
294Q8—41no—
295Q8—41no—
296Q8—1761no—
297D4—42no—
298D4—42no—
299D4—82no—
300D4—161no—
301D4—222no—
302D4—441no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—162no—
306C2×C4—441no—
307C2×C4—442no—
308C2×C4—882no—
309C2×C4—1762no—
310C2×C4C2×#432312yes—
311C2×C4C2×#432312yes—
312C2×C4C2×#432311yescharacteristic
313C2×C4C2×#432311yescharacteristic
314C2×C4C22×C22⋊D1111yescharacteristic
315C8—21no—
316C8—22no—
317C8#41×D1111yescharacteristic
318C8#6704311yescharacteristic
319C22—82no—
320C22—82no—
321C22—82no—
322C22—442no—
323C22—881no—
324C22—881no—
325C22C22×#432311yescharacteristic
326C4—22no—
327C4—22no—
328C4—21no—
329C4—81no—
330C4—81no—
331C4—881no—
332C4—882no—
333C4#1062280712yes—
334C4#1062336211yescharacteristic
335C4#1062336711yescharacteristic
336C2—162no—
337C2—882no—
338C2#1308124711yescharacteristic
339C2C2×#1062280711yescharacteristic
340C2#1308175511yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3396C2
socleC22×C11C22×D8
prime radical#13070648C2
hypercenter#3396D11
hypocenterC11#33928
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8 ◁ #3396

Complements

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

NH ≅ G/Ntype
1. #13081484C2semidirect
2. #13070847C2semidirect
3. #13070839C2semidirect
4. #13070773C2semidirect
5. #13070768C2semidirect
6. #13070668C2semidirect
8. Q8×C11⋊C16C2semidirect
9. C4×#66892C2semidirect
10. C4×#66890C2semidirect
11. C11×#3396C2semidirect
121. #3396D11semidirect
290. C11#33928semidirect

Maximal subgroups

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

subgroupindex
#130814842
#130708472
#130708392
#130707732
#130707682
#130706682
#130706482
Q8×C11⋊C162
C4×#668922
C4×#668902
C11×#33962
#3392811