Finite Group Databasebeta

← #14911441

Subgroups — #14911441

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#13081626C211yesmaximal, characteristic, complemented
2#13081481C211yesmaximal, characteristic, complemented
3#13070849C212yesmaximal, complemented
4#13070840C211yesmaximal, characteristic, complemented
5#13070772C212yesmaximal, complemented
6#13070768C211yesmaximal, characteristic, complemented
7#13070673C212yesmaximal, complemented
8#13070651C211yesmaximal, characteristic
9C16×Dic22C211yesmaximal, characteristic, complemented
10#13070460C212yesmaximal, complemented
11C4×C11×SD32C211yesmaximal, characteristic, complemented
12#10623116—21no—
13#10623074—21no—
14C2×C11×SD32C2211yescharacteristic
15C4×C11×Q16C2211yescharacteristic
16C4×C11×D8C2211yescharacteristic
17#10622804C2212yes—
18D8×Dic11C2212yes—
19C2×#66890C2212yes—
20#10622640—21no—
21#10622621—21no—
22#10622491C2212yes—
23#10622485C2212yes—
24#10622432—22no—
25#10622379—22no—
26#10622308C2211yescharacteristic
27#10622295C2211yescharacteristic
28C8×Dic22C2211yescharacteristic
29C11×#367C2211yescharacteristic
30C11×#358C2211yescharacteristic
31C11×#357C2211yescharacteristic
32C4×C11×C16C2211yescharacteristic
33#10622202C2212yes—
34#10622147C2212yes—
35#10622147C2212yes—
36Dic11⋊C16C2212yes—
37C16×Dic11C2212yes—
38#10622129C2212yes—
39#10622127C2212yes—
40C4⋊(C11⋊C16)C2211yescharacteristic
41C2×C11×Q16C2311yescharacteristic
42C2×C11×D8C2311yescharacteristic
43C4×Q8×C11—21no—
44C4×D4×C11—21no—
45#67000—22no—
46C2×#4325—22no—
47D4×Dic11—22no—
48C2×C4⋊Dic11—41no—
49#66977—41no—
50C2×D88—21no—
51C2×D88C2312yes—
52#66947—42no—
53#66946—22no—
54#66943—22no—
55#66931—42no—
56#66928—41no—
57#66927—21no—
58C4×D44—41no—
59#66922—21no—
60C4×Dic22D411yescharacteristic
61C11×SD32—22no—
62C2×C11×C16C2311yescharacteristic
63C2×C11×C16C2311yescharacteristic
64C11×#107C2311yescharacteristic
65C11×#107C2311yescharacteristic
66C11×#103—21no—
67C11×#102—21no—
68C4×C8×C11C2311yescharacteristic
69#66896—22no—
70#66890—24no—
71#66882—21no—
72#66882C2312yes—
73Dic11⋊C8D412yes—
74C8×Dic11C2312yes—
75C2×C11⋊C16C2312yes—
76#66873—22no—
77#66872—22no—
78C4⋊(C11⋊C8)D411yescharacteristic
79#33928—111nomaximal, Sylow
80C2×Q8×C11—21no—
81C2×D4×C11—21no—
82C22×C4×C11—41no—
83C22×Dic11—42no—
84C2×D44—22no—
85C2×D44—41no—
86C2×D44—41no—
87C2×C4×D11—42no—
88C2×Dic22—41no—
89C2×Dic22D811yescharacteristic
90C11×Q16—21no—
91C11×Q16—21no—
92C11×D8—21no—
93C11×D8#4112yes—
94C2×C8×C11C2×D411yescharacteristic
95C2×C8×C11C2411yescharacteristic
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—41no—
99C11×C22⋊C4—41no—
100C42×C11—41no—
101C42×C11C2×D411yescharacteristic
102C22⋊Dic11—42no—
103#4325—82no—
104(C2×D11)⋊C4—42no—
105(C2×D11)⋊C4—42no—
106(C2×D11)⋊C4—42no—
107C4⋊Dic11—22no—
108C4⋊Dic11—42no—
109C4⋊Dic11—41no—
110C4⋊Dic11D811yescharacteristic
111Dic11⋊C4—42no—
112Dic11⋊C4D812yes—
113C4×Dic11C2×D412yes—
114C2×C11⋊C8C2×D412yes—
115D88—22no—
116D88—22no—
117D88—81no—
118C11×C16—21no—
119C11×C16—21no—
120C11⋊C16—22no—
121#3396—111no—
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×SD32D1111yescharacteristic, complemented
131C4×D16—112no—
132C23×C11—41no—
133C22×D11—42no—
134Q8×C11—41no—
135Q8×C11—41no—
136D4×C11—22no—
137D4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—82no—
142C2×C4×C11C2×D811yescharacteristic
143C2×C4×C11C2×D811yescharacteristic
144C2×C4×C11C22×D411yescharacteristic
145C2×Dic11—42no—
146C2×Dic11—162no—
147C2×Dic11C2×D812yes—
148C2×Dic11C2×D812yes—
149D44—42no—
150D44—42no—
151D44—82no—
152D44—161no—
153C4×D11—162no—
154Dic22—22no—
155Dic22—161no—
156C8×C11—21no—
157C8×C11C2×#4111yescharacteristic
158C8×C112−1+411yescharacteristic
159C11⋊C8—22no—
160#559—221no—
161#554—221no—
162C2×SD32C2×D1111yescharacteristic
163C2×D16—112no—
164#500—111no—
165#499—112no—
166#495—112no—
167#493—111no—
168#478—222no—
169#476—221no—
170#463—222no—
171#460—221no—
172C8×Q8—111no—
173C4×Q16C2×D1111yescharacteristic
174C4×D8—112no—
175C4×D8—112no—
176C4×D8C2×D1111yescharacteristic
177#367C2×D1111yescharacteristic
178#366—112no—
179C4⋊C16—112no—
180C4⋊C16—111no—
181#358—112no—
182#358C2×D1111yescharacteristic
183#357—112no—
184#357—112no—
185#357—112no—
186#357C2×D1111yescharacteristic
187C4×C16—112no—
188C4×C16C2×D1111yescharacteristic
189C22×C11—42no—
190C22×C11—81no—
191C22×C11—81no—
192C22×C11C22×D811yescharacteristic
193C2×D11—82no—
194C2×D11—82no—
195C2×D11—82no—
196C4×C11—21no—
197C4×C11—81no—
198C4×C11—81no—
199C4×C11—81no—
200C4×C11#50812yes—
201C4×C11#54811yescharacteristic
202C4×C11#57711yescharacteristic
203Dic11—22no—
204Dic11—22no—
205Dic11—82no—
206C2×Q16C22×D1111yescharacteristic
207C2×SD16—222no—
208C2×D8—112no—
209C2×D8—221no—
210C2×D8C22×D1111yescharacteristic
211C4⋊Q8—221no—
212#127—221no—
213#125—222no—
214#124—222no—
215#124—441no—
216#123—442no—
217C22⋊Q8—442no—
218C22⋊Q8—441no—
219C4×Q8—21no—
220C4×Q8—111no—
221C4×D4—21no—
222C4×D4—222no—
223C4×D4—222no—
224C4×D4—441no—
225C2×C4⋊C4—441no—
226SD32—22no—
227D16—224no—
228C2×C16—112no—
229C2×C16C22×D1111yescharacteristic
230C2×C16C22×D1111yescharacteristic
231#107—112no—
232#107—221no—
233#107C22×D1111yescharacteristic
234#107C22×D1111yescharacteristic
235#106—222no—
236C4⋊C8—112no—
237C4⋊C8—111no—
238#103—21no—
239#102—21no—
240#102—222no—
241#102—222no—
242C4×C8—112no—
243C4×C8C22×D1111yescharacteristic
244C2×C11—82no—
245C2×C11#335811yescharacteristic
246C2×C11C2×#50811yescharacteristic
247C2×C11#341511yescharacteristic
248D11—162no—
249C2×Q8—21no—
250C2×Q8—111no—
251C2×Q8—441no—
252C2×D4—21no—
253C2×D4—222no—
254C2×D4—441no—
255C2×D4—441no—
256C22×C4—41no—
257C22×C4—442no—
258C22×C4—442no—
259Q16—21no—
260Q16—21no—
261SD16—882no—
262D8—21no—
263D8—222no—
264D8—222no—
265D8—881no—
266D8#433912yes—
267C2×C8—112no—
268C2×C8D4×D1111yescharacteristic
269C2×C8C23×D1111yescharacteristic
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—41no—
273C4⋊C4—111no—
274C4⋊C4—112no—
275C4⋊C4—222no—
276C4⋊C4—442no—
277C4⋊C4—442no—
278C4⋊C4—441no—
279C22⋊C4—41no—
280C22⋊C4—442no—
281C22⋊C4—442no—
282C22⋊C4—442no—
283C22⋊C4—442no—
284C42—41no—
285C42—112no—
286C42D4×D1111yescharacteristic
287C16—21no—
288C16—21no—
289C16—222no—
290C11#3392811yescharacteristic, complemented, Sylow
291C23—41no—
292C23—442no—
293Q8—41no—
294Q8—41no—
295Q8—222no—
296Q8—1761no—
297D4—22no—
298D4—41no—
299D4—442no—
300D4—442no—
301D4—882no—
302D4—1761no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—82no—
307C2×C4—112no—
308C2×C4—112no—
309C2×C4—442no—
310C2×C4—1762no—
311C2×C4—1762no—
312C2×C4D8×D1111yescharacteristic
313C2×C4D8×D1111yescharacteristic
314C2×C4C2×D4×D1111yescharacteristic
315C8—21no—
316C8—222no—
317C8C2×#433911yescharacteristic
318C8#6704311yescharacteristic
319C22—42no—
320C22—81no—
321C22—81no—
322C22—882no—
323C22—882no—
324C22—882no—
325C22C2×D8×D1111yescharacteristic
326C4—21no—
327C4—81no—
328C4—81no—
329C4—81no—
330C4—222no—
331C4—222no—
332C4—882no—
333C4#1062252912yes—
334C4#1062308311yescharacteristic
335C4#1062330111yescharacteristic
336C2—82no—
337C2—1762no—
338C2#1308124911yescharacteristic
339C2C2×#1062252911yescharacteristic
340C2#1308175411yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC4×C11×SD32C2
socleC22×C11C22×D8
prime radical#13070651C2
hypercenterC4×SD32D11
hypocenterC11#33928
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×SD32

Complements

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

NH ≅ G/Ntype
1. #13081626C2semidirect
2. #13081481C2semidirect
3. #13070849C2semidirect
4. #13070840C2semidirect
5. #13070772C2semidirect
6. #13070768C2semidirect
7. #13070673C2semidirect
9. C16×Dic22C2semidirect
10. #13070460C2semidirect
11. C4×C11×SD32C2semidirect
130. C4×SD32D11semidirect
290. C11#33928semidirect

Maximal subgroups

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

subgroupindex
#130816262
#130814812
#130708492
#130708402
#130707722
#130707682
#130706732
#130706512
C16×Dic222
#130704602
C4×C11×SD322
#3392811