Finite Group Databasebeta

← #14911448

Subgroups — #14911448

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#13081630C211yesmaximal, characteristic, complemented
2#13081485C211yesmaximal, characteristic, complemented
3#13070846C212yesmaximal, complemented
4#13070775C212yesmaximal, complemented
5#13070765C211yesmaximal, characteristic, complemented
6#13070670C212yesmaximal, complemented
7#13070648C211yesmaximal, characteristic
8C16×Dic22C211yesmaximal, characteristic, complemented
9C4×#66864C211yesmaximal, characteristic, complemented
10#13070460C212yesmaximal, complemented
11C11×#2240C211yesmaximal, characteristic, complemented
12#10623261—21no—
13#10623244—21no—
14C11×#500C2211yescharacteristic
15C11×#493C2211yescharacteristic
16#10622768C2212yes—
17#10622766—22no—
18D8×Dic11C2212yes—
19C2×#66890C2212yes—
20#10622697—21no—
21#10622688—21no—
22C2×#66864C2211yescharacteristic
23#10622504—22no—
24#10622491C2212yes—
25#10622485C2212yes—
26C4×Dic44C2211yescharacteristic
27C4×D88C2211yescharacteristic
28C8×Dic22C2211yescharacteristic
29C11×#357C2212yes—
30C11×#357C2212yes—
31C4×C11×C16C2211yescharacteristic
32#10622200C2212yes—
33#10622147C2211yescharacteristic
34#10622143C2211yescharacteristic
35#10622141C2211yescharacteristic
36Dic11⋊C16C2212yes—
37C16×Dic11C2212yes—
38#10622130C2212yes—
39#10622127C2212yes—
40C4⋊(C11⋊C16)C2211yescharacteristic
41C2×C11×D8—21no—
42C2×C11×D8C2312yes—
43C11×C4⋊Q8—21no—
44C11×#127—21no—
45#66999—42no—
46#66989—22no—
47#66989—41no—
48#66988—42no—
49D4×Dic11—22no—
50D4×Dic11—41no—
51C2×#4324—22no—
52C2×Dic44C2311yescharacteristic
53C2×D88C2311yescharacteristic
54#66950—41no—
55#66946—22no—
56C4⋊C4×D11—41no—
57#66943—22no—
58C4×D44—21no—
59C4×Dic22—21no—
60C4×Dic22D411yescharacteristic
61C2×C11×C16C2311yescharacteristic
62C2×C11×C16C2311yescharacteristic
63C11×#107—21no—
64C11×#107C2312yes—
65C4×C8×C11C2311yescharacteristic
66#66896—22no—
67#66890—24no—
68#66885—21no—
69#66882C2311yescharacteristic
70#66882C2311yescharacteristic
71#66880—21no—
72Dic11⋊C8D412yes—
73C8×Dic11C2312yes—
74C2×C11⋊C16C2312yes—
75#66873—22no—
76#66872—22no—
77C4⋊(C11⋊C8)D411yescharacteristic
78#66864—22no—
79#33928—111nomaximal, Sylow
80C2×Q8×C11—41no—
81C2×D4×C11—22no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C22×Dic11—42no—
85C2×D44—21no—
86C2×C4×D11—42no—
87C2×C4×D11—41no—
88C2×Dic22—21no—
89C2×Dic22D811yescharacteristic
90C11×D8—22no—
91C11×D8—22no—
92C11×D8—81no—
93C2×C8×C11C2×D411yescharacteristic
94C2×C8×C11C2411yescharacteristic
95C11×C4⋊C4—22no—
96C11×C4⋊C4—41no—
97C42×C11C2×D411yescharacteristic
98C22⋊Dic11—42no—
99C22⋊Dic11—42no—
100C22⋊Dic11—42no—
101#4324—82no—
102(C2×D11)⋊C4—42no—
103(C2×D11)⋊C4—41no—
104C4⋊Dic11—21no—
105C4⋊Dic11—21no—
106C4⋊Dic11—42no—
107C4⋊Dic11D811yescharacteristic
108Dic11⋊C4—42no—
109Dic11⋊C4—41no—
110Dic11⋊C4D812yes—
111C4×Dic11—41no—
112C4×Dic11C2×D412yes—
113C2×C11⋊C8C2×D412yes—
114Dic44—21no—
115Dic44—21no—
116D88—21no—
117D88#4112yes—
118C11×C16—21no—
119C11×C16—21no—
120C11⋊C16—22no—
121#3396—111no—
122#3380—111no—
123#2242—112no—
124#2240D1111yescharacteristic, complemented
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—161no—
135D4×C11—42no—
136D4×C11—42no—
137D4×C11—82no—
138D4×C11—161no—
139C2×C4×C11—42no—
140C2×C4×C11C2×D811yescharacteristic
141C2×C4×C11C2×D811yescharacteristic
142C2×C4×C11C22×D411yescharacteristic
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—162no—
147C2×Dic11C2×D812yes—
148C2×Dic11C2×D812yes—
149D44—22no—
150D44—41no—
151C4×D11—82no—
152C4×D11—162no—
153Dic22—22no—
154Dic22—41no—
155Dic22—41no—
156C8×C11—21no—
157C8×C11C2×#4111yescharacteristic
158C8×C112−1+411yescharacteristic
159C11⋊C8—22no—
160#559—221no—
161#554—221no—
162C2×SD32—111no—
163C2×D16—112no—
164#500C2×D1111yescharacteristic
165#499—112no—
166#495—112no—
167#493C2×D1111yescharacteristic
168#478—222no—
169#476—221no—
170#463—222no—
171#460—221no—
172C8×Q8—111no—
173C4×Q16—111no—
174C4×D8—112no—
175C4×D8—112no—
176C4×D8—111no—
177#367—111no—
178#366—112no—
179C4⋊C16—112no—
180C4⋊C16—111no—
181#358—111no—
182#358—112no—
183#357—112no—
184#357—111no—
185#357C2×D1112yes—
186#357C2×D1112yes—
187C4×C16—112no—
188C4×C16C2×D1111yescharacteristic
189C22×C11—82no—
190C22×C11—82no—
191C22×C11—82no—
192C22×C11C22×D811yescharacteristic
193C2×D11—42no—
194C2×D11—81no—
195C2×D11—81no—
196C4×C11—21no—
197C4×C11—82no—
198C4×C11#50812yes—
199C4×C11#54811yescharacteristic
200C4×C11#57711yescharacteristic
201Dic11—22no—
202Dic11—22no—
203Dic11—81no—
204Dic11—81no—
205Dic11—81no—
206C2×Q16—111no—
207C2×SD16—222no—
208C2×D8—21no—
209C2×D8—111no—
210C2×D8C22×D1112yes—
211C4⋊Q8—21no—
212#127—21no—
213#125—222no—
214#124—222no—
215#124—441no—
216#123—442no—
217C22⋊Q8—441no—
218C22⋊Q8—442no—
219C4×Q8—111no—
220C4×Q8—221no—
221C4×D4—222no—
222C4×D4—222no—
223C4×D4—221no—
224C4×D4—441no—
225C2×C4⋊C4—441no—
226SD32—222no—
227D16—224no—
228C2×C16—112no—
229C2×C16C22×D1111yescharacteristic
230C2×C16C22×D1111yescharacteristic
231#107—21no—
232#107—111no—
233#107—111no—
234#107C22×D1112yes—
235#106—222no—
236C4⋊C8—112no—
237C4⋊C8—111no—
238#103—221no—
239#102—222no—
240#102—222no—
241#102—221no—
242C4×C8—112no—
243C4×C8C22×D1111yescharacteristic
244C2×C11—162no—
245C2×C11#335811yescharacteristic
246C2×C11C2×#50811yescharacteristic
247C2×C11#341511yescharacteristic
248D11—82no—
249C2×Q8—41no—
250C2×Q8—111no—
251C2×Q8—221no—
252C2×D4—22no—
253C2×D4—41no—
254C2×D4—41no—
255C2×D4—221no—
256C22×C4—442no—
257C22×C4—442no—
258C22×C4—441no—
259Q16—221no—
260Q16—221no—
261SD16—882no—
262D8—22no—
263D8—22no—
264D8—81no—
265D8—112no—
266D8—221no—
267C2×C8—112no—
268C2×C8D4×D1111yescharacteristic
269C2×C8C23×D1111yescharacteristic
270C4⋊C4—22no—
271C4⋊C4—41no—
272C4⋊C4—111no—
273C4⋊C4—112no—
274C4⋊C4—221no—
275C4⋊C4—221no—
276C4⋊C4—442no—
277C4⋊C4—442no—
278C4⋊C4—441no—
279C22⋊C4—442no—
280C22⋊C4—442no—
281C22⋊C4—442no—
282C22⋊C4—442no—
283C22⋊C4—441no—
284C42—112no—
285C42—441no—
286C42D4×D1111yescharacteristic
287C16—21no—
288C16—21no—
289C16—222no—
290C11#3392811yescharacteristic, complemented, Sylow
291C23—42no—
292C23—441no—
293Q8—161no—
294Q8—222no—
295Q8—441no—
296Q8—441no—
297D4—42no—
298D4—42no—
299D4—82no—
300D4—161no—
301D4—222no—
302D4—441no—
303C2×C4—42no—
304C2×C4—112no—
305C2×C4—112no—
306C2×C4—441no—
307C2×C4—441no—
308C2×C4—441no—
309C2×C4—882no—
310C2×C4—1762no—
311C2×C4—1762no—
312C2×C4D8×D1111yescharacteristic
313C2×C4D8×D1111yescharacteristic
314C2×C4C2×D4×D1111yescharacteristic
315C8—21no—
316C8—222no—
317C8#41×D1111yescharacteristic
318C8#6704311yescharacteristic
319C22—82no—
320C22—82no—
321C22—82no—
322C22—442no—
323C22—881no—
324C22—881no—
325C22C2×D8×D1111yescharacteristic
326C4—21no—
327C4—82no—
328C4—222no—
329C4—222no—
330C4—881no—
331C4—881no—
332C4—881no—
333C4#1062252912yes—
334C4#1062320811yescharacteristic
335C4#1062329311yescharacteristic
336C2—162no—
337C2—882no—
338C2#1308124811yescharacteristic
339C2C2×#1062252911yescharacteristic
340C2#1308175311yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2240C2
socleC22×C11C22×D8
prime radical#13070648C2
hypercenter#2240D11
hypocenterC11#33928
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2240

Complements

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

NH ≅ G/Ntype
1. #13081630C2semidirect
2. #13081485C2semidirect
3. #13070846C2semidirect
4. #13070775C2semidirect
5. #13070765C2semidirect
6. #13070670C2semidirect
8. C16×Dic22C2semidirect
9. C4×#66864C2semidirect
10. #13070460C2semidirect
11. C11×#2240C2semidirect
124. #2240D11semidirect
290. C11#33928semidirect

Maximal subgroups

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

subgroupindex
#130816302
#130814852
#130708462
#130707752
#130707652
#130706702
#130706482
C16×Dic222
C4×#668642
#130704602
C11×#22402
#3392811