Finite Group Databasebeta

← #14673156

Subgroups — #14673156

Order 2816.

456 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622804C211yesmaximal, characteristic
2C2×#10622133C211yesmaximal, characteristic
3#13070336C211yesmaximal, characteristic, complemented
4#13070333C211yesmaximal, characteristic
5#13069362C211yesmaximal, characteristic, complemented
6#13066697C211yesmaximal, characteristic, complemented
7C2×C11×#362C211yesmaximal, characteristic, complemented
8C22×C11×Q16C2211yescharacteristic
9C2×#67000—21no—
10C22×#4325—21no—
11C22×D88C2211yescharacteristic
12C2×C11×M32C2211yescharacteristic
13C2×C11×#108C2211yescharacteristic
14#10622804—22no—
15#10622804—22no—
16#10622732—21no—
17#10622719C2211yescharacteristic
18C2×C8×Dic11C2211yescharacteristic
19C2×#66876C2211yescharacteristic
20C11×#362—22no—
21#10622202—22no—
22#10622193—21no—
23#10622147—22no—
24#10622133—22no—
25C22×Q8×C11—21no—
26C22×D44—21no—
27C2×C11×Q16—21no—
28C2×C11×Q16—21no—
29C2×C11×Q16—21no—
30C2×C11×Q16—21no—
31C2×C11×Q16—21no—
32C2×C11×Q16D412yes—
33C2×C11×M16—21no—
34C22×C8×C11C2311yescharacteristic
35#67000—24no—
36#67000—42no—
37C2×#4325—24no—
38C2×#4325—42no—
39C2×#4325—42no—
40C2×(C2×D11)⋊C4—42no—
41#66979—21no—
42C2×C4×Dic11D411yescharacteristic
43C22×C11⋊C8D411yescharacteristic
44C2×D88—21no—
45C2×D88—21no—
46C2×D88—21no—
47C2×D88—21no—
48C2×D88—21no—
49C2×D88D412yes—
50C11×M32—21no—
51C11×M32—21no—
52C2×C11×C16—21no—
53C11×#108—21no—
54C11×#108—21no—
55#66882D412yes—
56#66881—21no—
57Dic11⋊C8—42no—
58C8×Dic11—21no—
59C8×Dic11—21no—
60#66876—21no—
61#66876—21no—
62C2×C11⋊C16—21no—
63#13414—111nomaximal, Sylow
64C23×D11—41no—
65C2×Q8×C11—22no—
66C2×Q8×C11—41no—
67C2×Q8×C11—41no—
68C2×Q8×C11—41no—
69C2×Q8×C11—41no—
70C2×Q8×C11—41no—
71C22×C4×C11—41no—
72C22×C4×C11C2×D411yescharacteristic
73C22×Dic11—21no—
74C2×D44—22no—
75C2×D44—41no—
76C2×D44—41no—
77C2×D44—41no—
78C2×D44—41no—
79C2×D44—41no—
80C11×Q16—22no—
81C11×Q16—22no—
82C11×Q16—41no—
83C11×Q16—41no—
84C11×M16—41no—
85C11×M16—41no—
86C2×C8×C11—41no—
87C2×C8×C11C2×D411yescharacteristic
88C2×C8×C11C2×D411yescharacteristic
89C2×C8×C11C2×D411yescharacteristic
90C2×C8×C11#4111yescharacteristic
91C2×C8×C11#4111yescharacteristic
92C2×C8×C11#4111yescharacteristic
93C22⋊Dic11—41no—
94#4325—48no—
95(C2×D11)⋊C4—48no—
96C4⋊Dic11—22no—
97C4×Dic11—21no—
98C4×Dic11—41no—
99C4×Dic11SD1612yes—
100C2×C11⋊C8—21no—
101C2×C11⋊C8—21no—
102C2×C11⋊C8D812yes—
103D88—22no—
104D88—22no—
105D88—41no—
106D88—41no—
107C11×C16—41no—
108C11⋊C16—41no—
109C2×#495—111no—
110C2×#362D1111yescharacteristic, complemented
111C2×#361—111no—
112#2141—111no—
113#2140—111no—
114#1945—111no—
115#1376—111no—
116C23×C11AGL(1,ℤ/8)11yescharacteristic
117C22×D11—42no—
118C22×D11—84no—
119C22×D11—81no—
120C22×D11—81no—
121Q8×C11—42no—
122Q8×C11—42no—
123Q8×C11—81no—
124Q8×C11—81no—
125C2×C4×C11—42no—
126C2×C4×C11—81no—
127C2×C4×C11—81no—
128C2×C4×C11#12011yescharacteristic
129C2×C4×C11#12111yescharacteristic
130C2×C4×C11#12411yescharacteristic
131C2×C4×C11C2×D811yescharacteristic
132C2×C4×C11C2×SD1611yescharacteristic
133C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
134C2×Dic11—22no—
135C2×Dic11—42no—
136C2×Dic11—42no—
137D44—42no—
138D44—42no—
139D44—81no—
140D44—81no—
141C8×C11—81no—
142C8×C11#12111yescharacteristic
143C8×C11#12111yescharacteristic
144C8×C11#12311yescharacteristic
145C8×C11#12311yescharacteristic
146C11⋊C8—22no—
147C22×Q16C2×D1111yescharacteristic
148C22×SD16—221no—
149C22×D8—111no—
150C2×#124—221no—
151C2×M32—111no—
152C2×M32C2×D1111yescharacteristic
153#495—222no—
154#495—222no—
155C2×#108C2×D1111yescharacteristic
156#427—111no—
157#424—221no—
158C2×C4×C8—111no—
159#362—22no—
160#361—222no—
161#358—222no—
162#357—222no—
163#339—221no—
164C22×C11—22no—
165C22×C11#45011yescharacteristic
166C22×C11#45911yescharacteristic
167C22×C11#49011yescharacteristic
168C2×D11—84no—
169C2×D11—82no—
170C2×D11—162no—
171C2×D11—162no—
172C4×C11—82no—
173C4×C11#39411yescharacteristic
174C4×C11#44711yescharacteristic
175C4×C11#46011yescharacteristic
176C4×C11#48611yescharacteristic
177Dic11—42no—
178Dic11—82no—
179C22×Q8—21no—
180C22×D4—221no—
181C2×Q16—21no—
182C2×Q16—21no—
183C2×Q16—21no—
184C2×Q16—21no—
185C2×Q16—21no—
186C2×Q16C22⋊D1112yes—
187C2×SD16—224no—
188C2×SD16—442no—
189C2×SD16—442no—
190C2×D8—112no—
191C2×D8—221no—
192C2×D8—221no—
193C2×D8—221no—
194C2×D8—221no—
195C2×D8—221no—
196C2×M16—21no—
197C22×C8—111no—
198C22×C8C22×D1111yescharacteristic
199#124—224no—
200#124—442no—
201#117—221no—
202C2×C22⋊C4—442no—
203C2×C42—111no—
204M32—21no—
205M32—21no—
206M32—221no—
207M32—221no—
208C2×C16—21no—
209C2×C16—221no—
210#108—21no—
211#108—21no—
212#107—112no—
213#106—221no—
214C4⋊C8—442no—
215C4×C8—221no—
216C4×C8—221no—
217C2×C11—21no—
218C2×C11—21no—
219C2×C11#204111yescharacteristic
220C2×C11#221212yes—
221D11—162no—
222C24—441no—
223C2×Q8—22no—
224C2×Q8—41no—
225C2×Q8—41no—
226C2×Q8—41no—
227C2×Q8—41no—
228C2×Q8—41no—
229C2×D4—222no—
230C2×D4—441no—
231C2×D4—441no—
232C2×D4—441no—
233C2×D4—441no—
234C2×D4—441no—
235C22×C4—41no—
236C22×C4—221no—
237C22×C4D4×D1111yescharacteristic
238Q16—22no—
239Q16—22no—
240Q16—41no—
241Q16—41no—
242SD16—448no—
243D8—222no—
244D8—222no—
245D8—441no—
246D8—441no—
247M16—41no—
248M16—41no—
249C2×C8—41no—
250C2×C8—112no—
251C2×C8—221no—
252C2×C8—221no—
253C2×C8#433911yescharacteristic
254C2×C8#433911yescharacteristic
255C2×C8D4×D1111yescharacteristic
256C2×C8D4×D1111yescharacteristic
257C2×C8#434111yescharacteristic
258C2×C8C2×C22⋊D1111yescharacteristic
259C4⋊C4—222no—
260C22⋊C4—448no—
261C22⋊C4—441no—
262C42—112no—
263C42—221no—
264C42—441no—
265C16—41no—
266C16—441no—
267C11#1341411yescharacteristic, complemented, Sylow
268C23—442no—
269C23—884no—
270C23—881no—
271C23—881no—
272C23#6696711yescharacteristic
273Q8—42no—
274Q8—42no—
275Q8—81no—
276Q8—81no—
277D4—442no—
278D4—442no—
279D4—881no—
280D4—881no—
281C2×C4—42no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—222no—
285C2×C4—442no—
286C2×C4—442no—
287C2×C4#6693711yescharacteristic
288C2×C4#6693811yescharacteristic
289C2×C4D8×D1111yescharacteristic
290C2×C4#6696411yescharacteristic
291C2×C4SD16×D1111yescharacteristic
292C2×C4#6699011yescharacteristic
293C8—81no—
294C8—222no—
295C8#6693611yescharacteristic
296C8#6693711yescharacteristic
297C8#6698211yescharacteristic
298C8#6699211yescharacteristic
299C22—22no—
300C22—884no—
301C22—882no—
302C22—1762no—
303C22—1762no—
304C22#1062237711yescharacteristic
305C22#1062239911yescharacteristic
306C22#1062278211yescharacteristic
307C4—82no—
308C4—442no—
309C4—882no—
310C4#1062237311yescharacteristic
311C4#1062237511yescharacteristic
312C4#1062257211yescharacteristic
313C4#1062276911yescharacteristic
314C2—21no—
315C2—21no—
316C2—1762no—
317C2#1306984811yescharacteristic
318C2#1307068812yes—
subgroupG/H
centerC22#10622399
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC2×C11×#362C2
socleC22×C11#459
prime radicalC22×D88C22
hypercenterC2×#362D11
hypocenterC11#13414
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#362

Complements

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

NH ≅ G/Ntype
3. #13070336C2semidirect
5. #13069362C2semidirect
6. #13066697C2semidirect
7. C2×C11×#362C2semidirect
110. C2×#362D11semidirect
267. C11#13414semidirect

Maximal subgroups

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

subgroupindex
C2×#106228042
C2×#106221332
#130703362
#130703332
#130693622
#130666972
C2×C11×#3622
#1341411