Finite Group Databasebeta

← #14673161

Subgroups — #14673161

Order 2816.

456 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 97 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×#10622309C211yesmaximal, characteristic
2C2×#10622155C211yesmaximal, characteristic, complemented
3C2×#10622154C211yesmaximal, characteristic
4#13070337C211yesmaximal, characteristic, complemented
5#13070333C211yesmaximal, characteristic
6#13069364C211yesmaximal, characteristic, complemented
7C11×#1376C211yesmaximal, characteristic, complemented
8C22×Dic44C2211yescharacteristic
9C22×D88C2211yescharacteristic
10C22×#4314—21no—
11C2×#66928—21no—
12C2×C11×M32C2211yescharacteristic
13C2×C11×M32C2211yescharacteristic
14C2×C4×C8×C11C2211yescharacteristic
15C2×#66883C2211yescharacteristic
16#10622719C2211yescharacteristic
17#10622715—21no—
18#10622309—22no—
19#10622309—22no—
20#10622161—21no—
21#10622155—22no—
22#10622154—22no—
23#10622147—22no—
24#10622141—22no—
25C22×D44—21no—
26C22×Dic22—21no—
27C22×C8×C11D411yescharacteristic
28C22×C8×C11C2311yescharacteristic
29C2×C42×C11D411yescharacteristic
30C2×(C2×D11)⋊C4—42no—
31#66979—21no—
32C2×#4318—21no—
33C2×Dic44—21no—
34C2×Dic44—21no—
35C2×Dic44—21no—
36C2×Dic44—21no—
37C2×Dic44—21no—
38C2×Dic44D412yes—
39C2×D88—21no—
40C2×D88—21no—
41C2×D88—21no—
42C2×D88—21no—
43C2×D88—21no—
44C2×D88D412yes—
45C2×#4314—24no—
46C2×#4314—42no—
47C2×#4314—42no—
48#66928—24no—
49#66928—42no—
50C11×M32—21no—
51C11×M32—21no—
52C11×M32—21no—
53C11×M32—21no—
54C2×C11×C16—21no—
55C2×C11×C16—21no—
56C4×C8×C11—21no—
57C4×C8×C11—21no—
58#66883—21no—
59#66883—21no—
60#66882D412yes—
61#66881—21no—
62Dic11⋊C8—42no—
63#13414—111nomaximal, Sylow
64C23×D11—41no—
65C22×C4×C11—21no—
66C22×C4×C11C2×D411yescharacteristic
67C22×Dic11—41no—
68C2×D44—22no—
69C2×D44—41no—
70C2×D44—41no—
71C2×D44—41no—
72C2×D44—41no—
73C2×D44—41no—
74C2×Dic22—22no—
75C2×Dic22—41no—
76C2×Dic22—41no—
77C2×Dic22—41no—
78C2×Dic22—41no—
79C2×Dic22—41no—
80C2×C8×C11—21no—
81C2×C8×C11—21no—
82C2×C8×C11D812yes—
83C2×C8×C11C2×D411yescharacteristic
84C2×C8×C11C2×D411yescharacteristic
85C2×C8×C11C2×D411yescharacteristic
86C2×C8×C11#4111yescharacteristic
87C2×C8×C11#4111yescharacteristic
88C2×C8×C11#4111yescharacteristic
89C42×C11—21no—
90C42×C11SD1612yes—
91C22⋊Dic11—41no—
92(C2×D11)⋊C4—48no—
93C4⋊Dic11—22no—
94C4×Dic11—41no—
95#4318—41no—
96#4318—41no—
97C2×C11⋊C8—41no—
98Dic44—22no—
99Dic44—22no—
100Dic44—41no—
101Dic44—41no—
102D88—22no—
103D88—22no—
104D88—41no—
105D88—41no—
106#4314—48no—
107C11×C16—41no—
108C11×C16—41no—
109C2×#495—111no—
110C2×#362—111no—
111C2×#361—111no—
112#2141—111no—
113#2140—111no—
114#1945—111no—
115#1376D1111yescharacteristic, complemented
116C23×C11AGL(1,ℤ/8)11yescharacteristic
117C22×D11—42no—
118C22×D11—84no—
119C22×D11—81no—
120C22×D11—81no—
121C2×C4×C11—22no—
122C2×C4×C11—42no—
123C2×C4×C11#12011yescharacteristic
124C2×C4×C11#12111yescharacteristic
125C2×C4×C11#12411yescharacteristic
126C2×C4×C11C2×D811yescharacteristic
127C2×C4×C11C2×SD1611yescharacteristic
128C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
129C2×Dic11—42no—
130C2×Dic11—42no—
131C2×Dic11—81no—
132C2×Dic11—81no—
133D44—42no—
134D44—42no—
135D44—81no—
136D44—81no—
137Dic22—42no—
138Dic22—42no—
139Dic22—81no—
140Dic22—81no—
141C8×C11—22no—
142C8×C11#12111yescharacteristic
143C8×C11#12111yescharacteristic
144C8×C11#12311yescharacteristic
145C8×C11#12311yescharacteristic
146C11⋊C8—81no—
147C22×Q16—111no—
148C22×SD16—221no—
149C22×D8—111no—
150C2×#124—221no—
151C2×M32C2×D1111yescharacteristic
152C2×M32C2×D1111yescharacteristic
153#495—222no—
154#495—222no—
155C2×#108—111no—
156#427—111no—
157#424—221no—
158C2×C4×C8C2×D1111yescharacteristic
159#362—222no—
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—42no—
173C4×C11#39411yescharacteristic
174C4×C11#44711yescharacteristic
175C4×C11#46011yescharacteristic
176C4×C11#48611yescharacteristic
177Dic11—82no—
178Dic11—82no—
179C22×Q8—221no—
180C22×D4—221no—
181C2×Q16—112no—
182C2×Q16—221no—
183C2×Q16—221no—
184C2×Q16—221no—
185C2×Q16—221no—
186C2×Q16—221no—
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—221no—
197C22×C8D4411yescharacteristic
198C22×C8C22×D1111yescharacteristic
199#124—224no—
200#124—442no—
201#117—221no—
202C2×C22⋊C4—442no—
203C2×C42D4411yescharacteristic
204M32—21no—
205M32—21no—
206M32—21no—
207M32—21no—
208C2×C16—21no—
209C2×C16—21no—
210#108—221no—
211#108—221no—
212#107—112no—
213#106—221no—
214C4⋊C8—442no—
215C4×C8—21no—
216C4×C8—21no—
217C2×C11—21no—
218C2×C11—21no—
219C2×C11#204111yescharacteristic
220C2×C11#221212yes—
221D11—162no—
222C24—441no—
223C2×Q8—222no—
224C2×Q8—441no—
225C2×Q8—441no—
226C2×Q8—441no—
227C2×Q8—441no—
228C2×Q8—441no—
229C2×D4—222no—
230C2×D4—441no—
231C2×D4—441no—
232C2×D4—441no—
233C2×D4—441no—
234C2×D4—441no—
235C22×C4—21no—
236C22×C4—441no—
237C22×C4C2×D4411yescharacteristic
238Q16—222no—
239Q16—222no—
240Q16—441no—
241Q16—441no—
242SD16—448no—
243D8—222no—
244D8—222no—
245D8—441no—
246D8—441no—
247M16—441no—
248M16—441no—
249C2×C8—21no—
250C2×C8—21no—
251C2×C8—441no—
252C2×C8D8812yes—
253C2×C8#433911yescharacteristic
254C2×C8#433911yescharacteristic
255C2×C8D4×D1111yescharacteristic
256C2×C8D4×D1111yescharacteristic
257C2×C8D4×D1111yescharacteristic
258C2×C8#434311yescharacteristic
259C4⋊C4—222no—
260C22⋊C4—448no—
261C22⋊C4—441no—
262C42—21no—
263C42—441no—
264C42#431412yes—
265C16—41no—
266C16—41no—
267C11#1341411yescharacteristic, complemented, Sylow
268C23—442no—
269C23—884no—
270C23—881no—
271C23—881no—
272C23#6696111yescharacteristic
273Q8—442no—
274Q8—442no—
275Q8—881no—
276Q8—881no—
277D4—442no—
278D4—442no—
279D4—881no—
280D4—881no—
281C2×C4—22no—
282C2×C4—42no—
283C2×C4—442no—
284C2×C4—442no—
285C2×C4—881no—
286C2×C4—881no—
287C2×C4#6692811yescharacteristic
288C2×C4#6693511yescharacteristic
289C2×C4#6694811yescharacteristic
290C2×C4C2×#431411yescharacteristic
291C2×C4C2×D8811yescharacteristic
292C2×C4#6696111yescharacteristic
293C8—22no—
294C8—881no—
295C8#6693711yescharacteristic
296C8#6693711yescharacteristic
297C8#6694711yescharacteristic
298C8#6694711yescharacteristic
299C22—22no—
300C22—884no—
301C22—882no—
302C22—1762no—
303C22—1762no—
304C22#1062232611yescharacteristic
305C22#1062234411yescharacteristic
306C22#1062245611yescharacteristic
307C4—42no—
308C4—882no—
309C4—882no—
310C4#1062228511yescharacteristic
311C4#1062230711yescharacteristic
312C4#1062234511yescharacteristic
313C4#1062246111yescharacteristic
314C2—21no—
315C2—21no—
316C2—1762no—
317C2#1306985111yescharacteristic
318C2#1307068612yes—
subgroupG/H
centerC22#10622456
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#1376C2
socleC22×C11#459
prime radicalC22×D88C22
hypercenter#1376D11
hypocenterC11#13414
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8 ◁ #1376

Complements

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

NH ≅ G/Ntype
2. C2×#10622155C2semidirect
4. #13070337C2semidirect
6. #13069364C2semidirect
7. C11×#1376C2semidirect
115. #1376D11semidirect
267. C11#13414semidirect

Maximal subgroups

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

subgroupindex
C2×#106223092
C2×#106221552
C2×#106221542
#130703372
#130703332
#130693642
C11×#13762
#1341411