Finite Group Databasebeta

← #14656245

Subgroups — #14656245

Order 2816.

634 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 634 conjugacy classes of subgroups — too many to draw. Only its 103 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
1#13079926C211yesmaximal, characteristic, complemented
2#13078080C212yesmaximal, complemented
3#13067068C212yesmaximal, complemented
4#13066491C211yesmaximal, characteristic, complemented
5C11×#1954C211yesmaximal, characteristic, complemented
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66985—22no—
8#10623008C2212yes—
9C2×C11×C4⋊C8C2211yescharacteristic
10C2×C11×C22⋊C8—22no—
11C2×C4×C8×C11C2211yescharacteristic
12#10622728—22no—
13#10622632—22no—
14#10622629—24no—
15#10622628—22no—
16#10622579—22no—
17#10622537C2212yes—
18#10622459—22no—
19#10622456—22no—
20#10622097—24no—
21C22×D4×C11D411yescharacteristic
22C23×C4×C11—21no—
23C2×#4339—22no—
24C22×C8×C11—21no—
25C22×C8×C11D412yes—
26C4×D4×C11—22no—
27C4×D4×C11—22no—
28C2×C11×C4⋊C4D411yescharacteristic
29C2×C11×C22⋊C4—21no—
30C2×C42×C11C2311yescharacteristic
31C2×#4324—24no—
32#66985—44no—
33#66985—44no—
34C2×#4323—24no—
35#66983—22no—
36#66983—22no—
37C2×#4318—22no—
38C2×D88—22no—
39#66928—22no—
40#66927D412yes—
41C4×D44—22no—
42C4×D44—22no—
43#66922D412yes—
44C11×C4⋊C8—22no—
45C11×C22⋊C8—44no—
46C4×C8×C11—22no—
47#66885—24no—
48#66882—22no—
49#66874—24no—
50#66873—24no—
51C4⋊(C11⋊C8)—22no—
52C4⋊(C11⋊C8)D414yes—
53#10254—111nomaximal, Sylow
54C24×C11—21no—
55C2×D4×C11—22no—
56C2×D4×C11—21no—
57C2×D4×C11—22no—
58C2×D4×C11D812yescomplemented
59C22×C4×C11—21no—
60C22×C4×C11—42no—
61C22×C4×C11—42no—
62C22×C4×C11—41no—
63C22×C4×C11—41no—
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11#4111yescharacteristic
67C2×C22⋊D11—42no—
68#4339—42no—
69#4339—42no—
70#4339—42no—
71#4339—42no—
72C2×D44—22no—
73C2×D44—22no—
74C2×D44—22no—
75C2×C4×D11—42no—
76C2×Dic22—22no—
77C2×C8×C11—22no—
78C2×C8×C11—22no—
79C2×C8×C11—42no—
80C2×C8×C11—41no—
81C2×C8×C11—41no—
82C11×C4⋊C4—22no—
83C11×C22⋊C4—42no—
84C42×C11C2×D412yes—
85C42×C11C2×D412yes—
86#4324—48no—
87#4323—48no—
88(C2×D11)⋊C4—42no—
89(C2×D11)⋊C4—42no—
90C4⋊Dic11—22no—
91C4⋊Dic11—22no—
92#4318—42no—
93#4318—42no—
94C2×C11⋊C8—24no—
95D88—82no—
96#3245—111no—
97#3036—112no—
98#1954D1111yescharacteristic, complemented
99#1492—112no—
100#1292—111no—
101C23×C11—22no—
102C23×C11—42no—
103C23×C11—42no—
104C23×C11—41no—
105C23×C11—41no—
106C23×C11#12111yescharacteristic
107C22×D11—42no—
108D4×C11—24no—
109D4×C11—42no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—41no—
113C2×C4×C11—42no—
114C2×C4×C11—41no—
115C2×C4×C11—82no—
116C2×C4×C11—81no—
117C2×C4×C11—81no—
118C2×C4×C11#12012yes—
119C2×C4×C11#12011yescharacteristic
120C2×C4×C11#12112yes—
121C2×C4×C11#12711yescharacteristic
122C2×C4×C11C2×D811yescharacteristic
123C2×C4×C11#13511yescharacteristic
124C2×C4×C11AGL(1,ℤ/8)12yes—
125C22⋊D11—82no—
126C22⋊D11—82no—
127C2×Dic11—42no—
128D44—44no—
129D44—42no—
130D44—42no—
131D44—42no—
132D44—42no—
133C4×D11—82no—
134C4×D11—82no—
135Dic22—42no—
136Dic22—42no—
137C8×C11—42no—
138C8×C11—42no—
139C11⋊C8—44no—
140C2×AGL(1,ℤ/8)—222no—
141#532—112no—
142C2×C4×D4C2×D1111yescharacteristic
143#474—222no—
144#466—222no—
145#463—224no—
146#461—222no—
147#459—222no—
148#459—222no—
149#423—112no—
150C2×C4⋊C8C2×D1111yescharacteristic
151#417—222no—
152C2×C22⋊C8—22no—
153C2×C4×C8C2×D1111yescharacteristic
154D4⋊C8—224no—
155C22×C11—21no—
156C22×C11—21no—
157C22×C11—44no—
158C22×C11—42no—
159C22×C11—82no—
160C22×C11—81no—
161C22×C11—81no—
162C22×C11#39211yescharacteristic
163C22×C11#46611yescharacteristic
164C22×C11#46911yescharacteristic
165C2×D11—82no—
166C2×D11—82no—
167C2×D11—82no—
168C4×C11—21no—
169C4×C11—22no—
170C4×C11—81no—
171C4×C11#44712yes—
172C4×C11#44912yes—
173C4×C11#45311yescharacteristic
174C4×C11#45411yescharacteristic
175Dic11—82no—
176C2×#41—222no—
177C22×D4D4411yescharacteristic
178C23×C4—21no—
179AGL(1,ℤ/8)—444no—
180AGL(1,ℤ/8)—444no—
181C2×SD16—224no—
182C2×D8—222no—
183C2×D8—224no—
184C2×M16—222no—
185C22×C8—21no—
186C22×C8C22⋊D1112yes—
187C4⋊Q8—112no—
188#127—112no—
189#124—222no—
190#121—222no—
191#121—222no—
192C4×D4—22no—
193C4×D4—22no—
194C4×D4—222no—
195C4×D4—222no—
196C2×C4⋊C4D4411yescharacteristic
197C2×C22⋊C4—21no—
198C2×C42C22×D1111yescharacteristic
199#107—222no—
200C4⋊C8—22no—
201C4⋊C8—114no—
202C4⋊C8—222no—
203#103—224no—
204#102—224no—
205#102—224no—
206C22⋊C8—44no—
207C4×C8—22no—
208C2×C11—21no—
209C2×C11—21no—
210C2×C11—82no—
211C2×C11#199911yescharacteristic
212C2×C11#200611yescharacteristic
213C2×C11#201711yescharacteristic
214D11—162no—
215C24—21no—
216#41—442no—
217#41—442no—
218#41—442no—
219#41—442no—
220C2×Q8—222no—
221C2×D4—22no—
222C2×D4—21no—
223C2×D4—22no—
224C2×D4—222no—
225C2×D4—222no—
226C2×D4—222no—
227C2×D4—442no—
228C2×D4D8812yescomplemented
229C22×C4—21no—
230C22×C4—42no—
231C22×C4—42no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4—442no—
235C22×C4C2×D4411yescharacteristic
236C22×C4#433911yescharacteristic
237C22×C4C2×C22⋊D1111yescharacteristic
238SD16—448no—
239D8—448no—
240D8—882no—
241M16—442no—
242M16—442no—
243C2×C8—22no—
244C2×C8—22no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—42no—
248C2×C8—224no—
249C4⋊C4—22no—
250C4⋊C4—222no—
251C4⋊C4—222no—
252C22⋊C4—42no—
253C22⋊C4—442no—
254C22⋊C4—442no—
255C42D4×D1112yes—
256C42D4×D1112yes—
257C11#1025411yescharacteristic, complemented, Sylow
258C23—22no—
259C23—42no—
260C23—42no—
261C23—41no—
262C23—41no—
263C23—442no—
264C23#6698311yescharacteristic
265Q8—442no—
266Q8—442no—
267D4—24no—
268D4—42no—
269D4—444no—
270D4—442no—
271D4—442no—
272D4—442no—
273D4—442no—
274D4—882no—
275D4—882no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—41no—
281C2×C4—82no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—442no—
285C2×C4—882no—
286C2×C4—882no—
287C2×C4#6693512yes—
288C2×C4#6693712yes—
289C2×C4C2×D8811yescharacteristic
290C2×C4#6695711yescharacteristic
291C2×C4#6696112yes—
292C2×C4#6699011yescharacteristic
293C2×C4#6699311yescharacteristic
294C8—42no—
295C8—42no—
296C8—444no—
297C22—21no—
298C22—21no—
299C22—44no—
300C22—42no—
301C22—82no—
302C22—81no—
303C22—81no—
304C22—882no—
305C22—882no—
306C22—882no—
307C22#1062257311yescharacteristic
308C22#1062272811yescharacteristic
309C22#1062274811yescharacteristic
310C4—21no—
311C4—22no—
312C4—81no—
313C4—882no—
314C4#1062234512yes—
315C4#1062234712yes—
316C4#1062267511yescharacteristic
317C4#1062269011yescharacteristic
318C2—21no—
319C2—21no—
320C2—82no—
321C2—1762no—
322C2#1306961411yescharacteristic
323C2#1306965711yescharacteristic
324C2#1306972011yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1954C2
socleC22×C11#392
hypercenter#1954D11
hypocenterC11#10254
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1954

Complements

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

NH ≅ G/Ntype
1. #13079926C2semidirect
2. #13078080C2semidirect
3. #13067068C2semidirect
4. #13066491C2semidirect
5. C11×#1954C2semidirect
58. C2×D4×C11D8semidirect
98. #1954D11semidirect
228. C2×D4D88semidirect
257. C11#10254semidirect

Maximal subgroups

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

subgroupindex
#130799262
#130780802
#130670682
#130664912
C11×#19542
#1025411