Finite Group Databasebeta

← #14656279

Subgroups — #14656279

Order 2816.

794 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 794 conjugacy classes of subgroups — too many to draw. Only its 139 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×#10622308C211yesmaximal, characteristic, complemented
2C2×#10622628C212yesmaximal, complemented
3C2×#10622123C212yesmaximal, complemented
4#13066451C211yesmaximal, characteristic, complemented
5C11×#1954C211yesmaximal, characteristic, complemented
6C2×C4×D4×C11C2211yescharacteristic
7C22×#4323—22no—
8C22×D88—22no—
9C2×#66927C2212yes—
10C2×C11×C4⋊C8C2211yescharacteristic
11C2×C11×C22⋊C8—22no—
12C2×C4×C8×C11C2211yescharacteristic
13#10622628—24no—
14#10622628—24no—
15C2×#66873—22no—
16C2×C4⋊(C11⋊C8)C2212yes—
17#10622308—24no—
18#10622123—24no—
19C22×D4×C11D411yescharacteristic
20C23×C4×C11—21no—
21C22×D44—22no—
22C22×D44—22no—
23C22×D44—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×#4323—28no—
32C2×#4323—44no—
33C2×#4323—44no—
34C22×C11⋊C8—22no—
35C2×D88—28no—
36C2×D88—44no—
37C2×D88—44no—
38#66927—22no—
39#66927—22no—
40#66927—22no—
41#66927D414yes—
42C11×C4⋊C8—22no—
43C11×C22⋊C8—44no—
44C4×C8×C11—22no—
45#66873—28no—
46C4⋊(C11⋊C8)—22no—
47C4⋊(C11⋊C8)D414yes—
48#10260—111nomaximal, Sylow
49C24×C11—21no—
50C23×D11—42no—
51C2×D4×C11—22no—
52C2×D4×C11—21no—
53C2×D4×C11—22no—
54C2×D4×C11D812yescomplemented
55C22×C4×C11—21no—
56C22×C4×C11—41no—
57C22×C4×C11—41no—
58C22×C4×C11—42no—
59C22×C4×C11—42no—
60C22×C4×C11C2×D411yescharacteristic
61C22×C4×C11C2×D411yescharacteristic
62C22×C4×C11#4111yescharacteristic
63C2×D44—24no—
64C2×D44—24no—
65C2×D44—24no—
66C2×D44—42no—
67C2×D44—42no—
68C2×D44—42no—
69C2×D44—44no—
70C2×D44—42no—
71C2×D44—42no—
72C2×D44—44no—
73C2×D44—42no—
74C2×D44—42no—
75C2×D44—84no—
76C2×C8×C11—22no—
77C2×C8×C11—22no—
78C2×C8×C11—41no—
79C2×C8×C11—42no—
80C2×C8×C11D814yescomplemented
81C11×C4⋊C4—22no—
82C11×C22⋊C4—42no—
83C42×C11C2×D412yes—
84C42×C11C2×D412yes—
85#4323—416no—
86C2×C11⋊C8—24no—
87C2×C11⋊C8—42no—
88C2×C11⋊C8—42no—
89D88—416no—
90C2×#493—111no—
91C2×#459—112no—
92#1954D1111yescharacteristic, complemented
93C2×#331—112no—
94#1277—111no—
95C23×C11—22no—
96C23×C11—41no—
97C23×C11—42no—
98C23×C11—41no—
99C23×C11—42no—
100C23×C11#12111yescharacteristic
101C22×D11—44no—
102C22×D11—84no—
103C22×D11—82no—
104C22×D11—82no—
105C22×D11—84no—
106D4×C11—24no—
107D4×C11—42no—
108C2×C4×C11—22no—
109C2×C4×C11—41no—
110C2×C4×C11—42no—
111C2×C4×C11—82no—
112C2×C4×C11—81no—
113C2×C4×C11—81no—
114C2×C4×C11#12012yes—
115C2×C4×C11#12011yescharacteristic
116C2×C4×C11#12112yes—
117C2×C4×C11#12711yescharacteristic
118C2×C4×C11C2×D811yescharacteristic
119C2×C4×C11C2×D812yes—
120C2×C4×C11#13511yescharacteristic
121C2×C4×C11AGL(1,ℤ/8)12yes—
122C2×C4×C11AGL(1,ℤ/8)12yes—
123D44—48no—
124D44—44no—
125D44—44no—
126D44—84no—
127D44—84no—
128D44—82no—
129D44—82no—
130D44—82no—
131D44—82no—
132C8×C11—24no—
133C8×C11—81no—
134C11⋊C8—44no—
135C22×D8—222no—
136C22×D8—222no—
137C2×#127—112no—
138C2×C4×D4C2×D1111yescharacteristic
139#493—224no—
140#459—224no—
141#459—224no—
142C2×C4⋊C8—112no—
143C2×C4⋊C8C2×D1111yescharacteristic
144C2×#102—222no—
145C2×C22⋊C8—22no—
146C2×C4×C8C2×D1111yescharacteristic
147#331—224no—
148C22×C11—44no—
149C22×C11—42no—
150C22×C11—82no—
151C22×C11—81no—
152C22×C11—81no—
153C22×C11#39211yescharacteristic
154C22×C11#45912yes—
155C22×C11#46611yescharacteristic
156C22×C11#46911yescharacteristic
157C22×C11#47212yes—
158C2×D11—84no—
159C2×D11—84no—
160C2×D11—84no—
161C2×D11—164no—
162C2×D11—164no—
163C4×C11—22no—
164C4×C11—81no—
165C4×C11#44712yes—
166C4×C11#44712yes—
167C4×C11#44912yes—
168C4×C11#49311yescharacteristic
169C4×C11#49611yescharacteristic
170C22×D4—222no—
171C22×D4—222no—
172C22×D4—222no—
173C22×D4D4411yescharacteristic
174C23×C4—21no—
175C2×D8—228no—
176C2×D8—228no—
177C2×D8—444no—
178C2×D8—444no—
179C2×D8—444no—
180C2×D8—444no—
181C22×C8—21no—
182C22×C8—222no—
183C22×C8C22⋊D1112yes—
184#127—114no—
185#127—222no—
186#127—222no—
187#127—222no—
188C4×D4—22no—
189C4×D4—22no—
190C2×C4⋊C4D4411yescharacteristic
191C2×C22⋊C4—21no—
192C2×C42C22×D1111yescharacteristic
193C4⋊C8—22no—
194C4⋊C8—114no—
195C4⋊C8—222no—
196#102—228no—
197C22⋊C8—44no—
198C4×C8—22no—
199C2×C11—82no—
200C2×C11#166712yes—
201C2×C11#168712yes—
202C2×C11#199911yescharacteristic
203C2×C11#201111yescharacteristic
204C2×C11#201811yescharacteristic
205D11—164no—
206C24—21no—
207C24—442no—
208C2×D4—22no—
209C2×D4—21no—
210C2×D4—22no—
211C2×D4—224no—
212C2×D4—224no—
213C2×D4—224no—
214C2×D4—442no—
215C2×D4—442no—
216C2×D4—442no—
217C2×D4—442no—
218C2×D4—442no—
219C2×D4—442no—
220C2×D4—444no—
221C2×D4—442no—
222C2×D4—444no—
223C2×D4—884no—
224C2×D4D8812yescomplemented
225C22×C4—21no—
226C22×C4—42no—
227C22×C4—41no—
228C22×C4—41no—
229C22×C4—42no—
230C22×C4C2×D4411yescharacteristic
231C22×C4#433911yescharacteristic
232C22×C4C2×C22⋊D1111yescharacteristic
233D8—4416no—
234D8—4416no—
235C2×C8—22no—
236C2×C8—22no—
237C2×C8—42no—
238C2×C8—41no—
239C2×C8—224no—
240C2×C8—442no—
241C2×C8—442no—
242C2×C8#432314yescomplemented
243C4⋊C4—22no—
244C22⋊C4—42no—
245C42D4×D1112yes—
246C42D4×D1112yes—
247C11#1026011yescharacteristic, complemented, Sylow
248C23—22no—
249C23—41no—
250C23—42no—
251C23—41no—
252C23—42no—
253C23—444no—
254C23—882no—
255C23—882no—
256C23—884no—
257C23—884no—
258C23#6698311yescharacteristic
259D4—24no—
260D4—42no—
261D4—444no—
262D4—444no—
263D4—448no—
264D4—884no—
265D4—884no—
266D4—882no—
267D4—882no—
268D4—882no—
269D4—882no—
270C2×C4—22no—
271C2×C4—41no—
272C2×C4—42no—
273C2×C4—82no—
274C2×C4—81no—
275C2×C4—81no—
276C2×C4#6693512yes—
277C2×C4#6693712yes—
278C2×C4C2×D8811yescharacteristic
279C2×C4#6695711yescharacteristic
280C2×C4#6696112yes—
281C2×C4C2×#432312yes—
282C2×C4#6699011yescharacteristic
283C2×C4#6699311yescharacteristic
284C2×C4#6700212yes—
285C8—24no—
286C8—81no—
287C8—444no—
288C22—42no—
289C22—44no—
290C22—82no—
291C22—81no—
292C22—81no—
293C22—884no—
294C22—884no—
295C22—884no—
296C22—1764no—
297C22—1764no—
298C22#1062257311yescharacteristic
299C22#1062262812yes—
300C22#1062272811yescharacteristic
301C22#1062274811yescharacteristic
302C22#1062275512yes—
303C4—22no—
304C4—81no—
305C4#1062234512yes—
306C4#1062234712yes—
307C4#1062264912yes—
308C4#1062267111yescharacteristic
309C4#1062268611yescharacteristic
310C2—82no—
311C2—1764no—
312C2#1306797112yes—
313C2#1306809512yes—
314C2#1306961411yescharacteristic
315C2#1306968611yescharacteristic
316C2#1306972511yescharacteristic
subgroupG/H
centerC23#66983
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1954C2
socleC23×C11#121
hypercenter#1954D11
hypocenterC11#10260
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1954

Complements

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

NH ≅ G/Ntype
1. C2×#10622308C2semidirect
2. C2×#10622628C2semidirect
3. C2×#10622123C2semidirect
4. #13066451C2semidirect
5. C11×#1954C2semidirect
54. C2×D4×C11D8semidirect
80. C2×C8×C11D8semidirect
92. #1954D11semidirect
224. C2×D4D88semidirect
242. C2×C8#4323semidirect
247. C11#10260semidirect

Maximal subgroups

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

subgroupindex
C2×#106223082
C2×#106226282
C2×#106221232
#130664512
C11×#19542
#1026011