Finite Group Databasebeta

← #27169633

Subgroups — #27169633

Order 12928.

334 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 65 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#20265687C211yesmaximal, characteristic
2#20265139C211yesmaximal, characteristic, complemented
3#95×D101C211yesmaximal, characteristic, complemented
4#20264915C211yesmaximal, characteristic, complemented
5#20264913C211yesmaximal, characteristic, complemented
6#20264911C211yesmaximal, characteristic, complemented
7#327×C101C211yesmaximal, characteristic, complemented
8C2×#13108073C411yescharacteristic, complemented
9C22×C4×D101—21no—
10C22×C4×D101C2211yescharacteristic
11C2×#13108057—21no—
12#15692237—21no—
13#15692235C411yescharacteristic, complemented
14#15692234C2211yescharacteristic
15#15692226C411yescharacteristic, complemented
16#15692223—21no—
17D4×Dic101—21no—
18#15692215—21no—
19#15692213C411yescharacteristic, complemented
20C22⋊#11717579C2211yescharacteristic
21#15692167—21no—
22#15692162—21no—
23#15692162C2211yescharacteristic
24#121×C101C2211yescharacteristic
25C22⋊C8×C101C2211yescharacteristic
26#95×C101C2211yescharacteristic
27C23×D101D411yescharacteristic
28#13108073—42no—
29C2×Dic202C2×C411yescharacteristic, complemented
30C2×C22⋊D101—21no—
31C2×C22⋊D101—21no—
32C22×Dic101—21no—
33C22×Dic101—21no—
34C22×Dic101D411yescharacteristic
35C2×C4×D101—24no—
36C2×C4×D101—42no—
37C2×C4×D101—42no—
38C2×C4×D101—42no—
39C2×C4×D101C2×C411yescharacteristic
40C2×C4×D101C2×C411yescharacteristic
41C2×C4×D101D411yescharacteristic
42C2×C4×D101D411yescharacteristic
43#13108057—42no—
44C2×#11717579—21no—
45C4⋊Dic101—21no—
46C4⋊Dic101C2×C411yescharacteristic, complemented
47#13108053—21no—
48C22⋊Dic101—21no—
49C22⋊Dic101—21no—
50#13108051—21no—
51#13108051—21no—
52C4×Dic101—21no—
53C2×D4×C101—21no—
54C2×D4×C101C2×C411yescharacteristic, complemented
55C22×C4×C101—21no—
56C22×C4×C101C2311yescharacteristic
57C2×C8×C101—21no—
58C4⋊C4×C101C2×C411yescharacteristic, complemented
59C22⋊C4×C101—21no—
60C23×C101—21no—
61C23×C101C2×D411yescharacteristic
62C22×D101—21no—
63C22×D101—21no—
64C22×D101—22no—
65C22×D101—22no—
66C22×D101C22⋊C411yescharacteristic
67C22×D101C22⋊C411yescharacteristic
68D4×C101—41no—
69D4×C101—41no—
70D4×C101—41no—
71C2×C4×C101—22no—
72C2×C4×C101—21no—
73C2×C4×C101—41no—
74C2×C4×C101—41no—
75C2×C4×C101—41no—
76C2×C4×C101C22×C411yescharacteristic
77C2×C4×C101C2×D411yescharacteristic
78C22⋊D101—42no—
79C22⋊D101—42no—
80C2×Dic101—22no—
81C2×Dic101—21no—
82C2×Dic101—21no—
83C2×Dic101—41no—
84C2×Dic101—42no—
85C2×Dic101—41no—
86C2×Dic101—41no—
87C2×Dic101C22⋊C411yescharacteristic
88C2×Dic101C22⋊C411yescharacteristic
89C4×D101—22no—
90C4×D101—22no—
91C4×D101—41no—
92C4×D101—41no—
93C4×D101—48no—
94Dic202—41no—
95C8×C101—41no—
96#11717579—41no—
97C22×C101—21no—
98C22×C101—21no—
99C22×C101—41no—
100C22×C101—41no—
101C22×C101—41no—
102C22×C101C2×C22⋊C411yescharacteristic
103C22×C101AGL(1,ℤ/8)11yescharacteristic
104C22×C101#13711yescharacteristic
105C2×D101—24no—
106C2×D101—24no—
107C2×D101—21no—
108C2×D101—21no—
109C2×D101—21no—
110C2×D101—21no—
111C2×D101#9912yes—
112C2×D101#10412yes—
113C4×C101—21no—
114C4×C101—21no—
115C4×C101—42no—
116C4×C101—41no—
117Dic101—21no—
118Dic101—21no—
119Dic101—42no—
120Dic101—41no—
121Dic101—41no—
122C2×C101—21no—
123C2×C101—21no—
124C2×C101—81no—
125C2×C101C2×#9911yescharacteristic
126C2×C101#41711yescharacteristic
127C2×C101C2×#10411yescharacteristic
128D101—22no—
129D101—22no—
130#1504—1011nomaximal, Sylow
131C101#150411yescharacteristic, complemented, Sylow
132#525—1011no—
133#407—1011no—
134C2×#95—1011no—
135#328—1011no—
136#328—1011no—
137#327—1011no—
138#327D10111yescharacteristic, complemented
139C2×#41—1011no—
140C23×C4—1011no—
141C23×C4—2021no—
142C2×M16—2021no—
143#123—2021no—
144C22⋊Q8—1011no—
145C22⋊Q8—1011no—
146#121—1011no—
147#121C2×D10111yescharacteristic
148#120—2021no—
149C4×D4—2021no—
150C4×D4—2021no—
151#117—1011no—
152C22⋊C8—1011no—
153C22⋊C8—2021no—
154C22⋊C8C2×D10111yescharacteristic
155#95—1011no—
156#95—2021no—
157#95C2×D10111yescharacteristic
158C24—1011no—
159#41—4042no—
160C2×Q8—1011no—
161C2×D4—21no—
162C2×D4—2021no—
163C2×D4—2021no—
164C2×D4C4×D10111yescharacteristic, complemented
165C22×C4—21no—
166C22×C4—1011no—
167C22×C4—1011no—
168C22×C4—1011no—
169C22×C4—1011no—
170C22×C4—1011no—
171C22×C4—4042no—
172C22×C4—4042no—
173C22×C4—4042no—
174C22×C4—2024no—
175C22×C4—2021no—
176C22×C4—2021no—
177C22×C4C22×D10111yescharacteristic
178M16—4042no—
179C2×C8—21no—
180C2×C8—2021no—
181C4⋊C4—1011no—
182C4⋊C4—2021no—
183C4⋊C4—2021no—
184C4⋊C4C4×D10111yescharacteristic, complemented
185C22⋊C4—21no—
186C22⋊C4—2021no—
187C22⋊C4—2021no—
188C22⋊C4—2021no—
189C22⋊C4—2021no—
190C42—2021no—
191C23—21no—
192C23—1011no—
193C23—1011no—
194C23—2022no—
195C23—2022no—
196C23—2021no—
197C23—2021no—
198C23D4×D10111yescharacteristic
199Q8—4041no—
200D4—41no—
201D4—41no—
202D4—41no—
203D4—4042no—
204D4—4042no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—1011no—
211C2×C4—1011no—
212C2×C4—4041no—
213C2×C4—4041no—
214C2×C4—4048no—
215C2×C4—4041no—
216C2×C4—4041no—
217C2×C4—4042no—
218C2×C4—4041no—
219C2×C4—2022no—
220C2×C4—2022no—
221C2×C4—2022no—
222C2×C4—2021no—
223C2×C4—2021no—
224C2×C4C2×C4×D10111yescharacteristic
225C2×C4D4×D10111yescharacteristic
226C8—41no—
227C8—4041no—
228C22—21no—
229C22—21no—
230C22—41no—
231C22—41no—
232C22—41no—
233C22—1012no—
234C22—1012no—
235C22—2024no—
236C22—2024no—
237C22—2021no—
238C22—2021no—
239C22—2021no—
240C22—2021no—
241C22C22⋊C4×D10111yescharacteristic
242C22#1569227911yescharacteristic
243C22#1569228411yescharacteristic
244C4—21no—
245C4—21no—
246C4—42no—
247C4—41no—
248C4—4042no—
249C4—4041no—
250C4—4041no—
251C4—2021no—
252C4—2021no—
253C2—21no—
254C2—21no—
255C2—81no—
256C2—2022no—
257C2—2022no—
258C2#99×D10111yescharacteristic
259C2#2026517511yescharacteristic
260C2#104×D10111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D101
commutatorC2×C4×C101C22×C4
FrattiniC22×C4C22×D101
Fitting#327×C101C2
socleC22×C101C2×C22⋊C4
prime radical#20265687C2
cosocleC22×C4×C101C23
hypercenter#327D101
hypocenterC101#1504
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #20265139C2semidirect
3. #95×D101C2semidirect
4. #20264915C2semidirect
5. #20264913C2semidirect
6. #20264911C2semidirect
7. #327×C101C2semidirect
8. C2×#13108073C4semidirect
13. #15692235C4semidirect
15. #15692226C4semidirect
19. #15692213C4semidirect
29. C2×Dic202C2×C4semidirect
46. C4⋊Dic101C2×C4semidirect
54. C2×D4×C101C2×C4semidirect
58. C4⋊C4×C101C2×C4semidirect
131. C101#1504semidirect
138. #327D101semidirect
164. C2×D4C4×D101semidirect
184. C4⋊C4C4×D101semidirect

Maximal subgroups

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

subgroupindex
#202656872
#202651392
#95×D1012
#202649152
#202649132
#202649112
#327×C1012
#1504101