Finite Group Databasebeta

← #27171958

Subgroups — #27171958

Order 12928.

360 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 87 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#20265723C211yesmaximal, characteristic
2#20265200C211yesmaximal, characteristic, complemented
3C2×#15692183C211yesmaximal, characteristic, complemented
4C2×#15692182C211yesmaximal, characteristic, complemented
5C2×#15692181C211yesmaximal, characteristic, complemented
6C42×Dic101C211yesmaximal, characteristic, complemented
7C2×#104×C101C211yesmaximal, characteristic, complemented
8C2×#13108074C2211yescharacteristic
9C2×#13108058C2211yescharacteristic
10#15692253C411yescharacteristic, complemented
11#15692251C411yescharacteristic, complemented
12#15692244C411yescharacteristic, complemented
13#15692242C411yescharacteristic, complemented
14#15692227—22no—
15C4×C22⋊D101—22no—
16C2×C4×Dic101—22no—
17C2×C4×Dic101C2211yescharacteristic
18C2×C4×Dic101C2211yescharacteristic
19#15692184—22no—
20#15692183—22no—
21#15692182—22no—
22#15692181—22no—
23C2×#41×C101C2211yescharacteristic
24C2×M16×C101C2211yescharacteristic
25C2×C42×C101C2211yescharacteristic
26#104×C101—22no—
27#13108074—21no—
28#13108074—21no—
29#13108074—21no—
30#13108074—21no—
31C2×Dic202C2×C411yescharacteristic
32C2×D404C2×C411yescharacteristic
33C2×C22⋊D101—21no—
34C2×C22⋊D101—22no—
35C22×Dic101—21no—
36C22×Dic101D412yes—
37C2×C4×D101—21no—
38#13108058—21no—
39#13108058—21no—
40C2×#11717579—21no—
41#13108053—22no—
42C22⋊Dic101—22no—
43#13108051—22no—
44C4×Dic101—28no—
45C4×Dic101—21no—
46C4×Dic101C2×C411yescharacteristic
47C4×Dic101C2×C411yescharacteristic
48C4×Dic101D412yes—
49C4×Dic101D412yescomplemented
50#41×C101—21no—
51#41×C101—21no—
52#41×C101—21no—
53#41×C101—21no—
54C2×Q8×C101C2×C411yescharacteristic
55C2×D4×C101—21no—
56C2×D4×C101C2×C411yescharacteristic
57C22×C4×C101—21no—
58C22×C4×C101—21no—
59C22×C4×C101C2311yescharacteristic
60M16×C101—21no—
61M16×C101—21no—
62C2×C8×C101—21no—
63C42×C101—21no—
64C42×C101D412yescomplemented
65C23×C101—21no—
66C23×C101C2×D411yescharacteristic
67C22×D101—21no—
68Q8×C101—21no—
69Q8×C101—21no—
70D4×C101—21no—
71D4×C101—21no—
72D4×C101—41no—
73D4×C101—41no—
74C2×C4×C101—24no—
75C2×C4×C101—22no—
76C2×C4×C101—21no—
77C2×C4×C101—41no—
78C2×C4×C101—41no—
79C2×C4×C101C22×C411yescharacteristic
80C2×C4×C101C2×D411yescharacteristic
81C2×C4×C101C2×D411yescharacteristic
82C2×C4×C101C2×D411yescharacteristic
83C2×C4×C101#4111yescharacteristic
84C2×C4×C101#4111yescharacteristic
85C22⋊D101—41no—
86C22⋊D101—41no—
87C22⋊D101—44no—
88C2×Dic101—24no—
89C2×Dic101—22no—
90C2×Dic101—24no—
91C2×Dic101—21no—
92C2×Dic101C22⋊C412yes—
93C2×Dic101C22⋊C412yes—
94D404—21no—
95D404—21no—
96C4×D101—41no—
97C4×D101—41no—
98Dic202—21no—
99Dic202—21no—
100C8×C101—41no—
101#11717579—41no—
102C22×C101—22no—
103C22×C101—41no—
104C22×C101—42no—
105C22×C101C2×C22⋊C411yescharacteristic
106C22×C101#12111yescharacteristic
107C22×C101#12111yescharacteristic
108C2×D101—41no—
109C2×D101—42no—
110C4×C101—24no—
111C4×C101—41no—
112C4×C101C4×D411yescharacteristic
113C4×C101C4×D411yescharacteristic
114C4×C101#12411yescharacteristic
115C4×C101#12711yescharacteristic
116Dic101—24no—
117Dic101—22no—
118Dic101—41no—
119Dic101#10414yescomplemented
120C2×C101—21no—
121C2×C101—21no—
122C2×C101—81no—
123C2×C101#39011yescharacteristic
124C2×C101C2×#10412yes—
125D101—81no—
126#1962—1011nomaximal, Sylow
127C101#196211yescharacteristic, complemented, Sylow
128#532—1011no—
129#423—1011no—
130C2×#104—1011no—
131C2×#104—1011no—
132C2×#104—1011no—
133C2×#104D10111yescharacteristic, complemented
134C43—1011no—
135C2×#41—1011no—
136C2×#41C2×D10111yescharacteristic
137C2×M16—1011no—
138C2×M16C2×D10111yescharacteristic
139C4⋊Q8—1011no—
140#127—1011no—
141#124—1011no—
142#124—1011no—
143#121—2022no—
144C4×D4—2022no—
145C2×C42—1011no—
146C2×C42—1011no—
147C2×C42—2022no—
148C2×C42C2×D10111yescharacteristic
149C4⋊C8—2022no—
150#104—22no—
151#104—2022no—
152#104—2022no—
153#104—2022no—
154#41—21no—
155#41—21no—
156#41—21no—
157#41—21no—
158#41—2021no—
159#41—2021no—
160#41—2021no—
161#41—2021no—
162C2×Q8—1011no—
163C2×Q8C4×D10111yescharacteristic
164C2×D4—21no—
165C2×D4—1011no—
166C2×D4—2022no—
167C2×D4—2021no—
168C2×D4C4×D10111yescharacteristic
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—1012no—
172C22×C4—2021no—
173C22×C4—2021no—
174C22×C4C22×D10111yescharacteristic
175M16—21no—
176M16—21no—
177M16—2021no—
178M16—2021no—
179C2×C8—21no—
180C2×C8—2021no—
181C4⋊C4—2022no—
182C22⋊C4—2022no—
183C22⋊C4—2022no—
184C42—21no—
185C42—1011no—
186C42—1011no—
187C42—1012no—
188C42—1012no—
189C42—2028no—
190C42—2021no—
191C42C22⋊D10112yescomplemented
192C23—21no—
193C23—2021no—
194C23D4×D10111yescharacteristic
195Q8—21no—
196Q8—21no—
197Q8—2021no—
198Q8—2021no—
199D4—21no—
200D4—21no—
201D4—41no—
202D4—41no—
203D4—4044no—
204D4—4041no—
205D4—4041no—
206D4—2021no—
207D4—2021no—
208C2×C4—24no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—1012no—
214C2×C4—1012no—
215C2×C4—4041no—
216C2×C4—4041no—
217C2×C4—2024no—
218C2×C4—2021no—
219C2×C4—2024no—
220C2×C4—2022no—
221C2×C4C2×C4×D10111yescharacteristic
222C2×C4D4×D10111yescharacteristic
223C2×C4D4×D10111yescharacteristic
224C2×C4C2×C22⋊D10111yescharacteristic
225C2×C4#1310807311yescharacteristic
226C2×C4#1310807411yescharacteristic
227C8—41no—
228C8—4041no—
229C22—22no—
230C22—41no—
231C22—42no—
232C22—4041no—
233C22—4042no—
234C22C22⋊C4×D10111yescharacteristic
235C22#1569222711yescharacteristic
236C22#1569222811yescharacteristic
237C4—24no—
238C4—41no—
239C4—1014no—
240C4—4041no—
241C4—2024no—
242C4—2022no—
243C4#1569221511yescharacteristic
244C4C4×C22⋊D10111yescharacteristic
245C4#1569224111yescharacteristic
246C4#1569225111yescharacteristic
247C2—21no—
248C2—21no—
249C2—81no—
250C2—8081no—
251C2#2026507711yescharacteristic
252C2#104×D10112yes—
subgroupG/H
centerC2×C4D4×D101
commutatorC2×C4×C101C22×C4
FrattiniC22×C4C22×D101
FittingC2×#104×C101C2
socleC22×C101C2×C22⋊C4
prime radical#20265723C2
cosocleC22×C4×C101C23
hypercenterC2×#104D101
hypocenterC101#1962
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. #20265200C2semidirect
3. C2×#15692183C2semidirect
4. C2×#15692182C2semidirect
5. C2×#15692181C2semidirect
6. C42×Dic101C2semidirect
7. C2×#104×C101C2semidirect
10. #15692253C4semidirect
11. #15692251C4semidirect
12. #15692244C4semidirect
13. #15692242C4semidirect
49. C4×Dic101D4semidirect
64. C42×C101D4semidirect
119. Dic101#104semidirect
127. C101#1962semidirect
133. C2×#104D101semidirect
191. C42C22⋊D101semidirect

Maximal subgroups

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

subgroupindex
#202657232
#202652002
C2×#156921832
C2×#156921822
C2×#156921812
C42×Dic1012
C2×#104×C1012
#1962101