Finite Group Databasebeta

← #27186527

Subgroups — #27186527

Order 12928.

346 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 60 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#20266149C211yesmaximal, characteristic, complemented
2C4×C22⋊#87938C211yesmaximal, characteristic, complemented
3#20266029C212yesmaximal, complemented
4#20266028C212yesmaximal, complemented
5#121×D101C211yesmaximal, characteristic
6C2×#13108083—21no—
7C2×C22⋊#87938—21no—
8C2×C4×#87938—21no—
9#15692312—21no—
10#15692312C2212yescomplemented
11(C2×#87938)⋊C4C2212yescomplemented
12C2×D4×D101—21no—
13C2×D4×D101C411yescharacteristic, complemented
14C22×C4×D101C2211yescharacteristic
15#15692230C2211yescharacteristic
16#15692229C411yescharacteristic, complemented
17#15692228—21no—
18#15692227—21no—
19#15692226C2211yescharacteristic
20C4⋊C4×D101C411yescharacteristic, complemented
21C22⋊C4×D101—21no—
22#121×C101C411yescharacteristic, complemented
23C22×#87938—22no—
24#13108083—42no—
25C2×#11717581—22no—
26C22⋊#87938—24no—
27C4×#87938—42no—
28C23×D101—21no—
29C23×D101D411yescharacteristic
30C2×D404—21no—
31C2×D404C2×C411yescharacteristic
32C2×C22⋊D101—21no—
33C2×C22⋊D101—21no—
34C2×C22⋊D101—21no—
35D4×D101—42no—
36D4×D101—44no—
37C22×Dic101D411yescharacteristic
38C2×C4×D101—21no—
39C2×C4×D101—42no—
40C2×C4×D101C2×C411yescharacteristic
41C2×C4×D101D411yescharacteristic
42C2×C4×D101D411yescharacteristic
43C2×C4×D101C2311yescharacteristic
44C4⋊Dic101C2×C411yescharacteristic
45#13108053—21no—
46C22⋊Dic101—21no—
47#13108051—21no—
48#13108051—21no—
49C2×D4×C101—21no—
50C2×D4×C101C2×C411yescharacteristic
51C22×C4×C101C2×C411yescharacteristic
52C4⋊C4×C101C2×C411yescharacteristic
53C22⋊C4×C101—21no—
54C23×C101—21no—
55C23×C101C22⋊C411yescharacteristic
56C22×D101—22no—
57C22×D101—22no—
58C22×D101—21no—
59C22×D101—41no—
60C22×D101—42no—
61C22×D101—42no—
62C22×D101—42no—
63C22×D101C22⋊C411yescharacteristic
64C22×D101C2×D411yescharacteristic
65C2×#87938—24no—
66C2×#87938—42no—
67C2×#87938—42no—
68D4×C101—41no—
69D4×C101—42no—
70C2×C4×C101—21no—
71C2×C4×C101—41no—
72C2×C4×C101C22⋊C411yescharacteristic
73C2×C4×C101C22×C411yescharacteristic
74C22⋊D101—42no—
75C22⋊D101—42no—
76C22⋊D101—42no—
77C2×Dic101—22no—
78C2×Dic101—21no—
79C2×Dic101C22⋊C411yescharacteristic
80C2×Dic101C2×D411yescharacteristic
81D404—41no—
82D404—42no—
83C4×D101—22no—
84C4×D101—22no—
85C4×D101—41no—
86C4×D101—41no—
87C4×D101—42no—
88#11717581—42no—
89C22×C101—21no—
90C22×C101—21no—
91C22×C101—21no—
92C22×C101—41no—
93C22×C101—41no—
94C22×C101—41no—
95C22×C101C2×C22⋊C411yescharacteristic
96C2×D101—21no—
97C2×D101—21no—
98C2×D101—21no—
99C2×D101—21no—
100C2×D101—44no—
101C2×D101—41no—
102C2×D101—41no—
103C2×D101—41no—
104C2×D101—84no—
105C2×D101#10412yes—
106C2×D101AGL(1,ℤ/8)12yes—
107#87938—44no—
108C4×C101—21no—
109C4×C101—21no—
110C4×C101—41no—
111Dic101—21no—
112Dic101—41no—
113Dic101#9912yes—
114C2×C101—41no—
115C2×C101—81no—
116C2×C101C2×#9911yescharacteristic
117C2×C101#41811yescharacteristic
118C2×C101C2×#10411yescharacteristic
119D101—22no—
120D101—22no—
121D101—81no—
122#1507—1011nomaximal, Sylow
123C101#150711yescharacteristic, complemented, Sylow
124C2×#121—1011no—
125#407—1011no—
126C4×C22⋊C4—1011no—
127#327—1012no—
128#327—1012no—
129C22×D4—1011no—
130C22×D4—2021no—
131C23×C4—1011no—
132C2×M16—2021no—
133#121—1011no—
134#121—1011no—
135#121—1011no—
136#121—2021no—
137#121—2021no—
138#121#8793811yescharacteristic, complemented
139C2×C4⋊C4—1011no—
140C2×C22⋊C4—2021no—
141C2×C22⋊C4—2021no—
142C2×C42—2021no—
143C22⋊C8—1012no—
144C22⋊C8—2021no—
145#95—1012no—
146C24—1011no—
147C24—2021no—
148C2×D4—21no—
149C2×D4—1011no—
150C2×D4—4044no—
151C2×D4—4042no—
152C2×D4—2021no—
153C2×D4—2021no—
154C2×D4—2021no—
155C2×D4—2021no—
156C2×D4C2×#8793811yescharacteristic
157C22×C4—1011no—
158C22×C4—1011no—
159C22×C4—1011no—
160C22×C4—1011no—
161C22×C4—1011no—
162C22×C4—4042no—
163C22×C4—2021no—
164C22×C4—2022no—
165C22×C4C2×#8793811yescharacteristic
166M16—4042no—
167C2×C8—2022no—
168C4⋊C4—1011no—
169C4⋊C4—2021no—
170C4⋊C4C2×#8793811yescharacteristic
171C22⋊C4—21no—
172C22⋊C4—2021no—
173C22⋊C4—2021no—
174C22⋊C4—2024no—
175C22⋊C4—2021no—
176C42—4042no—
177C23—21no—
178C23—1011no—
179C23—1011no—
180C23—4041no—
181C23—4042no—
182C23—4042no—
183C23—4042no—
184C23—2022no—
185C23—2022no—
186C23—2021no—
187C23C22⋊#8793811yescharacteristic
188D4—41no—
189D4—42no—
190D4—4041no—
191D4—4042no—
192D4—4042no—
193D4—4042no—
194D4—4042no—
195C2×C4—21no—
196C2×C4—41no—
197C2×C4—1011no—
198C2×C4—1011no—
199C2×C4—4041no—
200C2×C4—4041no—
201C2×C4—4042no—
202C2×C4—4042no—
203C2×C4—4042no—
204C2×C4—2022no—
205C2×C4—2022no—
206C2×C4—2022no—
207C2×C4—2024no—
208C2×C4—2021no—
209C2×C4C22⋊#8793811yescharacteristic
210C2×C4C22×#8793811yescharacteristic
211C8—4042no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—41no—
216C22—41no—
217C22—41no—
218C22—8084no—
219C22—1012no—
220C22—1012no—
221C22—4044no—
222C22—4041no—
223C22—4041no—
224C22—4041no—
225C22—2021no—
226C22—2021no—
227C22—2021no—
228C22—2021no—
229C22C2×C22⋊#8793811yescharacteristic
230C4—21no—
231C4—21no—
232C4—41no—
233C4—1012no—
234C4—4044no—
235C4—4041no—
236C4—2021no—
237C2—41no—
238C2—81no—
239C2—8081no—
240C2—2022no—
241C2—2022no—
242C2D101⋊#9911yescharacteristic
243C2#2026616911yescharacteristic
244C2D101⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
Fitting#121×C101C4
socleC22×C101C2×C22⋊C4
prime radical#121×D101C2
cosocleC2×C4×D101C23
hypercenter#121#87938
hypocenterC101#1507
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #20266149C2semidirect
2. C4×C22⋊#87938C2semidirect
3. #20266029C2semidirect
4. #20266028C2semidirect
10. #15692312C22semidirect
11. (C2×#87938)⋊C4C22semidirect
13. C2×D4×D101C4semidirect
16. #15692229C4semidirect
20. C4⋊C4×D101C4semidirect
22. #121×C101C4semidirect
123. C101#1507semidirect
138. #121#87938semidirect

Maximal subgroups

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

subgroupindex
#202661492
C4×C22⋊#879382
#202660292
#202660282
#121×D1012
#1507101