Finite Group Databasebeta

← #27187323

Subgroups — #27187323

Order 12928.

324 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 72 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#20266119C211yesmaximal, characteristic
2C4×C22⋊#87938C211yesmaximal, characteristic
3#20266055C212yesmaximal
4#20266055C212yesmaximal
5C2×#15692233C211yesmaximal, characteristic
6C2×C4⋊#87938—21no—
7C2×C22⋊#87938C2212yes—
8C2×C22⋊#87938C2212yes—
9C2×C4×#87938—21no—
10(C2×#87938)⋊C4—21no—
11(C2×#87938)⋊C4—21no—
12C22×Dic202C411yescharacteristic, complemented
13C22×C4×D101C2211yescharacteristic
14#15692233—21no—
15#15692233—21no—
16#15692233—21no—
17#15692233—21no—
18C2×#13108053C411yescharacteristic, complemented
19C2×#13108053C411yescharacteristic, complemented
20C2×#13108051C2211yescharacteristic
21C2×#13108051C2211yescharacteristic
22C2×C4⋊C4×C101C411yescharacteristic, complemented
23C22×#87938—22no—
24C22×#87938—22no—
25C4⋊#87938—42no—
26C22⋊#87938—22no—
27C22⋊#87938—24no—
28C22⋊#87938Q814yescomplemented
29C4×#87938—42no—
30C23×D101C2311yescharacteristic
31C2×Dic202—21no—
32C2×Dic202—21no—
33C2×Dic202—42no—
34C22×Dic101C2×C411yescharacteristic
35C22×Dic101C2×C411yescharacteristic
36C22×Dic101C2×C411yescharacteristic
37C2×C4×D101—42no—
38C2×C4×D101D411yescharacteristic
39C2×C4×D101D411yescharacteristic
40C2×C4×D101D411yescharacteristic
41C2×C4×D101D411yescharacteristic
42#13108053—21no—
43#13108053—21no—
44#13108053—21no—
45#13108053—21no—
46#13108051—21no—
47#13108051—21no—
48#13108051—21no—
49#13108051—21no—
50C22×C4×C101C2×C411yescharacteristic
51C22×C4×C101C2×C411yescharacteristic
52C22×C4×C101C2×C411yescharacteristic
53C4⋊C4×C101—21no—
54C4⋊C4×C101—21no—
55C23×C101C22×C411yescharacteristic
56C22×D101—41no—
57C22×D101—41no—
58C22×D101C2×D411yescharacteristic
59C22×D101C2×D411yescharacteristic
60C22×D101C2×Q812yes—
61C22×D101#4112yes—
62C2×#87938—24no—
63C2×#87938—42no—
64C2×#87938—42no—
65C2×#87938—42no—
66C2×#87938—42no—
67C2×#87938—42no—
68C2×C4×C101—21no—
69C2×C4×C101—21no—
70C2×C4×C101—41no—
71C2×C4×C101—41no—
72C2×C4×C101—41no—
73C2×C4×C101C22⋊C411yescharacteristic
74C2×C4×C101C22⋊C411yescharacteristic
75C2×Dic101—22no—
76C2×Dic101—21no—
77C2×Dic101—21no—
78C2×Dic101—41no—
79C2×Dic101—41no—
80C2×Dic101C22⋊C411yescharacteristic
81C2×Dic101C22⋊C411yescharacteristic
82C4×D101—22no—
83C4×D101—22no—
84C4×D101—41no—
85C4×D101—41no—
86Dic202—42no—
87Dic202—42no—
88C22×C101—21no—
89C22×C101—21no—
90C22×C101C2×C22⋊C411yescharacteristic
91C22×C101C4×Q812yes—
92C2×D101—21no—
93C2×D101—21no—
94C2×D101—21no—
95C2×D101—21no—
96C2×D101—42no—
97C2×D101—42no—
98C2×D101C22⋊Q812yes—
99C2×D101#12411yescharacteristic
100C2×D101C4⋊Q811yescharacteristic
101#87938—44no—
102#87938—82no—
103C4×C101—21no—
104C4×C101—21no—
105C4×C101—41no—
106C4×C101—41no—
107Dic101—21no—
108Dic101—41no—
109Dic101—41no—
110Dic101#9912yes—
111C2×C101—22no—
112C2×C101#39111yescharacteristic
113C2×C101C2×#9911yescharacteristic
114C2×C101#41011yescharacteristic
115D101—22no—
116D101—21no—
117D101—21no—
118#1996—1011nomaximal, Sylow
119C101#199611yescharacteristic, complemented, Sylow
120C2×C22⋊Q8—1011no—
121#380—1011no—
122C4×C22⋊C4—1011no—
123#342—1012no—
124#342—1012no—
125C22×Q8—1011no—
126C23×C4—1011no—
127C22⋊Q8—2021no—
128C22⋊Q8—2021no—
129C22⋊Q8—2021no—
130C22⋊Q8—2021no—
131C2×C4⋊C4—1011no—
132C2×C4⋊C4—1011no—
133C2×C4⋊C4—2021no—
134C2×C4⋊C4#8793811yescharacteristic, complemented
135C2×C22⋊C4—1012no—
136C2×C22⋊C4—1011no—
137C2×C22⋊C4—1011no—
138C2×C22⋊C4—1012no—
139C2×C42—2021no—
140#95—2021no—
141#95—2021no—
142C24—1011no—
143C2×Q8—4042no—
144C2×Q8—2021no—
145C2×Q8—2021no—
146C22×C4—1011no—
147C22×C4—1011no—
148C22×C4—1011no—
149C22×C4—1011no—
150C22×C4—1011no—
151C22×C4—1011no—
152C22×C4—1011no—
153C22×C4—4042no—
154C22×C4—2022no—
155C22×C4—2022no—
156C22×C4C2×#8793811yescharacteristic
157C22×C4C2×#8793811yescharacteristic
158C22×C4C2×#8793811yescharacteristic
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—4042no—
162C4⋊C4—2021no—
163C4⋊C4—2021no—
164C4⋊C4—2021no—
165C4⋊C4—2021no—
166C22⋊C4—1014no—
167C22⋊C4—2021no—
168C22⋊C4—2021no—
169C22⋊C4—2021no—
170C22⋊C4—2021no—
171C22⋊C4—2024no—
172C22⋊C4—2022no—
173C42—4042no—
174C23—1012no—
175C23—1012no—
176C23—1011no—
177C23—1011no—
178C23—4041no—
179C23—4041no—
180C23C22×#8793811yescharacteristic
181Q8—4042no—
182Q8—4042no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—1011no—
189C2×C4—1011no—
190C2×C4—4041no—
191C2×C4—4041no—
192C2×C4—4042no—
193C2×C4—4042no—
194C2×C4—4042no—
195C2×C4—4042no—
196C2×C4—4042no—
197C2×C4—4041no—
198C2×C4—4041no—
199C2×C4—2022no—
200C2×C4—2022no—
201C2×C4—2022no—
202C2×C4—2024no—
203C2×C4—2021no—
204C2×C4—2021no—
205C2×C4C22⋊#8793811yescharacteristic
206C2×C4C22⋊#8793811yescharacteristic
207C22—21no—
208C22—21no—
209C22—1011no—
210C22—1012no—
211C22—1011no—
212C22—4042no—
213C22—4042no—
214C22—2021no—
215C22—2021no—
216C22—2021no—
217C22—2021no—
218C22C2×C22⋊#8793811yescharacteristic
219C22Q8×#8793812yes—
220C4—21no—
221C4—21no—
222C4—41no—
223C4—41no—
224C4—8082no—
225C4—1012no—
226C4—4044no—
227C4—4041no—
228C4—4041no—
229C4—2021no—
230C2—22no—
231C2—2021no—
232C2—2022no—
233C2—2021no—
234C2(C2×#87938)⋊Q811yescharacteristic
235C2D101⋊#9911yescharacteristic
236C2#2026615611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC23×C101C22×C4
FrattiniC23C22×#87938
FittingC2×C4⋊C4×C101C4
socleC22×C101C2×C22⋊C4
prime radical, cosocleC23×D101C23
hypercenterC2×C4⋊C4#87938
hypocenterC101#1996
LCSG ▷ C23×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
12. C22×Dic202C4semidirect
18. C2×#13108053C4semidirect
19. C2×#13108053C4semidirect
22. C2×C4⋊C4×C101C4semidirect
28. C22⋊#87938Q8semidirect
119. C101#1996semidirect
134. C2×C4⋊C4#87938semidirect

Maximal subgroups

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

subgroupindex
#202661192
C4×C22⋊#879382
#202660552
C2×#156922332
#1996101