Finite Group Databasebeta

← #27169529

Subgroups — #27169529

Order 12928.

260 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 73 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#20265724C211yesmaximal, characteristic
2#20265228C211yesmaximal, characteristic, complemented
3C4⋊C8×D101C211yesmaximal, characteristic, complemented
4#20264906C211yesmaximal, characteristic, complemented
5D4⋊#11717579C211yesmaximal, characteristic, complemented
6#20264904C211yesmaximal, characteristic, complemented
7D4⋊C8×C101C211yesmaximal, characteristic, complemented
8C2×#13108074—21no—
9C2×C8×D101—21no—
10#15692254C411yescharacteristic
11#15692251C411yescharacteristic
12#15692241—21no—
13#15692230C411yescharacteristic
14#15692228—21no—
15#15692226C411yescharacteristic
16C4×D404C2211yescharacteristic
17C4×C22⋊D101—21no—
18C42×D101C2211yescharacteristic
19C4⋊#11717579C2211yescharacteristic
20#15692184—21no—
21#15692184—21no—
22#15692167—21no—
23C4×#11717579C2211yescharacteristic
24C4×D4×C101C2211yescharacteristic
25C4⋊C8×C101C2211yescharacteristic
26C4×C8×C101C2211yescharacteristic
27#13108074—42no—
28#13108074—42no—
29C2×Dic202—21no—
30C2×D404—21no—
31C2×D404C2×C411yescharacteristic
32C2×C22⋊D101—21no—
33C2×C22⋊D101—21no—
34C2×C22⋊D101—21no—
35C2×C4×D101—21no—
36C2×C4×D101C2×C411yescharacteristic
37C2×C4×D101D411yescharacteristic
38C2×C4×D101D411yescharacteristic
39C2×#11717579—21no—
40C2×#11717579—21no—
41C8×D101—42no—
42C4⋊Dic101C2×C411yescharacteristic
43#13108053—21no—
44C22⋊Dic101—21no—
45#13108051—21no—
46#13108051—21no—
47C4×Dic101C2×C411yescharacteristic
48C4×Dic101D411yescharacteristic
49C4×Dic101D411yescharacteristic
50C2×D4×C101C2×C411yescharacteristic
51C22×C4×C101—21no—
52C2×C8×C101—21no—
53C2×C8×C101—21no—
54C4⋊C4×C101C2×C411yescharacteristic
55C22⋊C4×C101—21no—
56C42×C101C2311yescharacteristic
57C23×C101—21no—
58C22×D101—21no—
59C22×D101C22⋊C411yescharacteristic
60D4×C101—21no—
61D4×C101—21no—
62C2×C4×C101—21no—
63C2×C4×C101—41no—
64C2×C4×C101—41no—
65C2×C4×C101C22×C411yescharacteristic
66C2×C4×C101C2×D411yescharacteristic
67C2×C4×C101C2×D411yescharacteristic
68C22⋊D101—42no—
69C22⋊D101—42no—
70C22⋊D101—42no—
71C2×Dic101—21no—
72C2×Dic101C22⋊C411yescharacteristic
73C2×Dic101C22⋊C411yescharacteristic
74C2×Dic101C22⋊C411yescharacteristic
75D404—21no—
76D404—21no—
77D404—42no—
78C4×D101—21no—
79C4×D101—21no—
80C4×D101—41no—
81C4×D101—41no—
82C4×D101—41no—
83C4×D101D812yes—
84C4×D101SD1612yes—
85Dic202—42no—
86C8×C101—41no—
87C8×C101—41no—
88#11717579—41no—
89#11717579—41no—
90C22×C101—41no—
91C22×C101—41no—
92C22×C101—41no—
93C22×C101C2×C22⋊C411yescharacteristic
94C2×D101—21no—
95C2×D101—21no—
96C2×D101—41no—
97C2×D101—41no—
98C2×D101—41no—
99C2×D101#10212yes—
100C4×C101—21no—
101C4×C101—41no—
102C4×C101#13111yescharacteristic
103C4×C101#13111yescharacteristic
104C4×C101C2×D811yescharacteristic
105C4×C101C2×SD1611yescharacteristic
106Dic101—21no—
107Dic101—21no—
108Dic101—41no—
109Dic101#10212yes—
110C2×C101—81no—
111C2×C101#40811yescharacteristic
112C2×C101C2×#10211yescharacteristic
113C2×C101#42111yescharacteristic
114D101—22no—
115D101—81no—
116#1480—1011nomaximal, Sylow
117C101#148011yescharacteristic, complemented, Sylow
118#532—1011no—
119#431—1011no—
120C2×C4⋊C8—1011no—
121D4⋊C8—1011no—
122D4⋊C8—1011no—
123D4⋊C8—1011no—
124D4⋊C8D10111yescharacteristic, complemented
125C2×#41—2021no—
126C22×C8—2021no—
127C4⋊Q8—1011no—
128#127—1011no—
129#124—2021no—
130#121—1011no—
131#121—1011no—
132#121—2021no—
133C4×D4—1011no—
134C4×D4—2021no—
135C4×D4C2×D10111yescharacteristic
136C2×C42—1011no—
137C4⋊C8—1011no—
138C4⋊C8—2021no—
139C4⋊C8—2021no—
140C4⋊C8C2×D10111yescharacteristic
141C22⋊C8—2021no—
142C4×C8—1011no—
143C4×C8C2×D10111yescharacteristic
144#41—4042no—
145#41—4042no—
146C2×Q8—2021no—
147C2×D4—1011no—
148C2×D4—2021no—
149C2×D4—2021no—
150C2×D4—2021no—
151C2×D4—2021no—
152C2×D4C4×D10111yescharacteristic
153C22×C4—21no—
154C22×C4—1011no—
155C22×C4—1011no—
156C22×C4—1011no—
157C22×C4—2021no—
158C2×C8—21no—
159C2×C8—21no—
160C2×C8—4042no—
161C2×C8—2021no—
162C2×C8—2021no—
163C4⋊C4—1011no—
164C4⋊C4—2021no—
165C4⋊C4C4×D10111yescharacteristic
166C22⋊C4—21no—
167C22⋊C4—2021no—
168C22⋊C4—2021no—
169C22⋊C4—2021no—
170C42—1011no—
171C42—1011no—
172C42—1011no—
173C42C22×D10111yescharacteristic
174C23—21no—
175C23—1011no—
176C23—2021no—
177Q8—4042no—
178D4—21no—
179D4—21no—
180D4—4042no—
181D4—4042no—
182D4—4042no—
183D4—4042no—
184D4—2021no—
185D4—2021no—
186C2×C4—21no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—1011no—
190C2×C4—1012no—
191C2×C4—1012no—
192C2×C4—1011no—
193C2×C4—1011no—
194C2×C4—4041no—
195C2×C4—4041no—
196C2×C4—4041no—
197C2×C4—2021no—
198C2×C4—2021no—
199C2×C4—2021no—
200C2×C4C2×C4×D10111yescharacteristic
201C2×C4D4×D10111yescharacteristic
202C2×C4D4×D10111yescharacteristic
203C8—41no—
204C8—41no—
205C8—4041no—
206C8—4041no—
207C22—41no—
208C22—41no—
209C22—41no—
210C22—1012no—
211C22—4041no—
212C22—4041no—
213C22—4041no—
214C22—2021no—
215C22—2021no—
216C22C22⋊C4×D10111yescharacteristic
217C4—21no—
218C4—41no—
219C4—1012no—
220C4—4041no—
221C4—2021no—
222C4—2021no—
223C4#1569226111yescharacteristic
224C4#1569226311yescharacteristic
225C4D8×D10111yescharacteristic
226C4SD16×D10111yescharacteristic
227C2—81no—
228C2—8081no—
229C2—2022no—
230C2#2026514211yescharacteristic
231C2#102×D10111yescharacteristic
232C2#2026519211yescharacteristic
subgroupG/H
centerC2×C4D4×D101
commutatorC2×C4×C101C22×C4
FrattiniC42C22×D101
FittingD4⋊C8×C101C2
socleC22×C101C2×C22⋊C4
prime radical#20265724C2
cosocleC42×C101C23
hypercenterD4⋊C8D101
hypocenterC101#1480
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #20265228C2semidirect
3. C4⋊C8×D101C2semidirect
4. #20264906C2semidirect
5. D4⋊#11717579C2semidirect
6. #20264904C2semidirect
7. D4⋊C8×C101C2semidirect
117. C101#1480semidirect
124. D4⋊C8D101semidirect

Maximal subgroups

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

subgroupindex
#202657242
#202652282
C4⋊C8×D1012
#202649062
D4⋊#117175792
#202649042
D4⋊C8×C1012
#1480101