Finite Group Databasebeta

← #27169581

Subgroups — #27169581

Order 12928.

276 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 75 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#20265199C211yesmaximal, 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×#13108057—21no—
10C2×C8×D101—21no—
11#15692254C411yescharacteristic
12#15692251C411yescharacteristic
13#15692241—21no—
14#15692230C411yescharacteristic
15#15692228—21no—
16#15692226C411yescharacteristic
17C4×D404C2211yescharacteristic
18C4×C22⋊D101—21no—
19C42×D101C2211yescharacteristic
20C4⋊#11717579C2211yescharacteristic
21#15692184—21no—
22C4×#11717579C2211yescharacteristic
23C8×Dic101—21no—
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
39#13108057—42no—
40C2×#11717579—21no—
41C2×#11717579—21no—
42C8×D101—24no—
43C4⋊Dic101C2×C411yescharacteristic
44#13108053—21no—
45C22⋊Dic101—21no—
46#13108051—21no—
47#13108051—21no—
48C4×Dic101C2×C411yescharacteristic
49C4×Dic101D411yescharacteristic
50C4×Dic101D411yescharacteristic
51C2×D4×C101C2×C411yescharacteristic
52C22×C4×C101—21no—
53C2×C8×C101—21no—
54C2×C8×C101—21no—
55C4⋊C4×C101C2×C411yescharacteristic
56C22⋊C4×C101—21no—
57C42×C101C2311yescharacteristic
58C23×C101—21no—
59C22×D101—21no—
60C22×D101C22⋊C411yescharacteristic
61D4×C101—21no—
62D4×C101—21no—
63C2×C4×C101—21no—
64C2×C4×C101—41no—
65C2×C4×C101—41no—
66C2×C4×C101C22×C411yescharacteristic
67C2×C4×C101C2×D411yescharacteristic
68C2×C4×C101C2×D411yescharacteristic
69C22⋊D101—42no—
70C22⋊D101—42no—
71C22⋊D101—42no—
72C2×Dic101—21no—
73C2×Dic101C22⋊C411yescharacteristic
74C2×Dic101C22⋊C411yescharacteristic
75C2×Dic101C22⋊C411yescharacteristic
76D404—21no—
77D404—21no—
78D404—42no—
79C4×D101—21no—
80C4×D101—21no—
81C4×D101—22no—
82C4×D101—41no—
83C4×D101—41no—
84C4×D101D812yes—
85C4×D101SD1612yes—
86Dic202—42no—
87C8×C101—22no—
88C8×C101—41no—
89#11717579—22no—
90#11717579—41no—
91C22×C101—41no—
92C22×C101—41no—
93C22×C101—41no—
94C22×C101C2×C22⋊C411yescharacteristic
95C2×D101—21no—
96C2×D101—21no—
97C2×D101—41no—
98C2×D101—41no—
99C2×D101—41no—
100C2×D101#10212yes—
101C4×C101—21no—
102C4×C101—41no—
103C4×C101#13111yescharacteristic
104C4×C101#13111yescharacteristic
105C4×C101C2×D811yescharacteristic
106C4×C101C2×SD1611yescharacteristic
107Dic101—21no—
108Dic101—41no—
109Dic101#10212yes—
110Dic101#10412yes—
111C2×C101—81no—
112C2×C101#40811yescharacteristic
113C2×C101C2×#10211yescharacteristic
114C2×C101C2×#10411yescharacteristic
115D101—22no—
116D101—81no—
117#1492—1011nomaximal, Sylow
118C101#149211yescharacteristic, complemented, Sylow
119#532—1011no—
120#423—1011no—
121C2×C4×C8—1011no—
122D4⋊C8—1011no—
123D4⋊C8—1011no—
124D4⋊C8—1011no—
125D4⋊C8D10111yescharacteristic, complemented
126C2×#41—2021no—
127C2×M16—2021no—
128C22×C8—2021no—
129C4⋊Q8—1011no—
130#127—1011no—
131#124—2021no—
132#121—1011no—
133#121—1011no—
134#121—2021no—
135C4×D4—1011no—
136C4×D4—2021no—
137C4×D4C2×D10111yescharacteristic
138C2×C42—1011no—
139C4⋊C8—1011no—
140C4⋊C8—2021no—
141C4⋊C8C2×D10111yescharacteristic
142C4×C8—1011no—
143C4×C8—2021no—
144C4×C8C2×D10111yescharacteristic
145#41—4042no—
146#41—4042no—
147C2×Q8—2021no—
148C2×D4—1011no—
149C2×D4—2021no—
150C2×D4—2021no—
151C2×D4—2021no—
152C2×D4—2021no—
153C2×D4C4×D10111yescharacteristic
154C22×C4—21no—
155C22×C4—1011no—
156C22×C4—1011no—
157C22×C4—1011no—
158C22×C4—2021no—
159M16—4042no—
160C2×C8—21no—
161C2×C8—21no—
162C2×C8—2024no—
163C2×C8—2021no—
164C2×C8—2021no—
165C4⋊C4—1011no—
166C4⋊C4—2021no—
167C4⋊C4C4×D10111yescharacteristic
168C22⋊C4—21no—
169C22⋊C4—2021no—
170C22⋊C4—2021no—
171C22⋊C4—2021no—
172C42—1011no—
173C42—1011no—
174C42—1011no—
175C42C22×D10111yescharacteristic
176C23—21no—
177C23—1011no—
178C23—2021no—
179Q8—4042no—
180D4—21no—
181D4—21no—
182D4—4042no—
183D4—4042no—
184D4—4042no—
185D4—4042no—
186D4—2021no—
187D4—2021no—
188C2×C4—21no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—1011no—
192C2×C4—1011no—
193C2×C4—1012no—
194C2×C4—1012no—
195C2×C4—1011no—
196C2×C4—4041no—
197C2×C4—4041no—
198C2×C4—2022no—
199C2×C4—2021no—
200C2×C4—2021no—
201C2×C4—2021no—
202C2×C4C2×C4×D10111yescharacteristic
203C2×C4D4×D10111yescharacteristic
204C2×C4D4×D10111yescharacteristic
205C8—22no—
206C8—41no—
207C8—4041no—
208C8—2022no—
209C22—41no—
210C22—41no—
211C22—41no—
212C22—1012no—
213C22—4041no—
214C22—4041no—
215C22—4041no—
216C22—2021no—
217C22—2021no—
218C22C22⋊C4×D10111yescharacteristic
219C4—21no—
220C4—41no—
221C4—1012no—
222C4—1012no—
223C4—4041no—
224C4—2021no—
225C4#1569226111yescharacteristic
226C4#1569226311yescharacteristic
227C4D8×D10111yescharacteristic
228C4SD16×D10111yescharacteristic
229C2—81no—
230C2—8081no—
231C2—2022no—
232C2#2026514211yescharacteristic
233C2#102×D10111yescharacteristic
234C2#104×D10111yescharacteristic
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#1492
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. #20265199C2semidirect
3. C4×C8×D101C2semidirect
4. #20264906C2semidirect
5. D4⋊#11717579C2semidirect
6. #20264904C2semidirect
7. D4⋊C8×C101C2semidirect
118. C101#1492semidirect
125. D4⋊C8D101semidirect

Maximal subgroups

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

subgroupindex
#202657242
#202651992
C4×C8×D1012
#202649062
D4⋊#117175792
#202649042
D4⋊C8×C1012
#1492101