Finite Group Databasebeta

← #27186643

Subgroups — #27186643

Order 12928.

260 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 68 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#20266182C211yesmaximal, characteristic, complemented
2D101⋊(C4⋊C8)C211yesmaximal, characteristic, complemented
3#20266036C212yesmaximal, complemented
4#20266035C212yesmaximal, complemented
5#20265724C211yesmaximal, characteristic
6C2×#13108084—21no—
7C2×D101⋊C8—21no—
8#15692322—21no—
9#15692322C2212yes—
10#15692322C2212yes—
11C4⋊#11717581—21no—
12C2×#13108074—21no—
13#15692254C2211yescharacteristic
14#15692251C2211yescharacteristic
15#15692241—21no—
16#15692230C411yescharacteristic
17#15692228—21no—
18#15692226C411yescharacteristic
19C4×D404C411yescharacteristic
20C4×C22⋊D101—21no—
21C42×D101C2211yescharacteristic
22C4×D4×C101C411yescharacteristic
23#13108084—42no—
24D101⋊C8—42no—
25C2×#11717581—22no—
26C2×#11717581—22no—
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
39C4⋊Dic101C2×C411yescharacteristic
40#13108053—21no—
41C22⋊Dic101—21no—
42#13108051—21no—
43#13108051—21no—
44C4×Dic101D411yescharacteristic
45C4×Dic101D411yescharacteristic
46C4×Dic101C2311yescharacteristic
47C2×D4×C101C2×C411yescharacteristic
48C22×C4×C101—21no—
49C4⋊C4×C101C2×C411yescharacteristic
50C22⋊C4×C101—21no—
51C42×C101C2×C411yescharacteristic
52C23×C101—21no—
53C22×D101—21no—
54C22×D101C22⋊C411yescharacteristic
55D4×C101—41no—
56C2×C4×C101—21no—
57C2×C4×C101—42no—
58C2×C4×C101C22⋊C411yescharacteristic
59C2×C4×C101C22⋊C411yescharacteristic
60C2×C4×C101C22×C411yescharacteristic
61C22⋊D101—42no—
62C22⋊D101—41no—
63C22⋊D101—41no—
64C22⋊D101—41no—
65C22⋊D101—41no—
66C2×Dic101—21no—
67C2×Dic101C22⋊C411yescharacteristic
68C2×Dic101C2×D411yescharacteristic
69C2×Dic101C2×D411yescharacteristic
70D404—41no—
71D404—42no—
72C4×D101—21no—
73C4×D101—21no—
74C4×D101—41no—
75C4×D101—42no—
76C4×D101D812yes—
77C4×D101SD1612yes—
78Dic202—41no—
79Dic202—41no—
80#11717581—42no—
81#11717581—42no—
82C22×C101—41no—
83C22×C101—41no—
84C22×C101—41no—
85C22×C101C2×C22⋊C411yescharacteristic
86C2×D101—21no—
87C2×D101—21no—
88C2×D101—41no—
89C2×D101—41no—
90C2×D101—41no—
91C2×D101#10212yes—
92C4×C101—21no—
93C4×C101—21no—
94C4×C101—41no—
95C4×C101#10212yes—
96Dic101—21no—
97Dic101—41no—
98Dic101C2×D811yescharacteristic
99Dic101C2×SD1611yescharacteristic
100Dic101AGL(1,ℤ/8)11yescharacteristic
101Dic101#13711yescharacteristic
102C2×C101—81no—
103C2×C101#41311yescharacteristic
104C2×C101C2×#10211yescharacteristic
105C2×C101#41711yescharacteristic
106D101—22no—
107D101—81no—
108#1547—1011nomaximal, Sylow
109C101#154711yescharacteristic, complemented, Sylow
110#532—1011no—
111#423—1011no—
112C2×C4⋊C8—1011no—
113#332—1012no—
114#331—1012no—
115C2×#41—2021no—
116C2×M16—2021no—
117C22×C8—2021no—
118C4⋊Q8—1011no—
119#127—1011no—
120#124—2021no—
121#121—1011no—
122#121—1011no—
123#121—2021no—
124C4×D4—1011no—
125C4×D4—2021no—
126C4×D4#8793811yescharacteristic
127C2×C42—1011no—
128C4⋊C8—1012no—
129C4⋊C8—1012no—
130C4⋊C8—2021no—
131C4⋊C8—2021no—
132#41—4042no—
133#41—4042no—
134C2×Q8—2021no—
135C2×D4—1011no—
136C2×D4—2021no—
137C2×D4—2021no—
138C2×D4—2021no—
139C2×D4—2021no—
140C2×D4C2×#8793811yescharacteristic
141C22×C4—21no—
142C22×C4—1011no—
143C22×C4—1011no—
144C22×C4—1011no—
145C22×C4—2021no—
146M16—4042no—
147C2×C8—4042no—
148C2×C8—2022no—
149C2×C8—2022no—
150C4⋊C4—1011no—
151C4⋊C4—2021no—
152C4⋊C4C2×#8793811yescharacteristic
153C22⋊C4—21no—
154C22⋊C4—2021no—
155C22⋊C4—2021no—
156C22⋊C4—2021no—
157C42—1011no—
158C42—1011no—
159C42—1011no—
160C42C2×#8793811yescharacteristic
161C23—21no—
162C23—1011no—
163C23—2021no—
164Q8—4041no—
165Q8—4041no—
166D4—41no—
167D4—4041no—
168D4—4042no—
169D4—4041no—
170D4—4041no—
171D4—4041no—
172D4—4041no—
173D4—4042no—
174C2×C4—21no—
175C2×C4—42no—
176C2×C4—1011no—
177C2×C4—1011no—
178C2×C4—1012no—
179C2×C4—1012no—
180C2×C4—1011no—
181C2×C4—4041no—
182C2×C4—4042no—
183C2×C4—2021no—
184C2×C4—2021no—
185C2×C4—2021no—
186C2×C4C22⋊#8793811yescharacteristic
187C2×C4C22⋊#8793811yescharacteristic
188C2×C4C22×#8793811yescharacteristic
189C8—4042no—
190C8—4042no—
191C22—41no—
192C22—41no—
193C22—41no—
194C22—1012no—
195C22—4041no—
196C22—4041no—
197C22—4041no—
198C22—2021no—
199C22—2021no—
200C22C2×C22⋊#8793811yescharacteristic
201C4—21no—
202C4—21no—
203C4—41no—
204C4—1011no—
205C4—1011no—
206C4—1011no—
207C4—1011no—
208C4—4041no—
209C4—2021no—
210C4#1569231712yes—
211C2—81no—
212C2—8081no—
213C2—2022no—
214C2#2026616311yescharacteristic
215C2C2×#1569231711yescharacteristic
216C2#2026616811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
FittingC4×D4×C101C4
socleC22×C101C2×C22⋊C4
prime radical#20265724C2
cosocleC4×Dic101C23
hypercenterC4×D4#87938
hypocenterC101#1547
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #20266182C2semidirect
2. D101⋊(C4⋊C8)C2semidirect
3. #20266036C2semidirect
4. #20266035C2semidirect
109. C101#1547semidirect

Maximal subgroups

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

subgroupindex
#202661822
D101⋊(C4⋊C8)2
#202660362
#202660352
#202657242
#1547101