Finite Group Databasebeta

← #27186562

Subgroups — #27186562

Order 12928.

264 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 66 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#20266196C211yesmaximal, characteristic, complemented
2#20266121C211yesmaximal, characteristic, complemented
3#20266029C212yesmaximal, complemented
4#20266028C212yesmaximal, complemented
5#20265724C211yesmaximal, characteristic
6C2×C4⋊#87938—21no—
7C4⋊#11717581—21no—
8#15692312C2212yes—
9C4×#11717581—21no—
10(C2×#87938)⋊C4—21no—
11(C2×#87938)⋊C4C2212yes—
12C2×#13108074—21no—
13#15692254C411yescharacteristic, complemented
14#15692251C411yescharacteristic, complemented
15#15692241—21no—
16#15692230C2211yescharacteristic
17#15692228—21no—
18#15692226C2211yescharacteristic
19C4×D404C411yescharacteristic, complemented
20C4×C22⋊D101—21no—
21C42×D101C2211yescharacteristic
22C4×D4×C101C411yescharacteristic, complemented
23C22×#87938—22no—
24C2×#11717581—22no—
25C4⋊#87938—42no—
26#13108074—42no—
27#13108074—42no—
28C2×Dic202—21no—
29C2×D404—21no—
30C2×D404C2×C411yescharacteristic
31C2×C22⋊D101—21no—
32C2×C22⋊D101—21no—
33C2×C22⋊D101—21no—
34C2×C4×D101—21no—
35C2×C4×D101D411yescharacteristic
36C2×C4×D101D411yescharacteristic
37C2×C4×D101C2311yescharacteristic
38C4⋊Dic101C2×C411yescharacteristic
39#13108053—21no—
40C22⋊Dic101—21no—
41#13108051—21no—
42#13108051—21no—
43C4×Dic101C2×C411yescharacteristic
44C4×Dic101D411yescharacteristic
45C4×Dic101D411yescharacteristic
46C2×D4×C101C2×C411yescharacteristic
47C22×C4×C101—21no—
48C4⋊C4×C101C2×C411yescharacteristic
49C22⋊C4×C101—21no—
50C42×C101C2×C411yescharacteristic
51C23×C101—21no—
52C22×D101—21no—
53C22×D101C2×D411yescharacteristic
54C2×#87938—42no—
55C2×#87938—42no—
56C2×#87938—42no—
57D4×C101—41no—
58C2×C4×C101—21no—
59C2×C4×C101—42no—
60C2×C4×C101C22⋊C411yescharacteristic
61C2×C4×C101C22⋊C411yescharacteristic
62C2×C4×C101C22×C411yescharacteristic
63C22⋊D101—42no—
64C22⋊D101—41no—
65C22⋊D101—41no—
66C22⋊D101—42no—
67C2×Dic101—21no—
68C2×Dic101C22⋊C411yescharacteristic
69C2×Dic101C22⋊C411yescharacteristic
70C2×Dic101C2×D411yescharacteristic
71D404—41no—
72D404—41no—
73D404—41no—
74C4×D101—41no—
75C4×D101—41no—
76C4×D101—42no—
77C4×D101D812yes—
78C4×D101SD1612yes—
79Dic202—42no—
80#11717581—42no—
81C22×C101—41no—
82C22×C101—41no—
83C22×C101—41no—
84C22×C101C2×C22⋊C411yescharacteristic
85C2×D101—21no—
86C2×D101—21no—
87C2×D101—41no—
88C2×D101—41no—
89C2×D101—41no—
90C2×D101C2×D811yescharacteristic
91C2×D101C2×SD1611yescharacteristic
92#87938—82no—
93C4×C101—21no—
94C4×C101—21no—
95C4×C101—41no—
96C4×C101#10212yes—
97Dic101—21no—
98Dic101—21no—
99Dic101—41no—
100Dic101#10212yes—
101C2×C101—81no—
102C2×C101#41011yescharacteristic
103C2×C101C2×#10211yescharacteristic
104C2×C101#42111yescharacteristic
105D101—21no—
106D101—21no—
107D101—81no—
108#1517—1011nomaximal, Sylow
109C101#151711yescharacteristic, complemented, Sylow
110#532—1011no—
111#431—1011no—
112#382—1011no—
113#327—1012no—
114#327—1012no—
115C2×#41—2021no—
116C4⋊Q8—1011no—
117#127—1011no—
118#124—2021no—
119#121—1011no—
120#121—1011no—
121#121—2021no—
122C4×D4—1011no—
123C4×D4—2021no—
124C4×D4#8793811yescharacteristic, complemented
125C2×C4⋊C4—2021no—
126C2×C42—1011no—
127C4⋊C8—2021no—
128C22⋊C8—1012no—
129C4×C8—2021no—
130#95—1012no—
131#95—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—2022no—
146C22×C4—2021no—
147C2×C8—2022no—
148C4⋊C4—1011no—
149C4⋊C4—4042no—
150C4⋊C4—2021no—
151C4⋊C4C2×#8793811yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—2021no—
154C22⋊C4—2021no—
155C22⋊C4—2021no—
156C42—1011no—
157C42—1011no—
158C42—1011no—
159C42C2×#8793811yescharacteristic
160C23—21no—
161C23—1011no—
162C23—2021no—
163Q8—4042no—
164D4—41no—
165D4—4041no—
166D4—4041no—
167D4—4041no—
168D4—4042no—
169D4—4041no—
170D4—4041no—
171D4—4042no—
172C2×C4—21no—
173C2×C4—42no—
174C2×C4—1011no—
175C2×C4—1012no—
176C2×C4—1012no—
177C2×C4—1011no—
178C2×C4—1011no—
179C2×C4—4041no—
180C2×C4—4041no—
181C2×C4—4042no—
182C2×C4—4042no—
183C2×C4—4042no—
184C2×C4—4042no—
185C2×C4—2021no—
186C2×C4C22⋊#8793811yescharacteristic
187C2×C4C22⋊#8793811yescharacteristic
188C2×C4C22×#8793811yescharacteristic
189C8—4042no—
190C22—41no—
191C22—41no—
192C22—41no—
193C22—1011no—
194C22—1011no—
195C22—4041no—
196C22—4041no—
197C22—4041no—
198C22—2021no—
199C22—2021no—
200C22C2×C22⋊#8793811yescharacteristic
201C4—21no—
202C4—21no—
203C4—41no—
204C4—8082no—
205C4—1012no—
206C4—4041no—
207C4—2021no—
208C4—2021no—
209C4#1569231712yes—
210C2—81no—
211C2—8081no—
212C2—2021no—
213C2—2021no—
214C2#2026615611yescharacteristic
215C2C2×#1569231711yescharacteristic
216C2#2026617411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
FittingC4×D4×C101C4
socleC22×C101C2×C22⋊C4
prime radical#20265724C2
cosocleC2×C4×D101C23
hypercenterC4×D4#87938
hypocenterC101#1517
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. #20266196C2semidirect
2. #20266121C2semidirect
3. #20266029C2semidirect
4. #20266028C2semidirect
13. #15692254C4semidirect
14. #15692251C4semidirect
19. C4×D404C4semidirect
22. C4×D4×C101C4semidirect
109. C101#1517semidirect
124. C4×D4#87938semidirect

Maximal subgroups

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

subgroupindex
#202661962
#202661212
#202660292
#202660282
#202657242
#1517101