Finite Group Databasebeta

← #27186895

Subgroups — #27186895

Order 12928.

320 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 92 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
1C2×#15692319C212yesmaximal
2C4×#13108084C211yesmaximal, characteristic, complemented
3#20266113C211yesmaximal, characteristic, complemented
4#20266047C212yesmaximal, complemented
5C4×#13108073C211yesmaximal, characteristic
6C2×#13108084C2212yes—
7C2×C4×#87938C2212yes—
8#15692319C418yescomplemented
9#15692310—21no—
10C4×#11717581—21no—
11(C2×#87938)⋊C4—21no—
12(C2×#87938)⋊C4—21no—
13C2×#13108073C2211yescharacteristic
14C4×Dic202C411yescharacteristic, complemented
15#15692220C411yescharacteristic, complemented
16D4×Dic101C411yescharacteristic, complemented
17C4×C22⋊D101—21no—
18#15692215—21no—
19#15692213C2211yescharacteristic
20#15692211—21no—
21C2×C4×Dic101—21no—
22C42×D101C2211yescharacteristic
23C4×D4×C101C411yescharacteristic, complemented
24C22×#87938—22no—
25#13108084—22no—
26#13108084C2×C414yescomplemented
27C2×#11717581—22no—
28C4×#87938—22no—
29C4×#87938C2×C414yescomplemented
30#13108073—22no—
31#13108073C2×C414yes—
32C2×Dic202C2×C411yescharacteristic
33C2×C22⋊D101—21no—
34C22×Dic101—21no—
35C22×Dic101—21no—
36C2×C4×D101D411yescharacteristic
37C2×C4×D101D411yescharacteristic
38C2×C4×D101C2311yescharacteristic
39C4⋊Dic101C2×C411yescharacteristic
40#13108053—21no—
41#13108053—21no—
42C22⋊Dic101—21no—
43#13108051—21no—
44C4×Dic101—21no—
45C4×Dic101—21no—
46C4×Dic101—21no—
47C4×Dic101C2×C411yescharacteristic
48C4×Dic101D411yescharacteristic
49C4×Dic101D411yescharacteristic
50C2×D4×C101C2×C411yescharacteristic
51C22×C4×C101—21no—
52C4⋊C4×C101C2×C411yescharacteristic
53C22⋊C4×C101—21no—
54C42×C101C2×C411yescharacteristic
55C23×C101—21no—
56C22×D101C2×D411yescharacteristic
57C2×#87938—24no—
58C2×#87938—42no—
59C2×#87938—42no—
60D4×C101—21no—
61D4×C101C4212yes—
62C2×C4×C101—21no—
63C2×C4×C101—42no—
64C2×C4×C101C22⋊C411yescharacteristic
65C2×C4×C101C22⋊C411yescharacteristic
66C2×C4×C101C22×C411yescharacteristic
67C22⋊D101—24no—
68C2×Dic101—21no—
69C2×Dic101—24no—
70C2×Dic101—21no—
71C2×Dic101—42no—
72C2×Dic101C22⋊C411yescharacteristic
73C2×Dic101C22⋊C411yescharacteristic
74C2×Dic101C2×D411yescharacteristic
75C4×D101—41no—
76C4×D101—41no—
77C4×D101C22×C412yes—
78C4×D101#4112yes—
79Dic202—21no—
80Dic202C4212yes—
81#11717581—24no—
82C22×C101—22no—
83C22×C101—41no—
84C22×C101—41no—
85C22×C101C2×C22⋊C411yescharacteristic
86C2×D101—21no—
87C2×D101—21no—
88C2×D101C4×D412yes—
89#87938—44no—
90C4×C101—21no—
91C4×C101—21no—
92C4×C101—41no—
93C4×C101C2×C4211yescharacteristic
94C4×C101#11711yescharacteristic
95Dic101—22no—
96Dic101—21no—
97Dic101—21no—
98Dic101—41no—
99Dic101C4×D412yes—
100C2×C101—42no—
101C2×C101C4×C22⋊C411yescharacteristic
102C2×C101#42111yescharacteristic
103C2×C101#42111yescharacteristic
104D101—22no—
105#1759—1011nomaximal, Sylow
106C101#175911yescharacteristic, complemented, Sylow
107C4×#41—1011no—
108C2×#104—1012no—
109C4×M16—1011no—
110#376—1011no—
111#339—1012no—
112C2×#41—1011no—
113C2×M16—1012no—
114C4×Q8—1011no—
115C4×Q8—1011no—
116C4×D4—1011no—
117C4×D4—2021no—
118C4×D4—2021no—
119C4×D4#8793811yescharacteristic, complemented
120#117—1011no—
121#117—2021no—
122C2×C42—1011no—
123C2×C42—1012no—
124C2×C42—2021no—
125#104—1018no—
126#97—2021no—
127C4×C8—2021no—
128#95—2021no—
129#95—2021no—
130#41—1014no—
131#41—2022no—
132C2×Q8—1011no—
133C2×D4—2021no—
134C2×D4C2×#8793811yescharacteristic
135C22×C4—21no—
136C22×C4—1011no—
137C22×C4—1011no—
138C22×C4—1011no—
139C22×C4—2021no—
140C22×C4—2021no—
141C22×C4—2022no—
142M16—1014no—
143M16—2022no—
144C2×C8—2022no—
145C4⋊C4—1011no—
146C4⋊C4—2021no—
147C4⋊C4—2021no—
148C4⋊C4C2×#8793811yescharacteristic
149C22⋊C4—21no—
150C22⋊C4—2021no—
151C22⋊C4—2021no—
152C42—1011no—
153C42—1011no—
154C42—1011no—
155C42—1014no—
156C42—2021no—
157C42—2021no—
158C42—2022no—
159C42—2021no—
160C42C2×#8793811yescharacteristic
161C23—21no—
162C23—1011no—
163Q8—1012no—
164Q8—2021no—
165D4—21no—
166D4—2024no—
167D4C4×#8793812yes—
168C2×C4—21no—
169C2×C4—42no—
170C2×C4—1011no—
171C2×C4—1012no—
172C2×C4—1012no—
173C2×C4—1011no—
174C2×C4—1011no—
175C2×C4—4041no—
176C2×C4—4041no—
177C2×C4—4042no—
178C2×C4—4042no—
179C2×C4—4042no—
180C2×C4—2024no—
181C2×C4—2024no—
182C2×C4—2021no—
183C2×C4—2021no—
184C2×C4C22⋊#8793811yescharacteristic
185C2×C4C22⋊#8793811yescharacteristic
186C2×C4C22×#8793811yescharacteristic
187C8—2024no—
188C22—22no—
189C22—41no—
190C22—41no—
191C22—1012no—
192C22—2021no—
193C22—2021no—
194C22C2×C22⋊#8793811yescharacteristic
195C4—21no—
196C4—21no—
197C4—41no—
198C4—1012no—
199C4—4044no—
200C4—4041no—
201C4—2022no—
202C4—2021no—
203C4—2021no—
204C4C2×C4×#8793811yescharacteristic
205C4#1569233411yescharacteristic
206C2—42no—
207C2—2022no—
208C2C4×C22⋊#8793811yescharacteristic
209C2#2026617411yescharacteristic
210C2#2026617511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC4×C101C2×C42
FrattiniC2×C4C22×#87938
FittingC4×D4×C101C4
socleC22×C101C2×C22⋊C4
prime radicalC2×#13108073C22
cosocleC2×C4×D101C23
hypercenterC4×D4#87938
hypocenterC101#1759
LCSG ▷ C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C4×#13108084C2semidirect
3. #20266113C2semidirect
4. #20266047C2semidirect
8. #15692319C4semidirect
14. C4×Dic202C4semidirect
15. #15692220C4semidirect
16. D4×Dic101C4semidirect
23. C4×D4×C101C4semidirect
26. #13108084C2×C4semidirect
29. C4×#87938C2×C4semidirect
106. C101#1759semidirect
119. C4×D4#87938semidirect

Maximal subgroups

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

subgroupindex
C2×#156923192
C4×#131080842
#202661132
#202660472
C4×#131080732
#1759101