Finite Group Databasebeta

← #27170195

Subgroups — #27170195

Order 12928.

278 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 57 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#20265849C211yesmaximal, characteristic, complemented
2#20265553C211yesmaximal, characteristic, complemented
3#20265369C211yesmaximal, characteristic, complemented
4#20264920C211yesmaximal, characteristic, complemented
5Q8⋊#11717579C211yesmaximal, characteristic, complemented
6#20264904C211yesmaximal, characteristic, complemented
7#460×C101C211yesmaximal, characteristic, complemented
8C2×#13108075—21no—
9C2×#13108059—22no—
10C2×#13108059—21no—
11#15692252—21no—
12#15692252C2211yescharacteristic
13#15692230—22no—
14#15692230—21no—
15C4×D404—21no—
16C4×D404C2211yescharacteristic
17C4⋊#11717579C2211yescharacteristic
18#15692176—21no—
19C4×#11717579C2211yescharacteristic
20C2×SD16×C101—21no—
21#127×C101C2211yescharacteristic
22C4×Q8×C101C2211yescharacteristic
23C4⋊C8×C101C2211yescharacteristic
24#102×C101—21no—
25#13108075—42no—
26#13108075—42no—
27C2×D404—22no—
28C2×D404—21no—
29C2×D404—21no—
30C2×D404—22no—
31C2×D404D411yescharacteristic
32C2×D404D412yes—
33C2×C4×D101—22no—
34C2×C4×D101—21no—
35#13108059—44no—
36#13108059—42no—
37C2×#11717579—21no—
38C2×#11717579—21no—
39C4⋊Dic101D411yescharacteristic
40#13108051—22no—
41#13108051—21no—
42C2×Q8×C101D411yescharacteristic
43C2×D4×C101—21no—
44C2×D4×C101—21no—
45C2×D4×C101—21no—
46SD16×C101—42no—
47C2×C8×C101—21no—
48C4⋊C4×C101—21no—
49C4⋊C4×C101D411yescharacteristic
50C42×C101—21no—
51C42×C101C2311yescharacteristic
52C23×C101—41no—
53C22×D101—21no—
54C22×D101—22no—
55Q8×C101—21no—
56Q8×C101D812yescomplemented
57D4×C101—42no—
58D4×C101—41no—
59D4×C101—41no—
60D4×C101—41no—
61D4×C101—41no—
62C2×C4×C101—21no—
63C2×C4×C101—21no—
64C2×C4×C101C2×D411yescharacteristic
65C2×C4×C101C2×D411yescharacteristic
66C2×C4×C101C2×D411yescharacteristic
67C2×Dic101—21no—
68D404—21no—
69D404—21no—
70D404—42no—
71D404—44no—
72D404—41no—
73D404—41no—
74D404—41no—
75D404—41no—
76D404—82no—
77C4×D101—44no—
78C4×D101—41no—
79C4×D101—41no—
80C8×C101—41no—
81#11717579—22no—
82#11717579—41no—
83C22×C101—81no—
84C22×C101—81no—
85C22×C101—81no—
86C22×C101#12011yescharacteristic
87C2×D101—42no—
88C2×D101—41no—
89C2×D101—41no—
90C2×D101—42no—
91C2×D101—42no—
92C2×D101—41no—
93C4×C101—22no—
94C4×C101—21no—
95C4×C101—41no—
96C4×C101C2×D811yescharacteristic
97C4×C101#13511yescharacteristic
98C4×C101AGL(1,ℤ/8)11yescharacteristic
99C4×C101AGL(1,ℤ/8)11yescharacteristic
100Dic101—41no—
101C2×C101—161no—
102C2×C101#44711yescharacteristic
103C2×C101#44911yescharacteristic
104C2×C101#45311yescharacteristic
105D101—81no—
106D101—82no—
107#1621—1011nomaximal, Sylow
108C101#162111yescharacteristic, complemented, Sylow
109#550—1011no—
110#493—1011no—
111#460D10111yescharacteristic, complemented
112#459—1011no—
113#331—1011no—
114Q8⋊C8—1011no—
115D4⋊C8—1011no—
116C2×#41—2021no—
117C2×SD16—21no—
118C2×D8—2021no—
119C2×D8—2022no—
120#127—1011no—
121#127—2021no—
122#127C2×D10111yescharacteristic
123#121—2022no—
124#121—2021no—
125C4×Q8C2×D10111yescharacteristic
126C4×D4—1011no—
127C4×D4—2021no—
128C4⋊C8—1011no—
129C4⋊C8C2×D10111yescharacteristic
130#102—21no—
131#102—2021no—
132C4×C8—1011no—
133#41—4042no—
134#41—4042no—
135C2×Q8C22⋊D10111yescharacteristic
136C2×D4—21no—
137C2×D4—21no—
138C2×D4—21no—
139C2×D4—1012no—
140C2×D4—1011no—
141C2×D4—2022no—
142C2×D4—2022no—
143C2×D4—2021no—
144C2×D4—2021no—
145C22×C4—2022no—
146C22×C4—2021no—
147SD16—42no—
148D8—4042no—
149D8—4044no—
150C2×C8—21no—
151C2×C8—2021no—
152C2×C8—2021no—
153C4⋊C4—21no—
154C4⋊C4—1011no—
155C4⋊C4C22⋊D10111yescharacteristic
156C22⋊C4—2022no—
157C22⋊C4—2021no—
158C42—21no—
159C42C22×D10111yescharacteristic
160C23—41no—
161C23—2022no—
162C23—2021no—
163Q8—21no—
164Q8#1310805912yescomplemented
165D4—42no—
166D4—41no—
167D4—41no—
168D4—41no—
169D4—41no—
170D4—8082no—
171D4—4042no—
172D4—4044no—
173D4—4041no—
174D4—4041no—
175D4—4041no—
176D4—4041no—
177D4—2021no—
178D4—2021no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—4044no—
182C2×C4—4041no—
183C2×C4—4041no—
184C2×C4—2021no—
185C2×C4D4×D10111yescharacteristic
186C2×C4D4×D10111yescharacteristic
187C2×C4C2×C22⋊D10111yescharacteristic
188C8—41no—
189C8—4041no—
190C8—2022no—
191C22—81no—
192C22—81no—
193C22—81no—
194C22—4042no—
195C22—4041no—
196C22—4042no—
197C22—4041no—
198C22—4041no—
199C22—4042no—
200C22#1569222311yescharacteristic
201C4—22no—
202C4—21no—
203C4—41no—
204C4—4041no—
205C4C2×#1310805911yescharacteristic
206C4#1569227611yescharacteristic
207C4#1569228011yescharacteristic
208C4#1569228211yescharacteristic
209C2—161no—
210C2—8082no—
211C2—8081no—
212C2#2026531011yescharacteristic
213C2#2026532111yescharacteristic
214C2#2026534311yescharacteristic
subgroupG/H
centerC22#15692223
commutator, cosocleC42×C101C23
FrattiniC42C22×D101
Fitting#460×C101C2
socleC22×C101#120
hypercenter#460D101
hypocenterC101#1621
LCSG ▷ C42×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #20265849C2semidirect
2. #20265553C2semidirect
3. #20265369C2semidirect
4. #20264920C2semidirect
5. Q8⋊#11717579C2semidirect
6. #20264904C2semidirect
7. #460×C101C2semidirect
56. Q8×C101D8semidirect
108. C101#1621semidirect
111. #460D101semidirect
164. Q8#13108059semidirect

Maximal subgroups

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

subgroupindex
#202658492
#202655532
#202653692
#202649202
Q8⋊#117175792
#202649042
#460×C1012
#1621101