Finite Group Databasebeta

← #30640111

Subgroups — #30640111

Order 16256.

248 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 89 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×#16861140C211yesmaximal, characteristic
2C2×C4⋊(C127⋊C8)C211yesmaximal, characteristic
3C2×#16861133C211yesmaximal, characteristic
4C2×#16861133C211yesmaximal, characteristic
5#22549774C211yesmaximal, characteristic
6#22549638C211yesmaximal, characteristic
7#391×C127C211yesmaximal, characteristic
8C22×C127⋊C8C2211yescharacteristic
9C22×C127⋊C8C2211yescharacteristic
10C2×C4⋊Dic127C2211yescharacteristic
11C2×C4⋊Dic127C2211yescharacteristic
12C2×Dic127⋊C4—21no—
13#16861140—22no—
14C4⋊(C127⋊C8)—22no—
15#16861133—22no—
16#16861133—22no—
17C127⋊#95—21no—
18C22×Q8×C127C2211yescharacteristic
19C2×C4⋊C4×C127C2211yescharacteristic
20C2×C42×C127C2211yescharacteristic
21#95×C127—21no—
22#95×C127—21no—
23C22×Dic127—21no—
24C22×Dic127—21no—
25C2×C127⋊C8—21no—
26C2×C127⋊C8—21no—
27C2×C127⋊C8—21no—
28C2×C127⋊C8—21no—
29C2×C127⋊C8—21no—
30C2×C127⋊C8D412yes—
31C4⋊Dic127—21no—
32C4⋊Dic127—21no—
33C4⋊Dic127—21no—
34C4⋊Dic127D412yes—
35Dic127⋊C4—42no—
36C2×Q8×C127—21no—
37C2×Q8×C127—21no—
38C2×Q8×C127—21no—
39C2×Q8×C127—21no—
40C2×Q8×C127—21no—
41C2×Q8×C127Q812yes—
42C22×C4×C127—21no—
43C22×C4×C127—21no—
44C22×C4×C127D411yescharacteristic
45C22×C4×C127D411yescharacteristic
46C22×C4×C127C2311yescharacteristic
47C4⋊C4×C127—21no—
48C4⋊C4×C127—21no—
49C42×C127—21no—
50C42×C127—21no—
51C2×Dic127—22no—
52C2×Dic127—41no—
53C2×Dic127—41no—
54C2×Dic127—41no—
55C2×Dic127—41no—
56C2×Dic127—41no—
57C127⋊C8—22no—
58C127⋊C8—41no—
59C23×C127C2×D411yescharacteristic
60Q8×C127—22no—
61Q8×C127—22no—
62Q8×C127—41no—
63Q8×C127—41no—
64C2×C4×C127—21no—
65C2×C4×C127—21no—
66C2×C4×C127—21no—
67C2×C4×C127—22no—
68C2×C4×C127—21no—
69C2×C4×C127—21no—
70C2×C4×C127—41no—
71C2×C4×C127—41no—
72C2×C4×C127—41no—
73C2×C4×C127—41no—
74C2×C4×C127—41no—
75C2×C4×C127SD1612yes—
76C2×C4×C127C2×D411yescharacteristic
77C2×C4×C127C2×D411yescharacteristic
78C2×C4×C127C2×Q811yescharacteristic
79C2×C4×C127#4111yescharacteristic
80C2×C4×C127#4111yescharacteristic
81C2×C4×C127#4111yescharacteristic
82C22×C127#12111yescharacteristic
83C22×C127#12111yescharacteristic
84C22×C127C22⋊Q811yescharacteristic
85C22×C127C2×SD1611yescharacteristic
86C22×C127#13511yescharacteristic
87C22×C127#13711yescharacteristic
88C22×C127#13711yescharacteristic
89C4×C127—22no—
90C4×C127—42no—
91C4×C127—41no—
92C4×C127—81no—
93C4×C127#12111yescharacteristic
94C4×C127C22⋊Q811yescharacteristic
95C4×C127C22⋊Q811yescharacteristic
96C4×C127#12611yescharacteristic
97Dic127—42no—
98Dic127—81no—
99C2×C127#39611yescharacteristic
100C2×C127#46111yescharacteristic
101C2×C127#46411yescharacteristic
102C2×C127#46511yescharacteristic
103C2×C127#47011yescharacteristic
104C2×C127#47511yescharacteristic
105C2×C127#47911yescharacteristic
106#2066—1271nomaximal, Sylow
107C127#206611yescharacteristic, complemented, Sylow
108C2×#106—1271no—
109C2×C4⋊C8—1271no—
110C2×#103—1271no—
111C2×#103—1271no—
112#391D12711yescharacteristic
113#389—1271no—
114#340—1271no—
115C22×Q8C2×D12711yescharacteristic
116C22×C8—1271no—
117C22×C8—1271no—
118C2×C4⋊C4—1271no—
119C2×C4⋊C4—1271no—
120C2×C4⋊C4—2541no—
121C2×C4⋊C4C2×D12711yescharacteristic
122C2×C42C2×D12711yescharacteristic
123#106—2542no—
124C4⋊C8—2542no—
125#103—2542no—
126#103—2542no—
127#95—21no—
128#95—21no—
129#95—2541no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—21no—
135C2×Q8Dic25412yes—
136C22×C4—21no—
137C22×C4—21no—
138C22×C4—2541no—
139C22×C4—2541no—
140C22×C4C22⋊D12711yescharacteristic
141C22×C4C22⋊D12711yescharacteristic
142C22×C4C22×D12711yescharacteristic
143C2×C8—1272no—
144C2×C8—2541no—
145C2×C8—2541no—
146C2×C8—2541no—
147C2×C8—2541no—
148C2×C8—2541no—
149C4⋊C4—21no—
150C4⋊C4—21no—
151C4⋊C4—1272no—
152C4⋊C4—5082no—
153C4⋊C4—2541no—
154C4⋊C4—2541no—
155C4⋊C4—2541no—
156C42—21no—
157C42—21no—
158C23C2×C22⋊D12711yescharacteristic
159Q8—22no—
160Q8—22no—
161Q8—41no—
162Q8—41no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—22no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—5081no—
175C2×C4—5081no—
176C2×C4—5081no—
177C2×C4—5081no—
178C2×C4—5081no—
179C2×C4—2542no—
180C2×C4#1452323512yes—
181C2×C4D4×D12711yescharacteristic
182C2×C4D4×D12711yescharacteristic
183C2×C4C2×Dic25411yescharacteristic
184C2×C4#1452324711yescharacteristic
185C2×C4#1452324711yescharacteristic
186C2×C4#1452324811yescharacteristic
187C8—5081no—
188C8—2542no—
189C22#1686118011yescharacteristic
190C22#1686118111yescharacteristic
191C22#1686118811yescharacteristic
192C22C2×#1452323511yescharacteristic
193C22#1686122911yescharacteristic
194C22#1686123911yescharacteristic
195C22#1686124011yescharacteristic
196C4—22no—
197C4—42no—
198C4—41no—
199C4—81no—
200C4—10161no—
201C4—5082no—
202C4#1686118211yescharacteristic
203C4#1686118611yescharacteristic
204C4#1686118611yescharacteristic
205C4#1686120211yescharacteristic
206C2#2254979911yescharacteristic
207C2#2255007811yescharacteristic
208C2#2255009511yescharacteristic
209C2#2255010711yescharacteristic
210C2#2255013211yescharacteristic
211C2#2255016111yescharacteristic
212C2#2255018311yescharacteristic
subgroupG/H
centerC23C2×C22⋊D127
commutator, cosocleC22×C4×C127C23
FrattiniC22×C4C22×D127
Fitting#391×C127C2
socle, prime radicalC23×C127C2×D4
hypercenter#391D127
hypocenterC127#2066
LCSG ▷ C22×C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
107. C127#2066semidirect

Maximal subgroups

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

subgroupindex
C2×#168611402
C2×C4⋊(C127⋊C8)2
C2×#168611332
#225497742
#225496382
#391×C1272
#2066127