Finite Group Databasebeta

← C2×#22549674 #30640410

Subgroups — C2×#22549674 #30640410

Order 16256.

240 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 69 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×#16861207C211yesmaximal, characteristic
2C2×#16861128C211yesmaximal, characteristic
3#22549674C214yesmaximal, direct product factor
4C2×#101×C127C211yesmaximal, characteristic
5C22×Dic254C411yescharacteristic
6C2×#14523232—21no—
7#16861207—21no—
8#16861207—21no—
9#16861207C412yes—
10#16861207C2212yes—
11C2×Dic127⋊C4—21no—
12C2×Dic127⋊C4—21no—
13C2×C4×Dic127C411yescharacteristic
14#16861128—21no—
15#16861128C2212yes—
16C22×Q8×C127C2211yescharacteristic
17C2×M16×C127—21no—
18#101×C127—21no—
19#101×C127C2212yes—
20C2×Dic254—21no—
21C2×Dic254—41no—
22C2×Dic254—41no—
23C2×Dic254C2×C412yes—
24C22×Dic127—21no—
25C22×Dic127—21no—
26#14523232—22no—
27#14523232—41no—
28C2×C127⋊C8—41no—
29Dic127⋊C4—22no—
30Dic127⋊C4—22no—
31Dic127⋊C4—22no—
32Dic127⋊C4—22no—
33C4×Dic127—21no—
34C4×Dic127C2×C412yes—
35C2×Q8×C127—41no—
36C2×Q8×C127—41no—
37C2×Q8×C127C2×C411yescharacteristic
38C2×Q8×C127D411yescharacteristic
39C2×Q8×C127D411yescharacteristic
40C2×Q8×C127C2311yescharacteristic
41C22×C4×C127C2×C411yescharacteristic
42C22×C4×C127D411yescharacteristic
43C22×C4×C127D411yescharacteristic
44M16×C127—22no—
45M16×C127—41no—
46C2×C8×C127—41no—
47Dic254—42no—
48Dic254—42no—
49C2×Dic127—24no—
50C2×Dic127—22no—
51C2×Dic127—22no—
52C2×Dic127—41no—
53C2×Dic127—41no—
54C127⋊C8—42no—
55C23×C127C22⋊C411yescharacteristic
56Q8×C127—41no—
57Q8×C127—41no—
58Q8×C127—41no—
59Q8×C127—41no—
60C2×C4×C127—21no—
61C2×C4×C127—21no—
62C2×C4×C127—21no—
63C2×C4×C127—21no—
64C2×C4×C127—21no—
65C2×C4×C127—21no—
66C2×C4×C127C22⋊C411yescharacteristic
67C2×C4×C127C22⋊C411yescharacteristic
68C2×C4×C127C22⋊C411yescharacteristic
69C2×C4×C127C22×C411yescharacteristic
70C2×C4×C127C2×D411yescharacteristic
71C2×C4×C127C2×D411yescharacteristic
72C8×C127—42no—
73C22×C127—22no—
74C22×C127#9911yescharacteristic
75C22×C127#9911yescharacteristic
76C22×C127C2×C22⋊C411yescharacteristic
77C4×C127—21no—
78C4×C127—21no—
79C4×C127—21no—
80C4×C127—21no—
81C4×C127—21no—
82C4×C127—21no—
83Dic127—24no—
84Dic127—42no—
85C2×C127—21no—
86C2×C127—21no—
87C2×C127#35612yescomplemented
88C2×C127C2×#9911yescharacteristic
89C2×#356—1271nomaximal, Sylow
90C127C2×#35611yescharacteristic, complemented, Sylow
91C2×C4⋊Q8—1271no—
92C2×#101—1271no—
93C2×#101D12711yescharacteristic
94#356—1274no—
95C22×Q8—1271no—
96C22×Q8C2×D12711yescharacteristic
97C2×M16—21no—
98C2×M16—2541no—
99C4⋊Q8—1272no—
100C4⋊Q8—1272no—
101C4⋊Q8—2541no—
102C4⋊Q8—2541no—
103C2×C4⋊C4—2541no—
104C2×C4⋊C4—2541no—
105C2×C42—1271no—
106#101—21no—
107#101—1272no—
108#101—2541no—
109#101C2×D12712yes—
110C2×Q8—41no—
111C2×Q8—41no—
112C2×Q8—1272no—
113C2×Q8—5081no—
114C2×Q8—5081no—
115C2×Q8—2541no—
116C2×Q8C4×D12711yescharacteristic
117C2×Q8C22⋊D12711yescharacteristic
118C2×Q8D50811yescharacteristic
119C2×Q8C22×D12711yescharacteristic
120C22×C4—2541no—
121C22×C4—2541no—
122C22×C4C4×D12711yescharacteristic
123C22×C4C22⋊D12711yescharacteristic
124C22×C4D50811yescharacteristic
125M16—22no—
126M16—41no—
127M16—5081no—
128M16—2542no—
129C2×C8—41no—
130C2×C8—5081no—
131C4⋊C4—2542no—
132C4⋊C4—2542no—
133C4⋊C4—2542no—
134C4⋊C4—2542no—
135C42—1272no—
136C42—2541no—
137C23(C2×D127)⋊C411yescharacteristic
138Q8—41no—
139Q8—41no—
140Q8—41no—
141Q8—41no—
142Q8—5082no—
143Q8—5082no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—5081no—
151C2×C4—5081no—
152C2×C4—2542no—
153C2×C4—2544no—
154C2×C4—2542no—
155C2×C4(C2×D127)⋊C411yescharacteristic
156C2×C4(C2×D127)⋊C411yescharacteristic
157C2×C4(C2×D127)⋊C411yescharacteristic
158C2×C4C2×C4×D12711yescharacteristic
159C2×C4C2×C22⋊D12711yescharacteristic
160C2×C4C2×D50811yescharacteristic
161C8—42no—
162C8—5082no—
163C22—22no—
164C22#1686112311yescharacteristic
165C22#1686112311yescharacteristic
166C22C2×(C2×D127)⋊C411yescharacteristic
167C4—21no—
168C4—21no—
169C4—21no—
170C4—21no—
171C4—21no—
172C4—21no—
173C4—5082no—
174C4—2544no—
175C2—21no—
176C2—21no—
177C2#2254967412yesdirect product factor
178C2C2×#1686112311yescharacteristic
subgroupG/H
centerC22#16861123
commutatorC2×C4×C127C22×C4
FrattiniC2×Q8C22×D127
FittingC2×#101×C127C2
socleC22×C127#99
prime radicalC23×C127C22⋊C4
cosocleC2×Q8×C127C23
hypercenterC2×#101D127
hypocenterC127C2×#356
LCSG ▷ C2×C4×C127 ▷ C22×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
3. #22549674C2direct (N × H)
87. C2×C127#356semidirect
90. C127C2×#356semidirect
177. C2#22549674direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168612072
C2×#168611282
#225496742
C2×#101×C1272
C2×#356127