Finite Group Databasebeta

← C2×#22549670 #30640390

Subgroups — C2×#22549670 #30640390

Order 16256.

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

normal subgroups only

This group has 284 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×#16861196C211yesmaximal, characteristic
2C2×#16861124C211yesmaximal, characteristic
3#22549670C214yesmaximal, direct product factor
4C2×#99×C127C211yesmaximal, characteristic
5C22×Dic254C411yescharacteristic, complemented
6#16861196—21no—
7#16861196—21no—
8#16861196C412yescomplemented
9#16861196C2212yes—
10C2×C22⋊Dic127—21no—
11C2×C22⋊Dic127—21no—
12C2×C22⋊Dic127—21no—
13C2×C4×Dic127C411yescharacteristic, complemented
14#16861124—21no—
15#16861124C2212yes—
16C22×D4×C127C2211yescharacteristic
17C2×C22⋊C4×C127—21no—
18#99×C127—21no—
19#99×C127C2212yes—
20C2×Dic254—21no—
21C2×Dic254—41no—
22C2×Dic254—41no—
23C2×Dic254C2×C412yescomplemented
24C22×Dic127—21no—
25C22×Dic127—21no—
26C22×Dic127—41no—
27C22⋊Dic127—22no—
28C22⋊Dic127—22no—
29C22⋊Dic127—22no—
30C22⋊Dic127—22no—
31C22⋊Dic127—22no—
32C22⋊Dic127—41no—
33C4×Dic127—21no—
34C4×Dic127C2×C412yescomplemented
35C24×C127D411yescharacteristic
36C24×C127D411yescharacteristic
37C2×D4×C127—41no—
38C2×D4×C127—41no—
39C2×D4×C127C2×C411yescharacteristic
40C2×D4×C127D411yescharacteristic
41C2×D4×C127D411yescharacteristic
42C2×D4×C127C2311yescharacteristic
43C22×C4×C127—41no—
44C22×C4×C127C2×C411yescharacteristic
45C22⋊C4×C127—22no—
46C22⋊C4×C127—41no—
47Dic254—42no—
48Dic254—42no—
49C2×Dic127—22no—
50C2×Dic127—22no—
51C2×Dic127—42no—
52C2×Dic127—41no—
53C2×Dic127—41no—
54C2×Dic127—42no—
55C2×Dic127—82no—
56C23×C127—21no—
57C23×C127—21no—
58C23×C127—21no—
59C23×C127—21no—
60C23×C127—42no—
61C23×C127—42no—
62C23×C127C22⋊C411yescharacteristic
63C23×C127C22⋊C411yescharacteristic
64C23×C127C22⋊C411yescharacteristic
65C23×C127C2×D411yescharacteristic
66C23×C127C2×D411yescharacteristic
67D4×C127—41no—
68D4×C127—41no—
69D4×C127—41no—
70D4×C127—41no—
71C2×C4×C127—21no—
72C2×C4×C127—21no—
73C2×C4×C127—42no—
74C2×C4×C127—82no—
75C2×C4×C127C22⋊C411yescharacteristic
76C2×C4×C127C22×C411yescharacteristic
77C22×C127—22no—
78C22×C127—21no—
79C22×C127—21no—
80C22×C127—21no—
81C22×C127—21no—
82C22×C127—41no—
83C22×C127—41no—
84C22×C127—41no—
85C22×C127—41no—
86C22×C127—42no—
87C22×C127—42no—
88C22×C127—81no—
89C22×C127—81no—
90C22×C127#9911yescharacteristic
91C22×C127#9911yescharacteristic
92C22×C127C2×C22⋊C411yescharacteristic
93C4×C127—21no—
94C4×C127—21no—
95C4×C127—82no—
96Dic127—42no—
97Dic127—42no—
98Dic127—82no—
99C2×C127—21no—
100C2×C127—21no—
101C2×C127—41no—
102C2×C127—41no—
103C2×C127—41no—
104C2×C127—41no—
105C2×C127#35412yescomplemented
106C2×C127C2×#9911yescharacteristic
107C2×#354—1271nomaximal, Sylow
108C127C2×#35411yescharacteristic, complemented, Sylow
109C2×#124—1271no—
110C2×#99—1271no—
111C2×#99D12711yescharacteristic
112#354—1274no—
113C22×Q8—1271no—
114C22×D4C2×D12711yescharacteristic
115#124—1272no—
116#124—1272no—
117#124—2541no—
118#124—2541no—
119C2×C22⋊C4—21no—
120C2×C22⋊C4—2541no—
121C2×C22⋊C4—2541no—
122C2×C22⋊C4—2541no—
123C2×C42—1271no—
124#99—21no—
125#99—1272no—
126#99—2541no—
127#99C2×D12712yes—
128C24C22⋊D12711yescharacteristic
129C24D50811yescharacteristic
130C2×Q8—1272no—
131C2×Q8—5081no—
132C2×Q8—5081no—
133C2×Q8—2541no—
134C2×D4—41no—
135C2×D4—41no—
136C2×D4C4×D12711yescharacteristic
137C2×D4C22⋊D12711yescharacteristic
138C2×D4D50811yescharacteristic
139C2×D4C22×D12711yescharacteristic
140C22×C4—41no—
141C22×C4—5081no—
142C22×C4—2541no—
143C22×C4—2541no—
144C22×C4C4×D12711yescharacteristic
145C22⋊C4—22no—
146C22⋊C4—41no—
147C22⋊C4—5081no—
148C22⋊C4—2542no—
149C22⋊C4—2542no—
150C22⋊C4—2542no—
151C22⋊C4—2542no—
152C22⋊C4—2542no—
153C42—1272no—
154C42—2541no—
155C23—21no—
156C23—21no—
157C23—21no—
158C23—21no—
159C23—42no—
160C23—42no—
161C23(C2×D127)⋊C411yescharacteristic
162C23(C2×D127)⋊C411yescharacteristic
163C23(C2×D127)⋊C411yescharacteristic
164C23C2×C22⋊D12711yescharacteristic
165C23C2×D50811yescharacteristic
166Q8—5082no—
167Q8—5082no—
168D4—41no—
169D4—41no—
170D4—41no—
171D4—41no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—42no—
175C2×C4—82no—
176C2×C4—10162no—
177C2×C4—5082no—
178C2×C4—5082no—
179C2×C4—5081no—
180C2×C4—5081no—
181C2×C4—2542no—
182C2×C4—2542no—
183C2×C4(C2×D127)⋊C411yescharacteristic
184C2×C4C2×C4×D12711yescharacteristic
185C22—22no—
186C22—21no—
187C22—21no—
188C22—21no—
189C22—21no—
190C22—41no—
191C22—41no—
192C22—41no—
193C22—41no—
194C22—42no—
195C22—42no—
196C22—81no—
197C22—81no—
198C22#1686112311yescharacteristic
199C22#1686112311yescharacteristic
200C22C2×(C2×D127)⋊C411yescharacteristic
201C4—21no—
202C4—21no—
203C4—82no—
204C4—10162no—
205C4—5082no—
206C4—5082no—
207C2—21no—
208C2—21no—
209C2—41no—
210C2—41no—
211C2—41no—
212C2—41no—
213C2#2254967012yesdirect product factor
214C2C2×#1686112311yescharacteristic
subgroupG/H
centerC22#16861123
commutatorC2×C4×C127C22×C4
FrattiniC2×D4C22×D127
FittingC2×#99×C127C2
socleC22×C127#99
prime radicalC22×D4×C127C22
cosocleC2×D4×C127C23
hypercenterC2×#99D127
hypocenterC127C2×#354
LCSG ▷ C2×C4×C127 ▷ C22×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
3. #22549670C2direct (N × H)
5. C22×Dic254C4semidirect
8. #16861196C4semidirect
13. C2×C4×Dic127C4semidirect
23. C2×Dic254C2×C4semidirect
34. C4×Dic127C2×C4semidirect
105. C2×C127#354semidirect
108. C127C2×#354semidirect
213. C2#22549670direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168611962
C2×#168611242
#225496702
C2×#99×C1272
C2×#354127