Finite Group Databasebeta

← #487×D127 #30649038

Subgroups — #487×D127 #30649038

Order 16256.

424 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 145 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
1C4⋊Q8×D127C211yesmaximal, characteristic
2C4⋊Q8×D127C211yesmaximal, characteristic
3#22550228C211yesmaximal, characteristic, complemented
4#22550227C211yesmaximal, characteristic, complemented
5#22550226C211yesmaximal, characteristic, complemented
6#22550225C214yesmaximal, complemented
7#103×D127C214yesmaximal
8C4×C8×D127C211yesmaximal, characteristic
9#487×C127C211yesmaximal, characteristic, complemented
10C2×Q8×D127—21no—
11C2×Q8×D127C2212yes—
12C2×C8×D127C2212yes—
13#16861209C2211yescharacteristic
14#16861209C2211yescharacteristic
15#16861208—21no—
16#16861208—21no—
17#16861208—21no—
18#16861208C2212yes—
19#16861207—21no—
20#16861207C2212yes—
21C4⋊C4×D127—21no—
22C4⋊C4×D127—21no—
23C4⋊C4×D127—21no—
24C4⋊C4×D127C2212yes—
25C42×D127C2211yescharacteristic
26#16861134C2214yes—
27#16861133C2214yes—
28#16861132C2214yes—
29C4×C127⋊C8C2211yescharacteristic
30C8×Dic127C2212yes—
31C4⋊Q8×C127C2211yescharacteristic
32C4⋊Q8×C127C2211yescharacteristic
33#103×C127C2214yes—
34C4×C8×C127C2211yescharacteristic
35C2×Dic254—22no—
36C2×Dic254—22no—
37C2×Dic254—21no—
38C2×Dic254C2312yes—
39Q8×D127—28no—
40Q8×D127—44no—
41C2×C4×D127—22no—
42C2×C4×D127—22no—
43C2×C4×D127D411yescharacteristic
44C2×C4×D127D411yescharacteristic
45C2×C4×D127C2311yescharacteristic
46C2×C127⋊C8C2312yes—
47C8×D127—24no—
48C4⋊Dic127—21no—
49C4⋊Dic127—21no—
50C4⋊Dic127—21no—
51C4⋊Dic127C2312yes—
52Dic127⋊C4—22no—
53Dic127⋊C4—22no—
54Dic127⋊C4—22no—
55Dic127⋊C4—22no—
56C4×Dic127D411yescharacteristic
57C4×Dic127D411yescharacteristic
58C4×Dic127C2311yescharacteristic
59C2×Q8×C127—21no—
60C2×Q8×C127C2312yes—
61C2×C8×C127C2312yes—
62C4⋊C4×C127—21no—
63C4⋊C4×C127—21no—
64C4⋊C4×C127—21no—
65C4⋊C4×C127C2312yes—
66C42×C127C2311yescharacteristic
67C22×D127C2×D411yescharacteristic
68Dic254—24no—
69Dic254—42no—
70Dic254—44no—
71Dic254—44no—
72C2×Dic127—22no—
73C2×Dic127—22no—
74C2×Dic127C2×D411yescharacteristic
75C2×Dic127C2×D411yescharacteristic
76C2×Dic127C2×D411yescharacteristic
77C4×D127—44no—
78C4×D127—44no—
79C4×D127SD1614yes—
80C4×D127Q1614yes—
81C4×D127#4114yes—
82C127⋊C8—22no—
83Q8×C127—24no—
84Q8×C127—42no—
85C2×C4×C127—22no—
86C2×C4×C127—22no—
87C2×C4×C127C2×D411yescharacteristic
88C2×C4×C127C2×D411yescharacteristic
89C2×C4×C127C2411yescharacteristic
90C8×C127—22no—
91C22×C127C22×D411yescharacteristic
92C2×D127#12412yes—
93C2×D127C2×SD1612yes—
94C2×D127C2×Q1612yes—
95C4×C127—42no—
96C4×C127—42no—
97C4×C127C2×SD1612yes—
98C4×C127C2×Q1612yes—
99C4×C127C2×#4112yes—
100Dic127—42no—
101Dic127—42no—
102Dic127#12412yes—
103Dic127C2×SD1612yes—
104Dic127C2×Q1612yes—
105C2×C127C2×#12411yescharacteristic
106C2×C127C22×SD1611yescharacteristic
107C2×C127C22×Q1611yescharacteristic
108D127#48714yesdirect product factor
109C2×#487—1271nomaximal, Sylow
110C127C2×#48711yescharacteristic, complemented, Sylow
111C2×C4⋊Q8—1271no—
112C2×C4⋊Q8—1271no—
113#487—1271no—
114#487—1271no—
115#487—1274no—
116#487—1271no—
117#487D12711yescharacteristic, direct product factor
118C2×#103—1274no—
119C2×C4×C8—1271no—
120C22×Q8—1272no—
121C22×Q8—2541no—
122C22×C8—1272no—
123C4⋊Q8—1272no—
124C4⋊Q8—1272no—
125C4⋊Q8—1271no—
126C4⋊Q8—1271no—
127C4⋊Q8—2541no—
128C4⋊Q8—2541no—
129C4⋊Q8—2541no—
130C4⋊Q8—2541no—
131C4⋊Q8C2×D12711yescharacteristic
132C4⋊Q8C2×D12711yescharacteristic
133C2×C4⋊C4—1272no—
134C2×C4⋊C4—2541no—
135C2×C4⋊C4—2541no—
136C2×C4⋊C4—2541no—
137C2×C42—1271no—
138#103—1274no—
139#103—1274no—
140#103—1274no—
141#103C2×D12714yes—
142C4×C8—1272no—
143C4×C8—1271no—
144C4×C8C2×D12711yescharacteristic
145C2×Q8—21no—
146C2×Q8—1272no—
147C2×Q8—5084no—
148C2×Q8—2542no—
149C2×Q8—2542no—
150C2×Q8—2548no—
151C2×Q8—2541no—
152C2×Q8C22×D12712yes—
153C22×C4—1271no—
154C22×C4—1271no—
155C22×C4—1271no—
156C22×C4—2542no—
157C22×C4—2542no—
158C2×C8—1272no—
159C2×C8—2544no—
160C2×C8C22×D12712yes—
161C4⋊C4—21no—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—1272no—
165C4⋊C4—2542no—
166C4⋊C4—2542no—
167C4⋊C4—2542no—
168C4⋊C4—2542no—
169C4⋊C4—2541no—
170C4⋊C4—2541no—
171C4⋊C4—2541no—
172C4⋊C4C22×D12712yes—
173C42—1271no—
174C42—1271no—
175C42—1271no—
176C42C22×D12711yescharacteristic
177C23—1271no—
178Q8—24no—
179Q8—42no—
180Q8—5084no—
181Q8—5084no—
182Q8—5082no—
183Q8—2544no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—1271no—
187C2×C4—1271no—
188C2×C4—1271no—
189C2×C4—1274no—
190C2×C4—1274no—
191C2×C4—1274no—
192C2×C4—5084no—
193C2×C4—5084no—
194C2×C4—2542no—
195C2×C4—2542no—
196C2×C4D4×D12711yescharacteristic
197C2×C4D4×D12711yescharacteristic
198C2×C4C23×D12711yescharacteristic
199C8—22no—
200C8—2542no—
201C22—1272no—
202C22—1272no—
203C22—1272no—
204C22C2×D4×D12711yescharacteristic
205C4—42no—
206C4—42no—
207C4—1272no—
208C4—1272no—
209C4—1272no—
210C4—5082no—
211C4—5082no—
212C4SD16×D12712yes—
213C4Q16×D12712yes—
214C4#41×D12712yes—
215C2—1274no—
216C2#124×D12711yescharacteristic
217C2C2×SD16×D12711yescharacteristic
218C2C2×Q16×D12711yescharacteristic
subgroupG/H
centerC22C2×D4×D127
commutator, cosocleC2×C4×C127C24
FrattiniC2×C4C23×D127
Fitting#487×C127C2
socleC22×C127C22×D4
prime radicalC22×D127C2×D4
hypercenter#487D127
hypocenterC127C2×#487
LCSG ▷ C2×C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
3. #22550228C2semidirect
4. #22550227C2semidirect
5. #22550226C2semidirect
6. #22550225C2semidirect
9. #487×C127C2semidirect
108. D127#487direct (N × H)
110. C127C2×#487semidirect
117. #487D127direct (N × H)

Maximal subgroups

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

subgroupindex
C4⋊Q8×D1272
#225502282
#225502272
#225502262
#225502252
#103×D1272
C4×C8×D1272
#487×C1272
C2×#487127