Finite Group Databasebeta

← C127×#3203 #30636155

Subgroups — C127×#3203 #30636155

Order 16256.

402 conjugacy classes of subgroups.

The subgroup lattice has 240 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#537×C127C212yesmaximal, complemented
2#484×C127C212yesmaximal, complemented
3#480×C127C212yesmaximal, complemented
4#468×C127C212yesmaximal, complemented
5#467×C127C211yesmaximal, characteristic, complemented
6#466×C127C211yesmaximal, characteristic, complemented
7#452×C127C212yesmaximal, complemented
8#449×C127C212yesmaximal, complemented
9#408×C127C211yesmaximal, characteristic, complemented
10C2×#41×C127C2212yes—
11C2×#41×C127C2211yescharacteristic
12C2×Q16×C127C2211yescharacteristic
13C2×SD16×C127C2212yes—
14C2×D8×C127C2211yescharacteristic
15C2×M16×C127C2211yescharacteristic
16C22×C8×C127C2211yescharacteristic
17C22⋊Q8×C127—22no—
18C22⋊Q8×C127C2212yes—
19C22⋊Q8×C127C2212yes—
20#121×C127—22no—
21#121×C127—22no—
22#121×C127—22no—
23#121×C127C2212yes—
24#121×C127C2212yes—
25C2×C4⋊C4×C127C2212yes—
26#107×C127C2211yescharacteristic
27#107×C127C2211yescharacteristic
28#107×C127C2212yes—
29#103×C127C2212yes—
30#103×C127C2212yes—
31#102×C127C2212yes—
32#102×C127C2212yes—
33C22⋊C8×C127C2212yes—
34C22⋊C8×C127C2212yes—
35#41×C127—41no—
36#41×C127—41no—
37#41×C127—42no—
38#41×C127—42no—
39C2×Q8×C127D411yescharacteristic
40C2×Q8×C127C2312yes—
41C2×D4×C127—22no—
42C2×D4×C127—22no—
43C2×D4×C127—22no—
44C2×D4×C127D411yescharacteristic
45C2×D4×C127D412yes—
46C2×D4×C127C2312yes—
47C22×C4×C127—22no—
48C22×C4×C127—22no—
49C22×C4×C127C2312yes—
50C22×C4×C127C2311yescharacteristic
51Q16×C127—41no—
52SD16×C127—42no—
53D8×C127—41no—
54M16×C127—41no—
55C2×C8×C127—41no—
56C2×C8×C127C2311yescharacteristic
57C2×C8×C127C2312yes—
58C2×C8×C127C2311yescharacteristic
59C4⋊C4×C127—22no—
60C4⋊C4×C127—22no—
61C4⋊C4×C127—22no—
62C4⋊C4×C127C2312yes—
63C4⋊C4×C127C2312yes—
64C22⋊C4×C127—22no—
65C22⋊C4×C127—22no—
66C22⋊C4×C127—22no—
67C22⋊C4×C127—22no—
68C23×C127—22no—
69C23×C127C2×D411yescharacteristic
70C23×C127C2×D412yes—
71Q8×C127—22no—
72Q8×C127—22no—
73Q8×C127—41no—
74D4×C127—22no—
75D4×C127—22no—
76D4×C127—42no—
77D4×C127—41no—
78D4×C127—44no—
79D4×C127—82no—
80D4×C127—82no—
81C2×C4×C127—21no—
82C2×C4×C127—21no—
83C2×C4×C127—22no—
84C2×C4×C127—22no—
85C2×C4×C127—22no—
86C2×C4×C127—22no—
87C2×C4×C127—22no—
88C2×C4×C127—44no—
89C2×C4×C127—82no—
90C2×C4×C127C2×D411yescharacteristic
91C2×C4×C127C2×D412yes—
92C2×C4×C127C2411yescharacteristic
93C8×C127—21no—
94C8×C127—21no—
95C8×C127—22no—
96C22×C127—22no—
97C22×C127—21no—
98C22×C127—22no—
99C22×C127—21no—
100C22×C127—21no—
101C22×C127—22no—
102C22×C127—42no—
103C22×C127—42no—
104C22×C127—42no—
105C22×C127C22×D411yescharacteristic
106C4×C127—22no—
107C4×C127—21no—
108C4×C127—42no—
109C4×C127—42no—
110C4×C127—42no—
111C4×C127H(5,𝔽2)11yescharacteristic
112C4×C127H(5,𝔽2)11yescharacteristic
113C2×C127—42no—
114C2×C127—41no—
115C2×C127—82no—
116C2×C127#53411yescharacteristic
117C2×C127#57611yescharacteristic
118C2×C127#57811yescharacteristic
119#3203C12711yesmaximal, characteristic, direct product factor, Sylow
120C127#320311yescharacteristic, direct product factor, Sylow
121#537C2×C12712yescomplemented
122#484C2×C12712yescomplemented
123#480C2×C12712yescomplemented
124#468C2×C12712yescomplemented
125#467C2×C12711yescharacteristic, complemented
126#466C2×C12711yescharacteristic, complemented
127#452C2×C12712yescomplemented
128#449C2×C12712yescomplemented
129#408C2×C12711yescharacteristic, complemented
130C2×#41C22×C12712yes—
131C2×#41C22×C12711yescharacteristic
132C2×Q16C22×C12711yescharacteristic
133C2×SD16C22×C12712yes—
134C2×D8C22×C12711yescharacteristic
135C2×M16C22×C12711yescharacteristic
136C22×C8C22×C12711yescharacteristic
137C22⋊Q8—22no—
138C22⋊Q8C22×C12712yes—
139C22⋊Q8C22×C12712yes—
140#121—22no—
141#121—22no—
142#121—22no—
143#121C22×C12712yes—
144#121C22×C12712yes—
145C2×C4⋊C4C22×C12712yes—
146#107C22×C12711yescharacteristic
147#107C22×C12711yescharacteristic
148#107C22×C12712yes—
149#103C22×C12712yes—
150#103C22×C12712yes—
151#102C22×C12712yes—
152#102C22×C12712yes—
153C22⋊C8C22×C12712yes—
154C22⋊C8C22×C12712yes—
155#41—41no—
156#41—41no—
157#41—42no—
158#41—42no—
159C2×Q8D4×C12711yescharacteristic
160C2×Q8C23×C12712yes—
161C2×D4—22no—
162C2×D4—22no—
163C2×D4—22no—
164C2×D4D4×C12711yescharacteristic
165C2×D4D4×C12712yes—
166C2×D4C23×C12712yes—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4C23×C12712yes—
170C22×C4C23×C12711yescharacteristic
171Q16—41no—
172SD16—42no—
173D8—41no—
174M16—41no—
175C2×C8—41no—
176C2×C8C23×C12711yescharacteristic
177C2×C8C23×C12712yes—
178C2×C8C23×C12711yescharacteristic
179C4⋊C4—22no—
180C4⋊C4—22no—
181C4⋊C4—22no—
182C4⋊C4C23×C12712yes—
183C4⋊C4C23×C12712yes—
184C22⋊C4—22no—
185C22⋊C4—22no—
186C22⋊C4—22no—
187C22⋊C4—22no—
188C23—22no—
189C23C2×D4×C12711yescharacteristic
190C23C2×D4×C12712yes—
191Q8—22no—
192Q8—22no—
193Q8—41no—
194D4—22no—
195D4—22no—
196D4—42no—
197D4—41no—
198D4—44no—
199D4—82no—
200D4—82no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—44no—
209C2×C4—82no—
210C2×C4C2×D4×C12711yescharacteristic
211C2×C4C2×D4×C12712yes—
212C2×C4C24×C12711yescharacteristic
213C8—21no—
214C8—21no—
215C8—22no—
216C22—22no—
217C22—21no—
218C22—22no—
219C22—21no—
220C22—21no—
221C22—22no—
222C22—42no—
223C22—42no—
224C22—42no—
225C22C22×D4×C12711yescharacteristic
226C4—22no—
227C4—21no—
228C4—42no—
229C4—42no—
230C4—42no—
231C4H(5,𝔽2)×C12711yescharacteristic
232C4H(5,𝔽2)×C12711yescharacteristic
233C2—42no—
234C2—41no—
235C2—82no—
236C2#534×C12711yescharacteristic
237C2#576×C12711yescharacteristic
238C2#578×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C22×D4
commutator, Frattini, cosocleC2×C4C24×C127
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×#41×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. #537×C127C2semidirect
2. #484×C127C2semidirect
3. #480×C127C2semidirect
4. #468×C127C2semidirect
5. #467×C127C2semidirect
6. #466×C127C2semidirect
7. #452×C127C2semidirect
8. #449×C127C2semidirect
9. #408×C127C2semidirect
119. #3203C127direct (N × H)
120. C127#3203direct (N × H)
121. #537C2×C127semidirect
122. #484C2×C127semidirect
123. #480C2×C127semidirect
124. #468C2×C127semidirect
125. #467C2×C127semidirect
126. #466C2×C127semidirect
127. #452C2×C127semidirect
128. #449C2×C127semidirect
129. #408C2×C127semidirect

Maximal subgroups

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

subgroupindex
#537×C1272
#484×C1272
#480×C1272
#468×C1272
#467×C1272
#466×C1272
#452×C1272
#449×C1272
#408×C1272
#3203127