Finite Group Databasebeta

← C127×#3354 #30636306

Subgroups — C127×#3354 #30636306

Order 16256.

386 conjugacy classes of subgroups.

The subgroup lattice has 256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#555×C127C211yesmaximal, characteristic, complemented
2#547×C127C211yesmaximal, characteristic, complemented
3#498×C127C211yesmaximal, characteristic, complemented
4#482×C127C212yesmaximal, complemented
5#481×C127C212yesmaximal, complemented
6#476×C127C211yesmaximal, characteristic, complemented
7#474×C127C211yesmaximal, characteristic, complemented
8#469×C127C212yesmaximal, complemented
9C4×D8×C127C211yesmaximal, characteristic, complemented
10#436×C127C211yesmaximal, characteristic, complemented
11#428×C127C212yesmaximal, complemented
12C2×#41×C127—21no—
13C2×D8×C127C2211yescharacteristic
14C2×M16×C127C2212yes—
15C4⋊Q8×C127C2211yescharacteristic
16C4⋊Q8×C127C2211yescharacteristic
17#124×C127—22no—
18#123×C127—22no—
19C22⋊Q8×C127—21no—
20#121×C127—21no—
21#121×C127C2212yes—
22#121×C127C2212yes—
23C4×D4×C127C2211yescharacteristic
24C4×D4×C127C2211yescharacteristic
25C4×D4×C127C2211yescharacteristic
26#117×C127—21no—
27#117×C127C2212yes—
28C2×C4⋊C4×C127C2212yes—
29#107×C127C2211yescharacteristic
30#107×C127C2212yes—
31#106×C127C2212yes—
32#106×C127C2212yes—
33#106×C127C2212yes—
34C4⋊C8×C127C2211yescharacteristic
35#102×C127C2211yescharacteristic
36#102×C127C2211yescharacteristic
37#102×C127C2212yes—
38#102×C127C2212yes—
39C22⋊C8×C127C2212yes—
40C4×C8×C127C2211yescharacteristic
41#41×C127—44no—
42C2×Q8×C127—21no—
43C2×Q8×C127—21no—
44C2×D4×C127—22no—
45C2×D4×C127—22no—
46C2×D4×C127D411yescharacteristic
47C2×D4×C127C2311yescharacteristic
48C2×D4×C127C2311yescharacteristic
49C22×C4×C127—22no—
50C22×C4×C127—21no—
51C22×C4×C127—21no—
52C22×C4×C127C2312yes—
53D8×C127—22no—
54M16×C127—24no—
55C2×C8×C127C2311yescharacteristic
56C2×C8×C127C2312yes—
57C2×C8×C127C2311yescharacteristic
58C4⋊C4×C127—22no—
59C4⋊C4×C127—21no—
60C4⋊C4×C127—21no—
61C4⋊C4×C127D411yescharacteristic
62C4⋊C4×C127C2312yes—
63C4⋊C4×C127C2311yescharacteristic
64C4⋊C4×C127C2312yes—
65C4⋊C4×C127C2311yescharacteristic
66C22⋊C4×C127—22no—
67C22⋊C4×C127—22no—
68C22⋊C4×C127—21no—
69C22⋊C4×C127—21no—
70C22⋊C4×C127—22no—
71C22⋊C4×C127D412yes—
72C42×C127—22no—
73C42×C127C2311yescharacteristic
74C23×C127—21no—
75C23×C127—21no—
76C23×C127C2×D412yes—
77Q8×C127—42no—
78Q8×C127—81no—
79D4×C127—22no—
80D4×C127—21no—
81D4×C127—21no—
82D4×C127—21no—
83D4×C127—21no—
84D4×C127—44no—
85D4×C127—82no—
86C2×C4×C127—22no—
87C2×C4×C127—22no—
88C2×C4×C127—21no—
89C2×C4×C127—22no—
90C2×C4×C127—21no—
91C2×C4×C127—22no—
92C2×C4×C127—44no—
93C2×C4×C127—42no—
94C2×C4×C127—42no—
95C2×C4×C127C2×D412yes—
96C2×C4×C127C2×D411yescharacteristic
97C2×C4×C127C2×D411yescharacteristic
98C2×C4×C127C2411yescharacteristic
99C8×C127—22no—
100C8×C127—21no—
101C8×C127#4112yescomplemented
102C22×C127—22no—
103C22×C127—22no—
104C22×C127—22no—
105C22×C127—41no—
106C22×C127—41no—
107C22×C127—41no—
108C22×C127—41no—
109C22×C127—41no—
110C22×C127—41no—
111C22×C127C22×D411yescharacteristic
112C4×C127—22no—
113C4×C127—21no—
114C4×C127—41no—
115C4×C127—41no—
116C4×C127—42no—
117C4×C127—42no—
118C4×C127AGL(1,ℤ/8)12yes—
119C4×C127C2×#4111yescharacteristic
120C4×C1272−1+411yescharacteristic
121C2×C127—42no—
122C2×C127—81no—
123C2×C127—81no—
124C2×C127#54711yescharacteristic
125C2×C127C2×AGL(1,ℤ/8)11yescharacteristic
126C2×C127#57711yescharacteristic
127#3354C12711yesmaximal, characteristic, direct product factor, Sylow
128C127#335411yescharacteristic, direct product factor, Sylow
129#555C2×C12711yescharacteristic, complemented
130#547C2×C12711yescharacteristic, complemented
131#498C2×C12711yescharacteristic, complemented
132#482C2×C12712yescomplemented
133#481C2×C12712yescomplemented
134#476C2×C12711yescharacteristic, complemented
135#474C2×C12711yescharacteristic, complemented
136#469C2×C12712yescomplemented
137C4×D8C2×C12711yescharacteristic, complemented
138#436C2×C12711yescharacteristic, complemented
139#428C2×C12712yescomplemented
140C2×#41—21no—
141C2×D8C22×C12711yescharacteristic
142C2×M16C22×C12712yes—
143C4⋊Q8C22×C12711yescharacteristic
144C4⋊Q8C22×C12711yescharacteristic
145#124—22no—
146#123—22no—
147C22⋊Q8—21no—
148#121—21no—
149#121C22×C12712yes—
150#121C22×C12712yes—
151C4×D4C22×C12711yescharacteristic
152C4×D4C22×C12711yescharacteristic
153C4×D4C22×C12711yescharacteristic
154#117—21no—
155#117C22×C12712yes—
156C2×C4⋊C4C22×C12712yes—
157#107C22×C12711yescharacteristic
158#107C22×C12712yes—
159#106C22×C12712yes—
160#106C22×C12712yes—
161#106C22×C12712yes—
162C4⋊C8C22×C12711yescharacteristic
163#102C22×C12711yescharacteristic
164#102C22×C12711yescharacteristic
165#102C22×C12712yes—
166#102C22×C12712yes—
167C22⋊C8C22×C12712yes—
168C4×C8C22×C12711yescharacteristic
169#41—44no—
170C2×Q8—21no—
171C2×Q8—21no—
172C2×D4—22no—
173C2×D4—22no—
174C2×D4D4×C12711yescharacteristic
175C2×D4C23×C12711yescharacteristic
176C2×D4C23×C12711yescharacteristic
177C22×C4—22no—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4C23×C12712yes—
181D8—22no—
182M16—24no—
183C2×C8C23×C12711yescharacteristic
184C2×C8C23×C12712yes—
185C2×C8C23×C12711yescharacteristic
186C4⋊C4—22no—
187C4⋊C4—21no—
188C4⋊C4—21no—
189C4⋊C4D4×C12711yescharacteristic
190C4⋊C4C23×C12712yes—
191C4⋊C4C23×C12711yescharacteristic
192C4⋊C4C23×C12712yes—
193C4⋊C4C23×C12711yescharacteristic
194C22⋊C4—22no—
195C22⋊C4—22no—
196C22⋊C4—21no—
197C22⋊C4—21no—
198C22⋊C4—22no—
199C22⋊C4D4×C12712yes—
200C42—22no—
201C42C23×C12711yescharacteristic
202C23—21no—
203C23—21no—
204C23C2×D4×C12712yes—
205Q8—42no—
206Q8—81no—
207D4—22no—
208D4—21no—
209D4—21no—
210D4—21no—
211D4—21no—
212D4—44no—
213D4—82no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—44no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4C2×D4×C12712yes—
224C2×C4C2×D4×C12711yescharacteristic
225C2×C4C2×D4×C12711yescharacteristic
226C2×C4C24×C12711yescharacteristic
227C8—22no—
228C8—21no—
229C8#41×C12712yescomplemented
230C22—22no—
231C22—22no—
232C22—22no—
233C22—41no—
234C22—41no—
235C22—41no—
236C22—41no—
237C22—41no—
238C22—41no—
239C22C22×D4×C12711yescharacteristic
240C4—22no—
241C4—21no—
242C4—41no—
243C4—42no—
244C4—41no—
245C4—42no—
246C4AGL(1,ℤ/8)×C12712yes—
247C4C2×#41×C12711yescharacteristic
248C42−1+4×C12711yescharacteristic
249C2—42no—
250C2—81no—
251C2—81no—
252C2#547×C12711yescharacteristic
253C2C2×AGL(1,ℤ/8)×C12711yescharacteristic
254C2#577×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C22×D4
commutator, Frattini, cosocleC2×C4C24×C127
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C4×D4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. #555×C127C2semidirect
2. #547×C127C2semidirect
3. #498×C127C2semidirect
4. #482×C127C2semidirect
5. #481×C127C2semidirect
6. #476×C127C2semidirect
7. #474×C127C2semidirect
8. #469×C127C2semidirect
9. C4×D8×C127C2semidirect
10. #436×C127C2semidirect
11. #428×C127C2semidirect
101. C8×C127#41semidirect
127. #3354C127direct (N × H)
128. C127#3354direct (N × H)
129. #555C2×C127semidirect
130. #547C2×C127semidirect
131. #498C2×C127semidirect
132. #482C2×C127semidirect
133. #481C2×C127semidirect
134. #476C2×C127semidirect
135. #474C2×C127semidirect
136. #469C2×C127semidirect
137. C4×D8C2×C127semidirect
138. #436C2×C127semidirect
139. #428C2×C127semidirect
229. C8#41×C127semidirect

Maximal subgroups

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

subgroupindex
#555×C1272
#547×C1272
#498×C1272
#482×C1272
#481×C1272
#476×C1272
#474×C1272
#469×C1272
C4×D8×C1272
#436×C1272
#428×C1272
#3354127