Finite Group Databasebeta

← C127×#1876 #30634828

Subgroups — C127×#1876 #30634828

Order 16256.

324 conjugacy classes of subgroups.

The subgroup lattice has 262 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#135×C127C211yesmaximal, characteristic
2C2×#131×C127C211yesmaximal, characteristic, complemented
3C2×#104×C127C211yesmaximal, characteristic, complemented
4C2×#104×C127C211yesmaximal, characteristic, complemented
5#408×C127C211yesmaximal, characteristic, complemented
6#341×C127C211yesmaximal, characteristic, complemented
7#336×C127C211yesmaximal, characteristic, complemented
8C2×#41×C127C2211yescharacteristic
9C2×#41×C127C2211yescharacteristic
10#135×C127—22no—
11#135×C127—22no—
12C2×Q16×C127C411yescharacteristic, complemented
13C2×SD16×C127C411yescharacteristic, complemented
14C2×SD16×C127C411yescharacteristic, complemented
15C2×D8×C127C411yescharacteristic, complemented
16#131×C127—22no—
17#131×C127—22no—
18C2×M16×C127—21no—
19C2×M16×C127C2211yescharacteristic
20C2×M16×C127C2211yescharacteristic
21C22×C8×C127—21no—
22C22×C8×C127C2211yescharacteristic
23C22×C8×C127C2211yescharacteristic
24C2×C42×C127C2211yescharacteristic
25#104×C127—22no—
26#104×C127—22no—
27C22⋊C8×C127—21no—
28C22⋊C8×C127—21no—
29#41×C127—21no—
30#41×C127—21no—
31#41×C127—21no—
32#41×C127—21no—
33#41×C127—21no—
34#41×C127—21no—
35#41×C127D412yes—
36#41×C127D412yes—
37C2×Q8×C127C2×C411yescharacteristic
38C2×Q8×C127C2×C411yescharacteristic
39C2×D4×C127—21no—
40C2×D4×C127—21no—
41C2×D4×C127C2×C411yescharacteristic
42C2×D4×C127C2×C411yescharacteristic
43C22×C4×C127—21no—
44C22×C4×C127—21no—
45C22×C4×C127—21no—
46C22×C4×C127C2311yescharacteristic
47Q16×C127—22no—
48SD16×C127—22no—
49SD16×C127—22no—
50D8×C127—22no—
51M16×C127—24no—
52M16×C127—21no—
53M16×C127—21no—
54M16×C127—21no—
55M16×C127D412yes—
56C2×C8×C127—24no—
57C2×C8×C127—21no—
58C2×C8×C127—21no—
59C2×C8×C127—21no—
60C2×C8×C127—21no—
61C2×C8×C127—21no—
62C2×C8×C127—21no—
63C2×C8×C127C2×C411yescharacteristic
64C2×C8×C127C2×C411yescharacteristic
65C2×C8×C127D411yescharacteristic
66C2×C8×C127D411yescharacteristic
67C42×C127—21no—
68C42×C127—21no—
69C23×C127—21no—
70C23×C127—21no—
71C23×C127#4111yescharacteristic
72Q8×C127—21no—
73Q8×C127—21no—
74Q8×C127—21no—
75Q8×C127C22⋊C412yes—
76D4×C127—22no—
77D4×C127—22no—
78D4×C127—21no—
79D4×C127—21no—
80D4×C127—21no—
81D4×C127—41no—
82D4×C127—41no—
83D4×C127C22⋊C412yes—
84C2×C4×C127—21no—
85C2×C4×C127—22no—
86C2×C4×C127—22no—
87C2×C4×C127—22no—
88C2×C4×C127—21no—
89C2×C4×C127—41no—
90C2×C4×C127—41no—
91C2×C4×C127—41no—
92C2×C4×C127—41no—
93C2×C4×C127C22×C411yescharacteristic
94C2×C4×C127C2×D411yescharacteristic
95C2×C4×C127C2×D411yescharacteristic
96C2×C4×C127C2×D411yescharacteristic
97C2×C4×C127C2×D411yescharacteristic
98C2×C4×C127#4111yescharacteristic
99C8×C127—21no—
100C8×C127—21no—
101C8×C127—21no—
102C8×C127—22no—
103C8×C127—21no—
104C8×C127—41no—
105C22×C127—21no—
106C22×C127—21no—
107C22×C127—22no—
108C22×C127—41no—
109C22×C127—41no—
110C22×C127—41no—
111C22×C127—41no—
112C22×C127—41no—
113C22×C127C4×D411yescharacteristic
114C22×C127#12111yescharacteristic
115C22×C127#12311yescharacteristic
116C4×C127—22no—
117C4×C127—42no—
118C4×C127—41no—
119C4×C127C2×C22⋊C411yescharacteristic
120C4×C127C4×D411yescharacteristic
121C4×C127#12011yescharacteristic
122C4×C127#12111yescharacteristic
123C2×C127—21no—
124C2×C127—21no—
125C2×C127—42no—
126C2×C127—81no—
127C2×C127#38611yescharacteristic
128C2×C127#44311yescharacteristic
129C2×C127#44411yescharacteristic
130#1876C12711yesmaximal, characteristic, direct product factor, Sylow
131C127#187611yescharacteristic, direct product factor, Sylow
132C2×#135C2×C12711yescharacteristic
133C2×#131C2×C12711yescharacteristic, complemented
134C2×#104C2×C12711yescharacteristic, complemented
135C2×#104C2×C12711yescharacteristic, complemented
136#408C2×C12711yescharacteristic, complemented
137#341C2×C12711yescharacteristic, complemented
138#336C2×C12711yescharacteristic, complemented
139C2×#41C22×C12711yescharacteristic
140C2×#41C22×C12711yescharacteristic
141#135—22no—
142#135—22no—
143C2×Q16C4×C12711yescharacteristic, complemented
144C2×SD16C4×C12711yescharacteristic, complemented
145C2×SD16C4×C12711yescharacteristic, complemented
146C2×D8C4×C12711yescharacteristic, complemented
147#131—22no—
148#131—22no—
149C2×M16—21no—
150C2×M16C22×C12711yescharacteristic
151C2×M16C22×C12711yescharacteristic
152C22×C8—21no—
153C22×C8C22×C12711yescharacteristic
154C22×C8C22×C12711yescharacteristic
155C2×C42C22×C12711yescharacteristic
156#104—22no—
157#104—22no—
158C22⋊C8—21no—
159C22⋊C8—21no—
160#41—21no—
161#41—21no—
162#41—21no—
163#41—21no—
164#41—21no—
165#41—21no—
166#41D4×C12712yes—
167#41D4×C12712yes—
168C2×Q8C2×C4×C12711yescharacteristic
169C2×Q8C2×C4×C12711yescharacteristic
170C2×D4—21no—
171C2×D4—21no—
172C2×D4C2×C4×C12711yescharacteristic
173C2×D4C2×C4×C12711yescharacteristic
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4C23×C12711yescharacteristic
178Q16—22no—
179SD16—22no—
180SD16—22no—
181D8—22no—
182M16—24no—
183M16—21no—
184M16—21no—
185M16—21no—
186M16D4×C12712yes—
187C2×C8—24no—
188C2×C8—21no—
189C2×C8—21no—
190C2×C8—21no—
191C2×C8—21no—
192C2×C8—21no—
193C2×C8—21no—
194C2×C8C2×C4×C12711yescharacteristic
195C2×C8C2×C4×C12711yescharacteristic
196C2×C8D4×C12711yescharacteristic
197C2×C8D4×C12711yescharacteristic
198C42—21no—
199C42—21no—
200C23—21no—
201C23—21no—
202C23#41×C12711yescharacteristic
203Q8—21no—
204Q8—21no—
205Q8—21no—
206Q8C22⋊C4×C12712yes—
207D4—22no—
208D4—22no—
209D4—21no—
210D4—21no—
211D4—21no—
212D4—41no—
213D4—41no—
214D4C22⋊C4×C12712yes—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4C22×C4×C12711yescharacteristic
225C2×C4C2×D4×C12711yescharacteristic
226C2×C4C2×D4×C12711yescharacteristic
227C2×C4C2×D4×C12711yescharacteristic
228C2×C4C2×D4×C12711yescharacteristic
229C2×C4#41×C12711yescharacteristic
230C8—21no—
231C8—21no—
232C8—21no—
233C8—22no—
234C8—21no—
235C8—41no—
236C22—21no—
237C22—21no—
238C22—22no—
239C22—41no—
240C22—41no—
241C22—41no—
242C22—41no—
243C22—41no—
244C22C4×D4×C12711yescharacteristic
245C22#121×C12711yescharacteristic
246C22#123×C12711yescharacteristic
247C4—22no—
248C4—42no—
249C4—41no—
250C4C2×C22⋊C4×C12711yescharacteristic
251C4C4×D4×C12711yescharacteristic
252C4#120×C12711yescharacteristic
253C4#121×C12711yescharacteristic
254C2—21no—
255C2—21no—
256C2—42no—
257C2—81no—
258C2#386×C12711yescharacteristic
259C2#443×C12711yescharacteristic
260C2#444×C12711yescharacteristic
subgroupG/H
centerC2×C4×C127C2×D4
commutatorC2×C4C22×C4×C127
Frattini, cosocleC22×C4C23×C127
socleC22×C127C4×D4
prime radicalC2×#135×C127C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C22×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#131×C127C2semidirect
3. C2×#104×C127C2semidirect
4. C2×#104×C127C2semidirect
5. #408×C127C2semidirect
6. #341×C127C2semidirect
7. #336×C127C2semidirect
12. C2×Q16×C127C4semidirect
13. C2×SD16×C127C4semidirect
14. C2×SD16×C127C4semidirect
15. C2×D8×C127C4semidirect
130. #1876C127direct (N × H)
131. C127#1876direct (N × H)
133. C2×#131C2×C127semidirect
134. C2×#104C2×C127semidirect
135. C2×#104C2×C127semidirect
136. #408C2×C127semidirect
137. #341C2×C127semidirect
138. #336C2×C127semidirect
143. C2×Q16C4×C127semidirect
144. C2×SD16C4×C127semidirect
145. C2×SD16C4×C127semidirect
146. C2×D8C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#135×C1272
C2×#131×C1272
C2×#104×C1272
#408×C1272
#341×C1272
#336×C1272
#1876127