Finite Group Databasebeta

← C127×#2067 #30635019

Subgroups — C127×#2067 #30635019

Order 16256.

284 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 104 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×#107×C127C211yesmaximal, characteristic, complemented
2C2×C4⋊C8×C127C211yesmaximal, characteristic, complemented
3C2×#102×C127C211yesmaximal, characteristic
4C2×#102×C127C211yesmaximal, characteristic
5#390×C127C211yesmaximal, characteristic
6#389×C127C211yesmaximal, characteristic, complemented
7#340×C127C211yesmaximal, characteristic, complemented
8C22×D4×C127C2211yescharacteristic
9C22×C8×C127C2211yescharacteristic
10C22×C8×C127C2211yescharacteristic
11C2×C4⋊C4×C127—21no—
12C2×C4⋊C4×C127C2211yescharacteristic
13C2×C4⋊C4×C127C2211yescharacteristic
14C2×C4⋊C4×C127C2211yescharacteristic
15C2×C22⋊C4×C127—21no—
16C2×C22⋊C4×C127—21no—
17C2×C42×C127C2211yescharacteristic
18#107×C127—22no—
19C4⋊C8×C127—22no—
20#102×C127—22no—
21#102×C127—22no—
22#95×C127—21no—
23C24×C127—21no—
24C2×D4×C127—21no—
25C2×D4×C127—21no—
26C2×D4×C127—21no—
27C2×D4×C127—21no—
28C2×D4×C127—21no—
29C2×D4×C127Q812yes—
30C22×C4×C127—21no—
31C22×C4×C127—21no—
32C22×C4×C127—21no—
33C22×C4×C127D411yescharacteristic
34C22×C4×C127D411yescharacteristic
35C22×C4×C127C2311yescharacteristic
36C2×C8×C127—21no—
37C2×C8×C127—21no—
38C2×C8×C127—21no—
39C2×C8×C127—21no—
40C2×C8×C127—21no—
41C2×C8×C127D412yes—
42C4⋊C4×C127—21no—
43C4⋊C4×C127—21no—
44C4⋊C4×C127—21no—
45C4⋊C4×C127—21no—
46C4⋊C4×C127—21no—
47C4⋊C4×C127—42no—
48C4⋊C4×C127D412yes—
49C22⋊C4×C127—42no—
50C22⋊C4×C127—42no—
51C42×C127—21no—
52C42×C127—21no—
53C23×C127—22no—
54C23×C127—41no—
55C23×C127—41no—
56C23×C127—41no—
57C23×C127—41no—
58C23×C127—41no—
59C23×C127—41no—
60C23×C127C2×D411yescharacteristic
61D4×C127—22no—
62D4×C127—22no—
63D4×C127—41no—
64D4×C127—41no—
65C2×C4×C127—21no—
66C2×C4×C127—21no—
67C2×C4×C127—21no—
68C2×C4×C127—22no—
69C2×C4×C127—21no—
70C2×C4×C127—21no—
71C2×C4×C127—41no—
72C2×C4×C127—41no—
73C2×C4×C127—41no—
74C2×C4×C127—41no—
75C2×C4×C127—41no—
76C2×C4×C127—41no—
77C2×C4×C127—41no—
78C2×C4×C127—41no—
79C2×C4×C127D812yes—
80C2×C4×C127C2×D411yescharacteristic
81C2×C4×C127C2×D411yescharacteristic
82C2×C4×C127C2×Q811yescharacteristic
83C2×C4×C127#4111yescharacteristic
84C2×C4×C127#4111yescharacteristic
85C2×C4×C127#4111yescharacteristic
86C8×C127—22no—
87C8×C127—41no—
88C22×C127—42no—
89C22×C127—42no—
90C22×C127—42no—
91C22×C127—81no—
92C22×C127—81no—
93C22×C127—81no—
94C22×C127—81no—
95C22×C127#12111yescharacteristic
96C22×C127#12111yescharacteristic
97C22×C127C22⋊Q811yescharacteristic
98C22×C127C2×D811yescharacteristic
99C22×C127#13511yescharacteristic
100C22×C127AGL(1,ℤ/8)11yescharacteristic
101C22×C127#13711yescharacteristic
102C4×C127—22no—
103C4×C127—42no—
104C4×C127—41no—
105C4×C127—81no—
106C4×C127—81no—
107C4×C127#12111yescharacteristic
108C4×C127C22⋊Q811yescharacteristic
109C4×C127C22⋊Q811yescharacteristic
110C4×C127#12611yescharacteristic
111C2×C127—82no—
112C2×C127#39611yescharacteristic
113C2×C127#45911yescharacteristic
114C2×C127#46411yescharacteristic
115C2×C127#46611yescharacteristic
116C2×C127#46811yescharacteristic
117C2×C127#47411yescharacteristic
118C2×C127#47811yescharacteristic
119#2067C12711yesmaximal, characteristic, direct product factor, Sylow
120C127#206711yescharacteristic, direct product factor, Sylow
121C2×#107C2×C12711yescharacteristic, complemented
122C2×C4⋊C8C2×C12711yescharacteristic, complemented
123C2×#102C2×C12711yescharacteristic
124C2×#102C2×C12711yescharacteristic
125#390C2×C12711yescharacteristic
126#389C2×C12711yescharacteristic, complemented
127#340C2×C12711yescharacteristic, complemented
128C22×D4C22×C12711yescharacteristic
129C22×C8C22×C12711yescharacteristic
130C22×C8C22×C12711yescharacteristic
131C2×C4⋊C4—21no—
132C2×C4⋊C4C22×C12711yescharacteristic
133C2×C4⋊C4C22×C12711yescharacteristic
134C2×C4⋊C4C22×C12711yescharacteristic
135C2×C22⋊C4—21no—
136C2×C22⋊C4—21no—
137C2×C42C22×C12711yescharacteristic
138#107—22no—
139C4⋊C8—22no—
140#102—22no—
141#102—22no—
142#95—21no—
143C24—21no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4—21no—
148C2×D4—21no—
149C2×D4Q8×C12712yes—
150C22×C4—21no—
151C22×C4—21no—
152C22×C4—21no—
153C22×C4D4×C12711yescharacteristic
154C22×C4D4×C12711yescharacteristic
155C22×C4C23×C12711yescharacteristic
156C2×C8—21no—
157C2×C8—21no—
158C2×C8—21no—
159C2×C8—21no—
160C2×C8—21no—
161C2×C8D4×C12712yes—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—42no—
168C4⋊C4D4×C12712yes—
169C22⋊C4—42no—
170C22⋊C4—42no—
171C42—21no—
172C42—21no—
173C23—22no—
174C23—41no—
175C23—41no—
176C23—41no—
177C23—41no—
178C23—41no—
179C23—41no—
180C23C2×D4×C12711yescharacteristic
181D4—22no—
182D4—22no—
183D4—41no—
184D4—41no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4D8×C12712yes—
200C2×C4C2×D4×C12711yescharacteristic
201C2×C4C2×D4×C12711yescharacteristic
202C2×C4C2×Q8×C12711yescharacteristic
203C2×C4#41×C12711yescharacteristic
204C2×C4#41×C12711yescharacteristic
205C2×C4#41×C12711yescharacteristic
206C8—22no—
207C8—41no—
208C22—42no—
209C22—42no—
210C22—42no—
211C22—81no—
212C22—81no—
213C22—81no—
214C22—81no—
215C22#121×C12711yescharacteristic
216C22#121×C12711yescharacteristic
217C22C22⋊Q8×C12711yescharacteristic
218C22C2×D8×C12711yescharacteristic
219C22#135×C12711yescharacteristic
220C22AGL(1,ℤ/8)×C12711yescharacteristic
221C22#137×C12711yescharacteristic
222C4—22no—
223C4—42no—
224C4—41no—
225C4—81no—
226C4—81no—
227C4#121×C12711yescharacteristic
228C4C22⋊Q8×C12711yescharacteristic
229C4C22⋊Q8×C12711yescharacteristic
230C4#126×C12711yescharacteristic
231C2—82no—
232C2#396×C12711yescharacteristic
233C2#459×C12711yescharacteristic
234C2#464×C12711yescharacteristic
235C2#466×C12711yescharacteristic
236C2#468×C12711yescharacteristic
237C2#474×C12711yescharacteristic
238C2#478×C12711yescharacteristic
subgroupG/H
center, socleC23×C127C2×D4
commutator, Frattini, cosocleC22×C4C23×C127
prime radicalC22×D4×C127C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#107×C127C2semidirect
2. C2×C4⋊C8×C127C2semidirect
6. #389×C127C2semidirect
7. #340×C127C2semidirect
119. #2067C127direct (N × H)
120. C127#2067direct (N × H)
121. C2×#107C2×C127semidirect
122. C2×C4⋊C8C2×C127semidirect
126. #389C2×C127semidirect
127. #340C2×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#107×C1272
C2×C4⋊C8×C1272
C2×#102×C1272
#390×C1272
#389×C1272
#340×C1272
#2067127