Finite Group Databasebeta

← C127×#10622 #44574295

Subgroups — C127×#10622 #44574295

Order 32512.

402 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 134 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
1C127×#1954C211yesmaximal, characteristic
2C127×#1834C211yesmaximal, characteristic, complemented
3C127×#1802C212yesmaximal
4C127×#1296C212yesmaximal, complemented
5C127×#1277C211yesmaximal, characteristic, complemented
6C2×C4×D4×C127C2211yescharacteristic
7C2×C4⋊C8×C127C2212yes—
8C2×C4⋊C8×C127C2211yescharacteristic
9C2×#102×C127—22no—
10C2×C22⋊C8×C127—22no—
11C2×C4×C8×C127C2211yescharacteristic
12#384×C127C2212yes—
13#340×C127—22no—
14#340×C127—22no—
15C22×D4×C127D411yescharacteristic
16C23×C4×C127—21no—
17C22×C8×C127—22no—
18C22×C8×C127—21no—
19C22×C8×C127D412yes—
20C4×D4×C127—22no—
21C4×D4×C127—22no—
22C2×C4⋊C4×C127—22no—
23C2×C4⋊C4×C127—22no—
24C2×C4⋊C4×C127—22no—
25C2×C4⋊C4×C127D411yescharacteristic
26C2×C22⋊C4×C127—21no—
27C2×C42×C127C2311yescharacteristic
28C4⋊C8×C127—22no—
29C4⋊C8×C127—22no—
30C4⋊C8×C127—22no—
31#102×C127—44no—
32C22⋊C8×C127—44no—
33C4×C8×C127—22no—
34C24×C127—21no—
35C2×D4×C127—22no—
36C2×D4×C127—21no—
37C2×D4×C127—22no—
38C2×D4×C127Q1612yes—
39C22×C4×C127—21no—
40C22×C4×C127—41no—
41C22×C4×C127—41no—
42C22×C4×C127—42no—
43C22×C4×C127—42no—
44C22×C4×C127—42no—
45C22×C4×C127C2×D411yescharacteristic
46C22×C4×C127C2×D411yescharacteristic
47C22×C4×C127#4111yescharacteristic
48C2×C8×C127—22no—
49C2×C8×C127—22no—
50C2×C8×C127—22no—
51C2×C8×C127—42no—
52C2×C8×C127—41no—
53C2×C8×C127—42no—
54C2×C8×C127—42no—
55C2×C8×C127—42no—
56C4⋊C4×C127—22no—
57C4⋊C4×C127—42no—
58C4⋊C4×C127—42no—
59C4⋊C4×C127—42no—
60C4⋊C4×C127—42no—
61C4⋊C4×C127—82no—
62C22⋊C4×C127—42no—
63C42×C127#4112yes—
64C42×C127#4112yes—
65C23×C127—22no—
66C23×C127—41no—
67C23×C127—42no—
68C23×C127—41no—
69C23×C127—42no—
70C23×C127#12111yescharacteristic
71D4×C127—24no—
72D4×C127—42no—
73C2×C4×C127—22no—
74C2×C4×C127—41no—
75C2×C4×C127—42no—
76C2×C4×C127—82no—
77C2×C4×C127—81no—
78C2×C4×C127—81no—
79C2×C4×C127—82no—
80C2×C4×C127—82no—
81C2×C4×C127—82no—
82C2×C4×C127#12311yescharacteristic
83C2×C4×C127#12312yes—
84C2×C4×C127#12411yescharacteristic
85C2×C4×C127#12612yes—
86C2×C4×C127C2×Q1611yescharacteristic
87C2×C4×C127#13511yescharacteristic
88C2×C4×C127#13512yes—
89C2×C4×C127AGL(1,ℤ/8)12yes—
90C2×C4×C127AGL(1,ℤ/8)12yes—
91C8×C127—42no—
92C8×C127—82no—
93C8×C127—81no—
94C22×C127—42no—
95C22×C127—44no—
96C22×C127—81no—
97C22×C127—81no—
98C22×C127—82no—
99C22×C127#39711yescharacteristic
100C22×C127#46312yes—
101C22×C127#46711yescharacteristic
102C22×C127#46911yescharacteristic
103C22×C127#47112yes—
104C4×C127—22no—
105C4×C127—81no—
106C4×C127—162no—
107C4×C127#48212yes—
108C4×C127#48212yes—
109C4×C127#48412yes—
110C4×C127#48811yescharacteristic
111C4×C127#49011yescharacteristic
112#10622C12711yesmaximal, characteristic, direct product factor, Sylow
113C2×C127—82no—
114C2×C127#168312yes—
115C2×C127#170112yes—
116C2×C127#207311yescharacteristic
117C2×C127#207611yescharacteristic
118C2×C127#207911yescharacteristic
119#1954C2×C12711yescharacteristic
120#1834C2×C12711yescharacteristic, complemented
121#1802C2×C12712yes—
122#1296C2×C12712yescomplemented
123#1277C2×C12711yescharacteristic, complemented
124C127#1062211yescharacteristic, direct product factor, Sylow
125C2×C4×D4C22×C12711yescharacteristic
126C2×C4⋊C8C22×C12712yes—
127C2×C4⋊C8C22×C12711yescharacteristic
128C2×#102—22no—
129C2×C22⋊C8—22no—
130C2×C4×C8C22×C12711yescharacteristic
131#384C22×C12712yes—
132#340—22no—
133#340—22no—
134C22×D4D4×C12711yescharacteristic
135C23×C4—21no—
136C22×C8—22no—
137C22×C8—21no—
138C22×C8D4×C12712yes—
139C4×D4—22no—
140C4×D4—22no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4D4×C12711yescharacteristic
145C2×C22⋊C4—21no—
146C2×C42C23×C12711yescharacteristic
147C4⋊C8—22no—
148C4⋊C8—22no—
149C4⋊C8—22no—
150#102—44no—
151C22⋊C8—44no—
152C4×C8—22no—
153C24—21no—
154C2×D4—22no—
155C2×D4—21no—
156C2×D4—22no—
157C2×D4Q16×C12712yes—
158C22×C4—21no—
159C22×C4—41no—
160C22×C4—41no—
161C22×C4—42no—
162C22×C4—42no—
163C22×C4—42no—
164C22×C4C2×D4×C12711yescharacteristic
165C22×C4C2×D4×C12711yescharacteristic
166C22×C4#41×C12711yescharacteristic
167C2×C8—22no—
168C2×C8—22no—
169C2×C8—22no—
170C2×C8—42no—
171C2×C8—41no—
172C2×C8—42no—
173C2×C8—42no—
174C2×C8—42no—
175C4⋊C4—22no—
176C4⋊C4—42no—
177C4⋊C4—42no—
178C4⋊C4—42no—
179C4⋊C4—42no—
180C4⋊C4—82no—
181C22⋊C4—42no—
182C42#41×C12712yes—
183C42#41×C12712yes—
184C23—22no—
185C23—41no—
186C23—42no—
187C23—41no—
188C23—42no—
189C23#121×C12711yescharacteristic
190D4—24no—
191D4—42no—
192C2×C4—22no—
193C2×C4—41no—
194C2×C4—42no—
195C2×C4—82no—
196C2×C4—81no—
197C2×C4—81no—
198C2×C4—82no—
199C2×C4—82no—
200C2×C4—82no—
201C2×C4#123×C12711yescharacteristic
202C2×C4#123×C12712yes—
203C2×C4#124×C12711yescharacteristic
204C2×C4#126×C12712yes—
205C2×C4C2×Q16×C12711yescharacteristic
206C2×C4#135×C12711yescharacteristic
207C2×C4#135×C12712yes—
208C2×C4AGL(1,ℤ/8)×C12712yes—
209C2×C4AGL(1,ℤ/8)×C12712yes—
210C8—42no—
211C8—82no—
212C8—81no—
213C22—42no—
214C22—44no—
215C22—81no—
216C22—81no—
217C22—82no—
218C22#397×C12711yescharacteristic
219C22#463×C12712yes—
220C22#467×C12711yescharacteristic
221C22#469×C12711yescharacteristic
222C22#471×C12712yes—
223C4—22no—
224C4—81no—
225C4—162no—
226C4#482×C12712yes—
227C4#482×C12712yes—
228C4#484×C12712yes—
229C4#488×C12711yescharacteristic
230C4#490×C12711yescharacteristic
231C2—82no—
232C2C127×#168312yes—
233C2C127×#170112yes—
234C2C127×#207311yescharacteristic
235C2C127×#207611yescharacteristic
236C2C127×#207911yescharacteristic
subgroupG/H
center, socleC23×C127#121
commutator, Frattini, cosocleC2×C42C23×C127
prime radicalC22×D4×C127D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1834C2semidirect
4. C127×#1296C2semidirect
5. C127×#1277C2semidirect
112. #10622C127direct (N × H)
120. #1834C2×C127semidirect
122. #1296C2×C127semidirect
123. #1277C2×C127semidirect
124. C127#10622direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#19542
C127×#18342
C127×#18022
C127×#12962
C127×#12772
#10622127