Finite Group Databasebeta

← C127×#11679 #44575352

Subgroups — C127×#11679 #44575352

Order 32512.

318 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 122 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×#3170C211yesmaximal, characteristic
2C2×#346×C127C211yesmaximal, characteristic
3C127×#1568C211yesmaximal, characteristic
4C127×#1334C214yesmaximal, complemented
5#533×C127—21no—
6C22×C16×C127—21no—
7#500×C127C411yescharacteristic
8#494×C127C411yescharacteristic
9#487×C127—21no—
10#467×C127—21no—
11#467×C127C412yes—
12C4×Q16×C127—21no—
13C4×Q16×C127C2212yes—
14#432×C127—21no—
15C2×C4×C8×C127C2211yescharacteristic
16#346×C127—21no—
17#346×C127C2212yes—
18#335×C127—21no—
19#334×C127C2212yes—
20C2×Q16×C127—21no—
21C2×Q16×C127C2×C412yes—
22C22×C8×C127C2×C411yescharacteristic
23C22×C8×C127D411yescharacteristic
24C4⋊Q8×C127—21no—
25C4⋊Q8×C127—21no—
26#125×C127—41no—
27C22⋊Q8×C127—22no—
28C22⋊Q8×C127—41no—
29C4×Q8×C127—22no—
30C4×Q8×C127—41no—
31#117×C127—41no—
32C2×C42×C127D411yescharacteristic
33C2×C16×C127—24no—
34C2×C16×C127—22no—
35#107×C127—21no—
36#107×C127C2×C412yes—
37C4⋊C8×C127—22no—
38#103×C127—22no—
39#103×C127—22no—
40C22⋊C8×C127—41no—
41#97×C127—41no—
42C4×C8×C127C2×C411yescharacteristic
43C4×C8×C127D411yescharacteristic
44C4×C8×C127D411yescharacteristic
45C4×C8×C127C2311yescharacteristic
46C2×Q8×C127—22no—
47C2×Q8×C127—41no—
48C22×C4×C127C22⋊C411yescharacteristic
49C22×C4×C127D811yescharacteristic
50C22×C4×C127SD1611yescharacteristic
51Q16×C127—24no—
52Q16×C127—42no—
53C2×C8×C127—22no—
54C2×C8×C127—22no—
55C2×C8×C127—42no—
56C2×C8×C127C22⋊C411yescharacteristic
57C2×C8×C127C22⋊C411yescharacteristic
58C2×C8×C127C22×C411yescharacteristic
59C2×C8×C127C2×D411yescharacteristic
60C4⋊C4×C127—22no—
61C4⋊C4×C127—41no—
62C4⋊C4×C127—41no—
63C4⋊C4×C127—42no—
64C4⋊C4×C127—41no—
65C4⋊C4×C127—42no—
66C22⋊C4×C127—42no—
67C42×C127—42no—
68C42×C127C22⋊C411yescharacteristic
69C42×C127D811yescharacteristic
70C42×C127SD1611yescharacteristic
71C42×C127C2×D411yescharacteristic
72C16×C127—24no—
73C23×C127#10211yescharacteristic
74Q8×C127—42no—
75Q8×C127—42no—
76Q8×C127—82no—
77C2×C4×C127—22no—
78C2×C4×C127—21no—
79C2×C4×C127—21no—
80C2×C4×C127—41no—
81C2×C4×C127—42no—
82C2×C4×C127—42no—
83C2×C4×C127#10211yescharacteristic
84C2×C4×C127#10211yescharacteristic
85C2×C4×C127#10211yescharacteristic
86C2×C4×C127C2×C22⋊C411yescharacteristic
87C2×C4×C127C2×D811yescharacteristic
88C2×C4×C127C2×SD1611yescharacteristic
89C8×C127—21no—
90C8×C127—21no—
91C8×C127—82no—
92C8×C127#10412yes—
93C8×C127#13112yes—
94C22×C127—21no—
95C22×C127—21no—
96C22×C127#36212yes—
97C22×C127C2×#10211yescharacteristic
98C4×C127—21no—
99C4×C127—21no—
100C4×C127—21no—
101C4×C127—21no—
102C4×C127—21no—
103C4×C127—82no—
104C4×C127—82no—
105C4×C127#40811yescharacteristic
106C4×C127C2×#10411yescharacteristic
107#11679C12711yesmaximal, characteristic, direct product factor, Sylow
108C2×C127—22no—
109C2×C127#149211yescharacteristic
110C2×C127#214511yescharacteristic
111C2×C127C2×#36211yescharacteristic
112#3170C2×C12711yescharacteristic
113C2×#346C2×C12711yescharacteristic
114#1568C2×C12711yescharacteristic
115#1334C2×C12714yescomplemented
116C127#1167911yescharacteristic, direct product factor, Sylow
117#533—21no—
118C22×C16—21no—
119#500C4×C12711yescharacteristic
120#494C4×C12711yescharacteristic
121#487—21no—
122#467—21no—
123#467C4×C12712yes—
124C4×Q16—21no—
125C4×Q16C22×C12712yes—
126#432—21no—
127C2×C4×C8C22×C12711yescharacteristic
128#346—21no—
129#346C22×C12712yes—
130#335—21no—
131#334C22×C12712yes—
132C2×Q16—21no—
133C2×Q16C2×C4×C12712yes—
134C22×C8C2×C4×C12711yescharacteristic
135C22×C8D4×C12711yescharacteristic
136C4⋊Q8—21no—
137C4⋊Q8—21no—
138#125—41no—
139C22⋊Q8—22no—
140C22⋊Q8—41no—
141C4×Q8—22no—
142C4×Q8—41no—
143#117—41no—
144C2×C42D4×C12711yescharacteristic
145C2×C16—24no—
146C2×C16—22no—
147#107—21no—
148#107C2×C4×C12712yes—
149C4⋊C8—22no—
150#103—22no—
151#103—22no—
152C22⋊C8—41no—
153#97—41no—
154C4×C8C2×C4×C12711yescharacteristic
155C4×C8D4×C12711yescharacteristic
156C4×C8D4×C12711yescharacteristic
157C4×C8C23×C12711yescharacteristic
158C2×Q8—22no—
159C2×Q8—41no—
160C22×C4C22⋊C4×C12711yescharacteristic
161C22×C4D8×C12711yescharacteristic
162C22×C4SD16×C12711yescharacteristic
163Q16—24no—
164Q16—42no—
165C2×C8—22no—
166C2×C8—22no—
167C2×C8—42no—
168C2×C8C22⋊C4×C12711yescharacteristic
169C2×C8C22⋊C4×C12711yescharacteristic
170C2×C8C22×C4×C12711yescharacteristic
171C2×C8C2×D4×C12711yescharacteristic
172C4⋊C4—22no—
173C4⋊C4—41no—
174C4⋊C4—41no—
175C4⋊C4—42no—
176C4⋊C4—41no—
177C4⋊C4—42no—
178C22⋊C4—42no—
179C42—42no—
180C42C22⋊C4×C12711yescharacteristic
181C42D8×C12711yescharacteristic
182C42SD16×C12711yescharacteristic
183C42C2×D4×C12711yescharacteristic
184C16—24no—
185C23#102×C12711yescharacteristic
186Q8—42no—
187Q8—42no—
188Q8—82no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—41no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4#102×C12711yescharacteristic
196C2×C4#102×C12711yescharacteristic
197C2×C4#102×C12711yescharacteristic
198C2×C4C2×C22⋊C4×C12711yescharacteristic
199C2×C4C2×D8×C12711yescharacteristic
200C2×C4C2×SD16×C12711yescharacteristic
201C8—21no—
202C8—21no—
203C8—82no—
204C8#104×C12712yes—
205C8#131×C12712yes—
206C22—21no—
207C22—21no—
208C22#362×C12712yes—
209C22C2×#102×C12711yescharacteristic
210C4—21no—
211C4—21no—
212C4—21no—
213C4—21no—
214C4—21no—
215C4—82no—
216C4—82no—
217C4#408×C12711yescharacteristic
218C4C2×#104×C12711yescharacteristic
219C2—22no—
220C2C127×#149211yescharacteristic
221C2C127×#214511yescharacteristic
222C2C2×#362×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#102
commutatorC2×C8C22×C4×C127
Frattini, cosocleC4×C8C23×C127
prime radicalC23×C127#102
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ C2×C4×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#1334C2semidirect
107. #11679C127direct (N × H)
115. #1334C2×C127semidirect
116. C127#11679direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#31702
C2×#346×C1272
C127×#15682
C127×#13342
#11679127