Finite Group Databasebeta

← C127×#10669 #44574342

Subgroups — C127×#10669 #44574342

Order 32512.

296 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 106 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×#1995C211yesmaximal, characteristic
2C127×#1832C211yesmaximal, characteristic
3C127×#1571C211yesmaximal, characteristic
4C127×#1570C211yesmaximal, characteristic
5C127×#1481C211yesmaximal, characteristic
6C127×#1481C211yesmaximal, characteristic
7C127×#1274C211yesmaximal, characteristic
8#533×C127C2211yescharacteristic
9#431×C127C2211yescharacteristic
10#431×C127C2211yescharacteristic
11#423×C127C2211yescharacteristic
12C2×C4⋊C8×C127C2211yescharacteristic
13C2×C4⋊C8×C127C2211yescharacteristic
14#376×C127C2211yescharacteristic
15#339×C127—22no—
16#336×C127—22no—
17#335×C127—22no—
18#334×C127—22no—
19Q8⋊C8×C127—22no—
20Q8⋊C8×C127—22no—
21C2×M16×C127—21no—
22C22×C8×C127—21no—
23C22×C8×C127—21no—
24C4⋊Q8×C127Q811yescharacteristic
25C4⋊Q8×C127Q811yescharacteristic
26#125×C127—21no—
27C22⋊Q8×C127—21no—
28C22⋊Q8×C127—21no—
29C4×Q8×C127—21no—
30C4×Q8×C127—21no—
31#117×C127—21no—
32C2×C42×C127D412yes—
33C2×C42×C127C2311yescharacteristic
34C4⋊C8×C127—21no—
35C4⋊C8×C127—21no—
36C4⋊C8×C127—21no—
37C4⋊C8×C127—21no—
38C4⋊C8×C127—21no—
39C4⋊C8×C127—21no—
40C4⋊C8×C127—21no—
41C4⋊C8×C127—21no—
42C22⋊C8×C127—21no—
43C22⋊C8×C127—21no—
44C4×C8×C127D412yes—
45C4×C8×C127D412yes—
46#95×C127—21no—
47#95×C127—21no—
48C2×Q8×C127—21no—
49C2×Q8×C127—21no—
50C22×C4×C127—22no—
51C22×C4×C127C2×D411yescharacteristic
52C22×C4×C127#4111yescharacteristic
53C22×C4×C127#4111yescharacteristic
54M16×C127—42no—
55C2×C8×C127—22no—
56C2×C8×C127—22no—
57C2×C8×C127—41no—
58C2×C8×C127—41no—
59C2×C8×C127—41no—
60C2×C8×C127—42no—
61C2×C8×C127—42no—
62C4⋊C4×C127—21no—
63C4⋊C4×C127—21no—
64C4⋊C4×C127—21no—
65C4⋊C4×C127—21no—
66C4⋊C4×C127—41no—
67C4⋊C4×C127—41no—
68C22⋊C4×C127—41no—
69C42×C127—22no—
70C42×C127—22no—
71C42×C127—41no—
72C42×C127C2×D411yescharacteristic
73C42×C127C2×D411yescharacteristic
74C42×C127C2×Q811yescharacteristic
75C42×C127#4111yescharacteristic
76C23×C127#12311yescharacteristic
77Q8×C127—42no—
78Q8×C127—42no—
79C2×C4×C127—41no—
80C2×C4×C127—41no—
81C2×C4×C127—42no—
82C2×C4×C127—42no—
83C2×C4×C127—41no—
84C2×C4×C127—41no—
85C2×C4×C127—42no—
86C2×C4×C127C22⋊Q811yescharacteristic
87C2×C4×C127C22⋊Q811yescharacteristic
88C2×C4×C127C22⋊Q811yescharacteristic
89C2×C4×C127#12311yescharacteristic
90C2×C4×C127#12311yescharacteristic
91C2×C4×C127#12711yescharacteristic
92C2×C4×C127#13512yes—
93C2×C4×C127#13712yes—
94C8×C127—42no—
95C8×C127—42no—
96C8×C127—81no—
97C8×C127—81no—
98C8×C127—81no—
99C22×C127—21no—
100C22×C127—21no—
101C22×C127#39911yescharacteristic
102C22×C127#48512yes—
103C4×C127—21no—
104C4×C127—21no—
105C4×C127—21no—
106C4×C127—21no—
107C4×C127—82no—
108C4×C127—81no—
109C4×C127—81no—
110C4×C127#47912yes—
111C4×C127#49511yescharacteristic
112C4×C127#49711yescharacteristic
113#10669C12711yesmaximal, characteristic, direct product factor, Sylow
114C2×C127—22no—
115C2×C127#209711yescharacteristic
116C2×C127#209811yescharacteristic
117C2×C127#209811yescharacteristic
118#1995C2×C12711yescharacteristic
119#1832C2×C12711yescharacteristic
120#1571C2×C12711yescharacteristic
121#1570C2×C12711yescharacteristic
122#1481C2×C12711yescharacteristic
123#1481C2×C12711yescharacteristic
124#1274C2×C12711yescharacteristic
125C127#1066911yescharacteristic, direct product factor, Sylow
126#533C22×C12711yescharacteristic
127#431C22×C12711yescharacteristic
128#431C22×C12711yescharacteristic
129#423C22×C12711yescharacteristic
130C2×C4⋊C8C22×C12711yescharacteristic
131C2×C4⋊C8C22×C12711yescharacteristic
132#376C22×C12711yescharacteristic
133#339—22no—
134#336—22no—
135#335—22no—
136#334—22no—
137Q8⋊C8—22no—
138Q8⋊C8—22no—
139C2×M16—21no—
140C22×C8—21no—
141C22×C8—21no—
142C4⋊Q8Q8×C12711yescharacteristic
143C4⋊Q8Q8×C12711yescharacteristic
144#125—21no—
145C22⋊Q8—21no—
146C22⋊Q8—21no—
147C4×Q8—21no—
148C4×Q8—21no—
149#117—21no—
150C2×C42D4×C12712yes—
151C2×C42C23×C12711yescharacteristic
152C4⋊C8—21no—
153C4⋊C8—21no—
154C4⋊C8—21no—
155C4⋊C8—21no—
156C4⋊C8—21no—
157C4⋊C8—21no—
158C4⋊C8—21no—
159C4⋊C8—21no—
160C22⋊C8—21no—
161C22⋊C8—21no—
162C4×C8D4×C12712yes—
163C4×C8D4×C12712yes—
164#95—21no—
165#95—21no—
166C2×Q8—21no—
167C2×Q8—21no—
168C22×C4—22no—
169C22×C4C2×D4×C12711yescharacteristic
170C22×C4#41×C12711yescharacteristic
171C22×C4#41×C12711yescharacteristic
172M16—42no—
173C2×C8—22no—
174C2×C8—22no—
175C2×C8—41no—
176C2×C8—41no—
177C2×C8—41no—
178C2×C8—42no—
179C2×C8—42no—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—21no—
184C4⋊C4—41no—
185C4⋊C4—41no—
186C22⋊C4—41no—
187C42—22no—
188C42—22no—
189C42—41no—
190C42C2×D4×C12711yescharacteristic
191C42C2×D4×C12711yescharacteristic
192C42C2×Q8×C12711yescharacteristic
193C42#41×C12711yescharacteristic
194C23#123×C12711yescharacteristic
195Q8—42no—
196Q8—42no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—42no—
204C2×C4C22⋊Q8×C12711yescharacteristic
205C2×C4C22⋊Q8×C12711yescharacteristic
206C2×C4C22⋊Q8×C12711yescharacteristic
207C2×C4#123×C12711yescharacteristic
208C2×C4#123×C12711yescharacteristic
209C2×C4#127×C12711yescharacteristic
210C2×C4#135×C12712yes—
211C2×C4#137×C12712yes—
212C8—42no—
213C8—42no—
214C8—81no—
215C8—81no—
216C8—81no—
217C22—21no—
218C22—21no—
219C22#399×C12711yescharacteristic
220C22#485×C12712yes—
221C4—21no—
222C4—21no—
223C4—21no—
224C4—21no—
225C4—82no—
226C4—81no—
227C4—81no—
228C4#479×C12712yes—
229C4#495×C12711yescharacteristic
230C4#497×C12711yescharacteristic
231C2—22no—
232C2C127×#209711yescharacteristic
233C2C127×#209811yescharacteristic
234C2C127×#209811yescharacteristic
subgroupG/H
centerC2×C4×C127#127
commutator, Frattini, cosocleC2×C42C23×C127
socleC22×C127#399
prime radicalC23×C127#123
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
113. #10669C127direct (N × H)
125. C127#10669direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#19952
C127×#18322
C127×#15712
C127×#15702
C127×#14812
C127×#12742
#10669127