Finite Group Databasebeta

← C127×#11912 #44575585

Subgroups — C127×#11912 #44575585

Order 32512.

284 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 94 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×#3174C211yesmaximal, characteristic
2C127×#2166C211yesmaximal, characteristic, complemented
3C127×#2110C211yesmaximal, characteristic, complemented
4C127×#1356C212yesmaximal, complemented
5C127×#1355C212yesmaximal, complemented
6#541×C127C411yescharacteristic
7#540×C127C411yescharacteristic
8C2×M32×C127—21no—
9#499×C127C411yescharacteristic
10#492×C127C411yescharacteristic
11#491×C127C2211yescharacteristic
12#490×C127C2211yescharacteristic
13#468×C127—21no—
14#465×C127—21no—
15#440×C127—21no—
16C4×SD16×C127—21no—
17#405×C127C2211yescharacteristic
18#364×C127—21no—
19#349×C127—21no—
20#347×C127—21no—
21#347×C127C2212yes—
22#347×C127C2212yes—
23C2×SD16×C127—21no—
24C2×SD16×C127—21no—
25C2×M16×C127D411yescharacteristic
26C22×C8×C127D411yescharacteristic
27C4⋊Q8×C127C2×C411yescharacteristic
28#127×C127C2×C411yescharacteristic
29#126×C127—41no—
30#125×C127—41no—
31#125×C127C2×C411yescharacteristic
32#125×C127C2×C411yescharacteristic
33#123×C127—41no—
34C22⋊Q8×C127—21no—
35#121×C127—21no—
36#121×C127—41no—
37C4×Q8×C127—21no—
38C4×D4×C127—21no—
39#117×C127C2×C411yescharacteristic
40M32×C127—22no—
41M32×C127—22no—
42M32×C127—22no—
43C2×C16×C127—22no—
44#107×C127—21no—
45#106×C127—21no—
46#103×C127—21no—
47#103×C127—21no—
48#102×C127—21no—
49#102×C127—21no—
50#97×C127D411yescharacteristic
51#97×C127C2311yescharacteristic
52C4×C8×C127C2×C411yescharacteristic
53C4×C8×C127D411yescharacteristic
54C2×Q8×C127—21no—
55C2×D4×C127—21no—
56C2×D4×C127—41no—
57C2×D4×C127—41no—
58C22×C4×C127—41no—
59C22×C4×C127C22⋊C411yescharacteristic
60SD16×C127—42no—
61SD16×C127—41no—
62SD16×C127—41no—
63M16×C127—41no—
64C2×C8×C127—21no—
65C2×C8×C127—21no—
66C2×C8×C127C22⋊C411yescharacteristic
67C2×C8×C127C22⋊C411yescharacteristic
68C2×C8×C127C2×D411yescharacteristic
69C2×C8×C127C2×D411yescharacteristic
70C4⋊C4×C127—21no—
71C4⋊C4×C127—21no—
72C4⋊C4×C127—21no—
73C4⋊C4×C127—41no—
74C4⋊C4×C127—41no—
75C4⋊C4×C127—41no—
76C4⋊C4×C127—41no—
77C4⋊C4×C127—41no—
78C22⋊C4×C127—21no—
79C22⋊C4×C127—41no—
80C22⋊C4×C127—41no—
81C22⋊C4×C127—41no—
82C42×C127—41no—
83C42×C127C22⋊C411yescharacteristic
84C42×C127C22×C411yescharacteristic
85C16×C127—24no—
86C16×C127—42no—
87C23×C127—41no—
88C23×C127#10011yescharacteristic
89Q8×C127—41no—
90Q8×C127—41no—
91D4×C127—41no—
92D4×C127—41no—
93D4×C127—161no—
94D4×C127—161no—
95C2×C4×C127—21no—
96C2×C4×C127—21no—
97C2×C4×C127—21no—
98C2×C4×C127—21no—
99C2×C4×C127—41no—
100C2×C4×C127—41no—
101C2×C4×C127—41no—
102C2×C4×C127—161no—
103C2×C4×C127#10011yescharacteristic
104C2×C4×C127C2×C22⋊C411yescharacteristic
105C8×C127—21no—
106C8×C127—21no—
107C8×C127—21no—
108C8×C127#10411yescharacteristic
109C8×C127#10411yescharacteristic
110C22×C127—21no—
111C22×C127—41no—
112C22×C127—81no—
113C22×C127—81no—
114C22×C127—81no—
115C22×C127C2×#10011yescharacteristic
116C4×C127—21no—
117C4×C127—41no—
118C4×C127—41no—
119C4×C127—81no—
120C4×C127—81no—
121C4×C127—81no—
122C4×C127C2×#10411yescharacteristic
123C4×C127#42111yescharacteristic
124#11912C12711yesmaximal, characteristic, direct product factor, Sylow
125C2×C127—21no—
126C2×C127—41no—
127C2×C127—161no—
128C2×C127#153011yescharacteristic
129#3174C2×C12711yescharacteristic
130#2166C2×C12711yescharacteristic, complemented
131#2110C2×C12711yescharacteristic, complemented
132#1356C2×C12712yescomplemented
133#1355C2×C12712yescomplemented
134C127#1191211yescharacteristic, direct product factor, Sylow
135#541C4×C12711yescharacteristic
136#540C4×C12711yescharacteristic
137C2×M32—21no—
138#499C4×C12711yescharacteristic
139#492C4×C12711yescharacteristic
140#491C22×C12711yescharacteristic
141#490C22×C12711yescharacteristic
142#468—21no—
143#465—21no—
144#440—21no—
145C4×SD16—21no—
146#405C22×C12711yescharacteristic
147#364—21no—
148#349—21no—
149#347—21no—
150#347C22×C12712yes—
151#347C22×C12712yes—
152C2×SD16—21no—
153C2×SD16—21no—
154C2×M16D4×C12711yescharacteristic
155C22×C8D4×C12711yescharacteristic
156C4⋊Q8C2×C4×C12711yescharacteristic
157#127C2×C4×C12711yescharacteristic
158#126—41no—
159#125—41no—
160#125C2×C4×C12711yescharacteristic
161#125C2×C4×C12711yescharacteristic
162#123—41no—
163C22⋊Q8—21no—
164#121—21no—
165#121—41no—
166C4×Q8—21no—
167C4×D4—21no—
168#117C2×C4×C12711yescharacteristic
169M32—22no—
170M32—22no—
171M32—22no—
172C2×C16—22no—
173#107—21no—
174#106—21no—
175#103—21no—
176#103—21no—
177#102—21no—
178#102—21no—
179#97D4×C12711yescharacteristic
180#97C23×C12711yescharacteristic
181C4×C8C2×C4×C12711yescharacteristic
182C4×C8D4×C12711yescharacteristic
183C2×Q8—21no—
184C2×D4—21no—
185C2×D4—41no—
186C2×D4—41no—
187C22×C4—41no—
188C22×C4C22⋊C4×C12711yescharacteristic
189SD16—42no—
190SD16—41no—
191SD16—41no—
192M16—41no—
193C2×C8—21no—
194C2×C8—21no—
195C2×C8C22⋊C4×C12711yescharacteristic
196C2×C8C22⋊C4×C12711yescharacteristic
197C2×C8C2×D4×C12711yescharacteristic
198C2×C8C2×D4×C12711yescharacteristic
199C4⋊C4—21no—
200C4⋊C4—21no—
201C4⋊C4—21no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C22⋊C4—21no—
208C22⋊C4—41no—
209C22⋊C4—41no—
210C22⋊C4—41no—
211C42—41no—
212C42C22⋊C4×C12711yescharacteristic
213C42C22×C4×C12711yescharacteristic
214C16—24no—
215C16—42no—
216C23—41no—
217C23#100×C12711yescharacteristic
218Q8—41no—
219Q8—41no—
220D4—41no—
221D4—41no—
222D4—161no—
223D4—161no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—161no—
232C2×C4#100×C12711yescharacteristic
233C2×C4C2×C22⋊C4×C12711yescharacteristic
234C8—21no—
235C8—21no—
236C8—21no—
237C8#104×C12711yescharacteristic
238C8#104×C12711yescharacteristic
239C22—21no—
240C22—41no—
241C22—81no—
242C22—81no—
243C22—81no—
244C22C2×#100×C12711yescharacteristic
245C4—21no—
246C4—41no—
247C4—41no—
248C4—81no—
249C4—81no—
250C4—81no—
251C4C2×#104×C12711yescharacteristic
252C4#421×C12711yescharacteristic
253C2—21no—
254C2—41no—
255C2—161no—
256C2C127×#153011yescharacteristic
subgroupG/H
center, socleC2×C127#1530
commutatorC42C22×C4×C127
Frattini, cosocle#97C23×C127
prime radical#540×C127C4
LCSG ▷ C42 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C2×C4×C127 ◁ #405×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2166C2semidirect
3. C127×#2110C2semidirect
4. C127×#1356C2semidirect
5. C127×#1355C2semidirect
124. #11912C127direct (N × H)
130. #2166C2×C127semidirect
131. #2110C2×C127semidirect
132. #1356C2×C127semidirect
133. #1355C2×C127semidirect
134. C127#11912direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#31742
C127×#21662
C127×#21102
C127×#13562
C127×#13552
#11912127