Finite Group Databasebeta

← C127×#10665 #44574338

Subgroups — C127×#10665 #44574338

Order 32512.

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

normal subgroups only

This group has 334 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×#1963C211yesmaximal, characteristic
2C127×#1832C211yesmaximal, characteristic, complemented
3C127×#1571C211yesmaximal, characteristic, complemented
4C127×#1570C211yesmaximal, characteristic, complemented
5C127×#1480C211yesmaximal, characteristic
6C127×#1480C211yesmaximal, characteristic
7C127×#1274C211yesmaximal, characteristic, complemented
8#532×C127C2211yescharacteristic
9#431×C127C2211yescharacteristic
10#431×C127C2211yescharacteristic
11#423×C127C2211yescharacteristic
12C2×C4⋊C8×C127C2211yescharacteristic
13C2×C4⋊C8×C127C2211yescharacteristic
14C2×#104×C127—22no—
15#376×C127C2211yescharacteristic
16#336×C127—22no—
17#335×C127—22no—
18#334×C127—22no—
19D4⋊C8×C127—22no—
20D4⋊C8×C127—22no—
21C2×#41×C127—21no—
22C2×M16×C127—21no—
23C22×C8×C127—21no—
24C22×C8×C127—21no—
25C4⋊Q8×C127Q811yescharacteristic
26#127×C127Q811yescharacteristic
27#124×C127—21no—
28#121×C127—21no—
29#121×C127—21no—
30C4×D4×C127—21no—
31C4×D4×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—
42#104×C127—44no—
43C22⋊C8×C127—21no—
44C22⋊C8×C127—21no—
45C4×C8×C127D412yes—
46C4×C8×C127D412yes—
47#95×C127—21no—
48#95×C127—21no—
49#41×C127—42no—
50#41×C127—42no—
51C2×Q8×C127—21no—
52C2×D4×C127—21no—
53C2×D4×C127—21no—
54C2×D4×C127—21no—
55C2×D4×C127—41no—
56C22×C4×C127—22no—
57C22×C4×C127—41no—
58C22×C4×C127C2×D411yescharacteristic
59C22×C4×C127#4111yescharacteristic
60C22×C4×C127#4111yescharacteristic
61M16×C127—42no—
62C2×C8×C127—22no—
63C2×C8×C127—22no—
64C2×C8×C127—41no—
65C2×C8×C127—41no—
66C2×C8×C127—41no—
67C2×C8×C127—42no—
68C2×C8×C127—42no—
69C4⋊C4×C127—21no—
70C4⋊C4×C127—21no—
71C22⋊C4×C127—41no—
72C22⋊C4×C127—41no—
73C42×C127—22no—
74C42×C127—22no—
75C42×C127C2×D411yescharacteristic
76C42×C127C2×D411yescharacteristic
77C42×C127C2×Q811yescharacteristic
78C42×C127#4111yescharacteristic
79C23×C127—41no—
80C23×C127#12311yescharacteristic
81Q8×C127—42no—
82D4×C127—42no—
83D4×C127—42no—
84D4×C127—42no—
85D4×C127—82no—
86C2×C4×C127—41no—
87C2×C4×C127—41no—
88C2×C4×C127—42no—
89C2×C4×C127—42no—
90C2×C4×C127—41no—
91C2×C4×C127—42no—
92C2×C4×C127—81no—
93C2×C4×C127—81no—
94C2×C4×C127C22⋊Q811yescharacteristic
95C2×C4×C127C22⋊Q811yescharacteristic
96C2×C4×C127C22⋊Q811yescharacteristic
97C2×C4×C127#12311yescharacteristic
98C2×C4×C127#12311yescharacteristic
99C2×C4×C127#12711yescharacteristic
100C2×C4×C127#13512yes—
101C2×C4×C127AGL(1,ℤ/8)12yes—
102C8×C127—42no—
103C8×C127—42no—
104C8×C127—81no—
105C8×C127—81no—
106C8×C127—81no—
107C22×C127—21no—
108C22×C127—21no—
109C22×C127—81no—
110C22×C127—81no—
111C22×C127—81no—
112C22×C127#39911yescharacteristic
113C22×C127#48212yes—
114C4×C127—21no—
115C4×C127—21no—
116C4×C127—21no—
117C4×C127—21no—
118C4×C127—82no—
119C4×C127—81no—
120C4×C127#47812yes—
121C4×C127#49511yescharacteristic
122C4×C127#49611yescharacteristic
123#10665C12711yesmaximal, characteristic, direct product factor, Sylow
124C2×C127—22no—
125C2×C127—161no—
126C2×C127#209211yescharacteristic
127C2×C127#209811yescharacteristic
128C2×C127#209811yescharacteristic
129#1963C2×C12711yescharacteristic
130#1832C2×C12711yescharacteristic, complemented
131#1571C2×C12711yescharacteristic, complemented
132#1570C2×C12711yescharacteristic, complemented
133#1480C2×C12711yescharacteristic
134#1480C2×C12711yescharacteristic
135#1274C2×C12711yescharacteristic, complemented
136C127#1066511yescharacteristic, direct product factor, Sylow
137#532C22×C12711yescharacteristic
138#431C22×C12711yescharacteristic
139#431C22×C12711yescharacteristic
140#423C22×C12711yescharacteristic
141C2×C4⋊C8C22×C12711yescharacteristic
142C2×C4⋊C8C22×C12711yescharacteristic
143C2×#104—22no—
144#376C22×C12711yescharacteristic
145#336—22no—
146#335—22no—
147#334—22no—
148D4⋊C8—22no—
149D4⋊C8—22no—
150C2×#41—21no—
151C2×M16—21no—
152C22×C8—21no—
153C22×C8—21no—
154C4⋊Q8Q8×C12711yescharacteristic
155#127Q8×C12711yescharacteristic
156#124—21no—
157#121—21no—
158#121—21no—
159C4×D4—21no—
160C4×D4—21no—
161C2×C42D4×C12712yes—
162C2×C42C23×C12711yescharacteristic
163C4⋊C8—21no—
164C4⋊C8—21no—
165C4⋊C8—21no—
166C4⋊C8—21no—
167C4⋊C8—21no—
168C4⋊C8—21no—
169C4⋊C8—21no—
170C4⋊C8—21no—
171#104—44no—
172C22⋊C8—21no—
173C22⋊C8—21no—
174C4×C8D4×C12712yes—
175C4×C8D4×C12712yes—
176#95—21no—
177#95—21no—
178#41—42no—
179#41—42no—
180C2×Q8—21no—
181C2×D4—21no—
182C2×D4—21no—
183C2×D4—21no—
184C2×D4—41no—
185C22×C4—22no—
186C22×C4—41no—
187C22×C4C2×D4×C12711yescharacteristic
188C22×C4#41×C12711yescharacteristic
189C22×C4#41×C12711yescharacteristic
190M16—42no—
191C2×C8—22no—
192C2×C8—22no—
193C2×C8—41no—
194C2×C8—41no—
195C2×C8—41no—
196C2×C8—42no—
197C2×C8—42no—
198C4⋊C4—21no—
199C4⋊C4—21no—
200C22⋊C4—41no—
201C22⋊C4—41no—
202C42—22no—
203C42—22no—
204C42C2×D4×C12711yescharacteristic
205C42C2×D4×C12711yescharacteristic
206C42C2×Q8×C12711yescharacteristic
207C42#41×C12711yescharacteristic
208C23—41no—
209C23#123×C12711yescharacteristic
210Q8—42no—
211D4—42no—
212D4—42no—
213D4—42no—
214D4—82no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—41no—
220C2×C4—42no—
221C2×C4—81no—
222C2×C4—81no—
223C2×C4C22⋊Q8×C12711yescharacteristic
224C2×C4C22⋊Q8×C12711yescharacteristic
225C2×C4C22⋊Q8×C12711yescharacteristic
226C2×C4#123×C12711yescharacteristic
227C2×C4#123×C12711yescharacteristic
228C2×C4#127×C12711yescharacteristic
229C2×C4#135×C12712yes—
230C2×C4AGL(1,ℤ/8)×C12712yes—
231C8—42no—
232C8—42no—
233C8—81no—
234C8—81no—
235C8—81no—
236C22—21no—
237C22—21no—
238C22—81no—
239C22—81no—
240C22—81no—
241C22#399×C12711yescharacteristic
242C22#482×C12712yes—
243C4—21no—
244C4—21no—
245C4—21no—
246C4—21no—
247C4—82no—
248C4—81no—
249C4#478×C12712yes—
250C4#495×C12711yescharacteristic
251C4#496×C12711yescharacteristic
252C2—22no—
253C2—161no—
254C2C127×#209211yescharacteristic
255C2C127×#209811yescharacteristic
256C2C127×#209811yescharacteristic
subgroupG/H
centerC2×C4×C127#127
commutator, Frattini, cosocleC2×C42C23×C127
socleC22×C127#399
prime radical#532×C127C22
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
2. C127×#1832C2semidirect
3. C127×#1571C2semidirect
4. C127×#1570C2semidirect
7. C127×#1274C2semidirect
123. #10665C127direct (N × H)
130. #1832C2×C127semidirect
131. #1571C2×C127semidirect
132. #1570C2×C127semidirect
135. #1274C2×C127semidirect
136. C127#10665direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#19632
C127×#18322
C127×#15712
C127×#15702
C127×#14802
C127×#12742
#10665127