Finite Group Databasebeta

← C127×#10659 #44574332

Subgroups — C127×#10659 #44574332

Order 32512.

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

normal subgroups only

This group has 356 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×#1955C211yesmaximal, characteristic
2C127×#1838C211yesmaximal, characteristic, complemented
3C127×#1571C211yesmaximal, characteristic, complemented
4C127×#1570C211yesmaximal, characteristic, complemented
5C127×#1486C211yesmaximal, characteristic
6C127×#1486C211yesmaximal, characteristic
7C127×#1275C211yesmaximal, characteristic, complemented
8C2×C4×D4×C127C2211yescharacteristic
9#431×C127C2211yescharacteristic
10#431×C127C2211yescharacteristic
11#423×C127C2211yescharacteristic
12#423×C127C2211yescharacteristic
13C2×C4⋊C8×C127C2211yescharacteristic
14C2×C22⋊C8×C127—22no—
15C2×#97×C127C2211yescharacteristic
16#341×C127—22no—
17#335×C127—22no—
18#334×C127—22no—
19D4⋊C8×C127—22no—
20D4⋊C8×C127—22no—
21C22×D4×C127Q811yescharacteristic
22C23×C4×C127—21no—
23C2×M16×C127—21no—
24C2×M16×C127—21no—
25C22×C8×C127—21no—
26C22×C8×C127D412yes—
27C4×D4×C127—21no—
28C4×D4×C127—21no—
29C4×D4×C127—21no—
30C4×D4×C127—21no—
31C2×C4⋊C4×C127Q811yescharacteristic
32C2×C22⋊C4×C127—21no—
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—
44C22⋊C8×C127—44no—
45#97×C127—21no—
46#97×C127—21no—
47C4×C8×C127D412yes—
48C4×C8×C127D412yes—
49C24×C127—21no—
50C2×D4×C127—21no—
51C2×D4×C127—21no—
52C2×D4×C127—42no—
53C22×C4×C127—21no—
54C22×C4×C127—41no—
55C22×C4×C127—41no—
56C22×C4×C127—42no—
57C22×C4×C127—42no—
58C22×C4×C127C2×D411yescharacteristic
59C22×C4×C127C2×Q811yescharacteristic
60C22×C4×C127#4111yescharacteristic
61M16×C127—42no—
62M16×C127—42no—
63C2×C8×C127—22no—
64C2×C8×C127—22no—
65C2×C8×C127—22no—
66C2×C8×C127—22no—
67C2×C8×C127—22no—
68C2×C8×C127—41no—
69C2×C8×C127—41no—
70C2×C8×C127—41no—
71C2×C8×C127—42no—
72C4⋊C4×C127—21no—
73C4⋊C4×C127—21no—
74C22⋊C4×C127—41no—
75C22⋊C4×C127—41no—
76C42×C127C2×D411yescharacteristic
77C42×C127C2×D411yescharacteristic
78C42×C127#4111yescharacteristic
79C42×C127#4111yescharacteristic
80C23×C127—22no—
81C23×C127—41no—
82C23×C127—42no—
83C23×C127—41no—
84C23×C127—42no—
85C23×C127C22⋊Q811yescharacteristic
86D4×C127—22no—
87D4×C127—22no—
88D4×C127—41no—
89D4×C127—41no—
90C2×C4×C127—41no—
91C2×C4×C127—41no—
92C2×C4×C127—41no—
93C2×C4×C127—42no—
94C2×C4×C127—82no—
95C2×C4×C127—81no—
96C2×C4×C127—81no—
97C2×C4×C127C22⋊Q811yescharacteristic
98C2×C4×C127C22⋊Q811yescharacteristic
99C2×C4×C127#12311yescharacteristic
100C2×C4×C127#12311yescharacteristic
101C2×C4×C127#12311yescharacteristic
102C2×C4×C127#12711yescharacteristic
103C2×C4×C127#13512yes—
104C2×C4×C127AGL(1,ℤ/8)12yes—
105C8×C127—42no—
106C8×C127—42no—
107C8×C127—42no—
108C8×C127—81no—
109C8×C127—81no—
110C8×C127—81no—
111C22×C127—21no—
112C22×C127—21no—
113C22×C127—44no—
114C22×C127—42no—
115C22×C127—82no—
116C22×C127—81no—
117C22×C127—81no—
118C22×C127#39911yescharacteristic
119C22×C127#47812yes—
120C4×C127—21no—
121C4×C127—21no—
122C4×C127—21no—
123C4×C127—21no—
124C4×C127—81no—
125C4×C127#48212yes—
126C4×C127#49511yescharacteristic
127C4×C127#49611yescharacteristic
128#10659C12711yesmaximal, characteristic, direct product factor, Sylow
129C2×C127—22no—
130C2×C127—82no—
131C2×C127#209111yescharacteristic
132C2×C127#209211yescharacteristic
133C2×C127#209811yescharacteristic
134#1955C2×C12711yescharacteristic
135#1838C2×C12711yescharacteristic, complemented
136#1571C2×C12711yescharacteristic, complemented
137#1570C2×C12711yescharacteristic, complemented
138#1486C2×C12711yescharacteristic
139#1486C2×C12711yescharacteristic
140#1275C2×C12711yescharacteristic, complemented
141C127#1065911yescharacteristic, direct product factor, Sylow
142C2×C4×D4C22×C12711yescharacteristic
143#431C22×C12711yescharacteristic
144#431C22×C12711yescharacteristic
145#423C22×C12711yescharacteristic
146#423C22×C12711yescharacteristic
147C2×C4⋊C8C22×C12711yescharacteristic
148C2×C22⋊C8—22no—
149C2×#97C22×C12711yescharacteristic
150#341—22no—
151#335—22no—
152#334—22no—
153D4⋊C8—22no—
154D4⋊C8—22no—
155C22×D4Q8×C12711yescharacteristic
156C23×C4—21no—
157C2×M16—21no—
158C2×M16—21no—
159C22×C8—21no—
160C22×C8D4×C12712yes—
161C4×D4—21no—
162C4×D4—21no—
163C4×D4—21no—
164C4×D4—21no—
165C2×C4⋊C4Q8×C12711yescharacteristic
166C2×C22⋊C4—21no—
167C2×C42C23×C12711yescharacteristic
168C4⋊C8—21no—
169C4⋊C8—21no—
170C4⋊C8—21no—
171C4⋊C8—21no—
172C4⋊C8—21no—
173C4⋊C8—21no—
174C4⋊C8—21no—
175C4⋊C8—21no—
176C22⋊C8—21no—
177C22⋊C8—21no—
178C22⋊C8—44no—
179#97—21no—
180#97—21no—
181C4×C8D4×C12712yes—
182C4×C8D4×C12712yes—
183C24—21no—
184C2×D4—21no—
185C2×D4—21no—
186C2×D4—42no—
187C22×C4—21no—
188C22×C4—41no—
189C22×C4—41no—
190C22×C4—42no—
191C22×C4—42no—
192C22×C4C2×D4×C12711yescharacteristic
193C22×C4C2×Q8×C12711yescharacteristic
194C22×C4#41×C12711yescharacteristic
195M16—42no—
196M16—42no—
197C2×C8—22no—
198C2×C8—22no—
199C2×C8—22no—
200C2×C8—22no—
201C2×C8—22no—
202C2×C8—41no—
203C2×C8—41no—
204C2×C8—41no—
205C2×C8—42no—
206C4⋊C4—21no—
207C4⋊C4—21no—
208C22⋊C4—41no—
209C22⋊C4—41no—
210C42C2×D4×C12711yescharacteristic
211C42C2×D4×C12711yescharacteristic
212C42#41×C12711yescharacteristic
213C42#41×C12711yescharacteristic
214C23—22no—
215C23—41no—
216C23—42no—
217C23—41no—
218C23—42no—
219C23C22⋊Q8×C12711yescharacteristic
220D4—22no—
221D4—22no—
222D4—41no—
223D4—41no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—81no—
229C2×C4—82no—
230C2×C4—81no—
231C2×C4C22⋊Q8×C12711yescharacteristic
232C2×C4C22⋊Q8×C12711yescharacteristic
233C2×C4#123×C12711yescharacteristic
234C2×C4#123×C12711yescharacteristic
235C2×C4#123×C12711yescharacteristic
236C2×C4#127×C12711yescharacteristic
237C2×C4#135×C12712yes—
238C2×C4AGL(1,ℤ/8)×C12712yes—
239C8—42no—
240C8—42no—
241C8—42no—
242C8—81no—
243C8—81no—
244C8—81no—
245C22—21no—
246C22—21no—
247C22—44no—
248C22—42no—
249C22—82no—
250C22—81no—
251C22—81no—
252C22#399×C12711yescharacteristic
253C22#478×C12712yes—
254C4—21no—
255C4—21no—
256C4—21no—
257C4—21no—
258C4—81no—
259C4#482×C12712yes—
260C4#495×C12711yescharacteristic
261C4#496×C12711yescharacteristic
262C2—22no—
263C2—82no—
264C2C127×#209111yescharacteristic
265C2C127×#209211yescharacteristic
266C2C127×#209811yescharacteristic
subgroupG/H
centerC2×C4×C127#127
commutator, Frattini, cosocleC2×C42C23×C127
socleC22×C127#399
prime radicalC22×D4×C127Q8
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×#1838C2semidirect
3. C127×#1571C2semidirect
4. C127×#1570C2semidirect
7. C127×#1275C2semidirect
128. #10659C127direct (N × H)
135. #1838C2×C127semidirect
136. #1571C2×C127semidirect
137. #1570C2×C127semidirect
140. #1275C2×C127semidirect
141. C127#10659direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#19552
C127×#18382
C127×#15712
C127×#15702
C127×#14862
C127×#12752
#10659127