Finite Group Databasebeta

← C127×#11652 #44575325

Subgroups — C127×#11652 #44575325

Order 32512.

344 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 118 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×#3169C211yesmaximal, characteristic
2C127×#2163C211yesmaximal, characteristic, complemented
3C127×#1564C211yesmaximal, characteristic, complemented
4C127×#1333C214yesmaximal, complemented
5#532×C127—21no—
6#500×C127C411yescharacteristic
7#493×C127C411yescharacteristic
8#486×C127—21no—
9#466×C127—21no—
10#466×C127C412yes—
11C4×D8×C127—21no—
12C4×D8×C127C2212yes—
13#431×C127—21no—
14C2×C4×C8×C127C2211yescharacteristic
15C4⋊C16×C127—21no—
16C22⋊C16×C127—21no—
17#346×C127C2212yes—
18#335×C127—21no—
19#334×C127C2212yes—
20C2×#41×C127—41no—
21C2×D8×C127—21no—
22C2×D8×C127C2×C412yes—
23C22×C8×C127C2×C411yescharacteristic
24C22×C8×C127D411yescharacteristic
25C4⋊Q8×C127—21no—
26#127×C127—21no—
27#124×C127—41no—
28#121×C127—22no—
29#121×C127—41no—
30C4×D4×C127—22no—
31C4×D4×C127—41no—
32C2×C42×C127D411yescharacteristic
33C2×C16×C127—22no—
34#107×C127—21no—
35#107×C127C2×C412yes—
36C4⋊C8×C127—22no—
37#102×C127—22no—
38#102×C127—22no—
39C22⋊C8×C127—41no—
40C4×C8×C127—41no—
41C4×C8×C127C2×C411yescharacteristic
42C4×C8×C127D411yescharacteristic
43C4×C8×C127D411yescharacteristic
44C4×C8×C127C2311yescharacteristic
45#41×C127—84no—
46C2×Q8×C127—41no—
47C2×D4×C127—22no—
48C2×D4×C127—42no—
49C2×D4×C127—41no—
50C2×D4×C127—41no—
51C22×C4×C127—42no—
52C22×C4×C127C22⋊C411yescharacteristic
53C22×C4×C127D811yescharacteristic
54C22×C4×C127SD1611yescharacteristic
55D8×C127—24no—
56D8×C127—42no—
57C2×C8×C127—22no—
58C2×C8×C127—41no—
59C2×C8×C127—42no—
60C2×C8×C127C22⋊C411yescharacteristic
61C2×C8×C127C22⋊C411yescharacteristic
62C2×C8×C127C22×C411yescharacteristic
63C2×C8×C127C2×D411yescharacteristic
64C4⋊C4×C127—22no—
65C4⋊C4×C127—41no—
66C22⋊C4×C127—42no—
67C22⋊C4×C127—42no—
68C42×C127C22⋊C411yescharacteristic
69C42×C127D811yescharacteristic
70C42×C127SD1611yescharacteristic
71C42×C127C2×D411yescharacteristic
72C16×C127—42no—
73C23×C127—42no—
74C23×C127#10211yescharacteristic
75Q8×C127—82no—
76D4×C127—42no—
77D4×C127—42no—
78D4×C127—82no—
79D4×C127—84no—
80D4×C127—82no—
81C2×C4×C127—22no—
82C2×C4×C127—21no—
83C2×C4×C127—21no—
84C2×C4×C127—41no—
85C2×C4×C127—42no—
86C2×C4×C127—84no—
87C2×C4×C127#10211yescharacteristic
88C2×C4×C127#10211yescharacteristic
89C2×C4×C127#10211yescharacteristic
90C2×C4×C127C2×C22⋊C411yescharacteristic
91C2×C4×C127C2×D811yescharacteristic
92C2×C4×C127C2×SD1611yescharacteristic
93C8×C127—21no—
94C8×C127—21no—
95C8×C127—21no—
96C8×C127—82no—
97C8×C127#13112yes—
98C22×C127—21no—
99C22×C127—21no—
100C22×C127—21no—
101C22×C127—82no—
102C22×C127—82no—
103C22×C127—82no—
104C22×C127C2×#10211yescharacteristic
105C4×C127—21no—
106C4×C127—21no—
107C4×C127—21no—
108C4×C127—21no—
109C4×C127—82no—
110C4×C127#36112yes—
111C4×C127#40811yescharacteristic
112C4×C127#42111yescharacteristic
113#11652C12711yesmaximal, characteristic, direct product factor, Sylow
114C2×C127—41no—
115C2×C127—162no—
116C2×C127#148011yescharacteristic
117C2×C127#214511yescharacteristic
118C2×C127C2×#36111yescharacteristic
119#3169C2×C12711yescharacteristic
120#2163C2×C12711yescharacteristic, complemented
121#1564C2×C12711yescharacteristic, complemented
122#1333C2×C12714yescomplemented
123C127#1165211yescharacteristic, direct product factor, Sylow
124#532—21no—
125#500C4×C12711yescharacteristic
126#493C4×C12711yescharacteristic
127#486—21no—
128#466—21no—
129#466C4×C12712yes—
130C4×D8—21no—
131C4×D8C22×C12712yes—
132#431—21no—
133C2×C4×C8C22×C12711yescharacteristic
134C4⋊C16—21no—
135C22⋊C16—21no—
136#346C22×C12712yes—
137#335—21no—
138#334C22×C12712yes—
139C2×#41—41no—
140C2×D8—21no—
141C2×D8C2×C4×C12712yes—
142C22×C8C2×C4×C12711yescharacteristic
143C22×C8D4×C12711yescharacteristic
144C4⋊Q8—21no—
145#127—21no—
146#124—41no—
147#121—22no—
148#121—41no—
149C4×D4—22no—
150C4×D4—41no—
151C2×C42D4×C12711yescharacteristic
152C2×C16—22no—
153#107—21no—
154#107C2×C4×C12712yes—
155C4⋊C8—22no—
156#102—22no—
157#102—22no—
158C22⋊C8—41no—
159C4×C8—41no—
160C4×C8C2×C4×C12711yescharacteristic
161C4×C8D4×C12711yescharacteristic
162C4×C8D4×C12711yescharacteristic
163C4×C8C23×C12711yescharacteristic
164#41—84no—
165C2×Q8—41no—
166C2×D4—22no—
167C2×D4—42no—
168C2×D4—41no—
169C2×D4—41no—
170C22×C4—42no—
171C22×C4C22⋊C4×C12711yescharacteristic
172C22×C4D8×C12711yescharacteristic
173C22×C4SD16×C12711yescharacteristic
174D8—24no—
175D8—42no—
176C2×C8—22no—
177C2×C8—41no—
178C2×C8—42no—
179C2×C8C22⋊C4×C12711yescharacteristic
180C2×C8C22⋊C4×C12711yescharacteristic
181C2×C8C22×C4×C12711yescharacteristic
182C2×C8C2×D4×C12711yescharacteristic
183C4⋊C4—22no—
184C4⋊C4—41no—
185C22⋊C4—42no—
186C22⋊C4—42no—
187C42C22⋊C4×C12711yescharacteristic
188C42D8×C12711yescharacteristic
189C42SD16×C12711yescharacteristic
190C42C2×D4×C12711yescharacteristic
191C16—42no—
192C23—42no—
193C23#102×C12711yescharacteristic
194Q8—82no—
195D4—42no—
196D4—42no—
197D4—82no—
198D4—84no—
199D4—82no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—41no—
204C2×C4—42no—
205C2×C4—84no—
206C2×C4#102×C12711yescharacteristic
207C2×C4#102×C12711yescharacteristic
208C2×C4#102×C12711yescharacteristic
209C2×C4C2×C22⋊C4×C12711yescharacteristic
210C2×C4C2×D8×C12711yescharacteristic
211C2×C4C2×SD16×C12711yescharacteristic
212C8—21no—
213C8—21no—
214C8—21no—
215C8—82no—
216C8#131×C12712yes—
217C22—21no—
218C22—21no—
219C22—21no—
220C22—82no—
221C22—82no—
222C22—82no—
223C22C2×#102×C12711yescharacteristic
224C4—21no—
225C4—21no—
226C4—21no—
227C4—21no—
228C4—82no—
229C4#361×C12712yes—
230C4#408×C12711yescharacteristic
231C4#421×C12711yescharacteristic
232C2—41no—
233C2—162no—
234C2C127×#148011yescharacteristic
235C2C127×#214511yescharacteristic
236C2C2×#361×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#102
commutatorC2×C8C22×C4×C127
Frattini, cosocleC4×C8C23×C127
prime radicalC127×#3169C2
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
2. C127×#2163C2semidirect
3. C127×#1564C2semidirect
4. C127×#1333C2semidirect
113. #11652C127direct (N × H)
120. #2163C2×C127semidirect
121. #1564C2×C127semidirect
122. #1333C2×C127semidirect
123. C127#11652direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#31692
C127×#21632
C127×#15642
C127×#13332
#11652127