Finite Group Databasebeta

← C127×#13589 #44577262

Subgroups — C127×#13589 #44577262

Order 32512.

408 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 90 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×#3147C211yesmaximal, characteristic
2C127×#2132C212yesmaximal, complemented
3C127×#1411C212yesmaximal, complemented
4C127×#1410C212yesmaximal, complemented
5C2×#135×C127—22no—
6#532×C127C411yescharacteristic
7#532×C127C2211yescharacteristic
8#495×C127—22no—
9#494×C127C2211yescharacteristic
10#493×C127C411yescharacteristic
11#492×C127C411yescharacteristic
12#492×C127C2211yescharacteristic
13#413×C127—22no—
14C2×C4×C8×C127C411yescharacteristic
15#356×C127C2214yes—
16#355×C127—22no—
17C2×#41×C127—21no—
18C2×#41×C127D412yes—
19#135×C127—44no—
20#135×C127—44no—
21C2×Q16×C127—22no—
22C2×SD16×C127—22no—
23C2×SD16×C127—22no—
24C2×D8×C127—22no—
25C2×M16×C127—42no—
26C22×C8×C127—21no—
27C4⋊Q8×C127C2×C411yescharacteristic
28C4⋊Q8×C127C2311yescharacteristic
29#127×C127C2×C411yescharacteristic
30#127×C127C2×C411yescharacteristic
31#124×C127—21no—
32#124×C127D412yes—
33#121×C127—41no—
34#121×C127—41no—
35C4×D4×C127—41no—
36C4×D4×C127—41no—
37C2×C42×C127C2×C411yescharacteristic
38#101×C127—24no—
39#100×C127—42no—
40C4×C8×C127—21no—
41C4×C8×C127C2×C411yescharacteristic
42C4×C8×C127C2×C411yescharacteristic
43#41×C127—42no—
44#41×C127—42no—
45#41×C127—42no—
46#41×C127—42no—
47C2×Q8×C127—21no—
48C2×Q8×C127C2×D412yes—
49C2×D4×C127—22no—
50C2×D4×C127—21no—
51C2×D4×C127—41no—
52C2×D4×C127—41no—
53C2×D4×C127—41no—
54C2×D4×C127C22⋊C412yes—
55C22×C4×C127—21no—
56C22×C4×C127—22no—
57C22×C4×C127—41no—
58C22×C4×C127C22⋊C411yescharacteristic
59Q16×C127—44no—
60SD16×C127—44no—
61SD16×C127—44no—
62D8×C127—44no—
63M16×C127—44no—
64M16×C127—82no—
65C2×C8×C127—22no—
66C2×C8×C127—22no—
67C2×C8×C127—21no—
68C2×C8×C127—21no—
69C2×C8×C127—82no—
70C4⋊C4×C127—41no—
71C4⋊C4×C127—41no—
72C22⋊C4×C127—42no—
73C22⋊C4×C127—42no—
74C42×C127—21no—
75C42×C127C22⋊C411yescharacteristic
76C42×C127C22×C411yescharacteristic
77C23×C127—22no—
78C23×C127—41no—
79C23×C127#9911yescharacteristic
80Q8×C127—42no—
81Q8×C127—42no—
82D4×C127—42no—
83D4×C127—42no—
84D4×C127—82no—
85D4×C127—82no—
86D4×C127—82no—
87D4×C127—82no—
88C2×C4×C127—21no—
89C2×C4×C127—21no—
90C2×C4×C127—21no—
91C2×C4×C127—21no—
92C2×C4×C127—22no—
93C2×C4×C127—42no—
94C2×C4×C127—42no—
95C2×C4×C127—42no—
96C2×C4×C127—41no—
97C2×C4×C127—81no—
98C2×C4×C127—81no—
99C2×C4×C127#9911yescharacteristic
100C2×C4×C127C2×C22⋊C411yescharacteristic
101C8×C127—22no—
102C8×C127—22no—
103C8×C127—84no—
104C22×C127—21no—
105C22×C127—41no—
106C22×C127—42no—
107C22×C127—82no—
108C22×C127—82no—
109C22×C127—81no—
110C22×C127C2×#9911yescharacteristic
111C4×C127—22no—
112C4×C127—21no—
113C4×C127—41no—
114C4×C127—42no—
115C4×C127—81no—
116C4×C127#35311yescharacteristic
117C4×C127#35311yescharacteristic
118#13589C12711yesmaximal, characteristic, direct product factor, Sylow
119C2×C127—21no—
120C2×C127—41no—
121C2×C127—82no—
122C2×C127—161no—
123C2×C127C2×#35311yescharacteristic
124#3147C2×C12711yescharacteristic
125#2132C2×C12712yescomplemented
126#1411C2×C12712yescomplemented
127#1410C2×C12712yescomplemented
128C127#1358911yescharacteristic, direct product factor, Sylow
129C2×#135—22no—
130#532C4×C12711yescharacteristic
131#532C22×C12711yescharacteristic
132#495—22no—
133#494C22×C12711yescharacteristic
134#493C4×C12711yescharacteristic
135#492C4×C12711yescharacteristic
136#492C22×C12711yescharacteristic
137#413—22no—
138C2×C4×C8C4×C12711yescharacteristic
139#356C22×C12714yes—
140#355—22no—
141C2×#41—21no—
142C2×#41D4×C12712yes—
143#135—44no—
144#135—44no—
145C2×Q16—22no—
146C2×SD16—22no—
147C2×SD16—22no—
148C2×D8—22no—
149C2×M16—42no—
150C22×C8—21no—
151C4⋊Q8C2×C4×C12711yescharacteristic
152C4⋊Q8C23×C12711yescharacteristic
153#127C2×C4×C12711yescharacteristic
154#127C2×C4×C12711yescharacteristic
155#124—21no—
156#124D4×C12712yes—
157#121—41no—
158#121—41no—
159C4×D4—41no—
160C4×D4—41no—
161C2×C42C2×C4×C12711yescharacteristic
162#101—24no—
163#100—42no—
164C4×C8—21no—
165C4×C8C2×C4×C12711yescharacteristic
166C4×C8C2×C4×C12711yescharacteristic
167#41—42no—
168#41—42no—
169#41—42no—
170#41—42no—
171C2×Q8—21no—
172C2×Q8C2×D4×C12712yes—
173C2×D4—22no—
174C2×D4—21no—
175C2×D4—41no—
176C2×D4—41no—
177C2×D4—41no—
178C2×D4C22⋊C4×C12712yes—
179C22×C4—21no—
180C22×C4—22no—
181C22×C4—41no—
182C22×C4C22⋊C4×C12711yescharacteristic
183Q16—44no—
184SD16—44no—
185SD16—44no—
186D8—44no—
187M16—44no—
188M16—82no—
189C2×C8—22no—
190C2×C8—22no—
191C2×C8—21no—
192C2×C8—21no—
193C2×C8—82no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C22⋊C4—42no—
197C22⋊C4—42no—
198C42—21no—
199C42C22⋊C4×C12711yescharacteristic
200C42C22×C4×C12711yescharacteristic
201C23—22no—
202C23—41no—
203C23#99×C12711yescharacteristic
204Q8—42no—
205Q8—42no—
206D4—42no—
207D4—42no—
208D4—82no—
209D4—82no—
210D4—82no—
211D4—82no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—41no—
221C2×C4—81no—
222C2×C4—81no—
223C2×C4#99×C12711yescharacteristic
224C2×C4C2×C22⋊C4×C12711yescharacteristic
225C8—22no—
226C8—22no—
227C8—84no—
228C22—21no—
229C22—41no—
230C22—42no—
231C22—82no—
232C22—82no—
233C22—81no—
234C22C2×#99×C12711yescharacteristic
235C4—22no—
236C4—21no—
237C4—41no—
238C4—42no—
239C4—81no—
240C4#353×C12711yescharacteristic
241C4#353×C12711yescharacteristic
242C2—21no—
243C2—41no—
244C2—82no—
245C2—161no—
246C2C2×#353×C12711yescharacteristic
subgroupG/H
centerC4×C127#353
commutatorC42C22×C4×C127
Frattini, cosocleC4⋊Q8C23×C127
socleC2×C127C2×#353
prime radicalC127×#3147C2
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C127 ◁ C2×C4×C127 ◁ C22×C4×C127 ◁ #532×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2132C2semidirect
3. C127×#1411C2semidirect
4. C127×#1410C2semidirect
118. #13589C127direct (N × H)
125. #2132C2×C127semidirect
126. #1411C2×C127semidirect
127. #1410C2×C127semidirect
128. C127#13589direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#31472
C127×#21322
C127×#14112
C127×#14102
#13589127