Finite Group Databasebeta

← C127×#8337 #44572010

Subgroups — C127×#8337 #44572010

Order 32512.

1094 conjugacy classes of subgroups; only the 174 normal subgroups are shown.

normal subgroups only

This group has 1094 conjugacy classes of subgroups — too many to draw. Only its 174 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
1C2×#532×C127C211yesmaximal, characteristic
2C127×#1749C212yesmaximal, complemented
3C2×#329×C127C214yesmaximal, complemented
4C22×#41×C127C412yes—
5#532×C127—28no—
6C2×C4⋊Q8×C127C411yescharacteristic
7C2×#127×C127C411yescharacteristic
8C2×#124×C127C2212yes—
9C2×#121×C127—22no—
10C2×C4×D4×C127—22no—
11C22×C42×C127C2211yescharacteristic
12C2×C22⋊C8×C127—22no—
13C2×#97×C127C2214yes—
14#336×C127—22no—
15#329×C127—28no—
16C2×#41×C127—24no—
17C2×#41×C127—24no—
18C2×#41×C127—44no—
19C2×#41×C127—44no—
20C22×Q8×C127C2×C412yes—
21C22×D4×C127—22no—
22C22×D4×C127—22no—
23C22×D4×C127C2×C412yes—
24C23×C4×C127—22no—
25C23×C4×C127C2×C411yescharacteristic
26C23×C4×C127D412yes—
27C22×C8×C127—24no—
28C4⋊Q8×C127—24no—
29#127×C127—24no—
30#124×C127—24no—
31#124×C127D418yes—
32#121×C127—216no—
33C4×D4×C127—216no—
34C2×C4⋊C4×C127—22no—
35C2×C22⋊C4×C127—24no—
36C2×C42×C127—24no—
37C2×C42×C127C2×C411yescharacteristic
38C2×C42×C127D412yes—
39C2×C42×C127C2311yescharacteristic
40C22⋊C8×C127—28no—
41#97×C127—28no—
42C24×C127—22no—
43C24×C127C22⋊C411yescharacteristic
44#41×C127—416no—
45#41×C127—416no—
46C2×Q8×C127—22no—
47C2×Q8×C127—42no—
48C2×Q8×C127—42no—
49C2×Q8×C127C22⋊C414yes—
50C2×D4×C127—28no—
51C2×D4×C127—28no—
52C2×D4×C127—22no—
53C2×D4×C127—42no—
54C2×D4×C127—42no—
55C2×D4×C127—44no—
56C2×D4×C127—44no—
57C2×D4×C127—44no—
58C2×D4×C127—44no—
59C2×D4×C127C22⋊C414yes—
60C22×C4×C127—22no—
61C22×C4×C127—22no—
62C22×C4×C127—22no—
63C22×C4×C127—28no—
64C22×C4×C127—22no—
65C22×C4×C127—24no—
66C22×C4×C127—24no—
67C22×C4×C127—42no—
68C22×C4×C127—44no—
69C22×C4×C127—44no—
70C22×C4×C127C22⋊C411yescharacteristic
71C22×C4×C127C22⋊C412yes—
72C22×C4×C127C22×C411yescharacteristic
73C22×C4×C127C2×D412yes—
74C2×C8×C127—28no—
75C2×C8×C127—44no—
76C2×C8×C127—44no—
77C4⋊C4×C127—28no—
78C22⋊C4×C127—216no—
79C42×C127—22no—
80C42×C127—24no—
81C42×C127C2×D414yes—
82C23×C127—21no—
83C23×C127—21no—
84C23×C127—22no—
85C23×C127—22no—
86C23×C127—24no—
87C23×C127—42no—
88C23×C127—42no—
89C23×C127—44no—
90C23×C127—44no—
91C23×C127#10012yes—
92C23×C127C2×C22⋊C411yescharacteristic
93Q8×C127—44no—
94Q8×C127—44no—
95D4×C127—44no—
96D4×C127—416no—
97D4×C127—44no—
98D4×C127—416no—
99C2×C4×C127—28no—
100C2×C4×C127—22no—
101C2×C4×C127—21no—
102C2×C4×C127—21no—
103C2×C4×C127—21no—
104C2×C4×C127—21no—
105C2×C4×C127—22no—
106C2×C4×C127—22no—
107C2×C4×C127—22no—
108C2×C4×C127—24no—
109C2×C4×C127—48no—
110C2×C4×C127—416no—
111C2×C4×C127—42no—
112C2×C4×C127—42no—
113C2×C4×C127#10012yes—
114C2×C4×C127#10414yes—
115C2×C4×C127C2×C22⋊C412yes—
116C2×C4×C127#12014yes—
117C8×C127—48no—
118C22×C127—22no—
119C22×C127—24no—
120C22×C127—41no—
121C22×C127—41no—
122C22×C127—42no—
123C22×C127—44no—
124C22×C127—48no—
125C22×C127—82no—
126C22×C127—82no—
127C22×C127—84no—
128C22×C127#37911yescharacteristic
129C22×C127C2×#10011yescharacteristic
130C22×C127C2×#10011yescharacteristic
131C22×C127C2×#10412yes—
132C22×C127#42112yes—
133C4×C127—22no—
134C4×C127—22no—
135C4×C127—24no—
136C4×C127—24no—
137C4×C127—44no—
138#8337C12711yesmaximal, characteristic, direct product factor, Sylow
139C2×C127—42no—
140C2×C127—84no—
141C2×C127#152511yescharacteristic
142C2×C127#153012yes—
143C2×C127#153611yescharacteristic
144C2×C127#178311yescharacteristic
145C2×C127#178912yes—
146C2×#532C2×C12711yescharacteristic
147#1749C2×C12712yescomplemented
148C2×#329C2×C12714yescomplemented
149C127#833711yescharacteristic, direct product factor, Sylow
150C22×#41C4×C12712yes—
151#532—28no—
152C2×C4⋊Q8C4×C12711yescharacteristic
153C2×#127C4×C12711yescharacteristic
154C2×#124C22×C12712yes—
155C2×#121—22no—
156C2×C4×D4—22no—
157C22×C42C22×C12711yescharacteristic
158C2×C22⋊C8—22no—
159C2×#97C22×C12714yes—
160#336—22no—
161#329—28no—
162C2×#41—24no—
163C2×#41—24no—
164C2×#41—44no—
165C2×#41—44no—
166C22×Q8C2×C4×C12712yes—
167C22×D4—22no—
168C22×D4—22no—
169C22×D4C2×C4×C12712yes—
170C23×C4—22no—
171C23×C4C2×C4×C12711yescharacteristic
172C23×C4D4×C12712yes—
173C22×C8—24no—
174C4⋊Q8—24no—
175#127—24no—
176#124—24no—
177#124D4×C12718yes—
178#121—216no—
179C4×D4—216no—
180C2×C4⋊C4—22no—
181C2×C22⋊C4—24no—
182C2×C42—24no—
183C2×C42C2×C4×C12711yescharacteristic
184C2×C42D4×C12712yes—
185C2×C42C23×C12711yescharacteristic
186C22⋊C8—28no—
187#97—28no—
188C24—22no—
189C24C22⋊C4×C12711yescharacteristic
190#41—416no—
191#41—416no—
192C2×Q8—22no—
193C2×Q8—42no—
194C2×Q8—42no—
195C2×Q8C22⋊C4×C12714yes—
196C2×D4—28no—
197C2×D4—28no—
198C2×D4—22no—
199C2×D4—42no—
200C2×D4—42no—
201C2×D4—44no—
202C2×D4—44no—
203C2×D4—44no—
204C2×D4—44no—
205C2×D4C22⋊C4×C12714yes—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—28no—
210C22×C4—22no—
211C22×C4—24no—
212C22×C4—24no—
213C22×C4—42no—
214C22×C4—44no—
215C22×C4—44no—
216C22×C4C22⋊C4×C12711yescharacteristic
217C22×C4C22⋊C4×C12712yes—
218C22×C4C22×C4×C12711yescharacteristic
219C22×C4C2×D4×C12712yes—
220C2×C8—28no—
221C2×C8—44no—
222C2×C8—44no—
223C4⋊C4—28no—
224C22⋊C4—216no—
225C42—22no—
226C42—24no—
227C42C2×D4×C12714yes—
228C23—21no—
229C23—21no—
230C23—22no—
231C23—22no—
232C23—24no—
233C23—42no—
234C23—42no—
235C23—44no—
236C23—44no—
237C23#100×C12712yes—
238C23C2×C22⋊C4×C12711yescharacteristic
239Q8—44no—
240Q8—44no—
241D4—44no—
242D4—44no—
243D4—416no—
244D4—416no—
245C2×C4—28no—
246C2×C4—22no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—24no—
255C2×C4—48no—
256C2×C4—416no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4#100×C12712yes—
260C2×C4#104×C12714yes—
261C2×C4C2×C22⋊C4×C12712yes—
262C2×C4#120×C12714yes—
263C8—48no—
264C22—22no—
265C22—24no—
266C22—41no—
267C22—42no—
268C22—41no—
269C22—44no—
270C22—48no—
271C22—82no—
272C22—84no—
273C22—82no—
274C22#379×C12711yescharacteristic
275C22C2×#100×C12711yescharacteristic
276C22C2×#100×C12711yescharacteristic
277C22C2×#104×C12712yes—
278C22#421×C12712yes—
279C4—22no—
280C4—22no—
281C4—24no—
282C4—24no—
283C4—44no—
284C2—42no—
285C2—84no—
286C2C127×#152511yescharacteristic
287C2C127×#153012yes—
288C2C127×#153611yescharacteristic
289C2C127×#178311yescharacteristic
290C2C127×#178912yes—
subgroupG/H
center, socleC23×C127C2×C22⋊C4
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC2×#532×C127C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C127 ◁ C22×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1749C2semidirect
3. C2×#329×C127C2semidirect
138. #8337C127direct (N × H)
147. #1749C2×C127semidirect
148. C2×#329C2×C127semidirect
149. C127#8337direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#532×C1272
C127×#17492
C2×#329×C1272
#8337127