Finite Group Databasebeta

← C127×#9336 #44573009

Subgroups — C127×#9336 #44573009

Order 32512.

360 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 114 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×#3236C211yesmaximal, characteristic
2C127×#2987C211yesmaximal, characteristic
3C127×#1554C211yesmaximal, characteristic
4C127×#1534C211yesmaximal, characteristic
5C127×#1470C211yesmaximal, characteristic
6C127×#1308C211yesmaximal, characteristic
7C127×#1287C211yesmaximal, characteristic
8#533×C127C2211yescharacteristic
9C2×#125×C127C2211yescharacteristic
10#501×C127—21no—
11#491×C127—21no—
12#484×C127C412yes—
13#483×C127C412yes—
14#479×C127—22no—
15#446×C127—22no—
16#446×C127—22no—
17#433×C127—22no—
18#432×C127C2211yescharacteristic
19#432×C127C2211yescharacteristic
20#432×C127C2211yescharacteristic
21#432×C127C2211yescharacteristic
22#431×C127C2211yescharacteristic
23#333×C127—21no—
24#332×C127—21no—
25#330×C127—22no—
26#324×C127—22no—
27C4⋊Q8×C127D411yescharacteristic
28C4⋊Q8×C127D411yescharacteristic
29#125×C127—21no—
30#125×C127—21no—
31#125×C127—21no—
32#125×C127—21no—
33#125×C127—21no—
34C22⋊Q8×C127—21no—
35C22⋊Q8×C127C2×C412yes—
36C4×Q8×C127—21no—
37C4×Q8×C127D412yes—
38#117×C127—21no—
39C2×C4⋊C4×C127—21no—
40C2×C4⋊C4×C127—21no—
41C2×C4⋊C4×C127C2×C411yescharacteristic
42C2×C4⋊C4×C127C2×C411yescharacteristic
43C2×C42×C127C2311yescharacteristic
44#107×C127—22no—
45#106×C127—22no—
46C4⋊C8×C127—24no—
47C4⋊C8×C127—21no—
48C4⋊C8×C127—21no—
49C4⋊C8×C127—21no—
50C4⋊C8×C127—21no—
51C4⋊C8×C127—21no—
52#103×C127—22no—
53#103×C127—22no—
54C22⋊C8×C127—21no—
55C22⋊C8×C127—21no—
56C22⋊C8×C127—21no—
57C22⋊C8×C127C2×C412yes—
58C22⋊C8×C127D412yes—
59#97×C127—22no—
60#97×C127—21no—
61#97×C127—21no—
62#97×C127—21no—
63#97×C127D412yes—
64C4×C8×C127—22no—
65C4×C8×C127—21no—
66C2×Q8×C127—21no—
67C2×Q8×C127C22⋊C412yes—
68C22×C4×C127—21no—
69C22×C4×C127—21no—
70C22×C4×C127C22×C411yescharacteristic
71C22×C4×C127C2×D411yescharacteristic
72C22×C4×C127#4111yescharacteristic
73C2×C8×C127—22no—
74C2×C8×C127—22no—
75C2×C8×C127—22no—
76C2×C8×C127—41no—
77C2×C8×C127—41no—
78C4⋊C4×C127—22no—
79C4⋊C4×C127—21no—
80C4⋊C4×C127—21no—
81C4⋊C4×C127—21no—
82C4⋊C4×C127—22no—
83C4⋊C4×C127—21no—
84C4⋊C4×C127—21no—
85C4⋊C4×C127—21no—
86C4⋊C4×C127—21no—
87C4⋊C4×C127—41no—
88C4⋊C4×C127—41no—
89C4⋊C4×C127—41no—
90C4⋊C4×C127—41no—
91C4⋊C4×C127C22⋊C412yes—
92C22⋊C4×C127—22no—
93C42×C127—22no—
94C42×C127C2×D411yescharacteristic
95C42×C127C2×D411yescharacteristic
96C42×C127C2×D411yescharacteristic
97C42×C127#4111yescharacteristic
98C23×C127C4×D411yescharacteristic
99Q8×C127—42no—
100Q8×C127—81no—
101C2×C4×C127—22no—
102C2×C4×C127—22no—
103C2×C4×C127—41no—
104C2×C4×C127—41no—
105C2×C4×C127—41no—
106C2×C4×C127—42no—
107C2×C4×C127—41no—
108C2×C4×C127—41no—
109C2×C4×C127—81no—
110C2×C4×C127C2×C22⋊C411yescharacteristic
111C2×C4×C127C4×D411yescharacteristic
112C2×C4×C127#12011yescharacteristic
113C2×C4×C127#12111yescharacteristic
114C2×C4×C127#12111yescharacteristic
115C2×C4×C127#12311yescharacteristic
116C8×C127—42no—
117C8×C127—42no—
118C8×C127—42no—
119C8×C127—81no—
120C8×C127—81no—
121C22×C127—21no—
122C22×C127—21no—
123C22×C127—21no—
124C22×C127#38611yescharacteristic
125C4×C127—21no—
126C4×C127—21no—
127C4×C127—21no—
128C4×C127—21no—
129C4×C127—21no—
130C4×C127—21no—
131C4×C127—42no—
132C4×C127—42no—
133C4×C127—81no—
134C4×C127—81no—
135#9336C12711yesmaximal, characteristic, direct product factor, Sylow
136C2×C127—41no—
137C2×C127#188111yescharacteristic
138C2×C127#190511yescharacteristic
139C2×C127#191511yescharacteristic
140#3236C2×C12711yescharacteristic
141#2987C2×C12711yescharacteristic
142#1554C2×C12711yescharacteristic
143#1534C2×C12711yescharacteristic
144#1470C2×C12711yescharacteristic
145#1308C2×C12711yescharacteristic
146#1287C2×C12711yescharacteristic
147C127#933611yescharacteristic, direct product factor, Sylow
148#533C22×C12711yescharacteristic
149C2×#125C22×C12711yescharacteristic
150#501—21no—
151#491—21no—
152#484C4×C12712yes—
153#483C4×C12712yes—
154#479—22no—
155#446—22no—
156#446—22no—
157#433—22no—
158#432C22×C12711yescharacteristic
159#432C22×C12711yescharacteristic
160#432C22×C12711yescharacteristic
161#432C22×C12711yescharacteristic
162#431C22×C12711yescharacteristic
163#333—21no—
164#332—21no—
165#330—22no—
166#324—22no—
167C4⋊Q8D4×C12711yescharacteristic
168C4⋊Q8D4×C12711yescharacteristic
169#125—21no—
170#125—21no—
171#125—21no—
172#125—21no—
173#125—21no—
174C22⋊Q8—21no—
175C22⋊Q8C2×C4×C12712yes—
176C4×Q8—21no—
177C4×Q8D4×C12712yes—
178#117—21no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4C2×C4×C12711yescharacteristic
182C2×C4⋊C4C2×C4×C12711yescharacteristic
183C2×C42C23×C12711yescharacteristic
184#107—22no—
185#106—22no—
186C4⋊C8—24no—
187C4⋊C8—21no—
188C4⋊C8—21no—
189C4⋊C8—21no—
190C4⋊C8—21no—
191C4⋊C8—21no—
192#103—22no—
193#103—22no—
194C22⋊C8—21no—
195C22⋊C8—21no—
196C22⋊C8—21no—
197C22⋊C8C2×C4×C12712yes—
198C22⋊C8D4×C12712yes—
199#97—22no—
200#97—21no—
201#97—21no—
202#97—21no—
203#97D4×C12712yes—
204C4×C8—22no—
205C4×C8—21no—
206C2×Q8—21no—
207C2×Q8C22⋊C4×C12712yes—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4C22×C4×C12711yescharacteristic
211C22×C4C2×D4×C12711yescharacteristic
212C22×C4#41×C12711yescharacteristic
213C2×C8—22no—
214C2×C8—22no—
215C2×C8—22no—
216C2×C8—41no—
217C2×C8—41no—
218C4⋊C4—22no—
219C4⋊C4—21no—
220C4⋊C4—21no—
221C4⋊C4—21no—
222C4⋊C4—22no—
223C4⋊C4—21no—
224C4⋊C4—21no—
225C4⋊C4—21no—
226C4⋊C4—21no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—41no—
231C4⋊C4C22⋊C4×C12712yes—
232C22⋊C4—22no—
233C42—22no—
234C42C2×D4×C12711yescharacteristic
235C42C2×D4×C12711yescharacteristic
236C42C2×D4×C12711yescharacteristic
237C42#41×C12711yescharacteristic
238C23C4×D4×C12711yescharacteristic
239Q8—42no—
240Q8—81no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—42no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—81no—
250C2×C4C2×C22⋊C4×C12711yescharacteristic
251C2×C4C4×D4×C12711yescharacteristic
252C2×C4#120×C12711yescharacteristic
253C2×C4#121×C12711yescharacteristic
254C2×C4#121×C12711yescharacteristic
255C2×C4#123×C12711yescharacteristic
256C8—42no—
257C8—42no—
258C8—42no—
259C8—81no—
260C8—81no—
261C22—21no—
262C22—21no—
263C22—21no—
264C22#386×C12711yescharacteristic
265C4—21no—
266C4—21no—
267C4—21no—
268C4—21no—
269C4—21no—
270C4—21no—
271C4—42no—
272C4—42no—
273C4—81no—
274C4—81no—
275C2—41no—
276C2C127×#188111yescharacteristic
277C2C127×#190511yescharacteristic
278C2C127×#191511yescharacteristic
subgroupG/H
center, socleC22×C127#386
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC23×C127C4×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
135. #9336C127direct (N × H)
147. C127#9336direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#32362
C127×#29872
C127×#15542
C127×#15342
C127×#14702
C127×#13082
C127×#12872
#9336127