Finite Group Databasebeta

← C127×#11736 #44575409

Subgroups — C127×#11736 #44575409

Order 32512.

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

normal subgroups only

This group has 402 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×#2399C211yesmaximal, characteristic
2C4×#101×C127C211yesmaximal, characteristic
3C127×#1461C211yesmaximal, characteristic
4C127×#1354C212yesmaximal
5C127×#1346C212yesmaximal
6C2×C4×Q8×C127C411yescharacteristic
7C2×C4×Q8×C127C2211yescharacteristic
8#431×C127—21no—
9C2×#101×C127—21no—
10C4×M16×C127—21no—
11#398×C127—21no—
12#398×C127C411yescharacteristic
13#398×C127C2211yescharacteristic
14#395×C127—21no—
15#395×C127C411yescharacteristic
16#395×C127C2211yescharacteristic
17C4×C4⋊C4×C127—21no—
18C4×C4⋊C4×C127—21no—
19#376×C127C411yescharacteristic
20#343×C127C2212yes—
21#324×C127—21no—
22#324×C127C2212yes—
23C22×Q8×C127C2×C411yescharacteristic
24C22×Q8×C127D411yescharacteristic
25C2×M16×C127—22no—
26C4×Q8×C127—41no—
27C4×Q8×C127—41no—
28C4×Q8×C127—41no—
29C4×Q8×C127—41no—
30C2×C4⋊C4×C127—21no—
31C2×C4⋊C4×C127—21no—
32C2×C4⋊C4×C127—21no—
33C2×C4⋊C4×C127—21no—
34C2×C4⋊C4×C127—21no—
35C2×C4⋊C4×C127C2×C411yescharacteristic
36C2×C4⋊C4×C127C2×C411yescharacteristic
37C2×C4⋊C4×C127D411yescharacteristic
38C2×C4⋊C4×C127C2311yescharacteristic
39C2×C42×C127—21no—
40C2×C42×C127—21no—
41C2×C42×C127C2×C411yescharacteristic
42C2×C42×C127D411yescharacteristic
43C2×C42×C127D411yescharacteristic
44C4⋊C8×C127—41no—
45#101×C127—24no—
46C22⋊C8×C127—22no—
47#97×C127—41no—
48C4×C8×C127—41no—
49C4×C8×C127—41no—
50#95×C127—21no—
51#95×C127—21no—
52#95×C127—21no—
53#95×C127—21no—
54#95×C127—21no—
55#95×C127C2×C411yescharacteristic
56#95×C127C2×C411yescharacteristic
57C2×Q8×C127—22no—
58C2×Q8×C127—22no—
59C2×Q8×C127—41no—
60C2×Q8×C127—42no—
61C2×Q8×C127—41no—
62C22×C4×C127—21no—
63C22×C4×C127—21no—
64C22×C4×C127—21no—
65C22×C4×C127—21no—
66C22×C4×C127C22⋊C411yescharacteristic
67C22×C4×C127C22⋊C411yescharacteristic
68C22×C4×C127C22⋊C411yescharacteristic
69C22×C4×C127C22⋊C411yescharacteristic
70C22×C4×C127C22×C411yescharacteristic
71C22×C4×C127C2×D411yescharacteristic
72C22×C4×C127C2×D411yescharacteristic
73M16×C127—24no—
74M16×C127—42no—
75C2×C8×C127—42no—
76C2×C8×C127—42no—
77C4⋊C4×C127—41no—
78C4⋊C4×C127—41no—
79C4⋊C4×C127—41no—
80C4⋊C4×C127—41no—
81C4⋊C4×C127—42no—
82C4⋊C4×C127—42no—
83C4⋊C4×C127—42no—
84C4⋊C4×C127—42no—
85C4⋊C4×C127—42no—
86C42×C127—24no—
87C42×C127—21no—
88C42×C127—21no—
89C42×C127—21no—
90C42×C127—21no—
91C42×C127—21no—
92C42×C127—21no—
93C42×C127—41no—
94C42×C127—41no—
95C23×C127C2×C22⋊C411yescharacteristic
96Q8×C127—44no—
97Q8×C127—42no—
98Q8×C127—42no—
99C2×C4×C127—21no—
100C2×C4×C127—21no—
101C2×C4×C127—21no—
102C2×C4×C127—21no—
103C2×C4×C127—22no—
104C2×C4×C127—22no—
105C2×C4×C127—22no—
106C2×C4×C127—22no—
107C2×C4×C127—21no—
108C2×C4×C127—21no—
109C2×C4×C127—21no—
110C2×C4×C127—21no—
111C2×C4×C127—21no—
112C2×C4×C127—21no—
113C2×C4×C127—41no—
114C2×C4×C127—41no—
115C2×C4×C127—41no—
116C2×C4×C127—41no—
117C2×C4×C127—41no—
118C2×C4×C127—41no—
119C2×C4×C127—41no—
120C2×C4×C127—41no—
121C2×C4×C127—41no—
122C2×C4×C127—41no—
123C2×C4×C127—41no—
124C2×C4×C127—41no—
125C2×C4×C127#9911yescharacteristic
126C2×C4×C127#9911yescharacteristic
127C2×C4×C127#10412yes—
128C2×C4×C127#13512yes—
129C8×C127—44no—
130C8×C127—82no—
131C22×C127—21no—
132C22×C127—21no—
133C22×C127C2×#9911yescharacteristic
134C22×C127#41611yescharacteristic
135C22×C127C2×#10411yescharacteristic
136C4×C127—21no—
137C4×C127—22no—
138C4×C127—22no—
139C4×C127—42no—
140C4×C127—42no—
141C4×C127—41no—
142C4×C127—41no—
143C4×C127—42no—
144C4×C127—41no—
145C4×C127—41no—
146C4×C127—81no—
147C4×C127#35612yes—
148#11736C12711yesmaximal, characteristic, direct product factor, Sylow
149C2×C127—21no—
150C2×C127—21no—
151C2×C127#150111yescharacteristic
152C2×C127#212011yescharacteristic
153C2×C127C2×#35611yescharacteristic
154#2399C2×C12711yescharacteristic
155C4×#101C2×C12711yescharacteristic
156#1461C2×C12711yescharacteristic
157#1354C2×C12712yes—
158#1346C2×C12712yes—
159C127#1173611yescharacteristic, direct product factor, Sylow
160C2×C4×Q8C4×C12711yescharacteristic
161C2×C4×Q8C22×C12711yescharacteristic
162#431—21no—
163C2×#101—21no—
164C4×M16—21no—
165#398—21no—
166#398C4×C12711yescharacteristic
167#398C22×C12711yescharacteristic
168#395—21no—
169#395C4×C12711yescharacteristic
170#395C22×C12711yescharacteristic
171C4×C4⋊C4—21no—
172C4×C4⋊C4—21no—
173#376C4×C12711yescharacteristic
174#343C22×C12712yes—
175#324—21no—
176#324C22×C12712yes—
177C22×Q8C2×C4×C12711yescharacteristic
178C22×Q8D4×C12711yescharacteristic
179C2×M16—22no—
180C4×Q8—41no—
181C4×Q8—41no—
182C4×Q8—41no—
183C4×Q8—41no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4C2×C4×C12711yescharacteristic
190C2×C4⋊C4C2×C4×C12711yescharacteristic
191C2×C4⋊C4D4×C12711yescharacteristic
192C2×C4⋊C4C23×C12711yescharacteristic
193C2×C42—21no—
194C2×C42—21no—
195C2×C42C2×C4×C12711yescharacteristic
196C2×C42D4×C12711yescharacteristic
197C2×C42D4×C12711yescharacteristic
198C4⋊C8—41no—
199#101—24no—
200C22⋊C8—22no—
201#97—41no—
202C4×C8—41no—
203C4×C8—41no—
204#95—21no—
205#95—21no—
206#95—21no—
207#95—21no—
208#95—21no—
209#95C2×C4×C12711yescharacteristic
210#95C2×C4×C12711yescharacteristic
211C2×Q8—22no—
212C2×Q8—22no—
213C2×Q8—41no—
214C2×Q8—42no—
215C2×Q8—41no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4C22⋊C4×C12711yescharacteristic
221C22×C4C22⋊C4×C12711yescharacteristic
222C22×C4C22⋊C4×C12711yescharacteristic
223C22×C4C22⋊C4×C12711yescharacteristic
224C22×C4C22×C4×C12711yescharacteristic
225C22×C4C2×D4×C12711yescharacteristic
226C22×C4C2×D4×C12711yescharacteristic
227M16—24no—
228M16—42no—
229C2×C8—42no—
230C2×C8—42no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—42no—
236C4⋊C4—42no—
237C4⋊C4—42no—
238C4⋊C4—42no—
239C4⋊C4—42no—
240C42—24no—
241C42—21no—
242C42—21no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—21no—
247C42—41no—
248C42—41no—
249C23C2×C22⋊C4×C12711yescharacteristic
250Q8—44no—
251Q8—42no—
252Q8—42no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4#99×C12711yescharacteristic
280C2×C4#99×C12711yescharacteristic
281C2×C4#104×C12712yes—
282C2×C4#135×C12712yes—
283C8—44no—
284C8—82no—
285C22—21no—
286C22—21no—
287C22C2×#99×C12711yescharacteristic
288C22#416×C12711yescharacteristic
289C22C2×#104×C12711yescharacteristic
290C4—21no—
291C4—22no—
292C4—22no—
293C4—42no—
294C4—42no—
295C4—41no—
296C4—42no—
297C4—41no—
298C4—41no—
299C4—41no—
300C4—81no—
301C4#356×C12712yes—
302C2—21no—
303C2—21no—
304C2C127×#150111yescharacteristic
305C2C127×#212011yescharacteristic
306C2C2×#356×C12711yescharacteristic
subgroupG/H
centerC2×C4×C127#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C4⋊C4C23×C127
socleC22×C127C2×#99
prime radicalC23×C127C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C22×C4×C127 ◁ C2×C4×Q8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
148. #11736C127direct (N × H)
159. C127#11736direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#23992
C4×#101×C1272
C127×#14612
C127×#13542
C127×#13462
#11736127