Finite Group Databasebeta

← C127×#11700 #44575373

Subgroups — C127×#11700 #44575373

Order 32512.

452 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 126 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×#2621C211yesmaximal, characteristic
2C127×#1742C211yesmaximal, characteristic
3C127×#1458C211yesmaximal, characteristic
4C127×#1346C214yesmaximal, complemented
5C22×M16×C127—21no—
6C2×C4⋊Q8×C127C411yescharacteristic
7C2×C22⋊Q8×C127—21no—
8C2×#117×C127C2211yescharacteristic
9#431×C127—21no—
10#398×C127—21no—
11#398×C127C2212yes—
12#397×C127—21no—
13#397×C127C412yes—
14#391×C127—21no—
15#382×C127C411yescharacteristic
16#343×C127—21no—
17#343×C127C2212yes—
18#324×C127C2212yes—
19#323×C127—21no—
20C22×Q8×C127—21no—
21C23×C4×C127D411yescharacteristic
22C2×M16×C127—24no—
23C2×M16×C127—22no—
24C2×M16×C127—41no—
25C2×M16×C127—42no—
26C22×C8×C127—41no—
27C4⋊Q8×C127—41no—
28C4⋊Q8×C127—41no—
29C22⋊Q8×C127—42no—
30C22⋊Q8×C127—42no—
31#117×C127—41no—
32#117×C127—41no—
33C2×C4⋊C4×C127—21no—
34C2×C4⋊C4×C127—21no—
35C2×C4⋊C4×C127—22no—
36C2×C4⋊C4×C127C2×C412yes—
37C2×C4⋊C4×C127D411yescharacteristic
38C2×C4⋊C4×C127C2311yescharacteristic
39C2×C22⋊C4×C127—22no—
40C2×C22⋊C4×C127C2×C411yescharacteristic
41C2×C22⋊C4×C127D411yescharacteristic
42C2×C42×C127C2×C411yescharacteristic
43C2×C42×C127D411yescharacteristic
44C4⋊C8×C127—41no—
45C22⋊C8×C127—22no—
46C4×C8×C127—41no—
47#95×C127—21no—
48#95×C127—22no—
49#95×C127—22no—
50#95×C127C2×C412yes—
51C24×C127C22⋊C411yescharacteristic
52C2×Q8×C127—41no—
53C2×Q8×C127—41no—
54C2×Q8×C127—42no—
55C2×Q8×C127—42no—
56C22×C4×C127—21no—
57C22×C4×C127—21no—
58C22×C4×C127—22no—
59C22×C4×C127—22no—
60C22×C4×C127—22no—
61C22×C4×C127C22⋊C411yescharacteristic
62C22×C4×C127C22⋊C411yescharacteristic
63C22×C4×C127C22⋊C411yescharacteristic
64C22×C4×C127D812yes—
65C22×C4×C127SD1612yes—
66C22×C4×C127C22×C411yescharacteristic
67C22×C4×C127C2×D411yescharacteristic
68C22×C4×C127C2×D411yescharacteristic
69M16×C127—24no—
70M16×C127—44no—
71M16×C127—42no—
72C2×C8×C127—42no—
73C2×C8×C127—44no—
74C2×C8×C127—42no—
75C4⋊C4×C127—41no—
76C4⋊C4×C127—41no—
77C4⋊C4×C127—42no—
78C4⋊C4×C127—42no—
79C4⋊C4×C127—42no—
80C4⋊C4×C127—42no—
81C4⋊C4×C127—42no—
82C22⋊C4×C127—41no—
83C22⋊C4×C127—41no—
84C22⋊C4×C127—44no—
85C42×C127—21no—
86C42×C127—21no—
87C42×C127—21no—
88C42×C127—21no—
89C23×C127—21no—
90C23×C127—21no—
91C23×C127—41no—
92C23×C127—41no—
93C23×C127#10212yes—
94C23×C127C2×C22⋊C411yescharacteristic
95Q8×C127—82no—
96Q8×C127—82no—
97C2×C4×C127—21no—
98C2×C4×C127—21no—
99C2×C4×C127—22no—
100C2×C4×C127—22no—
101C2×C4×C127—22no—
102C2×C4×C127—22no—
103C2×C4×C127—21no—
104C2×C4×C127—21no—
105C2×C4×C127—21no—
106C2×C4×C127—21no—
107C2×C4×C127—41no—
108C2×C4×C127—41no—
109C2×C4×C127—41no—
110C2×C4×C127—41no—
111C2×C4×C127—42no—
112C2×C4×C127—42no—
113C2×C4×C127—42no—
114C2×C4×C127—42no—
115C2×C4×C127—42no—
116C2×C4×C127—42no—
117C2×C4×C127#9911yescharacteristic
118C2×C4×C127#9911yescharacteristic
119C2×C4×C127#10212yes—
120C2×C4×C127#10412yes—
121C2×C4×C127C2×D811yescharacteristic
122C2×C4×C127C2×SD1611yescharacteristic
123C8×C127—44no—
124C8×C127—82no—
125C22×C127—21no—
126C22×C127—21no—
127C22×C127—22no—
128C22×C127—42no—
129C22×C127—41no—
130C22×C127—41no—
131C22×C127—81no—
132C22×C127C2×#9911yescharacteristic
133C22×C127C2×#10211yescharacteristic
134C22×C127C2×#10411yescharacteristic
135C4×C127—21no—
136C4×C127—21no—
137C4×C127—41no—
138C4×C127—41no—
139C4×C127—41no—
140C4×C127—41no—
141C4×C127—82no—
142C4×C127—82no—
143C4×C127#32712yes—
144C4×C127#32712yes—
145#11700C12711yesmaximal, characteristic, direct product factor, Sylow
146C2×C127—21no—
147C2×C127—21no—
148C2×C127—42no—
149C2×C127C2×#32711yescharacteristic
150C2×C127#212311yescharacteristic
151C2×C127#213511yescharacteristic
152#2621C2×C12711yescharacteristic
153#1742C2×C12711yescharacteristic
154#1458C2×C12711yescharacteristic
155#1346C2×C12714yescomplemented
156C127#1170011yescharacteristic, direct product factor, Sylow
157C22×M16—21no—
158C2×C4⋊Q8C4×C12711yescharacteristic
159C2×C22⋊Q8—21no—
160C2×#117C22×C12711yescharacteristic
161#431—21no—
162#398—21no—
163#398C22×C12712yes—
164#397—21no—
165#397C4×C12712yes—
166#391—21no—
167#382C4×C12711yescharacteristic
168#343—21no—
169#343C22×C12712yes—
170#324C22×C12712yes—
171#323—21no—
172C22×Q8—21no—
173C23×C4D4×C12711yescharacteristic
174C2×M16—24no—
175C2×M16—22no—
176C2×M16—41no—
177C2×M16—42no—
178C22×C8—41no—
179C4⋊Q8—41no—
180C4⋊Q8—41no—
181C22⋊Q8—42no—
182C22⋊Q8—42no—
183#117—41no—
184#117—41no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4C2×C4×C12712yes—
189C2×C4⋊C4D4×C12711yescharacteristic
190C2×C4⋊C4C23×C12711yescharacteristic
191C2×C22⋊C4—22no—
192C2×C22⋊C4C2×C4×C12711yescharacteristic
193C2×C22⋊C4D4×C12711yescharacteristic
194C2×C42C2×C4×C12711yescharacteristic
195C2×C42D4×C12711yescharacteristic
196C4⋊C8—41no—
197C22⋊C8—22no—
198C4×C8—41no—
199#95—21no—
200#95—22no—
201#95—22no—
202#95C2×C4×C12712yes—
203C24C22⋊C4×C12711yescharacteristic
204C2×Q8—41no—
205C2×Q8—41no—
206C2×Q8—42no—
207C2×Q8—42no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4C22⋊C4×C12711yescharacteristic
214C22×C4C22⋊C4×C12711yescharacteristic
215C22×C4C22⋊C4×C12711yescharacteristic
216C22×C4D8×C12712yes—
217C22×C4SD16×C12712yes—
218C22×C4C22×C4×C12711yescharacteristic
219C22×C4C2×D4×C12711yescharacteristic
220C22×C4C2×D4×C12711yescharacteristic
221M16—24no—
222M16—44no—
223M16—42no—
224C2×C8—42no—
225C2×C8—44no—
226C2×C8—42no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—42no—
230C4⋊C4—42no—
231C4⋊C4—42no—
232C4⋊C4—42no—
233C4⋊C4—42no—
234C22⋊C4—41no—
235C22⋊C4—41no—
236C22⋊C4—44no—
237C42—21no—
238C42—21no—
239C42—21no—
240C42—21no—
241C23—21no—
242C23—21no—
243C23—41no—
244C23—41no—
245C23#102×C12712yes—
246C23C2×C22⋊C4×C12711yescharacteristic
247Q8—82no—
248Q8—82no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4#99×C12711yescharacteristic
270C2×C4#99×C12711yescharacteristic
271C2×C4#102×C12712yes—
272C2×C4#104×C12712yes—
273C2×C4C2×D8×C12711yescharacteristic
274C2×C4C2×SD16×C12711yescharacteristic
275C8—44no—
276C8—82no—
277C22—21no—
278C22—21no—
279C22—22no—
280C22—42no—
281C22—41no—
282C22—41no—
283C22—81no—
284C22C2×#99×C12711yescharacteristic
285C22C2×#102×C12711yescharacteristic
286C22C2×#104×C12711yescharacteristic
287C4—21no—
288C4—21no—
289C4—41no—
290C4—41no—
291C4—41no—
292C4—41no—
293C4—82no—
294C4—82no—
295C4#327×C12712yes—
296C4#327×C12712yes—
297C2—21no—
298C2—21no—
299C2—42no—
300C2C2×#327×C12711yescharacteristic
301C2C127×#212311yescharacteristic
302C2C127×#213511yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C4⋊C4C23×C127
prime radicalC24×C127C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C2×#117×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#1346C2semidirect
145. #11700C127direct (N × H)
155. #1346C2×C127semidirect
156. C127#11700direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#26212
C127×#17422
C127×#14582
C127×#13462
#11700127