Finite Group Databasebeta

← C127×#12330 #44576003

Subgroups — C127×#12330 #44576003

Order 32512.

322 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 86 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×#3395C211yesmaximal, characteristic, complemented
2C127×#2248C211yesmaximal, characteristic
3C127×#2207C211yesmaximal, characteristic
4C127×#1668C211yesmaximal, characteristic
5C127×#1362C211yesmaximal, characteristic, complemented
6C127×Q8⋊C16C211yesmaximal, characteristic, complemented
7C127×#1332C211yesmaximal, characteristic, complemented
8#557×C127—21no—
9C2×SD32×C127—21no—
10C2×SD32×C127—22no—
11#494×C127—21no—
12#494×C127C2211yescharacteristic
13#493×C127C2211yescharacteristic
14#462×C127—22no—
15#462×C127—21no—
16#460×C127—21no—
17C8×Q8×C127C2211yescharacteristic
18C4×Q16×C127—21no—
19C4×Q16×C127C2211yescharacteristic
20C4⋊C16×C127C2211yescharacteristic
21#357×C127—21no—
22C4×C16×C127C2211yescharacteristic
23#335×C127C2211yescharacteristic
24#331×C127—21no—
25C2×Q16×C127—22no—
26C2×Q16×C127—21no—
27C2×Q16×C127D411yescharacteristic
28C2×Q16×C127D412yes—
29C2×SD16×C127—41no—
30C2×D8×C127—21no—
31C2×D8×C127—21no—
32C4⋊Q8×C127—22no—
33C4⋊Q8×C127—21no—
34#127×C127—21no—
35#125×C127—42no—
36#125×C127—41no—
37C4×Q8×C127—22no—
38C4×Q8×C127—21no—
39C4×Q8×C127—41no—
40C4×Q8×C127D411yescharacteristic
41SD32×C127—44no—
42SD32×C127—42no—
43C2×C16×C127—21no—
44C2×C16×C127—21no—
45#107×C127D411yescharacteristic
46C4⋊C8×C127—21no—
47C4⋊C8×C127—21no—
48C4⋊C8×C127D411yescharacteristic
49#103×C127—22no—
50#103×C127—21no—
51#102×C127—41no—
52C4×C8×C127—21no—
53C4×C8×C127C2311yescharacteristic
54C2×Q8×C127—21no—
55C2×Q8×C127—22no—
56C2×Q8×C127D811yescharacteristic
57C2×D4×C127—41no—
58C2×D4×C127—41no—
59C2×D4×C127—41no—
60Q16×C127—21no—
61Q16×C127—21no—
62Q16×C127—42no—
63Q16×C127—41no—
64Q16×C127—41no—
65Q16×C127—82no—
66SD16×C127—82no—
67D8×C127—42no—
68D8×C127—41no—
69D8×C127—41no—
70C2×C8×C127—21no—
71C2×C8×C127—41no—
72C2×C8×C127C2×D411yescharacteristic
73C2×C8×C127C2×D411yescharacteristic
74C4⋊C4×C127—21no—
75C4⋊C4×C127—21no—
76C4⋊C4×C127—42no—
77C4⋊C4×C127—42no—
78C4⋊C4×C127—42no—
79C4⋊C4×C127—41no—
80C4⋊C4×C127—41no—
81C4⋊C4×C127—41no—
82C4⋊C4×C127D811yescharacteristic
83C42×C127—21no—
84C42×C127—42no—
85C42×C127—41no—
86C42×C127C2×D411yescharacteristic
87C16×C127—22no—
88C16×C127—41no—
89C23×C127—81no—
90Q8×C127—21no—
91Q8×C127—41no—
92Q8×C127—42no—
93Q8×C127—42no—
94Q8×C127—41no—
95Q8×C127SD3212yescomplemented
96D4×C127—81no—
97D4×C127—81no—
98D4×C127—81no—
99D4×C127—81no—
100D4×C127—161no—
101C2×C4×C127—21no—
102C2×C4×C127—21no—
103C2×C4×C127—41no—
104C2×C4×C127—42no—
105C2×C4×C127—41no—
106C2×C4×C127#12011yescharacteristic
107C2×C4×C127C2×D811yescharacteristic
108C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
109C8×C127—21no—
110C8×C127—41no—
111C8×C127—81no—
112C8×C127#13511yescharacteristic
113C8×C127AGL(1,ℤ/8)11yescharacteristic
114C22×C127—161no—
115C22×C127—161no—
116C22×C127—161no—
117C22×C127#44711yescharacteristic
118C4×C127—22no—
119C4×C127—21no—
120C4×C127—41no—
121C4×C127—81no—
122C4×C127—82no—
123C4×C127—81no—
124C4×C127#44911yescharacteristic
125C4×C127#45311yescharacteristic
126C4×C127C2×SD3211yescharacteristic
127C4×C127#51011yescharacteristic
128#12330C12711yesmaximal, characteristic, direct product factor, Sylow
129C2×C127—321no—
130C2×C127#162111yescharacteristic
131C2×C127#218511yescharacteristic
132C2×C127#219311yescharacteristic
133#3395C2×C12711yescharacteristic, complemented
134#2248C2×C12711yescharacteristic
135#2207C2×C12711yescharacteristic
136#1668C2×C12711yescharacteristic
137#1362C2×C12711yescharacteristic, complemented
138Q8⋊C16C2×C12711yescharacteristic, complemented
139#1332C2×C12711yescharacteristic, complemented
140C127#1233011yescharacteristic, direct product factor, Sylow
141#557—21no—
142C2×SD32—21no—
143C2×SD32—22no—
144#494—21no—
145#494C22×C12711yescharacteristic
146#493C22×C12711yescharacteristic
147#462—22no—
148#462—21no—
149#460—21no—
150C8×Q8C22×C12711yescharacteristic
151C4×Q16—21no—
152C4×Q16C22×C12711yescharacteristic
153C4⋊C16C22×C12711yescharacteristic
154#357—21no—
155C4×C16C22×C12711yescharacteristic
156#335C22×C12711yescharacteristic
157#331—21no—
158C2×Q16—22no—
159C2×Q16—21no—
160C2×Q16D4×C12711yescharacteristic
161C2×Q16D4×C12712yes—
162C2×SD16—41no—
163C2×D8—21no—
164C2×D8—21no—
165C4⋊Q8—22no—
166C4⋊Q8—21no—
167#127—21no—
168#125—42no—
169#125—41no—
170C4×Q8—22no—
171C4×Q8—21no—
172C4×Q8—41no—
173C4×Q8D4×C12711yescharacteristic
174SD32—44no—
175SD32—42no—
176C2×C16—21no—
177C2×C16—21no—
178#107D4×C12711yescharacteristic
179C4⋊C8—21no—
180C4⋊C8—21no—
181C4⋊C8D4×C12711yescharacteristic
182#103—22no—
183#103—21no—
184#102—41no—
185C4×C8—21no—
186C4×C8C23×C12711yescharacteristic
187C2×Q8—21no—
188C2×Q8—22no—
189C2×Q8D8×C12711yescharacteristic
190C2×D4—41no—
191C2×D4—41no—
192C2×D4—41no—
193Q16—21no—
194Q16—21no—
195Q16—42no—
196Q16—41no—
197Q16—41no—
198Q16—82no—
199SD16—82no—
200D8—42no—
201D8—41no—
202D8—41no—
203C2×C8—21no—
204C2×C8—41no—
205C2×C8C2×D4×C12711yescharacteristic
206C2×C8C2×D4×C12711yescharacteristic
207C4⋊C4—21no—
208C4⋊C4—21no—
209C4⋊C4—42no—
210C4⋊C4—42no—
211C4⋊C4—42no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C4⋊C4—41no—
215C4⋊C4D8×C12711yescharacteristic
216C42—21no—
217C42—42no—
218C42—41no—
219C42C2×D4×C12711yescharacteristic
220C16—22no—
221C16—41no—
222C23—81no—
223Q8—21no—
224Q8—41no—
225Q8—42no—
226Q8—42no—
227Q8—41no—
228Q8SD32×C12712yescomplemented
229D4—81no—
230D4—81no—
231D4—81no—
232D4—81no—
233D4—161no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—41no—
237C2×C4—42no—
238C2×C4—41no—
239C2×C4#120×C12711yescharacteristic
240C2×C4C2×D8×C12711yescharacteristic
241C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
242C8—21no—
243C8—41no—
244C8—81no—
245C8#135×C12711yescharacteristic
246C8AGL(1,ℤ/8)×C12711yescharacteristic
247C22—161no—
248C22—161no—
249C22—161no—
250C22#447×C12711yescharacteristic
251C4—22no—
252C4—21no—
253C4—41no—
254C4—81no—
255C4—82no—
256C4—81no—
257C4#449×C12711yescharacteristic
258C4#453×C12711yescharacteristic
259C4C2×SD32×C12711yescharacteristic
260C4#510×C12711yescharacteristic
261C2—321no—
262C2C127×#162111yescharacteristic
263C2C127×#218511yescharacteristic
264C2C127×#219311yescharacteristic
subgroupG/H
center, socleC22×C127#447
commutator, Frattini, cosocleC4×C8C23×C127
prime radical#493×C127C22
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C42×C127 ◁ C8×Q8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#3395C2semidirect
5. C127×#1362C2semidirect
6. C127×Q8⋊C16C2semidirect
7. C127×#1332C2semidirect
95. Q8×C127SD32semidirect
128. #12330C127direct (N × H)
133. #3395C2×C127semidirect
137. #1362C2×C127semidirect
138. Q8⋊C16C2×C127semidirect
139. #1332C2×C127semidirect
140. C127#12330direct (N × H)
228. Q8SD32×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#33952
C127×#22482
C127×#22072
C127×#16682
C127×#13622
C127×Q8⋊C162
C127×#13322
#12330127