Finite Group Databasebeta

← C127×#12428 #44576101

Subgroups — C127×#12428 #44576101

Order 32512.

256 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 82 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×#2208C211yesmaximal, characteristic, complemented
2C127×#2206C211yesmaximal, characteristic
3C127×#1709C211yesmaximal, characteristic, complemented
4C8×D8×C127C211yesmaximal, characteristic, complemented
5C127×#1370C211yesmaximal, characteristic, complemented
6C127×#1362C211yesmaximal, characteristic, complemented
7C127×#1361C211yesmaximal, characteristic, complemented
8C2×SD32×C127—21no—
9C2×D16×C127—21no—
10#494×C127C2211yescharacteristic
11#493×C127C2211yescharacteristic
12#486×C127—21no—
13#486×C127—21no—
14C4×D8×C127C2211yescharacteristic
15C8×D4×C127—21no—
16C4⋊C16×C127C2211yescharacteristic
17C4⋊C16×C127C2211yescharacteristic
18#358×C127—21no—
19#357×C127—21no—
20#335×C127C2211yescharacteristic
21D4⋊C8×C127—21no—
22C82×C127C2211yescharacteristic
23C2×Q16×C127—21no—
24C2×Q16×C127—21no—
25C2×D8×C127—21no—
26C2×D8×C127—21no—
27C2×D8×C127D411yescharacteristic
28C22×C8×C127—41no—
29C4⋊Q8×C127—21no—
30#127×C127—21no—
31C4×D4×C127—21no—
32SD32×C127—42no—
33D16×C127—42no—
34C2×C16×C127—21no—
35C2×C16×C127—21no—
36#107×C127D411yescharacteristic
37C4⋊C8×C127—21no—
38#102×C127—21no—
39#102×C127—42no—
40#102×C127—41no—
41#102×C127—41no—
42C22⋊C8×C127—41no—
43C4×C8×C127D411yescharacteristic
44C4×C8×C127D411yescharacteristic
45C4×C8×C127C2311yescharacteristic
46C2×Q8×C127—41no—
47C2×D4×C127—21no—
48C2×D4×C127—41no—
49C2×D4×C127—41no—
50C2×D4×C127—41no—
51C22×C4×C127—41no—
52Q16×C127—41no—
53Q16×C127—41no—
54Q16×C127—81no—
55D8×C127—21no—
56D8×C127—41no—
57D8×C127—41no—
58D8×C127—81no—
59D8×C127D812yes—
60C2×C8×C127—21no—
61C2×C8×C127—41no—
62C2×C8×C127—82no—
63C2×C8×C127D811yescharacteristic
64C2×C8×C127D811yescharacteristic
65C2×C8×C127C2×D411yescharacteristic
66C2×C8×C127#4111yescharacteristic
67C4⋊C4×C127—21no—
68C4⋊C4×C127—41no—
69C4⋊C4×C127—41no—
70C22⋊C4×C127—41no—
71C42×C127C2×D411yescharacteristic
72C16×C127—41no—
73C16×C127—41no—
74C23×C127—41no—
75C23×C127—81no—
76Q8×C127—81no—
77Q8×C127—81no—
78D4×C127—22no—
79D4×C127—41no—
80D4×C127—82no—
81D4×C127—81no—
82D4×C127—81no—
83D4×C127—81no—
84D4×C127—81no—
85C2×C4×C127—41no—
86C2×C4×C127—81no—
87C2×C4×C127—81no—
88C2×C4×C127—81no—
89C2×C4×C127#12111yescharacteristic
90C2×C4×C127C2×D811yescharacteristic
91C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
92C8×C127—21no—
93C8×C127—21no—
94C8×C127—21no—
95C8×C127—41no—
96C8×C127—81no—
97C8×C127C2×D811yescharacteristic
98C8×C127#13511yescharacteristic
99C22×C127—42no—
100C22×C127—81no—
101C22×C127—81no—
102C22×C127—161no—
103C22×C127—161no—
104C22×C127—161no—
105C22×C127#45911yescharacteristic
106C4×C127—21no—
107C4×C127—81no—
108C4×C127—161no—
109C4×C127#46611yescharacteristic
110C4×C127#47211yescharacteristic
111C4×C127#50811yescharacteristic
112C4×C127#50911yescharacteristic
113#12428C12711yesmaximal, characteristic, direct product factor, Sylow
114C2×C127—82no—
115C2×C127—321no—
116C2×C127#166711yescharacteristic
117C2×C127#221011yescharacteristic
118C2×C127#221211yescharacteristic
119#2208C2×C12711yescharacteristic, complemented
120#2206C2×C12711yescharacteristic
121#1709C2×C12711yescharacteristic, complemented
122C8×D8C2×C12711yescharacteristic, complemented
123#1370C2×C12711yescharacteristic, complemented
124#1362C2×C12711yescharacteristic, complemented
125#1361C2×C12711yescharacteristic, complemented
126C127#1242811yescharacteristic, direct product factor, Sylow
127C2×SD32—21no—
128C2×D16—21no—
129#494C22×C12711yescharacteristic
130#493C22×C12711yescharacteristic
131#486—21no—
132#486—21no—
133C4×D8C22×C12711yescharacteristic
134C8×D4—21no—
135C4⋊C16C22×C12711yescharacteristic
136C4⋊C16C22×C12711yescharacteristic
137#358—21no—
138#357—21no—
139#335C22×C12711yescharacteristic
140D4⋊C8—21no—
141C82C22×C12711yescharacteristic
142C2×Q16—21no—
143C2×Q16—21no—
144C2×D8—21no—
145C2×D8—21no—
146C2×D8D4×C12711yescharacteristic
147C22×C8—41no—
148C4⋊Q8—21no—
149#127—21no—
150C4×D4—21no—
151SD32—42no—
152D16—42no—
153C2×C16—21no—
154C2×C16—21no—
155#107D4×C12711yescharacteristic
156C4⋊C8—21no—
157#102—21no—
158#102—42no—
159#102—41no—
160#102—41no—
161C22⋊C8—41no—
162C4×C8D4×C12711yescharacteristic
163C4×C8D4×C12711yescharacteristic
164C4×C8C23×C12711yescharacteristic
165C2×Q8—41no—
166C2×D4—21no—
167C2×D4—41no—
168C2×D4—41no—
169C2×D4—41no—
170C22×C4—41no—
171Q16—41no—
172Q16—41no—
173Q16—81no—
174D8—21no—
175D8—41no—
176D8—41no—
177D8—81no—
178D8D8×C12712yes—
179C2×C8—21no—
180C2×C8—41no—
181C2×C8—82no—
182C2×C8D8×C12711yescharacteristic
183C2×C8D8×C12711yescharacteristic
184C2×C8C2×D4×C12711yescharacteristic
185C2×C8#41×C12711yescharacteristic
186C4⋊C4—21no—
187C4⋊C4—41no—
188C4⋊C4—41no—
189C22⋊C4—41no—
190C42C2×D4×C12711yescharacteristic
191C16—41no—
192C16—41no—
193C23—41no—
194C23—81no—
195Q8—81no—
196Q8—81no—
197D4—22no—
198D4—41no—
199D4—82no—
200D4—81no—
201D4—81no—
202D4—81no—
203D4—81no—
204C2×C4—41no—
205C2×C4—81no—
206C2×C4—81no—
207C2×C4—81no—
208C2×C4#121×C12711yescharacteristic
209C2×C4C2×D8×C12711yescharacteristic
210C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
211C8—21no—
212C8—21no—
213C8—21no—
214C8—41no—
215C8—81no—
216C8C2×D8×C12711yescharacteristic
217C8#135×C12711yescharacteristic
218C22—42no—
219C22—81no—
220C22—81no—
221C22—161no—
222C22—161no—
223C22—161no—
224C22#459×C12711yescharacteristic
225C4—21no—
226C4—81no—
227C4—161no—
228C4#466×C12711yescharacteristic
229C4#472×C12711yescharacteristic
230C4#508×C12711yescharacteristic
231C4#509×C12711yescharacteristic
232C2—82no—
233C2—321no—
234C2C127×#166711yescharacteristic
235C2C127×#221011yescharacteristic
236C2C127×#221211yescharacteristic
subgroupG/H
center, socleC22×C127#459
commutator, Frattini, cosocleC4×C8C23×C127
prime radicalC127×#2206C2
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C42×C127 ◁ C82×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#2208C2semidirect
3. C127×#1709C2semidirect
4. C8×D8×C127C2semidirect
5. C127×#1370C2semidirect
6. C127×#1362C2semidirect
7. C127×#1361C2semidirect
113. #12428C127direct (N × H)
119. #2208C2×C127semidirect
121. #1709C2×C127semidirect
122. C8×D8C2×C127semidirect
123. #1370C2×C127semidirect
124. #1362C2×C127semidirect
125. #1361C2×C127semidirect
126. C127#12428direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#22082
C127×#22062
C127×#17092
C8×D8×C1272
C127×#13702
C127×#13622
C127×#13612
#12428127