Finite Group Databasebeta

← C127×#10664 #44574337

Subgroups — C127×#10664 #44574337

Order 32512.

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

normal subgroups only

This group has 304 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×#1985C211yesmaximal, characteristic
2C127×#1838C211yesmaximal, characteristic
3C127×#1571C211yesmaximal, characteristic
4C127×#1570C211yesmaximal, characteristic
5C127×#1487C211yesmaximal, characteristic
6C127×#1487C211yesmaximal, characteristic
7C127×#1275C211yesmaximal, characteristic
8C2×C4×Q8×C127C2211yescharacteristic
9#431×C127C2211yescharacteristic
10#431×C127C2211yescharacteristic
11#423×C127C2211yescharacteristic
12#423×C127C2211yescharacteristic
13C2×C4⋊C8×C127C2211yescharacteristic
14C2×#97×C127C2211yescharacteristic
15#341×C127—22no—
16#336×C127—22no—
17#335×C127—22no—
18#334×C127—22no—
19Q8⋊C8×C127—22no—
20Q8⋊C8×C127—22no—
21C22×Q8×C127Q811yescharacteristic
22C2×M16×C127—21no—
23C2×M16×C127—21no—
24C22×C8×C127—21no—
25C22×C8×C127D412yes—
26C4×Q8×C127—21no—
27C4×Q8×C127—21no—
28C4×Q8×C127—21no—
29C4×Q8×C127—21no—
30C2×C4⋊C4×C127—21no—
31C2×C4⋊C4×C127Q811yescharacteristic
32C2×C42×C127—21no—
33C2×C42×C127C2311yescharacteristic
34C4⋊C8×C127—21no—
35C4⋊C8×C127—21no—
36C4⋊C8×C127—21no—
37C4⋊C8×C127—21no—
38C4⋊C8×C127—21no—
39C4⋊C8×C127—21no—
40C4⋊C8×C127—21no—
41C4⋊C8×C127—21no—
42C22⋊C8×C127—21no—
43C22⋊C8×C127—21no—
44#97×C127—21no—
45#97×C127—21no—
46C4×C8×C127D412yes—
47C4×C8×C127D412yes—
48C2×Q8×C127—21no—
49C2×Q8×C127—21no—
50C2×Q8×C127—42no—
51C22×C4×C127—21no—
52C22×C4×C127—21no—
53C22×C4×C127C2×D411yescharacteristic
54C22×C4×C127C2×Q811yescharacteristic
55C22×C4×C127#4111yescharacteristic
56M16×C127—42no—
57M16×C127—42no—
58C2×C8×C127—22no—
59C2×C8×C127—22no—
60C2×C8×C127—22no—
61C2×C8×C127—22no—
62C2×C8×C127—22no—
63C2×C8×C127—41no—
64C2×C8×C127—41no—
65C2×C8×C127—41no—
66C2×C8×C127—42no—
67C4⋊C4×C127—21no—
68C4⋊C4×C127—21no—
69C4⋊C4×C127—41no—
70C4⋊C4×C127—41no—
71C42×C127—41no—
72C42×C127—41no—
73C42×C127C2×D411yescharacteristic
74C42×C127C2×D411yescharacteristic
75C42×C127#4111yescharacteristic
76C42×C127#4111yescharacteristic
77C23×C127C22⋊Q811yescharacteristic
78Q8×C127—22no—
79Q8×C127—22no—
80Q8×C127—41no—
81Q8×C127—41no—
82C2×C4×C127—22no—
83C2×C4×C127—41no—
84C2×C4×C127—41no—
85C2×C4×C127—41no—
86C2×C4×C127—41no—
87C2×C4×C127—42no—
88C2×C4×C127—41no—
89C2×C4×C127C22⋊Q811yescharacteristic
90C2×C4×C127C22⋊Q811yescharacteristic
91C2×C4×C127#12311yescharacteristic
92C2×C4×C127#12311yescharacteristic
93C2×C4×C127#12311yescharacteristic
94C2×C4×C127#12711yescharacteristic
95C2×C4×C127#13512yes—
96C2×C4×C127#13712yes—
97C8×C127—42no—
98C8×C127—42no—
99C8×C127—42no—
100C8×C127—81no—
101C8×C127—81no—
102C8×C127—81no—
103C22×C127—21no—
104C22×C127—21no—
105C22×C127#39911yescharacteristic
106C22×C127#47912yes—
107C4×C127—21no—
108C4×C127—21no—
109C4×C127—21no—
110C4×C127—21no—
111C4×C127—42no—
112C4×C127—81no—
113C4×C127#48512yes—
114C4×C127#49511yescharacteristic
115C4×C127#49711yescharacteristic
116#10664C12711yesmaximal, characteristic, direct product factor, Sylow
117C2×C127—22no—
118C2×C127#209111yescharacteristic
119C2×C127#209711yescharacteristic
120C2×C127#209811yescharacteristic
121#1985C2×C12711yescharacteristic
122#1838C2×C12711yescharacteristic
123#1571C2×C12711yescharacteristic
124#1570C2×C12711yescharacteristic
125#1487C2×C12711yescharacteristic
126#1487C2×C12711yescharacteristic
127#1275C2×C12711yescharacteristic
128C127#1066411yescharacteristic, direct product factor, Sylow
129C2×C4×Q8C22×C12711yescharacteristic
130#431C22×C12711yescharacteristic
131#431C22×C12711yescharacteristic
132#423C22×C12711yescharacteristic
133#423C22×C12711yescharacteristic
134C2×C4⋊C8C22×C12711yescharacteristic
135C2×#97C22×C12711yescharacteristic
136#341—22no—
137#336—22no—
138#335—22no—
139#334—22no—
140Q8⋊C8—22no—
141Q8⋊C8—22no—
142C22×Q8Q8×C12711yescharacteristic
143C2×M16—21no—
144C2×M16—21no—
145C22×C8—21no—
146C22×C8D4×C12712yes—
147C4×Q8—21no—
148C4×Q8—21no—
149C4×Q8—21no—
150C4×Q8—21no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4Q8×C12711yescharacteristic
153C2×C42—21no—
154C2×C42C23×C12711yescharacteristic
155C4⋊C8—21no—
156C4⋊C8—21no—
157C4⋊C8—21no—
158C4⋊C8—21no—
159C4⋊C8—21no—
160C4⋊C8—21no—
161C4⋊C8—21no—
162C4⋊C8—21no—
163C22⋊C8—21no—
164C22⋊C8—21no—
165#97—21no—
166#97—21no—
167C4×C8D4×C12712yes—
168C4×C8D4×C12712yes—
169C2×Q8—21no—
170C2×Q8—21no—
171C2×Q8—42no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4C2×D4×C12711yescharacteristic
175C22×C4C2×Q8×C12711yescharacteristic
176C22×C4#41×C12711yescharacteristic
177M16—42no—
178M16—42no—
179C2×C8—22no—
180C2×C8—22no—
181C2×C8—22no—
182C2×C8—22no—
183C2×C8—22no—
184C2×C8—41no—
185C2×C8—41no—
186C2×C8—41no—
187C2×C8—42no—
188C4⋊C4—21no—
189C4⋊C4—21no—
190C4⋊C4—41no—
191C4⋊C4—41no—
192C42—41no—
193C42—41no—
194C42C2×D4×C12711yescharacteristic
195C42C2×D4×C12711yescharacteristic
196C42#41×C12711yescharacteristic
197C42#41×C12711yescharacteristic
198C23C22⋊Q8×C12711yescharacteristic
199Q8—22no—
200Q8—22no—
201Q8—41no—
202Q8—41no—
203C2×C4—22no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—42no—
209C2×C4—41no—
210C2×C4C22⋊Q8×C12711yescharacteristic
211C2×C4C22⋊Q8×C12711yescharacteristic
212C2×C4#123×C12711yescharacteristic
213C2×C4#123×C12711yescharacteristic
214C2×C4#123×C12711yescharacteristic
215C2×C4#127×C12711yescharacteristic
216C2×C4#135×C12712yes—
217C2×C4#137×C12712yes—
218C8—42no—
219C8—42no—
220C8—42no—
221C8—81no—
222C8—81no—
223C8—81no—
224C22—21no—
225C22—21no—
226C22#399×C12711yescharacteristic
227C22#479×C12712yes—
228C4—21no—
229C4—21no—
230C4—21no—
231C4—21no—
232C4—42no—
233C4—81no—
234C4#485×C12712yes—
235C4#495×C12711yescharacteristic
236C4#497×C12711yescharacteristic
237C2—22no—
238C2C127×#209111yescharacteristic
239C2C127×#209711yescharacteristic
240C2C127×#209811yescharacteristic
subgroupG/H
centerC2×C4×C127#127
commutator, Frattini, cosocleC2×C42C23×C127
socleC22×C127#399
prime radicalC23×C127C22⋊Q8
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
116. #10664C127direct (N × H)
128. C127#10664direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#19852
C127×#18382
C127×#15712
C127×#15702
C127×#14872
C127×#12752
#10664127