Finite Group Databasebeta

← C127×#7033 #44570706

Subgroups — C127×#7033 #44570706

Order 32512.

362 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 118 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×#1817C211yesmaximal, characteristic
2C127×#1797C211yesmaximal, characteristic
3C127×#1749C211yesmaximal, characteristic
4C22×C42×C127C2211yescharacteristic
5C2×C4⋊C8×C127—21no—
6C2×C22⋊C8×C127C412yes—
7C2×C22⋊C8×C127C412yes—
8C2×C22⋊C8×C127C412yes—
9C2×#97×C127—21no—
10#336×C127—21no—
11#336×C127—21no—
12#336×C127—21no—
13#336×C127—21no—
14C23×C4×C127C2×C411yescharacteristic
15C23×C4×C127C2×C411yescharacteristic
16C23×C4×C127C2×C411yescharacteristic
17C22×C8×C127—22no—
18C22×C8×C127—22no—
19C22×C8×C127—22no—
20C2×C42×C127—42no—
21C2×C42×C127D411yescharacteristic
22C2×C42×C127D411yescharacteristic
23C2×C42×C127D411yescharacteristic
24C2×C42×C127Q811yescharacteristic
25C4⋊C8×C127—42no—
26C22⋊C8×C127—22no—
27C22⋊C8×C127—42no—
28C22⋊C8×C127—42no—
29C22⋊C8×C127C814yescomplemented
30#97×C127—42no—
31C24×C127C4211yescharacteristic
32C22×C4×C127—22no—
33C22×C4×C127—21no—
34C22×C4×C127—21no—
35C22×C4×C127—41no—
36C22×C4×C127—41no—
37C22×C4×C127—41no—
38C22×C4×C127—41no—
39C22×C4×C127—41no—
40C22×C4×C127—41no—
41C22×C4×C127C22⋊C411yescharacteristic
42C22×C4×C127C22⋊C411yescharacteristic
43C22×C4×C127C22⋊C411yescharacteristic
44C22×C4×C127C4⋊C411yescharacteristic
45C22×C4×C127C4⋊C411yescharacteristic
46C22×C4×C127C4⋊C411yescharacteristic
47C22×C4×C127C2×C812yes—
48C22×C4×C127M1612yes—
49C2×C8×C127—24no—
50C2×C8×C127—42no—
51C2×C8×C127—42no—
52C2×C8×C127—42no—
53C2×C8×C127—42no—
54C2×C8×C127—42no—
55C2×C8×C127—42no—
56C2×C8×C127—42no—
57C2×C8×C127—42no—
58C42×C127—22no—
59C42×C127—22no—
60C42×C127—41no—
61C42×C127—41no—
62C23×C127—21no—
63C23×C127—21no—
64C23×C127—21no—
65C23×C127—21no—
66C23×C127—21no—
67C23×C127—21no—
68C23×C127#9511yescharacteristic
69C23×C127C4×C811yescharacteristic
70C23×C127#9711yescharacteristic
71C2×C4×C127—21no—
72C2×C4×C127—21no—
73C2×C4×C127—21no—
74C2×C4×C127—21no—
75C2×C4×C127—21no—
76C2×C4×C127—21no—
77C2×C4×C127—21no—
78C2×C4×C127—21no—
79C2×C4×C127—21no—
80C2×C4×C127—21no—
81C2×C4×C127—21no—
82C2×C4×C127—21no—
83C2×C4×C127—21no—
84C2×C4×C127—21no—
85C2×C4×C127—42no—
86C2×C4×C127—42no—
87C2×C4×C127—42no—
88C2×C4×C127—42no—
89C2×C4×C127—44no—
90C2×C4×C127C22⋊C812yes—
91C2×C4×C127#9912yes—
92C2×C4×C127#10011yescharacteristic
93C2×C4×C127#10111yescharacteristic
94C2×C4×C127C4⋊C812yes—
95C8×C127—44no—
96C8×C127—82no—
97C8×C127—82no—
98C22×C127—21no—
99C22×C127—21no—
100C22×C127—21no—
101C22×C127—21no—
102C22×C127—21no—
103C22×C127—21no—
104C22×C127—41no—
105C22×C127—41no—
106C22×C127—41no—
107C22×C127—41no—
108C22×C127#33611yescharacteristic
109C22×C127#34211yescharacteristic
110C22×C127#34311yescharacteristic
111C22×C127#34411yescharacteristic
112C22×C127#34411yescharacteristic
113C22×C127#34411yescharacteristic
114C22×C127#34411yescharacteristic
115C4×C127—22no—
116C4×C127—22no—
117C4×C127—21no—
118C4×C127—21no—
119C4×C127—22no—
120C4×C127—41no—
121C4×C127—41no—
122#7033C12711yesmaximal, characteristic, direct product factor, Sylow
123C2×C127—41no—
124C2×C127—41no—
125C2×C127#128111yescharacteristic
126C2×C127#128211yescharacteristic
127C2×C127#128311yescharacteristic
128C2×C127#130511yescharacteristic
129C2×C127#130611yescharacteristic
130C2×C127#130711yescharacteristic
131C2×C127#130811yescharacteristic
132#1817C2×C12711yescharacteristic
133#1797C2×C12711yescharacteristic
134#1749C2×C12711yescharacteristic
135C127#703311yescharacteristic, direct product factor, Sylow
136C22×C42C22×C12711yescharacteristic
137C2×C4⋊C8—21no—
138C2×C22⋊C8C4×C12712yes—
139C2×C22⋊C8C4×C12712yes—
140C2×C22⋊C8C4×C12712yes—
141C2×#97—21no—
142#336—21no—
143#336—21no—
144#336—21no—
145#336—21no—
146C23×C4C2×C4×C12711yescharacteristic
147C23×C4C2×C4×C12711yescharacteristic
148C23×C4C2×C4×C12711yescharacteristic
149C22×C8—22no—
150C22×C8—22no—
151C22×C8—22no—
152C2×C42—42no—
153C2×C42D4×C12711yescharacteristic
154C2×C42D4×C12711yescharacteristic
155C2×C42D4×C12711yescharacteristic
156C2×C42Q8×C12711yescharacteristic
157C4⋊C8—42no—
158C22⋊C8—22no—
159C22⋊C8—42no—
160C22⋊C8—42no—
161C22⋊C8C8×C12714yescomplemented
162#97—42no—
163C24C42×C12711yescharacteristic
164C22×C4—22no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—41no—
168C22×C4—41no—
169C22×C4—41no—
170C22×C4—41no—
171C22×C4—41no—
172C22×C4—41no—
173C22×C4C22⋊C4×C12711yescharacteristic
174C22×C4C22⋊C4×C12711yescharacteristic
175C22×C4C22⋊C4×C12711yescharacteristic
176C22×C4C4⋊C4×C12711yescharacteristic
177C22×C4C4⋊C4×C12711yescharacteristic
178C22×C4C4⋊C4×C12711yescharacteristic
179C22×C4C2×C8×C12712yes—
180C22×C4M16×C12712yes—
181C2×C8—24no—
182C2×C8—42no—
183C2×C8—42no—
184C2×C8—42no—
185C2×C8—42no—
186C2×C8—42no—
187C2×C8—42no—
188C2×C8—42no—
189C2×C8—42no—
190C42—22no—
191C42—22no—
192C42—41no—
193C42—41no—
194C23—21no—
195C23—21no—
196C23—21no—
197C23—21no—
198C23—21no—
199C23—21no—
200C23#95×C12711yescharacteristic
201C23C4×C8×C12711yescharacteristic
202C23#97×C12711yescharacteristic
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—44no—
222C2×C4C22⋊C8×C12712yes—
223C2×C4#99×C12712yes—
224C2×C4#100×C12711yescharacteristic
225C2×C4#101×C12711yescharacteristic
226C2×C4C4⋊C8×C12712yes—
227C8—44no—
228C8—82no—
229C8—82no—
230C22—21no—
231C22—21no—
232C22—21no—
233C22—21no—
234C22—21no—
235C22—21no—
236C22—41no—
237C22—41no—
238C22—41no—
239C22—41no—
240C22#336×C12711yescharacteristic
241C22#342×C12711yescharacteristic
242C22#343×C12711yescharacteristic
243C22#344×C12711yescharacteristic
244C22#344×C12711yescharacteristic
245C22#344×C12711yescharacteristic
246C22#344×C12711yescharacteristic
247C4—21no—
248C4—21no—
249C4—22no—
250C4—22no—
251C4—22no—
252C4—41no—
253C4—41no—
254C2—41no—
255C2—41no—
256C2C127×#128111yescharacteristic
257C2C127×#128211yescharacteristic
258C2C127×#128311yescharacteristic
259C2C127×#130511yescharacteristic
260C2C127×#130611yescharacteristic
261C2C127×#130711yescharacteristic
262C2C127×#130811yescharacteristic
subgroupG/H
center, socleC23×C127#95
commutatorC23C4×C8×C127
Frattini, cosocleC22×C42C22×C127
prime radicalC24×C127C42
LCSG ▷ C23 ▷ C22 ▷ C1
UCSC1 ◁ C23×C127 ◁ C22×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
29. C22⋊C8×C127C8semidirect
122. #7033C127direct (N × H)
135. C127#7033direct (N × H)
161. C22⋊C8C8×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#18172
C127×#17972
C127×#17492
#7033127