Finite Group Databasebeta

← C127×#13330 #44577003

Subgroups — C127×#13330 #44577003

Order 32512.

558 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 146 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
1C22×Q32×C127C212yesmaximal
2C2×#494×C127C211yesmaximal, characteristic
3C2×#358×C127C212yesmaximal
4C127×#1969C211yesmaximal, characteristic
5C127×#1374C211yesmaximal, characteristic
6C22×Q16×C127—21no—
7C22×Q16×C127C2212yes—
8C22×Q16×C127C2211yescharacteristic
9C2×C4⋊Q8×C127—21no—
10C2×Q32×C127—24no—
11C2×Q32×C127—24no—
12C2×Q32×C127—24no—
13C22×C16×C127C2212yes—
14#494×C127—24no—
15C2×#107×C127C2211yescharacteristic
16C2×#103×C127—21no—
17C2×C4×C8×C127C2211yescharacteristic
18#391×C127—21no—
19#358×C127—24no—
20C22×Q8×C127—22no—
21C22×Q8×C127—21no—
22C2×Q16×C127—24no—
23C2×Q16×C127—22no—
24C2×Q16×C127—22no—
25C2×Q16×C127—22no—
26C2×Q16×C127—22no—
27C2×Q16×C127—22no—
28C2×Q16×C127—22no—
29C2×Q16×C127—22no—
30C2×Q16×C127—21no—
31C2×Q16×C127—42no—
32C2×Q16×C127—42no—
33C2×Q16×C127D412yes—
34C2×Q16×C127D414yes—
35C22×C8×C127D411yescharacteristic
36C22×C8×C127C2311yescharacteristic
37C4⋊Q8×C127—24no—
38C4⋊Q8×C127—42no—
39C2×C4⋊C4×C127—21no—
40C2×C4⋊C4×C127—42no—
41C2×C42×C127D411yescharacteristic
42Q32×C127—216no—
43C2×C16×C127—22no—
44C2×C16×C127—22no—
45C2×C16×C127D414yes—
46#107×C127—22no—
47#103×C127—42no—
48C4×C8×C127—22no—
49#95×C127—42no—
50C2×Q8×C127—24no—
51C2×Q8×C127—22no—
52C2×Q8×C127—42no—
53C2×Q8×C127—41no—
54C2×Q8×C127—41no—
55C2×Q8×C127—42no—
56C2×Q8×C127—41no—
57C2×Q8×C127—42no—
58C2×Q8×C127—41no—
59C2×Q8×C127—42no—
60C2×Q8×C127—42no—
61C2×Q8×C127—41no—
62C22×C4×C127—41no—
63C22×C4×C127—42no—
64C22×C4×C127—41no—
65C22×C4×C127D812yes—
66C22×C4×C127C2×D411yescharacteristic
67Q16×C127—24no—
68Q16×C127—24no—
69Q16×C127—24no—
70Q16×C127—48no—
71Q16×C127—42no—
72Q16×C127—42no—
73Q16×C127—42no—
74C2×C8×C127—21no—
75C2×C8×C127—21no—
76C2×C8×C127D812yes—
77C2×C8×C127C2×D411yescharacteristic
78C2×C8×C127C2×D412yes—
79C2×C8×C127C2×D412yes—
80C2×C8×C127#4111yescharacteristic
81C4⋊C4×C127—48no—
82C4⋊C4×C127—41no—
83C4⋊C4×C127—41no—
84C42×C127—21no—
85C42×C127—21no—
86C16×C127—24no—
87C23×C127C2×D811yescharacteristic
88Q8×C127—42no—
89Q8×C127—44no—
90Q8×C127—44no—
91Q8×C127—42no—
92Q8×C127—81no—
93Q8×C127—82no—
94Q8×C127—82no—
95Q8×C127—81no—
96C2×C4×C127—22no—
97C2×C4×C127—22no—
98C2×C4×C127—44no—
99C2×C4×C127—42no—
100C2×C4×C127—81no—
101C2×C4×C127—82no—
102C2×C4×C127—81no—
103C2×C4×C127—82no—
104C2×C4×C127—81no—
105C2×C4×C127—82no—
106C2×C4×C127Q3214yescomplemented
107C2×C4×C127#12011yescharacteristic
108C2×C4×C127#12111yescharacteristic
109C2×C4×C127#12711yescharacteristic
110C2×C4×C127C2×D811yescharacteristic
111C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
112C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
113C8×C127—22no—
114C8×C127#12012yes—
115C8×C127#12112yes—
116C22×C127#44711yescharacteristic
117C22×C127#45911yescharacteristic
118C22×C127#49311yescharacteristic
119C22×C127C2×Q3212yes—
120C22×C127#51012yes—
121C4×C127—24no—
122C4×C127—84no—
123C4×C127—82no—
124C4×C127—161no—
125C4×C127#39211yescharacteristic
126C4×C127#44711yescharacteristic
127C4×C127#45911yescharacteristic
128C4×C127#49611yescharacteristic
129#13330C12711yesmaximal, characteristic, direct product factor, Sylow
130C2×C127#201111yescharacteristic
131C2×C127#218812yes—
132C2×C127#220912yes—
133C2×C127#224711yescharacteristic
134C2×C127#225111yescharacteristic
135C22×Q32C2×C12712yes—
136C2×#494C2×C12711yescharacteristic
137C2×#358C2×C12712yes—
138#1969C2×C12711yescharacteristic
139#1374C2×C12711yescharacteristic
140C127#1333011yescharacteristic, direct product factor, Sylow
141C22×Q16—21no—
142C22×Q16C22×C12712yes—
143C22×Q16C22×C12711yescharacteristic
144C2×C4⋊Q8—21no—
145C2×Q32—24no—
146C2×Q32—24no—
147C2×Q32—24no—
148C22×C16C22×C12712yes—
149#494—24no—
150C2×#107C22×C12711yescharacteristic
151C2×#103—21no—
152C2×C4×C8C22×C12711yescharacteristic
153#391—21no—
154#358—24no—
155C22×Q8—22no—
156C22×Q8—21no—
157C2×Q16—24no—
158C2×Q16—22no—
159C2×Q16—22no—
160C2×Q16—22no—
161C2×Q16—22no—
162C2×Q16—22no—
163C2×Q16—22no—
164C2×Q16—22no—
165C2×Q16—21no—
166C2×Q16—42no—
167C2×Q16—42no—
168C2×Q16D4×C12714yes—
169C2×Q16D4×C12712yes—
170C22×C8D4×C12711yescharacteristic
171C22×C8C23×C12711yescharacteristic
172C4⋊Q8—24no—
173C4⋊Q8—42no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—42no—
176C2×C42D4×C12711yescharacteristic
177Q32—216no—
178C2×C16—22no—
179C2×C16—22no—
180C2×C16D4×C12714yes—
181#107—22no—
182#103—42no—
183C4×C8—22no—
184#95—42no—
185C2×Q8—24no—
186C2×Q8—22no—
187C2×Q8—42no—
188C2×Q8—41no—
189C2×Q8—41no—
190C2×Q8—42no—
191C2×Q8—42no—
192C2×Q8—41no—
193C2×Q8—41no—
194C2×Q8—42no—
195C2×Q8—42no—
196C2×Q8—41no—
197C22×C4—41no—
198C22×C4—42no—
199C22×C4—41no—
200C22×C4D8×C12712yes—
201C22×C4C2×D4×C12711yescharacteristic
202Q16—24no—
203Q16—24no—
204Q16—24no—
205Q16—48no—
206Q16—42no—
207Q16—42no—
208Q16—42no—
209C2×C8—21no—
210C2×C8—21no—
211C2×C8D8×C12712yes—
212C2×C8C2×D4×C12711yescharacteristic
213C2×C8C2×D4×C12712yes—
214C2×C8C2×D4×C12712yes—
215C2×C8#41×C12711yescharacteristic
216C4⋊C4—48no—
217C4⋊C4—41no—
218C4⋊C4—41no—
219C42—21no—
220C42—21no—
221C16—24no—
222C23C2×D8×C12711yescharacteristic
223Q8—42no—
224Q8—44no—
225Q8—44no—
226Q8—42no—
227Q8—82no—
228Q8—81no—
229Q8—81no—
230Q8—82no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—44no—
234C2×C4—42no—
235C2×C4—81no—
236C2×C4—82no—
237C2×C4—81no—
238C2×C4—82no—
239C2×C4—82no—
240C2×C4—81no—
241C2×C4Q32×C12714yescomplemented
242C2×C4#120×C12711yescharacteristic
243C2×C4#121×C12711yescharacteristic
244C2×C4#127×C12711yescharacteristic
245C2×C4C2×D8×C12711yescharacteristic
246C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
247C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
248C8—22no—
249C8#120×C12712yes—
250C8#121×C12712yes—
251C22#447×C12711yescharacteristic
252C22#459×C12711yescharacteristic
253C22#493×C12711yescharacteristic
254C22C2×Q32×C12712yes—
255C22#510×C12712yes—
256C4—24no—
257C4—84no—
258C4—82no—
259C4—161no—
260C4#392×C12711yescharacteristic
261C4#447×C12711yescharacteristic
262C4#459×C12711yescharacteristic
263C4#496×C12711yescharacteristic
264C2C127×#201111yescharacteristic
265C2C127×#218812yes—
266C2C127×#220912yes—
267C2C127×#224711yescharacteristic
268C2C127×#225111yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C127C2×D8
commutator, Frattini, cosocleC22×C8C23×C127
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C2×C42×C127 ◁ C2×C4×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
106. C2×C4×C127Q32semidirect
129. #13330C127direct (N × H)
140. C127#13330direct (N × H)
241. C2×C4Q32×C127semidirect

Maximal subgroups

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

subgroupindex
C22×Q32×C1272
C2×#494×C1272
C2×#358×C1272
C127×#19692
C127×#13742
#13330127