Finite Group Databasebeta

← C127×#12334 #44576007

Subgroups — C127×#12334 #44576007

Order 32512.

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

normal subgroups only

This group has 306 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
2C127×#2247C211yesmaximal, characteristic
3C127×#2209C211yesmaximal, characteristic
4C127×#1670C211yesmaximal, characteristic
5C127×#1362C211yesmaximal, characteristic
6C127×Q8⋊C16C211yesmaximal, characteristic
7C127×#1332C211yesmaximal, characteristic
8#557×C127—21no—
9C2×Q32×C127—21no—
10C2×Q32×C127—22no—
11#494×C127—21no—
12#494×C127C2211yescharacteristic
13#494×C127C2211yescharacteristic
14#475×C127—21no—
15#462×C127—22no—
16#462×C127—21no—
17C8×Q8×C127C2211yescharacteristic
18C4×Q16×C127—21no—
19C4×Q16×C127C2211yescharacteristic
20C4⋊C16×C127C2211yescharacteristic
21#358×C127—21no—
22C4×C16×C127C2211yescharacteristic
23#335×C127C2211yescharacteristic
24#332×C127—21no—
25C2×Q16×C127—22no—
26C2×Q16×C127—21no—
27C2×Q16×C127—21no—
28C2×Q16×C127—21no—
29C2×Q16×C127D411yescharacteristic
30C2×Q16×C127D412yes—
31C4⋊Q8×C127—22no—
32C4⋊Q8×C127—21no—
33C4⋊Q8×C127—21no—
34#125×C127—42no—
35#125×C127—41no—
36C4×Q8×C127—22no—
37C4×Q8×C127—21no—
38C4×Q8×C127—41no—
39C4×Q8×C127D411yescharacteristic
40Q32×C127—44no—
41Q32×C127—42no—
42C2×C16×C127—21no—
43C2×C16×C127—21no—
44#107×C127D411yescharacteristic
45#106×C127—41no—
46C4⋊C8×C127—21no—
47C4⋊C8×C127—21no—
48C4⋊C8×C127D411yescharacteristic
49#103×C127—22no—
50#103×C127—21no—
51#103×C127—41no—
52C4×C8×C127—21no—
53C4×C8×C127C2311yescharacteristic
54C2×Q8×C127—21no—
55C2×Q8×C127—22no—
56C2×Q8×C127—41no—
57C2×Q8×C127D811yescharacteristic
58Q16×C127—21no—
59Q16×C127—21no—
60Q16×C127—42no—
61Q16×C127—42no—
62Q16×C127—41no—
63Q16×C127—41no—
64Q16×C127—41no—
65Q16×C127—41no—
66Q16×C127—82no—
67C2×C8×C127—21no—
68C2×C8×C127—41no—
69C2×C8×C127C2×D411yescharacteristic
70C2×C8×C127C2×D411yescharacteristic
71C4⋊C4×C127—21no—
72C4⋊C4×C127—21no—
73C4⋊C4×C127—42no—
74C4⋊C4×C127—42no—
75C4⋊C4×C127—42no—
76C4⋊C4×C127—41no—
77C4⋊C4×C127—41no—
78C4⋊C4×C127—41no—
79C4⋊C4×C127—41no—
80C4⋊C4×C127—41no—
81C4⋊C4×C127D811yescharacteristic
82C42×C127—21no—
83C42×C127—42no—
84C42×C127—41no—
85C42×C127C2×D411yescharacteristic
86C16×C127—22no—
87C16×C127—41no—
88Q8×C127—21no—
89Q8×C127—41no—
90Q8×C127—42no—
91Q8×C127—42no—
92Q8×C127—41no—
93Q8×C127—81no—
94Q8×C127—81no—
95Q8×C127Q3212yescomplemented
96C2×C4×C127—21no—
97C2×C4×C127—21no—
98C2×C4×C127—41no—
99C2×C4×C127—42no—
100C2×C4×C127—41no—
101C2×C4×C127—81no—
102C2×C4×C127#12011yescharacteristic
103C2×C4×C127C2×D811yescharacteristic
104C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
105C8×C127—21no—
106C8×C127—41no—
107C8×C127—81no—
108C8×C127#13511yescharacteristic
109C8×C127AGL(1,ℤ/8)11yescharacteristic
110C22×C127#44711yescharacteristic
111C4×C127—22no—
112C4×C127—21no—
113C4×C127—41no—
114C4×C127—81no—
115C4×C127—82no—
116C4×C127—81no—
117C4×C127—161no—
118C4×C127#44911yescharacteristic
119C4×C127#45311yescharacteristic
120C4×C127C2×Q3211yescharacteristic
121C4×C127#51011yescharacteristic
122#12334C12711yesmaximal, characteristic, direct product factor, Sylow
123C2×C127#162111yescharacteristic
124C2×C127#218811yescharacteristic
125C2×C127#219511yescharacteristic
126#3395C2×C12711yescharacteristic
127#2247C2×C12711yescharacteristic
128#2209C2×C12711yescharacteristic
129#1670C2×C12711yescharacteristic
130#1362C2×C12711yescharacteristic
131Q8⋊C16C2×C12711yescharacteristic
132#1332C2×C12711yescharacteristic
133C127#1233411yescharacteristic, direct product factor, Sylow
134#557—21no—
135C2×Q32—21no—
136C2×Q32—22no—
137#494—21no—
138#494C22×C12711yescharacteristic
139#494C22×C12711yescharacteristic
140#475—21no—
141#462—22no—
142#462—21no—
143C8×Q8C22×C12711yescharacteristic
144C4×Q16—21no—
145C4×Q16C22×C12711yescharacteristic
146C4⋊C16C22×C12711yescharacteristic
147#358—21no—
148C4×C16C22×C12711yescharacteristic
149#335C22×C12711yescharacteristic
150#332—21no—
151C2×Q16—22no—
152C2×Q16—21no—
153C2×Q16—21no—
154C2×Q16—21no—
155C2×Q16D4×C12711yescharacteristic
156C2×Q16D4×C12712yes—
157C4⋊Q8—22no—
158C4⋊Q8—21no—
159C4⋊Q8—21no—
160#125—42no—
161#125—41no—
162C4×Q8—22no—
163C4×Q8—21no—
164C4×Q8—41no—
165C4×Q8D4×C12711yescharacteristic
166Q32—44no—
167Q32—42no—
168C2×C16—21no—
169C2×C16—21no—
170#107D4×C12711yescharacteristic
171#106—41no—
172C4⋊C8—21no—
173C4⋊C8—21no—
174C4⋊C8D4×C12711yescharacteristic
175#103—22no—
176#103—21no—
177#103—41no—
178C4×C8—21no—
179C4×C8C23×C12711yescharacteristic
180C2×Q8—21no—
181C2×Q8—22no—
182C2×Q8—41no—
183C2×Q8D8×C12711yescharacteristic
184Q16—21no—
185Q16—21no—
186Q16—42no—
187Q16—42no—
188Q16—41no—
189Q16—41no—
190Q16—41no—
191Q16—41no—
192Q16—82no—
193C2×C8—21no—
194C2×C8—41no—
195C2×C8C2×D4×C12711yescharacteristic
196C2×C8C2×D4×C12711yescharacteristic
197C4⋊C4—21no—
198C4⋊C4—21no—
199C4⋊C4—42no—
200C4⋊C4—42no—
201C4⋊C4—42no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4D8×C12711yescharacteristic
208C42—21no—
209C42—42no—
210C42—41no—
211C42C2×D4×C12711yescharacteristic
212C16—22no—
213C16—41no—
214Q8—21no—
215Q8—41no—
216Q8—42no—
217Q8—42no—
218Q8—41no—
219Q8—81no—
220Q8—81no—
221Q8Q32×C12712yescomplemented
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—41no—
225C2×C4—42no—
226C2×C4—41no—
227C2×C4—81no—
228C2×C4#120×C12711yescharacteristic
229C2×C4C2×D8×C12711yescharacteristic
230C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
231C8—21no—
232C8—41no—
233C8—81no—
234C8#135×C12711yescharacteristic
235C8AGL(1,ℤ/8)×C12711yescharacteristic
236C22#447×C12711yescharacteristic
237C4—22no—
238C4—21no—
239C4—41no—
240C4—81no—
241C4—82no—
242C4—81no—
243C4—161no—
244C4#449×C12711yescharacteristic
245C4#453×C12711yescharacteristic
246C4C2×Q32×C12711yescharacteristic
247C4#510×C12711yescharacteristic
248C2C127×#162111yescharacteristic
249C2C127×#218811yescharacteristic
250C2C127×#219511yescharacteristic
subgroupG/H
center, socle, prime radicalC22×C127#447
commutator, Frattini, cosocleC4×C8C23×C127
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
95. Q8×C127Q32semidirect
122. #12334C127direct (N × H)
133. C127#12334direct (N × H)
221. Q8Q32×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#33952
C127×#22472
C127×#22092
C127×#16702
C127×#13622
C127×Q8⋊C162
C127×#13322
#12334127