Finite Group Databasebeta

← C127×#7829 #44571502

Subgroups — C127×#7829 #44571502

Order 32512.

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

normal subgroups only

This group has 394 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×#2734C211yesmaximal, characteristic
2C127×#2100C212yesmaximal
3C127×#2095C211yesmaximal, characteristic
4C127×#1272C211yesmaximal, characteristic
5C127×#1271C212yesmaximal
6C2×C4⋊Q8×C127—21no—
7C2×#107×C127—21no—
8C2×#103×C127—21no—
9#398×C127—21no—
10#395×C127—22no—
11#391×C127C2211yescharacteristic
12#389×C127C2212yes—
13#387×C127—22no—
14#384×C127C2211yescharacteristic
15#340×C127—22no—
16#340×C127—22no—
17#336×C127C2211yescharacteristic
18#336×C127C2212yes—
19C22×Q8×C127—21no—
20C22×Q8×C127D411yescharacteristic
21C22×C8×C127—21no—
22C22×C8×C127—22no—
23C4⋊Q8×C127—42no—
24C4⋊Q8×C127—42no—
25C2×C4⋊C4×C127—22no—
26C2×C4⋊C4×C127—22no—
27C2×C4⋊C4×C127—22no—
28C2×C4⋊C4×C127—21no—
29C2×C4⋊C4×C127—21no—
30C2×C4⋊C4×C127D412yes—
31C2×C4⋊C4×C127D412yes—
32C2×C4⋊C4×C127D411yescharacteristic
33C2×C42×C127—21no—
34C2×C42×C127C2311yescharacteristic
35#107×C127—42no—
36#103×C127—42no—
37#95×C127—21no—
38#95×C127—22no—
39#95×C127—22no—
40#95×C127—22no—
41C2×Q8×C127—21no—
42C2×Q8×C127—42no—
43C2×Q8×C127—41no—
44C2×Q8×C127—41no—
45C2×Q8×C127—81no—
46C2×Q8×C127—81no—
47C2×Q8×C127SD1612yes—
48C22×C4×C127—22no—
49C22×C4×C127—21no—
50C22×C4×C127—21no—
51C22×C4×C127—22no—
52C22×C4×C127—41no—
53C22×C4×C127C2×D411yescharacteristic
54C22×C4×C127C2×D412yes—
55C2×C8×C127—22no—
56C2×C8×C127—41no—
57C2×C8×C127—41no—
58C2×C8×C127—42no—
59C2×C8×C127—42no—
60C2×C8×C127—42no—
61C4⋊C4×C127—22no—
62C4⋊C4×C127—41no—
63C4⋊C4×C127—42no—
64C4⋊C4×C127—44no—
65C4⋊C4×C127—41no—
66C4⋊C4×C127—41no—
67C4⋊C4×C127—44no—
68C4⋊C4×C127—42no—
69C4⋊C4×C127—42no—
70C4⋊C4×C127—81no—
71C4⋊C4×C127Q1614yes—
72C42×C127—41no—
73C42×C127—42no—
74C23×C127#12011yescharacteristic
75Q8×C127—42no—
76Q8×C127—81no—
77Q8×C127—84no—
78C2×C4×C127—21no—
79C2×C4×C127—22no—
80C2×C4×C127—22no—
81C2×C4×C127—21no—
82C2×C4×C127—22no—
83C2×C4×C127—24no—
84C2×C4×C127—42no—
85C2×C4×C127—41no—
86C2×C4×C127—42no—
87C2×C4×C127—41no—
88C2×C4×C127—42no—
89C2×C4×C127—41no—
90C2×C4×C127—42no—
91C2×C4×C127—42no—
92C2×C4×C127—42no—
93C2×C4×C127—81no—
94C2×C4×C127—82no—
95C2×C4×C127C2×SD1611yescharacteristic
96C2×C4×C127C2×Q1612yes—
97C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
98C2×C4×C127#13712yes—
99C8×C127—42no—
100C8×C127—82no—
101C22×C127#45011yescharacteristic
102C22×C127#45112yes—
103C22×C127#45311yescharacteristic
104C22×C127#45412yes—
105C22×C127#45811yescharacteristic
106C4×C127—21no—
107C4×C127—21no—
108C4×C127—22no—
109C4×C127—22no—
110C4×C127—42no—
111C4×C127—44no—
112C4×C127—82no—
113C4×C127—81no—
114C4×C127—161no—
115#7829C12711yesmaximal, characteristic, direct product factor, Sylow
116C2×C127#161311yescharacteristic
117C2×C127#161712yes—
118C2×C127#163311yescharacteristic
119C2×C127#163712yes—
120C2×C127#165711yescharacteristic
121#2734C2×C12711yescharacteristic
122#2100C2×C12712yes—
123#2095C2×C12711yescharacteristic
124#1272C2×C12711yescharacteristic
125#1271C2×C12712yes—
126C127#782911yescharacteristic, direct product factor, Sylow
127C2×C4⋊Q8—21no—
128C2×#107—21no—
129C2×#103—21no—
130#398—21no—
131#395—22no—
132#391C22×C12711yescharacteristic
133#389C22×C12712yes—
134#387—22no—
135#384C22×C12711yescharacteristic
136#340—22no—
137#340—22no—
138#336C22×C12711yescharacteristic
139#336C22×C12712yes—
140C22×Q8—21no—
141C22×Q8D4×C12711yescharacteristic
142C22×C8—21no—
143C22×C8—22no—
144C4⋊Q8—42no—
145C4⋊Q8—42no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4D4×C12712yes—
152C2×C4⋊C4D4×C12712yes—
153C2×C4⋊C4D4×C12711yescharacteristic
154C2×C42—21no—
155C2×C42C23×C12711yescharacteristic
156#107—42no—
157#103—42no—
158#95—21no—
159#95—22no—
160#95—22no—
161#95—22no—
162C2×Q8—21no—
163C2×Q8—42no—
164C2×Q8—41no—
165C2×Q8—41no—
166C2×Q8—81no—
167C2×Q8—81no—
168C2×Q8SD16×C12712yes—
169C22×C4—22no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—22no—
173C22×C4—41no—
174C22×C4C2×D4×C12711yescharacteristic
175C22×C4C2×D4×C12712yes—
176C2×C8—22no—
177C2×C8—41no—
178C2×C8—41no—
179C2×C8—42no—
180C2×C8—42no—
181C2×C8—42no—
182C4⋊C4—22no—
183C4⋊C4—41no—
184C4⋊C4—42no—
185C4⋊C4—44no—
186C4⋊C4—41no—
187C4⋊C4—41no—
188C4⋊C4—44no—
189C4⋊C4—42no—
190C4⋊C4—42no—
191C4⋊C4—81no—
192C4⋊C4Q16×C12714yes—
193C42—41no—
194C42—42no—
195C23#120×C12711yescharacteristic
196Q8—42no—
197Q8—81no—
198Q8—84no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—24no—
205C2×C4—42no—
206C2×C4—41no—
207C2×C4—42no—
208C2×C4—41no—
209C2×C4—42no—
210C2×C4—41no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—81no—
215C2×C4—82no—
216C2×C4C2×SD16×C12711yescharacteristic
217C2×C4C2×Q16×C12712yes—
218C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
219C2×C4#137×C12712yes—
220C8—42no—
221C8—82no—
222C22#450×C12711yescharacteristic
223C22#451×C12712yes—
224C22#453×C12711yescharacteristic
225C22#454×C12712yes—
226C22#458×C12711yescharacteristic
227C4—21no—
228C4—21no—
229C4—22no—
230C4—22no—
231C4—42no—
232C4—44no—
233C4—82no—
234C4—81no—
235C4—161no—
236C2C127×#161311yescharacteristic
237C2C127×#161712yes—
238C2C127×#163311yescharacteristic
239C2C127×#163712yes—
240C2C127×#165711yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C127#120
commutator, Frattini, cosocleC2×C42C23×C127
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
115. #7829C127direct (N × H)
126. C127#7829direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#27342
C127×#21002
C127×#20952
C127×#12722
C127×#12712
#7829127