Finite Group Databasebeta

← C2×C127×#1411 #44577261

Subgroups — C2×C127×#1411 #44577261

Order 32512.

398 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 94 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
1C2×#494×C127C211yesmaximal, characteristic
2C2×#356×C127C212yesmaximal
3C127×#1411C214yesmaximal, direct product factor
4C22×Q16×C127—22no—
5C2×C4⋊Q8×C127C411yescharacteristic
6C2×C4⋊Q8×C127C2211yescharacteristic
7#494×C127—22no—
8#494×C127C412yes—
9#494×C127C2212yes—
10C2×#101×C127—22no—
11C2×C4×C8×C127C411yescharacteristic
12#356×C127—22no—
13#356×C127C2214yes—
14C22×Q8×C127—21no—
15C22×Q8×C127D412yes—
16C2×Q16×C127—24no—
17C2×Q16×C127—24no—
18C2×Q16×C127—44no—
19C2×Q16×C127—44no—
20C2×M16×C127—42no—
21C22×C8×C127—21no—
22C4⋊Q8×C127—21no—
23C4⋊Q8×C127—41no—
24C4⋊Q8×C127—41no—
25C4⋊Q8×C127C2×C412yes—
26C4⋊Q8×C127C2×C411yescharacteristic
27C4⋊Q8×C127D412yes—
28C4⋊Q8×C127C2311yescharacteristic
29C2×C4⋊C4×C127—41no—
30C2×C4⋊C4×C127—41no—
31C2×C42×C127C2×C411yescharacteristic
32#101×C127—24no—
33#101×C127—42no—
34C4×C8×C127—21no—
35C4×C8×C127C2×C412yes—
36C2×Q8×C127—22no—
37C2×Q8×C127—22no—
38C2×Q8×C127—42no—
39C2×Q8×C127—42no—
40C2×Q8×C127—42no—
41C2×Q8×C127—42no—
42C2×Q8×C127—41no—
43C2×Q8×C127C22⋊C412yes—
44C2×Q8×C127C2×D412yes—
45C22×C4×C127—21no—
46C22×C4×C127—22no—
47C22×C4×C127—41no—
48C22×C4×C127C22⋊C411yescharacteristic
49Q16×C127—48no—
50Q16×C127—48no—
51M16×C127—44no—
52M16×C127—82no—
53C2×C8×C127—22no—
54C2×C8×C127—22no—
55C2×C8×C127—22no—
56C2×C8×C127—82no—
57C4⋊C4×C127—41no—
58C4⋊C4×C127—42no—
59C4⋊C4×C127—41no—
60C4⋊C4×C127—42no—
61C4⋊C4×C127—42no—
62C42×C127—21no—
63C42×C127C22⋊C411yescharacteristic
64C42×C127C22×C411yescharacteristic
65C23×C127#9911yescharacteristic
66Q8×C127—42no—
67Q8×C127—42no—
68Q8×C127—44no—
69Q8×C127—82no—
70Q8×C127—82no—
71C2×C4×C127—24no—
72C2×C4×C127—21no—
73C2×C4×C127—21no—
74C2×C4×C127—21no—
75C2×C4×C127—21no—
76C2×C4×C127—22no—
77C2×C4×C127—22no—
78C2×C4×C127—42no—
79C2×C4×C127—42no—
80C2×C4×C127—42no—
81C2×C4×C127—81no—
82C2×C4×C127—81no—
83C2×C4×C127#9911yescharacteristic
84C2×C4×C127C2×C22⋊C411yescharacteristic
85C8×C127—24no—
86C8×C127—84no—
87C22×C127—22no—
88C22×C127#35311yescharacteristic
89C22×C127#35311yescharacteristic
90C22×C127C2×#9911yescharacteristic
91C4×C127—22no—
92C4×C127—22no—
93C4×C127—21no—
94C4×C127—21no—
95C4×C127—42no—
96C4×C127—42no—
97C4×C127—82no—
98C2×#1411C12711yesmaximal, characteristic, direct product factor, Sylow
99C2×C127—21no—
100C2×C127—21no—
101C2×C127#141112yesdirect product factor
102C2×C127C2×#35311yescharacteristic
103C2×#494C2×C12711yescharacteristic
104C2×#356C2×C12712yes—
105#1411C2×C12714yesdirect product factor
106C127C2×#141111yescharacteristic, direct product factor, Sylow
107C22×Q16—22no—
108C2×C4⋊Q8C4×C12711yescharacteristic
109C2×C4⋊Q8C22×C12711yescharacteristic
110#494—22no—
111#494C4×C12712yes—
112#494C22×C12712yes—
113C2×#101—22no—
114C2×C4×C8C4×C12711yescharacteristic
115#356—22no—
116#356C22×C12714yes—
117C22×Q8—21no—
118C22×Q8D4×C12712yes—
119C2×Q16—24no—
120C2×Q16—24no—
121C2×Q16—44no—
122C2×Q16—44no—
123C2×M16—42no—
124C22×C8—21no—
125C4⋊Q8—21no—
126C4⋊Q8—41no—
127C4⋊Q8—41no—
128C4⋊Q8C2×C4×C12712yes—
129C4⋊Q8C2×C4×C12711yescharacteristic
130C4⋊Q8D4×C12712yes—
131C4⋊Q8C23×C12711yescharacteristic
132C2×C4⋊C4—41no—
133C2×C4⋊C4—41no—
134C2×C42C2×C4×C12711yescharacteristic
135#101—24no—
136#101—42no—
137C4×C8—21no—
138C4×C8C2×C4×C12712yes—
139C2×Q8—22no—
140C2×Q8—22no—
141C2×Q8—42no—
142C2×Q8—42no—
143C2×Q8—42no—
144C2×Q8—42no—
145C2×Q8—41no—
146C2×Q8C22⋊C4×C12712yes—
147C2×Q8C2×D4×C12712yes—
148C22×C4—21no—
149C22×C4—22no—
150C22×C4—41no—
151C22×C4C22⋊C4×C12711yescharacteristic
152Q16—48no—
153Q16—48no—
154M16—44no—
155M16—82no—
156C2×C8—22no—
157C2×C8—22no—
158C2×C8—22no—
159C2×C8—82no—
160C4⋊C4—41no—
161C4⋊C4—42no—
162C4⋊C4—41no—
163C4⋊C4—42no—
164C4⋊C4—42no—
165C42—21no—
166C42C22⋊C4×C12711yescharacteristic
167C42C22×C4×C12711yescharacteristic
168C23#99×C12711yescharacteristic
169Q8—42no—
170Q8—42no—
171Q8—44no—
172Q8—82no—
173Q8—82no—
174C2×C4—24no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—81no—
185C2×C4—81no—
186C2×C4#99×C12711yescharacteristic
187C2×C4C2×C22⋊C4×C12711yescharacteristic
188C8—24no—
189C8—84no—
190C22—22no—
191C22#353×C12711yescharacteristic
192C22#353×C12711yescharacteristic
193C22C2×#99×C12711yescharacteristic
194C4—22no—
195C4—22no—
196C4—21no—
197C4—21no—
198C4—42no—
199C4—42no—
200C4—82no—
201C2—21no—
202C2—21no—
203C2C127×#141112yesdirect product factor
204C2C2×#353×C12711yescharacteristic
subgroupG/H
center, socleC22×C127#353
commutatorC42C22×C4×C127
Frattini, cosocleC4⋊Q8C23×C127
prime radicalC23×C127#99
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C127 ◁ C22×C4×C127 ◁ C2×C4⋊Q8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#1411C2direct (N × H)
98. C2×#1411C127direct (N × H)
101. C2×C127#1411direct (N × H)
105. #1411C2×C127direct (N × H)
106. C127C2×#1411direct (N × H)
203. C2C127×#1411direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#494×C1272
C2×#356×C1272
C127×#14112
C2×#1411127