Finite Group Databasebeta

← C127×#13592 #44577265

Subgroups — C127×#13592 #44577265

Order 32512.

398 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 90 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×#3152C211yesmaximal, characteristic
2C127×#2132C212yesmaximal
3C127×#1411C214yesmaximal, complemented
4C2×#137×C127—22no—
5#532×C127C2211yescharacteristic
6C2×C4⋊Q8×C127C411yescharacteristic
7#497×C127—22no—
8#494×C127C2212yes—
9#492×C127C412yes—
10#413×C127—22no—
11C4×M16×C127C411yescharacteristic
12#356×C127C2214yes—
13#355×C127—22no—
14C2×#41×C127D412yes—
15C22×Q8×C127—21no—
16#137×C127—44no—
17#137×C127—44no—
18C2×Q16×C127—24no—
19C2×SD16×C127—24no—
20C2×M16×C127—21no—
21C2×M16×C127—42no—
22C4⋊Q8×C127—21no—
23C4⋊Q8×C127—41no—
24C4⋊Q8×C127C2×C412yes—
25C4⋊Q8×C127C2311yescharacteristic
26#127×C127C2×C411yescharacteristic
27#124×C127D412yes—
28#121×C127—41no—
29C4×D4×C127—41no—
30C2×C4⋊C4×C127—41no—
31C2×C42×C127C2×C411yescharacteristic
32#101×C127—24no—
33#100×C127—42no—
34#97×C127—21no—
35C4×C8×C127C2×C412yes—
36#41×C127—42no—
37#41×C127—42no—
38C2×Q8×C127—22no—
39C2×Q8×C127—42no—
40C2×Q8×C127—42no—
41C2×Q8×C127—41no—
42C2×Q8×C127C2×D412yes—
43C2×D4×C127—22no—
44C2×D4×C127—41no—
45C2×D4×C127C22⋊C412yes—
46C22×C4×C127—21no—
47C22×C4×C127—22no—
48C22×C4×C127—41no—
49C22×C4×C127C22⋊C411yescharacteristic
50Q16×C127—48no—
51SD16×C127—48no—
52M16×C127—24no—
53M16×C127—44no—
54M16×C127—82no—
55C2×C8×C127—22no—
56C2×C8×C127—82no—
57C4⋊C4×C127—41no—
58C4⋊C4×C127—42no—
59C4⋊C4×C127—42no—
60C22⋊C4×C127—42no—
61C42×C127—21no—
62C42×C127C22⋊C411yescharacteristic
63C42×C127C22×C411yescharacteristic
64C23×C127—22no—
65C23×C127#9911yescharacteristic
66Q8×C127—42no—
67Q8×C127—44no—
68Q8×C127—82no—
69D4×C127—42no—
70D4×C127—82no—
71D4×C127—82no—
72C2×C4×C127—21no—
73C2×C4×C127—22no—
74C2×C4×C127—21no—
75C2×C4×C127—22no—
76C2×C4×C127—42no—
77C2×C4×C127—42no—
78C2×C4×C127—42no—
79C2×C4×C127—42no—
80C2×C4×C127—81no—
81C2×C4×C127—81no—
82C2×C4×C127#9911yescharacteristic
83C2×C4×C127C2×C22⋊C411yescharacteristic
84C8×C127—24no—
85C8×C127—84no—
86C22×C127—21no—
87C22×C127—41no—
88C22×C127—42no—
89C22×C127—82no—
90C22×C127C2×#9911yescharacteristic
91C4×C127—22no—
92C4×C127—21no—
93C4×C127—41no—
94C4×C127—42no—
95C4×C127—82no—
96C4×C127#35312yes—
97#13592C12711yesmaximal, characteristic, direct product factor, Sylow
98C2×C127—21no—
99C2×C127—41no—
100C2×C127—82no—
101C2×C127C2×#35311yescharacteristic
102#3152C2×C12711yescharacteristic
103#2132C2×C12712yes—
104#1411C2×C12714yescomplemented
105C127#1359211yescharacteristic, direct product factor, Sylow
106C2×#137—22no—
107#532C22×C12711yescharacteristic
108C2×C4⋊Q8C4×C12711yescharacteristic
109#497—22no—
110#494C22×C12712yes—
111#492C4×C12712yes—
112#413—22no—
113C4×M16C4×C12711yescharacteristic
114#356C22×C12714yes—
115#355—22no—
116C2×#41D4×C12712yes—
117C22×Q8—21no—
118#137—44no—
119#137—44no—
120C2×Q16—24no—
121C2×SD16—24no—
122C2×M16—21no—
123C2×M16—42no—
124C4⋊Q8—21no—
125C4⋊Q8—41no—
126C4⋊Q8C2×C4×C12712yes—
127C4⋊Q8C23×C12711yescharacteristic
128#127C2×C4×C12711yescharacteristic
129#124D4×C12712yes—
130#121—41no—
131C4×D4—41no—
132C2×C4⋊C4—41no—
133C2×C42C2×C4×C12711yescharacteristic
134#101—24no—
135#100—42no—
136#97—21no—
137C4×C8C2×C4×C12712yes—
138#41—42no—
139#41—42no—
140C2×Q8—22no—
141C2×Q8—42no—
142C2×Q8—42no—
143C2×Q8—41no—
144C2×Q8C2×D4×C12712yes—
145C2×D4—22no—
146C2×D4—41no—
147C2×D4C22⋊C4×C12712yes—
148C22×C4—21no—
149C22×C4—22no—
150C22×C4—41no—
151C22×C4C22⋊C4×C12711yescharacteristic
152Q16—48no—
153SD16—48no—
154M16—24no—
155M16—44no—
156M16—82no—
157C2×C8—22no—
158C2×C8—82no—
159C4⋊C4—41no—
160C4⋊C4—42no—
161C4⋊C4—42no—
162C22⋊C4—42no—
163C42—21no—
164C42C22⋊C4×C12711yescharacteristic
165C42C22×C4×C12711yescharacteristic
166C23—22no—
167C23#99×C12711yescharacteristic
168Q8—42no—
169Q8—44no—
170Q8—82no—
171D4—42no—
172D4—82no—
173D4—82no—
174C2×C4—21no—
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—22no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—81no—
183C2×C4—81no—
184C2×C4#99×C12711yescharacteristic
185C2×C4C2×C22⋊C4×C12711yescharacteristic
186C8—24no—
187C8—84no—
188C22—21no—
189C22—41no—
190C22—42no—
191C22—82no—
192C22C2×#99×C12711yescharacteristic
193C4—22no—
194C4—21no—
195C4—41no—
196C4—42no—
197C4—82no—
198C4#353×C12712yes—
199C2—21no—
200C2—41no—
201C2—82no—
202C2C2×#353×C12711yescharacteristic
subgroupG/H
center, socleC2×C127C2×#353
commutatorC42C22×C4×C127
Frattini, cosocleC4⋊Q8C23×C127
prime radical#532×C127C22
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C2×C4×C127 ◁ C22×C4×C127 ◁ #532×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#1411C2semidirect
97. #13592C127direct (N × H)
104. #1411C2×C127semidirect
105. C127#13592direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#31522
C127×#21322
C127×#14112
#13592127