Finite Group Databasebeta

← C127×#13598 #44577271

Subgroups — C127×#13598 #44577271

Order 32512.

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

normal subgroups only

This group has 318 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×#3135C211yesmaximal, characteristic
2C127×#2132C212yesmaximal
3C127×#1413C214yesmaximal, complemented
4#533×C127C411yescharacteristic
5#532×C127C2211yescharacteristic
6#491×C127C2212yes—
7#490×C127C412yes—
8#489×C127—22no—
9#416×C127—22no—
10#413×C127—22no—
11C2×#97×C127C411yescharacteristic
12#356×C127C2214yes—
13#355×C127—22no—
14C2×#41×C127D412yes—
15C2×M16×C127—42no—
16C22×C8×C127—21no—
17C4⋊Q8×C127—21no—
18C4⋊Q8×C127C2311yescharacteristic
19#127×C127C2×C411yescharacteristic
20#125×C127C2×C412yes—
21#124×C127D412yes—
22C22⋊Q8×C127—41no—
23#121×C127—41no—
24C4×Q8×C127—41no—
25C4×D4×C127—41no—
26#117×C127—21no—
27C2×C42×C127C2×C411yescharacteristic
28#103×C127—24no—
29#102×C127—24no—
30#101×C127—24no—
31#100×C127—42no—
32#97×C127—21no—
33#97×C127C2×C412yes—
34#41×C127—42no—
35#41×C127—42no—
36C2×Q8×C127—41no—
37C2×Q8×C127C2×D412yes—
38C2×D4×C127—22no—
39C2×D4×C127—41no—
40C2×D4×C127C22⋊C412yes—
41C22×C4×C127—21no—
42C22×C4×C127—22no—
43C22×C4×C127C22⋊C411yescharacteristic
44M16×C127—44no—
45M16×C127—82no—
46C2×C8×C127—22no—
47C2×C8×C127—41no—
48C2×C8×C127—41no—
49C2×C8×C127—82no—
50C4⋊C4×C127—22no—
51C4⋊C4×C127—41no—
52C4⋊C4×C127—42no—
53C4⋊C4×C127—41no—
54C22⋊C4×C127—42no—
55C22⋊C4×C127—41no—
56C42×C127—21no—
57C42×C127—41no—
58C42×C127C22⋊C411yescharacteristic
59C42×C127C22×C411yescharacteristic
60C23×C127—22no—
61C23×C127#9911yescharacteristic
62Q8×C127—42no—
63Q8×C127—82no—
64D4×C127—42no—
65D4×C127—82no—
66D4×C127—82no—
67C2×C4×C127—21no—
68C2×C4×C127—21no—
69C2×C4×C127—21no—
70C2×C4×C127—21no—
71C2×C4×C127—22no—
72C2×C4×C127—42no—
73C2×C4×C127—42no—
74C2×C4×C127—42no—
75C2×C4×C127—81no—
76C2×C4×C127#9911yescharacteristic
77C2×C4×C127C2×C22⋊C411yescharacteristic
78C8×C127—42no—
79C8×C127—84no—
80C22×C127—21no—
81C22×C127—41no—
82C22×C127—42no—
83C22×C127—82no—
84C22×C127C2×#9911yescharacteristic
85C4×C127—21no—
86C4×C127—41no—
87C4×C127—41no—
88C4×C127—42no—
89C4×C127—82no—
90C4×C127#35411yescharacteristic
91C4×C127#35411yescharacteristic
92#13598C12711yesmaximal, characteristic, direct product factor, Sylow
93C2×C127—21no—
94C2×C127—41no—
95C2×C127—82no—
96C2×C127C2×#35411yescharacteristic
97#3135C2×C12711yescharacteristic
98#2132C2×C12712yes—
99#1413C2×C12714yescomplemented
100C127#1359811yescharacteristic, direct product factor, Sylow
101#533C4×C12711yescharacteristic
102#532C22×C12711yescharacteristic
103#491C22×C12712yes—
104#490C4×C12712yes—
105#489—22no—
106#416—22no—
107#413—22no—
108C2×#97C4×C12711yescharacteristic
109#356C22×C12714yes—
110#355—22no—
111C2×#41D4×C12712yes—
112C2×M16—42no—
113C22×C8—21no—
114C4⋊Q8—21no—
115C4⋊Q8C23×C12711yescharacteristic
116#127C2×C4×C12711yescharacteristic
117#125C2×C4×C12712yes—
118#124D4×C12712yes—
119C22⋊Q8—41no—
120#121—41no—
121C4×Q8—41no—
122C4×D4—41no—
123#117—21no—
124C2×C42C2×C4×C12711yescharacteristic
125#103—24no—
126#102—24no—
127#101—24no—
128#100—42no—
129#97—21no—
130#97C2×C4×C12712yes—
131#41—42no—
132#41—42no—
133C2×Q8—41no—
134C2×Q8C2×D4×C12712yes—
135C2×D4—22no—
136C2×D4—41no—
137C2×D4C22⋊C4×C12712yes—
138C22×C4—21no—
139C22×C4—22no—
140C22×C4C22⋊C4×C12711yescharacteristic
141M16—44no—
142M16—82no—
143C2×C8—22no—
144C2×C8—41no—
145C2×C8—41no—
146C2×C8—82no—
147C4⋊C4—22no—
148C4⋊C4—41no—
149C4⋊C4—42no—
150C4⋊C4—41no—
151C22⋊C4—42no—
152C22⋊C4—41no—
153C42—21no—
154C42—41no—
155C42C22⋊C4×C12711yescharacteristic
156C42C22×C4×C12711yescharacteristic
157C23—22no—
158C23#99×C12711yescharacteristic
159Q8—42no—
160Q8—82no—
161D4—42no—
162D4—82no—
163D4—82no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—22no—
169C2×C4—42no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—81no—
173C2×C4#99×C12711yescharacteristic
174C2×C4C2×C22⋊C4×C12711yescharacteristic
175C8—42no—
176C8—84no—
177C22—21no—
178C22—41no—
179C22—42no—
180C22—82no—
181C22C2×#99×C12711yescharacteristic
182C4—21no—
183C4—41no—
184C4—41no—
185C4—42no—
186C4—82no—
187C4#354×C12711yescharacteristic
188C4#354×C12711yescharacteristic
189C2—21no—
190C2—41no—
191C2—82no—
192C2C2×#354×C12711yescharacteristic
subgroupG/H
centerC4×C127#354
commutatorC42C22×C4×C127
Frattini, cosocleC4⋊Q8C23×C127
socleC2×C127C2×#354
prime radical#532×C127C22
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×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×#1413C2semidirect
92. #13598C127direct (N × H)
99. #1413C2×C127semidirect
100. C127#13598direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#31352
C127×#21322
C127×#14132
#13598127