Finite Group Databasebeta

← #27179507

Subgroups — #27179507

Order 12928.

504 conjugacy classes of subgroups; only the 177 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 177 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×#15692254C211yesmaximal, characteristic
2C2×#15692253C211yesmaximal, characteristic
3#20265084C211yesmaximal, characteristic
4#20265083C211yesmaximal, characteristic
5#20265082C211yesmaximal, characteristic
6#20265081C214yesmaximal
7#20265041C214yesmaximal
8C42×Dic101C211yesmaximal, characteristic
9#391×C101C211yesmaximal, characteristic
10C22×Dic202C2212yes—
11C22×Dic202C2211yescharacteristic
12#15692254—24no—
13#15692253—24no—
14C2×C4⋊Dic101C2211yescharacteristic
15C2×#13108053C2212yes—
16C2×#13108053C2212yes—
17C2×#13108053C2212yes—
18C2×C4×Dic101C2212yes—
19C2×C4×Dic101C2211yescharacteristic
20C2×C4×Dic101C2211yescharacteristic
21C2×C4×Dic101C2212yes—
22#15692162C2214yes—
23#15692162C2214yes—
24#15692162C2214yes—
25C22×Q8×C101C2211yescharacteristic
26C2×C4⋊C4×C101C2211yescharacteristic
27C2×C42×C101C2211yescharacteristic
28#95×C101C2214yes—
29C2×Dic202—22no—
30C2×Dic202—22no—
31C2×Dic202—22no—
32C2×Dic202—24no—
33C2×Dic202—28no—
34C22×Dic101C2312yes—
35C22×Dic101C2312yes—
36C22×Dic101C2312yes—
37C22×Dic101C2311yescharacteristic
38C22×Dic101C2311yescharacteristic
39C4⋊Dic101—22no—
40#13108053—24no—
41#13108053—24no—
42#13108053—24no—
43C4×Dic101—22no—
44C4×Dic101—24no—
45C4×Dic101D414yes—
46C4×Dic101Q818yescomplemented
47C2×Q8×C101—22no—
48C2×Q8×C101—22no—
49C2×Q8×C101—22no—
50C22×C4×C101C2312yes—
51C22×C4×C101C2312yes—
52C22×C4×C101C2312yes—
53C22×C4×C101C2311yescharacteristic
54C4⋊C4×C101—22no—
55C42×C101—22no—
56C23×C101C2411yescharacteristic
57Q8×C101—44no—
58C2×C4×C101—22no—
59C2×C4×C101—22no—
60C2×C4×C101—22no—
61C2×C4×C101—22no—
62C2×C4×C101—22no—
63C2×C4×C101—22no—
64C2×C4×C101—24no—
65C2×C4×C101C2×D412yes—
66C2×C4×C101C2×Q814yes—
67C2×C4×C101#4112yes—
68C2×C4×C101#4112yes—
69C2×Dic101—22no—
70C2×Dic101—22no—
71C2×Dic101—22no—
72C2×Dic101—22no—
73C2×Dic101—24no—
74C2×Dic101—22no—
75C2×Dic101—22no—
76C2×Dic101C2×D412yes—
77C2×Dic101C2×D412yes—
78C2×Dic101C2×Q814yes—
79C2×Dic101C2×Q814yes—
80C2×Dic101#4114yes—
81Dic202—44no—
82Dic202—48no—
83C22×C101C22×D411yescharacteristic
84C22×C101C22×Q812yes—
85C22×C101C2×#4112yes—
86C22×C101C2×#4111yescharacteristic
87C22×C101C2×#4111yescharacteristic
88C4×C101—24no—
89C4×C101—42no—
90C4×C101—42no—
91C4×C101#12414yes—
92Dic101—24no—
93Dic101—42no—
94Dic101—42no—
95Dic101#12414yes—
96Dic101C4⋊Q814yes—
97C2×C101C2×#12411yescharacteristic
98C2×C101C2×#12411yescharacteristic
99C2×C101C2×C4⋊Q811yescharacteristic
100C2×C101#53312yes—
101C2×C101#53312yes—
102#2862—1011nomaximal, Sylow
103C101#286211yescharacteristic, complemented, Sylow
104C2×C4⋊Q8—1011no—
105C2×C4⋊Q8—1011no—
106#391—1011no—
107#391—1011no—
108#391—1011no—
109#391—1014no—
110#391D10111yescharacteristic
111#382—1014no—
112C43—1011no—
113C22×Q8—1012no—
114C22×Q8—1011no—
115C22×Q8C2×D10111yescharacteristic
116C4⋊Q8—2024no—
117C4⋊Q8—2024no—
118C2×C4⋊C4—1012no—
119C2×C4⋊C4—1012no—
120C2×C4⋊C4—1012no—
121C2×C4⋊C4—1011no—
122C2×C4⋊C4C2×D10111yescharacteristic
123C2×C42—1011no—
124C2×C42—1012no—
125C2×C42—1012no—
126C2×C42—1011no—
127C2×C42C2×D10111yescharacteristic
128#95—1014no—
129#95—1014no—
130#95—1014no—
131#95C2×D10114yes—
132C2×Q8—22no—
133C2×Q8—22no—
134C2×Q8—22no—
135C2×Q8—2024no—
136C2×Q8—2028no—
137C2×Q8—2022no—
138C2×Q8—2022no—
139C2×Q8—2022no—
140C22×C4—1011no—
141C22×C4—1011no—
142C22×C4—1012no—
143C22×C4—1012no—
144C22×C4—1012no—
145C22×C4C22×D10112yes—
146C22×C4C22×D10112yes—
147C22×C4C22×D10112yes—
148C22×C4C22×D10111yescharacteristic
149C4⋊C4—22no—
150C4⋊C4—2024no—
151C4⋊C4—2024no—
152C4⋊C4—2024no—
153C4⋊C4—2022no—
154C42—22no—
155C42—1014no—
156C42—1018no—
157C42—2024no—
158C42—2022no—
159C23C23×D10111yescharacteristic
160Q8—44no—
161Q8—4048no—
162Q8—4044no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—24no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—1012no—
171C2×C4—1012no—
172C2×C4—1014no—
173C2×C4—1014no—
174C2×C4—1014no—
175C2×C4—2022no—
176C2×C4—2022no—
177C2×C4—2024no—
178C2×C4—2022no—
179C2×C4—2022no—
180C2×C4—2022no—
181C2×C4—2022no—
182C2×C4D4×D10112yes—
183C2×C4Q8×D10114yes—
184C2×C4#1310807312yes—
185C2×C4#1310807412yes—
186C22C2×D4×D10111yescharacteristic
187C22C2×Q8×D10112yes—
188C22#41×D10112yes—
189C22C2×#1310807311yescharacteristic
190C22C2×#1310807411yescharacteristic
191C4—24no—
192C4—42no—
193C4—42no—
194C4—1014no—
195C4—1014no—
196C4—4042no—
197C4—4042no—
198C4—2024no—
199C4#1569224114yes—
200C2#124×D10111yescharacteristic
201C2C2×#1569224111yescharacteristic
202C2C4⋊Q8×D10111yescharacteristic
203C2#2026572912yes—
204C2#2026573112yes—
subgroupG/H
center, FrattiniC23C23×D101
commutator, socle, prime radical, cosocleC23×C101C24
Fitting#391×C101C2
hypercenter#391D101
hypocenterC101#2862
LCSG ▷ C23×C101 ▷ C101
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
46. C4×Dic101Q8semidirect
103. C101#2862semidirect

Maximal subgroups

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

subgroupindex
C2×#156922542
C2×#156922532
#202650842
#202650832
#202650822
#202650812
#202650412
C42×Dic1012
#391×C1012
#2862101