Finite Group Databasebeta

← #27172281

Subgroups — #27172281

Order 12928.

258 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 85 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×#15692246C211yesmaximal, characteristic
2C2×#15692179C211yesmaximal, characteristic
3#20265084C211yesmaximal, characteristic
4#20264940C211yesmaximal, characteristic
5#20264939C211yesmaximal, characteristic
6#20264931C211yesmaximal, characteristic
7C2×#103×C101C211yesmaximal, characteristic
8C22×#11717579C2211yescharacteristic
9#15692246—22no—
10#15692246—22no—
11C2×C4⋊Dic101—21no—
12C2×C4⋊Dic101C2211yescharacteristic
13C2×C4⋊Dic101C2211yescharacteristic
14C2×#13108053—21no—
15C2×C4×Dic101C2211yescharacteristic
16#15692179—22no—
17#15692162—21no—
18#15692162—21no—
19C22×Q8×C101C2211yescharacteristic
20C22×C8×C101C2211yescharacteristic
21C2×C4⋊C4×C101C2211yescharacteristic
22#103×C101—22no—
23C22×Dic101—21no—
24C22×Dic101—21no—
25C22×Dic101D411yescharacteristic
26C22×Dic101D411yescharacteristic
27C2×#11717579—21no—
28C2×#11717579—21no—
29C2×#11717579—21no—
30C4⋊Dic101—24no—
31C4⋊Dic101—21no—
32C4⋊Dic101—21no—
33C4⋊Dic101—21no—
34C4⋊Dic101D412yes—
35#13108053—24no—
36C4×Dic101—21no—
37C4×Dic101—21no—
38C2×Q8×C101—21no—
39C2×Q8×C101—21no—
40C2×Q8×C101—21no—
41C2×Q8×C101—21no—
42C2×Q8×C101—21no—
43C2×Q8×C101Q812yes—
44C22×C4×C101—21no—
45C22×C4×C101—21no—
46C22×C4×C101C2311yescharacteristic
47C2×C8×C101—21no—
48C2×C8×C101—21no—
49C2×C8×C101—21no—
50C4⋊C4×C101—21no—
51C4⋊C4×C101D412yes—
52C23×C101C2×D411yescharacteristic
53Q8×C101—22no—
54Q8×C101—22no—
55Q8×C101—41no—
56Q8×C101—41no—
57C2×C4×C101—22no—
58C2×C4×C101—22no—
59C2×C4×C101—41no—
60C2×C4×C101—41no—
61C2×C4×C101—41no—
62C2×C4×C101—41no—
63C2×C4×C101C2×D411yescharacteristic
64C2×C4×C101C2×D411yescharacteristic
65C2×C4×C101C2×Q811yescharacteristic
66C2×C4×C101#4111yescharacteristic
67C2×C4×C101#4111yescharacteristic
68C2×C4×C101#4111yescharacteristic
69C2×Dic101—21no—
70C2×Dic101—21no—
71C2×Dic101—22no—
72C2×Dic101—21no—
73C2×Dic101—21no—
74C2×Dic101—21no—
75C2×Dic101—21no—
76C2×Dic101—41no—
77C2×Dic101—41no—
78C2×Dic101—41no—
79C2×Dic101—41no—
80C2×Dic101—41no—
81C8×C101—41no—
82#11717579—41no—
83C22×C101#12011yescharacteristic
84C22×C101C22⋊Q811yescharacteristic
85C22×C101#12411yescharacteristic
86C22×C101#13511yescharacteristic
87C22×C101#13511yescharacteristic
88C22×C101#13711yescharacteristic
89C22×C101#13711yescharacteristic
90C4×C101—42no—
91C4×C101—42no—
92C4×C101C22⋊Q811yescharacteristic
93C4×C101C22⋊Q811yescharacteristic
94C4×C101#12411yescharacteristic
95C4×C101#12411yescharacteristic
96Dic101—41no—
97Dic101—41no—
98Dic101—42no—
99Dic101—81no—
100C2×C101#39311yescharacteristic
101C2×C101#45211yescharacteristic
102C2×C101#45211yescharacteristic
103C2×C101#47911yescharacteristic
104C2×C101#47911yescharacteristic
105C2×C101#48811yescharacteristic
106C2×C101#49111yescharacteristic
107#2026—1011nomaximal, Sylow
108C101#202611yescharacteristic, complemented, Sylow
109C2×#125—1011no—
110C2×#103—1011no—
111C2×#103D10111yescharacteristic
112#391—1011no—
113#340—1011no—
114#340—1011no—
115#336—1011no—
116C22×Q8C2×D10111yescharacteristic
117C22×C8—1011no—
118C22×C8C2×D10111yescharacteristic
119#125—2022no—
120#125—2022no—
121C2×C4⋊C4—1011no—
122C2×C4⋊C4—1011no—
123C2×C4⋊C4—2021no—
124C2×C4⋊C4—2021no—
125C2×C4⋊C4C2×D10111yescharacteristic
126C2×C42—1011no—
127#103—22no—
128#103—2022no—
129#95—2021no—
130#95—2021no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—21no—
135C2×Q8—21no—
136C2×Q8Dic20212yes—
137C22×C4—21no—
138C22×C4—21no—
139C22×C4—1011no—
140C22×C4—1011no—
141C22×C4—2021no—
142C22×C4—2021no—
143C22×C4C22×D10111yescharacteristic
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—21no—
147C2×C8—2021no—
148C2×C8—2021no—
149C2×C8—2021no—
150C4⋊C4—21no—
151C4⋊C4—1012no—
152C4⋊C4—2024no—
153C4⋊C4—2024no—
154C4⋊C4—2021no—
155C4⋊C4—2021no—
156C4⋊C4—2021no—
157C4⋊C4C22⋊D10112yes—
158C42—2021no—
159C42—2021no—
160C23D4×D10111yescharacteristic
161Q8—22no—
162Q8—22no—
163Q8—41no—
164Q8—41no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—4041no—
172C2×C4—4041no—
173C2×C4—4041no—
174C2×C4—4041no—
175C2×C4—4041no—
176C2×C4—2021no—
177C2×C4—2021no—
178C2×C4—2022no—
179C2×C4—2021no—
180C2×C4—2021no—
181C2×C4—2021no—
182C2×C4—2021no—
183C2×C4D4×D10111yescharacteristic
184C2×C4C2×C22⋊D10111yescharacteristic
185C2×C4C2×Dic20211yescharacteristic
186C2×C4#1310807311yescharacteristic
187C2×C4#1310807311yescharacteristic
188C2×C4#1310807411yescharacteristic
189C8—41no—
190C8—4041no—
191C22#1569222311yescharacteristic
192C22#1569223211yescharacteristic
193C22#1569224111yescharacteristic
194C22#1569227611yescharacteristic
195C22#1569227811yescharacteristic
196C22#1569228411yescharacteristic
197C22#1569228711yescharacteristic
198C4—42no—
199C4—42no—
200C4—8081no—
201C4—4041no—
202C4—4042no—
203C4—4041no—
204C4#1569223211yescharacteristic
205C4#1569223411yescharacteristic
206C4#1569224111yescharacteristic
207C4#1569224211yescharacteristic
208C2#2026508911yescharacteristic
209C2#2026533611yescharacteristic
210C2#2026533811yescharacteristic
211C2#2026548211yescharacteristic
212C2#2026548611yescharacteristic
213C2#2026553311yescharacteristic
214C2#2026554411yescharacteristic
subgroupG/H
centerC23D4×D101
commutator, cosocleC22×C4×C101C23
FrattiniC22×C4C22×D101
FittingC2×#103×C101C2
socle, prime radicalC23×C101C2×D4
hypercenterC2×#103D101
hypocenterC101#2026
LCSG ▷ C22×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
108. C101#2026semidirect

Maximal subgroups

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

subgroupindex
C2×#156922462
C2×#156921792
#202650842
#202649402
#202649392
#202649312
C2×#103×C1012
#2026101