Finite Group Databasebeta

← #27171524

Subgroups — #27171524

Order 12928.

324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 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×#15692255C211yesmaximal, characteristic
2#20265654C211yesmaximal, characteristic
3#20265187C211yesmaximal, characteristic
4#20265185C211yesmaximal, characteristic
5C2×#15692173C211yesmaximal, characteristic
6#20264937C211yesmaximal, characteristic
7#339×C101C211yesmaximal, characteristic
8C22×Dic202C2211yescharacteristic
9C22×Dic202C2211yescharacteristic
10C2×#13108058C2211yescharacteristic
11#15692255—22no—
12#15692255C414yescomplemented
13C4×Dic202—22no—
14#15692220—22no—
15#15692214C2211yescharacteristic
16#15692211—22no—
17C2×C4⋊Dic101—22no—
18#15692180—22no—
19#15692178—22no—
20#15692173—22no—
21C2×M16×C101C2211yescharacteristic
22#117×C101C2211yescharacteristic
23C2×C42×C101C2211yescharacteristic
24C2×Dic202—21no—
25C2×Dic202—21no—
26C2×Dic202—21no—
27C2×Dic202—21no—
28C2×Dic202—21no—
29C2×Dic202—21no—
30C2×Dic202—21no—
31C2×Dic202—21no—
32C2×Dic202—21no—
33C2×Dic202C2×C412yes—
34C2×Dic202C2×C412yes—
35C2×Dic202D412yes—
36C22×Dic101—21no—
37C22×Dic101D412yes—
38#13108058—21no—
39#13108058—21no—
40C2×#11717579—21no—
41C4⋊Dic101—28no—
42C4⋊Dic101D412yes—
43#13108053—24no—
44C22⋊Dic101—21no—
45C4×Dic101—24no—
46C4×Dic101—21no—
47C22×C4×C101—21no—
48C22×C4×C101C2311yescharacteristic
49M16×C101—21no—
50M16×C101—21no—
51C2×C8×C101—21no—
52C4⋊C4×C101D412yes—
53C22⋊C4×C101—21no—
54C42×C101—21no—
55C42×C101—21no—
56C42×C101C2×C412yes—
57C23×C101C2×D411yescharacteristic
58C2×C4×C101—24no—
59C2×C4×C101—22no—
60C2×C4×C101—22no—
61C2×C4×C101C22×C411yescharacteristic
62C2×C4×C101C2×D411yescharacteristic
63C2×C4×C101C2×D411yescharacteristic
64C2×C4×C101C2×D411yescharacteristic
65C2×C4×C101#4111yescharacteristic
66C2×C4×C101#4111yescharacteristic
67C2×Dic101—22no—
68C2×Dic101—22no—
69C2×Dic101—22no—
70C2×Dic101—22no—
71C2×Dic101—41no—
72C2×Dic101—41no—
73C2×Dic101C22⋊C414yes—
74Dic202—22no—
75Dic202—22no—
76Dic202—22no—
77Dic202—22no—
78Dic202—22no—
79Dic202—22no—
80Dic202—41no—
81Dic202—41no—
82C8×C101—41no—
83#11717579—41no—
84C22×C101—22no—
85C22×C101C2×C22⋊C411yescharacteristic
86C22×C101#12011yescharacteristic
87C22×C101#12311yescharacteristic
88C4×C101—24no—
89C4×C101—42no—
90C4×C101C4×D411yescharacteristic
91C4×C101C4×D411yescharacteristic
92C4×C101#12111yescharacteristic
93C4×C101#12111yescharacteristic
94Dic101—24no—
95Dic101—42no—
96Dic101—42no—
97C2×C101—21no—
98C2×C101—21no—
99C2×C101#38611yescharacteristic
100C2×C101#45612yes—
101#1886—1011nomaximal, Sylow
102C101#188611yescharacteristic, complemented, Sylow
103C2×C4⋊Q8—1011no—
104#519—1011no—
105#419—1011no—
106#419—1011no—
107C2×#101—1011no—
108#339—1011no—
109#339D10111yescharacteristic
110C22×Q8—1011no—
111C22×Q8—1011no—
112C2×M16—1011no—
113C2×M16C2×D10111yescharacteristic
114C4⋊Q8—1014no—
115C4⋊Q8—2022no—
116C4×Q8—2022no—
117C4×Q8—2022no—
118#117—1011no—
119#117—2022no—
120#117C2×D10111yescharacteristic
121C2×C4⋊C4—2022no—
122C2×C42C2×D10111yescharacteristic
123#103—2022no—
124#103—2022no—
125#101—2022no—
126C2×Q8—1012no—
127C2×Q8—1012no—
128C2×Q8—1012no—
129C2×Q8—2021no—
130C2×Q8—2021no—
131C2×Q8—2021no—
132C2×Q8—2021no—
133C2×Q8—2021no—
134C2×Q8—2021no—
135C2×Q8—2021no—
136C2×Q8—2021no—
137C2×Q8—2021no—
138C22×C4—21no—
139C22×C4—1012no—
140C22×C4—2021no—
141C22×C4C22×D10111yescharacteristic
142M16—21no—
143M16—21no—
144M16—2021no—
145M16—2021no—
146C2×C8—21no—
147C2×C8—2021no—
148C4⋊C4—1012no—
149C4⋊C4—2028no—
150C4⋊C4—2024no—
151C4⋊C4D40412yes—
152C22⋊C4—21no—
153C22⋊C4—2021no—
154C42—21no—
155C42—21no—
156C42—2024no—
157C42—2021no—
158C42C4×D10112yes—
159C23D4×D10111yescharacteristic
160Q8—4041no—
161Q8—4041no—
162Q8—2022no—
163Q8—2022no—
164Q8—2022no—
165Q8—2022no—
166Q8—2022no—
167Q8—2022no—
168C2×C4—24no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—1014no—
172C2×C4—4041no—
173C2×C4—4041no—
174C2×C4—2022no—
175C2×C4—2022no—
176C2×C4—2022no—
177C2×C4—2022no—
178C2×C4C2×C4×D10111yescharacteristic
179C2×C4D4×D10111yescharacteristic
180C2×C4D4×D10111yescharacteristic
181C2×C4C2×D40411yescharacteristic
182C2×C4#1310807411yescharacteristic
183C2×C4#1310807511yescharacteristic
184C8—41no—
185C8—4041no—
186C22—22no—
187C22C22⋊C4×D10111yescharacteristic
188C22#1569222511yescharacteristic
189C22#1569224011yescharacteristic
190C4—24no—
191C4—42no—
192C4—4042no—
193C4—4042no—
194C4—2024no—
195C4#1569221711yescharacteristic
196C4C4×D40411yescharacteristic
197C4#1569222811yescharacteristic
198C4#1569223011yescharacteristic
199C2—21no—
200C2—21no—
201C2#2026505511yescharacteristic
202C2#2026536112yes—
subgroupG/H
centerC22#15692225
commutatorC2×C4×C101C22×C4
FrattiniC22×C4C22×D101
Fitting#339×C101C2
socleC22×C101#120
prime radicalC23×C101C2×D4
cosocleC22×C4×C101C23
hypercenter#339D101
hypocenterC101#1886
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
12. #15692255C4semidirect
102. C101#1886semidirect

Maximal subgroups

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

subgroupindex
C2×#156922552
#202656542
#202651872
#202651852
C2×#156921732
#202649372
#339×C1012
#1886101