Finite Group Databasebeta

← #27172826

Subgroups — #27172826

Order 12928.

230 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 65 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
1#20265748C211yesmaximal, characteristic
2#20265161C211yesmaximal, characteristic
3#20264975C214yesmaximal, complemented
4#413×C101C211yesmaximal, characteristic
5C22×Dic202C411yescharacteristic
6C2×#13108058—21no—
7#15692253C2212yes—
8#15692242C412yes—
9#15692236—21no—
10#15692236—21no—
11#15692234—21no—
12#15692234—21no—
13#15692214C411yescharacteristic
14#15692174C2212yes—
15#15692172—21no—
16C2×#41×C101C2211yescharacteristic
17C2×M16×C101—21no—
18#101×C101C2212yes—
19#100×C101—21no—
20C2×Dic202—21no—
21C2×Dic202—41no—
22C2×Dic202—41no—
23C2×Dic202C2×C412yes—
24C22×Dic101—21no—
25#13108058—22no—
26#13108058—41no—
27C2×#11717579—41no—
28C4⋊Dic101—21no—
29#13108053—22no—
30#13108053—22no—
31C22⋊Dic101—21no—
32C22⋊Dic101—22no—
33C22⋊Dic101—22no—
34C4×Dic101C2×C412yes—
35#41×C101—41no—
36#41×C101—41no—
37C2×Q8×C101C2311yescharacteristic
38C2×D4×C101C2×C411yescharacteristic
39C2×D4×C101D411yescharacteristic
40C2×D4×C101D411yescharacteristic
41C22×C4×C101C2×C411yescharacteristic
42C22×C4×C101D411yescharacteristic
43C22×C4×C101D411yescharacteristic
44M16×C101—22no—
45M16×C101—41no—
46C2×C8×C101—41no—
47C23×C101C22⋊C411yescharacteristic
48C23×C101C22⋊C411yescharacteristic
49C23×C101C22⋊C411yescharacteristic
50Q8×C101—41no—
51D4×C101—41no—
52D4×C101—41no—
53D4×C101—41no—
54C2×C4×C101—21no—
55C2×C4×C101—21no—
56C2×C4×C101—21no—
57C2×C4×C101—21no—
58C2×C4×C101—21no—
59C2×C4×C101—21no—
60C2×C4×C101C22⋊C411yescharacteristic
61C2×C4×C101C22×C411yescharacteristic
62C2×C4×C101C2×D411yescharacteristic
63C2×C4×C101C2×D411yescharacteristic
64C2×Dic101—22no—
65C2×Dic101—22no—
66C2×Dic101—42no—
67Dic202—41no—
68Dic202—41no—
69Dic202—42no—
70C8×C101—42no—
71#11717579—42no—
72C22×C101—21no—
73C22×C101—21no—
74C22×C101—21no—
75C22×C101—41no—
76C22×C101—41no—
77C22×C101—41no—
78C22×C101C2×C22⋊C411yescharacteristic
79C4×C101—21no—
80C4×C101—21no—
81C4×C101—21no—
82C4×C101#9911yescharacteristic
83C4×C101#9911yescharacteristic
84Dic101—42no—
85Dic101—42no—
86C2×C101—21no—
87C2×C101—41no—
88C2×C101—41no—
89C2×C101—41no—
90C2×C101C2×#9911yescharacteristic
91#2135—1011nomaximal, Sylow
92C101#213511yescharacteristic, complemented, Sylow
93#536—1011no—
94#413—1011no—
95#413D10111yescharacteristic
96#356—1014no—
97C2×#41C2×D10111yescharacteristic
98C22×Q8—1011no—
99C2×M16—21no—
100C2×M16—2021no—
101C4⋊Q8—1012no—
102#124—1012no—
103#123—2021no—
104#123—2021no—
105C22⋊Q8—2021no—
106C22⋊Q8—2021no—
107#117—1011no—
108#101—1012no—
109#101C2×D10112yes—
110#100—21no—
111#100—2021no—
112#41—41no—
113#41—41no—
114C2×Q8—1012no—
115C2×Q8—4041no—
116C2×Q8—4041no—
117C2×Q8—2021no—
118C2×Q8C22×D10111yescharacteristic
119C2×D4C4×D10111yescharacteristic
120C2×D4D40411yescharacteristic
121C2×D4C22⋊D10111yescharacteristic
122C22×C4—2021no—
123C22×C4C4×D10111yescharacteristic
124C22×C4D40411yescharacteristic
125C22×C4C22⋊D10111yescharacteristic
126M16—22no—
127M16—41no—
128M16—4041no—
129M16—2022no—
130C2×C8—41no—
131C2×C8—4041no—
132C4⋊C4—2021no—
133C4⋊C4—2022no—
134C4⋊C4—2022no—
135C22⋊C4—2021no—
136C22⋊C4—2022no—
137C22⋊C4—2022no—
138C42—1012no—
139C23#1310805111yescharacteristic
140C23#1310805111yescharacteristic
141C23#1310805111yescharacteristic
142Q8—41no—
143Q8—4042no—
144Q8—4041no—
145Q8—4041no—
146D4—41no—
147D4—41no—
148D4—41no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—4042no—
156C2×C4—2022no—
157C2×C4—2022no—
158C2×C4#1310805111yescharacteristic
159C2×C4C2×C4×D10111yescharacteristic
160C2×C4C2×C22⋊D10111yescharacteristic
161C2×C4C2×D40411yescharacteristic
162C8—42no—
163C8—4042no—
164C22—21no—
165C22—21no—
166C22—21no—
167C22—41no—
168C22—41no—
169C22—41no—
170C22C2×#1310805111yescharacteristic
171C4—21no—
172C4—21no—
173C4—21no—
174C4—4042no—
175C4—4042no—
176C4#1569216911yescharacteristic
177C4#1569216911yescharacteristic
178C2—21no—
179C2—41no—
180C2—41no—
181C2—41no—
182C2C2×#1569216911yescharacteristic
subgroupG/H
centerC2C2×#15692169
commutatorC2×C4×C101C22×C4
FrattiniC2×Q8C22×D101
Fitting#413×C101C2
socleC2×C101C2×#99
prime radicalC2×#41×C101C22
cosocleC2×Q8×C101C23
hypercenter#413D101
hypocenterC101#2135
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
3. #20264975C2semidirect
92. C101#2135semidirect

Maximal subgroups

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

subgroupindex
#202657482
#202651612
#202649752
#413×C1012
#2135101