Finite Group Databasebeta

← #28362957

Subgroups — #28362957

Order 13952.

584 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C22×#13182028C211yesmaximal, characteristic
2C2×#16812617C212yesmaximal, complemented
3C2×#16812616C211yesmaximal, characteristic, complemented
4#20294989C212yesmaximal, complemented
5C2×#100×C109C211yesmaximal, characteristic, complemented
6C2×#13182028—24no—
7C2×#13182028—24no—
8C2×#13182028—22no—
9C2×#13182028—22no—
10C22×Dic218C2211yescharacteristic
11C22×C22⋊D109C412yes—
12C23×Dic109C412yes—
13C22×C4×D109C2211yescharacteristic
14C2×#13182013C2212yes—
15#16812617—24no—
16#16812616—22no—
17#16812611—24no—
18C22×D4×C109C2211yescharacteristic
19C2×M16×C109C2212yes—
20#100×C109—22no—
21C23×D109C2×C411yescharacteristic
22#13182028—216no—
23#13182028—216no—
24C2×Dic218—22no—
25C2×Dic218—21no—
26C2×Dic218—21no—
27C2×Dic218D414yes—
28C2×C22⋊D109—24no—
29C2×C22⋊D109—24no—
30C2×C22⋊D109—24no—
31C22×Dic109—24no—
32C22×Dic109—24no—
33C22×Dic109—24no—
34C22×Dic109C2×C411yescharacteristic
35C22×Dic109C2×C412yes—
36C2×C4×D109—22no—
37C2×C4×D109—21no—
38C2×C4×D109—21no—
39C2×C4×D109D414yes—
40#13182013—22no—
41#13182013—22no—
42C2×#11724784—22no—
43C24×C109C2×C412yes—
44C2×D4×C109—22no—
45C2×D4×C109—22no—
46C2×D4×C109D412yes—
47C2×D4×C109D412yes—
48C22×C4×C109C2311yescharacteristic
49M16×C109—22no—
50M16×C109—22no—
51C2×C8×C109—22no—
52C23×C109—22no—
53C23×C109—22no—
54C23×C109—44no—
55C23×C109C22⋊C414yes—
56C23×C109C22×C411yescharacteristic
57C22×D109—21no—
58C22×D109—21no—
59C22×D109—42no—
60C22×D109C22⋊C412yes—
61D4×C109—24no—
62D4×C109—24no—
63C2×C4×C109C2×D412yes—
64C2×C4×C109C2×D412yes—
65C2×C4×C109C2×D411yescharacteristic
66C2×C4×C109C2×D411yescharacteristic
67C22⋊D109—216no—
68C2×Dic109—216no—
69C2×Dic109—21no—
70C2×Dic109—21no—
71C2×Dic109—22no—
72C2×Dic109—22no—
73C2×Dic109C22⋊C412yes—
74C2×Dic109C22⋊C414yes—
75C4×D109—24no—
76C4×D109—24no—
77Dic218—24no—
78Dic218—24no—
79C8×C109—42no—
80#11724784—42no—
81C22×C109—22no—
82C22×C109—24no—
83C22×C109—44no—
84C22×C109—44no—
85C22×C109—44no—
86C22×C109C2×C22⋊C411yescharacteristic
87C22×C109C2×C22⋊C411yescharacteristic
88C22×C109C2×C22⋊C411yescharacteristic
89C2×D109—22no—
90C2×D109—24no—
91C2×D109—42no—
92C2×D109—42no—
93C4×C109#12012yes—
94C4×C109#12012yes—
95Dic109—24no—
96Dic109—22no—
97C2×C109—21no—
98C2×C109—21no—
99C2×C109—44no—
100C2×C109#37911yescharacteristic
101C2×C109#41312yes—
102D109—42no—
103#1785—1091nomaximal, Sylow
104C109#178511yescharacteristic, complemented, Sylow
105C22×#41—1091no—
106C2×#101—1092no—
107C2×#100—1091no—
108C2×#100D10911yescharacteristic, complemented
109#407—1092no—
110C2×#41—2184no—
111C2×#41—2184no—
112C2×#41—2182no—
113C2×#41—2182no—
114C22×Q8—1091no—
115C22×D4—1092no—
116C22×D4C2×D10911yescharacteristic
117C23×C4—1091no—
118C23×C4—1092no—
119C2×M16—1092no—
120C2×M16C2×D10912yes—
121#101—2184no—
122#100—22no—
123#100—2182no—
124C22⋊C8—2184no—
125C24—1091no—
126C24C4×D10912yes—
127#41—21816no—
128#41—21816no—
129C2×Q8—1094no—
130C2×Q8—2182no—
131C2×Q8—2181no—
132C2×Q8—2181no—
133C2×D4—22no—
134C2×D4—22no—
135C2×D4—2184no—
136C2×D4—2184no—
137C2×D4—2184no—
138C2×D4D43612yes—
139C2×D4C22⋊D10912yes—
140C22×C4—1091no—
141C22×C4—1092no—
142C22×C4—1094no—
143C22×C4—2184no—
144C22×C4—2184no—
145C22×C4—2184no—
146C22×C4—2182no—
147C22×C4—2181no—
148C22×C4—2181no—
149C22×C4C22×D10911yescharacteristic
150M16—22no—
151M16—22no—
152M16—2182no—
153M16—2182no—
154C2×C8—22no—
155C2×C8—2182no—
156C23—22no—
157C23—22no—
158C23—44no—
159C23—1092no—
160C23—4362no—
161C23—2181no—
162C23—2181no—
163C23#1318200614yes—
164C23C2×C4×D10911yescharacteristic
165Q8—2184no—
166Q8—2184no—
167D4—24no—
168D4—24no—
169D4—21816no—
170C2×C4—1094no—
171C2×C4—1092no—
172C2×C4—21816no—
173C2×C4—2181no—
174C2×C4—2182no—
175C2×C4—2181no—
176C2×C4—2182no—
177C2×C4—2184no—
178C2×C4—2184no—
179C2×C4D4×D10912yes—
180C2×C4D4×D10912yes—
181C2×C4C2×C22⋊D10911yescharacteristic
182C2×C4C2×D43611yescharacteristic
183C8—42no—
184C8—4362no—
185C22—22no—
186C22—24no—
187C22—44no—
188C22—44no—
189C22—44no—
190C22—4362no—
191C22—4362no—
192C22—2184no—
193C22—2182no—
194C22C22⋊C4×D10911yescharacteristic
195C22C22⋊C4×D10911yescharacteristic
196C22C2×#1318200611yescharacteristic
197C4—2182no—
198C4—2184no—
199C4#1681266712yes—
200C4#1681266912yes—
201C2—21no—
202C2—21no—
203C2—44no—
204C2—4362no—
205C2#2029488111yescharacteristic
206C2#2029500712yes—
subgroupG/H
centerC22C22⋊C4×D109
commutatorC23×C109C22×C4
FrattiniC22×C4C22×D109
FittingC2×#100×C109C2
socleC22×C109C2×C22⋊C4
prime radicalC22×#13182028C2
cosocleC22×C4×C109C23
hypercenterC2×#100D109
hypocenterC109#1785
LCSG ▷ C23×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
2. C2×#16812617C2semidirect
3. C2×#16812616C2semidirect
4. #20294989C2semidirect
5. C2×#100×C109C2semidirect
104. C109#1785semidirect
108. C2×#100D109semidirect

Maximal subgroups

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

subgroupindex
C22×#131820282
C2×#168126172
C2×#168126162
#202949892
C2×#100×C1092
#1785109