Finite Group Databasebeta

← #28379223

Subgroups — #28379223

Order 13952.

324 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 72 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#20295968C211yesmaximal, characteristic
2C4×C22⋊#89137C211yesmaximal, characteristic
3#20295904C212yesmaximal
4#20295904C212yesmaximal
5C2×#16812677C211yesmaximal, characteristic
6C2×C4⋊#89137—21no—
7C2×C22⋊#89137C2212yes—
8C2×C22⋊#89137C2212yes—
9C2×C4×#89137—21no—
10(C2×#89137)⋊C4—21no—
11(C2×#89137)⋊C4—21no—
12C22×Dic218C411yescharacteristic, complemented
13C22×C4×D109C2211yescharacteristic
14#16812677—21no—
15#16812677—21no—
16#16812677—21no—
17#16812677—21no—
18C2×#13182008C411yescharacteristic, complemented
19C2×#13182008C411yescharacteristic, complemented
20C2×#13182006C2211yescharacteristic
21C2×#13182006C2211yescharacteristic
22C2×C4⋊C4×C109C411yescharacteristic, complemented
23C22×#89137—22no—
24C22×#89137—22no—
25C4⋊#89137—42no—
26C22⋊#89137—22no—
27C22⋊#89137—24no—
28C22⋊#89137Q814yescomplemented
29C4×#89137—42no—
30C23×D109C2311yescharacteristic
31C2×Dic218—21no—
32C2×Dic218—21no—
33C2×Dic218—42no—
34C22×Dic109C2×C411yescharacteristic
35C22×Dic109C2×C411yescharacteristic
36C22×Dic109C2×C411yescharacteristic
37C2×C4×D109—42no—
38C2×C4×D109D411yescharacteristic
39C2×C4×D109D411yescharacteristic
40C2×C4×D109D411yescharacteristic
41C2×C4×D109D411yescharacteristic
42#13182008—21no—
43#13182008—21no—
44#13182008—21no—
45#13182008—21no—
46#13182006—21no—
47#13182006—21no—
48#13182006—21no—
49#13182006—21no—
50C22×C4×C109C2×C411yescharacteristic
51C22×C4×C109C2×C411yescharacteristic
52C22×C4×C109C2×C411yescharacteristic
53C4⋊C4×C109—21no—
54C4⋊C4×C109—21no—
55C23×C109C22×C411yescharacteristic
56C22×D109—41no—
57C22×D109—41no—
58C22×D109C2×D411yescharacteristic
59C22×D109C2×D411yescharacteristic
60C22×D109C2×Q812yes—
61C22×D109#4112yes—
62C2×#89137—24no—
63C2×#89137—42no—
64C2×#89137—42no—
65C2×#89137—42no—
66C2×#89137—42no—
67C2×#89137—42no—
68C2×C4×C109—21no—
69C2×C4×C109—21no—
70C2×C4×C109—41no—
71C2×C4×C109—41no—
72C2×C4×C109—41no—
73C2×C4×C109C22⋊C411yescharacteristic
74C2×C4×C109C22⋊C411yescharacteristic
75C2×Dic109—22no—
76C2×Dic109—21no—
77C2×Dic109—21no—
78C2×Dic109—41no—
79C2×Dic109—41no—
80C2×Dic109C22⋊C411yescharacteristic
81C2×Dic109C22⋊C411yescharacteristic
82C4×D109—22no—
83C4×D109—22no—
84C4×D109—41no—
85C4×D109—41no—
86Dic218—42no—
87Dic218—42no—
88C22×C109—21no—
89C22×C109—21no—
90C22×C109C2×C22⋊C411yescharacteristic
91C22×C109C4×Q812yes—
92C2×D109—21no—
93C2×D109—21no—
94C2×D109—21no—
95C2×D109—21no—
96C2×D109—42no—
97C2×D109—42no—
98C2×D109C22⋊Q812yes—
99C2×D109#12411yescharacteristic
100C2×D109C4⋊Q811yescharacteristic
101#89137—44no—
102#89137—82no—
103C4×C109—21no—
104C4×C109—21no—
105C4×C109—41no—
106C4×C109—41no—
107Dic109—21no—
108Dic109—41no—
109Dic109—41no—
110Dic109#9912yes—
111C2×C109—22no—
112C2×C109#39111yescharacteristic
113C2×C109C2×#9911yescharacteristic
114C2×C109#41011yescharacteristic
115D109—22no—
116D109—21no—
117D109—21no—
118#1996—1091nomaximal, Sylow
119C109#199611yescharacteristic, complemented, Sylow
120C2×C22⋊Q8—1091no—
121#380—1091no—
122C4×C22⋊C4—1091no—
123#342—1092no—
124#342—1092no—
125C22×Q8—1091no—
126C23×C4—1091no—
127C22⋊Q8—2181no—
128C22⋊Q8—2181no—
129C22⋊Q8—2181no—
130C22⋊Q8—2181no—
131C2×C4⋊C4—1091no—
132C2×C4⋊C4—1091no—
133C2×C4⋊C4—2181no—
134C2×C4⋊C4#8913711yescharacteristic, complemented
135C2×C22⋊C4—1092no—
136C2×C22⋊C4—1091no—
137C2×C22⋊C4—1091no—
138C2×C22⋊C4—1092no—
139C2×C42—2181no—
140#95—2181no—
141#95—2181no—
142C24—1091no—
143C2×Q8—4362no—
144C2×Q8—2181no—
145C2×Q8—2181no—
146C22×C4—1091no—
147C22×C4—1091no—
148C22×C4—1091no—
149C22×C4—1091no—
150C22×C4—1091no—
151C22×C4—1091no—
152C22×C4—1091no—
153C22×C4—4362no—
154C22×C4—2182no—
155C22×C4—2182no—
156C22×C4C2×#8913711yescharacteristic
157C22×C4C2×#8913711yescharacteristic
158C22×C4C2×#8913711yescharacteristic
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—4362no—
162C4⋊C4—2181no—
163C4⋊C4—2181no—
164C4⋊C4—2181no—
165C4⋊C4—2181no—
166C22⋊C4—1094no—
167C22⋊C4—2181no—
168C22⋊C4—2181no—
169C22⋊C4—2181no—
170C22⋊C4—2181no—
171C22⋊C4—2184no—
172C22⋊C4—2182no—
173C42—4362no—
174C23—1092no—
175C23—1092no—
176C23—1091no—
177C23—1091no—
178C23—4361no—
179C23—4361no—
180C23C22×#8913711yescharacteristic
181Q8—4362no—
182Q8—4362no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—1091no—
189C2×C4—1091no—
190C2×C4—4361no—
191C2×C4—4361no—
192C2×C4—4362no—
193C2×C4—4362no—
194C2×C4—4362no—
195C2×C4—4362no—
196C2×C4—4362no—
197C2×C4—4361no—
198C2×C4—4361no—
199C2×C4—2182no—
200C2×C4—2182no—
201C2×C4—2182no—
202C2×C4—2184no—
203C2×C4—2181no—
204C2×C4—2181no—
205C2×C4C22⋊#8913711yescharacteristic
206C2×C4C22⋊#8913711yescharacteristic
207C22—21no—
208C22—21no—
209C22—1091no—
210C22—1092no—
211C22—1091no—
212C22—4362no—
213C22—4362no—
214C22—2181no—
215C22—2181no—
216C22—2181no—
217C22—2181no—
218C22C2×C22⋊#8913711yescharacteristic
219C22Q8×#8913712yes—
220C4—21no—
221C4—21no—
222C4—41no—
223C4—41no—
224C4—8722no—
225C4—1092no—
226C4—4364no—
227C4—4361no—
228C4—4361no—
229C4—2181no—
230C2—22no—
231C2—2181no—
232C2—2182no—
233C2—2181no—
234C2(C2×#89137)⋊Q811yescharacteristic
235C2D109⋊#9911yescharacteristic
236C2#2029600511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC23×C109C22×C4
FrattiniC23C22×#89137
FittingC2×C4⋊C4×C109C4
socleC22×C109C2×C22⋊C4
prime radical, cosocleC23×D109C23
hypercenterC2×C4⋊C4#89137
hypocenterC109#1996
LCSG ▷ C23×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
12. C22×Dic218C4semidirect
18. C2×#13182008C4semidirect
19. C2×#13182008C4semidirect
22. C2×C4⋊C4×C109C4semidirect
28. C22⋊#89137Q8semidirect
119. C109#1996semidirect
134. C2×C4⋊C4#89137semidirect

Maximal subgroups

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

subgroupindex
#202959682
C4×C22⋊#891372
#202959042
C2×#168126772
#1996109