Finite Group Databasebeta

← C2×#20295254 #28372591

Subgroups — C2×#20295254 #28372591

Order 13952.

564 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 157 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×#13182017C211yesmaximal, characteristic, complemented
2C22×C8×D109C211yesmaximal, characteristic, complemented
3C2×#16812679C211yesmaximal, characteristic, complemented
4C2×#16812670C211yesmaximal, characteristic
5#20295254C218yesmaximal, direct product factor
6C2×#16812630C211yesmaximal, characteristic, complemented
7C2×#16812624C211yesmaximal, characteristic, complemented
8C2×#102×C109C211yesmaximal, characteristic, complemented
9C22×Dic218C2211yescharacteristic
10C22×C22⋊D109—21no—
11C22×C4×D109C2211yescharacteristic
12C2×#13182017—24no—
13C2×#13182017C2214yescomplemented
14C22×#11724784C2211yescharacteristic
15C2×C8×D109—24no—
16C2×C8×D109C2214yescomplemented
17#16812679—22no—
18#16812679C2214yescomplemented
19#16812670—22no—
20#16812670C2214yes—
21C2×C4⋊Dic109—21no—
22C2×C4⋊Dic109C2211yescharacteristic
23C2×C22⋊Dic109—21no—
24C2×#13182006—21no—
25#16812630C2214yescomplemented
26#16812624C2214yescomplemented
27C22×D4×C109C2211yescharacteristic
28C22×C8×C109C2211yescharacteristic
29C2×C4⋊C4×C109C2211yescharacteristic
30#102×C109C2214yescomplemented
31C23×D109D411yescharacteristic
32C2×Dic218—22no—
33C2×Dic218—22no—
34C2×Dic218—21no—
35C2×Dic218C2312yes—
36C2×C22⋊D109—24no—
37C2×C22⋊D109—44no—
38C22×Dic109—21no—
39C22×Dic109—21no—
40C22×Dic109D411yescharacteristic
41C2×C4×D109—22no—
42C2×C4×D109—22no—
43C2×C4×D109D412yes—
44C2×C4×D109C2312yes—
45#13182017—28no—
46C2×#11724784D414yescomplemented
47C2×#11724784C2312yes—
48C8×D109—28no—
49C4⋊Dic109—21no—
50C4⋊Dic109—24no—
51C4⋊Dic109C2312yes—
52C22⋊Dic109—24no—
53#13182006—24no—
54C24×C109—21no—
55C2×D4×C109—22no—
56C2×D4×C109—21no—
57C2×D4×C109—22no—
58C2×D4×C109C2312yes—
59C22×C4×C109—21no—
60C22×C4×C109C2311yescharacteristic
61C2×C8×C109—22no—
62C2×C8×C109C2312yes—
63C4⋊C4×C109—21no—
64C4⋊C4×C109C2312yes—
65C23×C109—22no—
66C23×C109—42no—
67C23×C109—42no—
68C23×C109—42no—
69C23×C109C2×D411yescharacteristic
70C22×D109—22no—
71C22×D109—22no—
72C22×D109SD1614yescomplemented
73C22×D109C2×D412yes—
74D4×C109—22no—
75D4×C109—22no—
76D4×C109—42no—
77C2×C4×C109—22no—
78C2×C4×C109—42no—
79C2×C4×C109C2×D411yescharacteristic
80C2×C4×C109C2×D412yes—
81C2×C4×C109#4112yes—
82C2×C4×C109C2411yescharacteristic
83C22⋊D109—48no—
84C2×Dic109—22no—
85C2×Dic109—22no—
86C2×Dic109—22no—
87C2×Dic109—42no—
88C2×Dic109—42no—
89C2×Dic109C2×D412yes—
90C4×D109—24no—
91C4×D109—22no—
92C4×D109—22no—
93Dic218—22no—
94Dic218—22no—
95Dic218—42no—
96C8×C109—22no—
97#11724784C2×D414yescomplemented
98C22×C109—42no—
99C22×C109—42no—
100C22×C109—42no—
101C22×C109—84no—
102C22×C109#12112yes—
103C22×C109C2×SD1612yes—
104C22×C109#13512yes—
105C22×C109C22×D411yescharacteristic
106C2×D109—22no—
107C2×D109—22no—
108C2×D109—28no—
109C2×D109C2×SD1614yescomplemented
110C4×C109—42no—
111C4×C109#12112yes—
112C4×C109C22×D411yescharacteristic
113C4×C109C2×#4111yescharacteristic
114Dic109—22no—
115Dic109—42no—
116Dic109—42no—
117C2×C109—82no—
118C2×C109#46514yescomplemented
119C2×C109C2×#12111yescharacteristic
120C2×C109C22×SD1611yescharacteristic
121C2×C109C2×#13511yescharacteristic
122D109—24no—
123C2×#465—1091nomaximal, Sylow
124C109C2×#46511yescharacteristic, complemented, Sylow
125C22×SD16—1091no—
126C23×C8—1091no—
127C2×C22⋊Q8—1091no—
128C2×#121—1091no—
129#465—1098no—
130C2×#106—1091no—
131C2×#103—1091no—
132C2×#102D10911yescharacteristic, complemented
133C22×Q8—1091no—
134C22×D4—2181no—
135C22×D4C2×D10911yescharacteristic
136C23×C4—1091no—
137C2×SD16—1094no—
138C2×SD16—2184no—
139C22×C8—1091no—
140C22×C8—1094no—
141C22×C8—2184no—
142C22×C8C2×D10911yescharacteristic
143C22⋊Q8—1094no—
144C22⋊Q8—2182no—
145#121—1094no—
146#121—2182no—
147C2×C4⋊C4—1091no—
148C2×C4⋊C4—2181no—
149C2×C4⋊C4C2×D10911yescharacteristic
150C2×C22⋊C4—2181no—
151C2×C22⋊C4—2181no—
152#106—1094no—
153#103—1094no—
154#102C2×D10914yescomplemented
155C24—21no—
156C24—1091no—
157C2×Q8—1092no—
158C2×Q8—2182no—
159C2×Q8—2182no—
160C2×Q8—2181no—
161C2×D4—22no—
162C2×D4—21no—
163C2×D4—22no—
164C2×D4—4364no—
165C2×D4—2184no—
166C2×D4C22×D10912yes—
167C22×C4—21no—
168C22×C4—1091no—
169C22×C4—1092no—
170C22×C4—1092no—
171C22×C4—2181no—
172C22×C4—2181no—
173C22×C4—2182no—
174C22×C4—2182no—
175C22×C4C22×D10911yescharacteristic
176SD16—2188no—
177C2×C8—22no—
178C2×C8—1094no—
179C2×C8—1092no—
180C2×C8—2188no—
181C2×C8C22×D10912yes—
182C4⋊C4—21no—
183C4⋊C4—1092no—
184C4⋊C4—2184no—
185C4⋊C4—2181no—
186C4⋊C4C22×D10912yes—
187C22⋊C4—2184no—
188C22⋊C4—2184no—
189C23—22no—
190C23—42no—
191C23—42no—
192C23—42no—
193C23—1094no—
194C23—1092no—
195C23—2182no—
196C23—2182no—
197C23D4×D10911yescharacteristic
198Q8—4362no—
199Q8—2182no—
200Q8—2182no—
201D4—22no—
202D4—22no—
203D4—42no—
204D4—4368no—
205C2×C4—22no—
206C2×C4—42no—
207C2×C4—1092no—
208C2×C4—4362no—
209C2×C4—4362no—
210C2×C4—2182no—
211C2×C4—2182no—
212C2×C4—2182no—
213C2×C4—2184no—
214C2×C4—2182no—
215C2×C4—2182no—
216C2×C4D4×D10911yescharacteristic
217C2×C4D4×D10912yes—
218C2×C4#1318202912yes—
219C2×C4C23×D10911yescharacteristic
220C8—22no—
221C8—1094no—
222C22—42no—
223C22—42no—
224C22—42no—
225C22—84no—
226C22—1094no—
227C22—2188no—
228C22—2182no—
229C22—2182no—
230C22#1681267212yes—
231C22SD16×D10912yes—
232C22#1681271812yes—
233C22C2×D4×D10911yescharacteristic
234C4—42no—
235C4—4362no—
236C4—4362no—
237C4—2182no—
238C4#1681267212yes—
239C4C2×D4×D10911yescharacteristic
240C4C2×#1318202911yescharacteristic
241C2—82no—
242C2—2184no—
243C2#2029525414yesdirect product factor
244C2C2×#1681267211yescharacteristic
245C2C2×SD16×D10911yescharacteristic
246C2C2×#1681271811yescharacteristic
subgroupG/H
centerC23D4×D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
FittingC2×#102×C109C2
socleC23×C109C2×D4
prime radicalC2×#16812670C2
hypercenterC2×#102D109
hypocenterC109C2×#465
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C22×#13182017C2semidirect
2. C22×C8×D109C2semidirect
3. C2×#16812679C2semidirect
5. #20295254C2direct (N × H)
6. C2×#16812630C2semidirect
7. C2×#16812624C2semidirect
8. C2×#102×C109C2semidirect
13. C2×#13182017C22semidirect
16. C2×C8×D109C22semidirect
18. #16812679C22semidirect
25. #16812630C22semidirect
26. #16812624C22semidirect
30. #102×C109C22semidirect
46. C2×#11724784D4semidirect
72. C22×D109SD16semidirect
97. #11724784C2×D4semidirect
109. C2×D109C2×SD16semidirect
118. C2×C109#465semidirect
124. C109C2×#465semidirect
132. C2×#102D109semidirect
154. #102C2×D109semidirect
243. C2#20295254direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131820172
C22×C8×D1092
C2×#168126792
C2×#168126702
#202952542
C2×#168126302
C2×#168126242
C2×#102×C1092
C2×#465109