Finite Group Databasebeta

← C2×#20295273 #28372621

Subgroups — C2×#20295273 #28372621

Order 13952.

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

normal subgroups only

This group has 544 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×#13182018C211yesmaximal, characteristic, complemented
2C22×#13182012C211yesmaximal, characteristic, complemented
3C2×#16812679C211yesmaximal, characteristic, complemented
4C2×#16812674C211yesmaximal, characteristic
5#20295273C218yesmaximal, direct product factor
6C2×#16812622C211yesmaximal, characteristic, complemented
7C2×#16812619C211yesmaximal, characteristic, complemented
8C2×#107×C109C211yesmaximal, characteristic, complemented
9C22×Dic218C2211yescharacteristic
10C22×D436—21no—
11C22×D436C2211yescharacteristic
12C22×C4×D109C2211yescharacteristic
13C2×#13182018—24no—
14C2×#13182018C2214yescomplemented
15C2×#13182012—24no—
16C2×#13182012C2214yescomplemented
17C22×#11724784C2211yescharacteristic
18#16812679—22no—
19#16812679C2214yescomplemented
20#16812674—22no—
21#16812674C2214yes—
22C2×C4⋊Dic109—21no—
23C2×#13182006—21no—
24C2×#13182006—21no—
25#16812622C2214yescomplemented
26#16812619C2214yescomplemented
27C22×C8×C109C2211yescharacteristic
28C2×C4⋊C4×C109C2211yescharacteristic
29C2×C4⋊C4×C109C2211yescharacteristic
30#107×C109C2214yescomplemented
31C23×D109—21no—
32C23×D109D411yescharacteristic
33C2×Dic218—22no—
34C2×Dic218—22no—
35C2×Dic218—21no—
36C2×Dic218C2312yes—
37C2×D436—22no—
38C2×D436—22no—
39C2×D436—24no—
40C2×D436—21no—
41C2×D436—44no—
42C2×D436C2312yes—
43C22×Dic109—21no—
44C22×Dic109D411yescharacteristic
45C2×C4×D109—22no—
46C2×C4×D109—22no—
47C2×C4×D109D412yes—
48C2×C4×D109C2312yes—
49#13182018—28no—
50#13182012—28no—
51C2×#11724784—22no—
52C2×#11724784C2312yes—
53C4⋊Dic109—24no—
54#13182006—24no—
55#13182006—24no—
56C22×C4×C109—21no—
57C22×C4×C109—21no—
58C22×C4×C109C2311yescharacteristic
59C2×C8×C109D414yescomplemented
60C2×C8×C109C2312yes—
61C4⋊C4×C109—21no—
62C4⋊C4×C109—21no—
63C4⋊C4×C109C2312yes—
64C4⋊C4×C109C2312yes—
65C23×C109C2×D411yescharacteristic
66C22×D109—22no—
67C22×D109—22no—
68C22×D109—22no—
69C22×D109—22no—
70C22×D109—42no—
71C22×D109—42no—
72C22×D109—42no—
73C22×D109C2×D412yes—
74C2×C4×C109—22no—
75C2×C4×C109—22no—
76C2×C4×C109—42no—
77C2×C4×C109—42no—
78C2×C4×C109C2×D411yescharacteristic
79C2×C4×C109C2×D412yes—
80C2×C4×C109#4112yes—
81C2×C4×C109C2411yescharacteristic
82C2×Dic109—22no—
83C2×Dic109—22no—
84C2×Dic109—42no—
85C2×Dic109C2×D412yes—
86D436—22no—
87D436—22no—
88D436—48no—
89D436—42no—
90C4×D109—24no—
91C4×D109—22no—
92C4×D109—22no—
93Dic218—22no—
94Dic218—22no—
95Dic218—42no—
96C8×C109C2×D414yescomplemented
97#11724784—22no—
98C22×C109#12112yes—
99C22×C109AGL(1,ℤ/8)12yes—
100C22×C109#13712yes—
101C22×C109C22×D411yescharacteristic
102C2×D109—22no—
103C2×D109—22no—
104C2×D109—22no—
105C2×D109—44no—
106C2×D109—42no—
107C2×D109—42no—
108C2×D109—42no—
109C2×D109—84no—
110C4×C109—42no—
111C4×C109—42no—
112C4×C109#12112yes—
113C4×C109C22×D411yescharacteristic
114C4×C109C2×#4111yescharacteristic
115Dic109—22no—
116Dic109—42no—
117C2×C109#46814yescomplemented
118C2×C109C2×#12111yescharacteristic
119C2×C109C2×AGL(1,ℤ/8)11yescharacteristic
120C2×C109C2×#13711yescharacteristic
121D109—42no—
122D109—82no—
123C2×#468—1091nomaximal, Sylow
124C109C2×#46811yescharacteristic, complemented, Sylow
125C22×SD16—1091no—
126C22×M16—1091no—
127C2×C22⋊Q8—1091no—
128C2×#121—1091no—
129#468—1098no—
130C2×#107D10911yescharacteristic, complemented
131C2×#103—1091no—
132C2×#102—1091no—
133C22×Q8—1091no—
134C22×D4—1091no—
135C22×D4—2181no—
136C23×C4—1091no—
137C2×SD16—1094no—
138C2×SD16—2184no—
139C2×M16—1094no—
140C2×M16—2184no—
141C22×C8—1091no—
142C22×C8C2×D10911yescharacteristic
143C22⋊Q8—1094no—
144C22⋊Q8—2182no—
145#121—1094no—
146#121—2182no—
147C2×C4⋊C4—2181no—
148C2×C4⋊C4C2×D10911yescharacteristic
149C2×C4⋊C4C2×D10911yescharacteristic
150C2×C22⋊C4—2181no—
151C2×C22⋊C4—2181no—
152#107C2×D10914yescomplemented
153#103—1094no—
154#102—1094no—
155C24—1091no—
156C24—2181no—
157C2×Q8—1092no—
158C2×Q8—2182no—
159C2×Q8—2182no—
160C2×Q8—2181no—
161C2×D4—1092no—
162C2×D4—4364no—
163C2×D4—2184no—
164C2×D4—2181no—
165C2×D4—2182no—
166C2×D4—2182no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—1091no—
170C22×C4—1092no—
171C22×C4—1092no—
172C22×C4—2181no—
173C22×C4—2182no—
174C22×C4—2182no—
175C22×C4C22×D10911yescharacteristic
176SD16—2188no—
177M16—2188no—
178C2×C8—1092no—
179C2×C8—2182no—
180C2×C8D43614yescomplemented
181C2×C8C22×D10912yes—
182C4⋊C4—21no—
183C4⋊C4—21no—
184C4⋊C4—2184no—
185C4⋊C4C22×D10912yes—
186C4⋊C4C22×D10912yes—
187C22⋊C4—2184no—
188C22⋊C4—2184no—
189C23—1092no—
190C23—4362no—
191C23—4362no—
192C23—4362no—
193C23—2182no—
194C23—2182no—
195C23—2182no—
196C23—2182no—
197C23D4×D10911yescharacteristic
198Q8—4362no—
199Q8—2182no—
200Q8—2182no—
201D4—4368no—
202D4—4362no—
203D4—2182no—
204D4—2182no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—1092no—
210C2×C4—4362no—
211C2×C4—2182no—
212C2×C4—2182no—
213C2×C4—2184no—
214C2×C4—2182no—
215C2×C4—2182no—
216C2×C4D4×D10911yescharacteristic
217C2×C4C2×D43612yes—
218C2×C4#1318203012yes—
219C2×C4C23×D10911yescharacteristic
220C8—2182no—
221C8C2×D43614yescomplemented
222C22—8724no—
223C22—4362no—
224C22—4362no—
225C22—4362no—
226C22—4364no—
227C22—2182no—
228C22—2182no—
229C22—2182no—
230C22#1681267412yes—
231C22#1681272312yes—
232C22#1681273112yes—
233C22C2×D4×D10911yescharacteristic
234C4—42no—
235C4—42no—
236C4—4362no—
237C4—2182no—
238C4#1681267412yes—
239C4C22×D43611yescharacteristic
240C4C2×#1318203011yescharacteristic
241C2—8722no—
242C2—4362no—
243C2#2029527314yesdirect product factor
244C2C2×#1681267411yescharacteristic
245C2C2×#1681272311yescharacteristic
246C2C2×#1681273111yescharacteristic
subgroupG/H
centerC23D4×D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
FittingC2×#107×C109C2
socleC23×C109C2×D4
prime radicalC2×#16812674C2
hypercenterC2×#107D109
hypocenterC109C2×#468
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
1. C22×#13182018C2semidirect
2. C22×#13182012C2semidirect
3. C2×#16812679C2semidirect
5. #20295273C2direct (N × H)
6. C2×#16812622C2semidirect
7. C2×#16812619C2semidirect
8. C2×#107×C109C2semidirect
14. C2×#13182018C22semidirect
16. C2×#13182012C22semidirect
19. #16812679C22semidirect
25. #16812622C22semidirect
26. #16812619C22semidirect
30. #107×C109C22semidirect
59. C2×C8×C109D4semidirect
96. C8×C109C2×D4semidirect
117. C2×C109#468semidirect
124. C109C2×#468semidirect
130. C2×#107D109semidirect
152. #107C2×D109semidirect
180. C2×C8D436semidirect
221. C8C2×D436semidirect
243. C2#20295273direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131820182
C22×#131820122
C2×#168126792
C2×#168126742
#202952732
C2×#168126222
C2×#168126192
C2×#107×C1092
C2×#468109