Finite Group Databasebeta

← C2×#34036374 #49168372

Subgroups — C2×#34036374 #49168372

Order 37504.

544 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 149 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×#17989790C211yesmaximal, characteristic, complemented
2C22×#17989785C211yesmaximal, characteristic, complemented
3C2×#22627604C211yesmaximal, characteristic, complemented
4C2×#22627595C211yesmaximal, characteristic
5#34036374C218yesmaximal, direct product factor
6C2×#22627557C211yesmaximal, characteristic, complemented
7C2×#22627549C211yesmaximal, characteristic, complemented
8C2×#102×C293C211yesmaximal, characteristic, complemented
9C22×Dic586C2211yescharacteristic
10C22×C22⋊D293—21no—
11C22×C4×D293C2211yescharacteristic
12C2×#17989790—24no—
13C2×#17989790C2214yescomplemented
14C2×#17989785—24no—
15C2×#17989785C2214yescomplemented
16C22×#14556873C2211yescharacteristic
17#22627604—22no—
18#22627604C2214yescomplemented
19#22627595—22no—
20#22627595C2214yes—
21C2×C4⋊Dic293—21no—
22C2×C4⋊Dic293C2211yescharacteristic
23C2×C22⋊Dic293—21no—
24C2×#17989779—21no—
25#22627557C2214yescomplemented
26#22627549C2214yescomplemented
27C22×D4×C293C2211yescharacteristic
28C22×C8×C293C2211yescharacteristic
29C2×C4⋊C4×C293C2211yescharacteristic
30#102×C293C2214yescomplemented
31C23×D293D411yescharacteristic
32C2×Dic586—21no—
33C2×Dic586—22no—
34C2×Dic586—22no—
35C2×Dic586C2312yes—
36C2×C22⋊D293—24no—
37C2×C22⋊D293—44no—
38C22×Dic293—21no—
39C22×Dic293—21no—
40C22×Dic293D411yescharacteristic
41C2×C4×D293—22no—
42C2×C4×D293—22no—
43C2×C4×D293D412yes—
44C2×C4×D293C2312yes—
45#17989790—28no—
46#17989785—28no—
47C2×#14556873D414yescomplemented
48C2×#14556873C2312yes—
49C4⋊Dic293—24no—
50C4⋊Dic293—21no—
51C4⋊Dic293C2312yes—
52C22⋊Dic293—24no—
53#17989779—24no—
54C24×C293—21no—
55C2×D4×C293—22no—
56C2×D4×C293—21no—
57C2×D4×C293—22no—
58C2×D4×C293C2312yes—
59C22×C4×C293—21no—
60C22×C4×C293C2311yescharacteristic
61C2×C8×C293—22no—
62C2×C8×C293C2312yes—
63C4⋊C4×C293—21no—
64C4⋊C4×C293C2312yes—
65C22×D293—22no—
66C22×D293—22no—
67C22×D293—22no—
68C22×D293C2×D412yes—
69Dic586—22no—
70Dic586—22no—
71Dic586—42no—
72C22⋊D293—48no—
73C2×Dic293—22no—
74C2×Dic293—22no—
75C2×Dic293—22no—
76C2×Dic293—42no—
77C2×Dic293—42no—
78C2×Dic293C2×D412yes—
79C4×D293—24no—
80C4×D293—22no—
81C4×D293—22no—
82#14556873C2×D414yescomplemented
83C23×C293—22no—
84C23×C293—42no—
85C23×C293—42no—
86C23×C293—42no—
87C23×C293C2×D411yescharacteristic
88D4×C293—22no—
89D4×C293—22no—
90D4×C293—42no—
91C2×C4×C293—22no—
92C2×C4×C293—42no—
93C2×C4×C293C2×D411yescharacteristic
94C2×C4×C293C2×D412yes—
95C2×C4×C293#4112yes—
96C2×C4×C293C2411yescharacteristic
97C8×C293—22no—
98C22×C293—42no—
99C22×C293—42no—
100C22×C293—42no—
101C22×C293—84no—
102C22×C293#12112yes—
103C22×C293AGL(1,ℤ/8)12yes—
104C22×C293#13712yes—
105C22×C293C22×D411yescharacteristic
106C2×D293—22no—
107C2×D293—22no—
108C2×D293—22no—
109C2×D293—44no—
110C4×C293—42no—
111C4×C293#12112yes—
112C4×C293C22×D411yescharacteristic
113C4×C293C2×#4111yescharacteristic
114Dic293—22no—
115Dic293—42no—
116Dic293—42no—
117C2×C293—82no—
118C2×C293#46814yescomplemented
119C2×C293C2×#12111yescharacteristic
120C2×C293C2×AGL(1,ℤ/8)11yescharacteristic
121C2×C293C2×#13711yescharacteristic
122D293—42no—
123C293C2×#46811yescharacteristic, complemented, Sylow
124C2×#468—2931nomaximal, Sylow
125C22×SD16—2931no—
126C22×M16—2931no—
127C2×C22⋊Q8—2931no—
128C2×#121—2931no—
129#468—2938no—
130C2×#107—2931no—
131C2×#103—2931no—
132C2×#102D29311yescharacteristic, complemented
133C22×Q8—2931no—
134C22×D4—5861no—
135C22×D4C2×D29311yescharacteristic
136C23×C4—2931no—
137C2×SD16—2934no—
138C2×SD16—5864no—
139C2×M16—2934no—
140C2×M16—5864no—
141C22×C8—2931no—
142C22×C8C2×D29311yescharacteristic
143C22⋊Q8—2934no—
144C22⋊Q8—5862no—
145#121—2934no—
146#121—5862no—
147C2×C4⋊C4—2931no—
148C2×C4⋊C4—5861no—
149C2×C4⋊C4C2×D29311yescharacteristic
150C2×C22⋊C4—5861no—
151C2×C22⋊C4—5861no—
152#107—2934no—
153#103—2934no—
154#102C2×D29314yescomplemented
155C24—21no—
156C24—2931no—
157C2×Q8—2932no—
158C2×Q8—5861no—
159C2×Q8—5862no—
160C2×Q8—5862no—
161C2×D4—22no—
162C2×D4—21no—
163C2×D4—22no—
164C2×D4—5864no—
165C2×D4—11724no—
166C2×D4C22×D29312yes—
167C22×C4—21no—
168C22×C4—2931no—
169C22×C4—2932no—
170C22×C4—2932no—
171C22×C4—5862no—
172C22×C4—5862no—
173C22×C4—5861no—
174C22×C4—5861no—
175C22×C4C22×D29311yescharacteristic
176SD16—5868no—
177M16—5868no—
178C2×C8—22no—
179C2×C8—2934no—
180C2×C8—2932no—
181C2×C8C22×D29312yes—
182C4⋊C4—21no—
183C4⋊C4—2932no—
184C4⋊C4—5864no—
185C4⋊C4—5861no—
186C4⋊C4C22×D29312yes—
187C22⋊C4—5864no—
188C22⋊C4—5864no—
189C23—22no—
190C23—42no—
191C23—42no—
192C23—42no—
193C23—2932no—
194C23—5862no—
195C23—5862no—
196C23—5862no—
197C23D4×D29311yescharacteristic
198Q8—5862no—
199Q8—5862no—
200Q8—11722no—
201D4—22no—
202D4—22no—
203D4—42no—
204D4—11728no—
205C2×C4—22no—
206C2×C4—42no—
207C2×C4—2932no—
208C2×C4—5862no—
209C2×C4—5864no—
210C2×C4—5862no—
211C2×C4—5862no—
212C2×C4—5862no—
213C2×C4—5862no—
214C2×C4—11722no—
215C2×C4—11722no—
216C2×C4D4×D29311yescharacteristic
217C2×C4D4×D29312yes—
218C2×C4#1798980212yes—
219C2×C4C23×D29311yescharacteristic
220C8—22no—
221C8—2934no—
222C22—42no—
223C22—42no—
224C22—42no—
225C22—84no—
226C22—5862no—
227C22—5862no—
228C22—5862no—
229C22—11724no—
230C22#2262759712yes—
231C22#2262764812yes—
232C22#2262765312yes—
233C22C2×D4×D29311yescharacteristic
234C4—42no—
235C4—5862no—
236C4—11722no—
237C4—11722no—
238C4#2262759712yes—
239C4C2×D4×D29311yescharacteristic
240C4C2×#1798980211yescharacteristic
241C2—82no—
242C2—11722no—
243C2#3403637414yesdirect product factor
244C2C2×#2262759711yescharacteristic
245C2C2×#2262764811yescharacteristic
246C2C2×#2262765311yescharacteristic
subgroupG/H
centerC23D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
FittingC2×#102×C293C2
socleC23×C293C2×D4
prime radicalC2×#22627595C2
hypercenterC2×#102D293
hypocenterC293C2×#468
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C22×#17989790C2semidirect
2. C22×#17989785C2semidirect
3. C2×#22627604C2semidirect
5. #34036374C2direct (N × H)
6. C2×#22627557C2semidirect
7. C2×#22627549C2semidirect
8. C2×#102×C293C2semidirect
13. C2×#17989790C22semidirect
15. C2×#17989785C22semidirect
18. #22627604C22semidirect
25. #22627557C22semidirect
26. #22627549C22semidirect
30. #102×C293C22semidirect
47. C2×#14556873D4semidirect
82. #14556873C2×D4semidirect
118. C2×C293#468semidirect
123. C293C2×#468semidirect
132. C2×#102D293semidirect
154. #102C2×D293semidirect
243. C2#34036374direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#179897902
C22×#179897852
C2×#226276042
C2×#226275952
#340363742
C2×#226275572
C2×#226275492
C2×#102×C2932
C2×#468293