Finite Group Databasebeta

← C2×#34036373 #49168371

Subgroups — C2×#34036373 #49168371

Order 37504.

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×#17989790C211yesmaximal, characteristic, complemented
2C22×#17989786C211yesmaximal, characteristic, complemented
3C2×#22627603C211yesmaximal, characteristic, complemented
4#34036373C218yesmaximal, direct product factor
5C2×#22627557C211yesmaximal, characteristic, complemented
6C2×#22627547C211yesmaximal, characteristic, complemented
7C2×#22627545C211yesmaximal, characteristic, complemented
8C2×#121×C293C211yesmaximal, characteristic
9C22×Dic586C2211yescharacteristic
10C2×#17989790—24no—
11C2×#17989790C2214yescomplemented
12C2×#17989786—24no—
13C2×#17989786C2214yescomplemented
14C22×#14556873C2211yescharacteristic
15C22×#14556873C2211yescharacteristic
16#22627603—22no—
17#22627603C2214yescomplemented
18C2×C4⋊Dic293C2211yescharacteristic
19C2×#17989781—21no—
20C2×C22⋊Dic293—21no—
21#22627557C2214yescomplemented
22#22627547C2214yescomplemented
23#22627545C2214yescomplemented
24C22×D4×C293—21no—
25C22×D4×C293C2211yescharacteristic
26C23×C4×C293C2211yescharacteristic
27#121×C293—22no—
28#121×C293C2214yes—
29C2×C4⋊C4×C293C2211yescharacteristic
30C2×C22⋊C4×C293—21no—
31C2×Dic586—21no—
32C2×Dic586—22no—
33C2×Dic586—22no—
34C2×Dic586C2312yes—
35C22×Dic293—21no—
36C22×Dic293—21no—
37#17989790—28no—
38#17989786—28no—
39C2×#14556873—22no—
40C2×#14556873D414yescomplemented
41C2×#14556873C2312yes—
42C2×#14556873C2312yes—
43C4⋊Dic293—21no—
44C4⋊Dic293C2312yes—
45#17989781—24no—
46C22⋊Dic293—24no—
47C24×C293—21no—
48C24×C293D411yescharacteristic
49C2×D4×C293—24no—
50C2×D4×C293—22no—
51C2×D4×C293—21no—
52C2×D4×C293—22no—
53C2×D4×C293—44no—
54C2×D4×C293C2312yes—
55C22×C4×C293—22no—
56C22×C4×C293—22no—
57C22×C4×C293—21no—
58C22×C4×C293D412yes—
59C22×C4×C293D411yescharacteristic
60C22×C4×C293C2312yes—
61C22×C4×C293C2311yescharacteristic
62C4⋊C4×C293—21no—
63C4⋊C4×C293C2312yes—
64C22⋊C4×C293—24no—
65Dic586—22no—
66Dic586—22no—
67Dic586—42no—
68C2×Dic293—22no—
69C2×Dic293—22no—
70C2×Dic293—42no—
71C2×Dic293—42no—
72#14556873—22no—
73#14556873C2×D414yescomplemented
74C23×C293—22no—
75C23×C293—22no—
76C23×C293—22no—
77C23×C293—22no—
78C23×C293—42no—
79C23×C293—42no—
80C23×C293—42no—
81C23×C293C2×D412yes—
82C23×C293C2×D411yescharacteristic
83D4×C293—22no—
84D4×C293—22no—
85D4×C293—48no—
86D4×C293—42no—
87C2×C4×C293—22no—
88C2×C4×C293—24no—
89C2×C4×C293—22no—
90C2×C4×C293—22no—
91C2×C4×C293—22no—
92C2×C4×C293—42no—
93C2×C4×C293C2×D412yes—
94C2×C4×C293C2×D412yes—
95C2×C4×C293C2×D411yescharacteristic
96C2×C4×C293#4112yes—
97C2×C4×C293C2411yescharacteristic
98C22×C293—22no—
99C22×C293—22no—
100C22×C293—22no—
101C22×C293—44no—
102C22×C293—42no—
103C22×C293—42no—
104C22×C293—42no—
105C22×C293—84no—
106C22×C293#12112yes—
107C22×C293AGL(1,ℤ/8)12yes—
108C22×C293#13712yes—
109C22×C293C22×D411yescharacteristic
110C4×C293—22no—
111C4×C293—42no—
112C4×C293#12112yes—
113C4×C293C22×D411yescharacteristic
114C4×C293C2×#4111yescharacteristic
115Dic293—42no—
116Dic293—42no—
117C2×C293—42no—
118C2×C293—82no—
119C2×C293#46814yescomplemented
120C2×C293C2×#12111yescharacteristic
121C2×C293C2×AGL(1,ℤ/8)11yescharacteristic
122C2×C293C2×#13711yescharacteristic
123C293C2×#46811yescharacteristic, complemented, Sylow
124C2×#468—2931nomaximal, Sylow
125C22×SD16—2931no—
126C22×M16—2931no—
127C2×C22⋊Q8—2931no—
128C2×#121D29311yescharacteristic
129#468—2938no—
130C2×#107—2931no—
131C2×#103—2931no—
132C2×#102—2931no—
133C22×Q8—2931no—
134C22×D4—21no—
135C22×D4C2×D29311yescharacteristic
136C23×C4C2×D29311yescharacteristic
137C2×SD16—2934no—
138C2×SD16—5864no—
139C2×M16—2934no—
140C2×M16—5864no—
141C22×C8—2931no—
142C22×C8—2931no—
143C22⋊Q8—2934no—
144C22⋊Q8—5862no—
145#121—22no—
146#121C2×D29314yes—
147C2×C4⋊C4—2931no—
148C2×C4⋊C4—5861no—
149C2×C4⋊C4C2×D29311yescharacteristic
150C2×C22⋊C4—21no—
151C2×C22⋊C4—5861no—
152#107—2934no—
153#103—2934no—
154#102—2934no—
155C24—21no—
156C24C22⋊D29311yescharacteristic
157C2×Q8—2932no—
158C2×Q8—5861no—
159C2×Q8—5862no—
160C2×Q8—5862no—
161C2×D4—24no—
162C2×D4—22no—
163C2×D4—21no—
164C2×D4—22no—
165C2×D4—44no—
166C2×D4C22×D29312yes—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—21no—
170C22×C4—5861no—
171C22×C4—5861no—
172C22×C4C22⋊D29312yes—
173C22×C4C22⋊D29311yescharacteristic
174C22×C4C22×D29312yes—
175C22×C4C22×D29311yescharacteristic
176SD16—5868no—
177M16—5868no—
178C2×C8—2934no—
179C2×C8—2932no—
180C2×C8—2932no—
181C2×C8—5862no—
182C4⋊C4—21no—
183C4⋊C4—2932no—
184C4⋊C4—5861no—
185C4⋊C4—5864no—
186C4⋊C4C22×D29312yes—
187C22⋊C4—24no—
188C22⋊C4—5864no—
189C23—22no—
190C23—22no—
191C23—22no—
192C23—22no—
193C23—42no—
194C23—42no—
195C23—42no—
196C23C2×C22⋊D29312yes—
197C23C2×C22⋊D29311yescharacteristic
198Q8—5862no—
199Q8—5862no—
200Q8—11722no—
201D4—22no—
202D4—22no—
203D4—48no—
204D4—42no—
205C2×C4—22no—
206C2×C4—24no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—42no—
211C2×C4—5862no—
212C2×C4—5862no—
213C2×C4—11722no—
214C2×C4—11722no—
215C2×C4D4×D29312yes—
216C2×C4C2×C22⋊D29312yes—
217C2×C4C2×C22⋊D29311yescharacteristic
218C2×C4#1798980112yes—
219C2×C4C23×D29311yescharacteristic
220C8—2934no—
221C8—5862no—
222C22—22no—
223C22—22no—
224C22—22no—
225C22—44no—
226C22—42no—
227C22—42no—
228C22—42no—
229C22—84no—
230C22#2262759612yes—
231C22#2262765012yes—
232C22#2262765412yes—
233C22C22×C22⋊D29311yescharacteristic
234C4—22no—
235C4—42no—
236C4—11722no—
237C4—11722no—
238C4#2262759612yes—
239C4C2×D4×D29311yescharacteristic
240C4C2×#1798980111yescharacteristic
241C2—42no—
242C2—82no—
243C2#3403637314yesdirect product factor
244C2C2×#2262759611yescharacteristic
245C2C2×#2262765011yescharacteristic
246C2C2×#2262765411yescharacteristic
subgroupG/H
centerC23C2×C22⋊D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting, prime radicalC2×#121×C293C2
socleC23×C293C2×D4
hypercenterC2×#121D293
hypocenterC293C2×#468
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C22×#17989790C2semidirect
2. C22×#17989786C2semidirect
3. C2×#22627603C2semidirect
4. #34036373C2direct (N × H)
5. C2×#22627557C2semidirect
6. C2×#22627547C2semidirect
7. C2×#22627545C2semidirect
11. C2×#17989790C22semidirect
13. C2×#17989786C22semidirect
17. #22627603C22semidirect
21. #22627557C22semidirect
22. #22627547C22semidirect
23. #22627545C22semidirect
40. C2×#14556873D4semidirect
73. #14556873C2×D4semidirect
119. C2×C293#468semidirect
123. C293C2×#468semidirect
243. C2#34036373direct (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×#179897862
C2×#226276032
#340363732
C2×#226275572
C2×#226275472
C2×#226275452
C2×#121×C2932
C2×#468293