Finite Group Databasebeta

← C2×#34036381 #49168380

Subgroups — C2×#34036381 #49168380

Order 37504.

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

normal subgroups only

This group has 596 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×#17989787C211yesmaximal, characteristic, complemented
2C22×#17989785C211yesmaximal, characteristic, complemented
3C2×#22627599C211yesmaximal, characteristic, complemented
4C2×#22627595C211yesmaximal, characteristic, complemented
5#34036381C218yesmaximal, direct product factor
6C2×#22627555C211yesmaximal, characteristic, complemented
7C2×#22627546C211yesmaximal, characteristic, complemented
8C2×#102×C293C211yesmaximal, characteristic, complemented
9C22×D1172—21no—
10C22×D1172C2211yescharacteristic
11C22×C22⋊D293—21no—
12C22×C4×D293C2211yescharacteristic
13C2×#17989787—24no—
14C2×#17989787C2214yescomplemented
15C2×#17989785—24no—
16C2×#17989785C2214yescomplemented
17C22×#14556873C2211yescharacteristic
18#22627599—22no—
19#22627599C2214yescomplemented
20#22627595—22no—
21#22627595C2214yescomplemented
22C2×C4⋊Dic293C2211yescharacteristic
23C2×C22⋊Dic293—21no—
24C2×#17989779—21no—
25#22627555C2214yescomplemented
26#22627546C2214yescomplemented
27C22×D4×C293C2211yescharacteristic
28C22×C8×C293C2211yescharacteristic
29C2×C4⋊C4×C293C2211yescharacteristic
30#102×C293C2214yescomplemented
31C23×D293—21no—
32C23×D293D411yescharacteristic
33C2×D1172—24no—
34C2×D1172—22no—
35C2×D1172—21no—
36C2×D1172—22no—
37C2×D1172—44no—
38C2×D1172C2312yes—
39C2×C22⋊D293—24no—
40C2×C22⋊D293—44no—
41C22×Dic293—21no—
42C22×Dic293D411yescharacteristic
43C2×C4×D293—22no—
44C2×C4×D293—22no—
45C2×C4×D293D412yes—
46C2×C4×D293C2312yes—
47#17989787—28no—
48#17989785—28no—
49C2×#14556873D414yescomplemented
50C2×#14556873C2312yes—
51C4⋊Dic293—21no—
52C4⋊Dic293C2312yes—
53C22⋊Dic293—24no—
54#17989779—24no—
55C24×C293—21no—
56C2×D4×C293—22no—
57C2×D4×C293—21no—
58C2×D4×C293—22no—
59C2×D4×C293C2312yes—
60C22×C4×C293—21no—
61C22×C4×C293C2311yescharacteristic
62C2×C8×C293—22no—
63C2×C8×C293C2312yes—
64C4⋊C4×C293—21no—
65C4⋊C4×C293C2312yes—
66C22×D293—22no—
67C22×D293—22no—
68C22×D293—22no—
69C22×D293—22no—
70C22×D293—42no—
71C22×D293—42no—
72C22×D293—42no—
73C22×D293C2×D412yes—
74D1172—22no—
75D1172—22no—
76D1172—48no—
77D1172—42no—
78C22⋊D293—48no—
79C2×Dic293—22no—
80C2×Dic293—22no—
81C2×Dic293—42no—
82C2×Dic293C2×D412yes—
83C4×D293—24no—
84C4×D293—22no—
85C4×D293—22no—
86#14556873C2×D414yescomplemented
87C23×C293—22no—
88C23×C293—42no—
89C23×C293—42no—
90C23×C293—42no—
91C23×C293C2×D411yescharacteristic
92D4×C293—22no—
93D4×C293—22no—
94D4×C293—42no—
95C2×C4×C293—22no—
96C2×C4×C293—42no—
97C2×C4×C293C2×D411yescharacteristic
98C2×C4×C293C2×D412yes—
99C2×C4×C293#4112yes—
100C2×C4×C293C2411yescharacteristic
101C8×C293—22no—
102C22×C293—42no—
103C22×C293—42no—
104C22×C293—42no—
105C22×C293—84no—
106C22×C293#12112yes—
107C22×C293AGL(1,ℤ/8)12yes—
108C22×C293AGL(1,ℤ/8)12yes—
109C22×C293C22×D411yescharacteristic
110C2×D293—22no—
111C2×D293—22no—
112C2×D293—22no—
113C2×D293—44no—
114C2×D293—42no—
115C2×D293—42no—
116C2×D293—42no—
117C2×D293—84no—
118C4×C293—42no—
119C4×C293#12112yes—
120C4×C293C22×D411yescharacteristic
121C4×C293C2×#4111yescharacteristic
122Dic293—22no—
123Dic293—42no—
124C2×C293—82no—
125C2×C293#46914yescomplemented
126C2×C293C2×#12111yescharacteristic
127C2×C293C2×AGL(1,ℤ/8)11yescharacteristic
128C2×C293C2×AGL(1,ℤ/8)11yescharacteristic
129D293—42no—
130D293—82no—
131C293C2×#46911yescharacteristic, complemented, Sylow
132C2×#469—2931nomaximal, Sylow
133C22×D8—2931no—
134C22×M16—2931no—
135C2×#121—2931no—
136C2×#121—2931no—
137#469—2938no—
138C2×#106—2931no—
139C2×#102—2931no—
140C2×#102D29311yescharacteristic, complemented
141C22×D4—2931no—
142C22×D4—5861no—
143C22×D4—5861no—
144C22×D4C2×D29311yescharacteristic
145C23×C4—2931no—
146C2×D8—2934no—
147C2×D8—5864no—
148C2×M16—2934no—
149C2×M16—5864no—
150C22×C8—2931no—
151C22×C8C2×D29311yescharacteristic
152#121—2934no—
153#121—2934no—
154#121—5862no—
155#121—5862no—
156C2×C4⋊C4—2931no—
157C2×C4⋊C4C2×D29311yescharacteristic
158C2×C22⋊C4—5861no—
159C2×C22⋊C4—5861no—
160#106—2934no—
161#102—2934no—
162#102C2×D29314yescomplemented
163C24—21no—
164C24—2931no—
165C24—5861no—
166C2×D4—22no—
167C2×D4—21no—
168C2×D4—22no—
169C2×D4—2932no—
170C2×D4—5864no—
171C2×D4—5864no—
172C2×D4—5862no—
173C2×D4—5861no—
174C2×D4—5862no—
175C2×D4—11724no—
176C2×D4—11724no—
177C2×D4C22×D29312yes—
178C22×C4—21no—
179C22×C4—2931no—
180C22×C4—2932no—
181C22×C4—2932no—
182C22×C4—5862no—
183C22×C4—5862no—
184C22×C4—5861no—
185C22×C4C22×D29311yescharacteristic
186D8—5868no—
187M16—5868no—
188C2×C8—22no—
189C2×C8—2934no—
190C2×C8—2932no—
191C2×C8C22×D29312yes—
192C4⋊C4—21no—
193C4⋊C4—2932no—
194C4⋊C4—5861no—
195C4⋊C4C22×D29312yes—
196C22⋊C4—5864no—
197C22⋊C4—5864no—
198C23—22no—
199C23—42no—
200C23—42no—
201C23—42no—
202C23—2932no—
203C23—5862no—
204C23—5862no—
205C23—5862no—
206C23—5862no—
207C23—11722no—
208C23—11722no—
209C23—11722no—
210C23D4×D29311yescharacteristic
211D4—22no—
212D4—22no—
213D4—42no—
214D4—5862no—
215D4—5862no—
216D4—11728no—
217D4—11728no—
218D4—11722no—
219C2×C4—22no—
220C2×C4—42no—
221C2×C4—2932no—
222C2×C4—5862no—
223C2×C4—5864no—
224C2×C4—5862no—
225C2×C4—5862no—
226C2×C4—5862no—
227C2×C4—11722no—
228C2×C4D4×D29311yescharacteristic
229C2×C4D4×D29312yes—
230C2×C4#1798980212yes—
231C2×C4C23×D29311yescharacteristic
232C8—22no—
233C8—2934no—
234C22—42no—
235C22—42no—
236C22—42no—
237C22—84no—
238C22—23444no—
239C22—5862no—
240C22—5862no—
241C22—5862no—
242C22—11722no—
243C22—11722no—
244C22—11722no—
245C22—11724no—
246C22#2262759712yes—
247C22#2262764812yes—
248C22#2262765112yes—
249C22C2×D4×D29311yescharacteristic
250C4—42no—
251C4—5862no—
252C4—11722no—
253C4#2262759712yes—
254C4C2×D4×D29311yescharacteristic
255C4C2×#1798980211yescharacteristic
256C2—82no—
257C2—23442no—
258C2—11722no—
259C2#3403638114yesdirect product factor
260C2C2×#2262759711yescharacteristic
261C2C2×#2262764811yescharacteristic
262C2C2×#2262765111yescharacteristic
subgroupG/H
centerC23D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
FittingC2×#102×C293C2
socleC23×C293C2×D4
hypercenterC2×#102D293
hypocenterC293C2×#469
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×#17989787C2semidirect
2. C22×#17989785C2semidirect
3. C2×#22627599C2semidirect
4. C2×#22627595C2semidirect
5. #34036381C2direct (N × H)
6. C2×#22627555C2semidirect
7. C2×#22627546C2semidirect
8. C2×#102×C293C2semidirect
14. C2×#17989787C22semidirect
16. C2×#17989785C22semidirect
19. #22627599C22semidirect
21. #22627595C22semidirect
25. #22627555C22semidirect
26. #22627546C22semidirect
30. #102×C293C22semidirect
49. C2×#14556873D4semidirect
86. #14556873C2×D4semidirect
125. C2×C293#469semidirect
131. C293C2×#469semidirect
140. C2×#102D293semidirect
162. #102C2×D293semidirect
259. C2#34036381direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#179897872
C22×#179897852
C2×#226275992
C2×#226275952
#340363812
C2×#226275552
C2×#226275462
C2×#102×C2932
C2×#469293