Finite Group Databasebeta

← C2×#23749877 #34054286

Subgroups — C2×#23749877 #34054286

Order 19072.

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×#14558721C211yesmaximal, characteristic, complemented
2C22×#14558719C211yesmaximal, characteristic, complemented
3C2×#18011886C211yesmaximal, characteristic, complemented
4C2×#18011882C211yesmaximal, characteristic, complemented
5#23749877C218yesmaximal, direct product factor
6C2×#18011842C211yesmaximal, characteristic, complemented
7C2×#18011833C211yesmaximal, characteristic, complemented
8C2×#102×C149C211yesmaximal, characteristic, complemented
9C22×D596—21no—
10C22×D596C2211yescharacteristic
11C22×C22⋊D149—21no—
12C22×C4×D149C2211yescharacteristic
13C2×#14558721—24no—
14C2×#14558721C2214yescomplemented
15C2×#14558719—24no—
16C2×#14558719C2214yescomplemented
17C22×#11924746C2211yescharacteristic
18#18011886—22no—
19#18011886C2214yescomplemented
20#18011882—22no—
21#18011882C2214yescomplemented
22C2×C4⋊Dic149C2211yescharacteristic
23C2×C22⋊Dic149—21no—
24C2×#14558713—21no—
25#18011842C2214yescomplemented
26#18011833C2214yescomplemented
27C22×D4×C149C2211yescharacteristic
28C22×C8×C149C2211yescharacteristic
29C2×C4⋊C4×C149C2211yescharacteristic
30#102×C149C2214yescomplemented
31C23×D149—21no—
32C23×D149D411yescharacteristic
33C2×D596—24no—
34C2×D596—22no—
35C2×D596—21no—
36C2×D596—22no—
37C2×D596—44no—
38C2×D596C2312yes—
39C2×C22⋊D149—24no—
40C2×C22⋊D149—44no—
41C22×Dic149—21no—
42C22×Dic149D411yescharacteristic
43C2×C4×D149—22no—
44C2×C4×D149—22no—
45C2×C4×D149D412yes—
46C2×C4×D149C2312yes—
47#14558721—28no—
48#14558719—28no—
49C2×#11924746D414yescomplemented
50C2×#11924746C2312yes—
51C4⋊Dic149—21no—
52C4⋊Dic149C2312yes—
53C22⋊Dic149—24no—
54#14558713—24no—
55C24×C149—21no—
56C2×D4×C149—22no—
57C2×D4×C149—21no—
58C2×D4×C149—22no—
59C2×D4×C149C2312yes—
60C22×C4×C149—21no—
61C22×C4×C149C2311yescharacteristic
62C2×C8×C149—22no—
63C2×C8×C149C2312yes—
64C4⋊C4×C149—21no—
65C4⋊C4×C149C2312yes—
66C22×D149—22no—
67C22×D149—22no—
68C22×D149—22no—
69C22×D149—22no—
70C22×D149—42no—
71C22×D149—42no—
72C22×D149—42no—
73C22×D149C2×D412yes—
74D596—22no—
75D596—22no—
76D596—48no—
77D596—42no—
78C22⋊D149—48no—
79C2×Dic149—22no—
80C2×Dic149—22no—
81C2×Dic149—42no—
82C2×Dic149C2×D412yes—
83C4×D149—24no—
84C4×D149—22no—
85C4×D149—22no—
86#11924746C2×D414yescomplemented
87C23×C149—22no—
88C23×C149—42no—
89C23×C149—42no—
90C23×C149—42no—
91C23×C149C2×D411yescharacteristic
92D4×C149—22no—
93D4×C149—22no—
94D4×C149—42no—
95C2×C4×C149—22no—
96C2×C4×C149—42no—
97C2×C4×C149C2×D411yescharacteristic
98C2×C4×C149C2×D412yes—
99C2×C4×C149#4112yes—
100C2×C4×C149C2411yescharacteristic
101C8×C149—22no—
102C22×C149—42no—
103C22×C149—42no—
104C22×C149—42no—
105C22×C149—84no—
106C22×C149#12112yes—
107C22×C149AGL(1,ℤ/8)12yes—
108C22×C149AGL(1,ℤ/8)12yes—
109C22×C149C22×D411yescharacteristic
110C2×D149—22no—
111C2×D149—22no—
112C2×D149—22no—
113C2×D149—44no—
114C2×D149—42no—
115C2×D149—42no—
116C2×D149—42no—
117C2×D149—84no—
118C4×C149—42no—
119C4×C149#12112yes—
120C4×C149C22×D411yescharacteristic
121C4×C149C2×#4111yescharacteristic
122Dic149—22no—
123Dic149—42no—
124C2×C149—82no—
125C2×C149#46914yescomplemented
126C2×C149C2×#12111yescharacteristic
127C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
128C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
129D149—42no—
130D149—82no—
131C149C2×#46911yescharacteristic, complemented, Sylow
132C2×#469—1491nomaximal, Sylow
133C22×D8—1491no—
134C22×M16—1491no—
135C2×#121—1491no—
136C2×#121—1491no—
137#469—1498no—
138C2×#106—1491no—
139C2×#102—1491no—
140C2×#102D14911yescharacteristic, complemented
141C22×D4—2981no—
142C22×D4—2981no—
143C22×D4—1491no—
144C22×D4C2×D14911yescharacteristic
145C23×C4—1491no—
146C2×D8—2984no—
147C2×D8—1494no—
148C2×M16—2984no—
149C2×M16—1494no—
150C22×C8—1491no—
151C22×C8C2×D14911yescharacteristic
152#121—2982no—
153#121—2982no—
154#121—1494no—
155#121—1494no—
156C2×C4⋊C4—1491no—
157C2×C4⋊C4C2×D14911yescharacteristic
158C2×C22⋊C4—2981no—
159C2×C22⋊C4—2981no—
160#106—1494no—
161#102—1494no—
162#102C2×D14914yescomplemented
163C24—21no—
164C24—2981no—
165C24—1491no—
166C2×D4—22no—
167C2×D4—21no—
168C2×D4—22no—
169C2×D4—2984no—
170C2×D4—2984no—
171C2×D4—2982no—
172C2×D4—2981no—
173C2×D4—2982no—
174C2×D4—5964no—
175C2×D4—5964no—
176C2×D4—1492no—
177C2×D4C22×D14912yes—
178C22×C4—21no—
179C22×C4—2982no—
180C22×C4—2982no—
181C22×C4—2981no—
182C22×C4—1491no—
183C22×C4—1492no—
184C22×C4—1492no—
185C22×C4C22×D14911yescharacteristic
186D8—2988no—
187M16—2988no—
188C2×C8—22no—
189C2×C8—1494no—
190C2×C8—1492no—
191C2×C8C22×D14912yes—
192C4⋊C4—21no—
193C4⋊C4—2981no—
194C4⋊C4—1492no—
195C4⋊C4C22×D14912yes—
196C22⋊C4—2984no—
197C22⋊C4—2984no—
198C23—22no—
199C23—42no—
200C23—42no—
201C23—42no—
202C23—2982no—
203C23—2982no—
204C23—2982no—
205C23—2982no—
206C23—5962no—
207C23—5962no—
208C23—5962no—
209C23—1492no—
210C23D4×D14911yescharacteristic
211D4—22no—
212D4—22no—
213D4—42no—
214D4—2982no—
215D4—2982no—
216D4—5968no—
217D4—5968no—
218D4—5962no—
219C2×C4—22no—
220C2×C4—42no—
221C2×C4—2982no—
222C2×C4—2982no—
223C2×C4—2982no—
224C2×C4—2984no—
225C2×C4—2982no—
226C2×C4—5962no—
227C2×C4—1492no—
228C2×C4D4×D14912yes—
229C2×C4D4×D14911yescharacteristic
230C2×C4#1455873612yes—
231C2×C4C23×D14911yescharacteristic
232C8—22no—
233C8—1494no—
234C22—42no—
235C22—42no—
236C22—42no—
237C22—84no—
238C22—2982no—
239C22—2982no—
240C22—2982no—
241C22—5964no—
242C22—5962no—
243C22—5962no—
244C22—5962no—
245C22—11924no—
246C22#1801188412yes—
247C22#1801193512yes—
248C22#1801193812yes—
249C22C2×D4×D14911yescharacteristic
250C4—42no—
251C4—2982no—
252C4—5962no—
253C4#1801188412yes—
254C4C2×D4×D14911yescharacteristic
255C4C2×#1455873611yescharacteristic
256C2—82no—
257C2—5962no—
258C2—11922no—
259C2#2374987714yesdirect product factor
260C2C2×#1801188411yescharacteristic
261C2C2×#1801193511yescharacteristic
262C2C2×#1801193811yescharacteristic
subgroupG/H
centerC23D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC2×#102×C149C2
socleC23×C149C2×D4
hypercenterC2×#102D149
hypocenterC149C2×#469
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C22×#14558721C2semidirect
2. C22×#14558719C2semidirect
3. C2×#18011886C2semidirect
4. C2×#18011882C2semidirect
5. #23749877C2direct (N × H)
6. C2×#18011842C2semidirect
7. C2×#18011833C2semidirect
8. C2×#102×C149C2semidirect
14. C2×#14558721C22semidirect
16. C2×#14558719C22semidirect
19. #18011886C22semidirect
21. #18011882C22semidirect
25. #18011842C22semidirect
26. #18011833C22semidirect
30. #102×C149C22semidirect
49. C2×#11924746D4semidirect
86. #11924746C2×D4semidirect
125. C2×C149#469semidirect
131. C149C2×#469semidirect
140. C2×#102D149semidirect
162. #102C2×D149semidirect
259. C2#23749877direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145587212
C22×#145587192
C2×#180118862
C2×#180118822
#237498772
C2×#180118422
C2×#180118332
C2×#102×C1492
C2×#469149