Finite Group Databasebeta

← C2×#23749996 #34055096

Subgroups — C2×#23749996 #34055096

Order 19072.

656 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 181 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×#14558725C211yesmaximal, characteristic, complemented
2C22×#14558724C211yesmaximal, characteristic, complemented
3C22×#14558723C211yesmaximal, characteristic, complemented
4C2×#18011909C211yesmaximal, characteristic, complemented
5C2×#18011907C211yesmaximal, characteristic
6#23749996C218yesmaximal, direct product factor
7C2×C8×Dic149C211yesmaximal, characteristic, complemented
8C22×SD16×C149C211yesmaximal, characteristic, complemented
9C22×Dic298C2211yescharacteristic
10C22×D596C2211yescharacteristic
11C22×C22⋊D149—22no—
12C2×#14558725—24no—
13C2×#14558725C2214yescomplemented
14C2×#14558724—24no—
15C2×#14558724C2214yescomplemented
16C2×#14558723—24no—
17C2×#14558723C2214yescomplemented
18C22×#11924746C2211yescharacteristic
19#18011909—22no—
20#18011909C2214yescomplemented
21#18011907—22no—
22#18011907C2214yes—
23C2×#14558715—22no—
24C2×C4×Dic149C2211yescharacteristic
25C8×Dic149C2214yescomplemented
26C22×Q8×C149C2211yescharacteristic
27C22×D4×C149C2211yescharacteristic
28C2×SD16×C149—24no—
29C2×SD16×C149C2214yescomplemented
30C22×C8×C149C2211yescharacteristic
31C23×D149—21no—
32C2×Dic298—21no—
33C2×Dic298—22no—
34C2×Dic298—22no—
35C2×Dic298C2312yes—
36C2×D596—22no—
37C2×D596—22no—
38C2×D596—21no—
39C2×D596C2312yes—
40C2×C22⋊D149—28no—
41C2×C22⋊D149—48no—
42C22×Dic149—21no—
43C22×Dic149D412yes—
44#14558725—28no—
45#14558724—28no—
46#14558723—28no—
47C2×#11924746D414yescomplemented
48C2×#11924746C2312yes—
49#14558715—28no—
50C4×Dic149D412yes—
51C4×Dic149C2312yes—
52C24×C149—21no—
53C2×Q8×C149—21no—
54C2×Q8×C149—22no—
55C2×Q8×C149—22no—
56C2×Q8×C149C2312yes—
57C2×D4×C149—22no—
58C2×D4×C149—22no—
59C2×D4×C149—21no—
60C2×D4×C149C2312yes—
61C22×C4×C149—21no—
62C22×C4×C149C2311yescharacteristic
63SD16×C149—28no—
64C2×C8×C149D414yescomplemented
65C2×C8×C149C2312yes—
66C22×D149—22no—
67C22×D149—42no—
68C22×D149—44no—
69Dic298—22no—
70Dic298—22no—
71Dic298—42no—
72D596—22no—
73D596—22no—
74D596—42no—
75C22⋊D149—416no—
76C2×Dic149—22no—
77C2×Dic149—42no—
78C2×Dic149SD1618yescomplemented
79C2×Dic149C2×D414yes—
80#11924746C2×D414yescomplemented
81C23×C149—22no—
82C23×C149—42no—
83C23×C149—44no—
84C23×C149C2×D411yescharacteristic
85Q8×C149—22no—
86Q8×C149—22no—
87Q8×C149—42no—
88D4×C149—22no—
89D4×C149—22no—
90D4×C149—42no—
91C2×C4×C149—22no—
92C2×C4×C149—42no—
93C2×C4×C149C2×D411yescharacteristic
94C2×C4×C149C2×D412yes—
95C2×C4×C149C2×D412yes—
96C2×C4×C149C2411yescharacteristic
97C8×C149C2×D414yescomplemented
98C22×C149—42no—
99C22×C149—44no—
100C22×C149—84no—
101C22×C149#12712yes—
102C22×C149C2×SD1614yes—
103C22×C149C22×D411yescharacteristic
104C2×D149—42no—
105C2×D149—44no—
106C2×D149—84no—
107C4×C149—42no—
108C4×C149#12712yes—
109C4×C149C22×D411yescharacteristic
110C4×C149C22×D411yescharacteristic
111Dic149—42no—
112Dic149C2×SD1618yescomplemented
113C2×C149—82no—
114C2×C149#49214yescomplemented
115C2×C149C2×#12711yescharacteristic
116C2×C149C22×SD1612yes—
117D149—82no—
118C149C2×#49211yescharacteristic, complemented, Sylow
119C2×#492—1491nomaximal, Sylow
120C22×SD16—1491no—
121C22×SD16—1491no—
122C22×SD16—1491no—
123C22×SD16D14911yescharacteristic, complemented
124C2×C4⋊Q8—1491no—
125C2×#127—1491no—
126#492—1498no—
127C2×C4×C8—1491no—
128C22×Q8—1491no—
129C22×Q8C2×D14911yescharacteristic
130C22×D4—2982no—
131C22×D4—1491no—
132C22×D4C2×D14911yescharacteristic
133C2×SD16—24no—
134C2×SD16—2984no—
135C2×SD16—2984no—
136C2×SD16—2984no—
137C2×SD16—1494no—
138C2×SD16—1494no—
139C2×SD16—1494no—
140C2×SD16C2×D14914yescomplemented
141C22×C8—1491no—
142C22×C8C2×D14911yescharacteristic
143C4⋊Q8—2982no—
144C4⋊Q8—1494no—
145#127—2982no—
146#127—1494no—
147C2×C4⋊C4—2982no—
148C2×C42—1491no—
149C4×C8—1494no—
150C24—21no—
151C24—2981no—
152C2×Q8—21no—
153C2×Q8—22no—
154C2×Q8—22no—
155C2×Q8—2981no—
156C2×Q8—2982no—
157C2×Q8—2982no—
158C2×Q8—1492no—
159C2×Q8C22×D14912yes—
160C2×D4—22no—
161C2×D4—21no—
162C2×D4—22no—
163C2×D4—2988no—
164C2×D4—2982no—
165C2×D4—2981no—
166C2×D4—2982no—
167C2×D4—5968no—
168C2×D4—1492no—
169C2×D4C22×D14912yes—
170C22×C4—21no—
171C22×C4—2981no—
172C22×C4—1492no—
173C22×C4C22×D14911yescharacteristic
174SD16—28no—
175SD16—2988no—
176SD16—2988no—
177SD16—2988no—
178C2×C8—1494no—
179C2×C8—1492no—
180C2×C8C22⋊D14914yescomplemented
181C2×C8C22×D14912yes—
182C4⋊C4—2988no—
183C42—1492no—
184C42—1492no—
185C23—22no—
186C23—42no—
187C23—44no—
188C23—2982no—
189C23—5962no—
190C23—5964no—
191C23D4×D14911yescharacteristic
192Q8—22no—
193Q8—22no—
194Q8—42no—
195Q8—2982no—
196Q8—2982no—
197Q8—5962no—
198D4—22no—
199D4—22no—
200D4—42no—
201D4—2982no—
202D4—2982no—
203D4—59616no—
204D4—5962no—
205C2×C4—22no—
206C2×C4—42no—
207C2×C4—2982no—
208C2×C4—5962no—
209C2×C4—1498no—
210C2×C4—1494no—
211C2×C4D4×D14911yescharacteristic
212C2×C4D4×D14912yes—
213C2×C4C2×C22⋊D14912yes—
214C2×C4C23×D14911yescharacteristic
215C8—1494no—
216C8C2×C22⋊D14914yescomplemented
217C22—42no—
218C22—44no—
219C22—84no—
220C22—5962no—
221C22—5964no—
222C22—11924no—
223C22#1801190712yes—
224C22SD16×D14914yes—
225C22C2×D4×D14911yescharacteristic
226C4—42no—
227C4—5962no—
228C4—1498no—
229C4#1801190712yes—
230C4C2×D4×D14911yescharacteristic
231C4C22×C22⋊D14911yescharacteristic
232C2—82no—
233C2—11922no—
234C2#2374999614yesdirect product factor
235C2C2×#1801190711yescharacteristic
236C2C2×SD16×D14912yes—
subgroupG/H
centerC23D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC22×SD16×C149C2
socleC23×C149C2×D4
prime radicalC2×#18011907C2
hypercenterC22×SD16D149
hypocenterC149C2×#492
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C22×#14558725C2semidirect
2. C22×#14558724C2semidirect
3. C22×#14558723C2semidirect
4. C2×#18011909C2semidirect
6. #23749996C2direct (N × H)
7. C2×C8×Dic149C2semidirect
8. C22×SD16×C149C2semidirect
13. C2×#14558725C22semidirect
15. C2×#14558724C22semidirect
17. C2×#14558723C22semidirect
20. #18011909C22semidirect
25. C8×Dic149C22semidirect
29. C2×SD16×C149C22semidirect
47. C2×#11924746D4semidirect
64. C2×C8×C149D4semidirect
78. C2×Dic149SD16semidirect
80. #11924746C2×D4semidirect
97. C8×C149C2×D4semidirect
112. Dic149C2×SD16semidirect
114. C2×C149#492semidirect
118. C149C2×#492semidirect
123. C22×SD16D149semidirect
140. C2×SD16C2×D149semidirect
180. C2×C8C22⋊D149semidirect
216. C8C2×C22⋊D149semidirect
234. C2#23749996direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145587252
C22×#145587242
C22×#145587232
C2×#180119092
C2×#180119072
#237499962
C2×C8×Dic1492
C22×SD16×C1492
C2×#492149