Finite Group Databasebeta

← C2×#23750011 #34055122

Subgroups — C2×#23750011 #34055122

Order 19072.

668 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 165 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×#14558723C211yesmaximal, characteristic, complemented
2C22×D1192C211yesmaximal, characteristic, complemented
3C22×#14558721C211yesmaximal, characteristic, complemented
4C2×#18011907C211yesmaximal, characteristic, complemented
5C2×#18011900C211yesmaximal, characteristic, complemented
6#23750011C218yesmaximal, direct product factor
7C2×#18011821C211yesmaximal, characteristic, complemented
8C22×SD16×C149C211yesmaximal, characteristic, complemented
9C22×D596C2211yescharacteristic
10C22×D596C2211yescharacteristic
11C22×C22⋊D149—22no—
12C2×#14558723—24no—
13C2×#14558723C2214yescomplemented
14C2×D1192—24no—
15C2×D1192C2214yescomplemented
16C2×#14558721—24no—
17C2×#14558721C2214yescomplemented
18C22×#11924746C2211yescharacteristic
19#18011907—22no—
20#18011907C2214yescomplemented
21#18011900—22no—
22#18011900C2214yescomplemented
23C2×#14558713—22no—
24C2×C4×Dic149C2211yescharacteristic
25#18011821C2214yescomplemented
26C22×Q8×C149C2211yescharacteristic
27C22×D4×C149C2211yescharacteristic
28C2×SD16×C149—24no—
29C2×SD16×C149C2214yescomplemented
30C22×C8×C149C2211yescharacteristic
31C23×D149—21no—
32C23×D149—21no—
33C2×D596—22no—
34C2×D596—22no—
35C2×D596—22no—
36C2×D596—22no—
37C2×D596—21no—
38C2×D596—21no—
39C2×D596C2312yes—
40C2×D596C2312yes—
41C2×C22⋊D149—28no—
42C2×C22⋊D149—48no—
43C22×Dic149D412yes—
44#14558723—28no—
45D1192—28no—
46#14558721—28no—
47C2×#11924746D414yescomplemented
48C2×#11924746C2312yes—
49#14558713—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—22no—
68C22×D149—42no—
69C22×D149—42no—
70C22×D149—44no—
71C22×D149—44no—
72D596—22no—
73D596—22no—
74D596—22no—
75D596—22no—
76D596—42no—
77D596—42no—
78C22⋊D149—416no—
79C2×Dic149—24no—
80C2×Dic149C2×D414yes—
81#11924746C2×D414yescomplemented
82C23×C149—22no—
83C23×C149—42no—
84C23×C149—44no—
85C23×C149C2×D411yescharacteristic
86Q8×C149—22no—
87Q8×C149—22no—
88Q8×C149—42no—
89D4×C149—22no—
90D4×C149—22no—
91D4×C149—42no—
92C2×C4×C149—22no—
93C2×C4×C149—42no—
94C2×C4×C149C2×D411yescharacteristic
95C2×C4×C149C2×D412yes—
96C2×C4×C149C2×D412yes—
97C2×C4×C149C2411yescharacteristic
98C8×C149C2×D414yescomplemented
99C22×C149—42no—
100C22×C149—44no—
101C22×C149—84no—
102C22×C149#12712yes—
103C22×C149AGL(1,ℤ/8)14yes—
104C22×C149C22×D411yescharacteristic
105C2×D149—42no—
106C2×D149—42no—
107C2×D149—44no—
108C2×D149—44no—
109C2×D149—84no—
110C2×D149—84no—
111C4×C149—42no—
112C4×C149#12712yes—
113C4×C149C22×D411yescharacteristic
114C4×C149C22×D411yescharacteristic
115Dic149—24no—
116C2×C149—82no—
117C2×C149#49614yescomplemented
118C2×C149C2×#12711yescharacteristic
119C2×C149C2×AGL(1,ℤ/8)12yes—
120D149—82no—
121D149—82no—
122C149C2×#49611yescharacteristic, complemented, Sylow
123C2×#496—1491nomaximal, Sylow
124C22×SD16—1491no—
125C22×SD16D14911yescharacteristic, complemented
126C22×D8—1491no—
127C22×D8—1491no—
128C2×#127—1491no—
129C2×#124—1491no—
130#496—1498no—
131C2×#97—1491no—
132C22×Q8C2×D14911yescharacteristic
133C22×D4—2982no—
134C22×D4—1491no—
135C22×D4—1491no—
136C22×D4C2×D14911yescharacteristic
137C2×SD16—24no—
138C2×SD16—2984no—
139C2×SD16—1494no—
140C2×SD16C2×D14914yescomplemented
141C2×D8—2984no—
142C2×D8—2984no—
143C2×D8—1494no—
144C2×D8—1494no—
145C22×C8—1491no—
146C22×C8C2×D14911yescharacteristic
147#127—2982no—
148#127—1494no—
149#124—2982no—
150#124—1494no—
151C2×C22⋊C4—2982no—
152C2×C42—1491no—
153#97—1494no—
154C24—21no—
155C24—2981no—
156C24—2981no—
157C2×Q8—21no—
158C2×Q8—22no—
159C2×Q8—22no—
160C2×Q8C22×D14912yes—
161C2×D4—22no—
162C2×D4—21no—
163C2×D4—22no—
164C2×D4—2988no—
165C2×D4—2982no—
166C2×D4—2982no—
167C2×D4—2981no—
168C2×D4—2981no—
169C2×D4—2982no—
170C2×D4—2982no—
171C2×D4—5968no—
172C2×D4—1492no—
173C2×D4—1492no—
174C2×D4C22×D14912yes—
175C22×C4—21no—
176C22×C4—1492no—
177C22×C4C22×D14911yescharacteristic
178SD16—28no—
179SD16—2988no—
180D8—2988no—
181D8—2988no—
182C2×C8—1494no—
183C2×C8—1492no—
184C2×C8C22⋊D14914yescomplemented
185C2×C8C22×D14912yes—
186C22⋊C4—2988no—
187C42—1492no—
188C42—1492no—
189C23—22no—
190C23—42no—
191C23—44no—
192C23—2982no—
193C23—2982no—
194C23—5962no—
195C23—5962no—
196C23—5964no—
197C23—5964no—
198C23D4×D14911yescharacteristic
199Q8—22no—
200Q8—22no—
201Q8—42no—
202D4—22no—
203D4—22no—
204D4—42no—
205D4—2982no—
206D4—2982no—
207D4—2982no—
208D4—2982no—
209D4—59616no—
210D4—5962no—
211D4—5962no—
212C2×C4—22no—
213C2×C4—42no—
214C2×C4—2984no—
215C2×C4—1494no—
216C2×C4D4×D14911yescharacteristic
217C2×C4D4×D14912yes—
218C2×C4C2×C22⋊D14912yes—
219C2×C4C23×D14911yescharacteristic
220C8—1494no—
221C8C2×C22⋊D14914yescomplemented
222C22—44no—
223C22—42no—
224C22—84no—
225C22—5964no—
226C22—5964no—
227C22—5962no—
228C22—5962no—
229C22—11924no—
230C22—11924no—
231C22#1801190712yes—
232C22#1801193814yes—
233C22C2×D4×D14911yescharacteristic
234C4—42no—
235C4—2984no—
236C4#1801190712yes—
237C4C2×D4×D14911yescharacteristic
238C4C22×C22⋊D14911yescharacteristic
239C2—82no—
240C2—11922no—
241C2—11922no—
242C2#2375001114yesdirect product factor
243C2C2×#1801190711yescharacteristic
244C2C2×#1801193812yes—
subgroupG/H
centerC23D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC22×SD16×C149C2
socleC23×C149C2×D4
hypercenterC22×SD16D149
hypocenterC149C2×#496
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×#14558723C2semidirect
2. C22×D1192C2semidirect
3. C22×#14558721C2semidirect
4. C2×#18011907C2semidirect
5. C2×#18011900C2semidirect
6. #23750011C2direct (N × H)
7. C2×#18011821C2semidirect
8. C22×SD16×C149C2semidirect
13. C2×#14558723C22semidirect
15. C2×D1192C22semidirect
17. C2×#14558721C22semidirect
20. #18011907C22semidirect
22. #18011900C22semidirect
25. #18011821C22semidirect
29. C2×SD16×C149C22semidirect
47. C2×#11924746D4semidirect
64. C2×C8×C149D4semidirect
81. #11924746C2×D4semidirect
98. C8×C149C2×D4semidirect
117. C2×C149#496semidirect
122. C149C2×#496semidirect
125. C22×SD16D149semidirect
140. C2×SD16C2×D149semidirect
184. C2×C8C22⋊D149semidirect
221. C8C2×C22⋊D149semidirect
242. C2#23750011direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145587232
C22×D11922
C22×#145587212
C2×#180119072
C2×#180119002
#237500112
C2×#180118212
C22×SD16×C1492
C2×#496149