Finite Group Databasebeta

← #34054172

Subgroups — #34054172

Order 19072.

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

normal subgroups only

This group has 584 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
1C2×#18011939C212yesmaximal, complemented
2C2×#18011908C211yesmaximal, characteristic, complemented
3C4×#14558736C211yesmaximal, characteristic, complemented
4#23749826C214yesmaximal, complemented
5#23749821C214yesmaximal, complemented
6#23749631C212yesmaximal, complemented
7#423×C149C211yesmaximal, characteristic, complemented
8C2×#14558736C2211yescharacteristic
9C22×D596—22no—
10C22×D596C2212yes—
11#18011939—28no—
12C2×#14558725C2214yescomplemented
13C2×D1192C2214yescomplemented
14#18011908—21no—
15#18011908—21no—
16#18011908C2214yes—
17C4×Dic298C2212yescomplemented
18C4×D596C2212yescomplemented
19C4×C22⋊D149—22no—
20#18011870C2211yescharacteristic
21#18011868—21no—
22C42×D149—21no—
23#18011833C2218yescomplemented
24C2×M16×C149C2212yes—
25C2×C42×C149C2211yescharacteristic
26C4⋊C8×C149C2214yescomplemented
27C23×D149—22no—
28#14558736—22no—
29#14558736D414yescomplemented
30C2×Dic298C2311yescharacteristic
31C2×D596—24no—
32C2×D596—22no—
33C2×D596—24no—
34C2×D596—24no—
35C2×D596—24no—
36C2×D596—48no—
37C2×D596C2314yes—
38C2×D596C2311yescharacteristic
39C2×C22⋊D149—21no—
40C2×C4×D149—21no—
41C2×C4×D149—22no—
42#14558725—28no—
43D1192—28no—
44C4⋊Dic149C2312yes—
45#14558715—22no—
46C22⋊Dic149—21no—
47#14558713—22no—
48C4×Dic149—21no—
49C4×Dic149—22no—
50C22×C4×C149D412yes—
51C22×C4×C149C2311yescharacteristic
52M16×C149—24no—
53C2×C8×C149C2314yes—
54C42×C149D411yescharacteristic
55C42×C149D411yescharacteristic
56C42×C149C2312yes—
57C22×D149—21no—
58C22×D149—24no—
59C22×D149—48no—
60C22×D149—44no—
61Dic298—21no—
62Dic298C2×D412yescomplemented
63D596—24no—
64D596—21no—
65D596—24no—
66D596—48no—
67D596—44no—
68D596—48no—
69D596C2×D412yescomplemented
70C22⋊D149—24no—
71C2×Dic149—21no—
72C2×Dic149—22no—
73C4×D149—24no—
74C4×D149—44no—
75C23×C149C2×D411yescharacteristic
76C2×C4×C149—24no—
77C2×C4×C149C2×D412yes—
78C2×C4×C149C2×D412yes—
79C2×C4×C149C2×D411yescharacteristic
80C2×C4×C149C2×D412yes—
81C2×C4×C149#4112yes—
82C2×C4×C149C2411yescharacteristic
83C8×C149—24no—
84C22×C149—22no—
85C22×C149#12112yes—
86C22×C149C22×D411yescharacteristic
87C2×D149—22no—
88C2×D149—42no—
89C2×D149—44no—
90C2×D149—48no—
91C2×D149—88no—
92C4×C149—22no—
93C4×C149#12112yes—
94C4×C149AGL(1,ℤ/8)14yescomplemented
95C4×C149C22×D411yescharacteristic
96C4×C149C2×#4111yescharacteristic
97Dic149—22no—
98Dic149—42no—
99C2×C149—22no—
100C2×C149C2×#12111yescharacteristic
101C2×C149C2×AGL(1,ℤ/8)12yes—
102D149—42no—
103D149—84no—
104C149#303811yescharacteristic, complemented, Sylow
105#3038—1491nomaximal, Sylow
106C2×AGL(1,ℤ/8)—1492no—
107C2×#127—1491no—
108C4×#41—1491no—
109#460—1494no—
110#459—1494no—
111#423D14911yescharacteristic, complemented
112#418—1492no—
113C2×#41—1491no—
114C22×D4—2982no—
115C22×D4—1492no—
116AGL(1,ℤ/8)—2988no—
117C2×SD16—1494no—
118C2×D8—1494no—
119C2×M16C2×D14912yes—
120#127—2981no—
121#127—2981no—
122#127—1494no—
123C4×Q8—1492no—
124C4×D4—2982no—
125C4×D4—1492no—
126#117—2981no—
127#117—1491no—
128C2×C42—2981no—
129C2×C42C2×D14911yescharacteristic
130C4⋊C8C2×D14914yescomplemented
131#102—1498no—
132C24—2982no—
133#41—2982no—
134#41—1494no—
135C2×Q8—1491no—
136C2×D4—2981no—
137C2×D4—2984no—
138C2×D4—2982no—
139C2×D4—2984no—
140C2×D4—2984no—
141C2×D4—2984no—
142C2×D4—5968no—
143C2×D4—1494no—
144C2×D4—1491no—
145C22×C4—2981no—
146C22×C4—2982no—
147C22×C4D59612yes—
148C22×C4C22×D14911yescharacteristic
149SD16—2988no—
150D8—2988no—
151M16—24no—
152C2×C8C22×D14914yes—
153C4⋊C4—2982no—
154C4⋊C4—1492no—
155C22⋊C4—2981no—
156C22⋊C4—2982no—
157C42—2981no—
158C42—2982no—
159C42D59611yescharacteristic
160C42D59611yescharacteristic
161C42C22×D14912yes—
162C23—2981no—
163C23—2984no—
164C23—5968no—
165C23—5964no—
166C23C2×D59611yescharacteristic
167Q8—2981no—
168Q8—1492no—
169D4—2984no—
170D4—2984no—
171D4—2981no—
172D4—2984no—
173D4—5968no—
174D4—5968no—
175D4—5964no—
176D4—1492no—
177C2×C4—24no—
178C2×C4—2981no—
179C2×C4—2984no—
180C2×C4—2982no—
181C2×C4—5964no—
182C2×C4D4×D14912yes—
183C2×C4C2×D59612yes—
184C2×C4C2×D59612yes—
185C2×C4C2×D59611yescharacteristic
186C2×C4#1455873712yes—
187C2×C4C23×D14911yescharacteristic
188C8—24no—
189C22—22no—
190C22—2982no—
191C22—5962no—
192C22—5968no—
193C22—5964no—
194C22—11928no—
195C22#1801188612yes—
196C22C22×D59611yescharacteristic
197C4—22no—
198C4—2982no—
199C4—5962no—
200C4#1801188612yes—
201C4#1801193914yescomplemented
202C4C2×D4×D14911yescharacteristic
203C4C2×#1455873711yescharacteristic
204C2—22no—
205C2—5962no—
206C2—11924no—
207C2C2×#1801188611yescharacteristic
208C2C2×#1801193912yes—
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#423×C149C2
socleC22×C149C22×D4
hypercenter#423D149
hypocenterC149#3038
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
1. C2×#18011939C2semidirect
2. C2×#18011908C2semidirect
3. C4×#14558736C2semidirect
4. #23749826C2semidirect
5. #23749821C2semidirect
6. #23749631C2semidirect
7. #423×C149C2semidirect
12. C2×#14558725C22semidirect
13. C2×D1192C22semidirect
17. C4×Dic298C22semidirect
18. C4×D596C22semidirect
23. #18011833C22semidirect
26. C4⋊C8×C149C22semidirect
29. #14558736D4semidirect
62. Dic298C2×D4semidirect
69. D596C2×D4semidirect
94. C4×C149AGL(1,ℤ/8)semidirect
104. C149#3038semidirect
111. #423D149semidirect
130. C4⋊C8C2×D149semidirect
201. C4#18011939semidirect

Maximal subgroups

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

subgroupindex
C2×#180119392
C2×#180119082
C4×#145587362
#237498262
#237498212
#237496312
#423×C1492
#3038149