Finite Group Databasebeta

← #324×D149 #34042999

Subgroups — #324×D149 #34042999

Order 19072.

328 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 87 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×C4⋊C4×D149C211yesmaximal, characteristic
2C22⋊C8×D149C212yesmaximal
3#23749351C211yesmaximal, characteristic, complemented
4#23749350C212yesmaximal, complemented
5#324×C149C211yesmaximal, characteristic, complemented
6C22×C4×D149C411yescharacteristic
7C22×C4×D149C411yescharacteristic
8C22×C4×D149C2211yescharacteristic
9C2×C8×D149—22no—
10C2×C4⋊Dic149C411yescharacteristic
11C2×#14558715C411yescharacteristic
12C2×#14558715C2211yescharacteristic
13C4⋊C4×D149—22no—
14C4⋊C4×D149—22no—
15C22⋊#11924746C2212yes—
16#18011823—22no—
17C2×C4⋊C4×C149C2211yescharacteristic
18C22⋊C8×C149C2212yes—
19C23×D149C2×C411yescharacteristic
20C22×Dic149C2×C411yescharacteristic
21C22×Dic149C2×C411yescharacteristic
22C22×Dic149C2×C411yescharacteristic
23C2×C4×D149—21no—
24C2×C4×D149—21no—
25C2×C4×D149—22no—
26C2×C4×D149—21no—
27C2×C4×D149—21no—
28C2×C4×D149—42no—
29C2×C4×D149—42no—
30C2×C4×D149C814yescomplemented
31C2×C4×D149D412yes—
32C2×C4×D149D412yes—
33C2×#11924746—22no—
34C8×D149—44no—
35C4⋊Dic149—22no—
36#14558715—22no—
37#14558715—22no—
38C22×C4×C149C2×C411yescharacteristic
39C22×C4×C149C2×C411yescharacteristic
40C22×C4×C149C2311yescharacteristic
41C2×C8×C149—22no—
42C4⋊C4×C149—22no—
43C22×D149—22no—
44C22×D149—22no—
45C22×D149C22⋊C411yescharacteristic
46C22×D149C22⋊C411yescharacteristic
47C22×D149C2×C812yes—
48C22×D149M1612yes—
49C2×Dic149—21no—
50C2×Dic149—21no—
51C2×Dic149—21no—
52C2×Dic149—41no—
53C2×Dic149—41no—
54C2×Dic149C22⋊C412yes—
55C2×Dic149C2×C812yescomplemented
56C4×D149—24no—
57C4×D149—24no—
58C4×D149—24no—
59C4×D149—42no—
60C4×D149—42no—
61C4×D149—42no—
62#11924746—42no—
63C23×C149C22×C411yescharacteristic
64C2×C4×C149—21no—
65C2×C4×C149—21no—
66C2×C4×C149—21no—
67C2×C4×C149—41no—
68C2×C4×C149—41no—
69C2×C4×C149C2×C812yescomplemented
70C2×C4×C149C2×D412yes—
71C8×C149—42no—
72C22×C149—21no—
73C22×C149—21no—
74C22×C149C2×C22⋊C411yescharacteristic
75C22×C149C22×C811yescharacteristic
76C22×C149C2×M1611yescharacteristic
77C2×D149—21no—
78C2×D149—21no—
79C2×D149—24no—
80C2×D149—24no—
81C2×D149C22⋊C812yes—
82C2×D149C22⋊C812yes—
83C2×D149#9912yes—
84C2×D149#10112yes—
85C4×C149—22no—
86C4×C149—22no—
87C4×C149—41no—
88Dic149—22no—
89Dic149—22no—
90Dic149—41no—
91C2×C149—21no—
92C2×C149—21no—
93C2×C149C2×C22⋊C811yescharacteristic
94C2×C149C2×#9911yescharacteristic
95C2×C149C2×#10111yescharacteristic
96D149—22no—
97D149#32414yesdirect product factor
98C149C2×#32411yescharacteristic, complemented, Sylow
99C2×#324—1491nomaximal, Sylow
100C22×C4⋊C4—1491no—
101C2×C22⋊C8—1492no—
102#324—1491no—
103#324—1492no—
104#324D14911yescharacteristic, direct product factor
105C23×C4—1491no—
106C23×C4—1491no—
107C23×C4—1491no—
108C22×C8—2982no—
109C2×C4⋊C4—2982no—
110C2×C4⋊C4—2982no—
111C2×C4⋊C4—1491no—
112C2×C4⋊C4—1491no—
113C2×C4⋊C4—1491no—
114C2×C4⋊C4C2×D14911yescharacteristic
115C22⋊C8—2982no—
116C22⋊C8—1492no—
117C22⋊C8C2×D14912yes—
118C24—1491no—
119C22×C4—2981no—
120C22×C4—2981no—
121C22×C4—2982no—
122C22×C4—2981no—
123C22×C4—2981no—
124C22×C4—5962no—
125C22×C4—5962no—
126C22×C4—1491no—
127C22×C4—1492no—
128C22×C4—1494no—
129C22×C4—1491no—
130C22×C4—1491no—
131C22×C4—1492no—
132C22×C4C4×D14911yescharacteristic
133C22×C4C4×D14911yescharacteristic
134C22×C4C22×D14911yescharacteristic
135C2×C8—22no—
136C2×C8—2982no—
137C2×C8—5964no—
138C4⋊C4—22no—
139C4⋊C4—2982no—
140C4⋊C4—2982no—
141C4⋊C4—2982no—
142C23—2982no—
143C23—2982no—
144C23—1492no—
145C23—1492no—
146C23—1491no—
147C23—1491no—
148C23C2×C4×D14911yescharacteristic
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—2984no—
155C2×C4—2984no—
156C2×C4—2984no—
157C2×C4—2981no—
158C2×C4—2981no—
159C2×C4—2981no—
160C2×C4—5962no—
161C2×C4—5962no—
162C2×C4—5962no—
163C2×C4—5961no—
164C2×C4—5961no—
165C2×C4—1492no—
166C2×C4—1492no—
167C2×C4C8×D14912yescomplemented
168C2×C4D4×D14912yes—
169C8—42no—
170C8—5962no—
171C22—21no—
172C22—21no—
173C22—2984no—
174C22—2984no—
175C22—2981no—
176C22—2981no—
177C22—1492no—
178C22—1492no—
179C22—1492no—
180C22—1492no—
181C22C22⋊C4×D14911yescharacteristic
182C22C2×C8×D14911yescharacteristic
183C22M16×D14911yescharacteristic
184C4—22no—
185C4—22no—
186C4—41no—
187C4—2982no—
188C4—2982no—
189C4—5961no—
190C2—21no—
191C2—21no—
192C2—2982no—
193C2—1494no—
194C2C22⋊C8×D14911yescharacteristic
195C2#99×D14911yescharacteristic
196C2#101×D14911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D149
commutatorC22×C149C22×C8
FrattiniC22×C4C22×D149
Fitting#324×C149C2
socleC22×C149C2×C22⋊C4
prime radicalC23×D149C2×C4
cosocleC22×C4×C149C23
hypercenter#324D149
hypocenterC149C2×#324
LCSG ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
3. #23749351C2semidirect
4. #23749350C2semidirect
5. #324×C149C2semidirect
30. C2×C4×D149C8semidirect
55. C2×Dic149C2×C8semidirect
69. C2×C4×C149C2×C8semidirect
97. D149#324direct (N × H)
98. C149C2×#324semidirect
104. #324D149direct (N × H)
167. C2×C4C8×D149semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D1492
C22⋊C8×D1492
#237493512
#237493502
#324×C1492
C2×#324149