Finite Group Databasebeta

← #34060034

Subgroups — #34060034

Order 19072.

252 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 68 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
1#23750647C211yesmaximal, characteristic
2C4×#14558746C211yesmaximal, characteristic
3#23750475C212yesmaximal, complemented
4Q8⋊#11924753C212yesmaximal, complemented
5C4×Q8×D149C211yesmaximal, characteristic
6C2×#14558746—21no—
7C4⋊#11924753C2212yes—
8#18011968—21no—
9#18011966—21no—
10#18011966—21no—
11C4×#11924753C2212yes—
12C2×Q8×D149C411yescharacteristic
13Q8×Dic149C2211yescharacteristic
14C4×Dic298—21no—
15C4×Dic298C411yescharacteristic
16#18011876—21no—
17#18011876C2211yescharacteristic
18C4⋊C4×D149—21no—
19C4⋊C4×D149C411yescharacteristic
20C42×D149—21no—
21C42×D149C2211yescharacteristic
22C4×Q8×C149C411yescharacteristic
23#14558746—24no—
24C2×#11924753—22no—
25C2×#11924753—22no—
26C2×Dic298—21no—
27C2×Dic298C2×C411yescharacteristic
28Q8×D149—22no—
29Q8×D149—22no—
30C2×C4×D149—21no—
31C2×C4×D149—21no—
32C2×C4×D149C2×C411yescharacteristic
33C2×C4×D149D411yescharacteristic
34C2×C4×D149D411yescharacteristic
35C4⋊Dic149—21no—
36C4⋊Dic149C2×C411yescharacteristic
37#14558715—21no—
38#14558715—21no—
39#14558715—21no—
40C4×Dic149—21no—
41C4×Dic149—21no—
42C4×Dic149—21no—
43C4×Dic149D411yescharacteristic
44C4×Dic149D411yescharacteristic
45C4×Dic149C2311yescharacteristic
46C2×Q8×C149C2×C411yescharacteristic
47C4⋊C4×C149—21no—
48C4⋊C4×C149C2×C411yescharacteristic
49C42×C149—21no—
50C42×C149C2×C411yescharacteristic
51#11924753—24no—
52#11924753—42no—
53C22×D149C22⋊C411yescharacteristic
54Dic298—24no—
55Dic298—21no—
56Dic298M1612yescomplemented
57C2×Dic149—21no—
58C2×Dic149—21no—
59C2×Dic149C22⋊C411yescharacteristic
60C2×Dic149C2×D411yescharacteristic
61C2×Dic149C2×D411yescharacteristic
62C4×D149—24no—
63C4×D149—22no—
64C4×D149—21no—
65C4×D149—21no—
66C4×D149—22no—
67C4×D149—42no—
68Q8×C149—21no—
69Q8×C149M1612yescomplemented
70C2×C4×C149—21no—
71C2×C4×C149—21no—
72C2×C4×C149C22⋊C411yescharacteristic
73C2×C4×C149C22⋊C411yescharacteristic
74C2×C4×C149C22×C411yescharacteristic
75C22×C149C2×C22⋊C411yescharacteristic
76C2×D149—21no—
77C2×D149—21no—
78C2×D149#10412yes—
79C4×C149—22no—
80C4×C149—21no—
81C4×C149—21no—
82C4×C149—41no—
83C4×C149C2×M1611yescharacteristic
84C4×C149C2×M1611yescharacteristic
85Dic149—22no—
86Dic149—21no—
87Dic149—21no—
88Dic149—41no—
89Dic149#13712yes—
90C2×C149#40711yescharacteristic
91C2×C149#41911yescharacteristic
92C2×C149C2×#10411yescharacteristic
93D149—22no—
94C149#149111yescharacteristic, complemented, Sylow
95#1491—1491nomaximal, Sylow
96C2×C4×Q8—1491no—
97#432—1491no—
98C4×M16—1491no—
99Q8⋊C8—1492no—
100Q8⋊C8—1492no—
101C22×Q8—1491no—
102C2×M16—2981no—
103C4×Q8—2981no—
104C4×Q8—2981no—
105C4×Q8—1491no—
106C4×Q8—1491no—
107C4×Q8—1491no—
108C4×Q8#1059701011yescharacteristic
109C2×C4⋊C4—2981no—
110C2×C4⋊C4—1491no—
111C2×C42—2981no—
112C2×C42—1491no—
113C4⋊C8—1492no—
114C22⋊C8—2981no—
115#97—2981no—
116#97—2981no—
117C4×C8—1492no—
118C2×Q8—2981no—
119C2×Q8—2982no—
120C2×Q8—2982no—
121C2×Q8—1491no—
122C2×Q8C2×#1059701011yescharacteristic
123C22×C4—2981no—
124C22×C4—2981no—
125C22×C4—1491no—
126C22×C4—1491no—
127C22×C4—1491no—
128M16—2984no—
129C2×C8—2982no—
130C2×C8—2982no—
131C4⋊C4—21no—
132C4⋊C4—2981no—
133C4⋊C4—2981no—
134C4⋊C4—2981no—
135C4⋊C4—2981no—
136C4⋊C4—1491no—
137C4⋊C4C2×#1059701011yescharacteristic
138C42—21no—
139C42—2981no—
140C42—2981no—
141C42—2981no—
142C42—1491no—
143C42—1491no—
144C42—1491no—
145C42C2×#1059701011yescharacteristic
146C23—1491no—
147Q8—21no—
148Q8—2984no—
149Q8—2981no—
150Q8—1492no—
151Q8#1455874612yescomplemented
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—2984no—
155C2×C4—2982no—
156C2×C4—2982no—
157C2×C4—2981no—
158C2×C4—2981no—
159C2×C4—2981no—
160C2×C4—2981no—
161C2×C4—5962no—
162C2×C4—1491no—
163C2×C4—1491no—
164C2×C4—1491no—
165C2×C4C22⋊#1059701011yescharacteristic
166C2×C4C22⋊#1059701011yescharacteristic
167C2×C4C22×#1059701011yescharacteristic
168C8—2984no—
169C8—5962no—
170C22—2981no—
171C22—2981no—
172C22—1492no—
173C22C2×C22⋊#1059701011yescharacteristic
174C4—22no—
175C4—21no—
176C4—21no—
177C4—41no—
178C4—2982no—
179C4—2981no—
180C4—2981no—
181C4—5961no—
182C4—1492no—
183C4D149⋊M1611yescharacteristic
184C4C2×#1455874611yescharacteristic
185C2—2982no—
186C2#2375059611yescharacteristic
187C2#2375061811yescharacteristic
188C2D149⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC4×Q8×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC22×D149C22⋊C4
cosocleC4×Dic149C23
hypercenterC4×Q8#10597010
hypocenterC149#1491
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
3. #23750475C2semidirect
4. Q8⋊#11924753C2semidirect
56. Dic298M16semidirect
69. Q8×C149M16semidirect
94. C149#1491semidirect
151. Q8#14558746semidirect

Maximal subgroups

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

subgroupindex
#237506472
C4×#145587462
#237504752
Q8⋊#119247532
C4×Q8×D1492
#1491149