Finite Group Databasebeta

← #34060047

Subgroups — #34060047

Order 19072.

216 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 60 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#23750643C211yesmaximal, characteristic, complemented
2#23750629C211yesmaximal, characteristic, complemented
3Q8⋊#11924753C212yesmaximal, complemented
4D4⋊#11924753C212yesmaximal, complemented
5#23750154C211yesmaximal, characteristic
6C2×#14558746—21no—
7#18011978—21no—
8C4⋊#11924753—21no—
9C4⋊#11924753C2212yes—
10#18011968—21no—
11C4×#11924753C2212yes—
12#18011904—21no—
13#18011903C411yescharacteristic
14#18011893—21no—
15#18011887C411yescharacteristic
16#18011882C411yescharacteristic
17Q8×Dic149C2211yescharacteristic
18D4×Dic149C2211yescharacteristic
19#18011871—21no—
20#18011867—21no—
21C42×D149C2211yescharacteristic
22#124×C149C411yescharacteristic
23#14558746—42no—
24C2×#11924753—22no—
25C2×#11924753—22no—
26C2×C22⋊D149—21no—
27C22×Dic149—21no—
28C2×C4×D149C2×C411yescharacteristic
29C2×C4×D149D411yescharacteristic
30C2×C4×D149D411yescharacteristic
31C4⋊Dic149—21no—
32C4⋊Dic149C2×C411yescharacteristic
33C4⋊Dic149C2×C411yescharacteristic
34#14558715—21no—
35#14558715—21no—
36#14558715—21no—
37C22⋊Dic149—21no—
38C22⋊Dic149—21no—
39#14558713—21no—
40C4×Dic149—21no—
41C4×Dic149D411yescharacteristic
42C4×Dic149D411yescharacteristic
43C4×Dic149C2311yescharacteristic
44C2×Q8×C149C2×C411yescharacteristic
45C2×D4×C149C2×C411yescharacteristic
46C22⋊C4×C149—21no—
47C22⋊C4×C149—21no—
48C42×C149C2×C411yescharacteristic
49#11924753—42no—
50#11924753—42no—
51C22×D149C22⋊C411yescharacteristic
52C22⋊D149—42no—
53C2×Dic149—21no—
54C2×Dic149—21no—
55C2×Dic149—41no—
56C2×Dic149—41no—
57C2×Dic149C22⋊C411yescharacteristic
58C2×Dic149C2×D411yescharacteristic
59C2×Dic149C2×D411yescharacteristic
60C4×D149—22no—
61C4×D149—21no—
62C4×D149—21no—
63C4×D149—41no—
64C23×C149—21no—
65Q8×C149—22no—
66D4×C149—22no—
67C2×C4×C149—21no—
68C2×C4×C149C22⋊C411yescharacteristic
69C2×C4×C149C22⋊C411yescharacteristic
70C2×C4×C149C22×C411yescharacteristic
71C22×C149—41no—
72C22×C149—41no—
73C22×C149—41no—
74C22×C149C2×C22⋊C411yescharacteristic
75C2×D149—21no—
76C2×D149—21no—
77C2×D149—21no—
78C4×C149—21no—
79C4×C149—21no—
80C4×C149—41no—
81C4×C149#13112yes—
82Dic149—21no—
83Dic149—21no—
84Dic149—41no—
85Dic149—41no—
86Dic149AGL(1,ℤ/8)11yescharacteristic
87Dic149#13711yescharacteristic
88C2×C149—81no—
89C2×C149#40811yescharacteristic
90C2×C149#41711yescharacteristic
91C2×C149#42111yescharacteristic
92D149—41no—
93C149#149511yescharacteristic, complemented, Sylow
94#1495—1491nomaximal, Sylow
95#529—1491no—
96#431—1491no—
97#423—1491no—
98Q8⋊C8—1492no—
99D4⋊C8—1492no—
100C2×M16—2981no—
101#126—2981no—
102#125—1491no—
103#124#1059701011yescharacteristic
104#123—2981no—
105C22⋊Q8—1491no—
106#121—1491no—
107C4×Q8—1491no—
108C4×D4—2981no—
109C4×D4—1491no—
110#117—2981no—
111C2×C42—1491no—
112C4⋊C8—2981no—
113C4⋊C8—2981no—
114C4⋊C8—1492no—
115C22⋊C8—2981no—
116C4×C8—1492no—
117C2×Q8C2×#1059701011yescharacteristic
118C2×D4—2981no—
119C2×D4C2×#1059701011yescharacteristic
120C22×C4—2981no—
121C22×C4—1491no—
122C22×C4—1491no—
123C22×C4—1491no—
124M16—5962no—
125C2×C8—2982no—
126C2×C8—2982no—
127C4⋊C4—2981no—
128C4⋊C4—2981no—
129C4⋊C4—2981no—
130C4⋊C4—2981no—
131C4⋊C4—1491no—
132C4⋊C4—1491no—
133C22⋊C4—21no—
134C22⋊C4—21no—
135C22⋊C4—2981no—
136C22⋊C4—2981no—
137C22⋊C4—2981no—
138C42—2981no—
139C42—1491no—
140C42—1491no—
141C42—1491no—
142C42C2×#1059701011yescharacteristic
143C23—21no—
144C23—1491no—
145Q8—22no—
146D4—22no—
147D4—5962no—
148C2×C4—21no—
149C2×C4—2981no—
150C2×C4—2981no—
151C2×C4—2982no—
152C2×C4—2981no—
153C2×C4—2981no—
154C2×C4—5961no—
155C2×C4—5961no—
156C2×C4—5961no—
157C2×C4—1491no—
158C2×C4—1491no—
159C2×C4—1491no—
160C2×C4C22⋊#1059701011yescharacteristic
161C2×C4C22⋊#1059701011yescharacteristic
162C2×C4C22×#1059701011yescharacteristic
163C8—5962no—
164C8—5962no—
165C22—41no—
166C22—41no—
167C22—41no—
168C22—2981no—
169C22—2981no—
170C22—2981no—
171C22C2×C22⋊#1059701011yescharacteristic
172C4—21no—
173C4—21no—
174C4—41no—
175C4—2981no—
176C4—2981no—
177C4—5961no—
178C4—5961no—
179C4—1491no—
180C4—1491no—
181C4#1801199812yes—
182C2—81no—
183C2—5961no—
184C2#2375059911yescharacteristic
185C2#2375061611yescharacteristic
186C2#2375062211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#124×C149C4
socleC22×C149C2×C22⋊C4
prime radical#18011882C4
cosocleC4×Dic149C23
hypercenter#124#10597010
hypocenterC149#1495
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #23750643C2semidirect
2. #23750629C2semidirect
3. Q8⋊#11924753C2semidirect
4. D4⋊#11924753C2semidirect
93. C149#1495semidirect

Maximal subgroups

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

subgroupindex
#237506432
#237506292
Q8⋊#119247532
D4⋊#119247532
#237501542
#1495149