Finite Group Databasebeta

← #34060010

Subgroups — #34060010

Order 19072.

262 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 62 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#23750641C211yesmaximal, characteristic, complemented
2C4×#14558745C211yesmaximal, characteristic, complemented
3#23750473C212yesmaximal, complemented
4D4⋊#11924753C212yesmaximal, complemented
5#23750170C211yesmaximal, characteristic
6C2×#14558745—21no—
7C4⋊#11924753C2212yes—
8C22⋊#11924753—21no—
9#18011966—21no—
10C4×#11924753—21no—
11C4×#11924753C2212yes—
12C2×#14558735—21no—
13#18011910C411yescharacteristic
14#18011907C411yescharacteristic
15#18011897—21no—
16#18011885C411yescharacteristic
17#18011883—21no—
18D4×Dic149C2211yescharacteristic
19#18011873C2211yescharacteristic
20#18011871—21no—
21C2×C4×Dic149C2211yescharacteristic
22#121×C149C411yescharacteristic
23#14558745—24no—
24C2×#11924753—22no—
25C2×#11924753—22no—
26#14558735—44no—
27C2×Dic298—21no—
28C2×D596C2×C411yescharacteristic
29C2×C22⋊D149—21no—
30C2×C22⋊D149—21no—
31C2×C22⋊D149—21no—
32C22×Dic149—21no—
33C22×Dic149D411yescharacteristic
34C22×Dic149D411yescharacteristic
35C2×C4×D149—21no—
36C4⋊Dic149C2×C411yescharacteristic
37#14558715—21no—
38C22⋊Dic149—21no—
39#14558713—21no—
40#14558713—21no—
41C4×Dic149C2×C411yescharacteristic
42C4×Dic149D411yescharacteristic
43C4×Dic149D411yescharacteristic
44C4×Dic149C2311yescharacteristic
45C2×D4×C149—21no—
46C2×D4×C149C2×C411yescharacteristic
47C22×C4×C149C2×C411yescharacteristic
48C4⋊C4×C149C2×C411yescharacteristic
49C22⋊C4×C149—21no—
50#11924753—24no—
51#11924753—42no—
52C22×D149—21no—
53Dic298—42no—
54D596—22no—
55C22⋊D149—42no—
56C22⋊D149—42no—
57C22⋊D149—42no—
58C2×Dic149—22no—
59C2×Dic149—22no—
60C2×Dic149—21no—
61C2×Dic149—42no—
62C2×Dic149C22⋊C411yescharacteristic
63C2×Dic149C22⋊C411yescharacteristic
64C2×Dic149C2×D411yescharacteristic
65C2×Dic149C2×D411yescharacteristic
66C4×D149—42no—
67C23×C149—21no—
68C23×C149C22⋊C411yescharacteristic
69D4×C149—22no—
70D4×C149—42no—
71C2×C4×C149—22no—
72C2×C4×C149—21no—
73C2×C4×C149C22⋊C411yescharacteristic
74C2×C4×C149C22×C411yescharacteristic
75C22×C149—21no—
76C22×C149—21no—
77C22×C149—21no—
78C22×C149—41no—
79C22×C149—41no—
80C22×C149—41no—
81C22×C149C2×C22⋊C411yescharacteristic
82C2×D149—41no—
83C2×D149—41no—
84C2×D149—41no—
85C4×C149—21no—
86C4×C149—41no—
87C4×C149#13112yes—
88Dic149—21no—
89Dic149—21no—
90Dic149—41no—
91Dic149#10412yes—
92Dic149AGL(1,ℤ/8)12yes—
93C2×C149—41no—
94C2×C149—81no—
95C2×C149#40811yescharacteristic
96C2×C149#41811yescharacteristic
97C2×C149C2×#10411yescharacteristic
98D149—81no—
99C149#148411yescharacteristic, complemented, Sylow
100#1484—1491nomaximal, Sylow
101#532—1491no—
102#431—1491no—
103C4×M16—1491no—
104D4⋊C8—1492no—
105D4⋊C8—1492no—
106C2×#41—2981no—
107C2×M16—2981no—
108C4⋊Q8—1491no—
109#127—1491no—
110#124—2981no—
111#121—2981no—
112#121—1491no—
113#121#1059701011yescharacteristic
114C4×D4—2981no—
115C4×D4—1491no—
116C4×D4—1491no—
117C2×C42—1491no—
118C4⋊C8—1492no—
119C22⋊C8—2981no—
120#97—2981no—
121C4×C8—2981no—
122C4×C8—1492no—
123#41—5964no—
124C2×Q8—2981no—
125C2×D4—21no—
126C2×D4—2981no—
127C2×D4—2981no—
128C2×D4—2981no—
129C2×D4—1491no—
130C2×D4C2×#1059701011yescharacteristic
131C22×C4—2981no—
132C22×C4—2981no—
133C22×C4—1491no—
134C22×C4—1491no—
135C22×C4C2×#1059701011yescharacteristic
136M16—2984no—
137C2×C8—2982no—
138C2×C8—2982no—
139C4⋊C4—2981no—
140C4⋊C4—1491no—
141C4⋊C4C2×#1059701011yescharacteristic
142C22⋊C4—21no—
143C22⋊C4—2981no—
144C22⋊C4—2981no—
145C22⋊C4—2981no—
146C42—1491no—
147C42—1491no—
148C42—1491no—
149C42—1491no—
150C23—21no—
151C23—2981no—
152C23C22⋊#1059701011yescharacteristic
153Q8—5962no—
154D4—22no—
155D4—42no—
156D4—2982no—
157D4—5962no—
158D4—5962no—
159D4—5962no—
160C2×C4—22no—
161C2×C4—21no—
162C2×C4—2982no—
163C2×C4—2982no—
164C2×C4—2981no—
165C2×C4—5962no—
166C2×C4—5962no—
167C2×C4—1491no—
168C2×C4—1491no—
169C2×C4—1491no—
170C2×C4—1491no—
171C2×C4C22⋊#1059701011yescharacteristic
172C2×C4C22×#1059701011yescharacteristic
173C8—2984no—
174C8—5962no—
175C22—21no—
176C22—21no—
177C22—21no—
178C22—41no—
179C22—41no—
180C22—41no—
181C22—5961no—
182C22—5961no—
183C22—5961no—
184C22C2×C22⋊#1059701011yescharacteristic
185C4—21no—
186C4—41no—
187C4—2981no—
188C4—2981no—
189C4—5961no—
190C4—1492no—
191C4—1492no—
192C4#1801199812yes—
193C2—41no—
194C2—81no—
195C2—11921no—
196C2#2375059811yescharacteristic
197C2#2375061711yescharacteristic
198C2D149⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#121×C149C4
socleC22×C149C2×C22⋊C4
prime radical#23750170C2
cosocleC4×Dic149C23
hypercenter#121#10597010
hypocenterC149#1484
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #23750641C2semidirect
2. C4×#14558745C2semidirect
3. #23750473C2semidirect
4. D4⋊#11924753C2semidirect
99. C149#1484semidirect

Maximal subgroups

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

subgroupindex
#237506412
C4×#145587452
#237504732
D4⋊#119247532
#237501702
#1484149