Finite Group Databasebeta

← #34060050

Subgroups — #34060050

Order 19072.

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

normal subgroups only

This group has 246 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#23750646C211yesmaximal, characteristic, complemented
2#23750641C211yesmaximal, characteristic, complemented
3#23750473C212yesmaximal, complemented
4D4⋊#11924753C212yesmaximal, complemented
5#23750170C211yesmaximal, characteristic
6C4⋊#11924753—21no—
7C4⋊#11924753C2212yes—
8C22⋊#11924753—21no—
9C22⋊#11924753—21no—
10#18011966—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
23C2×#11924753—22no—
24C2×#11924753—22no—
25#14558735—44no—
26C2×Dic298—21no—
27C2×D596C2×C411yescharacteristic
28C2×C22⋊D149—21no—
29C2×C22⋊D149—21no—
30C2×C22⋊D149—21no—
31C22×Dic149—21no—
32C22×Dic149D411yescharacteristic
33C22×Dic149D411yescharacteristic
34C2×C4×D149—21no—
35C4⋊Dic149C2×C411yescharacteristic
36#14558715—21no—
37C22⋊Dic149—21no—
38#14558713—21no—
39#14558713—21no—
40C4×Dic149C2×C411yescharacteristic
41C4×Dic149D411yescharacteristic
42C4×Dic149D411yescharacteristic
43C4×Dic149C2311yescharacteristic
44C2×D4×C149—21no—
45C2×D4×C149C2×C411yescharacteristic
46C22×C4×C149C2×C411yescharacteristic
47C4⋊C4×C149C2×C411yescharacteristic
48C22⋊C4×C149—21no—
49#11924753—42no—
50#11924753—42no—
51C22×D149—21no—
52Dic298—42no—
53D596—22no—
54C22⋊D149—42no—
55C22⋊D149—42no—
56C22⋊D149—42no—
57C2×Dic149—22no—
58C2×Dic149—21no—
59C2×Dic149—41no—
60C2×Dic149—42no—
61C2×Dic149C22⋊C411yescharacteristic
62C2×Dic149C22⋊C411yescharacteristic
63C2×Dic149C2×D411yescharacteristic
64C2×Dic149C2×D411yescharacteristic
65C4×D149—42no—
66C23×C149—21no—
67C23×C149C22⋊C411yescharacteristic
68D4×C149—22no—
69D4×C149—42no—
70C2×C4×C149—22no—
71C2×C4×C149—21no—
72C2×C4×C149C22⋊C411yescharacteristic
73C2×C4×C149C22×C411yescharacteristic
74C22×C149—21no—
75C22×C149—21no—
76C22×C149—21no—
77C22×C149—41no—
78C22×C149—41no—
79C22×C149—41no—
80C22×C149C2×C22⋊C411yescharacteristic
81C2×D149—41no—
82C2×D149—41no—
83C2×D149—41no—
84C4×C149—21no—
85C4×C149—41no—
86C4×C149#13112yes—
87Dic149—21no—
88Dic149—21no—
89Dic149—21no—
90Dic149—41no—
91Dic149AGL(1,ℤ/8)12yes—
92C2×C149—41no—
93C2×C149—81no—
94C2×C149#40811yescharacteristic
95C2×C149#41811yescharacteristic
96C2×C149#42111yescharacteristic
97D149—81no—
98C149#149611yescharacteristic, complemented, Sylow
99#1496—1491nomaximal, Sylow
100#532—1491no—
101#432—1491no—
102#431—1491no—
103D4⋊C8—1492no—
104D4⋊C8—1492no—
105C2×#41—2981no—
106C4⋊Q8—1491no—
107#127—1491no—
108#124—2981no—
109#121—2981no—
110#121—1491no—
111#121#1059701011yescharacteristic
112C4×D4—2981no—
113C4×D4—1491no—
114C4×D4—1491no—
115C2×C42—1491no—
116C4⋊C8—2981no—
117C4⋊C8—1492no—
118C22⋊C8—2981no—
119C22⋊C8—2981no—
120#97—2981no—
121C4×C8—1492no—
122#41—5964no—
123C2×Q8—2981no—
124C2×D4—21no—
125C2×D4—2981no—
126C2×D4—2981no—
127C2×D4—2981no—
128C2×D4—1491no—
129C2×D4C2×#1059701011yescharacteristic
130C22×C4—2981no—
131C22×C4—2981no—
132C22×C4—1491no—
133C22×C4—1491no—
134C22×C4C2×#1059701011yescharacteristic
135C2×C8—2982no—
136C2×C8—2982no—
137C4⋊C4—2981no—
138C4⋊C4—1491no—
139C4⋊C4C2×#1059701011yescharacteristic
140C22⋊C4—21no—
141C22⋊C4—2981no—
142C22⋊C4—2981no—
143C22⋊C4—2981no—
144C42—1491no—
145C42—1491no—
146C42—1491no—
147C42—1491no—
148C23—21no—
149C23—2981no—
150C23C22⋊#1059701011yescharacteristic
151Q8—5962no—
152D4—22no—
153D4—42no—
154D4—2982no—
155D4—5962no—
156D4—5962no—
157D4—5962no—
158C2×C4—22no—
159C2×C4—21no—
160C2×C4—2982no—
161C2×C4—2981no—
162C2×C4—5962no—
163C2×C4—5961no—
164C2×C4—5962no—
165C2×C4—1491no—
166C2×C4—1491no—
167C2×C4—1491no—
168C2×C4—1491no—
169C2×C4C22⋊#1059701011yescharacteristic
170C2×C4C22×#1059701011yescharacteristic
171C8—5962no—
172C8—5962no—
173C22—21no—
174C22—21no—
175C22—21no—
176C22—41no—
177C22—41no—
178C22—41no—
179C22—5961no—
180C22—5961no—
181C22—5961no—
182C22C2×C22⋊#1059701011yescharacteristic
183C4—21no—
184C4—41no—
185C4—2981no—
186C4—2981no—
187C4—2981no—
188C4—5961no—
189C4—1492no—
190C4#1801199812yes—
191C2—41no—
192C2—81no—
193C2—11921no—
194C2#2375059811yescharacteristic
195C2#2375061711yescharacteristic
196C2#2375062211yescharacteristic
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#1496
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. #23750646C2semidirect
2. #23750641C2semidirect
3. #23750473C2semidirect
4. D4⋊#11924753C2semidirect
98. C149#1496semidirect

Maximal subgroups

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

subgroupindex
#237506462
#237506412
#237504732
D4⋊#119247532
#237501702
#1496149