Finite Group Databasebeta

← #34060189

Subgroups — #34060189

Order 19072.

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

normal subgroups only

This group has 256 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#23750642C211yesmaximal, characteristic, complemented
2C2×#18011978C211yesmaximal, characteristic, complemented
3#23750484C212yesmaximal, complemented
4#23750483C212yesmaximal, complemented
5#23750170C211yesmaximal, characteristic
6C22×#11924753—21no—
7#18011978—21no—
8#18011978C2212yes—
9#18011978C2212yes—
10C22⋊#11924753—21no—
11C4×#11924753—21no—
12C2×#14558735—21no—
13#18011910C2211yescharacteristic
14#18011907C2211yescharacteristic
15#18011897—21no—
16#18011885C411yescharacteristic
17#18011883—21no—
18D4×Dic149C411yescharacteristic
19#18011873C411yescharacteristic
20#18011871—21no—
21C2×C4×Dic149C2211yescharacteristic
22#121×C149C411yescharacteristic
23C2×#11924753—22no—
24C2×#11924753—22no—
25C2×#11924753—42no—
26#14558735—42no—
27#14558735—42no—
28C2×Dic298—21no—
29C2×D596C2×C411yescharacteristic
30C2×C22⋊D149—21no—
31C2×C22⋊D149—21no—
32C2×C22⋊D149—21no—
33C22×Dic149—21no—
34C22×Dic149D411yescharacteristic
35C22×Dic149D411yescharacteristic
36C2×C4×D149—21no—
37C4⋊Dic149C2×C411yescharacteristic
38#14558715—21no—
39C22⋊Dic149—21no—
40#14558713—21no—
41#14558713—21no—
42C4×Dic149C2×C411yescharacteristic
43C4×Dic149D411yescharacteristic
44C4×Dic149D411yescharacteristic
45C4×Dic149C2311yescharacteristic
46C2×D4×C149—21no—
47C2×D4×C149C2×C411yescharacteristic
48C22×C4×C149C2×C411yescharacteristic
49C4⋊C4×C149C2×C411yescharacteristic
50C22⋊C4×C149—21no—
51#11924753—42no—
52#11924753—42no—
53C22×D149—21no—
54Dic298—41no—
55Dic298—41no—
56D596—41no—
57C22⋊D149—42no—
58C22⋊D149—41no—
59C22⋊D149—41no—
60C22⋊D149—42no—
61C2×Dic149—22no—
62C2×Dic149—21no—
63C2×Dic149—42no—
64C2×Dic149C22⋊C411yescharacteristic
65C2×Dic149C22⋊C411yescharacteristic
66C2×Dic149D812yes—
67C2×Dic149SD1612yes—
68C2×Dic149C2×D411yescharacteristic
69C2×Dic149C2×D411yescharacteristic
70C4×D149—42no—
71C23×C149—21no—
72C23×C149C22⋊C411yescharacteristic
73D4×C149—41no—
74D4×C149—42no—
75C2×C4×C149—21no—
76C2×C4×C149—41no—
77C2×C4×C149C22⋊C411yescharacteristic
78C2×C4×C149C22×C411yescharacteristic
79C22×C149—21no—
80C22×C149—21no—
81C22×C149—41no—
82C22×C149—41no—
83C22×C149—41no—
84C22×C149#10212yes—
85C22×C149C2×C22⋊C411yescharacteristic
86C2×D149—41no—
87C2×D149—41no—
88C2×D149—41no—
89C4×C149—21no—
90C4×C149—21no—
91C4×C149—41no—
92Dic149—21no—
93Dic149—41no—
94Dic149#10212yes—
95Dic149C2×D811yescharacteristic
96Dic149C2×SD1611yescharacteristic
97Dic149#13512yes—
98C2×C149—22no—
99C2×C149—81no—
100C2×C149#41311yescharacteristic
101C2×C149C2×#10211yescharacteristic
102C2×C149#41611yescharacteristic
103D149—81no—
104C149#154011yescharacteristic, complemented, Sylow
105#1540—1491nomaximal, Sylow
106#532—1491no—
107#431—1491no—
108C2×C4⋊C8—1491no—
109#332—1492no—
110#331—1492no—
111C2×#41—2981no—
112C22×C8—2981no—
113C4⋊Q8—1491no—
114#127—1491no—
115#124—2981no—
116#121—2981no—
117#121—1491no—
118#121#1059701011yescharacteristic
119C4×D4—2981no—
120C4×D4—1491no—
121C4×D4—1491no—
122C2×C42—1491no—
123C4⋊C8—2981no—
124C4⋊C8—1492no—
125C4⋊C8—1492no—
126C22⋊C8—2981no—
127C4×C8—2981no—
128#41—5962no—
129#41—5962no—
130C2×Q8—2981no—
131C2×D4—21no—
132C2×D4—2981no—
133C2×D4—2981no—
134C2×D4—2981no—
135C2×D4—1491no—
136C2×D4C2×#1059701011yescharacteristic
137C22×C4—2981no—
138C22×C4—2981no—
139C22×C4—1491no—
140C22×C4—1491no—
141C22×C4C2×#1059701011yescharacteristic
142C2×C8—2982no—
143C2×C8—2982no—
144C2×C8—5962no—
145C4⋊C4—2981no—
146C4⋊C4—1491no—
147C4⋊C4C2×#1059701011yescharacteristic
148C22⋊C4—21no—
149C22⋊C4—2981no—
150C22⋊C4—2981no—
151C22⋊C4—2981no—
152C42—1491no—
153C42—1491no—
154C42—1491no—
155C42—1491no—
156C23—21no—
157C23—2981no—
158C23C22⋊#1059701011yescharacteristic
159Q8—5961no—
160Q8—5961no—
161D4—41no—
162D4—42no—
163D4—5961no—
164D4—5962no—
165D4—5962no—
166D4—5961no—
167D4—5961no—
168C2×C4—21no—
169C2×C4—41no—
170C2×C4—2982no—
171C2×C4—2981no—
172C2×C4—5962no—
173C2×C4—5962no—
174C2×C4—1491no—
175C2×C4—1492no—
176C2×C4—1492no—
177C2×C4—1491no—
178C2×C4—1491no—
179C2×C4—1491no—
180C2×C4C22⋊#1059701011yescharacteristic
181C2×C4C22×#1059701011yescharacteristic
182C8—5962no—
183C8—5962no—
184C22—21no—
185C22—21no—
186C22—41no—
187C22—41no—
188C22—41no—
189C22—5961no—
190C22—5961no—
191C22—5961no—
192C22#1801197312yes—
193C22C2×C22⋊#1059701011yescharacteristic
194C4—21no—
195C4—21no—
196C4—41no—
197C4—2981no—
198C4—5961no—
199C4—1491no—
200C4—1492no—
201C4—1491no—
202C4—1492no—
203C2—22no—
204C2—81no—
205C2—11921no—
206C2#2375061211yescharacteristic
207C2C2×#1801197311yescharacteristic
208C2#2375061511yescharacteristic
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#1540
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #23750642C2semidirect
2. C2×#18011978C2semidirect
3. #23750484C2semidirect
4. #23750483C2semidirect
104. C149#1540semidirect

Maximal subgroups

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

subgroupindex
#237506422
C2×#180119782
#237504842
#237504832
#237501702
#1540149