Finite Group Databasebeta

← #34060134

Subgroups — #34060134

Order 19072.

218 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 56 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#23750644C211yesmaximal, characteristic, complemented
2#23750570C211yesmaximal, characteristic, complemented
3#23750478C212yesmaximal, complemented
4#23750477C212yesmaximal
5#23750160C211yesmaximal, characteristic
6C4⋊#11924753—21no—
7#18011968C2212yes—
8C4×#11924753—21no—
9(C2×#10597010)⋊C4—21no—
10(C2×#10597010)⋊C4—21no—
11(C2×#10597010)⋊C4C2212yes—
12#18011906—21no—
13#18011899C411yescharacteristic, complemented
14#18011896—21no—
15#18011891C2211yescharacteristic
16#18011886C2211yescharacteristic
17#18011876C411yescharacteristic, complemented
18#18011873—21no—
19#18011873C411yescharacteristic, complemented
20#18011869—21no—
21C42×D149C2211yescharacteristic
22#125×C149C411yescharacteristic, complemented
23C22×#10597010—22no—
24C2×#11924753—22no—
25C2×Dic298C2×C411yescharacteristic
26C2×D596—21no—
27C2×D596C2×C411yescharacteristic
28C2×C4×D149—21no—
29C2×C4×D149D411yescharacteristic
30C2×C4×D149D411yescharacteristic
31C2×C4×D149C2311yescharacteristic
32C4⋊Dic149—21no—
33#14558715—21no—
34#14558713—21no—
35#14558713—21no—
36#14558713—21no—
37#14558713—21no—
38#14558713—21no—
39C4×Dic149—21no—
40C4×Dic149C2×C411yescharacteristic
41C4×Dic149D411yescharacteristic
42C4×Dic149D411yescharacteristic
43C4⋊C4×C149—21no—
44C4⋊C4×C149—21no—
45C4⋊C4×C149C2×C411yescharacteristic
46C4⋊C4×C149C2×C411yescharacteristic
47C42×C149C2×C411yescharacteristic
48C2×#10597010—42no—
49C2×#10597010—42no—
50C2×#10597010—42no—
51#11924753—42no—
52C22×D149—21no—
53C22×D149C2×D411yescharacteristic
54Dic298—41no—
55D596—41no—
56D596—42no—
57C2×Dic149—21no—
58C2×Dic149C22⋊C411yescharacteristic
59C2×Dic149C22⋊C411yescharacteristic
60C2×Dic149C2×D411yescharacteristic
61C4×D149—22no—
62C4×D149—41no—
63C4×D149—41no—
64C4×D149—42no—
65C2×C4×C149—21no—
66C2×C4×C149—21no—
67C2×C4×C149C22⋊C411yescharacteristic
68C2×C4×C149C22⋊C411yescharacteristic
69C2×C4×C149C22×C411yescharacteristic
70C22×C149C2×C22⋊C411yescharacteristic
71C2×D149—21no—
72C2×D149—21no—
73C2×D149—41no—
74C2×D149—41no—
75C2×D149—41no—
76C2×D149#13512yes—
77#10597010—82no—
78C4×C149—21no—
79C4×C149—21no—
80C4×C149—21no—
81C4×C149—41no—
82C4×C149—41no—
83Dic149—21no—
84Dic149—21no—
85Dic149—21no—
86Dic149—41no—
87C2×C149#41011yescharacteristic
88C2×C149#41611yescharacteristic
89C2×C149#42111yescharacteristic
90D149—22no—
91D149—81no—
92C149#152111yescharacteristic, complemented, Sylow
93#1521—1491nomaximal, Sylow
94#529—1491no—
95#431—1491no—
96#383—1491no—
97#328—1492no—
98#327—1492no—
99#126—2981no—
100#125#1059701011yescharacteristic, complemented
101#124—1491no—
102#123—2981no—
103C22⋊Q8—1491no—
104#121—1491no—
105C4×Q8—1491no—
106C4×D4—2981no—
107C4×D4—1491no—
108#117—2981no—
109C2×C42—1491no—
110C4⋊C8—2981no—
111C22⋊C8—1492no—
112C4×C8—2981no—
113#95—2981no—
114#95—2981no—
115#95—1492no—
116C2×Q8—1491no—
117C2×D4—2981no—
118C2×D4—1491no—
119C22×C4—2981no—
120C22×C4—2982no—
121C22×C4—1491no—
122C22×C4—1491no—
123C22×C4—1491no—
124C2×C8—2982no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—2981no—
128C4⋊C4—2981no—
129C4⋊C4C2×#1059701011yescharacteristic
130C4⋊C4C2×#1059701011yescharacteristic
131C22⋊C4—2981no—
132C22⋊C4—2981no—
133C22⋊C4—2981no—
134C22⋊C4—2981no—
135C22⋊C4—2981no—
136C42—2981no—
137C42—1491no—
138C42—1491no—
139C42—1491no—
140C42C2×#1059701011yescharacteristic
141C23—2981no—
142C23—1491no—
143Q8—5961no—
144D4—5961no—
145D4—5962no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—2982no—
149C2×C4—2981no—
150C2×C4—5961no—
151C2×C4—5961no—
152C2×C4—5962no—
153C2×C4—5962no—
154C2×C4—5962no—
155C2×C4—5962no—
156C2×C4—1491no—
157C2×C4—1491no—
158C2×C4—1491no—
159C2×C4C22⋊#1059701011yescharacteristic
160C2×C4C22⋊#1059701011yescharacteristic
161C2×C4C22×#1059701011yescharacteristic
162C8—5962no—
163C22—2981no—
164C22—2981no—
165C22—5961no—
166C22—5961no—
167C22—5961no—
168C22—1492no—
169C22C2×C22⋊#1059701011yescharacteristic
170C4—21no—
171C4—21no—
172C4—21no—
173C4—41no—
174C4—41no—
175C4—2981no—
176C4—2981no—
177C4—2981no—
178C4—5961no—
179C4—11922no—
180C2—2982no—
181C2—11921no—
182C2#2375060611yescharacteristic
183C2#2375061511yescharacteristic
184C2#2375062211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#125×C149C4
socleC22×C149C2×C22⋊C4
prime radical#18011886C22
cosocleC2×C4×D149C23
hypercenter#125#10597010
hypocenterC149#1521
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
1. #23750644C2semidirect
2. #23750570C2semidirect
3. #23750478C2semidirect
13. #18011899C4semidirect
17. #18011876C4semidirect
19. #18011873C4semidirect
22. #125×C149C4semidirect
92. C149#1521semidirect
100. #125#10597010semidirect

Maximal subgroups

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

subgroupindex
#237506442
#237505702
#237504782
#237504772
#237501602
#1521149