Finite Group Databasebeta

← #34060965

Subgroups — #34060965

Order 19072.

258 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 52 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#23750606C212yesmaximal, complemented
2#23750531C212yesmaximal, complemented
3#23750530C212yesmaximal, complemented
4#23750176C211yesmaximal, characteristic
5#18011990—22no—
6#18011970—22no—
7#18011970C2214yes—
8C2×#14558737C411yescharacteristic, complemented
9C2×#14558737C2211yescharacteristic
10#18011908C2211yescharacteristic
11#18011900C411yescharacteristic, complemented
12#18011900C2211yescharacteristic
13#18011886—22no—
14#18011873—22no—
15C42×D149C411yescharacteristic, complemented
16C4⋊Q8×C149C411yescharacteristic, complemented
17C4⋊#10597010—42no—
18C22⋊#10597010—24no—
19C4×#10597010—42no—
20#14558737—41no—
21#14558737—41no—
22#14558737—41no—
23#14558737—41no—
24C2×D596—21no—
25C2×D596—22no—
26C2×D596C2×C411yescharacteristic
27C2×D596D412yes—
28C2×D596C2311yescharacteristic
29C2×C4×D149—21no—
30C2×C4×D149—21no—
31C2×C4×D149C2×C411yescharacteristic
32C2×C4×D149D412yes—
33#14558713—22no—
34#14558713—22no—
35C4×Dic149—21no—
36C4×Dic149C2×C411yescharacteristic
37C2×Q8×C149C2×C411yescharacteristic
38C2×Q8×C149C2×C411yescharacteristic
39C4⋊C4×C149—22no—
40C42×C149C2×C411yescharacteristic
41C2×#10597010—44no—
42C22×D149—21no—
43C22×D149C22⋊C411yescharacteristic
44C22×D149C2×D412yes—
45D596—42no—
46D596—41no—
47D596—41no—
48D596—44no—
49D596—42no—
50C2×Dic149—21no—
51C2×Dic149C22⋊C411yescharacteristic
52C4×D149—21no—
53C4×D149—21no—
54C4×D149—22no—
55C4×D149—22no—
56C4×D149—42no—
57C4×D149—41no—
58C4×D149—41no—
59Q8×C149—41no—
60Q8×C149—41no—
61C2×C4×C149—21no—
62C2×C4×C149—21no—
63C2×C4×C149C22⋊C412yes—
64C2×C4×C149C22×C411yescharacteristic
65C22×C149C2×C22⋊C411yescharacteristic
66C2×D149—21no—
67C2×D149—22no—
68C2×D149—41no—
69C2×D149—42no—
70C2×D149—42no—
71C2×D149—41no—
72#10597010—84no—
73C4×C149—22no—
74C4×C149—22no—
75C4×C149—21no—
76C4×C149—41no—
77Dic149—41no—
78Dic149#9911yescharacteristic
79Dic149#9911yescharacteristic
80C2×C149—21no—
81C2×C149C2×#9911yescharacteristic
82D149—42no—
83D149—41no—
84D149—81no—
85C149#212611yescharacteristic, complemented, Sylow
86#2126—1491nomaximal, Sylow
87#532—1491no—
88#410—1492no—
89#354—1492no—
90#353—1492no—
91C2×#41—1491no—
92C2×#41—1491no—
93C4⋊Q8#1059701011yescharacteristic, complemented
94#127—1491no—
95#124—1491no—
96#124—1491no—
97#121—2982no—
98C4×D4—2982no—
99#117—2982no—
100C2×C42—1491no—
101#99—2982no—
102#99—1494no—
103#41—5961no—
104#41—5961no—
105#41—5961no—
106#41—5961no—
107C2×Q8C2×#1059701011yescharacteristic
108C2×Q8C2×#1059701011yescharacteristic
109C2×D4—2982no—
110C2×D4—2981no—
111C2×D4—1492no—
112C2×D4—1491no—
113C2×D4—1491no—
114C22×C4—2981no—
115C22×C4—2981no—
116C22×C4—1492no—
117C22×C4—1491no—
118C4⋊C4—22no—
119C4⋊C4—5962no—
120C22⋊C4—2982no—
121C22⋊C4—2982no—
122C22⋊C4—2984no—
123C42—2981no—
124C42—5962no—
125C42—1491no—
126C42C2×#1059701011yescharacteristic
127C23—2981no—
128C23—1491no—
129C23—1492no—
130Q8—41no—
131Q8—41no—
132D4—5962no—
133D4—5961no—
134D4—5961no—
135D4—5964no—
136D4—5962no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—2982no—
140C2×C4—2982no—
141C2×C4—2981no—
142C2×C4—2981no—
143C2×C4—2981no—
144C2×C4—5962no—
145C2×C4—5961no—
146C2×C4—5961no—
147C2×C4—5964no—
148C2×C4—1491no—
149C2×C4C22⋊#1059701012yes—
150C2×C4C22×#1059701011yescharacteristic
151C22—2982no—
152C22—2981no—
153C22—5961no—
154C22—5962no—
155C22—5962no—
156C22—5961no—
157C22C2×C22⋊#1059701011yescharacteristic
158C4—22no—
159C4—22no—
160C4—21no—
161C4—41no—
162C4—5961no—
163C4—1491no—
164C4—1491no—
165C4—11924no—
166C2—21no—
167C2—5962no—
168C2—5961no—
169C2—11921no—
170C2D149⋊#9911yescharacteristic
subgroupG/H
centerC2D149⋊#99
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC4⋊Q8×C149C4
socleC2×C149C2×#99
prime radical#23750176C2
cosocleC2×D596C23
hypercenterC4⋊Q8#10597010
hypocenterC149#2126
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #23750606C2semidirect
2. #23750531C2semidirect
3. #23750530C2semidirect
8. C2×#14558737C4semidirect
11. #18011900C4semidirect
15. C42×D149C4semidirect
16. C4⋊Q8×C149C4semidirect
85. C149#2126semidirect
93. C4⋊Q8#10597010semidirect

Maximal subgroups

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

subgroupindex
#237506062
#237505312
#237505302
#237501762
#2126149