Finite Group Databasebeta

← #34060112

Subgroups — #34060112

Order 19072.

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

normal subgroups only

This group has 252 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#23750648C211yesmaximal, characteristic, complemented
2#23750570C211yesmaximal, characteristic, complemented
3#23750477C214yesmaximal, complemented
4#23750176C211yesmaximal, characteristic
5#18011978—21no—
6#18011968C2212yes—
7#18011966—21no—
8(C2×#10597010)⋊C4—21no—
9(C2×#10597010)⋊C4—21no—
10(C2×#10597010)⋊C4C2212yes—
11C2×#14558737—21no—
12#18011908C411yescharacteristic, complemented
13#18011900—21no—
14#18011886—21no—
15#18011886C2212yes—
16#18011873—21no—
17#18011873C412yescomplemented
18C42×D149C2211yescharacteristic
19C4⋊Q8×C149C411yescharacteristic, complemented
20C22×#10597010—22no—
21C2×#11924753—22no—
22#14558737—44no—
23C2×D596—22no—
24C2×D596—21no—
25C2×D596—21no—
26C2×D596C2×C412yes—
27C2×C4×D149—22no—
28C2×C4×D149D411yescharacteristic
29C2×C4×D149D411yescharacteristic
30C2×C4×D149C2311yescharacteristic
31#14558713—22no—
32#14558713—22no—
33C4×Dic149C2×C411yescharacteristic
34C4×Dic149D411yescharacteristic
35C4×Dic149D411yescharacteristic
36C2×Q8×C149—21no—
37C4⋊C4×C149—21no—
38C4⋊C4×C149C2×C412yes—
39C42×C149C2×C411yescharacteristic
40C2×#10597010—42no—
41C2×#10597010—42no—
42C2×#10597010—42no—
43#11924753—42no—
44C22×D149—22no—
45C22×D149C2×D411yescharacteristic
46D596—42no—
47D596—42no—
48D596—42no—
49D596—44no—
50C2×Dic149C22⋊C411yescharacteristic
51C2×Dic149C22⋊C411yescharacteristic
52C2×Dic149C2×D411yescharacteristic
53C4×D149—22no—
54C4×D149—41no—
55C4×D149—41no—
56C4×D149—44no—
57Q8×C149—42no—
58C2×C4×C149—22no—
59C2×C4×C149C22⋊C411yescharacteristic
60C2×C4×C149C22⋊C411yescharacteristic
61C2×C4×C149C22×C411yescharacteristic
62C22×C149C2×C22⋊C411yescharacteristic
63C2×D149—21no—
64C2×D149—21no—
65C2×D149—42no—
66C2×D149—42no—
67C2×D149—42no—
68C2×D149AGL(1,ℤ/8)12yes—
69#10597010—82no—
70C4×C149—21no—
71C4×C149—21no—
72C4×C149—21no—
73C4×C149—42no—
74Dic149—21no—
75Dic149—21no—
76Dic149—21no—
77C2×C149#41011yescharacteristic
78C2×C149#41811yescharacteristic
79C2×C149#42111yescharacteristic
80D149—22no—
81D149—82no—
82C149#151411yescharacteristic, complemented, Sylow
83#1514—1491nomaximal, Sylow
84#532—1491no—
85#432—1491no—
86#383—1491no—
87#327—1494no—
88C2×#41—2981no—
89C4⋊Q8#1059701011yescharacteristic, complemented
90#127—1491no—
91#124—2981no—
92#121—2981no—
93#121—1492no—
94C4×D4—2981no—
95C4×D4—1492no—
96C2×C42—1491no—
97C4⋊C8—2981no—
98C22⋊C8—1492no—
99#97—2981no—
100#95—2981no—
101#95—2981no—
102#95—1492no—
103#41—5964no—
104C2×Q8—21no—
105C2×D4—2982no—
106C2×D4—2981no—
107C2×D4—2981no—
108C2×D4—1492no—
109C22×C4—2982no—
110C22×C4—2982no—
111C22×C4—1491no—
112C22×C4—1491no—
113C22×C4—1491no—
114C2×C8—2982no—
115C4⋊C4—21no—
116C4⋊C4C2×#1059701012yes—
117C22⋊C4—2982no—
118C22⋊C4—2982no—
119C42—1491no—
120C42—1491no—
121C42—1491no—
122C42C2×#1059701011yescharacteristic
123C23—2982no—
124C23—1491no—
125Q8—42no—
126D4—5962no—
127D4—5962no—
128D4—5962no—
129D4—5964no—
130C2×C4—22no—
131C2×C4—2982no—
132C2×C4—5961no—
133C2×C4—5961no—
134C2×C4—5964no—
135C2×C4—5962no—
136C2×C4—5962no—
137C2×C4—5962no—
138C2×C4—1491no—
139C2×C4—1491no—
140C2×C4—1491no—
141C2×C4C22⋊#1059701011yescharacteristic
142C2×C4C22⋊#1059701011yescharacteristic
143C2×C4C22×#1059701011yescharacteristic
144C8—5962no—
145C22—2981no—
146C22—2981no—
147C22—5962no—
148C22—5962no—
149C22—5962no—
150C22—1492no—
151C22C2×C22⋊#1059701011yescharacteristic
152C4—21no—
153C4—21no—
154C4—21no—
155C4—42no—
156C4—2981no—
157C4—2981no—
158C4—2981no—
159C4—11922no—
160C2—2982no—
161C2—11922no—
162C2#2375060611yescharacteristic
163C2#2375061711yescharacteristic
164C2#2375062411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC4⋊Q8×C149C4
socleC22×C149C2×C22⋊C4
prime radical#23750176C2
cosocleC2×C4×D149C23
hypercenterC4⋊Q8#10597010
hypocenterC149#1514
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #23750648C2semidirect
2. #23750570C2semidirect
3. #23750477C2semidirect
12. #18011908C4semidirect
17. #18011873C4semidirect
19. C4⋊Q8×C149C4semidirect
82. C149#1514semidirect
89. C4⋊Q8#10597010semidirect

Maximal subgroups

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

subgroupindex
#237506482
#237505702
#237504772
#237501762
#1514149