Finite Group Databasebeta

← #34060052

Subgroups — #34060052

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#23750647C211yesmaximal, characteristic, complemented
2#23750643C211yesmaximal, characteristic, complemented
3#23750473C214yesmaximal, complemented
4#23750176C211yesmaximal, characteristic
5#18011978—21no—
6C4⋊#11924753C2212yes—
7#18011968—21no—
8#18011968—21no—
9#18011966—21no—
10C4×#11924753C2212yes—
11C2×#14558737—21no—
12#18011908C411yescharacteristic
13#18011900—21no—
14#18011886—21no—
15#18011886C412yes—
16#18011873—21no—
17#18011873C2212yes—
18C42×D149C2211yescharacteristic
19C4⋊Q8×C149C411yescharacteristic
20C2×#11924753—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×D149C2×C411yescharacteristic
29C2×C4×D149D411yescharacteristic
30C2×C4×D149D411yescharacteristic
31#14558713—22no—
32#14558713—22no—
33C4×Dic149D411yescharacteristic
34C4×Dic149D411yescharacteristic
35C4×Dic149C2311yescharacteristic
36C2×Q8×C149—21no—
37C4⋊C4×C149—21no—
38C4⋊C4×C149C2×C412yes—
39C42×C149C2×C411yescharacteristic
40#11924753—42no—
41#11924753—42no—
42C22×D149—22no—
43C22×D149C22⋊C411yescharacteristic
44D596—24no—
45D596—42no—
46D596—42no—
47D596—44no—
48C2×Dic149C22⋊C411yescharacteristic
49C2×Dic149C2×D411yescharacteristic
50C2×Dic149C2×D411yescharacteristic
51C4×D149—22no—
52C4×D149—22no—
53C4×D149—41no—
54C4×D149—44no—
55Q8×C149—42no—
56C2×C4×C149—22no—
57C2×C4×C149C22⋊C411yescharacteristic
58C2×C4×C149C22⋊C411yescharacteristic
59C2×C4×C149C22×C411yescharacteristic
60C22×C149C2×C22⋊C411yescharacteristic
61C2×D149—21no—
62C2×D149—21no—
63C2×D149—21no—
64C2×D149—42no—
65C2×D149—42no—
66C2×D149—42no—
67C4×C149—21no—
68C4×C149—21no—
69C4×C149—42no—
70C4×C149#13112yes—
71Dic149—21no—
72Dic149—21no—
73Dic149AGL(1,ℤ/8)12yes—
74C2×C149#40811yescharacteristic
75C2×C149#41811yescharacteristic
76C2×C149#42111yescharacteristic
77D149—41no—
78D149—82no—
79C149#149611yescharacteristic, complemented, Sylow
80#1496—1491nomaximal, Sylow
81#532—1491no—
82#432—1491no—
83#431—1491no—
84D4⋊C8—1494no—
85C2×#41—2981no—
86C4⋊Q8#1059701011yescharacteristic
87#127—1491no—
88#124—2981no—
89#121—2981no—
90#121—1492no—
91C4×D4—2981no—
92C4×D4—1492no—
93C2×C42—1491no—
94C4⋊C8—2981no—
95C4⋊C8—1492no—
96C22⋊C8—2981no—
97C22⋊C8—2981no—
98#97—2981no—
99C4×C8—1492no—
100#41—5964no—
101C2×Q8—21no—
102C2×D4—2982no—
103C2×D4—2981no—
104C2×D4—2981no—
105C2×D4—1492no—
106C22×C4—2982no—
107C22×C4—1491no—
108C22×C4—1491no—
109C22×C4—1491no—
110C2×C8—2982no—
111C2×C8—2982no—
112C4⋊C4—21no—
113C4⋊C4C2×#1059701012yes—
114C22⋊C4—2982no—
115C22⋊C4—2982no—
116C42—1491no—
117C42—1491no—
118C42—1491no—
119C42C2×#1059701011yescharacteristic
120C23—2982no—
121C23—1491no—
122Q8—42no—
123D4—2984no—
124D4—5962no—
125D4—5962no—
126D4—5964no—
127C2×C4—22no—
128C2×C4—2982no—
129C2×C4—2982no—
130C2×C4—5961no—
131C2×C4—5964no—
132C2×C4—1491no—
133C2×C4—1491no—
134C2×C4—1491no—
135C2×C4C22⋊#1059701011yescharacteristic
136C2×C4C22⋊#1059701011yescharacteristic
137C2×C4C22×#1059701011yescharacteristic
138C8—5962no—
139C8—5962no—
140C22—2981no—
141C22—2981no—
142C22—2981no—
143C22—5962no—
144C22—5962no—
145C22—5962no—
146C22C2×C22⋊#1059701011yescharacteristic
147C4—21no—
148C4—21no—
149C4—42no—
150C4—2981no—
151C4—2981no—
152C4—1492no—
153C4#1801199912yes—
154C2—5961no—
155C2—11922no—
156C2#2375060011yescharacteristic
157C2#2375061711yescharacteristic
158C2#2375062411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC4⋊Q8×C149C4
socleC22×C149C2×C22⋊C4
prime radical#23750176C2
cosocleC4×Dic149C23
hypercenterC4⋊Q8#10597010
hypocenterC149#1496
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #23750647C2semidirect
2. #23750643C2semidirect
3. #23750473C2semidirect
79. C149#1496semidirect

Maximal subgroups

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

subgroupindex
#237506472
#237506432
#237504732
#237501762
#1496149