Finite Group Databasebeta

← #34043865

Subgroups — #34043865

Order 19072.

194 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 53 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#23750345C211yesmaximal, characteristic
2#23749976C211yesmaximal, characteristic, complemented
3#23749921C211yesmaximal, characteristic, complemented
4#23749915C211yesmaximal, characteristic
5#23749370C211yesmaximal, characteristic, complemented
6#23749357C211yesmaximal, characteristic, complemented
7D4⋊C8×C149C211yesmaximal, characteristic
8#18011911C2211yescharacteristic
9#18011911C2211yescharacteristic
10#18011904—22no—
11#18011898—21no—
12#18011890—21no—
13C4×Dic298C2211yescharacteristic
14#18011876—21no—
15#18011870—21no—
16#18011845—21no—
17#18011842—21no—
18C4⋊#11924746C2211yescharacteristic
19#18011836—22no—
20#18011836—21no—
21#18011832—21no—
22C4×D4×C149C2211yescharacteristic
23C4⋊C8×C149C2211yescharacteristic
24C4×C8×C149C2211yescharacteristic
25C2×Dic298—21no—
26C2×Dic298—21no—
27C2×Dic298D411yescharacteristic
28C2×#11924746—21no—
29C4⋊Dic149—21no—
30C4⋊Dic149—21no—
31C4⋊Dic149—21no—
32C4⋊Dic149D412yes—
33C4⋊Dic149D411yescharacteristic
34#14558715—22no—
35#14558715—21no—
36C22⋊Dic149—22no—
37C22⋊Dic149—22no—
38C4×Dic149—22no—
39C4×Dic149—21no—
40C2×D4×C149D411yescharacteristic
41C22×C4×C149—21no—
42C2×C8×C149—21no—
43C2×C8×C149—21no—
44C4⋊C4×C149D411yescharacteristic
45C22⋊C4×C149—21no—
46C42×C149C2311yescharacteristic
47Dic298—21no—
48Dic298—21no—
49Dic298—41no—
50Dic298—41no—
51Dic298—42no—
52C2×Dic149—22no—
53C2×Dic149—21no—
54C2×Dic149—21no—
55C2×Dic149—41no—
56#11924746—41no—
57C23×C149—21no—
58D4×C149—21no—
59D4×C149—21no—
60C2×C4×C149—21no—
61C2×C4×C149—41no—
62C2×C4×C149—41no—
63C2×C4×C149C2×D411yescharacteristic
64C2×C4×C149C2×D411yescharacteristic
65C2×C4×C149C2×D411yescharacteristic
66C8×C149—41no—
67C8×C149—41no—
68C22×C149—41no—
69C22×C149—41no—
70C22×C149—41no—
71C22×C149#12011yescharacteristic
72C4×C149—21no—
73C4×C149—41no—
74C4×C149#13511yescharacteristic
75C4×C149#13511yescharacteristic
76C4×C149#13711yescharacteristic
77C4×C149#13711yescharacteristic
78Dic149—41no—
79Dic149—42no—
80Dic149—41no—
81Dic149—81no—
82C2×C149—81no—
83C2×C149#45211yescharacteristic
84C2×C149#45211yescharacteristic
85C2×C149#45411yescharacteristic
86C149#163811yescharacteristic, complemented, Sylow
87#1638—1491nomaximal, Sylow
88#556—1491no—
89#487—1491no—
90#477—1491no—
91#476—1491no—
92#332—1491no—
93Q8⋊C8—1491no—
94D4⋊C8D14911yescharacteristic
95C4⋊Q8—1491no—
96C4⋊Q8—1491no—
97#126—2982no—
98#124—2981no—
99C22⋊Q8—2981no—
100C4×Q8—2981no—
101C4×Q8—1491no—
102C4×D4C2×D14911yescharacteristic
103#117—2981no—
104#107—2981no—
105#106—2981no—
106C4⋊C8—1491no—
107C4⋊C8C2×D14911yescharacteristic
108#103—2981no—
109#103—2982no—
110#102—2981no—
111C4×C8C2×D14911yescharacteristic
112C2×Q8—2981no—
113C2×Q8—2981no—
114C2×Q8—1491no—
115C2×D4D59611yescharacteristic
116C22×C4—21no—
117C2×C8—21no—
118C2×C8—21no—
119C2×C8—2981no—
120C4⋊C4—2982no—
121C4⋊C4—2981no—
122C4⋊C4—2981no—
123C4⋊C4—2981no—
124C4⋊C4—2981no—
125C4⋊C4—1492no—
126C4⋊C4—1491no—
127C4⋊C4D59611yescharacteristic
128C22⋊C4—21no—
129C22⋊C4—2982no—
130C22⋊C4—2982no—
131C42—2982no—
132C42—2981no—
133C42C22×D14911yescharacteristic
134C23—21no—
135Q8—2981no—
136Q8—2981no—
137Q8—5962no—
138Q8—5961no—
139Q8—5961no—
140D4—21no—
141D4—21no—
142C2×C4—21no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—2981no—
146C2×C4—2981no—
147C2×C4—2982no—
148C2×C4—5961no—
149C2×C4D4×D14911yescharacteristic
150C2×C4D4×D14911yescharacteristic
151C2×C4C2×D59611yescharacteristic
152C8—41no—
153C8—41no—
154C8—5961no—
155C22—41no—
156C22—41no—
157C22—41no—
158C22#1801188111yescharacteristic
159C4—21no—
160C4—41no—
161C4—5961no—
162C4—5962no—
163C4—5961no—
164C4—11921no—
165C4#1801193011yescharacteristic
166C4#1801193311yescharacteristic
167C4#1801194011yescharacteristic
168C4#1801194411yescharacteristic
169C2—81no—
170C2#2374978811yescharacteristic
171C2#2374978911yescharacteristic
172C2#2374979911yescharacteristic
subgroupG/H
centerC22#18011881
commutator, cosocleC42×C149C23
FrattiniC42C22×D149
FittingD4⋊C8×C149C2
socleC22×C149#120
prime radicalC2×D4×C149D4
hypercenterD4⋊C8D149
hypocenterC149#1638
LCSG ▷ C42×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #23749976C2semidirect
3. #23749921C2semidirect
5. #23749370C2semidirect
6. #23749357C2semidirect
86. C149#1638semidirect

Maximal subgroups

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

subgroupindex
#237503452
#237499762
#237499212
#237499152
#237493702
#237493572
D4⋊C8×C1492
#1638149