Finite Group Databasebeta

← #34060227

Subgroups — #34060227

Order 19072.

202 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 58 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#23750645C211yesmaximal, characteristic
2#23750628C211yesmaximal, characteristic
3#23750485C212yesmaximal, complemented
4#23750484C212yesmaximal, complemented
5#23750177C211yesmaximal, characteristic
6C2×#14558745—21no—
7#18011978C2212yes—
8#18011978C2212yes—
9C4⋊#11924753—21no—
10C22⋊#11924753—21no—
11#18011966—21no—
12#18011910C2211yescharacteristic
13#18011909C2211yescharacteristic
14#18011901—21no—
15#18011890C411yescharacteristic
16#18011888—21no—
17Q8×Dic149C411yescharacteristic
18#18011876—21no—
19#18011876C411yescharacteristic
20#18011867—21no—
21C2×C4×Dic149C2211yescharacteristic
22C22⋊Q8×C149C411yescharacteristic
23#14558745—42no—
24C2×#11924753—22no—
25C2×#11924753—22no—
26C2×Dic298—21no—
27C2×Dic298C2×C411yescharacteristic
28C22×Dic149D411yescharacteristic
29C22×Dic149D411yescharacteristic
30C4⋊Dic149—21no—
31C4⋊Dic149C2×C411yescharacteristic
32#14558715—21no—
33#14558715—21no—
34#14558715—21no—
35#14558715—21no—
36#14558715—21no—
37C22⋊Dic149—21no—
38C4×Dic149—21no—
39C4×Dic149—21no—
40C4×Dic149C2×C411yescharacteristic
41C4×Dic149D411yescharacteristic
42C4×Dic149D411yescharacteristic
43C4×Dic149C2311yescharacteristic
44C2×Q8×C149C2×C411yescharacteristic
45C22×C4×C149C2×C411yescharacteristic
46C4⋊C4×C149—21no—
47C4⋊C4×C149C2×C411yescharacteristic
48C22⋊C4×C149—21no—
49#11924753—42no—
50#11924753—42no—
51Dic298—41no—
52Dic298—41no—
53Dic298—41no—
54C2×Dic149—21no—
55C2×Dic149—21no—
56C2×Dic149—22no—
57C2×Dic149—21no—
58C2×Dic149—21no—
59C2×Dic149C22⋊C411yescharacteristic
60C2×Dic149C22⋊C411yescharacteristic
61C2×Dic149C2×D411yescharacteristic
62C2×Dic149C2×D411yescharacteristic
63C23×C149C22⋊C411yescharacteristic
64Q8×C149—41no—
65C2×C4×C149—21no—
66C2×C4×C149—21no—
67C2×C4×C149—41no—
68C2×C4×C149C22⋊C411yescharacteristic
69C2×C4×C149C22×C411yescharacteristic
70C22×C149—21no—
71C22×C149—21no—
72C22×C149—21no—
73C22×C149C2×C22⋊C411yescharacteristic
74C4×C149—21no—
75C4×C149—21no—
76C4×C149—41no—
77C4×C149—41no—
78Dic149—21no—
79Dic149—21no—
80Dic149—41no—
81Dic149—41no—
82Dic149AGL(1,ℤ/8)11yescharacteristic
83Dic149#13711yescharacteristic
84Dic149#13712yes—
85C2×C149—41no—
86C2×C149#41311yescharacteristic
87C2×C149#41711yescharacteristic
88C2×C149#41911yescharacteristic
89C149#155911yescharacteristic, complemented, Sylow
90#1559—1491nomaximal, Sylow
91#533—1491no—
92#432—1491no—
93#423—1491no—
94#333—1492no—
95#332—1492no—
96C2×M16—2981no—
97C4⋊Q8—1491no—
98C4⋊Q8—1491no—
99#125—2981no—
100C22⋊Q8—2981no—
101C22⋊Q8—1491no—
102C22⋊Q8#1059701011yescharacteristic
103C4×Q8—2981no—
104C4×Q8—1491no—
105C4×Q8—1491no—
106#117—2981no—
107C2×C42—1491no—
108C4⋊C8—2981no—
109C4⋊C8—1492no—
110C4⋊C8—1492no—
111C22⋊C8—2981no—
112#97—2981no—
113C2×Q8—2981no—
114C2×Q8—1491no—
115C2×Q8C2×#1059701011yescharacteristic
116C22×C4—1491no—
117C22×C4—1491no—
118C22×C4C2×#1059701011yescharacteristic
119M16—5962no—
120C2×C8—2982no—
121C2×C8—2982no—
122C4⋊C4—21no—
123C4⋊C4—2981no—
124C4⋊C4—2981no—
125C4⋊C4—2981no—
126C4⋊C4—2981no—
127C4⋊C4—2981no—
128C4⋊C4—2981no—
129C4⋊C4—1491no—
130C4⋊C4C2×#1059701011yescharacteristic
131C22⋊C4—21no—
132C22⋊C4—2981no—
133C42—2981no—
134C42—2981no—
135C42—1491no—
136C42—1491no—
137C42—1491no—
138C42—1491no—
139C23C22⋊#1059701011yescharacteristic
140Q8—41no—
141Q8—5961no—
142Q8—5961no—
143Q8—5961no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—41no—
147C2×C4—2981no—
148C2×C4—2981no—
149C2×C4—2982no—
150C2×C4—2981no—
151C2×C4—2981no—
152C2×C4—1491no—
153C2×C4—1491no—
154C2×C4—1491no—
155C2×C4—1491no—
156C2×C4C22⋊#1059701011yescharacteristic
157C2×C4C22×#1059701011yescharacteristic
158C8—5962no—
159C8—5962no—
160C22—21no—
161C22—21no—
162C22—21no—
163C22C2×C22⋊#1059701011yescharacteristic
164C4—21no—
165C4—21no—
166C4—41no—
167C4—41no—
168C4—2981no—
169C4—2981no—
170C4—5961no—
171C4—5961no—
172C4—1491no—
173C4—1491no—
174C4—1492no—
175C2—41no—
176C2#2375061211yescharacteristic
177C2#2375061611yescharacteristic
178C2#2375061811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC22⋊Q8×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC23×C149C22⋊C4
cosocleC4×Dic149C23
hypercenterC22⋊Q8#10597010
hypocenterC149#1559
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #23750485C2semidirect
4. #23750484C2semidirect
89. C149#1559semidirect

Maximal subgroups

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

subgroupindex
#237506452
#237506282
#237504852
#237504842
#237501772
#1559149