Finite Group Databasebeta

← #34046361

Subgroups — #34046361

Order 19072.

270 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 55 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#23750188C211yesmaximal, characteristic
2#23749597C212yesmaximal, complemented
3#23749418C211yesmaximal, characteristic, complemented
4#23749417C212yesmaximal, complemented
5#353×C149C211yesmaximal, characteristic, complemented
6C2×#14558735C2211yescharacteristic
7C2×D4×D149C411yescharacteristic, complemented
8#18011907C2211yescharacteristic
9#18011899C411yescharacteristic, complemented
10#18011898C411yescharacteristic, complemented
11#18011883—22no—
12#18011879—22no—
13#18011868C411yescharacteristic, complemented
14#18011867—22no—
15#18011826C2212yescomplemented
16#18011825—22no—
17#127×C149C2211yescharacteristic
18#99×C149C2212yescomplemented
19C23×D149—21no—
20#14558735—42no—
21C2×Dic298C2×C411yescharacteristic
22C2×D596C2×C411yescharacteristic
23C2×C22⋊D149—21no—
24C2×C22⋊D149—22no—
25C2×C22⋊D149D412yes—
26D4×D149—42no—
27C22×Dic149D412yes—
28C2×C4×D149C2×C411yescharacteristic
29#14558715—21no—
30#14558715—42no—
31C22⋊Dic149—22no—
32C22⋊Dic149—22no—
33#14558713—21no—
34#14558713—22no—
35C4×Dic149—42no—
36C4×Dic149C2×C411yescharacteristic
37C2×D4×C149—22no—
38C2×D4×C149C2×C411yescharacteristic
39C2×D4×C149C2311yescharacteristic
40C22⋊C4×C149—22no—
41C42×C149C2×C411yescharacteristic
42C22×D149—21no—
43C22×D149—42no—
44C22×D149—82no—
45C22×D149C22⋊C411yescharacteristic
46Dic298—41no—
47D596—41no—
48C22⋊D149—42no—
49C22⋊D149—42no—
50C22⋊D149—82no—
51C2×Dic149—22no—
52C2×Dic149—22no—
53C2×Dic149—21no—
54C2×Dic149—42no—
55C2×Dic149C22⋊C412yes—
56C2×Dic149C22⋊C411yescharacteristic
57C4×D149—22no—
58C23×C149—21no—
59C23×C149C2×D412yes—
60D4×C149—41no—
61D4×C149—41no—
62D4×C149—82no—
63C2×C4×C149—21no—
64C2×C4×C149—42no—
65C2×C4×C149C22×C411yescharacteristic
66C22×C149—22no—
67C22×C149—42no—
68C22×C149—42no—
69C22×C149—41no—
70C22×C149C2×C22⋊C411yescharacteristic
71C2×D149—21no—
72C2×D149—41no—
73C2×D149—42no—
74C2×D149—41no—
75C2×D149—84no—
76C4×C149—21no—
77C4×C149—41no—
78C4×C149—82no—
79Dic149—22no—
80Dic149—41no—
81Dic149—82no—
82Dic149#9912yes—
83C2×C149—21no—
84C2×C149—42no—
85C2×C149—81no—
86C2×C149C2×#9911yescharacteristic
87D149—41no—
88D149—81no—
89C149#212811yescharacteristic, complemented, Sylow
90#2128—1491nomaximal, Sylow
91#535—1491no—
92#410—1492no—
93#353—1491no—
94#353—1492no—
95#353D14911yescharacteristic, complemented
96C2×#41—1491no—
97C22×D4—1491no—
98#127—1491no—
99#127C2×D14911yescharacteristic
100#124—1491no—
101#124—1491no—
102#121—2982no—
103#120—2982no—
104#117—2982no—
105#117—1491no—
106#99—2982no—
107#99—1492no—
108#99C2×D14912yescomplemented
109C24—2981no—
110#41—5962no—
111C2×Q8—1491no—
112C2×D4—22no—
113C2×D4—2982no—
114C2×D4—2981no—
115C2×D4—5962no—
116C2×D4—1492no—
117C2×D4—1491no—
118C2×D4C4×D14911yescharacteristic
119C2×D4C22×D14911yescharacteristic
120C22×C4—1492no—
121C22×C4—1491no—
122C4⋊C4—2981no—
123C4⋊C4—5962no—
124C22⋊C4—22no—
125C22⋊C4—2981no—
126C22⋊C4—2982no—
127C22⋊C4—2982no—
128C22⋊C4—2982no—
129C42—5962no—
130C42—1491no—
131C42C4×D14911yescharacteristic
132C23—21no—
133C23—2981no—
134C23—5962no—
135C23—1491no—
136C23—11922no—
137C23D4×D14912yes—
138Q8—5961no—
139D4—41no—
140D4—41no—
141D4—82no—
142D4—5961no—
143D4—5962no—
144D4—5962no—
145D4—11922no—
146C2×C4—21no—
147C2×C4—42no—
148C2×C4—2982no—
149C2×C4—2982no—
150C2×C4—2982no—
151C2×C4—2981no—
152C2×C4—5962no—
153C2×C4—1492no—
154C2×C4—1491no—
155C2×C4C2×C4×D14911yescharacteristic
156C22—22no—
157C22—42no—
158C22—42no—
159C22—41no—
160C22—2981no—
161C22—5961no—
162C22—5962no—
163C22—5961no—
164C22—11924no—
165C22C22⋊C4×D14911yescharacteristic
166C4—21no—
167C4—41no—
168C4—82no—
169C4—2982no—
170C4—5961no—
171C4—1492no—
172C4—11922no—
173C2—21no—
174C2—42no—
175C2—81no—
176C2—5961no—
177C2—11921no—
178C2#99×D14911yescharacteristic
subgroupG/H
centerC2#99×D149
commutatorC2×C4×C149C22×C4
FrattiniC2×D4C22×D149
Fitting#353×C149C2
socleC2×C149C2×#99
prime radical#23750188C2
cosocleC2×D4×C149C23
hypercenter#353D149
hypocenterC149#2128
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
2. #23749597C2semidirect
3. #23749418C2semidirect
4. #23749417C2semidirect
5. #353×C149C2semidirect
7. C2×D4×D149C4semidirect
9. #18011899C4semidirect
10. #18011898C4semidirect
13. #18011868C4semidirect
15. #18011826C22semidirect
18. #99×C149C22semidirect
89. C149#2128semidirect
95. #353D149semidirect
108. #99C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237501882
#237495972
#237494182
#237494172
#353×C1492
#2128149