Finite Group Databasebeta

← #44486232

Subgroups — #44486232

Order 30592.

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

normal subgroups only

This group has 250 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#29505323C211yesmaximal, characteristic
2#29504755C212yesmaximal, complemented
3#29504571C211yesmaximal, characteristic, complemented
4#29504568C212yesmaximal, complemented
5#356×C239C211yesmaximal, characteristic, complemented
6C2×#16838549C411yescharacteristic
7C2×#16838549C2211yescharacteristic
8M16×D239—22no—
9#21439957C411yescharacteristic
10#21439949C411yescharacteristic
11#21439949C2211yescharacteristic
12#21439935—22no—
13#21439922—22no—
14C42×D239C411yescharacteristic
15#21439879C2212yes—
16#21439876—22no—
17C4⋊Q8×C239C2211yescharacteristic
18#101×C239C2212yes—
19#16838549—41no—
20#16838549—41no—
21#16838549—41no—
22#16838549—41no—
23C2×D956—21no—
24C2×D956—22no—
25C2×D956C2×C411yescharacteristic
26C2×D956C2×C411yescharacteristic
27C2×D956D412yes—
28C2×C4×D239—21no—
29C2×C4×D239—21no—
30C2×C4×D239C2×C411yescharacteristic
31C2×C4×D239D412yes—
32#16838532—22no—
33#16838531—42no—
34C8×D239—42no—
35(C2×D239)⋊C4—22no—
36(C2×D239)⋊C4—22no—
37C4×Dic239—21no—
38C4×Dic239C2×C411yescharacteristic
39C2×Q8×C239C2×C411yescharacteristic
40C2×Q8×C239C2311yescharacteristic
41M16×C239—22no—
42C4⋊C4×C239—22no—
43C42×C239C2×C411yescharacteristic
44C22×D239—21no—
45C22×D239C22⋊C412yes—
46C22×D239C22⋊C411yescharacteristic
47D956—41no—
48D956—42no—
49D956—44no—
50D956—41no—
51D956—42no—
52C2×Dic239—21no—
53C2×Dic239C22⋊C411yescharacteristic
54C4×D239—22no—
55C4×D239—22no—
56C4×D239—21no—
57C4×D239—21no—
58C4×D239—42no—
59C4×D239—41no—
60C4×D239—41no—
61C239⋊C8—42no—
62Q8×C239—41no—
63Q8×C239—41no—
64C2×C4×C239—21no—
65C2×C4×C239—21no—
66C2×C4×C239C22×C411yescharacteristic
67C2×C4×C239C2×D412yes—
68C8×C239—42no—
69C22×C239C2×C22⋊C411yescharacteristic
70C2×D239—21no—
71C2×D239—22no—
72C2×D239—41no—
73C2×D239—42no—
74C2×D239—42no—
75C2×D239—41no—
76C4×C239—22no—
77C4×C239—22no—
78C4×C239—21no—
79C4×C239—41no—
80Dic239—41no—
81Dic239#9911yescharacteristic
82Dic239#9911yescharacteristic
83C2×C239—21no—
84C2×C239C2×#9911yescharacteristic
85D239—41no—
86D239—42no—
87D239—81no—
88C239#213211yescharacteristic, complemented, Sylow
89#2132—2391nomaximal, Sylow
90#532—2391no—
91#413—2392no—
92#356—2391no—
93#356D23911yescharacteristic, complemented
94#355—2392no—
95C2×#41—2391no—
96C2×#41—2391no—
97C2×M16—4782no—
98C4⋊Q8C2×D23911yescharacteristic
99#127—2391no—
100#124—2391no—
101#124—2391no—
102#121—4782no—
103C4×D4—4782no—
104C2×C42—2391no—
105#101—2392no—
106#101C2×D23912yes—
107#100—4782no—
108#41—9561no—
109#41—9561no—
110#41—9561no—
111#41—9561no—
112C2×Q8C4×D23911yescharacteristic
113C2×Q8C22×D23911yescharacteristic
114C2×D4—4782no—
115C2×D4—4781no—
116C2×D4—2391no—
117C2×D4—2391no—
118C2×D4—2392no—
119C22×C4—4781no—
120C22×C4—4781no—
121C22×C4—2391no—
122C22×C4—2392no—
123M16—22no—
124M16—9562no—
125M16—4782no—
126C2×C8—9562no—
127C4⋊C4—22no—
128C22⋊C4—4782no—
129C22⋊C4—4782no—
130C42—4781no—
131C42—2391no—
132C42C4×D23911yescharacteristic
133C23—4781no—
134C23—2392no—
135C23—2391no—
136Q8—41no—
137Q8—41no—
138D4—9561no—
139D4—9564no—
140D4—9562no—
141D4—9561no—
142D4—9562no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—9562no—
146C2×C4—9561no—
147C2×C4—9561no—
148C2×C4—4782no—
149C2×C4—4782no—
150C2×C4—4781no—
151C2×C4—4781no—
152C2×C4—4781no—
153C2×C4—2391no—
154C2×C4C2×C4×D23911yescharacteristic
155C2×C4D4×D23912yes—
156C8—42no—
157C8—9562no—
158C22—9562no—
159C22—9561no—
160C22—9562no—
161C22—9561no—
162C22—4781no—
163C22—4782no—
164C22C22⋊C4×D23911yescharacteristic
165C4—22no—
166C4—22no—
167C4—21no—
168C4—41no—
169C4—9561no—
170C4—2391no—
171C4—2391no—
172C2—21no—
173C2—19121no—
174C2—9561no—
175C2—9562no—
176C2#99×D23911yescharacteristic
subgroupG/H
centerC2#99×D239
commutatorC2×C4×C239C22×C4
FrattiniC2×Q8C22×D239
Fitting#356×C239C2
socleC2×C239C2×#99
prime radical#29505323C2
cosocleC2×Q8×C239C23
hypercenter#356D239
hypocenterC239#2132
LCSG ▷ C2×C4×C239 ▷ C22×C239 ▷ C2×C239 ▷ C239
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #356

Complements

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

NH ≅ G/Ntype
2. #29504755C2semidirect
3. #29504571C2semidirect
4. #29504568C2semidirect
5. #356×C239C2semidirect
88. C239#2132semidirect
93. #356D239semidirect

Maximal subgroups

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

subgroupindex
#295053232
#295047552
#295045712
#295045682
#356×C2392
#2132239