Finite Group Databasebeta

← #44483166

Subgroups — #44483166

Order 30592.

218 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 69 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#29505306C211yesmaximal, characteristic
2#29504829C211yesmaximal, characteristic, complemented
3#29504513C212yesmaximal, complemented
4#29504511C212yesmaximal, complemented
5C2×#97×C239C211yesmaximal, characteristic, complemented
6#21439954—21no—
7#21439952C2211yescharacteristic
8#21439948C2211yescharacteristic
9#21439943—21no—
10#21439939C411yescharacteristic
11#21439934C411yescharacteristic
12C4×Dic478C411yescharacteristic
13C4×D956C411yescharacteristic
14C4×C22⋊D239—21no—
15#21439917—21no—
16C4⋊(C239⋊C8)—21no—
17C22⋊(C239⋊C8)—21no—
18#21439871C2212yes—
19C22×C8×C239—21no—
20C2×C42×C239C2211yescharacteristic
21#97×C239—21no—
22#97×C239C2212yes—
23C2×Dic478C2×C411yescharacteristic
24C2×D956C2×C411yescharacteristic
25C2×C22⋊D239—21no—
26C2×C4×D239—21no—
27C2×C239⋊C8—22no—
28C4⋊Dic239C2×C411yescharacteristic
29C4⋊Dic239C2×C411yescharacteristic
30Dic239⋊C4—21no—
31Dic239⋊C4—21no—
32Dic239⋊C4—21no—
33Dic239⋊C4—21no—
34C22⋊Dic239—21no—
35(C2×D239)⋊C4—21no—
36(C2×D239)⋊C4—21no—
37(C2×D239)⋊C4—21no—
38(C2×D239)⋊C4—21no—
39C4×Dic239—21no—
40C22×C4×C239C2×C411yescharacteristic
41C22×C4×C239D411yescharacteristic
42C22×C4×C239D411yescharacteristic
43C2×C8×C239—24no—
44C2×C8×C239—22no—
45C42×C239C2×C411yescharacteristic
46C42×C239D411yescharacteristic
47C42×C239D411yescharacteristic
48C42×C239C2311yescharacteristic
49C22×D239—21no—
50Dic478—41no—
51D956—41no—
52C22⋊D239—42no—
53C2×Dic239—21no—
54C2×Dic239—21no—
55C2×Dic239—21no—
56C4×D239—42no—
57C239⋊C8—42no—
58C23×C239C22⋊C411yescharacteristic
59C2×C4×C239—22no—
60C2×C4×C239—41no—
61C2×C4×C239—41no—
62C2×C4×C239C22⋊C411yescharacteristic
63C2×C4×C239C22⋊C411yescharacteristic
64C2×C4×C239C22⋊C411yescharacteristic
65C2×C4×C239C22×C411yescharacteristic
66C2×C4×C239C2×D411yescharacteristic
67C2×C4×C239C2×D411yescharacteristic
68C8×C239—24no—
69C22×C239—21no—
70C22×C239—21no—
71C22×C239#10412yes—
72C22×C239C2×C22⋊C411yescharacteristic
73C2×D239—41no—
74C2×D239—41no—
75C2×D239—41no—
76C4×C239—21no—
77C4×C239—21no—
78C4×C239—21no—
79C4×C239—21no—
80C4×C239—21no—
81C4×C239—21no—
82Dic239—41no—
83Dic239—41no—
84Dic239—41no—
85C2×C239—22no—
86C2×C239#41311yescharacteristic
87C2×C239C2×#10411yescharacteristic
88C2×C239#42111yescharacteristic
89D239—81no—
90C239#153211yescharacteristic, complemented, Sylow
91#1532—2391nomaximal, Sylow
92#529—2391no—
93#432—2391no—
94C2×#97D23911yescharacteristic, complemented
95#330—2392no—
96#329—2392no—
97C22×C8—21no—
98#126—4781no—
99#125—2391no—
100#124—2391no—
101#123—4781no—
102C22⋊Q8—2391no—
103#121—2391no—
104C4×Q8—2391no—
105C4×D4—4781no—
106C4×D4—2391no—
107#117—4781no—
108C2×C42C2×D23911yescharacteristic
109C4⋊C8—4781no—
110C22⋊C8—4781no—
111#97—21no—
112#97—2392no—
113#97C2×D23912yes—
114C2×Q8—2391no—
115C2×D4—4781no—
116C2×D4—2391no—
117C22×C4—4781no—
118C22×C4C4×D23911yescharacteristic
119C22×C4C22⋊D23911yescharacteristic
120C22×C4D95611yescharacteristic
121C2×C8—24no—
122C2×C8—22no—
123C2×C8—4782no—
124C4⋊C4—4781no—
125C4⋊C4—4781no—
126C4⋊C4—4781no—
127C4⋊C4—4781no—
128C4⋊C4—2391no—
129C4⋊C4—2391no—
130C22⋊C4—4781no—
131C22⋊C4—4781no—
132C22⋊C4—4781no—
133C22⋊C4—4781no—
134C22⋊C4—4781no—
135C42—4781no—
136C42C4×D23911yescharacteristic
137C42C22⋊D23911yescharacteristic
138C42D95611yescharacteristic
139C42C22×D23911yescharacteristic
140C23—4781no—
141C23(C2×D239)⋊C411yescharacteristic
142Q8—9561no—
143D4—9561no—
144D4—9562no—
145C2×C4—22no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—9562no—
149C2×C4—4781no—
150C2×C4—4781no—
151C2×C4—4781no—
152C2×C4(C2×D239)⋊C411yescharacteristic
153C2×C4(C2×D239)⋊C411yescharacteristic
154C2×C4(C2×D239)⋊C411yescharacteristic
155C2×C4C2×C4×D23911yescharacteristic
156C2×C4C2×C22⋊D23911yescharacteristic
157C2×C4C2×D95611yescharacteristic
158C8—24no—
159C8—9562no—
160C22—21no—
161C22—21no—
162C22—9561no—
163C22—9561no—
164C22—9561no—
165C22#2143988812yes—
166C22C2×(C2×D239)⋊C411yescharacteristic
167C4—21no—
168C4—21no—
169C4—21no—
170C4—21no—
171C4—21no—
172C4—21no—
173C4—9561no—
174C4—9561no—
175C4—9561no—
176C2—22no—
177C2—19121no—
178C2#2950475411yescharacteristic
179C2C2×#2143988811yescharacteristic
180C2#2950478811yescharacteristic
subgroupG/H
centerC22C2×(C2×D239)⋊C4
commutatorC2×C4×C239C22×C4
FrattiniC42C22×D239
FittingC2×#97×C239C2
socleC22×C239C2×C22⋊C4
prime radical#21439934C4
cosocleC42×C239C23
hypercenterC2×#97D239
hypocenterC239#1532
LCSG ▷ C2×C4×C239 ▷ C22×C239 ▷ C239
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
2. #29504829C2semidirect
3. #29504513C2semidirect
4. #29504511C2semidirect
5. C2×#97×C239C2semidirect
90. C239#1532semidirect
94. C2×#97D239semidirect

Maximal subgroups

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

subgroupindex
#295053062
#295048292
#295045132
#295045112
C2×#97×C2392
#1532239