Finite Group Databasebeta

← #355×D239 #44486224

Subgroups — #355×D239 #44486224

Order 30592.

260 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 57 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#124×D239C211yesmaximal, characteristic
2#101×D239C212yesmaximal, complemented
3#29504569C211yesmaximal, characteristic, complemented
4#29504568C212yesmaximal, complemented
5#355×C239C211yesmaximal, characteristic, complemented
6C2×Q8×D239C2211yescharacteristic
7C2×D4×D239C411yescharacteristic
8M16×D239—22no—
9#21439949C2211yescharacteristic
10#21439948C411yescharacteristic
11#21439947C411yescharacteristic
12#21439946—22no—
13C22⋊C4×D239—22no—
14C42×D239C411yescharacteristic
15#21439879C2212yescomplemented
16#21439878—22no—
17#124×C239C2211yescharacteristic
18#101×C239C2212yescomplemented
19C23×D239—21no—
20C2×Dic478C2×C411yescharacteristic
21C2×Dic478D412yes—
22Q8×D239—41no—
23Q8×D239—41no—
24C2×D956C2×C411yescharacteristic
25C2×C22⋊D239—21no—
26D4×D239—41no—
27D4×D239—41no—
28C2×C4×D239—21no—
29C2×C4×D239C2×C411yescharacteristic
30C2×C4×D239D412yes—
31#16838532—22no—
32#16838531—42no—
33C8×D239—42no—
34C22⋊Dic239—22no—
35(C2×D239)⋊C4—22no—
36(C2×D239)⋊C4—22no—
37C4×Dic239—21no—
38C4×Dic239C2×C411yescharacteristic
39C2×Q8×C239C2311yescharacteristic
40C2×D4×C239C2×C411yescharacteristic
41M16×C239—22no—
42C22⋊C4×C239—22no—
43C42×C239C2×C411yescharacteristic
44C22×D239—21no—
45C22×D239—44no—
46C22×D239—41no—
47C22×D239—41no—
48C22×D239C22⋊C411yescharacteristic
49Dic478—41no—
50Dic478—42no—
51D956—41no—
52C22⋊D239—42no—
53C2×Dic239—21no—
54C2×Dic239C22⋊C411yescharacteristic
55C2×Dic239C22⋊C412yes—
56C4×D239—22no—
57C4×D239—22no—
58C4×D239—21no—
59C4×D239—21no—
60C4×D239—42no—
61C239⋊C8—42no—
62C23×C239—21no—
63Q8×C239—41no—
64D4×C239—41no—
65C2×C4×C239—21no—
66C2×C4×C239C22×C411yescharacteristic
67C2×C4×C239C2×D412yes—
68C8×C239—42no—
69C22×C239—42no—
70C22×C239—41no—
71C22×C239C2×C22⋊C411yescharacteristic
72C2×D239—22no—
73C2×D239—42no—
74C2×D239—41no—
75C2×D239—82no—
76C2×D239—82no—
77C2×D239#9911yescharacteristic
78C2×D239#9911yescharacteristic
79C4×C239—22no—
80C4×C239—21no—
81C4×C239—41no—
82Dic239—21no—
83Dic239—22no—
84Dic239—41no—
85C2×C239—21no—
86C2×C239—81no—
87C2×C239C2×#9911yescharacteristic
88D239—21no—
89D239—81no—
90D239#35512yesdirect product factor
91C239C2×#35511yescharacteristic, complemented, Sylow
92C2×#355—2391nomaximal, Sylow
93C2×#124—2391no—
94C2×#101—2392no—
95#355—2391no—
96#355—2392no—
97#355D23911yescharacteristic, direct product factor
98C22×Q8—2391no—
99C22×D4—2391no—
100C2×M16—4782no—
101#124—4782no—
102#124—2391no—
103#124—2391no—
104#124—2391no—
105#124C2×D23911yescharacteristic
106C2×C22⋊C4—4782no—
107C2×C42—2391no—
108#101—4782no—
109#101—2392no—
110#101C2×D23912yescomplemented
111C24—4781no—
112C2×Q8—9561no—
113C2×Q8—9561no—
114C2×Q8—2391no—
115C2×Q8—2392no—
116C2×Q8C22×D23911yescharacteristic
117C2×D4—9561no—
118C2×D4—9561no—
119C2×D4—4781no—
120C2×D4—2391no—
121C2×D4C4×D23911yescharacteristic
122C22×C4—4781no—
123C22×C4—2391no—
124C22×C4—2392no—
125M16—22no—
126M16—9562no—
127M16—4782no—
128C2×C8—9562no—
129C22⋊C4—22no—
130C22⋊C4—4782no—
131C22⋊C4—4782no—
132C22⋊C4—4782no—
133C42—4781no—
134C42—2391no—
135C42C4×D23911yescharacteristic
136C23—21no—
137C23—9564no—
138C23—9561no—
139C23—9561no—
140C23—4781no—
141C23—2391no—
142Q8—41no—
143Q8—9562no—
144Q8—9561no—
145D4—41no—
146D4—9561no—
147D4—9562no—
148C2×C4—21no—
149C2×C4—9562no—
150C2×C4—4782no—
151C2×C4—4782no—
152C2×C4—4781no—
153C2×C4—4781no—
154C2×C4—4781no—
155C2×C4—2391no—
156C2×C4—2392no—
157C2×C4C2×C4×D23911yescharacteristic
158C2×C4D4×D23912yes—
159C8—42no—
160C8—9562no—
161C22—42no—
162C22—41no—
163C22—19122no—
164C22—19122no—
165C22—9562no—
166C22—9561no—
167C22—4782no—
168C22—2391no—
169C22—2391no—
170C22C22⋊C4×D23911yescharacteristic
171C4—22no—
172C4—21no—
173C4—41no—
174C4—9561no—
175C4—4781no—
176C4—4782no—
177C2—21no—
178C2—81no—
179C2—19121no—
180C2—4781no—
181C2—2392no—
182C2#99×D23911yescharacteristic
subgroupG/H
centerC2#99×D239
commutatorC2×C4×C239C22×C4
FrattiniC2×Q8C22×D239
Fitting#355×C239C2
socleC2×C239C2×#99
prime radicalC2×D4×D239C4
cosocleC2×Q8×C239C23
hypercenter#355D239
hypocenterC239C2×#355
LCSG ▷ C2×C4×C239 ▷ C22×C239 ▷ C2×C239 ▷ C239
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
2. #101×D239C2semidirect
3. #29504569C2semidirect
4. #29504568C2semidirect
5. #355×C239C2semidirect
15. #21439879C22semidirect
18. #101×C239C22semidirect
90. D239#355direct (N × H)
91. C239C2×#355semidirect
97. #355D239direct (N × H)
110. #101C2×D239semidirect

Maximal subgroups

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

subgroupindex
#124×D2392
#101×D2392
#295045692
#295045682
#355×C2392
C2×#355239