Finite Group Databasebeta

← #353×D239 #44486204

Subgroups — #353×D239 #44486204

Order 30592.

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

normal subgroups only

This group has 368 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#127×D239C211yesmaximal, characteristic
2#99×D239C212yesmaximal, complemented
3#29504565C211yesmaximal, characteristic, complemented
4#29504564C212yesmaximal, complemented
5#353×C239C211yesmaximal, characteristic, complemented
6C2×D4×D239—22no—
7C2×D4×D239C411yescharacteristic, complemented
8C2×D4×D239C2211yescharacteristic
9#21439957C411yescharacteristic, complemented
10#21439956—22no—
11#21439956C411yescharacteristic, complemented
12#21439956C2211yescharacteristic
13C22⋊C4×D239—22no—
14C42×D239C411yescharacteristic, complemented
15#21439875C2212yescomplemented
16#21439874—22no—
17#127×C239C2211yescharacteristic
18#99×C239C2212yescomplemented
19C23×D239—21no—
20C23×D239D412yes—
21C2×D956—22no—
22C2×D956C2×C411yescharacteristic
23C2×D956C2×C411yescharacteristic, complemented
24C2×C22⋊D239—22no—
25C2×C22⋊D239—21no—
26C2×C22⋊D239—22no—
27C2×C22⋊D239D412yes—
28D4×D239—41no—
29D4×D239—41no—
30D4×D239—41no—
31D4×D239—41no—
32D4×D239—48no—
33C2×C4×D239—21no—
34C2×C4×D239—42no—
35C2×C4×D239C2×C411yescharacteristic
36C22⋊Dic239—22no—
37(C2×D239)⋊C4—42no—
38C4×Dic239—21no—
39C4×Dic239C2×C411yescharacteristic, complemented
40C2×D4×C239—22no—
41C2×D4×C239C2×C411yescharacteristic, complemented
42C2×D4×C239C2311yescharacteristic
43C22⋊C4×C239—22no—
44C42×C239C2×C411yescharacteristic, complemented
45C22×D239—22no—
46C22×D239—22no—
47C22×D239—21no—
48C22×D239—44no—
49C22×D239—44no—
50C22×D239—41no—
51C22×D239—41no—
52C22×D239C22⋊C411yescharacteristic
53C22×D239C22⋊C412yes—
54D956—41no—
55D956—44no—
56D956—41no—
57C22⋊D239—42no—
58C22⋊D239—44no—
59C22⋊D239—44no—
60C22⋊D239—42no—
61C2×Dic239—21no—
62C2×Dic239—42no—
63C2×Dic239C22⋊C411yescharacteristic
64C4×D239—24no—
65C4×D239—21no—
66C4×D239—21no—
67C4×D239—84no—
68C23×C239—21no—
69C23×C239C2×D412yes—
70D4×C239—41no—
71D4×C239—44no—
72D4×C239—41no—
73C2×C4×C239—21no—
74C2×C4×C239—42no—
75C2×C4×C239C22×C411yescharacteristic
76C22×C239—22no—
77C22×C239—42no—
78C22×C239—42no—
79C22×C239—41no—
80C22×C239C2×C22⋊C411yescharacteristic
81C2×D239—22no—
82C2×D239—22no—
83C2×D239—44no—
84C2×D239—42no—
85C2×D239—42no—
86C2×D239—41no—
87C2×D239—82no—
88C2×D239—82no—
89C2×D239—82no—
90C2×D239#9911yescharacteristic
91C2×D239#9911yescharacteristic
92C4×C239—22no—
93C4×C239—21no—
94C4×C239—82no—
95Dic239—22no—
96Dic239—21no—
97Dic239—82no—
98C2×C239—21no—
99C2×C239—42no—
100C2×C239—81no—
101C2×C239C2×#9911yescharacteristic
102D239—21no—
103D239—42no—
104D239—81no—
105D239#35312yesdirect product factor
106C239C2×#35311yescharacteristic, complemented, Sylow
107C2×#353—2391nomaximal, Sylow
108C2×#127—2391no—
109C2×#99—2392no—
110#353—2391no—
111#353—2392no—
112#353D23911yescharacteristic, direct product factor
113C22×D4—4782no—
114C22×D4—2391no—
115C22×D4—2391no—
116#127—4782no—
117#127—2391no—
118#127—2391no—
119#127—2391no—
120#127C2×D23911yescharacteristic
121C2×C22⋊C4—4782no—
122C2×C42—2391no—
123#99—4782no—
124#99—2392no—
125#99C2×D23912yescomplemented
126C24—4781no—
127C24—2392no—
128C2×D4—22no—
129C2×D4—9561no—
130C2×D4—9561no—
131C2×D4—9568no—
132C2×D4—9561no—
133C2×D4—9561no—
134C2×D4—4782no—
135C2×D4—4782no—
136C2×D4—4782no—
137C2×D4—4781no—
138C2×D4—2392no—
139C2×D4—2391no—
140C2×D4—2391no—
141C2×D4C4×D23911yescharacteristic, complemented
142C2×D4C22×D23911yescharacteristic
143C22×C4—9562no—
144C22×C4—4781no—
145C22×C4—2391no—
146C22⋊C4—22no—
147C22⋊C4—9562no—
148C22⋊C4—4782no—
149C42—4781no—
150C42—2391no—
151C42C4×D23911yescharacteristic, complemented
152C23—21no—
153C23—9564no—
154C23—9561no—
155C23—9561no—
156C23—9564no—
157C23—4782no—
158C23—4782no—
159C23—4781no—
160C23—2392no—
161C23—2391no—
162C23D4×D23912yes—
163D4—41no—
164D4—41no—
165D4—44no—
166D4—9561no—
167D4—9564no—
168D4—9561no—
169D4—9562no—
170D4—9564no—
171D4—9564no—
172D4—9562no—
173C2×C4—21no—
174C2×C4—42no—
175C2×C4—19124no—
176C2×C4—9562no—
177C2×C4—4784no—
178C2×C4—4781no—
179C2×C4—4781no—
180C2×C4—4781no—
181C2×C4—2391no—
182C2×C4C2×C4×D23911yescharacteristic
183C22—22no—
184C22—42no—
185C22—42no—
186C22—41no—
187C22—19122no—
188C22—19122no—
189C22—19122no—
190C22—9562no—
191C22—9562no—
192C22—9564no—
193C22—9561no—
194C22—4782no—
195C22—4782no—
196C22—2391no—
197C22—2391no—
198C22C22⋊C4×D23911yescharacteristic
199C4—22no—
200C4—21no—
201C4—82no—
202C4—19122no—
203C4—4782no—
204C4—4781no—
205C2—21no—
206C2—42no—
207C2—81no—
208C2—19121no—
209C2—9562no—
210C2—4781no—
211C2—2392no—
212C2#99×D23911yescharacteristic
subgroupG/H
centerC2#99×D239
commutatorC2×C4×C239C22×C4
FrattiniC2×D4C22×D239
Fitting#353×C239C2
socleC2×C239C2×#99
prime radical#127×D239C2
cosocleC2×D4×C239C23
hypercenter#353D239
hypocenterC239C2×#353
LCSG ▷ C2×C4×C239 ▷ C22×C239 ▷ C2×C239 ▷ C239
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
2. #99×D239C2semidirect
3. #29504565C2semidirect
4. #29504564C2semidirect
5. #353×C239C2semidirect
7. C2×D4×D239C4semidirect
9. #21439957C4semidirect
11. #21439956C4semidirect
14. C42×D239C4semidirect
15. #21439875C22semidirect
18. #99×C239C22semidirect
23. C2×D956C2×C4semidirect
39. C4×Dic239C2×C4semidirect
41. C2×D4×C239C2×C4semidirect
44. C42×C239C2×C4semidirect
105. D239#353direct (N × H)
106. C239C2×#353semidirect
112. #353D239direct (N × H)
125. #99C2×D239semidirect
141. C2×D4C4×D239semidirect
151. C42C4×D239semidirect

Maximal subgroups

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

subgroupindex
#127×D2392
#99×D2392
#295045652
#295045642
#353×C2392
C2×#353239