Finite Group Databasebeta

← #44483794

Subgroups — #44483794

Order 30592.

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

normal subgroups only

This group has 234 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#29505437C211yesmaximal, characteristic
2#29505049C211yesmaximal, characteristic
3#29504979C211yesmaximal, characteristic, complemented
4#29504518C211yesmaximal, characteristic, complemented
5#29504504C211yesmaximal, characteristic, complemented
6#29504501C211yesmaximal, characteristic
7#500×C239C211yesmaximal, characteristic, complemented
8C2×Q8×D239—21no—
9C2×#16838538—21no—
10#21439959—21no—
11#21439938—22no—
12#21439936—21no—
13C4×Dic478C2211yescharacteristic
14C4×D956C2211yescharacteristic
15#21439922—21no—
16#21439893—21no—
17C4⋊(C239⋊C8)C2211yescharacteristic
18C4⋊(C239⋊C8)C2211yescharacteristic
19#21439884—21no—
20#21439880—21no—
21C4⋊Q8×C239C2211yescharacteristic
22C4⋊Q8×C239C2211yescharacteristic
23#107×C239—22no—
24C4×C8×C239C2211yescharacteristic
25C2×Dic478—22no—
26C2×Dic478D411yescharacteristic
27Q8×D239—42no—
28Q8×D239—42no—
29C2×D956D411yescharacteristic
30C2×C4×D239—22no—
31C2×C4×D239—21no—
32#16838538—42no—
33C2×C239⋊C8—21no—
34C2×C239⋊C8—21no—
35C4⋊Dic239D411yescharacteristic
36C4⋊Dic239D411yescharacteristic
37Dic239⋊C4—22no—
38Dic239⋊C4—21no—
39(C2×D239)⋊C4—22no—
40(C2×D239)⋊C4—21no—
41C4×Dic239—21no—
42C2×Q8×C239—21no—
43C2×Q8×C239—21no—
44C2×C8×C239—21no—
45C4⋊C4×C239—21no—
46C4⋊C4×C239—21no—
47C4⋊C4×C239—21no—
48C4⋊C4×C239D412yes—
49C42×C239C2311yescharacteristic
50C22×D239—21no—
51Dic478—21no—
52Dic478—44no—
53Dic478D812yes—
54D956—21no—
55D956Q1612yescomplemented
56C2×Dic239—21no—
57C2×Dic239—21no—
58C2×Dic239—21no—
59C4×D239—44no—
60C4×D239—41no—
61C4×D239—41no—
62C239⋊C8—41no—
63C239⋊C8—41no—
64Q8×C239—41no—
65Q8×C239—41no—
66Q8×C239—41no—
67Q8×C239—41no—
68C2×C4×C239—22no—
69C2×C4×C239—41no—
70C2×C4×C239C2×D411yescharacteristic
71C2×C4×C239C2×D411yescharacteristic
72C2×C4×C239C2×D411yescharacteristic
73C8×C239—22no—
74C22×C239#12011yescharacteristic
75C2×D239—22no—
76C2×D239—41no—
77C2×D239—41no—
78C4×C239—21no—
79C4×C239—42no—
80C4×C239—81no—
81C4×C239C2×D811yescharacteristic
82C4×C239C2×Q1611yescharacteristic
83C4×C239AGL(1,ℤ/8)11yescharacteristic
84C4×C239#13711yescharacteristic
85Dic239—22no—
86Dic239—41no—
87Dic239—41no—
88C2×C239#44711yescharacteristic
89C2×C239#45111yescharacteristic
90C2×C239#45611yescharacteristic
91D239—42no—
92C239#164911yescharacteristic, complemented, Sylow
93#1649—2391nomaximal, Sylow
94D4×Q8—2391no—
95#500D23911yescharacteristic, complemented
96#474—2391no—
97#462—2391no—
98#332—2391no—
99Q8⋊C8—2391no—
100D4⋊C8—2391no—
101C22×Q8—4781no—
102C2×Q16—4781no—
103C4⋊Q8—4781no—
104C4⋊Q8C2×D23911yescharacteristic
105C4⋊Q8C2×D23911yescharacteristic
106C22⋊Q8—4781no—
107C22⋊Q8—4782no—
108C4×Q8—2391no—
109C4×D4—4781no—
110C4×D4—2391no—
111#107—22no—
112#107—4781no—
113C4⋊C8—2391no—
114C4⋊C8—2391no—
115#103—4781no—
116#102—4781no—
117C4×C8C2×D23911yescharacteristic
118C2×Q8—21no—
119C2×Q8—21no—
120C2×Q8—9562no—
121C2×Q8—9562no—
122C2×Q8—4782no—
123C2×Q8—2391no—
124C2×D4—2391no—
125C22×C4—4782no—
126C22×C4—4781no—
127Q16—9562no—
128C2×C8—21no—
129C2×C8—4781no—
130C2×C8—4781no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—4782no—
135C4⋊C4—4781no—
136C4⋊C4—2391no—
137C4⋊C4—2391no—
138C4⋊C4C22⋊D23912yes—
139C22⋊C4—4782no—
140C22⋊C4—4781no—
141C42—4781no—
142C42C22×D23911yescharacteristic
143C23—4781no—
144Q8—41no—
145Q8—41no—
146Q8—41no—
147Q8—41no—
148Q8—9564no—
149Q8—4781no—
150Q8—2392no—
151D4—4781no—
152D4—2392no—
153C2×C4—22no—
154C2×C4—41no—
155C2×C4—9564no—
156C2×C4—9561no—
157C2×C4—9561no—
158C2×C4—4781no—
159C2×C4—4781no—
160C2×C4—4781no—
161C2×C4D4×D23911yescharacteristic
162C2×C4D4×D23911yescharacteristic
163C2×C4C2×C22⋊D23911yescharacteristic
164C8—22no—
165C8—9561no—
166C8—9561no—
167C22—9561no—
168C22—9561no—
169C22—4782no—
170C22#2143992811yescharacteristic
171C4—21no—
172C4—42no—
173C4—81no—
174C4—9561no—
175C4—9561no—
176C4—4782no—
177C4D8×D23911yescharacteristic
178C4Q16×D23911yescharacteristic
179C4#2143998411yescharacteristic
180C4#2143999211yescharacteristic
181C2—9562no—
182C2#2950490411yescharacteristic
183C2#2950492611yescharacteristic
184C2#2950495411yescharacteristic
subgroupG/H
centerC22#21439928
commutator, cosocleC42×C239C23
FrattiniC42C22×D239
Fitting#500×C239C2
socleC22×C239#120
prime radicalC2×D956D4
hypercenter#500D239
hypocenterC239#1649
LCSG ▷ C42×C239 ▷ C22×C239 ▷ C239
UCSC1 ◁ C22 ◁ C42 ◁ #500

Complements

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

NH ≅ G/Ntype
3. #29504979C2semidirect
4. #29504518C2semidirect
5. #29504504C2semidirect
7. #500×C239C2semidirect
55. D956Q16semidirect
92. C239#1649semidirect
95. #500D239semidirect

Maximal subgroups

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

subgroupindex
#295054372
#295050492
#295049792
#295045182
#295045042
#295045012
#500×C2392
#1649239