Finite Group Databasebeta

← #44485462

Subgroups — #44485462

Order 30592.

276 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C22×#16838538C211yesmaximal, characteristic
2C2×#21439895C211yesmaximal, characteristic
3#29504780C211yesmaximal, characteristic
4C2×#21439879C211yesmaximal, characteristic
5C2×#21439878C211yesmaximal, characteristic
6#29504728C211yesmaximal, characteristic
7#419×C239C211yesmaximal, characteristic
8C22×Dic478C2211yescharacteristic
9C2×#16838538—21no—
10C2×#16838538—21no—
11C2×#16838538—22no—
12C2×#16838538C414yescomplemented
13C2×#16838532C2211yescharacteristic
14C2×#16838532C2211yescharacteristic
15C22×C239⋊C8C2211yescharacteristic
16#21439895—22no—
17#21439883—22no—
18#21439879—22no—
19#21439878—22no—
20#21439871—21no—
21C4×C239⋊C8—21no—
22C22×Q8×C239C2211yescharacteristic
23C2×M16×C239C2211yescharacteristic
24#117×C239C2211yescharacteristic
25#103×C239—22no—
26C2×Dic478—21no—
27C2×Dic478—21no—
28C2×Dic478—21no—
29C2×Dic478—21no—
30C2×Dic478—21no—
31C2×Dic478C2×C412yes—
32C22×Dic239—21no—
33#16838538—24no—
34#16838538—24no—
35#16838532—21no—
36#16838532—21no—
37#16838532—21no—
38#16838532D412yes—
39C2×C239⋊C8—21no—
40C2×C239⋊C8—21no—
41C2×C239⋊C8C2×C412yes—
42C2×C239⋊C8D411yescharacteristic
43C2×C239⋊C8D411yescharacteristic
44C2×C239⋊C8D412yes—
45C2×Q8×C239—21no—
46C2×Q8×C239—21no—
47C2×Q8×C239—21no—
48C2×Q8×C239—21no—
49C2×Q8×C239—21no—
50C2×Q8×C239C2×C412yes—
51C22×C4×C239—21no—
52C22×C4×C239C2311yescharacteristic
53M16×C239—21no—
54M16×C239—21no—
55C2×C8×C239—21no—
56C4⋊C4×C239D412yes—
57C22⋊C4×C239—21no—
58C42×C239—21no—
59Dic478—22no—
60Dic478—22no—
61Dic478—41no—
62Dic478—41no—
63C2×Dic239—22no—
64C2×Dic239—41no—
65C2×Dic239—41no—
66C239⋊C8—22no—
67C239⋊C8—41no—
68C239⋊C8C22⋊C412yes—
69C239⋊C8C22⋊C412yes—
70C23×C239#4111yescharacteristic
71Q8×C239—22no—
72Q8×C239—22no—
73Q8×C239—41no—
74Q8×C239—41no—
75C2×C4×C239—22no—
76C2×C4×C239—22no—
77C2×C4×C239—41no—
78C2×C4×C239—41no—
79C2×C4×C239C22×C411yescharacteristic
80C2×C4×C239C2×D411yescharacteristic
81C2×C4×C239C2×D411yescharacteristic
82C2×C4×C239C2×D411yescharacteristic
83C2×C4×C239C2×D411yescharacteristic
84C2×C4×C239#4111yescharacteristic
85C8×C239—41no—
86C22×C239—22no—
87C22×C239C4×D411yescharacteristic
88C22×C239#12111yescharacteristic
89C22×C239#12411yescharacteristic
90C4×C239—42no—
91C4×C239—42no—
92C4×C239C2×C22⋊C411yescharacteristic
93C4×C239C4×D411yescharacteristic
94C4×C239#12111yescharacteristic
95C4×C239#12711yescharacteristic
96Dic239—42no—
97C2×C239—21no—
98C2×C239—21no—
99C2×C239#39011yescharacteristic
100C2×C239#47312yes—
101C239#197911yescharacteristic, complemented, Sylow
102#1979—2391nomaximal, Sylow
103C22×Q16—2391no—
104C2×#108—2391no—
105#419—2391no—
106#419D23911yescharacteristic
107C2×#101—2391no—
108C2×#101—2391no—
109#405—2391no—
110C22×Q8—2391no—
111C22×Q8C2×D23911yescharacteristic
112C2×Q16—4781no—
113C2×Q16—4781no—
114C2×Q16—4782no—
115C2×Q16—2394no—
116C2×M16—2391no—
117C2×M16—2391no—
118C2×M16C2×D23911yescharacteristic
119C22×C8—2391no—
120#117C2×D23911yescharacteristic
121#108—4782no—
122#103—22no—
123#103—4782no—
124#101—4782no—
125#101—4782no—
126#97—4781no—
127C4×C8—4781no—
128C2×Q8—21no—
129C2×Q8—21no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—4781no—
134C2×Q8—4781no—
135C2×Q8—4781no—
136C2×Q8—4781no—
137C2×Q8—4781no—
138C2×Q8—2392no—
139C2×Q8C4×D23912yes—
140C22×C4—21no—
141C22×C4—4781no—
142C22×C4C22×D23911yescharacteristic
143Q16—4784no—
144Q16—4784no—
145M16—21no—
146M16—21no—
147M16—4781no—
148M16—4781no—
149M16—4781no—
150M16—2392no—
151C2×C8—21no—
152C2×C8—4781no—
153C2×C8—4781no—
154C2×C8—2392no—
155C2×C8—2391no—
156C2×C8—2391no—
157C2×C8—2392no—
158C4⋊C4C22⋊D23912yes—
159C22⋊C4—21no—
160C42—21no—
161C23#1683854711yescharacteristic
162Q8—22no—
163Q8—22no—
164Q8—41no—
165Q8—41no—
166Q8—9561no—
167Q8—9561no—
168Q8—4782no—
169Q8—4782no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—9561no—
175C2×C4—9561no—
176C2×C4—4782no—
177C2×C4C2×C4×D23911yescharacteristic
178C2×C4D4×D23911yescharacteristic
179C2×C4D4×D23911yescharacteristic
180C2×C4D4×D23911yescharacteristic
181C2×C4C2×C22⋊D23911yescharacteristic
182C2×C4#1683854811yescharacteristic
183C8—41no—
184C8—9561no—
185C8—4782no—
186C8—2392no—
187C8—2392no—
188C22—22no—
189C22(C22⋊D239)⋊C411yescharacteristic
190C22#2143993211yescharacteristic
191C22#2143994611yescharacteristic
192C4—42no—
193C4—42no—
194C4—9562no—
195C4C22⋊C4×D23911yescharacteristic
196C4C4×C22⋊D23911yescharacteristic
197C4#2143993311yescharacteristic
198C4#2143995611yescharacteristic
199C2—21no—
200C2—21no—
201C2#2950467211yescharacteristic
202C2#2950504512yes—
subgroupG/H
centerC22#21439932
commutatorC2×C4×C239C22×C4
FrattiniC22×C4C22×D239
Fitting#419×C239C2
socleC22×C239#121
prime radicalC23×C239#41
cosocleC22×C4×C239C23
hypercenter#419D239
hypocenterC239#1979
LCSG ▷ C2×C4×C239 ▷ C2×C239 ▷ C239
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
12. C2×#16838538C4semidirect
101. C239#1979semidirect

Maximal subgroups

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

subgroupindex
C22×#168385382
C2×#214398952
#295047802
C2×#214398792
C2×#214398782
#295047282
#419×C2392
#1979239