Finite Group Databasebeta

← #44485023

Subgroups — #44485023

Order 30592.

304 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 93 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#29505539C211yesmaximal, characteristic
2#29504789C211yesmaximal, characteristic
3#29504781C211yesmaximal, characteristic, complemented
4C2×#21439879C211yesmaximal, characteristic, complemented
5#29504543C211yesmaximal, characteristic, complemented
6C239⋊#338C211yesmaximal, characteristic, complemented
7C2×#137×C239C211yesmaximal, characteristic
8#21439967—22no—
9#21439967—22no—
10C2×#16838532—22no—
11C2×#16838532C2211yescharacteristic
12C2×#16838532C2211yescharacteristic
13C2×#16838532C2211yescharacteristic
14#21439919C2211yescharacteristic
15#21439887—22no—
16#21439884—22no—
17#21439879—22no—
18C2×#41×C239C2211yescharacteristic
19C22×Q8×C239C2211yescharacteristic
20#137×C239—22no—
21#137×C239—22no—
22C2×Q16×C239C412yescomplemented
23C2×SD16×C239C412yescomplemented
24C2×M16×C239C2211yescharacteristic
25#16838532—24no—
26#16838532—21no—
27#16838532—21no—
28#16838532—21no—
29#16838532—21no—
30#16838532—21no—
31#16838532D412yes—
32C2×C239⋊C8—24no—
33C2×C239⋊C8—21no—
34C2×C239⋊C8—21no—
35C2×C239⋊C8D412yes—
36C4⋊Dic239—21no—
37C22⋊Dic239—21no—
38C4×Dic239—21no—
39#41×C239—21no—
40#41×C239—21no—
41#41×C239D412yes—
42#41×C239D412yes—
43C2×Q8×C239—21no—
44C2×Q8×C239—21no—
45C2×Q8×C239—21no—
46C2×Q8×C239—21no—
47C2×Q8×C239—21no—
48C2×Q8×C239C2×C412yes—
49C2×Q8×C239C2×C411yescharacteristic
50C2×D4×C239—21no—
51C2×D4×C239C2×C411yescharacteristic
52C22×C4×C239—21no—
53C22×C4×C239—21no—
54C22×C4×C239C2311yescharacteristic
55Q16×C239—24no—
56SD16×C239—24no—
57M16×C239—21no—
58M16×C239—21no—
59C2×C8×C239C2×C412yes—
60C2×Dic239—41no—
61C239⋊C8—22no—
62C239⋊C8—22no—
63C239⋊C8—41no—
64C23×C239—21no—
65C23×C239#4111yescharacteristic
66Q8×C239—21no—
67Q8×C239—22no—
68Q8×C239—22no—
69Q8×C239—41no—
70Q8×C239—41no—
71Q8×C239C22⋊C412yes—
72D4×C239—22no—
73D4×C239—22no—
74D4×C239—21no—
75D4×C239C22⋊C412yes—
76C2×C4×C239—21no—
77C2×C4×C239—22no—
78C2×C4×C239—22no—
79C2×C4×C239—22no—
80C2×C4×C239—41no—
81C2×C4×C239—41no—
82C2×C4×C239C22×C411yescharacteristic
83C2×C4×C239C2×D411yescharacteristic
84C2×C4×C239C2×D411yescharacteristic
85C2×C4×C239C2×D411yescharacteristic
86C2×C4×C239C2×D411yescharacteristic
87C2×C4×C239#4111yescharacteristic
88C8×C239—22no—
89C22×C239—22no—
90C22×C239—41no—
91C22×C239—81no—
92C22×C239C4×D411yescharacteristic
93C22×C239#12111yescharacteristic
94C22×C239#12311yescharacteristic
95C4×C239—22no—
96C4×C239—42no—
97C4×C239C2×C22⋊C411yescharacteristic
98C4×C239C4×D411yescharacteristic
99C4×C239#12011yescharacteristic
100C4×C239#12111yescharacteristic
101Dic239—81no—
102C2×C239—21no—
103C2×C239—21no—
104C2×C239—21no—
105C2×C239—42no—
106C2×C239#38611yescharacteristic
107C239#190211yescharacteristic, complemented, Sylow
108#1902—2391nomaximal, Sylow
109C2×#137D23911yescharacteristic
110#568—2391no—
111#421—2391no—
112#419—2391no—
113C2×#101—2391no—
114#344—2391no—
115#338—2391no—
116C2×#41C2×D23911yescharacteristic
117C22×Q8C2×D23911yescharacteristic
118#137—22no—
119#137—22no—
120C2×Q16Dic23912yescomplemented
121C2×SD16Dic23912yescomplemented
122#131—4782no—
123#131—4782no—
124C2×M16—4782no—
125C2×M16—2391no—
126C2×M16—2391no—
127C2×M16—2391no—
128C2×M16C2×D23911yescharacteristic
129#117—2391no—
130#104—4782no—
131#103—4782no—
132#101—4782no—
133#41—21no—
134#41—21no—
135#41C22⋊D23912yes—
136#41C22⋊D23912yes—
137C2×Q8—21no—
138C2×Q8—21no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8C2×Dic23912yes—
143C2×Q8C2×Dic23911yescharacteristic
144C2×D4—21no—
145C2×D4C2×Dic23911yescharacteristic
146C22×C4—21no—
147C22×C4—21no—
148C22×C4C22×D23911yescharacteristic
149Q16—24no—
150SD16—24no—
151M16—21no—
152M16—21no—
153M16—4781no—
154M16—4781no—
155M16—4784no—
156M16—4781no—
157M16—4781no—
158M16—4781no—
159M16—2392no—
160C2×C8—4781no—
161C2×C8—4784no—
162C2×C8—4781no—
163C2×C8—2392no—
164C2×C8C2×Dic23912yes—
165C4⋊C4—4781no—
166C22⋊C4—4781no—
167C42—4781no—
168C23—21no—
169C23#1683854711yescharacteristic
170Q8—21no—
171Q8—22no—
172Q8—22no—
173Q8—41no—
174Q8—41no—
175Q8C22⋊Dic23912yes—
176D4—22no—
177D4—22no—
178D4—21no—
179D4C22⋊Dic23912yes—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—9561no—
187C2×C4C22×Dic23911yescharacteristic
188C2×C4D4×D23911yescharacteristic
189C2×C4D4×D23911yescharacteristic
190C2×C4C2×C22⋊D23911yescharacteristic
191C2×C4C2×C22⋊D23911yescharacteristic
192C2×C4#1683854711yescharacteristic
193C8—22no—
194C8—9561no—
195C8—4782no—
196C8—4782no—
197C22—22no—
198C22—41no—
199C22—81no—
200C22D4×Dic23911yescharacteristic
201C22#2143993211yescharacteristic
202C22#2143994111yescharacteristic
203C4—22no—
204C4—42no—
205C4—19121no—
206C4C2×C22⋊Dic23911yescharacteristic
207C4D4×Dic23911yescharacteristic
208C4#2143992811yescharacteristic
209C4#2143993211yescharacteristic
210C2—21no—
211C2—21no—
212C2—21no—
213C2—42no—
214C2#2950465211yescharacteristic
subgroupG/H
centerC2#29504652
commutatorC2×C4×C239C22×C4
FrattiniC22×C4C22×D239
FittingC2×#137×C239C2
socleC2×C239#386
prime radicalC2×#41×C239C22
cosocleC22×C4×C239C23
hypercenterC2×#137D239
hypocenterC239#1902
LCSG ▷ C2×C4×C239 ▷ C2×C239 ▷ C239
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
3. #29504781C2semidirect
4. C2×#21439879C2semidirect
5. #29504543C2semidirect
6. C239⋊#338C2semidirect
22. C2×Q16×C239C4semidirect
23. C2×SD16×C239C4semidirect
107. C239#1902semidirect
120. C2×Q16Dic239semidirect
121. C2×SD16Dic239semidirect

Maximal subgroups

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

subgroupindex
#295055392
#295047892
#295047812
C2×#214398792
#295045432
C239⋊#3382
C2×#137×C2392
#1902239