Finite Group Databasebeta

← #44484930

Subgroups — #44484930

Order 30592.

332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 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#29505538C211yesmaximal, characteristic, complemented
2#29505322C211yesmaximal, characteristic
3#29504790C211yesmaximal, characteristic, complemented
4#29504788C211yesmaximal, characteristic, complemented
5#29504745C211yesmaximal, characteristic, complemented
6#29504532C211yesmaximal, characteristic, complemented
7#339×C239C211yesmaximal, characteristic, complemented
8C2×#16838548C2211yescharacteristic
9C2×#16838548C2211yescharacteristic
10#21439968—22no—
11#21439966—22no—
12C2×#16838532C2211yescharacteristic
13M16×D239—22no—
14#21439960C411yescharacteristic, complemented
15#21439957C411yescharacteristic, complemented
16#21439948C411yescharacteristic, complemented
17#21439948C411yescharacteristic, complemented
18#21439934—22no—
19C4×D956—22no—
20#21439919C2211yescharacteristic
21#21439888—22no—
22#21439886—22no—
23#21439874—22no—
24C2×M16×C239C2211yescharacteristic
25#117×C239C2211yescharacteristic
26C2×C42×C239C2211yescharacteristic
27#16838548—21no—
28#16838548—21no—
29#16838548—21no—
30#16838548—21no—
31#16838548—21no—
32#16838548—21no—
33#16838548—21no—
34#16838548—21no—
35C2×Dic478C2×C411yescharacteristic
36C2×Dic478C2×C411yescharacteristic
37C2×D956—22no—
38C2×D956C2×C411yescharacteristic
39C2×D956C2×C411yescharacteristic
40C2×C22⋊D239—21no—
41C2×C22⋊D239D412yes—
42C2×C4×D239—21no—
43C2×C4×D239D412yes—
44#16838532—21no—
45#16838532D412yescomplemented
46#16838531—24no—
47C2×C239⋊C8—21no—
48C8×D239—24no—
49C4⋊Dic239—22no—
50C4⋊Dic239—21no—
51C22⋊Dic239—21no—
52(C2×D239)⋊C4—22no—
53(C2×D239)⋊C4—22no—
54C4×Dic239—21no—
55C22×C4×C239—21no—
56C22×C4×C239C2311yescharacteristic
57M16×C239—21no—
58M16×C239D412yescomplemented
59C2×C8×C239—21no—
60C4⋊C4×C239—21no—
61C22⋊C4×C239—21no—
62C42×C239—21no—
63C42×C239—21no—
64C42×C239C2×C411yescharacteristic
65C42×C239C2×C411yescharacteristic
66C22×D239—21no—
67C22×D239C22⋊C412yes—
68Dic478—21no—
69Dic478—21no—
70Dic478—21no—
71Dic478—21no—
72D956—21no—
73D956—21no—
74D956—21no—
75D956—21no—
76D956—44no—
77C22⋊D239—22no—
78C22⋊D239—22no—
79C22⋊D239—41no—
80C22⋊D239—41no—
81C2×Dic239—21no—
82C2×Dic239—41no—
83C2×Dic239C22⋊C412yes—
84C4×D239—22no—
85C4×D239—22no—
86C4×D239—41no—
87C4×D239—41no—
88C239⋊C8—22no—
89C23×C239C2×D411yescharacteristic
90C2×C4×C239—21no—
91C2×C4×C239—21no—
92C2×C4×C239—42no—
93C2×C4×C239—41no—
94C2×C4×C239C22×C411yescharacteristic
95C2×C4×C239C2×D411yescharacteristic
96C2×C4×C239C2×D411yescharacteristic
97C2×C4×C239C2×D411yescharacteristic
98C2×C4×C239#4111yescharacteristic
99C2×C4×C239#4111yescharacteristic
100C8×C239—22no—
101C22×C239—41no—
102C22×C239C2×C22⋊C411yescharacteristic
103C22×C239#12111yescharacteristic
104C22×C239#12111yescharacteristic
105C2×D239—22no—
106C2×D239—42no—
107C2×D239—42no—
108C2×D239—41no—
109C4×C239—22no—
110C4×C239—41no—
111C4×C239—81no—
112C4×C239C4×D411yescharacteristic
113C4×C239C4×D411yescharacteristic
114C4×C239#12011yescharacteristic
115C4×C239#12311yescharacteristic
116Dic239—22no—
117Dic239—41no—
118Dic239—81no—
119C2×C239—21no—
120C2×C239—21no—
121C2×C239—21no—
122C2×C239#38611yescharacteristic
123D239—42no—
124D239—81no—
125C239#188411yescharacteristic, complemented, Sylow
126#1884—2391nomaximal, Sylow
127#568—2391no—
128#532—2391no—
129#421—2391no—
130#421—2391no—
131#410—2391no—
132#339—2391no—
133#339D23911yescharacteristic, complemented
134C2×#41—2391no—
135C2×#41—2391no—
136#131—4782no—
137#131—4782no—
138C2×M16—4782no—
139C2×M16—2391no—
140C2×M16C2×D23911yescharacteristic
141C4⋊Q8—2391no—
142#127—2391no—
143#124—2391no—
144#124—2391no—
145#121—4782no—
146C4×D4—4782no—
147#117—2391no—
148#117C2×D23911yescharacteristic
149C2×C42C2×D23911yescharacteristic
150#104—4782no—
151#104—4782no—
152#99—4782no—
153#41—4781no—
154#41—4781no—
155#41—4781no—
156#41—4781no—
157#41—4781no—
158#41—4781no—
159#41—4781no—
160#41—4781no—
161C2×Q8—2391no—
162C2×Q8—2391no—
163C2×D4—4782no—
164C2×D4—4781no—
165C2×D4—2392no—
166C2×D4—2391no—
167C2×D4—2391no—
168C22×C4—21no—
169C22×C4—4781no—
170C22×C4—2392no—
171C22×C4C22×D23911yescharacteristic
172M16—21no—
173M16—4784no—
174M16—4781no—
175M16—2392no—
176M16D95612yescomplemented
177C2×C8—21no—
178C2×C8—4784no—
179C2×C8—4781no—
180C4⋊C4—21no—
181C4⋊C4—4782no—
182C4⋊C4—4781no—
183C22⋊C4—21no—
184C22⋊C4—4782no—
185C22⋊C4—4782no—
186C22⋊C4—4781no—
187C42—21no—
188C42—21no—
189C42—4781no—
190C42C4×D23911yescharacteristic
191C42C4×D23911yescharacteristic
192C23—4781no—
193C23—2392no—
194C23D4×D23911yescharacteristic
195Q8—4781no—
196Q8—4781no—
197Q8—4781no—
198Q8—4781no—
199D4—9564no—
200D4—9561no—
201D4—9561no—
202D4—4782no—
203D4—4782no—
204D4—4781no—
205D4—4781no—
206D4—4781no—
207D4—4781no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—42no—
211C2×C4—41no—
212C2×C4—9561no—
213C2×C4—9561no—
214C2×C4—9561no—
215C2×C4—4781no—
216C2×C4—4782no—
217C2×C4—4782no—
218C2×C4—2392no—
219C2×C4C2×C4×D23911yescharacteristic
220C2×C4D4×D23911yescharacteristic
221C2×C4D4×D23911yescharacteristic
222C2×C4C2×D95611yescharacteristic
223C2×C4#1683854811yescharacteristic
224C2×C4#1683854911yescharacteristic
225C8—22no—
226C8—4782no—
227C22—41no—
228C22—9562no—
229C22—9562no—
230C22—9561no—
231C22—4782no—
232C22C22⋊C4×D23911yescharacteristic
233C22#2143993311yescharacteristic
234C22#2143993511yescharacteristic
235C4—22no—
236C4—41no—
237C4—81no—
238C4—19121no—
239C4—9561no—
240C4—4782no—
241C4#2143992211yescharacteristic
242C4C4×D95611yescharacteristic
243C4#2143993011yescharacteristic
244C4#2143994511yescharacteristic
245C2—21no—
246C2—21no—
247C2—21no—
248C2—19121no—
249C2—9562no—
250C2#2950465011yescharacteristic
subgroupG/H
centerC4#21439930
commutatorC2×C4×C239C22×C4
FrattiniC22×C4C22×D239
Fitting#339×C239C2
socleC2×C239#386
prime radical#29505322C2
cosocleC22×C4×C239C23
hypercenter#339D239
hypocenterC239#1884
LCSG ▷ C2×C4×C239 ▷ C2×C239 ▷ C239
UCSC1 ◁ C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
1. #29505538C2semidirect
3. #29504790C2semidirect
4. #29504788C2semidirect
5. #29504745C2semidirect
6. #29504532C2semidirect
7. #339×C239C2semidirect
14. #21439960C4semidirect
15. #21439957C4semidirect
16. #21439948C4semidirect
17. #21439948C4semidirect
45. #16838532D4semidirect
58. M16×C239D4semidirect
125. C239#1884semidirect
133. #339D239semidirect
176. M16D956semidirect

Maximal subgroups

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

subgroupindex
#295055382
#295053222
#295047902
#295047882
#295047452
#295045322
#339×C2392
#1884239