Finite Group Databasebeta

← #44483085

Subgroups — #44483085

Order 30592.

222 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 61 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#29505308C211yesmaximal, characteristic
2#29504826C211yesmaximal, characteristic, complemented
3#29504636C211yesmaximal, characteristic, complemented
4#29504509C211yesmaximal, characteristic, complemented
5#29504507C211yesmaximal, characteristic
6#29504505C211yesmaximal, characteristic
7#328×C239C211yesmaximal, characteristic, complemented
8#21439955—21no—
9#21439951C411yescharacteristic, complemented
10#21439949C411yescharacteristic, complemented
11#21439944—21no—
12#21439934C2211yescharacteristic
13Q8×Dic239C411yescharacteristic, complemented
14#21439922C411yescharacteristic, complemented
15(C22⋊D239)⋊C4—21no—
16#21439918—21no—
17C2×Dic239⋊C4—21no—
18C2×C4×Dic239C2211yescharacteristic
19Dic239⋊C8—21no—
20C22⋊(C239⋊C8)C2211yescharacteristic
21#21439870—21no—
22C239⋊#95—21no—
23C239⋊#95C2211yescharacteristic
24C22⋊Q8×C239C2211yescharacteristic
25C22⋊C8×C239C2211yescharacteristic
26#95×C239C2211yescharacteristic
27C2×D956C2×C411yescharacteristic
28C2×C22⋊D239—21no—
29C22×Dic239—21no—
30C22×Dic239D411yescharacteristic
31C22×Dic239D411yescharacteristic
32C2×C4×D239—21no—
33C2×C239⋊C8—21no—
34C4⋊Dic239—21no—
35C4⋊Dic239—21no—
36C4⋊Dic239C2×C411yescharacteristic
37Dic239⋊C4—21no—
38Dic239⋊C4—42no—
39(C2×D239)⋊C4—21no—
40(C2×D239)⋊C4—21no—
41(C2×D239)⋊C4—21no—
42(C2×D239)⋊C4—21no—
43C4×Dic239—21no—
44C4×Dic239C2×C411yescharacteristic
45C4×Dic239C2×C411yescharacteristic
46C4×Dic239D411yescharacteristic
47C4×Dic239D411yescharacteristic
48C2×Q8×C239C2×C411yescharacteristic
49C22×C4×C239—21no—
50C22×C4×C239C2311yescharacteristic
51C2×C8×C239—21no—
52C4⋊C4×C239—21no—
53C4⋊C4×C239C2×C411yescharacteristic
54C22⋊C4×C239—21no—
55C22×D239—21no—
56D956—41no—
57C22⋊D239—41no—
58C22⋊D239—41no—
59C2×Dic239—21no—
60C2×Dic239—21no—
61C2×Dic239—21no—
62C2×Dic239—41no—
63C2×Dic239—41no—
64C2×Dic239—41no—
65C2×Dic239—41no—
66C2×Dic239C22⋊C411yescharacteristic
67C2×Dic239C22⋊C411yescharacteristic
68C2×Dic239C22⋊C411yescharacteristic
69C2×Dic239C22⋊C411yescharacteristic
70C4×D239—42no—
71C239⋊C8—41no—
72C23×C239C2×D411yescharacteristic
73Q8×C239—41no—
74C2×C4×C239—21no—
75C2×C4×C239—21no—
76C2×C4×C239—41no—
77C2×C4×C239—41no—
78C2×C4×C239—41no—
79C2×C4×C239—41no—
80C2×C4×C239C22×C411yescharacteristic
81C2×C4×C239C2×D411yescharacteristic
82C8×C239—41no—
83C22×C239—21no—
84C22×C239—21no—
85C22×C239C2×C22⋊C411yescharacteristic
86C22×C239AGL(1,ℤ/8)11yescharacteristic
87C22×C239#13711yescharacteristic
88C2×D239—41no—
89C2×D239—41no—
90C2×D239—41no—
91C4×C239—21no—
92C4×C239—21no—
93C4×C239—41no—
94C4×C239—41no—
95C4×C239—81no—
96Dic239—21no—
97Dic239—21no—
98Dic239—21no—
99Dic239—21no—
100Dic239—41no—
101Dic239—81no—
102C2×C239—21no—
103C2×C239—21no—
104C2×C239#41011yescharacteristic
105C2×C239#41711yescharacteristic
106C2×C239#42111yescharacteristic
107D239—81no—
108C239#151211yescharacteristic, complemented, Sylow
109#1512—2391nomaximal, Sylow
110#529—2391no—
111#432—2391no—
112#382—2391no—
113#328—2391no—
114#328D23911yescharacteristic, complemented
115#327—2391no—
116#327—2391no—
117#126—4781no—
118#125—2391no—
119#124—2391no—
120#123—4781no—
121C22⋊Q8C2×D23911yescharacteristic
122#121—2391no—
123C4×Q8—2391no—
124C4×D4—4781no—
125C4×D4—2391no—
126#117—4781no—
127C2×C4⋊C4—4781no—
128C2×C42—2391no—
129C4⋊C8—4781no—
130C22⋊C8—2391no—
131C22⋊C8C2×D23911yescharacteristic
132#97—4781no—
133#95—4781no—
134#95—2391no—
135#95C2×D23911yescharacteristic
136C2×Q8C4×D23911yescharacteristic
137C2×D4—4781no—
138C2×D4—2391no—
139C22×C4—21no—
140C22×C4—4781no—
141C22×C4—4781no—
142C22×C4—2391no—
143C22×C4—2391no—
144C22×C4C22×D23911yescharacteristic
145C2×C8—21no—
146C2×C8—4781no—
147C4⋊C4—21no—
148C4⋊C4—9562no—
149C4⋊C4—4781no—
150C4⋊C4—4781no—
151C4⋊C4—4781no—
152C4⋊C4—2391no—
153C4⋊C4C4×D23911yescharacteristic
154C22⋊C4—21no—
155C22⋊C4—4781no—
156C22⋊C4—4781no—
157C22⋊C4—4781no—
158C22⋊C4—4781no—
159C42—4781no—
160C42—2391no—
161C42—2391no—
162C42—2391no—
163C42—2391no—
164C23—4781no—
165C23D4×D23911yescharacteristic
166Q8—41no—
167D4—9561no—
168D4—9561no—
169D4—9561no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—9562no—
177C2×C4—9561no—
178C2×C4—9561no—
179C2×C4—9561no—
180C2×C4—9561no—
181C2×C4—4781no—
182C2×C4—4781no—
183C2×C4—4781no—
184C2×C4—2391no—
185C2×C4—2391no—
186C2×C4—2391no—
187C2×C4—2391no—
188C2×C4C2×C4×D23911yescharacteristic
189C2×C4D4×D23911yescharacteristic
190C8—41no—
191C8—9561no—
192C22—21no—
193C22—21no—
194C22—9561no—
195C22—9561no—
196C22—9561no—
197C22C22⋊C4×D23911yescharacteristic
198C22#2143998711yescharacteristic
199C22#2143999211yescharacteristic
200C4—21no—
201C4—21no—
202C4—41no—
203C4—41no—
204C4—81no—
205C4—19121no—
206C4—9561no—
207C4—4781no—
208C4—4781no—
209C4—4781no—
210C4—4781no—
211C2—21no—
212C2—21no—
213C2—19121no—
214C2#2950474411yescharacteristic
215C2#2950477211yescharacteristic
216C2#2950478711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D239
commutatorC2×C4×C239C22×C4
FrattiniC22×C4C22×D239
Fitting#328×C239C2
socleC22×C239C2×C22⋊C4
prime radical#21439934C22
cosocleC22×C4×C239C23
hypercenter#328D239
hypocenterC239#1512
LCSG ▷ C2×C4×C239 ▷ C22×C239 ▷ C239
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #29504826C2semidirect
3. #29504636C2semidirect
4. #29504509C2semidirect
7. #328×C239C2semidirect
9. #21439951C4semidirect
10. #21439949C4semidirect
13. Q8×Dic239C4semidirect
14. #21439922C4semidirect
108. C239#1512semidirect
114. #328D239semidirect

Maximal subgroups

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

subgroupindex
#295053082
#295048262
#295046362
#295045092
#295045072
#295045052
#328×C2392
#1512239