Finite Group Databasebeta

← #44486187

Subgroups — #44486187

Order 30592.

264 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 65 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#29505279C211yesmaximal, characteristic
2#29504756C211yesmaximal, characteristic, complemented
3#29504561C212yesmaximal, complemented
4#29504558C212yesmaximal, complemented
5#410×C239C211yesmaximal, characteristic, complemented
6C22×C4×D239C411yescharacteristic, complemented
7C2×#16838532—21no—
8#21439941C411yescharacteristic, complemented
9#21439941C2211yescharacteristic
10#21439936—21no—
11#21439931—21no—
12#21439928C411yescharacteristic, complemented
13#21439928C2211yescharacteristic
14C4×C22⋊D239—21no—
15C4×C22⋊D239—21no—
16#21439919C411yescharacteristic, complemented
17#21439879—21no—
18#21439877C2212yes—
19C2×#41×C239C2211yescharacteristic
20#117×C239—21no—
21#99×C239—21no—
22#99×C239C2212yes—
23C23×D239C2×C411yescharacteristic
24C2×C22⋊D239—21no—
25C2×C22⋊D239—21no—
26C22×Dic239C2×C411yescharacteristic
27C2×C4×D239—21no—
28C2×C4×D239—21no—
29C2×C4×D239—41no—
30C2×C4×D239—41no—
31#16838532—22no—
32#16838532—41no—
33C2×C239⋊C8—41no—
34C4⋊Dic239—21no—
35Dic239⋊C4—21no—
36Dic239⋊C4—21no—
37C22⋊Dic239—21no—
38C22⋊Dic239—21no—
39C22⋊Dic239C2×C411yescharacteristic
40C22⋊Dic239C2×C411yescharacteristic
41(C2×D239)⋊C4—21no—
42(C2×D239)⋊C4—21no—
43C4×Dic239—21no—
44#41×C239—41no—
45#41×C239—41no—
46C2×Q8×C239D411yescharacteristic
47C2×D4×C239C2×C411yescharacteristic
48C2×D4×C239D411yescharacteristic
49C2×D4×C239C2311yescharacteristic
50C22×C4×C239C2×C411yescharacteristic
51C22×C4×C239D411yescharacteristic
52C22×C4×C239D411yescharacteristic
53C4⋊C4×C239—41no—
54C22⋊C4×C239—22no—
55C42×C239—41no—
56C22×D239—21no—
57C22×D239—42no—
58C22×D239—41no—
59C22⋊D239—42no—
60C22⋊D239—42no—
61C2×Dic239—21no—
62C2×Dic239—21no—
63C2×Dic239—21no—
64C2×Dic239—41no—
65C4×D239—42no—
66C4×D239—41no—
67C4×D239—41no—
68C239⋊C8—42no—
69C23×C239C22⋊C411yescharacteristic
70C23×C239C22×C411yescharacteristic
71C23×C239C2×D411yescharacteristic
72Q8×C239—41no—
73D4×C239—41no—
74D4×C239—41no—
75D4×C239—41no—
76C2×C4×C239—21no—
77C2×C4×C239—21no—
78C2×C4×C239—21no—
79C2×C4×C239—21no—
80C2×C4×C239—21no—
81C2×C4×C239—21no—
82C2×C4×C239—42no—
83C2×C4×C239C22⋊C411yescharacteristic
84C2×C4×C239C22⋊C411yescharacteristic
85C2×C4×C239C22⋊C411yescharacteristic
86C2×C4×C239C2×D411yescharacteristic
87C22×C239—21no—
88C22×C239—21no—
89C22×C239—21no—
90C22×C239—41no—
91C22×C239—41no—
92C22×C239—41no—
93C22×C239C2×C22⋊C411yescharacteristic
94C2×D239—22no—
95C2×D239—41no—
96C2×D239—42no—
97C2×D239—41no—
98C2×D239—42no—
99C4×C239—21no—
100C4×C239—21no—
101C4×C239—21no—
102C4×C239—82no—
103C4×C239#9911yescharacteristic
104C4×C239#9911yescharacteristic
105Dic239—41no—
106Dic239—41no—
107Dic239—41no—
108C2×C239—21no—
109C2×C239—41no—
110C2×C239—41no—
111C2×C239—41no—
112C2×C239C2×#9911yescharacteristic
113D239—42no—
114C239#212011yescharacteristic, complemented, Sylow
115#2120—2391nomaximal, Sylow
116#525—2391no—
117#413—2391no—
118#410D23911yescharacteristic, complemented
119#352—2392no—
120AΣL(1,𝔽16)—2392no—
121C2×#41C2×D23911yescharacteristic
122C23×C4—2391no—
123C2×M16—4781no—
124#123—2391no—
125#123—2391no—
126C22⋊Q8—4781no—
127#121—4781no—
128#120—2391no—
129#120—2391no—
130C4×D4—4781no—
131C4×D4—4781no—
132#117—21no—
133#117—2391no—
134#101—4781no—
135#100—2392no—
136#99—21no—
137#99C2×D23912yes—
138C24—2391no—
139#41—41no—
140#41—41no—
141C2×Q8D95611yescharacteristic
142C2×D4—4781no—
143C2×D4—4781no—
144C2×D4C4×D23911yescharacteristic
145C2×D4C22⋊D23911yescharacteristic
146C2×D4C22×D23911yescharacteristic
147C22×C4—9561no—
148C22×C4—9561no—
149C22×C4—4781no—
150C22×C4—4781no—
151C22×C4—2391no—
152C22×C4C4×D23911yescharacteristic
153C22×C4C22⋊D23911yescharacteristic
154C22×C4D95611yescharacteristic
155M16—9561no—
156M16—4782no—
157C2×C8—9561no—
158C4⋊C4—41no—
159C4⋊C4—4781no—
160C4⋊C4—4781no—
161C4⋊C4—4781no—
162C22⋊C4—22no—
163C22⋊C4—4781no—
164C22⋊C4—4781no—
165C22⋊C4—4781no—
166C22⋊C4—4781no—
167C22⋊C4—2391no—
168C22⋊C4—2391no—
169C42—41no—
170C42—4781no—
171C23—9561no—
172C23—9562no—
173C23—4781no—
174C23(C2×D239)⋊C411yescharacteristic
175C23C2×C4×D23911yescharacteristic
176C23C2×C22⋊D23911yescharacteristic
177Q8—41no—
178D4—41no—
179D4—41no—
180D4—41no—
181D4—9562no—
182D4—9562no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—42no—
190C2×C4—9562no—
191C2×C4—9561no—
192C2×C4—9561no—
193C2×C4—9561no—
194C2×C4—4781no—
195C2×C4—4781no—
196C2×C4—4781no—
197C2×C4(C2×D239)⋊C411yescharacteristic
198C2×C4(C2×D239)⋊C411yescharacteristic
199C2×C4(C2×D239)⋊C411yescharacteristic
200C2×C4C2×D95611yescharacteristic
201C8—9562no—
202C22—21no—
203C22—21no—
204C22—21no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—9561no—
209C22—9562no—
210C22—9562no—
211C22—9561no—
212C22—4782no—
213C22C2×(C2×D239)⋊C411yescharacteristic
214C4—21no—
215C4—21no—
216C4—21no—
217C4—82no—
218C4—9561no—
219C4—9561no—
220C4—9561no—
221C4#2143987411yescharacteristic
222C4#2143987411yescharacteristic
223C2—21no—
224C2—41no—
225C2—41no—
226C2—41no—
227C2—9562no—
228C2C2×#2143987411yescharacteristic
subgroupG/H
centerC4#21439874
commutatorC23×C239C22×C4
FrattiniC2×D4C22×D239
Fitting#410×C239C2
socleC2×C239C2×#99
prime radical#29505279C2
cosocleC2×D4×C239C23
hypercenter#410D239
hypocenterC239#2120
LCSG ▷ C23×C239 ▷ C22×C239 ▷ C2×C239 ▷ C239
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #29504756C2semidirect
3. #29504561C2semidirect
4. #29504558C2semidirect
5. #410×C239C2semidirect
6. C22×C4×D239C4semidirect
8. #21439941C4semidirect
12. #21439928C4semidirect
16. #21439919C4semidirect
114. C239#2120semidirect
118. #410D239semidirect

Maximal subgroups

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

subgroupindex
#295052792
#295047562
#295045612
#295045582
#410×C2392
#2120239