Finite Group Databasebeta

← #30603964

Subgroups — #30603964

Order 15616.

386 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 86 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#21462047C212yesmaximal, complemented
2#21460758C212yesmaximal, complemented
3#21460741C212yesmaximal, complemented
4#21454511C211yesmaximal, characteristic
5C2×#14519852—22no—
6#16840657—22no—
7C22⋊#11758187C2214yes—
8C22×C8×D61C2211yescharacteristic
9#16840269C411yescharacteristic
10#16839831—22no—
11C8×C22⋊D61—22no—
12#16839790C2211yescharacteristic
13#16839729C2211yescharacteristic
14#16839725C411yescharacteristic
15#16839717C411yescharacteristic
16C2×#131×C61C411yescharacteristic
17#14519852—44no—
18C2×#11758187—24no—
19C22×C4×D61C2×C411yescharacteristic
20C2×#11758194C2×C411yescharacteristic
21C22×#92418C2311yescharacteristic
22C2×C8×D61—42no—
23C2×C8×D61D412yes—
24C2×C8×D61D412yes—
25#14519758—21no—
26#14519753C812yes—
27#14519748C812yes—
28#14519745—21no—
29C4×C22⋊D61—22no—
30#14519736C2×C411yescharacteristic
31#14519706—22no—
32C22⋊#92418—22no—
33#14519689—22no—
34#14519687—21no—
35C8×Dic61—21no—
36C2×#41×C61C2×C411yescharacteristic
37#131×C61—42no—
38C2×M16×C61—21no—
39C2×M16×C61C2×C411yescharacteristic
40C22×C8×C61—21no—
41C22×C8×C61C2×C411yescharacteristic
42C23×D61M1611yescharacteristic
43#41×C61—41no—
44#41×C61—41no—
45C2×Q8×C61C2×C811yescharacteristic
46C2×D4×C61—21no—
47C2×D4×C61C2×C811yescharacteristic
48C22×C4×C61—21no—
49C22×C4×C61C22×C411yescharacteristic
50C2×C22⋊D61—22no—
51C22×Dic61M1611yescharacteristic
52C2×C4×D61—41no—
53C2×C4×D61—41no—
54C2×C4×D61C22⋊C412yes—
55C2×C4×D61C2×C812yes—
56M16×C61—42no—
57M16×C61—41no—
58C2×C8×C61—22no—
59C2×C8×C61—21no—
60C2×C8×C61—42no—
61C2×C8×C61C22⋊C411yescharacteristic
62C2×C8×C61C22⋊C411yescharacteristic
63C22⋊Dic61—21no—
64C22⋊Dic61—22no—
65#11758198—22no—
66C4⋊Dic61C2×C812yes—
67#11758196—22no—
68C4×Dic61—21no—
69#11758194—41no—
70C2×#92418—21no—
71C2×#92418—41no—
72C2×#92418C2×D412yes—
73C8×D61—24no—
74C8×D61—42no—
75#11758187—44no—
76C23×C61—21no—
77C23×C61C2×M1611yescharacteristic
78C22×D61—41no—
79C22×D61—42no—
80C22×D61C22⋊C812yes—
81Q8×C61—41no—
82D4×C61—41no—
83D4×C61—42no—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61—21no—
87C2×C4×C61—41no—
88C2×C4×C61—41no—
89C2×C4×C61C2×C22⋊C411yescharacteristic
90C2×C4×C61C22×C811yescharacteristic
91C22⋊D61—44no—
92C2×Dic61—22no—
93C2×Dic61—41no—
94C2×Dic61C22⋊C812yes—
95C4×D61—22no—
96C4×D61—22no—
97C4×D61—42no—
98C8×C61—21no—
99C8×C61—41no—
100C8×C61#9912yes—
101#92418—22no—
102#92418—41no—
103#11469—611nomaximal, Sylow
104C22×C61—22no—
105C22×C61—21no—
106C22×C61—42no—
107C22×C61—41no—
108C22×C61C2×C22⋊C811yescharacteristic
109C2×D61—22no—
110C2×D61—22no—
111C2×D61—22no—
112C2×D61—44no—
113C4×C61—21no—
114C4×C61—41no—
115C4×C61C2×#9911yescharacteristic
116C4×C61#41311yescharacteristic
117Dic61—22no—
118Dic61—42no—
119#2929—611no—
120#2112—612no—
121#1323—612no—
122#1315—612no—
123C2×C61—41no—
124C2×C61—81no—
125C2×C61#145911yescharacteristic
126C2×C61#211712yes—
127D61—42no—
128C2×#131#692311yescharacteristic
129C23×C8—611no—
130#525—611no—
131C2×M32—1222no—
132#435—1222no—
133C8×D4—1222no—
134#424—611no—
135#408—611no—
136#407—611no—
137#405—611no—
138C22⋊C16—614no—
139C22⋊C16—1222no—
140C61#1146911yescharacteristic, complemented, Sylow
141C2×#41C2×#692311yescharacteristic
142C23×C4—611no—
143#131—42no—
144C2×M16—21no—
145C2×M16—611no—
146C2×M16C2×#692311yescharacteristic
147C22×C8—21no—
148C22×C8—611no—
149C22×C8—612no—
150C22×C8—612no—
151C22×C8—2442no—
152C22×C8C2×#692311yescharacteristic
153#123—1221no—
154C22⋊Q8—612no—
155#121—612no—
156#120—1221no—
157C4×D4—1222no—
158#117—611no—
159M32—2444no—
160C2×C16—1224no—
161C4⋊C8—1222no—
162C22⋊C8—1222no—
163C22⋊C8—1222no—
164#97—1221no—
165C4×C8—1221no—
166C24—611no—
167#41—41no—
168#41—41no—
169C2×Q8D61⋊C811yescharacteristic
170C2×D4—21no—
171C2×D4—1222no—
172C2×D4D61⋊C811yescharacteristic
173C22×C4—21no—
174C22×C4—611no—
175C22×C4—612no—
176C22×C4—612no—
177C22×C4—2441no—
178C22×C4—2441no—
179C22×C4C22×#692311yescharacteristic
180M16—42no—
181M16—41no—
182M16—2441no—
183C2×C8—22no—
184C2×C8—21no—
185C2×C8—42no—
186C2×C8—612no—
187C2×C8—1224no—
188C2×C8—1221no—
189C2×C8—2442no—
190C2×C8—2441no—
191C2×C8C22⋊#692311yescharacteristic
192C2×C8C22⋊#692311yescharacteristic
193C4⋊C4—612no—
194C4⋊C4—1222no—
195C22⋊C4—1222no—
196C22⋊C4—1222no—
197C22⋊C4—1221no—
198C42—1221no—
199C16—2444no—
200C23—21no—
201C23—612no—
202C23—2441no—
203C23—2442no—
204C23D61⋊M1611yescharacteristic
205Q8—41no—
206D4—41no—
207D4—42no—
208D4—2444no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—612no—
215C2×C4—1222no—
216C2×C4—1222no—
217C2×C4—1222no—
218C2×C4—2442no—
219C2×C4—2441no—
220C2×C4C2×C22⋊#692311yescharacteristic
221C2×C4C2×D61⋊C811yescharacteristic
222C8—21no—
223C8—41no—
224C8—1222no—
225C8—2441no—
226C8#1451983512yes—
227C22—22no—
228C22—21no—
229C22—42no—
230C22—41no—
231C22—1222no—
232C22—1222no—
233C22—1222no—
234C22—2444no—
235C22D61⋊(C22⋊C8)11yescharacteristic
236C4—21no—
237C4—41no—
238C4—1222no—
239C4—2442no—
240C4C2×#1451983511yescharacteristic
241C4#1684074811yescharacteristic
242C2—41no—
243C2—81no—
244C2—2442no—
245C2#2146105411yescharacteristic
246C2#2146206212yes—
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC2×#131×C61C4
socleC22×C61C2×C22⋊C8
prime radical#16840269C4
cosocleC22×#92418C23
hypercenterC2×#131#6923
hypocenterC61#11469
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×#131

Complements

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

NH ≅ G/Ntype
1. #21462047C2semidirect
2. #21460758C2semidirect
3. #21460741C2semidirect
140. C61#11469semidirect

Maximal subgroups

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

subgroupindex
#214620472
#214607582
#214607412
#214545112
#1146961