Finite Group Databasebeta

← #30603967

Subgroups — #30603967

Order 15616.

386 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 90 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#21462046C212yesmaximal, complemented
2#21460758C212yesmaximal, complemented
3#21460742C212yesmaximal, complemented
4#21454509C211yesmaximal, characteristic
5C2×#14519851—22no—
6C22⋊#11758187—22no—
7C22⋊#11758187C2214yes—
8C2×#14519785C411yescharacteristic
9C23×#92418C2211yescharacteristic
10#16840273C411yescharacteristic
11#16839830—22no—
12#16839825—22no—
13#16839790C2211yescharacteristic
14#16839730C2211yescharacteristic
15#16839720C411yescharacteristic
16C61×#407C411yescharacteristic
17#14519851—44no—
18C2×#11758187—24no—
19C2×#11758222C2×C411yescharacteristic
20#14519785—42no—
21C2×#11758189—21no—
22C22×#92418—42no—
23C22×#92418C2×C411yescharacteristic
24C22×#92418D412yes—
25C22×#92418D412yes—
26C22×#92418C2311yescharacteristic
27C2×C8×D61—21no—
28#14519760—21no—
29#14519756C812yes—
30#14519751C812yes—
31#14519746—21no—
32C4×C22⋊D61—22no—
33#14519736C2×C411yescharacteristic
34#14519706—22no—
35#14519689—22no—
36#14519687—21no—
37C8×Dic61—21no—
38C23×C4×C61C2×C411yescharacteristic
39C2×M16×C61C2×C411yescharacteristic
40C2×M16×C61C2×C411yescharacteristic
41C22⋊C8×C61—22no—
42C24×C61M1611yescharacteristic
43C22×C4×C61—41no—
44C22×C4×C61—41no—
45C22×C4×C61C22⋊C412yes—
46C22×C4×C61C2×C812yes—
47C22×C4×C61M1611yescharacteristic
48C22×C4×C61C22×C411yescharacteristic
49C2×C22⋊D61—22no—
50C2×C22⋊D61—21no—
51#11758222—41no—
52#11758222—41no—
53C2×D244C2×C811yescharacteristic
54C2×C4×D61—21no—
55C2×Dic122C2×C811yescharacteristic
56M16×C61—41no—
57M16×C61—41no—
58C2×C8×C61—21no—
59C2×C8×C61—21no—
60C22⋊Dic61—22no—
61C22⋊Dic61—21no—
62#11758198—22no—
63C4⋊Dic61C2×C812yes—
64#11758196—22no—
65C4×Dic61—21no—
66C2×#92418—24no—
67C2×#92418—22no—
68C2×#92418—42no—
69C2×#92418—41no—
70C2×#92418C22⋊C411yescharacteristic
71C2×#92418C22⋊C411yescharacteristic
72C2×#92418C2×D412yes—
73#11758189—42no—
74C8×D61—42no—
75#11758187—44no—
76C23×C61—41no—
77C23×C61—42no—
78C23×C61C22⋊C812yes—
79C23×C61C2×M1611yescharacteristic
80C22×D61—21no—
81C2×C4×C61—21no—
82C2×C4×C61—22no—
83C2×C4×C61—21no—
84C2×C4×C61—22no—
85C2×C4×C61—42no—
86C2×C4×C61—41no—
87C2×C4×C61C22⋊C812yes—
88C2×C4×C61C2×C22⋊C411yescharacteristic
89C2×C4×C61C22×C811yescharacteristic
90C22⋊D61—42no—
91C22⋊D61—44no—
92C2×Dic61—22no—
93C2×Dic61—21no—
94D244—41no—
95C4×D61—41no—
96C4×D61—41no—
97Dic122—41no—
98C8×C61—41no—
99C8×C61—41no—
100#92418—22no—
101#92418—21no—
102#92418#9912yes—
103#11469—611nomaximal, Sylow
104C22×C61—22no—
105C22×C61—22no—
106C22×C61—22no—
107C22×C61—21no—
108C22×C61—22no—
109C22×C61—44no—
110C22×C61C2×C22⋊C811yescharacteristic
111C2×D61—42no—
112C2×D61—41no—
113C4×C61—21no—
114C4×C61—22no—
115C4×C61C2×#9911yescharacteristic
116C4×C61#41311yescharacteristic
117Dic61—42no—
118Dic61—41no—
119#2929—611no—
120#2112—612no—
121#1323—612no—
122#1315—612no—
123C2×C61—42no—
124C2×C61—41no—
125C2×C61#145911yescharacteristic
126C2×C61#211712yes—
127D61—81no—
128C2×#131—611no—
129C23×C8—611no—
130#525—611no—
131C2×M32—1222no—
132#435—1222no—
133C8×D4—1222no—
134#424—611no—
135#408—611no—
136#407#692311yescharacteristic
137#405—611no—
138C22⋊C16—614no—
139C22⋊C16—1222no—
140C61#1146911yescharacteristic, complemented, Sylow
141C2×#41—611no—
142C23×C4C2×#692311yescharacteristic
143#131—2442no—
144C2×M16—1221no—
145C2×M16C2×#692311yescharacteristic
146C2×M16C2×#692311yescharacteristic
147C22×C8—612no—
148C22×C8—611no—
149C22×C8—612no—
150C22×C8—611no—
151C22×C8—1221no—
152C22×C8—2442no—
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—22no—
163C22⋊C8—1222no—
164#97—1221no—
165C4×C8—1221no—
166C24#1175821311yescharacteristic
167#41—2441no—
168#41—2441no—
169C2×Q8—611no—
170C2×D4—611no—
171C2×D4—1222no—
172C2×D4—1221no—
173C22×C4—41no—
174C22×C4—41no—
175C22×C4—1221no—
176C22×C4D61⋊C812yes—
177C22×C4#1175821311yescharacteristic
178C22×C4C22⋊#692312yes—
179C22×C4C22×#692311yescharacteristic
180M16—41no—
181M16—41no—
182M16—2442no—
183C2×C8—21no—
184C2×C8—21no—
185C2×C8—611no—
186C2×C8—611no—
187C2×C8—612no—
188C2×C8—1224no—
189C2×C8—1222no—
190C2×C8—2442no—
191C2×C8—2441no—
192C2×C8—2442no—
193C4⋊C4—612no—
194C4⋊C4—1222no—
195C22⋊C4—1222no—
196C22⋊C4—1221no—
197C22⋊C4—1222no—
198C42—1221no—
199C16—2444no—
200C23—41no—
201C23—42no—
202C23—1221no—
203C23#1451983412yes—
204C23C2×#1175821311yescharacteristic
205Q8—2441no—
206D4—2441no—
207D4—2444no—
208D4—2442no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—42no—
214C2×C4—41no—
215C2×C4—1222no—
216C2×C4—1221no—
217C2×C4—2441no—
218C2×C4—2441no—
219C2×C4#1451983412yes—
220C2×C4C2×C22⋊#692311yescharacteristic
221C2×C4C2×D61⋊C811yescharacteristic
222C8—41no—
223C8—41no—
224C8—612no—
225C8—1222no—
226C8—1221no—
227C22—22no—
228C22—22no—
229C22—22no—
230C22—21no—
231C22—22no—
232C22—44no—
233C22—2442no—
234C22—2441no—
235C22C2×#1451983411yescharacteristic
236C4—22no—
237C4—21no—
238C4—2442no—
239C4—2441no—
240C4D61⋊#9911yescharacteristic
241C4#1684074911yescharacteristic
242C2—42no—
243C2—41no—
244C2—4881no—
245C2#2146105711yescharacteristic
246C2#2146206312yes—
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#407C4
socleC22×C61C2×C22⋊C8
prime radical#16840273C4
cosocleC22×#92418C23
hypercenter#407#6923
hypocenterC61#11469
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. #21462046C2semidirect
2. #21460758C2semidirect
3. #21460742C2semidirect
140. C61#11469semidirect

Maximal subgroups

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

subgroupindex
#214620462
#214607582
#214607422
#214545092
#1146961