Finite Group Databasebeta

← #30604210

Subgroups — #30604210

Order 15616.

348 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 70 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#21462193C212yesmaximal, complemented
2#21460753C212yesmaximal, complemented
3#21460752C212yesmaximal, complemented
4#21454511C211yesmaximal, characteristic
5#16840684—22no—
6#16840658C2214yes—
7#16840655—22no—
8C22×C8×D61C411yescharacteristic
9#16840269C411yescharacteristic
10#16839831—22no—
11C8×C22⋊D61—22no—
12#16839790C411yescharacteristic
13#16839729C2211yescharacteristic
14#16839725C2211yescharacteristic
15#16839717C2211yescharacteristic
16C2×#131×C61C411yescharacteristic
17#14519851—24no—
18C22×C4×D61C2×C411yescharacteristic
19C2×#11758194C2311yescharacteristic
20C22×#92418C2×C411yescharacteristic
21C2×C8×D61—21no—
22C2×C8×D61—21no—
23C2×C8×D61—42no—
24#14519758—21no—
25#14519753—21no—
26#14519748—21no—
27#14519745—21no—
28C4×C22⋊D61—22no—
29#14519736C2×C411yescharacteristic
30#14519706—22no—
31C22⋊#92418—22no—
32#14519689—22no—
33#14519687D412yes—
34C8×Dic61D412yes—
35C2×#41×C61C2×C411yescharacteristic
36#131×C61—42no—
37C2×M16×C61—21no—
38C2×M16×C61C2×C411yescharacteristic
39C22×C8×C61—21no—
40C22×C8×C61C2×C411yescharacteristic
41C23×D61M1611yescharacteristic
42#41×C61—41no—
43#41×C61—41no—
44C2×Q8×C61M1611yescharacteristic
45C2×D4×C61—21no—
46C2×D4×C61M1611yescharacteristic
47C22×C4×C61—21no—
48C22×C4×C61C22×C411yescharacteristic
49C2×C22⋊D61—22no—
50C22×Dic61M1611yescharacteristic
51C2×C4×D61—21no—
52C2×C4×D61—21no—
53C2×C4×D61—41no—
54C2×C4×D61—41no—
55M16×C61—42no—
56M16×C61—41no—
57C2×C8×C61—22no—
58C2×C8×C61—21no—
59C2×C8×C61—42no—
60C2×C8×C61C22⋊C411yescharacteristic
61C2×C8×C61C22⋊C411yescharacteristic
62C22⋊Dic61—22no—
63C22⋊Dic61—21no—
64#11758198—22no—
65C4⋊Dic61—21no—
66#11758196—22no—
67C4×Dic61C22⋊C412yes—
68#11758194—41no—
69C2×#92418—21no—
70C2×#92418—41no—
71C2×#92418C2×D412yes—
72C8×D61—42no—
73C8×D61—42no—
74#11758187—44no—
75C23×C61—21no—
76C23×C61C2×M1611yescharacteristic
77C22×D61—21no—
78C22×D61—42no—
79C22×D61—41no—
80Q8×C61—41no—
81D4×C61—41no—
82D4×C61—42no—
83C2×C4×C61—21no—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61—41no—
87C2×C4×C61—41no—
88C2×C4×C61C2×C22⋊C411yescharacteristic
89C2×C4×C61C2×M1611yescharacteristic
90C22⋊D61—44no—
91C2×Dic61—22no—
92C2×Dic61—21no—
93C2×Dic61—41no—
94C4×D61—42no—
95C4×D61—41no—
96C4×D61—41no—
97C8×C61—21no—
98C8×C61—41no—
99C8×C61#10012yes—
100#92418—22no—
101#92418—41no—
102#11537—611nomaximal, Sylow
103C22×C61—21no—
104C22×C61—41no—
105C22×C61—42no—
106C22×C61—41no—
107C22×C61#40711yescharacteristic
108C2×D61—22no—
109C2×D61—41no—
110C2×D61—42no—
111C2×D61—41no—
112C2×D61—42no—
113C4×C61—21no—
114C4×C61—41no—
115C4×C61#41011yescharacteristic
116C4×C61C2×#10011yescharacteristic
117Dic61—42no—
118Dic61—41no—
119#2929—611no—
120#2166—612no—
121#1321—612no—
122#1320—612no—
123C2×C61—21no—
124C2×C61—41no—
125C2×C61—81no—
126C2×C61#146611yescharacteristic
127D61—42no—
128C2×#131#692311yescharacteristic
129C23×C8—611no—
130#525—611no—
131#435—1222no—
132C8×D4—1222no—
133#424—611no—
134#408—611no—
135#407—611no—
136#405—611no—
137#364—1222no—
138#349—614no—
139#347—1222no—
140C61#1153711yescharacteristic, 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—1221no—
150C22×C8—1221no—
151C22×C8—2442no—
152C22×C8C2×#692311yescharacteristic
153#123—1221no—
154C22⋊Q8—1221no—
155#121—1221no—
156#120—1221no—
157C4×D4—1222no—
158#117—611no—
159M32—1224no—
160C4⋊C8—1222no—
161C22⋊C8—1222no—
162C22⋊C8—1222no—
163#97—612no—
164C4×C8—612no—
165C24—611no—
166#41—41no—
167#41—41no—
168C2×Q8#1175821311yescharacteristic
169C2×D4—21no—
170C2×D4—1222no—
171C2×D4#1175821311yescharacteristic
172C22×C4—21no—
173C22×C4—611no—
174C22×C4—1221no—
175C22×C4—1221no—
176C22×C4—2441no—
177C22×C4—2441no—
178C22×C4C22×#692311yescharacteristic
179M16—42no—
180M16—41no—
181M16—2441no—
182C2×C8—22no—
183C2×C8—21no—
184C2×C8—42no—
185C2×C8—612no—
186C2×C8—1221no—
187C2×C8—2442no—
188C2×C8—2442no—
189C2×C8—2441no—
190C2×C8C22⋊#692311yescharacteristic
191C2×C8C22⋊#692311yescharacteristic
192C4⋊C4—1222no—
193C4⋊C4—1221no—
194C22⋊C4—1222no—
195C22⋊C4—1222no—
196C22⋊C4—1221no—
197C42—612no—
198C16—2444no—
199C23—21no—
200C23—1221no—
201C23—2441no—
202C23—2442no—
203C23D61⋊M1611yescharacteristic
204Q8—41no—
205D4—41no—
206D4—42no—
207D4—2444no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—1222no—
214C2×C4—1221no—
215C2×C4—2442no—
216C2×C4—2441no—
217C2×C4—2441no—
218C2×C4—2441no—
219C2×C4C2×C22⋊#692311yescharacteristic
220C2×C4C2×#1175821311yescharacteristic
221C8—21no—
222C8—41no—
223C8—1222no—
224C8—2441no—
225C8#1451983712yes—
226C22—21no—
227C22—41no—
228C22—42no—
229C22—41no—
230C22—1222no—
231C22—2441no—
232C22—2442no—
233C22—2442no—
234C22—2441no—
235C22#1684073311yescharacteristic
236C4—21no—
237C4—41no—
238C4—2442no—
239C4—2441no—
240C4#1684074111yescharacteristic
241C4C2×#1451983711yescharacteristic
242C2—21no—
243C2—41no—
244C2—81no—
245C2—2442no—
246C2#2146107811yescharacteristic
subgroupG/H
centerC4#16840741
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#131×C61C4
socleC2×C61#1466
prime radical#16840269C4
cosocleC2×#11758194C23
hypercenterC2×#131#6923
hypocenterC61#11537
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C8 ◁ C22×C8 ◁ C2×#131

Complements

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

NH ≅ G/Ntype
1. #21462193C2semidirect
2. #21460753C2semidirect
3. #21460752C2semidirect
140. C61#11537semidirect

Maximal subgroups

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

subgroupindex
#214621932
#214607532
#214607522
#214545112
#1153761