Finite Group Databasebeta

← #30604211

Subgroups — #30604211

Order 15616.

348 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 66 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#21462192C212yesmaximal, complemented
2#21460754C212yesmaximal, complemented
3#21460752C212yesmaximal, complemented
4#21454512C211yesmaximal, characteristic
5#16840685—22no—
6#16840658C2214yes—
7#16840654—22no—
8C2×#14519785C411yescharacteristic
9C22×C8×D61C411yescharacteristic
10#16840274C411yescharacteristic
11#16839832—22no—
12#16839827—22no—
13#16839728C2211yescharacteristic
14#16839725C2211yescharacteristic
15#16839718C2211yescharacteristic
16C61×#424C411yescharacteristic
17#14519851—24no—
18C2×#11758222C2×C411yescharacteristic
19C22×C4×D61C2×C411yescharacteristic
20#14519785—42no—
21C2×#11758194C2311yescharacteristic
22C2×#11758189—21no—
23C22×#92418C2×C411yescharacteristic
24C2×C8×D61—21no—
25C2×C8×D61—21no—
26C2×C8×D61—21no—
27C2×C8×D61—42no—
28#14519761—21no—
29#14519757—21no—
30#14519752—21no—
31#14519747—21no—
32C4×D244—22no—
33#14519689—22no—
34#14519689—22no—
35#14519688D412yes—
36C4×#92418D412yes—
37C2×M16×C61C2×C411yescharacteristic
38C22×C8×C61C2×C411yescharacteristic
39#117×C61C2×C411yescharacteristic
40C4⋊C8×C61—22no—
41C23×D61M1611yescharacteristic
42C22×C4×C61C22×C411yescharacteristic
43C2×C22⋊D61—21no—
44C22×Dic61M1611yescharacteristic
45#11758222—41no—
46#11758222—41no—
47C2×D244—22no—
48C2×D244M1611yescharacteristic
49C2×C4×D61—21no—
50C2×C4×D61—21no—
51C2×C4×D61—21no—
52C2×C4×D61—41no—
53C2×C4×D61—41no—
54C2×Dic122M1611yescharacteristic
55M16×C61—41no—
56C2×C8×C61—21no—
57C2×C8×C61—21no—
58C2×C8×C61—41no—
59C4⋊C4×C61—21no—
60C22⋊C4×C61—21no—
61C42×C61C22⋊C412yes—
62#11758198—22no—
63#11758198—22no—
64C4⋊Dic61—22no—
65#11758194—41no—
66C2×#92418—22no—
67C2×#92418C22⋊C411yescharacteristic
68C2×#92418C22⋊C411yescharacteristic
69C2×#92418C2×D412yes—
70#11758189—42no—
71C8×D61—42no—
72C8×D61—42no—
73C8×D61—42no—
74#11758187—44no—
75C23×C61C2×M1611yescharacteristic
76C22×D61—21no—
77C22×D61—21no—
78C22×D61—42no—
79C22×D61—41no—
80C2×C4×C61—21no—
81C2×C4×C61—21no—
82C2×C4×C61—22no—
83C2×C4×C61C2×C22⋊C411yescharacteristic
84C2×C4×C61C2×M1611yescharacteristic
85C22⋊D61—42no—
86C2×Dic61—21no—
87C2×Dic61—21no—
88C2×Dic61—41no—
89D244—41no—
90D244—44no—
91C4×D61—42no—
92C4×D61—41no—
93C4×D61—41no—
94C4×D61—41no—
95C4×D61—41no—
96Dic122—41no—
97C8×C61—41no—
98C8×C61—41no—
99#92418—22no—
100#92418—21no—
101#92418#10012yes—
102#11537—611nomaximal, Sylow
103C22×C61—21no—
104C22×C61—41no—
105C22×C61#40711yescharacteristic
106C2×D61—22no—
107C2×D61—41no—
108C2×D61—42no—
109C2×D61—41no—
110C2×D61—42no—
111C2×D61—42no—
112C2×D61—41no—
113C4×C61—21no—
114C4×C61—42no—
115C4×C61#41011yescharacteristic
116C4×C61C2×#10011yescharacteristic
117Dic61—41no—
118Dic61—41no—
119#2929—611no—
120#2166—612no—
121#1321—612no—
122#1320—612no—
123C2×C61—21no—
124C2×C61—41no—
125C2×C61#146611yescharacteristic
126D61—42no—
127D61—81no—
128C2×#131—611no—
129C23×C8—611no—
130#525—611no—
131#435—1222no—
132C8×D4—1222no—
133#424#692311yescharacteristic
134#408—611no—
135#407—611no—
136#405—611no—
137#364—1222no—
138#349—614no—
139#347—1222no—
140C61#1153711yescharacteristic, complemented, Sylow
141C2×#41—611no—
142C23×C4—611no—
143#131—2442no—
144C2×M16—611no—
145C2×M16—1221no—
146C2×M16C2×#692311yescharacteristic
147C22×C8—611no—
148C22×C8—1221no—
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#117C2×#692311yescharacteristic
159M32—1224no—
160C4⋊C8—22no—
161C22⋊C8—1222no—
162C22⋊C8—1222no—
163#97—612no—
164C4×C8—612no—
165C24—611no—
166#41—2441no—
167#41—2441no—
168C2×Q8—611no—
169C2×D4—611no—
170C2×D4—1222no—
171C2×D4—1221no—
172C22×C4—611no—
173C22×C4—1221no—
174C22×C4—1221no—
175C22×C4—1221no—
176C22×C4—2441no—
177C22×C4—2441no—
178C22×C4C22×#692311yescharacteristic
179M16—41no—
180M16—2442no—
181M16—2441no—
182C2×C8—21no—
183C2×C8—21no—
184C2×C8—41no—
185C2×C8—611no—
186C2×C8—612no—
187C2×C8—611no—
188C2×C8—1222no—
189C2×C8—2442no—
190C2×C8—2442no—
191C2×C8—2442no—
192C4⋊C4—21no—
193C4⋊C4—1222no—
194C22⋊C4—21no—
195C22⋊C4—1222no—
196C22⋊C4—1222no—
197C42C22⋊#692312yes—
198C16—2444no—
199C23—1221no—
200C23—1221no—
201C23—2441no—
202C23—2442no—
203C23D61⋊M1611yescharacteristic
204Q8—2441no—
205D4—2441no—
206D4—2444no—
207D4—2442no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—1221no—
212C2×C4—1221no—
213C2×C4—2442no—
214C2×C4—2441no—
215C2×C4—2441no—
216C2×C4—2441no—
217C2×C4—2441no—
218C2×C4—2441no—
219C2×C4C2×C22⋊#692311yescharacteristic
220C2×C4D61⋊M1611yescharacteristic
221C8—41no—
222C8—41no—
223C8—612no—
224C8—1222no—
225C8—1221no—
226C22—21no—
227C22—41no—
228C22—1222no—
229C22—2442no—
230C22—2441no—
231C22—2442no—
232C22—2442no—
233C22—2441no—
234C22—2441no—
235C22#1684073411yescharacteristic
236C4—21no—
237C4—42no—
238C4—2441no—
239C4—2441no—
240C4#1684074311yescharacteristic
241C4D61⋊#10011yescharacteristic
242C2—21no—
243C2—41no—
244C2—4881no—
245C2—2442no—
246C2#2146108011yescharacteristic
subgroupG/H
centerC4#16840743
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#424C4
socleC2×C61#1466
prime radical#16840274C4
cosocleC2×#11758194C23
hypercenter#424#6923
hypocenterC61#11537
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
1. #21462192C2semidirect
2. #21460754C2semidirect
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
#214621922
#214607542
#214607522
#214545122
#1153761