Finite Group Databasebeta

← #30608370

Subgroups — #30608370

Order 15616.

408 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 60 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#21462112C212yesmaximal, complemented
2#21460956C212yesmaximal, complemented
3#21460954C212yesmaximal, complemented
4#21456245C211yesmaximal, characteristic
5#16840748—22no—
6#16840673C2214yes—
7#16840671—22no—
8C2×#14519797—22no—
9#16840312C2211yescharacteristic
10#16840144—22no—
11#16840141C2211yescharacteristic
12#16840138C411yescharacteristic
13#16840136C411yescharacteristic
14#16840134C2211yescharacteristic
15C2×C4×#92418C411yescharacteristic
16C61×#532C411yescharacteristic
17D61⋊M16—42no—
18#14519838—24no—
19#14519837—42no—
20C2×#11758222D412yes—
21#14519797—44no—
22#14519797—44no—
23C2×#11758202—22no—
24C2×#11758200—22no—
25C2×#11758201—22no—
26C2×#11758199—22no—
27C22×#92418—21no—
28#14519777C2311yescharacteristic
29#14519774C2×C411yescharacteristic
30#14519765D412yes—
31#14519751—41no—
32C4×D244—41no—
33C4×#92418—21no—
34C4×#92418C2×C411yescharacteristic
35C4×#92418C2×C411yescharacteristic
36C2×#41×C61—21no—
37C4⋊Q8×C61C2×C411yescharacteristic
38#127×C61C2×C411yescharacteristic
39#124×C61—21no—
40#121×C61—41no—
41C4×D4×C61—41no—
42C2×C42×C61C2×C411yescharacteristic
43#41×C61—42no—
44#41×C61—42no—
45C2×Q8×C61—21no—
46C2×D4×C61—21no—
47C2×D4×C61—41no—
48C2×D4×C61—41no—
49C22×C4×C61—21no—
50C22×C4×C61—41no—
51C22×C4×C61C22⋊C411yescharacteristic
52C2×C22⋊D61—22no—
53#11758222—42no—
54#11758222—42no—
55C2×D244—41no—
56C2×D244C22⋊C412yes—
57C2×C4×D61—22no—
58C2×Dic122C2×D412yes—
59#11758217—44no—
60#11758213—82no—
61D61⋊C8—82no—
62C4⋊C4×C61—41no—
63C22⋊C4×C61—42no—
64C42×C61—21no—
65C42×C61C22⋊C411yescharacteristic
66C42×C61C22×C411yescharacteristic
67#11758202—44no—
68#11758201—44no—
69#11758200—44no—
70#11758199—44no—
71#11758198—42no—
72C4⋊Dic61—41no—
73C2×#92418—22no—
74C2×#92418—22no—
75C2×#92418—21no—
76C2×#92418—21no—
77C23×C61—41no—
78C23×C61#9911yescharacteristic
79C22×D61—22no—
80Q8×C61—42no—
81D4×C61—42no—
82D4×C61—82no—
83D4×C61—82no—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61—21no—
87C2×C4×C61—21no—
88C2×C4×C61—42no—
89C2×C4×C61—41no—
90C2×C4×C61—81no—
91C2×C4×C61—81no—
92C2×C4×C61#9911yescharacteristic
93C2×C4×C61C2×C22⋊C411yescharacteristic
94C22⋊D61—82no—
95C2×Dic61—22no—
96D244—42no—
97D244—82no—
98C4×D61—42no—
99C4×D61—42no—
100Dic122—42no—
101#92420—84no—
102#92418—22no—
103#92418—22no—
104#13589—611nomaximal, Sylow
105C22×C61—21no—
106C22×C61—41no—
107C22×C61—82no—
108C22×C61—81no—
109C22×C61C2×#9911yescharacteristic
110C2×D61—42no—
111C2×D61—82no—
112C4×C61—22no—
113C4×C61—21no—
114C4×C61—41no—
115C4×C61—81no—
116C4×C61#35311yescharacteristic
117C4×C61#35311yescharacteristic
118Dic61—42no—
119#3147—611no—
120#2132—612no—
121#1411—612no—
122#1410—612no—
123C2×C61—21no—
124C2×C61—41no—
125C2×C61—161no—
126C2×C61C2×#35311yescharacteristic
127D61—82no—
128C2×#135—1222no—
129#532—611no—
130#532#692311yescharacteristic
131#495—1222no—
132#494—611no—
133#493—611no—
134#492—611no—
135#492—611no—
136#413—1222no—
137C2×C4×C8—611no—
138#356—614no—
139#355—1222no—
140C61#1358911yescharacteristic, complemented, Sylow
141C2×#41—21no—
142C2×#41—612no—
143#135—2444no—
144#135—2444no—
145C2×Q16—1222no—
146C2×SD16—1222no—
147C2×SD16—1222no—
148C2×D8—1222no—
149C2×M16—2442no—
150C22×C8—1221no—
151C4⋊Q8—611no—
152C4⋊Q8C2×#692311yescharacteristic
153#127—611no—
154#127C2×#692311yescharacteristic
155#124—21no—
156#124—612no—
157#121—41no—
158#121—2441no—
159C4×D4—41no—
160C4×D4—2441no—
161C2×C42C2×#692311yescharacteristic
162#101—1224no—
163#100—2442no—
164C4×C8—611no—
165C4×C8—611no—
166C4×C8—1221no—
167#41—42no—
168#41—42no—
169#41—2442no—
170#41—2442no—
171C2×Q8—21no—
172C2×Q8—612no—
173C2×D4—21no—
174C2×D4—41no—
175C2×D4—41no—
176C2×D4—612no—
177C2×D4—1222no—
178C2×D4—2441no—
179C22×C4—21no—
180C22×C4—41no—
181C22×C4—1222no—
182C22×C4C22⋊#692311yescharacteristic
183Q16—2444no—
184SD16—2444no—
185SD16—2444no—
186D8—2444no—
187M16—4882no—
188M16—2444no—
189C2×C8—1222no—
190C2×C8—1222no—
191C2×C8—1221no—
192C2×C8—1221no—
193C2×C8—4882no—
194C4⋊C4—41no—
195C4⋊C4—2441no—
196C22⋊C4—42no—
197C22⋊C4—2442no—
198C42—21no—
199C42C22⋊#692311yescharacteristic
200C42C22×#692311yescharacteristic
201C23—41no—
202C23—1222no—
203C23#1451983511yescharacteristic
204Q8—42no—
205Q8—2442no—
206D4—42no—
207D4—82no—
208D4—82no—
209D4—4882no—
210D4—4882no—
211D4—2442no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—42no—
217C2×C4—41no—
218C2×C4—81no—
219C2×C4—81no—
220C2×C4—1222no—
221C2×C4—2442no—
222C2×C4—2442no—
223C2×C4#1451983511yescharacteristic
224C2×C4C2×C22⋊#692311yescharacteristic
225C8—1222no—
226C8—1222no—
227C8—4884no—
228C22—21no—
229C22—41no—
230C22—82no—
231C22—81no—
232C22—4882no—
233C22—2442no—
234C22C2×#1451983511yescharacteristic
235C4—22no—
236C4—21no—
237C4—41no—
238C4—81no—
239C4—2442no—
240C4#1684066611yescharacteristic
241C4#1684066611yescharacteristic
242C2—21no—
243C2—41no—
244C2—161no—
245C2—4882no—
246C2C2×#1684066611yescharacteristic
subgroupG/H
centerC4#16840666
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#532C4
socleC2×C61C2×#353
prime radical#21456245C2
cosocle#14519777C23
hypercenter#532#6923
hypocenterC61#13589
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #21462112C2semidirect
2. #21460956C2semidirect
3. #21460954C2semidirect
140. C61#13589semidirect

Maximal subgroups

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

subgroupindex
#214621122
#214609562
#214609542
#214562452
#1358961