Finite Group Databasebeta

← #30608376

Subgroups — #30608376

Order 15616.

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

normal subgroups only

This group has 398 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
1C2×#16840673C212yesmaximal, complemented
2#21460957C212yesmaximal, complemented
3#21460955C212yesmaximal, complemented
4#21456278C211yesmaximal, characteristic
5C2×#14519838—22no—
6#16840673—22no—
7#16840673C2214yes—
8C2×#14519810—22no—
9#16840312C411yescharacteristic
10C2×#14519777C2211yescharacteristic
11#16840156—22no—
12#16840142C411yescharacteristic
13#16840142C2211yescharacteristic
14#16840135C411yescharacteristic
15#16840135C2211yescharacteristic
16C4×M16×C61C411yescharacteristic
17C2×#11758217—42no—
18#14519838—24no—
19#14519838—42no—
20C2×#11758222—21no—
21C22×Dic122D412yes—
22#14519810—44no—
23#14519810—44no—
24C2×Dic244—22no—
25C2×Dic244—22no—
26C2×#11758190—22no—
27C2×#11758190—22no—
28#14519777—41no—
29#14519777C2×C411yescharacteristic
30#14519777C2×C411yescharacteristic
31#14519777D412yes—
32#14519777C2311yescharacteristic
33#14519774C2×C411yescharacteristic
34#14519765—21no—
35#14519751—41no—
36C4×D244—41no—
37C2×C4⋊Dic61—41no—
38C2×M16×C61—21no—
39C2×C42×C61C2×C411yescharacteristic
40#97×C61—21no—
41C4×C8×C61C2×C411yescharacteristic
42C4×C8×C61C2×C411yescharacteristic
43C22×C4×C61—21no—
44C22×C4×C61C22⋊C411yescharacteristic
45C2×C22⋊D61—41no—
46C22×Dic61—22no—
47#11758222—42no—
48#11758222—42no—
49C2×D244—21no—
50C2×D244—41no—
51C2×C4×D61—41no—
52C2×Dic122—21no—
53C2×Dic122—22no—
54C2×Dic122—42no—
55C2×Dic122—42no—
56C2×Dic122C22⋊C412yes—
57C2×Dic122C2×D412yes—
58#11758217—44no—
59#11758217—82no—
60C2×#92420—82no—
61M16×C61—24no—
62C2×C8×C61—21no—
63C2×C8×C61—21no—
64C42×C61—21no—
65C42×C61C22⋊C411yescharacteristic
66C42×C61C22×C411yescharacteristic
67#11758198—42no—
68C4⋊Dic61—41no—
69C4⋊Dic61—42no—
70C4⋊Dic61—41no—
71C4⋊Dic61—41no—
72Dic244—44no—
73Dic244—44no—
74#11758190—44no—
75#11758190—44no—
76C23×C61#9911yescharacteristic
77C22×D61—41no—
78C2×C4×C61—22no—
79C2×C4×C61—21no—
80C2×C4×C61—21no—
81C2×C4×C61—42no—
82C2×C4×C61#9911yescharacteristic
83C2×C4×C61C2×C22⋊C411yescharacteristic
84C22⋊D61—82no—
85C2×Dic61—22no—
86C2×Dic61—22no—
87C2×Dic61—42no—
88C2×Dic61—42no—
89C2×Dic61—41no—
90D244—42no—
91D244—82no—
92C4×D61—81no—
93C4×D61—81no—
94Dic122—42no—
95Dic122—42no—
96Dic122—42no—
97Dic122—82no—
98#92420—84no—
99C8×C61—22no—
100C8×C61—22no—
101#13590—611nomaximal, Sylow
102C22×C61—41no—
103C22×C61#35312yes—
104C22×C61C2×#9911yescharacteristic
105C2×D61—82no—
106C2×D61—81no—
107C4×C61—22no—
108C4×C61—21no—
109C4×C61—21no—
110C4×C61—41no—
111Dic61—42no—
112Dic61—42no—
113Dic61—81no—
114#3152—611no—
115C2×#356—612no—
116#1411—612no—
117#1410—612no—
118C2×C61—21no—
119C2×C61—22no—
120C2×C61C2×#35311yescharacteristic
121D61—161no—
122C2×#137—1222no—
123#532—611no—
124C2×C4⋊Q8—611no—
125#497—1222no—
126#494—611no—
127#494—611no—
128#492—611no—
129#492—611no—
130C2×#101—1222no—
131C4×M16#692311yescharacteristic
132#356—614no—
133#356—1222no—
134C61#1359011yescharacteristic, complemented, Sylow
135C2×#41—1221no—
136C22×Q8—612no—
137#137—2444no—
138#137—2444no—
139C2×Q16—1222no—
140C2×Q16—1222no—
141C2×SD16—1222no—
142C2×SD16—1222no—
143C2×M16—21no—
144C2×M16—2442no—
145C4⋊Q8—612no—
146C4⋊Q8—611no—
147C4⋊Q8—611no—
148C4⋊Q8—611no—
149C4⋊Q8—2441no—
150#127—611no—
151#124—1221no—
152#121—2441no—
153C4×D4—2441no—
154C2×C4⋊C4—2441no—
155C2×C42C2×#692311yescharacteristic
156#101—1224no—
157#101—2442no—
158#97—21no—
159C4×C8C2×#692311yescharacteristic
160C4×C8C2×#692311yescharacteristic
161#41—2442no—
162#41—2442no—
163C2×Q8—612no—
164C2×Q8—612no—
165C2×Q8—1222no—
166C2×Q8—1221no—
167C2×Q8—2442no—
168C2×Q8—2442no—
169C2×D4—1221no—
170C2×D4—2441no—
171C2×D4—2441no—
172C22×C4—21no—
173C22×C4—1222no—
174C22×C4—2441no—
175C22×C4C22⋊#692311yescharacteristic
176Q16—2444no—
177Q16—2444no—
178SD16—2444no—
179SD16—2444no—
180M16—24no—
181M16—4882no—
182M16—2444no—
183C2×C8—21no—
184C2×C8—21no—
185C2×C8—4882no—
186C4⋊C4—2441no—
187C4⋊C4—2441no—
188C4⋊C4—2442no—
189C4⋊C4—2441no—
190C22⋊C4—2442no—
191C42—21no—
192C42C22⋊#692311yescharacteristic
193C42C22×#692311yescharacteristic
194C23—2441no—
195C23#1451983611yescharacteristic
196Q8—4882no—
197Q8—2442no—
198Q8—2442no—
199Q8—2442no—
200D4—4882no—
201D4—4882no—
202D4—2442no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—42no—
207C2×C4—1222no—
208C2×C4—1222no—
209C2×C4—4881no—
210C2×C4—4881no—
211C2×C4—2441no—
212C2×C4—2442no—
213C2×C4—2442no—
214C2×C4#1451983611yescharacteristic
215C2×C4C2×C22⋊#692311yescharacteristic
216C8—22no—
217C8—22no—
218C8—4884no—
219C22—41no—
220C22—4882no—
221C22—4881no—
222C22#1684066712yes—
223C22C2×#1451983611yescharacteristic
224C4—22no—
225C4—21no—
226C4—21no—
227C4—41no—
228C4—4881no—
229C4—2442no—
230C4—2442no—
231C2—21no—
232C2—22no—
233C2—9761no—
234C2C2×#1684066711yescharacteristic
subgroupG/H
centerC2C2×#16840667
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC4×M16×C61C4
socleC2×C61C2×#353
prime radical#16840312C4
cosocle#14519777C23
hypercenterC4×M16#6923
hypocenterC61#13590
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
1. C2×#16840673C2semidirect
2. #21460957C2semidirect
3. #21460955C2semidirect
134. C61#13590semidirect

Maximal subgroups

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

subgroupindex
C2×#168406732
#214609572
#214609552
#214562782
#1359061