Finite Group Databasebeta

← #30605531

Subgroups — #30605531

Order 15616.

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

normal subgroups only

This group has 326 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#21462188C212yesmaximal, complemented
2#21460823C212yesmaximal, complemented
3#21460822C212yesmaximal, complemented
4#21456195C211yesmaximal, characteristic
5#16840685—22no—
6#16840658—22no—
7#16840654C2214yescomplemented
8C2×#14519774C411yescharacteristic
9#16840128C411yescharacteristic
10#16840128C411yescharacteristic
11#16840128C2211yescharacteristic
12#16840128C2211yescharacteristic
13#16840110—22no—
14#16839766—22no—
15C4×#11758194C2211yescharacteristic
16C61×#533C411yescharacteristic
17#14519851—24no—
18C22×D244—21no—
19C22×D244—41no—
20C2×#11758194D412yes—
21#14519774—21no—
22#14519774—41no—
23#14519774C2×C411yescharacteristic
24#14519774C2×C411yescharacteristic
25#14519697—22no—
26#14519697—22no—
27#14519697—22no—
28#14519697—22no—
29#14519688C2×C411yescharacteristic
30#14519688C2311yescharacteristic
31C4×#92418D412yes—
32C4⋊Q8×C61—21no—
33#125×C61C2×C411yescharacteristic
34#125×C61C2×C411yescharacteristic
35C22⋊Q8×C61—41no—
36C4×Q8×C61—41no—
37#117×C61—21no—
38C2×C42×C61C2×C411yescharacteristic
39C23×D61—41no—
40C2×Q8×C61—41no—
41C22×C4×C61—21no—
42C22×C4×C61C22⋊C411yescharacteristic
43C2×D244—21no—
44C2×D244—21no—
45C2×D244—44no—
46C2×D244—42no—
47C2×D244—41no—
48C2×D244—41no—
49C2×D244—41no—
50C2×D244—84no—
51C4⋊C4×C61—21no—
52C4⋊C4×C61—21no—
53C4⋊C4×C61—41no—
54C4⋊C4×C61—41no—
55C4⋊C4×C61—41no—
56C22⋊C4×C61—41no—
57C42×C61—21no—
58C42×C61—41no—
59C42×C61C22⋊C411yescharacteristic
60C42×C61C22×C411yescharacteristic
61#11758194—42no—
62C2×#92418C22⋊C412yes—
63C2×#92418C2×D412yes—
64#11758187—44no—
65C23×C61#10011yescharacteristic
66C22×D61—41no—
67C22×D61—41no—
68C22×D61—82no—
69C22×D61—84no—
70Q8×C61—82no—
71C2×C4×C61—21no—
72C2×C4×C61—22no—
73C2×C4×C61—21no—
74C2×C4×C61—42no—
75C2×C4×C61—41no—
76C2×C4×C61—41no—
77C2×C4×C61#10011yescharacteristic
78C2×C4×C61C2×C22⋊C411yescharacteristic
79D244—42no—
80D244—42no—
81D244—82no—
82D244—84no—
83D244—82no—
84D244—82no—
85#92418—22no—
86#92418—22no—
87#11915—611nomaximal, Sylow
88C22×C61—21no—
89C22×C61—41no—
90C22×C61C2×#10011yescharacteristic
91C2×D61—82no—
92C2×D61—82no—
93C2×D61—81no—
94C2×D61—81no—
95C2×D61—164no—
96C4×C61—22no—
97C4×C61—21no—
98C4×C61—41no—
99C4×C61—81no—
100C4×C61—81no—
101C4×C61#42112yes—
102#3138—611no—
103#2165—612no—
104#1355—612no—
105#1355—612no—
106C2×C61—21no—
107C2×C61—41no—
108C2×C61#153311yescharacteristic
109D61—161no—
110D61—161no—
111#533#692311yescharacteristic
112C2×#127—611no—
113#490—611no—
114#490—611no—
115#490—611no—
116#490—611no—
117#486—1222no—
118#418—1222no—
119C4×M16—611no—
120#364—1222no—
121#349—1222no—
122#347—614no—
123C61#1191511yescharacteristic, complemented, Sylow
124C22×D4—1221no—
125C22×D4—2441no—
126C2×M16—612no—
127C4⋊Q8—21no—
128#127—611no—
129#127—611no—
130#127—1221no—
131#127—2441no—
132#125C2×#692311yescharacteristic
133#125C2×#692311yescharacteristic
134C22⋊Q8—41no—
135C4×Q8—41no—
136#117—21no—
137C2×C42C2×#692311yescharacteristic
138M32—1224no—
139#102—1222no—
140#102—1222no—
141#102—1222no—
142#102—1222no—
143#97—611no—
144#97—611no—
145C4×C8—612no—
146C24—2441no—
147C2×Q8—41no—
148C2×D4—1221no—
149C2×D4—1221no—
150C2×D4—4884no—
151C2×D4—2441no—
152C2×D4—2441no—
153C2×D4—2442no—
154C2×D4—2444no—
155C2×D4—2441no—
156C22×C4—21no—
157C22×C4C22⋊#692311yescharacteristic
158M16—2442no—
159C2×C8—612no—
160C2×C8—612no—
161C4⋊C4—21no—
162C4⋊C4—21no—
163C4⋊C4—41no—
164C4⋊C4—41no—
165C4⋊C4—41no—
166C22⋊C4—41no—
167C42—21no—
168C42—41no—
169C42C22⋊#692311yescharacteristic
170C42C22×#692311yescharacteristic
171C16—2444no—
172C23—4882no—
173C23—4884no—
174C23—2441no—
175C23—2441no—
176C23#1451983711yescharacteristic
177Q8—82no—
178D4—4884no—
179D4—4882no—
180D4—4882no—
181D4—4882no—
182D4—2442no—
183D4—2442no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—42no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4#1451983711yescharacteristic
191C2×C4C2×C22⋊#692311yescharacteristic
192C8—1222no—
193C8—1222no—
194C22—21no—
195C22—41no—
196C22—9764no—
197C22—4882no—
198C22—4882no—
199C22—4881no—
200C22—4881no—
201C22C2×#1451983711yescharacteristic
202C4—22no—
203C4—21no—
204C4—41no—
205C4—81no—
206C4—81no—
207C4#1684076112yes—
208C2—21no—
209C2—41no—
210C2—9761no—
211C2—9761no—
212C2#2146130011yescharacteristic
subgroupG/H
centerC2#21461300
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#533C4
socleC2×C61#1533
prime radicalC2×#14519774C4
cosocle#14519688C23
hypercenter#533#6923
hypocenterC61#11915
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
1. #21462188C2semidirect
2. #21460823C2semidirect
3. #21460822C2semidirect
7. #16840654C22semidirect
123. C61#11915semidirect

Maximal subgroups

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

subgroupindex
#214621882
#214608232
#214608222
#214561952
#1191561