Finite Group Databasebeta

← #30594949

Subgroups — #30594949

Order 15616.

304 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 36 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#21460916C211yesmaximal, characteristic, complemented
2#21460750C211yesmaximal, characteristic, complemented
3#21446909C211yesmaximal, characteristic
4C2×#14519838—21no—
5#16840607—21no—
6C22×#11758190—21no—
7C2×#14519774C411yescharacteristic
8C2×#14519699—21no—
9#16839668C2211yescharacteristic
10C61×#336C411yescharacteristic
11C2×#11758217—41no—
12#14519838—22no—
13#14519838—41no—
14C22⋊#92420—41no—
15C22×Dic122D411yescharacteristic
16C22×D244—21no—
17C22×D244—41no—
18C2×#11758190—42no—
19C2×#11758190—42no—
20C2×#11758190—41no—
21C2×#11758190—41no—
22#14519774—42no—
23C2×C4⋊Dic61D411yescharacteristic
24#14519699—42no—
25#14519684—41no—
26C22×C8×C61—21no—
27C2×C42×C61C2×C411yescharacteristic
28C23×D61—41no—
29C22×C4×C61—21no—
30C22×C4×C61C22⋊C411yescharacteristic
31C22×Dic61—21no—
32C22×Dic61—21no—
33C2×D244—22no—
34C2×D244—41no—
35C2×D244—41no—
36C2×D244—41no—
37C2×D244—41no—
38C2×D244—41no—
39C2×D244—42no—
40C2×D244—42no—
41C2×D244—82no—
42C2×D244—82no—
43C2×Dic122—21no—
44C2×Dic122—41no—
45C2×Dic122—41no—
46C2×Dic122D811yescharacteristic
47C2×Dic122SD1611yescharacteristic
48#11758217—42no—
49#11758217—81no—
50C2×#92420—81no—
51C2×#92420—81no—
52C2×C8×C61—22no—
53C2×C8×C61—41no—
54C2×C8×C61—41no—
55C42×C61—41no—
56C4⋊Dic61—41no—
57#11758190—44no—
58#11758190—44no—
59C23×C61#9911yescharacteristic
60C22×D61—42no—
61C22×D61—82no—
62C22×D61—82no—
63C22×D61—81no—
64C22×D61—81no—
65C2×C4×C61—21no—
66C2×C4×C61—21no—
67C2×C4×C61—22no—
68C2×C4×C61—41no—
69C2×C4×C61—41no—
70C2×C4×C61#10211yescharacteristic
71C2×C4×C61#10411yescharacteristic
72C2×Dic61—21no—
73C2×Dic61—21no—
74C2×Dic61—41no—
75C2×Dic61—41no—
76C2×Dic61—41no—
77C2×Dic61—81no—
78D244—42no—
79D244—42no—
80D244—81no—
81D244—81no—
82D244—84no—
83D244—84no—
84Dic122—41no—
85Dic122—41no—
86Dic122—81no—
87#92420—82no—
88#92420—161no—
89C8×C61—42no—
90#7404—611nomaximal, Sylow
91C22×C61—21no—
92C22×C61—21no—
93C22×C61#32711yescharacteristic
94C22×C61AΣL(1,𝔽16)11yescharacteristic
95C22×C61#35311yescharacteristic
96C2×D61—84no—
97C2×D61—82no—
98C2×D61—162no—
99C2×D61—161no—
100C2×D61—161no—
101C4×C61—21no—
102C4×C61—21no—
103C4×C61—42no—
104Dic61—41no—
105Dic61—41no—
106Dic61—81no—
107#2014—611no—
108#1394—611no—
109#1319—611no—
110C2×C61—21no—
111C2×C61—21no—
112C2×C61#134311yescharacteristic
113C2×C61#140611yescharacteristic
114C2×C61#141011yescharacteristic
115D61—162no—
116C22×SD16—1221no—
117C2×#127—611no—
118C2×#102—1221no—
119C2×#101—1221no—
120#391—611no—
121#336#692311yescharacteristic
122#324—1221no—
123C61#740411yescharacteristic, complemented, Sylow
124C22×Q8—611no—
125C22×D4—1221no—
126C22×D4—2441no—
127C2×SD16—2442no—
128C2×SD16—2442no—
129C2×SD16—2441no—
130C2×SD16—2441no—
131C2×M16—2441no—
132C22×C8—21no—
133#127—2442no—
134C2×C4⋊C4—611no—
135C2×C42C2×#692311yescharacteristic
136#102—2442no—
137#101—1222no—
138#101—2441no—
139C22⋊C8—2441no—
140#95—2441no—
141C24—2441no—
142C2×Q8—611no—
143C2×Q8—611no—
144C2×Q8—1221no—
145C2×Q8—2441no—
146C2×Q8—2441no—
147C2×D4—1222no—
148C2×D4—4882no—
149C2×D4—4882no—
150C2×D4—2441no—
151C2×D4—2441no—
152C2×D4—2441no—
153C2×D4—2442no—
154C2×D4—2442no—
155C2×D4—2441no—
156C2×D4—2441no—
157C22×C4—21no—
158C22×C4—1221no—
159C22×C4—1221no—
160C22×C4C22⋊#692311yescharacteristic
161SD16—2444no—
162SD16—2444no—
163M16—4881no—
164M16—2442no—
165C2×C8—22no—
166C2×C8—41no—
167C2×C8—41no—
168C2×C8—4881no—
169C2×C8—4881no—
170C4⋊C4—2441no—
171C42—41no—
172C23—4882no—
173C23—4882no—
174C23—4881no—
175C23—4881no—
176C23—2442no—
177C23#1451983611yescharacteristic
178Q8—4881no—
179Q8—2441no—
180Q8—2441no—
181D4—4881no—
182D4—4881no—
183D4—4884no—
184D4—4884no—
185D4—2442no—
186D4—2442no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—1221no—
193C2×C4—1221no—
194C2×C4—4881no—
195C2×C4—2441no—
196C2×C4—2441no—
197C2×C4—2441no—
198C2×C4#1451983911yescharacteristic
199C2×C4#1451984211yescharacteristic
200C8—42no—
201C8—9761no—
202C8—4882no—
203C22—21no—
204C22—21no—
205C22—9762no—
206C22—9761no—
207C22—9761no—
208C22—4884no—
209C22—4882no—
210C22#1684061411yescharacteristic
211C22#1684066311yescharacteristic
212C22#1684066711yescharacteristic
213C4—21no—
214C4—21no—
215C4—42no—
216C4—4881no—
217C4—2441no—
218C4—2441no—
219C2—21no—
220C2—21no—
221C2—9762no—
222C2#2146079811yescharacteristic
223C2#2146094711yescharacteristic
224C2#2146095511yescharacteristic
subgroupG/H
centerC22#16840667
commutatorC2×C42×C61C2×C4
FrattiniC2×C42C2×#6923
FittingC61×#336C4
socleC22×C61#353
prime radicalC2×#14519774C4
cosocle#16839668C22
hypercenter#336#6923
hypocenterC61#7404
LCSG ▷ C2×C42×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ #336

Complements

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

NH ≅ G/Ntype
1. #21460916C2semidirect
2. #21460750C2semidirect
123. C61#7404semidirect

Maximal subgroups

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

subgroupindex
#214609162
#214607502
#214469092
#740461