Finite Group Databasebeta

← #29573030

Subgroups — #29573030

Order 15616.

404 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 101 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#21454530C211yesmaximal, characteristic
2#21444574C212yesmaximal, complemented
3#21444552C212yesmaximal
4#21443732C211yesmaximal, characteristic, complemented
5C61×#1309C211yesmaximal, characteristic, complemented
6C2×#14519785C412yes—
7#16840312C2211yescharacteristic
8#16839839—22no—
9#16839827—22no—
10#16839786C2212yes—
11#16839730C412yes—
12C2×C4×#92418C2211yescharacteristic
13#16839512—22no—
14#16839512—22no—
15#16839510—22no—
16#16839505—22no—
17C61×#423C2212yes—
18C61×#423C2211yescharacteristic
19C2×#11758222C2×C412yes—
20#14519785—44no—
21C2×#11758194—22no—
22C2×#11758189—22no—
23C22×#92418C2×C411yescharacteristic
24C22×#92418C2×C411yescharacteristic
25C2×C8×D61—22no—
26#14519777D411yescharacteristic
27#14519774D411yescharacteristic
28#14519765Q812yes—
29#14519751—22no—
30C4×D244—22no—
31C4⋊#92418—22no—
32C4⋊#92418—22no—
33#14519689—24no—
34C4×#92418D412yes—
35C4×#92418D412yes—
36C2×M16×C61—22no—
37C2×M16×C61C2×C412yes—
38C2×C42×C61C2311yescharacteristic
39C4⋊C8×C61—22no—
40C4⋊C8×C61—22no—
41C4⋊C8×C61—22no—
42C22×C4×C61C22×C411yescharacteristic
43C22×C4×C61#4112yes—
44C2×C22⋊D61—22no—
45#11758222—42no—
46#11758222—42no—
47C2×D244—22no—
48C2×D244C4⋊C412yes—
49C2×C4×D61—22no—
50C2×Dic122C4⋊C412yes—
51M16×C61—42no—
52M16×C61—82no—
53C2×C8×C61—22no—
54C2×C8×C61—42no—
55C42×C61C2×D412yes—
56C42×C61C2×D411yescharacteristic
57C42×C61C2×Q811yescharacteristic
58#11758198—24no—
59C4⋊Dic61—22no—
60#11758194—82no—
61C2×#92418—22no—
62C2×#92418—41no—
63C2×#92418—42no—
64C2×#92418C22⋊C412yes—
65C2×#92418C22⋊C411yescharacteristic
66C2×#92418C22⋊C411yescharacteristic
67#11758189—44no—
68C8×D61—44no—
69C23×C61#11711yescharacteristic
70C22×D61—22no—
71C2×C4×C61—21no—
72C2×C4×C61—21no—
73C2×C4×C61—22no—
74C2×C4×C61—22no—
75C2×C4×C61C2×C22⋊C411yescharacteristic
76C2×C4×C61C2×C4⋊C411yescharacteristic
77C2×C4×C61#12112yes—
78C2×C4×C61C22⋊Q812yes—
79C22⋊D61—44no—
80C2×Dic61—22no—
81D244—42no—
82D244—42no—
83D244—42no—
84C4×D61—42no—
85C4×D61—42no—
86Dic122—42no—
87C8×C61—42no—
88C8×C61—82no—
89#92418—21no—
90#92418—22no—
91#92418—82no—
92#92418#10012yes—
93#8636—611nomaximal, Sylow
94C22×C61—21no—
95C22×C61—22no—
96C22×C61#38011yescharacteristic
97C2×D61—42no—
98C2×D61—44no—
99C4×C61—21no—
100C4×C61—22no—
101C4×C61C2×#10011yescharacteristic
102C4×C61#41311yescharacteristic
103C4×C61#47112yes—
104C4×C61#47112yes—
105Dic61—42no—
106#2931—611no—
107#1566—612no—
108#1560—612no—
109#1309—611no—
110#1309D6111yescharacteristic, complemented
111C2×C61—41no—
112C2×C61#180011yescharacteristic
113C2×C61#181512yes—
114D61—82no—
115C2×#131—612no—
116#532—611no—
117#436—1222no—
118C8×D4—1222no—
119#423—612no—
120#423C2×D6112yes—
121#423C2×D6111yescharacteristic
122#408—612no—
123C2×C4×C8—611no—
124#334—1222no—
125#334—1222no—
126#333—1222no—
127#331—1222no—
128C61#863611yescharacteristic, complemented, Sylow
129C2×#41—612no—
130#131—2444no—
131C2×M16—22no—
132C2×M16—1222no—
133C2×M16—1222no—
134C2×M16C4×D6112yes—
135C22×C8—611no—
136C22×C8—611no—
137C22×C8—1222no—
138C4⋊Q8—611no—
139#127—611no—
140#124—612no—
141#121—1222no—
142C4×D4—1222no—
143C2×C42C22×D6111yescharacteristic
144C4⋊C8—22no—
145C4⋊C8—22no—
146C4⋊C8—22no—
147C4⋊C8—1222no—
148C4⋊C8—1222no—
149C22⋊C8—1224no—
150C4×C8—612no—
151C4×C8—612no—
152#41—2442no—
153#41—2442no—
154C2×Q8—612no—
155C2×D4—612no—
156C2×D4—1222no—
157C2×D4—1222no—
158C22×C4—1222no—
159C22×C4C2×C4×D6111yescharacteristic
160C22×C4#1175822212yes—
161M16—42no—
162M16—82no—
163M16—4882no—
164M16—2444no—
165C2×C8—22no—
166C2×C8—42no—
167C2×C8—611no—
168C2×C8—612no—
169C2×C8—611no—
170C2×C8—1222no—
171C2×C8—2444no—
172C2×C8—2441no—
173C2×C8—2442no—
174C4⋊C4—1222no—
175C22⋊C4—1224no—
176C42D4×D6112yes—
177C42D4×D6111yescharacteristic
178C42Q8×D6111yescharacteristic
179C23—1222no—
180C23#1451973411yescharacteristic
181Q8—2442no—
182D4—2442no—
183D4—2444no—
184D4—2442no—
185D4—2442no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—1222no—
191C2×C4—2442no—
192C2×C4—2442no—
193C2×C4C22⋊C4×D6111yescharacteristic
194C2×C4C4⋊C4×D6111yescharacteristic
195C2×C4#1451975012yes—
196C2×C4#1451975512yes—
197C8—42no—
198C8—82no—
199C8—612no—
200C8—1221no—
201C8—1222no—
202C8—4882no—
203C22—21no—
204C22—22no—
205C22—2442no—
206C22—2444no—
207C22#1683962111yescharacteristic
208C4—21no—
209C4—22no—
210C4—2442no—
211C4#100×D6111yescharacteristic
212C4#1683974511yescharacteristic
213C4#1684002412yes—
214C4#1684002812yes—
215C2—41no—
216C2—4882no—
217C2#2144581011yescharacteristic
218C2#2144587712yes—
subgroupG/H
centerC22#16839621
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1309C2
socleC22×C61#380
prime radical#16840312C22
cosocleC2×C42×C61C23
hypercenter#1309D61
hypocenterC61#8636
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1309

Complements

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

NH ≅ G/Ntype
2. #21444574C2semidirect
4. #21443732C2semidirect
5. C61×#1309C2semidirect
110. #1309D61semidirect
128. C61#8636semidirect

Maximal subgroups

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

subgroupindex
#214545302
#214445742
#214445522
#214437322
C61×#13092
#863661