Finite Group Databasebeta

← #30599067

Subgroups — #30599067

Order 15616.

404 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 90 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#21461373C212yesmaximal, complemented
2#21461356C212yesmaximal
3#21460727C212yesmaximal, complemented
4#21454529C211yesmaximal, characteristic
5#16840765C2214yes—
6#16840624—22no—
7#16840623—22no—
8#16840622—22no—
9#16840620—22no—
10C2×#14519783C411yescharacteristic
11#16840308C2211yescharacteristic
12#16839838—22no—
13C8×C22⋊D61—22no—
14#16839785C2211yescharacteristic
15#16839730C411yescharacteristic
16#16839729C411yescharacteristic
17C2×C8×Dic61C2211yescharacteristic
18C2×#131×C61C411yescharacteristic
19C2×#11758217—24no—
20#14519844—24no—
21C4⋊#92420—24no—
22C2×#11758222C2×C411yescharacteristic
23#14519783—42no—
24C2×#11758194C2×C411yescharacteristic
25C2×#11758189—21no—
26C22×#92418C2×C411yescharacteristic
27C2×C8×D61—21no—
28#14519775D411yescharacteristic
29#14519773D411yescharacteristic
30#14519766Q811yescharacteristic
31#14519764Q811yescharacteristic
32#14519749—22no—
33C4×C22⋊D61—22no—
34C2×C4×Dic61C2311yescharacteristic
35#14519706—22no—
36C22⋊#92418—22no—
37#14519689—22no—
38C8×Dic61D412yes—
39C8×Dic61D412yes—
40C2×#41×C61C2×C411yescharacteristic
41#131×C61—42no—
42C2×M16×C61—21no—
43C2×M16×C61C2×C411yescharacteristic
44C22×C8×C61—21no—
45C22×C8×C61C2×C411yescharacteristic
46#41×C61—41no—
47#41×C61—41no—
48C2×Q8×C61C4⋊C411yescharacteristic
49C2×D4×C61—21no—
50C2×D4×C61C4⋊C411yescharacteristic
51C22×C4×C61—21no—
52C22×C4×C61C22×C411yescharacteristic
53C2×C22⋊D61—21no—
54C2×C22⋊D61—22no—
55C22×Dic61#4112yes—
56#11758222—41no—
57#11758222—41no—
58C2×D244C4⋊C411yescharacteristic
59C2×C4×D61—21no—
60C2×Dic122C4⋊C411yescharacteristic
61#11758217—84no—
62C2×#92420—44no—
63M16×C61—42no—
64M16×C61—41no—
65C2×C8×C61—22no—
66C2×C8×C61—21no—
67C2×C8×C61—42no—
68C2×C8×C61C22⋊C411yescharacteristic
69C2×C8×C61C22⋊C411yescharacteristic
70C22⋊Dic61—22no—
71#11758198—22no—
72#11758196—22no—
73C4×Dic61C2×D411yescharacteristic
74C4×Dic61C2×D412yes—
75C4×Dic61C2×Q811yescharacteristic
76#11758194—41no—
77C2×#92418—21no—
78C2×#92418—41no—
79C2×#92418C22⋊C412yes—
80#11758189—42no—
81C8×D61—42no—
82C23×C61—21no—
83C23×C61#11711yescharacteristic
84C22×D61—21no—
85Q8×C61—41no—
86D4×C61—41no—
87D4×C61—42no—
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—21no—
91C2×C4×C61—41no—
92C2×C4×C61—41no—
93C2×C4×C61C2×C22⋊C411yescharacteristic
94C2×C4×C61C2×C4⋊C411yescharacteristic
95C22⋊D61—42no—
96C22⋊D61—44no—
97C2×Dic61—24no—
98C2×Dic61—21no—
99C2×Dic61#12112yes—
100C2×Dic61C22⋊Q812yes—
101D244—41no—
102C4×D61—41no—
103C4×D61—41no—
104Dic122—41no—
105#92420—84no—
106C8×C61—21no—
107C8×C61—41no—
108C8×C61#10012yes—
109#92418—22no—
110#92418—41no—
111#8636—611nomaximal, Sylow
112C22×C61—21no—
113C22×C61—22no—
114C22×C61—41no—
115C22×C61—42no—
116C22×C61#38011yescharacteristic
117C2×D61—41no—
118C2×D61—42no—
119C4×C61—21no—
120C4×C61—41no—
121C4×C61C2×#10011yescharacteristic
122C4×C61#41311yescharacteristic
123Dic61—22no—
124Dic61—41no—
125Dic61#47114yes—
126#2931—611no—
127#1566—612no—
128#1560—612no—
129#1309—612no—
130C2×C61—41no—
131C2×C61—81no—
132C2×C61#180011yescharacteristic
133C2×C61#181512yes—
134D61—81no—
135C2×#131—611no—
136C2×#131#692311yescharacteristic
137#532—611no—
138#436—1222no—
139C8×D4—1222no—
140#423—611no—
141#423—614no—
142#408—611no—
143#408—611no—
144C2×C4×C8—611no—
145#334—1222no—
146#334—1222no—
147#333—1222no—
148#331—1222no—
149C61#863611yescharacteristic, complemented, Sylow
150C2×#41—611no—
151C2×#41C2×#692311yescharacteristic
152#131—42no—
153#131—2442no—
154C2×M16—21no—
155C2×M16—611no—
156C2×M16—1221no—
157C2×M16—1224no—
158C2×M16C2×#692311yescharacteristic
159C22×C8—21no—
160C22×C8—611no—
161C22×C8—1221no—
162C22×C8C2×#692311yescharacteristic
163C4⋊Q8—611no—
164#127—611no—
165#124—611no—
166#124—611no—
167#121—1222no—
168C4×D4—1222no—
169C2×C42—611no—
170C4⋊C8—1222no—
171C4⋊C8—1224no—
172C4⋊C8—1224no—
173C22⋊C8—1222no—
174C22⋊C8—1222no—
175C4×C8—612no—
176C4×C8—612no—
177#41—41no—
178#41—41no—
179#41—2441no—
180#41—2441no—
181C2×Q8—611no—
182C2×Q8C4⋊#692311yescharacteristic
183C2×D4—21no—
184C2×D4—611no—
185C2×D4—1222no—
186C2×D4—1221no—
187C2×D4C4⋊#692311yescharacteristic
188C22×C4—21no—
189C22×C4—612no—
190C22×C4—1221no—
191C22×C4C22×#692311yescharacteristic
192M16—42no—
193M16—41no—
194M16—4884no—
195M16—2442no—
196M16—2441no—
197C2×C8—22no—
198C2×C8—21no—
199C2×C8—42no—
200C2×C8—612no—
201C2×C8—1221no—
202C2×C8—2441no—
203C2×C8—2444no—
204C2×C8—2442no—
205C2×C8C22⋊#692311yescharacteristic
206C2×C8C22⋊#692311yescharacteristic
207C4⋊C4—1222no—
208C22⋊C4—1222no—
209C22⋊C4—1222no—
210C42—612no—
211C42—611no—
212C42—611no—
213C23—21no—
214C23—1221no—
215C23#1451985611yescharacteristic
216Q8—41no—
217Q8—2441no—
218D4—41no—
219D4—42no—
220D4—2441no—
221D4—2444no—
222D4—2442no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—612no—
229C2×C4—612no—
230C2×C4—1224no—
231C2×C4—1221no—
232C2×C4—2441no—
233C2×C4—2441no—
234C2×C4C2×C22⋊#692311yescharacteristic
235C2×C4C2×C4⋊#692311yescharacteristic
236C8—21no—
237C8—41no—
238C8—1222no—
239C8—4884no—
240C8—2441no—
241C8#1451983712yes—
242C22—21no—
243C22—22no—
244C22—41no—
245C22—42no—
246C22—2441no—
247C22—2442no—
248C22#1684070411yescharacteristic
249C4—21no—
250C4—41no—
251C4—614no—
252C4—1222no—
253C4—2441no—
254C4C2×#1451983711yescharacteristic
255C4#1684074811yescharacteristic
256C2—41no—
257C2—81no—
258C2—4881no—
259C2#2146168311yescharacteristic
260C2#2146170712yes—
subgroupG/H
centerC22#16840704
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#131×C61C4
socleC22×C61#380
prime radical#16840308C22
cosocleC2×C4×Dic61C23
hypercenterC2×#131#6923
hypocenterC61#8636
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131

Complements

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

NH ≅ G/Ntype
1. #21461373C2semidirect
3. #21460727C2semidirect
149. C61#8636semidirect

Maximal subgroups

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

subgroupindex
#214613732
#214613562
#214607272
#214545292
#863661