Finite Group Databasebeta

← #30599071

Subgroups — #30599071

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#21461376C212yesmaximal, complemented
2#21461356C212yesmaximal
3#21460727C212yesmaximal, complemented
4#21454529C211yesmaximal, characteristic
5#16840765C2214yes—
6#16840626—22no—
7#16840625—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—42no—
97C22⋊D61—42no—
98C2×Dic61—22no—
99C2×Dic61—22no—
100C2×Dic61—21no—
101C2×Dic61#12112yes—
102C2×Dic61C22⋊Q812yes—
103D244—41no—
104C4×D61—41no—
105C4×D61—41no—
106Dic122—41no—
107#92420—84no—
108C8×C61—21no—
109C8×C61—41no—
110C8×C61#10012yes—
111#92418—22no—
112#92418—41no—
113#8638—611nomaximal, Sylow
114C22×C61—21no—
115C22×C61—22no—
116C22×C61—41no—
117C22×C61—42no—
118C22×C61#38011yescharacteristic
119C2×D61—41no—
120C2×D61—42no—
121C4×C61—21no—
122C4×C61—41no—
123C4×C61C2×#10011yescharacteristic
124C4×C61#41311yescharacteristic
125Dic61—22no—
126Dic61—41no—
127Dic61#47212yes—
128Dic61#47312yes—
129#2931—611no—
130#1567—612no—
131#1560—612no—
132#1309—612no—
133C2×C61—41no—
134C2×C61—81no—
135C2×C61#180011yescharacteristic
136C2×C61#181612yes—
137D61—81no—
138C2×#131—611no—
139C2×#131#692311yescharacteristic
140#532—611no—
141#436—1222no—
142C8×D4—1222no—
143#423—611no—
144#423—614no—
145#408—611no—
146#408—611no—
147C2×C4×C8—611no—
148#335—1222no—
149#335—1222no—
150#333—1222no—
151#331—1222no—
152C61#863811yescharacteristic, complemented, Sylow
153C2×#41—611no—
154C2×#41C2×#692311yescharacteristic
155#131—42no—
156#131—2442no—
157C2×M16—21no—
158C2×M16—611no—
159C2×M16—1221no—
160C2×M16—1224no—
161C2×M16C2×#692311yescharacteristic
162C22×C8—21no—
163C22×C8—611no—
164C22×C8—1221no—
165C22×C8C2×#692311yescharacteristic
166C4⋊Q8—611no—
167#127—611no—
168#124—611no—
169#124—611no—
170#121—1222no—
171C4×D4—1222no—
172C2×C42—611no—
173C4⋊C8—1222no—
174C4⋊C8—1224no—
175C4⋊C8—1224no—
176C22⋊C8—1222no—
177C22⋊C8—1222no—
178C4×C8—612no—
179C4×C8—612no—
180#41—41no—
181#41—41no—
182#41—2441no—
183#41—2441no—
184C2×Q8—611no—
185C2×Q8C4⋊#692311yescharacteristic
186C2×D4—21no—
187C2×D4—611no—
188C2×D4—1222no—
189C2×D4—1221no—
190C2×D4C4⋊#692311yescharacteristic
191C22×C4—21no—
192C22×C4—612no—
193C22×C4—1221no—
194C22×C4C22×#692311yescharacteristic
195M16—42no—
196M16—41no—
197M16—4884no—
198M16—2442no—
199M16—2441no—
200C2×C8—22no—
201C2×C8—21no—
202C2×C8—42no—
203C2×C8—612no—
204C2×C8—1221no—
205C2×C8—2441no—
206C2×C8—2444no—
207C2×C8—2442no—
208C2×C8C22⋊#692311yescharacteristic
209C2×C8C22⋊#692311yescharacteristic
210C4⋊C4—1222no—
211C22⋊C4—1222no—
212C22⋊C4—1222no—
213C42—612no—
214C42—611no—
215C42—611no—
216C23—21no—
217C23—1221no—
218C23#1451985611yescharacteristic
219Q8—41no—
220Q8—2441no—
221D4—41no—
222D4—42no—
223D4—2441no—
224D4—2442no—
225D4—2442no—
226D4—2442no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—612no—
233C2×C4—612no—
234C2×C4—1222no—
235C2×C4—1222no—
236C2×C4—1221no—
237C2×C4—2441no—
238C2×C4—2441no—
239C2×C4C2×C22⋊#692311yescharacteristic
240C2×C4C2×C4⋊#692311yescharacteristic
241C8—21no—
242C8—41no—
243C8—1222no—
244C8—4884no—
245C8—2441no—
246C8#1451983712yes—
247C22—21no—
248C22—22no—
249C22—41no—
250C22—42no—
251C22—2441no—
252C22—2442no—
253C22#1684070411yescharacteristic
254C4—21no—
255C4—41no—
256C4—612no—
257C4—612no—
258C4—1222no—
259C4—2441no—
260C4C2×#1451983711yescharacteristic
261C4#1684074811yescharacteristic
262C2—41no—
263C2—81no—
264C2—4881no—
265C2#2146168311yescharacteristic
266C2#2146170812yes—
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#8638
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. #21461376C2semidirect
3. #21460727C2semidirect
152. C61#8638semidirect

Maximal subgroups

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

subgroupindex
#214613762
#214613562
#214607272
#214545292
#863861