Finite Group Databasebeta

← #30599402

Subgroups — #30599402

Order 15616.

378 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 80 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#21461685C211yesmaximal, characteristic
2#21461061C211yesmaximal, characteristic
3#21460717C212yesmaximal
4#21460672C212yesmaximal
5#21448779C211yesmaximal, characteristic
6#16840779C2212yes—
7#16840765C2212yes—
8C2×#14519838—21no—
9#16840642—21no—
10#16840608—21no—
11#16840607—21no—
12C2×C4×Dic122C2211yescharacteristic
13#16839666—21no—
14#16839645—21no—
15#16839644—21no—
16#16839629C411yescharacteristic
17#16839626C2211yescharacteristic
18#16839613—21no—
19#16839613C2211yescharacteristic
20#16839608C411yescharacteristic
21#16839607C411yescharacteristic
22C61×#383C411yescharacteristic
23C2×#11758217—22no—
24#14519844—22no—
25#14519844—22no—
26C4⋊#92420—22no—
27#14519838—42no—
28C22⋊#92420—22no—
29C4×#92420—22no—
30C22×Dic122D411yescharacteristic
31C4×Dic122—22no—
32C4×Dic122—22no—
33C2×C4⋊Dic61D411yescharacteristic
34C2×#11758196—21no—
35C2×#11758196—21no—
36C2×#11758196D411yescharacteristic
37C2×#11758196D411yescharacteristic
38C2×C4×Dic61—21no—
39C2×C4×Dic61—21no—
40C2×C4×Dic61—21no—
41C2×C4×Dic61C2×C411yescharacteristic
42C2×C4×Dic61C2311yescharacteristic
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684C2×C411yescharacteristic
49#14519684C2×C411yescharacteristic
50C2×C42×C61C2×C411yescharacteristic
51#95×C61—21no—
52#95×C61—21no—
53#95×C61C2×C411yescharacteristic
54#95×C61C2×C411yescharacteristic
55C22×C4×C61—21no—
56C22×C4×C61—21no—
57C22×C4×C61C22⋊C411yescharacteristic
58C22×C4×C61C22⋊C411yescharacteristic
59C22×C4×C61C22×C411yescharacteristic
60C22×Dic61—21no—
61C22×Dic61—21no—
62C22×Dic61C22⋊C411yescharacteristic
63C22×Dic61C22⋊C411yescharacteristic
64C22×Dic61C2×D411yescharacteristic
65C22×Dic61C2×D411yescharacteristic
66C2×Dic122—22no—
67C2×Dic122—22no—
68C2×Dic122—21no—
69C2×Dic122—21no—
70#11758217—42no—
71#11758217—42no—
72C2×#92420—42no—
73C2×#92420—42no—
74C42×C61—21no—
75C42×C61—21no—
76C4⋊Dic61—22no—
77#11758196—22no—
78#11758196—22no—
79#11758196—42no—
80#11758196—41no—
81#11758196—41no—
82C4×Dic61—21no—
83C4×Dic61—21no—
84C4×Dic61—42no—
85C4×Dic61—42no—
86C4×Dic61—42no—
87C4×Dic61#4112yes—
88C4×Dic61#4112yes—
89C23×C61C2×C22⋊C411yescharacteristic
90C2×C4×C61—21no—
91C2×C4×C61—21no—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—41no—
95C2×C4×C61—41no—
96C2×C4×C61—41no—
97C2×C4×C61—41no—
98C2×C4×C61—41no—
99C2×C4×C61—41no—
100C2×C4×C61—41no—
101C2×C4×C61—41no—
102C2×C4×C61#11711yescharacteristic
103C2×C4×C61#11711yescharacteristic
104C2×Dic61—22no—
105C2×Dic61—21no—
106C2×Dic61—21no—
107C2×Dic61—21no—
108C2×Dic61—21no—
109C2×Dic61—41no—
110C2×Dic61—41no—
111C2×Dic61—41no—
112C2×Dic61—41no—
113C2×Dic61—41no—
114C2×Dic61—41no—
115C2×Dic61—41no—
116C2×Dic61#12312yes—
117C2×Dic61#12312yes—
118C2×Dic61#13512yes—
119C2×Dic61AGL(1,ℤ/8)11yescharacteristic
120C2×Dic61#13711yescharacteristic
121Dic122—42no—
122Dic122—42no—
123#92420—82no—
124#92420—82no—
125#8769—611nomaximal, Sylow
126C22×C61—21no—
127C22×C61—21no—
128C22×C61#38111yescharacteristic
129C22×C61#41611yescharacteristic
130C22×C61#41711yescharacteristic
131C4×C61—21no—
132C4×C61—21no—
133C4×C61—41no—
134C4×C61—41no—
135C4×C61—81no—
136C4×C61—81no—
137Dic61—22no—
138Dic61—42no—
139Dic61—41no—
140Dic61—41no—
141Dic61—81no—
142Dic61#48212yes—
143Dic61#48512yes—
144#2356—611no—
145#1801—611no—
146#1461—611no—
147#1303—612no—
148#1286—612no—
149C2×C61—21no—
150C2×C61—21no—
151C2×C61#182511yescharacteristic
152C2×C61#182711yescharacteristic
153C2×C61#183011yescharacteristic
154C2×C4×Q8—611no—
155#431—612no—
156#423—612no—
157C2×#101—1221no—
158#391—1221no—
159#387—1221no—
160#387—1221no—
161#383—611no—
162#383#692311yescharacteristic
163#382—611no—
164C4×C4⋊C4—611no—
165C4×C4⋊C4—1221no—
166#376—611no—
167#376—611no—
168#343—1221no—
169#324—1221no—
170#324—1221no—
171C61#876911yescharacteristic, complemented, Sylow
172C22×Q8—611no—
173C2×M16—1222no—
174C4×Q8—1222no—
175C4×Q8—1222no—
176C2×C4⋊C4—611no—
177C2×C4⋊C4—611no—
178C2×C4⋊C4—611no—
179C2×C4⋊C4—1221no—
180C2×C4⋊C4—1221no—
181C2×C42—611no—
182C2×C42—611no—
183C2×C42—1221no—
184C2×C42—1221no—
185C2×C42—1221no—
186C2×C42C2×#692311yescharacteristic
187C4⋊C8—1222no—
188C4⋊C8—1222no—
189C4⋊C8—1222no—
190#101—2442no—
191C22⋊C8—1222no—
192C4×C8—1222no—
193#95—21no—
194#95—21no—
195#95—611no—
196#95—611no—
197#95—1221no—
198#95—1221no—
199#95—1221no—
200#95—1221no—
201#95—1221no—
202#95C2×#692311yescharacteristic
203#95C2×#692311yescharacteristic
204C2×Q8—1221no—
205C2×Q8—1222no—
206C2×Q8—1222no—
207C2×Q8—1221no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—611no—
211C22×C4—611no—
212C22×C4—611no—
213C22×C4—611no—
214C22×C4—1221no—
215C22×C4—1221no—
216C22×C4C22⋊#692311yescharacteristic
217C22×C4C22⋊#692311yescharacteristic
218C22×C4C22×#692311yescharacteristic
219M16—2442no—
220M16—2442no—
221C2×C8—2442no—
222C2×C8—2442no—
223C4⋊C4—1222no—
224C4⋊C4—1222no—
225C4⋊C4—1222no—
226C4⋊C4—2441no—
227C4⋊C4—2441no—
228C4⋊C4—2442no—
229C42—21no—
230C42—21no—
231C42—612no—
232C42—612no—
233C42—1221no—
234C42—1221no—
235C42—2442no—
236C42—2442no—
237C42—2442no—
238C23C2×C22⋊#692311yescharacteristic
239Q8—2442no—
240Q8—2442no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—612no—
254C2×C4—612no—
255C2×C4—611no—
256C2×C4—611no—
257C2×C4—612no—
258C2×C4—1222no—
259C2×C4—1221no—
260C2×C4—1221no—
261C2×C4—1221no—
262C2×C4—1221no—
263C2×C4—2441no—
264C2×C4—2441no—
265C2×C4—2441no—
266C2×C4—2441no—
267C2×C4—2441no—
268C2×C4—2441no—
269C2×C4—2441no—
270C2×C4#1451985611yescharacteristic
271C2×C4#1451985611yescharacteristic
272C8—4882no—
273C8—4882no—
274C22—21no—
275C22—21no—
276C22#1684070511yescharacteristic
277C22#1684075211yescharacteristic
278C22#1684075311yescharacteristic
279C4—21no—
280C4—21no—
281C4—41no—
282C4—41no—
283C4—81no—
284C4—81no—
285C4—612no—
286C4—612no—
287C4—1222no—
288C4—4881no—
289C4—2442no—
290C4—2441no—
291C4—2441no—
292C2—21no—
293C2—21no—
294C2#2146172411yescharacteristic
295C2#2146172911yescharacteristic
296C2#2146173311yescharacteristic
subgroupG/H
centerC22#16840705
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#383C4
socleC22×C61#381
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#383#6923
hypocenterC61#8769
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #383

Complements

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

NH ≅ G/Ntype
171. C61#8769semidirect

Maximal subgroups

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

subgroupindex
#214616852
#214610612
#214607172
#214606722
#214487792
#876961