Finite Group Databasebeta

← #30600284

Subgroups — #30600284

Order 15616.

474 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 98 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#21462717C211yesmaximal, characteristic
2#21461123C212yesmaximal
3#21461063C211yesmaximal, characteristic
4#21460643C212yesmaximal
5#21448536C211yesmaximal, characteristic
6#16840812—24no—
7#16840783—22no—
8#16840778C2212yes—
9#16840778C2212yes—
10#16840612—24no—
11#16840608—22no—
12C2×#14519777C411yescharacteristic
13C2×#14519742C2211yescharacteristic
14C2×#14519742C2211yescharacteristic
15#16839667C411yescharacteristic
16#16839667C411yescharacteristic
17#16839645—22no—
18#16839645—22no—
19#16839608C2211yescharacteristic
20C61×#382C411yescharacteristic
21C4⋊#92420—24no—
22C4⋊#92420—22no—
23C4⋊#92420—22no—
24C22⋊#92420—22no—
25C22⋊#92420—22no—
26#14519832—24no—
27C4×#92420—22no—
28C4×#92420D414yes—
29C22×Dic122C2×C411yescharacteristic
30C22×Dic122C2×C411yescharacteristic
31#14519777—22no—
32#14519777—22no—
33#14519742—22no—
34#14519742—22no—
35#14519742—22no—
36#14519742—22no—
37C2×C4⋊Dic61—22no—
38C2×#11758196—21no—
39C2×#11758196D412yes—
40C2×C4×Dic61—21no—
41C2×C4×Dic61C2×C411yescharacteristic
42C2×C4×Dic61D412yes—
43C2×C4×Dic61C2311yescharacteristic
44#14519684—22no—
45#14519684—22no—
46#14519684—21no—
47#14519684—21no—
48C2×C4⋊C4×C61C2×C411yescharacteristic
49C2×C4⋊C4×C61C2×C411yescharacteristic
50C2×C42×C61C2×C411yescharacteristic
51#95×C61—22no—
52C22×C4×C61—21no—
53C22×C4×C61—21no—
54C22×C4×C61C22⋊C412yes—
55C22×C4×C61C22×C411yescharacteristic
56C22×Dic61—21no—
57C22×Dic61—21no—
58C22×Dic61C22⋊C412yes—
59C22×Dic61C2×D411yescharacteristic
60C22×Dic61C2×D411yescharacteristic
61C2×Dic122—22no—
62C2×Dic122—22no—
63C2×Dic122—22no—
64C2×Dic122—21no—
65C2×Dic122—21no—
66C2×Dic122—21no—
67C2×Dic122—22no—
68C2×Dic122M1612yes—
69C2×#92420—24no—
70C2×#92420—42no—
71C4⋊C4×C61—22no—
72C4⋊C4×C61—22no—
73C42×C61—21no—
74C42×C61M1612yes—
75C4⋊Dic61—28no—
76#11758196—24no—
77#11758196—41no—
78#11758196—41no—
79C4×Dic61—22no—
80C4×Dic61—22no—
81C4×Dic61—22no—
82C4×Dic61—42no—
83C4×Dic61C2×D412yes—
84C4×Dic61#4112yes—
85C23×C61C2×C22⋊C411yescharacteristic
86C2×C4×C61—22no—
87C2×C4×C61—22no—
88C2×C4×C61—41no—
89C2×C4×C61—41no—
90C2×C4×C61—42no—
91C2×C4×C61—42no—
92C2×C4×C61—41no—
93C2×C4×C61C4×D412yes—
94C2×C4×C61C2×M1611yescharacteristic
95C2×C4×C61C2×M1611yescharacteristic
96C2×C4×C61#13112yes—
97C2×Dic61—22no—
98C2×Dic61—22no—
99C2×Dic61—22no—
100C2×Dic61—22no—
101C2×Dic61—41no—
102C2×Dic61—41no—
103C2×Dic61—41no—
104C2×Dic61—41no—
105C2×Dic61—41no—
106C2×Dic61—41no—
107C2×Dic61—41no—
108C2×Dic61#12011yescharacteristic
109C2×Dic61#12112yes—
110C2×Dic61#12311yescharacteristic
111Dic122—24no—
112Dic122—42no—
113Dic122—42no—
114Dic122—42no—
115#92420—44no—
116#92420—82no—
117#9104—611nomaximal, Sylow
118C22×C61—21no—
119C22×C61—21no—
120C22×C61#38611yescharacteristic
121C22×C61#40711yescharacteristic
122C22×C61#40811yescharacteristic
123C4×C61—42no—
124C4×C61—42no—
125C4×C61—81no—
126C4×C61#43512yes—
127C4×C61#43612yes—
128Dic61—22no—
129Dic61—21no—
130Dic61—21no—
131Dic61—42no—
132Dic61—42no—
133Dic61—81no—
134#2983—611no—
135#2327—611no—
136#1479—612no—
137#1461—611no—
138#1274—612no—
139C2×C61—21no—
140C2×C61—21no—
141C2×C61#187011yescharacteristic
142C2×C61#190911yescharacteristic
143C2×C61#191211yescharacteristic
144C2×C4⋊Q8—611no—
145C2×C4×Q8—611no—
146C2×C4×Q8—611no—
147#446—1224no—
148#432—1222no—
149#431—612no—
150#431—612no—
151#391—611no—
152#391—611no—
153#387—1222no—
154#387—1222no—
155#382#692311yescharacteristic
156#376—611no—
157Q8⋊C8—1224no—
158#324—1222no—
159C61#910411yescharacteristic, complemented, Sylow
160C22×Q8—611no—
161C22×Q8—611no—
162C4⋊Q8—1222no—
163C4⋊Q8—1222no—
164C4×Q8—1222no—
165C4×Q8—1222no—
166C4×Q8—1222no—
167C4×Q8—1222no—
168C2×C4⋊C4—612no—
169C2×C4⋊C4—1222no—
170C2×C4⋊C4—1221no—
171C2×C4⋊C4C2×#692311yescharacteristic
172C2×C4⋊C4C2×#692311yescharacteristic
173C2×C42—611no—
174C2×C42—612no—
175C2×C42—611no—
176C2×C42—1221no—
177C2×C42C2×#692311yescharacteristic
178C4⋊C8—1222no—
179C4⋊C8—1222no—
180C4⋊C8—1224no—
181C22⋊C8—1222no—
182C22⋊C8—1222no—
183#97—1224no—
184C4×C8—614no—
185C4×C8—1222no—
186#95—22no—
187#95—1221no—
188#95—1221no—
189#95—1222no—
190#95—1222no—
191C2×Q8—612no—
192C2×Q8—1222no—
193C2×Q8—1221no—
194C2×Q8—1221no—
195C2×Q8—1221no—
196C2×Q8—1222no—
197C2×Q8—1222no—
198C2×Q8—1222no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—611no—
202C22×C4—611no—
203C22×C4—612no—
204C22×C4—1221no—
205C22×C4—1221no—
206C22×C4C22⋊#692312yes—
207C22×C4C22×#692311yescharacteristic
208C2×C8—1224no—
209C2×C8—2442no—
210C4⋊C4—22no—
211C4⋊C4—22no—
212C4⋊C4—1224no—
213C4⋊C4—1228no—
214C4⋊C4—2441no—
215C4⋊C4—2441no—
216C42—21no—
217C42—612no—
218C42—612no—
219C42—1222no—
220C42—1222no—
221C42—1222no—
222C42—2442no—
223C42#1175821312yes—
224C23C2×C22⋊#692311yescharacteristic
225Q8—1224no—
226Q8—2442no—
227Q8—2442no—
228Q8—2442no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—41no—
236C2×C4—611no—
237C2×C4—612no—
238C2×C4—611no—
239C2×C4—1222no—
240C2×C4—1222no—
241C2×C4—1222no—
242C2×C4—1222no—
243C2×C4—2441no—
244C2×C4—2441no—
245C2×C4—2441no—
246C2×C4—2441no—
247C2×C4—2441no—
248C2×C4—2441no—
249C2×C4—2441no—
250C2×C4D4×#692312yes—
251C2×C4D61⋊M1611yescharacteristic
252C2×C4C2×#1175821311yescharacteristic
253C2×C4#1451986512yes—
254C8—4882no—
255C8—2444no—
256C22—21no—
257C22—21no—
258C22#1684071011yescharacteristic
259C22#1684073311yescharacteristic
260C22#1684073711yescharacteristic
261C4—42no—
262C4—42no—
263C4—81no—
264C4—1222no—
265C4—1221no—
266C4—1221no—
267C4—4881no—
268C4—2442no—
269C4—2442no—
270C4#1684079212yes—
271C4#1684079612yes—
272C2—21no—
273C2—21no—
274C2#2146179911yescharacteristic
275C2#2146186011yescharacteristic
276C2#2146186711yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#382C4
socleC22×C61#386
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#382#6923
hypocenterC61#9104
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #382

Complements

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

NH ≅ G/Ntype
159. C61#9104semidirect

Maximal subgroups

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

subgroupindex
#214627172
#214611232
#214610632
#214606432
#214485362
#910461