Finite Group Databasebeta

← #30595910

Subgroups — #30595910

Order 15616.

388 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 96 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#21461747C211yesmaximal, characteristic
2#21461734C211yesmaximal, characteristic
3#21460638C212yesmaximal
4#21460637C212yesmaximal
5#21454178C211yesmaximal, characteristic
6C2×C4⋊#92420—21no—
7#16840628—21no—
8#16840628—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519767—21no—
13#16839661C2211yescharacteristic
14#16839660C411yescharacteristic
15#16839659—21no—
16#16839658C2211yescharacteristic
17#16839657—21no—
18#16839631C411yescharacteristic
19#16839631C411yescharacteristic
20#16839626—21no—
21C42×Dic61C2211yescharacteristic
22C61×#389C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25C4⋊#92420—42no—
26#14519767—42no—
27#14519767—42no—
28C2×C4⋊Dic61—21no—
29C2×C4⋊Dic61C2×C411yescharacteristic
30C2×C4⋊Dic61C2×C411yescharacteristic
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×#11758196—21no—
34C2×#11758196—21no—
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×C4×Dic61C2×C411yescharacteristic
38C2×C4×Dic61D411yescharacteristic
39C2×C4×Dic61D411yescharacteristic
40C2×C4×Dic61D411yescharacteristic
41C2×C4×Dic61D411yescharacteristic
42C2×C4×Dic61C2311yescharacteristic
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46C2×C4⋊C4×C61—21no—
47C2×C4⋊C4×C61C2×C411yescharacteristic
48C2×C4⋊C4×C61C2×C411yescharacteristic
49C2×C42×C61C2×C411yescharacteristic
50#95×C61—21no—
51C22×C4×C61—21no—
52C22×C4×C61—21no—
53C22×C4×C61C22⋊C411yescharacteristic
54C22×C4×C61C22⋊C411yescharacteristic
55C22×C4×C61C22×C411yescharacteristic
56C22×Dic61—21no—
57C22×Dic61—21no—
58C22×Dic61C22⋊C411yescharacteristic
59C22×Dic61C22⋊C411yescharacteristic
60C22×Dic61C2×D411yescharacteristic
61C22×Dic61C2×D411yescharacteristic
62C2×#92420—42no—
63C2×#92420—42no—
64C2×#92420—42no—
65C2×#92420—42no—
66C2×#92420—42no—
67C2×#92420—42no—
68C4⋊C4×C61—22no—
69C4⋊C4×C61—41no—
70C4⋊C4×C61—42no—
71C42×C61—22no—
72C4⋊Dic61—22no—
73C4⋊Dic61—41no—
74C4⋊Dic61—41no—
75C4⋊Dic61—41no—
76#11758196—42no—
77#11758196—42no—
78#11758196—42no—
79#11758196—42no—
80#11758196—42no—
81#11758196—41no—
82#11758196—41no—
83C4×Dic61—22no—
84C4×Dic61—22no—
85C4×Dic61—41no—
86C4×Dic61—41no—
87C4×Dic61—41no—
88C4×Dic61D812yes—
89C4×Dic61SD1612yes—
90C23×C61C2×C22⋊C411yescharacteristic
91C2×C4×C61—21no—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—41no—
99C2×C4×C61—41no—
100C2×C4×C61—41no—
101C2×C4×C61—41no—
102C2×C4×C61—41no—
103C2×C4×C61—41no—
104C2×C4×C61#10212yes—
105C2×C4×C61#13112yes—
106C2×Dic61—21no—
107C2×Dic61—21no—
108C2×Dic61—21no—
109C2×Dic61—21no—
110C2×Dic61—21no—
111C2×Dic61—21no—
112C2×Dic61—21no—
113C2×Dic61—21no—
114C2×Dic61—41no—
115C2×Dic61—41no—
116C2×Dic61—41no—
117C2×Dic61—41no—
118C2×Dic61—41no—
119C2×Dic61—41no—
120C2×Dic61#10112yes—
121C2×Dic61#10212yes—
122C2×Dic61C2×D811yescharacteristic
123C2×Dic61C2×SD1611yescharacteristic
124C2×Dic61#13712yes—
125#92420—82no—
126#92420—82no—
127#7723—611nomaximal, Sylow
128C22×C61#40811yescharacteristic
129C22×C61#41011yescharacteristic
130C22×C61C2×#10111yescharacteristic
131C22×C61C2×#10211yescharacteristic
132C22×C61#41911yescharacteristic
133C22×C61#42111yescharacteristic
134C22×C61#42111yescharacteristic
135C4×C61—22no—
136C4×C61—22no—
137C4×C61—41no—
138C4×C61—81no—
139C4×C61—81no—
140Dic61—22no—
141Dic61—22no—
142Dic61—21no—
143Dic61—21no—
144Dic61—22no—
145Dic61—81no—
146Dic61—81no—
147#2859—611no—
148#1839—611no—
149#1831—611no—
150#1271—612no—
151#1271—612no—
152C2×C61#147011yescharacteristic
153C2×C61#148011yescharacteristic
154C2×C61#149711yescharacteristic
155C2×C61#151511yescharacteristic
156C2×C61#151711yescharacteristic
157C2×C61#153411yescharacteristic
158C2×C61#154611yescharacteristic
159C2×#125—1221no—
160C2×C4⋊C8—1221no—
161#389—611no—
162#389—611no—
163#389—611no—
164#389—1221no—
165#389—1221no—
166#389#692311yescharacteristic
167#384—611no—
168#384—611no—
169#382—1221no—
170C43—611no—
171#336—612no—
172#336—612no—
173#336—1221no—
174#336—1221no—
175#336—1221no—
176C61#772311yescharacteristic, complemented, Sylow
177C22×C8—1222no—
178C22×C8—1222no—
179#125—2442no—
180#125—2442no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—611no—
183C2×C4⋊C4—611no—
184C2×C4⋊C4—1221no—
185C2×C4⋊C4—1221no—
186C2×C4⋊C4—1221no—
187C2×C4⋊C4—1221no—
188C2×C4⋊C4—1221no—
189C2×C4⋊C4—1221no—
190C2×C4⋊C4—1221no—
191C2×C4⋊C4C2×#692311yescharacteristic
192C2×C4⋊C4C2×#692311yescharacteristic
193C2×C42—611no—
194C2×C42—611no—
195C2×C42—611no—
196C2×C42—611no—
197C2×C42—611no—
198C2×C42—611no—
199C2×C42C2×#692311yescharacteristic
200C4⋊C8—2442no—
201#95—21no—
202#95—1221no—
203#95—1221no—
204#95—1221no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—611no—
208C22×C4—611no—
209C22×C4—611no—
210C22×C4—611no—
211C22×C4—1221no—
212C22×C4—1221no—
213C22×C4C22⋊#692311yescharacteristic
214C22×C4C22⋊#692311yescharacteristic
215C22×C4C22×#692311yescharacteristic
216C2×C8—2442no—
217C2×C8—2442no—
218C2×C8—2442no—
219C2×C8—2442no—
220C2×C8—2442no—
221C2×C8—2442no—
222C4⋊C4—22no—
223C4⋊C4—41no—
224C4⋊C4—42no—
225C4⋊C4—1222no—
226C4⋊C4—2441no—
227C4⋊C4—2442no—
228C4⋊C4—2442no—
229C4⋊C4—2441no—
230C4⋊C4—2441no—
231C4⋊C4—2441no—
232C4⋊C4—2441no—
233C4⋊C4—2442no—
234C4⋊C4—2442no—
235C4⋊C4—2442no—
236C42—22no—
237C42—612no—
238C42—612no—
239C42—1222no—
240C42—1222no—
241C42—2441no—
242C42—2441no—
243C42—2441no—
244C23C2×C22⋊#692311yescharacteristic
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—612no—
259C2×C4—612no—
260C2×C4—611no—
261C2×C4—611no—
262C2×C4—612no—
263C2×C4—1221no—
264C2×C4—1221no—
265C2×C4—1221no—
266C2×C4—1221no—
267C2×C4—1221no—
268C2×C4—1221no—
269C2×C4—1221no—
270C2×C4—1221no—
271C2×C4—2441no—
272C2×C4—2441no—
273C2×C4—2441no—
274C2×C4—2441no—
275C2×C4—2441no—
276C2×C4—2441no—
277C2×C4#1451983912yes—
278C2×C4#1451986412yes—
279C8—4882no—
280C8—4882no—
281C22#1684073511yescharacteristic
282C22#1684074111yescharacteristic
283C22D61⋊#10111yescharacteristic
284C22C2×#1451983911yescharacteristic
285C22#1684075511yescharacteristic
286C22#1684075911yescharacteristic
287C22#1684075911yescharacteristic
288C4—22no—
289C4—22no—
290C4—41no—
291C4—81no—
292C4—81no—
293C4—1221no—
294C4—1221no—
295C4—1222no—
296C4—1222no—
297C4—1222no—
298C4—4881no—
299C4—4881no—
300C2#2146109111yescharacteristic
301C2#2146112411yescharacteristic
302C2#2146118111yescharacteristic
303C2#2146124111yescharacteristic
304C2#2146124911yescharacteristic
305C2#2146130211yescharacteristic
306C2#2146132911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#389C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#389#6923
hypocenterC61#7723
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
176. C61#7723semidirect

Maximal subgroups

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

subgroupindex
#214617472
#214617342
#214606382
#214606372
#214541782
#772361