Finite Group Databasebeta

← #30604334

Subgroups — #30604334

Order 15616.

350 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 70 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#21461081C211yesmaximal, characteristic
2#21461061C211yesmaximal, characteristic
3#21460761C212yesmaximal
4#21460759C212yesmaximal
5#21451010C211yesmaximal, characteristic
6#16840783—21no—
7#16840779—21no—
8#16840608—21no—
9#16840608—21no—
10#16840607C2212yes—
11#16840607C2212yes—
12C2×#14519769C411yescharacteristic
13C2×C4×Dic122C2211yescharacteristic
14#16839692—21no—
15#16839692—21no—
16#16839668C411yescharacteristic
17#16839668C411yescharacteristic
18#16839647—21no—
19#16839647—21no—
20#16839632C2211yescharacteristic
21#16839628C2211yescharacteristic
22C4×C4⋊C4×C61C411yescharacteristic
23#14519844—41no—
24C4⋊#92420—41no—
25C22⋊#92420—22no—
26C22⋊#92420—22no—
27#14519832—41no—
28C4×#92420—41no—
29C22×Dic122C2×C411yescharacteristic
30#14519769—41no—
31#14519769—41no—
32C4×Dic122—41no—
33C4×Dic122—41no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61C2×C411yescharacteristic
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×C4⋊Dic61C2311yescharacteristic
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758196D411yescharacteristic
42C2×#11758196D411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51C2×C4⋊C4×C61—21no—
52C2×C42×C61C2×C411yescharacteristic
53C2×C42×C61C2×C411yescharacteristic
54C2×C42×C61C2×C411yescharacteristic
55#95×C61—21no—
56C22×C4×C61—21no—
57C22×C4×C61—21no—
58C22×C4×C61C22⋊C411yescharacteristic
59C22×C4×C61C22⋊C411yescharacteristic
60C22×C4×C61C22×C411yescharacteristic
61C22×Dic61—21no—
62C22×Dic61—21no—
63C22×Dic61C22⋊C411yescharacteristic
64C22×Dic61C22⋊C411yescharacteristic
65C22×Dic61C2×D411yescharacteristic
66C22×Dic61C2×D411yescharacteristic
67C2×Dic122—22no—
68C2×Dic122—22no—
69C2×Dic122—41no—
70C2×#92420—42no—
71C2×#92420—42no—
72C4⋊C4×C61—42no—
73C42×C61—21no—
74C42×C61—21no—
75C42×C61—22no—
76C42×C61—22no—
77C4⋊Dic61—41no—
78C4⋊Dic61—42no—
79C4⋊Dic61—42no—
80C4⋊Dic61—41no—
81C4⋊Dic61—41no—
82#11758196—41no—
83#11758196—41no—
84#11758196—42no—
85#11758196—41no—
86#11758196—41no—
87C4×Dic61—21no—
88C4×Dic61—21no—
89C4×Dic61—21no—
90C4×Dic61—21no—
91C23×C61C2×C22⋊C411yescharacteristic
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—22no—
95C2×C4×C61—21no—
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—41no—
103C2×C4×C61#9911yescharacteristic
104C2×C4×C61#9911yescharacteristic
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—41no—
114C2×Dic61—41no—
115C2×Dic61—41no—
116C2×Dic61—41no—
117C2×Dic61—42no—
118C2×Dic61—41no—
119C2×Dic61—41no—
120C2×Dic61#10112yes—
121Dic122—44no—
122#92420—82no—
123#92420—82no—
124#11571—611nomaximal, Sylow
125C22×C61—21no—
126C22×C61—21no—
127C22×C61#40811yescharacteristic
128C22×C61C2×#9911yescharacteristic
129C22×C61C2×#10111yescharacteristic
130C4×C61—21no—
131C4×C61—21no—
132C4×C61—22no—
133C4×C61—42no—
134C4×C61—41no—
135C4×C61—81no—
136Dic61—22no—
137Dic61—41no—
138Dic61—41no—
139Dic61—41no—
140Dic61—81no—
141Dic61—81no—
142#2565—611no—
143#1467—611no—
144#1461—611no—
145#1325—612no—
146#1324—612no—
147C2×C61—21no—
148C2×C61—21no—
149C2×C61#147211yescharacteristic
150C2×C61#212611yescharacteristic
151C2×C61#213311yescharacteristic
152C2×#125—611no—
153C2×C4×Q8—611no—
154#432—1221no—
155#431—1221no—
156#398—1221no—
157#398—1221no—
158#391—611no—
159#391—611no—
160#387—1221no—
161#387—1221no—
162#384—611no—
163#382—611no—
164C4×C4⋊C4#692311yescharacteristic
165#324—612no—
166#324—612no—
167#324—1221no—
168#324—1221no—
169C61#1157111yescharacteristic, complemented, Sylow
170C22×Q8—611no—
171#125—2441no—
172#125—2441no—
173C4×Q8—2441no—
174C4×Q8—2441no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—611no—
177C2×C4⋊C4—611no—
178C2×C4⋊C4—611no—
179C2×C4⋊C4—611no—
180C2×C4⋊C4—611no—
181C2×C4⋊C4—1221no—
182C2×C4⋊C4—1221no—
183C2×C4⋊C4—1221no—
184C2×C4⋊C4—1221no—
185C2×C42—611no—
186C2×C42—611no—
187C2×C42C2×#692311yescharacteristic
188C2×C42C2×#692311yescharacteristic
189C2×C42C2×#692311yescharacteristic
190C4⋊C8—2441no—
191C4⋊C8—2441no—
192C22⋊C8—1222no—
193C22⋊C8—1222no—
194#97—2441no—
195C4×C8—2441no—
196#95—21no—
197#95—1221no—
198#95—1221no—
199#95—1221no—
200#95—1221no—
201#95—1221no—
202#95—1221no—
203C2×Q8—1222no—
204C2×Q8—1222no—
205C2×Q8—2441no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—611no—
209C22×C4—611no—
210C22×C4—611no—
211C22×C4—611no—
212C22×C4—1221no—
213C22×C4—1221no—
214C22×C4C22⋊#692311yescharacteristic
215C22×C4C22⋊#692311yescharacteristic
216C22×C4C22×#692311yescharacteristic
217C2×C8—2442no—
218C2×C8—2442no—
219C4⋊C4—42no—
220C4⋊C4—2441no—
221C4⋊C4—2441no—
222C4⋊C4—2441no—
223C4⋊C4—2441no—
224C4⋊C4—2441no—
225C4⋊C4—2442no—
226C4⋊C4—2442no—
227C4⋊C4—2442no—
228C4⋊C4—2441no—
229C4⋊C4—2441no—
230C42—21no—
231C42—21no—
232C42—22no—
233C42—22no—
234C42—1221no—
235C42—1221no—
236C42—1221no—
237C42—1221no—
238C23C2×C22⋊#692311yescharacteristic
239Q8—2444no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—612no—
252C2×C4—1221no—
253C2×C4—1221no—
254C2×C4—1221no—
255C2×C4—1221no—
256C2×C4—1221no—
257C2×C4—1221no—
258C2×C4—1221no—
259C2×C4—2441no—
260C2×C4—2441no—
261C2×C4—2442no—
262C2×C4—2441no—
263C2×C4—2441no—
264C2×C4—2441no—
265C2×C4—2441no—
266C2×C4#1451983611yescharacteristic
267C2×C4#1451983611yescharacteristic
268C2×C4#1451986412yes—
269C8—4882no—
270C8—4882no—
271C22—21no—
272C22—21no—
273C22#1684073611yescharacteristic
274C22C2×#1451983611yescharacteristic
275C22D61⋊#10111yescharacteristic
276C4—21no—
277C4—21no—
278C4—22no—
279C4—42no—
280C4—41no—
281C4—81no—
282C4—1222no—
283C4—4881no—
284C4—4881no—
285C4—2441no—
286C4—2441no—
287C4—2441no—
288C2—21no—
289C2—21no—
290C2#2146109711yescharacteristic
291C2#2146209211yescharacteristic
292C2#2146211611yescharacteristic
subgroupG/H
centerC22C2×#14519836
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC4×C4⋊C4×C61C4
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4⋊Dic61C23
hypercenterC4×C4⋊C4#6923
hypocenterC61#11571
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
169. C61#11571semidirect

Maximal subgroups

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

subgroupindex
#214610812
#214610612
#214607612
#214607592
#214510102
#1157161