Finite Group Databasebeta

← #30599398

Subgroups — #30599398

Order 15616.

422 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 422 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#21461685C211yesmaximal, characteristic
2#21461061C211yesmaximal, characteristic
3#21460717C212yesmaximal
4#21460672C212yesmaximal
5#21448736C211yesmaximal, characteristic
6#16840779C2212yes—
7#16840765C2212yes—
8C2×#14519838—21no—
9#16840642—21no—
10#16840608—21no—
11#16840607—21no—
12C2×C4×Dic122C2211yescharacteristic
13C2×#14519742—21no—
14#16839659—21no—
15#16839659—21no—
16#16839658—21no—
17#16839626C411yescharacteristic
18#16839626C2211yescharacteristic
19C4×C4⋊Dic61C411yescharacteristic
20#16839613C411yescharacteristic
21#16839613C2211yescharacteristic
22C61×#382C411yescharacteristic
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—
33#14519742—44no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61D411yescharacteristic
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196D411yescharacteristic
41C2×#11758196D411yescharacteristic
42C2×C4×Dic61—21no—
43C2×C4×Dic61—21no—
44C2×C4×Dic61—21no—
45C2×C4×Dic61C2×C411yescharacteristic
46C2×C4×Dic61C2311yescharacteristic
47#14519684—21no—
48#14519684—21no—
49#14519684C2×C411yescharacteristic
50#14519684C2×C411yescharacteristic
51C2×C4⋊C4×C61—21no—
52C2×C42×C61C2×C411yescharacteristic
53#95×C61—21no—
54#95×C61C2×C411yescharacteristic
55#95×C61C2×C411yescharacteristic
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×Dic122SD1612yes—
70C2×Dic122Q1612yes—
71#11758217—42no—
72#11758217—42no—
73C2×#92420—42no—
74C2×#92420—42no—
75C4⋊C4×C61—42no—
76C42×C61—21no—
77C42×C61—21no—
78C4⋊Dic61—22no—
79C4⋊Dic61—42no—
80#11758196—22no—
81#11758196—22no—
82#11758196—42no—
83#11758196—42no—
84#11758196—42no—
85#11758196—42no—
86C4×Dic61—21no—
87C4×Dic61—21no—
88C4×Dic61—42no—
89C4×Dic61—42no—
90C4×Dic61—42no—
91C4×Dic61#4112yes—
92C4×Dic61#4112yes—
93C23×C61C2×C22⋊C411yescharacteristic
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
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—41no—
104C2×C4×C61—41no—
105C2×C4×C61#10312yes—
106C2×C4×C61#11711yescharacteristic
107C2×C4×C61#11711yescharacteristic
108C2×Dic61—21no—
109C2×Dic61—21no—
110C2×Dic61—22no—
111C2×Dic61—21no—
112C2×Dic61—41no—
113C2×Dic61—41no—
114C2×Dic61—41no—
115C2×Dic61—41no—
116C2×Dic61—41no—
117C2×Dic61—41no—
118C2×Dic61—41no—
119C2×Dic61#10312yes—
120C2×Dic61#12312yes—
121C2×Dic61#12312yes—
122C2×Dic61C2×SD1611yescharacteristic
123C2×Dic61C2×Q1611yescharacteristic
124C2×Dic61AGL(1,ℤ/8)12yes—
125Dic122—24no—
126Dic122—24no—
127#92420—82no—
128#92420—82no—
129#8767—611nomaximal, Sylow
130C22×C61—21no—
131C22×C61—21no—
132C22×C61#38111yescharacteristic
133C22×C61C2×#10311yescharacteristic
134C22×C61#41811yescharacteristic
135C4×C61—22no—
136C4×C61—21no—
137C4×C61—21no—
138C4×C61—41no—
139C4×C61—81no—
140C4×C61—81no—
141Dic61—22no—
142Dic61—22no—
143Dic61—42no—
144Dic61—41no—
145Dic61—81no—
146Dic61#48112yes—
147Dic61#48412yes—
148#2351—611no—
149#1801—611no—
150#1461—611no—
151#1303—612no—
152#1286—612no—
153C2×C61—21no—
154C2×C61—21no—
155C2×C61#182411yescharacteristic
156C2×C61#182711yescharacteristic
157C2×C61#183011yescharacteristic
158C2×C4×Q8—611no—
159C2×C4×Q8—1221no—
160#431—612no—
161#423—612no—
162C2×#101—1221no—
163#389—1221no—
164#389—1221no—
165#389—1221no—
166#382—611no—
167#382—611no—
168#382#692311yescharacteristic
169C4×C4⋊C4—611no—
170C4×C4⋊C4—611no—
171C4×C4⋊C4—611no—
172#343—1221no—
173#324—1221no—
174#324—1221no—
175C61#876711yescharacteristic, complemented, Sylow
176C22×Q8—611no—
177C2×M16—1222no—
178C4×Q8—1222no—
179C4×Q8—1222no—
180C4×Q8—2444no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—611no—
183C2×C4⋊C4—611no—
184C2×C4⋊C4—611no—
185C2×C4⋊C4—1221no—
186C2×C4⋊C4—1221no—
187C2×C4⋊C4—1221no—
188C2×C4⋊C4—1221no—
189C2×C4⋊C4—1221no—
190C2×C42—611no—
191C2×C42—611no—
192C2×C42—1221no—
193C2×C42—1221no—
194C2×C42—1221no—
195C2×C42C2×#692311yescharacteristic
196C4⋊C8—1222no—
197C4⋊C8—1222no—
198C4⋊C8—1222no—
199#101—2442no—
200C22⋊C8—1222no—
201C4×C8—1222no—
202#95—21no—
203#95—611no—
204#95—611no—
205#95—1221no—
206#95—1221no—
207#95C2×#692311yescharacteristic
208#95C2×#692311yescharacteristic
209C2×Q8—612no—
210C2×Q8—612no—
211C2×Q8—1222no—
212C2×Q8—1222no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—611no—
216C22×C4—611no—
217C22×C4—611no—
218C22×C4—611no—
219C22×C4—1221no—
220C22×C4—1221no—
221C22×C4C22⋊#692311yescharacteristic
222C22×C4C22⋊#692311yescharacteristic
223C22×C4C22×#692311yescharacteristic
224M16—2442no—
225M16—2442no—
226C2×C8—2442no—
227C2×C8—2442no—
228C4⋊C4—42no—
229C4⋊C4—1222no—
230C4⋊C4—1222no—
231C4⋊C4—1222no—
232C4⋊C4—2442no—
233C4⋊C4—2442no—
234C4⋊C4—2442no—
235C4⋊C4—2442no—
236C4⋊C4—2442no—
237C42—21no—
238C42—21no—
239C42—612no—
240C42—612no—
241C42—1221no—
242C42—1221no—
243C42—2442no—
244C42—2442no—
245C42—2442no—
246C23C2×C22⋊#692311yescharacteristic
247Q8—1224no—
248Q8—1224no—
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—41no—
259C2×C4—41no—
260C2×C4—612no—
261C2×C4—611no—
262C2×C4—611no—
263C2×C4—612no—
264C2×C4—612no—
265C2×C4—612no—
266C2×C4—1221no—
267C2×C4—1221no—
268C2×C4—1222no—
269C2×C4—1221no—
270C2×C4—2441no—
271C2×C4—2441no—
272C2×C4—2441no—
273C2×C4—2441no—
274C2×C4—2441no—
275C2×C4—2441no—
276C2×C4—2441no—
277C2×C4#1451984012yes—
278C2×C4#1451985611yescharacteristic
279C2×C4#1451985611yescharacteristic
280C8—4882no—
281C8—4882no—
282C22—21no—
283C22—21no—
284C22#1684070511yescharacteristic
285C22C2×#1451984011yescharacteristic
286C22#1684075411yescharacteristic
287C4—22no—
288C4—21no—
289C4—21no—
290C4—41no—
291C4—81no—
292C4—81no—
293C4—612no—
294C4—612no—
295C4—1222no—
296C4—1222no—
297C4—4881no—
298C4—2442no—
299C4—2441no—
300C2—21no—
301C2—21no—
302C2#2146172311yescharacteristic
303C2#2146172911yescharacteristic
304C2#2146173311yescharacteristic
subgroupG/H
centerC22#16840705
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#382C4
socleC22×C61#381
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#382#6923
hypocenterC61#8767
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #382

Complements

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

NH ≅ G/Ntype
175. C61#8767semidirect

Maximal subgroups

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

subgroupindex
#214616852
#214610612
#214607172
#214606722
#214487362
#876761