Finite Group Databasebeta

← #30597786

Subgroups — #30597786

Order 15616.

444 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 104 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#125×#6923C211yesmaximal, characteristic
2#21461535C212yesmaximal
3D61⋊#330C211yesmaximal, characteristic
4#21460696C212yesmaximal
5#330×D61C211yesmaximal, characteristic
6#16840721C2212yes—
7#16840713C412yes—
8#16840711—22no—
9#16840706C2211yescharacteristic
10C4⋊C4×#6923—22no—
11C4⋊C4×#6923C412yes—
12C42×#6923C2211yescharacteristic
13(C2×#6923)⋊C8—22no—
14(C2×#6923)⋊C8—22no—
15#16840619C414yescomplemented
16#125×D61C2211yescharacteristic
17#97×D61C2212yes—
18#16839504C411yescharacteristic, complemented
19#16839503C412yescomplemented
20C61×#330C411yescharacteristic, complemented
21C2×D61⋊C8—22no—
22C2×C4⋊#6923—22no—
23C2×C4⋊#6923C2×C412yes—
24C2×C4×#6923—22no—
25C2×C4×#6923C2×C411yescharacteristic
26C2×C4×#6923C2×C411yescharacteristic
27C2×C4×#6923D412yes—
28C2×C4×#6923D412yes—
29#14519832—22no—
30#14519832C2×C414yes—
31(C2×#6923)⋊C4—22no—
32(C2×#6923)⋊C4—22no—
33(C2×#6923)⋊C4—22no—
34C2×C8×D61—22no—
35#14519769C2×C411yescharacteristic
36#14519768C2×C412yes—
37#14519767—22no—
38C4⋊C4×D61—22no—
39C4⋊C4×D61C2×C412yes—
40C42×D61C2311yescharacteristic
41#14519688C2×C412yes—
42#14519687—22no—
43#125×C61C2×C411yescharacteristic
44#97×C61C2×C412yes—
45C22×#6923—22no—
46C22×#6923C22⋊C411yescharacteristic
47C22×#6923C22⋊C412yes—
48C22×#6923C22⋊C411yescharacteristic
49C2×C4×D61—22no—
50C2×C4×D61C22×C411yescharacteristic
51C2×C4×D61C2×D412yes—
52C2×#92420—24no—
53C4⋊#6923—42no—
54C4⋊#6923—44no—
55C4×#6923—22no—
56C4×#6923—41no—
57C4×#6923—42no—
58C4×#6923—42no—
59C4×#6923—44no—
60D61⋊C8—42no—
61D61⋊C8—42no—
62C2×C8×C61—22no—
63C4⋊C4×C61—22no—
64C4⋊C4×C61C4212yes—
65C42×C61C22×C411yescharacteristic
66C4⋊Dic61—22no—
67C4⋊Dic61C4212yes—
68#11758196—22no—
69#11758196—22no—
70#11758196—22no—
71C4×Dic61C22×C411yescharacteristic
72C4×Dic61#4112yes—
73C2×#92418—22no—
74C8×D61—42no—
75C8×D61—42no—
76C22×D61C2×C22⋊C411yescharacteristic
77C2×#6923—22no—
78C2×#6923—21no—
79C2×#6923—22no—
80C2×#6923—22no—
81C2×#6923—22no—
82C2×#6923—22no—
83C2×#6923—42no—
84C2×#6923—42no—
85C2×#6923—42no—
86C2×#6923#10112yes—
87C2×C4×C61—22no—
88C2×C4×C61C2×C4211yescharacteristic
89C2×C4×C61C4×D412yes—
90C2×Dic61—22no—
91C2×Dic61#11711yescharacteristic
92C2×Dic61C4×D412yes—
93C4×D61—21no—
94C4×D61—21no—
95C4×D61—22no—
96C4×D61—22no—
97C4×D61—42no—
98C4×D61—42no—
99#92420—44no—
100C8×C61—42no—
101#92418—42no—
102#8225—611nomaximal, Sylow
103C22×C61C4×C22⋊C411yescharacteristic
104C2×D61C2×#10111yescharacteristic
105C2×D61#41311yescharacteristic
106C2×D61#42112yes—
107C2×D61#42112yes—
108#6923—22no—
109#6923—41no—
110#6923—42no—
111#6923—82no—
112C4×C61—21no—
113C4×C61—22no—
114C4×C61—42no—
115Dic61—21no—
116Dic61—22no—
117Dic61—42no—
118C4×#125—611no—
119#1745—612no—
120C2×#330—611no—
121C2×#330—611no—
122#1295—612no—
123C2×C61C4×#10111yescharacteristic
124C2×C61#175912yes—
125D61#153411yescharacteristic
126D61#153512yes—
127D61#153711yescharacteristic
128C2×#125—611no—
129C2×#97—612no—
130C2×#97—612no—
131#389—612no—
132#387—1222no—
133#382—611no—
134C4×C4⋊C4—612no—
135C4×C4⋊C4—1222no—
136C43—611no—
137#336—1222no—
138#336—1222no—
139#330—614no—
140#330—611no—
141#330—612no—
142#330#692311yescharacteristic, complemented
143C61#822511yescharacteristic, complemented, Sylow
144C22×C8—1222no—
145C22×C8—1222no—
146#125—612no—
147#125—611no—
148#125—1222no—
149#125C2×#692311yescharacteristic
150C2×C4⋊C4—612no—
151C2×C4⋊C4—612no—
152C2×C4⋊C4—1222no—
153C2×C4⋊C4—1222no—
154C2×C42—611no—
155C2×C42—611no—
156C2×C42—611no—
157C2×C42—612no—
158C2×C42—612no—
159C2×C42—1222no—
160#97—614no—
161#97—612no—
162#97—1222no—
163#97—1222no—
164#97C2×#692312yes—
165#95—1222no—
166#95—1222no—
167#95—1222no—
168C22×C4—611no—
169C22×C4—611no—
170C22×C4—612no—
171C22×C4—611no—
172C22×C4—612no—
173C22×C4—1222no—
174C22×C4—1222no—
175C2×C8—22no—
176C2×C8—1224no—
177C2×C8—1222no—
178C2×C8—2442no—
179C2×C8—2442no—
180C2×C8—2442no—
181C2×C8—2442no—
182C4⋊C4—22no—
183C4⋊C4—612no—
184C4⋊C4—1222no—
185C4⋊C4—1222no—
186C4⋊C4—1222no—
187C4⋊C4—1222no—
188C4⋊C4—2442no—
189C4⋊C4—2444no—
190C4⋊C4C4×#692312yes—
191C42—611no—
192C42—612no—
193C42—1222no—
194C42—2441no—
195C42—2442no—
196C42—2442no—
197C42—2444no—
198C42C22×#692311yescharacteristic
199C23—611no—
200C2×C4—22no—
201C2×C4—612no—
202C2×C4—611no—
203C2×C4—612no—
204C2×C4—1221no—
205C2×C4—1221no—
206C2×C4—1222no—
207C2×C4—1222no—
208C2×C4—1222no—
209C2×C4—1221no—
210C2×C4—1222no—
211C2×C4—1222no—
212C2×C4—1222no—
213C2×C4—1222no—
214C2×C4—1222no—
215C2×C4—2442no—
216C2×C4—2442no—
217C2×C4—2442no—
218C2×C4—2442no—
219C2×C4—2442no—
220C2×C4C2×C4×#692311yescharacteristic
221C2×C4D4×#692312yes—
222C8—42no—
223C8—2442no—
224C8—2444no—
225C22—611no—
226C22—611no—
227C22—612no—
228C22—612no—
229C22C22⋊C4×#692311yescharacteristic
230C4—21no—
231C4—22no—
232C4—42no—
233C4—1222no—
234C4—1221no—
235C4—1222no—
236C4—4882no—
237C4—2442no—
238C4—2441no—
239C4—2442no—
240C2—611no—
241C2—612no—
242C2—611no—
243C2#101×#692311yescharacteristic
244C2#2146158412yes—
subgroupG/H
centerC22C22⋊C4×#6923
commutatorC2×C4×C61C2×C42
FrattiniC42C22×#6923
FittingC61×#330C4
socleC22×C61C4×C22⋊C4
prime radicalC22×D61C2×C22⋊C4
cosocleC42×D61C23
hypercenter#330#6923
hypocenterC61#8225
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
15. #16840619C4semidirect
18. #16839504C4semidirect
19. #16839503C4semidirect
20. C61×#330C4semidirect
142. #330#6923semidirect
143. C61#8225semidirect

Maximal subgroups

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

subgroupindex
#125×#69232
#214615352
D61⋊#3302
#214606962
#330×D612
#822561