Finite Group Databasebeta

← #29568139

Subgroups — #29568139

Order 15616.

440 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 111 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#21448388C211yesmaximal, characteristic
2#21445961C212yesmaximal
3#21443645C211yesmaximal, characteristic
4#21443644C212yesmaximal
5C61×#1272C211yesmaximal, characteristic
6C2×#14519775C411yescharacteristic
7C2×Q8×Dic61C411yescharacteristic
8C2×#14519742C411yescharacteristic
9#16839668C2211yescharacteristic
10#16839659—22no—
11#16839631C411yescharacteristic
12#16839613—22no—
13C42×Dic61C2211yescharacteristic
14#16839517C2212yes—
15#16839516—22no—
16#16839516—22no—
17C61×#391C2211yescharacteristic
18C61×#336C2212yes—
19C22×Dic122C2×C411yescharacteristic
20C22×#92418—22no—
21#14519775—22no—
22#14519775C814yescomplemented
23Q8×Dic61—42no—
24#14519742—42no—
25C2×C4⋊Dic61—21no—
26C2×C4⋊Dic61C2×C411yescharacteristic
27C2×#11758196—22no—
28C2×#11758196—21no—
29C2×#11758196—22no—
30C2×C4×Dic61—21no—
31C2×C4×Dic61—21no—
32C2×C4×Dic61C2×C411yescharacteristic
33C2×C4×Dic61C2×C411yescharacteristic
34C2×C4×Dic61D412yes—
35C2×C4×Dic61D412yes—
36#14519684—22no—
37C22×Q8×C61C2×C411yescharacteristic
38C22×C8×C61—22no—
39C2×C4⋊C4×C61C2×C411yescharacteristic
40C2×C42×C61C2311yescharacteristic
41#95×C61—22no—
42C2×Q8×C61—21no—
43C2×Q8×C61—41no—
44C2×Q8×C61—41no—
45C2×Q8×C61C2×C812yes—
46C22×C4×C61—21no—
47C22×C4×C61—21no—
48C22×C4×C61C22×C411yescharacteristic
49C22×C4×C61C2×D412yes—
50C22×Dic61—21no—
51C22×Dic61—21no—
52C22×Dic61C22⋊C411yescharacteristic
53C22×Dic61C22⋊C412yes—
54C22×Dic61C22⋊C411yescharacteristic
55C2×Dic122—21no—
56C2×Dic122—41no—
57C2×Dic122—41no—
58C2×Dic122C2×C812yes—
59C2×C8×C61—42no—
60C2×C8×C61—42no—
61C2×C8×C61—42no—
62C4⋊C4×C61—41no—
63C42×C61—41no—
64C4⋊Dic61—42no—
65C4⋊Dic61—41no—
66#11758196—28no—
67#11758196—44no—
68#11758196—42no—
69C4×Dic61—22no—
70C4×Dic61—22no—
71C4×Dic61—22no—
72C4×Dic61—42no—
73C4×Dic61—42no—
74C4×Dic61—42no—
75C4×Dic61C2×C812yes—
76C4×Dic61M1612yes—
77C2×#92418—42no—
78C2×#92418—42no—
79C2×#92418—42no—
80C23×C61C2×C22⋊C411yescharacteristic
81Q8×C61—42no—
82Q8×C61—42no—
83C2×C4×C61—22no—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61—22no—
87C2×C4×C61—22no—
88C2×C4×C61—41no—
89C2×C4×C61—41no—
90C2×C4×C61—41no—
91C2×C4×C61—42no—
92C2×C4×C61C22×C811yescharacteristic
93C2×C4×C61C2×M1611yescharacteristic
94C2×C4×C61#13712yes—
95C2×C4×C61#13712yes—
96C2×Dic61—22no—
97C2×Dic61—22no—
98C2×Dic61—22no—
99C2×Dic61—22no—
100C2×Dic61—21no—
101C2×Dic61—22no—
102C2×Dic61—41no—
103C2×Dic61—41no—
104C2×Dic61—41no—
105C2×Dic61—42no—
106C2×Dic61C22⋊C814yes—
107C2×Dic61#10012yes—
108Dic122—42no—
109Dic122—42no—
110C8×C61—82no—
111#92418—82no—
112#7605—611nomaximal, Sylow
113C22×C61C2×C22⋊C811yescharacteristic
114C22×C61#41011yescharacteristic
115C22×C61C2×#10011yescharacteristic
116C22×C61#41912yes—
117C22×C61#42112yes—
118C4×C61—21no—
119C4×C61—21no—
120C4×C61—22no—
121C4×C61—22no—
122C4×C61—42no—
123C4×C61—81no—
124Dic61—22no—
125Dic61—24no—
126Dic61—41no—
127Dic61—42no—
128Dic61—81no—
129C4×C4⋊Q8—611no—
130#1839—612no—
131#1272—611no—
132#1272—612no—
133#1272D6111yescharacteristic
134C2×C61#146011yescharacteristic
135C2×C61#147912yes—
136C2×C61#151512yes—
137C2×C61#153611yescharacteristic
138C2×C61#155811yescharacteristic
139C2×C4⋊Q8—611no—
140C2×C4×Q8—611no—
141C2×C4×Q8—611no—
142#391—611no—
143#391C2×D6111yescharacteristic
144#389—1222no—
145#384—611no—
146C4×C4⋊C4—1222no—
147C43—611no—
148#336—612no—
149#336—1222no—
150#336—1222no—
151#336C2×D6112yes—
152C61#760511yescharacteristic, complemented, Sylow
153C22×Q8—611no—
154C22×Q8C4×D6111yescharacteristic
155C22×C8—22no—
156C22×C8—1222no—
157C4⋊Q8—614no—
158C4⋊Q8—1222no—
159C4×Q8—2442no—
160C4×Q8—2442no—
161C2×C4⋊C4—611no—
162C2×C4⋊C4—1222no—
163C2×C4⋊C4—1221no—
164C2×C4⋊C4—1221no—
165C2×C4⋊C4—1222no—
166C2×C4⋊C4C4×D6111yescharacteristic
167C2×C42—611no—
168C2×C42—611no—
169C2×C42—612no—
170C2×C42—612no—
171C2×C42—1221no—
172C2×C42—1221no—
173C2×C42C22×D6111yescharacteristic
174#95—22no—
175#95—1222no—
176C2×Q8—21no—
177C2×Q8—41no—
178C2×Q8—41no—
179C2×Q8—612no—
180C2×Q8—1221no—
181C2×Q8—2441no—
182C2×Q8—2441no—
183C2×Q8C8×D6112yes—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—611no—
187C22×C4—612no—
188C22×C4—611no—
189C22×C4—1221no—
190C22×C4—1221no—
191C22×C4C2×C4×D6111yescharacteristic
192C22×C4D4×D6112yes—
193C2×C8—42no—
194C2×C8—42no—
195C2×C8—42no—
196C2×C8—2442no—
197C2×C8—2442no—
198C2×C8—2442no—
199C4⋊C4—41no—
200C4⋊C4—1228no—
201C4⋊C4—2441no—
202C4⋊C4—2444no—
203C4⋊C4—2442no—
204C4⋊C4—2442no—
205C42—41no—
206C42—612no—
207C42—612no—
208C42—1222no—
209C42—1222no—
210C42—1222no—
211C42—2442no—
212C42—2442no—
213C42—2442no—
214C23C22⋊C4×D6111yescharacteristic
215Q8—42no—
216Q8—42no—
217Q8—2442no—
218Q8—2442no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—614no—
229C2×C4—612no—
230C2×C4—1222no—
231C2×C4—1222no—
232C2×C4—1222no—
233C2×C4—1222no—
234C2×C4—1221no—
235C2×C4—1222no—
236C2×C4—2441no—
237C2×C4—2442no—
238C2×C4—2441no—
239C2×C4—2441no—
240C2×C4C2×C8×D6111yescharacteristic
241C2×C4M16×D6111yescharacteristic
242C2×C4#1451980612yes—
243C2×C4#1451980912yes—
244C8—82no—
245C8—4882no—
246C22C22⋊C8×D6111yescharacteristic
247C22#1683973411yescharacteristic
248C22#100×D6111yescharacteristic
249C22#1683976912yes—
250C22#1683977712yes—
251C4—22no—
252C4—22no—
253C4—21no—
254C4—21no—
255C4—42no—
256C4—81no—
257C4—1224no—
258C4—1222no—
259C4—4881no—
260C4—2442no—
261C4—2441no—
262C2#2144413811yescharacteristic
263C2#2144421212yes—
264C2#2144436812yes—
265C2#2144445211yescharacteristic
266C2#2144454311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC2×C4×C61C22×C8
FrattiniC2×C42C22×D61
FittingC61×#1272C2
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1272D61
hypocenterC61#7605
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
22. #14519775C8semidirect
152. C61#7605semidirect

Maximal subgroups

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

subgroupindex
#214483882
#214459612
#214436452
#214436442
C61×#12722
#760561