Finite Group Databasebeta

← #29569296

Subgroups — #29569296

Order 15616.

462 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 87 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#21452191C211yesmaximal, characteristic
2#21447383C212yesmaximal, complemented
3#21447352C211yesmaximal, characteristic
4#21443643C212yesmaximal, complemented
5C61×#1270C211yesmaximal, characteristic
6C2×#14519754—22no—
7C2×#14519708—21no—
8C2×#14519698—21no—
9#16839685—22no—
10#16839682—21no—
11#16839660C2212yes—
12#16839642—21no—
13#16839632C2211yescharacteristic
14#16839525—22no—
15#16839525—22no—
16#16839517C2211yescharacteristic
17C61×#390C2211yescharacteristic
18C61×#336C2212yes—
19C22×Dic122—21no—
20C23×Dic61—21no—
21C22×#92418—21no—
22#14519754—44no—
23#14519754—44no—
24C2×C4⋊Dic61—21no—
25C2×C4⋊Dic61—22no—
26C2×C4⋊Dic61D412yes—
27C2×C4⋊Dic61D412yes—
28C2×#11758196—22no—
29C2×#11758196—22no—
30C2×C22⋊Dic61—22no—
31C2×C22⋊Dic61—21no—
32#14519708—42no—
33#14519698—42no—
34#14519684—21no—
35#14519684—22no—
36C22×D4×C61D411yescharacteristic
37C22×C8×C61—22no—
38C2×C4⋊C4×C61D411yescharacteristic
39C2×C22⋊C4×C61—22no—
40C2×C42×C61C2311yescharacteristic
41C24×C61—21no—
42C2×D4×C61—21no—
43C2×D4×C61—41no—
44C2×D4×C61—41no—
45C2×D4×C61Q1612yes—
46C22×C4×C61—21no—
47C22×C4×C61C2×D412yes—
48C22×C4×C61C2×D411yescharacteristic
49C22×Dic61—22no—
50C22×Dic61—22no—
51C22×Dic61—44no—
52C22×Dic61—41no—
53C22×Dic61—81no—
54C2×Dic122—44no—
55C2×Dic122—81no—
56C2×C8×C61—42no—
57C2×C8×C61—42no—
58C2×C8×C61—42no—
59C4⋊C4×C61—41no—
60C22⋊C4×C61—42no—
61C22⋊C4×C61—42no—
62C42×C61—41no—
63C22⋊Dic61—44no—
64C22⋊Dic61—81no—
65C4⋊Dic61—22no—
66C4⋊Dic61—42no—
67C4⋊Dic61—41no—
68C4⋊Dic61—41no—
69C4⋊Dic61—44no—
70C4⋊Dic61SD1614yes—
71#11758196—44no—
72#11758196—42no—
73#11758196—42no—
74C2×#92418—22no—
75C2×#92418—41no—
76C2×#92418—41no—
77C23×C61—22no—
78C23×C61—42no—
79C23×C61—41no—
80C23×C61—42no—
81C23×C61—41no—
82C23×C61#12011yescharacteristic
83D4×C61—42no—
84D4×C61—81no—
85C2×C4×C61—21no—
86C2×C4×C61—22no—
87C2×C4×C61—21no—
88C2×C4×C61—22no—
89C2×C4×C61—42no—
90C2×C4×C61—41no—
91C2×C4×C61C2×SD1612yes—
92C2×C4×C61C2×Q1611yescharacteristic
93C2×C4×C61AGL(1,ℤ/8)12yes—
94C2×C4×C61#13711yescharacteristic
95C2×Dic61—24no—
96C2×Dic61—42no—
97C2×Dic61—42no—
98C2×Dic61—42no—
99C2×Dic61—42no—
100C2×Dic61—42no—
101C2×Dic61—84no—
102C2×Dic61—81no—
103C2×Dic61—82no—
104Dic122—84no—
105C8×C61—82no—
106#92418—42no—
107#7826—611nomaximal, Sylow
108C22×C61—42no—
109C22×C61—44no—
110C22×C61—82no—
111C22×C61—81no—
112C22×C61—81no—
113C22×C61#45012yes—
114C22×C61#45111yescharacteristic
115C22×C61#45311yescharacteristic
116C22×C61#45412yes—
117C22×C61#45811yescharacteristic
118C4×C61—21no—
119C4×C61—21no—
120C4×C61—22no—
121C4×C61—22no—
122C4×C61—81no—
123Dic61—44no—
124Dic61—82no—
125Dic61—161no—
126#2683—611no—
127#2100—612no—
128#2094—611no—
129#1271—612no—
130#1270D6111yescharacteristic
131C2×C61—82no—
132C2×C61#161411yescharacteristic
133C2×C61#161612yes—
134C2×C61#162911yescharacteristic
135C2×C61#163712yes—
136C2×C61#165711yescharacteristic
137C2×C22⋊Q8—1222no—
138C2×#106—1221no—
139C2×#102—1221no—
140#396—1222no—
141#395—1221no—
142#390C2×D6111yescharacteristic
143#389—612no—
144#386—1221no—
145#384—611no—
146#340—1222no—
147#340—1222no—
148#336—611no—
149#336C2×D6112yes—
150C61#782611yescharacteristic, complemented, Sylow
151C22×Q8—1221no—
152C22×D4D24411yescharacteristic
153C23×C4—1221no—
154C22×C8—22no—
155C22×C8—1221no—
156C22⋊Q8—2444no—
157C22⋊Q8—2444no—
158C2×C4⋊C4—612no—
159C2×C4⋊C4—612no—
160C2×C4⋊C4—1222no—
161C2×C4⋊C4—1222no—
162C2×C4⋊C4—1221no—
163C2×C4⋊C4—1222no—
164C2×C4⋊C4D24411yescharacteristic
165C2×C22⋊C4—22no—
166C2×C22⋊C4—1221no—
167C2×C22⋊C4—1222no—
168C2×C42C22×D6111yescharacteristic
169#106—2442no—
170#102—2442no—
171#95—1221no—
172#95—1222no—
173C24—21no—
174C2×Q8—4881no—
175C2×Q8—2444no—
176C2×D4—21no—
177C2×D4—41no—
178C2×D4—41no—
179C2×D4Dic24412yes—
180C22×C4—21no—
181C22×C4—1222no—
182C22×C4—1222no—
183C22×C4—4881no—
184C22×C4—2444no—
185C22×C4—2441no—
186C22×C4C2×D24411yescharacteristic
187C22×C4D4×D6112yes—
188C2×C8—42no—
189C2×C8—42no—
190C2×C8—42no—
191C2×C8—1222no—
192C2×C8—2441no—
193C2×C8—2441no—
194C4⋊C4—41no—
195C4⋊C4—614no—
196C4⋊C4—1222no—
197C4⋊C4—2441no—
198C4⋊C4—2441no—
199C4⋊C4—2444no—
200C4⋊C4—2442no—
201C4⋊C4—2444no—
202C4⋊C4—2442no—
203C4⋊C4—2442no—
204C22⋊C4—42no—
205C22⋊C4—42no—
206C22⋊C4—4881no—
207C22⋊C4—2444no—
208C42—41no—
209C23—22no—
210C23—42no—
211C23—41no—
212C23—42no—
213C23—41no—
214C23#1451974711yescharacteristic
215Q8—4884no—
216D4—42no—
217D4—81no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—42no—
223C2×C4—41no—
224C2×C4—1224no—
225C2×C4—4882no—
226C2×C4—4881no—
227C2×C4—4884no—
228C2×C4—2442no—
229C2×C4—2442no—
230C2×C4—2442no—
231C2×C4—2442no—
232C2×C4—2442no—
233C2×C4SD16×D6112yes—
234C2×C4C2×Dic24411yescharacteristic
235C2×C4#1451980112yes—
236C2×C4#1451981011yescharacteristic
237C8—82no—
238C8—2442no—
239C22—44no—
240C22—42no—
241C22—81no—
242C22—82no—
243C22—81no—
244C22#1683991412yes—
245C22#1683992011yescharacteristic
246C22#1683993211yescharacteristic
247C22#1683993612yes—
248C22#1683995311yescharacteristic
249C4—21no—
250C4—21no—
251C4—22no—
252C4—22no—
253C4—81no—
254C4—9761no—
255C4—4882no—
256C4—2444no—
257C2—82no—
258C2#2144484611yescharacteristic
259C2#2144485712yes—
260C2#2144493611yescharacteristic
261C2#2144498712yes—
262C2#2144511811yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1270C2
socleC23×C61#120
prime radicalC22×D4×C61D4
hypercenter#1270D61
hypocenterC61#7826
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #21447383C2semidirect
4. #21443643C2semidirect
150. C61#7826semidirect

Maximal subgroups

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

subgroupindex
#214521912
#214473832
#214473522
#214436432
C61×#12702
#782661