Finite Group Databasebeta

← #29590664

Subgroups — #29590664

Order 15616.

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

normal subgroups only

This group has 394 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#21451024C211yesmaximal, characteristic
2#21444163C211yesmaximal, characteristic
3#21443848C214yesmaximal
4C4×#101×C61C211yesmaximal, characteristic
5C2×#14519777C411yescharacteristic
6#16839819—21no—
7#16839682C412yes—
8#16839682C2212yes—
9#16839669—21no—
10#16839660—21no—
11#16839660—21no—
12#16839631—21no—
13C4×C4⋊Dic61C411yescharacteristic
14#16839488—21no—
15#16839488C2212yes—
16C2×C4×Q8×C61C2211yescharacteristic
17C2×#101×C61—21no—
18C4×M16×C61—21no—
19C61×#343C2212yes—
20C22×Dic122C2×C412yes—
21#14519777—41no—
22#14519777—41no—
23C2×C4⋊Dic61—21no—
24C2×C4⋊Dic61—21no—
25C2×C4⋊Dic61—21no—
26C2×#11758196—22no—
27C2×#11758196—22no—
28C2×C4×Dic61—21no—
29C4⋊#92418—41no—
30C22⋊#92418—22no—
31#14519688—41no—
32#14519684—22no—
33#14519684—22no—
34#14519684C2×C412yes—
35C22×Q8×C61D411yescharacteristic
36C2×M16×C61—22no—
37C4×Q8×C61—41no—
38C4×Q8×C61—41no—
39C2×C4⋊C4×C61C2×C411yescharacteristic
40C2×C4⋊C4×C61D411yescharacteristic
41C2×C4⋊C4×C61C2311yescharacteristic
42C2×C42×C61C2×C411yescharacteristic
43C2×C42×C61D411yescharacteristic
44C2×C42×C61D411yescharacteristic
45#101×C61—24no—
46#97×C61—41no—
47C4×C8×C61—41no—
48C2×Q8×C61—22no—
49C2×Q8×C61—22no—
50C2×Q8×C61—41no—
51C22×C4×C61C22⋊C411yescharacteristic
52C22×C4×C61C22⋊C411yescharacteristic
53C22×C4×C61C22⋊C411yescharacteristic
54C22×C4×C61C22⋊C411yescharacteristic
55C22×C4×C61C22×C411yescharacteristic
56C22×C4×C61C2×D411yescharacteristic
57C22×C4×C61C2×D411yescharacteristic
58C22×Dic61—22no—
59C22×Dic61—22no—
60C2×Dic122—42no—
61C2×Dic122—82no—
62M16×C61—24no—
63M16×C61—42no—
64C2×C8×C61—42no—
65C4⋊C4×C61—41no—
66C4⋊C4×C61—41no—
67C4⋊C4×C61—41no—
68C42×C61—21no—
69C42×C61—21no—
70C42×C61—21no—
71C42×C61—21no—
72C42×C61—21no—
73C42×C61—21no—
74C4⋊Dic61—24no—
75C4⋊Dic61—42no—
76C4⋊Dic61—41no—
77C4⋊Dic61—41no—
78#11758196—82no—
79#11758196—82no—
80C4×Dic61—42no—
81C2×#92418—42no—
82C23×C61C2×C22⋊C411yescharacteristic
83Q8×C61—44no—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61—21no—
87C2×C4×C61—21no—
88C2×C4×C61—22no—
89C2×C4×C61—21no—
90C2×C4×C61—21no—
91C2×C4×C61—21no—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—41no—
96C2×C4×C61—41no—
97C2×C4×C61—41no—
98C2×C4×C61#9911yescharacteristic
99C2×C4×C61#9911yescharacteristic
100C2×C4×C61#10412yes—
101C2×C4×C61#13712yes—
102C2×Dic61—24no—
103C2×Dic61—42no—
104C2×Dic61—42no—
105C2×Dic61—42no—
106C2×Dic61—42no—
107C2×Dic61—42no—
108Dic122—84no—
109C8×C61—44no—
110#92418—82no—
111#11795—611nomaximal, Sylow
112C22×C61—21no—
113C22×C61—21no—
114C22×C61C2×#9911yescharacteristic
115C22×C61#41911yescharacteristic
116C22×C61C2×#10411yescharacteristic
117C4×C61—21no—
118C4×C61—22no—
119C4×C61—22no—
120C4×C61—41no—
121C4×C61—41no—
122C4×C61—41no—
123C4×C61—41no—
124C4×C61#35612yes—
125Dic61—44no—
126Dic61—82no—
127#2567—611no—
128C4×#101D6111yescharacteristic
129#1467—611no—
130#1354—614no—
131C2×C61—21no—
132C2×C61—21no—
133C2×C61#150811yescharacteristic
134C2×C61#212211yescharacteristic
135C2×C61C2×#35611yescharacteristic
136C2×C4⋊Q8—611no—
137C2×C4×Q8C2×D6111yescharacteristic
138#432—1221no—
139C2×#101—21no—
140C4×M16—21no—
141#395—612no—
142#395—612no—
143#391—1221no—
144#389—1221no—
145#389—1221no—
146#384—1221no—
147C4×C4⋊C4—611no—
148#343C2×D6112yes—
149#324—612no—
150#324—1221no—
151C61#1179511yescharacteristic, complemented, Sylow
152C22×Q8—612no—
153C22×Q8C22⋊D6111yescharacteristic
154C2×M16—22no—
155C4⋊Q8—2441no—
156C4⋊Q8—2441no—
157C4×Q8—41no—
158C4×Q8—41no—
159C2×C4⋊C4—1221no—
160C2×C4⋊C4—1222no—
161C2×C4⋊C4—1222no—
162C2×C4⋊C4—1221no—
163C2×C4⋊C4—1221no—
164C2×C4⋊C4C4×D6111yescharacteristic
165C2×C4⋊C4D24411yescharacteristic
166C2×C4⋊C4C22×D6111yescharacteristic
167C2×C42—1221no—
168C2×C42C4×D6111yescharacteristic
169C2×C42D24411yescharacteristic
170C2×C42C22⋊D6111yescharacteristic
171C4⋊C8—2441no—
172#101—24no—
173C22⋊C8—1222no—
174#97—41no—
175#97—2441no—
176C4×C8—41no—
177#95—612no—
178#95—1222no—
179#95—1222no—
180C2×Q8—22no—
181C2×Q8—22no—
182C2×Q8—41no—
183C2×Q8—4882no—
184C2×Q8—2442no—
185C22×C4—1222no—
186C22×C4—1222no—
187C22×C4#1175819811yescharacteristic
188C22×C4#1175819811yescharacteristic
189C22×C4#1175819811yescharacteristic
190C22×C4#1175819811yescharacteristic
191C22×C4C2×C4×D6111yescharacteristic
192C22×C4C2×D24411yescharacteristic
193C22×C4C2×C22⋊D6111yescharacteristic
194M16—24no—
195M16—42no—
196C2×C8—42no—
197C2×C8—2442no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—41no—
201C4⋊C4—1224no—
202C4⋊C4—4882no—
203C4⋊C4—4882no—
204C4⋊C4—2442no—
205C4⋊C4—2441no—
206C4⋊C4—2441no—
207C42—21no—
208C42—21no—
209C42—21no—
210C42—21no—
211C42—21no—
212C42—21no—
213C42—2442no—
214C23C2×#1175819811yescharacteristic
215Q8—44no—
216Q8—4884no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—1224no—
232C2×C4—2442no—
233C2×C4—2442no—
234C2×C4—2442no—
235C2×C4—2442no—
236C2×C4—2442no—
237C2×C4#1451969111yescharacteristic
238C2×C4#1451969111yescharacteristic
239C2×C4#1451970512yes—
240C2×C4#1451980712yes—
241C8—44no—
242C8—4882no—
243C22—21no—
244C22—21no—
245C22C2×#1451969111yescharacteristic
246C22#1683977011yescharacteristic
247C22C2×#1451970511yescharacteristic
248C4—21no—
249C4—22no—
250C4—22no—
251C4—41no—
252C4—41no—
253C4—41no—
254C4—41no—
255C4—4882no—
256C4—2444no—
257C4#1683956012yes—
258C2—21no—
259C2—21no—
260C2#2144433811yescharacteristic
261C2#2144747011yescharacteristic
262C2C2×#1683956011yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC4×#101×C61C2
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenterC4×#101D61
hypocenterC61#11795
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
151. C61#11795semidirect

Maximal subgroups

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

subgroupindex
#214510242
#214441632
#214438482
C4×#101×C612
#1179561