Finite Group Databasebeta

← #29591179

Subgroups — #29591179

Order 15616.

388 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 99 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#21444143C211yesmaximal, characteristic
3#21443848C214yesmaximal
4C61×#1801C211yesmaximal, characteristic
5C2×#14519777C411yescharacteristic
6#16839815—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
17C61×#423—21no—
18C2×#101×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—
31C4×#92418—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
45C4⋊C8×C61—41no—
46C4⋊C8×C61—41no—
47#101×C61—42no—
48C2×Q8×C61—41no—
49C2×Q8×C61—41no—
50C2×Q8×C61SD1612yes—
51C2×Q8×C61Q1612yes—
52C22×C4×C61C22⋊C411yescharacteristic
53C22×C4×C61C22⋊C411yescharacteristic
54C22×C4×C61C22⋊C411yescharacteristic
55C22×C4×C61C22⋊C411yescharacteristic
56C22×C4×C61C22×C411yescharacteristic
57C22×C4×C61C2×D411yescharacteristic
58C22×C4×C61C2×D411yescharacteristic
59C22×Dic61—22no—
60C22×Dic61—22no—
61C2×Dic122—42no—
62C2×Dic122—82no—
63M16×C61—42no—
64M16×C61—42no—
65C2×C8×C61—42no—
66C4⋊C4×C61—41no—
67C4⋊C4×C61—41no—
68C4⋊C4×C61—41no—
69C42×C61—21no—
70C42×C61—21no—
71C42×C61—21no—
72C42×C61—21no—
73C42×C61—21no—
74C42×C61—21no—
75C4⋊Dic61—24no—
76C4⋊Dic61—42no—
77C4⋊Dic61—41no—
78C4⋊Dic61—41no—
79#11758196—82no—
80#11758196—82no—
81C4×Dic61—42no—
82C2×#92418—42no—
83C23×C61C2×C22⋊C411yescharacteristic
84Q8×C61—42no—
85Q8×C61—42no—
86C2×C4×C61—21no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—21no—
91C2×C4×C61—21no—
92C2×C4×C61—22no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—41no—
97C2×C4×C61—41no—
98C2×C4×C61—41no—
99C2×C4×C61#9911yescharacteristic
100C2×C4×C61#9911yescharacteristic
101C2×C4×C61#10312yes—
102C2×C4×C61#10312yes—
103C2×C4×C61C2×SD1611yescharacteristic
104C2×C4×C61C2×Q1611yescharacteristic
105C2×Dic61—24no—
106C2×Dic61—42no—
107C2×Dic61—42no—
108C2×Dic61—42no—
109C2×Dic61—42no—
110C2×Dic61—42no—
111Dic122—84no—
112C8×C61—82no—
113#92418—82no—
114#11908—611nomaximal, Sylow
115C22×C61—21no—
116C22×C61—21no—
117C22×C61C2×#9911yescharacteristic
118C22×C61C2×#10311yescharacteristic
119C22×C61#42111yescharacteristic
120C4×C61—21no—
121C4×C61—21no—
122C4×C61—22no—
123C4×C61—22no—
124C4×C61—21no—
125C4×C61—41no—
126C4×C61—41no—
127C4×C61—41no—
128C4×C61#35612yes—
129Dic61—44no—
130Dic61—82no—
131#2567—611no—
132#1801D6111yescharacteristic
133#1461—611no—
134#1354—614no—
135C2×C61—21no—
136C2×C61—21no—
137C2×C61#152011yescharacteristic
138C2×C61#212211yescharacteristic
139C2×C61C2×#35611yescharacteristic
140C2×C4⋊Q8—611no—
141C2×C4×Q8C2×D6111yescharacteristic
142#431—1221no—
143#423—21no—
144C2×#101—21no—
145#395—612no—
146#395—612no—
147#391—1221no—
148#389—1221no—
149#389—1221no—
150#384—1221no—
151C4×C4⋊C4—611no—
152#343C2×D6112yes—
153#324—612no—
154#324—1221no—
155C61#1190811yescharacteristic, complemented, Sylow
156C22×Q8—612no—
157C22×Q8C22⋊D6111yescharacteristic
158C2×M16—22no—
159C4⋊Q8—2441no—
160C4⋊Q8—2441no—
161C4×Q8—41no—
162C4×Q8—41no—
163C2×C4⋊C4—1221no—
164C2×C4⋊C4—1222no—
165C2×C4⋊C4—1222no—
166C2×C4⋊C4—1221no—
167C2×C4⋊C4—1221no—
168C2×C4⋊C4C4×D6111yescharacteristic
169C2×C4⋊C4D24411yescharacteristic
170C2×C4⋊C4C22×D6111yescharacteristic
171C2×C42—1221no—
172C2×C42C4×D6111yescharacteristic
173C2×C42D24411yescharacteristic
174C2×C42C22⋊D6111yescharacteristic
175C4⋊C8—41no—
176C4⋊C8—41no—
177C4⋊C8—2441no—
178#101—42no—
179C22⋊C8—1222no—
180C4×C8—2441no—
181#95—612no—
182#95—1222no—
183#95—1222no—
184C2×Q8—41no—
185C2×Q8—41no—
186C2×Q8—4882no—
187C2×Q8—2442no—
188C2×Q8#1175820012yes—
189C2×Q8#1175820212yes—
190C22×C4—1222no—
191C22×C4—1222no—
192C22×C4#1175819811yescharacteristic
193C22×C4#1175819811yescharacteristic
194C22×C4#1175819811yescharacteristic
195C22×C4#1175819811yescharacteristic
196C22×C4C2×C4×D6111yescharacteristic
197C22×C4C2×D24411yescharacteristic
198C22×C4C2×C22⋊D6111yescharacteristic
199M16—42no—
200M16—42no—
201C2×C8—42no—
202C2×C8—2442no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—1224no—
207C4⋊C4—4882no—
208C4⋊C4—4882no—
209C4⋊C4—2442no—
210C4⋊C4—2441no—
211C4⋊C4—2441no—
212C42—21no—
213C42—21no—
214C42—21no—
215C42—21no—
216C42—21no—
217C42—21no—
218C42—2442no—
219C23C2×#1175819811yescharacteristic
220Q8—42no—
221Q8—42no—
222Q8—4884no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—1224no—
237C2×C4—2442no—
238C2×C4—2442no—
239C2×C4—2442no—
240C2×C4—2442no—
241C2×C4—2442no—
242C2×C4#1451969111yescharacteristic
243C2×C4#1451969111yescharacteristic
244C2×C4#1451970012yes—
245C2×C4#1451970012yes—
246C2×C4C2×#1175820011yescharacteristic
247C2×C4C2×#1175820211yescharacteristic
248C8—82no—
249C8—4882no—
250C22—21no—
251C22—21no—
252C22C2×#1451969111yescharacteristic
253C22C2×#1451970011yescharacteristic
254C22#1683978011yescharacteristic
255C4—21no—
256C4—22no—
257C4—22no—
258C4—21no—
259C4—21no—
260C4—41no—
261C4—41no—
262C4—41no—
263C4—4882no—
264C4—2444no—
265C4#1683956012yes—
266C2—21no—
267C2—21no—
268C2#2144439011yescharacteristic
269C2#2144747011yescharacteristic
270C2C2×#1683956011yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1801C2
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1801D61
hypocenterC61#11908
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1801

Complements

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

NH ≅ G/Ntype
155. C61#11908semidirect

Maximal subgroups

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

subgroupindex
#214510242
#214441432
#214438482
C61×#18012
#1190861