Finite Group Databasebeta

← #29591177

Subgroups — #29591177

Order 15616.

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

normal subgroups only

This group has 372 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#21451031C211yesmaximal, characteristic
2#21445815C211yesmaximal, characteristic
3#21443847C214yesmaximal
4C61×#1461C211yesmaximal, characteristic
5C2×#14519777C411yescharacteristic
6#16839786—21no—
7C2×#14519696—21no—
8#16839701C412yes—
9#16839701C2212yes—
10#16839669—21no—
11#16839668—21no—
12#16839668—21no—
13#16839627—21no—
14C4×C4⋊Dic61C411yescharacteristic
15#16839531C2212yes—
16C2×C4×Q8×C61C2211yescharacteristic
17C61×#431—21no—
18C61×#324—21no—
19C61×#324C2212yes—
20C22×Dic122—21no—
21C2×#11758194—22no—
22#14519777—41no—
23#14519777—41no—
24C2×C4⋊Dic61—21no—
25C2×C4⋊Dic61—21no—
26C2×C4⋊Dic61C2×C412yes—
27C2×C4×Dic61—21no—
28C4⋊#92418—41no—
29C4⋊#92418—41no—
30#14519696—42no—
31#14519684—22no—
32#14519684—22no—
33#14519684—22no—
34#14519684—22no—
35#14519684C2×C412yes—
36C22×Q8×C61D411yescharacteristic
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—
46C22⋊C8×C61—22no—
47C4×C8×C61—41no—
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—44no—
62C2×Dic122—41no—
63C2×Dic122—41no—
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—42no—
75C4⋊Dic61—42no—
76C4⋊Dic61—42no—
77C4×Dic61—42no—
78#11758194—42no—
79#11758194—42no—
80C2×#92418—42no—
81C23×C61C2×C22⋊C411yescharacteristic
82Q8×C61—42no—
83Q8×C61—42no—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61—21no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—22no—
91C2×C4×C61—21no—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—41no—
95C2×C4×C61—41no—
96C2×C4×C61—41no—
97C2×C4×C61#9911yescharacteristic
98C2×C4×C61#9911yescharacteristic
99C2×C4×C61#10312yes—
100C2×C4×C61#10312yes—
101C2×C4×C61C2×SD1611yescharacteristic
102C2×C4×C61C2×Q1611yescharacteristic
103C2×Dic61—42no—
104C2×Dic61—44no—
105C2×Dic61—42no—
106C2×Dic61—42no—
107C2×Dic61—42no—
108Dic122—82no—
109Dic122—82no—
110C8×C61—82no—
111#92418—82no—
112#11907—611nomaximal, Sylow
113C22×C61—21no—
114C22×C61—21no—
115C22×C61C2×#9911yescharacteristic
116C22×C61C2×#10311yescharacteristic
117C22×C61#42111yescharacteristic
118C4×C61—21no—
119C4×C61—21no—
120C4×C61—22no—
121C4×C61—22no—
122C4×C61—21no—
123C4×C61—41no—
124C4×C61—41no—
125C4×C61—41no—
126C4×C61#35512yes—
127Dic61—82no—
128Dic61—82no—
129#2568—611no—
130#1801—611no—
131#1461D6111yescharacteristic
132#1353—614no—
133C2×C61—21no—
134C2×C61—21no—
135C2×C61#152011yescharacteristic
136C2×C61#212311yescharacteristic
137C2×C61C2×#35511yescharacteristic
138C2×C4⋊Q8—611no—
139C2×C4×Q8C2×D6111yescharacteristic
140#431—21no—
141#423—1221no—
142C2×#101—1221no—
143#400—612no—
144#400—612no—
145#391—1221no—
146#391—1221no—
147#391—1221no—
148#382—1221no—
149C4×C4⋊C4—611no—
150#343—612no—
151#324—21no—
152#324C2×D6112yes—
153C61#1190711yescharacteristic, complemented, Sylow
154C22×Q8—1221no—
155C22×Q8D24411yescharacteristic
156C2×M16—1222no—
157C4⋊Q8—2441no—
158C4⋊Q8—2441no—
159C4×Q8—41no—
160C4×Q8—41no—
161C2×C4⋊C4—612no—
162C2×C4⋊C4—1221no—
163C2×C4⋊C4—1221no—
164C2×C4⋊C4C4×D6111yescharacteristic
165C2×C4⋊C4C22⋊D6111yescharacteristic
166C2×C4⋊C4C22×D6111yescharacteristic
167C2×C42—1221no—
168C2×C42C4×D6111yescharacteristic
169C2×C42D24411yescharacteristic
170C2×C42C22⋊D6111yescharacteristic
171C4⋊C8—41no—
172C4⋊C8—2441no—
173C4⋊C8—2441no—
174#101—2442no—
175C22⋊C8—22no—
176C4×C8—41no—
177#95—612no—
178#95—1222no—
179#95—1222no—
180#95—1222no—
181#95—1222no—
182C2×Q8—41no—
183C2×Q8—41no—
184C2×Q8—2444no—
185C2×Q8—2441no—
186C2×Q8—2441no—
187C2×Q8#1175819012yes—
188C2×Q8Dic24412yes—
189C22×C4—1222no—
190C22×C4—1222no—
191C22×C4#1175819811yescharacteristic
192C22×C4#1175819811yescharacteristic
193C22×C4#1175819811yescharacteristic
194C22×C4#1175819811yescharacteristic
195C22×C4C2×C4×D6111yescharacteristic
196C22×C4C2×D24411yescharacteristic
197C22×C4C2×C22⋊D6111yescharacteristic
198M16—2442no—
199M16—2442no—
200C2×C8—42no—
201C2×C8—2442no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—2442no—
206C4⋊C4—2442no—
207C4⋊C4—2442no—
208C42—21no—
209C42—21no—
210C42—21no—
211C42—21no—
212C42—21no—
213C42—21no—
214C42—2442no—
215C23C2×#1175819811yescharacteristic
216Q8—42no—
217Q8—42no—
218Q8—4882no—
219Q8—4882no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—2442no—
234C2×C4—2442no—
235C2×C4—2444no—
236C2×C4—2442no—
237C2×C4—2442no—
238C2×C4#1451969111yescharacteristic
239C2×C4#1451969111yescharacteristic
240C2×C4#1451970212yes—
241C2×C4#1451970212yes—
242C2×C4C2×#1175819011yescharacteristic
243C2×C4C2×Dic24411yescharacteristic
244C8—82no—
245C8—4882no—
246C22—21no—
247C22—21no—
248C22C2×#1451969111yescharacteristic
249C22C2×#1451970211yescharacteristic
250C22#1683977811yescharacteristic
251C4—21no—
252C4—22no—
253C4—22no—
254C4—21no—
255C4—21no—
256C4—41no—
257C4—41no—
258C4—41no—
259C4—4882no—
260C4—4882no—
261C4#1683955812yes—
262C2—21no—
263C2—21no—
264C2#2144439211yescharacteristic
265C2#2144747211yescharacteristic
266C2C2×#1683955811yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1461C2
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1461D61
hypocenterC61#11907
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1461

Complements

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

NH ≅ G/Ntype
153. C61#11907semidirect

Maximal subgroups

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

subgroupindex
#214510312
#214458152
#214438472
C61×#14612
#1190761