Finite Group Databasebeta

← #29590718

Subgroups — #29590718

Order 15616.

388 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 79 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#21451585C211yesmaximal, characteristic
2#21445902C211yesmaximal, characteristic
3#21443826C214yesmaximal, complemented
4C61×#1464C211yesmaximal, characteristic
5C2×#14519777C411yescharacteristic
6C2×#14519756—21no—
7#16839726—21no—
8#16839692—21no—
9#16839692C2212yes—
10#16839687—21no—
11#16839687C412yes—
12#16839668—21no—
13#16839628C411yescharacteristic
14#16839531—21no—
15#16839531C2212yes—
16C2×#117×C61C2211yescharacteristic
17C61×#432—21no—
18C61×#324C2212yes—
19C61×#323—21no—
20C22×Dic122—21no—
21C2×#11758194—22no—
22#14519777—41no—
23#14519777—41no—
24#14519756—44no—
25C2×C4⋊Dic61—21no—
26C2×C4⋊Dic61—21no—
27C2×C4⋊Dic61C2×C412yes—
28C2×#11758196—22no—
29C2×C22⋊Dic61—22no—
30C22⋊#92418—41no—
31C22⋊#92418—41no—
32#14519684—21no—
33#14519684—22no—
34#14519684—22no—
35#14519684C2×C412yes—
36C23×C4×C61D411yescharacteristic
37#117×C61—41no—
38#117×C61—41no—
39C2×C4⋊C4×C61D411yescharacteristic
40C2×C4⋊C4×C61C2311yescharacteristic
41C2×C22⋊C4×C61C2×C411yescharacteristic
42C2×C22⋊C4×C61D411yescharacteristic
43C2×C42×C61C2×C411yescharacteristic
44C2×C42×C61D411yescharacteristic
45C4⋊C8×C61—41no—
46C22⋊C8×C61—22no—
47#97×C61—41no—
48C24×C61C22⋊C411yescharacteristic
49C22×C4×C61—21no—
50C22×C4×C61—21no—
51C22×C4×C61—22no—
52C22×C4×C61—41no—
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—42no—
63C2×Dic122—41no—
64C2×Dic122—41no—
65C2×C8×C61—42no—
66C4⋊C4×C61—41no—
67C4⋊C4×C61—41no—
68C22⋊C4×C61—41no—
69C22⋊C4×C61—41no—
70C42×C61—21no—
71C42×C61—21no—
72C42×C61—21no—
73C42×C61—21no—
74C22⋊Dic61—44no—
75C4⋊Dic61—42no—
76C4⋊Dic61—42no—
77C4⋊Dic61—42no—
78#11758196—44no—
79#11758194—42no—
80#11758194—42no—
81C2×#92418—42no—
82C23×C61—21no—
83C23×C61—21no—
84C23×C61—21no—
85C23×C61—41no—
86C23×C61—41no—
87C23×C61C2×C22⋊C411yescharacteristic
88C2×C4×C61—21no—
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—21no—
96C2×C4×C61—42no—
97C2×C4×C61—42no—
98C2×C4×C61—41no—
99C2×C4×C61—41no—
100C2×C4×C61—41no—
101C2×C4×C61—41no—
102C2×C4×C61#9911yescharacteristic
103C2×C4×C61#9911yescharacteristic
104C2×C4×C61AGL(1,ℤ/8)12yes—
105C2×Dic61—42no—
106C2×Dic61—42no—
107C2×Dic61—42no—
108C2×Dic61—42no—
109C2×Dic61—42no—
110C2×Dic61—42no—
111Dic122—82no—
112Dic122—82no—
113C8×C61—82no—
114#92418—82no—
115#11807—611nomaximal, Sylow
116C22×C61—21no—
117C22×C61—21no—
118C22×C61—42no—
119C22×C61—41no—
120C22×C61—41no—
121C22×C61—41no—
122C22×C61—81no—
123C22×C61C2×#9911yescharacteristic
124C22×C61#41811yescharacteristic
125C22×C61#42111yescharacteristic
126C4×C61—22no—
127C4×C61—21no—
128C4×C61—21no—
129C4×C61—41no—
130C4×C61—41no—
131C4×C61—41no—
132C4×C61—41no—
133Dic61—82no—
134Dic61—82no—
135#2621—611no—
136#1822—611no—
137#1464D6111yescharacteristic
138#1346—614no—
139C2×C61—21no—
140C2×C61—21no—
141C2×C61—81no—
142C2×C61#151011yescharacteristic
143C2×C61#212311yescharacteristic
144C2×C61#213511yescharacteristic
145C2×C4⋊Q8—611no—
146C2×C22⋊Q8—1221no—
147C2×#117C2×D6111yescharacteristic
148#432—21no—
149#407—1221no—
150#398—612no—
151#398—1221no—
152#397—612no—
153#397—1221no—
154#391—1221no—
155#382—611no—
156#343—612no—
157#343—1221no—
158#324C2×D6112yes—
159#323—21no—
160C61#1180711yescharacteristic, complemented, Sylow
161C22×Q8—1221no—
162C23×C4D24411yescharacteristic
163C2×M16—1222no—
164C4⋊Q8—2441no—
165C4⋊Q8—2441no—
166C22⋊Q8—2444no—
167#117—41no—
168#117—41no—
169C2×C4⋊C4—612no—
170C2×C4⋊C4—1221no—
171C2×C4⋊C4—1221no—
172C2×C4⋊C4—1222no—
173C2×C4⋊C4D24411yescharacteristic
174C2×C4⋊C4C22×D6111yescharacteristic
175C2×C22⋊C4—1222no—
176C2×C22⋊C4C4×D6111yescharacteristic
177C2×C22⋊C4C22⋊D6111yescharacteristic
178C2×C42C4×D6111yescharacteristic
179C2×C42C22⋊D6111yescharacteristic
180C4⋊C8—41no—
181C22⋊C8—22no—
182C22⋊C8—2441no—
183C22⋊C8—2441no—
184#97—41no—
185#95—612no—
186#95—1221no—
187#95—1222no—
188#95—1222no—
189C24#1175819811yescharacteristic
190C2×Q8—2442no—
191C2×Q8—2442no—
192C2×Q8—2441no—
193C2×Q8—2441no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—22no—
197C22×C4—41no—
198C22×C4—1222no—
199C22×C4—1222no—
200C22×C4#1175819811yescharacteristic
201C22×C4#1175819811yescharacteristic
202C22×C4#1175819811yescharacteristic
203C22×C4C2×C4×D6111yescharacteristic
204C22×C4C2×D24411yescharacteristic
205C22×C4C2×C22⋊D6111yescharacteristic
206M16—2442no—
207M16—2442no—
208C2×C8—42no—
209C2×C8—2442no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—2442no—
213C4⋊C4—2442no—
214C4⋊C4—2442no—
215C4⋊C4—2444no—
216C22⋊C4—41no—
217C22⋊C4—41no—
218C22⋊C4—2444no—
219C42—21no—
220C42—21no—
221C42—21no—
222C42—21no—
223C23—21no—
224C23—21no—
225C23—21no—
226C23—41no—
227C23—41no—
228C23C2×#1175819811yescharacteristic
229Q8—4882no—
230Q8—4882no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—2442no—
246C2×C4—2442no—
247C2×C4—2442no—
248C2×C4—2442no—
249C2×C4—2442no—
250C2×C4—2442no—
251C2×C4#1451969111yescharacteristic
252C2×C4#1451969111yescharacteristic
253C2×C4#1451980512yes—
254C8—82no—
255C8—4882no—
256C22—21no—
257C22—21no—
258C22—42no—
259C22—41no—
260C22—41no—
261C22—41no—
262C22—81no—
263C22C2×#1451969111yescharacteristic
264C22#1683976811yescharacteristic
265C22#1683977811yescharacteristic
266C4—22no—
267C4—21no—
268C4—21no—
269C4—41no—
270C4—41no—
271C4—41no—
272C4—41no—
273C4—4882no—
274C4—4882no—
275C2—21no—
276C2—21no—
277C2—81no—
278C2#2144434911yescharacteristic
279C2#2144747211yescharacteristic
280C2#2144751311yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1464C2
socleC22×C61C2×#99
prime radicalC24×C61C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1464D61
hypocenterC61#11807
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
3. #21443826C2semidirect
160. C61#11807semidirect

Maximal subgroups

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

subgroupindex
#214515852
#214459022
#214438262
C61×#14642
#1180761