Finite Group Databasebeta

← #29590768

Subgroups — #29590768

Order 15616.

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

normal subgroups only

This group has 368 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#21451640C211yesmaximal, characteristic
2#21444153C211yesmaximal, characteristic
3#21443848C214yesmaximal, complemented
4C61×#1822C211yesmaximal, characteristic
5C2×#14519777C411yescharacteristic
6#16839819—21no—
7#16839701—21no—
8#16839698—21no—
9#16839682C2212yes—
10#16839674C412yes—
11#16839660—21no—
12#16839628C411yescharacteristic
13#16839622—21no—
14#16839488C2212yes—
15#16839486—21no—
16C2×#117×C61C2211yescharacteristic
17C61×#407—21no—
18C61×#343—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×C22⋊Dic61—22no—
28C4⋊#92418—41no—
29C22⋊#92418—22no—
30#14519688—41no—
31#14519684—21no—
32#14519684—22no—
33#14519684—22no—
34#14519684C2×C412yes—
35C23×C4×C61D411yescharacteristic
36C2×M16×C61—22no—
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
45C22⋊C8×C61—41no—
46C22⋊C8×C61—41no—
47C24×C61C22⋊C411yescharacteristic
48C22×C4×C61—21no—
49C22×C4×C61—21no—
50C22×C4×C61—22no—
51C22×C4×C61—41no—
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—42no—
63M16×C61—42no—
64C2×C8×C61—42no—
65C4⋊C4×C61—41no—
66C4⋊C4×C61—41no—
67C22⋊C4×C61—41no—
68C22⋊C4×C61—41no—
69C42×C61—21no—
70C42×C61—21no—
71C42×C61—21no—
72C42×C61—21no—
73C22⋊Dic61—82no—
74C4⋊Dic61—42no—
75C4⋊Dic61—42no—
76C4⋊Dic61—41no—
77C4⋊Dic61—41no—
78#11758196—82no—
79C2×#92418—42no—
80C23×C61—21no—
81C23×C61—21no—
82C23×C61—21no—
83C23×C61—41no—
84C23×C61—41no—
85C23×C61C2×C22⋊C411yescharacteristic
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—21no—
93C2×C4×C61—21no—
94C2×C4×C61—42no—
95C2×C4×C61—42no—
96C2×C4×C61—41no—
97C2×C4×C61—41no—
98C2×C4×C61—41no—
99C2×C4×C61—41no—
100C2×C4×C61#9911yescharacteristic
101C2×C4×C61#9911yescharacteristic
102C2×C4×C61#13712yes—
103C2×Dic61—42no—
104C2×Dic61—42no—
105C2×Dic61—42no—
106C2×Dic61—42no—
107C2×Dic61—42no—
108C2×Dic61—42no—
109Dic122—84no—
110C8×C61—82no—
111#92418—82no—
112#11819—611nomaximal, Sylow
113C22×C61—21no—
114C22×C61—21no—
115C22×C61—42no—
116C22×C61—41no—
117C22×C61—41no—
118C22×C61—41no—
119C22×C61—81no—
120C22×C61C2×#9911yescharacteristic
121C22×C61#41911yescharacteristic
122C22×C61#42111yescharacteristic
123C4×C61—22no—
124C4×C61—21no—
125C4×C61—21no—
126C4×C61—41no—
127C4×C61—41no—
128C4×C61—41no—
129C4×C61—41no—
130Dic61—82no—
131Dic61—82no—
132#2628—611no—
133#1822D6111yescharacteristic
134#1464—611no—
135#1354—614no—
136C2×C61—21no—
137C2×C61—21no—
138C2×C61—81no—
139C2×C61#151111yescharacteristic
140C2×C61#212211yescharacteristic
141C2×C61#213511yescharacteristic
142C2×C4⋊Q8—611no—
143C2×#117C2×D6111yescharacteristic
144#432—1221no—
145#407—21no—
146#400—1221no—
147#399—1221no—
148#395—612no—
149#393—612no—
150#389—1221no—
151#382—611no—
152#380—1221no—
153#343—21no—
154#343C2×D6112yes—
155#324—612no—
156#323—1221no—
157C61#1181911yescharacteristic, complemented, Sylow
158C22×Q8—612no—
159C23×C4C22⋊D6111yescharacteristic
160C2×M16—22no—
161C4⋊Q8—2441no—
162C4⋊Q8—2441no—
163#117—41no—
164#117—41no—
165C2×C4⋊C4—1222no—
166C2×C4⋊C4—1221no—
167C2×C4⋊C4—1221no—
168C2×C4⋊C4—1221no—
169C2×C4⋊C4C22⋊D6111yescharacteristic
170C2×C4⋊C4C22×D6111yescharacteristic
171C2×C22⋊C4—1222no—
172C2×C22⋊C4C4×D6111yescharacteristic
173C2×C22⋊C4D24411yescharacteristic
174C2×C42C4×D6111yescharacteristic
175C2×C42D24411yescharacteristic
176C4⋊C8—2441no—
177C22⋊C8—41no—
178C22⋊C8—41no—
179C22⋊C8—1222no—
180#97—2441no—
181#95—612no—
182#95—1221no—
183#95—1222no—
184#95—1222no—
185C24#1175819811yescharacteristic
186C2×Q8—4882no—
187C2×Q8—2442no—
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—22no—
191C22×C4—41no—
192C22×C4—1222no—
193C22×C4—1222no—
194C22×C4#1175819811yescharacteristic
195C22×C4#1175819811yescharacteristic
196C22×C4#1175819811yescharacteristic
197C22×C4C2×C4×D6111yescharacteristic
198C22×C4C2×D24411yescharacteristic
199C22×C4C2×C22⋊D6111yescharacteristic
200M16—42no—
201M16—42no—
202C2×C8—42no—
203C2×C8—2442no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—4882no—
207C4⋊C4—2442no—
208C4⋊C4—2442no—
209C4⋊C4—2441no—
210C4⋊C4—2441no—
211C22⋊C4—41no—
212C22⋊C4—41no—
213C22⋊C4—4882no—
214C42—21no—
215C42—21no—
216C42—21no—
217C42—21no—
218C23—21no—
219C23—21no—
220C23—21no—
221C23—41no—
222C23—41no—
223C23C2×#1175819811yescharacteristic
224Q8—4884no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—2442no—
240C2×C4—2442no—
241C2×C4—2442no—
242C2×C4—2442no—
243C2×C4—2442no—
244C2×C4—2442no—
245C2×C4#1451969111yescharacteristic
246C2×C4#1451969111yescharacteristic
247C2×C4#1451980712yes—
248C8—82no—
249C8—4882no—
250C22—21no—
251C22—21no—
252C22—42no—
253C22—41no—
254C22—41no—
255C22—41no—
256C22—81no—
257C22C2×#1451969111yescharacteristic
258C22#1683977011yescharacteristic
259C22#1683978011yescharacteristic
260C4—22no—
261C4—21no—
262C4—21no—
263C4—41no—
264C4—41no—
265C4—41no—
266C4—41no—
267C4—4882no—
268C4—4882no—
269C2—21no—
270C2—21no—
271C2—81no—
272C2#2144435111yescharacteristic
273C2#2144747011yescharacteristic
274C2#2144751311yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1822C2
socleC22×C61C2×#99
prime radicalC24×C61C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1822D61
hypocenterC61#11819
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1822

Complements

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

NH ≅ G/Ntype
3. #21443848C2semidirect
157. C61#11819semidirect

Maximal subgroups

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

subgroupindex
#214516402
#214441532
#214438482
C61×#18222
#1181961