Finite Group Databasebeta

← #29567140

Subgroups — #29567140

Order 15616.

344 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 95 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#21445803C211yesmaximal, characteristic
2#21445552C211yesmaximal, characteristic
3C61×#1458C211yesmaximal, characteristic
4C2×#14519736—21no—
5C2×C4⋊#92418C411yescharacteristic, complemented
6C2×C4⋊#92418C411yescharacteristic, complemented
7C2×C22⋊#92418—21no—
8#16839529—21no—
9#16839529C412yes—
10#16839517—21no—
11C2×#117×C61C2211yescharacteristic
12C61×#431—21no—
13C61×#324C412yescomplemented
14C61×#323—21no—
15C22×#92418—21no—
16C22×#92418—21no—
17#14519736—22no—
18#14519736—22no—
19#14519736—41no—
20#14519736—41no—
21C2×C4⋊Dic61—41no—
22C2×C22⋊Dic61—22no—
23C2×C4×Dic61—41no—
24C4⋊#92418—41no—
25C4⋊#92418—41no—
26C22⋊#92418—41no—
27C22⋊#92418—41no—
28C23×C4×C61D411yescharacteristic
29#117×C61—41no—
30#117×C61—41no—
31C2×C4⋊C4×C61C2×C411yescharacteristic
32C2×C4⋊C4×C61Q811yescharacteristic
33C2×C22⋊C4×C61C2×C411yescharacteristic
34C2×C22⋊C4×C61D411yescharacteristic
35C2×C42×C61C2×C411yescharacteristic
36C2×C42×C61D411yescharacteristic
37C4⋊C8×C61—41no—
38C22⋊C8×C61—22no—
39C4×C8×C61—41no—
40C24×C61C22⋊C411yescharacteristic
41C22×C4×C61—21no—
42C22×C4×C61—21no—
43C22×C4×C61—21no—
44C22×C4×C61—21no—
45C22×C4×C61C4211yescharacteristic
46C22×C4×C61C22⋊C411yescharacteristic
47C22×C4×C61C22⋊C411yescharacteristic
48C22×C4×C61C4⋊C411yescharacteristic
49C22×C4×C61C4⋊C411yescharacteristic
50C22×C4×C61C4⋊C411yescharacteristic
51C22×C4×C61D811yescharacteristic
52C22×C4×C61SD1611yescharacteristic
53C22×C4×C61SD1611yescharacteristic
54C22×C4×C61Q1611yescharacteristic
55C22×Dic61—42no—
56C2×C8×C61—42no—
57C4⋊C4×C61—41no—
58C4⋊C4×C61—41no—
59C22⋊C4×C61—41no—
60C22⋊C4×C61—41no—
61C42×C61—21no—
62C42×C61—21no—
63C42×C61—21no—
64C42×C61—21no—
65C22⋊Dic61—24no—
66C22⋊Dic61—42no—
67C4⋊Dic61—42no—
68C4⋊Dic61—42no—
69C4×Dic61—42no—
70C4×Dic61—42no—
71C2×#92418—41no—
72C2×#92418—41no—
73C2×#92418—41no—
74C2×#92418—41no—
75C2×#92418—41no—
76C2×#92418—41no—
77C23×C61—21no—
78C23×C61—21no—
79C23×C61—41no—
80C23×C61—41no—
81C23×C61#9511yescharacteristic
82C23×C61#10211yescharacteristic
83C23×C61#10311yescharacteristic
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—21no—
91C2×C4×C61—21no—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
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×C61#10211yescharacteristic
105C2×C4×C61#10311yescharacteristic
106C2×C4×C61#10411yescharacteristic
107C2×C4×C61#10411yescharacteristic
108C2×C4×C61#10611yescharacteristic
109C2×C4×C61#10711yescharacteristic
110C2×Dic61—44no—
111C2×Dic61—82no—
112C2×Dic61—82no—
113C8×C61—82no—
114#92418—81no—
115#92418—81no—
116#7252—611nomaximal, Sylow
117C22×C61—21no—
118C22×C61—21no—
119C22×C61—21no—
120C22×C61—21no—
121C22×C61—41no—
122C22×C61—41no—
123C22×C61—41no—
124C22×C61—41no—
125C22×C61—81no—
126C22×C61#33911yescharacteristic
127C22×C61#34011yescharacteristic
128C22×C61#34211yescharacteristic
129C4×C61—21no—
130C4×C61—21no—
131C4×C61—41no—
132C4×C61—41no—
133C4×C61—41no—
134C4×C61—41no—
135C4×C61#32711yescharacteristic
136C4×C61#32711yescharacteristic
137C4×C61#32811yescharacteristic
138C4×C61#32811yescharacteristic
139Dic61—84no—
140#1798—611no—
141#1740—611no—
142#1458D6111yescharacteristic
143C2×C61—21no—
144C2×C61—21no—
145C2×C61—41no—
146C2×C61—41no—
147C2×C61#129411yescharacteristic
148C2×C61#139111yescharacteristic
149C2×C61#139511yescharacteristic
150C2×#117—1221no—
151C2×#117C2×D6111yescharacteristic
152#431—21no—
153C2×C4⋊C8—611no—
154C2×C4⋊C8—611no—
155C2×C22⋊C8—1221no—
156#342—612no—
157#342—1221no—
158#336—1221no—
159#324Dic6112yescomplemented
160#323—21no—
161C61#725211yescharacteristic, complemented, Sylow
162C23×C4D24411yescharacteristic
163C22×C8—1221no—
164C22×C8—1221no—
165#117—41no—
166#117—41no—
167#117—1222no—
168#117—1222no—
169#117—2441no—
170#117—2441no—
171C2×C4⋊C4—2441no—
172C2×C4⋊C4Dic12211yescharacteristic
173C2×C4⋊C4C2×Dic6111yescharacteristic
174C2×C22⋊C4—1222no—
175C2×C22⋊C4C4×D6111yescharacteristic
176C2×C22⋊C4C22⋊D6111yescharacteristic
177C2×C42—2441no—
178C2×C42C4×D6111yescharacteristic
179C2×C42C22⋊D6111yescharacteristic
180C4⋊C8—41no—
181C4⋊C8—2441no—
182C4⋊C8—2441no—
183C22⋊C8—22no—
184C22⋊C8—2441no—
185C22⋊C8—2441no—
186C4×C8—41no—
187C24#1175819811yescharacteristic
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—2442no—
193C22×C4#1175819011yescharacteristic
194C22×C4#1175819011yescharacteristic
195C22×C4D48811yescharacteristic
196C22×C4Dic24411yescharacteristic
197C22×C4C4×Dic6111yescharacteristic
198C22×C4#1175819611yescharacteristic
199C22×C4#1175819611yescharacteristic
200C22×C4C4⋊Dic6111yescharacteristic
201C22×C4#1175819811yescharacteristic
202C22×C4C22⋊Dic6111yescharacteristic
203C2×C8—42no—
204C2×C8—2441no—
205C2×C8—2441no—
206C2×C8—2441no—
207C2×C8—2441no—
208C2×C8—2441no—
209C2×C8—2441no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—2442no—
213C4⋊C4—2442no—
214C22⋊C4—41no—
215C22⋊C4—41no—
216C22⋊C4—1224no—
217C22⋊C4—2442no—
218C42—21no—
219C42—21no—
220C42—21no—
221C42—21no—
222C42—2442no—
223C42—2442no—
224C23—21no—
225C23—21no—
226C23—41no—
227C23—41no—
228C23#1451968411yescharacteristic
229C23#1451969911yescharacteristic
230C23#1451970211yescharacteristic
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—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—4882no—
250C2×C4—4882no—
251C2×C4—2444no—
252C2×C4#1451969111yescharacteristic
253C2×C4#1451969111yescharacteristic
254C2×C4#1451969911yescharacteristic
255C2×C4#1451970211yescharacteristic
256C2×C4#1451970311yescharacteristic
257C2×C4#1451970311yescharacteristic
258C2×C4#1451970911yescharacteristic
259C2×C4#1451971111yescharacteristic
260C8—82no—
261C8—4881no—
262C8—4881no—
263C22—21no—
264C22—21no—
265C22—21no—
266C22—21no—
267C22—41no—
268C22—41no—
269C22—41no—
270C22—41no—
271C22—81no—
272C22#1683952311yescharacteristic
273C22#1683952511yescharacteristic
274C22#1683952811yescharacteristic
275C4—21no—
276C4—21no—
277C4—41no—
278C4—41no—
279C4—41no—
280C4—41no—
281C4—4884no—
282C4#1683949711yescharacteristic
283C4#1683949711yescharacteristic
284C4#1683950011yescharacteristic
285C4#1683950011yescharacteristic
286C2—21no—
287C2—21no—
288C2—41no—
289C2—41no—
290C2#2144369911yescharacteristic
291C2#2144393911yescharacteristic
292C2#2144394911yescharacteristic
subgroupG/H
centerC2×C4#14519691
commutatorC22×C4×C61C42
FrattiniC2×#117C2×D61
FittingC61×#1458C2
socleC22×C61#342
prime radicalC24×C61C22⋊C4
cosocleC2×#117×C61C22
hypercenter#1458D61
hypocenterC61#7252
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#117 ◁ #1458

Complements

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

NH ≅ G/Ntype
5. C2×C4⋊#92418C4semidirect
6. C2×C4⋊#92418C4semidirect
13. C61×#324C4semidirect
159. #324Dic61semidirect
161. C61#7252semidirect

Maximal subgroups

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

subgroupindex
#214458032
#214455522
C61×#14582
#725261