Finite Group Databasebeta

← #29592451

Subgroups — #29592451

Order 15616.

372 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 59 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#21453887C211yesmaximal, characteristic, complemented
2#21447048C211yesmaximal, characteristic
3#21444824C212yesmaximal
4#21443826C212yesmaximal, complemented
5C61×#1324C211yesmaximal, characteristic, complemented
6#16840343C2211yescharacteristic
7C2×#14519769—21no—
8#16840076—22no—
9C2×#14519705—21no—
10#16839761—21no—
11#16839702—22no—
12#16839694—22no—
13#16839692—21no—
14#16839692C2212yes—
15#16839531C2211yescharacteristic
16#16839497—22no—
17C61×#382C2211yescharacteristic
18C61×#324C2212yes—
19C2×#11758222—21no—
20C2×#11758194—21no—
21#14519769—42no—
22#14519769—42no—
23#14519757—41no—
24#14519752—41no—
25#14519751—22no—
26C2×C4⋊Dic61—21no—
27C2×C4⋊Dic61—21no—
28C2×C4⋊Dic61—21no—
29C2×C4⋊Dic61D412yes—
30C2×#11758196—22no—
31C2×#11758196—22no—
32#14519711—42no—
33#14519705—42no—
34#14519700—41no—
35#14519699—42no—
36#14519697—41no—
37#14519684—22no—
38#14519684—21no—
39#14519684—22no—
40#14519684D412yes—
41C2×C4⋊C4×C61D411yescharacteristic
42C2×C4⋊C4×C61C2311yescharacteristic
43C2×C42×C61D411yescharacteristic
44C22⋊C8×C61—22no—
45#95×C61—22no—
46C22×C4×C61—21no—
47C22×C4×C61—21no—
48C22×C4×C61C2×D411yescharacteristic
49C22×C4×C61C2×D412yes—
50C2×C22⋊D61—41no—
51C22×Dic61—22no—
52C22×Dic61—22no—
53#11758222—41no—
54#11758222—41no—
55#11758222—41no—
56#11758222—41no—
57C2×D244—21no—
58C2×D244—22no—
59C2×C4×D61—41no—
60C2×Dic122—21no—
61C2×C8×C61—42no—
62C4⋊C4×C61—41no—
63C4⋊C4×C61—41no—
64C42×C61—21no—
65C42×C61D812yes—
66#11758198—42no—
67C4⋊Dic61—22no—
68C4⋊Dic61—42no—
69C4⋊Dic61—42no—
70C4⋊Dic61—42no—
71C4⋊Dic61—81no—
72#11758196—44no—
73#11758196—42no—
74#11758196—42no—
75#11758194—41no—
76#11758194—41no—
77C2×#92418—41no—
78C23×C61#12011yescharacteristic
79C22×D61—41no—
80C2×C4×C61—21no—
81C2×C4×C61—21no—
82C2×C4×C61—22no—
83C2×C4×C61—22no—
84C2×C4×C61—41no—
85C2×C4×C61—41no—
86C2×C4×C61—42no—
87C2×C4×C61—42no—
88C2×C4×C61—41no—
89C2×C4×C61C2×D811yescharacteristic
90C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
91C22⋊D61—81no—
92C22⋊D61—81no—
93C2×Dic61—42no—
94C2×Dic61—42no—
95C2×Dic61—42no—
96C2×Dic61—42no—
97C2×Dic61—42no—
98C2×Dic61—41no—
99C2×Dic61—42no—
100D244—41no—
101D244—41no—
102D244—82no—
103C4×D61—81no—
104C4×D61—81no—
105Dic122—41no—
106Dic122—41no—
107C8×C61—82no—
108#92418—81no—
109#12157—611nomaximal, Sylow
110C22×C61—21no—
111C22×C61—21no—
112C22×C61#44711yescharacteristic
113C22×C61#45411yescharacteristic
114C22×C61B(4,𝔽2)11yescharacteristic
115C2×D61—81no—
116C2×D61—81no—
117C2×D61—81no—
118C4×C61—21no—
119C4×C61—21no—
120C4×C61—42no—
121C4×C61—42no—
122C4×C61—81no—
123Dic61—82no—
124Dic61—81no—
125Dic61—82no—
126#2822—611no—
127#2040—611no—
128#1610—612no—
129#1346—612no—
130#1324D6111yescharacteristic, complemented
131C2×C61—21no—
132C2×C61—21no—
133C2×C61#159811yescharacteristic
134C2×C61#220111yescharacteristic
135C2×C61#220311yescharacteristic
136D61—161no—
137#537—611no—
138C2×#125—1221no—
139#480—1222no—
140C2×#104—1221no—
141#417—1221no—
142#400—1222no—
143#398—612no—
144#398—1222no—
145#398—1221no—
146#382C2×D6111yescharacteristic
147#343—611no—
148#327—1222no—
149#324C2×D6112yes—
150C61#1215711yescharacteristic, complemented, Sylow
151C2×#41—1221no—
152C2×M16—1221no—
153#125—2442no—
154#125—2442no—
155C22⋊Q8—2441no—
156#121—1222no—
157#121—2441no—
158C2×C4⋊C4—612no—
159C2×C4⋊C4—1221no—
160C2×C4⋊C4—1221no—
161C2×C4⋊C4—1222no—
162C2×C4⋊C4—1221no—
163C2×C4⋊C4—1222no—
164C2×C4⋊C4D24411yescharacteristic
165C2×C4⋊C4C22×D6111yescharacteristic
166C2×C42D24411yescharacteristic
167#107—2442no—
168#104—2442no—
169#103—2441no—
170#102—2441no—
171#102—2442no—
172C22⋊C8—22no—
173#95—22no—
174#95—612no—
175#95—1222no—
176#95—1221no—
177#95—1222no—
178#41—2441no—
179#41—2441no—
180#41—2441no—
181#41—2441no—
182C2×Q8—1221no—
183C2×D4—1222no—
184C2×D4—1221no—
185C2×D4—2441no—
186C22×C4—21no—
187C22×C4—21no—
188C22×C4—1222no—
189C22×C4—1222no—
190C22×C4—2441no—
191C22×C4C2×D24411yescharacteristic
192C22×C4D4×D6112yes—
193M16—2441no—
194M16—2441no—
195C2×C8—42no—
196C2×C8—2441no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—1222no—
200C4⋊C4—4881no—
201C4⋊C4—2442no—
202C4⋊C4—2444no—
203C4⋊C4—2442no—
204C4⋊C4—2442no—
205C4⋊C4—2442no—
206C4⋊C4—2442no—
207C22⋊C4—2442no—
208C42—21no—
209C42D48812yes—
210C23—2441no—
211C23#1451974711yescharacteristic
212Q8—2441no—
213Q8—2441no—
214D4—4882no—
215D4—4881no—
216D4—4881no—
217D4—2441no—
218D4—2441no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—41no—
228C2×C4—4881no—
229C2×C4—4881no—
230C2×C4—2442no—
231C2×C4—2442no—
232C2×C4—2442no—
233C2×C4—2441no—
234C2×C4—2442no—
235C2×C4—2442no—
236C2×C4—2442no—
237C2×C4C2×D48811yescharacteristic
238C2×C4#1451980511yescharacteristic
239C8—82no—
240C8—4881no—
241C22—21no—
242C22—21no—
243C22—4881no—
244C22—4881no—
245C22—4881no—
246C22#1683989811yescharacteristic
247C22#1683993711yescharacteristic
248C22#1683995011yescharacteristic
249C4—21no—
250C4—21no—
251C4—42no—
252C4—42no—
253C4—81no—
254C4—4882no—
255C4—4881no—
256C4—4882no—
257C2—21no—
258C2—21no—
259C2—9761no—
260C2#2144475611yescharacteristic
261C2#2144783411yescharacteristic
262C2#2144784211yescharacteristic
subgroupG/H
centerC22#16839950
commutator, cosocleC2×C4⋊C4×C61C23
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1324C2
socleC22×C61B(4,𝔽2)
prime radical#16840343C22
hypercenter#1324D61
hypocenterC61#12157
LCSG ▷ C2×C4⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1324

Complements

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

NH ≅ G/Ntype
1. #21453887C2semidirect
4. #21443826C2semidirect
5. C61×#1324C2semidirect
130. #1324D61semidirect
150. C61#12157semidirect

Maximal subgroups

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

subgroupindex
#214538872
#214470482
#214448242
#214438262
C61×#13242
#1215761