Finite Group Databasebeta

← #29583092

Subgroups — #29583092

Order 15616.

476 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 89 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#21454094C211yesmaximal, characteristic, complemented
2#21446643C212yesmaximal
3#21446642C211yesmaximal, characteristic
4#21443701C212yesmaximal, complemented
5C61×#1295C211yesmaximal, characteristic, complemented
6C2×#14519774C2211yescharacteristic
7C2×#14519699—22no—
8C2×#14519699—22no—
9C2×#14519697—22no—
10C2×#14519688C2211yescharacteristic
11#16839696—22no—
12#16839695—22no—
13#16839694—22no—
14#16839628C2212yes—
15C2×#97×C61C2212yes—
16C61×#382C2211yescharacteristic
17C22×D244—21no—
18C22×D244—22no—
19C22×#92418—21no—
20#14519774—22no—
21#14519774—21no—
22#14519774Q812yes—
23C2×C4⋊Dic61—22no—
24C2×C4⋊Dic61D412yes—
25C2×C4⋊Dic61D412yes—
26C2×#11758196—22no—
27C2×#11758196—22no—
28#14519699—44no—
29#14519699—44no—
30#14519697—44no—
31#14519688—22no—
32#14519684—22no—
33#14519684—22no—
34#14519684—22no—
35C22×C8×C61—22no—
36C2×C4⋊C4×C61D412yes—
37C2×C42×C61C2311yescharacteristic
38#97×C61—22no—
39#97×C61—22no—
40#95×C61—22no—
41C23×D61—41no—
42C22×C4×C61—22no—
43C22×C4×C61C2×D411yescharacteristic
44C22×C4×C61C2×D412yes—
45C22×Dic61—22no—
46C22×Dic61—22no—
47C2×D244—24no—
48C2×D244—22no—
49C2×D244—42no—
50C2×D244—42no—
51C2×D244—42no—
52C2×D244—42no—
53C2×D244—42no—
54C2×D244—42no—
55C2×D244—42no—
56C2×D244—41no—
57C2×C8×C61—24no—
58C2×C8×C61—42no—
59C2×C8×C61—42no—
60C4⋊C4×C61—42no—
61C42×C61C2×Q811yescharacteristic
62C42×C61#4112yes—
63C42×C61#4111yescharacteristic
64C4⋊Dic61—42no—
65C4⋊Dic61—42no—
66C4⋊Dic61—82no—
67#11758196—82no—
68#11758196—82no—
69C2×#92418—22no—
70C2×#92418—41no—
71C2×#92418—41no—
72C23×C61#12011yescharacteristic
73C22×D61—42no—
74C22×D61—82no—
75C22×D61—81no—
76C22×D61—82no—
77C22×D61—81no—
78C2×C4×C61—21no—
79C2×C4×C61—22no—
80C2×C4×C61—21no—
81C2×C4×C61—22no—
82C2×C4×C61—42no—
83C2×C4×C61—42no—
84C2×C4×C61—42no—
85C2×C4×C61C22⋊Q812yes—
86C2×C4×C61C22⋊Q811yescharacteristic
87C2×C4×C61#12412yes—
88C2×C4×C61#12411yescharacteristic
89C2×Dic61—42no—
90C2×Dic61—42no—
91C2×Dic61—42no—
92C2×Dic61—42no—
93C2×Dic61—42no—
94C2×Dic61—42no—
95D244—44no—
96D244—44no—
97D244—44no—
98D244—82no—
99D244—82no—
100D244—82no—
101C8×C61—44no—
102#92418—42no—
103#10360—611nomaximal, Sylow
104C22×C61#39311yescharacteristic
105C22×C61#45312yes—
106C22×C61#45311yescharacteristic
107C22×C61#45412yes—
108C22×C61#45411yescharacteristic
109C2×D61—84no—
110C2×D61—82no—
111C2×D61—162no—
112C2×D61—161no—
113C2×D61—161no—
114C4×C61—21no—
115C4×C61—22no—
116C4×C61—22no—
117C4×C61—21no—
118C4×C61—82no—
119Dic61—82no—
120Dic61—82no—
121#2845—611no—
122#1961—612no—
123#1961—611no—
124#1295—612no—
125#1295D6111yescharacteristic, complemented
126C2×C61#165612yes—
127C2×C61#165611yescharacteristic
128C2×C61#165811yescharacteristic
129C2×C61#202712yes—
130C2×C61#202711yescharacteristic
131D61—162no—
132C2×#127—611no—
133C2×#102—1222no—
134C2×#102—1222no—
135C2×#102—1222no—
136C2×#97—611no—
137C2×#97C2×D6112yes—
138#398—1222no—
139#398—1222no—
140#398—1222no—
141#382—612no—
142#382C2×D6111yescharacteristic
143C61#1036011yescharacteristic, complemented, Sylow
144C22×D4—1221no—
145C22×D4—1222no—
146C22×C8—22no—
147C22×C8—1221no—
148#127—612no—
149#127—1222no—
150#127—1221no—
151C2×C4⋊C4—612no—
152C2×C4⋊C4—612no—
153C2×C4⋊C4—1222no—
154C2×C4⋊C4—1222no—
155C2×C4⋊C4—1222no—
156C2×C4⋊C4D24412yes—
157C2×C42C22×D6111yescharacteristic
158#102—2444no—
159#102—2444no—
160#102—2444no—
161#97—22no—
162#97—22no—
163#97—1222no—
164#95—22no—
165#95—1222no—
166#95—1222no—
167#95—1222no—
168C24—2441no—
169C2×D4—1224no—
170C2×D4—1222no—
171C2×D4—2442no—
172C2×D4—2442no—
173C2×D4—2442no—
174C2×D4—2442no—
175C2×D4—2442no—
176C2×D4—2442no—
177C2×D4—2442no—
178C2×D4—2441no—
179C22×C4—22no—
180C22×C4—1222no—
181C22×C4—1222no—
182C22×C4C2×D24411yescharacteristic
183C22×C4D4×D6112yes—
184C2×C8—24no—
185C2×C8—42no—
186C2×C8—42no—
187C2×C8—1222no—
188C2×C8—2441no—
189C2×C8—2441no—
190C4⋊C4—42no—
191C4⋊C4—4882no—
192C4⋊C4—4882no—
193C4⋊C4—4882no—
194C4⋊C4—2442no—
195C4⋊C4—2442no—
196C42#1175822212yes—
197C42#1175822411yescharacteristic
198C42Q8×D6111yescharacteristic
199C23—4882no—
200C23—4881no—
201C23—4882no—
202C23—4881no—
203C23—2442no—
204C23#1451974711yescharacteristic
205D4—4882no—
206D4—4882no—
207D4—4882no—
208D4—2444no—
209D4—2444no—
210D4—2444no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—2442no—
219C2×C4—2442no—
220C2×C4—2442no—
221C2×C4—2442no—
222C2×C4—2442no—
223C2×C4—2442no—
224C2×C4#1451975512yes—
225C2×C4#1451975711yescharacteristic
226C2×C4#1451976312yes—
227C2×C4#1451976511yescharacteristic
228C8—44no—
229C8—2442no—
230C22—9761no—
231C22—9762no—
232C22—9761no—
233C22—4884no—
234C22—4882no—
235C22#1683967511yescharacteristic
236C22#1683993112yes—
237C22#1683993211yescharacteristic
238C22#1683993612yes—
239C22#1683993711yescharacteristic
240C4—22no—
241C4—22no—
242C4—21no—
243C4—21no—
244C4—82no—
245C4—4882no—
246C4—4882no—
247C2—9762no—
248C2#2144511312yes—
249C2#2144511411yescharacteristic
250C2#2144512211yescharacteristic
251C2#2144697412yes—
252C2#2144697611yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1295C2
socleC23×C61#120
prime radicalC2×#14519774C22
hypercenter#1295D61
hypocenterC61#10360
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
1. #21454094C2semidirect
4. #21443701C2semidirect
5. C61×#1295C2semidirect
125. #1295D61semidirect
143. C61#10360semidirect

Maximal subgroups

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

subgroupindex
#214540942
#214466432
#214466422
#214437012
C61×#12952
#1036061