Finite Group Databasebeta

← #29580674

Subgroups — #29580674

Order 15616.

502 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 502 conjugacy classes of subgroups — too many to draw. Only its 81 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#21455763C212yesmaximal
2#21445894C211yesmaximal, characteristic
3#21444352C212yesmaximal
4#21443727C211yesmaximal, characteristic
5C61×#2817C211yesmaximal, characteristic
6C2×#14519736C2211yescharacteristic
7#16840100—24no—
8#16840095—22no—
9#16840090—22no—
10#16839802—22no—
11#16839771—22no—
12#16839726C2212yes—
13#16839625C2211yescharacteristic
14#16839528—22no—
15#16839499—24no—
16C2×C22⋊Q8×C61C2212yes—
17C61×#400—22no—
18C61×#397—22no—
19C61×#395—22no—
20C61×#381C2211yescharacteristic
21C2×#11758194—22no—
22#14519736—22no—
23#14519736—22no—
24C2×C4⋊Dic61D412yes—
25C2×C22⋊Dic61—21no—
26C2×C22⋊Dic61—21no—
27C2×C4×Dic61—21no—
28#14519710—24no—
29#14519708—24no—
30#14519701—24no—
31#14519701—24no—
32C22⋊#92418—22no—
33C22⋊#92418D414yes—
34#14519684—22no—
35C22×Q8×C61D412yes—
36C23×C4×C61C2311yescharacteristic
37C22⋊Q8×C61—22no—
38C22⋊Q8×C61—22no—
39C22⋊Q8×C61—22no—
40C22⋊Q8×C61—22no—
41C2×C4⋊C4×C61—22no—
42C2×C4⋊C4×C61—22no—
43C2×C4⋊C4×C61D412yes—
44C2×C22⋊C4×C61—22no—
45C2×C22⋊C4×C61D412yes—
46#95×C61—24no—
47#95×C61—22no—
48#95×C61—22no—
49C24×C61C2×D411yescharacteristic
50C2×Q8×C61—22no—
51C2×Q8×C61—22no—
52C2×Q8×C61—44no—
53C22×C4×C61—22no—
54C22×C4×C61—22no—
55C22×C4×C61—22no—
56C22×C4×C61—42no—
57C22×C4×C61C2×D412yes—
58C22×C4×C61C2×D411yescharacteristic
59C22×C4×C61C2×D412yes—
60C22×C4×C61#4111yescharacteristic
61C22×Dic61—22no—
62C22×Dic61—41no—
63C4⋊C4×C61—22no—
64C4⋊C4×C61—22no—
65C4⋊C4×C61—42no—
66C4⋊C4×C61—42no—
67C4⋊C4×C61—82no—
68C22⋊C4×C61—42no—
69C22⋊C4×C61—42no—
70C22⋊C4×C61—42no—
71C22⋊Dic61—41no—
72C22⋊Dic61—41no—
73C22⋊Dic61—42no—
74C4⋊Dic61—22no—
75C4⋊Dic61—22no—
76C4×Dic61—42no—
77#11758194—44no—
78C2×#92418—24no—
79C23×C61—22no—
80C23×C61—42no—
81C23×C61#12011yescharacteristic
82C23×C61#12111yescharacteristic
83C23×C61#12711yescharacteristic
84Q8×C61—44no—
85Q8×C61—82no—
86C2×C4×C61—24no—
87C2×C4×C61—41no—
88C2×C4×C61—42no—
89C2×C4×C61—41no—
90C2×C4×C61—44no—
91C2×C4×C61—44no—
92C2×C4×C61—42no—
93C2×C4×C61—42no—
94C2×C4×C61—42no—
95C2×C4×C61—44no—
96C2×C4×C61#12012yes—
97C2×C4×C61#12112yes—
98C2×Dic61—42no—
99C2×Dic61—82no—
100C2×Dic61—81no—
101C2×Dic61—82no—
102#92418—44no—
103#9985—611nomaximal, Sylow
104C22×C61—22no—
105C22×C61—22no—
106C22×C61—22no—
107C22×C61—21no—
108C22×C61—21no—
109C22×C61—82no—
110C22×C61#39211yescharacteristic
111C22×C61#45812yes—
112C4×C61—22no—
113C4×C61—22no—
114C4×C61—82no—
115C4×C61—82no—
116C4×C61—82no—
117Dic61—82no—
118Dic61—161no—
119#3095—612no—
120#2817D6111yescharacteristic
121#1820—611no—
122#1511—612no—
123#1306—611no—
124C2×C61—22no—
125C2×C61—41no—
126C2×C61—41no—
127C2×C61#200912yes—
128C2×C61#202211yescharacteristic
129C2×C22⋊Q8C2×D6112yes—
130C2×#117—611no—
131#485—1224no—
132#484—1222no—
133#483—1222no—
134#428—1222no—
135#419—1222no—
136#407—612no—
137#400—22no—
138#397—22no—
139#395—22no—
140#381—611no—
141#381C2×D6111yescharacteristic
142#342—1222no—
143#328—1224no—
144C61#998511yescharacteristic, complemented, Sylow
145C22×Q8C22⋊D6112yes—
146C23×C4C22×D6111yescharacteristic
147C2×M16—1222no—
148C22⋊Q8—22no—
149C22⋊Q8—22no—
150C22⋊Q8—22no—
151C22⋊Q8—22no—
152#117—1222no—
153#117—1222no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—612no—
157C2×C4⋊C4C22⋊D6112yes—
158C2×C22⋊C4—22no—
159C2×C22⋊C4—1221no—
160C2×C22⋊C4—1221no—
161C2×C22⋊C4C22⋊D6112yes—
162C2×C42—1221no—
163#107—1224no—
164#106—1224no—
165#103—1224no—
166#103—1224no—
167C22⋊C8—614no—
168C22⋊C8—1222no—
169#95—24no—
170#95—22no—
171#95—22no—
172#95—1222no—
173C24C2×C22⋊D6111yescharacteristic
174C2×Q8—22no—
175C2×Q8—22no—
176C2×Q8—44no—
177C22×C4—22no—
178C22×C4—22no—
179C22×C4—22no—
180C22×C4—42no—
181C22×C4—1222no—
182C22×C4—2441no—
183C22×C4D4×D6111yescharacteristic
184C22×C4D4×D6112yes—
185C22×C4#1175822411yescharacteristic
186C22×C4C2×C22⋊D6112yes—
187M16—2444no—
188C2×C8—1224no—
189C4⋊C4—22no—
190C4⋊C4—22no—
191C4⋊C4—42no—
192C4⋊C4—42no—
193C4⋊C4—82no—
194C4⋊C4—1222no—
195C4⋊C4—1222no—
196C22⋊C4—42no—
197C22⋊C4—42no—
198C22⋊C4—42no—
199C22⋊C4—2442no—
200C22⋊C4—2441no—
201C22⋊C4—2441no—
202C42—2442no—
203C23—22no—
204C23—42no—
205C23#1451974611yescharacteristic
206C23#1451974811yescharacteristic
207C23#1451977311yescharacteristic
208Q8—44no—
209Q8—82no—
210C2×C4—24no—
211C2×C4—41no—
212C2×C4—42no—
213C2×C4—41no—
214C2×C4—44no—
215C2×C4—44no—
216C2×C4—42no—
217C2×C4—44no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—4881no—
221C2×C4—4882no—
222C2×C4—4882no—
223C2×C4—2442no—
224C2×C4#1451974512yes—
225C2×C4#1451974912yes—
226C8—2444no—
227C22—22no—
228C22—21no—
229C22—21no—
230C22—22no—
231C22—22no—
232C22—82no—
233C22#1683967011yescharacteristic
234C22#1683995212yes—
235C4—22no—
236C4—22no—
237C4—82no—
238C4—82no—
239C4—82no—
240C4—9761no—
241C4—4882no—
242C2—22no—
243C2—41no—
244C2—41no—
245C2#2144687912yes—
246C2#2144694811yescharacteristic
subgroupG/H
centerC22#16839670
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#2817C2
socleC22×C61#392
prime radicalC24×C61C2×D4
hypercenter#2817D61
hypocenterC61#9985
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2817

Complements

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

NH ≅ G/Ntype
144. C61#9985semidirect

Maximal subgroups

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

subgroupindex
#214557632
#214458942
#214443522
#214437272
C61×#28172
#998561