Finite Group Databasebeta

← #29599700

Subgroups — #29599700

Order 15616.

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

normal subgroups only

This group has 384 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#21446033C212yesmaximal
2#21446033C211yesmaximal, characteristic
3#21443946C211yesmaximal, characteristic
4#21443946C212yesmaximal
5C61×#2809C211yesmaximal, characteristic
6#16840240C2211yescharacteristic
7#16839802—22no—
8#16839802—21no—
9C2×#14519696C2212yes—
10C2×#14519696C2211yescharacteristic
11#16839522—22no—
12#16839522—21no—
13C61×#400—21no—
14C61×#398—22no—
15C61×#391C2211yescharacteristic
16C61×#391C2212yes—
17C61×#389—21no—
18C61×#387—22no—
19C2×#11758194—22no—
20C2×#11758194—21no—
21Q8×Dic61—41no—
22Q8×Dic61—41no—
23#14519736—22no—
24#14519736—21no—
25#14519710—42no—
26#14519710—41no—
27#14519708—42no—
28#14519708—41no—
29#14519696—22no—
30#14519696—21no—
31#14519696Q814yes—
32#14519696Q812yes—
33C22×Q8×C61C2311yescharacteristic
34C2×C4⋊C4×C61—22no—
35C2×C4⋊C4×C61—21no—
36C2×C4⋊C4×C61—21no—
37C2×C4⋊C4×C61—21no—
38C2×C4⋊C4×C61D412yes—
39C2×C4⋊C4×C61D411yescharacteristic
40C2×C42×C61D412yes—
41C2×C42×C61D411yescharacteristic
42#95×C61—21no—
43#95×C61—22no—
44#95×C61—22no—
45#95×C61—22no—
46#95×C61—22no—
47C2×Q8×C61—41no—
48C2×Q8×C61—41no—
49C2×Q8×C61C2×Q812yes—
50C2×Q8×C61C2×Q811yescharacteristic
51C2×Q8×C61#4111yescharacteristic
52C22×C4×C61—21no—
53C22×C4×C61—21no—
54C22×C4×C61—22no—
55C22×C4×C61—22no—
56C22×C4×C61C2×D412yes—
57C22×C4×C61C2×D411yescharacteristic
58C4⋊C4×C61—44no—
59C4⋊C4×C61—42no—
60C4⋊C4×C61—42no—
61C4⋊C4×C61—41no—
62C4⋊C4×C61—81no—
63C4⋊C4×C61—81no—
64C42×C61—41no—
65C42×C61—42no—
66C22⋊Dic61—41no—
67C4⋊Dic61—22no—
68C4⋊Dic61—21no—
69C4⋊Dic61—21no—
70C4⋊Dic61—22no—
71C4×Dic61—42no—
72C4×Dic61—41no—
73#11758194—24no—
74#11758194—22no—
75#11758194—41no—
76#11758194—42no—
77C2×#92418—42no—
78C2×#92418—41no—
79C23×C61#12011yescharacteristic
80Q8×C61—42no—
81Q8×C61—41no—
82Q8×C61—41no—
83C2×C4×C61—22no—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61—22no—
87C2×C4×C61—22no—
88C2×C4×C61—41no—
89C2×C4×C61—41no—
90C2×C4×C61—42no—
91C2×C4×C61—42no—
92C2×C4×C61—42no—
93C2×C4×C61—42no—
94C2×C4×C61—42no—
95C2×C4×C61—41no—
96C2×C4×C61—42no—
97C2×C4×C61—42no—
98C2×C4×C61C22⋊Q812yes—
99C2×C4×C61C22⋊Q811yescharacteristic
100C2×C4×C61C4⋊Q812yes—
101C2×C4×C61C4⋊Q811yescharacteristic
102C2×Dic61—41no—
103C2×Dic61—41no—
104#92418—44no—
105#92418—42no—
106#13465—611nomaximal, Sylow
107C22×C61—21no—
108C22×C61—21no—
109C22×C61#39511yescharacteristic
110C22×C61B(4,𝔽2)11yescharacteristic
111C22×C61#45811yescharacteristic
112C4×C61—22no—
113C4×C61—21no—
114C4×C61—22no—
115C4×C61—21no—
116C4×C61—42no—
117C4×C61—82no—
118C4×C61—81no—
119C4×C61—82no—
120Dic61—81no—
121Dic61—81no—
122#2809D6111yescharacteristic
123#1857—612no—
124#1857—611no—
125#1394—611no—
126#1394—612no—
127C2×C61—21no—
128C2×C61—21no—
129C2×C61#206211yescharacteristic
130C2×C61#220311yescharacteristic
131C2×C61#220411yescharacteristic
132#519—611no—
133#428—1222no—
134#428—1221no—
135C2×#101—612no—
136C2×#101—611no—
137#400—21no—
138#398—22no—
139#391C2×D6111yescharacteristic
140#391C2×D6112yes—
141#389—21no—
142#387—22no—
143#339—1222no—
144#339—1221no—
145C61#1346511yescharacteristic, complemented, Sylow
146C22×Q8C22×D6111yescharacteristic
147C2×M16—1222no—
148C2×M16—1221no—
149C4×Q8—2441no—
150C4×Q8—2441no—
151#117—1222no—
152#117—1221no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4C22⋊D6112yes—
158C2×C4⋊C4C22⋊D6111yescharacteristic
159C2×C42C22⋊D6112yes—
160C2×C42C22⋊D6111yescharacteristic
161#107—2442no—
162#107—2441no—
163#106—2442no—
164#106—2441no—
165#101—614no—
166#101—612no—
167#101—1222no—
168#101—1221no—
169#95—21no—
170#95—22no—
171#95—22no—
172#95—22no—
173#95—22no—
174C2×Q8—41no—
175C2×Q8—41no—
176C2×Q8Q8×D6112yes—
177C2×Q8Q8×D6111yescharacteristic
178C2×Q8#1175822611yescharacteristic
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—22no—
182C22×C4—22no—
183C22×C4C2×C22⋊D6112yes—
184C22×C4C2×C22⋊D6111yescharacteristic
185M16—1224no—
186M16—1222no—
187M16—2441no—
188M16—2442no—
189C2×C8—2442no—
190C2×C8—2441no—
191C4⋊C4—42no—
192C4⋊C4—41no—
193C4⋊C4—44no—
194C4⋊C4—42no—
195C4⋊C4—81no—
196C4⋊C4—81no—
197C4⋊C4—1222no—
198C4⋊C4—1221no—
199C4⋊C4—1221no—
200C4⋊C4—1222no—
201C22⋊C4—2441no—
202C42—41no—
203C42—42no—
204C42—2442no—
205C42—2441no—
206C23#1451974611yescharacteristic
207Q8—42no—
208Q8—41no—
209Q8—41no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—41no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—2441no—
226C2×C4—2441no—
227C2×C4#1451975312yes—
228C2×C4#1451975311yescharacteristic
229C2×C4#1451977512yes—
230C2×C4#1451977511yescharacteristic
231C8—2444no—
232C8—2442no—
233C22—21no—
234C22—21no—
235C22#1683968111yescharacteristic
236C22#1683994911yescharacteristic
237C22#1683995211yescharacteristic
238C4—22no—
239C4—21no—
240C4—22no—
241C4—21no—
242C4—42no—
243C4—82no—
244C4—81no—
245C4—82no—
246C4—4881no—
247C4—4881no—
248C2—21no—
249C2—21no—
250C2#2144717111yescharacteristic
251C2#2144784011yescharacteristic
252C2#2144784511yescharacteristic
subgroupG/H
centerC22#16839949
commutator, cosocleC22×Q8×C61C23
FrattiniC22×Q8C22×D61
FittingC61×#2809C2
socleC22×C61B(4,𝔽2)
prime radicalC23×C61#120
hypercenter#2809D61
hypocenterC61#13465
LCSG ▷ C22×Q8×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #2809

Complements

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

NH ≅ G/Ntype
145. C61#13465semidirect

Maximal subgroups

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

subgroupindex
#214460332
#214439462
C61×#28092
#1346561