Finite Group Databasebeta

← #29583093

Subgroups — #29583093

Order 15616.

392 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 93 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#21446791C212yesmaximal
2#21446638C211yesmaximal, characteristic
3#21443700C211yesmaximal, characteristic
4#21443700C212yesmaximal
5C61×#2845C211yesmaximal, characteristic
6C2×#14519777C2211yescharacteristic
7C2×#14519700—22no—
8C2×#14519688C2212yes—
9C2×#14519688C2211yescharacteristic
10#16839524—22no—
11#16839524—22no—
12C61×#398—22no—
13C61×#398—22no—
14C61×#398—22no—
15C61×#382C2212yes—
16C61×#382C2211yescharacteristic
17C22×Dic122—21no—
18C22×#92418—21no—
19C22×#92418—22no—
20#14519777—22no—
21#14519777—21no—
22#14519777Q812yes—
23C2×C4⋊Dic61—22no—
24#14519700—44no—
25#14519688—22no—
26#14519688—22no—
27#14519688—22no—
28C2×C4⋊C4×C61—22no—
29C2×C4⋊C4×C61—22no—
30C2×C4⋊C4×C61—22no—
31C2×C4⋊C4×C61D412yes—
32C2×C4⋊C4×C61D412yes—
33C2×C4⋊C4×C61D412yes—
34C2×C42×C61C2311yescharacteristic
35#95×C61—22no—
36#95×C61—22no—
37#95×C61—22no—
38#95×C61—22no—
39C22×C4×C61—22no—
40C22×C4×C61—22no—
41C22×C4×C61—22no—
42C22×C4×C61C2×D411yescharacteristic
43C22×C4×C61C2×D412yes—
44C22×Dic61—41no—
45C2×Dic122—22no—
46C2×Dic122—42no—
47C2×Dic122—42no—
48C2×Dic122—41no—
49C4⋊C4×C61—42no—
50C4⋊C4×C61—42no—
51C4⋊C4×C61—42no—
52C4⋊C4×C61—82no—
53C4⋊C4×C61—82no—
54C4⋊C4×C61—82no—
55C42×C61C2×Q811yescharacteristic
56C42×C61#4112yes—
57C42×C61#4111yescharacteristic
58C4⋊Dic61—24no—
59C4⋊Dic61—42no—
60C2×#92418—22no—
61C2×#92418—24no—
62C2×#92418—41no—
63C2×#92418—42no—
64C2×#92418—42no—
65C2×#92418—41no—
66C23×C61#12011yescharacteristic
67C2×C4×C61—21no—
68C2×C4×C61—21no—
69C2×C4×C61—22no—
70C2×C4×C61—22no—
71C2×C4×C61—42no—
72C2×C4×C61—42no—
73C2×C4×C61—42no—
74C2×C4×C61—42no—
75C2×C4×C61—42no—
76C2×C4×C61—42no—
77C2×C4×C61—42no—
78C2×C4×C61—42no—
79C2×C4×C61—42no—
80C2×C4×C61C22⋊Q812yes—
81C2×C4×C61C22⋊Q811yescharacteristic
82C2×C4×C61#12412yes—
83C2×C4×C61#12411yescharacteristic
84C2×Dic61—42no—
85C2×Dic61—81no—
86C2×Dic61—81no—
87Dic122—44no—
88Dic122—82no—
89#92418—42no—
90#92418—44no—
91#10361—611nomaximal, Sylow
92C22×C61#39311yescharacteristic
93C22×C61#45311yescharacteristic
94C22×C61#45411yescharacteristic
95C22×C61#45512yes—
96C22×C61#45612yes—
97C4×C61—21no—
98C4×C61—21no—
99C4×C61—22no—
100C4×C61—22no—
101C4×C61—82no—
102C4×C61—82no—
103C4×C61—82no—
104Dic61—82no—
105#2845D6111yescharacteristic
106#1993—612no—
107#1960—611no—
108#1295—611no—
109#1295—612no—
110C2×C61#166112yes—
111C2×C61#166211yescharacteristic
112C2×C61#166311yescharacteristic
113C2×C61#202711yescharacteristic
114C2×C61#202812yes—
115C2×C4⋊Q8—611no—
116C2×#103—1222no—
117C2×#97—611no—
118C2×#97—612no—
119#398—22no—
120#398—22no—
121#398—22no—
122#382C2×D6111yescharacteristic
123#382C2×D6112yes—
124#340—1222no—
125#340—1222no—
126C61#1036111yescharacteristic, complemented, Sylow
127C22×Q8—1221no—
128C22×C8—1222no—
129C22×C8—1221no—
130C4⋊Q8—612no—
131C4⋊Q8—1222no—
132C4⋊Q8—1221no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4—1222no—
137C2×C4⋊C4C22⋊D6112yes—
138C2×C4⋊C4C22⋊D6112yes—
139C2×C4⋊C4C22⋊D6112yes—
140C2×C42C22×D6111yescharacteristic
141#103—2444no—
142#97—1222no—
143#97—1222no—
144#97—1222no—
145#95—22no—
146#95—22no—
147#95—22no—
148#95—22no—
149C2×Q8—1222no—
150C2×Q8—2442no—
151C2×Q8—2442no—
152C2×Q8—2441no—
153C22×C4—22no—
154C22×C4—22no—
155C22×C4—22no—
156C22×C4—2441no—
157C22×C4C2×C22⋊D6112yes—
158C22×C4C2×C22⋊D6111yescharacteristic
159C2×C8—1222no—
160C2×C8—1224no—
161C2×C8—2442no—
162C2×C8—2441no—
163C2×C8—2442no—
164C2×C8—2441no—
165C4⋊C4—42no—
166C4⋊C4—42no—
167C4⋊C4—42no—
168C4⋊C4—82no—
169C4⋊C4—82no—
170C4⋊C4—82no—
171C4⋊C4—1224no—
172C4⋊C4—2442no—
173C42Q8×D6111yescharacteristic
174C42#1175822612yes—
175C42#1175822611yescharacteristic
176C23#1451974611yescharacteristic
177Q8—4882no—
178Q8—2444no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—4881no—
193C2×C4—4881no—
194C2×C4—2442no—
195C2×C4#1451975312yes—
196C2×C4#1451975311yescharacteristic
197C2×C4#1451976612yes—
198C2×C4#1451976611yescharacteristic
199C8—2442no—
200C8—2444no—
201C22#1683967311yescharacteristic
202C22#1683993011yescharacteristic
203C22#1683993511yescharacteristic
204C22#1683994012yes—
205C22#1683994512yes—
206C4—21no—
207C4—21no—
208C4—22no—
209C4—22no—
210C4—82no—
211C4—82no—
212C4—82no—
213C4—4882no—
214C2#2144513612yes—
215C2#2144514211yescharacteristic
216C2#2144514711yescharacteristic
217C2#2144697211yescharacteristic
218C2#2144697712yes—
subgroupG/H
centerC23#14519746
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2845C2
socle, prime radicalC23×C61#120
hypercenter#2845D61
hypocenterC61#10361
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2845

Complements

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

NH ≅ G/Ntype
126. C61#10361semidirect

Maximal subgroups

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

subgroupindex
#214467912
#214466382
#214437002
C61×#28452
#1036161