Finite Group Databasebeta

← #29583095

Subgroups — #29583095

Order 15616.

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

normal subgroups only

This group has 392 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
2#21446792C212yesmaximal
3#21446638C211yesmaximal, characteristic
4#21443701C212yesmaximal
5C61×#1295C211yesmaximal, characteristic
6C2×#14519777C2211yescharacteristic
7C2×#14519700—22no—
8C2×#14519688C2211yescharacteristic
9#16839696—22no—
10#16839695—22no—
11#16839694—22no—
12#16839628C2212yes—
13#16839525—22no—
14#16839525—22no—
15C2×#97×C61C2212yes—
16C61×#382C2211yescharacteristic
17C22×Dic122—21no—
18C22×#92418—21no—
19#14519777—22no—
20#14519777—21no—
21#14519777Q812yes—
22C2×C4⋊Dic61—22no—
23C2×C4⋊Dic61—22no—
24C2×C4⋊Dic61D412yes—
25C2×C4⋊Dic61D412yes—
26C2×#11758196—22no—
27C2×#11758196—22no—
28#14519700—44no—
29#14519688—22no—
30#14519684—22no—
31#14519684—22no—
32#14519684—22no—
33C22×C8×C61—22no—
34C2×C4⋊C4×C61D412yes—
35C2×C42×C61C2311yescharacteristic
36#97×C61—22no—
37#97×C61—22no—
38#95×C61—22no—
39C22×C4×C61—22no—
40C22×C4×C61C2×D411yescharacteristic
41C22×C4×C61C2×D412yes—
42C22×Dic61—22no—
43C22×Dic61—22no—
44C22×Dic61—41no—
45C2×Dic122—22no—
46C2×Dic122—42no—
47C2×Dic122—42no—
48C2×Dic122—41no—
49C2×C8×C61—24no—
50C2×C8×C61—42no—
51C2×C8×C61—42no—
52C4⋊C4×C61—42no—
53C42×C61C2×Q811yescharacteristic
54C42×C61#4112yes—
55C42×C61#4111yescharacteristic
56C4⋊Dic61—24no—
57C4⋊Dic61—42no—
58C4⋊Dic61—42no—
59C4⋊Dic61—42no—
60C4⋊Dic61—82no—
61#11758196—82no—
62#11758196—82no—
63C2×#92418—22no—
64C2×#92418—41no—
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×C61C22⋊Q812yes—
75C2×C4×C61C22⋊Q811yescharacteristic
76C2×C4×C61#12412yes—
77C2×C4×C61#12411yescharacteristic
78C2×Dic61—42no—
79C2×Dic61—42no—
80C2×Dic61—42no—
81C2×Dic61—42no—
82C2×Dic61—42no—
83C2×Dic61—42no—
84C2×Dic61—42no—
85C2×Dic61—81no—
86C2×Dic61—81no—
87Dic122—44no—
88Dic122—82no—
89C8×C61—44no—
90#92418—42no—
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—
102Dic61—82no—
103Dic61—82no—
104Dic61—82no—
105#2845—611no—
106#1993—612no—
107#1960—611no—
108#1295—612no—
109#1295D6111yescharacteristic
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×#97C2×D6112yes—
119#398—1222no—
120#398—1222no—
121#398—1222no—
122#382—612no—
123#382C2×D6111yescharacteristic
124#340—1222no—
125#340—1222no—
126C61#1036111yescharacteristic, complemented, Sylow
127C22×Q8—1221no—
128C22×C8—22no—
129C22×C8—1221no—
130C4⋊Q8—612no—
131C4⋊Q8—1222no—
132C4⋊Q8—1221no—
133C2×C4⋊C4—612no—
134C2×C4⋊C4—612no—
135C2×C4⋊C4—1222no—
136C2×C4⋊C4—1222no—
137C2×C4⋊C4—1222no—
138C2×C4⋊C4—1222no—
139C2×C4⋊C4D24412yes—
140C2×C42C22×D6111yescharacteristic
141#103—2444no—
142#97—22no—
143#97—22no—
144#97—1222no—
145#95—22no—
146#95—1222no—
147#95—1222no—
148#95—1222no—
149C2×Q8—1222no—
150C2×Q8—2442no—
151C2×Q8—2442no—
152C2×Q8—2441no—
153C22×C4—22no—
154C22×C4—1222no—
155C22×C4—1222no—
156C22×C4—2441no—
157C22×C4C2×D24411yescharacteristic
158C22×C4D4×D6112yes—
159C2×C8—24no—
160C2×C8—42no—
161C2×C8—42no—
162C2×C8—1222no—
163C2×C8—2441no—
164C2×C8—2441no—
165C4⋊C4—42no—
166C4⋊C4—1224no—
167C4⋊C4—4882no—
168C4⋊C4—4882no—
169C4⋊C4—4882no—
170C4⋊C4—2442no—
171C4⋊C4—2442no—
172C4⋊C4—2442no—
173C42#1175822212yes—
174C42#1175822411yescharacteristic
175C42Q8×D6111yescharacteristic
176C23#1451974711yescharacteristic
177Q8—4882no—
178Q8—2444no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—21no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—4881no—
187C2×C4—4881no—
188C2×C4—2442no—
189C2×C4—2442no—
190C2×C4—2442no—
191C2×C4—2442no—
192C2×C4—2442no—
193C2×C4—2442no—
194C2×C4—2442no—
195C2×C4#1451975512yes—
196C2×C4#1451975711yescharacteristic
197C2×C4#1451976312yes—
198C2×C4#1451976511yescharacteristic
199C8—44no—
200C8—2442no—
201C22#1683967511yescharacteristic
202C22#1683993211yescharacteristic
203C22#1683993711yescharacteristic
204C22#1683994112yes—
205C22#1683994612yes—
206C4—21no—
207C4—21no—
208C4—22no—
209C4—22no—
210C4—82no—
211C4—4882no—
212C4—4882no—
213C4—4882no—
214C2#2144513712yes—
215C2#2144514311yescharacteristic
216C2#2144514811yescharacteristic
217C2#2144697611yescharacteristic
218C2#2144697912yes—
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1295C2
socle, prime radicalC23×C61#120
hypercenter#1295D61
hypocenterC61#10361
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
126. C61#10361semidirect

Maximal subgroups

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

subgroupindex
#214540942
#214467922
#214466382
#214437012
C61×#12952
#1036161