Finite Group Databasebeta

← #29580972

Subgroups — #29580972

Order 15616.

468 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 85 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#21455945C212yesmaximal
2#21446758C211yesmaximal, characteristic
3#21444434C212yesmaximal
4#21443689C211yesmaximal, characteristic
5C61×#3249C211yesmaximal, characteristic
6C2×C4×Dic122C2211yescharacteristic
7#16840090—22no—
8#16840044—22no—
9#16839969—22no—
10#16839917—22no—
11#16839867—24no—
12#16839819C2212yes—
13C2×#14519688C2211yescharacteristic
14#16839516—22no—
15#16839504—24no—
16C61×#533C2212yes—
17C61×#477—22no—
18C61×#467—22no—
19C61×#462—22no—
20C2×C4⋊C8×C61C2211yescharacteristic
21C22×Dic122D411yescharacteristic
22C2×#11758202—24no—
23C22×#92418—21no—
24C4×Dic122—22no—
25C4×Dic122—22no—
26C2×C4⋊Dic61D411yescharacteristic
27C2×#11758196—21no—
28C2×C4×Dic61—21no—
29#14519708—24no—
30C4⋊#92418—22no—
31#14519701—24no—
32#14519700—24no—
33C22⋊#92418—22no—
34#14519688—22no—
35#14519688D414yes—
36C2×Q16×C61—22no—
37C22×C8×C61D412yes—
38C4⋊Q8×C61D412yes—
39C4⋊Q8×C61D412yes—
40#125×C61—22no—
41C22⋊Q8×C61—22no—
42C22⋊Q8×C61—22no—
43C4×Q8×C61—22no—
44C4×Q8×C61—22no—
45#117×C61—22no—
46C2×C42×C61C2311yescharacteristic
47#107×C61—22no—
48C4⋊C8×C61—22no—
49#103×C61—24no—
50C2×Q8×C61—22no—
51C2×Q8×C61—22no—
52C22×C4×C61C2×D411yescharacteristic
53C22×C4×C61C2×D411yescharacteristic
54C22×C4×C61#4111yescharacteristic
55C22×Dic61—21no—
56C22×Dic61—21no—
57C2×Dic122—22no—
58C2×Dic122—42no—
59Q16×C61—82no—
60C2×C8×C61—22no—
61C2×C8×C61—42no—
62C4⋊C4×C61—22no—
63C4⋊C4×C61—22no—
64C4⋊C4×C61—22no—
65C4⋊C4×C61—22no—
66C4⋊C4×C61—42no—
67C4⋊C4×C61—42no—
68C22⋊C4×C61—42no—
69C42×C61—42no—
70C42×C61C2×D412yes—
71C42×C61C2×D412yes—
72#11758202—48no—
73C4⋊Dic61—22no—
74#11758196—42no—
75C4×Dic61—41no—
76C4×Dic61—41no—
77C2×#92418—22no—
78C2×#92418—24no—
79C2×#92418—41no—
80C2×#92418—41no—
81C23×C61#12111yescharacteristic
82Q8×C61—44no—
83Q8×C61—42no—
84Q8×C61—42no—
85C2×C4×C61—22no—
86C2×C4×C61—21no—
87C2×C4×C61—21no—
88C2×C4×C61—41no—
89C2×C4×C61—42no—
90C2×C4×C61—42no—
91C2×C4×C61#12012yes—
92C2×C4×C61#12011yescharacteristic
93C2×C4×C61#12112yes—
94C2×C4×C61#12711yescharacteristic
95C2×Dic61—22no—
96C2×Dic61—41no—
97C2×Dic61—41no—
98C2×Dic61—41no—
99C2×Dic61—42no—
100Dic122—24no—
101Dic122—42no—
102C8×C61—42no—
103#92418—42no—
104#92418—44no—
105#10031—611nomaximal, Sylow
106C22×C61—21no—
107C22×C61—21no—
108C22×C61#39211yescharacteristic
109C22×C61#47312yes—
110C4×C61—21no—
111C4×C61—22no—
112C4×C61—22no—
113C4×C61—82no—
114C4×C61—82no—
115C4×C61#45511yescharacteristic
116C4×C61#45611yescharacteristic
117Dic61—42no—
118Dic61—81no—
119#3249D6111yescharacteristic
120#3113—612no—
121#1985—611no—
122#1531—612no—
123#1290—611no—
124C2×C61—22no—
125C2×C61#200711yescharacteristic
126C2×C61#201011yescharacteristic
127C2×C61#202011yescharacteristic
128#533C2×D6112yes—
129C2×C4×Q8—611no—
130#483—1222no—
131#477—22no—
132#475—1222no—
133#467—22no—
134#462—22no—
135#462—1222no—
136#451—1222no—
137#441—1224no—
138#432—612no—
139C2×C4⋊C8C2×D6111yescharacteristic
140C2×#97—611no—
141#336—1222no—
142#330—1224no—
143C61#1003111yescharacteristic, complemented, Sylow
144C22×Q8—611no—
145C2×Q16—22no—
146C2×Q16—1224no—
147C22×C8—1221no—
148C22×C8C22⋊D6112yes—
149C4⋊Q8C22⋊D6112yes—
150C4⋊Q8C22⋊D6112yes—
151#125—22no—
152C22⋊Q8—22no—
153C22⋊Q8—22no—
154C4×Q8—22no—
155C4×Q8—22no—
156C4×Q8—1222no—
157C4×Q8—1222no—
158#117—22no—
159C2×C4⋊C4—611no—
160C2×C4⋊C4—1221no—
161C2×C42—1221no—
162C2×C42C22×D6111yescharacteristic
163#107—22no—
164#106—1224no—
165C4⋊C8—22no—
166C4⋊C8—1222no—
167#103—24no—
168#103—1224no—
169#103—1224no—
170C22⋊C8—1222no—
171#97—614no—
172#97—1222no—
173C2×Q8—22no—
174C2×Q8—22no—
175C2×Q8—1222no—
176C2×Q8—2442no—
177C22×C4—1221no—
178C22×C4—1221no—
179C22×C4D4×D6111yescharacteristic
180C22×C4#1175822411yescharacteristic
181C22×C4C2×C22⋊D6111yescharacteristic
182Q16—82no—
183Q16—2448no—
184C2×C8—22no—
185C2×C8—42no—
186C2×C8—1222no—
187C2×C8—1224no—
188C2×C8—2441no—
189C2×C8—2441no—
190C4⋊C4—22no—
191C4⋊C4—22no—
192C4⋊C4—22no—
193C4⋊C4—22no—
194C4⋊C4—42no—
195C4⋊C4—42no—
196C4⋊C4—1222no—
197C4⋊C4—2442no—
198C22⋊C4—42no—
199C42—42no—
200C42—2441no—
201C42—2441no—
202C42D4×D6112yes—
203C42C2×C22⋊D6112yes—
204C23#1451974811yescharacteristic
205Q8—44no—
206Q8—42no—
207Q8—42no—
208Q8—1224no—
209Q8—2442no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—1222no—
217C2×C4—2442no—
218C2×C4—2441no—
219C2×C4—2441no—
220C2×C4—2441no—
221C2×C4#1451974512yes—
222C2×C4#1451974611yescharacteristic
223C2×C4#1451974912yes—
224C2×C4#1451977311yescharacteristic
225C8—42no—
226C8—2442no—
227C8—2444no—
228C22—21no—
229C22—21no—
230C22#1683967011yescharacteristic
231C22#1684003412yes—
232C4—22no—
233C4—21no—
234C4—22no—
235C4—82no—
236C4—82no—
237C4—4881no—
238C4—2442no—
239C4#1683994011yescharacteristic
240C4#1683994511yescharacteristic
241C2—22no—
242C2#2144686611yescharacteristic
243C2#2144688311yescharacteristic
244C2#2144693811yescharacteristic
subgroupG/H
centerC22#16839670
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#3249C2
socleC22×C61#392
prime radicalC23×C61#121
hypercenter#3249D61
hypocenterC61#10031
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3249

Complements

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

NH ≅ G/Ntype
143. C61#10031semidirect

Maximal subgroups

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

subgroupindex
#214559452
#214467582
#214444342
#214436892
C61×#32492
#1003161