Finite Group Databasebeta

← #29573596

Subgroups — #29573596

Order 15616.

378 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 107 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#21448784C211yesmaximal, characteristic
2#21444143C211yesmaximal, characteristic
3#21443720C212yesmaximal
4#21443679C212yesmaximal
5C61×#1801C211yesmaximal, characteristic
6#16839815C2212yes—
7#16839669—21no—
8#16839648—22no—
9#16839630C412yes—
10#16839628C2211yescharacteristic
11C4⋊C4×Dic61—21no—
12C4×C4⋊Dic61C2211yescharacteristic
13#16839608C412yes—
14#16839488—22no—
15C2×C4×Q8×C61C2211yescharacteristic
16C61×#423C2212yes—
17C2×#101×C61—21no—
18C61×#343—21no—
19C2×C4⋊Dic61—21no—
20C2×C4⋊Dic61—21no—
21C2×C4×Dic61—22no—
22C2×C4×Dic61—21no—
23C4⋊#92418—22no—
24C22⋊#92418—22no—
25C4×#92418—22no—
26#14519684—22no—
27#14519684—22no—
28#14519684—22no—
29#14519684—21no—
30#14519684C2×C411yescharacteristic
31#14519684C2×C412yes—
32#14519684C2×C411yescharacteristic
33C22×Q8×C61D411yescharacteristic
34C2×M16×C61—22no—
35C4×Q8×C61—22no—
36C4×Q8×C61—22no—
37C2×C4⋊C4×C61D412yes—
38C2×C4⋊C4×C61D411yescharacteristic
39C2×C42×C61C2×C412yes—
40C2×C42×C61C2311yescharacteristic
41C4⋊C8×C61—22no—
42C4⋊C8×C61—22no—
43#101×C61—42no—
44C2×Q8×C61—22no—
45C2×Q8×C61—22no—
46C2×Q8×C61—21no—
47C2×Q8×C61—21no—
48C22×C4×C61C22⋊C412yes—
49C22×C4×C61C22⋊C412yes—
50C22×C4×C61C22×C411yescharacteristic
51C22×C4×C61C2×D411yescharacteristic
52C22×C4×C61C2×D411yescharacteristic
53C22×Dic61—21no—
54C22×Dic61—22no—
55C22×Dic61—21no—
56M16×C61—42no—
57M16×C61—42no—
58C2×C8×C61—42no—
59C4⋊C4×C61—22no—
60C4⋊C4×C61—24no—
61C42×C61—22no—
62C42×C61—22no—
63C42×C61#4112yes—
64C42×C61#4112yes—
65C4⋊Dic61—42no—
66C4⋊Dic61—42no—
67C4×Dic61—44no—
68C4×Dic61—41no—
69C4×Dic61—41no—
70C2×#92418—42no—
71C23×C61C2×C22⋊C411yescharacteristic
72Q8×C61—42no—
73Q8×C61—42no—
74C2×C4×C61—22no—
75C2×C4×C61—22no—
76C2×C4×C61—22no—
77C2×C4×C61—22no—
78C2×C4×C61—41no—
79C2×C4×C61—41no—
80C2×C4×C61—42no—
81C2×C4×C61#11711yescharacteristic
82C2×C4×C61#11711yescharacteristic
83C2×C4×C61#12312yes—
84C2×C4×C61#12312yes—
85C2×C4×C61#13512yes—
86C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
87C2×C4×C61#13711yescharacteristic
88C2×Dic61—22no—
89C2×Dic61—41no—
90C2×Dic61—41no—
91C2×Dic61—42no—
92C2×Dic61—41no—
93C2×Dic61—41no—
94C2×Dic61—42no—
95C2×Dic61—42no—
96C2×Dic61—41no—
97C8×C61—82no—
98#92418—82no—
99#8768—611nomaximal, Sylow
100C22×C61—21no—
101C22×C61—21no—
102C22×C61#38111yescharacteristic
103C22×C61#41611yescharacteristic
104C22×C61#41711yescharacteristic
105C4×C61—22no—
106C4×C61—21no—
107C4×C61—21no—
108C4×C61—42no—
109C4×C61—42no—
110C4×C61#48212yes—
111C4×C61#48512yes—
112Dic61—42no—
113Dic61—81no—
114Dic61—82no—
115#2356—611no—
116#1801D6111yescharacteristic
117#1461—611no—
118#1303—612no—
119#1286—612no—
120C2×C61—21no—
121C2×C61—21no—
122C2×C61#182511yescharacteristic
123C2×C61#182711yescharacteristic
124C2×C61#183011yescharacteristic
125C2×C4×Q8C2×D6111yescharacteristic
126#431—612no—
127#423C2×D6112yes—
128C2×#101—21no—
129#391—1221no—
130#387—1222no—
131#383—612no—
132#382—611no—
133C4×C4⋊C4—611no—
134C4×C4⋊C4—1221no—
135#376—612no—
136#343—21no—
137#324—1222no—
138C61#876811yescharacteristic, complemented, Sylow
139C22×Q8C22⋊D6111yescharacteristic
140C2×M16—22no—
141C4×Q8—22no—
142C4×Q8—22no—
143C2×C4⋊C4—1221no—
144C2×C4⋊C4—1221no—
145C2×C4⋊C4D24412yes—
146C2×C4⋊C4C22⋊D6111yescharacteristic
147C2×C42—1222no—
148C2×C42—1221no—
149C2×C42C4×D6112yes—
150C2×C42C22×D6111yescharacteristic
151C4⋊C8—22no—
152C4⋊C8—22no—
153C4⋊C8—1222no—
154#101—42no—
155C22⋊C8—1222no—
156C4×C8—1222no—
157#95—611no—
158#95—612no—
159#95—611no—
160#95—1222no—
161#95—1222no—
162#95—1222no—
163#95—1221no—
164C2×Q8—21no—
165C2×Q8—22no—
166C2×Q8—22no—
167C2×Q8—21no—
168C22×C4—1221no—
169C22×C4—1222no—
170C22×C4—1221no—
171C22×C4#1175819812yes—
172C22×C4#1175819812yes—
173C22×C4C2×C4×D6111yescharacteristic
174C22×C4C2×D24411yescharacteristic
175C22×C4C2×C22⋊D6111yescharacteristic
176M16—42no—
177M16—42no—
178C2×C8—42no—
179C2×C8—2442no—
180C4⋊C4—22no—
181C4⋊C4—24no—
182C4⋊C4—2442no—
183C4⋊C4—2442no—
184C42—22no—
185C42—22no—
186C42—2444no—
187C42—2441no—
188C42—2441no—
189C42#1175822412yes—
190C42#1175822412yes—
191C23C2×#1175819811yescharacteristic
192Q8—42no—
193Q8—42no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—42no—
201C2×C4—1222no—
202C2×C4—2442no—
203C2×C4—2441no—
204C2×C4—2442no—
205C2×C4—2441no—
206C2×C4—2442no—
207C2×C4—2441no—
208C2×C4—2441no—
209C2×C4—2441no—
210C2×C4#1451973311yescharacteristic
211C2×C4#1451973311yescharacteristic
212C2×C4#1451975812yes—
213C2×C4#1451976112yes—
214C2×C4#1451979712yes—
215C2×C4#1451980311yescharacteristic
216C2×C4#1451980811yescharacteristic
217C8—82no—
218C8—4882no—
219C22—21no—
220C22—21no—
221C22#1683962311yescharacteristic
222C22#1683975611yescharacteristic
223C22#1683976111yescharacteristic
224C4—22no—
225C4—21no—
226C4—21no—
227C4—42no—
228C4—42no—
229C4—4882no—
230C4—4881no—
231C4—2442no—
232C4#1684008312yes—
233C4#1684010012yes—
234C2—21no—
235C2—21no—
236C2#2144591111yescharacteristic
237C2#2144592411yescharacteristic
238C2#2144593111yescharacteristic
subgroupG/H
centerC22#16839623
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1801C2
socleC22×C61#381
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1801D61
hypocenterC61#8768
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1801

Complements

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

NH ≅ G/Ntype
138. C61#8768semidirect

Maximal subgroups

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

subgroupindex
#214487842
#214441432
#214437202
#214436792
C61×#18012
#876861