Finite Group Databasebeta

← #29577393

Subgroups — #29577393

Order 15616.

470 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 135 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#21451031C211yesmaximal, characteristic
2#21445815C211yesmaximal, characteristic
3#21444503C212yesmaximal
4#21443721C212yesmaximal
5C61×#2982C211yesmaximal, characteristic
6C2×#14519777C2211yescharacteristic
7#16839786C2212yes—
8C2×#14519696—21no—
9#16839701C414yes—
10#16839669—21no—
11#16839668—22no—
12#16839627—21no—
13C4×C4⋊Dic61C2211yescharacteristic
14#16839531—21no—
15#16839509—24no—
16C2×C4×Q8×C61C2211yescharacteristic
17C8×Q8×C61—24no—
18C61×#431—22no—
19C61×#431C2212yes—
20C22×Dic122—21no—
21C2×#11758194—22no—
22#14519777—22no—
23#14519777—22no—
24C2×C4⋊Dic61—21no—
25C2×C4⋊Dic61—21no—
26C2×C4⋊Dic61C2×C412yes—
27C2×C4×Dic61—21no—
28C4⋊#92418—22no—
29C4⋊#92418—22no—
30#14519696—42no—
31#14519684—24no—
32#14519684—24no—
33#14519684C2×C412yes—
34C22×Q8×C61D411yescharacteristic
35C4×Q8×C61—22no—
36C4×Q8×C61—22no—
37C2×C4⋊C4×C61C2×C412yes—
38C2×C4⋊C4×C61D411yescharacteristic
39C2×C42×C61D412yes—
40C2×C42×C61C2311yescharacteristic
41C4⋊C8×C61—24no—
42C4⋊C8×C61D414yes—
43C22⋊C8×C61—22no—
44C4×C8×C61—24no—
45C4×C8×C61—22no—
46C2×Q8×C61—22no—
47C2×Q8×C61—22no—
48C2×Q8×C61SD1612yes—
49C2×Q8×C61Q1612yes—
50C22×C4×C61C22⋊C412yes—
51C22×C4×C61C22⋊C412yes—
52C22×C4×C61C22×C411yescharacteristic
53C22×C4×C61C2×D411yescharacteristic
54C22×C4×C61C2×D411yescharacteristic
55C22×Dic61—22no—
56C22×Dic61—22no—
57C2×Dic122—44no—
58C2×Dic122—41no—
59C2×Dic122—41no—
60C2×C8×C61—24no—
61C4⋊C4×C61—24no—
62C4⋊C4×C61—22no—
63C42×C61—22no—
64C42×C61—22no—
65C42×C61C2×D412yes—
66C42×C61#4112yes—
67C4⋊Dic61—24no—
68C4⋊Dic61—42no—
69C4⋊Dic61—42no—
70C4×Dic61—42no—
71#11758194—42no—
72#11758194—42no—
73C2×#92418—42no—
74C23×C61C2×C22⋊C411yescharacteristic
75Q8×C61—24no—
76Q8×C61—24no—
77C2×C4×C61—22no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61—41no—
82C2×C4×C61—42no—
83C2×C4×C61#10314yes—
84C2×C4×C61C4×D412yes—
85C2×C4×C61#12011yescharacteristic
86C2×C4×C61#12112yes—
87C2×C4×C61#12311yescharacteristic
88C2×C4×C61C2×SD1611yescharacteristic
89C2×C4×C61C2×Q1611yescharacteristic
90C2×C4×C61#13512yes—
91C2×Dic61—42no—
92C2×Dic61—44no—
93C2×Dic61—42no—
94C2×Dic61—42no—
95C2×Dic61—42no—
96Dic122—82no—
97Dic122—82no—
98C8×C61—44no—
99#92418—82no—
100#9396—611nomaximal, Sylow
101C22×C61—21no—
102C22×C61—21no—
103C22×C61#38611yescharacteristic
104C22×C61C2×#10311yescharacteristic
105C22×C61#41611yescharacteristic
106C4×C61—21no—
107C4×C61—24no—
108C4×C61—22no—
109C4×C61—42no—
110C4×C61#45412yes—
111C4×C61#46512yes—
112C4×C61#46712yes—
113Dic61—82no—
114Dic61—82no—
115#2982D6111yescharacteristic
116#2568—611no—
117#1801—611no—
118#1549—612no—
119#1303—612no—
120C2×C61—21no—
121C2×C61—21no—
122C2×C61#188811yescharacteristic
123C2×C61#189211yescharacteristic
124C2×C61#191511yescharacteristic
125C2×C4⋊Q8—611no—
126C2×C4×Q8C2×D6111yescharacteristic
127C8×Q8—24no—
128#431—22no—
129#431C2×D6112yes—
130#423—612no—
131C2×#101—1221no—
132#400—614no—
133#391—1221no—
134#391—1222no—
135#382—1221no—
136C4×C4⋊C4—611no—
137#343—1221no—
138#332—1224no—
139C61#939611yescharacteristic, complemented, Sylow
140C22×Q8—1221no—
141C22×Q8D24411yescharacteristic
142C2×M16—1222no—
143C4⋊Q8—1222no—
144C4⋊Q8—1222no—
145C4×Q8—22no—
146C4×Q8—22no—
147C2×C4⋊C4—612no—
148C2×C4⋊C4—1221no—
149C2×C4⋊C4—1221no—
150C2×C4⋊C4C4×D6112yes—
151C2×C4⋊C4D24411yescharacteristic
152C2×C42—1221no—
153C2×C42C22⋊D6112yes—
154C2×C42C22×D6111yescharacteristic
155C4⋊C8—24no—
156C4⋊C8—1222no—
157C4⋊C8—1222no—
158C4⋊C8C22⋊D6114yes—
159#101—2442no—
160C22⋊C8—22no—
161C4×C8—24no—
162C4×C8—22no—
163#95—612no—
164#95—1224no—
165#95—1224no—
166C2×Q8—22no—
167C2×Q8—22no—
168C2×Q8—2444no—
169C2×Q8—2441no—
170C2×Q8—2441no—
171C2×Q8#1175819012yes—
172C2×Q8Dic24412yes—
173C22×C4—1222no—
174C22×C4—1222no—
175C22×C4#1175819812yes—
176C22×C4#1175819812yes—
177C22×C4C2×C4×D6111yescharacteristic
178C22×C4C2×D24411yescharacteristic
179C22×C4C2×C22⋊D6111yescharacteristic
180M16—2442no—
181M16—2442no—
182C2×C8—24no—
183C2×C8—2442no—
184C4⋊C4—24no—
185C4⋊C4—22no—
186C4⋊C4—1224no—
187C4⋊C4—2442no—
188C4⋊C4—2442no—
189C42—22no—
190C42—22no—
191C42—2442no—
192C42#1175822212yes—
193C42C2×C22⋊D6112yes—
194C23C2×#1175819811yescharacteristic
195Q8—24no—
196Q8—24no—
197Q8—4882no—
198Q8—4882no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—41no—
204C2×C4—42no—
205C2×C4—2442no—
206C2×C4—2442no—
207C2×C4—2444no—
208C2×C4—2442no—
209C2×C4—2442no—
210C2×C4#1451970214yes—
211C2×C4C4×C22⋊D6112yes—
212C2×C4#1451974611yescharacteristic
213C2×C4#1451975112yes—
214C2×C4#1451976011yescharacteristic
215C2×C4C2×#1175819011yescharacteristic
216C2×C4C2×Dic24411yescharacteristic
217C2×C4#1451979912yes—
218C8—44no—
219C8—4882no—
220C22—21no—
221C22—21no—
222C22#1683964111yescharacteristic
223C22C2×#1451970211yescharacteristic
224C22#1683975911yescharacteristic
225C4—21no—
226C4—24no—
227C4—22no—
228C4—42no—
229C4—4882no—
230C4—4882no—
231C4#1683993512yes—
232C4#1683999112yes—
233C4#1684000312yes—
234C2—21no—
235C2—21no—
236C2#2144622211yescharacteristic
237C2#2144624211yescharacteristic
238C2#2144637111yescharacteristic
subgroupG/H
centerC22#16839641
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#2982C2
socleC22×C61#386
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenter#2982D61
hypocenterC61#9396
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2982

Complements

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

NH ≅ G/Ntype
139. C61#9396semidirect

Maximal subgroups

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

subgroupindex
#214510312
#214458152
#214445032
#214437212
C61×#29822
#939661