Finite Group Databasebeta

← #29577383

Subgroups — #29577383

Order 15616.

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

normal subgroups only

This group has 506 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#21450804C211yesmaximal, characteristic
2#21445815C211yesmaximal, characteristic
3#21444490C212yesmaximal
4#21443721C212yesmaximal
5C61×#2982C211yesmaximal, characteristic
6C2×#14519777C2211yescharacteristic
7C2×#14519775—21no—
8#16839786C2212yes—
9C2×#14519696—21no—
10#16839692C414yes—
11#16839667—21no—
12#16839660—22no—
13C4×C4⋊Dic61C2211yescharacteristic
14#16839531—21no—
15#16839507—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—
24#14519775—42no—
25#14519775—42no—
26C2×C4⋊Dic61—21no—
27C2×C4⋊Dic61—21no—
28C2×C4⋊Dic61C2×C412yes—
29C2×#11758196—24no—
30C2×C4×Dic61—21no—
31C4⋊#92418—22no—
32C4⋊#92418—22no—
33#14519696—42no—
34#14519684—24no—
35#14519684C2×C412yes—
36C22×Q8×C61D411yescharacteristic
37C4×Q8×C61—22no—
38C4×Q8×C61—22no—
39C2×C4⋊C4×C61C2×C412yes—
40C2×C4⋊C4×C61D411yescharacteristic
41C2×C42×C61D412yes—
42C2×C42×C61C2311yescharacteristic
43C4⋊C8×C61—24no—
44C4⋊C8×C61D414yes—
45C22⋊C8×C61—22no—
46C4×C8×C61—24no—
47C4×C8×C61—22no—
48C2×Q8×C61—22no—
49C2×Q8×C61—22no—
50C2×Q8×C61D812yes—
51C2×Q8×C61SD1612yes—
52C22×C4×C61C22⋊C412yes—
53C22×C4×C61C22⋊C412yes—
54C22×C4×C61C22×C411yescharacteristic
55C22×C4×C61C2×D411yescharacteristic
56C22×C4×C61C2×D411yescharacteristic
57C22×Dic61—22no—
58C22×Dic61—22no—
59C2×Dic122—42no—
60C2×Dic122—41no—
61C2×Dic122—41no—
62C2×Dic122—42no—
63C2×C8×C61—24no—
64C4⋊C4×C61—24no—
65C4⋊C4×C61—22no—
66C42×C61—22no—
67C42×C61—22no—
68C42×C61C2×D412yes—
69C42×C61#4112yes—
70C4⋊Dic61—24no—
71C4⋊Dic61—24no—
72C4⋊Dic61—41no—
73C4⋊Dic61—41no—
74#11758196—48no—
75C4×Dic61—41no—
76C4×Dic61—41no—
77#11758194—42no—
78#11758194—42no—
79C2×#92418—42no—
80C23×C61C2×C22⋊C411yescharacteristic
81Q8×C61—24no—
82Q8×C61—24no—
83C2×C4×C61—22no—
84C2×C4×C61—22no—
85C2×C4×C61—22no—
86C2×C4×C61—22no—
87C2×C4×C61—41no—
88C2×C4×C61—42no—
89C2×C4×C61#10214yes—
90C2×C4×C61C4×D412yes—
91C2×C4×C61#12011yescharacteristic
92C2×C4×C61#12112yes—
93C2×C4×C61#12311yescharacteristic
94C2×C4×C61C2×D811yescharacteristic
95C2×C4×C61C2×SD1611yescharacteristic
96C2×C4×C61#13512yes—
97C2×Dic61—24no—
98C2×Dic61—42no—
99C2×Dic61—42no—
100C2×Dic61—42no—
101C2×Dic61—42no—
102C2×Dic61—42no—
103Dic122—82no—
104Dic122—82no—
105C8×C61—44no—
106#92418—82no—
107#9394—611nomaximal, Sylow
108C22×C61—21no—
109C22×C61—21no—
110C22×C61#38611yescharacteristic
111C22×C61C2×#10211yescharacteristic
112C22×C61#41611yescharacteristic
113C4×C61—21no—
114C4×C61—24no—
115C4×C61—22no—
116C4×C61—42no—
117C4×C61#45612yes—
118C4×C61#46512yes—
119C4×C61#46612yes—
120Dic61—44no—
121Dic61—82no—
122#2982D6111yescharacteristic
123#2546—611no—
124#1801—611no—
125#1546—612no—
126#1303—612no—
127C2×C61—21no—
128C2×C61—21no—
129C2×C61#188611yescharacteristic
130C2×C61#189311yescharacteristic
131C2×C61#191511yescharacteristic
132C2×C4⋊Q8—611no—
133C2×C4⋊Q8—1221no—
134C2×C4×Q8C2×D6111yescharacteristic
135C8×Q8—24no—
136#431—22no—
137#431C2×D6112yes—
138#423—612no—
139C2×#101—1221no—
140#398—614no—
141#391—1221no—
142#389—1222no—
143C4×C4⋊C4—611no—
144#343—1221no—
145#332—1224no—
146C61#939411yescharacteristic, complemented, Sylow
147C22×Q8—1221no—
148C22×Q8D24411yescharacteristic
149C2×M16—1222no—
150C4⋊Q8—1222no—
151C4⋊Q8—1222no—
152C4⋊Q8—2442no—
153C4⋊Q8—2442no—
154C4×Q8—22no—
155C4×Q8—22no—
156C2×C4⋊C4—612no—
157C2×C4⋊C4—1221no—
158C2×C4⋊C4—1224no—
159C2×C4⋊C4—1221no—
160C2×C4⋊C4C4×D6112yes—
161C2×C4⋊C4D24411yescharacteristic
162C2×C42—1221no—
163C2×C42C22⋊D6112yes—
164C2×C42C22×D6111yescharacteristic
165C4⋊C8—24no—
166C4⋊C8—1222no—
167C4⋊C8—1222no—
168C4⋊C8C22⋊D6114yes—
169#101—2442no—
170C22⋊C8—22no—
171C4×C8—24no—
172C4×C8—22no—
173#95—612no—
174#95—1224no—
175C2×Q8—22no—
176C2×Q8—22no—
177C2×Q8—2442no—
178C2×Q8—2441no—
179C2×Q8—2441no—
180C2×Q8—2442no—
181C2×Q8#1175819012yes—
182C2×Q8D48812yes—
183C22×C4—1222no—
184C22×C4—1222no—
185C22×C4#1175819812yes—
186C22×C4#1175819812yes—
187C22×C4C2×C4×D6111yescharacteristic
188C22×C4C2×D24411yescharacteristic
189C22×C4C2×C22⋊D6111yescharacteristic
190M16—2442no—
191M16—2442no—
192C2×C8—24no—
193C2×C8—2442no—
194C4⋊C4—24no—
195C4⋊C4—22no—
196C4⋊C4—1224no—
197C4⋊C4—1224no—
198C4⋊C4—2448no—
199C4⋊C4—2441no—
200C4⋊C4—2441no—
201C42—22no—
202C42—22no—
203C42—2441no—
204C42—2441no—
205C42#1175822212yes—
206C42C2×C22⋊D6112yes—
207C23C2×#1175819811yescharacteristic
208Q8—24no—
209Q8—24no—
210Q8—4882no—
211Q8—4882no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—41no—
217C2×C4—42no—
218C2×C4—1224no—
219C2×C4—2442no—
220C2×C4—2442no—
221C2×C4—2442no—
222C2×C4—2442no—
223C2×C4—2442no—
224C2×C4#1451969914yes—
225C2×C4C4×C22⋊D6112yes—
226C2×C4#1451974611yescharacteristic
227C2×C4#1451975112yes—
228C2×C4#1451976011yescharacteristic
229C2×C4C2×D48811yescharacteristic
230C2×C4C2×#1175819011yescharacteristic
231C2×C4#1451979912yes—
232C8—44no—
233C8—4882no—
234C22—21no—
235C22—21no—
236C22#1683964111yescharacteristic
237C22C2×#1451969911yescharacteristic
238C22#1683975911yescharacteristic
239C4—21no—
240C4—24no—
241C4—22no—
242C4—42no—
243C4—4882no—
244C4—2444no—
245C4#1683994512yes—
246C4#1683999112yes—
247C4#1683999812yes—
248C2—21no—
249C2—21no—
250C2#2144621211yescharacteristic
251C2#2144624711yescharacteristic
252C2#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#9394
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
146. C61#9394semidirect

Maximal subgroups

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

subgroupindex
#214508042
#214458152
#214444902
#214437212
C61×#29822
#939461