Finite Group Databasebeta

← #29577421

Subgroups — #29577421

Order 15616.

486 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 115 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#21454904C211yesmaximal, characteristic
2#21450804C211yesmaximal, characteristic
3#21444492C212yesmaximal
4#21443720C212yesmaximal
5C61×#1801C211yesmaximal, characteristic
6C2×#14519777C2211yescharacteristic
7C2×#14519775—21no—
8#16839893—24no—
9#16839819—22no—
10#16839815C2212yes—
11#16839692C414yes—
12#16839667—21no—
13#16839660—22no—
14C4×C4⋊Dic61C2211yescharacteristic
15#16839509—24no—
16C2×C4×Q8×C61C2211yescharacteristic
17C61×#423C2212yes—
18C2×#101×C61—21no—
19C61×#343—21no—
20C22×Dic122—21no—
21#14519777—22no—
22#14519777—22no—
23#14519775—44no—
24C2×C4⋊Dic61—21no—
25C2×C4⋊Dic61—21no—
26C2×C4⋊Dic61C2×C412yes—
27C2×#11758196—24no—
28C2×C4×Dic61—21no—
29C4⋊#92418—24no—
30C4⋊#92418D414yes—
31C22⋊#92418—22no—
32#14519688—24no—
33C4×#92418—22no—
34#14519684—24no—
35#14519684C2×C412yes—
36C22×Q8×C61D411yescharacteristic
37C2×M16×C61—22no—
38C4×Q8×C61—22no—
39C4×Q8×C61—22no—
40C2×C4⋊C4×C61C2×C412yes—
41C2×C4⋊C4×C61D411yescharacteristic
42C2×C42×C61D412yes—
43C2×C42×C61C2311yescharacteristic
44C4⋊C8×C61—22no—
45C4⋊C8×C61—22no—
46#101×C61—42no—
47C2×Q8×C61—22no—
48C2×Q8×C61—21no—
49C2×Q8×C61—22no—
50C2×Q8×C61—21no—
51C22×C4×C61C22⋊C412yes—
52C22×C4×C61C22⋊C412yes—
53C22×C4×C61C22×C411yescharacteristic
54C22×C4×C61C2×D411yescharacteristic
55C22×C4×C61C2×D411yescharacteristic
56C22×Dic61—22no—
57C22×Dic61—22no—
58C2×Dic122—42no—
59C2×Dic122—41no—
60C2×Dic122—42no—
61C2×Dic122—41no—
62M16×C61—42no—
63M16×C61—42no—
64C2×C8×C61—42no—
65C4⋊C4×C61—24no—
66C4⋊C4×C61—22no—
67C42×C61—22no—
68C42×C61—22no—
69C42×C61C2×D412yes—
70C42×C61#4112yes—
71C4⋊Dic61—24no—
72C4⋊Dic61—24no—
73C4⋊Dic61—41no—
74C4⋊Dic61—41no—
75#11758196—48no—
76C4×Dic61—42no—
77C2×#92418—24no—
78C23×C61C2×C22⋊C411yescharacteristic
79Q8×C61—42no—
80Q8×C61—42no—
81C2×C4×C61—22no—
82C2×C4×C61—22no—
83C2×C4×C61—22no—
84C2×C4×C61—22no—
85C2×C4×C61—22no—
86C2×C4×C61—41no—
87C2×C4×C61—42no—
88C2×C4×C61C4×D412yes—
89C2×C4×C61#12011yescharacteristic
90C2×C4×C61#12112yes—
91C2×C4×C61#12311yescharacteristic
92C2×C4×C61AGL(1,ℤ/8)12yes—
93C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
94C2×C4×C61#13711yescharacteristic
95C2×Dic61—24no—
96C2×Dic61—42no—
97C2×Dic61—42no—
98C2×Dic61—42no—
99C2×Dic61—42no—
100C2×Dic61—42no—
101Dic122—82no—
102Dic122—82no—
103C8×C61—82no—
104#92418—44no—
105#9402—611nomaximal, Sylow
106C22×C61—21no—
107C22×C61—21no—
108C22×C61#38611yescharacteristic
109C22×C61#41711yescharacteristic
110C22×C61#41811yescharacteristic
111C4×C61—21no—
112C4×C61—22no—
113C4×C61—42no—
114C4×C61—42no—
115C4×C61#45612yes—
116C4×C61#46812yes—
117C4×C61#46912yes—
118Dic61—44no—
119Dic61—82no—
120#2983—611no—
121#2546—611no—
122#1801D6111yescharacteristic
123#1546—612no—
124#1303—612no—
125C2×C61—21no—
126C2×C61—21no—
127C2×C61#188611yescharacteristic
128C2×C61#189511yescharacteristic
129C2×C61#191511yescharacteristic
130C2×C4⋊Q8—611no—
131C2×C4⋊Q8—1221no—
132C2×C4×Q8C2×D6111yescharacteristic
133#446—1224no—
134#432—1222no—
135#431—612no—
136#423C2×D6112yes—
137C2×#101—21no—
138#398—614no—
139#391—1221no—
140#389—1222no—
141C4×C4⋊C4—611no—
142#343—21no—
143#332—1224no—
144C61#940211yescharacteristic, complemented, Sylow
145C22×Q8—1221no—
146C22×Q8C22⋊D6111yescharacteristic
147C2×M16—22no—
148C4⋊Q8—1222no—
149C4⋊Q8—1222no—
150C4⋊Q8—2444no—
151C4×Q8—22no—
152C4×Q8—22no—
153C2×C4⋊C4—612no—
154C2×C4⋊C4—1221no—
155C2×C4⋊C4—1224no—
156C2×C4⋊C4—1221no—
157C2×C4⋊C4C4×D6112yes—
158C2×C4⋊C4C22⋊D6111yescharacteristic
159C2×C42—1221no—
160C2×C42D24412yes—
161C2×C42C22×D6111yescharacteristic
162C4⋊C8—22no—
163C4⋊C8—22no—
164C4⋊C8—614no—
165C4⋊C8—1224no—
166#101—42no—
167C22⋊C8—1222no—
168#97—1224no—
169C4×C8—1222no—
170#95—612no—
171#95—1224no—
172C2×Q8—21no—
173C2×Q8—22no—
174C2×Q8—22no—
175C2×Q8—21no—
176C2×Q8—2441no—
177C2×Q8—2442no—
178C2×Q8—2442no—
179C2×Q8—2441no—
180C22×C4—1222no—
181C22×C4—1222no—
182C22×C4#1175819812yes—
183C22×C4#1175819812yes—
184C22×C4C2×C4×D6111yescharacteristic
185C22×C4C2×D24411yescharacteristic
186C22×C4C2×C22⋊D6111yescharacteristic
187M16—42no—
188M16—42no—
189C2×C8—42no—
190C2×C8—1224no—
191C4⋊C4—24no—
192C4⋊C4—22no—
193C4⋊C4—1224no—
194C4⋊C4—1224no—
195C4⋊C4—2448no—
196C4⋊C4—2441no—
197C4⋊C4—2441no—
198C42—22no—
199C42—22no—
200C42—2442no—
201C42D4×D6112yes—
202C42#1175822412yes—
203C23C2×#1175819811yescharacteristic
204Q8—42no—
205Q8—42no—
206Q8—4882no—
207Q8—4882no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—1224no—
216C2×C4—2442no—
217C2×C4—2442no—
218C2×C4—2442no—
219C2×C4—2442no—
220C2×C4—2442no—
221C2×C4#1451973712yes—
222C2×C4#1451974711yescharacteristic
223C2×C4#1451974912yes—
224C2×C4#1451976111yescharacteristic
225C2×C4#1451980212yes—
226C2×C4#1451980311yescharacteristic
227C2×C4#1451980811yescharacteristic
228C8—82no—
229C8—2444no—
230C22—21no—
231C22—21no—
232C22#1683963911yescharacteristic
233C22#1683976111yescharacteristic
234C22#1683976611yescharacteristic
235C4—21no—
236C4—22no—
237C4—42no—
238C4—42no—
239C4—4882no—
240C4—2444no—
241C4#1683994712yes—
242C4#1684001012yes—
243C4#1684001312yes—
244C2—21no—
245C2—21no—
246C2#2144621011yescharacteristic
247C2#2144625511yescharacteristic
248C2#2144636911yescharacteristic
subgroupG/H
centerC22#16839639
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1801C2
socleC22×C61#386
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1801D61
hypocenterC61#9402
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
144. C61#9402semidirect

Maximal subgroups

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

subgroupindex
#214549042
#214508042
#214444922
#214437202
C61×#18012
#940261