Finite Group Databasebeta

← #29577424

Subgroups — #29577424

Order 15616.

486 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 123 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#21445815C211yesmaximal, characteristic
3#21444491C212yesmaximal
4#21443722C212yesmaximal
5C61×#2546C211yesmaximal, characteristic
6#16839893—24no—
7#16839819—22no—
8#16839815C2212yes—
9#16839786C2212yes—
10C2×#14519696—21no—
11#16839531—21no—
12#16839508—24no—
13C2×C4⋊Q8×C61—21no—
14C2×C4⋊Q8×C61C2211yescharacteristic
15C2×C4×Q8×C61C2211yescharacteristic
16C61×#398C414yes—
17C61×#391—21no—
18C61×#389—22no—
19C4×C4⋊C4×C61C2211yescharacteristic
20C2×#11758194—22no—
21C4⋊#92418—24no—
22C4⋊#92418—22no—
23C4⋊#92418—22no—
24C4⋊#92418D414yes—
25#14519696—42no—
26C22⋊#92418—22no—
27#14519688—24no—
28C4×#92418—22no—
29C22×Q8×C61—21no—
30C22×Q8×C61D411yescharacteristic
31C4⋊Q8×C61—22no—
32C4⋊Q8×C61—22no—
33C4⋊Q8×C61—44no—
34C4×Q8×C61—22no—
35C4×Q8×C61—22no—
36C2×C4⋊C4×C61—21no—
37C2×C4⋊C4×C61—24no—
38C2×C4⋊C4×C61—21no—
39C2×C4⋊C4×C61C2×C412yes—
40C2×C4⋊C4×C61C2×C412yes—
41C2×C4⋊C4×C61D411yescharacteristic
42C2×C42×C61—21no—
43C2×C42×C61D412yes—
44C2×C42×C61C2311yescharacteristic
45#95×C61—24no—
46#95×C61C2×C412yes—
47C2×Q8×C61—22no—
48C2×Q8×C61—22no—
49C2×Q8×C61—21no—
50C2×Q8×C61—21no—
51C2×Q8×C61—42no—
52C2×Q8×C61—42no—
53C2×Q8×C61—41no—
54C2×Q8×C61—41no—
55C22×C4×C61—22no—
56C22×C4×C61—22no—
57C22×C4×C61C22⋊C412yes—
58C22×C4×C61C22⋊C412yes—
59C22×C4×C61C22×C411yescharacteristic
60C22×C4×C61C2×D411yescharacteristic
61C22×C4×C61C2×D411yescharacteristic
62C4⋊C4×C61—24no—
63C4⋊C4×C61—24no—
64C4⋊C4×C61—22no—
65C4⋊C4×C61—24no—
66C4⋊C4×C61—48no—
67C4⋊C4×C61—41no—
68C4⋊C4×C61—41no—
69C42×C61—22no—
70C42×C61—22no—
71C42×C61—42no—
72C42×C61C2×D412yes—
73C42×C61#4112yes—
74#11758194—42no—
75#11758194—42no—
76C2×#92418—24no—
77C2×#92418—42no—
78C23×C61C2×C22⋊C411yescharacteristic
79Q8×C61—42no—
80Q8×C61—42no—
81Q8×C61—82no—
82Q8×C61—82no—
83C2×C4×C61—22no—
84C2×C4×C61—24no—
85C2×C4×C61—22no—
86C2×C4×C61—22no—
87C2×C4×C61—22no—
88C2×C4×C61—22no—
89C2×C4×C61—41no—
90C2×C4×C61—42no—
91C2×C4×C61—42no—
92C2×C4×C61—42no—
93C2×C4×C61—42no—
94C2×C4×C61—42no—
95C2×C4×C61—42no—
96C2×C4×C61C4×D412yes—
97C2×C4×C61#12011yescharacteristic
98C2×C4×C61#12112yes—
99C2×C4×C61#12311yescharacteristic
100C2×C4×C61AGL(1,ℤ/8)12yes—
101C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
102C2×C4×C61#13711yescharacteristic
103#92418—44no—
104#92418—82no—
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—44no—
114C4×C61—42no—
115C4×C61—42no—
116C4×C61—82no—
117C4×C61#45612yes—
118C4×C61#46812yes—
119C4×C61#46912yes—
120#2983—611no—
121#2546D6111yescharacteristic
122#1801—611no—
123#1546—612no—
124#1303—612no—
125C2×C61—21no—
126C2×C61—21no—
127C2×C61#188611yescharacteristic
128C2×C61#189511yescharacteristic
129C2×C61#191511yescharacteristic
130C2×C4⋊Q8—21no—
131C2×C4⋊Q8C2×D6111yescharacteristic
132C2×C4×Q8C2×D6111yescharacteristic
133#446—1224no—
134#432—1222no—
135#431—612no—
136#423—612no—
137C2×#101—1221no—
138#398Dic6114yes—
139#391—21no—
140#389—22no—
141C4×C4⋊C4C2×D6111yescharacteristic
142#343—1221no—
143#332—1224no—
144C61#940211yescharacteristic, complemented, Sylow
145C22×Q8—21no—
146C22×Q8C22⋊D6111yescharacteristic
147C2×M16—1222no—
148C4⋊Q8—22no—
149C4⋊Q8—22no—
150C4⋊Q8—44no—
151C4×Q8—22no—
152C4×Q8—22no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—24no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4C2×Dic6112yes—
157C2×C4⋊C4C2×Dic6112yes—
158C2×C4⋊C4C22⋊D6111yescharacteristic
159C2×C42—21no—
160C2×C42C22⋊D6112yes—
161C2×C42C22×D6111yescharacteristic
162C4⋊C8—614no—
163C4⋊C8—1224no—
164C4⋊C8—1222no—
165C4⋊C8—1222no—
166#101—2442no—
167C22⋊C8—1222no—
168#97—1224no—
169C4×C8—1222no—
170#95—24no—
171#95C2×Dic6112yes—
172C2×Q8—22no—
173C2×Q8—21no—
174C2×Q8—22no—
175C2×Q8—21no—
176C2×Q8—42no—
177C2×Q8—41no—
178C2×Q8—42no—
179C2×Q8—41no—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4C22⋊Dic6112yes—
183C22×C4C22⋊Dic6112yes—
184C22×C4C22×Dic6111yescharacteristic
185C22×C4C2×C22⋊D6111yescharacteristic
186C22×C4C2×C22⋊D6111yescharacteristic
187M16—2442no—
188M16—2442no—
189C2×C8—1224no—
190C2×C8—2442no—
191C4⋊C4—24no—
192C4⋊C4—24no—
193C4⋊C4—22no—
194C4⋊C4—24no—
195C4⋊C4—48no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C42—22no—
199C42—22no—
200C42—42no—
201C42D4×D6112yes—
202C42#1175822412yes—
203C23C2×C22⋊Dic6111yescharacteristic
204Q8—42no—
205Q8—42no—
206Q8—82no—
207Q8—82no—
208C2×C4—22no—
209C2×C4—24no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—41no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4D4×Dic6112yes—
222C2×C4#1451974511yescharacteristic
223C2×C4#1451974912yes—
224C2×C4#1451975811yescharacteristic
225C2×C4#1451980211yescharacteristic
226C2×C4#1451980312yes—
227C2×C4#1451980711yescharacteristic
228C8—4882no—
229C8—2444no—
230C22—21no—
231C22—21no—
232C22#1683964211yescharacteristic
233C22#1683976311yescharacteristic
234C22#1683976711yescharacteristic
235C4—21no—
236C4—22no—
237C4—44no—
238C4—42no—
239C4—42no—
240C4—82no—
241C4#1683994412yes—
242C4#1684000612yes—
243C4#1684001312yes—
244C2—21no—
245C2—21no—
246C2#2144621311yescharacteristic
247C2#2144625811yescharacteristic
248C2#2144637211yescharacteristic
subgroupG/H
centerC22#16839642
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#2546C2
socleC22×C61#386
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenter#2546D61
hypocenterC61#9402
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2546

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
#214458152
#214444912
#214437222
C61×#25462
#940261