Finite Group Databasebeta

← #29577698

Subgroups — #29577698

Order 15616.

468 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 111 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#21444545C212yesmaximal
3#21444163C211yesmaximal, characteristic
4#21443675C212yesmaximal
5C61×#2546C211yesmaximal, characteristic
6#16839893—24no—
7#16839819—21no—
8#16839819C2212yes—
9#16839819C2212yes—
10#16839815—21no—
11#16839511—24no—
12#16839488—21no—
13#16839488—21no—
14C2×C4⋊Q8×C61C412yes—
15C2×C4⋊Q8×C61C2211yescharacteristic
16C2×C4×Q8×C61C2211yescharacteristic
17C61×#398—21no—
18C61×#398—21no—
19C61×#391C412yes—
20C61×#389—21no—
21C61×#389—21no—
22C4×C4⋊C4×C61C2211yescharacteristic
23C4⋊#92418—22no—
24C4⋊#92418—22no—
25C4⋊#92418—22no—
26C4⋊#92418D414yes—
27C22⋊#92418—22no—
28C22⋊#92418—22no—
29#14519688—22no—
30#14519688—22no—
31#14519688—22no—
32C4×#92418—22no—
33C22×Q8×C61C2×C412yes—
34C22×Q8×C61C2×C411yescharacteristic
35C4⋊Q8×C61—22no—
36C4⋊Q8×C61—22no—
37C4⋊Q8×C61—44no—
38C4×Q8×C61—22no—
39C4×Q8×C61—22no—
40C2×C4⋊C4×C61—21no—
41C2×C4⋊C4×C61—22no—
42C2×C4⋊C4×C61—22no—
43C2×C4⋊C4×C61—21no—
44C2×C4⋊C4×C61—21no—
45C2×C4⋊C4×C61C2×C411yescharacteristic
46C2×C4⋊C4×C61D411yescharacteristic
47C2×C4⋊C4×C61D411yescharacteristic
48C2×C42×C61C2×C412yes—
49C2×C42×C61D411yescharacteristic
50C2×C42×C61D411yescharacteristic
51C2×C42×C61C2311yescharacteristic
52#95×C61—22no—
53#95×C61—22no—
54#95×C61—21no—
55C2×Q8×C61—22no—
56C2×Q8×C61—22no—
57C2×Q8×C61—24no—
58C2×Q8×C61—41no—
59C2×Q8×C61—42no—
60C2×Q8×C61—42no—
61C22×C4×C61—22no—
62C22×C4×C61—22no—
63C22×C4×C61C22⋊C411yescharacteristic
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22×C411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C4⋊C4×C61—24no—
71C4⋊C4×C61—22no—
72C4⋊C4×C61—22no—
73C4⋊C4×C61—22no—
74C4⋊C4×C61—44no—
75C4⋊C4×C61—44no—
76C4⋊C4×C61—41no—
77C4⋊C4×C61—42no—
78C4⋊C4×C61—41no—
79C42×C61—21no—
80C42×C61—21no—
81C42×C61—21no—
82C42×C61—21no—
83C42×C61—42no—
84C42×C61C2×D412yes—
85C42×C61#4112yes—
86C2×#92418—24no—
87C2×#92418—42no—
88C23×C61C2×C22⋊C411yescharacteristic
89Q8×C61—44no—
90Q8×C61—84no—
91C2×C4×C61—21no—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—22no—
96C2×C4×C61—24no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—41no—
103C2×C4×C61—42no—
104C2×C4×C61—42no—
105C2×C4×C61—41no—
106C2×C4×C61—41no—
107C2×C4×C61—42no—
108C2×C4×C61—42no—
109C2×C4×C61—42no—
110C2×C4×C61#10012yes—
111C2×C4×C61C4×D412yes—
112C2×C4×C61#12011yescharacteristic
113C2×C4×C61#12112yes—
114C2×C4×C61#12311yescharacteristic
115#92418—44no—
116#92418—82no—
117#9452—611nomaximal, Sylow
118C22×C61—21no—
119C22×C61—21no—
120C22×C61#38611yescharacteristic
121C22×C61C2×#10011yescharacteristic
122C22×C61#41311yescharacteristic
123C4×C61—21no—
124C4×C61—22no—
125C4×C61—22no—
126C4×C61—22no—
127C4×C61—44no—
128C4×C61—41no—
129C4×C61—41no—
130C4×C61—41no—
131C4×C61—82no—
132C4×C61#45612yes—
133#2983—611no—
134#2546D6111yescharacteristic
135#1558—612no—
136#1467—611no—
137#1285—612no—
138C2×C61—21no—
139C2×C61—21no—
140C2×C61#188611yescharacteristic
141C2×C61#190011yescharacteristic
142C2×C61#190911yescharacteristic
143C2×C4⋊Q8Dic6112yes—
144C2×C4⋊Q8C2×D6111yescharacteristic
145C2×C4×Q8C2×D6111yescharacteristic
146#446—1224no—
147#432—612no—
148#432—612no—
149#432—1221no—
150#431—1221no—
151#398—21no—
152#398—21no—
153#391Dic6112yes—
154#389—21no—
155#389—21no—
156C4×C4⋊C4C2×D6111yescharacteristic
157#333—1224no—
158#324—1221no—
159#324—1221no—
160C61#945211yescharacteristic, complemented, Sylow
161C22×Q8C2×Dic6112yes—
162C22×Q8C2×Dic6111yescharacteristic
163C4⋊Q8—22no—
164C4⋊Q8—22no—
165C4⋊Q8—44no—
166C4×Q8—22no—
167C4×Q8—22no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4C2×Dic6111yescharacteristic
174C2×C4⋊C4C22⋊D6111yescharacteristic
175C2×C4⋊C4C22⋊D6111yescharacteristic
176C2×C42C2×Dic6112yes—
177C2×C42C22⋊D6111yescharacteristic
178C2×C42C22⋊D6111yescharacteristic
179C2×C42C22×D6111yescharacteristic
180C4⋊C8—614no—
181C4⋊C8—1222no—
182C4⋊C8—1222no—
183C4⋊C8—1222no—
184C22⋊C8—1222no—
185C22⋊C8—1222no—
186#97—1222no—
187#97—1222no—
188#97—1222no—
189C4×C8—1222no—
190#95—22no—
191#95—22no—
192#95—21no—
193C2×Q8—22no—
194C2×Q8—22no—
195C2×Q8—24no—
196C2×Q8—41no—
197C2×Q8—42no—
198C2×Q8—42no—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4C22⋊Dic6111yescharacteristic
202C22×C4C22⋊Dic6111yescharacteristic
203C22×C4C22⋊Dic6111yescharacteristic
204C22×C4C22⋊Dic6111yescharacteristic
205C22×C4C22×Dic6111yescharacteristic
206C22×C4C2×C22⋊D6111yescharacteristic
207C22×C4C2×C22⋊D6111yescharacteristic
208C2×C8—1224no—
209C2×C8—2442no—
210C4⋊C4—24no—
211C4⋊C4—22no—
212C4⋊C4—22no—
213C4⋊C4—22no—
214C4⋊C4—44no—
215C4⋊C4—44no—
216C4⋊C4—41no—
217C4⋊C4—42no—
218C4⋊C4—41no—
219C42—21no—
220C42—21no—
221C42—21no—
222C42—21no—
223C42—42no—
224C42D4×D6112yes—
225C42#1175822412yes—
226C23C2×C22⋊Dic6111yescharacteristic
227Q8—44no—
228Q8—84no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—24no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4#1451969412yes—
249C2×C4D4×Dic6112yes—
250C2×C4#1451974511yescharacteristic
251C2×C4#1451974912yes—
252C2×C4#1451975811yescharacteristic
253C8—4882no—
254C8—2444no—
255C22—21no—
256C22—21no—
257C22#1683964211yescharacteristic
258C22C2×#1451969411yescharacteristic
259C22#1683974611yescharacteristic
260C4—21no—
261C4—22no—
262C4—22no—
263C4—22no—
264C4—44no—
265C4—41no—
266C4—41no—
267C4—41no—
268C4—82no—
269C4#1683994412yes—
270C2—21no—
271C2—21no—
272C2#2144621311yescharacteristic
273C2#2144628311yescharacteristic
274C2#2144634211yescharacteristic
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#9452
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
160. C61#9452semidirect

Maximal subgroups

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

subgroupindex
#214549042
#214445452
#214441632
#214436752
C61×#25462
#945261