Finite Group Databasebeta

← #29575534

Subgroups — #29575534

Order 15616.

474 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 127 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#21444214C212yesmaximal
3#21444143C211yesmaximal, characteristic
4#21443648C212yesmaximal
5C61×#2327C211yesmaximal, characteristic
6#16839893—24no—
7#16839819—22no—
8#16839815C2212yes—
9#16839815C2212yes—
10Q8⋊#92418—24no—
11#16839488—22no—
12C2×C4⋊Q8×C61C411yescharacteristic
13C2×C4×Q8×C61C2211yescharacteristic
14C2×C4×Q8×C61C2211yescharacteristic
15C61×#391C411yescharacteristic
16C61×#391C411yescharacteristic
17C61×#387—22no—
18C61×#387—22no—
19C61×#382C411yescharacteristic
20C61×#376C2211yescharacteristic
21C4⋊#92418—24no—
22C4⋊#92418—22no—
23C4⋊#92418—22no—
24C22⋊#92418—22no—
25C22⋊#92418—22no—
26#14519688—24no—
27C4×#92418—22no—
28C4×#92418D414yes—
29C22×Q8×C61C2×C411yescharacteristic
30C22×Q8×C61C2×C411yescharacteristic
31C4⋊Q8×C61—22no—
32C4⋊Q8×C61—22no—
33C4×Q8×C61—22no—
34C4×Q8×C61—22no—
35C4×Q8×C61—22no—
36C4×Q8×C61—22no—
37C2×C4⋊C4×C61—22no—
38C2×C4⋊C4×C61—21no—
39C2×C4⋊C4×C61C2×C411yescharacteristic
40C2×C4⋊C4×C61C2×C411yescharacteristic
41C2×C4⋊C4×C61D412yes—
42C2×C42×C61—21no—
43C2×C42×C61C2×C411yescharacteristic
44C2×C42×C61C2×C411yescharacteristic
45C2×C42×C61D412yes—
46C2×C42×C61C2311yescharacteristic
47#95×C61—22no—
48#95×C61—22no—
49#95×C61—22no—
50#95×C61—21no—
51#95×C61—21no—
52C2×Q8×C61—22no—
53C2×Q8×C61—21no—
54C2×Q8×C61—21no—
55C2×Q8×C61—21no—
56C2×Q8×C61—22no—
57C2×Q8×C61—22no—
58C2×Q8×C61—22no—
59C2×Q8×C61M1612yes—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61C22⋊C412yes—
65C22×C4×C61C22⋊C412yes—
66C22×C4×C61C22×C411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C4⋊C4×C61—28no—
70C4⋊C4×C61—22no—
71C4⋊C4×C61—24no—
72C4⋊C4×C61—22no—
73C4⋊C4×C61—41no—
74C4⋊C4×C61—41no—
75C42×C61—22no—
76C42×C61—22no—
77C42×C61—21no—
78C42×C61—22no—
79C42×C61—42no—
80C42×C61M1612yes—
81C42×C61C2×D412yes—
82C42×C61#4112yes—
83C2×#92418—24no—
84C2×#92418—42no—
85C23×C61C2×C22⋊C411yescharacteristic
86Q8×C61—24no—
87Q8×C61—42no—
88Q8×C61—42no—
89Q8×C61—42no—
90C2×C4×C61—22no—
91C2×C4×C61—22no—
92C2×C4×C61—22no—
93C2×C4×C61—22no—
94C2×C4×C61—22no—
95C2×C4×C61—22no—
96C2×C4×C61—41no—
97C2×C4×C61—41no—
98C2×C4×C61—41no—
99C2×C4×C61—41no—
100C2×C4×C61—41no—
101C2×C4×C61—41no—
102C2×C4×C61—42no—
103C2×C4×C61—41no—
104C2×C4×C61—41no—
105C2×C4×C61—42no—
106C2×C4×C61—41no—
107C2×C4×C61—41no—
108C2×C4×C61C4×D412yes—
109C2×C4×C61#12011yescharacteristic
110C2×C4×C61#12112yes—
111C2×C4×C61#12311yescharacteristic
112C2×C4×C61C2×M1611yescharacteristic
113C2×C4×C61C2×M1611yescharacteristic
114C2×C4×C61#13112yes—
115#92418—44no—
116#92418—82no—
117#9104—611nomaximal, Sylow
118C22×C61—21no—
119C22×C61—21no—
120C22×C61#38611yescharacteristic
121C22×C61#40711yescharacteristic
122C22×C61#40811yescharacteristic
123C4×C61—22no—
124C4×C61—21no—
125C4×C61—21no—
126C4×C61—42no—
127C4×C61—42no—
128C4×C61—42no—
129C4×C61—42no—
130C4×C61—81no—
131C4×C61—81no—
132C4×C61#43512yes—
133C4×C61#43612yes—
134#2983—611no—
135#2327D6111yescharacteristic
136#1479—612no—
137#1461—611no—
138#1274—612no—
139C2×C61—21no—
140C2×C61—21no—
141C2×C61#187011yescharacteristic
142C2×C61#190911yescharacteristic
143C2×C61#191211yescharacteristic
144C2×C4⋊Q8Dic6111yescharacteristic
145C2×C4×Q8C2×D6111yescharacteristic
146C2×C4×Q8C2×D6111yescharacteristic
147#446—1224no—
148#432—1222no—
149#431—612no—
150#431—612no—
151#391Dic6111yescharacteristic
152#391Dic6111yescharacteristic
153#387—22no—
154#387—22no—
155#382Dic6111yescharacteristic
156#376C2×D6111yescharacteristic
157Q8⋊C8—1224no—
158#324—1222no—
159C61#910411yescharacteristic, complemented, Sylow
160C22×Q8C2×Dic6111yescharacteristic
161C22×Q8C2×Dic6111yescharacteristic
162C4⋊Q8—22no—
163C4⋊Q8—22no—
164C4×Q8—22no—
165C4×Q8—22no—
166C4×Q8—22no—
167C4×Q8—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4C2×Dic6111yescharacteristic
171C2×C4⋊C4C2×Dic6111yescharacteristic
172C2×C4⋊C4C22⋊D6112yes—
173C2×C42—21no—
174C2×C42C2×Dic6111yescharacteristic
175C2×C42C2×Dic6111yescharacteristic
176C2×C42C22⋊D6112yes—
177C2×C42C22×D6111yescharacteristic
178C4⋊C8—1224no—
179C4⋊C8—1222no—
180C4⋊C8—1222no—
181C22⋊C8—1222no—
182C22⋊C8—1222no—
183#97—1224no—
184C4×C8—614no—
185C4×C8—1222no—
186#95—22no—
187#95—22no—
188#95—22no—
189#95—21no—
190#95—21no—
191C2×Q8—22no—
192C2×Q8—21no—
193C2×Q8—21no—
194C2×Q8—21no—
195C2×Q8—22no—
196C2×Q8—22no—
197C2×Q8—22no—
198C2×Q8#1175819412yes—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4C22⋊Dic6112yes—
204C22×C4C22⋊Dic6112yes—
205C22×C4C22×Dic6111yescharacteristic
206C22×C4C2×C22⋊D6111yescharacteristic
207C22×C4C2×C22⋊D6111yescharacteristic
208C2×C8—1224no—
209C2×C8—2442no—
210C4⋊C4—28no—
211C4⋊C4—22no—
212C4⋊C4—24no—
213C4⋊C4—22no—
214C4⋊C4—41no—
215C4⋊C4—41no—
216C42—22no—
217C42—22no—
218C42—21no—
219C42—22no—
220C42—42no—
221C42#1175819412yes—
222C42D4×D6112yes—
223C42#1175822412yes—
224C23C2×C22⋊Dic6111yescharacteristic
225Q8—24no—
226Q8—42no—
227Q8—42no—
228Q8—42no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—42no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4D4×Dic6112yes—
248C2×C4#1451974511yescharacteristic
249C2×C4#1451974912yes—
250C2×C4#1451975811yescharacteristic
251C2×C4C2×#1175819411yescharacteristic
252C2×C4C2×#1175819411yescharacteristic
253C2×C4#1451978412yes—
254C8—4882no—
255C8—2444no—
256C22—21no—
257C22—21no—
258C22#1683964211yescharacteristic
259C22#1683972611yescharacteristic
260C22#1683972911yescharacteristic
261C4—22no—
262C4—21no—
263C4—21no—
264C4—42no—
265C4—42no—
266C4—42no—
267C4—42no—
268C4—81no—
269C4—81no—
270C4#1683983412yes—
271C4#1683984012yes—
272C2—21no—
273C2—21no—
274C2#2144611711yescharacteristic
275C2#2144634211yescharacteristic
276C2#2144635711yescharacteristic
subgroupG/H
centerC22#16839642
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#2327C2
socleC22×C61#386
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenter#2327D61
hypocenterC61#9104
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2327

Complements

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

NH ≅ G/Ntype
159. C61#9104semidirect

Maximal subgroups

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

subgroupindex
#214549042
#214442142
#214441432
#214436482
C61×#23272
#910461