Finite Group Databasebeta

← #29573239

Subgroups — #29573239

Order 15616.

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

normal subgroups only

This group has 350 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#21454753C211yesmaximal, characteristic
2#21444567C211yesmaximal, characteristic
3#21444382C212yesmaximal
4#21443677C212yesmaximal
5C61×#1835C211yesmaximal, characteristic
6#16840319C2211yescharacteristic
7#16839892—21no—
8#16839892C412yescomplemented
9C8×Dic122—21no—
10C8×Dic122C412yescomplemented
11#16839815C2212yes—
12#16839788—21no—
13#16839786C2211yescharacteristic
14#16839717—21no—
15#16839515—21no—
16#16839513—21no—
17#16839498—24no—
18C2×C4×C8×C61C2211yescharacteristic
19C61×#382C2212yes—
20C61×#340—21no—
21C61×#340—21no—
22C2×#11758194—21no—
23#14519777Q811yescharacteristic
24#14519777Q811yescharacteristic
25#14519769—21no—
26#14519756—21no—
27#14519756D412yes—
28C4×Dic122—21no—
29C4×Dic122C2×C412yes—
30#14519736—21no—
31C4⋊#92418—21no—
32C4⋊#92418—22no—
33C4⋊#92418C2×C412yes—
34#14519706—22no—
35#14519706—22no—
36C22⋊#92418—22no—
37#14519687—22no—
38C4×#92418—22no—
39C8×Dic61—22no—
40C22×C8×C61D411yescharacteristic
41C22×C8×C61D411yescharacteristic
42C2×C4⋊C4×C61—22no—
43C2×C42×C61C2311yescharacteristic
44C4×C8×C61C2×C411yescharacteristic
45C4×C8×C61C2×C411yescharacteristic
46C4×C8×C61D411yescharacteristic
47C4×C8×C61D411yescharacteristic
48#95×C61—22no—
49#95×C61—22no—
50C22×C4×C61—42no—
51C22×C4×C61C2×D411yescharacteristic
52C22×C4×C61C2×D411yescharacteristic
53C22×C4×C61#4111yescharacteristic
54C2×Dic122—21no—
55C2×Dic122C4⋊C412yes—
56C2×C8×C61—22no—
57C2×C8×C61—22no—
58C2×C8×C61C22⋊C411yescharacteristic
59C2×C8×C61C22⋊C411yescharacteristic
60C2×C8×C61C22⋊C411yescharacteristic
61C2×C8×C61C22⋊C411yescharacteristic
62C4⋊C4×C61—42no—
63C4⋊C4×C61—42no—
64C42×C61C22×C411yescharacteristic
65C42×C61C2×D411yescharacteristic
66C42×C61C2×Q811yescharacteristic
67C42×C61#4111yescharacteristic
68C22⋊Dic61—22no—
69C4⋊Dic61—21no—
70C4⋊Dic61—21no—
71C4⋊Dic61—21no—
72C4⋊Dic61C4⋊C412yes—
73#11758196—22no—
74#11758196—22no—
75C4×Dic61—22no—
76#11758194—42no—
77C2×#92418—22no—
78C2×#92418—42no—
79C23×C61#12111yescharacteristic
80C2×C4×C61—41no—
81C2×C4×C61—41no—
82C2×C4×C61—82no—
83C2×C4×C61—82no—
84C2×C4×C61—82no—
85C2×C4×C61C2×C22⋊C411yescharacteristic
86C2×C4×C61C2×C4⋊C411yescharacteristic
87C2×C4×C61#11711yescharacteristic
88C2×C4×C61#12111yescharacteristic
89C2×C4×C61C22⋊Q811yescharacteristic
90C2×C4×C61C22⋊Q811yescharacteristic
91C2×C4×C61#13512yes—
92C2×C4×C61#13712yes—
93C2×Dic61—22no—
94C2×Dic61—22no—
95Dic122—42no—
96Dic122—42no—
97C8×C61—21no—
98C8×C61—21no—
99C8×C61—21no—
100C8×C61—21no—
101#92418—42no—
102#92418—82no—
103#8679—611nomaximal, Sylow
104C22×C61—21no—
105C22×C61—21no—
106C22×C61#38011yescharacteristic
107C22×C61#46412yes—
108C4×C61—21no—
109C4×C61—21no—
110C4×C61—21no—
111C4×C61—21no—
112C4×C61—162no—
113C4×C61#41611yescharacteristic
114C4×C61#41911yescharacteristic
115C4×C61#47912yes—
116Dic61—42no—
117Dic61—42no—
118#2960—611no—
119#1835D6111yescharacteristic
120#1564—611no—
121#1518—612no—
122#1286—612no—
123C2×C61—22no—
124C2×C61#180511yescharacteristic
125C2×C61#181211yescharacteristic
126C2×C61#181411yescharacteristic
127#533—611no—
128#446—612no—
129#446—1221no—
130C8×Q8—612no—
131C8×Q8—1221no—
132#431—612no—
133#424—1221no—
134#423—611no—
135#405—1221no—
136C2×C4×C8C2×D6111yescharacteristic
137#382C2×D6112yes—
138#340—21no—
139#340—21no—
140#335—1221no—
141#334—1221no—
142#328—1224no—
143C61#867911yescharacteristic, complemented, Sylow
144C2×M16—1221no—
145C22×C8C22⋊D6111yescharacteristic
146C22×C8C22⋊D6111yescharacteristic
147C4⋊Q8—611no—
148C4⋊Q8—611no—
149#125—1221no—
150C22⋊Q8—612no—
151C22⋊Q8—1221no—
152C4×Q8—612no—
153C4×Q8—1221no—
154#117—1221no—
155C2×C4⋊C4—22no—
156C2×C42C22×D6111yescharacteristic
157C4⋊C8—612no—
158C4⋊C8—1222no—
159C4⋊C8—1222no—
160C4⋊C8—1221no—
161C4⋊C8—1222no—
162C22⋊C8—1222no—
163#97—1222no—
164C4×C8—1222no—
165C4×C8—1222no—
166C4×C8C4×D6111yescharacteristic
167C4×C8C4×D6111yescharacteristic
168C4×C8D24411yescharacteristic
169C4×C8D24411yescharacteristic
170#95—22no—
171#95—22no—
172C2×Q8—612no—
173C2×Q8—1221no—
174C22×C4—42no—
175C22×C4D4×D6111yescharacteristic
176C22×C4#1175822411yescharacteristic
177C22×C4C2×C22⋊D6111yescharacteristic
178M16—2442no—
179C2×C8—22no—
180C2×C8—22no—
181C2×C8—1222no—
182C2×C8—2442no—
183C2×C8#1175819811yescharacteristic
184C2×C8#1175819811yescharacteristic
185C2×C8#1175819811yescharacteristic
186C2×C8#1175819811yescharacteristic
187C4⋊C4—42no—
188C4⋊C4—42no—
189C4⋊C4—612no—
190C4⋊C4—1222no—
191C4⋊C4—1222no—
192C4⋊C4—1221no—
193C4⋊C4—1221no—
194C4⋊C4—1221no—
195C22⋊C4—1222no—
196C42—1222no—
197C42C2×C4×D6111yescharacteristic
198C42C2×D24411yescharacteristic
199C42Q8×D6111yescharacteristic
200C42#1175822611yescharacteristic
201C23#1451974811yescharacteristic
202Q8—2442no—
203Q8—2442no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—82no—
207C2×C4—82no—
208C2×C4—82no—
209C2×C4—1222no—
210C2×C4—1222no—
211C2×C4C2×#1175819811yescharacteristic
212C2×C4C4⋊C4×D6111yescharacteristic
213C2×C4#1451973511yescharacteristic
214C2×C4#1451975211yescharacteristic
215C2×C4#1451975311yescharacteristic
216C2×C4#1451975711yescharacteristic
217C2×C4#1451979712yes—
218C2×C4#1451980712yes—
219C8—21no—
220C8—21no—
221C8—21no—
222C8—21no—
223C8—4882no—
224C8—2442no—
225C22—21no—
226C22—21no—
227C22#1683961911yescharacteristic
228C22#1683998112yes—
229C4—21no—
230C4—21no—
231C4—21no—
232C4—21no—
233C4—162no—
234C4—2442no—
235C4—2442no—
236C4#1683975611yescharacteristic
237C4#1683977011yescharacteristic
238C4#1684006612yes—
239C2—22no—
240C2#2144583111yescharacteristic
241C2#2144586211yescharacteristic
242C2#2144587011yescharacteristic
subgroupG/H
centerC22#16839619
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1835C2
socleC22×C61#380
prime radicalC23×C61#121
cosocleC2×C42×C61C23
hypercenter#1835D61
hypocenterC61#8679
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1835

Complements

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

NH ≅ G/Ntype
8. #16839892C4semidirect
10. C8×Dic122C4semidirect
143. C61#8679semidirect

Maximal subgroups

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

subgroupindex
#214547532
#214445672
#214443822
#214436772
C61×#18352
#867961