Finite Group Databasebeta

← #30604344

Subgroups — #30604344

Order 15616.

358 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 74 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#21461081C211yesmaximal, characteristic
2#21461061C211yesmaximal, characteristic
3#21460760C214yesmaximal
4#21451035C211yesmaximal, characteristic
5#16840783—21no—
6#16840779—21no—
7#16840608—21no—
8#16840608—21no—
9#16840607C2212yes—
10#16840607C2212yes—
11C2×C4×Dic122C2211yescharacteristic
12#16839700—21no—
13#16839700—21no—
14#16839669—21no—
15#16839669—21no—
16#16839667C412yes—
17#16839627C2212yes—
18C4×C4⋊Dic61C411yescharacteristic
19C2×C4⋊Q8×C61C411yescharacteristic
20#14519844—41no—
21C4⋊#92420—41no—
22C22⋊#92420—22no—
23C22⋊#92420—22no—
24#14519832—41no—
25C4×#92420—41no—
26C22×Dic122C2×C411yescharacteristic
27C4×Dic122—41no—
28C4×Dic122—41no—
29C2×C4⋊Dic61—21no—
30C2×C4⋊Dic61C2311yescharacteristic
31C2×#11758196D411yescharacteristic
32C2×#11758196D411yescharacteristic
33C2×C4×Dic61C2×C412yes—
34C2×C4×Dic61D411yescharacteristic
35C2×C4×Dic61D411yescharacteristic
36#14519684—21no—
37#14519684—22no—
38#14519684—22no—
39#14519684—22no—
40#14519684—22no—
41C22×Q8×C61—21no—
42C4⋊Q8×C61—41no—
43C4⋊Q8×C61—41no—
44C2×C4⋊C4×C61—21no—
45C2×C4⋊C4×C61C2×C412yes—
46C2×C42×C61C2×C411yescharacteristic
47C2×Q8×C61—44no—
48C2×Q8×C61—41no—
49C2×Q8×C61—41no—
50C22×C4×C61—22no—
51C22×C4×C61C22⋊C411yescharacteristic
52C22×C4×C61C22⋊C411yescharacteristic
53C22×C4×C61C22×C411yescharacteristic
54C22×Dic61—22no—
55C22×Dic61C22⋊C411yescharacteristic
56C22×Dic61C22⋊C411yescharacteristic
57C22×Dic61C2×D411yescharacteristic
58C22×Dic61C2×D411yescharacteristic
59C2×Dic122—22no—
60C2×Dic122—22no—
61C2×Dic122—41no—
62C2×#92420—42no—
63C2×#92420—42no—
64C4⋊C4×C61—42no—
65C4⋊C4×C61—42no—
66C42×C61—21no—
67C42×C61—21no—
68C4⋊Dic61—41no—
69C4⋊Dic61—42no—
70#11758196—41no—
71#11758196—41no—
72C4×Dic61—21no—
73C4×Dic61—21no—
74C4×Dic61—21no—
75C4×Dic61—21no—
76C4×Dic61—24no—
77C23×C61C2×C22⋊C411yescharacteristic
78Q8×C61—82no—
79Q8×C61—82no—
80C2×C4×C61—21no—
81C2×C4×C61—21no—
82C2×C4×C61—22no—
83C2×C4×C61—21no—
84C2×C4×C61—41no—
85C2×C4×C61—44no—
86C2×C4×C61—42no—
87C2×C4×C61#9911yescharacteristic
88C2×C4×C61#9911yescharacteristic
89C2×C4×C61#13112yes—
90C2×Dic61—21no—
91C2×Dic61—21no—
92C2×Dic61—21no—
93C2×Dic61—21no—
94C2×Dic61—21no—
95C2×Dic61—21no—
96C2×Dic61—21no—
97C2×Dic61—41no—
98C2×Dic61—41no—
99C2×Dic61—42no—
100C2×Dic61—42no—
101C2×Dic61—42no—
102C2×Dic61#10112yes—
103Dic122—44no—
104#92420—82no—
105#92420—82no—
106#11573—611nomaximal, Sylow
107C22×C61—21no—
108C22×C61—21no—
109C22×C61#40811yescharacteristic
110C22×C61C2×#9911yescharacteristic
111C22×C61C2×#10111yescharacteristic
112C4×C61—21no—
113C4×C61—22no—
114C4×C61—41no—
115C4×C61—82no—
116C4×C61#35512yes—
117Dic61—22no—
118Dic61—41no—
119Dic61—41no—
120Dic61—41no—
121Dic61—82no—
122#2568—611no—
123#1467—611no—
124#1461—611no—
125#1324—614no—
126C2×C61—21no—
127C2×C61—21no—
128C2×C61#147211yescharacteristic
129C2×C61#212911yescharacteristic
130C2×C61C2×#35511yescharacteristic
131C2×C4⋊Q8#692311yescharacteristic
132C2×C4×Q8—611no—
133#432—1221no—
134#431—1221no—
135#400—1221no—
136#400—1221no—
137#391—612no—
138#391—1221no—
139#391—1221no—
140#382—612no—
141C4×C4⋊C4—611no—
142#324—612no—
143#324—612no—
144#324—1221no—
145#324—1221no—
146C61#1157311yescharacteristic, complemented, Sylow
147C22×Q8—21no—
148C22×Q8—611no—
149C4⋊Q8—41no—
150C4⋊Q8—41no—
151C4×Q8—2441no—
152C4×Q8—2441no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—611no—
155C2×C4⋊C4—611no—
156C2×C4⋊C4—611no—
157C2×C4⋊C4—1221no—
158C2×C4⋊C4C2×#692312yes—
159C2×C42—611no—
160C2×C42—611no—
161C2×C42—612no—
162C2×C42C2×#692311yescharacteristic
163C4⋊C8—2441no—
164C4⋊C8—2441no—
165C22⋊C8—1222no—
166C22⋊C8—1222no—
167#97—2441no—
168C4×C8—2441no—
169#95—1222no—
170#95—1222no—
171#95—1222no—
172#95—1222no—
173#95—1221no—
174C2×Q8—44no—
175C2×Q8—41no—
176C2×Q8—41no—
177C2×Q8—1222no—
178C2×Q8—1222no—
179C2×Q8—2441no—
180C22×C4—22no—
181C22×C4—611no—
182C22×C4—611no—
183C22×C4—611no—
184C22×C4—611no—
185C22×C4—1222no—
186C22×C4C22⋊#692311yescharacteristic
187C22×C4C22⋊#692311yescharacteristic
188C22×C4C22×#692311yescharacteristic
189C2×C8—2442no—
190C2×C8—2442no—
191C4⋊C4—42no—
192C4⋊C4—42no—
193C4⋊C4—2441no—
194C4⋊C4—2441no—
195C4⋊C4—2441no—
196C4⋊C4—2442no—
197C42—21no—
198C42—21no—
199C42—1221no—
200C42—1221no—
201C42—1221no—
202C42—1221no—
203C42—1224no—
204C23C2×C22⋊#692311yescharacteristic
205Q8—82no—
206Q8—82no—
207Q8—2444no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—41no—
213C2×C4—44no—
214C2×C4—42no—
215C2×C4—612no—
216C2×C4—1221no—
217C2×C4—1221no—
218C2×C4—1221no—
219C2×C4—1221no—
220C2×C4—1221no—
221C2×C4—1221no—
222C2×C4—1221no—
223C2×C4—2442no—
224C2×C4—2442no—
225C2×C4—2442no—
226C2×C4—2441no—
227C2×C4—2441no—
228C2×C4#1451983511yescharacteristic
229C2×C4#1451983511yescharacteristic
230C2×C4#1451986512yes—
231C8—4882no—
232C8—4882no—
233C22—21no—
234C22—21no—
235C22#1684073711yescharacteristic
236C22C2×#1451983511yescharacteristic
237C22D61⋊#10111yescharacteristic
238C4—21no—
239C4—22no—
240C4—41no—
241C4—82no—
242C4—1222no—
243C4—4882no—
244C4—2441no—
245C4—2441no—
246C4—2441no—
247C4#1684067012yes—
248C2—21no—
249C2—21no—
250C2#2146109911yescharacteristic
251C2#2146210111yescharacteristic
252C2C2×#1684067011yescharacteristic
subgroupG/H
centerC22C2×#14519835
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C4⋊Q8×C61C4
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4⋊Dic61C23
hypercenterC2×C4⋊Q8#6923
hypocenterC61#11573
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
146. C61#11573semidirect

Maximal subgroups

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

subgroupindex
#214610812
#214610612
#214607602
#214510352
#1157361