Finite Group Databasebeta

← #30606852

Subgroups — #30606852

Order 15616.

962 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 962 conjugacy classes of subgroups — too many to draw. Only its 100 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
1C2×#16840673C214yesmaximal, complemented
2#21461655C212yesmaximal
3C2×#16840338C211yesmaximal, characteristic
4C2×#14519838C2214yes—
5C2×#14519837—22no—
6#16840734—22no—
7#16840673—28no—
8C22×#11758222C2211yescharacteristic
9C23×Dic122C411yescharacteristic
10#16840338—28no—
11C2×#14519777C2212yes—
12C2×#14519765C412yes—
13C2×#14519761—22no—
14C2×#14519757—22no—
15C2×#117×C61C411yescharacteristic
16C2×#11758217—24no—
17#14519838—28no—
18#14519837—44no—
19#14519834—44no—
20C2×#11758222—24no—
21C2×#11758222—42no—
22C2×#11758222—42no—
23C22×Dic122—21no—
24C22×Dic122—24no—
25C22×Dic122—42no—
26C22×Dic122—42no—
27C22×Dic122C2×C412yes—
28C22×Dic122C2311yescharacteristic
29C22×D244C2×C411yescharacteristic
30C22×C22⋊D61D412yes—
31C23×Dic61—21no—
32C22×C4×D61D412yes—
33#14519777—24no—
34#14519777D418yes—
35#14519765—24no—
36#14519765—24no—
37#14519761—216no—
38#14519757—216no—
39C2×C4⋊Dic61—24no—
40C2×#11758198—24no—
41C23×C4×C61C2×C411yescharacteristic
42#117×C61—24no—
43C2×C4⋊C4×C61—21no—
44C2×C22⋊C4×C61—21no—
45C2×C42×C61C2×C412yes—
46C24×C61C22⋊C411yescharacteristic
47C23×D61C22⋊C412yes—
48C22×C4×C61—22no—
49C22×C4×C61—22no—
50C22×C4×C61—22no—
51C22×C4×C61—22no—
52C22×C4×C61C22⋊C411yescharacteristic
53C22×C4×C61C22×C411yescharacteristic
54C2×C22⋊D61—24no—
55C2×C22⋊D61—24no—
56C2×C22⋊D61—42no—
57C22×Dic61—24no—
58C22×Dic61—22no—
59C22×Dic61—42no—
60C22×Dic61—42no—
61C22×Dic61C2×D412yes—
62#11758222—416no—
63C2×D244—22no—
64C2×D244—41no—
65C2×D244—41no—
66C2×C4×D61—24no—
67C2×C4×D61—24no—
68C2×C4×D61—42no—
69C2×Dic122—24no—
70C2×Dic122—22no—
71C2×Dic122—41no—
72C2×Dic122—41no—
73C2×Dic122—42no—
74C2×Dic122—416no—
75C2×Dic122—42no—
76C2×Dic122—42no—
77C2×Dic122—42no—
78C2×Dic122C22⋊C414yes—
79C2×Dic122C2×D414yes—
80#11758217—44no—
81#11758217—44no—
82C2×#92420—44no—
83C4⋊C4×C61—24no—
84C22⋊C4×C61—24no—
85C42×C61—22no—
86C42×C61C22⋊C414yes—
87#11758198—216no—
88C4⋊Dic61—216no—
89C23×C61—21no—
90C23×C61—21no—
91C23×C61—42no—
92C23×C61#9912yes—
93C23×C61C2×C22⋊C411yescharacteristic
94C22×D61—22no—
95C22×D61—22no—
96C22×D61—22no—
97C22×D61—44no—
98C2×C4×C61—28no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—24no—
104C2×C4×C61—44no—
105C2×C4×C61#9912yes—
106C2×C4×C61C2×C22⋊C412yes—
107C22⋊D61—48no—
108C2×Dic61—22no—
109C2×Dic61—22no—
110C2×Dic61—24no—
111C2×Dic61—48no—
112C2×Dic61—42no—
113C2×Dic61—42no—
114C2×Dic61#12014yes—
115D244—44no—
116C4×D61—48no—
117Dic122—44no—
118Dic122—44no—
119Dic122—48no—
120Dic122—44no—
121#92420—84no—
122#12704—611nomaximal, Sylow
123C22×C61—22no—
124C22×C61—22no—
125C22×C61—42no—
126C22×C61—42no—
127C22×C61—42no—
128C22×C61#37911yescharacteristic
129C22×C61C2×#9911yescharacteristic
130C22×C61C2×#9911yescharacteristic
131C2×D61—44no—
132C2×D61—44no—
133C2×D61—42no—
134C2×D61—82no—
135C4×C61—22no—
136C4×C61—22no—
137C4×C61—44no—
138Dic61—24no—
139Dic61—44no—
140C2×#536—611no—
141C2×#356—614no—
142#1785—612no—
143C2×C61—21no—
144C2×C61—21no—
145C2×C61—42no—
146C2×C61#178111yescharacteristic
147C2×C61#213512yes—
148D61—82no—
149C22×#41—611no—
150C23×Q8—611no—
151#536—1228no—
152C2×C4⋊Q8—612no—
153C2×#124—612no—
154C2×#123—1222no—
155C2×C22⋊Q8—1222no—
156C2×#117#692311yescharacteristic
157C2×#101—614no—
158C2×#100—1222no—
159#407—1222no—
160#356—1228no—
161C61#1270411yescharacteristic, complemented, Sylow
162C2×#41—1224no—
163C2×#41—2442no—
164C2×#41—2442no—
165C22×Q8—611no—
166C22×Q8—612no—
167C22×Q8—1224no—
168C22×Q8—1221no—
169C22×Q8—2442no—
170C22×Q8—2442no—
171C22×D4—612no—
172C22×D4—611no—
173C23×C4—612no—
174C23×C4—1221no—
175C23×C4C2×#692311yescharacteristic
176C2×M16—1224no—
177C4⋊Q8—618no—
178C4⋊Q8—1224no—
179#124—1224no—
180#124—1224no—
181#123—12216no—
182C22⋊Q8—12216no—
183#117—24no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—1224no—
186C2×C22⋊C4—21no—
187C2×C22⋊C4—1224no—
188C2×C42C2×#692312yes—
189#101—1228no—
190#100—2444no—
191C22⋊C8—2444no—
192C24—612no—
193C24C22⋊#692311yescharacteristic
194#41—24416no—
195C2×Q8—614no—
196C2×Q8—614no—
197C2×Q8—1224no—
198C2×Q8—1222no—
199C2×Q8—2441no—
200C2×Q8—2441no—
201C2×Q8—24416no—
202C2×Q8—2442no—
203C2×Q8—2442no—
204C2×Q8—2442no—
205C2×Q8—2442no—
206C2×D4—1224no—
207C2×D4—1224no—
208C2×D4—1222no—
209C2×D4—2441no—
210C2×D4—2441no—
211C2×D4—2442no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—612no—
217C22×C4—1224no—
218C22×C4—1224no—
219C22×C4—1222no—
220C22×C4—1224no—
221C22×C4—2442no—
222C22×C4—2442no—
223C22×C4—2442no—
224C22×C4C22⋊#692311yescharacteristic
225C22×C4C22×#692311yescharacteristic
226M16—2444no—
227M16—2444no—
228C2×C8—2444no—
229C4⋊C4—24no—
230C4⋊C4—12216no—
231C22⋊C4—24no—
232C22⋊C4—12216no—
233C42—22no—
234C42C22⋊#692314yes—
235C23—21no—
236C23—21no—
237C23—42no—
238C23—1222no—
239C23—1222no—
240C23—1222no—
241C23—2444no—
242C23#1451983612yes—
243C23C2×C22⋊#692311yescharacteristic
244Q8—2444no—
245Q8—2444no—
246Q8—2448no—
247Q8—2444no—
248D4—2444no—
249D4—2448no—
250C2×C4—28no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—24no—
256C2×C4—44no—
257C2×C4—614no—
258C2×C4—1222no—
259C2×C4—1222no—
260C2×C4—1224no—
261C2×C4—2448no—
262C2×C4—2448no—
263C2×C4—2442no—
264C2×C4—2442no—
265C2×C4#1451983612yes—
266C2×C4C2×C22⋊#692312yes—
267C8—4884no—
268C22—22no—
269C22—22no—
270C22—42no—
271C22—42no—
272C22—42no—
273C22—4882no—
274C22—2444no—
275C22—2444no—
276C22—2442no—
277C22#1684070311yescharacteristic
278C22C2×#1451983611yescharacteristic
279C22C2×#1451983611yescharacteristic
280C4—22no—
281C4—22no—
282C4—44no—
283C4—1224no—
284C4—2444no—
285C2—21no—
286C2—21no—
287C2—42no—
288C2—4882no—
289C2#2146164711yescharacteristic
290C2#2146212312yes—
subgroupG/H
centerC22C2×#14519836
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#117×C61C4
socleC22×C61C2×#99
prime radicalC22×#11758222C22
cosocleC22×Dic122C23
hypercenterC2×#117#6923
hypocenterC61#12704
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. C2×#16840673C2semidirect
161. C61#12704semidirect

Maximal subgroups

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

subgroupindex
C2×#168406732
#214616552
C2×#168403382
#1270461