Finite Group Databasebeta

← #30598147

Subgroups — #30598147

Order 15616.

1518 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 1518 conjugacy classes of subgroups — too many to draw. Only its 136 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#21461642C212yesmaximal, complemented
2C2×#16840606C214yesmaximal, complemented
3C22×#14519752C211yesmaximal, characteristic
4C2×#14519834—24no—
5C2×C22⋊#92420C2214yes—
6#16840606—28no—
7C23×D244C411yescharacteristic
8C23×D244C412yes—
9C23×C4×D61C2211yescharacteristic
10C2×#14519752—28no—
11C2×#14519752—24no—
12C22×#11758198C2212yes—
13C22×C4⋊C4×C61C411yescharacteristic
14C22×#92420—24no—
15#14519834—48no—
16C22⋊#92420—28no—
17C24×D61C2×C411yescharacteristic
18C24×D61C2×C412yes—
19C22×D244—24no—
20C22×D244—24no—
21C22×D244—24no—
22C22×D244—22no—
23C22×D244—24no—
24C22×D244—44no—
25C22×D244—48no—
26C23×Dic61C2311yescharacteristic
27C22×C4×D61—24no—
28C22×C4×D61—44no—
29C22×C4×D61D414yes—
30#14519752—232no—
31C2×#11758198—24no—
32C2×#11758198—24no—
33C2×#11758198D418yes—
34C23×C4×C61C2×C412yes—
35C23×C4×C61C2×C411yescharacteristic
36C2×C4⋊C4×C61—24no—
37C2×C4⋊C4×C61—22no—
38C24×C61C22×C411yescharacteristic
39C23×D61—22no—
40C23×D61—24no—
41C23×D61—22no—
42C23×D61—22no—
43C23×D61—24no—
44C23×D61—28no—
45C23×D61—42no—
46C23×D61—44no—
47C23×D61—44no—
48C23×D61C22⋊C412yes—
49C23×D61C22⋊C414yes—
50C22×C4×C61—22no—
51C22×C4×C61—24no—
52C22×C4×C61—22no—
53C22×C4×C61—22no—
54C22×C4×C61—44no—
55C22×C4×C61C22⋊C412yes—
56C22×C4×C61C22⋊C414yes—
57C22×Dic61—42no—
58C22×Dic61C2×D412yes—
59C22×Dic61C2×D414yes—
60C2×D244—28no—
61C2×D244—216no—
62C2×D244—416no—
63C2×D244—44no—
64C2×D244—416no—
65C2×D244—48no—
66C2×D244—416no—
67C2×D244—48no—
68C2×D244—44no—
69C2×C4×D61—28no—
70C2×C4×D61—28no—
71C2×C4×D61—44no—
72C2×C4×D61—416no—
73C2×#92420—48no—
74C2×#92420—44no—
75C4⋊C4×C61—28no—
76#11758198—216no—
77C23×C61—22no—
78C23×C61—22no—
79C23×C61C2×C22⋊C412yes—
80C23×C61C2×C22⋊C411yescharacteristic
81C23×C61#13114yes—
82C22×D61—28no—
83C22×D61—22no—
84C22×D61—24no—
85C22×D61—24no—
86C22×D61—22no—
87C22×D61—24no—
88C22×D61—28no—
89C22×D61—416no—
90C22×D61—44no—
91C22×D61—44no—
92C22×D61—44no—
93C22×D61—44no—
94C22×D61—44no—
95C22×D61—44no—
96C22×D61—44no—
97C22×D61—44no—
98C22×D61—44no—
99C22×D61—44no—
100C22×D61—816no—
101C22×D61#10014yes—
102C2×C4×C61—28no—
103C2×C4×C61—22no—
104C2×C4×C61—22no—
105C2×C4×C61—24no—
106C2×C4×C61—44no—
107C2×C4×C61—44no—
108C2×C4×C61—44no—
109C2×C4×C61#9914yes—
110C2×Dic61—24no—
111C2×Dic61—44no—
112C2×Dic61#12014yes—
113D244—416no—
114D244—432no—
115C4×D61—416no—
116#92420—84no—
117#8307—611nomaximal, Sylow
118C22×C61—28no—
119C22×C61—22no—
120C22×C61—22no—
121C22×C61#37911yescharacteristic
122C22×C61#40814yes—
123C22×C61#40812yes—
124C22×C61C2×#9912yes—
125C22×C61C2×#10012yes—
126C2×D61—28no—
127C2×D61—24no—
128C2×D61—416no—
129C2×D61—44no—
130C2×D61—42no—
131C2×D61—42no—
132C2×D61—44no—
133C2×D61—44no—
134C2×D61—44no—
135C2×D61—88no—
136C2×D61—88no—
137C2×D61—88no—
138C4×C61—24no—
139C4×C61—44no—
140Dic61—24no—
141C22×#121—611no—
142#1779—612no—
143C2×#323—614no—
144C2×C61—24no—
145C2×C61#147114yes—
146C2×C61#178011yescharacteristic
147C2×C61#178111yescharacteristic
148C2×C61#178311yescharacteristic
149D61—44no—
150D61—84no—
151C23×D4—612no—
152C23×D4—611no—
153C24×C4—611no—
154C2×#121—1228no—
155C2×#121—1224no—
156C22×C4⋊C4#692311yescharacteristic
157C22×C22⋊C4—612no—
158C2×C22⋊C8—614no—
159C2×C22⋊C8—1224no—
160#323—1228no—
161C61#830711yescharacteristic, complemented, Sylow
162C25—611no—
163C25—612no—
164C22×D4—1224no—
165C22×D4—1224no—
166C22×D4—1224no—
167C22×D4—1222no—
168C22×D4—1224no—
169C22×D4—2444no—
170C22×D4—2448no—
171C23×C4—611no—
172C23×C4—614no—
173C23×C4—1224no—
174C23×C4—2444no—
175C23×C4C2×#692312yes—
176C23×C4C2×#692311yescharacteristic
177C22×C8—1224no—
178#121—12232no—
179C2×C4⋊C4—24no—
180C2×C4⋊C4—22no—
181C2×C22⋊C4—618no—
182C2×C22⋊C4—1224no—
183C2×C22⋊C4—1224no—
184C22⋊C8—1228no—
185C22⋊C8—2448no—
186C24—612no—
187C24—614no—
188C24—1224no—
189C24—1222no—
190C24—1228no—
191C24—1222no—
192C24—1222no—
193C24—1224no—
194C24—2442no—
195C24—2444no—
196C24—2444no—
197C24C22×#692311yescharacteristic
198C2×D4—1228no—
199C2×D4—12216no—
200C2×D4—24416no—
201C2×D4—2444no—
202C2×D4—2448no—
203C2×D4—24416no—
204C2×D4—2448no—
205C2×D4—24416no—
206C2×D4—2444no—
207C22×C4—22no—
208C22×C4—24no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—44no—
212C22×C4—612no—
213C22×C4—614no—
214C22×C4—1228no—
215C22×C4—1228no—
216C22×C4—2444no—
217C22×C4—24416no—
218C22×C4—2442no—
219C22×C4C22⋊#692312yes—
220C22×C4C22⋊#692314yes—
221C2×C8—2444no—
222C2×C8—2448no—
223C4⋊C4—28no—
224C22⋊C4—12216no—
225C23—22no—
226C23—22no—
227C23—614no—
228C23—1228no—
229C23—1224no—
230C23—1224no—
231C23—1222no—
232C23—1222no—
233C23—1228no—
234C23—1224no—
235C23—48816no—
236C23—24416no—
237C23—2444no—
238C23—2444no—
239C23—2444no—
240C23—2444no—
241C23—2444no—
242C23—2444no—
243C23—2444no—
244C23—2444no—
245C23—2444no—
246C23—2444no—
247C23C2×C22⋊#692312yes—
248C23C2×C22⋊#692311yescharacteristic
249C23#1451986514yes—
250D4—24416no—
251D4—24432no—
252C2×C4—28no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—24no—
256C2×C4—44no—
257C2×C4—44no—
258C2×C4—44no—
259C2×C4—614no—
260C2×C4—1224no—
261C2×C4—24416no—
262C2×C4—2444no—
263C2×C4#1451983614yes—
264C8—4884no—
265C22—28no—
266C22—22no—
267C22—22no—
268C22—1228no—
269C22—1224no—
270C22—4888no—
271C22—4888no—
272C22—4888no—
273C22—24416no—
274C22—2444no—
275C22—2444no—
276C22—2444no—
277C22—2444no—
278C22—2442no—
279C22—2442no—
280C22#1684070311yescharacteristic
281C22#1684073714yes—
282C22#1684073712yes—
283C22C2×#1451983612yes—
284C22D61⋊#10012yes—
285C4—24no—
286C4—44no—
287C4—1224no—
288C2—24no—
289C2—4884no—
290C2—2444no—
291C2#2146109614yes—
292C2#2146164411yescharacteristic
293C2#2146164711yescharacteristic
294C2#2146165211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC24×C61C22×C4
FrattiniC24C22×#6923
FittingC22×C4⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC22×#14519752C2
cosocleC23×Dic61C23
hypercenterC22×C4⋊C4#6923
hypocenterC61#8307
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #21461642C2semidirect
2. C2×#16840606C2semidirect
161. C61#8307semidirect

Maximal subgroups

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

subgroupindex
#214616422
C2×#168406062
C22×#145197522
#830761