Finite Group Databasebeta

← #30602153

Subgroups — #30602153

Order 15616.

506 conjugacy classes of subgroups; only the 140 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 140 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#21461752C211yesmaximal, characteristic
2#21461534C211yesmaximal, characteristic
3#21460655C214yesmaximal
4#21448386C211yesmaximal, characteristic
5C2×#14519844—21no—
6C2×#14519844—21no—
7C2×C4⋊#92420C2212yes—
8C2×C4×#92420C2212yes—
9#16840628—21no—
10#16840628—21no—
11C2×#14519777C411yescharacteristic
12C2×#14519742—21no—
13#16839667—21no—
14#16839658—21no—
15#16839658C412yes—
16C4⋊C4×Dic61—21no—
17C4⋊C4×Dic61C2212yes—
18C42×Dic61C2211yescharacteristic
19C61×#384C411yescharacteristic
20C22×#92420—22no—
21C22×#92420—22no—
22#14519844—42no—
23#14519844—42no—
24C4⋊#92420—24no—
25C4×#92420—22no—
26C4×#92420Q814yescomplemented
27C22×Dic122—21no—
28#14519777—24no—
29#14519742—42no—
30#14519742—42no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61C2×C412yes—
33C2×#11758196—22no—
34C2×C4×Dic61—22no—
35C2×C4×Dic61C2×C411yescharacteristic
36C2×C4×Dic61D411yescharacteristic
37C2×C4×Dic61D411yescharacteristic
38C2×C4×Dic61D411yescharacteristic
39C2×C4×Dic61D411yescharacteristic
40C2×C4×Dic61C2311yescharacteristic
41#14519684—22no—
42#14519684—22no—
43C2×C4⋊C4×C61—21no—
44C2×C4⋊C4×C61—21no—
45C2×C4⋊C4×C61C2×C412yes—
46C2×C42×C61C2×C411yescharacteristic
47C22×C4×C61—22no—
48C22×C4×C61C22⋊C411yescharacteristic
49C22×C4×C61C22⋊C411yescharacteristic
50C22×C4×C61C22×C411yescharacteristic
51C22×Dic61—22no—
52C22×Dic61C22⋊C411yescharacteristic
53C22×Dic61C22⋊C411yescharacteristic
54C22×Dic61C2×D411yescharacteristic
55C22×Dic61C2×D411yescharacteristic
56C2×Dic122—24no—
57C2×Dic122—42no—
58C2×Dic122—42no—
59C2×#92420—24no—
60C2×#92420—42no—
61C2×#92420—42no—
62C2×#92420—42no—
63C2×#92420—42no—
64C2×#92420—42no—
65C4⋊C4×C61—24no—
66C4⋊C4×C61—42no—
67C4⋊C4×C61—42no—
68C42×C61—22no—
69C4⋊Dic61—24no—
70C4⋊Dic61—22no—
71C4⋊Dic61M1614yes—
72#11758196—44no—
73C4×Dic61—22no—
74C4×Dic61—41no—
75C4×Dic61—41no—
76C4×Dic61—42no—
77C4×Dic61—42no—
78C4×Dic61D812yes—
79C4×Dic61SD1612yes—
80C4×Dic61SD1612yes—
81C4×Dic61Q1612yes—
82C4×Dic61C2×Q812yes—
83C4×Dic61#4112yes—
84C23×C61C2×C22⋊C411yescharacteristic
85C2×C4×C61—21no—
86C2×C4×C61—21no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—42no—
90C2×C4×C61—42no—
91C2×C4×C61—42no—
92C2×C4×C61#10212yes—
93C2×C4×C61#10312yes—
94C2×C4×C61C4×Q812yes—
95C2×C4×C61C2×M1612yes—
96C2×C4×C61#13112yes—
97C2×Dic61—21no—
98C2×Dic61—21no—
99C2×Dic61—21no—
100C2×Dic61—21no—
101C2×Dic61—21no—
102C2×Dic61—21no—
103C2×Dic61—24no—
104C2×Dic61—42no—
105C2×Dic61—42no—
106C2×Dic61#10212yes—
107C2×Dic61#10312yes—
108C2×Dic61C22⋊Q812yes—
109C2×Dic61#12411yescharacteristic
110C2×Dic61C4⋊Q811yescharacteristic
111C2×Dic61C2×D811yescharacteristic
112C2×Dic61C2×SD1611yescharacteristic
113C2×Dic61C2×SD1611yescharacteristic
114C2×Dic61C2×Q1611yescharacteristic
115Dic122—48no—
116#92420—44no—
117#92420—82no—
118#9874—611nomaximal, Sylow
119C22×C61#39111yescharacteristic
120C22×C61#40711yescharacteristic
121C22×C61#40811yescharacteristic
122C22×C61C2×#10211yescharacteristic
123C22×C61C2×#10311yescharacteristic
124C22×C61#42111yescharacteristic
125C22×C61#42111yescharacteristic
126C4×C61—22no—
127C4×C61—22no—
128C4×C61—82no—
129C4×C61#44614yes—
130Dic61—22no—
131Dic61—22no—
132Dic61—22no—
133Dic61—44no—
134Dic61#48611yescharacteristic
135Dic61#48711yescharacteristic
136Dic61#49811yescharacteristic
137Dic61#50011yescharacteristic
138C4×C4⋊Q8—611no—
139#1842—611no—
140#1744—611no—
141#1279—614no—
142C2×C61#148011yescharacteristic
143C2×C61#148111yescharacteristic
144C2×C61#148611yescharacteristic
145C2×C61#148711yescharacteristic
146C2×C61#198511yescharacteristic
147C2×C61#199011yescharacteristic
148C2×C61#199511yescharacteristic
149C2×C4⋊Q8—611no—
150C2×C4×Q8—1221no—
151C2×C4⋊C8—612no—
152C2×C4⋊C8—1221no—
153C2×C4⋊C8—1221no—
154C2×C4×C8—612no—
155#391—1221no—
156#389—612no—
157#389—1221no—
158#384#692311yescharacteristic
159C4×C4⋊C4—612no—
160C4×C4⋊C4—1221no—
161C43—611no—
162#336—1221no—
163#336—1221no—
164C61#987411yescharacteristic, complemented, Sylow
165C22×Q8—1221no—
166C22×C8—1222no—
167C22×C8—1222no—
168C4⋊Q8—1224no—
169C4×Q8—2442no—
170C4×Q8—2442no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—612no—
174C2×C4⋊C4—1221no—
175C2×C4⋊C4—1222no—
176C2×C4⋊C4C2×#692312yes—
177C2×C42—611no—
178C2×C42—611no—
179C2×C42—611no—
180C2×C42—611no—
181C2×C42—611no—
182C2×C42—611no—
183C2×C42—1222no—
184C2×C42C2×#692311yescharacteristic
185C4⋊C8—1224no—
186C4⋊C8—2442no—
187C4⋊C8—2442no—
188C4×C8—614no—
189C4×C8—1222no—
190#95—1222no—
191#95—1222no—
192C2×Q8—1224no—
193C2×Q8—2442no—
194C2×Q8—2442no—
195C22×C4—22no—
196C22×C4—611no—
197C22×C4—611no—
198C22×C4—611no—
199C22×C4—611no—
200C22×C4—1222no—
201C22×C4C22⋊#692311yescharacteristic
202C22×C4C22⋊#692311yescharacteristic
203C22×C4C22×#692311yescharacteristic
204C2×C8—1224no—
205C2×C8—2442no—
206C2×C8—2442no—
207C2×C8—2442no—
208C2×C8—2442no—
209C2×C8—2442no—
210C4⋊C4—24no—
211C4⋊C4—42no—
212C4⋊C4—42no—
213C4⋊C4—614no—
214C4⋊C4—1224no—
215C4⋊C4—1222no—
216C4⋊C4—2444no—
217C42—22no—
218C42—612no—
219C42—612no—
220C42—612no—
221C42—612no—
222C42—612no—
223C42—612no—
224C42—1222no—
225C42—2441no—
226C42—2441no—
227C42—2442no—
228C42—2442no—
229C23C2×C22⋊#692311yescharacteristic
230Q8—2448no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—611no—
239C2×C4—611no—
240C2×C4—611no—
241C2×C4—611no—
242C2×C4—611no—
243C2×C4—611no—
244C2×C4—612no—
245C2×C4—612no—
246C2×C4—612no—
247C2×C4—1221no—
248C2×C4—1221no—
249C2×C4—1221no—
250C2×C4—1221no—
251C2×C4—1221no—
252C2×C4—1221no—
253C2×C4—1224no—
254C2×C4—2442no—
255C2×C4—2442no—
256C2×C4#1451983912yes—
257C2×C4#1451984012yes—
258C2×C4Q8×#692312yes—
259C2×C4D61⋊M1612yes—
260C2×C4#1451986412yes—
261C8—4882no—
262C8—2444no—
263C22(C2×#6923)⋊Q811yescharacteristic
264C22#1684073411yescharacteristic
265C22#1684073611yescharacteristic
266C22C2×#1451983911yescharacteristic
267C22C2×#1451984011yescharacteristic
268C22#1684076011yescharacteristic
269C22#1684076111yescharacteristic
270C4—22no—
271C4—22no—
272C4—82no—
273C4—611no—
274C4—611no—
275C4—611no—
276C4—611no—
277C4—1222no—
278C4—1222no—
279C4—1222no—
280C4—2444no—
281C4#1684081414yes—
282C2#2146112511yescharacteristic
283C2#2146112811yescharacteristic
284C2#2146114611yescharacteristic
285C2#2146114911yescharacteristic
286C2#2146199111yescharacteristic
287C2#2146200011yescharacteristic
288C2#2146200711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#384C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#384#6923
hypocenterC61#9874
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
26. C4×#92420Q8semidirect
164. C61#9874semidirect

Maximal subgroups

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

subgroupindex
#214617522
#214615342
#214606552
#214483862
#987461