Finite Group Databasebeta

← #30601797

Subgroups — #30601797

Order 15616.

538 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 538 conjugacy classes of subgroups — too many to draw. Only its 124 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#21461735C211yesmaximal, characteristic
2#21461604C211yesmaximal, characteristic
3C2×#16840621C214yesmaximal
4#21454216C211yesmaximal, characteristic
5C2×#14519844C2212yes—
6C2×#14519844C2212yes—
7C2×#14519832—21no—
8#16840628—21no—
9#16840628—21no—
10#16840628—21no—
11#16840621—28no—
12C2×#14519776—21no—
13C2×#14519776—21no—
14C2×#14519776C2212yes—
15#16839632C411yescharacteristic
16#16839631—21no—
17#16839631—21no—
18#16839631C412yes—
19C42×Dic61C2211yescharacteristic
20C61×#384C411yescharacteristic
21C22×#92420—22no—
22C22×#92420—22no—
23#14519844—24no—
24#14519844—22no—
25#14519844D414yes—
26#14519832—42no—
27C22×Dic122—22no—
28#14519776—24no—
29#14519776—24no—
30#14519776—44no—
31#14519776—44no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61C2×C412yes—
35C2×#11758196—22no—
36C2×#11758196—22no—
37C2×#11758196—22no—
38C2×C4×Dic61C2×C411yescharacteristic
39C2×C4×Dic61D411yescharacteristic
40C2×C4×Dic61D411yescharacteristic
41C2×C4×Dic61D411yescharacteristic
42C2×C4×Dic61D411yescharacteristic
43C2×C4×Dic61C2311yescharacteristic
44C2×C4⋊C4×C61—21no—
45C2×C4⋊C4×C61—21no—
46C2×C4⋊C4×C61C2×C412yes—
47C2×C42×C61C2×C411yescharacteristic
48C22×C4×C61—22no—
49C22×C4×C61C22⋊C411yescharacteristic
50C22×C4×C61C22⋊C411yescharacteristic
51C22×C4×C61C22×C411yescharacteristic
52C22×Dic61—22no—
53C22×Dic61C22⋊C411yescharacteristic
54C22×Dic61C22⋊C411yescharacteristic
55C22×Dic61C2×D411yescharacteristic
56C22×Dic61C2×D411yescharacteristic
57C2×Dic122—42no—
58C2×Dic122—42no—
59C2×Dic122—44no—
60C2×Dic122—44no—
61C2×#92420—24no—
62C2×#92420—42no—
63C2×#92420—42no—
64C2×#92420—42no—
65C2×#92420—42no—
66C2×#92420—42no—
67C4⋊C4×C61—24no—
68C4⋊C4×C61—42no—
69C4⋊C4×C61—42no—
70C42×C61—22no—
71C4⋊Dic61—24no—
72C4⋊Dic61—42no—
73C4⋊Dic61—42no—
74#11758196—44no—
75#11758196—44no—
76#11758196—44no—
77C4×Dic61—22no—
78C4×Dic61—22no—
79C4×Dic61—22no—
80C4×Dic61—22no—
81C4×Dic61SD1612yes—
82C4×Dic61Q1612yes—
83C4×Dic61C2×D412yes—
84C4×Dic61#4112yes—
85C23×C61C2×C22⋊C411yescharacteristic
86C2×C4×C61—21no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—21no—
91C2×C4×C61—21no—
92C2×C4×C61—42no—
93C2×C4×C61—42no—
94C2×C4×C61—42no—
95C2×C4×C61#10112yes—
96C2×C4×C61#10312yes—
97C2×C4×C61C4×D412yes—
98C2×Dic61—21no—
99C2×Dic61—21no—
100C2×Dic61—21no—
101C2×Dic61—21no—
102C2×Dic61—42no—
103C2×Dic61—42no—
104C2×Dic61—42no—
105C2×Dic61#10112yes—
106C2×Dic61#10312yes—
107C2×Dic61#12112yes—
108C2×Dic61#12411yescharacteristic
109C2×Dic61#12711yescharacteristic
110C2×Dic61C2×SD1611yescharacteristic
111C2×Dic61C2×Q1611yescharacteristic
112C2×Dic61AGL(1,ℤ/8)12yes—
113C2×Dic61AGL(1,ℤ/8)12yes—
114C2×Dic61#13712yes—
115Dic122—84no—
116Dic122—84no—
117#92420—44no—
118#92420—82no—
119#9703—611nomaximal, Sylow
120C22×C61#39011yescharacteristic
121C22×C61C2×#10111yescharacteristic
122C22×C61C2×#10111yescharacteristic
123C22×C61C2×#10311yescharacteristic
124C22×C61#41811yescharacteristic
125C22×C61#41811yescharacteristic
126C22×C61#41911yescharacteristic
127C4×C61—22no—
128C4×C61—22no—
129C4×C61—22no—
130C4×C61—82no—
131Dic61—22no—
132Dic61—22no—
133Dic61—82no—
134Dic61#46112yes—
135Dic61#46212yes—
136Dic61#49012yes—
137Dic61#49612yes—
138#2868—611no—
139#1831—611no—
140#1767—611no—
141C2×#332—614no—
142C2×C61#154911yescharacteristic
143C2×C61#154911yescharacteristic
144C2×C61#155611yescharacteristic
145C2×C61#155611yescharacteristic
146C2×C61#196111yescharacteristic
147C2×C61#196611yescharacteristic
148C2×C61#198111yescharacteristic
149C2×C4⋊Q8—612no—
150C2×C4⋊Q8—1221no—
151C2×C4⋊Q8—1221no—
152C2×C4⋊C8—612no—
153C2×C4⋊C8—612no—
154C2×#97—1221no—
155#384—612no—
156#384—611no—
157#384—1221no—
158#384—1221no—
159#384#692311yescharacteristic
160C43—611no—
161#336—1221no—
162#336—1221no—
163#336—1221no—
164#332—1228no—
165C61#970311yescharacteristic, complemented, Sylow
166C22×Q8—1222no—
167C22×C8—1222no—
168C22×C8—1222no—
169C4⋊Q8—1224no—
170C4⋊Q8—1224no—
171C4⋊Q8—2444no—
172C4⋊Q8—2444no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—612no—
176C2×C4⋊C4—1222no—
177C2×C4⋊C4—1222no—
178C2×C4⋊C4—1222no—
179C2×C4⋊C4—1221no—
180C2×C4⋊C4—1221no—
181C2×C4⋊C4C2×#692312yes—
182C2×C42—611no—
183C2×C42—611no—
184C2×C42—611no—
185C2×C42—611no—
186C2×C42—611no—
187C2×C42—611no—
188C2×C42C2×#692311yescharacteristic
189C4⋊C8—614no—
190C4⋊C8—1222no—
191C4⋊C8—1224no—
192#97—2442no—
193C2×Q8—2442no—
194C2×Q8—2442no—
195C2×Q8—2444no—
196C2×Q8—2444no—
197C22×C4—22no—
198C22×C4—611no—
199C22×C4—611no—
200C22×C4—611no—
201C22×C4—611no—
202C22×C4—1222no—
203C22×C4C22⋊#692311yescharacteristic
204C22×C4C22⋊#692311yescharacteristic
205C22×C4C22×#692311yescharacteristic
206C2×C8—1224no—
207C2×C8—2442no—
208C2×C8—2442no—
209C2×C8—2442no—
210C2×C8—2442no—
211C2×C8—2442no—
212C4⋊C4—24no—
213C4⋊C4—42no—
214C4⋊C4—42no—
215C4⋊C4—1224no—
216C4⋊C4—2442no—
217C4⋊C4—2442no—
218C4⋊C4—2444no—
219C4⋊C4—2444no—
220C4⋊C4—2444no—
221C42—22no—
222C42—612no—
223C42—612no—
224C42—612no—
225C42—612no—
226C42—1222no—
227C42—1222no—
228C42—1222no—
229C42—1222no—
230C23C2×C22⋊#692311yescharacteristic
231Q8—4884no—
232Q8—4884no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—612no—
243C2×C4—611no—
244C2×C4—611no—
245C2×C4—611no—
246C2×C4—611no—
247C2×C4—612no—
248C2×C4—612no—
249C2×C4—612no—
250C2×C4—612no—
251C2×C4—612no—
252C2×C4—1221no—
253C2×C4—1221no—
254C2×C4—1221no—
255C2×C4—1221no—
256C2×C4—2442no—
257C2×C4—2442no—
258C2×C4—2442no—
259C2×C4#1451983812yes—
260C2×C4#1451984012yes—
261C2×C4D4×#692312yes—
262C8—4882no—
263C8—2444no—
264C22#1684071411yescharacteristic
265C22C2×#1451983811yescharacteristic
266C22D61⋊#10111yescharacteristic
267C22C2×#1451984011yescharacteristic
268C22#1684075411yescharacteristic
269C22#1684075411yescharacteristic
270C22#1684075511yescharacteristic
271C4—22no—
272C4—22no—
273C4—22no—
274C4—82no—
275C4—612no—
276C4—612no—
277C4—612no—
278C4—612no—
279C4—1222no—
280C4—1222no—
281C4—4882no—
282C2#2146133411yescharacteristic
283C2#2146133511yescharacteristic
284C2#2146134811yescharacteristic
285C2#2146134911yescharacteristic
286C2#2146195111yescharacteristic
287C2#2146196211yescharacteristic
288C2#2146198511yescharacteristic
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#9703
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
165. C61#9703semidirect

Maximal subgroups

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

subgroupindex
#214617352
#214616042
C2×#168406212
#214542162
#970361