Finite Group Databasebeta

← #30601799

Subgroups — #30601799

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—42no—
32#14519776—42no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61C2×C412yes—
36C2×#11758196—22no—
37C2×#11758196—22no—
38C2×#11758196—22no—
39C2×C4×Dic61C2×C411yescharacteristic
40C2×C4×Dic61D411yescharacteristic
41C2×C4×Dic61D411yescharacteristic
42C2×C4×Dic61D411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61C2311yescharacteristic
45C2×C4⋊C4×C61—21no—
46C2×C4⋊C4×C61—21no—
47C2×C4⋊C4×C61C2×C412yes—
48C2×C42×C61C2×C411yescharacteristic
49C22×C4×C61—22no—
50C22×C4×C61C22⋊C411yescharacteristic
51C22×C4×C61C22⋊C411yescharacteristic
52C22×C4×C61C22×C411yescharacteristic
53C22×Dic61—22no—
54C22×Dic61C22⋊C411yescharacteristic
55C22×Dic61C22⋊C411yescharacteristic
56C22×Dic61C2×D411yescharacteristic
57C22×Dic61C2×D411yescharacteristic
58C2×Dic122—44no—
59C2×Dic122—42no—
60C2×Dic122—42no—
61C2×Dic122—44no—
62C2×#92420—24no—
63C2×#92420—42no—
64C2×#92420—42no—
65C2×#92420—42no—
66C2×#92420—42no—
67C2×#92420—42no—
68C4⋊C4×C61—24no—
69C4⋊C4×C61—42no—
70C4⋊C4×C61—42no—
71C42×C61—22no—
72C4⋊Dic61—24no—
73C4⋊Dic61—42no—
74C4⋊Dic61—42no—
75#11758196—44no—
76#11758196—44no—
77#11758196—42no—
78#11758196—42no—
79C4×Dic61—22no—
80C4×Dic61—22no—
81C4×Dic61—22no—
82C4×Dic61—22no—
83C4×Dic61D812yes—
84C4×Dic61SD1612yes—
85C4×Dic61C2×D412yes—
86C4×Dic61#4112yes—
87C23×C61C2×C22⋊C411yescharacteristic
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—21no—
91C2×C4×C61—21no—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—42no—
95C2×C4×C61—42no—
96C2×C4×C61—42no—
97C2×C4×C61#10112yes—
98C2×C4×C61#10212yes—
99C2×C4×C61C4×D412yes—
100C2×Dic61—21no—
101C2×Dic61—21no—
102C2×Dic61—21no—
103C2×Dic61—21no—
104C2×Dic61—42no—
105C2×Dic61—42no—
106C2×Dic61—42no—
107C2×Dic61#10112yes—
108C2×Dic61#10212yes—
109C2×Dic61#12112yes—
110C2×Dic61#12411yescharacteristic
111C2×Dic61#12711yescharacteristic
112C2×Dic61C2×D811yescharacteristic
113C2×Dic61C2×SD1611yescharacteristic
114C2×Dic61AGL(1,ℤ/8)12yes—
115C2×Dic61#13712yes—
116C2×Dic61#13712yes—
117Dic122—84no—
118Dic122—84no—
119#92420—44no—
120#92420—82no—
121#9705—611nomaximal, Sylow
122C22×C61#39011yescharacteristic
123C22×C61C2×#10111yescharacteristic
124C22×C61C2×#10111yescharacteristic
125C22×C61C2×#10211yescharacteristic
126C22×C61#41811yescharacteristic
127C22×C61#41911yescharacteristic
128C22×C61#41911yescharacteristic
129C4×C61—22no—
130C4×C61—22no—
131C4×C61—22no—
132C4×C61—82no—
133Dic61—22no—
134Dic61—22no—
135Dic61—82no—
136Dic61#45912yes—
137Dic61#46012yes—
138Dic61#49112yes—
139Dic61#49712yes—
140#2868—611no—
141#1831—611no—
142#1767—611no—
143C2×#332—614no—
144C2×C61#154611yescharacteristic
145C2×C61#154611yescharacteristic
146C2×C61#155611yescharacteristic
147C2×C61#155611yescharacteristic
148C2×C61#196011yescharacteristic
149C2×C61#196611yescharacteristic
150C2×C61#198211yescharacteristic
151C2×C4⋊Q8—612no—
152C2×C4⋊Q8—1221no—
153C2×C4⋊Q8—1221no—
154C2×C4⋊C8—612no—
155C2×C4⋊C8—612no—
156C2×#97—1221no—
157#384—612no—
158#384—611no—
159#384—1221no—
160#384—1221no—
161#384#692311yescharacteristic
162C43—611no—
163#336—1221no—
164#336—1221no—
165#336—1221no—
166#332—1228no—
167C61#970511yescharacteristic, complemented, Sylow
168C22×Q8—1222no—
169C22×C8—1222no—
170C22×C8—1222no—
171C4⋊Q8—1224no—
172C4⋊Q8—1224no—
173C4⋊Q8—2442no—
174C4⋊Q8—2442no—
175C4⋊Q8—2444no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—612no—
179C2×C4⋊C4—1222no—
180C2×C4⋊C4—1222no—
181C2×C4⋊C4—1222no—
182C2×C4⋊C4—1221no—
183C2×C4⋊C4—1221no—
184C2×C4⋊C4C2×#692312yes—
185C2×C42—611no—
186C2×C42—611no—
187C2×C42—611no—
188C2×C42—611no—
189C2×C42—611no—
190C2×C42—611no—
191C2×C42C2×#692311yescharacteristic
192C4⋊C8—614no—
193C4⋊C8—1222no—
194C4⋊C8—1224no—
195#97—2442no—
196C2×Q8—2444no—
197C2×Q8—2442no—
198C2×Q8—2442no—
199C2×Q8—2444no—
200C22×C4—22no—
201C22×C4—611no—
202C22×C4—611no—
203C22×C4—611no—
204C22×C4—611no—
205C22×C4—1222no—
206C22×C4C22⋊#692311yescharacteristic
207C22×C4C22⋊#692311yescharacteristic
208C22×C4C22×#692311yescharacteristic
209C2×C8—1224no—
210C2×C8—2442no—
211C2×C8—2442no—
212C2×C8—2442no—
213C2×C8—2442no—
214C2×C8—2442no—
215C4⋊C4—24no—
216C4⋊C4—42no—
217C4⋊C4—42no—
218C4⋊C4—1224no—
219C4⋊C4—2442no—
220C4⋊C4—2442no—
221C4⋊C4—2442no—
222C4⋊C4—2444no—
223C4⋊C4—2444no—
224C4⋊C4—2442no—
225C42—22no—
226C42—612no—
227C42—612no—
228C42—612no—
229C42—612no—
230C42—1222no—
231C42—1222no—
232C42—1222no—
233C42—1222no—
234C23C2×C22⋊#692311yescharacteristic
235Q8—4884no—
236Q8—4884no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—612no—
247C2×C4—611no—
248C2×C4—611no—
249C2×C4—611no—
250C2×C4—611no—
251C2×C4—612no—
252C2×C4—612no—
253C2×C4—612no—
254C2×C4—612no—
255C2×C4—612no—
256C2×C4—1221no—
257C2×C4—1221no—
258C2×C4—1221no—
259C2×C4—1221no—
260C2×C4—2442no—
261C2×C4—2442no—
262C2×C4—2442no—
263C2×C4#1451983812yes—
264C2×C4#1451983912yes—
265C2×C4D4×#692312yes—
266C8—4882no—
267C8—2444no—
268C22#1684071411yescharacteristic
269C22C2×#1451983811yescharacteristic
270C22D61⋊#10111yescharacteristic
271C22C2×#1451983911yescharacteristic
272C22#1684075411yescharacteristic
273C22#1684075511yescharacteristic
274C22#1684075511yescharacteristic
275C4—22no—
276C4—22no—
277C4—22no—
278C4—82no—
279C4—612no—
280C4—612no—
281C4—612no—
282C4—612no—
283C4—1222no—
284C4—1222no—
285C4—4882no—
286C2#2146132811yescharacteristic
287C2#2146132911yescharacteristic
288C2#2146134811yescharacteristic
289C2#2146134911yescharacteristic
290C2#2146195011yescharacteristic
291C2#2146196211yescharacteristic
292C2#2146198611yescharacteristic
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#9705
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
167. C61#9705semidirect

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
#970561