Finite Group Databasebeta

← #29575007

Subgroups — #29575007

Order 15616.

756 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 756 conjugacy classes of subgroups — too many to draw. Only its 131 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×#16839682C211yesmaximal, characteristic
2#21445753C212yesmaximal
3C2×#16839488C211yesmaximal, characteristic
4#21443697C212yesmaximal
5C61×#2313C211yesmaximal, characteristic
6C23×Dic122C2211yescharacteristic
7C22×#11758196—21no—
8C2×#14519700—24no—
9C2×C22⋊#92418C2212yes—
10#16839682—22no—
11#16839682C414yescomplemented
12C2×#14519684—21no—
13C2×#14519684C2211yescharacteristic
14#16839488—22no—
15C22×C4⋊C4×C61C2211yescharacteristic
16C61×#387—24no—
17C61×#381—21no—
18C61×#380C2212yes—
19C4×C22⋊C4×C61—21no—
20C22×Dic122—22no—
21C22×Dic122—22no—
22C22×Dic122—21no—
23C22×Dic122—44no—
24C22×Dic122C2×C412yes—
25C23×Dic61—21no—
26C23×Dic61—21no—
27C22×#92418—22no—
28C2×#11758196—24no—
29C2×#11758196—44no—
30#14519700—48no—
31C22⋊#92418—22no—
32C22⋊#92418—22no—
33#14519684—24no—
34#14519684—21no—
35#14519684C2×C412yes—
36C23×C4×C61D411yescharacteristic
37C23×C4×C61D411yescharacteristic
38C23×C4×C61C2311yescharacteristic
39C2×C4⋊C4×C61—22no—
40C2×C4⋊C4×C61—22no—
41C2×C4⋊C4×C61C2×C412yes—
42C2×C4⋊C4×C61D412yes—
43C2×C4⋊C4×C61D414yes—
44C2×C22⋊C4×C61—22no—
45C2×C42×C61—22no—
46#95×C61—22no—
47#95×C61—24no—
48#95×C61—22no—
49C24×C61C2×D411yescharacteristic
50C22×C4×C61—21no—
51C22×C4×C61—21no—
52C22×C4×C61—21no—
53C22×C4×C61—22no—
54C22×C4×C61—22no—
55C22×C4×C61—21no—
56C22×C4×C61—24no—
57C22×C4×C61—42no—
58C22×C4×C61—42no—
59C22×C4×C61C22⋊C412yes—
60C22×C4×C61C22⋊C412yes—
61C22×C4×C61C22×C411yescharacteristic
62C22×C4×C61C2×D412yes—
63C22×C4×C61C2×D411yescharacteristic
64C22×C4×C61#4112yes—
65C22×Dic61—24no—
66C22×Dic61—24no—
67C22×Dic61—22no—
68C22×Dic61—22no—
69C22×Dic61—42no—
70C22×Dic61—42no—
71C22×Dic61—41no—
72C22×Dic61—41no—
73C22×Dic61—42no—
74C2×Dic122—28no—
75C2×Dic122—24no—
76C2×Dic122—44no—
77C2×Dic122—48no—
78C2×Dic122—44no—
79C2×Dic122—44no—
80C2×Dic122—42no—
81C4⋊C4×C61—24no—
82C4⋊C4×C61—24no—
83C4⋊C4×C61—44no—
84C22⋊C4×C61—42no—
85C22⋊C4×C61—42no—
86C42×C61—82no—
87#11758196—48no—
88C2×#92418—44no—
89C2×#92418—42no—
90C23×C61—22no—
91C23×C61—22no—
92C23×C61C2×C22⋊C411yescharacteristic
93C23×C61#12011yescharacteristic
94C23×C61#12311yescharacteristic
95C23×C61#13512yes—
96C23×C61#13712yes—
97C2×C4×C61—24no—
98C2×C4×C61—22no—
99C2×C4×C61—22no—
100C2×C4×C61—22no—
101C2×C4×C61—22no—
102C2×C4×C61—41no—
103C2×C4×C61—41no—
104C2×C4×C61—42no—
105C2×C4×C61—42no—
106C2×C4×C61—42no—
107C2×C4×C61—42no—
108C2×C4×C61—42no—
109C2×C4×C61—44no—
110C2×C4×C61—44no—
111C2×C4×C61—44no—
112C2×C4×C61—81no—
113C2×C4×C61C4×D412yes—
114C2×C4×C61#12112yes—
115C2×Dic61—24no—
116C2×Dic61—24no—
117C2×Dic61—42no—
118C2×Dic61—42no—
119C2×Dic61—44no—
120C2×Dic61—48no—
121C2×Dic61—42no—
122C2×Dic61—42no—
123C2×Dic61—44no—
124Dic122—28no—
125Dic122—48no—
126Dic122—44no—
127#92418—82no—
128#9014—611nomaximal, Sylow
129C22×C61—24no—
130C22×C61—24no—
131C22×C61—21no—
132C22×C61—21no—
133C22×C61—21no—
134C22×C61—21no—
135C22×C61#38611yescharacteristic
136C22×C61#41611yescharacteristic
137C22×C61#41911yescharacteristic
138C22×C61#45212yes—
139C22×C61#45612yes—
140C22×C61B(4,𝔽2)12yes—
141C22×C61#48512yes—
142C4×C61—22no—
143C4×C61—22no—
144C4×C61—42no—
145C4×C61—42no—
146C4×C61—84no—
147Dic61—44no—
148Dic61—44no—
149C2×#395—611no—
150#2313D6111yescharacteristic
151#1787—612no—
152C2×#324—611no—
153#1294—612no—
154C2×C61—21no—
155C2×C61—21no—
156C2×C61—22no—
157C2×C61#160314yes—
158C2×C61#187311yescharacteristic
159C2×C61#188611yescharacteristic
160C2×C61#188911yescharacteristic
161C23×Q8—611no—
162C22×C4⋊C4—1221no—
163C22×C4⋊C4C2×D6111yescharacteristic
164C2×#103—1224no—
165C2×C22⋊C8—612no—
166#395—614no—
167#395—1222no—
168#387—24no—
169#381—21no—
170#380C2×D6112yes—
171C4×C22⋊C4—21no—
172C2×#95—611no—
173C2×#95—1221no—
174#324—1222no—
175C61#901411yescharacteristic, complemented, Sylow
176C22×Q8—612no—
177C22×Q8—1221no—
178C22×Q8—1222no—
179C22×Q8—1222no—
180C22×Q8—2444no—
181C23×C4—1221no—
182C23×C4—1221no—
183C23×C4C22⋊D6111yescharacteristic
184C23×C4C22⋊D6111yescharacteristic
185C23×C4C22×D6111yescharacteristic
186C22×C8—1222no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—1224no—
190C2×C4⋊C4—2444no—
191C2×C4⋊C4C4×D6112yes—
192C2×C4⋊C4D24412yes—
193C2×C4⋊C4C22⋊D6114yes—
194C2×C22⋊C4—22no—
195C2×C42—22no—
196#103—2448no—
197C22⋊C8—1222no—
198C22⋊C8—1222no—
199#95—22no—
200#95—24no—
201#95—22no—
202#95—612no—
203#95—1224no—
204#95—1221no—
205C24C2×C22⋊D6111yescharacteristic
206C2×Q8—1228no—
207C2×Q8—1224no—
208C2×Q8—2444no—
209C2×Q8—2444no—
210C2×Q8—2444no—
211C2×Q8—2448no—
212C2×Q8—2442no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—21no—
219C22×C4—24no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4—1224no—
223C22×C4—1224no—
224C22×C4—1222no—
225C22×C4—1222no—
226C22×C4—2442no—
227C22×C4—2442no—
228C22×C4—2441no—
229C22×C4—2441no—
230C22×C4—2442no—
231C22×C4#1175819812yes—
232C22×C4#1175819812yes—
233C22×C4C2×C4×D6111yescharacteristic
234C22×C4C2×D24411yescharacteristic
235C22×C4#1175822212yes—
236C22×C4C2×C22⋊D6112yes—
237C2×C8—2444no—
238C2×C8—2442no—
239C4⋊C4—24no—
240C4⋊C4—24no—
241C4⋊C4—44no—
242C4⋊C4—2448no—
243C22⋊C4—42no—
244C22⋊C4—42no—
245C42—82no—
246C23—22no—
247C23—22no—
248C23C2×#1175819811yescharacteristic
249C23#1451974611yescharacteristic
250C23#1451976011yescharacteristic
251C23#1451979712yes—
252C23#1451980712yes—
253Q8—1228no—
254Q8—2448no—
255Q8—2444no—
256C2×C4—24no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—44no—
269C2×C4—44no—
270C2×C4—44no—
271C2×C4—81no—
272C2×C4—1224no—
273C2×C4—1224no—
274C2×C4—2442no—
275C2×C4—2448no—
276C2×C4—2442no—
277C2×C4—2444no—
278C2×C4—2444no—
279C2×C4—2442no—
280C2×C4—2442no—
281C2×C4C4×C22⋊D6112yes—
282C2×C4#1451975112yes—
283C8—4882no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22—24no—
289C22—24no—
290C22#1683964111yescharacteristic
291C22#1683975611yescharacteristic
292C22#1683977011yescharacteristic
293C22#1683992412yes—
294C22#1683994512yes—
295C22#1683994912yes—
296C22#1684010312yes—
297C4—22no—
298C4—22no—
299C4—42no—
300C4—42no—
301C4—84no—
302C4—2444no—
303C4—2444no—
304C2—21no—
305C2—21no—
306C2—22no—
307C2#2144478214yes—
308C2#2144613111yescharacteristic
309C2#2144621211yescharacteristic
310C2#2144622711yescharacteristic
subgroupG/H
centerC23#14519746
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#2313C2
socleC23×C61#120
prime radicalC24×C61C2×D4
cosocleC23×C4×C61C23
hypercenter#2313D61
hypocenterC61#9014
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2313

Complements

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

NH ≅ G/Ntype
11. #16839682C4semidirect
175. C61#9014semidirect

Maximal subgroups

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

subgroupindex
C2×#168396822
#214457532
C2×#168394882
#214436972
C61×#23132
#901461