Finite Group Databasebeta

← #30595784

Subgroups — #30595784

Order 15616.

562 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 562 conjugacy classes of subgroups — too many to draw. Only its 116 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
1C4×#14519834C211yesmaximal, characteristic
2#21461483C211yesmaximal, characteristic
3#21460638C214yesmaximal, complemented
4#21454166C211yesmaximal, characteristic
5C22×#11758213—21no—
6C2×#14519834—21no—
7C2×C4×#92420—21no—
8#16840628—21no—
9#16840628C2212yes—
10#16840628C2212yes—
11C2×#14519753—21no—
12C2×C42×D61C2211yescharacteristic
13#16839669—21no—
14#16839658—21no—
15#16839658C2212yes—
16#16839632C411yescharacteristic
17#16839619—21no—
18#16839619C412yes—
19C2×C4⋊Q8×C61C411yescharacteristic
20C2×#11758213—24no—
21C2×#11758213—42no—
22C2×#11758213—42no—
23C22×#92420—22no—
24C22×#92420—22no—
25#14519834—24no—
26C4×#92420—42no—
27C22×C4×D61C2×C411yescharacteristic
28C22×C4×D61D411yescharacteristic
29C22×C4×D61D411yescharacteristic
30#14519753—44no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61C2×C412yes—
34C2×#11758196—22no—
35C2×#11758198—22no—
36C2×C4×Dic61D411yescharacteristic
37C2×C4×Dic61D411yescharacteristic
38C2×C4×Dic61C2311yescharacteristic
39C42×D61—42no—
40#14519684—22no—
41#14519684—22no—
42C22×Q8×C61—21no—
43C4⋊Q8×C61—42no—
44C2×C4⋊C4×C61—21no—
45C2×C4⋊C4×C61C2×C412yes—
46C2×C42×C61C2×C411yescharacteristic
47C23×D61C22⋊C411yescharacteristic
48C2×Q8×C61—42no—
49C2×Q8×C61—42no—
50C2×Q8×C61—42no—
51C22×C4×C61—22no—
52C22×C4×C61C22⋊C411yescharacteristic
53C22×C4×C61C22⋊C411yescharacteristic
54C22×C4×C61C22×C411yescharacteristic
55C22×Dic61—22no—
56C22×Dic61C22⋊C411yescharacteristic
57C22×Dic61C2×D411yescharacteristic
58C22×Dic61C2×D411yescharacteristic
59C2×C4×D61—22no—
60C2×C4×D61—22no—
61C2×C4×D61—22no—
62C2×C4×D61—22no—
63C2×C4×D61—22no—
64C2×C4×D61—22no—
65C2×C4×D61—41no—
66C2×C4×D61—41no—
67C2×C4×D61SD1612yes—
68C2×C4×D61Q1612yes—
69C2×#92420—24no—
70C2×#92420—24no—
71C2×#92420—42no—
72C2×#92420—42no—
73C2×#92420—42no—
74C2×#92420—42no—
75#11758213—48no—
76C4⋊C4×C61—42no—
77C4⋊C4×C61—42no—
78C42×C61—22no—
79#11758198—44no—
80C4⋊Dic61—24no—
81C4⋊Dic61—42no—
82C4⋊Dic61—42no—
83#11758196—44no—
84C4×Dic61—22no—
85C4×Dic61—41no—
86C4×Dic61—41no—
87C23×C61C2×C22⋊C411yescharacteristic
88C22×D61—21no—
89C22×D61—21no—
90C22×D61—21no—
91C22×D61—21no—
92C22×D61—21no—
93C22×D61—21no—
94C22×D61#10312yes—
95Q8×C61—84no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—42no—
101C2×C4×C61—42no—
102C2×C4×C61—42no—
103C2×C4×C61#9912yes—
104C2×C4×C61#10312yes—
105C2×C4×C61#10412yes—
106C2×C4×C61#10412yes—
107C2×C4×C61#13112yes—
108C2×Dic61—21no—
109C2×Dic61—21no—
110C2×Dic61—21no—
111C2×Dic61—21no—
112C2×Dic61—21no—
113C2×Dic61—21no—
114C2×Dic61—42no—
115C2×Dic61—42no—
116C2×Dic61—42no—
117C2×Dic61#10112yes—
118C2×Dic61C2×SD1611yescharacteristic
119C2×Dic61C2×Q1611yescharacteristic
120C2×Dic61AGL(1,ℤ/8)12yes—
121C4×D61—24no—
122C4×D61—24no—
123C4×D61—44no—
124C4×D61—44no—
125#92420—44no—
126#92420—44no—
127#7688—611nomaximal, Sylow
128C22×C61#40811yescharacteristic
129C22×C61C2×#9911yescharacteristic
130C22×C61C2×#10111yescharacteristic
131C22×C61C2×#10311yescharacteristic
132C22×C61#41811yescharacteristic
133C22×C61C2×#10411yescharacteristic
134C22×C61C2×#10411yescharacteristic
135C2×D61—22no—
136C2×D61—22no—
137C2×D61—22no—
138C2×D61—41no—
139C2×D61—41no—
140C2×D61—41no—
141C2×D61—41no—
142C4×C61—22no—
143C4×C61—22no—
144C4×C61—82no—
145C4×C61#32814yes—
146Dic61—22no—
147Dic61—21no—
148Dic61—21no—
149Dic61—22no—
150Dic61—82no—
151#2857—611no—
152C4×C22⋊C8—611no—
153#1728—611no—
154#1271—614no—
155C2×C61#147211yescharacteristic
156C2×C61#148411yescharacteristic
157C2×C61#149311yescharacteristic
158C2×C61C2×#32811yescharacteristic
159C2×C61#150711yescharacteristic
160C2×C61#152611yescharacteristic
161C2×C61#154911yescharacteristic
162D61—42no—
163C22×M16—1221no—
164C2×C4⋊Q8#692311yescharacteristic
165C2×C22⋊Q8—1221no—
166C22×C42—611no—
167C2×C22⋊C8—1221no—
168C2×C4×C8—1221no—
169#391—1221no—
170#389—612no—
171#389—1221no—
172#384—611no—
173#380—612no—
174#380—1221no—
175#336—612no—
176#336—612no—
177#336—1221no—
178C61#768811yescharacteristic, complemented, Sylow
179C22×Q8—21no—
180C23×C4—611no—
181C23×C4—611no—
182C23×C4—611no—
183C2×M16—1224no—
184C2×M16—2442no—
185C2×M16—2442no—
186C22×C8—1222no—
187C22×C8—1222no—
188C4⋊Q8—42no—
189C22⋊Q8—2444no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—612no—
192C2×C4⋊C4—1222no—
193C2×C4⋊C4—1221no—
194C2×C4⋊C4—1221no—
195C2×C4⋊C4C2×#692312yes—
196C2×C22⋊C4—1222no—
197C2×C42—611no—
198C2×C42—611no—
199C2×C42—611no—
200C2×C42—2442no—
201C2×C42C2×#692311yescharacteristic
202C22⋊C8—1224no—
203C4×C8—2442no—
204#95—1222no—
205#95—1222no—
206C24—611no—
207C2×Q8—42no—
208C2×Q8—42no—
209C2×Q8—42no—
210C22×C4—22no—
211C22×C4—611no—
212C22×C4—611no—
213C22×C4—611no—
214C22×C4—612no—
215C22×C4—612no—
216C22×C4—1222no—
217C22×C4—1222no—
218C22×C4—1222no—
219C22×C4—1222no—
220C22×C4—1222no—
221C22×C4—1222no—
222C22×C4—1222no—
223C22×C4—2441no—
224C22×C4—2441no—
225C22×C4C22⋊#692311yescharacteristic
226C22×C4C22⋊#692311yescharacteristic
227C22×C4C22×#692311yescharacteristic
228M16—2448no—
229C2×C8—1224no—
230C2×C8—1224no—
231C2×C8—2442no—
232C2×C8—2442no—
233C2×C8—2442no—
234C2×C8—2442no—
235C4⋊C4—42no—
236C4⋊C4—42no—
237C4⋊C4—1224no—
238C4⋊C4—2442no—
239C4⋊C4—2444no—
240C4⋊C4—2442no—
241C22⋊C4—2444no—
242C42—22no—
243C42—1222no—
244C42—2441no—
245C42—2441no—
246C23—612no—
247C23—1221no—
248C23—1221no—
249C23—1221no—
250C23—1221no—
251C23—1221no—
252C23—1221no—
253C23C2×C22⋊#692311yescharacteristic
254Q8—84no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—612no—
263C2×C4—611no—
264C2×C4—611no—
265C2×C4—612no—
266C2×C4—1221no—
267C2×C4—1221no—
268C2×C4—1221no—
269C2×C4—1221no—
270C2×C4—1221no—
271C2×C4—1221no—
272C2×C4—1224no—
273C2×C4—1224no—
274C2×C4—2444no—
275C2×C4—2444no—
276C2×C4—2442no—
277C2×C4—2442no—
278C2×C4—2442no—
279C2×C4#1451983512yes—
280C2×C4#1451984012yes—
281C2×C4#1451984112yes—
282C2×C4#1451984212yes—
283C2×C4#1451986512yes—
284C8—2444no—
285C8—2444no—
286C22—1222no—
287C22—1222no—
288C22—1222no—
289C22—2441no—
290C22—2441no—
291C22—2441no—
292C22—2441no—
293C22#1684073711yescharacteristic
294C22C2×#1451983511yescharacteristic
295C22D61⋊#10111yescharacteristic
296C22C2×#1451984011yescharacteristic
297C22#1684075411yescharacteristic
298C22C2×#1451984111yescharacteristic
299C22C2×#1451984211yescharacteristic
300C4—22no—
301C4—22no—
302C4—82no—
303C4—1222no—
304C4—1221no—
305C4—1221no—
306C4—1222no—
307C4—4882no—
308C4#1684061614yes—
309C2—2442no—
310C2#2146109911yescharacteristic
311C2#2146114011yescharacteristic
312C2#2146116911yescharacteristic
313C2C2×#1684061611yescharacteristic
314C2#2146121511yescharacteristic
315C2#2146127711yescharacteristic
316C2#2146133511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C4⋊Q8×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×C4⋊Q8#6923
hypocenterC61#7688
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. #21460638C2semidirect
178. C61#7688semidirect

Maximal subgroups

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

subgroupindex
C4×#145198342
#214614832
#214606382
#214541662
#768861