Finite Group Databasebeta

← #30597308

Subgroups — #30597308

Order 15616.

914 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 914 conjugacy classes of subgroups — too many to draw. Only its 156 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
1D61⋊#407C212yesmaximal
2#21460722C214yesmaximal, complemented
3#21448198C211yesmaximal, characteristic
4C2×D61⋊M16—22no—
5#16840734—22no—
6#16840733—22no—
7#16840733C414yescomplemented
8#16840732C2214yes—
9D61⋊(C22⋊C8)—22no—
10D61⋊(C22⋊C8)C414yescomplemented
11C23×C4×D61C2211yescharacteristic
12C2×#14519736C411yescharacteristic
13#16839623C2212yes—
14#16839619—22no—
15#16839617C412yes—
16C4×#11758198—22no—
17C2×#117×C61C411yescharacteristic
18C2×#11758213—24no—
19D61⋊M16—44no—
20D61⋊M16—44no—
21C2×#11758217—24no—
22C2×D61⋊C8—24no—
23#14519834—24no—
24#14519834—24no—
25C22⋊#92420—24no—
26C22⋊#92420C2×C418yes—
27C24×D61C2×C411yescharacteristic
28C23×Dic61C2311yescharacteristic
29C22×C4×D61—42no—
30C22×C4×D61—42no—
31C22×C4×D61C2×C412yes—
32C22×C4×D61C2×C412yes—
33C22×C4×D61D412yes—
34C22×C4×D61D412yes—
35C22×C4×D61D412yes—
36C22×C4×D61Q812yes—
37#14519736—42no—
38C2×C4⋊Dic61—21no—
39C2×C22⋊Dic61C2×C412yes—
40C2×#11758198—24no—
41C2×C4×Dic61—21no—
42#14519684—24no—
43C23×C4×C61C2×C411yescharacteristic
44#117×C61—42no—
45C2×C4⋊C4×C61—21no—
46C2×C22⋊C4×C61C2×C412yes—
47C2×C42×C61—21no—
48C24×C61C22×C411yescharacteristic
49C23×D61—44no—
50C23×D61—41no—
51C23×D61—41no—
52C23×D61C4211yescharacteristic
53C23×D61C4211yescharacteristic
54C23×D61C22⋊C412yes—
55C23×D61C4⋊C412yes—
56C22×C4×C61—22no—
57C22×C4×C61—22no—
58C22×C4×C61—22no—
59C22×C4×C61C4212yes—
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C4⋊C412yes—
63C22×Dic61—22no—
64C22×Dic61—41no—
65C22×Dic61—41no—
66C22×Dic61C22×C412yes—
67C22×Dic61C2×D412yes—
68C22×Dic61C2×D411yescharacteristic
69C22×Dic61C2×Q811yescharacteristic
70C2×C4×D61—24no—
71C2×C4×D61—24no—
72C2×C4×D61—44no—
73C2×C4×D61—44no—
74C2×C4×D61—44no—
75C2×C4×D61—44no—
76C2×C4×D61—42no—
77C2×C4×D61—42no—
78C2×C4×D61C22⋊C412yes—
79C2×C4×D61C22⋊C412yes—
80C2×C4×D61C22⋊C412yes—
81C2×C4×D61C22⋊C412yes—
82C2×C4×D61C4⋊C412yes—
83C2×C4×D61C4⋊C412yes—
84C2×C4×D61C4⋊C412yes—
85C2×C4×D61C4⋊C412yes—
86#11758217—44no—
87#11758217—44no—
88C2×#92420—28no—
89#11758213—48no—
90D61⋊C8—48no—
91C4⋊C4×C61—42no—
92C22⋊C4×C61—42no—
93C42×C61—42no—
94C22⋊Dic61—42no—
95#11758198—48no—
96C4⋊Dic61—42no—
97C4×Dic61—42no—
98C23×C61—21no—
99C23×C61—21no—
100C23×C61—42no—
101C23×C61C2×C4211yescharacteristic
102C23×C61C2×C22⋊C411yescharacteristic
103C23×C61C2×C4⋊C411yescharacteristic
104C22×D61—22no—
105C22×D61—22no—
106C22×D61—24no—
107C22×D61—24no—
108C22×D61—24no—
109C22×D61—41no—
110C22×D61—41no—
111C22×D61—42no—
112C22×D61—42no—
113C22×D61—42no—
114C22×D61—42no—
115C22×D61—48no—
116C22×D61—48no—
117C22×D61#9512yes—
118C22×D61#9512yes—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—24no—
122C2×C4×C61—24no—
123C2×C4×C61—44no—
124C2×C4×C61—42no—
125C2×C4×C61#9512yes—
126C2×C4×C61#9512yes—
127C2×C4×C61#9912yes—
128C2×C4×C61#9912yes—
129C2×Dic61—22no—
130C2×Dic61—22no—
131C2×Dic61—42no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—44no—
135C2×Dic61—42no—
136C2×Dic61C2×C22⋊C412yes—
137C2×Dic61C2×C4⋊C412yes—
138C4×D61—24no—
139C4×D61—24no—
140C4×D61—24no—
141C4×D61—24no—
142C4×D61—42no—
143C4×D61—42no—
144C4×D61—42no—
145C4×D61—42no—
146#92420—48no—
147#8115—611nomaximal, Sylow
148C22×C61—22no—
149C22×C61—21no—
150C22×C61—21no—
151C22×C61—22no—
152C22×C61—22no—
153C22×C61—42no—
154C22×C61—42no—
155C22×C61C2×#9511yescharacteristic
156C22×C61C2×#9911yescharacteristic
157C22×C61C2×#9911yescharacteristic
158C2×D61—22no—
159C2×D61—22no—
160C2×D61—22no—
161C2×D61—22no—
162C2×D61—22no—
163C2×D61—44no—
164C2×D61—44no—
165C2×D61—44no—
166C2×D61—48no—
167C2×D61—44no—
168C2×D61#34414yes—
169C4×C61—22no—
170C4×C61—82no—
171C4×C61#34214yes—
172Dic61—22no—
173Dic61—22no—
174Dic61—82no—
175C2×#407—612no—
176#2280—611no—
177#1306—614no—
178C2×C61—21no—
179C2×C61—21no—
180C2×C61—41no—
181C2×C61—41no—
182C2×C61C2×#34211yescharacteristic
183C2×C61C2×#34412yes—
184D61—24no—
185D61—42no—
186C24×C4—611no—
187C22×M16—1222no—
188C2×#117—611no—
189C2×#117#692311yescharacteristic
190#407—614no—
191#407—614no—
192#407—1222no—
193#407—1222no—
194C2×C22⋊C8—614no—
195C2×C22⋊C8—1222no—
196#381—612no—
197#380—1222no—
198#379—612no—
199C4×C22⋊C4—1222no—
200C61#811511yescharacteristic, complemented, Sylow
201C25—611no—
202C23×C4—611no—
203C23×C4—612no—
204C23×C4—612no—
205C23×C4—612no—
206C23×C4—612no—
207C23×C4—612no—
208C23×C4—612no—
209C23×C4—2442no—
210C23×C4—2442no—
211C23×C4C2×#692311yescharacteristic
212C2×M16—1224no—
213C2×M16—1224no—
214C2×M16—2444no—
215C2×M16—2444no—
216C22×C8—1224no—
217#117—42no—
218#117—2442no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—1221no—
221C2×C22⋊C4—612no—
222C2×C22⋊C4—1224no—
223C2×C22⋊C4C2×#692312yes—
224C2×C42—21no—
225C2×C42—1221no—
226C22⋊C8—618no—
227C22⋊C8—1224no—
228C22⋊C8—1224no—
229C22⋊C8—1224no—
230#95—1224no—
231C24—611no—
232C24—612no—
233C24—612no—
234C24—611no—
235C24—2441no—
236C24—2441no—
237C24—2444no—
238C24C22×#692311yescharacteristic
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—612no—
243C22×C4—612no—
244C22×C4—611no—
245C22×C4—611no—
246C22×C4—612no—
247C22×C4—612no—
248C22×C4—612no—
249C22×C4—612no—
250C22×C4—612no—
251C22×C4—612no—
252C22×C4—612no—
253C22×C4—612no—
254C22×C4—1224no—
255C22×C4—1224no—
256C22×C4—1222no—
257C22×C4—2444no—
258C22×C4—2444no—
259C22×C4—2444no—
260C22×C4—2444no—
261C22×C4—2442no—
262C22×C4—2442no—
263C22×C4—2441no—
264C22×C4—2441no—
265C22×C4C4×#692312yes—
266C22×C4C4⋊#692312yes—
267C22×C4C22⋊#692311yescharacteristic
268C22×C4C22⋊#692311yescharacteristic
269M16—2448no—
270M16—2444no—
271M16—2444no—
272C2×C8—1228no—
273C2×C8—2448no—
274C4⋊C4—42no—
275C4⋊C4—2442no—
276C22⋊C4—42no—
277C22⋊C4—2448no—
278C22⋊C4—2442no—
279C42—42no—
280C42—2442no—
281C23—21no—
282C23—21no—
283C23—42no—
284C23—612no—
285C23—612no—
286C23—1224no—
287C23—1224no—
288C23—1224no—
289C23—1222no—
290C23—1222no—
291C23—2441no—
292C23—2441no—
293C23—2442no—
294C23—2442no—
295C23—2442no—
296C23—2442no—
297C23—2448no—
298C23—2448no—
299C23C2×C4×#692311yescharacteristic
300C23C2×C22⋊#692311yescharacteristic
301C23C2×C4⋊#692311yescharacteristic
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—24no—
305C2×C4—24no—
306C2×C4—44no—
307C2×C4—42no—
308C2×C4—612no—
309C2×C4—612no—
310C2×C4—1222no—
311C2×C4—1222no—
312C2×C4—1224no—
313C2×C4—1224no—
314C2×C4—1224no—
315C2×C4—1224no—
316C2×C4—2442no—
317C2×C4—2442no—
318C2×C4—2442no—
319C2×C4—2442no—
320C2×C4—2441no—
321C2×C4—2442no—
322C2×C4—2441no—
323C2×C4—2444no—
324C2×C4—2442no—
325C2×C4(C2×#6923)⋊C412yes—
326C2×C4(C2×#6923)⋊C412yes—
327C2×C4#1451983512yes—
328C2×C4#1451983612yes—
329C8—2448no—
330C22—22no—
331C22—21no—
332C22—21no—
333C22—22no—
334C22—22no—
335C22—42no—
336C22—42no—
337C22—614no—
338C22—1222no—
339C22—1222no—
340C22—1222no—
341C22—1222no—
342C22—1222no—
343C22—2444no—
344C22—2444no—
345C22—2444no—
346C22—2448no—
347C22—2444no—
348C22C2×(C2×#6923)⋊C411yescharacteristic
349C22C2×#1451983511yescharacteristic
350C22C2×#1451983611yescharacteristic
351C4—22no—
352C4—82no—
353C4—1222no—
354C4—1222no—
355C4—4882no—
356C4#1684064014yes—
357C2—21no—
358C2—21no—
359C2—41no—
360C2—41no—
361C2—1224no—
362C2—2442no—
363C2C2×#1684064011yescharacteristic
364C2#2146152712yes—
subgroupG/H
centerC22C2×(C2×#6923)⋊C4
commutatorC23×C61C2×C42
FrattiniC24C22×#6923
FittingC2×#117×C61C4
socleC22×C61C2×#95
prime radicalC24×D61C2×C4
cosocleC23×Dic61C23
hypercenterC2×#117#6923
hypocenterC61#8115
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #21460722C2semidirect
7. #16840733C4semidirect
10. D61⋊(C22⋊C8)C4semidirect
200. C61#8115semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4072
#214607222
#214481982
#811561