Finite Group Databasebeta

← #30596971

Subgroups — #30596971

Order 15616.

874 conjugacy classes of subgroups; only the 148 normal subgroups are shown.

normal subgroups only

This group has 874 conjugacy classes of subgroups — too many to draw. Only its 148 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#21460701C214yesmaximal, complemented
3#407×D61C211yesmaximal, characteristic
4C2×D61⋊M16—22no—
5#16840734C414yes—
6#16840733—22no—
7#16840733C414yes—
8#16840732—22no—
9D61⋊(C22⋊C8)—22no—
10D61⋊(C22⋊C8)C2214yes—
11C23×C4×D61C2211yescharacteristic
12C2×M16×D61C412yes—
13#16839726C411yescharacteristic
14#16839725C2212yes—
15#16839724—22no—
16C22⋊C8×D61—22no—
17C61×#407C411yescharacteristic
18C2×#11758213—24no—
19D61⋊M16—48no—
20C2×#11758217—24no—
21C2×D61⋊C8—24no—
22#14519834—24no—
23#14519834C2×C418yes—
24C22⋊#92420—24no—
25C22⋊#92420—24no—
26C24×D61Q811yescharacteristic
27C23×Dic61D411yescharacteristic
28C22×C4×D61—44no—
29C22×C4×D61C2×C411yescharacteristic
30C22×C4×D61C2×C412yes—
31C22×C4×D61C2×C412yes—
32C22×C4×D61D412yes—
33C22×C4×D61D411yescharacteristic
34C22×C4×D61D412yes—
35C22×C4×D61Q811yescharacteristic
36C22×C4×D61C2311yescharacteristic
37C2×#11758194C2×C412yes—
38C2×#11758189—22no—
39M16×D61—44no—
40C2×C8×D61—22no—
41C22⋊#92418—22no—
42#14519689—24no—
43C23×C4×C61C2×C411yescharacteristic
44C2×M16×C61C2×C412yes—
45C22⋊C8×C61—22no—
46C24×C61C4⋊C411yescharacteristic
47C23×D61—42no—
48C23×D61—44no—
49C23×D61C4⋊C412yes—
50C23×D61C4⋊C411yescharacteristic
51C23×D61C4⋊C412yes—
52C23×D61C2×Q811yescharacteristic
53C22×C4×C61—42no—
54C22×C4×C61C4212yes—
55C22×C4×C61C22⋊C412yes—
56C22×C4×C61C4⋊C411yescharacteristic
57C22×C4×C61C22×C411yescharacteristic
58C22×Dic61—42no—
59C22×Dic61C22⋊C412yes—
60C22×Dic61C22⋊C412yes—
61C22×Dic61C4⋊C411yescharacteristic
62C22×Dic61C2×D411yescharacteristic
63C2×C4×D61—24no—
64C2×C4×D61—28no—
65C2×C4×D61—44no—
66C2×C4×D61—42no—
67C2×C4×D61—44no—
68C2×C4×D61—42no—
69C2×C4×D61—44no—
70C2×C4×D61—42no—
71C2×C4×D61C4211yescharacteristic
72C2×C4×D61C4211yescharacteristic
73C2×C4×D61C22⋊C411yescharacteristic
74C2×C4×D61C22⋊C412yes—
75C2×C4×D61C22⋊C412yes—
76C2×C4×D61C22⋊C411yescharacteristic
77C2×C4×D61C4⋊C412yes—
78C2×C4×D61C4⋊C412yes—
79C2×C4×D61C22×C412yes—
80C2×C4×D61C2×D412yes—
81#11758217—48no—
82C2×#92420—28no—
83#11758213—48no—
84D61⋊C8—48no—
85M16×C61—42no—
86C2×C8×C61—22no—
87#11758194—42no—
88C2×#92418—22no—
89#11758189—44no—
90C8×D61—44no—
91C23×C61—41no—
92C23×C61—42no—
93C23×C61#9512yes—
94C23×C61C2×C4⋊C411yescharacteristic
95C22×D61—24no—
96C22×D61—22no—
97C22×D61—24no—
98C22×D61—24no—
99C22×D61—24no—
100C22×D61—42no—
101C22×D61—41no—
102C22×D61—42no—
103C22×D61—42no—
104C22×D61—42no—
105C22×D61—416no—
106C22×D61#9511yescharacteristic
107C22×D61#9511yescharacteristic
108C22×D61C2×C4⋊C412yes—
109C2×C4×C61—22no—
110C2×C4×C61—24no—
111C2×C4×C61—42no—
112C2×C4×C61—41no—
113C2×C4×C61#9512yes—
114C2×C4×C61C2×C4211yescharacteristic
115C2×C4×C61C2×C22⋊C411yescharacteristic
116C2×Dic61—24no—
117C2×Dic61—22no—
118C2×Dic61—42no—
119C2×Dic61—41no—
120C2×Dic61#9511yescharacteristic
121C2×Dic61#9511yescharacteristic
122C2×Dic61C2×C22⋊C412yes—
123C4×D61—24no—
124C4×D61—22no—
125C4×D61—22no—
126C4×D61—24no—
127C4×D61—22no—
128C4×D61—24no—
129C4×D61—42no—
130C4×D61—42no—
131C4×D61—42no—
132C4×D61#9914yes—
133#92420—48no—
134C8×C61—42no—
135#92418—42no—
136#8055—611nomaximal, Sylow
137C22×C61—22no—
138C22×C61—22no—
139C22×C61—22no—
140C22×C61—22no—
141C22×C61—21no—
142C22×C61—44no—
143C22×C61C2×#9511yescharacteristic
144C2×D61—22no—
145C2×D61—22no—
146C2×D61—22no—
147C2×D61—22no—
148C2×D61—21no—
149C2×D61—48no—
150C2×D61—44no—
151C2×D61—44no—
152C2×D61—48no—
153C2×D61#34212yes—
154C2×D61#43014yes—
155C4×C61—22no—
156C4×C61—21no—
157C4×C61C2×#9912yes—
158Dic61—22no—
159Dic61—21no—
160Dic61#34212yes—
161C2×#407—611no—
162C2×#407—612no—
163#1298—614no—
164C2×C61—42no—
165C2×C61—41no—
166C2×C61#173812yes—
167C2×C61C2×#34211yescharacteristic
168D61—22no—
169D61—24no—
170D61—41no—
171C24×C4—611no—
172C22×M16—612no—
173C22×M16—1222no—
174#407—614no—
175#407—614no—
176#407—611no—
177#407—612no—
178#407—1222no—
179#407—1222no—
180#407—1222no—
181#407#692311yescharacteristic
182C2×C22⋊C8—614no—
183C2×C22⋊C8—1222no—
184C2×C22⋊C8—1222no—
185C61#805511yescharacteristic, complemented, Sylow
186C25—611no—
187C23×C4—611no—
188C23×C4—612no—
189C23×C4—611no—
190C23×C4—612no—
191C23×C4—612no—
192C23×C4—611no—
193C23×C4—611no—
194C23×C4—612no—
195C23×C4—611no—
196C23×C4—2444no—
197C23×C4C2×#692311yescharacteristic
198C2×M16—612no—
199C2×M16—1222no—
200C2×M16—1224no—
201C2×M16—1224no—
202C2×M16—2448no—
203C2×M16—2444no—
204C2×M16C2×#692312yes—
205C22×C8—1222no—
206C22×C8—1224no—
207C22⋊C8—22no—
208C22⋊C8—618no—
209C22⋊C8—1224no—
210C22⋊C8—1224no—
211C22⋊C8—1224no—
212C22⋊C8—1224no—
213C22⋊C8—1222no—
214C24—612no—
215C24—611no—
216C24—612no—
217C24—611no—
218C24—2442no—
219C24—2444no—
220C24C4⋊#692311yescharacteristic
221C22×C4—42no—
222C22×C4—611no—
223C22×C4—612no—
224C22×C4—611no—
225C22×C4—612no—
226C22×C4—611no—
227C22×C4—612no—
228C22×C4—612no—
229C22×C4—611no—
230C22×C4—611no—
231C22×C4—612no—
232C22×C4—611no—
233C22×C4—612no—
234C22×C4—612no—
235C22×C4—612no—
236C22×C4—1224no—
237C22×C4—1228no—
238C22×C4—2442no—
239C22×C4—2444no—
240C22×C4—2444no—
241C22×C4—2442no—
242C22×C4—2444no—
243C22×C4—2442no—
244C22×C4—2442no—
245C22×C4C4×#692312yes—
246C22×C4C4⋊#692311yescharacteristic
247C22×C4C22⋊#692312yes—
248C22×C4C22×#692311yescharacteristic
249M16—42no—
250M16—2444no—
251M16—2448no—
252M16—2448no—
253M16—2442no—
254C2×C8—22no—
255C2×C8—1228no—
256C2×C8—1222no—
257C2×C8—2444no—
258C2×C8—2448no—
259C23—41no—
260C23—42no—
261C23—611no—
262C23—612no—
263C23—611no—
264C23—1224no—
265C23—1222no—
266C23—1224no—
267C23—1224no—
268C23—1224no—
269C23—2442no—
270C23—2441no—
271C23—2442no—
272C23—2442no—
273C23—2442no—
274C23—24416no—
275C23(C2×#6923)⋊C412yes—
276C23C2×C4⋊#692311yescharacteristic
277C2×C4—22no—
278C2×C4—24no—
279C2×C4—42no—
280C2×C4—41no—
281C2×C4—611no—
282C2×C4—614no—
283C2×C4—611no—
284C2×C4—612no—
285C2×C4—1224no—
286C2×C4—1222no—
287C2×C4—1224no—
288C2×C4—1222no—
289C2×C4—1224no—
290C2×C4—1222no—
291C2×C4—1224no—
292C2×C4—1222no—
293C2×C4—2442no—
294C2×C4—2442no—
295C2×C4—2442no—
296C2×C4—2441no—
297C2×C4—2442no—
298C2×C4(C2×#6923)⋊C412yes—
299C2×C4C2×C4×#692311yescharacteristic
300C2×C4C2×C22⋊#692311yescharacteristic
301C8—42no—
302C8—2448no—
303C8—2442no—
304C22—22no—
305C22—22no—
306C22—22no—
307C22—22no—
308C22—21no—
309C22—44no—
310C22—614no—
311C22—612no—
312C22—1222no—
313C22—1222no—
314C22—1222no—
315C22—1222no—
316C22—1221no—
317C22—2448no—
318C22—2444no—
319C22—2444no—
320C22—2448no—
321C22C2×(C2×#6923)⋊C411yescharacteristic
322C4—22no—
323C4—21no—
324C4—612no—
325C4—1222no—
326C4—1221no—
327C4D61⋊#9912yes—
328C2—42no—
329C2—41no—
330C2—1224no—
331C2—1222no—
332C2—2441no—
333C2#2146151212yes—
334C2#2146151611yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC61×#407C4
socleC22×C61C2×#95
prime radicalC24×D61Q8
cosocleC22×C4×D61C23
hypercenter#407#6923
hypocenterC61#8055
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. #21460701C2semidirect
185. C61#8055semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4072
#214607012
#407×D612
#805561