Finite Group Databasebeta

← #30596773

Subgroups — #30596773

Order 15616.

906 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 906 conjugacy classes of subgroups — too many to draw. Only its 162 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#21460691C214yesmaximal, complemented
3C2×C22⋊C8×D61C211yesmaximal, characteristic
4C2×D61⋊M16—22no—
5#16840734C414yes—
6#16840733—22no—
7#16840733C2214yes—
8#16840732—22no—
9D61⋊(C22⋊C8)—22no—
10D61⋊(C22⋊C8)C414yes—
11C23×C4×D61C2211yescharacteristic
12C22×C8×D61C412yes—
13C2×C22⋊#92418C411yescharacteristic
14C2×#14519689C2212yes—
15C22⋊C8×D61—22no—
16C22⋊C8×D61—22no—
17C2×C22⋊C8×C61C411yescharacteristic
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
37C22×#92418C2×C412yes—
38C2×C8×D61—22no—
39C2×C8×D61—22no—
40C2×C8×D61—44no—
41C22⋊#92418—22no—
42#14519689—24no—
43C23×C4×C61C2×C411yescharacteristic
44C22×C8×C61C2×C412yes—
45C22⋊C8×C61—22no—
46C24×C61C4⋊C411yescharacteristic
47C23×D61—24no—
48C23×D61—42no—
49C23×D61—42no—
50C23×D61C4⋊C412yes—
51C23×D61C4⋊C411yescharacteristic
52C23×D61C4⋊C412yes—
53C23×D61C2×Q811yescharacteristic
54C22×C4×C61—42no—
55C22×C4×C61C4212yes—
56C22×C4×C61C22⋊C412yes—
57C22×C4×C61C4⋊C411yescharacteristic
58C22×C4×C61C22×C411yescharacteristic
59C22×Dic61—42no—
60C22×Dic61C22⋊C412yes—
61C22×Dic61C22⋊C412yes—
62C22×Dic61C4⋊C411yescharacteristic
63C22×Dic61C2×D411yescharacteristic
64C2×C4×D61—24no—
65C2×C4×D61—28no—
66C2×C4×D61—44no—
67C2×C4×D61—42no—
68C2×C4×D61—44no—
69C2×C4×D61—42no—
70C2×C4×D61—44no—
71C2×C4×D61—42no—
72C2×C4×D61C4211yescharacteristic
73C2×C4×D61C4211yescharacteristic
74C2×C4×D61C22⋊C411yescharacteristic
75C2×C4×D61C22⋊C412yes—
76C2×C4×D61C22⋊C412yes—
77C2×C4×D61C22⋊C411yescharacteristic
78C2×C4×D61C4⋊C412yes—
79C2×C4×D61C4⋊C412yes—
80C2×C4×D61C22×C412yes—
81C2×C4×D61C2×D412yes—
82#11758217—48no—
83C2×#92420—28no—
84#11758213—48no—
85D61⋊C8—48no—
86C2×C8×C61—22no—
87C2×C8×C61—42no—
88C2×#92418—22no—
89C2×#92418—42no—
90C8×D61—44no—
91C8×D61—44no—
92C23×C61—22no—
93C23×C61—41no—
94C23×C61—41no—
95C23×C61#9512yes—
96C23×C61C2×C4⋊C411yescharacteristic
97C22×D61—22no—
98C22×D61—22no—
99C22×D61—22no—
100C22×D61—24no—
101C22×D61—24no—
102C22×D61—24no—
103C22×D61—24no—
104C22×D61—42no—
105C22×D61—41no—
106C22×D61—42no—
107C22×D61—41no—
108C22×D61—416no—
109C22×D61#9511yescharacteristic
110C22×D61#9511yescharacteristic
111C22×D61#10814yes—
112C22×D61C2×C4⋊C412yes—
113C2×C4×C61—22no—
114C2×C4×C61—24no—
115C2×C4×C61—42no—
116C2×C4×C61—41no—
117C2×C4×C61#9512yes—
118C2×C4×C61C2×C4211yescharacteristic
119C2×C4×C61C2×C22⋊C411yescharacteristic
120C2×Dic61—24no—
121C2×Dic61—22no—
122C2×Dic61—42no—
123C2×Dic61—41no—
124C2×Dic61#9511yescharacteristic
125C2×Dic61#9511yescharacteristic
126C2×Dic61C2×C22⋊C412yes—
127C4×D61—24no—
128C4×D61—22no—
129C4×D61—22no—
130C4×D61—24no—
131C4×D61—22no—
132C4×D61—24no—
133C4×D61—42no—
134C4×D61—42no—
135C4×D61—42no—
136C4×D61#9914yes—
137#92420—48no—
138C8×C61—42no—
139#92418—42no—
140C2×#1293—611nomaximal, Sylow
141C22×C61—21no—
142C22×C61—21no—
143C22×C61—22no—
144C22×C61—22no—
145C22×C61—22no—
146C22×C61—44no—
147C22×C61C2×#9511yescharacteristic
148C22×C61C2×#10812yes—
149C2×D61—21no—
150C2×D61—21no—
151C2×D61—28no—
152C2×D61—22no—
153C2×D61—22no—
154C2×D61—22no—
155C2×D61—48no—
156C2×D61—44no—
157C2×D61—48no—
158C2×D61#33812yes—
159C2×D61#34112yes—
160C2×D61#34112yes—
161C2×D61#34212yes—
162C4×C61—22no—
163C4×C61—21no—
164C4×C61C2×#9912yes—
165Dic61—22no—
166Dic61—21no—
167Dic61#34212yes—
168C2×#407—612no—
169C22×C22⋊C8—611no—
170#1293—614no—
171C2×C61—22no—
172C2×C61—42no—
173C2×C61C2×#33811yescharacteristic
174C2×C61C2×#34111yescharacteristic
175C2×C61C2×#34211yescharacteristic
176D61—22no—
177D61—42no—
178D61#129314yescomplemented
179C24×C4—611no—
180C22×M16—1222no—
181C23×C8—612no—
182#407—614no—
183#407—614no—
184#407—1222no—
185#407—1222no—
186C2×C22⋊C8—614no—
187C2×C22⋊C8—611no—
188C2×C22⋊C8—612no—
189C2×C22⋊C8—1222no—
190C2×C22⋊C8—1222no—
191C2×C22⋊C8—1222no—
192C2×C22⋊C8#692311yescharacteristic
193C61C2×#129311yescharacteristic, complemented, Sylow
194C25—611no—
195C23×C4—611no—
196C23×C4—612no—
197C23×C4—611no—
198C23×C4—612no—
199C23×C4—612no—
200C23×C4—611no—
201C23×C4—611no—
202C23×C4—612no—
203C23×C4—611no—
204C23×C4—2444no—
205C23×C4C2×#692311yescharacteristic
206C2×M16—1224no—
207C2×M16—1224no—
208C2×M16—2448no—
209C22×C8—612no—
210C22×C8—1222no—
211C22×C8—1222no—
212C22×C8—1224no—
213C22×C8—2444no—
214C22×C8C2×#692312yes—
215C22⋊C8—22no—
216C22⋊C8—618no—
217C22⋊C8—1224no—
218C22⋊C8—1224no—
219C22⋊C8—1224no—
220C22⋊C8—1224no—
221C22⋊C8—1222no—
222C24—611no—
223C24—612no—
224C24—612no—
225C24—611no—
226C24—1224no—
227C24—2442no—
228C24—2442no—
229C24C4⋊#692311yescharacteristic
230C22×C4—42no—
231C22×C4—611no—
232C22×C4—612no—
233C22×C4—611no—
234C22×C4—612no—
235C22×C4—611no—
236C22×C4—612no—
237C22×C4—612no—
238C22×C4—611no—
239C22×C4—611no—
240C22×C4—612no—
241C22×C4—611no—
242C22×C4—612no—
243C22×C4—612no—
244C22×C4—612no—
245C22×C4—1224no—
246C22×C4—1228no—
247C22×C4—2442no—
248C22×C4—2444no—
249C22×C4—2444no—
250C22×C4—2442no—
251C22×C4—2444no—
252C22×C4—2442no—
253C22×C4—2442no—
254C22×C4C4×#692312yes—
255C22×C4C4⋊#692311yescharacteristic
256C22×C4C22⋊#692312yes—
257C22×C4C22×#692311yescharacteristic
258M16—2448no—
259M16—2448no—
260C2×C8—22no—
261C2×C8—42no—
262C2×C8—1228no—
263C2×C8—1222no—
264C2×C8—2444no—
265C2×C8—2444no—
266C2×C8—2448no—
267C2×C8—2442no—
268C23—22no—
269C23—41no—
270C23—41no—
271C23—611no—
272C23—614no—
273C23—611no—
274C23—612no—
275C23—1222no—
276C23—1222no—
277C23—1224no—
278C23—1224no—
279C23—1224no—
280C23—1224no—
281C23—1222no—
282C23—2441no—
283C23—2442no—
284C23—2441no—
285C23—2442no—
286C23—24416no—
287C23(C2×#6923)⋊C412yes—
288C23C2×C4⋊#692311yescharacteristic
289C2×C4—22no—
290C2×C4—24no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—611no—
294C2×C4—614no—
295C2×C4—611no—
296C2×C4—612no—
297C2×C4—1224no—
298C2×C4—1222no—
299C2×C4—1224no—
300C2×C4—1222no—
301C2×C4—1224no—
302C2×C4—1222no—
303C2×C4—1222no—
304C2×C4—1224no—
305C2×C4—2442no—
306C2×C4—2442no—
307C2×C4—2442no—
308C2×C4—2441no—
309C2×C4—2442no—
310C2×C4(C2×#6923)⋊C412yes—
311C2×C4C2×C4×#692311yescharacteristic
312C2×C4C2×C22⋊#692311yescharacteristic
313C8—42no—
314C8—2448no—
315C8—2442no—
316C22—21no—
317C22—21no—
318C22—22no—
319C22—22no—
320C22—22no—
321C22—44no—
322C22—612no—
323C22—612no—
324C22—612no—
325C22—612no—
326C22—1228no—
327C22—1221no—
328C22—1221no—
329C22—1222no—
330C22—1222no—
331C22—1222no—
332C22—2444no—
333C22—2448no—
334C22—2448no—
335C22C2×(C2×#6923)⋊C411yescharacteristic
336C22D61⋊#10812yes—
337C4—22no—
338C4—21no—
339C4—612no—
340C4—1222no—
341C4—1221no—
342C4D61⋊#9912yes—
343C2—22no—
344C2—42no—
345C2—614no—
346C2—1222no—
347C2—2442no—
348C2D61⋊#33811yescharacteristic
349C2#2146151111yescharacteristic
350C2#2146151611yescharacteristic
subgroupG/H
centerC22C2×(C2×#6923)⋊C4
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC2×C22⋊C8×C61C4
socleC22×C61C2×#95
prime radicalC24×D61Q8
cosocleC22×C4×D61C23
hypercenterC2×C22⋊C8#6923
hypocenterC61C2×#1293
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #21460691C2semidirect
178. D61#1293semidirect
193. C61C2×#1293semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4072
#214606912
C2×C22⋊C8×D612
C2×#129361