Finite Group Databasebeta

← #30596970

Subgroups — #30596970

Order 15616.

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

normal subgroups only

This group has 874 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#21460701C214yesmaximal, complemented
3C2×#16839725C211yesmaximal, 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
12C22×#11758194C411yescharacteristic
13#16839725—22no—
14#16839725C412yes—
15#16839725C2212yes—
16C2×#14519689—22no—
17C22×M16×C61C411yescharacteristic
18C2×#11758213—24no—
19D61⋊M16—44no—
20D61⋊M16—44no—
21C2×#11758217—24no—
22C2×D61⋊C8—24no—
23#14519834—24no—
24#14519834C2×C418yes—
25C22⋊#92420—24no—
26C22⋊#92420—24no—
27C24×D61Q811yescharacteristic
28C23×Dic61D411yescharacteristic
29C22×C4×D61—42no—
30C22×C4×D61—42no—
31C22×C4×D61C2×C411yescharacteristic
32C22×C4×D61C2×C412yes—
33C22×C4×D61C2×C412yes—
34C22×C4×D61D412yes—
35C22×C4×D61D411yescharacteristic
36C22×C4×D61D412yes—
37C22×C4×D61Q811yescharacteristic
38C22×C4×D61C2311yescharacteristic
39C2×#11758194—21no—
40C2×#11758194—42no—
41C2×#11758194C2×C412yes—
42C22×#92418—21no—
43#14519689—24no—
44#14519689—24no—
45C23×C4×C61C2×C411yescharacteristic
46C2×M16×C61—21no—
47C2×M16×C61—42no—
48C2×M16×C61C2×C412yes—
49C22×C8×C61—21no—
50C24×C61C4⋊C411yescharacteristic
51C23×D61—44no—
52C23×D61—42no—
53C23×D61C4⋊C412yes—
54C23×D61C4⋊C412yes—
55C23×D61C4⋊C411yescharacteristic
56C23×D61C2×Q811yescharacteristic
57C22×C4×C61—22no—
58C22×C4×C61—22no—
59C22×C4×C61C4211yescharacteristic
60C22×C4×C61C4211yescharacteristic
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22⋊C411yescharacteristic
63C22×C4×C61C4⋊C411yescharacteristic
64C22×C4×C61C22×C411yescharacteristic
65C22×Dic61—42no—
66C22×Dic61C22⋊C412yes—
67C22×Dic61C22⋊C412yes—
68C22×Dic61C4⋊C411yescharacteristic
69C22×Dic61C2×D411yescharacteristic
70C2×C4×D61—24no—
71C2×C4×D61—24no—
72C2×C4×D61—44no—
73C2×C4×D61—41no—
74C2×C4×D61—41no—
75C2×C4×D61—42no—
76C2×C4×D61—42no—
77C2×C4×D61—42no—
78C2×C4×D61—42no—
79C2×C4×D61—41no—
80C2×C4×D61—41no—
81C2×C4×D61—44no—
82C2×C4×D61C4212yes—
83C2×C4×D61C22⋊C412yes—
84C2×C4×D61C22⋊C412yes—
85C2×C4×D61C22⋊C412yes—
86C2×C4×D61C4⋊C412yes—
87C2×C4×D61C4⋊C412yes—
88C2×C4×D61C22×C412yes—
89C2×C4×D61C2×D412yes—
90#11758217—48no—
91C2×#92420—28no—
92#11758213—48no—
93D61⋊C8—44no—
94D61⋊C8—44no—
95M16×C61—42no—
96M16×C61—42no—
97C2×C8×C61—22no—
98C2×C8×C61—42no—
99#11758194—42no—
100#11758194—42no—
101C2×#92418—22no—
102C2×#92418—42no—
103C23×C61—22no—
104C23×C61—42no—
105C23×C61#9511yescharacteristic
106C23×C61#9511yescharacteristic
107C23×C61C2×C4⋊C411yescharacteristic
108C22×D61—24no—
109C22×D61—24no—
110C22×D61—24no—
111C22×D61—24no—
112C22×D61—42no—
113C22×D61—41no—
114C22×D61—41no—
115C22×D61—42no—
116C22×D61—42no—
117C22×D61—42no—
118C22×D61—416no—
119C22×D61#9512yes—
120C22×D61C2×C4⋊C412yes—
121C2×C4×C61—22no—
122C2×C4×C61—22no—
123C2×C4×C61—22no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61#9511yescharacteristic
129C2×C4×C61#9511yescharacteristic
130C2×C4×C61#9912yes—
131C2×C4×C61#9912yes—
132C2×C4×C61C2×C4211yescharacteristic
133C2×C4×C61C2×C22⋊C411yescharacteristic
134C2×Dic61—24no—
135C2×Dic61—42no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61#9512yes—
139C2×Dic61C2×C22⋊C412yes—
140C4×D61—24no—
141C4×D61—24no—
142C4×D61—22no—
143C4×D61—22no—
144C4×D61—22no—
145C4×D61—22no—
146C4×D61—42no—
147C4×D61—42no—
148C4×D61—42no—
149C4×D61—42no—
150#92420—48no—
151C8×C61—42no—
152#92418—42no—
153#8055—611nomaximal, Sylow
154C22×C61—22no—
155C22×C61—22no—
156C22×C61—22no—
157C22×C61—21no—
158C22×C61—21no—
159C22×C61—44no—
160C22×C61#34212yes—
161C22×C61C2×#9511yescharacteristic
162C2×D61—22no—
163C2×D61—22no—
164C2×D61—22no—
165C2×D61—22no—
166C2×D61—22no—
167C2×D61—44no—
168C2×D61—48no—
169C2×D61—48no—
170C2×D61—44no—
171C2×D61#43014yes—
172C4×C61—21no—
173C4×C61—21no—
174C4×C61#34212yes—
175C4×C61C2×#9911yescharacteristic
176C4×C61C2×#9911yescharacteristic
177Dic61—22no—
178Dic61—22no—
179C2×#407—611no—
180C2×#407—612no—
181#1298—614no—
182C2×C61—22no—
183C2×C61—41no—
184C2×C61—41no—
185C2×C61#173812yes—
186C2×C61C2×#34211yescharacteristic
187D61—24no—
188D61—42no—
189C24×C4—611no—
190C22×M16—611no—
191C22×M16—1222no—
192C22×M16#692311yescharacteristic
193#407—614no—
194#407—614no—
195#407—612no—
196#407—612no—
197#407—1222no—
198#407—1222no—
199#407—1222no—
200C2×C22⋊C8—614no—
201C2×C22⋊C8—1222no—
202C2×C22⋊C8—1222no—
203C61#805511yescharacteristic, complemented, Sylow
204C25—611no—
205C23×C4—611no—
206C23×C4—612no—
207C23×C4—612no—
208C23×C4—612no—
209C23×C4—611no—
210C23×C4—611no—
211C23×C4—612no—
212C23×C4—611no—
213C23×C4—611no—
214C23×C4—2442no—
215C23×C4—2442no—
216C23×C4C2×#692311yescharacteristic
217C2×M16—21no—
218C2×M16—42no—
219C2×M16—612no—
220C2×M16—1224no—
221C2×M16—1224no—
222C2×M16—1221no—
223C2×M16—2444no—
224C2×M16—2444no—
225C2×M16—2442no—
226C2×M16C2×#692312yes—
227C22×C8—21no—
228C22×C8—1224no—
229C22×C8—1221no—
230C22⋊C8—618no—
231C22⋊C8—1224no—
232C22⋊C8—1224no—
233C22⋊C8—1224no—
234C22⋊C8—1224no—
235C22⋊C8—1224no—
236C24—612no—
237C24—611no—
238C24—612no—
239C24—611no—
240C24—2442no—
241C24—2444no—
242C24C4⋊#692311yescharacteristic
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—612no—
246C22×C4—612no—
247C22×C4—611no—
248C22×C4—611no—
249C22×C4—612no—
250C22×C4—612no—
251C22×C4—612no—
252C22×C4—612no—
253C22×C4—612no—
254C22×C4—612no—
255C22×C4—612no—
256C22×C4—612no—
257C22×C4—1224no—
258C22×C4—1224no—
259C22×C4—2442no—
260C22×C4—2441no—
261C22×C4—2441no—
262C22×C4—2442no—
263C22×C4—2441no—
264C22×C4—2441no—
265C22×C4—2444no—
266C22×C4—2442no—
267C22×C4—2442no—
268C22×C4—2444no—
269C22×C4—2442no—
270C22×C4C4×#692311yescharacteristic
271C22×C4C4×#692311yescharacteristic
272C22×C4C4⋊#692311yescharacteristic
273C22×C4C22⋊#692311yescharacteristic
274C22×C4C22⋊#692311yescharacteristic
275C22×C4C22×#692311yescharacteristic
276M16—42no—
277M16—42no—
278M16—2442no—
279M16—2448no—
280M16—2448no—
281M16—2442no—
282C2×C8—22no—
283C2×C8—42no—
284C2×C8—1228no—
285C2×C8—1222no—
286C2×C8—2444no—
287C2×C8—2444no—
288C2×C8—2442no—
289C23—22no—
290C23—42no—
291C23—612no—
292C23—612no—
293C23—1224no—
294C23—1224no—
295C23—1224no—
296C23—1224no—
297C23—2442no—
298C23—2441no—
299C23—2441no—
300C23—2442no—
301C23—2442no—
302C23—2442no—
303C23—24416no—
304C23(C2×#6923)⋊C411yescharacteristic
305C23(C2×#6923)⋊C411yescharacteristic
306C23C2×C4⋊#692311yescharacteristic
307C2×C4—22no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—612no—
315C2×C4—612no—
316C2×C4—1224no—
317C2×C4—1222no—
318C2×C4—1222no—
319C2×C4—1222no—
320C2×C4—1222no—
321C2×C4—1224no—
322C2×C4—1224no—
323C2×C4—2442no—
324C2×C4—2442no—
325C2×C4—2442no—
326C2×C4—2442no—
327C2×C4—2441no—
328C2×C4—2442no—
329C2×C4—2441no—
330C2×C4(C2×#6923)⋊C411yescharacteristic
331C2×C4(C2×#6923)⋊C411yescharacteristic
332C2×C4#1451983512yes—
333C2×C4#1451983612yes—
334C2×C4C2×C4×#692311yescharacteristic
335C2×C4C2×C22⋊#692311yescharacteristic
336C8—42no—
337C8—2448no—
338C8—2442no—
339C22—22no—
340C22—22no—
341C22—22no—
342C22—21no—
343C22—21no—
344C22—44no—
345C22—614no—
346C22—1222no—
347C22—1222no—
348C22—1222no—
349C22—1222no—
350C22—1222no—
351C22—2448no—
352C22—2444no—
353C22—2448no—
354C22—2444no—
355C22#1684064012yes—
356C22C2×(C2×#6923)⋊C411yescharacteristic
357C4—21no—
358C4—21no—
359C4—1222no—
360C4—1222no—
361C4#1684064012yes—
362C4C2×#1451983511yescharacteristic
363C4C2×#1451983611yescharacteristic
364C2—22no—
365C2—41no—
366C2—41no—
367C2—1224no—
368C2—2442no—
369C2#2146151212yes—
370C2C2×#1684064011yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC22×M16×C61C4
socleC22×C61C2×#95
prime radicalC24×D61Q8
cosocleC22×C4×D61C23
hypercenterC22×M16#6923
hypocenterC61#8055
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
2. #21460701C2semidirect
203. 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
C2×#168397252
#805561