Finite Group Databasebeta

← #30597304

Subgroups — #30597304

Order 15616.

942 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 942 conjugacy classes of subgroups — too many to draw. Only its 160 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
1C2×#16840732C212yesmaximal
2#21460722C214yesmaximal, complemented
3C2×#16839623C211yesmaximal, characteristic
4C22×#11758217—22no—
5#16840732—22no—
6#16840732—22no—
7#16840732C414yescomplemented
8#16840732C2214yes—
9C2×C22⋊#92420—22no—
10C2×C22⋊#92420C414yescomplemented
11C24×Dic61C2211yescharacteristic
12C22×C22⋊Dic61C411yescharacteristic
13#16839623—22no—
14#16839623C412yes—
15#16839623C2212yes—
16C2×#14519684—22no—
17C22×C22⋊C4×C61C411yescharacteristic
18C2×#11758217—24no—
19C2×#11758217—24no—
20C2×#11758217—44no—
21C2×#11758217—44no—
22C22×#92420—24no—
23C22⋊#92420—24no—
24C22⋊#92420—24no—
25C22⋊#92420—24no—
26C22⋊#92420C2×C418yescomplemented
27C23×Dic61—21no—
28C23×Dic61—42no—
29C23×Dic61—42no—
30C23×Dic61C2×C411yescharacteristic
31C23×Dic61C2×C412yes—
32C23×Dic61C2×C412yes—
33C23×Dic61D412yes—
34C23×Dic61D412yes—
35C23×Dic61D412yes—
36C23×Dic61Q812yes—
37C23×Dic61C2311yescharacteristic
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61—42no—
40C2×C22⋊Dic61C2×C412yes—
41#14519684—24no—
42#14519684—24no—
43C25×C61C2×C411yescharacteristic
44C23×C4×C61—21no—
45C2×C22⋊C4×C61—21no—
46C2×C22⋊C4×C61—42no—
47C2×C22⋊C4×C61C2×C412yes—
48C24×C61—22no—
49C24×C61—22no—
50C24×C61—44no—
51C24×C61C4212yes—
52C24×C61C22⋊C411yescharacteristic
53C24×C61C22⋊C411yescharacteristic
54C24×C61C4⋊C412yes—
55C24×C61C22×C411yescharacteristic
56C22×C4×C61—22no—
57C22×C4×C61—42no—
58C22×C4×C61—44no—
59C22×Dic61—24no—
60C22×Dic61—24no—
61C22×Dic61—22no—
62C22×Dic61—44no—
63C22×Dic61—44no—
64C22×Dic61—41no—
65C22×Dic61—41no—
66C22×Dic61—44no—
67C22×Dic61—42no—
68C22×Dic61—42no—
69C22×Dic61—44no—
70C22×Dic61—41no—
71C22×Dic61—41no—
72C22×Dic61—44no—
73C22×Dic61—42no—
74C22×Dic61C4211yescharacteristic
75C22×Dic61C4211yescharacteristic
76C22×Dic61C22⋊C412yes—
77C22×Dic61C22⋊C412yes—
78C22×Dic61C22⋊C412yes—
79C22×Dic61C22⋊C412yes—
80C22×Dic61C22⋊C412yes—
81C22×Dic61C4⋊C412yes—
82C22×Dic61C4⋊C412yes—
83C22×Dic61C4⋊C412yes—
84C22×Dic61C4⋊C412yes—
85C22×Dic61C4⋊C412yes—
86C22×Dic61C22×C412yes—
87C22×Dic61C2×D412yes—
88C22×Dic61C2×D411yescharacteristic
89C22×Dic61C2×Q811yescharacteristic
90#11758217—48no—
91#11758217—44no—
92#11758217—44no—
93C2×#92420—28no—
94C2×#92420—48no—
95C22⋊C4×C61—42no—
96C22⋊C4×C61—42no—
97C22⋊Dic61—42no—
98C22⋊Dic61—42no—
99C23×C61—24no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61—24no—
103C23×C61—24no—
104C23×C61—24no—
105C23×C61—24no—
106C23×C61—21no—
107C23×C61—21no—
108C23×C61—42no—
109C23×C61—42no—
110C23×C61—42no—
111C23×C61—42no—
112C23×C61—48no—
113C23×C61—48no—
114C23×C61#9512yes—
115C23×C61#9512yes—
116C23×C61#9912yes—
117C23×C61#9912yes—
118C23×C61C2×C4211yescharacteristic
119C23×C61C2×C22⋊C411yescharacteristic
120C23×C61C2×C4⋊C411yescharacteristic
121C2×C4×C61—44no—
122C2×C4×C61—42no—
123C2×C4×C61—84no—
124C2×Dic61—24no—
125C2×Dic61—24no—
126C2×Dic61—24no—
127C2×Dic61—24no—
128C2×Dic61—22no—
129C2×Dic61—22no—
130C2×Dic61—22no—
131C2×Dic61—22no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—42no—
135C2×Dic61—42no—
136C2×Dic61—42no—
137C2×Dic61—42no—
138C2×Dic61—42no—
139C2×Dic61—42no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—44no—
143C2×Dic61—42no—
144C2×Dic61—84no—
145C2×Dic61#9512yes—
146C2×Dic61#9512yes—
147C2×Dic61C2×C22⋊C412yes—
148C2×Dic61C2×C4⋊C412yes—
149#92420—48no—
150#8114—611nomaximal, Sylow
151C22×C61—24no—
152C22×C61—24no—
153C22×C61—22no—
154C22×C61—22no—
155C22×C61—22no—
156C22×C61—22no—
157C22×C61—22no—
158C22×C61—21no—
159C22×C61—21no—
160C22×C61—22no—
161C22×C61—22no—
162C22×C61—42no—
163C22×C61—42no—
164C22×C61—48no—
165C22×C61—48no—
166C22×C61—42no—
167C22×C61—42no—
168C22×C61#34214yes—
169C22×C61#34414yes—
170C22×C61C2×#9511yescharacteristic
171C22×C61C2×#9911yescharacteristic
172C22×C61C2×#9911yescharacteristic
173C4×C61—82no—
174Dic61—22no—
175Dic61—22no—
176Dic61—22no—
177Dic61—22no—
178Dic61—82no—
179C2×#407—612no—
180C2×#381—611no—
181#1306—614no—
182C2×C61—21no—
183C2×C61—21no—
184C2×C61—24no—
185C2×C61—24no—
186C2×C61—41no—
187C2×C61—41no—
188C2×C61C2×#34211yescharacteristic
189C2×C61C2×#34412yes—
190C24×C4—611no—
191C22×M16—1222no—
192C22×C22⋊C4—611no—
193C22×C22⋊C4#692311yescharacteristic
194#407—614no—
195#407—614no—
196#407—1222no—
197#407—1222no—
198C2×C22⋊C8—614no—
199C2×C22⋊C8—1222no—
200#381—612no—
201#381—612no—
202#381—1222no—
203C2×#95—1222no—
204C61#811411yescharacteristic, complemented, Sylow
205C25C2×#692311yescharacteristic
206C23×C4—21no—
207C23×C4—612no—
208C23×C4—612no—
209C23×C4—612no—
210C23×C4—612no—
211C23×C4—612no—
212C23×C4—612no—
213C23×C4—611no—
214C23×C4—611no—
215C23×C4—1221no—
216C23×C4—2442no—
217C23×C4—2442no—
218C2×M16—1224no—
219C2×M16—1224no—
220C2×M16—2444no—
221C2×M16—2444no—
222C22×C8—1224no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4—42no—
225C2×C22⋊C4—612no—
226C2×C22⋊C4—1221no—
227C2×C22⋊C4—2442no—
228C2×C22⋊C4C2×#692312yes—
229C22⋊C8—618no—
230C22⋊C8—1224no—
231C22⋊C8—1224no—
232C22⋊C8—1224no—
233#95—1224no—
234#95—1224no—
235C24—22no—
236C24—22no—
237C24—44no—
238C24C4×#692312yes—
239C24C4⋊#692312yes—
240C24C22⋊#692311yescharacteristic
241C24C22⋊#692311yescharacteristic
242C24C22×#692311yescharacteristic
243C22×C4—22no—
244C22×C4—42no—
245C22×C4—44no—
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—612no—
255C22×C4—612no—
256C22×C4—612no—
257C22×C4—611no—
258C22×C4—611no—
259C22×C4—611no—
260C22×C4—612no—
261C22×C4—611no—
262C22×C4—1224no—
263C22×C4—1224no—
264C22×C4—1222no—
265C22×C4—2441no—
266C22×C4—2442no—
267C22×C4—2441no—
268C22×C4—2441no—
269C22×C4—2442no—
270C22×C4—2441no—
271C22×C4—2444no—
272C22×C4—2444no—
273C22×C4—2444no—
274C22×C4—2444no—
275C22×C4—2442no—
276C22×C4—2444no—
277M16—2444no—
278M16—2444no—
279M16—2448no—
280C2×C8—1228no—
281C2×C8—2448no—
282C22⋊C4—42no—
283C22⋊C4—42no—
284C22⋊C4—2442no—
285C22⋊C4—2442no—
286C23—21no—
287C23—21no—
288C23—24no—
289C23—21no—
290C23—21no—
291C23—24no—
292C23—24no—
293C23—24no—
294C23—24no—
295C23—42no—
296C23—42no—
297C23—42no—
298C23—42no—
299C23—48no—
300C23—48no—
301C23(C2×#6923)⋊C412yes—
302C23(C2×#6923)⋊C412yes—
303C23#1451983512yes—
304C23#1451983612yes—
305C23C2×C4×#692311yescharacteristic
306C23C2×C22⋊#692311yescharacteristic
307C23C2×C4⋊#692311yescharacteristic
308C2×C4—44no—
309C2×C4—42no—
310C2×C4—84no—
311C2×C4—612no—
312C2×C4—612no—
313C2×C4—612no—
314C2×C4—612no—
315C2×C4—1222no—
316C2×C4—1222no—
317C2×C4—1222no—
318C2×C4—1222no—
319C2×C4—1224no—
320C2×C4—1224no—
321C2×C4—1224no—
322C2×C4—1224no—
323C2×C4—4884no—
324C2×C4—2441no—
325C2×C4—2442no—
326C2×C4—2442no—
327C2×C4—2442no—
328C2×C4—2442no—
329C2×C4—2442no—
330C2×C4—2441no—
331C2×C4—2441no—
332C2×C4—2442no—
333C2×C4—2441no—
334C2×C4—2444no—
335C2×C4—2442no—
336C8—2448no—
337C22—24no—
338C22—24no—
339C22—22no—
340C22—22no—
341C22—22no—
342C22—22no—
343C22—22no—
344C22—21no—
345C22—21no—
346C22—22no—
347C22—22no—
348C22—42no—
349C22—42no—
350C22—48no—
351C22—48no—
352C22—42no—
353C22—42no—
354C22#1684064014yes—
355C22#1684064314yes—
356C22C2×(C2×#6923)⋊C411yescharacteristic
357C22C2×#1451983511yescharacteristic
358C22C2×#1451983611yescharacteristic
359C4—82no—
360C4—1222no—
361C4—1222no—
362C4—1222no—
363C4—1222no—
364C4—4882no—
365C2—21no—
366C2—21no—
367C2—24no—
368C2—24no—
369C2—41no—
370C2—41no—
371C2C2×#1684064011yescharacteristic
372C2C2×#1684064312yes—
subgroupG/H
centerC22C2×(C2×#6923)⋊C4
commutatorC23×C61C2×C42
FrattiniC24C22×#6923
FittingC22×C22⋊C4×C61C4
socleC22×C61C2×#95
prime radicalC25×C61C2×C4
cosocleC23×Dic61C23
hypercenterC22×C22⋊C4#6923
hypocenterC61#8114
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C25 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #21460722C2semidirect
7. #16840732C4semidirect
10. C2×C22⋊#92420C4semidirect
26. C22⋊#92420C2×C4semidirect
204. C61#8114semidirect

Maximal subgroups

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

subgroupindex
C2×#168407322
#214607222
C2×#168396232
#811461