Finite Group Databasebeta

← #30617857

Subgroups — #30617857

Order 15616.

1270 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840782C211yesmaximal, characteristic
2C2×#16840778C211yesmaximal, characteristic
3#21461992C214yesmaximal, complemented
4#21461990C214yesmaximal, complemented
5#21461710C212yesmaximal
6#21461709C212yesmaximal
7C22×#14519742C211yesmaximal, characteristic
8#16840782—24no—
9#16840778—24no—
10C2×#14519844C2212yes—
11C2×C4⋊#92420C2212yes—
12C2×C22⋊#92420C2212yes—
13C2×C22⋊#92420C2212yes—
14C2×#14519832C2212yes—
15C2×C4×#92420C2212yes—
16#16840628C2218yes—
17#16840628C2218yes—
18C23×Dic122C411yescharacteristic
19C2×#14519742—24no—
20C2×#14519742—24no—
21C2×#14519742C412yes—
22C2×#14519742C412yes—
23C2×#14519742C2212yes—
24C2×#14519742C2212yes—
25C22×#11758196C411yescharacteristic
26C22×#11758196C411yescharacteristic
27C22×C4×Dic61C2211yescharacteristic
28C22×C4×Dic61C2211yescharacteristic
29C22×C4×Dic61C2211yescharacteristic
30C22×C4⋊C4×C61C411yescharacteristic
31C22×#92420C2314yes—
32C22×#92420C2314yes—
33#14519844—24no—
34C4⋊#92420—24no—
35C22⋊#92420—24no—
36C22⋊#92420—24no—
37#14519832—24no—
38C4×#92420—24no—
39C22×Dic122—24no—
40C22×Dic122—28no—
41C22×Dic122C2×C412yes—
42C22×Dic122C2×C412yes—
43C23×Dic61C2×C411yescharacteristic
44C23×Dic61C2×C411yescharacteristic
45C23×Dic61C2×C411yescharacteristic
46C23×Dic61C2311yescharacteristic
47#14519742—28no—
48#14519742—28no—
49#14519742—24no—
50#14519742—24no—
51#14519742—24no—
52#14519742—24no—
53C2×#11758196—24no—
54C2×#11758196—24no—
55C2×#11758196C2×C412yes—
56C2×#11758196C2×C412yes—
57C2×#11758196C2×C412yes—
58C2×#11758196C2×C412yes—
59C2×C4×Dic61—22no—
60C2×C4×Dic61—22no—
61C2×C4×Dic61—22no—
62C2×C4×Dic61—22no—
63C2×C4×Dic61C2×C412yes—
64C2×C4×Dic61C2×C412yes—
65C2×C4×Dic61C2×C411yescharacteristic
66C2×C4×Dic61C2×C411yescharacteristic
67C2×C4×Dic61D414yes—
68C2×C4×Dic61D414yes—
69C2×C4×Dic61C2312yes—
70C2×C4×Dic61C2312yes—
71C2×C4×Dic61C2311yescharacteristic
72C2×C4×Dic61C2311yescharacteristic
73C23×C4×C61C2×C411yescharacteristic
74C23×C4×C61C2×C411yescharacteristic
75C23×C4×C61C2×C411yescharacteristic
76C2×C4⋊C4×C61—24no—
77C2×C4⋊C4×C61C2×C412yes—
78C2×C4⋊C4×C61C2×C412yes—
79C24×C61C22×C411yescharacteristic
80C22×C4×C61—22no—
81C22×C4×C61—24no—
82C22×C4×C61—24no—
83C22×C4×C61—22no—
84C22×C4×C61—24no—
85C22×C4×C61C22⋊C414yes—
86C22×C4×C61C22×C412yes—
87C22×C4×C61C22×C411yescharacteristic
88C22×C4×C61C22×C411yescharacteristic
89C22×C4×C61C22×C412yes—
90C22×Dic61—22no—
91C22×Dic61—24no—
92C22×Dic61—24no—
93C22×Dic61—24no—
94C22×Dic61—22no—
95C22×Dic61—24no—
96C22×Dic61C22⋊C414yes—
97C22×Dic61C22×C412yes—
98C22×Dic61C22×C411yescharacteristic
99C22×Dic61C22×C411yescharacteristic
100C22×Dic61C22×C412yes—
101C22×Dic61C22×C411yescharacteristic
102C22×Dic61C2×D412yes—
103C22×Dic61C2×D412yes—
104C22×Dic61C2411yescharacteristic
105C2×Dic122—232no—
106C2×Dic122—24no—
107C2×Dic122—24no—
108C2×Dic122—24no—
109C2×Dic122—24no—
110C2×Dic122—24no—
111C2×Dic122M1618yes—
112C2×#92420—24no—
113C2×#92420—24no—
114C2×#92420—28no—
115C2×#92420—28no—
116C4⋊C4×C61—24no—
117C4⋊C4×C61—24no—
118#11758196—24no—
119#11758196—24no—
120#11758196—24no—
121#11758196—24no—
122C4×Dic61—24no—
123C4×Dic61—24no—
124C4×Dic61—22no—
125C4×Dic61—22no—
126C4×Dic61—22no—
127C4×Dic61—22no—
128C4×Dic61C22⋊C414yes—
129C4×Dic61C22⋊C414yes—
130C4×Dic61C2×D412yes—
131C4×Dic61C2×D412yes—
132C4×Dic61C2×D412yes—
133C4×Dic61C2×D412yes—
134C23×C61—22no—
135C23×C61—22no—
136C23×C61C2×C22⋊C412yes—
137C23×C61#13114yes—
138C23×C61C23×C411yescharacteristic
139C2×C4×C61—28no—
140C2×C4×C61—22no—
141C2×C4×C61—22no—
142C2×C4×C61—22no—
143C2×C4×C61—22no—
144C2×C4×C61—28no—
145C2×C4×C61—22no—
146C2×C4×C61—24no—
147C2×C4×C61—44no—
148C2×C4×C61C2×C22⋊C412yes—
149C2×C4×C61C2×C22⋊C412yes—
150C2×C4×C61C2×M1614yes—
151C2×Dic61—28no—
152C2×Dic61—22no—
153C2×Dic61—22no—
154C2×Dic61—22no—
155C2×Dic61—22no—
156C2×Dic61—24no—
157C2×Dic61—24no—
158C2×Dic61—28no—
159C2×Dic61—22no—
160C2×Dic61—24no—
161C2×Dic61—44no—
162C2×Dic61C2×C22⋊C412yes—
163C2×Dic61C2×C22⋊C412yes—
164C2×Dic61C2×C22⋊C412yes—
165C2×Dic61C2×M1614yes—
166C2×Dic61C2×M1614yes—
167C2×Dic61C22×D411yescharacteristic
168C2×Dic61C22×D411yescharacteristic
169C2×Dic612−1+414yes—
170Dic122—216no—
171Dic122—216no—
172#92420—44no—
173#92420—44no—
174#21820—611nomaximal, Sylow
175C22×C61—22no—
176C22×C61—22no—
177C22×C61—28no—
178C22×C61#40814yes—
179C22×C61C22×C22⋊C411yescharacteristic
180C22×C61#51912yes—
181C22×C61C22×M1612yes—
182C22×C61C2×#13112yes—
183C4×C61—24no—
184C4×C61—22no—
185C4×C61—22no—
186C4×C61—42no—
187Dic61—22no—
188Dic61—22no—
189Dic61—24no—
190Dic61—42no—
191Dic61#40714yes—
192Dic61#53612yes—
193Dic61#53612yes—
194C22×C4×Q8—611no—
195C2×#432—611no—
196C2×#431—611no—
197#1985—614no—
198#1984—614no—
199#1817—612no—
200#1817—612no—
201C2×C61—24no—
202C2×C61#231011yescharacteristic
203C2×C61C2×#40711yescharacteristic
204C2×C61C2×#40811yescharacteristic
205C2×C61#298414yes—
206C23×Q8—611no—
207C2×C4×Q8—612no—
208C2×C4×Q8—612no—
209C2×C4×Q8—612no—
210C2×C4×Q8—612no—
211C2×C4×Q8—1224no—
212C2×C4×Q8—1224no—
213C22×C4⋊C4—611no—
214C22×C4⋊C4—611no—
215C22×C4⋊C4#692311yescharacteristic
216C22×C42—611no—
217C22×C42—611no—
218C22×C42—611no—
219#432—1224no—
220#431—1224no—
221C2×C4⋊C8—612no—
222C2×C4⋊C8—612no—
223C2×C22⋊C8—612no—
224C2×C22⋊C8—612no—
225C2×#97—612no—
226C2×C4×C8—612no—
227#336—618no—
228#336—618no—
229C61#2182011yescharacteristic, complemented, Sylow
230C22×Q8—612no—
231C22×Q8—612no—
232C22×Q8—1224no—
233C22×Q8—1228no—
234C23×C4—611no—
235C23×C4—611no—
236C23×C4—611no—
237C23×C4—611no—
238C23×C4C2×#692311yescharacteristic
239C23×C4C2×#692311yescharacteristic
240C23×C4C2×#692311yescharacteristic
241C22×C8—614no—
242C22×C8—614no—
243C4×Q8—1224no—
244C4×Q8—1224no—
245C4×Q8—1224no—
246C4×Q8—1224no—
247C4×Q8—1228no—
248C4×Q8—1228no—
249C2×C4⋊C4—24no—
250C2×C4⋊C4—612no—
251C2×C4⋊C4—612no—
252C2×C4⋊C4—612no—
253C2×C4⋊C4—612no—
254C2×C4⋊C4—1224no—
255C2×C4⋊C4—1224no—
256C2×C4⋊C4C2×#692312yes—
257C2×C4⋊C4C2×#692312yes—
258C2×C42—614no—
259C2×C42—614no—
260C2×C42—611no—
261C2×C42—611no—
262C2×C42—611no—
263C2×C42—611no—
264C2×C42—612no—
265C2×C42—612no—
266C2×C42—612no—
267C2×C42—612no—
268C2×C42—1222no—
269C2×C42—1222no—
270C2×C42—1222no—
271C2×C42—1222no—
272C4⋊C8—1224no—
273C4⋊C8—1224no—
274C22⋊C8—1224no—
275C22⋊C8—1224no—
276#97—1224no—
277C4×C8—1224no—
278C24C22×#692311yescharacteristic
279C2×Q8—618no—
280C2×Q8—1224no—
281C2×Q8—1224no—
282C2×Q8—1224no—
283C2×Q8—1224no—
284C2×Q8—12232no—
285C2×Q8—1224no—
286C22×C4—22no—
287C22×C4—24no—
288C22×C4—24no—
289C22×C4—22no—
290C22×C4—24no—
291C22×C4—611no—
292C22×C4—611no—
293C22×C4—612no—
294C22×C4—612no—
295C22×C4—614no—
296C22×C4—611no—
297C22×C4—611no—
298C22×C4—612no—
299C22×C4—612no—
300C22×C4—1224no—
301C22×C4—1224no—
302C22×C4—1224no—
303C22×C4—1222no—
304C22×C4—1222no—
305C22×C4—1224no—
306C22×C4C22⋊#692314yes—
307C22×C4C22×#692312yes—
308C22×C4C22×#692311yescharacteristic
309C22×C4C22×#692311yescharacteristic
310C22×C4C22×#692312yes—
311C2×C8—1224no—
312C2×C8—1224no—
313C2×C8—1228no—
314C2×C8—1228no—
315C4⋊C4—24no—
316C4⋊C4—24no—
317C4⋊C4—1224no—
318C4⋊C4—1224no—
319C4⋊C4—1224no—
320C4⋊C4—1224no—
321C42—612no—
322C42—612no—
323C42—612no—
324C42—612no—
325C42—614no—
326C42—614no—
327C42—1222no—
328C42—1222no—
329C42—1224no—
330C42—1222no—
331C42—1222no—
332C42—1224no—
333C23—22no—
334C23—22no—
335C23C2×C22⋊#692312yes—
336C23#1451986414yes—
337C23C23×#692311yescharacteristic
338Q8—12216no—
339Q8—12216no—
340C2×C4—28no—
341C2×C4—28no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—24no—
348C2×C4—44no—
349C2×C4—612no—
350C2×C4—611no—
351C2×C4—611no—
352C2×C4—614no—
353C2×C4—614no—
354C2×C4—612no—
355C2×C4—612no—
356C2×C4—614no—
357C2×C4—1224no—
358C2×C4—1224no—
359C2×C4—1228no—
360C2×C4—1228no—
361C2×C4—1222no—
362C2×C4—1222no—
363C2×C4—1222no—
364C2×C4—1222no—
365C2×C4—1222no—
366C2×C4—1224no—
367C2×C4—2444no—
368C2×C4C2×C22⋊#692312yes—
369C2×C4C2×C22⋊#692312yes—
370C2×C4D61⋊M1614yes—
371C8—2444no—
372C8—2444no—
373C22—22no—
374C22—22no—
375C22—28no—
376C22#1684073514yes—
377C22C22×C22⋊#692311yescharacteristic
378C22#1684083012yes—
379C22C2×D61⋊M1612yes—
380C22C2×#1451986412yes—
381C4—24no—
382C4—22no—
383C4—22no—
384C4—42no—
385C4—612no—
386C4—612no—
387C4—614no—
388C4—1222no—
389C4—1222no—
390C4—1224no—
391C4—2442no—
392C2—24no—
393C2#2146229311yescharacteristic
394C2D61⋊#40711yescharacteristic
395C2C2×#1684073511yescharacteristic
396C2#2146271914yes—
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC22×C4⋊C4×C61C4
prime radicalC24×C61C22×C4
cosocleC22×Dic61C24
hypercenterC22×C4⋊C4#6923
hypocenterC61#21820
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #21461992C2semidirect
4. #21461990C2semidirect
229. C61#21820semidirect

Maximal subgroups

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

subgroupindex
C2×#168407822
C2×#168407782
#214619922
#214619902
#214617102
#214617092
C22×#145197422
#2182061