Finite Group Databasebeta

← #30602516

Subgroups — #30602516

Order 15616.

1258 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519838C212yesmaximal
2C2×#16840642C212yesmaximal
3#21461482C212yesmaximal
4C22×#14519742C211yesmaximal, characteristic
5C22×#11758217C2214yes—
6C2×#14519838—24no—
7C2×#14519838—24no—
8C2×#14519838C418yescomplemented
9#16840642—24no—
10#16840628—24no—
11C23×Dic122C2211yescharacteristic
12C2×#14519742—24no—
13C2×#14519742—24no—
14C2×#14519742—24no—
15C22×#11758196C411yescharacteristic
16C22×#11758196C2211yescharacteristic
17C22×C4×Dic61C411yescharacteristic
18C22×C4×Dic61C411yescharacteristic
19C22×C4×Dic61C2211yescharacteristic
20C22×C4⋊C4×C61C411yescharacteristic
21C2×#11758217—24no—
22C2×#11758217—24no—
23C2×#11758217—24no—
24C2×#11758217—24no—
25C2×#11758217—24no—
26C2×#11758217C2×C418yes—
27C22×#92420—24no—
28#14519838—216no—
29C22×Dic122—22no—
30C22×Dic122—22no—
31C22×Dic122—22no—
32C22×Dic122—22no—
33C22×Dic122C2×C414yes—
34C22×Dic122D412yes—
35C22×Dic122D414yes—
36C22×Dic122Q812yes—
37C23×Dic61C2×C411yescharacteristic
38C23×Dic61C2×C411yescharacteristic
39C23×Dic61C2×C411yescharacteristic
40C23×Dic61C2311yescharacteristic
41#14519742—232no—
42C2×#11758196—22no—
43C2×#11758196—22no—
44C2×#11758196—22no—
45C2×#11758196—22no—
46C2×#11758196—22no—
47C2×#11758196D414yes—
48C2×C4×Dic61—22no—
49C2×C4×Dic61—22no—
50C2×C4×Dic61—22no—
51C2×C4×Dic61—22no—
52C2×C4×Dic61—22no—
53C2×C4×Dic61—22no—
54C2×C4×Dic61—22no—
55C2×C4×Dic61—22no—
56C2×C4×Dic61D414yes—
57C23×C4×C61C2×C411yescharacteristic
58C23×C4×C61C2×C411yescharacteristic
59C23×C4×C61C2×C411yescharacteristic
60C2×C4⋊C4×C61—22no—
61C2×C4⋊C4×C61—22no—
62C2×C4⋊C4×C61—22no—
63C24×C61C22×C411yescharacteristic
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61—42no—
73C22×C4×C61—42no—
74C22×C4×C61C4212yes—
75C22×C4×C61C22⋊C412yes—
76C22×C4×C61C22⋊C412yes—
77C22×C4×C61C22⋊C412yes—
78C22×C4×C61C4⋊C412yes—
79C22×Dic61—21no—
80C22×Dic61—21no—
81C22×Dic61—21no—
82C22×Dic61—21no—
83C22×Dic61—21no—
84C22×Dic61—21no—
85C22×Dic61—24no—
86C22×Dic61—21no—
87C22×Dic61—21no—
88C22×Dic61—42no—
89C22×Dic61C4212yes—
90C22×Dic61C22⋊C412yes—
91C22×Dic61C22⋊C412yes—
92C22×Dic61C22⋊C412yes—
93C22×Dic61C4⋊C412yes—
94C22×Dic61C22×C412yes—
95C22×Dic61C2×D411yescharacteristic
96C22×Dic61C2×D412yes—
97C22×Dic61C2×D412yes—
98C22×Dic61C2×D412yes—
99C22×Dic61C2×Q811yescharacteristic
100C22×Dic61#4112yes—
101C22×Dic61#4112yes—
102C2×Dic122—28no—
103C2×Dic122—28no—
104C2×Dic122—28no—
105C2×Dic122—24no—
106C2×Dic122—24no—
107C2×Dic122—24no—
108C2×Dic122—24no—
109C2×Dic122—28no—
110C2×Dic122C22⋊C418yes—
111C2×Dic122C4⋊C418yes—
112#11758217—28no—
113#11758217—28no—
114#11758217—44no—
115#11758217—44no—
116C2×#92420—28no—
117C2×#92420—44no—
118C2×#92420—44no—
119C4⋊C4×C61—28no—
120#11758196—28no—
121#11758196—28no—
122C4×Dic61—28no—
123C4×Dic61—28no—
124C4×Dic61—28no—
125C23×C61—22no—
126C23×C61—22no—
127C23×C61C2×C4211yescharacteristic
128C23×C61C2×C22⋊C411yescharacteristic
129C23×C61C2×C22⋊C411yescharacteristic
130C23×C61C2×C22⋊C411yescharacteristic
131C23×C61C2×C4⋊C411yescharacteristic
132C23×C61#11711yescharacteristic
133C23×C61#11711yescharacteristic
134C2×C4×C61—22no—
135C2×C4×C61—22no—
136C2×C4×C61—22no—
137C2×C4×C61—22no—
138C2×C4×C61—22no—
139C2×C4×C61—22no—
140C2×C4×C61—22no—
141C2×C4×C61—22no—
142C2×C4×C61—24no—
143C2×C4×C61—42no—
144C2×C4×C61—42no—
145C2×C4×C61—42no—
146C2×C4×C61—42no—
147C2×C4×C61—42no—
148C2×C4×C61#9514yes—
149C2×Dic61—24no—
150C2×Dic61—24no—
151C2×Dic61—22no—
152C2×Dic61—22no—
153C2×Dic61—22no—
154C2×Dic61—22no—
155C2×Dic61—22no—
156C2×Dic61—22no—
157C2×Dic61—22no—
158C2×Dic61—22no—
159C2×Dic61—22no—
160C2×Dic61—42no—
161C2×Dic61—42no—
162C2×Dic61—42no—
163C2×Dic61#9514yes—
164C2×Dic61#10114yescomplemented
165C2×Dic61C2×C22⋊C412yes—
166C2×Dic61C2×C4⋊C412yes—
167C2×Dic61C4×D414yes—
168C2×Dic61C4×D414yes—
169C2×Dic61#12014yes—
170C2×Dic61#12112yes—
171C2×Dic61#12112yes—
172C2×Dic61C22⋊Q812yes—
173C2×Dic61C22⋊Q812yes—
174C2×Dic61#12314yes—
175Dic122—216no—
176Dic122—216no—
177#92420—48no—
178#10763—611nomaximal, Sylow
179C22×C61—22no—
180C22×C61—22no—
181C22×C61—22no—
182C22×C61—22no—
183C22×C61—21no—
184C22×C61—21no—
185C22×C61—21no—
186C22×C61—21no—
187C22×C61C2×#9511yescharacteristic
188C22×C61C4×C22⋊C411yescharacteristic
189C22×C61C4×C22⋊C411yescharacteristic
190C22×C61#37911yescharacteristic
191C22×C61#38011yescharacteristic
192C22×C61#38011yescharacteristic
193C22×C61#38111yescharacteristic
194C22×C61C2×#10112yes—
195C22×C61#41312yes—
196C4×C61—24no—
197C4×C61—42no—
198C4×C61—42no—
199Dic61—24no—
200Dic61—24no—
201Dic61—42no—
202Dic61#38514yes—
203Dic61#38614yes—
204C22×C4×Q8—611no—
205C22×#101—612no—
206C2×#343—612no—
207#1728—612no—
208C2×C61—21no—
209C2×C61—21no—
210C2×C61—21no—
211C2×C61—21no—
212C2×C61C22⋊#9511yescharacteristic
213C2×C61C4×#10112yes—
214C2×C61#178411yescharacteristic
215C2×C61#178511yescharacteristic
216C2×C61#180112yes—
217C23×Q8—611no—
218C22×M16—614no—
219C2×C4×Q8—1224no—
220C2×C4×Q8—1224no—
221C2×C4×Q8—1224no—
222C22×C4⋊C4—611no—
223C22×C4⋊C4—611no—
224C22×C4⋊C4#692311yescharacteristic
225C22×C42—611no—
226C22×C42—611no—
227C22×C42—611no—
228C2×#101—618no—
229C2×#101—1224no—
230C2×#101—1224no—
231#343—1224no—
232#336—1224no—
233C61#1076311yescharacteristic, complemented, Sylow
234C22×Q8—614no—
235C22×Q8—612no—
236C22×Q8—612no—
237C22×Q8—614no—
238C22×Q8—1222no—
239C22×Q8—1222no—
240C22×Q8—1222no—
241C22×Q8—1222no—
242C23×C4—611no—
243C23×C4—611no—
244C23×C4—611no—
245C23×C4—611no—
246C23×C4C2×#692311yescharacteristic
247C23×C4C2×#692311yescharacteristic
248C23×C4C2×#692311yescharacteristic
249C2×M16—618no—
250C2×M16—1224no—
251C2×M16—1224no—
252C2×M16—1224no—
253C2×M16—1224no—
254C2×M16—1224no—
255C22×C8—1224no—
256C4×Q8—12232no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—614no—
261C2×C4⋊C4—1222no—
262C2×C4⋊C4—1222no—
263C2×C4⋊C4—1222no—
264C2×C4⋊C4—1222no—
265C2×C4⋊C4—1222no—
266C2×C42—614no—
267C2×C42—1222no—
268C2×C42—1222no—
269C2×C42—1222no—
270C2×C42—1222no—
271C2×C42—1222no—
272C2×C42—1222no—
273C2×C42—1222no—
274C2×C42—1222no—
275#101—12216no—
276C24C22×#692311yescharacteristic
277C2×Q8—618no—
278C2×Q8—618no—
279C2×Q8—1228no—
280C2×Q8—1224no—
281C2×Q8—1224no—
282C2×Q8—1224no—
283C2×Q8—1224no—
284C2×Q8—1228no—
285C2×Q8—1228no—
286C2×Q8—1228no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4—612no—
298C22×C4—612no—
299C22×C4—612no—
300C22×C4—612no—
301C22×C4—611no—
302C22×C4—611no—
303C22×C4—612no—
304C22×C4—612no—
305C22×C4—612no—
306C22×C4—612no—
307C22×C4—612no—
308C22×C4—612no—
309C22×C4—612no—
310C22×C4—1224no—
311C22×C4—1221no—
312C22×C4—1221no—
313C22×C4—1221no—
314C22×C4—1221no—
315C22×C4—1221no—
316C22×C4—1221no—
317C22×C4—1221no—
318C22×C4—1221no—
319C22×C4—2442no—
320C22×C4C4×#692312yes—
321C22×C4C4⋊#692312yes—
322C22×C4C22⋊#692312yes—
323C22×C4C22⋊#692312yes—
324C22×C4C22⋊#692312yes—
325M16—1228no—
326M16—1228no—
327M16—2444no—
328M16—2444no—
329C2×C8—1228no—
330C2×C8—2444no—
331C2×C8—2444no—
332C4⋊C4—28no—
333C4⋊C4—1228no—
334C4⋊C4—1228no—
335C42—1228no—
336C42—1228no—
337C42—1228no—
338C23—22no—
339C23—22no—
340C23C2×C4×#692311yescharacteristic
341C23C2×C22⋊#692311yescharacteristic
342C23C2×C22⋊#692311yescharacteristic
343C23C2×C22⋊#692311yescharacteristic
344C23C2×C4⋊#692311yescharacteristic
345C23#1451985611yescharacteristic
346C23#1451985611yescharacteristic
347Q8—12216no—
348Q8—12216no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—24no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—612no—
364C2×C4—612no—
365C2×C4—612no—
366C2×C4—612no—
367C2×C4—614no—
368C2×C4—612no—
369C2×C4—612no—
370C2×C4—614no—
371C2×C4—614no—
372C2×C4—614no—
373C2×C4—614no—
374C2×C4—614no—
375C2×C4—1224no—
376C2×C4—1224no—
377C2×C4—1222no—
378C2×C4—1222no—
379C2×C4—1222no—
380C2×C4—1222no—
381C2×C4—1222no—
382C2×C4—1222no—
383C2×C4—1222no—
384C2×C4—1222no—
385C2×C4—1222no—
386C2×C4—2442no—
387C2×C4—2442no—
388C2×C4—2442no—
389C2×C4(C2×#6923)⋊C414yes—
390C8—2448no—
391C22—22no—
392C22—22no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—22no—
398C22—22no—
399C22C2×(C2×#6923)⋊C411yescharacteristic
400C22C4×C22⋊#692311yescharacteristic
401C22C4×C22⋊#692311yescharacteristic
402C22#1684070311yescharacteristic
403C22#1684070411yescharacteristic
404C22#1684070411yescharacteristic
405C22#1684070511yescharacteristic
406C22D61⋊#10112yes—
407C22#1684074912yes—
408C4—24no—
409C4—42no—
410C4—42no—
411C4—614no—
412C4—614no—
413C4—1224no—
414C4—1224no—
415C4—2442no—
416C2—21no—
417C2—21no—
418C2—21no—
419C2—21no—
420C2#2146099311yescharacteristic
421C2#2146157212yes—
422C2#2146165411yescharacteristic
423C2#2146165611yescharacteristic
424C2#2146168612yes—
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC23×C61C2×C42
FrattiniC24C22×#6923
FittingC22×C4⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22×C4
cosocleC23×Dic61C23
hypercenterC22×C4⋊C4#6923
hypocenterC61#10763
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
8. C2×#14519838C4semidirect
164. C2×Dic61#101semidirect
233. C61#10763semidirect

Maximal subgroups

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

subgroupindex
C22×#145198382
C2×#168406422
#214614822
C22×#145197422
#1076361