Finite Group Databasebeta

← #29663798

Subgroups — #29663798

Order 15616.

798 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
1#21455279C212yesmaximal, complemented
2C2×C8×D244C211yesmaximal, characteristic, complemented
3#21445253C214yesmaximal, complemented
4#21445205C212yesmaximal, complemented
5#21445171C212yesmaximal, complemented
6#21444578C211yesmaximal, characteristic, complemented
7#21444496C212yesmaximal, complemented
8C61×#3169C211yesmaximal, characteristic, complemented
9C2×#14519802—22no—
10C22×C8×D61—21no—
11C2×C4×D244C2211yescharacteristic
12#16839974—24no—
13#16839964C2214yes—
14#16839954C2214yes—
15C8×D244—21no—
16C8×D244—21no—
17C8×D244C2212yes—
18C8×D244C2212yes—
19#16839786C2212yes—
20C2×C4⋊#92418C2211yescharacteristic
21#16839763—22no—
22C2×#14519689—21no—
23#16839515C2212yescomplemented
24#16839515C2212yescomplemented
25#16839508C2214yescomplemented
26#16839506C2214yescomplemented
27C61×#532C2212yes—
28C61×#500C2211yescharacteristic, complemented
29C61×#493C2211yescharacteristic, complemented
30C61×#486C2212yescomplemented
31C61×#466—21no—
32C61×#466—21no—
33C4×D8×C61—21no—
34C4×D8×C61—21no—
35C2×C4×C8×C61C2211yescharacteristic
36C22×D244D411yescharacteristic
37C22×C4×D61—21no—
38#14519802—48no—
39C2×#11758201—24no—
40C2×#11758199—24no—
41C2×#11758194—22no—
42C22×#92418—21no—
43C2×C8×D61—22no—
44C2×C8×D61—22no—
45C2×C8×D61—44no—
46C4×D244—21no—
47C4×D244—21no—
48C4×D244D412yes—
49C4×D244C2312yes—
50C2×C4⋊Dic61D411yescharacteristic
51C2×#11758198—21no—
52C4⋊#92418—22no—
53C4⋊#92418—21no—
54C4⋊#92418C2314yes—
55C4⋊#92418C2312yes—
56#14519701—24no—
57#14519698—24no—
58#14519689—22no—
59#14519689—22no—
60C2×#41×C61—22no—
61C2×D8×C61—21no—
62C2×D8×C61—21no—
63C22×C8×C61D411yescharacteristic
64C22×C8×C61D411yescharacteristic
65C4⋊Q8×C61C2312yes—
66#127×C61C2312yes—
67#124×C61—22no—
68#121×C61—22no—
69#121×C61—22no—
70C4×D4×C61—22no—
71C4×D4×C61—22no—
72C2×C42×C61C2311yescharacteristic
73#107×C61—21no—
74#107×C61—21no—
75#102×C61—22no—
76#102×C61—22no—
77C4×C8×C61D411yescharacteristic
78C4×C8×C61D411yescharacteristic
79C4×C8×C61C2311yescharacteristic
80C4×C8×C61C2311yescharacteristic
81C23×D61—21no—
82#41×C61—44no—
83#41×C61—44no—
84C2×Q8×C61—22no—
85C2×D4×C61—22no—
86C2×D4×C61—22no—
87C2×D4×C61—22no—
88C2×D4×C61—42no—
89C22×C4×C61—42no—
90C22×C4×C61C2×D411yescharacteristic
91C22×C4×C61C2×D411yescharacteristic
92C22×C4×C61#4111yescharacteristic
93C22×Dic61—21no—
94C2×D244—21no—
95C2×D244—22no—
96C2×D244D814yescomplemented
97C2×D244C2×D412yes—
98C2×C4×D61—22no—
99C2×C4×D61—22no—
100C2×C4×D61—42no—
101C2×C4×D61—42no—
102D8×C61—42no—
103D8×C61—42no—
104C2×C8×C61—22no—
105C2×C8×C61—41no—
106C2×C8×C61C2×D411yescharacteristic
107C2×C8×C61C2×D411yescharacteristic
108C2×C8×C61C2×D411yescharacteristic
109C2×C8×C61C2×D411yescharacteristic
110C4⋊C4×C61—22no—
111C4⋊C4×C61—22no—
112C22⋊C4×C61—42no—
113C22⋊C4×C61—42no—
114C42×C61C2×D411yescharacteristic
115C42×C61C2×D411yescharacteristic
116C42×C61#4111yescharacteristic
117C42×C61C2411yescharacteristic
118#11758201—48no—
119#11758199—48no—
120#11758198—22no—
121#11758198—22no—
122C4⋊Dic61—21no—
123C4⋊Dic61C2×D412yes—
124#11758194—44no—
125C2×#92418—22no—
126C2×#92418—24no—
127C2×#92418—42no—
128C8×D61—44no—
129C8×D61—44no—
130C23×C61—42no—
131C23×C61#12111yescharacteristic
132C22×D61—22no—
133C22×D61—24no—
134C22×D61—42no—
135C22×D61—42no—
136Q8×C61—42no—
137Q8×C61—42no—
138D4×C61—42no—
139D4×C61—42no—
140D4×C61—42no—
141D4×C61—42no—
142D4×C61—82no—
143D4×C61—84no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—41no—
147C2×C4×C61—42no—
148C2×C4×C61—84no—
149C2×C4×C61#12111yescharacteristic
150C2×C4×C61#12111yescharacteristic
151C2×C4×C61#12111yescharacteristic
152C2×C4×C61C2×D812yes—
153C2×C4×C61#13512yes—
154C2×C4×C61C22×D411yescharacteristic
155C2×C4×C61C22×D411yescharacteristic
156C2×C4×C61C2×#4111yescharacteristic
157C2×Dic61—22no—
158C2×Dic61—42no—
159D244—22no—
160D244—24no—
161D244C2×D814yes—
162C4×D61—44no—
163C4×D61—42no—
164C4×D61—42no—
165C8×C61—21no—
166C8×C61—21no—
167C8×C61—21no—
168C8×C61AGL(1,ℤ/8)12yescomplemented
169#92418—44no—
170#92418—42no—
171#19255—611nomaximal, Sylow
172C22×C61—21no—
173C22×C61—21no—
174C22×C61—82no—
175C22×C61—82no—
176C22×C61—82no—
177C22×C61#46612yes—
178C22×C61C2×#12111yescharacteristic
179C2×D61—24no—
180C2×D61—48no—
181C2×D61—42no—
182C2×D61—42no—
183C4×C61—21no—
184C4×C61—21no—
185C4×C61—21no—
186C4×C61—82no—
187C4×C61#46612yes—
188C4×C61C22×D811yescharacteristic
189C4×C61C2×#13511yescharacteristic
190C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
191C4×C61#57511yescharacteristic
192Dic61—42no—
193#3169D6111yescharacteristic, complemented
194#3036—612no—
195C2×C8×D4—611no—
196#1681—614no—
197#1673—612no—
198#1667—612no—
199#1567—611no—
200#1547—612no—
201C2×C61—22no—
202C2×C61—162no—
203C2×C61#303611yescharacteristic
204C2×C61C2×#46611yescharacteristic
205C2×C61#306711yescharacteristic
206D61—44no—
207C2×AGL(1,ℤ/8)—1222no—
208C23×C8—1221no—
209#532C2×D6112yes—
210C2×C4×D4—611no—
211#500C2×D6111yescharacteristic, complemented
212#493C2×D6111yescharacteristic, complemented
213#486C2×D6112yescomplemented
214#466—21no—
215#466—21no—
216#463—1224no—
217#461—614no—
218#459—614no—
219C4×D8—21no—
220C4×D8—21no—
221C8×D4—612no—
222C8×D4—612no—
223C8×D4—1221no—
224C8×D4—1221no—
225#423—612no—
226C2×C4⋊C8—611no—
227#417—1222no—
228C2×C22⋊C8—1221no—
229C2×C4×C8C2×D6111yescharacteristic
230#335—612no—
231#335—612no—
232#332—614no—
233#331—614no—
234C61#1925511yescharacteristic, complemented, Sylow
235C2×#41—22no—
236C22×D4—611no—
237C23×C4—1221no—
238AGL(1,ℤ/8)—2448no—
239C2×SD16—1224no—
240C2×D8—21no—
241C2×D8—21no—
242C2×D8—1224no—
243C2×M16—1222no—
244C22×C8—1221no—
245C22×C8—1222no—
246C22×C8—1222no—
247C22×C8—2444no—
248C22×C8C22⋊D6111yescharacteristic
249C22×C8C22⋊D6111yescharacteristic
250C4⋊Q8C22×D6112yes—
251#127C22×D6112yes—
252#124—22no—
253#121—22no—
254#121—22no—
255C4×D4—22no—
256C4×D4—22no—
257C4×D4—612no—
258C4×D4—612no—
259C4×D4—1221no—
260C4×D4—1221no—
261C2×C4⋊C4—611no—
262C2×C22⋊C4—1221no—
263C2×C42C22×D6111yescharacteristic
264#107—21no—
265#107—21no—
266C4⋊C8—612no—
267C4⋊C8—614no—
268C4⋊C8—1222no—
269C4⋊C8—1221no—
270#103—1224no—
271#102—22no—
272#102—22no—
273#102—1224no—
274C22⋊C8—1222no—
275C22⋊C8—1222no—
276C4×C8C22⋊D6111yescharacteristic
277C4×C8C22⋊D6111yescharacteristic
278C4×C8C22×D6111yescharacteristic
279C4×C8C22×D6111yescharacteristic
280C24—1221no—
281#41—44no—
282#41—44no—
283C2×Q8—22no—
284C2×D4—22no—
285C2×D4—22no—
286C2×D4—22no—
287C2×D4—42no—
288C2×D4—612no—
289C2×D4—614no—
290C2×D4—1221no—
291C2×D4—1222no—
292C22×C4—42no—
293C22×C4—1221no—
294C22×C4—1222no—
295C22×C4—1222no—
296C22×C4—2442no—
297C22×C4—2442no—
298C22×C4D4×D6111yescharacteristic
299C22×C4#1175822411yescharacteristic
300C22×C4C2×C22⋊D6111yescharacteristic
301SD16—2448no—
302D8—42no—
303D8—42no—
304D8—2448no—
305M16—2444no—
306C2×C8—22no—
307C2×C8—41no—
308C2×C8—1224no—
309C2×C8—1222no—
310C2×C8—2444no—
311C2×C8—2442no—
312C2×C8—2444no—
313C2×C8C2×C22⋊D6111yescharacteristic
314C2×C8C2×C22⋊D6111yescharacteristic
315C2×C8C2×C22⋊D6111yescharacteristic
316C2×C8C2×C22⋊D6111yescharacteristic
317C4⋊C4—22no—
318C4⋊C4—22no—
319C4⋊C4—612no—
320C4⋊C4—1221no—
321C22⋊C4—42no—
322C22⋊C4—42no—
323C22⋊C4—1222no—
324C22⋊C4—1222no—
325C42D4×D6111yescharacteristic
326C42#1175822411yescharacteristic
327C42C2×C22⋊D6111yescharacteristic
328C42C23×D6111yescharacteristic
329C23—42no—
330C23—1224no—
331C23—1222no—
332C23—2442no—
333C23—2442no—
334C23#1451974811yescharacteristic
335Q8—42no—
336Q8—42no—
337D4—42no—
338D4—42no—
339D4—42no—
340D4—42no—
341D4—82no—
342D4—84no—
343D4—614no—
344D4—1224no—
345D4—1222no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—41no—
349C2×C4—42no—
350C2×C4—84no—
351C2×C4—1222no—
352C2×C4—2444no—
353C2×C4—2442no—
354C2×C4—2442no—
355C2×C4—2442no—
356C2×C4#1451974811yescharacteristic
357C2×C4#1451974811yescharacteristic
358C2×C4#1451974811yescharacteristic
359C2×C4D8×D6112yes—
360C2×C4#1451979612yes—
361C2×C4C2×D4×D6111yescharacteristic
362C2×C4C22×C22⋊D6111yescharacteristic
363C2×C4C2×#1175822411yescharacteristic
364C8—21no—
365C8—21no—
366C8—21no—
367C8—2444no—
368C8—2442no—
369C8#1451980212yescomplemented
370C22—21no—
371C22—21no—
372C22—82no—
373C22—82no—
374C22—82no—
375C22—1224no—
376C22—2448no—
377C22—2442no—
378C22—2442no—
379C22#1683999512yes—
380C22C2×#1451974811yescharacteristic
381C4—21no—
382C4—21no—
383C4—21no—
384C4—82no—
385C4—2442no—
386C4#1683999512yes—
387C4C2×D8×D6111yescharacteristic
388C4C2×#1451979611yescharacteristic
389C4C2×#1451980211yescharacteristic
390C4#1684056011yescharacteristic
391C2—22no—
392C2—162no—
393C2—2444no—
394C2#2145527911yescharacteristic
395C2C2×#1683999511yescharacteristic
396C2#2145553511yescharacteristic
subgroupG/H
centerC22C2×#14519748
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3169C2
socleC22×C61C2×#121
hypercenter#3169D61
hypocenterC61#19255
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3169

Complements

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

NH ≅ G/Ntype
1. #21455279C2semidirect
2. C2×C8×D244C2semidirect
3. #21445253C2semidirect
4. #21445205C2semidirect
5. #21445171C2semidirect
6. #21444578C2semidirect
7. #21444496C2semidirect
8. C61×#3169C2semidirect
23. #16839515C22semidirect
24. #16839515C22semidirect
25. #16839508C22semidirect
26. #16839506C22semidirect
28. C61×#500C22semidirect
29. C61×#493C22semidirect
30. C61×#486C22semidirect
96. C2×D244D8semidirect
168. C8×C61AGL(1,ℤ/8)semidirect
193. #3169D61semidirect
211. #500C2×D61semidirect
212. #493C2×D61semidirect
213. #486C2×D61semidirect
234. C61#19255semidirect
369. C8#14519802semidirect

Maximal subgroups

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

subgroupindex
#214552792
C2×C8×D2442
#214452532
#214452052
#214451712
#214445782
#214444962
C61×#31692
#1925561