Finite Group Databasebeta

← #29590245

Subgroups — #29590245

Order 15616.

504 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 89 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
1#21455402C211yesmaximal, characteristic
2#21447428C211yesmaximal, characteristic, complemented
3#340×D61C211yesmaximal, characteristic, complemented
4#21443831C211yesmaximal, characteristic, complemented
5#21443829C211yesmaximal, characteristic, complemented
6#21443827C211yesmaximal, characteristic, complemented
7C61×#1348C211yesmaximal, characteristic, complemented
8C2×#14519800C411yescharacteristic, complemented
9C22×C8×D61C2211yescharacteristic
10#16840275—21no—
11C2×C4⋊C4×D61—21no—
12C2×#14519716—21no—
13#16840000C411yescharacteristic, complemented
14#16839999C411yescharacteristic, complemented
15#16839998C2211yescharacteristic
16#16839994—21no—
17#16839993—21no—
18#16839799C411yescharacteristic, complemented
19#16839757—21no—
20C22⋊#11758185C2211yescharacteristic
21#16839541—21no—
22#16839525C2211yescharacteristic
23#16839524—21no—
24C61×#467C2211yescharacteristic
25C61×C22⋊C16C2211yescharacteristic
26C61×#340C2211yescharacteristic
27C2×#11758226—21no—
28C22×C4×D61—41no—
29C22×C4×D61D411yescharacteristic
30#14519800—42no—
31C2×#11758201—21no—
32C2×D488C2×C411yescharacteristic, complemented
33C22×#92418D411yescharacteristic
34C2×C8×D61—42no—
35C2×C8×D61C2×C411yescharacteristic
36C2×C8×D61C2×C411yescharacteristic
37C2×C8×D61D411yescharacteristic
38C2×C8×D61D411yescharacteristic
39#14519762—41no—
40#14519753—21no—
41#14519752—21no—
42#14519751—21no—
43#14519747—41no—
44#14519739—41no—
45#14519737—41no—
46#14519735—21no—
47C2×C4⋊Dic61—21no—
48C2×#11758196—41no—
49C4⋊C4×D61—24no—
50C4⋊C4×D61—42no—
51#14519716—42no—
52C2×#11758185—21no—
53#14519711C2×C411yescharacteristic, complemented
54#14519708—21no—
55#14519701—21no—
56#14519699—21no—
57#14519697—21no—
58C2×Q16×C61C2×C411yescharacteristic, complemented
59C22×C8×C61C2311yescharacteristic
60C22⋊Q8×C61—21no—
61C2×C4⋊C4×C61—21no—
62C2×C16×C61—21no—
63#107×C61C2×C411yescharacteristic, complemented
64#103×C61—21no—
65C23×D61D811yescharacteristic
66C2×Q8×C61—21no—
67C22×C4×C61—41no—
68C22×C4×C61C2×D411yescharacteristic
69C2×C22⋊D61—41no—
70C22×Dic61—41no—
71C22×Dic61D811yescharacteristic
72#11758226—42no—
73#11758226—42no—
74C2×D244—21no—
75C2×D244—41no—
76C2×D244—41no—
77C2×C4×D61—22no—
78C2×C4×D61—22no—
79C2×C4×D61—44no—
80C2×C4×D61—41no—
81C2×C4×D61—82no—
82C2×C4×D61—82no—
83C2×C4×D61C22⋊C411yescharacteristic
84C2×C4×D61C22⋊C411yescharacteristic
85C2×C4×D61SD1611yescharacteristic
86C2×C4×D61SD1611yescharacteristic
87Q16×C61—41no—
88C2×C8×C61—41no—
89C2×C8×C61C22×C411yescharacteristic
90C2×C8×C61C2×D411yescharacteristic
91C4⋊C4×C61—22no—
92C4⋊C4×C61—21no—
93C4⋊C4×C61—41no—
94C4⋊C4×C61—41no—
95C22⋊C4×C61—41no—
96#11758201—42no—
97#11758198—41no—
98#11758198—41no—
99#11758198—41no—
100#11758198—41no—
101C4⋊Dic61—22no—
102C4⋊Dic61—21no—
103C4⋊Dic61—41no—
104#11758196—44no—
105#11758196—41no—
106C4×Dic61—41no—
107C2×#92418—41no—
108C2×#92418C22⋊C411yescharacteristic
109C2×#92418C22⋊C411yescharacteristic
110D488—41no—
111C8×D61—22no—
112C8×D61—22no—
113C8×D61—41no—
114C8×D61—41no—
115C16×C61—41no—
116#11758185—41no—
117C23×C61C2×D811yescharacteristic
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—22no—
121C22×D61—22no—
122C22×D61—41no—
123C22×D61#10211yescharacteristic
124C22×D61#10211yescharacteristic
125Q8×C61—41no—
126Q8×C61—41no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—42no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—81no—
133C2×C4×C61—81no—
134C2×C4×C61C2×C22⋊C411yescharacteristic
135C2×C4×C61C2×SD1611yescharacteristic
136C22⋊D61—81no—
137C22⋊D61—81no—
138C2×Dic61—22no—
139C2×Dic61—42no—
140C2×Dic61—41no—
141C2×Dic61—81no—
142C2×Dic61—81no—
143C2×Dic61#10211yescharacteristic
144C2×Dic61#10211yescharacteristic
145D244—41no—
146D244—41no—
147D244—82no—
148D244—82no—
149C4×D61—22no—
150C4×D61—21no—
151C4×D61—21no—
152C4×D61—22no—
153C4×D61—88no—
154C4×D61—82no—
155C4×D61#9912yes—
156C4×D61#10412yes—
157C8×C61—21no—
158C8×C61—21no—
159#92418—21no—
160#92418—21no—
161#11704—611nomaximal, Sylow
162C22×C61—21no—
163C22×C61—21no—
164C22×C61C2×#10211yescharacteristic
165C22×C61#50911yescharacteristic
166C22×C61#51011yescharacteristic
167C2×D61—24no—
168C2×D61—24no—
169C2×D61—21no—
170C2×D61—21no—
171C2×D61—21no—
172C2×D61—21no—
173C2×D61—81no—
174C2×D61—81no—
175C2×D61—81no—
176C2×D61#32712yes—
177C2×D61#36012yes—
178C4×C61—21no—
179C4×C61—82no—
180C4×C61—81no—
181C4×C61—81no—
182C4×C61C2×#9911yescharacteristic
183C4×C61C2×#10411yescharacteristic
184Dic61—21no—
185Dic61—82no—
186Dic61—81no—
187Dic61#32712yes—
188#3050—611no—
189#2112—611no—
190C2×#340—611no—
191#1348—611no—
192#1348D6111yescharacteristic, complemented
193#1347—611no—
194#1347—611no—
195C2×C61—21no—
196C2×C61—21no—
197C2×C61C2×#32711yescharacteristic
198C2×C61#213911yescharacteristic
199C2×C61C2×#36011yescharacteristic
200D61—22no—
201D61—22no—
202D61—161no—
203C2×#135—611no—
204C23×C8—611no—
205#525—1221no—
206C22×C4⋊C4—1221no—
207C2×M32—1221no—
208#467—611no—
209#467C2×D6111yescharacteristic
210#466—611no—
211#466—611no—
212#465—1221no—
213#465—1221no—
214#427—611no—
215#416—1221no—
216C22⋊C16—611no—
217C22⋊C16—1221no—
218C22⋊C16C2×D6111yescharacteristic
219#340—611no—
220#340—1221no—
221#340C2×D6111yescharacteristic
222C61#1170411yescharacteristic, complemented, Sylow
223C2×#41—1221no—
224C23×C4—611no—
225C23×C4—2441no—
226#135—2442no—
227C2×Q16C4×D6111yescharacteristic, complemented
228C2×SD16—1221no—
229C2×D8—611no—
230C22×C8—611no—
231C22×C8—611no—
232C22×C8—611no—
233C22×C8—611no—
234C22×C8—611no—
235C22×C8—2442no—
236C22×C8C22×D6111yescharacteristic
237#123—2441no—
238C22⋊Q8—21no—
239C22⋊Q8—1221no—
240#121—1221no—
241#121—1221no—
242#120—2441no—
243C4×D4—2441no—
244C4×D4—2441no—
245#117—1221no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—1224no—
248C2×C4⋊C4—1221no—
249C2×C4⋊C4—2442no—
250C2×C4⋊C4—2441no—
251M32—2442no—
252C2×C16—21no—
253C2×C16—1221no—
254#107—611no—
255#107C4×D6111yescharacteristic, complemented
256#106—1221no—
257#103—21no—
258#103—1221no—
259#102—1221no—
260#102—1221no—
261C24—611no—
262#41—2442no—
263#41—2442no—
264C2×Q8—21no—
265C2×D4—1221no—
266C2×D4—2441no—
267C2×D4—2441no—
268C2×D4—2441no—
269C22×C4—41no—
270C22×C4—611no—
271C22×C4—611no—
272C22×C4—611no—
273C22×C4—611no—
274C22×C4—611no—
275C22×C4—1222no—
276C22×C4—1222no—
277C22×C4—4882no—
278C22×C4—4882no—
279C22×C4—2441no—
280C22×C4—2444no—
281C22×C4—2441no—
282C22×C4D4×D6111yescharacteristic
283Q16—41no—
284SD16—2442no—
285D8—2441no—
286C2×C8—41no—
287C2×C8—611no—
288C2×C8—611no—
289C2×C8—1222no—
290C2×C8—1222no—
291C2×C8—2441no—
292C2×C8—2441no—
293C2×C8—2441no—
294C2×C8C2×C4×D6111yescharacteristic
295C2×C8D4×D6111yescharacteristic
296C4⋊C4—22no—
297C4⋊C4—21no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—1222no—
301C4⋊C4—1221no—
302C4⋊C4—2441no—
303C4⋊C4—2441no—
304C4⋊C4—2444no—
305C22⋊C4—41no—
306C22⋊C4—2441no—
307C22⋊C4—2441no—
308C22⋊C4—2441no—
309C22⋊C4—2441no—
310C42—2441no—
311C16—41no—
312C16—2441no—
313C23—611no—
314C23—611no—
315C23—1222no—
316C23—1222no—
317C23—1221no—
318C23—1221no—
319C23—2441no—
320C23D8×D6111yescharacteristic
321Q8—41no—
322Q8—41no—
323D4—4882no—
324D4—4882no—
325D4—4881no—
326D4—4881no—
327D4—2441no—
328D4—2441no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—611no—
337C2×C4—612no—
338C2×C4—612no—
339C2×C4—611no—
340C2×C4—1222no—
341C2×C4—1222no—
342C2×C4—1222no—
343C2×C4—1221no—
344C2×C4—1221no—
345C2×C4—4882no—
346C2×C4—4888no—
347C2×C4—4881no—
348C2×C4—4881no—
349C2×C4—2442no—
350C2×C4—2441no—
351C2×C4C22⋊C4×D6111yescharacteristic
352C2×C4SD16×D6111yescharacteristic
353C8—21no—
354C8—21no—
355C8—1221no—
356C8—1221no—
357C22—21no—
358C22—21no—
359C22—612no—
360C22—612no—
361C22—1224no—
362C22—1224no—
363C22—1221no—
364C22—1221no—
365C22—1221no—
366C22—1221no—
367C22—4881no—
368C22—4881no—
369C22—4881no—
370C22#102×D6111yescharacteristic
371C22#1684019911yescharacteristic
372C22#1684020411yescharacteristic
373C4—21no—
374C4—82no—
375C4—81no—
376C4—81no—
377C4—612no—
378C4—1221no—
379C4—4882no—
380C4—4881no—
381C4#99×D6111yescharacteristic
382C4#104×D6111yescharacteristic
383C2—21no—
384C2—21no—
385C2—1222no—
386C2—1222no—
387C2—9761no—
388C2#327×D6111yescharacteristic
389C2#2144753011yescharacteristic
390C2#360×D6111yescharacteristic
subgroupG/H
centerC22#102×D61
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC61×#1348C2
socleC22×C61C2×#102
prime radical#21455402C2
cosocleC22×C8×C61C23
hypercenter#1348D61
hypocenterC61#11704
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1348

Complements

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

NH ≅ G/Ntype
2. #21447428C2semidirect
3. #340×D61C2semidirect
4. #21443831C2semidirect
5. #21443829C2semidirect
6. #21443827C2semidirect
7. C61×#1348C2semidirect
8. C2×#14519800C4semidirect
13. #16840000C4semidirect
14. #16839999C4semidirect
18. #16839799C4semidirect
32. C2×D488C2×C4semidirect
53. #14519711C2×C4semidirect
58. C2×Q16×C61C2×C4semidirect
63. #107×C61C2×C4semidirect
192. #1348D61semidirect
222. C61#11704semidirect
227. C2×Q16C4×D61semidirect
255. #107C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214554022
#214474282
#340×D612
#214438312
#214438292
#214438272
C61×#13482
#1170461