Finite Group Databasebeta

← #30608463

Subgroups — #30608463

Order 15616.

336 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 54 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#21462099C211yesmaximal, characteristic
2#21462097C211yesmaximal, characteristic
3#21460959C211yesmaximal, characteristic, complemented
4#21460958C211yesmaximal, characteristic, complemented
5#21460953C211yesmaximal, characteristic, complemented
6#21460953C211yesmaximal, characteristic, complemented
7#21456894C211yesmaximal, characteristic
8#16840743—21no—
9D61⋊#99—21no—
10#16840668—21no—
11#16840667C2211yescharacteristic
12#16840667C2211yescharacteristic
13#16840667C2211yescharacteristic
14#16840667C2211yescharacteristic
15#16840666—21no—
16#16840375C411yescharacteristic, complemented
17#16840330C2211yescharacteristic
18#16840157C411yescharacteristic, complemented
19#16840135C2211yescharacteristic
20#16840128C2211yescharacteristic
21#16839987—21no—
22#16839961—21no—
23#16839927—21no—
24#16839914—21no—
25#16839821C411yescharacteristic, complemented
26C61×#488C411yescharacteristic, complemented
27#14519856—41no—
28C2×C22⋊#6923—41no—
29#14519836—21no—
30#14519836—21no—
31#14519836—21no—
32#14519836—21no—
33#14519836—41no—
34#14519835—41no—
35C2×#11758226D411yescharacteristic
36C2×D4×D61D411yescharacteristic
37C2×#11758202—21no—
38C2×#11758190—21no—
39C2×#11758190—21no—
40C2×#11758200—21no—
41#14519777C2×C411yescharacteristic, complemented
42#14519774C2311yescharacteristic
43#14519773D411yescharacteristic
44#14519772—41no—
45#14519768—41no—
46#14519766D411yescharacteristic
47#14519757—21no—
48#14519750—41no—
49#14519747—41no—
50#14519742—21no—
51#14519734C2×C411yescharacteristic
52#14519706—21no—
53#14519697—21no—
54#14519697—21no—
55#14519689—21no—
56#14519688C2×C411yescharacteristic, complemented
57#125×C61C2×C411yescharacteristic, complemented
58#124×C61C2×C411yescharacteristic
59#103×C61—21no—
60#102×C61—21no—
61C4×C8×C61C2×C411yescharacteristic, complemented
62C23×D61—21no—
63C22×#6923—81no—
64C2×Q8×C61C22⋊C411yescharacteristic
65C2×D4×C61C22⋊C411yescharacteristic
66C2×C22⋊D61—21no—
67C2×C22⋊D61—41no—
68#11758226—81no—
69D4×D61—81no—
70C2×D244—21no—
71C2×D244—41no—
72C2×D244C2×D411yescharacteristic
73C2×D244C2×D411yescharacteristic
74C2×C4×D61—21no—
75C2×C4×D61C22⋊C411yescharacteristic
76C2×Dic122—21no—
77C22⋊#6923—41no—
78C22⋊#6923—41no—
79C22⋊#6923—41no—
80C22⋊#6923—41no—
81C22⋊#6923—81no—
82C4⋊#6923—81no—
83C4×#6923—81no—
84C2×C8×C61—21no—
85C4⋊C4×C61—21no—
86C4⋊C4×C61—41no—
87C22⋊C4×C61—41no—
88C42×C61C22×C411yescharacteristic
89#11758202—81no—
90#11758200—81no—
91#11758198—21no—
92#11758198—41no—
93#11758198—41no—
94C4⋊Dic61—41no—
95C4⋊Dic61—41no—
96#11758196—21no—
97#11758196—41no—
98C4×Dic61—41no—
99C4×Dic61C22⋊C411yescharacteristic
100C2×#92418—21no—
101#11758190—81no—
102#11758190—81no—
103C23×C61—21no—
104C22×D61—21no—
105C22×D61—21no—
106C22×D61—41no—
107C22×D61—41no—
108C22×D61—161no—
109C22×D61#9911yescharacteristic
110C2×#6923—81no—
111C2×#6923—81no—
112C2×#6923—81no—
113C2×#6923—81no—
114C2×#6923—162no—
115Q8×C61—41no—
116D4×C61—41no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—41no—
120C2×C4×C61C2×C22⋊C411yescharacteristic
121C22⋊D61—81no—
122C22⋊D61—161no—
123C2×Dic61—21no—
124C2×Dic61—41no—
125C2×Dic61#9911yescharacteristic
126D244—41no—
127D244—41no—
128D244—81no—
129D244—161no—
130C4×D61—41no—
131C4×D61—41no—
132C4×D61—41no—
133Dic122—41no—
134Dic122—41no—
135C8×C61—41no—
136#92418—41no—
137#13610—611nomaximal, Sylow
138C22×C61—41no—
139C22×C61—81no—
140C22×C61C2×#9911yescharacteristic
141C2×D61—21no—
142C2×D61—41no—
143C2×D61—41no—
144C2×D61—41no—
145C2×D61—82no—
146C2×D61—81no—
147C2×D61—81no—
148C2×D61—161no—
149#6923—161no—
150#6923—161no—
151#6923—161no—
152#6923—161no—
153C4×C61—21no—
154C4×C61—41no—
155C4×C61—41no—
156C4×C61—81no—
157Dic61—21no—
158Dic61—41no—
159Dic61—81no—
160#3222—611no—
161#2128—611no—
162#2127—611no—
163#1412—611no—
164#1412—611no—
165#1409—611no—
166#1409—611no—
167C2×C61—21no—
168C2×C61—81no—
169C2×C61#212711yescharacteristic
170D61—41no—
171D61—81no—
172D61—81no—
173#541—611no—
174#535—611no—
175#497—611no—
176#492—611no—
177#490—611no—
178#488#692311yescharacteristic, complemented
179#464—1221no—
180#460—1221no—
181#452—1221no—
182#450—1221no—
183#433—611no—
184#410—1221no—
185C2×#99—1221no—
186#354—1221no—
187#353—611no—
188#353—611no—
189#353—611no—
190#353—611no—
191#353—1221no—
192C61#1361011yescharacteristic, complemented, Sylow
193C2×#41—611no—
194C22×D4—611no—
195C2×Q16—1221no—
196C2×SD16—1221no—
197C2×SD16—1221no—
198C2×SD16—1221no—
199C4⋊Q8—611no—
200#127—611no—
201#127—611no—
202#126—2441no—
203#125—2441no—
204#125C2×#692311yescharacteristic, complemented
205#124—611no—
206#124C2×#692311yescharacteristic
207C22⋊Q8—1221no—
208#121—2441no—
209#120—2441no—
210C4×Q8—1221no—
211#117—611no—
212#117—2441no—
213C2×C22⋊C4—2441no—
214C4⋊C8—1221no—
215#103—21no—
216#102—21no—
217#102—1221no—
218#102—1221no—
219#99—1221no—
220#99—1221no—
221#99—1221no—
222#99—1221no—
223#99—2441no—
224#99—2441no—
225C22⋊C8—1221no—
226#97—611no—
227C4×C8C2×#692311yescharacteristic, complemented
228C24—1221no—
229#41—4881no—
230C2×Q8—1221no—
231C2×Q8C22⋊#692311yescharacteristic
232C2×D4—611no—
233C2×D4—611no—
234C2×D4—1221no—
235C2×D4—1221no—
236C2×D4—4881no—
237C2×D4—2441no—
238C2×D4—2441no—
239C2×D4C22⋊#692311yescharacteristic
240C22×C4—611no—
241C22×C4—1221no—
242C22×C4—4881no—
243Q16—4881no—
244SD16—4881no—
245SD16—4881no—
246SD16—4881no—
247C2×C8—21no—
248C2×C8—1221no—
249C4⋊C4—21no—
250C4⋊C4—41no—
251C4⋊C4—1221no—
252C4⋊C4—4881no—
253C4⋊C4—2441no—
254C4⋊C4—2441no—
255C4⋊C4—2441no—
256C22⋊C4—41no—
257C22⋊C4—1221no—
258C22⋊C4—4881no—
259C22⋊C4—2441no—
260C22⋊C4—2441no—
261C22⋊C4—2441no—
262C22⋊C4—2441no—
263C22⋊C4—2441no—
264C22⋊C4—2441no—
265C42—611no—
266C42—4881no—
267C42—2441no—
268C42C22×#692311yescharacteristic
269C23—21no—
270C23—611no—
271C23—1221no—
272C23—1221no—
273C23—9761no—
274C23—2441no—
275C23—2441no—
276Q8—41no—
277Q8—2441no—
278Q8—2441no—
279D4—41no—
280D4—9761no—
281D4—9761no—
282D4—4881no—
283D4—4881no—
284D4—2441no—
285D4—2441no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—41no—
289C2×C4—611no—
290C2×C4—1221no—
291C2×C4—9762no—
292C2×C4—4881no—
293C2×C4—4881no—
294C2×C4—4881no—
295C2×C4—4881no—
296C2×C4—2441no—
297C2×C4—2441no—
298C2×C4—2441no—
299C2×C4—2441no—
300C2×C4C2×C22⋊#692311yescharacteristic
301C8—41no—
302C8—2441no—
303C22—41no—
304C22—81no—
305C22—1221no—
306C22—9761no—
307C22—4881no—
308C22—4881no—
309C22—4882no—
310C22—2441no—
311C22—2441no—
312C22—2441no—
313C22D61⋊#9911yescharacteristic
314C4—21no—
315C4—41no—
316C4—41no—
317C4—81no—
318C4—1221no—
319C4—9761no—
320C4—9761no—
321C4—9761no—
322C4—9761no—
323C4—4881no—
324C4—2441no—
325C2—21no—
326C2—81no—
327C2—4881no—
328C2—4881no—
329C2—2441no—
330C2#2146209711yescharacteristic
subgroupG/H
centerC2#21462097
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#488C4
socleC2×C61#2127
prime radical#16840330C22
cosocle#14519774C23
hypercenter#488#6923
hypocenterC61#13610
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #488

Complements

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

NH ≅ G/Ntype
3. #21460959C2semidirect
4. #21460958C2semidirect
5. #21460953C2semidirect
6. #21460953C2semidirect
16. #16840375C4semidirect
18. #16840157C4semidirect
25. #16839821C4semidirect
26. C61×#488C4semidirect
41. #14519777C2×C4semidirect
56. #14519688C2×C4semidirect
57. #125×C61C2×C4semidirect
61. C4×C8×C61C2×C4semidirect
178. #488#6923semidirect
192. C61#13610semidirect
204. #125C2×#6923semidirect
227. C4×C8C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214620992
#214620972
#214609592
#214609582
#214609532
#214568942
#1361061