Finite Group Databasebeta

← #30608420

Subgroups — #30608420

Order 15616.

334 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 60 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
1C2×#16840671C211yesmaximal, characteristic
2C2×#16840669C211yesmaximal, characteristic
3#21460965C212yesmaximal, complemented
4#21460964C212yesmaximal, complemented
5#21456208C211yesmaximal, characteristic
6C2×#14519838—21no—
7C2×#14519836—21no—
8#16840671—21no—
9#16840671C2212yes—
10#16840669—21no—
11#16840669C2212yes—
12C2×#14519765C2211yescharacteristic
13#16840124—21no—
14#16840124—21no—
15#16840119C411yescharacteristic, complemented
16#16840119C411yescharacteristic, complemented
17#16840119C2211yescharacteristic
18#16840119C2211yescharacteristic
19#16839770—21no—
20#16839766—21no—
21C4×#11758194C411yescharacteristic, complemented
22C61×#533C411yescharacteristic, complemented
23C2×#11758217—41no—
24C2×C22⋊#6923—41no—
25#14519838—22no—
26#14519838—41no—
27#14519836—22no—
28#14519836—41no—
29C22×Dic122D411yescharacteristic
30C22×D244D411yescharacteristic
31C2×#11758194—21no—
32#14519765—41no—
33#14519765C2×C411yescharacteristic
34#14519765D411yescharacteristic
35#14519765D411yescharacteristic
36#14519765C2311yescharacteristic
37C2×#11758198—41no—
38#14519700—21no—
39#14519700—21no—
40#14519700—21no—
41#14519700—21no—
42#14519697—21no—
43#14519697—21no—
44#14519697—21no—
45#14519697—21no—
46#14519688—21no—
47C4×#92418C2×C411yescharacteristic, complemented
48C4×#92418C2×C411yescharacteristic, complemented
49C4⋊Q8×C61—21no—
50#125×C61C2×C411yescharacteristic, complemented
51#125×C61C2×C411yescharacteristic, complemented
52C22⋊Q8×C61—41no—
53C4×Q8×C61—41no—
54#117×C61—21no—
55C2×C42×C61C2×C411yescharacteristic
56C23×D61—21no—
57C22×#6923—81no—
58C2×Q8×C61—41no—
59C22×C4×C61—21no—
60C22×C4×C61C22⋊C411yescharacteristic
61C22×Dic61—21no—
62C2×D244—21no—
63C2×D244—41no—
64C2×D244—41no—
65C2×D244C22⋊C411yescharacteristic
66C2×D244C2×D411yescharacteristic
67C2×Dic122—21no—
68C2×Dic122—41no—
69C2×Dic122—41no—
70C2×Dic122C22⋊C411yescharacteristic
71C2×Dic122C2×D411yescharacteristic
72C22⋊#6923—42no—
73C22⋊#6923—81no—
74#11758217—42no—
75#11758217—81no—
76C2×#92420—81no—
77C4⋊C4×C61—21no—
78C4⋊C4×C61—21no—
79C4⋊C4×C61—41no—
80C4⋊C4×C61—41no—
81C4⋊C4×C61—41no—
82C22⋊C4×C61—41no—
83C42×C61—21no—
84C42×C61—41no—
85C42×C61C22⋊C411yescharacteristic
86C42×C61C22×C411yescharacteristic
87#11758198—41no—
88#11758198—41no—
89#11758198—41no—
90#11758198—41no—
91#11758194—41no—
92#11758194—41no—
93C2×#92418—21no—
94C2×#92418—21no—
95C23×C61#9911yescharacteristic
96C22×D61—21no—
97C22×D61—21no—
98C22×D61—41no—
99C22×D61—41no—
100C22×D61—82no—
101C2×#6923—82no—
102C2×#6923—162no—
103Q8×C61—82no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61—81no—
111C2×C4×C61#9911yescharacteristic
112C2×C4×C61C2×C22⋊C411yescharacteristic
113C2×Dic61—21no—
114C2×Dic61—21no—
115C2×Dic61—41no—
116C2×Dic61—41no—
117D244—41no—
118D244—41no—
119D244—81no—
120Dic122—41no—
121Dic122—41no—
122Dic122—81no—
123#92420—82no—
124#92418—41no—
125#92418—41no—
126#13603—611nomaximal, Sylow
127C22×C61—41no—
128C22×C61#35411yescharacteristic
129C22×C61#35411yescharacteristic
130C22×C61C2×#9911yescharacteristic
131C2×D61—41no—
132C2×D61—41no—
133C2×D61—82no—
134C2×D61—81no—
135C2×D61—81no—
136C2×D61—161no—
137#6923—162no—
138C4×C61—21no—
139C4×C61—21no—
140C4×C61—41no—
141C4×C61—41no—
142C4×C61—81no—
143C4×C61—81no—
144Dic61—41no—
145Dic61—41no—
146#3140—611no—
147C2×#355—611no—
148C2×#354—611no—
149#1414—612no—
150#1414—612no—
151C2×C61—21no—
152C2×C61—21no—
153C2×C61—21no—
154C2×C61C2×#35411yescharacteristic
155D61—81no—
156D61—81no—
157#533#692311yescharacteristic, complemented
158C2×#124—611no—
159#489—1221no—
160#489—1221no—
161#488—611no—
162#488—611no—
163#488—611no—
164#488—611no—
165#419—1221no—
166#418—1221no—
167C2×#101—1221no—
168C2×#99—1221no—
169C4×M16—611no—
170#355—612no—
171#355—1221no—
172#354—612no—
173#354—1221no—
174C61#1360311yescharacteristic, complemented, Sylow
175C22×Q8—611no—
176C22×D4—611no—
177C2×M16—1221no—
178C2×M16—2441no—
179C4⋊Q8—21no—
180#125C2×#692311yescharacteristic, complemented
181#125C2×#692311yescharacteristic, complemented
182#124—611no—
183#124—611no—
184#124—611no—
185#124—611no—
186#124—2441no—
187C22⋊Q8—41no—
188C4×Q8—41no—
189#117—21no—
190C2×C22⋊C4—2441no—
191C2×C22⋊C4—2441no—
192C2×C42C2×#692311yescharacteristic
193#103—1221no—
194#103—1221no—
195#103—1221no—
196#103—1221no—
197#102—1221no—
198#102—1221no—
199#102—1221no—
200#102—1221no—
201#101—1222no—
202#101—2441no—
203#99—1222no—
204#99—2441no—
205#97—1221no—
206C4×C8—611no—
207C4×C8—611no—
208C24—1221no—
209C2×Q8—41no—
210C2×Q8—611no—
211C2×Q8—611no—
212C2×Q8—1221no—
213C2×Q8—2441no—
214C2×Q8—2441no—
215C2×D4—611no—
216C2×D4—611no—
217C2×D4—1221no—
218C2×D4—2441no—
219C2×D4—2441no—
220C22×C4—21no—
221C22×C4—1221no—
222C22×C4—4881no—
223C22×C4C22⋊#692311yescharacteristic
224M16—4881no—
225M16—2442no—
226M16—2441no—
227M16—2441no—
228C2×C8—1221no—
229C2×C8—1221no—
230C2×C8—4881no—
231C4⋊C4—21no—
232C4⋊C4—21no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C22⋊C4—41no—
237C22⋊C4—4881no—
238C22⋊C4—2441no—
239C22⋊C4—2441no—
240C22⋊C4—2441no—
241C22⋊C4—2441no—
242C22⋊C4—2442no—
243C42—21no—
244C42—41no—
245C42C22⋊#692311yescharacteristic
246C42C22×#692311yescharacteristic
247C23—1221no—
248C23—1221no—
249C23—4882no—
250C23—2441no—
251C23—2441no—
252C23#1451983511yescharacteristic
253Q8—82no—
254Q8—4881no—
255Q8—2441no—
256Q8—2441no—
257D4—4881no—
258D4—2441no—
259D4—2441no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—81no—
267C2×C4—1221no—
268C2×C4—1221no—
269C2×C4—9762no—
270C2×C4—4882no—
271C2×C4—2441no—
272C2×C4—2441no—
273C2×C4#1451983511yescharacteristic
274C2×C4C2×C22⋊#692311yescharacteristic
275C8—4882no—
276C8—2441no—
277C8—2441no—
278C22—41no—
279C22—9761no—
280C22—4881no—
281C22—4881no—
282C22—4882no—
283C22—2441no—
284C22—2441no—
285C22#1684066811yescharacteristic
286C22#1684066811yescharacteristic
287C22C2×#1451983511yescharacteristic
288C4—21no—
289C4—21no—
290C4—41no—
291C4—41no—
292C4—81no—
293C4—81no—
294C4—9762no—
295C4—2441no—
296C4—2441no—
297C2—21no—
298C2—21no—
299C2—21no—
300C2—4881no—
301C2—4881no—
302C2C2×#1684066811yescharacteristic
subgroupG/H
centerC2C2×#16840668
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#533C4
socleC2×C61C2×#354
prime radicalC22×D244D4
cosocle#14519765C23
hypercenter#533#6923
hypocenterC61#13603
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
3. #21460965C2semidirect
4. #21460964C2semidirect
15. #16840119C4semidirect
16. #16840119C4semidirect
21. C4×#11758194C4semidirect
22. C61×#533C4semidirect
47. C4×#92418C2×C4semidirect
48. C4×#92418C2×C4semidirect
50. #125×C61C2×C4semidirect
51. #125×C61C2×C4semidirect
157. #533#6923semidirect
174. C61#13603semidirect
180. #125C2×#6923semidirect
181. #125C2×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168406712
C2×#168406692
#214609652
#214609642
#214562082
#1360361