Finite Group Databasebeta

← #30606575

Subgroups — #30606575

Order 15616.

460 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 92 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#21462543C211yesmaximal, characteristic
2#21462113C211yesmaximal, characteristic
3#21461577C212yesmaximal, complemented
4#21460918C212yesmaximal, complemented
5#21447483C211yesmaximal, characteristic
6C2×#14519865C411yescharacteristic, complemented
7C2×#14519864C2211yescharacteristic
8#16840795—22no—
9#16840789—22no—
10#16840767C411yescharacteristic, complemented
11#16840749C2212yes—
12#16840737C411yescharacteristic, complemented
13#16840736C2211yescharacteristic
14#16840726—22no—
15C4×D61⋊C8C411yescharacteristic, complemented
16#16840672C412yescomplemented
17#16840671C412yescomplemented
18#16840643—22no—
19#16840311C2211yescharacteristic
20#16839734C2212yes—
21#16839557C411yescharacteristic
22#16839554C412yes—
23C61×#354C411yescharacteristic
24#14519865—41no—
25#14519865—41no—
26#14519864—41no—
27#14519864—41no—
28C2×#11758213—21no—
29C2×#11758213C2×C411yescharacteristic
30C2×#11758213C2×C411yescharacteristic
31C2×#11758217—22no—
32C2×#11758217D412yes—
33C2×D61⋊C8—21no—
34C2×D61⋊C8C2×C411yescharacteristic
35C2×D61⋊C8C2×C411yescharacteristic
36C22×#92420D412yes—
37#14519844—22no—
38#14519838C2×C414yes—
39#14519837—22no—
40#14519834—22no—
41C22⋊#92420—22no—
42#14519832—42no—
43C4×#92420—21no—
44C4×#92420—21no—
45C4×#92420—42no—
46C2×#11758226C2×C411yescharacteristic
47C2×#11758224C2311yescharacteristic
48#14519775C2×C411yescharacteristic
49#14519773C2×C411yescharacteristic
50#14519765C2×C411yescharacteristic
51#14519750—22no—
52#14519737—22no—
53#14519733—22no—
54C42×D61C2×C411yescharacteristic
55#14519692C2×C412yes—
56#14519691—22no—
57#124×C61C2×C411yescharacteristic
58#99×C61C2×C412yes—
59C2×Q8×C61C4211yescharacteristic
60C2×D4×C61C22×C411yescharacteristic
61C2×C22⋊D61—22no—
62C2×C22⋊D61#4112yes—
63C22×Dic61C2×D412yes—
64#11758226—41no—
65#11758226—41no—
66#11758224—41no—
67#11758224—41no—
68C2×D244—21no—
69C2×D244C4211yescharacteristic
70C2×C4×D61—21no—
71C2×C4×D61—21no—
72C2×C4×D61C22×C411yescharacteristic
73C2×Dic122C22×C411yescharacteristic
74#11758217—24no—
75#11758217—42no—
76#11758217—42no—
77C2×#92420—22no—
78C2×#92420—22no—
79C2×#92420—21no—
80C2×#92420—21no—
81C2×#92420—42no—
82C2×#92420C22⋊C411yescharacteristic
83C2×#92420C22⋊C412yes—
84C2×#92420C22⋊C411yescharacteristic
85#11758213—41no—
86#11758213—42no—
87#11758213—41no—
88D61⋊C8—21no—
89D61⋊C8—21no—
90D61⋊C8—41no—
91D61⋊C8—41no—
92D61⋊C8—41no—
93C22⋊C4×C61—22no—
94C22⋊C4×C61—22no—
95C42×C61C4211yescharacteristic
96C22⋊Dic61—22no—
97#11758198—22no—
98#11758196—22no—
99#11758196—42no—
100C4×Dic61—21no—
101C4×Dic61—42no—
102C4×Dic61C4211yescharacteristic
103C23×C61C4×D412yes—
104C22×D61—21no—
105C22×D61#11711yescharacteristic
106Q8×C61—41no—
107D4×C61—41no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—42no—
111C2×C4×C61C2×C4211yescharacteristic
112C22⋊D61—42no—
113C22⋊D61—44no—
114C2×Dic61—21no—
115C2×Dic61—22no—
116C2×Dic61—22no—
117C2×Dic61—42no—
118C2×Dic61C2×C22⋊C411yescharacteristic
119C2×Dic61C4×D412yes—
120D244—41no—
121D244—42no—
122C4×D61—21no—
123C4×D61—21no—
124C4×D61—42no—
125C4×D61—41no—
126C4×D61—41no—
127Dic122—41no—
128#92420—21no—
129#92420—22no—
130#92420—44no—
131#92420—41no—
132#92420—41no—
133#92420#9911yescharacteristic
134#92420#9911yescharacteristic
135#12633—611nomaximal, Sylow
136C22×C61—22no—
137C22×C61—42no—
138C22×C61C4×C22⋊C411yescharacteristic
139C2×D61—21no—
140C2×D61—41no—
141C2×D61—42no—
142C2×D61—41no—
143C4×C61—21no—
144C4×C61—41no—
145C4×C61—41no—
146C4×C61—82no—
147Dic61—22no—
148Dic61—22no—
149Dic61—82no—
150Dic61C2×#9911yescharacteristic
151Dic61#41011yescharacteristic
152#2931—611no—
153#2132—611no—
154#2126—611no—
155#1757—612no—
156#1395—612no—
157C2×C61—21no—
158C2×C61—42no—
159C2×C61C4×#9911yescharacteristic
160D61—41no—
161D61—81no—
162C2×#131—611no—
163C2×#131—611no—
164#532—611no—
165#436—1222no—
166C8×D4—1222no—
167#423—611no—
168#413—612no—
169#410—612no—
170#408—611no—
171#408—611no—
172#405—1222no—
173C2×C4×C8—611no—
174#356—612no—
175#355—612no—
176#354—611no—
177#354#692311yescharacteristic
178#353—612no—
179#344—1222no—
180C61#1263311yescharacteristic, complemented, Sylow
181C2×#41—611no—
182C2×#41—611no—
183#131—2441no—
184#131—2441no—
185#131—2441no—
186#131—2441no—
187C2×M16—612no—
188C2×M16—611no—
189C2×M16—611no—
190C2×M16—1221no—
191C2×M16—1222no—
192C22×C8—612no—
193C22×C8—611no—
194C22×C8—611no—
195C22×C8—1221no—
196C4⋊Q8—611no—
197#127—611no—
198#124—611no—
199#124C2×#692311yescharacteristic
200#121—1222no—
201C4×D4—1222no—
202#117—1222no—
203C2×C42—611no—
204C4⋊C8—1222no—
205#101—614no—
206#100—1222no—
207#99—612no—
208#99—1222no—
209#99C2×#692312yes—
210C22⋊C8—1222no—
211C22⋊C8—1222no—
212#97—2442no—
213C4×C8—1221no—
214C4×C8—1221no—
215C4×C8—2442no—
216#41—2441no—
217#41—2441no—
218#41—2441no—
219#41—2441no—
220C2×Q8—611no—
221C2×Q8C4×#692311yescharacteristic
222C2×D4—612no—
223C2×D4—611no—
224C2×D4—1221no—
225C2×D4—1222no—
226C2×D4C22×#692311yescharacteristic
227C22×C4—612no—
228C22×C4—611no—
229C22×C4—1221no—
230C22×C4—1221no—
231M16—1224no—
232M16—2441no—
233M16—2442no—
234M16—2442no—
235M16—2442no—
236M16—2441no—
237C2×C8—611no—
238C2×C8—611no—
239C2×C8—612no—
240C2×C8—1222no—
241C2×C8—1222no—
242C2×C8—1221no—
243C2×C8—1221no—
244C2×C8—1221no—
245C2×C8—1221no—
246C2×C8—2441no—
247C2×C8—2441no—
248C2×C8—2442no—
249C2×C8—2441no—
250C4⋊C4—1222no—
251C4⋊C4—2442no—
252C22⋊C4—22no—
253C22⋊C4—22no—
254C22⋊C4—1222no—
255C22⋊C4—1222no—
256C42—611no—
257C42—1221no—
258C42—2442no—
259C42C4×#692311yescharacteristic
260C23—611no—
261C23—1221no—
262C23D4×#692312yes—
263Q8—41no—
264Q8—2441no—
265D4—41no—
266D4—2441no—
267D4—2442no—
268D4—2442no—
269D4—2444no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—42no—
273C2×C4—611no—
274C2×C4—612no—
275C2×C4—1221no—
276C2×C4—1221no—
277C2×C4—1222no—
278C2×C4—1222no—
279C2×C4—1221no—
280C2×C4—2441no—
281C2×C4—2441no—
282C2×C4—2442no—
283C2×C4—2442no—
284C2×C4C2×C4×#692311yescharacteristic
285C8—611no—
286C8—611no—
287C8—1222no—
288C8—1221no—
289C8—2441no—
290C8—2441no—
291C8—2444no—
292C22—22no—
293C22—42no—
294C22—1221no—
295C22—2442no—
296C22—2441no—
297C22—2441no—
298C22C22⋊C4×#692311yescharacteristic
299C4—21no—
300C4—41no—
301C4—41no—
302C4—82no—
303C4—611no—
304C4—611no—
305C4—1222no—
306C4—1222no—
307C4—4882no—
308C2—21no—
309C2—42no—
310C2—4881no—
311C2—2441no—
312C2#99×#692311yescharacteristic
subgroupG/H
centerC2#99×#6923
commutatorC2×C4×C61C2×C42
FrattiniC2×D4C22×#6923
FittingC61×#354C4
socleC2×C61C4×#99
prime radical#16840311C22
cosocleC2×#11758224C23
hypercenter#354#6923
hypocenterC61#12633
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
3. #21461577C2semidirect
4. #21460918C2semidirect
6. C2×#14519865C4semidirect
10. #16840767C4semidirect
12. #16840737C4semidirect
15. C4×D61⋊C8C4semidirect
16. #16840672C4semidirect
17. #16840671C4semidirect
180. C61#12633semidirect

Maximal subgroups

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

subgroupindex
#214625432
#214621132
#214615772
#214609182
#214474832
#1263361