Finite Group Databasebeta

← #30608434

Subgroups — #30608434

Order 15616.

320 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 56 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#21462116C211yesmaximal, characteristic, complemented
2#21462103C211yesmaximal, characteristic, complemented
3#21460965C212yesmaximal, complemented
4#21460946C212yesmaximal, complemented
5#21456874C211yesmaximal, characteristic
6C2×#14519838—21no—
7#16840741—21no—
8#16840673—21no—
9#16840671C2212yes—
10#16840669—21no—
11#16840669C2212yes—
12#16840338C2211yescharacteristic
13#16840149C2211yescharacteristic
14#16840134C411yescharacteristic, complemented
15#16840132C411yescharacteristic, complemented
16#16840119C2211yescharacteristic
17#16839977—21no—
18#16839967—21no—
19#16839905—21no—
20#16839900—21no—
21#16839823C411yescharacteristic, complemented
22C61×#540C411yescharacteristic, complemented
23C2×#11758217—41no—
24#14519856—41no—
25#14519838—22no—
26#14519838—41no—
27#14519836—22no—
28#14519835—41no—
29C2×#11758222D411yescharacteristic
30C22×Dic122D411yescharacteristic
31C2×#11758200—21no—
32C2×#11758200—21no—
33C2×#11758200—21no—
34C2×#11758199—21no—
35#14519777C2×C411yescharacteristic
36#14519777D411yescharacteristic
37#14519765D411yescharacteristic
38#14519765C2311yescharacteristic
39#14519761—41no—
40#14519757—41no—
41C4⋊#92418—21no—
42#14519700—21no—
43#14519700—21no—
44#14519700—21no—
45#14519697—21no—
46C22⋊#92418—21no—
47#14519688C2×C411yescharacteristic
48C4×#92418C2×C411yescharacteristic
49#127×C61C2×C411yescharacteristic
50#125×C61C2×C411yescharacteristic
51#123×C61—41no—
52#121×C61—21no—
53#121×C61—41no—
54C4×D4×C61—21no—
55#117×C61C2×C411yescharacteristic
56C2×D4×C61—21no—
57C2×D4×C61—41no—
58C2×D4×C61—41no—
59C22×C4×C61—41no—
60C22×C4×C61C22⋊C411yescharacteristic
61C2×C22⋊D61—21no—
62C22×Dic61—21no—
63#11758222—81no—
64C2×D244C2×D411yescharacteristic
65C2×C4×D61—21no—
66C2×Dic122—21no—
67C2×Dic122—81no—
68C2×Dic122C22⋊C411yescharacteristic
69C2×Dic122C22⋊C411yescharacteristic
70C2×Dic122C2×D411yescharacteristic
71C22⋊#6923—42no—
72#11758217—42no—
73#11758217—81no—
74C2×#92420—81no—
75C4⋊#6923—81no—
76C4×#6923—81no—
77C4⋊C4×C61—21no—
78C4⋊C4×C61—21no—
79C4⋊C4×C61—41no—
80C22⋊C4×C61—21no—
81C22⋊C4×C61—41no—
82C22⋊C4×C61—41no—
83C42×C61C22⋊C411yescharacteristic
84C42×C61C22×C411yescharacteristic
85#11758200—81no—
86#11758200—81no—
87#11758200—81no—
88#11758199—81no—
89#11758198—41no—
90#11758198—41no—
91C4⋊Dic61—41no—
92C4⋊Dic61—41no—
93C2×#92418—21no—
94C2×#92418—21no—
95C23×C61—41no—
96C23×C61#9911yescharacteristic
97C22×D61—21no—
98C2×#6923—82no—
99D4×C61—41no—
100D4×C61—41no—
101D4×C61—161no—
102D4×C61—161no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—41no—
106C2×C4×C61—41no—
107C2×C4×C61—161no—
108C2×C4×C61#9911yescharacteristic
109C2×C4×C61C2×C22⋊C411yescharacteristic
110C22⋊D61—81no—
111C2×Dic61—21no—
112C2×Dic61—21no—
113C2×Dic61—21no—
114C2×Dic61—41no—
115C2×Dic61—41no—
116D244—41no—
117C4×D61—41no—
118C4×D61—41no—
119Dic122—41no—
120Dic122—41no—
121Dic122—41no—
122Dic122—81no—
123#92420—82no—
124#92418—41no—
125#92418—41no—
126#13606—611nomaximal, Sylow
127C22×C61—21no—
128C22×C61—41no—
129C22×C61—81no—
130C22×C61—81no—
131C22×C61—81no—
132C22×C61C2×#9911yescharacteristic
133C2×D61—41no—
134C2×D61—81no—
135#6923—162no—
136C4×C61—21no—
137C4×C61—21no—
138C4×C61—41no—
139C4×C61—41no—
140C4×C61—81no—
141Dic61—41no—
142Dic61—41no—
143Dic61—41no—
144#3221—611no—
145#2133—611no—
146#2129—611no—
147#1414—612no—
148#1406—612no—
149C2×C61—21no—
150C2×C61—41no—
151C2×C61—161no—
152C2×C61#212711yescharacteristic
153D61—81no—
154#540#692311yescharacteristic, complemented
155#536—611no—
156#496—611no—
157#492—611no—
158#491—611no—
159#488—611no—
160#463—1221no—
161#461—1221no—
162#449—1221no—
163#448—1221no—
164#433—611no—
165C2×#101—1221no—
166#410—1221no—
167#356—1221no—
168#355—612no—
169#354—612no—
170#354—1221no—
171C61#1360611yescharacteristic, complemented, Sylow
172C2×#41—611no—
173C22×Q8—611no—
174C2×SD16—1221no—
175C2×SD16—1221no—
176C2×SD16—1221no—
177C2×D8—1221no—
178C2×M16—2441no—
179C4⋊Q8—611no—
180C4⋊Q8—611no—
181#127C2×#692311yescharacteristic
182#125C2×#692311yescharacteristic
183#124—611no—
184#124—611no—
185#123—41no—
186#123—2441no—
187C22⋊Q8—2441no—
188#121—21no—
189#121—41no—
190C4×D4—21no—
191#117—2441no—
192#117C2×#692311yescharacteristic
193C4⋊C8—1221no—
194#103—1221no—
195#103—1221no—
196#103—1221no—
197#102—1221no—
198#101—1222no—
199#101—2441no—
200#99—1222no—
201#99—2441no—
202C22⋊C8—1221no—
203#97—611no—
204C4×C8—611no—
205#41—4881no—
206C2×Q8—611no—
207C2×Q8—611no—
208C2×Q8—611no—
209C2×Q8—1221no—
210C2×Q8—4881no—
211C2×D4—21no—
212C2×D4—41no—
213C2×D4—41no—
214C2×D4—611no—
215C2×D4—1221no—
216C22×C4—41no—
217C22×C4—1221no—
218C22×C4—1221no—
219C22×C4C22⋊#692311yescharacteristic
220SD16—4881no—
221SD16—4881no—
222SD16—4881no—
223D8—4881no—
224M16—4881no—
225M16—2442no—
226C2×C8—1221no—
227C2×C8—1221no—
228C2×C8—4881no—
229C4⋊C4—21no—
230C4⋊C4—21no—
231C4⋊C4—41no—
232C4⋊C4—4881no—
233C4⋊C4—2441no—
234C4⋊C4—2441no—
235C22⋊C4—21no—
236C22⋊C4—41no—
237C22⋊C4—41no—
238C22⋊C4—2441no—
239C22⋊C4—2441no—
240C22⋊C4—2442no—
241C42—4881no—
242C42C22⋊#692311yescharacteristic
243C42C22×#692311yescharacteristic
244C23—41no—
245C23—1221no—
246C23#1451983511yescharacteristic
247Q8—4881no—
248Q8—2441no—
249Q8—2441no—
250Q8—2441no—
251D4—41no—
252D4—41no—
253D4—161no—
254D4—161no—
255D4—4881no—
256D4—2441no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—161no—
262C2×C4—1221no—
263C2×C4—1221no—
264C2×C4—1221no—
265C2×C4—4882no—
266C2×C4—2441no—
267C2×C4—2441no—
268C2×C4—2441no—
269C2×C4—2441no—
270C2×C4#1451983511yescharacteristic
271C2×C4C2×C22⋊#692311yescharacteristic
272C8—4882no—
273C8—2441no—
274C8—2441no—
275C22—21no—
276C22—41no—
277C22—81no—
278C22—81no—
279C22—81no—
280C22—4881no—
281C22—2441no—
282C22C2×#1451983511yescharacteristic
283C4—21no—
284C4—21no—
285C4—41no—
286C4—41no—
287C4—81no—
288C4—9762no—
289C4—2441no—
290C4—2441no—
291C4—2441no—
292C2—21no—
293C2—41no—
294C2—161no—
295C2—4881no—
296C2#2146209411yescharacteristic
subgroupG/H
centerC2#21462094
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#540C4
socleC2×C61#2127
prime radical#21456874C2
cosocle#14519765C23
hypercenter#540#6923
hypocenterC61#13606
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C22×C4 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #21462116C2semidirect
2. #21462103C2semidirect
3. #21460965C2semidirect
4. #21460946C2semidirect
14. #16840134C4semidirect
15. #16840132C4semidirect
21. #16839823C4semidirect
22. C61×#540C4semidirect
154. #540#6923semidirect
171. C61#13606semidirect

Maximal subgroups

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

subgroupindex
#214621162
#214621032
#214609652
#214609462
#214568742
#1360661