Finite Group Databasebeta

← #30608446

Subgroups — #30608446

Order 15616.

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

normal subgroups only

This group has 308 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
2#21462103C211yesmaximal, characteristic
3#21460964C212yesmaximal, complemented
4#21460948C212yesmaximal, complemented
5#21456896C211yesmaximal, characteristic
6C2×#14519838—21no—
7#16840741—21no—
8#16840673—21no—
9#16840671C2212yes—
10#16840669—21no—
11#16840669C2212yes—
12#16840338C2211yescharacteristic
13#16840154C2211yescharacteristic
14#16840141C411yescharacteristic, complemented
15#16840132C411yescharacteristic, complemented
16#16840119C2211yescharacteristic
17#16839984—21no—
18#16839972—21no—
19#16839922—21no—
20#16839917—21no—
21#16839823C411yescharacteristic, complemented
22C61×#541C411yescharacteristic, complemented
23C2×#11758217—41no—
24#14519856—41no—
25#14519838—22no—
26#14519838—41no—
27#14519836—22no—
28#14519835—41no—
29C2×#11758222D411yescharacteristic
30C22×Dic122D411yescharacteristic
31C2×#11758202—21no—
32C2×#11758202—21no—
33C2×#11758202—21no—
34C2×#11758201—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
49C4⋊Q8×C61C2×C411yescharacteristic
50#126×C61—41no—
51#125×C61—41no—
52#125×C61C2×C411yescharacteristic
53C22⋊Q8×C61—21no—
54C4×Q8×C61—21no—
55#117×C61C2×C411yescharacteristic
56C2×Q8×C61—21no—
57C22×C4×C61C22⋊C411yescharacteristic
58C2×C22⋊D61—21no—
59C22×Dic61—21no—
60#11758222—81no—
61C2×D244C2×D411yescharacteristic
62C2×C4×D61—21no—
63C2×Dic122—21no—
64C2×Dic122—81no—
65C2×Dic122C22⋊C411yescharacteristic
66C2×Dic122C22⋊C411yescharacteristic
67C2×Dic122C2×D411yescharacteristic
68C22⋊#6923—42no—
69#11758217—42no—
70#11758217—81no—
71C2×#92420—81no—
72C4⋊#6923—81no—
73C4×#6923—81no—
74C4⋊C4×C61—21no—
75C4⋊C4×C61—21no—
76C4⋊C4×C61—41no—
77C4⋊C4×C61—41no—
78C4⋊C4×C61—41no—
79C4⋊C4×C61—41no—
80C22⋊C4×C61—21no—
81C22⋊C4×C61—41no—
82C42×C61—41no—
83C42×C61C22⋊C411yescharacteristic
84C42×C61C22×C411yescharacteristic
85#11758202—81no—
86#11758202—81no—
87#11758202—81no—
88#11758201—81no—
89#11758198—41no—
90#11758198—41no—
91C4⋊Dic61—41no—
92C4⋊Dic61—41no—
93C2×#92418—21no—
94C2×#92418—21no—
95C23×C61#9911yescharacteristic
96C22×D61—21no—
97C2×#6923—82no—
98Q8×C61—41no—
99Q8×C61—41no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—41no—
103C2×C4×C61—41no—
104C2×C4×C61—41no—
105C2×C4×C61#9911yescharacteristic
106C2×C4×C61C2×C22⋊C411yescharacteristic
107C22⋊D61—81no—
108C2×Dic61—21no—
109C2×Dic61—21no—
110C2×Dic61—21no—
111C2×Dic61—41no—
112C2×Dic61—41no—
113D244—41no—
114C4×D61—41no—
115C4×D61—41no—
116Dic122—41no—
117Dic122—41no—
118Dic122—41no—
119Dic122—81no—
120#92420—82no—
121#92418—41no—
122#92418—41no—
123#13608—611nomaximal, Sylow
124C22×C61—21no—
125C22×C61—41no—
126C22×C61C2×#9911yescharacteristic
127C2×D61—41no—
128C2×D61—81no—
129#6923—162no—
130C4×C61—21no—
131C4×C61—21no—
132C4×C61—41no—
133C4×C61—41no—
134C4×C61—81no—
135C4×C61—81no—
136Dic61—41no—
137Dic61—41no—
138Dic61—41no—
139#3223—611no—
140#2133—611no—
141#2129—611no—
142#1414—612no—
143#1407—612no—
144C2×C61—21no—
145C2×C61—41no—
146C2×C61#212711yescharacteristic
147D61—81no—
148#541#692311yescharacteristic, complemented
149#536—611no—
150#497—611no—
151#494—611no—
152#491—611no—
153#488—611no—
154#464—1221no—
155#462—1221no—
156#452—1221no—
157#451—1221no—
158#433—611no—
159C2×#101—1221no—
160#410—1221no—
161#356—1221no—
162#355—612no—
163#354—612no—
164#354—1221no—
165C61#1360811yescharacteristic, complemented, Sylow
166C2×#41—611no—
167C22×Q8—611no—
168C2×Q16—1221no—
169C2×Q16—1221no—
170C2×Q16—1221no—
171C2×SD16—1221no—
172C2×M16—2441no—
173C4⋊Q8—611no—
174C4⋊Q8—611no—
175C4⋊Q8C2×#692311yescharacteristic
176#126—41no—
177#125—41no—
178#125C2×#692311yescharacteristic
179#124—611no—
180#124—611no—
181#123—2441no—
182C22⋊Q8—21no—
183C22⋊Q8—2441no—
184C4×Q8—21no—
185#117—2441no—
186#117C2×#692311yescharacteristic
187C4⋊C8—1221no—
188#103—1221no—
189#103—1221no—
190#103—1221no—
191#102—1221no—
192#101—1222no—
193#101—2441no—
194#99—1222no—
195#99—2441no—
196C22⋊C8—1221no—
197#97—611no—
198C4×C8—611no—
199#41—4881no—
200C2×Q8—21no—
201C2×Q8—611no—
202C2×Q8—611no—
203C2×Q8—611no—
204C2×Q8—1221no—
205C2×Q8—4881no—
206C2×D4—611no—
207C2×D4—1221no—
208C22×C4—1221no—
209C22×C4—1221no—
210C22×C4C22⋊#692311yescharacteristic
211Q16—4881no—
212Q16—4881no—
213Q16—4881no—
214SD16—4881no—
215M16—4881no—
216M16—2442no—
217C2×C8—1221no—
218C2×C8—1221no—
219C2×C8—4881no—
220C4⋊C4—21no—
221C4⋊C4—21no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—4881no—
227C4⋊C4—2441no—
228C4⋊C4—2441no—
229C22⋊C4—21no—
230C22⋊C4—41no—
231C22⋊C4—2441no—
232C22⋊C4—2441no—
233C22⋊C4—2442no—
234C42—41no—
235C42—4881no—
236C42C22⋊#692311yescharacteristic
237C42C22×#692311yescharacteristic
238C23—1221no—
239C23#1451983511yescharacteristic
240Q8—41no—
241Q8—41no—
242Q8—4881no—
243Q8—2441no—
244Q8—2441no—
245Q8—2441no—
246D4—4881no—
247D4—2441no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—1221no—
254C2×C4—1221no—
255C2×C4—1221no—
256C2×C4—4882no—
257C2×C4—2441no—
258C2×C4—2441no—
259C2×C4—2441no—
260C2×C4—2441no—
261C2×C4#1451983511yescharacteristic
262C2×C4C2×C22⋊#692311yescharacteristic
263C8—4882no—
264C8—2441no—
265C8—2441no—
266C22—21no—
267C22—41no—
268C22—4881no—
269C22—2441no—
270C22C2×#1451983511yescharacteristic
271C4—21no—
272C4—21no—
273C4—41no—
274C4—41no—
275C4—81no—
276C4—81no—
277C4—9762no—
278C4—2441no—
279C4—2441no—
280C4—2441no—
281C2—21no—
282C2—41no—
283C2—4881no—
284C2#2146209411yescharacteristic
subgroupG/H
centerC2#21462094
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#541C4
socleC2×C61#2127
prime radicalC2×#11758222D4
cosocle#14519765C23
hypercenter#541#6923
hypocenterC61#13608
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C22×C4 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
3. #21460964C2semidirect
4. #21460948C2semidirect
14. #16840141C4semidirect
15. #16840132C4semidirect
21. #16839823C4semidirect
22. C61×#541C4semidirect
148. #541#6923semidirect
165. C61#13608semidirect

Maximal subgroups

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

subgroupindex
#214621162
#214621032
#214609642
#214609482
#214568962
#1360861