Finite Group Databasebeta

← #30601631

Subgroups — #30601631

Order 15616.

558 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 122 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#21461734C211yesmaximal, characteristic, complemented
2#21461534C211yesmaximal, characteristic, complemented
3C2×Q8⋊#92420C212yesmaximal, complemented
4C2×#16840610C212yesmaximal
5#21448362C211yesmaximal, characteristic
6C2×C4⋊#92420C2212yes—
7C2×C4×#92420C2212yes—
8#16840628—22no—
9#16840628—22no—
10Q8⋊#92420—24no—
11#16840610—24no—
12C2×#14519766C411yescharacteristic
13C2×Q8×Dic61C2211yescharacteristic
14C2×#14519739C2211yescharacteristic
15#16839664C411yescharacteristic
16#16839654—22no—
17#16839627C411yescharacteristic
18#16839609—22no—
19C42×Dic61C2211yescharacteristic
20C61×#391C411yescharacteristic
21C22×#92420—22no—
22C22×#92420—22no—
23C4⋊#92420—22no—
24C4⋊#92420—22no—
25C4×#92420—22no—
26C4×#92420D414yes—
27C22×D244C2×C411yescharacteristic
28C22×C4×D61—21no—
29#14519766—22no—
30#14519766—22no—
31Q8×Dic61—22no—
32Q8×Dic61—22no—
33#14519739—22no—
34#14519739—22no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61C2×C411yescharacteristic
37C2×#11758198—22no—
38C2×#11758198—22no—
39C2×#11758198—21no—
40C2×C4×Dic61—21no—
41C2×C4×Dic61C2×C411yescharacteristic
42C2×C4×Dic61D412yes—
43C2×C4×Dic61D412yes—
44C2×C4×Dic61C2311yescharacteristic
45#14519684—22no—
46C22×Q8×C61C2×C411yescharacteristic
47C2×C4⋊C4×C61C2×C411yescharacteristic
48C2×C42×C61C2×C411yescharacteristic
49#95×C61—22no—
50C23×D61—21no—
51C2×Q8×C61—21no—
52C2×Q8×C61—22no—
53C2×Q8×C61—22no—
54C2×Q8×C61M1612yes—
55C22×C4×C61—21no—
56C22×C4×C61—21no—
57C22×C4×C61C22⋊C412yes—
58C22×C4×C61C22×C411yescharacteristic
59C22×Dic61—21no—
60C22×Dic61C22⋊C412yes—
61C22×Dic61C2×D411yescharacteristic
62C22×Dic61C2×D411yescharacteristic
63C2×D244—22no—
64C2×D244—22no—
65C2×D244—21no—
66C2×D244M1612yes—
67C2×C4×D61—41no—
68C2×C4×D61—41no—
69C2×C4×D61—44no—
70C2×#92420—24no—
71C2×#92420—44no—
72C2×#92420—42no—
73C2×#92420—44no—
74C4⋊C4×C61—22no—
75C42×C61—22no—
76#11758198—28no—
77#11758198—44no—
78#11758198—42no—
79C4⋊Dic61—22no—
80C4⋊Dic61—42no—
81C4×Dic61—21no—
82C4×Dic61—21no—
83C4×Dic61—24no—
84C4×Dic61—42no—
85C4×Dic61—41no—
86C4×Dic61—41no—
87C4×Dic61C2×D412yes—
88C4×Dic61#4112yes—
89C23×C61C2×C22⋊C411yescharacteristic
90C22×D61—22no—
91C22×D61—41no—
92C22×D61—41no—
93C22×D61—42no—
94C22×D61—42no—
95Q8×C61—24no—
96Q8×C61—42no—
97C2×C4×C61—22no—
98C2×C4×C61—22no—
99C2×C4×C61—22no—
100C2×C4×C61—22no—
101C2×C4×C61—41no—
102C2×C4×C61—41no—
103C2×C4×C61—41no—
104C2×C4×C61—42no—
105C2×C4×C61C4×D412yes—
106C2×C4×C61C2×M1611yescharacteristic
107C2×C4×C61C2×M1611yescharacteristic
108C2×C4×C61#13112yes—
109C2×Dic61—22no—
110C2×Dic61—22no—
111C2×Dic61—22no—
112C2×Dic61—22no—
113C2×Dic61—41no—
114C2×Dic61—42no—
115C2×Dic61#12112yes—
116C2×Dic61#12411yescharacteristic
117C2×Dic61#12711yescharacteristic
118C2×Dic61#13514yes—
119D244—24no—
120D244—42no—
121C4×D61—82no—
122C4×D61—82no—
123#92420—44no—
124#92420—82no—
125#9645—611nomaximal, Sylow
126C22×C61#39011yescharacteristic
127C22×C61#40711yescharacteristic
128C22×C61#40811yescharacteristic
129C22×C61#41612yes—
130C22×C61#42112yes—
131C2×D61—42no—
132C2×D61—44no—
133C2×D61—81no—
134C2×D61—81no—
135C2×D61—82no—
136C4×C61—42no—
137C4×C61—42no—
138C4×C61—81no—
139C4×C61#43512yes—
140C4×C61#43512yes—
141Dic61—22no—
142Dic61—42no—
143Dic61—81no—
144Dic61#48812yes—
145Dic61#49512yes—
146C4×#124—611no—
147#1831—611no—
148#1744—611no—
149C2×Q8⋊C8—612no—
150C2×D4⋊C8—612no—
151C2×C61#148212yes—
152C2×C61#148812yes—
153C2×C61#195511yescharacteristic
154C2×C61#195811yescharacteristic
155C2×C61#196311yescharacteristic
156D61—82no—
157C2×#124—611no—
158C2×C4×Q8—611no—
159C2×C4×D4—611no—
160C2×C4⋊C8—612no—
161C2×C4×C8—612no—
162#391#692311yescharacteristic
163#390—611no—
164#388—1222no—
165#382—611no—
166C4×C22⋊C4—1222no—
167C43—611no—
168#336—1222no—
169#336—1222no—
170Q8⋊C8—1224no—
171D4⋊C8—1224no—
172C61#964511yescharacteristic, complemented, Sylow
173C22×Q8C2×#692311yescharacteristic
174C22×D4—611no—
175C23×C4—1221no—
176C22×C8—1222no—
177C22×C8—1222no—
178#124—1222no—
179#124—1222no—
180C4×Q8—1222no—
181C4×Q8—1222no—
182C4×D4—1222no—
183C4×D4—1222no—
184C2×C4⋊C4—611no—
185C2×C4⋊C4—1221no—
186C2×C4⋊C4C2×#692311yescharacteristic
187C2×C22⋊C4—1222no—
188C2×C22⋊C4—1221no—
189C2×C22⋊C4—1222no—
190C2×C42—611no—
191C2×C42—612no—
192C2×C42—611no—
193C2×C42—612no—
194C2×C42—1221no—
195C2×C42C2×#692311yescharacteristic
196C4⋊C8—1222no—
197C4⋊C8—1222no—
198C4×C8—614no—
199C4×C8—1222no—
200#95—22no—
201#95—1222no—
202C24—1221no—
203C2×Q8—21no—
204C2×Q8—22no—
205C2×Q8—22no—
206C2×Q8#1175821312yes—
207C2×D4—612no—
208C2×D4—1222no—
209C2×D4—1221no—
210C2×D4—1222no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—611no—
214C22×C4—611no—
215C22×C4—612no—
216C22×C4—1221no—
217C22×C4—2441no—
218C22×C4—2441no—
219C22×C4—2444no—
220C22×C4C22⋊#692312yes—
221C22×C4C22×#692311yescharacteristic
222C2×C8—1224no—
223C2×C8—2442no—
224C2×C8—2444no—
225C2×C8—2444no—
226C4⋊C4—22no—
227C4⋊C4—1222no—
228C4⋊C4—2442no—
229C22⋊C4—1228no—
230C22⋊C4—2444no—
231C22⋊C4—2442no—
232C42—22no—
233C42—612no—
234C42—612no—
235C42—1224no—
236C42—1221no—
237C42—1221no—
238C42—2442no—
239C42—2441no—
240C42—2441no—
241C23—1222no—
242C23—2441no—
243C23—2441no—
244C23—2442no—
245C23—2442no—
246C23C2×C22⋊#692311yescharacteristic
247Q8—24no—
248Q8—42no—
249D4—1224no—
250D4—2442no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—42no—
259C2×C4—611no—
260C2×C4—611no—
261C2×C4—614no—
262C2×C4—612no—
263C2×C4—1222no—
264C2×C4—1222no—
265C2×C4—1222no—
266C2×C4—1222no—
267C2×C4—4882no—
268C2×C4—4882no—
269C2×C4—2441no—
270C2×C4—2442no—
271C2×C4D4×#692312yes—
272C2×C4D61⋊M1611yescharacteristic
273C2×C4C2×#1175821311yescharacteristic
274C2×C4#1451986412yes—
275C8—4882no—
276C8—2444no—
277C22—4882no—
278C22—4881no—
279C22—4881no—
280C22—2444no—
281C22—2442no—
282C22#1684071411yescharacteristic
283C22#1684073311yescharacteristic
284C22#1684073511yescharacteristic
285C22#1684075212yes—
286C22#1684076112yes—
287C4—42no—
288C4—42no—
289C4—81no—
290C4—612no—
291C4—612no—
292C4—1222no—
293C4—4881no—
294C4—2442no—
295C4#1684079112yes—
296C4#1684079412yes—
297C2—4882no—
298C2#2146113212yes—
299C2#2146115312yes—
300C2#2146194411yescharacteristic
301C2#2146194811yescharacteristic
302C2#2146195511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#391C4
socleC23×C61C2×C22⋊C4
prime radicalC22×D244C2×C4
cosocleC2×C4×Dic61C23
hypercenter#391#6923
hypocenterC61#9645
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
1. #21461734C2semidirect
2. #21461534C2semidirect
3. C2×Q8⋊#92420C2semidirect
172. C61#9645semidirect

Maximal subgroups

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

subgroupindex
#214617342
#214615342
C2×Q8⋊#924202
C2×#168406102
#214483622
#964561