Finite Group Databasebeta

← #29576984

Subgroups — #29576984

Order 15616.

398 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 85 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#21456824C211yesmaximal, characteristic
2#21454924C211yesmaximal, characteristic, complemented
3#21444530C211yesmaximal, characteristic, complemented
4#21444442C211yesmaximal, characteristic
5#21444172C211yesmaximal, characteristic
6#21443682C211yesmaximal, characteristic, complemented
7C61×#1308C211yesmaximal, characteristic, complemented
8#16840319C2211yescharacteristic
9C2×#14519765C2211yescharacteristic
10#16840156—21no—
11#16840122—21no—
12#16839985—22no—
13#16839920C412yes—
14#16839915C412yes—
15#16839891—22no—
16#16839890—22no—
17#16839820—22no—
18#16839819C2211yescharacteristic
19#16839815C2211yescharacteristic
20#16839510—21no—
21#16839509—21no—
22#16839501—22no—
23#16839485—22no—
24C61×#432C2211yescharacteristic
25C61×#432C2211yescharacteristic
26C61×#432C2211yescharacteristic
27C22×Dic122C2×C411yescharacteristic
28C22×D244C2×C411yescharacteristic
29C2×Dic244—22no—
30C2×#11758190—22no—
31#14519777D411yescharacteristic
32#14519777D411yescharacteristic
33#14519769—21no—
34#14519765—21no—
35#14519765—21no—
36#14519765—21no—
37#14519765—21no—
38#14519756—21no—
39#14519756C2×C412yes—
40C4×Dic122—21no—
41C4×Dic122D412yes—
42#14519736—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C4⋊#92418—21no—
46C4⋊#92418—21no—
47#14519706—24no—
48#14519702—22no—
49#14519699—22no—
50C22⋊#92418—21no—
51C22⋊#92418—21no—
52#14519688D412yes—
53#14519687—22no—
54C4×#92418—21no—
55C8×Dic61—22no—
56C2×C42×C61C2311yescharacteristic
57C4⋊C8×C61—21no—
58C4⋊C8×C61—21no—
59C4⋊C8×C61—21no—
60C22⋊C8×C61—21no—
61C22⋊C8×C61C2×C412yes—
62C22⋊C8×C61D412yes—
63#97×C61—21no—
64#97×C61—21no—
65#97×C61—21no—
66C23×D61—21no—
67C22×C4×C61C22×C411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61#4111yescharacteristic
70C22×Dic61—21no—
71C2×D244—21no—
72C2×D244—21no—
73C2×D244—81no—
74C2×Dic122—21no—
75C2×Dic122—21no—
76C2×Dic122—21no—
77C2×Dic122—81no—
78C2×Dic122C22⋊C412yes—
79C2×C8×C61—22no—
80C2×C8×C61—22no—
81C2×C8×C61—41no—
82C42×C61C2×D411yescharacteristic
83C42×C61C2×D411yescharacteristic
84C42×C61C2×D411yescharacteristic
85C42×C61#4111yescharacteristic
86C22⋊Dic61—22no—
87#11758198—41no—
88#11758198—41no—
89#11758198—41no—
90#11758198—41no—
91C4⋊Dic61—21no—
92C4⋊Dic61—21no—
93C4⋊Dic61—21no—
94C4⋊Dic61C22⋊C412yes—
95#11758196—22no—
96#11758196—22no—
97C4×Dic61—22no—
98C2×#92418—22no—
99C2×#92418—41no—
100Dic244—82no—
101#11758190—82no—
102C23×C61C4×D411yescharacteristic
103C22×D61—41no—
104C22×D61—42no—
105C22×D61—81no—
106C22×D61—81no—
107C2×C4×C61—41no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61C2×C22⋊C411yescharacteristic
111C2×C4×C61C4×D411yescharacteristic
112C2×C4×C61#12011yescharacteristic
113C2×C4×C61#12111yescharacteristic
114C2×C4×C61#12111yescharacteristic
115C2×C4×C61#12311yescharacteristic
116C2×Dic61—22no—
117C2×Dic61—22no—
118C2×Dic61—41no—
119C2×Dic61—81no—
120D244—42no—
121D244—81no—
122Dic122—42no—
123Dic122—42no—
124Dic122—81no—
125Dic122—81no—
126C8×C61—42no—
127C8×C61—42no—
128C8×C61—81no—
129#92418—42no—
130#92418—81no—
131#9334—611nomaximal, Sylow
132C22×C61—21no—
133C22×C61—21no—
134C22×C61—21no—
135C22×C61#38611yescharacteristic
136C2×D61—81no—
137C2×D61—81no—
138C2×D61—81no—
139C2×D61—162no—
140C4×C61—21no—
141C4×C61—21no—
142C4×C61—21no—
143C4×C61—21no—
144C4×C61—21no—
145C4×C61—21no—
146Dic61—42no—
147Dic61—42no—
148Dic61—81no—
149#3215—611no—
150#2987—611no—
151#1554—611no—
152#1533—611no—
153#1469—611no—
154#1308D6111yescharacteristic, complemented
155#1287—611no—
156C2×C61—41no—
157C2×C61#188111yescharacteristic
158C2×C61#190511yescharacteristic
159C2×C61#191411yescharacteristic
160D61—161no—
161#533—611no—
162C2×#124—611no—
163#497—1221no—
164#489—1221no—
165#464—1222no—
166#451—612no—
167#450—612no—
168#446—1222no—
169#446—1222no—
170#433—1222no—
171#432—611no—
172#432C2×D6111yescharacteristic
173#432C2×D6111yescharacteristic
174#432C2×D6111yescharacteristic
175#431—611no—
176#333—1221no—
177#332—1221no—
178#329—1222no—
179#323—1222no—
180C61#933411yescharacteristic, complemented, Sylow
181C22×Q8—611no—
182C22×D4—611no—
183C2×Q16—1222no—
184C2×SD16—1222no—
185C4⋊Q8—611no—
186C4⋊Q8—611no—
187#125—1221no—
188#124—1221no—
189#124—1221no—
190#124—1221no—
191#124—1221no—
192C22⋊Q8—612no—
193C22⋊Q8—1221no—
194C4×Q8—612no—
195C4×Q8—1221no—
196#117—1221no—
197C2×C22⋊C4—1221no—
198C2×C22⋊C4—1221no—
199C2×C42C22×D6111yescharacteristic
200C4⋊C8—21no—
201C4⋊C8—21no—
202C4⋊C8—21no—
203C4⋊C8—1224no—
204C4⋊C8—1221no—
205C4⋊C8—1221no—
206#103—1222no—
207#102—1222no—
208C22⋊C8—21no—
209C22⋊C8—1221no—
210C22⋊C8—1221no—
211C22⋊C8C4×D6112yes—
212C22⋊C8D24412yes—
213#97—21no—
214#97—21no—
215#97—21no—
216#97—612no—
217#97—1222no—
218C4×C8—1222no—
219C4×C8—1221no—
220C24—1221no—
221C2×Q8—612no—
222C2×Q8—1221no—
223C2×Q8—1221no—
224C2×Q8—1221no—
225C2×Q8—4881no—
226C2×D4—1221no—
227C2×D4—1221no—
228C2×D4—4881no—
229C22×C4—1221no—
230C22×C4C2×C4×D6111yescharacteristic
231C22×C4C2×D24411yescharacteristic
232C22×C4#1175822211yescharacteristic
233Q16—4882no—
234SD16—4882no—
235C2×C8—22no—
236C2×C8—22no—
237C2×C8—41no—
238C2×C8—1222no—
239C2×C8—2441no—
240C4⋊C4—612no—
241C4⋊C4—1222no—
242C4⋊C4—1221no—
243C4⋊C4—1221no—
244C4⋊C4—1221no—
245C4⋊C4—1222no—
246C22⋊C4—1222no—
247C22⋊C4—2441no—
248C22⋊C4—2441no—
249C22⋊C4—2441no—
250C22⋊C4—2441no—
251C42—1222no—
252C42D4×D6111yescharacteristic
253C42D4×D6111yescharacteristic
254C42D4×D6111yescharacteristic
255C42#1175822611yescharacteristic
256C23—4881no—
257C23—4881no—
258C23—2442no—
259C23—2441no—
260C23C4×D24411yescharacteristic
261Q8—4881no—
262Q8—4881no—
263Q8—2442no—
264Q8—2442no—
265D4—4881no—
266D4—2442no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—1222no—
271C2×C4—1222no—
272C2×C4—4881no—
273C2×C4—2441no—
274C2×C4C22⋊C4×D6111yescharacteristic
275C2×C4#1451973911yescharacteristic
276C2×C4#1451974711yescharacteristic
277C2×C4#1451975011yescharacteristic
278C2×C4#1451975211yescharacteristic
279C2×C4#1451976211yescharacteristic
280C8—42no—
281C8—42no—
282C8—81no—
283C8—4881no—
284C8—2442no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22—9762no—
289C22—4881no—
290C22—4881no—
291C22—4881no—
292C22#1683964011yescharacteristic
293C4—21no—
294C4—21no—
295C4—21no—
296C4—21no—
297C4—21no—
298C4—21no—
299C4—4881no—
300C4—2442no—
301C4—2442no—
302C2—41no—
303C2—9761no—
304C2#2144618011yescharacteristic
305C2#2144631211yescharacteristic
306C2#2144636511yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1308C2
socleC22×C61#386
prime radicalC22×D244C2×C4
cosocleC2×C42×C61C23
hypercenter#1308D61
hypocenterC61#9334
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1308

Complements

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

NH ≅ G/Ntype
2. #21454924C2semidirect
3. #21444530C2semidirect
6. #21443682C2semidirect
7. C61×#1308C2semidirect
154. #1308D61semidirect
180. C61#9334semidirect

Maximal subgroups

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

subgroupindex
#214568242
#214549242
#214445302
#214444422
#214441722
#214436822
C61×#13082
#933461