Finite Group Databasebeta

← #29591168

Subgroups — #29591168

Order 15616.

372 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 95 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#21451181C211yesmaximal, characteristic
2#21445815C211yesmaximal, characteristic
3#21443850C212yesmaximal
4#21443847C212yesmaximal
5C61×#1461C211yesmaximal, characteristic
6C2×C4×Dic122C411yescharacteristic
7#16839786—21no—
8C2×#14519696—21no—
9#16839701C411yescharacteristic
10#16839701C2211yescharacteristic
11#16839682C411yescharacteristic
12#16839682C2211yescharacteristic
13#16839669—21no—
14#16839658—21no—
15#16839646—21no—
16#16839646—21no—
17#16839628C411yescharacteristic
18#16839531C2212yes—
19C2×C4×Q8×C61C2211yescharacteristic
20C61×#431—21no—
21C61×#324—21no—
22C61×#324C2212yes—
23C22×Dic122C2×C411yescharacteristic
24C2×#11758194—22no—
25C4×Dic122—41no—
26C4×Dic122—41no—
27C2×C4⋊Dic61—21no—
28C2×C4⋊Dic61C2×C411yescharacteristic
29C2×#11758196—21no—
30C2×#11758196—21no—
31C2×#11758196—21no—
32C2×C4×Dic61—21no—
33C4⋊#92418—41no—
34C4⋊#92418—41no—
35#14519696—42no—
36#14519684—21no—
37#14519684—21no—
38#14519684—21no—
39#14519684—21no—
40#14519684—21no—
41#14519684—21no—
42#14519684—21no—
43#14519684C2×C411yescharacteristic
44#14519684C2×C411yescharacteristic
45C22×Q8×C61D411yescharacteristic
46C4×Q8×C61—41no—
47C4×Q8×C61—41no—
48C2×C4⋊C4×C61C2×C411yescharacteristic
49C2×C4⋊C4×C61D411yescharacteristic
50C2×C4⋊C4×C61C2311yescharacteristic
51C2×C42×C61C2×C411yescharacteristic
52C2×C42×C61D411yescharacteristic
53C2×C42×C61D411yescharacteristic
54C4⋊C8×C61—41no—
55C22⋊C8×C61—22no—
56C4×C8×C61—41no—
57C2×Q8×C61—41no—
58C2×Q8×C61—41no—
59C2×Q8×C61SD1612yes—
60C2×Q8×C61Q1612yes—
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22⋊C411yescharacteristic
63C22×C4×C61C22⋊C411yescharacteristic
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22×C411yescharacteristic
66C22×C4×C61C2×D411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61—21no—
72C2×Dic122—41no—
73C2×Dic122—42no—
74C2×C8×C61—42no—
75C4⋊C4×C61—41no—
76C4⋊C4×C61—41no—
77C4⋊C4×C61—41no—
78C42×C61—21no—
79C42×C61—21no—
80C42×C61—21no—
81C42×C61—21no—
82C42×C61—21no—
83C42×C61—21no—
84C4⋊Dic61—42no—
85C4⋊Dic61—41no—
86#11758196—42no—
87#11758196—42no—
88#11758196—41no—
89#11758196—41no—
90C4×Dic61—42no—
91#11758194—42no—
92#11758194—42no—
93C2×#92418—42no—
94C23×C61C2×C22⋊C411yescharacteristic
95Q8×C61—42no—
96Q8×C61—42no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—41no—
107C2×C4×C61—41no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61#9911yescharacteristic
111C2×C4×C61#9911yescharacteristic
112C2×C4×C61#10312yes—
113C2×C4×C61#10312yes—
114C2×C4×C61C2×SD1611yescharacteristic
115C2×C4×C61C2×Q1611yescharacteristic
116C2×Dic61—22no—
117C2×Dic61—41no—
118C2×Dic61—41no—
119C2×Dic61—41no—
120C2×Dic61—41no—
121C2×Dic61—41no—
122C2×Dic61—41no—
123C2×Dic61—42no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127Dic122—42no—
128Dic122—42no—
129C8×C61—82no—
130#92418—82no—
131#11905—611nomaximal, Sylow
132C22×C61—21no—
133C22×C61—21no—
134C22×C61C2×#9911yescharacteristic
135C22×C61C2×#10311yescharacteristic
136C22×C61#42111yescharacteristic
137C4×C61—21no—
138C4×C61—21no—
139C4×C61—21no—
140C4×C61—22no—
141C4×C61—22no—
142C4×C61—21no—
143C4×C61—41no—
144C4×C61—41no—
145C4×C61—41no—
146Dic61—42no—
147Dic61—81no—
148Dic61—81no—
149Dic61—81no—
150#2581—611no—
151#1801—611no—
152#1461D6111yescharacteristic
153#1354—612no—
154#1353—612no—
155C2×C61—21no—
156C2×C61—21no—
157C2×C61#152011yescharacteristic
158C2×C61#212011yescharacteristic
159C2×C61#213311yescharacteristic
160C2×C4×Q8—611no—
161C2×C4×Q8C2×D6111yescharacteristic
162#431—21no—
163#423—1221no—
164C2×#101—1221no—
165#400—611no—
166#400—611no—
167#395—611no—
168#395—611no—
169#391—1221no—
170#389—1221no—
171#387—1221no—
172#387—1221no—
173#382—611no—
174#343—612no—
175#324—21no—
176#324C2×D6112yes—
177C61#1190511yescharacteristic, complemented, Sylow
178C22×Q8—611no—
179C22×Q8D24411yescharacteristic
180C2×M16—1222no—
181C4×Q8—41no—
182C4×Q8—41no—
183C4×Q8—2441no—
184C4×Q8—2441no—
185C2×C4⋊C4—611no—
186C2×C4⋊C4—1221no—
187C2×C4⋊C4—1221no—
188C2×C4⋊C4—1221no—
189C2×C4⋊C4—1221no—
190C2×C4⋊C4C4×D6111yescharacteristic
191C2×C4⋊C4C22⋊D6111yescharacteristic
192C2×C4⋊C4C22×D6111yescharacteristic
193C2×C42—1221no—
194C2×C42C4×D6111yescharacteristic
195C2×C42D24411yescharacteristic
196C2×C42C22⋊D6111yescharacteristic
197C4⋊C8—41no—
198C4⋊C8—2441no—
199C4⋊C8—2441no—
200#101—2442no—
201C22⋊C8—22no—
202C4×C8—41no—
203#95—611no—
204#95—611no—
205#95—1221no—
206#95—1221no—
207#95—1221no—
208#95—1221no—
209#95—1221no—
210#95—1221no—
211#95—1221no—
212C2×Q8—41no—
213C2×Q8—41no—
214C2×Q8—2441no—
215C2×Q8—2442no—
216C2×Q8#1175819012yes—
217C2×Q8Dic24412yes—
218C22×C4—1221no—
219C22×C4—1221no—
220C22×C4—1221no—
221C22×C4—1221no—
222C22×C4#1175819811yescharacteristic
223C22×C4#1175819811yescharacteristic
224C22×C4#1175819811yescharacteristic
225C22×C4#1175819811yescharacteristic
226C22×C4C2×C4×D6111yescharacteristic
227C22×C4C2×D24411yescharacteristic
228C22×C4C2×C22⋊D6111yescharacteristic
229M16—2442no—
230M16—2442no—
231C2×C8—42no—
232C2×C8—2442no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—2441no—
237C4⋊C4—2442no—
238C4⋊C4—2442no—
239C4⋊C4—2442no—
240C4⋊C4—2441no—
241C4⋊C4—2441no—
242C42—21no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—21no—
247C42—21no—
248C42—2442no—
249C23C2×#1175819811yescharacteristic
250Q8—42no—
251Q8—42no—
252Q8—2442no—
253Q8—2442no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—1222no—
268C2×C4—2441no—
269C2×C4—2441no—
270C2×C4—2441no—
271C2×C4—2441no—
272C2×C4—2442no—
273C2×C4—2441no—
274C2×C4—2441no—
275C2×C4—2441no—
276C2×C4—2441no—
277C2×C4—2441no—
278C2×C4#1451969111yescharacteristic
279C2×C4#1451969111yescharacteristic
280C2×C4#1451970212yes—
281C2×C4#1451970212yes—
282C2×C4C2×#1175819011yescharacteristic
283C2×C4C2×Dic24411yescharacteristic
284C8—82no—
285C8—4882no—
286C22—21no—
287C22—21no—
288C22C2×#1451969111yescharacteristic
289C22C2×#1451970211yescharacteristic
290C22#1683977811yescharacteristic
291C4—21no—
292C4—22no—
293C4—22no—
294C4—21no—
295C4—21no—
296C4—21no—
297C4—41no—
298C4—41no—
299C4—41no—
300C4—4881no—
301C4—4881no—
302C4—4881no—
303C4—2442no—
304C2—21no—
305C2—21no—
306C2#2144439211yescharacteristic
307C2#2144745811yescharacteristic
308C2#2144750611yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1461C2
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1461D61
hypocenterC61#11905
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1461

Complements

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

NH ≅ G/Ntype
177. C61#11905semidirect

Maximal subgroups

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

subgroupindex
#214511812
#214458152
#214438502
#214438472
C61×#14612
#1190561