Finite Group Databasebeta

← #29598705

Subgroups — #29598705

Order 15616.

396 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 103 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#21451006C211yesmaximal, characteristic
2#21445815C211yesmaximal, characteristic
3#21443945C212yesmaximal
4#21443945C212yesmaximal
5C4×#101×C61C211yesmaximal, characteristic
6C2×#14519769C411yescharacteristic
7#16839786—21no—
8C2×#14519696C2212yes—
9#16839695—21no—
10#16839695—21no—
11#16839669C2211yescharacteristic
12#16839669C2211yescharacteristic
13#16839646—21no—
14#16839646—21no—
15#16839631C411yescharacteristic
16#16839627C411yescharacteristic
17C4×C4⋊Dic61C411yescharacteristic
18#16839531—21no—
19C2×C4×Q8×C61C2211yescharacteristic
20C2×#101×C61C2212yes—
21C4×M16×C61—21no—
22C61×#343—21no—
23C2×#11758194—22no—
24#14519769—41no—
25#14519769—41no—
26C2×C4⋊Dic61—21no—
27C2×C4⋊Dic61C2×C411yescharacteristic
28C2×C4⋊Dic61C2×C411yescharacteristic
29C2×#11758196—21no—
30C2×#11758196—21no—
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×C4×Dic61C2×C411yescharacteristic
34C2×C4×Dic61C2×C411yescharacteristic
35C4⋊#92418—41no—
36C4⋊#92418—41no—
37#14519696—24no—
38#14519684—21no—
39#14519684—21no—
40#14519684—21no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45C22×Q8×C61C2311yescharacteristic
46C2×M16×C61—22no—
47C4×Q8×C61—41no—
48C4×Q8×C61—41no—
49C2×C4⋊C4×C61C2×C411yescharacteristic
50C2×C4⋊C4×C61D411yescharacteristic
51C2×C4⋊C4×C61D411yescharacteristic
52C2×C42×C61C2×C411yescharacteristic
53C2×C42×C61D411yescharacteristic
54C2×C42×C61D411yescharacteristic
55#101×C61—22no—
56#101×C61Q814yes—
57#97×C61—41no—
58C4×C8×C61—41no—
59C2×Q8×C61—41no—
60C2×Q8×C61—41no—
61C2×Q8×C61C2×Q812yes—
62C2×Q8×C61#4112yes—
63C22×C4×C61C22⋊C411yescharacteristic
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22×C411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74M16×C61—24no—
75M16×C61—42no—
76C2×C8×C61—42no—
77C4⋊C4×C61—41no—
78C4⋊C4×C61—41no—
79C4⋊C4×C61—41no—
80C42×C61—21no—
81C42×C61—21no—
82C42×C61—21no—
83C42×C61—21no—
84C42×C61—21no—
85C42×C61—21no—
86C4⋊Dic61—42no—
87C4⋊Dic61—41no—
88C4⋊Dic61—41no—
89#11758196—42no—
90#11758196—42no—
91#11758196—42no—
92#11758196—41no—
93#11758196—41no—
94C4×Dic61—41no—
95C4×Dic61—41no—
96#11758194—42no—
97#11758194—42no—
98C2×#92418—42no—
99C23×C61C2×C22⋊C411yescharacteristic
100Q8×C61—42no—
101Q8×C61—42no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61#9911yescharacteristic
116C2×C4×C61#9911yescharacteristic
117C2×C4×C61C4×Q812yes—
118C2×C4×C61C22⋊Q812yes—
119C2×C4×C61#12411yescharacteristic
120C2×C4×C61C4⋊Q811yescharacteristic
121C2×Dic61—22no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—42no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C8×C61—44no—
133#92418—82no—
134#13303—611nomaximal, Sylow
135C22×C61—21no—
136C22×C61—21no—
137C22×C61#39111yescharacteristic
138C22×C61C2×#9911yescharacteristic
139C22×C61#41011yescharacteristic
140C4×C61—21no—
141C4×C61—21no—
142C4×C61—21no—
143C4×C61—22no—
144C4×C61—22no—
145C4×C61—21no—
146C4×C61—41no—
147C4×C61—41no—
148C4×C61—41no—
149Dic61—42no—
150Dic61—81no—
151Dic61—81no—
152Dic61—81no—
153#2565—611no—
154#1801—611no—
155C4×#101D6111yescharacteristic
156#1394—612no—
157#1394—612no—
158C2×C61—21no—
159C2×C61—21no—
160C2×C61#199611yescharacteristic
161C2×C61#213211yescharacteristic
162C2×C61#213311yescharacteristic
163C2×#125—611no—
164C2×C4×Q8C2×D6111yescharacteristic
165#423—1221no—
166C2×#101—612no—
167C2×#101C2×D6112yes—
168C4×M16—21no—
169#398—1221no—
170#398—1221no—
171#391—611no—
172#391—611no—
173#387—1221no—
174#387—1221no—
175#384—611no—
176#382—611no—
177C4×C4⋊C4—611no—
178#343—21no—
179#343—1221no—
180C61#1330311yescharacteristic, complemented, Sylow
181C22×Q8C22×D6111yescharacteristic
182C2×M16—22no—
183C2×M16—1222no—
184#125—2441no—
185#125—2441no—
186C4×Q8—41no—
187C4×Q8—41no—
188C2×C4⋊C4—611no—
189C2×C4⋊C4—611no—
190C2×C4⋊C4—1221no—
191C2×C4⋊C4—1221no—
192C2×C4⋊C4—1221no—
193C2×C4⋊C4—1221no—
194C2×C4⋊C4—1221no—
195C2×C4⋊C4C4×D6111yescharacteristic
196C2×C4⋊C4D24411yescharacteristic
197C2×C4⋊C4C22⋊D6111yescharacteristic
198C2×C42—611no—
199C2×C42—611no—
200C2×C42C4×D6111yescharacteristic
201C2×C42D24411yescharacteristic
202C2×C42C22⋊D6111yescharacteristic
203C4⋊C8—2441no—
204C4⋊C8—2441no—
205#101—22no—
206#101—1224no—
207#101Dic12214yes—
208#97—41no—
209C4×C8—41no—
210#95—1221no—
211#95—1221no—
212#95—1221no—
213#95—1221no—
214#95—1221no—
215#95—1221no—
216#95—1221no—
217C2×Q8—41no—
218C2×Q8—41no—
219C2×Q8C2×Dic12212yes—
220C2×Q8#1175822212yes—
221C22×C4—1221no—
222C22×C4—1221no—
223C22×C4—1221no—
224C22×C4—1221no—
225C22×C4#1175819811yescharacteristic
226C22×C4#1175819811yescharacteristic
227C22×C4#1175819811yescharacteristic
228C22×C4#1175819811yescharacteristic
229C22×C4C2×C4×D6111yescharacteristic
230C22×C4C2×D24411yescharacteristic
231C22×C4C2×C22⋊D6111yescharacteristic
232M16—24no—
233M16—42no—
234M16—2442no—
235M16—2442no—
236C2×C8—42no—
237C2×C8—2442no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—2441no—
242C4⋊C4—2441no—
243C4⋊C4—2442no—
244C4⋊C4—2442no—
245C4⋊C4—2442no—
246C4⋊C4—2442no—
247C4⋊C4—2441no—
248C4⋊C4—2441no—
249C42—21no—
250C42—21no—
251C42—21no—
252C42—21no—
253C42—21no—
254C42—21no—
255C42—2441no—
256C42—2441no—
257C23C2×#1175819811yescharacteristic
258Q8—42no—
259Q8—42no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—1222no—
274C2×C4—2441no—
275C2×C4—2441no—
276C2×C4—2441no—
277C2×C4—2441no—
278C2×C4—2442no—
279C2×C4—2441no—
280C2×C4—2441no—
281C2×C4—2441no—
282C2×C4—2441no—
283C2×C4—2441no—
284C2×C4#1451969111yescharacteristic
285C2×C4#1451969111yescharacteristic
286C2×C4C4×Dic12212yes—
287C2×C4#1451975612yes—
288C2×C4#1451976511yescharacteristic
289C2×C4#1451977711yescharacteristic
290C8—44no—
291C8—4882no—
292C22—21no—
293C22—21no—
294C22#1683966811yescharacteristic
295C22C2×#1451969111yescharacteristic
296C22#1683973511yescharacteristic
297C4—21no—
298C4—21no—
299C4—22no—
300C4—21no—
301C4—22no—
302C4—21no—
303C4—41no—
304C4—41no—
305C4—41no—
306C4—4881no—
307C4—4881no—
308C4—4881no—
309C4—2442no—
310C2—21no—
311C2—21no—
312C2#2144680411yescharacteristic
313C2#2144750211yescharacteristic
314C2#2144750611yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC22×Q8C22×D61
FittingC4×#101×C61C2
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC22×Q8×C61C23
hypercenterC4×#101D61
hypocenterC61#13303
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
180. C61#13303semidirect

Maximal subgroups

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

subgroupindex
#214510062
#214458152
#214439452
C4×#101×C612
#1330361