Finite Group Databasebeta

← #29599880

Subgroups — #29599880

Order 15616.

342 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839541C211yesmaximal, characteristic
2#21445845C211yesmaximal, characteristic
3#21445845C211yesmaximal, characteristic
4#21443911C211yesmaximal, characteristic, complemented
5#21443910C211yesmaximal, characteristic, complemented
6#21443910C211yesmaximal, characteristic, complemented
7C2×C61×#367C211yesmaximal, characteristic, complemented
8C22×C8×D61C2211yescharacteristic
9C22×#11758185C2211yescharacteristic
10C2×#14519711C2211yescharacteristic
11C2×#14519711C2211yescharacteristic
12#16839619—21no—
13#16839619—21no—
14#16839541—22no—
15#16839524—21no—
16#16839524—21no—
17C22×C16×C61C2211yescharacteristic
18C2×#107×C61C2211yescharacteristic
19C2×#107×C61C2211yescharacteristic
20C61×#367—22no—
21C22×C4×D61D411yescharacteristic
22C22×#92418D411yescharacteristic
23C2×C8×D61—21no—
24C2×C8×D61—21no—
25C2×C8×D61—21no—
26C2×C8×D61—21no—
27C2×C8×D61—21no—
28C2×C8×D61—21no—
29C2×C4⋊Dic61—21no—
30C2×C4⋊Dic61—21no—
31C2×#11758198—41no—
32C2×#11758198—41no—
33C2×#11758185—21no—
34C2×#11758185—21no—
35C2×#11758185—21no—
36#14519711—21no—
37#14519711—21no—
38#14519711—21no—
39#14519711—21no—
40#14519684—41no—
41#14519684—41no—
42C22×C8×C61C2311yescharacteristic
43C2×C4⋊C4×C61—21no—
44C2×C4⋊C4×C61—21no—
45C2×C16×C61—21no—
46C2×C16×C61—21no—
47C2×C16×C61D412yes—
48#107×C61—21no—
49#107×C61—21no—
50#107×C61—21no—
51#107×C61—21no—
52C23×D61D811yescharacteristic
53C22×C4×C61—41no—
54C22×C4×C61—41no—
55C22×C4×C61C2×D411yescharacteristic
56C22×Dic61—41no—
57C22×Dic61—41no—
58C22×Dic61D811yescharacteristic
59C2×C4×D61—21no—
60C2×C4×D61—21no—
61C2×C4×D61—21no—
62C2×C4×D61—21no—
63C2×C4×D61—21no—
64C2×C4×D61—21no—
65C2×C8×C61C2×D411yescharacteristic
66C2×C8×C61#4111yescharacteristic
67C2×C8×C61#4111yescharacteristic
68C2×C8×C61#4111yescharacteristic
69C2×C8×C61#4111yescharacteristic
70C2×C8×C61#4111yescharacteristic
71C4⋊C4×C61—41no—
72C4⋊C4×C61—41no—
73C4⋊C4×C61—41no—
74C4⋊C4×C61—41no—
75#11758198—82no—
76#11758198—82no—
77C4⋊Dic61—41no—
78C4⋊Dic61—41no—
79C4⋊Dic61—41no—
80C4⋊Dic61—41no—
81C2×#92418—21no—
82C2×#92418—21no—
83C2×#92418—21no—
84C8×D61—41no—
85C8×D61—41no—
86C8×D61—41no—
87C8×D61—41no—
88C16×C61—22no—
89#11758185—41no—
90C23×C61C2×D811yescharacteristic
91C22×D61—21no—
92C22×D61—21no—
93C22×D61—21no—
94C22×D61—21no—
95C22×D61—21no—
96C22×D61—21no—
97C22×D61SD3212yes—
98C2×C4×C61—81no—
99C2×C4×C61—81no—
100C2×C4×C61—81no—
101C2×C4×C61—81no—
102C2×C4×C61—81no—
103C2×C4×C61—81no—
104C2×C4×C61#12111yescharacteristic
105C2×C4×C61#12311yescharacteristic
106C2×C4×C61#12311yescharacteristic
107C2×C4×C61#13511yescharacteristic
108C2×C4×C61#13711yescharacteristic
109C2×C4×C61#13711yescharacteristic
110C2×Dic61—21no—
111C2×Dic61—21no—
112C2×Dic61—21no—
113C2×Dic61—81no—
114C2×Dic61—81no—
115C2×Dic61—81no—
116C2×Dic61—81no—
117C2×Dic61—81no—
118C2×Dic61—81no—
119C4×D61—41no—
120C4×D61—41no—
121C4×D61—41no—
122C4×D61—41no—
123C8×C61#12311yescharacteristic
124C8×C61#12411yescharacteristic
125C8×C61#12611yescharacteristic
126C8×C61#12611yescharacteristic
127#92418—41no—
128#13494—611nomaximal, Sylow
129C22×C61#46611yescharacteristic
130C22×C61#48011yescharacteristic
131C22×C61#48011yescharacteristic
132C22×C61C2×SD3211yescharacteristic
133C22×C61#50811yescharacteristic
134C22×C61#50911yescharacteristic
135C22×C61#51011yescharacteristic
136C2×D61—22no—
137C2×D61—22no—
138C2×D61—22no—
139C2×D61—41no—
140C2×D61—41no—
141C2×D61—41no—
142C2×D61—41no—
143C4×C61—161no—
144C4×C61—161no—
145C4×C61#39711yescharacteristic
146C4×C61#47011yescharacteristic
147C4×C61#48511yescharacteristic
148C4×C61#48511yescharacteristic
149Dic61—41no—
150Dic61—161no—
151Dic61—161no—
152C2×#367D6111yescharacteristic, complemented
153C2×C22⋊C16—611no—
154#1808—611no—
155#1808—611no—
156#1380—611no—
157#1380—611no—
158#1380—611no—
159C2×C61#207511yescharacteristic
160C2×C61#221711yescharacteristic
161C2×C61#222011yescharacteristic
162C2×C61#223311yescharacteristic
163C2×C61#223411yescharacteristic
164C2×C61#223511yescharacteristic
165C2×C61#223711yescharacteristic
166D61—42no—
167C23×C8—611no—
168C22×C16—611no—
169C22×C16C2×D6111yescharacteristic
170C2×#107—611no—
171C2×#107—611no—
172C2×#107C2×D6111yescharacteristic
173C2×#107C2×D6111yescharacteristic
174#380—1221no—
175#380—1221no—
176#367—22no—
177C22⋊C16—1222no—
178#340—1221no—
179#340—1221no—
180C61#1349411yescharacteristic, complemented, Sylow
181C23×C4—611no—
182C22×C8—611no—
183C22×C8—1221no—
184C22×C8—1221no—
185C22×C8—1221no—
186C22×C8—1221no—
187C22×C8—1221no—
188C22×C8—1221no—
189C22×C8C22×D6111yescharacteristic
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—1221no—
193C2×C4⋊C4—1221no—
194C2×C22⋊C4—2441no—
195C2×C22⋊C4—2441no—
196C2×C16—21no—
197C2×C16—21no—
198C2×C16—1221no—
199C2×C16—1221no—
200C2×C16—1221no—
201C2×C16C22⋊D6112yes—
202#107—21no—
203#107—21no—
204#107—21no—
205#107—21no—
206#107—1221no—
207#107—1221no—
208#107—1221no—
209#107—1221no—
210#95—2441no—
211#95—2441no—
212C24—611no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4—611no—
216C22×C4—1221no—
217C22×C4—1221no—
218C22×C4—1221no—
219C22×C4—1221no—
220C22×C4—1221no—
221C22×C4—1221no—
222C22×C4—2441no—
223C22×C4—2441no—
224C22×C4D4×D6111yescharacteristic
225C2×C8—1221no—
226C2×C8—1221no—
227C2×C8—1221no—
228C2×C8—2441no—
229C2×C8—2441no—
230C2×C8—2441no—
231C2×C8—2441no—
232C2×C8#1175822211yescharacteristic
233C2×C8#1175822211yescharacteristic
234C2×C8#1175822411yescharacteristic
235C2×C8#1175822611yescharacteristic
236C2×C8#1175822611yescharacteristic
237C2×C8C2×C22⋊D6111yescharacteristic
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—2441no—
243C4⋊C4—2441no—
244C4⋊C4—2441no—
245C4⋊C4—2441no—
246C22⋊C4—4882no—
247C22⋊C4—4882no—
248C16—22no—
249C16—2441no—
250C23—612no—
251C23—1221no—
252C23—1221no—
253C23—1221no—
254C23—1221no—
255C23—1221no—
256C23—1221no—
257C23D8×D6111yescharacteristic
258C2×C4—81no—
259C2×C4—81no—
260C2×C4—81no—
261C2×C4—81no—
262C2×C4—81no—
263C2×C4—81no—
264C2×C4—1221no—
265C2×C4—1221no—
266C2×C4—1221no—
267C2×C4—4881no—
268C2×C4—4881no—
269C2×C4—4881no—
270C2×C4—4881no—
271C2×C4—4881no—
272C2×C4—4881no—
273C2×C4—2441no—
274C2×C4—2441no—
275C2×C4—2441no—
276C2×C4—2441no—
277C2×C4#1451974811yescharacteristic
278C2×C4#1451976211yescharacteristic
279C2×C4#1451976211yescharacteristic
280C2×C4#1451979611yescharacteristic
281C2×C4#1451980911yescharacteristic
282C2×C4#1451980911yescharacteristic
283C8—2441no—
284C8#1451976011yescharacteristic
285C8#1451976611yescharacteristic
286C8#1451977211yescharacteristic
287C8#1451977211yescharacteristic
288C22—1222no—
289C22—1222no—
290C22—1222no—
291C22—2441no—
292C22—2441no—
293C22—2441no—
294C22—2441no—
295C22#1683999511yescharacteristic
296C22#1684007711yescharacteristic
297C22#1684007711yescharacteristic
298C22SD32×D6111yescharacteristic
299C22#1684019311yescharacteristic
300C22#1684019911yescharacteristic
301C22#1684020111yescharacteristic
302C4—161no—
303C4—161no—
304C4—9761no—
305C4—9761no—
306C4—2441no—
307C4#1683968811yescharacteristic
308C4#1684001711yescharacteristic
309C4#1684010511yescharacteristic
310C4#1684010511yescharacteristic
311C2—2442no—
312C2#2144724311yescharacteristic
313C2#2144791211yescharacteristic
314C2#2144792911yescharacteristic
315C2#2144800611yescharacteristic
316C2#2144801211yescharacteristic
317C2#2144801811yescharacteristic
318C2#2144803011yescharacteristic
subgroupG/H
centerC23D8×D61
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC2×C61×#367C2
socleC23×C61C2×D8
prime radicalC23×D61D8
hypercenterC2×#367D61
hypocenterC61#13494
LCSG ▷ C22×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#367

Complements

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

NH ≅ G/Ntype
4. #21443911C2semidirect
5. #21443910C2semidirect
6. #21443910C2semidirect
7. C2×C61×#367C2semidirect
152. C2×#367D61semidirect
180. C61#13494semidirect

Maximal subgroups

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

subgroupindex
C2×#168395412
#214458452
#214439112
#214439102
C2×C61×#3672
#1349461