Finite Group Databasebeta

← #29649246

Subgroups — #29649246

Order 15616.

610 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C8×#11758222C211yesmaximal, characteristic
2#21454487C212yesmaximal
3#21444596C214yesmaximal, complemented
4#21444595C212yesmaximal, complemented
5#21444579C212yesmaximal, complemented
6#21444564C212yesmaximal, complemented
7C2×#16839513C211yesmaximal, characteristic, complemented
8C61×#1566C211yesmaximal, characteristic, complemented
9C4×#11758222C2211yescharacteristic
10C8×Dic122C411yescharacteristic
11C8×Dic122C411yescharacteristic
12C8×D244C411yescharacteristic
13C8×D244C411yescharacteristic
14C8×C22⋊D61C412yes—
15C8×C22⋊D61C412yes—
16#16839822—24no—
17#16839818C2214yes—
18#16839815C2211yescharacteristic
19#16839814C2214yes—
20#16839813C2212yes—
21C2×C4⋊#92418C2212yes—
22#16839730—22no—
23#16839720—22no—
24C4×C8×D61C2212yes—
25#16839514C2214yes—
26#16839514C2214yes—
27#16839513C2211yescharacteristic
28#16839513C2211yescharacteristic
29#16839513C2212yes—
30C61×#423C2212yes—
31C2×C4×C8×C61C2211yescharacteristic
32C61×#334C2212yes—
33C61×#334C2212yes—
34C2×#11758222D411yescharacteristic
35C22×#92418—22no—
36C2×C8×D61C2×C412yes—
37C2×C8×D61C2×C412yes—
38C4×Dic122C2×C411yescharacteristic
39C4×Dic122Q811yescharacteristic
40C4×D244C2×C411yescharacteristic
41C4×D244Q811yescharacteristic
42C4×C22⋊D61C2×C412yes—
43C4×C22⋊D61Q812yes—
44#14519736D411yescharacteristic
45#14519734D412yes—
46C42×D61C2312yes—
47C4⋊#92418—22no—
48C4⋊#92418C2×C411yescharacteristic
49C4⋊#92418C2×C411yescharacteristic
50C4⋊#92418C2312yes—
51C4⋊#92418C2312yes—
52#14519706C2×C412yes—
53#14519706C2×C412yes—
54C22⋊#92418C2×C412yes—
55#14519689—24no—
56#14519689—24no—
57#14519689C2×C412yes—
58#14519689C2×C412yes—
59#14519687—24no—
60C4×#92418C2312yes—
61C8×Dic61—24no—
62C8×Dic61C2×C412yes—
63C8×Dic61C2×C412yes—
64C2×M16×C61—22no—
65C22×C8×C61C2×C411yescharacteristic
66C22×C8×C61C2×C411yescharacteristic
67C2×C42×C61C2311yescharacteristic
68C4⋊C8×C61—22no—
69C4⋊C8×C61C2314yes—
70C4×C8×C61C2×C411yescharacteristic
71C4×C8×C61C2×C411yescharacteristic
72C4×C8×C61C2311yescharacteristic
73C4×C8×C61C2311yescharacteristic
74C22×C4×C61C22×C411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61C2×Q811yescharacteristic
77C2×C22⋊D61C4⋊C412yes—
78#11758222—24no—
79C2×D244C4⋊C411yescharacteristic
80C2×C4×D61C22×C412yes—
81C2×C4×D61C2×D412yes—
82C2×C4×D61C2×Q812yes—
83C2×Dic122C4⋊C411yescharacteristic
84M16×C61—44no—
85C2×C8×C61—22no—
86C2×C8×C61—24no—
87C2×C8×C61—41no—
88C2×C8×C61C22×C411yescharacteristic
89C2×C8×C61C22×C411yescharacteristic
90C2×C8×C61C22×C411yescharacteristic
91C2×C8×C61C22×C411yescharacteristic
92C42×C61C22×C411yescharacteristic
93C42×C61C2×D411yescharacteristic
94C42×C61C2×Q811yescharacteristic
95C42×C61C2411yescharacteristic
96C22⋊Dic61C4⋊C412yes—
97#11758198C4⋊C412yes—
98#11758198C4⋊C412yes—
99C4⋊Dic61C4⋊C411yescharacteristic
100C4⋊Dic61C4⋊C411yescharacteristic
101#11758196C4⋊C412yes—
102#11758196C4⋊C412yes—
103C4×Dic61C22×C412yes—
104C4×Dic61C2×D412yes—
105C4×Dic61C2×Q812yes—
106C2×#92418—22no—
107C2×#92418—22no—
108C2×#92418—44no—
109C2×#92418C22×C412yes—
110C2×#92418C22×C412yes—
111C8×D61—24no—
112C8×D61—42no—
113C23×C61C2×C4⋊C411yescharacteristic
114C22×D61C2×C4⋊C412yes—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—41no—
118C2×C4×C61C2×C4⋊C411yescharacteristic
119C2×C4×C61C2×C4⋊C411yescharacteristic
120C2×C4×C61C2×C4⋊C411yescharacteristic
121C2×C4×C61#13514yes—
122C2×C4×C61C23×C411yescharacteristic
123C2×C4×C61C22×D411yescharacteristic
124C2×C4×C61C22×Q811yescharacteristic
125C22⋊D61—24no—
126C2×Dic61C2×C4⋊C412yes—
127C2×Dic61C2×C4⋊C412yes—
128C2×Dic61C2×C4⋊C412yes—
129D244—22no—
130C4×D61—22no—
131C4×D61—22no—
132C4×D61—24no—
133C4×D61—42no—
134Dic122—22no—
135C8×C61—21no—
136C8×C61—21no—
137C8×C61—21no—
138C8×C61—44no—
139C8×C61#13112yes—
140#92418—22no—
141#92418—22no—
142#92418—42no—
143#92418—42no—
144#17827—611nomaximal, Sylow
145C22×C61—21no—
146C22×C61—21no—
147C22×C61#42712yes—
148C22×C61C22×C4⋊C411yescharacteristic
149C2×D61—22no—
150C2×D61—22no—
151C2×D61—22no—
152C4×C61—21no—
153C4×C61—21no—
154C4×C61—21no—
155C4×C61#42712yes—
156C4×C61C2×#13111yescharacteristic
157C4×C61#56811yescharacteristic
158C4×C61C2×#13512yes—
159Dic61—22no—
160Dic61—22no—
161Dic61—22no—
162C8×#41—611no—
163#2925—612no—
164#1572—614no—
165#1571—612no—
166#1568—612no—
167#1566D6111yescharacteristic, complemented
168#1564—612no—
169C2×#334—611no—
170C2×C61—22no—
171C2×C61#290611yescharacteristic
172C2×C61C2×#42711yescharacteristic
173C2×C61#291611yescharacteristic
174D61—42no—
175C4×#41—611no—
176C8×Q8—611no—
177C8×Q8—611no—
178C8×D4—612no—
179C8×D4—612no—
180C8×D4—611no—
181C8×D4—611no—
182#433—1224no—
183#432—614no—
184#431—611no—
185#431—612no—
186#431—614no—
187#423C2×D6112yes—
188C2×C4⋊C8—612no—
189#408—1222no—
190#405—1222no—
191C2×C4×C8—612no—
192C2×C4×C8C2×D6111yescharacteristic
193#335—614no—
194#335—614no—
195#334—611no—
196#334—611no—
197#334—612no—
198#334C2×D6112yes—
199#334C2×D6112yes—
200C61#1782711yescharacteristic, complemented, Sylow
201C2×#41—611no—
202C2×M16—22no—
203C22×C8—612no—
204C22×C8—612no—
205C22×C8—1222no—
206C22×C8C4×D6111yescharacteristic
207C22×C8C4×D6111yescharacteristic
208C4×Q8—611no—
209C4×Q8—611no—
210C4×D4—612no—
211C4×D4—612no—
212C4×D4—611no—
213C4×D4—611no—
214#117—611no—
215#117—612no—
216C2×C42—612no—
217C2×C42C22×D6111yescharacteristic
218C4⋊C8—22no—
219C4⋊C8—612no—
220C4⋊C8—612no—
221C4⋊C8—611no—
222C4⋊C8—611no—
223C4⋊C8—612no—
224C4⋊C8—612no—
225C4⋊C8—1222no—
226C4⋊C8C22×D6114yes—
227C22⋊C8—612no—
228C22⋊C8—612no—
229C22⋊C8—612no—
230C22⋊C8—1224no—
231C22⋊C8—1224no—
232#97—1224no—
233C4×C8—612no—
234C4×C8—612no—
235C4×C8—612no—
236C4×C8—1224no—
237C4×C8C4×D6111yescharacteristic
238C4×C8C4×D6111yescharacteristic
239C4×C8C22×D6111yescharacteristic
240C4×C8C22×D6111yescharacteristic
241#41—1224no—
242C2×Q8—611no—
243C2×D4—612no—
244C2×D4—611no—
245C22×C4—612no—
246C22×C4—612no—
247C22×C4—612no—
248C22×C4C2×C4×D6111yescharacteristic
249C22×C4D4×D6111yescharacteristic
250C22×C4Q8×D6111yescharacteristic
251M16—44no—
252C2×C8—22no—
253C2×C8—24no—
254C2×C8—41no—
255C2×C8—612no—
256C2×C8—612no—
257C2×C8—1224no—
258C2×C8—1222no—
259C2×C8—1222no—
260C2×C8—2442no—
261C2×C8—2444no—
262C2×C8C2×C4×D6111yescharacteristic
263C2×C8C2×C4×D6111yescharacteristic
264C2×C8C2×C4×D6111yescharacteristic
265C2×C8C2×C4×D6111yescharacteristic
266C4⋊C4—612no—
267C4⋊C4—612no—
268C4⋊C4—611no—
269C4⋊C4—611no—
270C22⋊C4—612no—
271C22⋊C4—612no—
272C22⋊C4—612no—
273C42—612no—
274C42—612no—
275C42—612no—
276C42C2×C4×D6111yescharacteristic
277C42D4×D6111yescharacteristic
278C42Q8×D6111yescharacteristic
279C42C23×D6111yescharacteristic
280C23—612no—
281C23C4⋊C4×D6111yescharacteristic
282Q8—1222no—
283D4—1224no—
284D4—1222no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—41no—
288C2×C4—612no—
289C2×C4—612no—
290C2×C4—612no—
291C2×C4—1222no—
292C2×C4—1222no—
293C2×C4—1224no—
294C2×C4—2442no—
295C2×C4C4⋊C4×D6111yescharacteristic
296C2×C4C4⋊C4×D6111yescharacteristic
297C2×C4C4⋊C4×D6111yescharacteristic
298C2×C4#1451979814yes—
299C2×C4C22×C4×D6111yescharacteristic
300C2×C4C2×D4×D6111yescharacteristic
301C2×C4C2×Q8×D6111yescharacteristic
302C8—21no—
303C8—21no—
304C8—21no—
305C8—44no—
306C8—1222no—
307C8—1222no—
308C8—2442no—
309C8—2442no—
310C8#1451978512yes—
311C22—21no—
312C22—21no—
313C22—1222no—
314C22—1222no—
315C22—1222no—
316C22#1683979712yes—
317C22C2×C4⋊C4×D6111yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—1222no—
322C4—1222no—
323C4—1222no—
324C4#1683979712yes—
325C4C2×#1451978511yescharacteristic
326C4#1684052811yescharacteristic
327C4C2×#1451979812yes—
328C2—22no—
329C2—2442no—
330C2#2145438811yescharacteristic
331C2C2×#1683979711yescharacteristic
332C2#2145442711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1566C2
socleC22×C61C22×C4⋊C4
prime radicalC2×#11758222D4
cosocleC42×C61C24
hypercenter#1566D61
hypocenterC61#17827
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1566

Complements

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

NH ≅ G/Ntype
3. #21444596C2semidirect
4. #21444595C2semidirect
5. #21444579C2semidirect
6. #21444564C2semidirect
7. C2×#16839513C2semidirect
8. C61×#1566C2semidirect
167. #1566D61semidirect
200. C61#17827semidirect

Maximal subgroups

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

subgroupindex
C8×#117582222
#214544872
#214445962
#214445952
#214445792
#214445642
C2×#168395132
C61×#15662
#1782761