Finite Group Databasebeta

← #29573179

Subgroups — #29573179

Order 15616.

454 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C8×#11758222C211yesmaximal, characteristic
2#21445836C212yesmaximal
3C4×#14519711C211yesmaximal, characteristic, complemented
4#21443720C212yesmaximal, complemented
5C61×#1567C211yesmaximal, characteristic, complemented
6C4×#11758222C2211yescharacteristic
7C8×Dic122C411yescharacteristic, complemented
8C8×Dic122C411yescharacteristic, complemented
9C8×D244C411yescharacteristic, complemented
10C8×D244C411yescharacteristic, complemented
11C8×C22⋊D61—21no—
12C8×C22⋊D61—21no—
13#16839815C2211yescharacteristic
14#16839813—21no—
15C2×#14519711—21no—
16C2×#14519703—22no—
17C4×C8×D61—21no—
18C4×C4⋊Dic61C2212yes—
19#16839525—21no—
20#16839523—22no—
21C61×#423C2212yes—
22C2×C4×C8×C61C2211yescharacteristic
23C61×#335—21no—
24C61×#335—21no—
25C2×#11758222D411yescharacteristic
26C2×C8×D61—21no—
27C2×C8×D61—21no—
28C4×Dic122C2×C411yescharacteristic
29C4×Dic122Q811yescharacteristic
30C4×D244C2×C411yescharacteristic
31C4×D244Q811yescharacteristic
32C4×C22⋊D61—21no—
33C4×C22⋊D61—21no—
34#14519736D411yescharacteristic
35#14519734—21no—
36C2×C4⋊Dic61—22no—
37C2×C4×Dic61—22no—
38C42×D61—21no—
39#14519711—24no—
40C4⋊#92418C2×C411yescharacteristic
41C4⋊#92418C2×C411yescharacteristic
42#14519706—21no—
43#14519706—21no—
44#14519703—44no—
45C22⋊#92418—21no—
46#14519689—21no—
47#14519689—21no—
48C4×#92418—21no—
49C8×Dic61—21no—
50C8×Dic61—21no—
51#14519684—22no—
52C2×M16×C61—22no—
53C22×C8×C61D411yescharacteristic
54C22×C8×C61D411yescharacteristic
55C2×C42×C61C2311yescharacteristic
56C4⋊C8×C61—22no—
57C4⋊C8×C61—22no—
58C4×C8×C61C2×C411yescharacteristic
59C4×C8×C61C2×C411yescharacteristic
60C4×C8×C61D411yescharacteristic
61C4×C8×C61D411yescharacteristic
62C22×C4×C61C2×D411yescharacteristic
63C22×C4×C61C2×D411yescharacteristic
64C22×C4×C61#4111yescharacteristic
65C2×C22⋊D61—21no—
66C22×Dic61—42no—
67#11758222—21no—
68#11758222—21no—
69#11758222D812yes—
70#11758222Q1612yes—
71C2×D244C4⋊C411yescharacteristic
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×Dic122C4⋊C411yescharacteristic
76M16×C61—42no—
77M16×C61—42no—
78C2×C8×C61—22no—
79C2×C8×C61—41no—
80C2×C8×C61—42no—
81C2×C8×C61C22⋊C411yescharacteristic
82C2×C8×C61C22⋊C411yescharacteristic
83C2×C8×C61C22⋊C411yescharacteristic
84C2×C8×C61C22⋊C411yescharacteristic
85C42×C61C22×C411yescharacteristic
86C42×C61C2×D411yescharacteristic
87C42×C61C2×Q811yescharacteristic
88C42×C61#4111yescharacteristic
89C22⋊Dic61—21no—
90#11758198—21no—
91#11758198—21no—
92C4⋊Dic61—24no—
93C4⋊Dic61—42no—
94C4⋊Dic61C4⋊C411yescharacteristic
95C4⋊Dic61C4⋊C411yescharacteristic
96#11758196—21no—
97#11758196—21no—
98C4×Dic61—21no—
99C4×Dic61—21no—
100C4×Dic61—21no—
101C4×Dic61—42no—
102C4×Dic61—42no—
103C2×#92418—21no—
104C2×#92418—21no—
105C8×D61—42no—
106C8×D61—42no—
107C23×C61#12111yescharacteristic
108C22×D61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—41no—
112C2×C4×C61C2×C22⋊C411yescharacteristic
113C2×C4×C61C2×C4⋊C411yescharacteristic
114C2×C4×C61#11711yescharacteristic
115C2×C4×C61#12111yescharacteristic
116C2×C4×C61C22⋊Q811yescharacteristic
117C2×C4×C61C22⋊Q811yescharacteristic
118C2×C4×C61C2×D811yescharacteristic
119C2×C4×C61C2×Q1611yescharacteristic
120C2×C4×C61#13511yescharacteristic
121C2×C4×C61#13511yescharacteristic
122C22⋊D61—22no—
123C22⋊D61—22no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—44no—
128C2×Dic61—82no—
129C2×Dic61—82no—
130D244—21no—
131D244#10712yescomplemented
132C4×D61—22no—
133C4×D61—22no—
134C4×D61—42no—
135C4×D61—41no—
136C4×D61—41no—
137Dic122—21no—
138Dic122#10712yescomplemented
139C8×C61—21no—
140C8×C61—21no—
141C8×C61—21no—
142C8×C61—82no—
143C8×C61#10412yescomplemented
144#92418—41no—
145#92418—41no—
146#8667—611nomaximal, Sylow
147C22×C61—21no—
148C22×C61—21no—
149C22×C61#38011yescharacteristic
150C22×C61#46611yescharacteristic
151C22×C61#46711yescharacteristic
152C2×D61—22no—
153C2×D61—41no—
154C2×D61—41no—
155C4×C61—21no—
156C4×C61—21no—
157C4×C61—21no—
158C4×C61C2×#10411yescharacteristic
159C4×C61#42111yescharacteristic
160C4×C61C2×#10711yescharacteristic
161C4×C61#42711yescharacteristic
162C4×C61#46611yescharacteristic
163C4×C61#46711yescharacteristic
164Dic61—22no—
165Dic61—41no—
166Dic61—41no—
167Dic61—84no—
168C8×#41—611no—
169#1806—612no—
170C4×#107—611no—
171#1567D6111yescharacteristic, complemented
172#1303—612no—
173C2×C61—21no—
174C2×C61—21no—
175C2×C61#180611yescharacteristic
176C2×C61#180811yescharacteristic
177C2×C61#181411yescharacteristic
178D61—42no—
179C4×#41—611no—
180C8×Q8—611no—
181C8×Q8—611no—
182C8×D4—611no—
183C8×D4—611no—
184C8×D4—1221no—
185C8×D4—1221no—
186#431—611no—
187#431—1221no—
188C2×#107—1221no—
189#423C2×D6112yes—
190C2×#104—1222no—
191C2×C4×C8—1221no—
192C2×C4×C8C2×D6111yescharacteristic
193C4×C4⋊C4—612no—
194#340—1221no—
195#339—1222no—
196#335—21no—
197#335—21no—
198C61#866711yescharacteristic, complemented, Sylow
199C2×#41—611no—
200C2×M16—22no—
201C22×C8—1221no—
202C22×C8—1221no—
203C22×C8D24411yescharacteristic
204C22×C8D24411yescharacteristic
205C4×Q8—611no—
206C4×Q8—611no—
207C4×D4—611no—
208C4×D4—611no—
209C4×D4—1221no—
210C4×D4—1221no—
211#117—611no—
212#117—1221no—
213C2×C4⋊C4—1222no—
214C2×C42—1221no—
215C2×C42—1222no—
216C2×C42C22×D6111yescharacteristic
217#107—1224no—
218C4⋊C8—22no—
219C4⋊C8—22no—
220C4⋊C8—611no—
221C4⋊C8—611no—
222C4⋊C8—1221no—
223C4⋊C8—1221no—
224#104—2444no—
225C22⋊C8—1221no—
226C22⋊C8—1221no—
227C22⋊C8—1221no—
228C4×C8—1221no—
229C4×C8—1221no—
230C4×C8—1221no—
231C4×C8C4×D6111yescharacteristic
232C4×C8C4×D6111yescharacteristic
233C4×C8C22⋊D6111yescharacteristic
234C4×C8C22⋊D6111yescharacteristic
235#95—1222no—
236#41—612no—
237#41—612no—
238#41—1221no—
239#41—1221no—
240C2×Q8—611no—
241C2×D4—611no—
242C2×D4—1221no—
243C22×C4—1221no—
244C22×C4—1221no—
245C22×C4—1221no—
246C22×C4—2442no—
247C22×C4C2×D24411yescharacteristic
248C22×C4D4×D6111yescharacteristic
249C22×C4#1175822611yescharacteristic
250M16—42no—
251M16—42no—
252C2×C8—22no—
253C2×C8—41no—
254C2×C8—42no—
255C2×C8—1221no—
256C2×C8—1221no—
257C2×C8—2442no—
258C2×C8—2442no—
259C2×C8#1175819811yescharacteristic
260C2×C8#1175819811yescharacteristic
261C2×C8#1175819811yescharacteristic
262C2×C8#1175819811yescharacteristic
263C4⋊C4—611no—
264C4⋊C4—611no—
265C4⋊C4—1224no—
266C4⋊C4—1221no—
267C4⋊C4—1221no—
268C4⋊C4—2442no—
269C22⋊C4—1221no—
270C22⋊C4—1221no—
271C22⋊C4—1221no—
272C42—1221no—
273C42—1221no—
274C42—1221no—
275C42—2442no—
276C42—2442no—
277C42C2×C4×D6111yescharacteristic
278C42#1175822411yescharacteristic
279C42Q8×D6111yescharacteristic
280C42C2×C22⋊D6111yescharacteristic
281C23—1221no—
282C23#1451975211yescharacteristic
283Q8—612no—
284Q8—1221no—
285D4—612no—
286D4—1222no—
287D4—1222no—
288D4—1221no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—41no—
292C2×C4—1221no—
293C2×C4—1222no—
294C2×C4—1222no—
295C2×C4—1221no—
296C2×C4—1221no—
297C2×C4—4882no—
298C2×C4—4882no—
299C2×C4—2442no—
300C2×C4—2444no—
301C2×C4—2441no—
302C2×C4—2441no—
303C2×C4C2×#1175819811yescharacteristic
304C2×C4C4⋊C4×D6111yescharacteristic
305C2×C4#1451973511yescharacteristic
306C2×C4#1451974811yescharacteristic
307C2×C4#1451975311yescharacteristic
308C2×C4#1451975711yescharacteristic
309C2×C4D8×D6111yescharacteristic
310C2×C4Q16×D6111yescharacteristic
311C2×C4#1451979611yescharacteristic
312C2×C4#1451980011yescharacteristic
313C8—21no—
314C8—21no—
315C8—21no—
316C8—82no—
317C8—2441no—
318C8—2441no—
319C8#1451970312yescomplemented
320C22—21no—
321C22—21no—
322C22—1222no—
323C22—2441no—
324C22—2441no—
325C22#1683961911yescharacteristic
326C22#1683999911yescharacteristic
327C22#1684000411yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—1222no—
332C4—4884no—
333C4—2441no—
334C4—2441no—
335C4C2×#1451970311yescharacteristic
336C4#1683977811yescharacteristic
337C4#107×D6111yescharacteristic
338C4#1683979911yescharacteristic
339C4#1683999511yescharacteristic
340C4#1684000011yescharacteristic
341C2—21no—
342C2—21no—
343C2—2442no—
344C2#2144583611yescharacteristic
345C2#2144584511yescharacteristic
346C2#2144587411yescharacteristic
subgroupG/H
centerC2×C4#14519748
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1567C2
socleC22×C61#380
prime radicalC2×#11758222D4
cosocleC2×C42×C61C23
hypercenter#1567D61
hypocenterC61#8667
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1567

Complements

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

NH ≅ G/Ntype
3. C4×#14519711C2semidirect
4. #21443720C2semidirect
5. C61×#1567C2semidirect
7. C8×Dic122C4semidirect
8. C8×Dic122C4semidirect
9. C8×D244C4semidirect
10. C8×D244C4semidirect
131. D244#107semidirect
138. Dic122#107semidirect
143. C8×C61#104semidirect
171. #1567D61semidirect
198. C61#8667semidirect
319. C8#14519703semidirect

Maximal subgroups

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

subgroupindex
C8×#117582222
#214458362
C4×#145197112
#214437202
C61×#15672
#866761