Finite Group Databasebeta

← #30597661

Subgroups — #30597661

Order 15616.

468 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14519841C211yesmaximal, characteristic
2#21461532C211yesmaximal, characteristic, complemented
3#21461111C211yesmaximal, characteristic
4C8×#11758213C211yesmaximal, characteristic, complemented
5#21460650C211yesmaximal, characteristic, complemented
6#21460646C211yesmaximal, characteristic, complemented
7#21454782C211yesmaximal, characteristic
8#16840781C2211yescharacteristic
9C2×#14519841C412yes—
10C4×#11758213C2211yescharacteristic
11C4×D61⋊C8C2211yescharacteristic
12C42×#6923C2211yescharacteristic
13#16840632C412yes—
14(C2×#6923)⋊C8—21no—
15(C2×#6923)⋊C8—21no—
16#16840612C412yescomplemented
17D4⋊#92420C412yescomplemented
18#92420⋊C8—21no—
19C8×#92420—21no—
20C4×#11758224C2211yescharacteristic
21#16839892C411yescharacteristic, complemented
22#16839889C411yescharacteristic, complemented
23#16839840C411yescharacteristic, complemented
24#16839836—21no—
25#16839831—21no—
26#16839814C2211yescharacteristic
27#16839812—21no—
28M16×Dic61—21no—
29C4×C8×D61C2211yescharacteristic
30C61×#436C411yescharacteristic, complemented
31C2×#11758213C2×C412yes—
32C2×D61⋊C8—21no—
33C2×C4×#6923—21no—
34C2×C4×#6923—21no—
35C2×C4×#6923C2×C412yes—
36C4⋊#92420C2×C412yes—
37#14519841—24no—
38#14519834—21no—
39#14519832—21no—
40C4×#92420—21no—
41C4×#92420—21no—
42C4×#92420—21no—
43C4×#92420C2×C412yes—
44C2×#11758224C2×C411yescharacteristic
45C2×#11758194—21no—
46C2×C8×D61D411yescharacteristic
47C2×C8×D61D411yescharacteristic
48C4×Dic122C2×C411yescharacteristic
49#14519742C2×C411yescharacteristic
50D4×Dic61C2×C411yescharacteristic
51C4×C22⋊D61—21no—
52#14519737—21no—
53#14519735C2×C411yescharacteristic
54#14519733—21no—
55C2×C4×Dic61—21no—
56C42×D61C2311yescharacteristic
57C4⋊#92418C2×C411yescharacteristic
58#14519706—21no—
59#14519706—21no—
60C22⋊#92418—21no—
61#14519689—21no—
62#14519687—21no—
63#14519687—21no—
64C4×#92418C2×C411yescharacteristic
65C8×Dic61—21no—
66C8×Dic61D411yescharacteristic
67C8×Dic61D411yescharacteristic
68C2×M16×C61—21no—
69C4×D4×C61C2×C411yescharacteristic
70C4⋊C8×C61C2×C411yescharacteristic
71C22⋊C8×C61—21no—
72C4×C8×C61C2×C411yescharacteristic
73C22×#6923—22no—
74C2×D4×C61C4211yescharacteristic
75C22×C4×C61—21no—
76C2×C22⋊D61—21no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79#11758224—22no—
80#11758224—22no—
81C2×C4×D61C22×C411yescharacteristic
82C2×C4×D61C2×D411yescharacteristic
83C2×C4×D61#4111yescharacteristic
84C2×Dic122C4211yescharacteristic
85C2×#92420—22no—
86C2×#92420—22no—
87C2×#92420—22no—
88C4×#6923—24no—
89C4×#6923—22no—
90C4×#6923—22no—
91C4×#6923—41no—
92C4×#6923—41no—
93#11758213—22no—
94#11758213M1614yescomplemented
95D61⋊C8—41no—
96D61⋊C8—41no—
97M16×C61—42no—
98C2×C8×C61—21no—
99C2×C8×C61C22⋊C411yescharacteristic
100C2×C8×C61C22⋊C411yescharacteristic
101C4⋊C4×C61C4211yescharacteristic
102C22⋊C4×C61—21no—
103C42×C61C22×C411yescharacteristic
104C22⋊Dic61—21no—
105#11758198—21no—
106C4⋊Dic61C4211yescharacteristic
107#11758196—21no—
108#11758196—21no—
109C4×Dic61—21no—
110C4×Dic61—21no—
111C4×Dic61—21no—
112C4×Dic61C22×C411yescharacteristic
113C4×Dic61C2×D411yescharacteristic
114C4×Dic61#4111yescharacteristic
115#11758194—42no—
116C2×#92418—21no—
117C2×#92418C22⋊C411yescharacteristic
118C2×#92418C22⋊C411yescharacteristic
119C8×D61—41no—
120C8×D61—41no—
121C23×C61—21no—
122C22×D61C4×D411yescharacteristic
123C2×#6923—24no—
124C2×#6923—42no—
125C2×#6923—42no—
126D4×C61—21no—
127D4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61C2×C4211yescharacteristic
132C2×C4×C61C2×C22⋊C411yescharacteristic
133C2×C4×C61#11711yescharacteristic
134C22⋊D61—42no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—42no—
138C2×Dic61—42no—
139C2×Dic61C4×D411yescharacteristic
140C2×Dic61C4×D411yescharacteristic
141C2×Dic61C4×D411yescharacteristic
142C4×D61—21no—
143C4×D61—21no—
144C4×D61—22no—
145C4×D61C2×M1612yes—
146C4×D61#13112yes—
147Dic122—21no—
148Dic122—21no—
149#92420—24no—
150#92420—42no—
151#92420—42no—
152C8×C61—21no—
153C8×C61—21no—
154C8×C61—41no—
155#92418—21no—
156#92418—21no—
157#92418—41no—
158#8197—611nomaximal, Sylow
159C22×C61—41no—
160C22×C61—41no—
161C22×C61—41no—
162C22×C61C4×C22⋊C411yescharacteristic
163C2×D61—21no—
164C2×D61—21no—
165C2×D61#43612yes—
166#6923—44no—
167C4×C61—21no—
168C4×C61—41no—
169C4×C61C4×M1611yescharacteristic
170C4×C61#40511yescharacteristic
171C4×C61#42111yescharacteristic
172C4×C61#42111yescharacteristic
173Dic61—21no—
174Dic61—41no—
175Dic61—41no—
176Dic61#43512yes—
177Dic61#44312yes—
178#2965—611no—
179C4×#104—611no—
180#1744—611no—
181#1476—611no—
182C8×M16—611no—
183#1278—611no—
184#1276—611no—
185C2×C61—81no—
186C2×C61#175311yescharacteristic
187C2×C61#175911yescharacteristic
188C2×C61#176411yescharacteristic
189D61—22no—
190C4×#41—611no—
191#446—611no—
192#446—611no—
193#436—611no—
194#436#692311yescharacteristic, complemented
195#435—1221no—
196#435—1221no—
197#431—611no—
198#431—611no—
199#431—1221no—
200C2×#104—612no—
201C4×M16—611no—
202C4×M16—1221no—
203C2×C4×C8—611no—
204C2×C4×C8—611no—
205C43—611no—
206#339—612no—
207#336—1221no—
208#336—1221no—
209Q8⋊C8—612no—
210D4⋊C8—612no—
211#322—1221no—
212C82—1221no—
213C61#819711yescharacteristic, complemented, Sylow
214C2×#41—611no—
215C2×M16—21no—
216C2×M16—612no—
217C2×M16—1221no—
218C22×C8—611no—
219C22×C8—611no—
220C22×C8—1221no—
221C4×Q8—611no—
222C4×Q8—611no—
223C4×D4—611no—
224C4×D4—1221no—
225C4×D4—1221no—
226C4×D4C2×#692311yescharacteristic
227#117—611no—
228#117—1221no—
229C2×C42—611no—
230C2×C42—612no—
231C2×C42—1221no—
232C2×C42—1221no—
233C2×C42—1221no—
234C4⋊C8—612no—
235C4⋊C8—611no—
236C4⋊C8—1221no—
237C4⋊C8—1221no—
238C4⋊C8C2×#692311yescharacteristic
239#104—1224no—
240C22⋊C8—21no—
241C22⋊C8—1221no—
242C22⋊C8—1221no—
243C22⋊C8—1221no—
244#97—1221no—
245#97—1221no—
246#97—1221no—
247C4×C8—611no—
248C4×C8—611no—
249C4×C8—612no—
250C4×C8—611no—
251C4×C8—1221no—
252C4×C8—1221no—
253C4×C8—1221no—
254C4×C8—1221no—
255C4×C8C2×#692311yescharacteristic
256#41—1222no—
257#41—1222no—
258C2×Q8—611no—
259C2×D4—1221no—
260C2×D4C4×#692311yescharacteristic
261C22×C4—21no—
262C22×C4—611no—
263C22×C4—611no—
264C22×C4—611no—
265C22×C4—1221no—
266C22×C4—1221no—
267C22×C4—1222no—
268M16—42no—
269M16—614no—
270M16—1222no—
271M16—2442no—
272C2×C8—21no—
273C2×C8—611no—
274C2×C8—611no—
275C2×C8—1222no—
276C2×C8—1222no—
277C2×C8—1222no—
278C2×C8—1221no—
279C2×C8—2441no—
280C2×C8—2441no—
281C2×C8—2441no—
282C2×C8—2441no—
283C2×C8C22⋊#692311yescharacteristic
284C2×C8C22⋊#692311yescharacteristic
285C4⋊C4—611no—
286C4⋊C4—1221no—
287C4⋊C4—1221no—
288C4⋊C4C4×#692311yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—1221no—
291C22⋊C4—1221no—
292C42—611no—
293C42—611no—
294C42—611no—
295C42—1221no—
296C42—1221no—
297C42—1222no—
298C42—1222no—
299C42—1224no—
300C42—1221no—
301C42—2441no—
302C42—2441no—
303C42C22×#692311yescharacteristic
304C23—21no—
305C23—611no—
306Q8—1221no—
307Q8—1221no—
308D4—21no—
309D4—21no—
310D4—2442no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—611no—
315C2×C4—611no—
316C2×C4—612no—
317C2×C4—612no—
318C2×C4—611no—
319C2×C4—1222no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—1224no—
323C2×C4—1221no—
324C2×C4—1221no—
325C2×C4—2442no—
326C2×C4—2442no—
327C2×C4—2442no—
328C2×C4—2442no—
329C2×C4C2×C4×#692311yescharacteristic
330C2×C4C2×C22⋊#692311yescharacteristic
331C2×C4#1451985611yescharacteristic
332C8—21no—
333C8—21no—
334C8—41no—
335C8—1224no—
336C8—1221no—
337C8—1221no—
338C8—2442no—
339C8—2442no—
340C8—2441no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—612no—
345C22—1221no—
346C22—1221no—
347C22C4×C22⋊#692311yescharacteristic
348C4—21no—
349C4—41no—
350C4—612no—
351C4—612no—
352C4—1221no—
353C4—2444no—
354C4—2441no—
355C4—2441no—
356C4M16×#692311yescharacteristic
357C4#1684072811yescharacteristic
358C4#1684075911yescharacteristic
359C4#1684076011yescharacteristic
360C2—81no—
361C2—1222no—
362C2#2146155911yescharacteristic
363C2#2146158211yescharacteristic
364C2#2146159311yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C2×C42
FrattiniC42C22×#6923
FittingC61×#436C4
socleC22×C61C4×C22⋊C4
prime radicalC2×#11758224C2×C4
cosocleC42×D61C23
hypercenter#436#6923
hypocenterC61#8197
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #436

Complements

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

NH ≅ G/Ntype
2. #21461532C2semidirect
4. C8×#11758213C2semidirect
5. #21460650C2semidirect
6. #21460646C2semidirect
16. #16840612C4semidirect
17. D4⋊#92420C4semidirect
21. #16839892C4semidirect
22. #16839889C4semidirect
23. #16839840C4semidirect
30. C61×#436C4semidirect
94. #11758213M16semidirect
194. #436#6923semidirect
213. C61#8197semidirect

Maximal subgroups

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

subgroupindex
C4×#145198412
#214615322
#214611112
C8×#117582132
#214606502
#214606462
#214547822
#819761