Finite Group Databasebeta

← #30597628

Subgroups — #30597628

Order 15616.

498 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×#14519842C211yesmaximal, characteristic
2#21461532C211yesmaximal, characteristic, complemented
3#21461113C211yesmaximal, characteristic
4C8×#11758213C211yesmaximal, characteristic, complemented
5#21460650C211yesmaximal, characteristic, complemented
6#21460646C211yesmaximal, characteristic, complemented
7C8×#11758226C211yesmaximal, characteristic
8#16840781C2211yescharacteristic
9C2×#14519842C412yes—
10C4×#11758213C2211yescharacteristic
11C4×D61⋊C8C2211yescharacteristic
12C42×#6923C2211yescharacteristic
13#16840632C412yes—
14(C2×#6923)⋊C8—21no—
15(C2×#6923)⋊C8—21no—
16Q8⋊#92420C412yescomplemented
17#16840610C412yescomplemented
18#92420⋊C8—21no—
19C8×#92420—21no—
20C4×#11758226C2211yescharacteristic
21Q8×#92418C411yescharacteristic, complemented
22C8×D244—21no—
23C8×D244C411yescharacteristic, complemented
24#16839827—21no—
25#16839827C411yescharacteristic, complemented
26#16839814—21no—
27#16839814C2211yescharacteristic
28C4×C8×D61—21no—
29C4×C8×D61C2211yescharacteristic
30C8×Q8×C61C411yescharacteristic, complemented
31C2×#11758213C2×C412yes—
32C2×D61⋊C8—21no—
33C2×C4×#6923—21no—
34C2×C4×#6923—21no—
35C2×C4×#6923C2×C412yes—
36C4⋊#92420C2×C412yes—
37#14519842C818yescomplemented
38#14519834—21no—
39#14519832—21no—
40C4×#92420—21no—
41C4×#92420—21no—
42C4×#92420—21no—
43C4×#92420C2×C412yes—
44C2×#11758226C2×C411yescharacteristic
45C2×C8×D61—21no—
46C2×C8×D61—21no—
47C2×C8×D61D411yescharacteristic
48C2×C8×D61D411yescharacteristic
49Q8×Dic61C2×C411yescharacteristic
50C4×D244—21no—
51C4×D244C2×C411yescharacteristic
52#14519739—21no—
53#14519739C2×C411yescharacteristic
54#14519735—21no—
55#14519735C2×C411yescharacteristic
56C42×D61—21no—
57C42×D61C2311yescharacteristic
58C4⋊#92418—21no—
59C4⋊#92418C2×C411yescharacteristic
60#14519689—21no—
61#14519689—21no—
62#14519689—21no—
63C4×#92418—21no—
64C4×#92418C2×C411yescharacteristic
65C8×Dic61—21no—
66C8×Dic61D411yescharacteristic
67C8×Dic61D411yescharacteristic
68C4×Q8×C61C2×C411yescharacteristic
69C4⋊C8×C61—21no—
70C4⋊C8×C61C2×C411yescharacteristic
71C4×C8×C61—21no—
72C4×C8×C61C2×C411yescharacteristic
73C22×#6923—22no—
74C2×Q8×C61C4211yescharacteristic
75#11758226—22no—
76#11758226C2×C814yes—
77C2×D244—21no—
78C2×D244C4211yescharacteristic
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61C22×C411yescharacteristic
83C2×C4×D61C2×D411yescharacteristic
84C2×C4×D61#4111yescharacteristic
85C2×#92420—22no—
86C2×#92420—22no—
87C2×#92420—22no—
88C4×#6923—22no—
89C4×#6923—41no—
90C4×#6923—41no—
91C4×#6923—42no—
92C4×#6923C2×C814yescomplemented
93#11758213—22no—
94#11758213C2×C814yescomplemented
95D61⋊C8—41no—
96D61⋊C8—41no—
97C2×C8×C61—21no—
98C2×C8×C61C22⋊C411yescharacteristic
99C2×C8×C61C22⋊C411yescharacteristic
100C4⋊C4×C61—21no—
101C4⋊C4×C61C4211yescharacteristic
102C42×C61—21no—
103C42×C61C22×C411yescharacteristic
104#11758198—21no—
105#11758198—21no—
106#11758198—21no—
107C4⋊Dic61—21no—
108C4⋊Dic61C4211yescharacteristic
109C4×Dic61—21no—
110C4×Dic61—21no—
111C4×Dic61C22×C411yescharacteristic
112C4×Dic61C2×D411yescharacteristic
113C4×Dic61#4111yescharacteristic
114C2×#92418—21no—
115C2×#92418C22⋊C411yescharacteristic
116C2×#92418C22⋊C411yescharacteristic
117C8×D61—41no—
118C8×D61—41no—
119C8×D61—42no—
120C8×D61—42no—
121C22×D61—21no—
122C22×D61C4×D411yescharacteristic
123C2×#6923—24no—
124C2×#6923—42no—
125C2×#6923—42no—
126Q8×C61—21no—
127Q8×C61C4×C812yes—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61C2×C4211yescharacteristic
131C2×C4×C61C2×C22⋊C411yescharacteristic
132C2×C4×C61#11711yescharacteristic
133C2×Dic61—21no—
134C2×Dic61C4×D411yescharacteristic
135C2×Dic61C4×D411yescharacteristic
136C2×Dic61C4×D411yescharacteristic
137D244—24no—
138D244—21no—
139D244C4×C812yes—
140C4×D61—21no—
141C4×D61—21no—
142C4×D61—24no—
143C4×D61—22no—
144C4×D61—41no—
145C4×D61—41no—
146C4×D61—42no—
147C4×D61C22×C812yes—
148C4×D61#13112yes—
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#8191—611nomaximal, Sylow
159C22×C61C4×C22⋊C411yescharacteristic
160C2×D61—21no—
161C2×D61—21no—
162C2×D61—22no—
163C2×D61—41no—
164C2×D61—41no—
165C2×D61C8×D412yes—
166#6923—44no—
167C4×C61—22no—
168C4×C61—21no—
169C4×C61—41no—
170C4×C61C2×C4×C811yescharacteristic
171C4×C61#40511yescharacteristic
172C4×C61#42111yescharacteristic
173C4×C61#42111yescharacteristic
174Dic61—21no—
175Dic61—41no—
176Dic61C8×D412yes—
177Dic61#44412yes—
178C8×#41—611no—
179C4×#104—611no—
180#1744—611no—
181#1476—611no—
182C8×M16—611no—
183#1278—611no—
184#1276—611no—
185C2×C61C8×C22⋊C411yescharacteristic
186C2×C61#175911yescharacteristic
187C2×C61#176511yescharacteristic
188D61—22no—
189D61—42no—
190C4×#41—611no—
191C8×Q8—611no—
192C8×Q8#692311yescharacteristic, complemented
193C8×D4—611no—
194C8×D4—611no—
195C8×D4—1221no—
196C8×D4—1221no—
197#431—611no—
198#431—611no—
199#431—1221no—
200C2×#104—612no—
201C4×M16—611no—
202C2×C4×C8—611no—
203C2×C4×C8—611no—
204C2×C4×C8—1221no—
205C43—611no—
206#339—612no—
207#336—1221no—
208#336—1221no—
209Q8⋊C8—612no—
210D4⋊C8—612no—
211#322—1221no—
212C82—1221no—
213C61#819111yescharacteristic, complemented, Sylow
214C2×#41—611no—
215C2×M16—612no—
216C22×C8—611no—
217C22×C8—611no—
218C22×C8—1221no—
219C22×C8—1221no—
220C22×C8—1221no—
221C4×Q8—611no—
222C4×Q8C2×#692311yescharacteristic
223C4×D4—611no—
224C4×D4—611no—
225C4×D4—1221no—
226C4×D4—1221no—
227#117—611no—
228#117—1221no—
229C2×C42—611no—
230C2×C42—612no—
231C2×C42—1221no—
232C2×C42—1221no—
233C2×C42—1221no—
234C4⋊C8—21no—
235C4⋊C8—612no—
236C4⋊C8—611no—
237C4⋊C8—1221no—
238C4⋊C8C2×#692311yescharacteristic
239#104—618no—
240C22⋊C8—1221no—
241C22⋊C8—1221no—
242C22⋊C8—1221no—
243C22⋊C8—1221no—
244#97—1221no—
245C4×C8—21no—
246C4×C8—611no—
247C4×C8—611no—
248C4×C8—612no—
249C4×C8—611no—
250C4×C8—1221no—
251C4×C8—1221no—
252C4×C8—1221no—
253C4×C8—1221no—
254C4×C8—1221no—
255C4×C8C2×#692311yescharacteristic
256#41—614no—
257#41—1222no—
258C2×Q8C4×#692311yescharacteristic
259C2×D4—611no—
260C2×D4—1221no—
261C22×C4—611no—
262C22×C4—611no—
263C22×C4—611no—
264C22×C4—1221no—
265C22×C4—1221no—
266C22×C4—1222no—
267C22×C4—1221no—
268M16—614no—
269M16—1222no—
270C2×C8—21no—
271C2×C8—611no—
272C2×C8—611no—
273C2×C8—1222no—
274C2×C8—1222no—
275C2×C8—1222no—
276C2×C8—1221no—
277C2×C8—2441no—
278C2×C8—2441no—
279C2×C8—2442no—
280C2×C8—2442no—
281C2×C8—2441no—
282C2×C8—2441no—
283C2×C8C22⋊#692311yescharacteristic
284C2×C8C22⋊#692311yescharacteristic
285C4⋊C4—21no—
286C4⋊C4—611no—
287C4⋊C4—1221no—
288C4⋊C4C4×#692311yescharacteristic
289C22⋊C4—1221no—
290C22⋊C4—1221no—
291C22⋊C4—1221no—
292C42—21no—
293C42—611no—
294C42—611no—
295C42—611no—
296C42—614no—
297C42—1221no—
298C42—1221no—
299C42—1222no—
300C42—2442no—
301C42—2441no—
302C42—2441no—
303C42C22×#692311yescharacteristic
304C23—611no—
305C23—1221no—
306Q8—21no—
307Q8C8×#692312yes—
308D4—612no—
309D4—1224no—
310D4—1221no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—611no—
314C2×C4—611no—
315C2×C4—612no—
316C2×C4—612no—
317C2×C4—611no—
318C2×C4—1222no—
319C2×C4—1224no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—1224no—
323C2×C4—1221no—
324C2×C4—2442no—
325C2×C4—2442no—
326C2×C4—2442no—
327C2×C4—2441no—
328C2×C4—2441no—
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—612no—
342C22—1221no—
343C22—1221no—
344C22—1222no—
345C22—2441no—
346C22—2441no—
347C22C4×C22⋊#692311yescharacteristic
348C4—22no—
349C4—21no—
350C4—41no—
351C4—612no—
352C4—612no—
353C4—1221no—
354C4—2444no—
355C4—2441no—
356C4C2×C8×#692311yescharacteristic
357C4#1684072511yescharacteristic
358C4#1684075911yescharacteristic
359C4#1684076111yescharacteristic
360C2—1222no—
361C2—2442no—
362C2C8×C22⋊#692311yescharacteristic
363C2#2146158311yescharacteristic
364C2#2146159711yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC4×C61C2×C4×C8
FrattiniC42C22×#6923
FittingC8×Q8×C61C4
socleC22×C61C4×C22⋊C4
prime radicalC2×#11758226C2×C4
cosocleC42×D61C23
hypercenterC8×Q8#6923
hypocenterC61#8191
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×Q8

Complements

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

NH ≅ G/Ntype
2. #21461532C2semidirect
4. C8×#11758213C2semidirect
5. #21460650C2semidirect
6. #21460646C2semidirect
16. Q8⋊#92420C4semidirect
17. #16840610C4semidirect
21. Q8×#92418C4semidirect
23. C8×D244C4semidirect
25. #16839827C4semidirect
30. C8×Q8×C61C4semidirect
37. #14519842C8semidirect
92. C4×#6923C2×C8semidirect
94. #11758213C2×C8semidirect
192. C8×Q8#6923semidirect
213. C61#8191semidirect

Maximal subgroups

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

subgroupindex
C4×#145198422
#214615322
#214611132
C8×#117582132
#214606502
#214606462
C8×#117582262
#819161