Finite Group Databasebeta

← #416×D103 #27203636

Subgroups — #416×D103 #27203636

Order 13184.

792 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×D103C211yesmaximal, characteristic
2C22×C8×D103C211yesmaximal, characteristic, complemented
3#117×D103C211yesmaximal, characteristic, complemented
4#20267788C211yesmaximal, characteristic, complemented
5#20267787C211yesmaximal, characteristic, complemented
6#20267786C212yesmaximal, complemented
7#20267785C211yesmaximal, characteristic, complemented
8#20267784C212yesmaximal, complemented
9#103×D103C212yesmaximal, complemented
10#102×D103C212yesmaximal, complemented
11#416×C103C211yesmaximal, characteristic, complemented
12C2×#13110106C2211yescharacteristic
13C2×#13110105—21no—
14C2×#13110105C2211yescharacteristic
15C2×#13110104—21no—
16C2×#13110104C2211yescharacteristic
17#41×D103—24no—
18#41×D103C418yescomplemented
19C2×Q8×D103C2211yescharacteristic
20C2×D4×D103—21no—
21C2×D4×D103C2211yescharacteristic
22C22×C4×D103—21no—
23C22×C4×D103C2211yescharacteristic
24C22×C103⋊C8C2211yescharacteristic, complemented
25C2×C8×D103—24no—
26C2×C8×D103C2212yes—
27C2×C8×D103C2212yescomplemented
28#15692980C2211yescharacteristic, complemented
29#15692979C2212yescomplemented
30#15692978—21no—
31#15692977—21no—
32C4⋊C4×D103C2212yes—
33C22⋊C4×D103—21no—
34C42×D103—21no—
35#15692946C2212yescomplemented
36#15692945C2212yescomplemented
37#15692944C2212yescomplemented
38#15692943C2212yescomplemented
39#15692942C2212yescomplemented
40#15692941C2212yescomplemented
41C2×#41×C103C2211yescharacteristic
42C22×C8×C103C2211yescharacteristic, complemented
43#117×C103C2211yescharacteristic, complemented
44#103×C103C2212yescomplemented
45#102×C103C2212yescomplemented
46C23×D103—21no—
47C23×D103D411yescharacteristic
48#13110106—22no—
49#13110106C2×C414yescomplemented
50#13110105—22no—
51#13110105—28no—
52#13110105C2×C414yescomplemented
53#13110104—28no—
54#13110104—22no—
55#13110104C2×C414yescomplemented
56C2×Dic206—21no—
57C2×Dic206C2311yescharacteristic
58Q8×D103—22no—
59Q8×D103C2×C414yes—
60C2×D412—21no—
61C2×D412C2311yescharacteristic
62C2×C22⋊D103—21no—
63C2×C22⋊D103—21no—
64C2×C22⋊D103—21no—
65D4×D103—28no—
66D4×D103—22no—
67D4×D103C2×C414yes—
68C22×Dic103—21no—
69C22×Dic103D411yescharacteristic
70C2×C4×D103—21no—
71C2×C4×D103—21no—
72C2×C4×D103—21no—
73C2×C4×D103—28no—
74C2×C4×D103—22no—
75C2×C4×D103C2×C414yes—
76C2×C4×D103D411yescharacteristic
77C2×C4×D103D411yescharacteristic
78C2×C4×D103D414yes—
79C2×C4×D103C2311yescharacteristic
80C2×C4×D103C2311yescharacteristic
81C2×C103⋊C8—22no—
82C2×C103⋊C8C2312yes—
83C8×D103—24no—
84C8×D103—24no—
85C4⋊Dic103C2312yes—
86Dic103⋊C4—22no—
87C22⋊Dic103—21no—
88(C2×D103)⋊C4—22no—
89C4×Dic103—21no—
90C4×Dic103—22no—
91#41×C103—22no—
92#41×C103C2×C414yescomplemented
93C2×Q8×C103C2311yescharacteristic
94C2×D4×C103—21no—
95C2×D4×C103C2311yescharacteristic
96C22×C4×C103—21no—
97C22×C4×C103C2311yescharacteristic
98C2×C8×C103—22no—
99C2×C8×C103C2312yes—
100C4⋊C4×C103C2312yes—
101C22⋊C4×C103—21no—
102C42×C103—21no—
103C23×C103—21no—
104C23×C103C2×D411yescharacteristic
105C22×D103—24no—
106C22×D103—21no—
107C22×D103—24no—
108C22×D103—44no—
109C22×D103C22⋊C414yes—
110C22×D103C2×D411yescharacteristic
111C22×D103C2×D411yescharacteristic
112Q8×C103—21no—
113Q8×C103C22×C412yes—
114D4×C103—24no—
115D4×C103—21no—
116D4×C103C22×C412yes—
117C2×C4×C103—21no—
118C2×C4×C103—24no—
119C2×C4×C103—22no—
120C2×C4×C103C22×C412yes—
121C2×C4×C103C2×D412yes—
122C2×C4×C103C2×D411yescharacteristic
123C2×C4×C103C2411yescharacteristic
124C22⋊D103—24no—
125C22⋊D103—24no—
126C22⋊D103—24no—
127C2×Dic103—21no—
128C2×Dic103—24no—
129C2×Dic103—22no—
130C2×Dic103C22⋊C414yes—
131C2×Dic103C2×D411yescharacteristic
132C2×Dic103C2×D411yescharacteristic
133D412—24no—
134D412—21no—
135D412C22×C412yes—
136C4×D103—24no—
137C4×D103—24no—
138C4×D103—24no—
139C4×D103—44no—
140C4×D103C22⋊C414yes—
141C4×D103C22⋊C414yes—
142C4×D103C22×C412yes—
143C4×D103C22×C412yes—
144C4×D103C2×D412yes—
145C4×D103C2×D412yes—
146Dic206—21no—
147Dic206—24no—
148Dic206C22×C412yes—
149C8×C103—22no—
150C103⋊C8—22no—
151C22×C103—22no—
152C22×C103—22no—
153C22×C103—42no—
154C22×C103C2×C22⋊C412yes—
155C22×C103C22×D411yescharacteristic
156C2×D103—22no—
157C2×D103—28no—
158C2×D103—22no—
159C2×D103—42no—
160C2×D103—48no—
161C2×D103C2×C22⋊C412yes—
162C2×D103C2×C22⋊C412yes—
163C2×D103#13514yes—
164C4×C103—22no—
165C4×C103—42no—
166C4×C103C2×C22⋊C412yes—
167C4×C103C23×C411yescharacteristic
168C4×C103C22×D411yescharacteristic
169Dic103—22no—
170Dic103—42no—
171Dic103C2×C22⋊C412yes—
172Dic103C2×C22⋊C412yes—
173C2×C103—22no—
174C2×C103—42no—
175C2×C103C22×C22⋊C411yescharacteristic
176C2×C103C2×#13512yes—
177D103—22no—
178D103—42no—
179D103#41614yesdirect product factor
180C2×#416—1031nomaximal, Sylow
181C103C2×#41611yescharacteristic, complemented, Sylow
182C22×#41—1031no—
183C23×C8—1031no—
184C2×#117—1031no—
185#416—1031no—
186#416—1031no—
187#416—1031no—
188#416—1032no—
189#416—1032no—
190#416D10311yescharacteristic, direct product factor
191C2×#103—1032no—
192C2×#102—1032no—
193C2×#41—1038no—
194C2×#41—1031no—
195C2×#41—1031no—
196C2×#41—1031no—
197C2×#41—2061no—
198C2×#41—2061no—
199C2×#41—2064no—
200C2×#41C2×D10311yescharacteristic
201C22×Q8—1031no—
202C22×D4—1031no—
203C22×D4—2061no—
204C23×C4—1031no—
205C23×C4—2061no—
206C22×C8—1031no—
207C22×C8—1032no—
208C22×C8—1032no—
209C22×C8—2064no—
210C22×C8C2×D10311yescharacteristic, complemented
211#117—1031no—
212#117—1032no—
213#117—2061no—
214#117—2061no—
215#117C2×D10311yescharacteristic, complemented
216C2×C4⋊C4—1032no—
217C2×C22⋊C4—2061no—
218C2×C42—2061no—
219#103—1032no—
220#103—1032no—
221#103—1032no—
222#103C2×D10312yescomplemented
223#102—1032no—
224#102—1032no—
225#102—1032no—
226#102C2×D10312yescomplemented
227C24—1031no—
228C24—2061no—
229#41—22no—
230#41—1034no—
231#41—1034no—
232#41—1034no—
233#41—2068no—
234#41—2068no—
235#41—2062no—
236#41—2062no—
237#41—2062no—
238#41C4×D10314yescomplemented
239C2×Q8—1034no—
240C2×Q8—1031no—
241C2×Q8—2061no—
242C2×Q8—2062no—
243C2×Q8C22×D10311yescharacteristic
244C2×D4—21no—
245C2×D4—1034no—
246C2×D4—1031no—
247C2×D4—2061no—
248C2×D4—2062no—
249C2×D4—2061no—
250C2×D4—2068no—
251C2×D4—2061no—
252C2×D4—2061no—
253C2×D4C22×D10311yescharacteristic
254C22×C4—21no—
255C22×C4—1031no—
256C22×C4—1034no—
257C22×C4—1034no—
258C22×C4—1031no—
259C22×C4—1031no—
260C22×C4—1031no—
261C22×C4—1031no—
262C22×C4—2061no—
263C22×C4—2068no—
264C22×C4—2062no—
265C22×C4—2061no—
266C22×C4—2061no—
267C22×C4—2061no—
268C22×C4C22×D10311yescharacteristic
269C2×C8—22no—
270C2×C8—1032no—
271C2×C8—2064no—
272C2×C8—2064no—
273C2×C8—2062no—
274C2×C8C22×D10312yes—
275C4⋊C4—1032no—
276C4⋊C4—2062no—
277C4⋊C4C22×D10312yes—
278C22⋊C4—21no—
279C22⋊C4—2062no—
280C22⋊C4—2061no—
281C42—21no—
282C42—2062no—
283C42—2061no—
284C23—21no—
285C23—1031no—
286C23—1031no—
287C23—1034no—
288C23—4124no—
289C23—2064no—
290C23—2064no—
291C23—2061no—
292C23D4×D10311yescharacteristic
293Q8—21no—
294Q8—1032no—
295Q8—2064no—
296Q8—2061no—
297Q8C2×C4×D10312yes—
298D4—24no—
299D4—21no—
300D4—1032no—
301D4—2064no—
302D4—2064no—
303D4—2064no—
304D4—2064no—
305D4—2061no—
306D4C2×C4×D10312yes—
307C2×C4—21no—
308C2×C4—24no—
309C2×C4—22no—
310C2×C4—1031no—
311C2×C4—1031no—
312C2×C4—1034no—
313C2×C4—1032no—
314C2×C4—1032no—
315C2×C4—1034no—
316C2×C4—1034no—
317C2×C4—1032no—
318C2×C4—1032no—
319C2×C4—4124no—
320C2×C4—2064no—
321C2×C4—2064no—
322C2×C4—2064no—
323C2×C4—2062no—
324C2×C4—2061no—
325C2×C4—2064no—
326C2×C4C2×C4×D10312yes—
327C2×C4D4×D10312yes—
328C2×C4D4×D10311yescharacteristic
329C2×C4C23×D10311yescharacteristic
330C8—22no—
331C8—2062no—
332C22—22no—
333C22—22no—
334C22—42no—
335C22—1034no—
336C22—1032no—
337C22—1032no—
338C22—4128no—
339C22—4122no—
340C22—2068no—
341C22—2062no—
342C22—2062no—
343C22C22⋊C4×D10312yes—
344C22C2×D4×D10311yescharacteristic
345C4—22no—
346C4—42no—
347C4—1032no—
348C4—1032no—
349C4—4122no—
350C4—2062no—
351C4C22⋊C4×D10312yes—
352C4C22×C4×D10311yescharacteristic
353C4C2×D4×D10311yescharacteristic
354C2—22no—
355C2—42no—
356C2—1034no—
357C2—4122no—
358C2—2062no—
359C2C2×C22⋊C4×D10311yescharacteristic
360C2#135×D10312yes—
subgroupG/H
centerC2×C4D4×D103
commutatorC4×C103C23×C4
FrattiniC2×C4C23×D103
Fitting#416×C103C2
socleC22×C103C22×D4
prime radicalC2×#41×D103C2
cosocleC2×C4×C103C24
hypercenter#416D103
hypocenterC103C2×#416
LCSG ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
2. C22×C8×D103C2semidirect
3. #117×D103C2semidirect
4. #20267788C2semidirect
5. #20267787C2semidirect
6. #20267786C2semidirect
7. #20267785C2semidirect
8. #20267784C2semidirect
9. #103×D103C2semidirect
10. #102×D103C2semidirect
11. #416×C103C2semidirect
18. #41×D103C4semidirect
24. C22×C103⋊C8C22semidirect
27. C2×C8×D103C22semidirect
28. #15692980C22semidirect
29. #15692979C22semidirect
35. #15692946C22semidirect
36. #15692945C22semidirect
37. #15692944C22semidirect
38. #15692943C22semidirect
39. #15692942C22semidirect
40. #15692941C22semidirect
42. C22×C8×C103C22semidirect
43. #117×C103C22semidirect
44. #103×C103C22semidirect
45. #102×C103C22semidirect
49. #13110106C2×C4semidirect
52. #13110105C2×C4semidirect
55. #13110104C2×C4semidirect
92. #41×C103C2×C4semidirect
179. D103#416direct (N × H)
181. C103C2×#416semidirect
190. #416D103direct (N × H)
210. C22×C8C2×D103semidirect
215. #117C2×D103semidirect
222. #103C2×D103semidirect
226. #102C2×D103semidirect
238. #41C4×D103semidirect

Maximal subgroups

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

subgroupindex
C2×#41×D1032
C22×C8×D1032
#117×D1032
#202677882
#202677872
#202677862
#202677852
#202677842
#103×D1032
#102×D1032
#416×C1032
C2×#416103