Finite Group Databasebeta

← #485×D103 #27205032

Subgroups — #485×D103 #27205032

Order 13184.

416 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22⋊Q8×D103C211yesmaximal, characteristic
2#117×D103C211yesmaximal, characteristic
3#20268135C211yesmaximal, characteristic, complemented
4#20268134C211yesmaximal, characteristic, complemented
5#20268133C211yesmaximal, characteristic, complemented
6#20268132C211yesmaximal, characteristic, complemented
7#20268131C211yesmaximal, characteristic, complemented
8#20268130C211yesmaximal, characteristic, complemented
9#20268129C211yesmaximal, characteristic, complemented
10#107×D103C211yesmaximal, characteristic, complemented
11#106×D103C211yesmaximal, characteristic, complemented
12#103×D103C211yesmaximal, characteristic, complemented
13#103×D103C211yesmaximal, characteristic, complemented
14C22⋊C8×D103C211yesmaximal, characteristic
15#485×C103C211yesmaximal, characteristic, complemented
16C2×Q8×D103C2211yescharacteristic
17C22×C4×D103C2211yescharacteristic
18C2×C8×D103C2211yescharacteristic
19C2×C8×D103C2211yescharacteristic
20#15693001C2211yescharacteristic
21#15693000C2211yescharacteristic
22#15692999—21no—
23#15692998—21no—
24#15692997C2211yescharacteristic
25#15692980C2211yescharacteristic
26#15692979C2211yescharacteristic
27#15692979C2211yescharacteristic
28#15692978—21no—
29#15692977—21no—
30C4⋊C4×D103—21no—
31C4⋊C4×D103C2211yescharacteristic
32C4⋊C4×D103C2211yescharacteristic
33C4⋊C4×D103C2211yescharacteristic
34C22⋊C4×D103—21no—
35C22⋊C4×D103—21no—
36C42×D103—21no—
37#15692955C2211yescharacteristic, complemented
38#15692954C2211yescharacteristic, complemented
39#15692954C2211yescharacteristic, complemented
40#15692953C2211yescharacteristic, complemented
41#15692952C2211yescharacteristic, complemented
42#15692952C2211yescharacteristic, complemented
43#15692946C2211yescharacteristic, complemented
44#15692946C2211yescharacteristic, complemented
45#15692945C2211yescharacteristic, complemented
46#15692945C2211yescharacteristic, complemented
47#15692944C2211yescharacteristic, complemented
48#15692944C2211yescharacteristic, complemented
49C22⋊(C103⋊C8)C2211yescharacteristic
50(C2×D103)⋊C8C2211yescharacteristic
51(C2×D103)⋊C8C2211yescharacteristic
52C22⋊Q8×C103C2211yescharacteristic
53#117×C103C2211yescharacteristic
54#107×C103C2211yescharacteristic, complemented
55#106×C103C2211yescharacteristic, complemented
56#103×C103C2211yescharacteristic, complemented
57#103×C103C2211yescharacteristic, complemented
58C22⋊C8×C103C2211yescharacteristic
59C23×D103D411yescharacteristic
60C2×Dic206—21no—
61C2×Dic206C2311yescharacteristic
62Q8×D103—22no—
63Q8×D103—22no—
64C22×Dic103D411yescharacteristic
65C2×C4×D103—22no—
66C2×C4×D103—22no—
67C2×C4×D103—21no—
68C2×C4×D103—21no—
69C2×C4×D103—21no—
70C2×C4×D103—21no—
71C2×C4×D103D411yescharacteristic
72C2×C4×D103D411yescharacteristic
73C2×C4×D103C2311yescharacteristic
74C2×C4×D103C2311yescharacteristic
75C2×C103⋊C8C2311yescharacteristic
76C2×C103⋊C8C2311yescharacteristic
77C8×D103—22no—
78C8×D103—22no—
79C4⋊Dic103—21no—
80C4⋊Dic103C2311yescharacteristic
81C4⋊Dic103C2311yescharacteristic
82C4⋊Dic103C2311yescharacteristic
83Dic103⋊C4—21no—
84Dic103⋊C4—21no—
85Dic103⋊C4—21no—
86Dic103⋊C4—21no—
87Dic103⋊C4—21no—
88C22⋊Dic103—21no—
89C22⋊Dic103—21no—
90(C2×D103)⋊C4—21no—
91(C2×D103)⋊C4—21no—
92(C2×D103)⋊C4—21no—
93(C2×D103)⋊C4—21no—
94C4×Dic103—21no—
95C4×Dic103—21no—
96C4×Dic103—21no—
97C2×Q8×C103C2311yescharacteristic
98C22×C4×C103C2311yescharacteristic
99C2×C8×C103C2311yescharacteristic
100C2×C8×C103C2311yescharacteristic
101C4⋊C4×C103—21no—
102C4⋊C4×C103C2311yescharacteristic
103C4⋊C4×C103C2311yescharacteristic
104C4⋊C4×C103C2311yescharacteristic
105C22⋊C4×C103—21no—
106C22⋊C4×C103—21no—
107C42×C103—21no—
108C23×C103C2×D411yescharacteristic
109C22×D103—22no—
110C22×D103—22no—
111C22×D103—22no—
112C22×D103C2×D411yescharacteristic
113C22×D103C2×D411yescharacteristic
114Q8×C103—21no—
115Q8×C103—21no—
116C2×C4×C103—21no—
117C2×C4×C103—21no—
118C2×C4×C103—21no—
119C2×C4×C103—21no—
120C2×C4×C103—21no—
121C2×C4×C103—21no—
122C2×C4×C103C2×D411yescharacteristic
123C2×C4×C103C2411yescharacteristic
124C2×Dic103—22no—
125C2×Dic103—21no—
126C2×Dic103—21no—
127C2×Dic103—21no—
128C2×Dic103—21no—
129C2×Dic103C2×D411yescharacteristic
130C2×Dic103C2×D411yescharacteristic
131C4×D103—22no—
132C4×D103—21no—
133C4×D103—21no—
134C4×D103—22no—
135C4×D103—42no—
136C4×D103—42no—
137C4×D103—42no—
138C4×D103—42no—
139C4×D103#4112yes—
140C4×D103#4112yes—
141Dic206—21no—
142Dic206—21no—
143Dic206—42no—
144C8×C103—21no—
145C8×C103—21no—
146C103⋊C8—21no—
147C103⋊C8—21no—
148C22×C103—21no—
149C22×C103—21no—
150C22×C103—21no—
151C22×C103C22×D411yescharacteristic
152C2×D103—21no—
153C2×D103—21no—
154C2×D103—21no—
155C2×D103—44no—
156C2×D103#12312yes—
157C2×D103#13512yes—
158C2×D103#13712yes—
159C4×C103—21no—
160C4×C103—41no—
161C4×C103—41no—
162C4×C103—41no—
163C4×C103—41no—
164C4×C103C2×#4111yescharacteristic
165C4×C103C2×#4111yescharacteristic
166Dic103—21no—
167Dic103—41no—
168Dic103—41no—
169Dic103—41no—
170Dic103—41no—
171Dic103#12312yes—
172C2×C103—41no—
173C2×C103C2×#12311yescharacteristic
174C2×C103C2×#13511yescharacteristic
175C2×C103C2×#13711yescharacteristic
176D103—41no—
177D103#48514yesdirect product factor
178C2×#485—1031nomaximal, Sylow
179C103C2×#48511yescharacteristic, complemented, Sylow
180C2×C22⋊Q8—1031no—
181C2×#117—1031no—
182#485—1031no—
183#485—1031no—
184#485—1031no—
185#485—1031no—
186#485—1031no—
187#485—1031no—
188#485—1031no—
189#485D10311yescharacteristic, direct product factor
190C2×#107—1031no—
191C2×#106—1031no—
192C2×#103—1031no—
193C2×#103—1031no—
194C2×C22⋊C8—1031no—
195C22×Q8—1031no—
196C23×C4—1031no—
197C22×C8—1031no—
198C22×C8—1031no—
199C22⋊Q8—1031no—
200C22⋊Q8—1031no—
201C22⋊Q8—1031no—
202C22⋊Q8—2061no—
203C22⋊Q8—2061no—
204C22⋊Q8C2×D10311yescharacteristic
205#117—1031no—
206#117—1031no—
207#117—1031no—
208#117—2061no—
209#117—2061no—
210#117C2×D10311yescharacteristic
211C2×C4⋊C4—1031no—
212C2×C4⋊C4—1031no—
213C2×C4⋊C4—1031no—
214C2×C4⋊C4—2061no—
215C2×C22⋊C4—2061no—
216C2×C22⋊C4—2061no—
217C2×C42—2061no—
218#107—1031no—
219#107—1031no—
220#107—1031no—
221#107C2×D10311yescharacteristic, complemented
222#106—1031no—
223#106—1031no—
224#106—1031no—
225#106C2×D10311yescharacteristic, complemented
226#103—1031no—
227#103—1031no—
228#103—1031no—
229#103—1031no—
230#103—1031no—
231#103—1031no—
232#103C2×D10311yescharacteristic, complemented
233#103C2×D10311yescharacteristic, complemented
234C22⋊C8—1031no—
235C22⋊C8—1031no—
236C22⋊C8—1031no—
237C22⋊C8C2×D10311yescharacteristic
238C24—1031no—
239C2×Q8—1031no—
240C2×Q8—2061no—
241C2×Q8—2062no—
242C2×Q8—2062no—
243C2×Q8C22×D10311yescharacteristic
244C22×C4—1031no—
245C22×C4—1031no—
246C22×C4—1031no—
247C22×C4—1031no—
248C22×C4—1031no—
249C22×C4—2062no—
250C22×C4—2062no—
251C22×C4—2061no—
252C22×C4—2061no—
253C22×C4—2061no—
254C22×C4—2061no—
255C22×C4C22×D10311yescharacteristic
256C2×C8—1031no—
257C2×C8—1031no—
258C2×C8—2062no—
259C2×C8—2062no—
260C2×C8C22×D10311yescharacteristic
261C2×C8C22×D10311yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—1031no—
264C4⋊C4—1031no—
265C4⋊C4—1031no—
266C4⋊C4—2061no—
267C4⋊C4—2061no—
268C4⋊C4—2061no—
269C4⋊C4—2061no—
270C4⋊C4—2061no—
271C4⋊C4—2061no—
272C4⋊C4C22×D10311yescharacteristic
273C4⋊C4C22×D10311yescharacteristic
274C4⋊C4C22×D10311yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—2061no—
278C22⋊C4—2061no—
279C22⋊C4—2061no—
280C22⋊C4—2061no—
281C22⋊C4—2061no—
282C22⋊C4—2061no—
283C42—21no—
284C42—2061no—
285C42—2061no—
286C42—2061no—
287C23—1031no—
288C23—1031no—
289C23—2062no—
290C23—2062no—
291C23—2062no—
292C23D4×D10311yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—4122no—
296Q8—2061no—
297Q8—2061no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—1031no—
305C2×C4—1032no—
306C2×C4—1032no—
307C2×C4—1031no—
308C2×C4—4122no—
309C2×C4—4122no—
310C2×C4—4122no—
311C2×C4—4122no—
312C2×C4—2062no—
313C2×C4—2062no—
314C2×C4—2062no—
315C2×C4—2061no—
316C2×C4—2061no—
317C2×C4—2061no—
318C2×C4—2061no—
319C2×C4—2061no—
320C2×C4—2061no—
321C2×C4D4×D10311yescharacteristic
322C2×C4C23×D10311yescharacteristic
323C8—21no—
324C8—21no—
325C8—2061no—
326C8—2061no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—1032no—
331C22—1032no—
332C22—1032no—
333C22—4124no—
334C22—2061no—
335C22—2061no—
336C22—2061no—
337C22C2×D4×D10311yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—1032no—
344C4—4121no—
345C4—4121no—
346C4—4121no—
347C4—4121no—
348C4—2061no—
349C4#41×D10311yescharacteristic
350C4#41×D10311yescharacteristic
351C2—41no—
352C2—1034no—
353C2—4121no—
354C2#123×D10311yescharacteristic
355C2#135×D10311yescharacteristic
356C2#137×D10311yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#485×C103C2
socleC22×C103C22×D4
prime radicalC23×D103D4
hypercenter#485D103
hypocenterC103C2×#485
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
3. #20268135C2semidirect
4. #20268134C2semidirect
5. #20268133C2semidirect
6. #20268132C2semidirect
7. #20268131C2semidirect
8. #20268130C2semidirect
9. #20268129C2semidirect
10. #107×D103C2semidirect
11. #106×D103C2semidirect
12. #103×D103C2semidirect
13. #103×D103C2semidirect
15. #485×C103C2semidirect
37. #15692955C22semidirect
38. #15692954C22semidirect
39. #15692954C22semidirect
40. #15692953C22semidirect
41. #15692952C22semidirect
42. #15692952C22semidirect
43. #15692946C22semidirect
44. #15692946C22semidirect
45. #15692945C22semidirect
46. #15692945C22semidirect
47. #15692944C22semidirect
48. #15692944C22semidirect
54. #107×C103C22semidirect
55. #106×C103C22semidirect
56. #103×C103C22semidirect
57. #103×C103C22semidirect
177. D103#485direct (N × H)
179. C103C2×#485semidirect
189. #485D103direct (N × H)
221. #107C2×D103semidirect
225. #106C2×D103semidirect
232. #103C2×D103semidirect
233. #103C2×D103semidirect

Maximal subgroups

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

subgroupindex
C22⋊Q8×D1032
#117×D1032
#202681352
#202681342
#202681332
#202681322
#202681312
#202681302
#202681292
#107×D1032
#106×D1032
#103×D1032
C22⋊C8×D1032
#485×C1032
C2×#485103