Finite Group Databasebeta

← #27205327

Subgroups — #27205327

Order 13184.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268410C211yesmaximal, characteristic, complemented
2#20268263C211yesmaximal, characteristic, complemented
3#20268130C211yesmaximal, characteristic, complemented
4#20268114C211yesmaximal, characteristic, complemented
5#20268082C211yesmaximal, characteristic, complemented
6#20268071C211yesmaximal, characteristic, complemented
7#20268003C211yesmaximal, characteristic, complemented
8#20267940C211yesmaximal, characteristic, complemented
9#20267923C211yesmaximal, characteristic
10#20267903C211yesmaximal, characteristic, complemented
11#20267894C211yesmaximal, characteristic, complemented
12SD16×Dic103C211yesmaximal, characteristic, complemented
13#20267871C211yesmaximal, characteristic, complemented
14#20267851C211yesmaximal, characteristic, complemented
15#463×C103C211yesmaximal, characteristic, complemented
16C2×D4×D103C2211yescharacteristic
17C2×#13110092C2211yescharacteristic
18C2×#13110090C2211yescharacteristic
19#15693021C2211yescharacteristic, complemented
20#15693014—21no—
21#15693007—21no—
22#15693005—21no—
23#15692998—21no—
24#15692997C2211yescharacteristic
25#15692992C2211yescharacteristic
26Q8×Dic103C2211yescharacteristic, complemented
27C4×D412C2211yescharacteristic
28D4×Dic103C2211yescharacteristic
29D4×Dic103C2211yescharacteristic, complemented
30#15692983C2211yescharacteristic
31C4×C22⋊D103—21no—
32(C22⋊D103)⋊C4—21no—
33#15692979C2211yescharacteristic
34#15692978C2211yescharacteristic
35C2×(C2×D103)⋊C4—21no—
36C22⋊C4×D103—21no—
37#15692954C2211yescharacteristic, complemented
38#15692954C2211yescharacteristic, complemented
39#15692953C2211yescharacteristic, complemented
40#15692953C2211yescharacteristic, complemented
41C4⋊(C103⋊C8)C2211yescharacteristic, complemented
42#15692945C2211yescharacteristic, complemented
43#15692943C2211yescharacteristic
44#15692943C2211yescharacteristic
45#15692942C2211yescharacteristic
46#15692942C2211yescharacteristic
47#15692942C2211yescharacteristic, complemented
48(C2×D103)⋊C8C2211yescharacteristic
49(C2×D103)⋊C8C2211yescharacteristic
50#15692931C2211yescharacteristic, complemented
51C8×Dic103C2211yescharacteristic, complemented
52C2×SD16×C103C2211yescharacteristic
53C2×D8×C103C2211yescharacteristic
54#124×C103C2211yescharacteristic, complemented
55C4×D4×C103C2211yescharacteristic
56C4⋊C8×C103C2211yescharacteristic, complemented
57#103×C103C2211yescharacteristic, complemented
58#102×C103C2211yescharacteristic, complemented
59C23×D103—21no—
60C2×Dic206—21no—
61C2×D412C2311yescharacteristic
62C2×C22⋊D103—21no—
63C2×C22⋊D103—21no—
64D4×D103—22no—
65D4×D103—22no—
66C22×Dic103—21no—
67C22×Dic103—21no—
68C2×C4×D103—21no—
69C2×C4×D103—21no—
70C2×C4×D103C2311yescharacteristic
71#13110092—22no—
72#13110090—22no—
73C2×C103⋊C8C2311yescharacteristic
74C2×C103⋊C8C2311yescharacteristic
75C4⋊Dic103—21no—
76C4⋊Dic103—21no—
77C4⋊Dic103C2311yescharacteristic
78C4⋊Dic103C2311yescharacteristic
79C4⋊Dic103C2311yescharacteristic
80Dic103⋊C4—21no—
81Dic103⋊C4D411yescharacteristic
82Dic103⋊C4D411yescharacteristic
83C22⋊Dic103—21no—
84C22⋊Dic103—21no—
85C22⋊Dic103—21no—
86(C2×D103)⋊C4—21no—
87(C2×D103)⋊C4—21no—
88(C2×D103)⋊C4—21no—
89(C2×D103)⋊C4—21no—
90(C2×D103)⋊C4D411yescharacteristic
91(C2×D103)⋊C4D411yescharacteristic
92C4×Dic103—21no—
93C4×Dic103—21no—
94C4×Dic103C2311yescharacteristic
95C2×Q8×C103C2311yescharacteristic
96C2×D4×C103C2311yescharacteristic
97C2×D4×C103C2311yescharacteristic
98C22×C4×C103—21no—
99SD16×C103—22no—
100D8×C103—22no—
101C2×C8×C103C2311yescharacteristic
102C2×C8×C103C2311yescharacteristic
103C4⋊C4×C103C2311yescharacteristic
104C22⋊C4×C103—21no—
105C22⋊C4×C103—21no—
106C22⋊C4×C103—21no—
107C42×C103C2311yescharacteristic
108C23×C103—21no—
109C23×C103—21no—
110C22×D103—21no—
111C22×D103—24no—
112C22×D103—81no—
113C22×D103—81no—
114C22×D103C2×D411yescharacteristic
115Q8×C103—21no—
116Q8×C103—21no—
117D4×C103—21no—
118D4×C103—21no—
119D4×C103—21no—
120D4×C103#4112yes—
121C2×C4×C103—21no—
122C2×C4×C103—21no—
123C2×C4×C103—81no—
124C2×C4×C103C2×D411yescharacteristic
125C2×C4×C103C2×D411yescharacteristic
126C2×C4×C103C2411yescharacteristic
127C22⋊D103—24no—
128C22⋊D103—81no—
129C2×Dic103—21no—
130C2×Dic103—21no—
131C2×Dic103—21no—
132C2×Dic103—81no—
133C2×Dic103—81no—
134C2×Dic103C2×D411yescharacteristic
135C2×Dic103C2×D411yescharacteristic
136C2×Dic103C2×D411yescharacteristic
137D412—21no—
138D412#4112yes—
139C4×D103—21no—
140C4×D103—21no—
141C4×D103—81no—
142C4×D103—81no—
143Dic206—81no—
144C8×C103—21no—
145C8×C103—21no—
146C103⋊C8—21no—
147C103⋊C8—21no—
148C22×C103—22no—
149C22×C103—41no—
150C22×C103—41no—
151C22×C103—41no—
152C22×C103—41no—
153C22×C103—41no—
154C22×C103C22×D411yescharacteristic
155C2×D103—21no—
156C2×D103—22no—
157C2×D103—21no—
158C2×D103—21no—
159C2×D103—41no—
160C2×D103—41no—
161C2×D103—84no—
162C4×C103—21no—
163C4×C103—21no—
164C4×C103—41no—
165C4×C103—41no—
166C4×C103C2×#4111yescharacteristic
167C4×C103C2×#4111yescharacteristic
168Dic103—21no—
169Dic103—21no—
170Dic103—21no—
171Dic103—41no—
172Dic103—41no—
173Dic103—41no—
174C2×C103—42no—
175C2×C103—81no—
176C2×C103#52511yescharacteristic
177C2×C103#57611yescharacteristic
178C2×C103#57711yescharacteristic
179D103—41no—
180D103—42no—
181#3118—1031nomaximal, Sylow
182C103#311811yescharacteristic, complemented, Sylow
183#542—1031no—
184#518—1031no—
185#485—1031no—
186#482—1031no—
187#476—1031no—
188#474—1031no—
189#463—1031no—
190#463D10311yescharacteristic, complemented
191#450—1031no—
192#447—1031no—
193#442—1031no—
194#440—1031no—
195C4×SD16—1031no—
196C4×D8—1031no—
197#433—1031no—
198C22×D4—1031no—
199C2×SD16—1031no—
200C2×SD16C2×D10311yescharacteristic
201C2×D8—1031no—
202C2×D8C2×D10311yescharacteristic
203C4⋊Q8—1031no—
204#126—2061no—
205#124—2061no—
206#124C2×D10311yescharacteristic, complemented
207#123—2061no—
208C22⋊Q8—1031no—
209C22⋊Q8—2061no—
210#121—1031no—
211C4×Q8—1031no—
212C4×D4—1031no—
213C4×D4—1031no—
214C4×D4—1031no—
215C4×D4—1031no—
216C4×D4—2061no—
217C4×D4—2061no—
218C4×D4C2×D10311yescharacteristic
219#117—1031no—
220#117—1031no—
221C2×C22⋊C4—2061no—
222C2×C22⋊C4—2061no—
223#107—1031no—
224#107—1031no—
225#106—1031no—
226#106—1031no—
227C4⋊C8—1031no—
228C4⋊C8C2×D10311yescharacteristic, complemented
229#103—1031no—
230#103C2×D10311yescharacteristic, complemented
231#102—1031no—
232#102—1031no—
233#102—1031no—
234#102—1031no—
235#102—1031no—
236#102C2×D10311yescharacteristic, complemented
237C22⋊C8—1031no—
238C22⋊C8—1031no—
239#97—1031no—
240C4×C8—1031no—
241C24—2061no—
242C2×Q8—2061no—
243C2×Q8C22×D10311yescharacteristic
244C2×D4—1031no—
245C2×D4—2061no—
246C2×D4—2062no—
247C2×D4—2061no—
248C2×D4—2062no—
249C2×D4C22×D10311yescharacteristic
250C2×D4C22×D10311yescharacteristic
251C22×C4—21no—
252C22×C4—1031no—
253C22×C4—2061no—
254C22×C4—2061no—
255C22×C4—2061no—
256C22×C4—2061no—
257SD16—22no—
258SD16—2062no—
259D8—22no—
260D8—2062no—
261C2×C8—1031no—
262C2×C8—1031no—
263C2×C8C22×D10311yescharacteristic
264C2×C8C22×D10311yescharacteristic
265C4⋊C4—1031no—
266C4⋊C4—1031no—
267C4⋊C4—1031no—
268C4⋊C4—1031no—
269C4⋊C4—1031no—
270C4⋊C4—2061no—
271C4⋊C4—2061no—
272C4⋊C4—2061no—
273C4⋊C4C22×D10311yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—1031no—
278C22⋊C4—1031no—
279C22⋊C4—2061no—
280C22⋊C4—2061no—
281C22⋊C4—2061no—
282C22⋊C4—2061no—
283C22⋊C4—2061no—
284C22⋊C4—2061no—
285C22⋊C4—2061no—
286C42—1031no—
287C42—2061no—
288C42—2061no—
289C42C22×D10311yescharacteristic
290C23—21no—
291C23—21no—
292C23—8241no—
293C23—8241no—
294C23—1031no—
295C23—2064no—
296C23—2061no—
297Q8—21no—
298Q8—21no—
299Q8—8241no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—8241no—
304D4—1032no—
305D4—2064no—
306D4—2061no—
307D4#1311010412yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—8241no—
312C2×C4—8241no—
313C2×C4—8241no—
314C2×C4—8241no—
315C2×C4—1031no—
316C2×C4—1031no—
317C2×C4—1031no—
318C2×C4—2061no—
319C2×C4—2061no—
320C2×C4—2061no—
321C2×C4—2061no—
322C2×C4—2061no—
323C2×C4D4×D10311yescharacteristic
324C2×C4D4×D10311yescharacteristic
325C2×C4C23×D10311yescharacteristic
326C8—21no—
327C8—21no—
328C8—2061no—
329C8—2061no—
330C22—22no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—8244no—
337C22—4121no—
338C22—4121no—
339C22—2061no—
340C22—2062no—
341C22—2061no—
342C22—2061no—
343C22C2×D4×D10311yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—4121no—
349C4—4121no—
350C4—4121no—
351C4—2061no—
352C4—2061no—
353C4—2061no—
354C4#41×D10311yescharacteristic
355C4C2×#1311010411yescharacteristic
356C2—42no—
357C2—81no—
358C2—4121no—
359C2—4122no—
360C2#2026830111yescharacteristic
361C2#2026859511yescharacteristic
362C2#2026859811yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#463×C103C2
socleC22×C103C22×D4
prime radical#20267923C2
hypercenter#463D103
hypocenterC103#3118
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #20268410C2semidirect
2. #20268263C2semidirect
3. #20268130C2semidirect
4. #20268114C2semidirect
5. #20268082C2semidirect
6. #20268071C2semidirect
7. #20268003C2semidirect
8. #20267940C2semidirect
10. #20267903C2semidirect
11. #20267894C2semidirect
12. SD16×Dic103C2semidirect
13. #20267871C2semidirect
14. #20267851C2semidirect
15. #463×C103C2semidirect
19. #15693021C22semidirect
26. Q8×Dic103C22semidirect
29. D4×Dic103C22semidirect
37. #15692954C22semidirect
38. #15692954C22semidirect
39. #15692953C22semidirect
40. #15692953C22semidirect
41. C4⋊(C103⋊C8)C22semidirect
42. #15692945C22semidirect
47. #15692942C22semidirect
50. #15692931C22semidirect
51. C8×Dic103C22semidirect
54. #124×C103C22semidirect
56. C4⋊C8×C103C22semidirect
57. #103×C103C22semidirect
58. #102×C103C22semidirect
182. C103#3118semidirect
190. #463D103semidirect
206. #124C2×D103semidirect
228. C4⋊C8C2×D103semidirect
230. #103C2×D103semidirect
236. #102C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202684102
#202682632
#202681302
#202681142
#202680822
#202680712
#202680032
#202679402
#202679232
#202679032
#202678942
SD16×Dic1032
#202678712
#202678512
#463×C1032
#3118103