Finite Group Databasebeta

← #27205334

Subgroups — #27205334

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#20268413C211yesmaximal, characteristic, complemented
2#20268263C211yesmaximal, characteristic, complemented
3#20268131C211yesmaximal, characteristic, complemented
4#20268117C211yesmaximal, characteristic, complemented
5#20268080C211yesmaximal, characteristic, complemented
6#20268069C211yesmaximal, characteristic, complemented
7#20268009C211yesmaximal, characteristic, complemented
8#20268008C211yesmaximal, characteristic, complemented
9#20267940C211yesmaximal, characteristic, complemented
10#20267926C211yesmaximal, characteristic
11#20267901C211yesmaximal, characteristic, complemented
12#20267889C211yesmaximal, characteristic, complemented
13C4×D824C211yesmaximal, characteristic, complemented
14#20267850C211yesmaximal, characteristic, complemented
15C4×SD16×C103C211yesmaximal, characteristic, complemented
16C2×D4×D103C2211yescharacteristic
17C2×#13110092C2211yescharacteristic
18C2×D824C2211yescharacteristic
19C2×#13110090C2211yescharacteristic
20#15693020C2211yescharacteristic, complemented
21#15693015—21no—
22#15693010C2211yescharacteristic, complemented
23#15693009—21no—
24#15693006—21no—
25#15692999—21no—
26#15692997C2211yescharacteristic
27#15692996C2211yescharacteristic
28C4×D412C2211yescharacteristic
29C4×D412C2211yescharacteristic, complemented
30D4×Dic103C2211yescharacteristic
31#15692983C2211yescharacteristic
32C4×C22⋊D103—21no—
33(C22⋊D103)⋊C4—21no—
34#15692979C2211yescharacteristic
35#15692978C2211yescharacteristic
36C2×(C2×D103)⋊C4—21no—
37C22⋊C4×D103—21no—
38#15692955C2211yescharacteristic, complemented
39#15692954C2211yescharacteristic, complemented
40#15692952C2211yescharacteristic, complemented
41Dic103⋊C8C2211yescharacteristic, complemented
42Dic103⋊C8C2211yescharacteristic, complemented
43#15692945C2211yescharacteristic, complemented
44#15692943C2211yescharacteristic
45#15692943C2211yescharacteristic, complemented
46#15692942C2211yescharacteristic
47#15692941C2211yescharacteristic
48#15692941C2211yescharacteristic, complemented
49(C2×D103)⋊C8C2211yescharacteristic
50(C2×D103)⋊C8C2211yescharacteristic
51#15692932C2211yescharacteristic, complemented
52C2×SD16×C103C2211yescharacteristic
53C4×Q8×C103C2211yescharacteristic, complemented
54C4×D4×C103C2211yescharacteristic
55#106×C103C2211yescharacteristic, complemented
56#103×C103C2211yescharacteristic, complemented
57#102×C103C2211yescharacteristic
58C4×C8×C103C2211yescharacteristic, complemented
59C23×D103—21no—
60C2×Dic206—21no—
61C2×D412—21no—
62C2×D412C2311yescharacteristic
63C2×D412C2311yescharacteristic
64C2×C22⋊D103—21no—
65D4×D103—22no—
66D4×D103—22no—
67C22×Dic103—21no—
68C2×C4×D103—21no—
69C2×C4×D103—21no—
70C2×C4×D103—21no—
71C2×C4×D103C2311yescharacteristic
72#13110092—22no—
73D824—22no—
74#13110090—22no—
75C2×C103⋊C8C2311yescharacteristic
76C2×C103⋊C8C2311yescharacteristic
77C4⋊Dic103C2311yescharacteristic
78C4⋊Dic103C2311yescharacteristic
79Dic103⋊C4—21no—
80Dic103⋊C4—21no—
81Dic103⋊C4D411yescharacteristic
82Dic103⋊C4D411yescharacteristic
83C22⋊Dic103—21no—
84(C2×D103)⋊C4—21no—
85(C2×D103)⋊C4—21no—
86(C2×D103)⋊C4—21no—
87(C2×D103)⋊C4—21no—
88(C2×D103)⋊C4—21no—
89(C2×D103)⋊C4—21no—
90(C2×D103)⋊C4—21no—
91(C2×D103)⋊C4—21no—
92(C2×D103)⋊C4D411yescharacteristic
93(C2×D103)⋊C4D411yescharacteristic
94C4×Dic103—21no—
95C4×Dic103C2311yescharacteristic
96C2×Q8×C103C2311yescharacteristic
97C2×D4×C103C2311yescharacteristic
98C22×C4×C103—21no—
99SD16×C103—22no—
100C2×C8×C103C2311yescharacteristic
101C2×C8×C103C2311yescharacteristic
102C4⋊C4×C103—21no—
103C4⋊C4×C103C2311yescharacteristic
104C4⋊C4×C103C2311yescharacteristic
105C22⋊C4×C103—21no—
106C42×C103—21no—
107C42×C103C2311yescharacteristic
108C23×C103—21no—
109C22×D103—21no—
110C22×D103—24no—
111C22×D103—21no—
112C22×D103—81no—
113C22×D103—81no—
114C22×D103C2×D411yescharacteristic
115Q8×C103—21no—
116Q8×C103—21no—
117D4×C103—21no—
118D4×C103#4112yes—
119C2×C4×C103—21no—
120C2×C4×C103—21no—
121C2×C4×C103—21no—
122C2×C4×C103—81no—
123C2×C4×C103C2×D411yescharacteristic
124C2×C4×C103C2×D411yescharacteristic
125C2×C4×C103C2411yescharacteristic
126C22⋊D103—24no—
127C2×Dic103—21no—
128C2×Dic103—21no—
129C2×Dic103—81no—
130C2×Dic103C2×D411yescharacteristic
131C2×Dic103C2×D411yescharacteristic
132C2×Dic103C2×D411yescharacteristic
133D412—21no—
134D412—21no—
135D412—21no—
136D412—81no—
137D412#4112yes—
138C4×D103—21no—
139C4×D103—21no—
140C4×D103—81no—
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×C103C22×D411yescharacteristic
152C2×D103—21no—
153C2×D103—22no—
154C2×D103—21no—
155C2×D103—21no—
156C2×D103—41no—
157C2×D103—41no—
158C2×D103—41no—
159C2×D103—41no—
160C2×D103—41no—
161C2×D103—84no—
162C4×C103—21no—
163C4×C103—21no—
164C4×C103—41no—
165C4×C103—41no—
166C4×C103—41no—
167C4×C103C2×#4111yescharacteristic
168C4×C103C2×#4111yescharacteristic
169Dic103—21no—
170Dic103—21no—
171Dic103—21no—
172Dic103—41no—
173Dic103—41no—
174C2×C103—42no—
175C2×C103#52511yescharacteristic
176C2×C103#57611yescharacteristic
177C2×C103#57711yescharacteristic
178D103—41no—
179D103—42no—
180D103—81no—
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#463—1031no—
191#450—1031no—
192#447—1031no—
193#442—1031no—
194#440—1031no—
195C4×SD16D10311yescharacteristic, complemented
196C4×D8—1031no—
197#433—1031no—
198C22×D4—1031no—
199C2×SD16—1031no—
200C2×SD16C2×D10311yescharacteristic
201C2×D8—1031no—
202C2×D8—1031no—
203C4⋊Q8—1031no—
204#126—2061no—
205#124—1031no—
206#124—2061no—
207#123—2061no—
208C22⋊Q8—1031no—
209C22⋊Q8—2061no—
210#121—1031no—
211C4×Q8C2×D10311yescharacteristic, complemented
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#106C2×D10311yescharacteristic, complemented
227C4⋊C8—1031no—
228C4⋊C8—1031no—
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
237C22⋊C8—1031no—
238C22⋊C8—1031no—
239#97—1031no—
240C4×C8C2×D10311yescharacteristic, complemented
241C24—2061no—
242C2×Q8—2061no—
243C2×Q8C22×D10311yescharacteristic
244C2×D4—1031no—
245C2×D4—1031no—
246C2×D4—2061no—
247C2×D4—2061no—
248C2×D4—2062no—
249C2×D4—2062no—
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—2062no—
260D8—2062no—
261C2×C8—1031no—
262C2×C8—1031no—
263C2×C8C22×D10311yescharacteristic
264C2×C8C22×D10311yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—1031no—
267C4⋊C4—1031no—
268C4⋊C4—1031no—
269C4⋊C4—1031no—
270C4⋊C4—2061no—
271C4⋊C4—2061no—
272C4⋊C4C22×D10311yescharacteristic
273C4⋊C4C22×D10311yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—1031no—
276C22⋊C4—1031no—
277C22⋊C4—2061no—
278C22⋊C4—2061no—
279C22⋊C4—2061no—
280C22⋊C4—2061no—
281C22⋊C4—2061no—
282C22⋊C4—2061no—
283C22⋊C4—2061no—
284C22⋊C4—2061no—
285C22⋊C4—2061no—
286C42—21no—
287C42—1031no—
288C42—2061no—
289C42C22×D10311yescharacteristic
290C23—21no—
291C23—8241no—
292C23—8241no—
293C23—1031no—
294C23—2064no—
295C23—2061no—
296C23—2061no—
297Q8—21no—
298Q8—21no—
299Q8—8241no—
300D4—21no—
301D4—8241no—
302D4—1032no—
303D4—2064no—
304D4—2061no—
305D4—2061no—
306D4—2061no—
307D4#1311010512yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—81no—
312C2×C4—8241no—
313C2×C4—8241no—
314C2×C4—8241no—
315C2×C4—8241no—
316C2×C4—1031no—
317C2×C4—1031no—
318C2×C4—1031no—
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—8244no—
334C22—4121no—
335C22—4121no—
336C22—4121no—
337C22—4121no—
338C22—4121no—
339C22—2061no—
340C22—2062no—
341C22—2061no—
342C22—2061no—
343C22C2×D4×D10311yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—4121no—
350C4—4121no—
351C4—2061no—
352C4—2061no—
353C4—2061no—
354C4#41×D10311yescharacteristic
355C4C2×#1311010511yescharacteristic
356C2—42no—
357C2—8241no—
358C2—4121no—
359C2—4122no—
360C2#2026830011yescharacteristic
361C2#2026859311yescharacteristic
362C2#2026859711yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC4×SD16×C103C2
socleC22×C103C22×D4
prime radical#20267926C2
hypercenterC4×SD16D103
hypocenterC103#3118
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #20268413C2semidirect
2. #20268263C2semidirect
3. #20268131C2semidirect
4. #20268117C2semidirect
5. #20268080C2semidirect
6. #20268069C2semidirect
7. #20268009C2semidirect
8. #20268008C2semidirect
9. #20267940C2semidirect
11. #20267901C2semidirect
12. #20267889C2semidirect
13. C4×D824C2semidirect
14. #20267850C2semidirect
15. C4×SD16×C103C2semidirect
20. #15693020C22semidirect
22. #15693010C22semidirect
29. C4×D412C22semidirect
38. #15692955C22semidirect
39. #15692954C22semidirect
40. #15692952C22semidirect
41. Dic103⋊C8C22semidirect
42. Dic103⋊C8C22semidirect
43. #15692945C22semidirect
45. #15692943C22semidirect
48. #15692941C22semidirect
51. #15692932C22semidirect
53. C4×Q8×C103C22semidirect
55. #106×C103C22semidirect
56. #103×C103C22semidirect
58. C4×C8×C103C22semidirect
182. C103#3118semidirect
195. C4×SD16D103semidirect
211. C4×Q8C2×D103semidirect
226. #106C2×D103semidirect
230. #103C2×D103semidirect
240. C4×C8C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202684132
#202682632
#202681312
#202681172
#202680802
#202680692
#202680092
#202680082
#202679402
#202679262
#202679012
#202678892
C4×D8242
#202678502
C4×SD16×C1032
#3118103