Finite Group Databasebeta

← #27205330

Subgroups — #27205330

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#20268412C211yesmaximal, characteristic, complemented
2#20268265C211yesmaximal, characteristic, complemented
3#20268133C211yesmaximal, characteristic, complemented
4#20268116C211yesmaximal, characteristic, complemented
5#20268082C211yesmaximal, characteristic, complemented
6#20268072C211yesmaximal, characteristic, complemented
7#20268007C211yesmaximal, characteristic, complemented
8#20268007C211yesmaximal, characteristic, complemented
9#20267944C211yesmaximal, characteristic, complemented
10#20267927C211yesmaximal, characteristic
11#20267904C211yesmaximal, characteristic, complemented
12#20267893C211yesmaximal, characteristic, complemented
13C4×#13110094C211yesmaximal, characteristic, complemented
14C4×D824C211yesmaximal, characteristic, complemented
15#433×C103C211yesmaximal, characteristic, complemented
16C22×D412C2211yescharacteristic
17C2×#13110094C2211yescharacteristic
18C2×#13110094C2211yescharacteristic
19C2×D824C2211yescharacteristic
20C2×D824C2211yescharacteristic
21#15693021C2211yescharacteristic, complemented
22#15693016—21no—
23#15693009C2211yescharacteristic, complemented
24#15693007—21no—
25#15693003—21no—
26#15693000C2211yescharacteristic
27#15692999—21no—
28#15692995C2211yescharacteristic
29C4×Dic206C2211yescharacteristic, complemented
30C4×D412C2211yescharacteristic
31C4×D412C2211yescharacteristic
32C4×D412C2211yescharacteristic
33C4×D412C2211yescharacteristic
34C4×D412C2211yescharacteristic, complemented
35#15692983—21no—
36#15692983—21no—
37#15692980C2211yescharacteristic
38C22⋊C4×D103—21no—
39C22⋊C4×D103—21no—
40#15692955C2211yescharacteristic, complemented
41#15692955C2211yescharacteristic, complemented
42#15692953C2211yescharacteristic, complemented
43#15692953C2211yescharacteristic, complemented
44#15692946C2211yescharacteristic, complemented
45#15692946C2211yescharacteristic, complemented
46#15692943C2211yescharacteristic
47#15692943C2211yescharacteristic
48#15692943C2211yescharacteristic
49#15692943C2211yescharacteristic
50#15692943C2211yescharacteristic, complemented
51#15692943C2211yescharacteristic, complemented
52#117×C103C2211yescharacteristic
53C4⋊C8×C103C2211yescharacteristic, complemented
54C4⋊C8×C103C2211yescharacteristic, complemented
55C22⋊C8×C103C2211yescharacteristic
56C22⋊C8×C103C2211yescharacteristic
57#97×C103C2211yescharacteristic, complemented
58C4×C8×C103C2211yescharacteristic, complemented
59C23×D103—21no—
60C2×Dic206—21no—
61C2×Dic206C2311yescharacteristic
62C2×D412—21no—
63C2×D412—22no—
64C2×D412—22no—
65C2×D412C2311yescharacteristic
66C2×D412C2311yescharacteristic
67C2×D412C2311yescharacteristic
68C2×C22⋊D103—21no—
69C2×C4×D103—21no—
70C2×C4×D103—21no—
71C2×C4×D103—21no—
72C2×C4×D103—21no—
73C2×C4×D103—21no—
74#13110094—22no—
75#13110094—22no—
76D824—22no—
77D824—22no—
78C4⋊Dic103—21no—
79C4⋊Dic103C2311yescharacteristic
80C4⋊Dic103C2311yescharacteristic
81C4⋊Dic103C2311yescharacteristic
82C4⋊Dic103C2311yescharacteristic
83Dic103⋊C4—21no—
84Dic103⋊C4—21no—
85C22⋊Dic103—21no—
86C22⋊Dic103—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)⋊C4—21no—
93(C2×D103)⋊C4—21no—
94(C2×D103)⋊C4—21no—
95C4×Dic103—21no—
96C4×Dic103—21no—
97C22×C4×C103C2311yescharacteristic
98C2×C8×C103C2311yescharacteristic
99C2×C8×C103C2311yescharacteristic
100C2×C8×C103C2311yescharacteristic
101C2×C8×C103C2311yescharacteristic
102C4⋊C4×C103D411yescharacteristic
103C4⋊C4×C103D411yescharacteristic
104C22⋊C4×C103D411yescharacteristic
105C22⋊C4×C103D411yescharacteristic
106C42×C103C2311yescharacteristic
107C42×C103C2311yescharacteristic
108C23×C103C2×D411yescharacteristic
109C22×D103—21no—
110C22×D103—21no—
111C22×D103—24no—
112C22×D103—21no—
113C22×D103—81no—
114C22×D103—81no—
115C2×C4×C103—21no—
116C2×C4×C103—21no—
117C2×C4×C103C2×D411yescharacteristic
118C2×C4×C103C2×D411yescharacteristic
119C2×C4×C103C2×D411yescharacteristic
120C2×C4×C103C2×D411yescharacteristic
121C2×C4×C103C2×D411yescharacteristic
122C2×C4×C103C2411yescharacteristic
123C22⋊D103—81no—
124C2×Dic103—21no—
125C2×Dic103—21no—
126C2×Dic103—21no—
127C2×Dic103—21no—
128C2×Dic103—21no—
129D412—24no—
130D412—21no—
131D412—21no—
132D412—21no—
133D412—21no—
134D412#4112yes—
135D412#4112yes—
136C4×D103—81no—
137C4×D103—81no—
138C4×D103—81no—
139C4×D103—81no—
140C4×D103—81no—
141Dic206—21no—
142Dic206—21no—
143Dic206—81no—
144C8×C103—21no—
145C8×C103—21no—
146C8×C103—21no—
147C8×C103—21no—
148C22×C103—21no—
149C22×C103—21no—
150C22×C103—21no—
151C22×C103C22×D411yescharacteristic
152C2×D103—22no—
153C2×D103—22no—
154C2×D103—41no—
155C2×D103—41no—
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—21no—
165C4×C103—21no—
166C4×C103—21no—
167C4×C103C2×#4111yescharacteristic
168C4×C103C2×#4111yescharacteristic
169Dic103—41no—
170Dic103—41no—
171Dic103—41no—
172Dic103—41no—
173Dic103—41no—
174C2×C103—41no—
175C2×C103#52511yescharacteristic
176C2×C103#57611yescharacteristic
177C2×C103#57711yescharacteristic
178D103—42no—
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×SD16—1031no—
196C4×D8—1031no—
197#433D10311yescharacteristic, complemented
198C22×D4—1031no—
199C2×SD16—1031no—
200C2×SD16—1031no—
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×Q8—1031no—
212C4×D4—1031no—
213C4×D4—1031no—
214C4×D4—1031no—
215C4×D4—1031no—
216C4×D4—1031no—
217C4×D4—2061no—
218C4×D4—2061no—
219#117—1031no—
220#117C2×D10311yescharacteristic
221C2×C22⋊C4—2061no—
222C2×C22⋊C4—2061no—
223#107—1031no—
224#107—1031no—
225#106—1031no—
226#106—1031no—
227C4⋊C8C2×D10311yescharacteristic, complemented
228C4⋊C8C2×D10311yescharacteristic, complemented
229#103—1031no—
230#103—1031no—
231#102—1031no—
232#102—1031no—
233#102—1031no—
234#102—1031no—
235#102—1031no—
236#102—1031no—
237C22⋊C8C2×D10311yescharacteristic
238C22⋊C8C2×D10311yescharacteristic
239#97C2×D10311yescharacteristic, complemented
240C4×C8C2×D10311yescharacteristic, complemented
241C24—2061no—
242C2×Q8—1031no—
243C2×Q8—2061no—
244C2×D4—1031no—
245C2×D4—1031no—
246C2×D4—1031no—
247C2×D4—2062no—
248C2×D4—2062no—
249C2×D4—2061no—
250C2×D4—2061no—
251C22×C4—2061no—
252C22×C4—2061no—
253C22×C4—2061no—
254C22×C4—2061no—
255C22×C4—2061no—
256C22×C4C22×D10311yescharacteristic
257SD16—2062no—
258SD16—2062no—
259D8—2062no—
260D8—2062no—
261C2×C8C22×D10311yescharacteristic
262C2×C8C22×D10311yescharacteristic
263C2×C8C22×D10311yescharacteristic
264C2×C8C22×D10311yescharacteristic
265C4⋊C4—1031no—
266C4⋊C4—1031no—
267C4⋊C4—1031no—
268C4⋊C4—1031no—
269C4⋊C4—2061no—
270C4⋊C4—2061no—
271C4⋊C4—2061no—
272C4⋊C4D41211yescharacteristic
273C4⋊C4D41211yescharacteristic
274C22⋊C4—2061no—
275C22⋊C4—2061no—
276C22⋊C4—2061no—
277C22⋊C4—2061no—
278C22⋊C4—2061no—
279C22⋊C4—2061no—
280C22⋊C4—2061no—
281C22⋊C4—2061no—
282C22⋊C4—2061no—
283C22⋊C4—2061no—
284C22⋊C4D41211yescharacteristic
285C22⋊C4D41211yescharacteristic
286C42—2061no—
287C42—2061no—
288C42C22×D10311yescharacteristic
289C42C22×D10311yescharacteristic
290C23—8241no—
291C23—8241no—
292C23—2064no—
293C23—2061no—
294C23—2061no—
295C23—2061no—
296C23C2×D41211yescharacteristic
297Q8—8241no—
298Q8—2061no—
299Q8—2061no—
300D4—8241no—
301D4—1032no—
302D4—1032no—
303D4—2064no—
304D4—2061no—
305D4—2061no—
306D4—2061no—
307D4—2061no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—8241no—
311C2×C4—8241no—
312C2×C4—8241no—
313C2×C4—8241no—
314C2×C4—8241no—
315C2×C4—2061no—
316C2×C4—2061no—
317C2×C4—2061no—
318C2×C4—2061no—
319C2×C4—2061no—
320C2×C4C2×D41211yescharacteristic
321C2×C4C2×D41211yescharacteristic
322C2×C4C2×D41211yescharacteristic
323C2×C4C2×D41211yescharacteristic
324C2×C4C2×D41211yescharacteristic
325C2×C4C23×D10311yescharacteristic
326C8—21no—
327C8—21no—
328C8—21no—
329C8—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—8244no—
334C22—4121no—
335C22—4121no—
336C22—4121no—
337C22—4121no—
338C22—4121no—
339C22—4121no—
340C22—4121no—
341C22—2062no—
342C22—2062no—
343C22C22×D41211yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—4121no—
350C4—4121no—
351C4—4121no—
352C4—4121no—
353C4—4121no—
354C4#41×D10311yescharacteristic
355C4#41×D10311yescharacteristic
356C2—41no—
357C2—8241no—
358C2—4122no—
359C2—4122no—
360C2#2026830311yescharacteristic
361C2#2026859611yescharacteristic
362C2#2026860311yescharacteristic
subgroupG/H
centerC22C22×D412
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#433×C103C2
socleC22×C103C22×D4
prime radical#20267927C2
hypercenter#433D103
hypocenterC103#3118
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #20268412C2semidirect
2. #20268265C2semidirect
3. #20268133C2semidirect
4. #20268116C2semidirect
5. #20268082C2semidirect
6. #20268072C2semidirect
7. #20268007C2semidirect
8. #20268007C2semidirect
9. #20267944C2semidirect
11. #20267904C2semidirect
12. #20267893C2semidirect
13. C4×#13110094C2semidirect
14. C4×D824C2semidirect
15. #433×C103C2semidirect
21. #15693021C22semidirect
23. #15693009C22semidirect
29. C4×Dic206C22semidirect
34. C4×D412C22semidirect
40. #15692955C22semidirect
41. #15692955C22semidirect
42. #15692953C22semidirect
43. #15692953C22semidirect
44. #15692946C22semidirect
45. #15692946C22semidirect
50. #15692943C22semidirect
51. #15692943C22semidirect
53. C4⋊C8×C103C22semidirect
54. C4⋊C8×C103C22semidirect
57. #97×C103C22semidirect
58. C4×C8×C103C22semidirect
182. C103#3118semidirect
197. #433D103semidirect
227. C4⋊C8C2×D103semidirect
228. C4⋊C8C2×D103semidirect
239. #97C2×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
#202684122
#202682652
#202681332
#202681162
#202680822
#202680722
#202680072
#202679442
#202679272
#202679042
#202678932
C4×#131100942
C4×D8242
#433×C1032
#3118103