Finite Group Databasebeta

← #27203971

Subgroups — #27203971

Order 13184.

506 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15693048C211yesmaximal, characteristic
2#20268273C211yesmaximal, characteristic, complemented
3#20268263C211yesmaximal, characteristic, complemented
4#20267902C211yesmaximal, characteristic, complemented
5#20267901C211yesmaximal, characteristic, complemented
6#20267892C211yesmaximal, characteristic, complemented
7#20267889C211yesmaximal, characteristic, complemented
8#20267876C211yesmaximal, characteristic, complemented
9C4×D824C211yesmaximal, characteristic, complemented
10#20267871C211yesmaximal, characteristic, complemented
11#20267830C211yesmaximal, characteristic, complemented
12#20267786C211yesmaximal, characteristic, complemented
13#102×D103C211yesmaximal, characteristic, complemented
14#20267745C211yesmaximal, characteristic, complemented
15C4×SD16×C103C211yesmaximal, characteristic, complemented
16C2×#13110106C2211yescharacteristic
17C2×D4×D103C2211yescharacteristic
18#15693048C418yescomplemented
19C2×#13110092C2211yescharacteristic
20C2×D824C2211yescharacteristic
21C2×#13110090C2211yescharacteristic
22C2×#13110088C2211yescharacteristic
23C2×C8×D103C2211yescharacteristic
24Q8×Dic103C2211yescharacteristic, complemented
25C4×D412—21no—
26C4×D412C2211yescharacteristic
27C4×D412C2211yescharacteristic, complemented
28D4×Dic103C2211yescharacteristic
29#15692983—21no—
30#15692983C2211yescharacteristic
31#15692983C2211yescharacteristic, complemented
32C4×C22⋊D103—21no—
33(C22⋊D103)⋊C4—21no—
34#15692979C2211yescharacteristic
35#15692978—21no—
36#15692978C2211yescharacteristic
37C4⋊C4×D103—21no—
38C4⋊C4×D103C2211yescharacteristic
39C2×(C2×D103)⋊C4—21no—
40C22⋊C4×D103—21no—
41#15692955C2211yescharacteristic, complemented
42#15692954C2211yescharacteristic, complemented
43#15692952C2211yescharacteristic, complemented
44#15692945C2211yescharacteristic, complemented
45#15692943C2211yescharacteristic
46#15692943C2211yescharacteristic, complemented
47#15692942C2211yescharacteristic
48#15692941C2211yescharacteristic
49#15692941C2211yescharacteristic, complemented
50#15692932C2211yescharacteristic, complemented
51#15692931C2211yescharacteristic, complemented
52C8×Dic103C2211yescharacteristic, complemented
53C2×SD16×C103C2211yescharacteristic
54C4×Q8×C103C2211yescharacteristic, complemented
55C4×D4×C103C2211yescharacteristic
56#106×C103C2211yescharacteristic, complemented
57#103×C103C2211yescharacteristic, complemented
58#102×C103C2211yescharacteristic
59C4×C8×C103C2211yescharacteristic, complemented
60C23×D103—21no—
61#13110106—22no—
62#13110106C2×C414yescomplemented
63C2×D412—21no—
64C2×D412C2311yescharacteristic
65C2×D412C2311yescharacteristic
66C2×C22⋊D103—21no—
67D4×D103—22no—
68D4×D103C2×C414yescomplemented
69C22×Dic103—21no—
70C2×C4×D103—21no—
71C2×C4×D103—21no—
72C2×C4×D103—21no—
73C2×C4×D103—21no—
74C2×C4×D103—21no—
75C2×C4×D103—21no—
76C2×C4×D103C2311yescharacteristic
77#13110092C2×C414yescomplemented
78D824C2×C414yescomplemented
79#13110090C2×C414yescomplemented
80#13110088C2×C414yescomplemented
81C2×C103⋊C8C2311yescharacteristic
82C2×C103⋊C8C2311yescharacteristic
83C8×D103—22no—
84C4⋊Dic103—21no—
85C4⋊Dic103C2311yescharacteristic
86C4⋊Dic103C2311yescharacteristic
87Dic103⋊C4—21no—
88Dic103⋊C4D411yescharacteristic
89Dic103⋊C4D411yescharacteristic
90C22⋊Dic103—21no—
91(C2×D103)⋊C4—21no—
92(C2×D103)⋊C4—21no—
93(C2×D103)⋊C4—21no—
94(C2×D103)⋊C4—21no—
95(C2×D103)⋊C4—21no—
96(C2×D103)⋊C4D411yescharacteristic
97(C2×D103)⋊C4D411yescharacteristic
98C4×Dic103—21no—
99C4×Dic103—21no—
100C4×Dic103C2311yescharacteristic
101C2×Q8×C103C2311yescharacteristic
102C2×D4×C103C2311yescharacteristic
103C22×C4×C103—21no—
104SD16×C103C2×C414yescomplemented
105C2×C8×C103C2311yescharacteristic
106C2×C8×C103C2311yescharacteristic
107C4⋊C4×C103—21no—
108C4⋊C4×C103C2311yescharacteristic
109C4⋊C4×C103C2311yescharacteristic
110C22⋊C4×C103—21no—
111C42×C103—21no—
112C42×C103C2311yescharacteristic
113C23×C103—21no—
114C22×D103—21no—
115C22×D103—21no—
116C22×D103—24no—
117C22×D103—81no—
118C22×D103—81no—
119C22×D103C2×D411yescharacteristic
120Q8×C103—21no—
121Q8×C103C22×C412yes—
122D4×C103—21no—
123D4×C103C22×C412yes—
124C2×C4×C103—21no—
125C2×C4×C103—21no—
126C2×C4×C103—21no—
127C2×C4×C103—81no—
128C2×C4×C103C2×D411yescharacteristic
129C2×C4×C103C2×D411yescharacteristic
130C2×C4×C103C2411yescharacteristic
131C22⋊D103—24no—
132C2×Dic103—21no—
133C2×Dic103—21no—
134C2×Dic103—81no—
135C2×Dic103C2×D411yescharacteristic
136C2×Dic103C2×D411yescharacteristic
137C2×Dic103C2×D411yescharacteristic
138D412—24no—
139D412—21no—
140D412—21no—
141D412C22×C412yes—
142D412C22×C412yes—
143C4×D103—24no—
144C4×D103—81no—
145C4×D103—81no—
146C4×D103—81no—
147C4×D103—81no—
148C4×D103—81no—
149C4×D103C22×C412yes—
150C4×D103#4112yes—
151C8×C103—21no—
152C8×C103C22×C412yes—
153C103⋊C8—21no—
154C103⋊C8C22×C412yes—
155C22×C103—22no—
156C22×C103—41no—
157C22×C103—41no—
158C22×C103C22×D411yescharacteristic
159C2×D103—21no—
160C2×D103—21no—
161C2×D103—22no—
162C2×D103—22no—
163C2×D103—41no—
164C2×D103—41no—
165C2×D103—41no—
166C2×D103—41no—
167C2×D103—84no—
168C2×D103C4×D412yes—
169C4×C103—22no—
170C4×C103—21no—
171C4×C103—21no—
172C4×C103—41no—
173C4×C103—41no—
174C4×C103C23×C411yescharacteristic
175C4×C103C2×#4111yescharacteristic
176Dic103—21no—
177Dic103—21no—
178Dic103—41no—
179Dic103—41no—
180Dic103C4×D412yes—
181C2×C103—42no—
182C2×C103C2×C4×D411yescharacteristic
183C2×C103#57611yescharacteristic
184C2×C103#57711yescharacteristic
185D103—22no—
186D103—42no—
187D103—42no—
188#2946—1031nomaximal, Sylow
189C103#294611yescharacteristic, complemented, Sylow
190C2×AGL(1,ℤ/8)—1031no—
191#520—1031no—
192#518—1031no—
193#442—1031no—
194#442—1031no—
195#440—1031no—
196#440—1031no—
197C4×SD16—1031no—
198C4×SD16D10311yescharacteristic, complemented
199C4×D8—1031no—
200C4×D8—1031no—
201#428—1031no—
202#416—1031no—
203C2×#102—1031no—
204#405—1031no—
205C2×#41—1031no—
206C22×D4—1031no—
207AGL(1,ℤ/8)—1038no—
208C2×SD16—1031no—
209C2×SD16C2×D10311yescharacteristic
210C2×D8—1031no—
211C2×D8—1031no—
212C2×M16—1031no—
213C22×C8—1031no—
214C4×Q8—1031no—
215C4×Q8C2×D10311yescharacteristic, complemented
216C4×D4—1031no—
217C4×D4—1031no—
218C4×D4—1031no—
219C4×D4—1031no—
220C4×D4—1031no—
221C4×D4—2061no—
222C4×D4—2061no—
223C4×D4—2061no—
224C4×D4—2061no—
225C4×D4C2×D10311yescharacteristic
226#117—1031no—
227#117—1031no—
228#117—2061no—
229C2×C4⋊C4—1031no—
230C2×C4⋊C4—2061no—
231C2×C22⋊C4—2061no—
232C2×C22⋊C4—2061no—
233#107—1031no—
234#107—1031no—
235#106—1031no—
236#106C2×D10311yescharacteristic, complemented
237#103—1031no—
238#103C2×D10311yescharacteristic, complemented
239#102—1031no—
240#102—1031no—
241#102—1031no—
242#102—1031no—
243#102—1031no—
244#102C2×D10311yescharacteristic
245#97—1031no—
246#97—1031no—
247C4×C8—1031no—
248C4×C8C2×D10311yescharacteristic, complemented
249C24—2061no—
250#41—1034no—
251#41—2062no—
252C2×Q8C22×D10311yescharacteristic
253C2×D4—1034no—
254C2×D4—1031no—
255C2×D4—1031no—
256C2×D4—2061no—
257C2×D4—2062no—
258C2×D4—2061no—
259C2×D4C22×D10311yescharacteristic
260C22×C4—21no—
261C22×C4—1031no—
262C22×C4—2061no—
263C22×C4—2061no—
264C22×C4—2061no—
265C22×C4—2061no—
266C22×C4—2061no—
267C22×C4—2061no—
268C22×C4—2061no—
269SD16—1034no—
270SD16C4×D10314yescomplemented
271D8—1034no—
272D8—1034no—
273M16—1034no—
274C2×C8—1031no—
275C2×C8—1031no—
276C2×C8—2062no—
277C2×C8C22×D10311yescharacteristic
278C2×C8C22×D10311yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—1031no—
281C4⋊C4—1031no—
282C4⋊C4—1031no—
283C4⋊C4—1031no—
284C4⋊C4—2061no—
285C4⋊C4—2061no—
286C4⋊C4C22×D10311yescharacteristic
287C4⋊C4C22×D10311yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—1031no—
290C22⋊C4—1031no—
291C22⋊C4—2061no—
292C22⋊C4—2061no—
293C22⋊C4—2061no—
294C22⋊C4—2061no—
295C22⋊C4—2061no—
296C22⋊C4—2061no—
297C42—21no—
298C42—1031no—
299C42—2061no—
300C42—2061no—
301C42C22×D10311yescharacteristic
302C23—21no—
303C23—8241no—
304C23—8241no—
305C23—1031no—
306C23—2064no—
307C23—2061no—
308C23—2061no—
309Q8—21no—
310Q8C2×C4×D10312yes—
311D4—21no—
312D4—1032no—
313D4—1032no—
314D4—2064no—
315D4—2064no—
316D4—2061no—
317D4—2061no—
318D4C2×C4×D10312yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—81no—
323C2×C4—8241no—
324C2×C4—8241no—
325C2×C4—8241no—
326C2×C4—8241no—
327C2×C4—8241no—
328C2×C4—8241no—
329C2×C4—1031no—
330C2×C4—1032no—
331C2×C4—1032no—
332C2×C4—1031no—
333C2×C4—1031no—
334C2×C4—2064no—
335C2×C4—2061no—
336C2×C4—2061no—
337C2×C4D4×D10311yescharacteristic
338C2×C4D4×D10311yescharacteristic
339C2×C4C23×D10311yescharacteristic
340C8—21no—
341C8—1032no—
342C8—2061no—
343C8C2×C4×D10312yes—
344C22—22no—
345C22—41no—
346C22—41no—
347C22—8244no—
348C22—1032no—
349C22—4121no—
350C22—4121no—
351C22—4121no—
352C22—4121no—
353C22—2062no—
354C22—2062no—
355C22—2061no—
356C22—2061no—
357C22C2×D4×D10311yescharacteristic
358C4—21no—
359C4—21no—
360C4—22no—
361C4—41no—
362C4—41no—
363C4—1032no—
364C4—4121no—
365C4—4121no—
366C4—2061no—
367C4—2061no—
368C4C22×C4×D10311yescharacteristic
369C4#41×D10311yescharacteristic
370C2—42no—
371C2—4122no—
372C2—4122no—
373C2—2062no—
374C2C4×D4×D10311yescharacteristic
375C2#2026859311yescharacteristic
376C2#2026859711yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutatorC4×C103C23×C4
FrattiniC2×C4C23×D103
FittingC4×SD16×C103C2
socleC22×C103C22×D4
prime radicalC2×#15693048C2
cosocleC2×C4×C103C24
hypercenterC4×SD16D103
hypocenterC103#2946
LCSG ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. #20268273C2semidirect
3. #20268263C2semidirect
4. #20267902C2semidirect
5. #20267901C2semidirect
6. #20267892C2semidirect
7. #20267889C2semidirect
8. #20267876C2semidirect
9. C4×D824C2semidirect
10. #20267871C2semidirect
11. #20267830C2semidirect
12. #20267786C2semidirect
13. #102×D103C2semidirect
14. #20267745C2semidirect
15. C4×SD16×C103C2semidirect
18. #15693048C4semidirect
24. Q8×Dic103C22semidirect
27. C4×D412C22semidirect
31. #15692983C22semidirect
41. #15692955C22semidirect
42. #15692954C22semidirect
43. #15692952C22semidirect
44. #15692945C22semidirect
46. #15692943C22semidirect
49. #15692941C22semidirect
50. #15692932C22semidirect
51. #15692931C22semidirect
52. C8×Dic103C22semidirect
54. C4×Q8×C103C22semidirect
56. #106×C103C22semidirect
57. #103×C103C22semidirect
59. C4×C8×C103C22semidirect
62. #13110106C2×C4semidirect
68. D4×D103C2×C4semidirect
77. #13110092C2×C4semidirect
78. D824C2×C4semidirect
79. #13110090C2×C4semidirect
80. #13110088C2×C4semidirect
104. SD16×C103C2×C4semidirect
189. C103#2946semidirect
198. C4×SD16D103semidirect
215. C4×Q8C2×D103semidirect
236. #106C2×D103semidirect
238. #103C2×D103semidirect
248. C4×C8C2×D103semidirect
270. SD16C4×D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156930482
#202682732
#202682632
#202679022
#202679012
#202678922
#202678892
#202678762
C4×D8242
#202678712
#202678302
#202677862
#102×D1032
#202677452
C4×SD16×C1032
#2946103