Finite Group Databasebeta

← #27203955

Subgroups — #27203955

Order 13184.

548 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15693045C211yesmaximal, characteristic
2C4×#13110104C211yesmaximal, characteristic, complemented
3C4×D4×D103C211yesmaximal, characteristic, complemented
4#20267901C211yesmaximal, characteristic, complemented
5#20267893C211yesmaximal, characteristic, complemented
6#20267891C211yesmaximal, characteristic, complemented
7#20267882C211yesmaximal, characteristic, complemented
8#20267878C211yesmaximal, characteristic, complemented
9D8×Dic103C211yesmaximal, characteristic, complemented
10#20267871C211yesmaximal, characteristic, complemented
11#20267830C211yesmaximal, characteristic, complemented
12#20267794C211yesmaximal, characteristic, complemented
13#20267789C211yesmaximal, characteristic, complemented
14#20267743C211yesmaximal, characteristic, complemented
15#442×C103C211yesmaximal, characteristic, complemented
16C2×#13110104C2211yescharacteristic
17C2×D4×D103C2211yescharacteristic
18C22×C4×D103—21no—
19#15693045C418yescomplemented
20C2×#13110094C2211yescharacteristic
21C2×#13110093C2211yescharacteristic
22C2×#13110090C2211yescharacteristic
23C2×#13110088C2211yescharacteristic
24C2×#13110088C2211yescharacteristic
25C4×Dic206C2211yescharacteristic, complemented
26#15692986C2211yescharacteristic, complemented
27C4×D412C2211yescharacteristic
28D4×Dic103C2211yescharacteristic
29D4×Dic103C2211yescharacteristic, complemented
30#15692983C2211yescharacteristic
31C4×C22⋊D103—21no—
32C4×C22⋊D103—21no—
33(C22⋊D103)⋊C4—21no—
34(C22⋊D103)⋊C4—21no—
35#15692979C2211yescharacteristic
36#15692977—21no—
37C4⋊C4×D103C2211yescharacteristic
38C22⋊C4×D103—21no—
39C2×C4×Dic103—21no—
40C42×D103C2211yescharacteristic
41#15692955C2211yescharacteristic, complemented
42#15692954C2211yescharacteristic, complemented
43#15692952C2211yescharacteristic, complemented
44#15692946C2211yescharacteristic, complemented
45#15692944C2211yescharacteristic, complemented
46#15692943C2211yescharacteristic
47#15692942C2211yescharacteristic
48#15692942C2211yescharacteristic, complemented
49#15692941C2211yescharacteristic
50#15692932C2211yescharacteristic, complemented
51C8×Dic103C2211yescharacteristic, complemented
52C8×Dic103C2211yescharacteristic, complemented
53C2×D8×C103C2211yescharacteristic
54C4×D4×C103C2211yescharacteristic
55C4×D4×C103C2211yescharacteristic, complemented
56#106×C103C2211yescharacteristic, complemented
57#102×C103C2211yescharacteristic
58#102×C103C2211yescharacteristic, complemented
59#97×C103C2211yescharacteristic, complemented
60C23×D103—21no—
61#13110104—22no—
62#13110104C2×C414yescomplemented
63C2×Dic206C2311yescharacteristic
64C2×D412C2311yescharacteristic
65C2×C22⋊D103—21no—
66C2×C22⋊D103—21no—
67D4×D103—22no—
68D4×D103C2×C414yescomplemented
69C22×Dic103—21no—
70C22×Dic103—21no—
71C22×Dic103—21no—
72C2×C4×D103—21no—
73C2×C4×D103—21no—
74C2×C4×D103—21no—
75C2×C4×D103—44no—
76C2×C4×D103D411yescharacteristic
77C2×C4×D103D411yescharacteristic
78C2×C4×D103C2311yescharacteristic
79#13110094C2×C414yescomplemented
80#13110093C2×C414yescomplemented
81#13110090C2×C414yescomplemented
82#13110088—22no—
83#13110088C2×C414yescomplemented
84C2×C103⋊C8C2311yescharacteristic
85C2×C103⋊C8C2311yescharacteristic
86C4⋊Dic103C2311yescharacteristic
87C4⋊Dic103C2311yescharacteristic
88Dic103⋊C4—21no—
89Dic103⋊C4—21no—
90Dic103⋊C4—21no—
91C22⋊Dic103—21no—
92C22⋊Dic103—21no—
93(C2×D103)⋊C4—21no—
94(C2×D103)⋊C4—21no—
95(C2×D103)⋊C4—21no—
96C4×Dic103—21no—
97C4×Dic103—21no—
98C4×Dic103—21no—
99C4×Dic103D411yescharacteristic
100C4×Dic103D411yescharacteristic
101C4×Dic103C2311yescharacteristic
102C2×D4×C103C2311yescharacteristic
103C2×D4×C103C2311yescharacteristic
104C22×C4×C103—21no—
105C22×C4×C103—21no—
106D8×C103C2×C414yescomplemented
107C2×C8×C103C2311yescharacteristic
108C2×C8×C103C2311yescharacteristic
109C4⋊C4×C103C2311yescharacteristic
110C4⋊C4×C103C2311yescharacteristic
111C22⋊C4×C103—21no—
112C22⋊C4×C103—21no—
113C42×C103C2311yescharacteristic
114C23×C103—21no—
115C23×C103—21no—
116C22×D103—21no—
117C22×D103—24no—
118C22×D103—42no—
119C22×D103—42no—
120C22×D103C2×D411yescharacteristic
121D4×C103—21no—
122D4×C103—21no—
123D4×C103C22×C412yes—
124D4×C103C22×C412yescomplemented
125C2×C4×C103—21no—
126C2×C4×C103—21no—
127C2×C4×C103—42no—
128C2×C4×C103—42no—
129C2×C4×C103C2×D411yescharacteristic
130C2×C4×C103C2×D411yescharacteristic
131C2×C4×C103C2411yescharacteristic
132C22⋊D103—24no—
133C22⋊D103—24no—
134C2×Dic103—21no—
135C2×Dic103—24no—
136C2×Dic103—21no—
137C2×Dic103—21no—
138C2×Dic103—42no—
139C2×Dic103—42no—
140C2×Dic103C2×D411yescharacteristic
141C2×Dic103C2×D411yescharacteristic
142C2×Dic103C2×D411yescharacteristic
143D412—21no—
144D412C22×C412yes—
145C4×D103—22no—
146C4×D103—41no—
147C4×D103—42no—
148C4×D103—42no—
149C4×D103—42no—
150C4×D103C22×C412yes—
151C4×D103#4112yes—
152Dic206—21no—
153Dic206C22×C412yescomplemented
154C8×C103—21no—
155C8×C103C22×C412yescomplemented
156C103⋊C8—21no—
157C103⋊C8C22×C412yescomplemented
158C22×C103—22no—
159C22×C103—22no—
160C22×C103—41no—
161C22×C103—41no—
162C22×C103—41no—
163C22×C103—41no—
164C22×C103C22×D411yescharacteristic
165C2×D103—21no—
166C2×D103—21no—
167C2×D103—22no—
168C2×D103—48no—
169C2×D103—41no—
170C2×D103—41no—
171C2×D103C4×D412yes—
172C4×C103—21no—
173C4×C103—21no—
174C4×C103—41no—
175C4×C103—41no—
176C4×C103C23×C411yescharacteristic
177C4×C103C2×#4111yescharacteristic
178Dic103—22no—
179Dic103—21no—
180Dic103—41no—
181Dic103—41no—
182Dic103C4×D412yes—
183Dic103AGL(1,ℤ/8)12yescomplemented
184C2×C103—42no—
185C2×C103—42no—
186C2×C103C2×C4×D411yescharacteristic
187C2×C103C2×AGL(1,ℤ/8)11yescharacteristic
188C2×C103#57511yescharacteristic
189D103—22no—
190D103—42no—
191C4×AGL(1,ℤ/8)—1031nomaximal, Sylow
192C103C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
193C2×AGL(1,ℤ/8)—1031no—
194C4×#41—1031no—
195C2×C4×D4—1031no—
196#442—1031no—
197#442D10311yescharacteristic, complemented
198#440—1031no—
199#440—1031no—
200C4×SD16—1031no—
201C4×SD16—1031no—
202C4×D8—1031no—
203C4×D8—1031no—
204#428—1031no—
205#418—1031no—
206#417—1031no—
207C4×M16—1031no—
208C2×#41—1031no—
209C22×D4—1031no—
210C23×C4—2061no—
211AGL(1,ℤ/8)—1038no—
212C2×SD16—1031no—
213C2×SD16—1031no—
214C2×D8—1031no—
215C2×D8C2×D10311yescharacteristic
216C2×M16—1031no—
217C2×M16—1031no—
218C4×Q8—1031no—
219C4×Q8—1031no—
220C4×D4—1031no—
221C4×D4—1031no—
222C4×D4—1031no—
223C4×D4—1031no—
224C4×D4—2061no—
225C4×D4—2061no—
226C4×D4—2061no—
227C4×D4—2061no—
228C4×D4C2×D10311yescharacteristic
229C4×D4C2×D10311yescharacteristic, complemented
230#117—1031no—
231#117—2061no—
232C2×C4⋊C4—1031no—
233C2×C22⋊C4—2061no—
234C2×C42—1031no—
235C2×C42—2061no—
236#107—1031no—
237#107—1031no—
238#106—1031no—
239#106C2×D10311yescharacteristic, complemented
240#103—1031no—
241#103—1031no—
242#102—1031no—
243#102—1031no—
244#102—1031no—
245#102—1031no—
246#102C2×D10311yescharacteristic
247#102C2×D10311yescharacteristic, complemented
248#97—1031no—
249#97C2×D10311yescharacteristic, complemented
250C4×C8—1031no—
251C4×C8—1031no—
252C24—2061no—
253#41—1034no—
254#41—2062no—
255C2×Q8—1031no—
256C2×D4—1034no—
257C2×D4—1031no—
258C2×D4—2062no—
259C2×D4—2061no—
260C2×D4—2061no—
261C2×D4C22×D10311yescharacteristic
262C2×D4C22×D10311yescharacteristic
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—1031no—
266C22×C4—1031no—
267C22×C4—1031no—
268C22×C4—4124no—
269C22×C4—2061no—
270C22×C4—2061no—
271C22×C4—2061no—
272C22×C4—2061no—
273C22×C4—2061no—
274C22×C4—2061no—
275SD16—1034no—
276SD16—1034no—
277D8—1034no—
278D8C4×D10314yescomplemented
279M16—1034no—
280M16—2062no—
281C2×C8—1031no—
282C2×C8—1031no—
283C2×C8C22×D10311yescharacteristic
284C2×C8C22×D10311yescharacteristic
285C4⋊C4—1031no—
286C4⋊C4—1031no—
287C4⋊C4—2061no—
288C4⋊C4—2061no—
289C4⋊C4—2061no—
290C4⋊C4C22×D10311yescharacteristic
291C4⋊C4C22×D10311yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—2061no—
295C22⋊C4—2061no—
296C22⋊C4—2061no—
297C22⋊C4—2061no—
298C22⋊C4—2061no—
299C42—1031no—
300C42—1031no—
301C42—1031no—
302C42—2061no—
303C42—2061no—
304C42—2061no—
305C42C22×D10311yescharacteristic
306C23—21no—
307C23—21no—
308C23—1031no—
309C23—4122no—
310C23—4122no—
311C23—2064no—
312C23—2061no—
313Q8—1032no—
314Q8—2061no—
315D4—21no—
316D4—21no—
317D4—1032no—
318D4—2064no—
319D4—2064no—
320D4—2061no—
321D4C2×C4×D10312yes—
322D4C2×C4×D10312yescomplemented
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—1031no—
328C2×C4—1031no—
329C2×C4—1032no—
330C2×C4—1032no—
331C2×C4—1031no—
332C2×C4—4122no—
333C2×C4—4121no—
334C2×C4—4122no—
335C2×C4—4122no—
336C2×C4—4122no—
337C2×C4—4122no—
338C2×C4—2062no—
339C2×C4—2064no—
340C2×C4—2061no—
341C2×C4—2061no—
342C2×C4—2061no—
343C2×C4D4×D10311yescharacteristic
344C2×C4D4×D10311yescharacteristic
345C2×C4C23×D10311yescharacteristic
346C8—21no—
347C8—1032no—
348C8—2061no—
349C8C2×C4×D10312yescomplemented
350C22—22no—
351C22—22no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—1032no—
357C22—4128no—
358C22—4121no—
359C22—4121no—
360C22—2062no—
361C22—2061no—
362C22—2061no—
363C22C2×D4×D10311yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—1032no—
369C4—1032no—
370C4—4121no—
371C4—4121no—
372C4—2061no—
373C4—2062no—
374C4C22×C4×D10311yescharacteristic
375C4#41×D10311yescharacteristic
376C2—42no—
377C2—42no—
378C2—4122no—
379C2—2062no—
380C2C4×D4×D10311yescharacteristic
381C2AGL(1,ℤ/8)×D10311yescharacteristic
382C2#2026858711yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutatorC4×C103C23×C4
FrattiniC2×C4C23×D103
Fitting#442×C103C2
socleC22×C103C22×D4
prime radicalC2×#15693045C2
cosocleC2×C4×C103C24
hypercenter#442D103
hypocenterC103C4×AGL(1,ℤ/8)
LCSG ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
2. C4×#13110104C2semidirect
3. C4×D4×D103C2semidirect
4. #20267901C2semidirect
5. #20267893C2semidirect
6. #20267891C2semidirect
7. #20267882C2semidirect
8. #20267878C2semidirect
9. D8×Dic103C2semidirect
10. #20267871C2semidirect
11. #20267830C2semidirect
12. #20267794C2semidirect
13. #20267789C2semidirect
14. #20267743C2semidirect
15. #442×C103C2semidirect
19. #15693045C4semidirect
25. C4×Dic206C22semidirect
26. #15692986C22semidirect
29. D4×Dic103C22semidirect
41. #15692955C22semidirect
42. #15692954C22semidirect
43. #15692952C22semidirect
44. #15692946C22semidirect
45. #15692944C22semidirect
48. #15692942C22semidirect
50. #15692932C22semidirect
51. C8×Dic103C22semidirect
52. C8×Dic103C22semidirect
55. C4×D4×C103C22semidirect
56. #106×C103C22semidirect
58. #102×C103C22semidirect
59. #97×C103C22semidirect
62. #13110104C2×C4semidirect
68. D4×D103C2×C4semidirect
79. #13110094C2×C4semidirect
80. #13110093C2×C4semidirect
81. #13110090C2×C4semidirect
83. #13110088C2×C4semidirect
106. D8×C103C2×C4semidirect
124. D4×C103C22×C4semidirect
153. Dic206C22×C4semidirect
155. C8×C103C22×C4semidirect
157. C103⋊C8C22×C4semidirect
183. Dic103AGL(1,ℤ/8)semidirect
192. C103C4×AGL(1,ℤ/8)semidirect
197. #442D103semidirect
229. C4×D4C2×D103semidirect
239. #106C2×D103semidirect
247. #102C2×D103semidirect
249. #97C2×D103semidirect
278. D8C4×D103semidirect
322. D4C2×C4×D103semidirect
349. C8C2×C4×D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156930452
C4×#131101042
C4×D4×D1032
#202679012
#202678932
#202678912
#202678822
#202678782
D8×Dic1032
#202678712
#202678302
#202677942
#202677892
#202677432
#442×C1032
C4×AGL(1,ℤ/8)103