Finite Group Databasebeta

← C4×#20263353 #38751521

Subgroups — C4×#20263353 #38751521

Order 25216.

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×#20263353C211yesmaximal, characteristic
2C4×#15691359C211yesmaximal, characteristic, complemented
3C4×D4×D197C211yesmaximal, characteristic, complemented
4#27161190C211yesmaximal, characteristic, complemented
5#27161188C211yesmaximal, characteristic, complemented
6#27161182C211yesmaximal, characteristic, complemented
7#27161180C211yesmaximal, characteristic, complemented
8C4×#15691345C211yesmaximal, characteristic, complemented
9C4×D1576C211yesmaximal, characteristic, complemented
10C4×#15691343C211yesmaximal, characteristic, complemented
11#27161118C211yesmaximal, characteristic, complemented
12#27161082C211yesmaximal, characteristic, complemented
13#27161079C211yesmaximal, characteristic, complemented
14C4×#15691341C211yesmaximal, characteristic, complemented
15C4×SD16×C197C211yesmaximal, characteristic, complemented
16C2×#15691359C2211yescharacteristic
17C2×D4×D197C2211yescharacteristic
18C22×C4×D197—21no—
19#20263353C418yesdirect product factor
20C2×#15691345C2211yescharacteristic
21C2×D1576C2211yescharacteristic
22C2×#15691343C2211yescharacteristic
23C2×#15691341C2211yescharacteristic
24C2×#15691341C2211yescharacteristic
25Q8×Dic197C2211yescharacteristic, complemented
26C4×D788—21no—
27C4×D788C2211yescharacteristic
28C4×D788C2211yescharacteristic, complemented
29D4×Dic197C2211yescharacteristic
30#20263288—21no—
31#20263288C2211yescharacteristic
32#20263288C2211yescharacteristic, complemented
33C4×C22⋊D197—21no—
34#20263286—21no—
35#20263284—21no—
36#20263284C2211yescharacteristic
37C4⋊C4×D197C2211yescharacteristic
38C22⋊C4×D197—21no—
39C42×D197—21no—
40C42×D197C2211yescharacteristic
41#20263260C2211yescharacteristic, complemented
42#20263259C2211yescharacteristic, complemented
43#20263257C2211yescharacteristic, complemented
44#20263250C2211yescharacteristic, complemented
45#20263248C2211yescharacteristic
46#20263248C2211yescharacteristic, complemented
47#20263247C2211yescharacteristic
48#20263246C2211yescharacteristic
49#20263246C2211yescharacteristic, complemented
50#20263236C2211yescharacteristic, complemented
51#20263236C2211yescharacteristic, complemented
52C4×#13096802C2211yescharacteristic, complemented
53C2×SD16×C197C2211yescharacteristic
54C4×Q8×C197C2211yescharacteristic, complemented
55C4×D4×C197C2211yescharacteristic
56#106×C197C2211yescharacteristic, complemented
57#103×C197C2211yescharacteristic, complemented
58#102×C197C2211yescharacteristic
59C4×C8×C197C2211yescharacteristic, complemented
60C23×D197—21no—
61#15691359—22no—
62#15691359C2×C414yescomplemented
63C2×D788—21no—
64C2×D788C2311yescharacteristic
65C2×D788C2311yescharacteristic
66C2×C22⋊D197—21no—
67D4×D197—22no—
68D4×D197C2×C414yescomplemented
69C22×Dic197—21no—
70C2×C4×D197—21no—
71C2×C4×D197—21no—
72C2×C4×D197—21no—
73C2×C4×D197—21no—
74C2×C4×D197—21no—
75C2×C4×D197—21no—
76C2×C4×D197—44no—
77C2×C4×D197D411yescharacteristic
78C2×C4×D197D411yescharacteristic
79C2×C4×D197C2311yescharacteristic
80#15691345C2×C414yescomplemented
81D1576C2×C414yescomplemented
82#15691343C2×C414yescomplemented
83#15691341—22no—
84#15691341C2×C414yescomplemented
85C2×#13096802C2311yescharacteristic
86C2×#13096802C2311yescharacteristic
87C4⋊Dic197—21no—
88C4⋊Dic197C2311yescharacteristic
89C4⋊Dic197C2311yescharacteristic
90#15691337—21no—
91C22⋊Dic197—21no—
92#15691335—21no—
93#15691335—21no—
94#15691335—21no—
95#15691335—21no—
96#15691335—21no—
97C4×Dic197—21no—
98C4×Dic197—21no—
99C4×Dic197D411yescharacteristic
100C4×Dic197D411yescharacteristic
101C4×Dic197C2311yescharacteristic
102C2×Q8×C197C2311yescharacteristic
103C2×D4×C197C2311yescharacteristic
104C22×C4×C197—21no—
105SD16×C197C2×C414yescomplemented
106C2×C8×C197C2311yescharacteristic
107C2×C8×C197C2311yescharacteristic
108C4⋊C4×C197—21no—
109C4⋊C4×C197C2311yescharacteristic
110C4⋊C4×C197C2311yescharacteristic
111C22⋊C4×C197—21no—
112C42×C197—21no—
113C42×C197C2311yescharacteristic
114C22×D197—21no—
115C22×D197—21no—
116C22×D197—24no—
117C22×D197—42no—
118C22×D197—42no—
119C22×D197C2×D411yescharacteristic
120D788—24no—
121D788—21no—
122D788—21no—
123D788C22×C412yes—
124D788C22×C412yescomplemented
125C22⋊D197—24no—
126C2×Dic197—21no—
127C2×Dic197—21no—
128C2×Dic197—42no—
129C2×Dic197C2×D411yescharacteristic
130C2×Dic197C2×D411yescharacteristic
131C2×Dic197C2×D411yescharacteristic
132C4×D197—22no—
133C4×D197—24no—
134C4×D197—41no—
135C4×D197—42no—
136C4×D197—42no—
137C4×D197—42no—
138C4×D197—42no—
139C4×D197—42no—
140C4×D197C22×C412yes—
141C4×D197#4112yes—
142#13096802—21no—
143#13096802C22×C412yescomplemented
144C23×C197—21no—
145Q8×C197—21no—
146Q8×C197C22×C412yescomplemented
147D4×C197—21no—
148D4×C197C22×C412yes—
149C2×C4×C197—21no—
150C2×C4×C197—21no—
151C2×C4×C197—21no—
152C2×C4×C197—42no—
153C2×C4×C197C2×D411yescharacteristic
154C2×C4×C197C2×D411yescharacteristic
155C2×C4×C197C2411yescharacteristic
156C8×C197—21no—
157C8×C197C22×C412yescomplemented
158C22×C197—22no—
159C22×C197—41no—
160C22×C197—41no—
161C22×C197C22×D411yescharacteristic
162C2×D197—21no—
163C2×D197—21no—
164C2×D197—22no—
165C2×D197—22no—
166C2×D197—48no—
167C2×D197—41no—
168C2×D197—41no—
169C2×D197—41no—
170C2×D197—41no—
171C2×D197C4×D412yes—
172C4×C197—22no—
173C4×C197—21no—
174C4×C197—41no—
175C4×C197—41no—
176C4×C197AGL(1,ℤ/8)12yescomplemented
177C4×C197C23×C411yescharacteristic
178C4×C197C2×#4111yescharacteristic
179Dic197—21no—
180Dic197—21no—
181Dic197—41no—
182Dic197—41no—
183Dic197C4×D412yes—
184C2×C197—42no—
185C2×C197C2×C4×D411yescharacteristic
186C2×C197C2×AGL(1,ℤ/8)11yescharacteristic
187C2×C197#57511yescharacteristic
188D197—22no—
189D197—42no—
190D197—42no—
191C197C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
192C4×AGL(1,ℤ/8)—1971nomaximal, Sylow
193C2×AGL(1,ℤ/8)—1971no—
194C4×#41—1971no—
195C2×C4×D4—1971no—
196#442—1971no—
197#442—1971no—
198#440—1971no—
199#440—1971no—
200C4×SD16—1971no—
201C4×SD16D19711yescharacteristic, complemented
202C4×D8—1971no—
203C4×D8—1971no—
204#428—1971no—
205#418—1971no—
206#417—1971no—
207C4×M16—1971no—
208C2×#41—1971no—
209C22×D4—1971no—
210C23×C4—3941no—
211AGL(1,ℤ/8)—1978no—
212C2×SD16—1971no—
213C2×SD16C2×D19711yescharacteristic
214C2×D8—1971no—
215C2×D8—1971no—
216C2×M16—1971no—
217C2×M16—1971no—
218C4×Q8—1971no—
219C4×Q8C2×D19711yescharacteristic, complemented
220C4×D4—3941no—
221C4×D4—3941no—
222C4×D4—3941no—
223C4×D4—3941no—
224C4×D4—1971no—
225C4×D4—1971no—
226C4×D4—1971no—
227C4×D4—1971no—
228C4×D4—1971no—
229C4×D4C2×D19711yescharacteristic
230#117—3941no—
231#117—1971no—
232C2×C4⋊C4—1971no—
233C2×C22⋊C4—3941no—
234C2×C42—3941no—
235C2×C42—1971no—
236#107—1971no—
237#107—1971no—
238#106—1971no—
239#106C2×D19711yescharacteristic, complemented
240#103—1971no—
241#103C2×D19711yescharacteristic, complemented
242#102—1971no—
243#102—1971no—
244#102—1971no—
245#102—1971no—
246#102—1971no—
247#102C2×D19711yescharacteristic
248#97—1971no—
249#97—1971no—
250C4×C8—1971no—
251C4×C8C2×D19711yescharacteristic, complemented
252C24—3941no—
253#41—3942no—
254#41—1974no—
255C2×Q8C22×D19711yescharacteristic
256C2×D4—3941no—
257C2×D4—3942no—
258C2×D4—3941no—
259C2×D4—1974no—
260C2×D4—1971no—
261C2×D4—1971no—
262C2×D4C22×D19711yescharacteristic
263C22×C4—21no—
264C22×C4—7884no—
265C22×C4—3941no—
266C22×C4—3941no—
267C22×C4—3941no—
268C22×C4—3941no—
269C22×C4—3941no—
270C22×C4—3941no—
271C22×C4—3941no—
272C22×C4—1971no—
273C22×C4—1971no—
274C22×C4—1971no—
275SD16—1974no—
276SD16C4×D19714yescomplemented
277D8—1974no—
278D8—1974no—
279M16—3942no—
280M16—1974no—
281C2×C8—1971no—
282C2×C8—1971no—
283C2×C8C22×D19711yescharacteristic
284C2×C8C22×D19711yescharacteristic
285C4⋊C4—21no—
286C4⋊C4—3941no—
287C4⋊C4—3941no—
288C4⋊C4—1971no—
289C4⋊C4—1971no—
290C4⋊C4C22×D19711yescharacteristic
291C4⋊C4C22×D19711yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—3941no—
294C22⋊C4—3941no—
295C22⋊C4—3941no—
296C22⋊C4—3941no—
297C22⋊C4—3941no—
298C22⋊C4—3941no—
299C42—21no—
300C42—3941no—
301C42—3941no—
302C42—1971no—
303C42—1971no—
304C42—1971no—
305C42C22×D19711yescharacteristic
306C23—21no—
307C23—7882no—
308C23—7882no—
309C23—3944no—
310C23—3941no—
311C23—3941no—
312C23—1971no—
313Q8—21no—
314Q8C2×C4×D19712yescomplemented
315D4—21no—
316D4—3944no—
317D4—3944no—
318D4—3941no—
319D4—3941no—
320D4—1972no—
321D4—1972no—
322D4C2×C4×D19712yes—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—42no—
327C2×C4—7881no—
328C2×C4—7882no—
329C2×C4—7882no—
330C2×C4—7882no—
331C2×C4—7882no—
332C2×C4—7882no—
333C2×C4—7882no—
334C2×C4—3944no—
335C2×C4—3941no—
336C2×C4—3941no—
337C2×C4—3942no—
338C2×C4—1971no—
339C2×C4—1971no—
340C2×C4—1971no—
341C2×C4—1972no—
342C2×C4—1972no—
343C2×C4D4×D19711yescharacteristic
344C2×C4D4×D19711yescharacteristic
345C2×C4C23×D19711yescharacteristic
346C8—21no—
347C8—3941no—
348C8—1972no—
349C8C2×C4×D19712yescomplemented
350C22—22no—
351C22—41no—
352C22—41no—
353C22—7888no—
354C22—7881no—
355C22—7881no—
356C22—7881no—
357C22—7881no—
358C22—3942no—
359C22—3942no—
360C22—3941no—
361C22—3941no—
362C22—1972no—
363C22C2×D4×D19711yescharacteristic
364C4—21no—
365C4—22no—
366C4—41no—
367C4—41no—
368C4—7881no—
369C4—7881no—
370C4—3941no—
371C4—3941no—
372C4—1972no—
373C4#2026335312yesdirect product factor
374C4C22×C4×D19711yescharacteristic
375C4#41×D19711yescharacteristic
376C2—42no—
377C2—7882no—
378C2—7882no—
379C2—3942no—
380C2C4×D4×D19711yescharacteristic
381C2C2×#2026335311yescharacteristic
382C2#2716187611yescharacteristic
subgroupG/H
centerC2×C4D4×D197
commutatorC4×C197C23×C4
FrattiniC2×C4C23×D197
FittingC4×SD16×C197C2
socleC22×C197C22×D4
prime radicalC2×#20263353C2
cosocleC2×C4×C197C24
hypercenterC4×SD16D197
hypocenterC197C4×AGL(1,ℤ/8)
LCSG ▷ C4×C197 ▷ C2×C197 ▷ C197
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. C4×#15691359C2semidirect
3. C4×D4×D197C2semidirect
4. #27161190C2semidirect
5. #27161188C2semidirect
6. #27161182C2semidirect
7. #27161180C2semidirect
8. C4×#15691345C2semidirect
9. C4×D1576C2semidirect
10. C4×#15691343C2semidirect
11. #27161118C2semidirect
12. #27161082C2semidirect
13. #27161079C2semidirect
14. C4×#15691341C2semidirect
15. C4×SD16×C197C2semidirect
19. #20263353C4direct (N × H)
25. Q8×Dic197C22semidirect
28. C4×D788C22semidirect
32. #20263288C22semidirect
41. #20263260C22semidirect
42. #20263259C22semidirect
43. #20263257C22semidirect
44. #20263250C22semidirect
46. #20263248C22semidirect
49. #20263246C22semidirect
50. #20263236C22semidirect
51. #20263236C22semidirect
52. C4×#13096802C22semidirect
54. C4×Q8×C197C22semidirect
56. #106×C197C22semidirect
57. #103×C197C22semidirect
59. C4×C8×C197C22semidirect
62. #15691359C2×C4semidirect
68. D4×D197C2×C4semidirect
80. #15691345C2×C4semidirect
81. D1576C2×C4semidirect
82. #15691343C2×C4semidirect
84. #15691341C2×C4semidirect
105. SD16×C197C2×C4semidirect
124. D788C22×C4semidirect
143. #13096802C22×C4semidirect
146. Q8×C197C22×C4semidirect
157. C8×C197C22×C4semidirect
176. C4×C197AGL(1,ℤ/8)semidirect
191. C197C4×AGL(1,ℤ/8)semidirect
201. C4×SD16D197semidirect
219. C4×Q8C2×D197semidirect
239. #106C2×D197semidirect
241. #103C2×D197semidirect
251. C4×C8C2×D197semidirect
276. SD16C4×D197semidirect
314. Q8C2×C4×D197semidirect
349. C8C2×C4×D197semidirect
373. C4#20263353direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#202633532
C4×#156913592
C4×D4×D1972
#271611902
#271611882
#271611822
#271611802
C4×#156913452
C4×D15762
C4×#156913432
#271611182
#271610822
#271610792
C4×#156913412
C4×SD16×C1972
C4×AGL(1,ℤ/8)197