Finite Group Databasebeta

← C4×#19097798 #34108945

Subgroups — C4×#19097798 #34108945

Order 20096.

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×#19097798C211yesmaximal, characteristic
2C4×#14578955C211yesmaximal, characteristic, complemented
3C4×D4×D157C211yesmaximal, characteristic, complemented
4#23757384C211yesmaximal, characteristic, complemented
5#23757382C211yesmaximal, characteristic, complemented
6#23757376C211yesmaximal, characteristic, complemented
7#23757374C211yesmaximal, characteristic, complemented
8C4×#14578941C211yesmaximal, characteristic, complemented
9C4×D1256C211yesmaximal, characteristic, complemented
10C4×#14578939C211yesmaximal, characteristic, complemented
11#23757312C211yesmaximal, characteristic, complemented
12#23757276C211yesmaximal, characteristic, complemented
13#23757273C211yesmaximal, characteristic, complemented
14C4×#14578937C211yesmaximal, characteristic, complemented
15C4×SD16×C157C211yesmaximal, characteristic, complemented
16C2×#14578955C2211yescharacteristic
17C2×D4×D157C2211yescharacteristic
18C22×C4×D157—21no—
19#19097798C418yesdirect product factor
20C2×#14578941C2211yescharacteristic
21C2×D1256C2211yescharacteristic
22C2×#14578939C2211yescharacteristic
23C2×#14578937C2211yescharacteristic
24C2×#14578937C2211yescharacteristic
25Q8×Dic157C2211yescharacteristic, complemented
26C4×D628—21no—
27C4×D628C2211yescharacteristic
28C4×D628C2211yescharacteristic, complemented
29D4×Dic157C2211yescharacteristic
30#19097733—21no—
31#19097733C2211yescharacteristic
32#19097733C2211yescharacteristic, complemented
33C4×C22⋊D157—21no—
34#19097731—21no—
35#19097729—21no—
36#19097729C2211yescharacteristic
37C4⋊C4×D157C2211yescharacteristic
38C22⋊C4×D157—21no—
39C42×D157—21no—
40C42×D157C2211yescharacteristic
41#19097705C2211yescharacteristic, complemented
42#19097704C2211yescharacteristic, complemented
43#19097702C2211yescharacteristic, complemented
44#19097695C2211yescharacteristic, complemented
45#19097693C2211yescharacteristic
46#19097693C2211yescharacteristic, complemented
47#19097692C2211yescharacteristic
48#19097691C2211yescharacteristic
49#19097691C2211yescharacteristic, complemented
50#19097681C2211yescharacteristic, complemented
51#19097681C2211yescharacteristic, complemented
52C4×#11929434C2211yescharacteristic, complemented
53C2×SD16×C157C2211yescharacteristic
54C4×Q8×C157C2211yescharacteristic, complemented
55C4×D4×C157C2211yescharacteristic
56#106×C157C2211yescharacteristic, complemented
57#103×C157C2211yescharacteristic, complemented
58#102×C157C2211yescharacteristic
59C4×C8×C157C2211yescharacteristic, complemented
60C23×D157—21no—
61#14578955—22no—
62#14578955C2×C414yescomplemented
63C2×D628—21no—
64C2×D628C2311yescharacteristic
65C2×D628C2311yescharacteristic
66C2×C22⋊D157—21no—
67D4×D157—22no—
68D4×D157C2×C414yescomplemented
69C22×Dic157—21no—
70C2×C4×D157—21no—
71C2×C4×D157—21no—
72C2×C4×D157—21no—
73C2×C4×D157—21no—
74C2×C4×D157—21no—
75C2×C4×D157—21no—
76C2×C4×D157—44no—
77C2×C4×D157D411yescharacteristic
78C2×C4×D157D411yescharacteristic
79C2×C4×D157C2311yescharacteristic
80#14578941C2×C414yescomplemented
81D1256C2×C414yescomplemented
82#14578939C2×C414yescomplemented
83#14578937—22no—
84#14578937C2×C414yescomplemented
85C2×#11929434C2311yescharacteristic
86C2×#11929434C2311yescharacteristic
87C4⋊Dic157—21no—
88C4⋊Dic157C2311yescharacteristic
89C4⋊Dic157C2311yescharacteristic
90#14578933—21no—
91C22⋊Dic157—21no—
92#14578931—21no—
93#14578931—21no—
94#14578931—21no—
95#14578931—21no—
96#14578931—21no—
97C4×Dic157—21no—
98C4×Dic157—21no—
99C4×Dic157D411yescharacteristic
100C4×Dic157D411yescharacteristic
101C4×Dic157C2311yescharacteristic
102C2×Q8×C157C2311yescharacteristic
103C2×D4×C157C2311yescharacteristic
104C22×C4×C157—21no—
105SD16×C157C2×C414yescomplemented
106C2×C8×C157C2311yescharacteristic
107C2×C8×C157C2311yescharacteristic
108C4⋊C4×C157—21no—
109C4⋊C4×C157C2311yescharacteristic
110C4⋊C4×C157C2311yescharacteristic
111C22⋊C4×C157—21no—
112C42×C157—21no—
113C42×C157C2311yescharacteristic
114C22×D157—21no—
115C22×D157—21no—
116C22×D157—24no—
117C22×D157—42no—
118C22×D157—42no—
119C22×D157C2×D411yescharacteristic
120D628—24no—
121D628—21no—
122D628—21no—
123D628C22×C412yes—
124D628C22×C412yescomplemented
125C22⋊D157—24no—
126C2×Dic157—21no—
127C2×Dic157—21no—
128C2×Dic157—42no—
129C2×Dic157C2×D411yescharacteristic
130C2×Dic157C2×D411yescharacteristic
131C2×Dic157C2×D411yescharacteristic
132C4×D157—22no—
133C4×D157—24no—
134C4×D157—41no—
135C4×D157—42no—
136C4×D157—42no—
137C4×D157—42no—
138C4×D157—42no—
139C4×D157—42no—
140C4×D157C22×C412yes—
141C4×D157#4112yes—
142#11929434—21no—
143#11929434C22×C412yescomplemented
144C23×C157—21no—
145Q8×C157—21no—
146Q8×C157C22×C412yescomplemented
147D4×C157—21no—
148D4×C157C22×C412yes—
149C2×C4×C157—21no—
150C2×C4×C157—21no—
151C2×C4×C157—21no—
152C2×C4×C157—42no—
153C2×C4×C157C2×D411yescharacteristic
154C2×C4×C157C2×D411yescharacteristic
155C2×C4×C157C2411yescharacteristic
156C8×C157—21no—
157C8×C157C22×C412yescomplemented
158C22×C157—22no—
159C22×C157—41no—
160C22×C157—41no—
161C22×C157C22×D411yescharacteristic
162C2×D157—21no—
163C2×D157—21no—
164C2×D157—22no—
165C2×D157—22no—
166C2×D157—48no—
167C2×D157—41no—
168C2×D157—41no—
169C2×D157—41no—
170C2×D157—41no—
171C2×D157C4×D412yes—
172C4×C157—22no—
173C4×C157—21no—
174C4×C157—41no—
175C4×C157—41no—
176C4×C157AGL(1,ℤ/8)12yescomplemented
177C4×C157C23×C411yescharacteristic
178C4×C157C2×#4111yescharacteristic
179Dic157—21no—
180Dic157—21no—
181Dic157—41no—
182Dic157—41no—
183Dic157C4×D412yes—
184C2×C157—42no—
185C2×C157C2×C4×D411yescharacteristic
186C2×C157C2×AGL(1,ℤ/8)11yescharacteristic
187C2×C157#57511yescharacteristic
188D157—22no—
189D157—42no—
190D157—42no—
191C157C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
192C4×AGL(1,ℤ/8)—1571nomaximal, Sylow
193C2×AGL(1,ℤ/8)—1571no—
194C4×#41—1571no—
195C2×C4×D4—1571no—
196#442—1571no—
197#442—1571no—
198#440—1571no—
199#440—1571no—
200C4×SD16—1571no—
201C4×SD16D15711yescharacteristic, complemented
202C4×D8—1571no—
203C4×D8—1571no—
204#428—1571no—
205#418—1571no—
206#417—1571no—
207C4×M16—1571no—
208C2×#41—1571no—
209C22×D4—1571no—
210C23×C4—3141no—
211AGL(1,ℤ/8)—1578no—
212C2×SD16—1571no—
213C2×SD16C2×D15711yescharacteristic
214C2×D8—1571no—
215C2×D8—1571no—
216C2×M16—1571no—
217C2×M16—1571no—
218C4×Q8—1571no—
219C4×Q8C2×D15711yescharacteristic, complemented
220C4×D4—3141no—
221C4×D4—3141no—
222C4×D4—3141no—
223C4×D4—3141no—
224C4×D4—1571no—
225C4×D4—1571no—
226C4×D4—1571no—
227C4×D4—1571no—
228C4×D4—1571no—
229C4×D4C2×D15711yescharacteristic
230#117—3141no—
231#117—1571no—
232C2×C4⋊C4—1571no—
233C2×C22⋊C4—3141no—
234C2×C42—3141no—
235C2×C42—1571no—
236#107—1571no—
237#107—1571no—
238#106—1571no—
239#106C2×D15711yescharacteristic, complemented
240#103—1571no—
241#103C2×D15711yescharacteristic, complemented
242#102—1571no—
243#102—1571no—
244#102—1571no—
245#102—1571no—
246#102—1571no—
247#102C2×D15711yescharacteristic
248#97—1571no—
249#97—1571no—
250C4×C8—1571no—
251C4×C8C2×D15711yescharacteristic, complemented
252C24—3141no—
253#41—3142no—
254#41—1574no—
255C2×Q8C22×D15711yescharacteristic
256C2×D4—3141no—
257C2×D4—3142no—
258C2×D4—3141no—
259C2×D4—1574no—
260C2×D4—1571no—
261C2×D4—1571no—
262C2×D4C22×D15711yescharacteristic
263C22×C4—21no—
264C22×C4—3141no—
265C22×C4—3141no—
266C22×C4—3141no—
267C22×C4—3141no—
268C22×C4—3141no—
269C22×C4—3141no—
270C22×C4—3141no—
271C22×C4—6284no—
272C22×C4—1571no—
273C22×C4—1571no—
274C22×C4—1571no—
275SD16—1574no—
276SD16C4×D15714yescomplemented
277D8—1574no—
278D8—1574no—
279M16—3142no—
280M16—1574no—
281C2×C8—1571no—
282C2×C8—1571no—
283C2×C8C22×D15711yescharacteristic
284C2×C8C22×D15711yescharacteristic
285C4⋊C4—21no—
286C4⋊C4—3141no—
287C4⋊C4—3141no—
288C4⋊C4—1571no—
289C4⋊C4—1571no—
290C4⋊C4C22×D15711yescharacteristic
291C4⋊C4C22×D15711yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—3141no—
294C22⋊C4—3141no—
295C22⋊C4—3141no—
296C22⋊C4—3141no—
297C22⋊C4—3141no—
298C22⋊C4—3141no—
299C42—21no—
300C42—3141no—
301C42—3141no—
302C42—1571no—
303C42—1571no—
304C42—1571no—
305C42C22×D15711yescharacteristic
306C23—21no—
307C23—3144no—
308C23—3141no—
309C23—3141no—
310C23—6282no—
311C23—6282no—
312C23—1571no—
313Q8—21no—
314Q8C2×C4×D15712yescomplemented
315D4—21no—
316D4—3144no—
317D4—3144no—
318D4—3141no—
319D4—3141no—
320D4—1572no—
321D4—1572no—
322D4C2×C4×D15712yes—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—42no—
327C2×C4—3144no—
328C2×C4—3142no—
329C2×C4—3141no—
330C2×C4—3141no—
331C2×C4—6281no—
332C2×C4—6282no—
333C2×C4—6282no—
334C2×C4—6282no—
335C2×C4—6282no—
336C2×C4—6282no—
337C2×C4—6282no—
338C2×C4—1571no—
339C2×C4—1571no—
340C2×C4—1571no—
341C2×C4—1572no—
342C2×C4—1572no—
343C2×C4D4×D15711yescharacteristic
344C2×C4D4×D15711yescharacteristic
345C2×C4C23×D15711yescharacteristic
346C8—21no—
347C8—3141no—
348C8—1572no—
349C8C2×C4×D15712yescomplemented
350C22—22no—
351C22—41no—
352C22—41no—
353C22—3141no—
354C22—3141no—
355C22—3142no—
356C22—3142no—
357C22—6288no—
358C22—6281no—
359C22—6281no—
360C22—6281no—
361C22—6281no—
362C22—1572no—
363C22C2×D4×D15711yescharacteristic
364C4—22no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—3141no—
369C4—3141no—
370C4—6281no—
371C4—6281no—
372C4—1572no—
373C4#1909779812yesdirect product factor
374C4C22×C4×D15711yescharacteristic
375C4#41×D15711yescharacteristic
376C2—42no—
377C2—3142no—
378C2—6282no—
379C2—6282no—
380C2C4×D4×D15711yescharacteristic
381C2C2×#1909779811yescharacteristic
382C2#2375807011yescharacteristic
subgroupG/H
centerC2×C4D4×D157
commutatorC4×C157C23×C4
FrattiniC2×C4C23×D157
FittingC4×SD16×C157C2
socleC22×C157C22×D4
prime radicalC2×#19097798C2
cosocleC2×C4×C157C24
hypercenterC4×SD16D157
hypocenterC157C4×AGL(1,ℤ/8)
LCSG ▷ C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. C4×#14578955C2semidirect
3. C4×D4×D157C2semidirect
4. #23757384C2semidirect
5. #23757382C2semidirect
6. #23757376C2semidirect
7. #23757374C2semidirect
8. C4×#14578941C2semidirect
9. C4×D1256C2semidirect
10. C4×#14578939C2semidirect
11. #23757312C2semidirect
12. #23757276C2semidirect
13. #23757273C2semidirect
14. C4×#14578937C2semidirect
15. C4×SD16×C157C2semidirect
19. #19097798C4direct (N × H)
25. Q8×Dic157C22semidirect
28. C4×D628C22semidirect
32. #19097733C22semidirect
41. #19097705C22semidirect
42. #19097704C22semidirect
43. #19097702C22semidirect
44. #19097695C22semidirect
46. #19097693C22semidirect
49. #19097691C22semidirect
50. #19097681C22semidirect
51. #19097681C22semidirect
52. C4×#11929434C22semidirect
54. C4×Q8×C157C22semidirect
56. #106×C157C22semidirect
57. #103×C157C22semidirect
59. C4×C8×C157C22semidirect
62. #14578955C2×C4semidirect
68. D4×D157C2×C4semidirect
80. #14578941C2×C4semidirect
81. D1256C2×C4semidirect
82. #14578939C2×C4semidirect
84. #14578937C2×C4semidirect
105. SD16×C157C2×C4semidirect
124. D628C22×C4semidirect
143. #11929434C22×C4semidirect
146. Q8×C157C22×C4semidirect
157. C8×C157C22×C4semidirect
176. C4×C157AGL(1,ℤ/8)semidirect
191. C157C4×AGL(1,ℤ/8)semidirect
201. C4×SD16D157semidirect
219. C4×Q8C2×D157semidirect
239. #106C2×D157semidirect
241. #103C2×D157semidirect
251. C4×C8C2×D157semidirect
276. SD16C4×D157semidirect
314. Q8C2×C4×D157semidirect
349. C8C2×C4×D157semidirect
373. C4#19097798direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190977982
C4×#145789552
C4×D4×D1572
#237573842
#237573822
#237573762
#237573742
C4×#145789412
C4×D12562
C4×#145789392
#237573122
#237572762
#237572732
C4×#145789372
C4×SD16×C1572
C4×AGL(1,ℤ/8)157