Finite Group Databasebeta

← C2×#23757442 #34109461

Subgroups — C2×#23757442 #34109461

Order 20096.

844 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 844 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19097817C211yesmaximal, characteristic, complemented
2C2×#19097799C211yesmaximal, characteristic, complemented
3C2×#19097796C211yesmaximal, characteristic, complemented
4C2×#19097768C211yesmaximal, characteristic, complemented
5#23757442C218yesmaximal, direct product factor
6C2×#19097699C211yesmaximal, characteristic, complemented
7C2×#19097687C211yesmaximal, characteristic, complemented
8C2×#104×C157C211yesmaximal, characteristic, complemented
9#19097817—22no—
10#19097817—22no—
11#19097817—22no—
12#19097817C2214yescomplemented
13C2×#14578955—21no—
14C2×#14578954—21no—
15C2×#14578954C2211yescharacteristic
16C22×D628—21no—
17C22×D628—22no—
18C22×D628C2211yescharacteristic
19C22×D628C2211yescharacteristic, complemented
20C2×D4×D157—21no—
21C2×D4×D157—22no—
22#19097799—22no—
23#19097799C2214yescomplemented
24#19097796—22no—
25#19097796C2214yescomplemented
26C2×#14578943—21no—
27C2×#14578941—21no—
28C2×D1256—21no—
29C2×#14578939—21no—
30C2×#14578938C2211yescharacteristic, complemented
31#19097768—22no—
32#19097768C2214yescomplemented
33#19097699C2214yescomplemented
34#19097687C2214yescomplemented
35C2×#41×C157C2211yescharacteristic
36C2×M16×C157C2211yescharacteristic, complemented
37C2×C42×C157C2211yescharacteristic, complemented
38#104×C157C2214yescomplemented
39C23×D157—22no—
40C23×D157—21no—
41C23×D157D412yes—
42#14578955—24no—
43#14578955—24no—
44#14578954—24no—
45#14578954—24no—
46#14578954—21no—
47#14578954—21no—
48#14578954D412yescomplemented
49#14578954C2312yes—
50C2×Dic314D411yescharacteristic, complemented
51C2×D628—22no—
52C2×D628—24no—
53C2×D628—24no—
54C2×D628—28no—
55C2×D628—21no—
56C2×D628—21no—
57C2×D628—21no—
58C2×D628—21no—
59C2×D628—21no—
60C2×D628—21no—
61C2×D628—21no—
62C2×D628—21no—
63C2×D628—21no—
64C2×D628—48no—
65C2×D628D412yes—
66C2×D628D411yescharacteristic, complemented
67C2×D628C2312yes—
68C2×D628C2312yescomplemented
69C2×C22⋊D157—22no—
70C2×C22⋊D157—21no—
71D4×D157—28no—
72D4×D157—24no—
73D4×D157—28no—
74D4×D157—24no—
75C2×C4×D157—22no—
76C2×C4×D157—21no—
77#14578943—24no—
78#14578941—24no—
79D1256—24no—
80#14578939—24no—
81#14578938—21no—
82#14578938C2312yescomplemented
83C2×#11929434—21no—
84#41×C157—21no—
85#41×C157—21no—
86#41×C157D412yescomplemented
87#41×C157C2312yes—
88C2×Q8×C157D411yescharacteristic, complemented
89C2×D4×C157—21no—
90C2×D4×C157D411yescharacteristic, complemented
91C22×C4×C157—21no—
92C22×C4×C157—21no—
93C22×C4×C157C2311yescharacteristic
94M16×C157—21no—
95M16×C157C2312yescomplemented
96C2×C8×C157—21no—
97C42×C157—21no—
98C42×C157C2312yescomplemented
99C22×D157—22no—
100C22×D157—21no—
101C22×D157—28no—
102C22×D157—22no—
103C22×D157—22no—
104C22×D157—44no—
105C22×D157—44no—
106C22×D157—41no—
107C22×D157—41no—
108C22×D157—84no—
109C22×D157C2×D414yes—
110Dic314—21no—
111Dic314C2×D412yescomplemented
112D628—28no—
113D628—22no—
114D628—22no—
115D628—21no—
116D628—22no—
117D628—22no—
118D628—22no—
119D628—22no—
120D628—416no—
121D628—41no—
122D628—41no—
123D628C2×D412yescomplemented
124C22⋊D157—28no—
125C22⋊D157—22no—
126C22⋊D157—22no—
127C2×Dic157—21no—
128C4×D157—28no—
129C4×D157—22no—
130C4×D157—22no—
131#11929434—22no—
132C23×C157—21no—
133C23×C157C2×D411yescharacteristic
134Q8×C157—21no—
135Q8×C157C2×D412yescomplemented
136D4×C157—22no—
137D4×C157—22no—
138D4×C157—21no—
139D4×C157C2×D412yescomplemented
140C2×C4×C157—24no—
141C2×C4×C157—21no—
142C2×C4×C157—22no—
143C2×C4×C157—22no—
144C2×C4×C157—22no—
145C2×C4×C157C2×D411yescharacteristic
146C2×C4×C157C2×D411yescharacteristic
147C2×C4×C157C2×D411yescharacteristic
148C2×C4×C157C2×D411yescharacteristic
149C2×C4×C157C2×D411yescharacteristic
150C2×C4×C157C2411yescharacteristic
151C8×C157—22no—
152C22×C157—22no—
153C22×C157—22no—
154C22×C157—42no—
155C22×C157#12011yescharacteristic
156C22×C157#12011yescharacteristic
157C22×C157C22×D411yescharacteristic
158C2×D157—24no—
159C2×D157—22no—
160C2×D157—44no—
161C2×D157—42no—
162C2×D157—44no—
163C2×D157—44no—
164C2×D157—42no—
165C2×D157—82no—
166C2×D157—88no—
167C2×D157—82no—
168C2×D157—82no—
169C4×C157—24no—
170C4×C157—22no—
171C4×C157#12011yescharacteristic
172C4×C157#12011yescharacteristic
173C4×C157C22×D411yescharacteristic
174C4×C157C22×D411yescharacteristic
175Dic157—22no—
176C2×C157—21no—
177C2×C157—21no—
178C2×C157—42no—
179C2×C157#45312yescomplemented
180C2×C157C2×#12011yescharacteristic
181D157—44no—
182D157—42no—
183D157—82no—
184C157C2×#45311yescharacteristic, complemented, Sylow
185C2×#453—1571nomaximal, Sylow
186C2×H(5,𝔽2)—1571no—
187C2×AGL(1,ℤ/8)—1571no—
188C2×AGL(1,ℤ/8)—1571no—
189C2×#127—1571no—
190#453—1578no—
191C2×#104—1571no—
192C2×#104D15711yescharacteristic, complemented
193C2×#100—1571no—
194H(5,𝔽2)—3142no—
195H(5,𝔽2)—3142no—
196H(5,𝔽2)—3142no—
197H(5,𝔽2)—1574no—
198C2×#41—3141no—
199C2×#41—3141no—
200C2×#41—1571no—
201C2×#41C2×D15711yescharacteristic
202C22×D4—3141no—
203C22×D4—3142no—
204C22×D4—3142no—
205C22×D4—3141no—
206C22×D4—1571no—
207C22×D4—1571no—
208AGL(1,ℤ/8)—3142no—
209AGL(1,ℤ/8)—3142no—
210AGL(1,ℤ/8)—1574no—
211AGL(1,ℤ/8)—1574no—
212C2×SD16—3141no—
213C2×SD16—3141no—
214C2×D8—3141no—
215C2×D8—3141no—
216C2×M16—1571no—
217C2×M16C2×D15711yescharacteristic, complemented
218#127—3142no—
219#127—1574no—
220C2×C42C2×D15711yescharacteristic, complemented
221#104—1574no—
222#104C2×D15714yescomplemented
223#100—1574no—
224C24—3142no—
225C24—3141no—
226C24—1572no—
227#41—21no—
228#41—21no—
229#41—3144no—
230#41—3144no—
231#41—3144no—
232#41—3144no—
233#41—3141no—
234#41—3141no—
235#41—1572no—
236#41—1572no—
237#41D62812yescomplemented
238#41C22×D15712yes—
239C2×Q8—1571no—
240C2×Q8D62811yescharacteristic, complemented
241C2×D4—21no—
242C2×D4—3142no—
243C2×D4—3144no—
244C2×D4—3144no—
245C2×D4—3148no—
246C2×D4—3148no—
247C2×D4—3144no—
248C2×D4—3148no—
249C2×D4—3142no—
250C2×D4—3141no—
251C2×D4—3144no—
252C2×D4—3141no—
253C2×D4—3141no—
254C2×D4—3141no—
255C2×D4—3141no—
256C2×D4—3141no—
257C2×D4—3141no—
258C2×D4—3141no—
259C2×D4—3141no—
260C2×D4—3141no—
261C2×D4—6288no—
262C2×D4—1572no—
263C2×D4—1571no—
264C2×D4—1572no—
265C2×D4—1572no—
266C2×D4D62811yescharacteristic, complemented
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—3142no—
270C22×C4—3141no—
271C22×C4C22×D15711yescharacteristic
272SD16—3144no—
273SD16—3144no—
274D8—3144no—
275D8—3144no—
276M16—21no—
277M16—3141no—
278M16—1572no—
279M16C22×D15712yescomplemented
280C2×C8—21no—
281C2×C8—3141no—
282C42—21no—
283C42C22×D15712yescomplemented
284C23—21no—
285C23—3148no—
286C23—3142no—
287C23—3141no—
288C23—3142no—
289C23—3142no—
290C23—6284no—
291C23—6284no—
292C23—6281no—
293C23—6281no—
294C23—1574no—
295C23—12564no—
296C23D4×D15711yescharacteristic
297Q8—21no—
298Q8—3141no—
299Q8—1572no—
300Q8C2×D62812yescomplemented
301D4—22no—
302D4—22no—
303D4—21no—
304D4—3148no—
305D4—3148no—
306D4—3142no—
307D4—3142no—
308D4—3142no—
309D4—3141no—
310D4—3142no—
311D4—3142no—
312D4—3142no—
313D4—3142no—
314D4—3142no—
315D4—62816no—
316D4—6281no—
317D4—6281no—
318D4—1572no—
319D4C2×D62812yescomplemented
320C2×C4—24no—
321C2×C4—21no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—3148no—
326C2×C4—3141no—
327C2×C4—3142no—
328C2×C4—3142no—
329C2×C4D4×D15711yescharacteristic
330C2×C4D4×D15711yescharacteristic
331C2×C4D4×D15711yescharacteristic
332C2×C4C2×D62811yescharacteristic
333C2×C4C2×D62811yescharacteristic
334C2×C4C23×D15711yescharacteristic
335C8—22no—
336C8—3142no—
337C22—22no—
338C22—22no—
339C22—42no—
340C22—3144no—
341C22—3142no—
342C22—6284no—
343C22—6284no—
344C22—6284no—
345C22—6282no—
346C22—6282no—
347C22—12562no—
348C22—12562no—
349C22—12568no—
350C22—12562no—
351C22#1909774111yescharacteristic
352C22#1909774111yescharacteristic
353C22C2×D4×D15711yescharacteristic
354C4—24no—
355C4—22no—
356C4—3142no—
357C4#1909774111yescharacteristic
358C4#1909774111yescharacteristic
359C4C2×D4×D15711yescharacteristic
360C4C22×D62811yescharacteristic
361C2—21no—
362C2—21no—
363C2—42no—
364C2—6284no—
365C2—6282no—
366C2—12562no—
367C2#2375744212yesdirect product factor
368C2C2×#1909774111yescharacteristic
subgroupG/H
centerC22#19097741
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
FittingC2×#104×C157C2
socleC22×C157#120
hypercenterC2×#104D157
hypocenterC157C2×#453
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
1. C2×#19097817C2semidirect
2. C2×#19097799C2semidirect
3. C2×#19097796C2semidirect
4. C2×#19097768C2semidirect
5. #23757442C2direct (N × H)
6. C2×#19097699C2semidirect
7. C2×#19097687C2semidirect
8. C2×#104×C157C2semidirect
12. #19097817C22semidirect
19. C22×D628C22semidirect
23. #19097799C22semidirect
25. #19097796C22semidirect
30. C2×#14578938C22semidirect
32. #19097768C22semidirect
33. #19097699C22semidirect
34. #19097687C22semidirect
36. C2×M16×C157C22semidirect
37. C2×C42×C157C22semidirect
38. #104×C157C22semidirect
48. #14578954D4semidirect
50. C2×Dic314D4semidirect
66. C2×D628D4semidirect
68. C2×D628C23semidirect
82. #14578938C23semidirect
86. #41×C157D4semidirect
88. C2×Q8×C157D4semidirect
90. C2×D4×C157D4semidirect
95. M16×C157C23semidirect
98. C42×C157C23semidirect
111. Dic314C2×D4semidirect
123. D628C2×D4semidirect
135. Q8×C157C2×D4semidirect
139. D4×C157C2×D4semidirect
179. C2×C157#453semidirect
184. C157C2×#453semidirect
192. C2×#104D157semidirect
217. C2×M16C2×D157semidirect
220. C2×C42C2×D157semidirect
222. #104C2×D157semidirect
237. #41D628semidirect
240. C2×Q8D628semidirect
266. C2×D4D628semidirect
279. M16C22×D157semidirect
283. C42C22×D157semidirect
300. Q8C2×D628semidirect
319. D4C2×D628semidirect
367. C2#23757442direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190978172
C2×#190977992
C2×#190977962
C2×#190977682
#237574422
C2×#190976992
C2×#190976872
C2×#104×C1572
C2×#453157