Finite Group Databasebeta

← #34108961

Subgroups — #34108961

Order 20096.

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×#19097795C211yesmaximal, characteristic
2#23757752C211yesmaximal, characteristic, complemented
3#23757745C211yesmaximal, characteristic, complemented
4#23757385C211yesmaximal, characteristic, complemented
5#23757383C211yesmaximal, characteristic, complemented
6#23757373C211yesmaximal, characteristic, complemented
7#23757372C211yesmaximal, characteristic, complemented
8#23757364C211yesmaximal, characteristic, complemented
9C4×#14578943C211yesmaximal, characteristic, complemented
10#23757353C211yesmaximal, characteristic, complemented
11#23757314C211yesmaximal, characteristic, complemented
12#23757266C211yesmaximal, characteristic, complemented
13#102×D157C211yesmaximal, characteristic, complemented
14#23757227C211yesmaximal, characteristic, complemented
15C4×D8×C157C211yesmaximal, characteristic, complemented
16C2×#14578953C2211yescharacteristic
17C2×D4×D157C2211yescharacteristic
18#19097795C418yescomplemented
19C2×#14578943C2211yescharacteristic
20C2×#14578942C2211yescharacteristic
21C2×#14578939C2211yescharacteristic
22C2×#14578937C2211yescharacteristic
23C2×C8×D157C2211yescharacteristic
24C4×Dic314C2211yescharacteristic, complemented
25#19097736C2211yescharacteristic, complemented
26C4×D628C2211yescharacteristic
27D4×Dic157C2211yescharacteristic
28D4×Dic157C2211yescharacteristic, complemented
29#19097733C2211yescharacteristic
30C4×C22⋊D157—21no—
31C4×C22⋊D157—21no—
32#19097731—21no—
33#19097731—21no—
34#19097729C2211yescharacteristic
35#19097728C2211yescharacteristic
36#19097727—21no—
37C2×#14578933—21no—
38C4⋊C4×D157C2211yescharacteristic
39C2×#14578931—21no—
40C22⋊C4×D157—21no—
41#19097704C2211yescharacteristic, complemented
42#19097703C2211yescharacteristic, complemented
43#19097702C2211yescharacteristic, complemented
44#19097696C2211yescharacteristic, complemented
45#19097694C2211yescharacteristic, complemented
46#19097693C2211yescharacteristic
47#19097692C2211yescharacteristic
48#19097692C2211yescharacteristic, complemented
49#19097691C2211yescharacteristic
50#19097682C2211yescharacteristic, complemented
51#19097681C2211yescharacteristic, complemented
52C8×Dic157C2211yescharacteristic, complemented
53C2×D8×C157C2211yescharacteristic
54C4×D4×C157C2211yescharacteristic
55C4×D4×C157C2211yescharacteristic, complemented
56#107×C157C2211yescharacteristic, complemented
57#102×C157C2211yescharacteristic
58#102×C157C2211yescharacteristic, complemented
59C4×C8×C157C2211yescharacteristic, complemented
60C23×D157—21no—
61#14578953—22no—
62#14578953C2×C414yescomplemented
63C2×Dic314C2311yescharacteristic
64C2×D628C2311yescharacteristic
65C2×C22⋊D157—21no—
66C2×C22⋊D157—21no—
67D4×D157—22no—
68D4×D157C2×C414yescomplemented
69C22×Dic157—21no—
70C22×Dic157—21no—
71C22×Dic157—21no—
72C2×C4×D157—21no—
73C2×C4×D157—21no—
74C2×C4×D157—21no—
75C2×C4×D157C2311yescharacteristic
76#14578943C2×C414yescomplemented
77#14578942C2×C414yescomplemented
78#14578939C2×C414yescomplemented
79#14578937C2×C414yescomplemented
80C2×#11929434C2311yescharacteristic
81C2×#11929434C2311yescharacteristic
82C8×D157—22no—
83C4⋊Dic157C2311yescharacteristic
84C4⋊Dic157C2311yescharacteristic
85#14578933—21no—
86#14578933—21no—
87#14578933—21no—
88#14578933D411yescharacteristic
89#14578933D411yescharacteristic
90C22⋊Dic157—21no—
91C22⋊Dic157—21no—
92#14578931—21no—
93#14578931—21no—
94#14578931—21no—
95#14578931D411yescharacteristic
96#14578931D411yescharacteristic
97C4×Dic157—21no—
98C4×Dic157—21no—
99C4×Dic157—21no—
100C4×Dic157C2311yescharacteristic
101C2×D4×C157C2311yescharacteristic
102C2×D4×C157C2311yescharacteristic
103C22×C4×C157—21no—
104C22×C4×C157—21no—
105D8×C157C2×C414yescomplemented
106C2×C8×C157C2311yescharacteristic
107C2×C8×C157C2311yescharacteristic
108C4⋊C4×C157C2311yescharacteristic
109C4⋊C4×C157C2311yescharacteristic
110C22⋊C4×C157—21no—
111C22⋊C4×C157—21no—
112C42×C157C2311yescharacteristic
113C22×D157—21no—
114C22×D157—24no—
115C22×D157—81no—
116C22×D157—81no—
117C22×D157C2×D411yescharacteristic
118Dic314—21no—
119Dic314C22×C412yes—
120D628—21no—
121D628C22×C412yes—
122C22⋊D157—24no—
123C22⋊D157—24no—
124C2×Dic157—21no—
125C2×Dic157—24no—
126C2×Dic157—21no—
127C2×Dic157—21no—
128C2×Dic157—81no—
129C2×Dic157—81no—
130C2×Dic157C2×D411yescharacteristic
131C2×Dic157C2×D411yescharacteristic
132C2×Dic157C2×D411yescharacteristic
133C4×D157—81no—
134C4×D157—81no—
135C4×D157—81no—
136C4×D157C22×C412yes—
137C4×D157#4112yes—
138#11929434—21no—
139#11929434C22×C412yes—
140C23×C157—21no—
141C23×C157—21no—
142D4×C157—21no—
143D4×C157—21no—
144D4×C157C22×C412yes—
145D4×C157C22×C412yes—
146C2×C4×C157—21no—
147C2×C4×C157—21no—
148C2×C4×C157—81no—
149C2×C4×C157—81no—
150C2×C4×C157C2×D411yescharacteristic
151C2×C4×C157C2×D411yescharacteristic
152C2×C4×C157C2411yescharacteristic
153C8×C157—21no—
154C8×C157C22×C412yes—
155C22×C157—22no—
156C22×C157—22no—
157C22×C157—41no—
158C22×C157—41no—
159C22×C157—41no—
160C22×C157—41no—
161C22×C157C22×D411yescharacteristic
162C2×D157—21no—
163C2×D157—21no—
164C2×D157—22no—
165C2×D157—41no—
166C2×D157—41no—
167C2×D157—84no—
168C2×D157C4×D412yes—
169C4×C157—21no—
170C4×C157—21no—
171C4×C157—41no—
172C4×C157—41no—
173C4×C157C23×C411yescharacteristic
174C4×C157C2×#4111yescharacteristic
175Dic157—22no—
176Dic157—21no—
177Dic157—21no—
178Dic157—41no—
179Dic157—41no—
180Dic157C4×D412yes—
181C2×C157—42no—
182C2×C157—42no—
183C2×C157C2×C4×D411yescharacteristic
184C2×C157#57611yescharacteristic
185C2×C157#57711yescharacteristic
186D157—22no—
187D157—42no—
188C157#294611yescharacteristic, complemented, Sylow
189#2946—1571nomaximal, Sylow
190C2×AGL(1,ℤ/8)—1571no—
191#520—1571no—
192#518—1571no—
193#442—1571no—
194#442—1571no—
195#440—1571no—
196#440—1571no—
197C4×SD16—1571no—
198C4×SD16—1571no—
199C4×D8—1571no—
200C4×D8D15711yescharacteristic, complemented
201#428—1571no—
202#416—1571no—
203C2×#102—1571no—
204#405—1571no—
205C2×#41—1571no—
206C22×D4—1571no—
207AGL(1,ℤ/8)—1578no—
208C2×SD16—1571no—
209C2×SD16—1571no—
210C2×D8—1571no—
211C2×D8C2×D15711yescharacteristic
212C2×M16—1571no—
213C22×C8—1571no—
214C4×Q8—1571no—
215C4×Q8—1571no—
216C4×D4—3141no—
217C4×D4—3141no—
218C4×D4—3141no—
219C4×D4—3141no—
220C4×D4—1571no—
221C4×D4—1571no—
222C4×D4—1571no—
223C4×D4—1571no—
224C4×D4C2×D15711yescharacteristic
225C4×D4C2×D15711yescharacteristic, complemented
226#117—3141no—
227#117—1571no—
228#117—1571no—
229C2×C4⋊C4—3141no—
230C2×C4⋊C4—1571no—
231C2×C22⋊C4—3141no—
232C2×C22⋊C4—3141no—
233#107—1571no—
234#107C2×D15711yescharacteristic, complemented
235#106—1571no—
236#106—1571no—
237#103—1571no—
238#103—1571no—
239#102—1571no—
240#102—1571no—
241#102—1571no—
242#102—1571no—
243#102C2×D15711yescharacteristic
244#102C2×D15711yescharacteristic, complemented
245#97—1571no—
246#97—1571no—
247C4×C8—1571no—
248C4×C8C2×D15711yescharacteristic, complemented
249C24—3141no—
250#41—3142no—
251#41—1574no—
252C2×Q8—1571no—
253C2×D4—3141no—
254C2×D4—3142no—
255C2×D4—3141no—
256C2×D4—1574no—
257C2×D4—1571no—
258C2×D4C22×D15711yescharacteristic
259C2×D4C22×D15711yescharacteristic
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—3141no—
263C22×C4—3141no—
264C22×C4—3141no—
265C22×C4—3141no—
266C22×C4—3141no—
267C22×C4—3141no—
268C22×C4—1571no—
269SD16—1574no—
270SD16—1574no—
271D8—1574no—
272D8C4×D15714yescomplemented
273M16—1574no—
274C2×C8—3142no—
275C2×C8—1571no—
276C2×C8—1571no—
277C2×C8C22×D15711yescharacteristic
278C2×C8C22×D15711yescharacteristic
279C4⋊C4—3141no—
280C4⋊C4—3141no—
281C4⋊C4—3141no—
282C4⋊C4—1571no—
283C4⋊C4—1571no—
284C4⋊C4—1571no—
285C4⋊C4—1571no—
286C4⋊C4C22×D15711yescharacteristic
287C4⋊C4C22×D15711yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—3141no—
291C22⋊C4—3141no—
292C22⋊C4—3141no—
293C22⋊C4—3141no—
294C22⋊C4—3141no—
295C22⋊C4—1571no—
296C22⋊C4—1571no—
297C42—3141no—
298C42—3141no—
299C42—3141no—
300C42—1571no—
301C42C22×D15711yescharacteristic
302C23—21no—
303C23—21no—
304C23—3144no—
305C23—3141no—
306C23—1571no—
307C23—12561no—
308C23—12561no—
309Q8—3141no—
310Q8—1572no—
311D4—21no—
312D4—21no—
313D4—3144no—
314D4—3144no—
315D4—3141no—
316D4—1572no—
317D4C2×C4×D15712yes—
318D4C2×C4×D15712yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—3141no—
324C2×C4—3144no—
325C2×C4—3141no—
326C2×C4—3141no—
327C2×C4—1571no—
328C2×C4—1571no—
329C2×C4—1571no—
330C2×C4—1572no—
331C2×C4—1572no—
332C2×C4—12561no—
333C2×C4—12561no—
334C2×C4—12561no—
335C2×C4—12561no—
336C2×C4—12561no—
337C2×C4D4×D15711yescharacteristic
338C2×C4D4×D15711yescharacteristic
339C2×C4C23×D15711yescharacteristic
340C8—21no—
341C8—3141no—
342C8—1572no—
343C8C2×C4×D15712yes—
344C22—22no—
345C22—22no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—3141no—
351C22—3141no—
352C22—3142no—
353C22—6281no—
354C22—6281no—
355C22—1572no—
356C22—12564no—
357C22C2×D4×D15711yescharacteristic
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—3141no—
363C4—3142no—
364C4—3141no—
365C4—6281no—
366C4—6281no—
367C4—1572no—
368C4C22×C4×D15711yescharacteristic
369C4#41×D15711yescharacteristic
370C2—42no—
371C2—42no—
372C2—3142no—
373C2—6282no—
374C2C4×D4×D15711yescharacteristic
375C2#2375807411yescharacteristic
376C2#2375808011yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutatorC4×C157C23×C4
FrattiniC2×C4C23×D157
FittingC4×D8×C157C2
socleC22×C157C22×D4
prime radicalC2×#19097795C2
cosocleC2×C4×C157C24
hypercenterC4×D8D157
hypocenterC157#2946
LCSG ▷ C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
2. #23757752C2semidirect
3. #23757745C2semidirect
4. #23757385C2semidirect
5. #23757383C2semidirect
6. #23757373C2semidirect
7. #23757372C2semidirect
8. #23757364C2semidirect
9. C4×#14578943C2semidirect
10. #23757353C2semidirect
11. #23757314C2semidirect
12. #23757266C2semidirect
13. #102×D157C2semidirect
14. #23757227C2semidirect
15. C4×D8×C157C2semidirect
18. #19097795C4semidirect
24. C4×Dic314C22semidirect
25. #19097736C22semidirect
28. D4×Dic157C22semidirect
41. #19097704C22semidirect
42. #19097703C22semidirect
43. #19097702C22semidirect
44. #19097696C22semidirect
45. #19097694C22semidirect
48. #19097692C22semidirect
50. #19097682C22semidirect
51. #19097681C22semidirect
52. C8×Dic157C22semidirect
55. C4×D4×C157C22semidirect
56. #107×C157C22semidirect
58. #102×C157C22semidirect
59. C4×C8×C157C22semidirect
62. #14578953C2×C4semidirect
68. D4×D157C2×C4semidirect
76. #14578943C2×C4semidirect
77. #14578942C2×C4semidirect
78. #14578939C2×C4semidirect
79. #14578937C2×C4semidirect
105. D8×C157C2×C4semidirect
188. C157#2946semidirect
200. C4×D8D157semidirect
225. C4×D4C2×D157semidirect
234. #107C2×D157semidirect
244. #102C2×D157semidirect
248. C4×C8C2×D157semidirect
272. D8C4×D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190977952
#237577522
#237577452
#237573852
#237573832
#237573732
#237573722
#237573642
C4×#145789432
#237573532
#237573142
#237572662
#102×D1572
#237572272
C4×D8×C1572
#2946157