Finite Group Databasebeta

← #34111909

Subgroups — #34111909

Order 20096.

448 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23758088C211yesmaximal, characteristic, complemented
2#23758087C211yesmaximal, characteristic, complemented
3#23758084C211yesmaximal, characteristic, complemented
4#23757664C211yesmaximal, characteristic, complemented
5#23757548C211yesmaximal, characteristic, complemented
6#23757546C211yesmaximal, characteristic, complemented
7#23757534C211yesmaximal, characteristic, complemented
8#23757533C211yesmaximal, characteristic, complemented
9#23757456C211yesmaximal, characteristic, complemented
10#23757454C211yesmaximal, characteristic, complemented
11#23757451C211yesmaximal, characteristic, complemented
12#23757444C211yesmaximal, characteristic, complemented
13#23757395C211yesmaximal, characteristic, complemented
14#23757393C211yesmaximal, characteristic, complemented
15#577×C157C211yesmaximal, characteristic, complemented
16#19097818C2211yescharacteristic
17#19097818C2211yescharacteristic, complemented
18#19097802—21no—
19#19097802C2211yescharacteristic, complemented
20#19097801—21no—
21#19097801—21no—
22#19097801C2211yescharacteristic
23#19097801C2211yescharacteristic
24#19097801C2211yescharacteristic
25#19097801C2211yescharacteristic, complemented
26#19097800—21no—
27#19097800—21no—
28#19097797—21no—
29#19097797C2211yescharacteristic
30#19097791—21no—
31#19097791—21no—
32#19097791C2211yescharacteristic
33#19097790—21no—
34C2×Dic628C2211yescharacteristic, complemented
35C2×#14578944—21no—
36C2×#14578944C2211yescharacteristic, complemented
37Q16×D157—21no—
38C2×#14578942—21no—
39C2×#14578942C2211yescharacteristic
40#19097778C2211yescharacteristic
41#19097778C2211yescharacteristic, complemented
42#19097777C2211yescharacteristic, complemented
43#19097769C2211yescharacteristic, complemented
44#19097758C2211yescharacteristic
45#19097707C2211yescharacteristic, complemented
46#19097706C2211yescharacteristic, complemented
47#19097698C2211yescharacteristic
48#19097698C2211yescharacteristic
49#19097698C2211yescharacteristic, complemented
50#19097697C2211yescharacteristic, complemented
51#19097690C2211yescharacteristic, complemented
52#19097689C2211yescharacteristic, complemented
53#19097689C2211yescharacteristic, complemented
54#19097688C2211yescharacteristic
55#19097681C2211yescharacteristic, complemented
562−1+4×C157C2211yescharacteristic
57H(5,𝔽2)×C157C2211yescharacteristic
58#137×C157—21no—
59#137×C157C2211yescharacteristic
60AGL(1,ℤ/8)×C157—21no—
61AGL(1,ℤ/8)×C157C2211yescharacteristic
62#135×C157—21no—
63#135×C157C2211yescharacteristic
64C2×SD16×C157—21no—
65C2×SD16×C157C2211yescharacteristic
66#131×C157C2211yescharacteristic
67#14578954—21no—
68#14578954—21no—
69#14578954C2311yescharacteristic
70#14578953—21no—
71#14578953—21no—
72#14578953—41no—
73#14578953—41no—
74C2×Dic314—21no—
75C2×Dic314—21no—
76C2×Dic314C2311yescharacteristic
77C2×Dic314C2311yescharacteristic
78Q8×D157—21no—
79Q8×D157—21no—
80Dic628—21no—
81Dic628—21no—
82#14578944—21no—
83#14578944—21no—
84#14578944—21no—
85#14578944—21no—
86#14578944—21no—
87#14578944—21no—
88#14578944—21no—
89#14578944D411yescharacteristic
90#14578942—21no—
91#14578942—21no—
92#14578942—21no—
93#14578942—21no—
94#14578942—21no—
95#14578942—21no—
96#14578942—21no—
97#14578942D411yescharacteristic
98#14578941—21no—
99#14578941D411yescharacteristic
100#14578939—21no—
101#14578939D411yescharacteristic
102#14578938—21no—
103#14578938—21no—
104#14578938C2311yescharacteristic
105#14578938C2311yescharacteristic
106#14578938C2311yescharacteristic
107#14578937—21no—
108C2×#11929434—21no—
109C2×#11929434—21no—
110C2×#11929434C2311yescharacteristic
111C8×D157—21no—
112#14578933—41no—
113C22⋊Dic157—41no—
114C4×Dic157C2311yescharacteristic
115#41×C157—21no—
116#41×C157—21no—
117#41×C157—21no—
118#41×C157—21no—
119#41×C157—41no—
120#41×C157C2311yescharacteristic
121#41×C157C2311yescharacteristic
122#41×C157C2311yescharacteristic
123C2×Q8×C157—21no—
124C2×Q8×C157—21no—
125C2×Q8×C157C2311yescharacteristic
126C2×D4×C157—21no—
127C2×D4×C157—21no—
128C2×D4×C157—41no—
129C2×D4×C157C2311yescharacteristic
130Q16×C157—21no—
131Q16×C157D411yescharacteristic
132SD16×C157—21no—
133SD16×C157—21no—
134SD16×C157—21no—
135SD16×C157—21no—
136SD16×C157D411yescharacteristic
137SD16×C157D411yescharacteristic
138D8×C157—21no—
139D8×C157D411yescharacteristic
140M16×C157—21no—
141M16×C157C2311yescharacteristic
142C2×C8×C157—21no—
143C2×C8×C157C2311yescharacteristic
144Dic314—21no—
145Dic314—21no—
146Dic314—21no—
147Dic314—21no—
148Dic314—41no—
149Dic314—41no—
150Dic314C2×D411yescharacteristic
151D628C2×D411yescharacteristic
152C22⋊D157—21no—
153C22⋊D157—41no—
154C22⋊D157—41no—
155C2×Dic157—21no—
156C2×Dic157—21no—
157C2×Dic157—21no—
158C2×Dic157—41no—
159C2×Dic157—41no—
160C4×D157—21no—
161C4×D157—41no—
162C4×D157—41no—
163#11929434—21no—
164#11929434—21no—
165#11929434—21no—
166#11929434C2×D411yescharacteristic
167#11929434C2×D411yescharacteristic
168C23×C157—21no—
169C23×C157—41no—
170Q8×C157—21no—
171Q8×C157—21no—
172Q8×C157—41no—
173Q8×C157C2×D411yescharacteristic
174Q8×C157C2×D411yescharacteristic
175Q8×C157C2×D411yescharacteristic
176D4×C157—21no—
177D4×C157—21no—
178D4×C157—21no—
179D4×C157—21no—
180D4×C157—21no—
181D4×C157—41no—
182D4×C157—41no—
183D4×C157—41no—
184D4×C157C2×D411yescharacteristic
185D4×C157C2×D411yescharacteristic
186D4×C157C2×D411yescharacteristic
187C2×C4×C157—21no—
188C2×C4×C157—21no—
189C2×C4×C157—21no—
190C2×C4×C157—21no—
191C2×C4×C157—41no—
192C2×C4×C157—41no—
193C2×C4×C157—41no—
194C2×C4×C157C2411yescharacteristic
195C8×C157—21no—
196C8×C157C2×D411yescharacteristic
197C8×C157C2×D411yescharacteristic
198C22×C157—21no—
199C22×C157—21no—
200C22×C157—21no—
201C22×C157—41no—
202C22×C157—81no—
203C22×C157—161no—
204C22×C157H(5,𝔽2)11yescharacteristic
205C2×D157—21no—
206C4×C157—21no—
207C4×C157—21no—
208C4×C157—21no—
209C4×C157—41no—
210C4×C157C22×D411yescharacteristic
211C4×C157C22×D411yescharacteristic
212Dic157—21no—
213Dic157—41no—
214Dic157—41no—
215Dic157—41no—
216C2×C157—21no—
217C2×C157—41no—
218C2×C157—41no—
219C2×C157—41no—
220C2×C157—81no—
221C2×C157D4211yescharacteristic
222D157—41no—
223C157#328911yescharacteristic, complemented, Sylow
224#3289—1571nomaximal, Sylow
225#578—1571no—
226#578—1571no—
227#577—1571no—
228#577D15711yescharacteristic, complemented
229#497—1571no—
230#473—1571no—
231#473—1571no—
232#471—1571no—
233#471—1571no—
234#456—1571no—
235#456—1571no—
236#455—1571no—
237#454—1571no—
238#444—1571no—
239#444—1571no—
2402−1+4—1571no—
2412−1+4—1571no—
2422−1+4C2×D15711yescharacteristic
243H(5,𝔽2)C2×D15711yescharacteristic
244#137—21no—
245#137—3141no—
246#137—3141no—
247#137—3141no—
248#137—3141no—
249#137—3141no—
250#137—1571no—
251#137—1571no—
252#137—1571no—
253#137—1571no—
254#137—1571no—
255#137C2×D15711yescharacteristic
256AGL(1,ℤ/8)—21no—
257AGL(1,ℤ/8)—3141no—
258AGL(1,ℤ/8)—1571no—
259AGL(1,ℤ/8)C2×D15711yescharacteristic
260#135—21no—
261#135—3141no—
262#135—3141no—
263#135—3141no—
264#135—1571no—
265#135C2×D15711yescharacteristic
266C2×Q16—3141no—
267C2×Q16—3141no—
268C2×Q16—1571no—
269C2×Q16—1571no—
270C2×SD16—21no—
271C2×SD16—3141no—
272C2×SD16—1571no—
273C2×SD16C2×D15711yescharacteristic
274#131—1571no—
275#131—1571no—
276#131—1571no—
277#131C2×D15711yescharacteristic
278C4⋊Q8—1571no—
279#124—1571no—
280#108—1571no—
281#108—1571no—
282#104—1571no—
283#104—1571no—
284#104—1571no—
285#104—1571no—
286#101—1571no—
287#101—1571no—
288#101—1571no—
289#100—1571no—
290#97—1571no—
291#41—21no—
292#41—21no—
293#41—21no—
294#41—21no—
295#41—41no—
296#41—3141no—
297#41—3141no—
298#41—3141no—
299#41—3141no—
300#41—6281no—
301#41—6281no—
302#41—1571no—
303#41C22×D15711yescharacteristic
304#41C22×D15711yescharacteristic
305#41C22×D15711yescharacteristic
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—3141no—
309C2×Q8—3141no—
310C2×Q8—3141no—
311C2×Q8—3141no—
312C2×Q8—1571no—
313C2×Q8—1571no—
314C2×Q8C22×D15711yescharacteristic
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—41no—
318C2×D4C22×D15711yescharacteristic
319Q16—21no—
320Q16—3141no—
321Q16—3141no—
322Q16—3141no—
323Q16—3141no—
324Q16—3141no—
325Q16—3141no—
326Q16—3141no—
327Q16—3141no—
328Q16—3141no—
329Q16—1571no—
330Q16C22⋊D15711yescharacteristic
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—21no—
335SD16—3141no—
336SD16—3141no—
337SD16—3141no—
338SD16—3141no—
339SD16—3141no—
340SD16—3141no—
341SD16—3141no—
342SD16—3141no—
343SD16—1571no—
344SD16—1571no—
345SD16C22⋊D15711yescharacteristic
346SD16C22⋊D15711yescharacteristic
347D8—21no—
348D8—3141no—
349D8—1571no—
350D8C22⋊D15711yescharacteristic
351M16—21no—
352M16—3141no—
353M16—3141no—
354M16—3141no—
355M16—1571no—
356M16—1571no—
357M16—1571no—
358M16C22×D15711yescharacteristic
359C2×C8—21no—
360C2×C8—3141no—
361C2×C8—3141no—
362C2×C8—3141no—
363C2×C8—1571no—
364C2×C8C22×D15711yescharacteristic
365C4⋊C4—6281no—
366C22⋊C4—6281no—
367C42—1571no—
368C23—21no—
369C23—41no—
370Q8—21no—
371Q8—21no—
372Q8—41no—
373Q8—3141no—
374Q8—3141no—
375Q8—3141no—
376Q8—3141no—
377Q8—6281no—
378Q8—6281no—
379Q8—1571no—
380Q8D4×D15711yescharacteristic
381Q8C2×C22⋊D15711yescharacteristic
382Q8C2×C22⋊D15711yescharacteristic
383D4—21no—
384D4—21no—
385D4—21no—
386D4—21no—
387D4—21no—
388D4—41no—
389D4—41no—
390D4—41no—
391D4—3141no—
392D4—6281no—
393D4—6281no—
394D4—1571no—
395D4D4×D15711yescharacteristic
396D4C2×C22⋊D15711yescharacteristic
397D4C2×C22⋊D15711yescharacteristic
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—3141no—
406C2×C4—3141no—
407C2×C4—3141no—
408C2×C4—3141no—
409C2×C4—6281no—
410C2×C4—6281no—
411C2×C4—6281no—
412C2×C4—6281no—
413C2×C4C23×D15711yescharacteristic
414C8—21no—
415C8—3141no—
416C8—3141no—
417C8—3141no—
418C8—1571no—
419C8—1571no—
420C8C2×C22⋊D15711yescharacteristic
421C8C2×C22⋊D15711yescharacteristic
422C22—21no—
423C22—21no—
424C22—21no—
425C22—41no—
426C22—81no—
427C22—161no—
428C22—3141no—
429C22#1909781611yescharacteristic
430C4—21no—
431C4—21no—
432C4—21no—
433C4—41no—
434C4—3141no—
435C4—6281no—
436C4—6281no—
437C4—6281no—
438C4C2×D4×D15711yescharacteristic
439C4C22×C22⋊D15711yescharacteristic
440C2—21no—
441C2—41no—
442C2—41no—
443C2—41no—
444C2—81no—
445C2—6281no—
446C2D4×C22⋊D15711yescharacteristic
subgroupG/H
centerC2D4×C22⋊D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#577×C157C2
socleC2×C157D42
hypercenter#577D157
hypocenterC157#3289
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C2×C4 ◁ #577

Complements

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

NH ≅ G/Ntype
1. #23758088C2semidirect
2. #23758087C2semidirect
3. #23758084C2semidirect
4. #23757664C2semidirect
5. #23757548C2semidirect
6. #23757546C2semidirect
7. #23757534C2semidirect
8. #23757533C2semidirect
9. #23757456C2semidirect
10. #23757454C2semidirect
11. #23757451C2semidirect
12. #23757444C2semidirect
13. #23757395C2semidirect
14. #23757393C2semidirect
15. #577×C157C2semidirect
17. #19097818C22semidirect
19. #19097802C22semidirect
25. #19097801C22semidirect
34. C2×Dic628C22semidirect
36. C2×#14578944C22semidirect
41. #19097778C22semidirect
42. #19097777C22semidirect
43. #19097769C22semidirect
45. #19097707C22semidirect
46. #19097706C22semidirect
49. #19097698C22semidirect
50. #19097697C22semidirect
51. #19097690C22semidirect
52. #19097689C22semidirect
53. #19097689C22semidirect
55. #19097681C22semidirect
223. C157#3289semidirect
228. #577D157semidirect

Maximal subgroups

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

subgroupindex
#237580882
#237580872
#237580842
#237576642
#237575482
#237575462
#237575342
#237575332
#237574562
#237574542
#237574512
#237574442
#237573952
#237573932
#577×C1572
#3289157