Finite Group Databasebeta

← #34103114

Subgroups — #34103114

Order 20096.

928 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19097741C211yesmaximal, characteristic
2C2×C4×D628C211yesmaximal, characteristic, complemented
3C2×#19097733C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D157C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D157C211yesmaximal, characteristic, complemented
6#23757173C211yesmaximal, characteristic, complemented
7#23757166C211yesmaximal, characteristic, complemented
8#23757151C211yesmaximal, characteristic, complemented
9#23757151C211yesmaximal, characteristic, complemented
10#23757149C211yesmaximal, characteristic, complemented
11#23757147C211yesmaximal, characteristic, complemented
12#23757144C211yesmaximal, characteristic, complemented
13C4×#14578931C211yesmaximal, characteristic, complemented
14#23757120C211yesmaximal, characteristic, complemented
15#388×C157C211yesmaximal, characteristic, complemented
16C24×D157C2211yescharacteristic
17C22×D628C2211yescharacteristic
18C22×D628C2211yescharacteristic
19C22×C22⋊D157C2211yescharacteristic
20C22×C4×D157C2211yescharacteristic
21C22×C4×D157C2211yescharacteristic
22C22×C4×D157C2211yescharacteristic
23C22×C4×D157C2211yescharacteristic
24C22×C4×D157C2211yescharacteristic, complemented
25#19097741C418yescomplemented
26C4×D628—24no—
27#19097733—24no—
28C2×C4⋊Dic157C2211yescharacteristic, complemented
29C2×#14578933C2211yescharacteristic, complemented
30C2×C22⋊Dic157C2211yescharacteristic
31C2×C22⋊Dic157C2211yescharacteristic
32C2×#14578931C2211yescharacteristic
33C2×#14578931C2211yescharacteristic
34C2×#14578931C2211yescharacteristic
35C2×#14578931C2211yescharacteristic
36C2×#14578931C2211yescharacteristic
37C2×#14578931C2211yescharacteristic
38C2×#14578931C2211yescharacteristic, complemented
39C2×#14578931C2211yescharacteristic, complemented
40C2×#14578931C2211yescharacteristic, complemented
41C22⋊C4×D157—24no—
42C22⋊C4×D157—24no—
43C2×C4×Dic157C2211yescharacteristic, complemented
44C2×C4×Dic157C2211yescharacteristic, complemented
45#19097678C2211yescharacteristic, complemented
46#19097678C2211yescharacteristic, complemented
47#19097678C2211yescharacteristic, complemented
48#19097678C2211yescharacteristic, complemented
49C2×C4⋊C4×C157C2211yescharacteristic, complemented
50C2×C22⋊C4×C157C2211yescharacteristic
51C2×C22⋊C4×C157C2211yescharacteristic
52C2×C22⋊C4×C157C2211yescharacteristic
53C2×C42×C157C2211yescharacteristic, complemented
54#95×C157C2211yescharacteristic, complemented
55#95×C157C2211yescharacteristic, complemented
56C23×D157—22no—
57C23×D157—22no—
58C23×D157—22no—
59C23×D157—22no—
60C23×D157—41no—
61C23×D157—41no—
62C23×D157C2×C414yescomplemented
63C23×D157C2311yescharacteristic
64C23×D157C2311yescharacteristic
65C23×D157C2311yescharacteristic
66C2×D628—22no—
67C2×D628—22no—
68C2×D628—22no—
69C2×D628—22no—
70C2×D628C2×C414yescomplemented
71C2×D628C2×C414yescomplemented
72C2×C22⋊D157—41no—
73C2×C22⋊D157—41no—
74C2×C22⋊D157C2×C414yescomplemented
75C22×Dic157C2311yescharacteristic
76C22×Dic157C2311yescharacteristic
77C22×Dic157C2311yescharacteristic
78C22×Dic157C2311yescharacteristic
79C22×Dic157C2311yescharacteristic
80C2×C4×D157—22no—
81C2×C4×D157—22no—
82C2×C4×D157—22no—
83C2×C4×D157—22no—
84C2×C4×D157—22no—
85C2×C4×D157—22no—
86C2×C4×D157—22no—
87C2×C4×D157—22no—
88C2×C4×D157—22no—
89C2×C4×D157—22no—
90C2×C4×D157—41no—
91C2×C4×D157—41no—
92C2×C4×D157—41no—
93C2×C4×D157—41no—
94C2×C4×D157—41no—
95C4⋊Dic157—22no—
96#14578933—41no—
97C22⋊Dic157—22no—
98C22⋊Dic157—22no—
99#14578931—22no—
100#14578931—22no—
101#14578931—22no—
102#14578931—22no—
103#14578931—41no—
104#14578931C2×C414yescomplemented
105#14578931C2×C414yescomplemented
106#14578931D414yescomplemented
107#14578931D414yescomplemented
108C4×Dic157—22no—
109C4×Dic157—41no—
110C24×C157C2311yescharacteristic
111C22×C4×C157C2311yescharacteristic
112C22×C4×C157C2311yescharacteristic
113C22×C4×C157C2311yescharacteristic
114C22×C4×C157C2311yescharacteristic
115C22×C4×C157C2311yescharacteristic
116C22×C4×C157C2311yescharacteristic
117C4⋊C4×C157—22no—
118C22⋊C4×C157—22no—
119C22⋊C4×C157—22no—
120C22⋊C4×C157C2×C414yescomplemented
121C42×C157—22no—
122C22×D157—21no—
123C22×D157—21no—
124C22×D157—21no—
125C22×D157—21no—
126C22×D157—21no—
127C22×D157—21no—
128C22×D157—21no—
129C22×D157—21no—
130C22×D157—21no—
131C22×D157—21no—
132C22×D157—21no—
133C22×D157—21no—
134C22×D157—21no—
135C22×D157—21no—
136C22×D157—28no—
137C22×D157—28no—
138C22×D157—44no—
139C22×D157—44no—
140C22×D157—44no—
141C22×D157—44no—
142C22×D157—44no—
143C22×D157C22×C412yes—
144C22×D157C22×C412yes—
145C22×D157C22×C412yes—
146C22×D157C2×D412yes—
147C22×D157C2×D412yes—
148C22×D157#4112yes—
149C22×D157#4112yes—
150D628—28no—
151D628—28no—
152C22⋊D157—44no—
153C2×Dic157—21no—
154C2×Dic157—21no—
155C2×Dic157—21no—
156C2×Dic157—21no—
157C2×Dic157—21no—
158C2×Dic157—21no—
159C2×Dic157—21no—
160C2×Dic157—21no—
161C2×Dic157—21no—
162C2×Dic157—21no—
163C2×Dic157—21no—
164C2×Dic157—21no—
165C2×Dic157C22×C412yes—
166C2×Dic157C2×D412yes—
167C2×Dic157C2×D412yes—
168C4×D157—44no—
169C4×D157—44no—
170C4×D157—44no—
171C4×D157—44no—
172C4×D157—44no—
173C23×C157—21no—
174C23×C157—21no—
175C23×C157—21no—
176C23×C157—21no—
177C23×C157—21no—
178C23×C157—21no—
179C23×C157C22×C412yes—
180C23×C157C2411yescharacteristic
181C2×C4×C157—21no—
182C2×C4×C157—21no—
183C2×C4×C157—21no—
184C2×C4×C157—21no—
185C2×C4×C157—21no—
186C2×C4×C157—21no—
187C2×C4×C157—21no—
188C2×C4×C157—21no—
189C2×C4×C157—21no—
190C2×C4×C157—21no—
191C2×C4×C157—21no—
192C2×C4×C157—21no—
193C2×C4×C157—21no—
194C2×C4×C157—21no—
195C2×C4×C157C22×C412yes—
196C2×C4×C157C22×C412yes—
197C2×C4×C157C2×D412yes—
198C2×C4×C157C2×D412yes—
199C22×C157—22no—
200C22×C157—22no—
201C22×C157—22no—
202C22×C157—41no—
203C22×C157—41no—
204C22×C157—41no—
205C22×C157—41no—
206C22×C157C23×C411yescharacteristic
207C22×C157C22×D411yescharacteristic
208C22×C157C22×D411yescharacteristic
209C22×C157C2×#4111yescharacteristic
210C22×C157C2×#4111yescharacteristic
211C22×C157H(5,𝔽2)11yescharacteristic
212C22×C157H(5,𝔽2)11yescharacteristic
213C2×D157—22no—
214C2×D157—22no—
215C2×D157—22no—
216C2×D157—22no—
217C2×D157—22no—
218C2×D157—22no—
219C2×D157—22no—
220C2×D157—22no—
221C2×D157—22no—
222C2×D157—22no—
223C2×D157—22no—
224C2×D157—22no—
225C2×D157—22no—
226C2×D157—22no—
227C2×D157—22no—
228C2×D157—416no—
229C2×D157—41no—
230C2×D157—41no—
231C2×D157—41no—
232C2×D157—41no—
233C2×D157C4×D414yescomplemented
234C2×D157C4×D414yescomplemented
235C4×C157—22no—
236C4×C157—22no—
237C4×C157—22no—
238C4×C157—22no—
239C4×C157—41no—
240C4×C157—41no—
241Dic157—22no—
242Dic157—22no—
243Dic157—22no—
244Dic157—41no—
245Dic157—41no—
246C2×C157—42no—
247C2×C157C2×C4×D411yescharacteristic
248C2×C157C2×C4×D411yescharacteristic
249C2×C157#51811yescharacteristic
250C2×C157D4211yescharacteristic
251C2×C157#54611yescharacteristic
252C2×C157#54611yescharacteristic
253C2×C157#55111yescharacteristic
254D157—24no—
255D157—24no—
256D157—42no—
257C157#235811yescharacteristic, complemented, Sylow
258#2358—1571nomaximal, Sylow
259C2×#120—1571no—
260C2×C4×D4—1571no—
261C2×C4×D4—1571no—
262C22×C22⋊C4—1571no—
263C22×C22⋊C4—1571no—
264#390—1571no—
265#388—1571no—
266#388D15711yescharacteristic, complemented
267#386—1571no—
268#386—1571no—
269#386—1571no—
270#385—1571no—
271#385—1571no—
272C4×C22⋊C4—1571no—
273C4×C22⋊C4—1571no—
274C25—1571no—
275C22×D4—1571no—
276C22×D4—1571no—
277C22×D4—1571no—
278C23×C4—1571no—
279C23×C4—1571no—
280C23×C4—1571no—
281C23×C4—1571no—
282C23×C4—1571no—
283#120—1578no—
284C4×D4—3144no—
285C4×D4—3144no—
286C2×C4⋊C4—1571no—
287C2×C4⋊C4—1571no—
288C2×C4⋊C4C2×D15711yescharacteristic, complemented
289C2×C22⋊C4—3144no—
290C2×C22⋊C4—3144no—
291C2×C22⋊C4—1571no—
292C2×C22⋊C4—1571no—
293C2×C22⋊C4—1571no—
294C2×C22⋊C4—1571no—
295C2×C22⋊C4—1571no—
296C2×C22⋊C4—1571no—
297C2×C22⋊C4—1571no—
298C2×C22⋊C4—1571no—
299C2×C22⋊C4—1571no—
300C2×C22⋊C4—1571no—
301C2×C22⋊C4—1571no—
302C2×C22⋊C4C2×D15711yescharacteristic
303C2×C22⋊C4C2×D15711yescharacteristic
304C2×C22⋊C4C2×D15711yescharacteristic
305C2×C42—1571no—
306C2×C42—1571no—
307C2×C42C2×D15711yescharacteristic, complemented
308#95—1571no—
309#95—1571no—
310#95—1571no—
311#95—1571no—
312#95C2×D15711yescharacteristic, complemented
313#95C2×D15711yescharacteristic, complemented
314C24—3142no—
315C24—3142no—
316C24—3142no—
317C24—3142no—
318C24—6281no—
319C24—6281no—
320C24—1571no—
321C24—1574no—
322C24—1571no—
323C24—1571no—
324C24C22×D15711yescharacteristic
325C2×D4—3142no—
326C2×D4—3142no—
327C2×D4—3142no—
328C2×D4—3142no—
329C2×D4—6281no—
330C2×D4—6281no—
331C2×D4—1574no—
332C2×D4—1574no—
333C2×D4—1574no—
334C22×C4—3142no—
335C22×C4—3142no—
336C22×C4—3142no—
337C22×C4—3142no—
338C22×C4—3142no—
339C22×C4—3142no—
340C22×C4—3142no—
341C22×C4—3142no—
342C22×C4—3142no—
343C22×C4—3142no—
344C22×C4—6281no—
345C22×C4—6281no—
346C22×C4—6281no—
347C22×C4—6281no—
348C22×C4—6281no—
349C22×C4—1571no—
350C22×C4—1571no—
351C22×C4—1571no—
352C22×C4—1571no—
353C22×C4—1571no—
354C22×C4C22×D15711yescharacteristic
355C22×C4C22×D15711yescharacteristic
356C22×C4C22×D15711yescharacteristic
357C22×C4C22×D15711yescharacteristic
358C22×C4C22×D15711yescharacteristic
359C22×C4C22×D15711yescharacteristic
360C4⋊C4—22no—
361C4⋊C4—3142no—
362C4⋊C4—6281no—
363C22⋊C4—22no—
364C22⋊C4—22no—
365C22⋊C4—3142no—
366C22⋊C4—3142no—
367C22⋊C4—3142no—
368C22⋊C4—3142no—
369C22⋊C4—3142no—
370C22⋊C4—3142no—
371C22⋊C4—6281no—
372C22⋊C4—1574no—
373C22⋊C4—1574no—
374C22⋊C4—1574no—
375C22⋊C4—1574no—
376C22⋊C4C4×D15714yescomplemented
377C42—22no—
378C42—3142no—
379C42—6281no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—3148no—
387C23—3148no—
388C23—3141no—
389C23—3141no—
390C23—3141no—
391C23—3141no—
392C23—3141no—
393C23—3141no—
394C23—3141no—
395C23—3141no—
396C23—3141no—
397C23—3141no—
398C23—3141no—
399C23—3141no—
400C23—3141no—
401C23—3141no—
402C23—6284no—
403C23—6284no—
404C23—6284no—
405C23—6284no—
406C23—6284no—
407C23—1572no—
408C23—1572no—
409C23—1572no—
410C23—1572no—
411C23—1572no—
412C23—1572no—
413C23—1572no—
414C23C2×C4×D15712yes—
415C23C23×D15711yescharacteristic
416D4—3148no—
417D4—3148no—
418D4—6284no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—3141no—
434C2×C4—3141no—
435C2×C4—3141no—
436C2×C4—3141no—
437C2×C4—3141no—
438C2×C4—3141no—
439C2×C4—3141no—
440C2×C4—3141no—
441C2×C4—3141no—
442C2×C4—3141no—
443C2×C4—3141no—
444C2×C4—3141no—
445C2×C4—6284no—
446C2×C4—6284no—
447C2×C4—6284no—
448C2×C4—6284no—
449C2×C4—6284no—
450C2×C4—1572no—
451C2×C4—1572no—
452C2×C4—1572no—
453C2×C4C2×C4×D15712yes—
454C2×C4C2×C4×D15712yes—
455C2×C4D4×D15712yes—
456C2×C4D4×D15712yes—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—3142no—
465C22—3142no—
466C22—3142no—
467C22—3142no—
468C22—3142no—
469C22—3142no—
470C22—3142no—
471C22—3142no—
472C22—3142no—
473C22—3142no—
474C22—3142no—
475C22—3142no—
476C22—3142no—
477C22—3142no—
478C22—3142no—
479C22—62816no—
480C22—6281no—
481C22—6281no—
482C22—6281no—
483C22—6281no—
484C22—1574no—
485C22—1574no—
486C22C22×C4×D15711yescharacteristic
487C22C2×D4×D15711yescharacteristic
488C22C2×D4×D15711yescharacteristic
489C22#41×D15711yescharacteristic
490C22#41×D15711yescharacteristic
491C22#1909781711yescharacteristic
492C22#1909781711yescharacteristic
493C4—22no—
494C4—22no—
495C4—22no—
496C4—22no—
497C4—41no—
498C4—41no—
499C4—3142no—
500C4—3142no—
501C4—3142no—
502C4—6281no—
503C4—6281no—
504C2—42no—
505C2—3144no—
506C2—3144no—
507C2—6282no—
508C2C4×D4×D15711yescharacteristic
509C2C4×D4×D15711yescharacteristic
510C2#2375774711yescharacteristic
511C2#2375790711yescharacteristic
512C2#2375791511yescharacteristic
513C2#2375791611yescharacteristic
514C2#2375794811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D157
commutatorC22×C157C23×C4
Fitting#388×C157C2
socle, cosocleC23×C157C24
prime radicalC2×#19097741C2
hypercenter#388D157
hypocenterC157#2358
LCSG ▷ C22×C157 ▷ C157
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C2×C4×D628C2semidirect
3. C2×#19097733C2semidirect
4. C2×C22⋊C4×D157C2semidirect
5. C2×C22⋊C4×D157C2semidirect
6. #23757173C2semidirect
7. #23757166C2semidirect
8. #23757151C2semidirect
9. #23757151C2semidirect
10. #23757149C2semidirect
11. #23757147C2semidirect
12. #23757144C2semidirect
13. C4×#14578931C2semidirect
14. #23757120C2semidirect
15. #388×C157C2semidirect
24. C22×C4×D157C22semidirect
25. #19097741C4semidirect
28. C2×C4⋊Dic157C22semidirect
29. C2×#14578933C22semidirect
38. C2×#14578931C22semidirect
39. C2×#14578931C22semidirect
40. C2×#14578931C22semidirect
43. C2×C4×Dic157C22semidirect
44. C2×C4×Dic157C22semidirect
45. #19097678C22semidirect
46. #19097678C22semidirect
47. #19097678C22semidirect
48. #19097678C22semidirect
49. C2×C4⋊C4×C157C22semidirect
53. C2×C42×C157C22semidirect
54. #95×C157C22semidirect
55. #95×C157C22semidirect
62. C23×D157C2×C4semidirect
70. C2×D628C2×C4semidirect
71. C2×D628C2×C4semidirect
74. C2×C22⋊D157C2×C4semidirect
104. #14578931C2×C4semidirect
105. #14578931C2×C4semidirect
106. #14578931D4semidirect
107. #14578931D4semidirect
120. C22⋊C4×C157C2×C4semidirect
233. C2×D157C4×D4semidirect
234. C2×D157C4×D4semidirect
257. C157#2358semidirect
266. #388D157semidirect
288. C2×C4⋊C4C2×D157semidirect
307. C2×C42C2×D157semidirect
312. #95C2×D157semidirect
313. #95C2×D157semidirect
376. C22⋊C4C4×D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190977412
C2×C4×D6282
C2×#190977332
C2×C22⋊C4×D1572
#237571732
#237571662
#237571512
#237571492
#237571472
#237571442
C4×#145789312
#237571202
#388×C1572
#2358157