Finite Group Databasebeta

← #34103116

Subgroups — #34103116

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×#19097739C211yesmaximal, characteristic
2C2×D4×Dic157C211yesmaximal, characteristic, complemented
3C2×#19097731C211yesmaximal, characteristic, complemented
4C22×#14578931C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D157C211yesmaximal, characteristic, complemented
6#23757173C211yesmaximal, characteristic, complemented
7#23757165C211yesmaximal, characteristic, complemented
8#23757162C211yesmaximal, characteristic, complemented
9#23757150C211yesmaximal, characteristic, complemented
10#23757149C211yesmaximal, characteristic, complemented
11#23757147C211yesmaximal, characteristic, complemented
12#23757145C211yesmaximal, characteristic, complemented
13C4×C22⋊Dic157C211yesmaximal, characteristic, complemented
14#23757120C211yesmaximal, characteristic, complemented
15#386×C157C211yesmaximal, characteristic, complemented
16C24×D157C2211yescharacteristic
17C22×C22⋊D157C2211yescharacteristic
18C22×C22⋊D157C2211yescharacteristic
19C23×Dic157C2211yescharacteristic
20C23×Dic157C2211yescharacteristic, complemented
21C22×C4×D157C2211yescharacteristic
22C22×C4×D157C2211yescharacteristic
23#19097739C418yescomplemented
24D4×Dic157—24no—
25#19097731—24no—
26C2×C4⋊Dic157C2211yescharacteristic, complemented
27C2×#14578933C2211yescharacteristic, complemented
28C2×#14578933C2211yescharacteristic, complemented
29C2×C22⋊Dic157C2211yescharacteristic
30C2×C22⋊Dic157C2211yescharacteristic
31C2×C22⋊Dic157C2211yescharacteristic, complemented
32C2×#14578931—24no—
33C2×#14578931C2211yescharacteristic
34C2×#14578931C2211yescharacteristic
35C2×#14578931C2211yescharacteristic
36C2×#14578931C2211yescharacteristic
37C2×#14578931C2211yescharacteristic
38C2×#14578931C2211yescharacteristic
39C2×#14578931C2211yescharacteristic
40C2×#14578931C2211yescharacteristic
41C22⋊C4×D157—24no—
42C2×C4×Dic157C2211yescharacteristic, complemented
43C2×C4×Dic157C2211yescharacteristic, complemented
44C2×C4×Dic157C2211yescharacteristic, complemented
45#19097678C2211yescharacteristic, complemented
46#19097678C2211yescharacteristic, complemented
47#19097678C2211yescharacteristic, complemented
48#19097678C2211yescharacteristic, complemented
49C22×D4×C157C2211yescharacteristic
50C23×C4×C157C2211yescharacteristic
51C2×C22⋊C4×C157C2211yescharacteristic
52C2×C22⋊C4×C157C2211yescharacteristic, complemented
53C2×C22⋊C4×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
65C2×C22⋊D157—22no—
66C2×C22⋊D157—22no—
67C2×C22⋊D157—41no—
68C2×C22⋊D157—41no—
69C2×C22⋊D157C2×C414yescomplemented
70C2×C22⋊D157C2×C414yescomplemented
71C22×Dic157—22no—
72C22×Dic157—22no—
73C22×Dic157—22no—
74C22×Dic157—22no—
75C22×Dic157—41no—
76C22×Dic157—41no—
77C22×Dic157C2311yescharacteristic
78C22×Dic157C2311yescharacteristic
79C22×Dic157C2311yescharacteristic
80C22×Dic157C2311yescharacteristic
81C22×Dic157C2311yescharacteristic
82C22×Dic157C2311yescharacteristic
83C2×C4×D157—22no—
84C2×C4×D157—22no—
85C2×C4×D157—22no—
86C2×C4×D157—22no—
87C2×C4×D157—41no—
88C2×C4×D157—41no—
89C4⋊Dic157—22no—
90#14578933—22no—
91#14578933—41no—
92C22⋊Dic157—22no—
93C22⋊Dic157C2×C414yescomplemented
94C22⋊Dic157D414yescomplemented
95#14578931—22no—
96#14578931—22no—
97#14578931—22no—
98#14578931—22no—
99#14578931—22no—
100#14578931C2×C414yescomplemented
101#14578931C2×C414yescomplemented
102#14578931D414yescomplemented
103C4×Dic157—22no—
104C4×Dic157—22no—
105C4×Dic157—41no—
106C24×C157C2311yescharacteristic
107C24×C157C2311yescharacteristic
108C2×D4×C157—22no—
109C2×D4×C157—22no—
110C2×D4×C157C2×C414yescomplemented
111C22×C4×C157—22no—
112C22×C4×C157—22no—
113C22×C4×C157—41no—
114C22×C4×C157C2311yescharacteristic
115C22×C4×C157C2311yescharacteristic
116C22×C4×C157C2311yescharacteristic
117C22×C4×C157C2311yescharacteristic
118C22×C4×C157C2311yescharacteristic
119C22⋊C4×C157—22no—
120C22⋊C4×C157—22no—
121C22⋊C4×C157—41no—
122C22×D157—21no—
123C22×D157—21no—
124C22×D157—21no—
125C22×D157—21no—
126C22×D157—28no—
127C22×D157—21no—
128C22×D157—21no—
129C22×D157—21no—
130C22×D157—21no—
131C22×D157—21no—
132C22×D157—21no—
133C22×D157—28no—
134C22×D157—44no—
135C22×D157—44no—
136C22×D157—44no—
137C22×D157—44no—
138C22×D157—44no—
139C22×D157C22×C412yes—
140C22×D157C22×C412yes—
141C22×D157C2×D412yes—
142C22×D157#4112yes—
143C22⋊D157—28no—
144C22⋊D157—44no—
145C2×Dic157—21no—
146C2×Dic157—21no—
147C2×Dic157—21no—
148C2×Dic157—21no—
149C2×Dic157—21no—
150C2×Dic157—21no—
151C2×Dic157—21no—
152C2×Dic157—21no—
153C2×Dic157—21no—
154C2×Dic157—21no—
155C2×Dic157—21no—
156C2×Dic157—21no—
157C2×Dic157—21no—
158C2×Dic157—44no—
159C2×Dic157—44no—
160C2×Dic157C22×C412yes—
161C2×Dic157C22×C412yes—
162C2×Dic157C2×D412yes—
163C2×Dic157C2×D412yes—
164C2×Dic157C2×D412yes—
165C4×D157—44no—
166C4×D157—44no—
167C23×C157—21no—
168C23×C157—21no—
169C23×C157—21no—
170C23×C157—21no—
171C23×C157—21no—
172C23×C157—21no—
173C23×C157—21no—
174C23×C157—21no—
175C23×C157—21no—
176C23×C157—21no—
177C23×C157C22×C412yes—
178C23×C157C22×C412yes—
179C23×C157C2×D412yes—
180C23×C157#4112yes—
181C23×C157C2411yescharacteristic
182D4×C157—28no—
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×C157—21no—
196C2×C4×C157—44no—
197C2×C4×C157C22×C412yes—
198C2×C4×C157C2×D412yes—
199C22×C157—22no—
200C22×C157—22no—
201C22×C157—22no—
202C22×C157—22no—
203C22×C157—22no—
204C22×C157—22no—
205C22×C157—22no—
206C22×C157—22no—
207C22×C157—22no—
208C22×C157—41no—
209C22×C157—41no—
210C22×C157—41no—
211C22×C157—41no—
212C22×C157C4×D414yescomplemented
213C22×C157C23×C411yescharacteristic
214C22×C157C22×D411yescharacteristic
215C22×C157C22×D411yescharacteristic
216C22×C157C2×#4111yescharacteristic
217C22×C157C2×#4111yescharacteristic
218C22×C157H(5,𝔽2)11yescharacteristic
219C22×C157H(5,𝔽2)11yescharacteristic
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—22no—
229C2×D157—416no—
230C2×D157—41no—
231C2×D157—41no—
232C2×D157—41no—
233C2×D157—41no—
234C2×D157C4×D414yescomplemented
235C4×C157—22no—
236C4×C157—22no—
237C4×C157—41no—
238C4×C157—41no—
239C4×C157—41no—
240Dic157—22no—
241Dic157—22no—
242Dic157—22no—
243Dic157—22no—
244Dic157—22no—
245Dic157—41no—
246C2×C157—24no—
247C2×C157—42no—
248C2×C157C2×C4×D411yescharacteristic
249C2×C157C2×C4×D411yescharacteristic
250C2×C157#51811yescharacteristic
251C2×C157D4211yescharacteristic
252C2×C157#54611yescharacteristic
253C2×C157#54611yescharacteristic
254C2×C157#55111yescharacteristic
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#388—1571no—
267#386—1571no—
268#386—1571no—
269#386D15711yescharacteristic, complemented
270#385—1571no—
271#385—1571no—
272C4×C22⋊C4—1571no—
273C4×C22⋊C4—1571no—
274C25—1571no—
275C22×D4—1571no—
276C22×D4—1571no—
277C22×D4C2×D15711yescharacteristic
278C23×C4—1571no—
279C23×C4—1571no—
280C23×C4—1571no—
281C23×C4—1571no—
282C23×C4C2×D15711yescharacteristic
283#120—1578no—
284C4×D4—3144no—
285C4×D4—3144no—
286C2×C4⋊C4—1571no—
287C2×C4⋊C4—1571no—
288C2×C4⋊C4—1571no—
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, complemented
304C2×C22⋊C4C2×D15711yescharacteristic, complemented
305C2×C42—1571no—
306C2×C42—1571no—
307C2×C42—1571no—
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—
323C24C22×D15711yescharacteristic
324C24C22×D15711yescharacteristic
325C2×D4—22no—
326C2×D4—22no—
327C2×D4—3142no—
328C2×D4—3142no—
329C2×D4—6281no—
330C2×D4—6281no—
331C2×D4—1574no—
332C2×D4—1574no—
333C2×D4C4×D15714yescomplemented
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—41no—
337C22×C4—3142no—
338C22×C4—3142no—
339C22×C4—3142no—
340C22×C4—3142no—
341C22×C4—3142no—
342C22×C4—3142no—
343C22×C4—3142no—
344C22×C4—3142no—
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×C4—1571no—
355C22×C4C22×D15711yescharacteristic
356C22×C4C22×D15711yescharacteristic
357C22×C4C22×D15711yescharacteristic
358C22×C4C22×D15711yescharacteristic
359C22×C4C22×D15711yescharacteristic
360C4⋊C4—3142no—
361C4⋊C4—3142no—
362C4⋊C4—6281no—
363C22⋊C4—22no—
364C22⋊C4—22no—
365C22⋊C4—41no—
366C22⋊C4—3142no—
367C22⋊C4—3142no—
368C22⋊C4—3142no—
369C22⋊C4—3142no—
370C22⋊C4—3142no—
371C22⋊C4—3142no—
372C22⋊C4—1574no—
373C22⋊C4—1574no—
374C22⋊C4—1574no—
375C22⋊C4—1574no—
376C22⋊C4—1574no—
377C42—3142no—
378C42—3142no—
379C42—6281no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—3148no—
391C23—3141no—
392C23—3141no—
393C23—3141no—
394C23—3141no—
395C23—3148no—
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—
411C23C2×C4×D15712yes—
412C23C2×C4×D15712yes—
413C23D4×D15712yes—
414C23#1457895312yes—
415C23C23×D15711yescharacteristic
416D4—28no—
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—44no—
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—3141no—
446C2×C4—6284no—
447C2×C4—6284no—
448C2×C4—6284no—
449C2×C4—6284no—
450C2×C4—1572no—
451C2×C4—1572no—
452C2×C4—1572no—
453C2×C4—1572no—
454C2×C4—1572no—
455C2×C4C2×C4×D15712yes—
456C2×C4D4×D15712yes—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—22no—
464C22—22no—
465C22—22no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—41no—
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#1909773114yescomplemented
486C22C22×C4×D15711yescharacteristic
487C22C2×D4×D15711yescharacteristic
488C22C2×D4×D15711yescharacteristic
489C22#41×D15711yescharacteristic
490C22C2×#1457895311yescharacteristic
491C22#1909781611yescharacteristic
492C22#1909781711yescharacteristic
493C4—22no—
494C4—22no—
495C4—41no—
496C4—41no—
497C4—41no—
498C4—3142no—
499C4—3142no—
500C4—3142no—
501C4—3142no—
502C4—3142no—
503C4—6281no—
504C2—24no—
505C2—42no—
506C2—3144no—
507C2—6282no—
508C2C4×D4×D15711yescharacteristic
509C2C2×#1909773111yescharacteristic
510C2#2375774511yescharacteristic
511C2#2375790711yescharacteristic
512C2#2375791011yescharacteristic
513C2#2375791211yescharacteristic
514C2#2375794611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D157
commutatorC22×C157C23×C4
Fitting#386×C157C2
socle, cosocleC23×C157C24
prime radicalC2×#19097739C2
hypercenter#386D157
hypocenterC157#2358
LCSG ▷ C22×C157 ▷ C157
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×D4×Dic157C2semidirect
3. C2×#19097731C2semidirect
4. C22×#14578931C2semidirect
5. C2×C22⋊C4×D157C2semidirect
6. #23757173C2semidirect
7. #23757165C2semidirect
8. #23757162C2semidirect
9. #23757150C2semidirect
10. #23757149C2semidirect
11. #23757147C2semidirect
12. #23757145C2semidirect
13. C4×C22⋊Dic157C2semidirect
14. #23757120C2semidirect
15. #386×C157C2semidirect
20. C23×Dic157C22semidirect
23. #19097739C4semidirect
26. C2×C4⋊Dic157C22semidirect
27. C2×#14578933C22semidirect
28. C2×#14578933C22semidirect
31. C2×C22⋊Dic157C22semidirect
42. C2×C4×Dic157C22semidirect
43. C2×C4×Dic157C22semidirect
44. C2×C4×Dic157C22semidirect
45. #19097678C22semidirect
46. #19097678C22semidirect
47. #19097678C22semidirect
48. #19097678C22semidirect
52. C2×C22⋊C4×C157C22semidirect
53. C2×C22⋊C4×C157C22semidirect
54. #95×C157C22semidirect
55. #95×C157C22semidirect
62. C23×D157C2×C4semidirect
69. C2×C22⋊D157C2×C4semidirect
70. C2×C22⋊D157C2×C4semidirect
93. C22⋊Dic157C2×C4semidirect
94. C22⋊Dic157D4semidirect
100. #14578931C2×C4semidirect
101. #14578931C2×C4semidirect
102. #14578931D4semidirect
110. C2×D4×C157C2×C4semidirect
212. C22×C157C4×D4semidirect
234. C2×D157C4×D4semidirect
257. C157#2358semidirect
269. #386D157semidirect
303. C2×C22⋊C4C2×D157semidirect
304. C2×C22⋊C4C2×D157semidirect
312. #95C2×D157semidirect
313. #95C2×D157semidirect
333. C2×D4C4×D157semidirect
485. C22#19097731semidirect

Maximal subgroups

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

subgroupindex
C2×#190977392
C2×D4×Dic1572
C2×#190977312
C22×#145789312
C2×C22⋊C4×D1572
#237571732
#237571652
#237571622
#237571502
#237571492
#237571472
#237571452
C4×C22⋊Dic1572
#237571202
#386×C1572
#2358157