Finite Group Databasebeta

← #23766376

Subgroups — #23766376

Order 10112.

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×#14579131C211yesmaximal, characteristic
2C2×#14579123C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊D79C211yesmaximal, characteristic, complemented
4C22×(C2×D79)⋊C4C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D79C211yesmaximal, characteristic, complemented
6#19098464C211yesmaximal, characteristic, complemented
7#19098453C211yesmaximal, characteristic, complemented
8#19098452C211yesmaximal, characteristic, complemented
9#19098441C211yesmaximal, characteristic, complemented
10#19098441C211yesmaximal, characteristic, complemented
11#19098440C211yesmaximal, characteristic, complemented
12#19098434C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic79C211yesmaximal, characteristic, complemented
14#19098410C211yesmaximal, characteristic, complemented
15#385×C79C211yesmaximal, characteristic, complemented
16C24×D79C2211yescharacteristic
17C22×D316C2211yescharacteristic
18C22×D316C2211yescharacteristic
19C22×C22⋊D79C2211yescharacteristic
20C23×Dic79C2211yescharacteristic
21C22×C4×D79C2211yescharacteristic
22C22×C4×D79C2211yescharacteristic
23C22×C4×D79C2211yescharacteristic, complemented
24#14579131C418yescomplemented
25#14579123—24no—
26C4×C22⋊D79—24no—
27C2×Dic79⋊C4C2211yescharacteristic, complemented
28C2×C22⋊Dic79C2211yescharacteristic
29C2×(C2×D79)⋊C4—24no—
30C2×(C2×D79)⋊C4C2211yescharacteristic
31C2×(C2×D79)⋊C4C2211yescharacteristic
32C2×(C2×D79)⋊C4C2211yescharacteristic
33C2×(C2×D79)⋊C4C2211yescharacteristic
34C2×(C2×D79)⋊C4C2211yescharacteristic
35C2×(C2×D79)⋊C4C2211yescharacteristic
36C2×(C2×D79)⋊C4C2211yescharacteristic
37C2×(C2×D79)⋊C4C2211yescharacteristic
38C2×(C2×D79)⋊C4C2211yescharacteristic, complemented
39C2×(C2×D79)⋊C4C2211yescharacteristic, complemented
40C2×(C2×D79)⋊C4C2211yescharacteristic, complemented
41C22⋊C4×D79—24no—
42C2×C4×Dic79C2211yescharacteristic, complemented
43C2×C4×Dic79C2211yescharacteristic, complemented
44C2×C4×Dic79C2211yescharacteristic, complemented
45C79⋊#95C2211yescharacteristic, complemented
46C79⋊#95C2211yescharacteristic, complemented
47C79⋊#95C2211yescharacteristic, complemented
48C79⋊#95C2211yescharacteristic, complemented
49C23×C4×C79C2211yescharacteristic
50C2×C4⋊C4×C79C2211yescharacteristic, complemented
51C2×C4⋊C4×C79C2211yescharacteristic, complemented
52C2×C22⋊C4×C79C2211yescharacteristic
53C2×C22⋊C4×C79C2211yescharacteristic
54#95×C79C2211yescharacteristic, complemented
55#95×C79C2211yescharacteristic, complemented
56C23×D79—22no—
57C23×D79—22no—
58C23×D79—22no—
59C23×D79—22no—
60C23×D79—41no—
61C23×D79—41no—
62C23×D79C2×C414yescomplemented
63C23×D79C2311yescharacteristic
64C23×D79C2311yescharacteristic
65C23×D79C2311yescharacteristic
66C2×D316—22no—
67C2×D316—22no—
68C2×D316—41no—
69C2×D316—41no—
70C2×D316C2×C414yescomplemented
71C2×D316C2×C414yescomplemented
72C2×C22⋊D79—22no—
73C2×C22⋊D79—22no—
74C2×C22⋊D79C2×C414yescomplemented
75C22×Dic79—22no—
76C22×Dic79—22no—
77C22×Dic79—41no—
78C22×Dic79C2311yescharacteristic
79C22×Dic79C2311yescharacteristic
80C22×Dic79C2311yescharacteristic
81C22×Dic79C2311yescharacteristic
82C22×Dic79C2311yescharacteristic
83C2×C4×D79—22no—
84C2×C4×D79—22no—
85C2×C4×D79—22no—
86C2×C4×D79—22no—
87C2×C4×D79—22no—
88C2×C4×D79—22no—
89C2×C4×D79—41no—
90C2×C4×D79—41no—
91C2×C4×D79—41no—
92Dic79⋊C4—22no—
93C22⋊Dic79D414yescomplemented
94(C2×D79)⋊C4—22no—
95(C2×D79)⋊C4—22no—
96(C2×D79)⋊C4—22no—
97(C2×D79)⋊C4—22no—
98(C2×D79)⋊C4—22no—
99(C2×D79)⋊C4—22no—
100(C2×D79)⋊C4—22no—
101(C2×D79)⋊C4—41no—
102(C2×D79)⋊C4C2×C414yescomplemented
103(C2×D79)⋊C4C2×C414yescomplemented
104(C2×D79)⋊C4D414yescomplemented
105C4×Dic79—22no—
106C4×Dic79—22no—
107C4×Dic79—41no—
108C24×C79C2311yescharacteristic
109C22×C4×C79—22no—
110C22×C4×C79—22no—
111C22×C4×C79—41no—
112C22×C4×C79C2311yescharacteristic
113C22×C4×C79C2311yescharacteristic
114C22×C4×C79C2311yescharacteristic
115C22×C4×C79C2311yescharacteristic
116C22×C4×C79C2311yescharacteristic
117C22×C4×C79C2311yescharacteristic
118C4⋊C4×C79—22no—
119C4⋊C4×C79—41no—
120C22⋊C4×C79—22no—
121C22⋊C4×C79C2×C414yescomplemented
122C23×C79—21no—
123C23×C79—21no—
124C23×C79—21no—
125C23×C79—21no—
126C23×C79C22×C412yes—
127C23×C79C2×D412yes—
128C23×C79#4112yes—
129C23×C79C2411yescharacteristic
130C22×D79—21no—
131C22×D79—21no—
132C22×D79—21no—
133C22×D79—21no—
134C22×D79—28no—
135C22×D79—21no—
136C22×D79—21no—
137C22×D79—21no—
138C22×D79—21no—
139C22×D79—21no—
140C22×D79—21no—
141C22×D79—21no—
142C22×D79—21no—
143C22×D79—21no—
144C22×D79—21no—
145C22×D79—21no—
146C22×D79—21no—
147C22×D79—28no—
148C22×D79—44no—
149C22×D79—44no—
150C22×D79—44no—
151C22×D79—44no—
152C22×D79—44no—
153C22×D79C22×C412yes—
154C22×D79C22×C412yes—
155C22×D79C22×C412yes—
156C22×D79C2×D412yes—
157C22×D79#4112yes—
158C2×C4×C79—21no—
159C2×C4×C79—21no—
160C2×C4×C79—21no—
161C2×C4×C79—21no—
162C2×C4×C79—21no—
163C2×C4×C79—21no—
164C2×C4×C79—21no—
165C2×C4×C79—21no—
166C2×C4×C79—21no—
167C2×C4×C79—21no—
168C2×C4×C79—21no—
169C2×C4×C79—21no—
170C2×C4×C79—21no—
171C2×C4×C79—21no—
172C2×C4×C79—21no—
173C2×C4×C79—44no—
174C2×C4×C79C22×C412yes—
175C2×C4×C79C22×C412yes—
176C2×C4×C79C2×D412yes—
177C22⋊D79—28no—
178C2×Dic79—21no—
179C2×Dic79—21no—
180C2×Dic79—21no—
181C2×Dic79—21no—
182C2×Dic79—21no—
183C2×Dic79—21no—
184C2×Dic79—21no—
185C2×Dic79—21no—
186C2×Dic79—21no—
187C2×Dic79—21no—
188C2×Dic79—21no—
189C2×Dic79—44no—
190C2×Dic79C22×C412yes—
191C2×Dic79C2×D412yes—
192C2×Dic79C2×D412yes—
193C2×Dic79C2×D412yes—
194D316—28no—
195D316—44no—
196C4×D79—44no—
197C4×D79—44no—
198C4×D79—44no—
199C22×C79—22no—
200C22×C79—22no—
201C22×C79—22no—
202C22×C79—22no—
203C22×C79—22no—
204C22×C79—22no—
205C22×C79C4×D414yescomplemented
206C22×C79C23×C411yescharacteristic
207C22×C79C22×D411yescharacteristic
208C22×C79C22×D411yescharacteristic
209C22×C79C2×#4111yescharacteristic
210C22×C79C2×#4111yescharacteristic
211C22×C79H(5,𝔽2)11yescharacteristic
212C22×C79H(5,𝔽2)11yescharacteristic
213C2×D79—22no—
214C2×D79—22no—
215C2×D79—22no—
216C2×D79—22no—
217C2×D79—22no—
218C2×D79—22no—
219C2×D79—22no—
220C2×D79—22no—
221C2×D79—22no—
222C2×D79—22no—
223C2×D79—22no—
224C2×D79—22no—
225C2×D79—416no—
226C2×D79—41no—
227C2×D79—41no—
228C2×D79—41no—
229C2×D79—41no—
230C2×D79—41no—
231C2×D79—41no—
232C2×D79—41no—
233C2×D79—41no—
234C2×D79C4×D414yescomplemented
235C4×C79—22no—
236C4×C79—22no—
237C4×C79—22no—
238C4×C79—41no—
239C4×C79—41no—
240C4×C79—41no—
241Dic79—22no—
242Dic79—22no—
243Dic79—22no—
244Dic79—22no—
245Dic79—41no—
246C2×C79—24no—
247C2×C79C2×C4×D411yescharacteristic
248C2×C79C2×C4×D411yescharacteristic
249C2×C79#51811yescharacteristic
250C2×C79D4211yescharacteristic
251C2×C79#54611yescharacteristic
252C2×C79#54611yescharacteristic
253C2×C79#55111yescharacteristic
254D79—24no—
255D79—42no—
256D79—42no—
257#2358—791nomaximal, Sylow
258C79#235811yescharacteristic, complemented, Sylow
259C2×#120—791no—
260C2×C4×D4—791no—
261C2×C4×D4—791no—
262C22×C22⋊C4—791no—
263C22×C22⋊C4—791no—
264#390—791no—
265#388—791no—
266#388—791no—
267#386—791no—
268#386—791no—
269#386—791no—
270#385—791no—
271#385D7911yescharacteristic, complemented
272C4×C22⋊C4—791no—
273C4×C22⋊C4—791no—
274C25—791no—
275C22×D4—791no—
276C22×D4—791no—
277C22×D4—791no—
278C23×C4—791no—
279C23×C4—791no—
280C23×C4—791no—
281C23×C4—791no—
282C23×C4C2×D7911yescharacteristic
283#120—798no—
284C4×D4—1584no—
285C4×D4—1584no—
286C2×C4⋊C4—791no—
287C2×C4⋊C4C2×D7911yescharacteristic, complemented
288C2×C4⋊C4C2×D7911yescharacteristic, complemented
289C2×C22⋊C4—791no—
290C2×C22⋊C4—791no—
291C2×C22⋊C4—791no—
292C2×C22⋊C4—791no—
293C2×C22⋊C4—791no—
294C2×C22⋊C4—791no—
295C2×C22⋊C4—791no—
296C2×C22⋊C4—791no—
297C2×C22⋊C4—791no—
298C2×C22⋊C4—791no—
299C2×C22⋊C4—791no—
300C2×C22⋊C4—791no—
301C2×C22⋊C4—1584no—
302C2×C22⋊C4—1584no—
303C2×C22⋊C4C2×D7911yescharacteristic
304C2×C22⋊C4C2×D7911yescharacteristic
305C2×C42—791no—
306C2×C42—791no—
307C2×C42—791no—
308#95—791no—
309#95—791no—
310#95—791no—
311#95—791no—
312#95C2×D7911yescharacteristic, complemented
313#95C2×D7911yescharacteristic, complemented
314C24—3161no—
315C24—3161no—
316C24—794no—
317C24—791no—
318C24—791no—
319C24—791no—
320C24—1582no—
321C24—1582no—
322C24—1582no—
323C24—1582no—
324C24C22×D7911yescharacteristic
325C2×D4—3161no—
326C2×D4—3161no—
327C2×D4—794no—
328C2×D4—794no—
329C2×D4—794no—
330C2×D4—1582no—
331C2×D4—1582no—
332C2×D4—1582no—
333C2×D4—1582no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—41no—
337C22×C4—3161no—
338C22×C4—3161no—
339C22×C4—3161no—
340C22×C4—3161no—
341C22×C4—791no—
342C22×C4—791no—
343C22×C4—791no—
344C22×C4—791no—
345C22×C4—791no—
346C22×C4—1582no—
347C22×C4—1582no—
348C22×C4—1582no—
349C22×C4—1582no—
350C22×C4—1582no—
351C22×C4—1582no—
352C22×C4—1582no—
353C22×C4—1582no—
354C22×C4C22×D7911yescharacteristic
355C22×C4C22×D7911yescharacteristic
356C22×C4C22×D7911yescharacteristic
357C22×C4C22×D7911yescharacteristic
358C22×C4C22×D7911yescharacteristic
359C22×C4C22×D7911yescharacteristic
360C4⋊C4—22no—
361C4⋊C4—41no—
362C4⋊C4—1582no—
363C22⋊C4—22no—
364C22⋊C4—3161no—
365C22⋊C4—794no—
366C22⋊C4—794no—
367C22⋊C4—794no—
368C22⋊C4—794no—
369C22⋊C4—1582no—
370C22⋊C4—1582no—
371C22⋊C4—1582no—
372C22⋊C4—1582no—
373C22⋊C4—1582no—
374C22⋊C4—1582no—
375C22⋊C4—1582no—
376C22⋊C4C4×D7914yescomplemented
377C42—3161no—
378C42—1582no—
379C42—1582no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—3164no—
385C23—3164no—
386C23—3164no—
387C23—3164no—
388C23—3164no—
389C23—792no—
390C23—792no—
391C23—792no—
392C23—792no—
393C23—792no—
394C23—1588no—
395C23—1581no—
396C23—1581no—
397C23—1581no—
398C23—1581no—
399C23—1581no—
400C23—1581no—
401C23—1581no—
402C23—1581no—
403C23—1588no—
404C23—1581no—
405C23—1581no—
406C23—1581no—
407C23—1581no—
408C23—1581no—
409C23—1581no—
410C23—1581no—
411C23—1581no—
412C23C2×C4×D7912yes—
413C23D4×D7912yes—
414C23#1192962512yes—
415C23C23×D7911yescharacteristic
416D4—3164no—
417D4—1588no—
418D4—1588no—
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—21no—
434C2×C4—44no—
435C2×C4—3164no—
436C2×C4—3164no—
437C2×C4—3164no—
438C2×C4—3164no—
439C2×C4—792no—
440C2×C4—792no—
441C2×C4—792no—
442C2×C4—792no—
443C2×C4—1581no—
444C2×C4—1581no—
445C2×C4—1581no—
446C2×C4—1581no—
447C2×C4—1581no—
448C2×C4—1581no—
449C2×C4—1581no—
450C2×C4—1581no—
451C2×C4—1581no—
452C2×C4—1581no—
453C2×C4—1581no—
454C2×C4C2×C4×D7912yes—
455C2×C4C2×C4×D7912yes—
456C2×C4D4×D7912yes—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—31616no—
464C22—3161no—
465C22—3161no—
466C22—3161no—
467C22—3161no—
468C22—3161no—
469C22—3161no—
470C22—3161no—
471C22—3161no—
472C22—794no—
473C22—1582no—
474C22—1582no—
475C22—1582no—
476C22—1582no—
477C22—1582no—
478C22—1582no—
479C22—1582no—
480C22—1582no—
481C22—1582no—
482C22—1582no—
483C22—1582no—
484C22—1582no—
485C22#1457912314yescomplemented
486C22C22×C4×D7911yescharacteristic
487C22C2×D4×D7911yescharacteristic
488C22C2×D4×D7911yescharacteristic
489C22#41×D7911yescharacteristic
490C22C2×#1192962511yescharacteristic
491C22#1457920611yescharacteristic
492C22#1457920711yescharacteristic
493C4—22no—
494C4—22no—
495C4—22no—
496C4—41no—
497C4—41no—
498C4—41no—
499C4—3161no—
500C4—1582no—
501C4—1582no—
502C4—1582no—
503C4—1582no—
504C2—24no—
505C2—3162no—
506C2—3162no—
507C2—1584no—
508C2C4×D4×D7911yescharacteristic
509C2C2×#1457912311yescharacteristic
510C2#1909903511yescharacteristic
511C2#1909919511yescharacteristic
512C2#1909920411yescharacteristic
513C2#1909920511yescharacteristic
514C2#1909924011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutatorC22×C79C23×C4
Fitting#385×C79C2
socle, cosocleC23×C79C24
prime radicalC2×#14579131C2
hypercenter#385D79
hypocenterC79#2358
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C2×#14579123C2semidirect
3. C2×C4×C22⋊D79C2semidirect
4. C22×(C2×D79)⋊C4C2semidirect
5. C2×C22⋊C4×D79C2semidirect
6. #19098464C2semidirect
7. #19098453C2semidirect
8. #19098452C2semidirect
9. #19098441C2semidirect
10. #19098441C2semidirect
11. #19098440C2semidirect
12. #19098434C2semidirect
13. C22⋊C4×Dic79C2semidirect
14. #19098410C2semidirect
15. #385×C79C2semidirect
23. C22×C4×D79C22semidirect
24. #14579131C4semidirect
27. C2×Dic79⋊C4C22semidirect
38. C2×(C2×D79)⋊C4C22semidirect
39. C2×(C2×D79)⋊C4C22semidirect
40. C2×(C2×D79)⋊C4C22semidirect
42. C2×C4×Dic79C22semidirect
43. C2×C4×Dic79C22semidirect
44. C2×C4×Dic79C22semidirect
45. C79⋊#95C22semidirect
46. C79⋊#95C22semidirect
47. C79⋊#95C22semidirect
48. C79⋊#95C22semidirect
50. C2×C4⋊C4×C79C22semidirect
51. C2×C4⋊C4×C79C22semidirect
54. #95×C79C22semidirect
55. #95×C79C22semidirect
62. C23×D79C2×C4semidirect
70. C2×D316C2×C4semidirect
71. C2×D316C2×C4semidirect
74. C2×C22⋊D79C2×C4semidirect
93. C22⋊Dic79D4semidirect
102. (C2×D79)⋊C4C2×C4semidirect
103. (C2×D79)⋊C4C2×C4semidirect
104. (C2×D79)⋊C4D4semidirect
121. C22⋊C4×C79C2×C4semidirect
205. C22×C79C4×D4semidirect
234. C2×D79C4×D4semidirect
258. C79#2358semidirect
271. #385D79semidirect
287. C2×C4⋊C4C2×D79semidirect
288. C2×C4⋊C4C2×D79semidirect
312. #95C2×D79semidirect
313. #95C2×D79semidirect
376. C22⋊C4C4×D79semidirect
485. C22#14579123semidirect