Finite Group Databasebeta

← #23767523

Subgroups — #23767523

Order 10112.

786 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579147C211yesmaximal, characteristic, complemented
2C2×#14579138C211yesmaximal, characteristic, complemented
3C2×#14579130C211yesmaximal, characteristic
4C22×C22⋊Dic79C211yesmaximal, characteristic, complemented
5#19098491C211yesmaximal, characteristic, complemented
6#19098479C211yesmaximal, characteristic, complemented
7#19098478C211yesmaximal, characteristic, complemented
8#19098475C211yesmaximal, characteristic, complemented
9#19098463C211yesmaximal, characteristic, complemented
10#19098456C211yesmaximal, characteristic, complemented
11#19098451C211yesmaximal, characteristic, complemented
12#19098440C211yesmaximal, characteristic, complemented
13#19098440C211yesmaximal, characteristic, complemented
14C22⋊C4×Dic79C211yesmaximal, characteristic, complemented
15#379×C79C211yesmaximal, characteristic, complemented
16C22×Dic158C2211yescharacteristic, complemented
17C22×C22⋊D79C2211yescharacteristic
18C22×C22⋊D79C2211yescharacteristic
19C22×C22⋊D79C2211yescharacteristic
20C23×Dic79C2211yescharacteristic
21C23×Dic79C2211yescharacteristic
22#14579147—24no—
23#14579138—24no—
24#14579130—24no—
25C2×C4⋊Dic79C2211yescharacteristic, complemented
26C2×Dic79⋊C4C2211yescharacteristic, complemented
27C2×Dic79⋊C4C2211yescharacteristic, complemented
28C2×C22⋊Dic79—24no—
29C2×C22⋊Dic79C2211yescharacteristic
30C2×C22⋊Dic79C2211yescharacteristic
31C2×C22⋊Dic79C2211yescharacteristic
32C2×C22⋊Dic79C2211yescharacteristic
33C2×C22⋊Dic79C2211yescharacteristic
34C2×C22⋊Dic79C2211yescharacteristic
35C2×C22⋊Dic79C2211yescharacteristic
36C2×(C2×D79)⋊C4C2211yescharacteristic, complemented
37C2×(C2×D79)⋊C4C2211yescharacteristic, complemented
38C2×(C2×D79)⋊C4C2211yescharacteristic, complemented
39C2×(C2×D79)⋊C4C2211yescharacteristic, complemented
40C2×C4×Dic79C2211yescharacteristic, complemented
41C2×C4×Dic79C2211yescharacteristic, complemented
42C79⋊#95C2211yescharacteristic, complemented
43C79⋊#95C2211yescharacteristic, complemented
44C79⋊#95C2211yescharacteristic, complemented
45C79⋊#95C2211yescharacteristic, complemented
46C79⋊#95C2211yescharacteristic, complemented
47C79⋊#95C2211yescharacteristic, complemented
48C25×C79C2211yescharacteristic
49C2×C22⋊C4×C79C2211yescharacteristic
50C2×C22⋊C4×C79C2211yescharacteristic
51C2×C22⋊C4×C79C2211yescharacteristic
52C2×C22⋊C4×C79C2211yescharacteristic
53C2×C22⋊C4×C79C2211yescharacteristic
54C2×C22⋊C4×C79C2211yescharacteristic
55C23×D79C2311yescharacteristic
56C2×Dic158—22no—
57C2×Dic158—22no—
58C2×Dic158—41no—
59C2×C22⋊D79—22no—
60C2×C22⋊D79—22no—
61C2×C22⋊D79—22no—
62C2×C22⋊D79—22no—
63C2×C22⋊D79—22no—
64C2×C22⋊D79—22no—
65C2×C22⋊D79—22no—
66C2×C22⋊D79—41no—
67C2×C22⋊D79—41no—
68C22×Dic79—22no—
69C22×Dic79—22no—
70C22×Dic79—22no—
71C22×Dic79—22no—
72C22×Dic79—41no—
73C22×Dic79—41no—
74C22×Dic79C2311yescharacteristic
75C22×Dic79C2311yescharacteristic
76C22×Dic79C2311yescharacteristic
77C22×Dic79C2311yescharacteristic
78C22×Dic79C2311yescharacteristic
79C22×Dic79C2311yescharacteristic
80C22×Dic79C2311yescharacteristic
81C4⋊Dic79—22no—
82Dic79⋊C4—22no—
83Dic79⋊C4—22no—
84C22⋊Dic79—22no—
85C22⋊Dic79—22no—
86C22⋊Dic79—22no—
87C22⋊Dic79—22no—
88C22⋊Dic79—22no—
89C22⋊Dic79D414yes—
90C22⋊Dic79D414yescomplemented
91(C2×D79)⋊C4—22no—
92(C2×D79)⋊C4—22no—
93(C2×D79)⋊C4—41no—
94(C2×D79)⋊C4—41no—
95C4×Dic79—22no—
96C4×Dic79—41no—
97C24×C79—22no—
98C24×C79—22no—
99C24×C79—22no—
100C24×C79—22no—
101C24×C79—22no—
102C24×C79—41no—
103C24×C79—41no—
104C24×C79C2311yescharacteristic
105C24×C79C2311yescharacteristic
106C24×C79C2311yescharacteristic
107C22×C4×C79C2311yescharacteristic
108C22×C4×C79C2311yescharacteristic
109C22×C4×C79C2311yescharacteristic
110C22×C4×C79C2311yescharacteristic
111C22⋊C4×C79—22no—
112C22⋊C4×C79—22no—
113C22⋊C4×C79—22no—
114C22⋊C4×C79—22no—
115C22⋊C4×C79—41no—
116C22⋊C4×C79—41no—
117C23×C79—21no—
118C23×C79—21no—
119C23×C79—21no—
120C23×C79—21no—
121C23×C79—28no—
122C23×C79—21no—
123C23×C79—21no—
124C23×C79—21no—
125C23×C79—21no—
126C23×C79—21no—
127C23×C79—21no—
128C23×C79—21no—
129C23×C79—21no—
130C23×C79—21no—
131C23×C79—21no—
132C23×C79—21no—
133C23×C79—21no—
134C23×C79—44no—
135C23×C79—44no—
136C23×C79—44no—
137C23×C79—44no—
138C23×C79—44no—
139C23×C79—44no—
140C23×C79C2×D412yes—
141C23×C79C2×D412yes—
142C23×C79#4112yes—
143C23×C79#4112yes—
144C23×C79#4112yes—
145C23×C79C2411yescharacteristic
146C22×D79—21no—
147C22×D79—21no—
148C22×D79—21no—
149C22×D79—21no—
150C22×D79—21no—
151C22×D79—21no—
152C22×D79—21no—
153C2×C4×C79—21no—
154C2×C4×C79—21no—
155C2×C4×C79—21no—
156C2×C4×C79—21no—
157C2×C4×C79—21no—
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—
165C22⋊D79—44no—
166C22⋊D79—44no—
167C22⋊D79—44no—
168C2×Dic79—21no—
169C2×Dic79—21no—
170C2×Dic79—21no—
171C2×Dic79—21no—
172C2×Dic79—21no—
173C2×Dic79—21no—
174C2×Dic79—21no—
175C2×Dic79—21no—
176C2×Dic79—21no—
177C2×Dic79—21no—
178C2×Dic79—21no—
179C2×Dic79—21no—
180C2×Dic79—21no—
181C2×Dic79—21no—
182C2×Dic79—21no—
183C2×Dic79—21no—
184C2×Dic79—21no—
185C2×Dic79—44no—
186C2×Dic79—44no—
187C2×Dic79C2×D412yes—
188C2×Dic79C2×D412yes—
189C2×Dic79C2×D412yes—
190C2×Dic79C2×D412yes—
191Dic158—44no—
192C22×C79—22no—
193C22×C79—22no—
194C22×C79—22no—
195C22×C79—22no—
196C22×C79—22no—
197C22×C79—22no—
198C22×C79—22no—
199C22×C79—22no—
200C22×C79—22no—
201C22×C79—22no—
202C22×C79—22no—
203C22×C79—22no—
204C22×C79—416no—
205C22×C79—41no—
206C22×C79—41no—
207C22×C79—41no—
208C22×C79—41no—
209C22×C79—41no—
210C22×C79—41no—
211C22×C79—41no—
212C22×C79—41no—
213C22×C79#12414yescomplemented
214C22×C79C22×D411yescharacteristic
215C22×C79C22×D411yescharacteristic
216C22×C79C2×#4111yescharacteristic
217C22×C79C2×#4111yescharacteristic
218C22×C79C2×#4111yescharacteristic
219C22×C79H(5,𝔽2)11yescharacteristic
220C22×C79H(5,𝔽2)11yescharacteristic
221C2×D79—41no—
222C2×D79—41no—
223C2×D79—41no—
224C2×D79—41no—
225C2×D79—41no—
226C2×D79—41no—
227C2×D79—41no—
228C4×C79—41no—
229C4×C79—41no—
230C4×C79—41no—
231C4×C79—41no—
232Dic79—22no—
233Dic79—22no—
234Dic79—22no—
235Dic79—22no—
236Dic79—41no—
237Dic79—41no—
238Dic79—41no—
239C2×C79—24no—
240C2×C79—42no—
241C2×C79—42no—
242C2×C79#52511yescharacteristic
243C2×C79C2×#12411yescharacteristic
244C2×C79#53811yescharacteristic
245C2×C79D4211yescharacteristic
246C2×C79#54611yescharacteristic
247C2×C79#54611yescharacteristic
248C2×C79#55111yescharacteristic
249D79—81no—
250#2472—791nomaximal, Sylow
251C79#247211yescharacteristic, complemented, Sylow
252C2×#124—791no—
253C2×C22⋊Q8—791no—
254C2×#120—791no—
255C22×C22⋊C4—791no—
256#397—791no—
257#394—791no—
258#394—791no—
259#393—791no—
260#390—791no—
261#388—791no—
262#388—791no—
263#386—791no—
264#386—791no—
265#379D7911yescharacteristic, complemented
266C4×C22⋊C4—791no—
267C25C2×D7911yescharacteristic
268C22×Q8—791no—
269C22×D4—791no—
270C22×D4—791no—
271C22×D4—791no—
272C23×C4—791no—
273C23×C4—791no—
274#124—1584no—
275C22⋊Q8—1584no—
276#120—1584no—
277C2×C4⋊C4—791no—
278C2×C4⋊C4—791no—
279C2×C4⋊C4—791no—
280C2×C22⋊C4—791no—
281C2×C22⋊C4—791no—
282C2×C22⋊C4—791no—
283C2×C22⋊C4—791no—
284C2×C22⋊C4—791no—
285C2×C22⋊C4—791no—
286C2×C22⋊C4—791no—
287C2×C22⋊C4—791no—
288C2×C22⋊C4—791no—
289C2×C22⋊C4—791no—
290C2×C22⋊C4—791no—
291C2×C22⋊C4—1584no—
292C2×C22⋊C4C2×D7911yescharacteristic
293C2×C22⋊C4C2×D7911yescharacteristic
294C2×C22⋊C4C2×D7911yescharacteristic
295C2×C22⋊C4C2×D7911yescharacteristic
296C2×C22⋊C4C2×D7911yescharacteristic
297C2×C22⋊C4C2×D7911yescharacteristic
298C2×C42—791no—
299C2×C42—791no—
300#95—791no—
301#95—791no—
302#95—791no—
303#95—791no—
304#95—791no—
305#95—791no—
306C24—22no—
307C24—22no—
308C24—22no—
309C24—22no—
310C24—22no—
311C24—41no—
312C24—41no—
313C24—791no—
314C24C22×D7911yescharacteristic
315C24C22×D7911yescharacteristic
316C24C22×D7911yescharacteristic
317C2×Q8—3161no—
318C2×Q8—1582no—
319C2×Q8—1582no—
320C2×D4—3161no—
321C2×D4—3161no—
322C2×D4—1582no—
323C2×D4—1582no—
324C2×D4—1582no—
325C2×D4—1582no—
326C2×D4—1582no—
327C2×D4—1582no—
328C2×D4—1582no—
329C22×C4—3161no—
330C22×C4—3161no—
331C22×C4—791no—
332C22×C4—791no—
333C22×C4—791no—
334C22×C4—791no—
335C22×C4—791no—
336C22×C4—791no—
337C22×C4—791no—
338C22×C4—1582no—
339C22×C4—1582no—
340C22×C4—1582no—
341C22×C4—1582no—
342C22×C4C22×D7911yescharacteristic
343C22×C4C22×D7911yescharacteristic
344C22×C4C22×D7911yescharacteristic
345C22×C4C22×D7911yescharacteristic
346C4⋊C4—1582no—
347C4⋊C4—1582no—
348C4⋊C4—1582no—
349C22⋊C4—22no—
350C22⋊C4—22no—
351C22⋊C4—22no—
352C22⋊C4—22no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—3161no—
356C22⋊C4—3161no—
357C22⋊C4—794no—
358C22⋊C4—794no—
359C22⋊C4—1582no—
360C22⋊C4—1582no—
361C22⋊C4—1582no—
362C22⋊C4—1582no—
363C22⋊C4—1582no—
364C22⋊C4—1582no—
365C22⋊C4—1582no—
366C42—3161no—
367C42—1582no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—28no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—44no—
386C23—44no—
387C23—44no—
388C23—44no—
389C23—44no—
390C23—44no—
391C23—1581no—
392C23—1581no—
393C23—1581no—
394C23—1581no—
395C23—1581no—
396C23—1581no—
397C23—1581no—
398C23D4×D7912yes—
399C23D4×D7912yes—
400C23#1192962312yes—
401C23#1192962312yes—
402C23#1192962412yes—
403C23C23×D7911yescharacteristic
404Q8—3164no—
405D4—3164no—
406D4—3164no—
407D4—3164no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—3164no—
421C2×C4—3164no—
422C2×C4—792no—
423C2×C4—792no—
424C2×C4—792no—
425C2×C4—792no—
426C2×C4—1581no—
427C2×C4—1581no—
428C2×C4—1581no—
429C2×C4—1581no—
430C2×C4—1581no—
431C2×C4—1581no—
432C2×C4—1581no—
433C2×C4—1581no—
434C2×C4—1581no—
435C2×C4—1581no—
436C2×C4—1581no—
437C2×C4—1581no—
438C2×C4—1581no—
439C2×C4—1581no—
440C2×C4—1581no—
441C2×C4—1581no—
442C2×C4—1581no—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—22no—
452C22—22no—
453C22—22no—
454C22—22no—
455C22—416no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—3161no—
465C22—3161no—
466C22—3161no—
467C22—3161no—
468C22—3161no—
469C22—3161no—
470C22—3161no—
471C22#1457914714yescomplemented
472C22C2×D4×D7911yescharacteristic
473C22C2×D4×D7911yescharacteristic
474C22C2×#1192962311yescharacteristic
475C22C2×#1192962311yescharacteristic
476C22C2×#1192962411yescharacteristic
477C22#1457920611yescharacteristic
478C22#1457920611yescharacteristic
479C4—41no—
480C4—41no—
481C4—41no—
482C4—41no—
483C4—3161no—
484C4—3161no—
485C4—3161no—
486C4—1582no—
487C4—1582no—
488C4—1582no—
489C4—1582no—
490C2—24no—
491C2—42no—
492C2—42no—
493C2—6321no—
494C2#1909906911yescharacteristic
495C2C2×#1457914711yescharacteristic
496C2#1909914811yescharacteristic
497C2#1909919511yescharacteristic
498C2#1909920011yescharacteristic
499C2#1909920311yescharacteristic
500C2#1909923911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#379×C79C2
prime radicalC2×#14579130C2
hypercenter#379D79
hypocenterC79#2472
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
1. C2×#14579147C2semidirect
2. C2×#14579138C2semidirect
4. C22×C22⋊Dic79C2semidirect
5. #19098491C2semidirect
6. #19098479C2semidirect
7. #19098478C2semidirect
8. #19098475C2semidirect
9. #19098463C2semidirect
10. #19098456C2semidirect
11. #19098451C2semidirect
12. #19098440C2semidirect
13. #19098440C2semidirect
14. C22⋊C4×Dic79C2semidirect
15. #379×C79C2semidirect
16. C22×Dic158C22semidirect
25. C2×C4⋊Dic79C22semidirect
26. C2×Dic79⋊C4C22semidirect
27. C2×Dic79⋊C4C22semidirect
36. C2×(C2×D79)⋊C4C22semidirect
37. C2×(C2×D79)⋊C4C22semidirect
38. C2×(C2×D79)⋊C4C22semidirect
39. C2×(C2×D79)⋊C4C22semidirect
40. C2×C4×Dic79C22semidirect
41. C2×C4×Dic79C22semidirect
42. C79⋊#95C22semidirect
43. C79⋊#95C22semidirect
44. C79⋊#95C22semidirect
45. C79⋊#95C22semidirect
46. C79⋊#95C22semidirect
47. C79⋊#95C22semidirect
90. C22⋊Dic79D4semidirect
213. C22×C79#124semidirect
251. C79#2472semidirect
265. #379D79semidirect
471. C22#14579147semidirect