Finite Group Databasebeta

← #23767644

Subgroups — #23767644

Order 10112.

664 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
1C2×#14579154C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×D79C211yesmaximal, characteristic
3#19098490C211yesmaximal, characteristic, complemented
4#19098488C211yesmaximal, characteristic, complemented
5#19098488C211yesmaximal, characteristic, complemented
6#19098485C211yesmaximal, characteristic, complemented
7#19098455C211yesmaximal, characteristic, complemented
8#19098454C211yesmaximal, characteristic, complemented
9#19098437C211yesmaximal, characteristic, complemented
10#19098437C211yesmaximal, characteristic, complemented
11#19098420C211yesmaximal, characteristic, complemented
12#19098418C211yesmaximal, characteristic
13#19098418C211yesmaximal, characteristic
14C4×(C2×D79)⋊C4C211yesmaximal, characteristic, complemented
15#388×C79C211yesmaximal, characteristic, complemented
16C24×D79C2211yescharacteristic
17C22×C4×D79C2211yescharacteristic
18C22×C4×D79C2211yescharacteristic
19#14579154—24no—
20C2×C4⋊Dic79C2211yescharacteristic, complemented
21C2×C4⋊Dic79C2211yescharacteristic, complemented
22C2×C4⋊Dic79C2211yescharacteristic, complemented
23C2×Dic79⋊C4C2211yescharacteristic, complemented
24C2×Dic79⋊C4C2211yescharacteristic, complemented
25C2×C22⋊Dic79C2211yescharacteristic
26C2×C22⋊Dic79C2211yescharacteristic
27C2×C22⋊Dic79C2211yescharacteristic
28C2×(C2×D79)⋊C4C2211yescharacteristic
29C2×(C2×D79)⋊C4C2211yescharacteristic
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
38C22⋊C4×D79—24no—
39C2×C4×Dic79C2211yescharacteristic, complemented
40C79⋊#95C2211yescharacteristic, complemented
41C79⋊#95C2211yescharacteristic, complemented
42C79⋊#95C2211yescharacteristic, complemented
43C79⋊#95C2211yescharacteristic, complemented
44C79⋊#95C2211yescharacteristic, complemented
45C79⋊#95C2211yescharacteristic, complemented
46C2×C4⋊C4×C79C2211yescharacteristic, complemented
47C2×C22⋊C4×C79C2211yescharacteristic
48C2×C22⋊C4×C79C2211yescharacteristic
49C2×C22⋊C4×C79C2211yescharacteristic
50C2×C42×C79C2211yescharacteristic, complemented
51#95×C79C2211yescharacteristic, complemented
52#95×C79C2211yescharacteristic, complemented
53C23×D79—22no—
54C23×D79—22no—
55C23×D79—22no—
56C23×D79—22no—
57C23×D79—22no—
58C23×D79—41no—
59C23×D79—41no—
60C23×D79C2311yescharacteristic
61C23×D79C2311yescharacteristic
62C22×Dic79C2311yescharacteristic
63C22×Dic79C2311yescharacteristic
64C22×Dic79C2311yescharacteristic
65C22×Dic79C2311yescharacteristic
66C22×Dic79C2311yescharacteristic
67C22×Dic79C2311yescharacteristic
68C2×C4×D79—22no—
69C2×C4×D79—22no—
70C2×C4×D79—22no—
71C2×C4×D79—22no—
72C2×C4×D79—41no—
73C2×C4×D79—41no—
74C4⋊Dic79—22no—
75C4⋊Dic79—41no—
76C4⋊Dic79—41no—
77Dic79⋊C4—22no—
78Dic79⋊C4—22no—
79C22⋊Dic79—22no—
80C22⋊Dic79—22no—
81C22⋊Dic79—22no—
82(C2×D79)⋊C4—22no—
83(C2×D79)⋊C4—22no—
84(C2×D79)⋊C4—22no—
85(C2×D79)⋊C4—22no—
86(C2×D79)⋊C4—22no—
87(C2×D79)⋊C4—22no—
88(C2×D79)⋊C4—22no—
89(C2×D79)⋊C4—22no—
90(C2×D79)⋊C4—41no—
91(C2×D79)⋊C4—41no—
92C4×Dic79—22no—
93C24×C79C2311yescharacteristic
94C22×C4×C79C2311yescharacteristic
95C22×C4×C79C2311yescharacteristic
96C22×C4×C79C2311yescharacteristic
97C22×C4×C79C2311yescharacteristic
98C22×C4×C79C2311yescharacteristic
99C22×C4×C79C2311yescharacteristic
100C4⋊C4×C79—41no—
101C22⋊C4×C79—41no—
102C22⋊C4×C79—41no—
103C22⋊C4×C79D414yes—
104C42×C79—41no—
105C23×C79—21no—
106C23×C79—21no—
107C23×C79—21no—
108C23×C79—21no—
109C23×C79—21no—
110C23×C79—21no—
111C23×C79C2×D412yes—
112C23×C79C2411yescharacteristic
113C22×D79—21no—
114C22×D79—21no—
115C22×D79—21no—
116C22×D79—21no—
117C22×D79—28no—
118C22×D79—21no—
119C22×D79—21no—
120C22×D79—21no—
121C22×D79—21no—
122C22×D79—21no—
123C22×D79—21no—
124C22×D79—44no—
125C22×D79—44no—
126C22×D79—44no—
127C22×D79—44no—
128C22×D79—44no—
129C22×D79—44no—
130C22×D79#4112yes—
131C22×D79#4112yes—
132C22×D79#4112yes—
133C22×D79#4112yes—
134C2×C4×C79—21no—
135C2×C4×C79—21no—
136C2×C4×C79—21no—
137C2×C4×C79—21no—
138C2×C4×C79—21no—
139C2×C4×C79—21no—
140C2×C4×C79—21no—
141C2×C4×C79—21no—
142C2×C4×C79—21no—
143C2×C4×C79—21no—
144C2×C4×C79—21no—
145C2×C4×C79—21no—
146C2×C4×C79—21no—
147C2×C4×C79—21no—
148C2×C4×C79—21no—
149C2×C4×C79—21no—
150C2×C4×C79C2×D412yes—
151C2×C4×C79C2×D412yes—
152C2×Dic79—21no—
153C2×Dic79—21no—
154C2×Dic79—21no—
155C2×Dic79—21no—
156C2×Dic79—21no—
157C2×Dic79—21no—
158C2×Dic79—21no—
159C2×Dic79—21no—
160C2×Dic79—21no—
161C2×Dic79—21no—
162C2×Dic79—21no—
163C2×Dic79—21no—
164C2×Dic79—21no—
165C2×Dic79—21no—
166C2×Dic79—21no—
167C2×Dic79—21no—
168C2×Dic79—21no—
169C2×Dic79—21no—
170C4×D79—44no—
171C4×D79—44no—
172C22×C79—22no—
173C22×C79—22no—
174C22×C79—22no—
175C22×C79—41no—
176C22×C79—41no—
177C22×C79—41no—
178C22×C79—41no—
179C22×C79C22×D411yescharacteristic
180C22×C79C2×#4111yescharacteristic
181C22×C79C2×#4111yescharacteristic
182C22×C79C2×#4111yescharacteristic
183C22×C79C2×#4111yescharacteristic
184C22×C79H(5,𝔽2)11yescharacteristic
185C22×C79H(5,𝔽2)11yescharacteristic
186C2×D79—22no—
187C2×D79—22no—
188C2×D79—22no—
189C2×D79—22no—
190C2×D79—22no—
191C2×D79—22no—
192C2×D79—22no—
193C2×D79—22no—
194C2×D79—22no—
195C2×D79—416no—
196C2×D79—41no—
197C2×D79—41no—
198C2×D79—41no—
199C2×D79—41no—
200C2×D79#12614yescomplemented
201C4×C79—22no—
202C4×C79—22no—
203C4×C79—41no—
204C4×C79—41no—
205C4×C79—41no—
206C4×C79—41no—
207Dic79—41no—
208Dic79—41no—
209Dic79—41no—
210Dic79—41no—
211Dic79—41no—
212Dic79—41no—
213C2×C79—42no—
214C2×C79#52511yescharacteristic
215C2×C79C2×#12611yescharacteristic
216C2×C79#53811yescharacteristic
217C2×C79#54611yescharacteristic
218C2×C79#54611yescharacteristic
219C2×C79#55111yescharacteristic
220C2×C79#55111yescharacteristic
221D79—24no—
222D79—42no—
223#2480—791nomaximal, Sylow
224C79#248011yescharacteristic, complemented, Sylow
225C2×#126—791no—
226C22×C22⋊C4—791no—
227#397—791no—
228#397—791no—
229#397—791no—
230#396—791no—
231#388—791no—
232#388—791no—
233#388D7911yescharacteristic, complemented
234#385—791no—
235#385—791no—
236#380—791no—
237#379—791no—
238#379—791no—
239C4×C22⋊C4—791no—
240C25—791no—
241C23×C4—791no—
242C23×C4—791no—
243#126—1584no—
244C2×C4⋊C4—791no—
245C2×C4⋊C4—791no—
246C2×C4⋊C4—791no—
247C2×C4⋊C4—791no—
248C2×C4⋊C4—791no—
249C2×C4⋊C4C2×D7911yescharacteristic, complemented
250C2×C22⋊C4—791no—
251C2×C22⋊C4—791no—
252C2×C22⋊C4—791no—
253C2×C22⋊C4—791no—
254C2×C22⋊C4—791no—
255C2×C22⋊C4—791no—
256C2×C22⋊C4—791no—
257C2×C22⋊C4—791no—
258C2×C22⋊C4—791no—
259C2×C22⋊C4—791no—
260C2×C22⋊C4—791no—
261C2×C22⋊C4—791no—
262C2×C22⋊C4—791no—
263C2×C22⋊C4—1584no—
264C2×C22⋊C4C2×D7911yescharacteristic
265C2×C22⋊C4C2×D7911yescharacteristic
266C2×C22⋊C4C2×D7911yescharacteristic
267C2×C42—791no—
268C2×C42C2×D7911yescharacteristic, complemented
269#95—791no—
270#95—791no—
271#95—791no—
272#95—791no—
273#95—791no—
274#95—791no—
275#95C2×D7911yescharacteristic, complemented
276#95C2×D7911yescharacteristic, complemented
277C24—3161no—
278C24—3161no—
279C24—791no—
280C24—791no—
281C24—1582no—
282C24—1582no—
283C24—1582no—
284C24—1582no—
285C24—1582no—
286C24C22×D7911yescharacteristic
287C22×C4—3161no—
288C22×C4—3161no—
289C22×C4—791no—
290C22×C4—791no—
291C22×C4—791no—
292C22×C4—791no—
293C22×C4—791no—
294C22×C4—791no—
295C22×C4—1582no—
296C22×C4—1582no—
297C22×C4—1582no—
298C22×C4—1582no—
299C22×C4C22×D7911yescharacteristic
300C22×C4C22×D7911yescharacteristic
301C22×C4C22×D7911yescharacteristic
302C22×C4C22×D7911yescharacteristic
303C22×C4C22×D7911yescharacteristic
304C22×C4C22×D7911yescharacteristic
305C4⋊C4—41no—
306C4⋊C4—3161no—
307C4⋊C4—3161no—
308C4⋊C4—1582no—
309C4⋊C4—1582no—
310C4⋊C4—1582no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—3161no—
314C22⋊C4—3161no—
315C22⋊C4—1582no—
316C22⋊C4—1582no—
317C22⋊C4—1582no—
318C22⋊C4—1582no—
319C22⋊C4—1582no—
320C22⋊C4—1582no—
321C22⋊C4—1582no—
322C22⋊C4—1582no—
323C22⋊C4—1582no—
324C22⋊C4—1582no—
325C22⋊C4—1582no—
326C22⋊C4D31614yes—
327C42—41no—
328C42—1582no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—3164no—
336C23—3164no—
337C23—3164no—
338C23—3164no—
339C23—3164no—
340C23—3164no—
341C23—792no—
342C23—792no—
343C23—792no—
344C23—792no—
345C23—1588no—
346C23—1581no—
347C23—1581no—
348C23—1581no—
349C23—1581no—
350C23—1581no—
351C23—1581no—
352C23—1581no—
353C23—1581no—
354C23—1581no—
355C23—1581no—
356C23C2×D31612yes—
357C23C23×D7911yescharacteristic
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—3164no—
375C2×C4—3164no—
376C2×C4—1581no—
377C2×C4—1581no—
378C2×C4—1581no—
379C2×C4—1581no—
380C2×C4—1581no—
381C2×C4—1581no—
382C2×C4—1581no—
383C2×C4—1581no—
384C2×C4—1581no—
385C2×C4—1581no—
386C2×C4—1581no—
387C2×C4—1581no—
388C2×C4—1581no—
389C2×C4—1581no—
390C2×C4—1581no—
391C2×C4—1581no—
392C2×C4—1581no—
393C2×C4—1581no—
394C2×C4C2×D31612yes—
395C2×C4C2×D31612yes—
396C22—22no—
397C22—22no—
398C22—22no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—31616no—
404C22—3161no—
405C22—3161no—
406C22—3161no—
407C22—3161no—
408C22—794no—
409C22—1582no—
410C22—1582no—
411C22—1582no—
412C22—1582no—
413C22—1582no—
414C22—1582no—
415C22—1582no—
416C22—1582no—
417C22—1582no—
418C22C22×D31611yescharacteristic
419C22#41×D7911yescharacteristic
420C22#41×D7911yescharacteristic
421C22#41×D7911yescharacteristic
422C22#41×D7911yescharacteristic
423C22#1457920611yescharacteristic
424C22#1457920611yescharacteristic
425C4—22no—
426C4—22no—
427C4—41no—
428C4—41no—
429C4—41no—
430C4—41no—
431C4—3161no—
432C4—3161no—
433C4—3161no—
434C4—3161no—
435C4—3161no—
436C4—3161no—
437C2—42no—
438C2—3162no—
439C2—1584no—
440C2#1909907511yescharacteristic
441C2#126×D7911yescharacteristic
442C2#1909914511yescharacteristic
443C2#1909920811yescharacteristic
444C2#1909920811yescharacteristic
445C2#1909924111yescharacteristic
446C2#1909924311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#388×C79C2
prime radicalC24×D79C22
hypercenter#388D79
hypocenterC79#2480
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#14579154C2semidirect
3. #19098490C2semidirect
4. #19098488C2semidirect
5. #19098488C2semidirect
6. #19098485C2semidirect
7. #19098455C2semidirect
8. #19098454C2semidirect
9. #19098437C2semidirect
10. #19098437C2semidirect
11. #19098420C2semidirect
14. C4×(C2×D79)⋊C4C2semidirect
15. #388×C79C2semidirect
20. C2×C4⋊Dic79C22semidirect
21. C2×C4⋊Dic79C22semidirect
22. C2×C4⋊Dic79C22semidirect
23. C2×Dic79⋊C4C22semidirect
24. C2×Dic79⋊C4C22semidirect
39. C2×C4×Dic79C22semidirect
40. C79⋊#95C22semidirect
41. C79⋊#95C22semidirect
42. C79⋊#95C22semidirect
43. C79⋊#95C22semidirect
44. C79⋊#95C22semidirect
45. C79⋊#95C22semidirect
46. C2×C4⋊C4×C79C22semidirect
50. C2×C42×C79C22semidirect
51. #95×C79C22semidirect
52. #95×C79C22semidirect
200. C2×D79#126semidirect
224. C79#2480semidirect
233. #388D79semidirect
249. C2×C4⋊C4C2×D79semidirect
268. C2×C42C2×D79semidirect
275. #95C2×D79semidirect
276. #95C2×D79semidirect