Finite Group Databasebeta

← #23770445

Subgroups — #23770445

Order 10112.

560 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19098492C211yesmaximal, characteristic, complemented
2#19098491C211yesmaximal, characteristic, complemented
3#19098489C211yesmaximal, characteristic, complemented
4#19098476C211yesmaximal, characteristic, complemented
5#19098476C211yesmaximal, characteristic, complemented
6#19098475C211yesmaximal, characteristic, complemented
7#19098454C211yesmaximal, characteristic, complemented
8#19098454C211yesmaximal, characteristic, complemented
9#19098453C211yesmaximal, characteristic, complemented
10#19098452C211yesmaximal, characteristic, complemented
11#19098451C211yesmaximal, characteristic, complemented
12#19098418C211yesmaximal, characteristic
13#19098418C211yesmaximal, characteristic
14#19098418C211yesmaximal, characteristic
15#388×C79C211yesmaximal, characteristic, complemented
16C24×D79C2211yescharacteristic
17C22×Dic158C2211yescharacteristic, complemented
18C2×Dic79⋊C4C2211yescharacteristic, complemented
19C2×Dic79⋊C4C2211yescharacteristic, complemented
20C2×C22⋊Dic79C2211yescharacteristic
21C2×C22⋊Dic79C2211yescharacteristic
22C2×C22⋊Dic79C2211yescharacteristic
23C2×(C2×D79)⋊C4C2211yescharacteristic
24C2×(C2×D79)⋊C4C2211yescharacteristic
25C2×(C2×D79)⋊C4C2211yescharacteristic
26C2×(C2×D79)⋊C4C2211yescharacteristic
27C2×(C2×D79)⋊C4C2211yescharacteristic
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×C4×Dic79C2211yescharacteristic, complemented
36C79⋊#95C2211yescharacteristic, complemented
37C79⋊#95C2211yescharacteristic, complemented
38C79⋊#95C2211yescharacteristic, complemented
39C79⋊#95C2211yescharacteristic, complemented
40C79⋊#95C2211yescharacteristic, complemented
41C79⋊#95C2211yescharacteristic, complemented
42C79⋊#95C2211yescharacteristic, complemented
43C79⋊#95C2211yescharacteristic, complemented
44C2×C4⋊C4×C79C2211yescharacteristic, complemented
45C2×C22⋊C4×C79C2211yescharacteristic
46C2×C22⋊C4×C79C2211yescharacteristic
47C2×C22⋊C4×C79C2211yescharacteristic
48C2×C42×C79C2211yescharacteristic, complemented
49#95×C79C2211yescharacteristic, complemented
50#95×C79C2211yescharacteristic, complemented
51C23×D79—22no—
52C23×D79—22no—
53C23×D79—22no—
54C23×D79—41no—
55C23×D79—41no—
56C23×D79—41no—
57C23×D79—41no—
58C23×D79C2311yescharacteristic
59C23×D79C2311yescharacteristic
60C2×Dic158—41no—
61C2×Dic158—41no—
62C2×Dic158—41no—
63C22×Dic79C2311yescharacteristic
64C22×Dic79C2311yescharacteristic
65C22×Dic79C2311yescharacteristic
66C22×Dic79C2311yescharacteristic
67C22×Dic79C2311yescharacteristic
68C22×Dic79C2311yescharacteristic
69Dic79⋊C4—41no—
70Dic79⋊C4—41no—
71C22⋊Dic79—22no—
72C22⋊Dic79—41no—
73C22⋊Dic79—41no—
74(C2×D79)⋊C4—22no—
75(C2×D79)⋊C4—22no—
76(C2×D79)⋊C4—22no—
77(C2×D79)⋊C4—22no—
78(C2×D79)⋊C4—41no—
79(C2×D79)⋊C4—41no—
80(C2×D79)⋊C4—41no—
81(C2×D79)⋊C4—41no—
82(C2×D79)⋊C4—41no—
83(C2×D79)⋊C4—41no—
84(C2×D79)⋊C4—41no—
85(C2×D79)⋊C4—41no—
86C4×Dic79—41no—
87C24×C79C2311yescharacteristic
88C22×C4×C79C2311yescharacteristic
89C22×C4×C79C2311yescharacteristic
90C22×C4×C79C2311yescharacteristic
91C22×C4×C79C2311yescharacteristic
92C22×C4×C79C2311yescharacteristic
93C22×C4×C79C2311yescharacteristic
94C4⋊C4×C79—41no—
95C22⋊C4×C79—22no—
96C22⋊C4×C79—41no—
97C22⋊C4×C79—41no—
98C42×C79—41no—
99C23×C79—21no—
100C23×C79—21no—
101C23×C79—21no—
102C23×C79—21no—
103C23×C79—21no—
104C23×C79—21no—
105C23×C79#4112yes—
106C23×C79C2411yescharacteristic
107C22×D79—21no—
108C22×D79—21no—
109C22×D79—21no—
110C22×D79—21no—
111C22×D79—21no—
112C22×D79—21no—
113C22×D79—21no—
114C22×D79—21no—
115C22×D79—21no—
116C22×D79—21no—
117C22×D79—21no—
118C22×D79—21no—
119C22×D79—44no—
120C22×D79—44no—
121C22×D79—44no—
122C22×D79—44no—
123C22×D79—44no—
124C22×D79—44no—
125C22×D79—44no—
126C22×D79#4112yes—
127C22×D79#4112yes—
128C2×C4×C79—21no—
129C2×C4×C79—21no—
130C2×C4×C79—21no—
131C2×C4×C79—21no—
132C2×C4×C79—21no—
133C2×C4×C79—21no—
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×Dic79—21no—
147C2×Dic79—21no—
148C2×Dic79—21no—
149C2×Dic79—21no—
150C2×Dic79—21no—
151C2×Dic79—21no—
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—
164Dic158—44no—
165C22×C79—22no—
166C22×C79—22no—
167C22×C79—22no—
168C22×C79—41no—
169C22×C79—41no—
170C22×C79—41no—
171C22×C79—41no—
172C22×C79C2×#4111yescharacteristic
173C22×C79C2×#4111yescharacteristic
174C22×C79C2×#4111yescharacteristic
175C22×C79H(5,𝔽2)11yescharacteristic
176C22×C79H(5,𝔽2)11yescharacteristic
177C22×C79H(5,𝔽2)11yescharacteristic
178C22×C79H(5,𝔽2)11yescharacteristic
179C2×D79—22no—
180C2×D79—22no—
181C2×D79—22no—
182C2×D79—22no—
183C2×D79—22no—
184C2×D79—22no—
185C2×D79—416no—
186C2×D79—41no—
187C2×D79—41no—
188C2×D79—41no—
189C2×D79—41no—
190C2×D79—41no—
191C2×D79—41no—
192C2×D79—41no—
193C2×D79—41no—
194C4×C79—41no—
195C4×C79—41no—
196C4×C79—41no—
197C4×C79—41no—
198C4×C79—41no—
199C4×C79—41no—
200Dic79—41no—
201Dic79—41no—
202Dic79—41no—
203Dic79—41no—
204Dic79—41no—
205Dic79—41no—
206C2×C79—42no—
207C2×C79#53811yescharacteristic
208C2×C79#53811yescharacteristic
209C2×C79#53811yescharacteristic
210C2×C79#55111yescharacteristic
211C2×C79#55111yescharacteristic
212C2×C79#55111yescharacteristic
213C2×C79H(3,𝔽4)11yescharacteristic
214D79—42no—
215D79—42no—
216#2736—791nomaximal, Sylow
217C79#273611yescharacteristic, complemented, Sylow
218#397—791no—
219#397—791no—
220#397—791no—
221#393—791no—
222#393—791no—
223#393—791no—
224#388—791no—
225#388—791no—
226#388—791no—
227#388—791no—
228#388—791no—
229#388D7911yescharacteristic, complemented
230#379—791no—
231#379—791no—
232#379—791no—
233C25—791no—
234C22×Q8—791no—
235C2×C4⋊C4—791no—
236C2×C4⋊C4—791no—
237C2×C4⋊C4C2×D7911yescharacteristic, complemented
238C2×C22⋊C4—791no—
239C2×C22⋊C4—791no—
240C2×C22⋊C4—791no—
241C2×C22⋊C4—791no—
242C2×C22⋊C4—791no—
243C2×C22⋊C4—791no—
244C2×C22⋊C4—791no—
245C2×C22⋊C4—791no—
246C2×C22⋊C4—791no—
247C2×C22⋊C4—791no—
248C2×C22⋊C4—791no—
249C2×C22⋊C4—791no—
250C2×C22⋊C4—791no—
251C2×C22⋊C4—791no—
252C2×C22⋊C4—791no—
253C2×C22⋊C4C2×D7911yescharacteristic
254C2×C22⋊C4C2×D7911yescharacteristic
255C2×C22⋊C4C2×D7911yescharacteristic
256C2×C42—791no—
257C2×C42C2×D7911yescharacteristic, complemented
258#95—791no—
259#95—791no—
260#95—791no—
261#95—791no—
262#95—791no—
263#95—791no—
264#95—791no—
265#95—791no—
266#95C2×D7911yescharacteristic, complemented
267#95C2×D7911yescharacteristic, complemented
268C24—3161no—
269C24—3161no—
270C24—3161no—
271C24—3161no—
272C24—791no—
273C24—791no—
274C24—1582no—
275C24—1582no—
276C24—1582no—
277C24C22×D7911yescharacteristic
278C2×Q8—3161no—
279C2×Q8—3161no—
280C2×Q8—3161no—
281C22×C4—791no—
282C22×C4—791no—
283C22×C4—791no—
284C22×C4—791no—
285C22×C4—791no—
286C22×C4—791no—
287C22×C4C22×D7911yescharacteristic
288C22×C4C22×D7911yescharacteristic
289C22×C4C22×D7911yescharacteristic
290C22×C4C22×D7911yescharacteristic
291C22×C4C22×D7911yescharacteristic
292C22×C4C22×D7911yescharacteristic
293C4⋊C4—41no—
294C4⋊C4—3161no—
295C4⋊C4—3161no—
296C22⋊C4—22no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—3161no—
300C22⋊C4—3161no—
301C22⋊C4—3161no—
302C22⋊C4—3161no—
303C22⋊C4—3161no—
304C22⋊C4—3161no—
305C22⋊C4—3161no—
306C22⋊C4—3161no—
307C22⋊C4—3161no—
308C22⋊C4—3161no—
309C22⋊C4—1582no—
310C22⋊C4—1582no—
311C22⋊C4—1582no—
312C22⋊C4—1582no—
313C22⋊C4—1582no—
314C42—41no—
315C42—3161no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—3164no—
323C23—3164no—
324C23—3164no—
325C23—3164no—
326C23—3164no—
327C23—3164no—
328C23—3164no—
329C23—792no—
330C23—792no—
331C23—1581no—
332C23—1581no—
333C23—1581no—
334C23—1581no—
335C23—1581no—
336C23—1581no—
337C23—1581no—
338C23—1581no—
339C23—1581no—
340C23—1581no—
341C23—1581no—
342C23—1581no—
343C23#1192962412yes—
344C23C23×D7911yescharacteristic
345Q8—3164no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—1581no—
365C2×C4—1581no—
366C2×C4—1581no—
367C2×C4—1581no—
368C2×C4—1581no—
369C2×C4—1581no—
370C2×C4—1581no—
371C2×C4—1581no—
372C2×C4—1581no—
373C2×C4—1581no—
374C2×C4—1581no—
375C2×C4—1581no—
376C2×C4—1581no—
377C2×C4—1581no—
378C2×C4—1581no—
379C2×C4—1581no—
380C2×C4—1581no—
381C2×C4—1581no—
382C22—22no—
383C22—22no—
384C22—22no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—31616no—
390C22—3161no—
391C22—3161no—
392C22—3161no—
393C22—3161no—
394C22—3161no—
395C22—3161no—
396C22—3161no—
397C22—3161no—
398C22—1582no—
399C22—1582no—
400C22—1582no—
401C22—1582no—
402C22—1582no—
403C22—1582no—
404C22#41×D7911yescharacteristic
405C22#41×D7911yescharacteristic
406C22C2×#1192962411yescharacteristic
407C22#1457920611yescharacteristic
408C22#1457920611yescharacteristic
409C22#1457920711yescharacteristic
410C22#1457920711yescharacteristic
411C4—41no—
412C4—41no—
413C4—41no—
414C4—41no—
415C4—41no—
416C4—41no—
417C4—3161no—
418C4—3161no—
419C4—3161no—
420C4—3161no—
421C4—3161no—
422C4—3161no—
423C2—42no—
424C2—3162no—
425C2—3162no—
426C2#1909914511yescharacteristic
427C2#1909914611yescharacteristic
428C2#1909914911yescharacteristic
429C2#1909923711yescharacteristic
430C2#1909923811yescharacteristic
431C2#1909924211yescharacteristic
432C2#1909930511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#388×C79C2
prime radicalC24×D79C22
hypercenter#388D79
hypocenterC79#2736
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. #19098492C2semidirect
2. #19098491C2semidirect
3. #19098489C2semidirect
4. #19098476C2semidirect
5. #19098476C2semidirect
6. #19098475C2semidirect
7. #19098454C2semidirect
8. #19098454C2semidirect
9. #19098453C2semidirect
10. #19098452C2semidirect
11. #19098451C2semidirect
15. #388×C79C2semidirect
17. C22×Dic158C22semidirect
18. C2×Dic79⋊C4C22semidirect
19. C2×Dic79⋊C4C22semidirect
35. C2×C4×Dic79C22semidirect
36. C79⋊#95C22semidirect
37. C79⋊#95C22semidirect
38. C79⋊#95C22semidirect
39. C79⋊#95C22semidirect
40. C79⋊#95C22semidirect
41. C79⋊#95C22semidirect
42. C79⋊#95C22semidirect
43. C79⋊#95C22semidirect
44. C2×C4⋊C4×C79C22semidirect
48. C2×C42×C79C22semidirect
49. #95×C79C22semidirect
50. #95×C79C22semidirect
217. C79#2736semidirect
229. #388D79semidirect
237. C2×C4⋊C4C2×D79semidirect
257. C2×C42C2×D79semidirect
266. #95C2×D79semidirect
267. #95C2×D79semidirect