Finite Group Databasebeta

← #23773311

Subgroups — #23773311

Order 10112.

420 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099070C211yesmaximal, characteristic
2#117×D79C211yesmaximal, characteristic, complemented
3#19098903C211yesmaximal, characteristic, complemented
4#19098902C211yesmaximal, characteristic, complemented
5#19098897C211yesmaximal, characteristic, complemented
6#19098892C211yesmaximal, characteristic, complemented
7#19098886C211yesmaximal, characteristic, complemented
8#19098885C211yesmaximal, characteristic, complemented
9#19098880C211yesmaximal, characteristic, complemented
10#19098875C211yesmaximal, characteristic, complemented
11#19098601C211yesmaximal, characteristic, complemented
12#19098599C211yesmaximal, characteristic, complemented
13#19098559C211yesmaximal, characteristic, complemented
14C2×(C2×D79)⋊C8C211yesmaximal, characteristic, complemented
15#416×C79C211yesmaximal, characteristic, complemented
16C22×C4×D79C2211yescharacteristic
17C22×C79⋊C8C2211yescharacteristic
18#14579142—21no—
19#14579137C2211yescharacteristic
20#14579137C2211yescharacteristic
21#14579132C2211yescharacteristic
22#14579132C2211yescharacteristic
23#14579129—21no—
24C4×C22⋊D79—21no—
25C4×C22⋊D79—21no—
26#14579120C2211yescharacteristic
27#14579120C2211yescharacteristic
28#14579119C2211yescharacteristic
29#14579119C2211yescharacteristic
30#14579118—21no—
31#14579117—21no—
32C4⋊C4×D79C2211yescharacteristic
33C4⋊C4×D79C2211yescharacteristic
34C22⋊C4×D79—21no—
35C42×D79—21no—
36#14579095C2211yescharacteristic, complemented
37#14579095C2211yescharacteristic, complemented
38#14579094C2211yescharacteristic, complemented
39#14579094C2211yescharacteristic, complemented
40#14579093C2211yescharacteristic, complemented
41#14579093C2211yescharacteristic, complemented
42#14579092C2211yescharacteristic, complemented
43#14579092C2211yescharacteristic, complemented
44#14579085C2211yescharacteristic, complemented
45#14579085C2211yescharacteristic, complemented
46#14579082C2211yescharacteristic, complemented
47#14579082C2211yescharacteristic, complemented
48(C2×D79)⋊C8C2211yescharacteristic
49(C2×D79)⋊C8C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic
51(C2×D79)⋊C8C2211yescharacteristic
52C2×#41×C79C2211yescharacteristic
53C22×C8×C79C2211yescharacteristic
54#117×C79C2211yescharacteristic
55#103×C79C2211yescharacteristic, complemented
56#103×C79C2211yescharacteristic, complemented
57#102×C79C2211yescharacteristic, complemented
58#102×C79C2211yescharacteristic, complemented
59C23×D79D411yescharacteristic
60C2×C22⋊D79—21no—
61C2×C22⋊D79—21no—
62C22×Dic79D411yescharacteristic
63C2×C4×D79—21no—
64C2×C4×D79—21no—
65C2×C4×D79—22no—
66C2×C4×D79—22no—
67C2×C4×D79D411yescharacteristic
68C2×C4×D79D411yescharacteristic
69C2×C4×D79C2311yescharacteristic
70C2×C4×D79C2311yescharacteristic
71C2×C79⋊C8—22no—
72C2×C79⋊C8C2311yescharacteristic
73C2×C79⋊C8C2311yescharacteristic
74C4⋊Dic79C2311yescharacteristic
75C4⋊Dic79C2311yescharacteristic
76C4⋊Dic79C2311yescharacteristic
77C4⋊Dic79C2311yescharacteristic
78Dic79⋊C4—21no—
79Dic79⋊C4—21no—
80Dic79⋊C4—21no—
81Dic79⋊C4—21no—
82C22⋊Dic79—21no—
83C22⋊Dic79—21no—
84C22⋊Dic79—21no—
85C22⋊Dic79—21no—
86(C2×D79)⋊C4—21no—
87(C2×D79)⋊C4—21no—
88(C2×D79)⋊C4—21no—
89(C2×D79)⋊C4—21no—
90C4×Dic79—21no—
91C4×Dic79—21no—
92C4×Dic79—21no—
93C4×Dic79—21no—
94#41×C79—22no—
95#41×C79—22no—
96C2×Q8×C79C2311yescharacteristic
97C2×D4×C79—21no—
98C2×D4×C79C2311yescharacteristic
99C22×C4×C79—21no—
100C22×C4×C79C2311yescharacteristic
101C2×C8×C79—22no—
102C2×C8×C79C2311yescharacteristic
103C2×C8×C79C2311yescharacteristic
104C4⋊C4×C79C2311yescharacteristic
105C4⋊C4×C79C2311yescharacteristic
106C22⋊C4×C79—21no—
107C42×C79—21no—
108C23×C79—21no—
109C23×C79C2×D411yescharacteristic
110C22×D79—22no—
111C22×D79—22no—
112C22×D79—41no—
113C22×D79C2×D411yescharacteristic
114C22×D79C2×D411yescharacteristic
115Q8×C79—21no—
116Q8×C79—21no—
117D4×C79—21no—
118D4×C79—21no—
119D4×C79—42no—
120C2×C4×C79—21no—
121C2×C4×C79—21no—
122C2×C4×C79—21no—
123C2×C4×C79—42no—
124C2×C4×C79C2×D411yescharacteristic
125C2×C4×C79#4112yes—
126C2×C4×C79#4112yes—
127C2×C4×C79C2411yescharacteristic
128C22⋊D79—42no—
129C22⋊D79—42no—
130C2×Dic79—22no—
131C2×Dic79—21no—
132C2×Dic79—21no—
133C2×Dic79—21no—
134C2×Dic79—21no—
135C2×Dic79C2×D411yescharacteristic
136C2×Dic79C2×D411yescharacteristic
137C4×D79—22no—
138C4×D79—22no—
139C4×D79—21no—
140C4×D79—21no—
141C4×D79—21no—
142C4×D79—21no—
143C4×D79—42no—
144C4×D79—42no—
145C8×C79—21no—
146C8×C79—21no—
147C79⋊C8—21no—
148C79⋊C8—21no—
149C22×C79—21no—
150C22×C79—21no—
151C22×C79—41no—
152C22×C79—41no—
153C22×C79—41no—
154C22×C79#12312yes—
155C22×C79C22×D411yescharacteristic
156C2×D79—21no—
157C2×D79—21no—
158C2×D79—21no—
159C2×D79—21no—
160C2×D79—21no—
161C2×D79—44no—
162C2×D79#13512yes—
163C4×C79—41no—
164C4×C79—41no—
165C4×C79—41no—
166C4×C79#12312yes—
167C4×C79C2×#4111yescharacteristic
168C4×C79C2×#4111yescharacteristic
169Dic79—21no—
170Dic79—21no—
171Dic79—41no—
172Dic79—41no—
173Dic79—41no—
174Dic79—41no—
175C2×C79—22no—
176C2×C79—81no—
177C2×C79C2×#12311yescharacteristic
178C2×C79C2×#13511yescharacteristic
179C2×C79#57511yescharacteristic
180D79—22no—
181D79—41no—
182#3091—791nomaximal, Sylow
183C79#309111yescharacteristic, complemented, Sylow
184#525—791no—
185C2×#117—791no—
186#485—791no—
187#485—791no—
188#484—791no—
189#483—791no—
190#482—791no—
191#482—791no—
192#481—791no—
193#480—791no—
194#427—791no—
195#427—791no—
196#416—791no—
197#416D7911yescharacteristic, complemented
198C2×C22⋊C8—791no—
199C2×#41C2×D7911yescharacteristic
200C23×C4—791no—
201C22×C8—791no—
202C22×C8C2×D7911yescharacteristic
203#123—1581no—
204C22⋊Q8—791no—
205C22⋊Q8—791no—
206#121—791no—
207#121—791no—
208#120—1581no—
209C4×D4—1581no—
210C4×D4—1581no—
211#117—791no—
212#117—791no—
213#117—791no—
214#117—791no—
215#117—1581no—
216#117—1581no—
217#117C2×D7911yescharacteristic
218C2×C4⋊C4—791no—
219C2×C4⋊C4—791no—
220C2×C22⋊C4—1581no—
221C2×C42—1581no—
222#107—791no—
223#107—791no—
224#107—791no—
225#107—791no—
226#106—791no—
227#106—791no—
228#106—791no—
229#106—791no—
230#103—791no—
231#103—791no—
232#103C2×D7911yescharacteristic, complemented
233#103C2×D7911yescharacteristic, complemented
234#102—791no—
235#102—791no—
236#102C2×D7911yescharacteristic, complemented
237#102C2×D7911yescharacteristic, complemented
238C22⋊C8—791no—
239C22⋊C8—791no—
240C22⋊C8—791no—
241C22⋊C8—791no—
242C24—791no—
243#41—22no—
244#41—22no—
245C2×Q8C22×D7911yescharacteristic
246C2×D4—21no—
247C2×D4—1581no—
248C2×D4—1581no—
249C2×D4C22×D7911yescharacteristic
250C22×C4—21no—
251C22×C4—791no—
252C22×C4—791no—
253C22×C4—791no—
254C22×C4—791no—
255C22×C4—791no—
256C22×C4—1581no—
257C22×C4—1581no—
258C22×C4—1582no—
259C22×C4—1582no—
260C22×C4C22×D7911yescharacteristic
261C2×C8—22no—
262C2×C8—791no—
263C2×C8—791no—
264C2×C8—1582no—
265C2×C8C22×D7911yescharacteristic
266C2×C8C22×D7911yescharacteristic
267C4⋊C4—791no—
268C4⋊C4—791no—
269C4⋊C4—791no—
270C4⋊C4—791no—
271C4⋊C4—1581no—
272C4⋊C4—1581no—
273C4⋊C4—1581no—
274C4⋊C4—1581no—
275C4⋊C4C22×D7911yescharacteristic
276C4⋊C4C22×D7911yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—1581no—
279C22⋊C4—1581no—
280C22⋊C4—1581no—
281C22⋊C4—1581no—
282C22⋊C4—1581no—
283C22⋊C4—1581no—
284C22⋊C4—1581no—
285C22⋊C4—1581no—
286C42—21no—
287C42—1581no—
288C42—1581no—
289C42—1581no—
290C42—1581no—
291C23—21no—
292C23—3161no—
293C23—791no—
294C23—791no—
295C23—1582no—
296C23—1582no—
297C23D4×D7911yescharacteristic
298Q8—21no—
299Q8—21no—
300D4—21no—
301D4—21no—
302D4—42no—
303D4—3162no—
304D4—3162no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—42no—
309C2×C4—3162no—
310C2×C4—3162no—
311C2×C4—791no—
312C2×C4—791no—
313C2×C4—1581no—
314C2×C4—1581no—
315C2×C4—1581no—
316C2×C4—1581no—
317C2×C4—1582no—
318C2×C4—1581no—
319C2×C4—1581no—
320C2×C4—1581no—
321C2×C4—1581no—
322C2×C4—1582no—
323C2×C4—1582no—
324C2×C4D4×D7911yescharacteristic
325C2×C4#1192962312yes—
326C2×C4#1192962412yes—
327C2×C4C23×D7911yescharacteristic
328C8—21no—
329C8—21no—
330C8—1581no—
331C8—1581no—
332C22—21no—
333C22—21no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—3164no—
338C22—792no—
339C22—1581no—
340C22—1581no—
341C22—1581no—
342C22—1581no—
343C22—1581no—
344C22#1457914312yes—
345C22C2×D4×D7911yescharacteristic
346C4—41no—
347C4—41no—
348C4—41no—
349C4—3161no—
350C4—3161no—
351C4—3161no—
352C4—3161no—
353C4—1581no—
354C4—1581no—
355C4#1457914312yes—
356C4C2×#1192962311yescharacteristic
357C4C2×#1192962411yescharacteristic
358C2—22no—
359C2—81no—
360C2—3161no—
361C2—1582no—
362C2C2×#1457914311yescharacteristic
363C2#135×D7911yescharacteristic
364C2#1909936011yescharacteristic
subgroupG/H
centerC2×C4D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#416×C79C2
socleC22×C79C22×D4
prime radical#19099070C2
hypercenter#416D79
hypocenterC79#3091
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
2. #117×D79C2semidirect
3. #19098903C2semidirect
4. #19098902C2semidirect
5. #19098897C2semidirect
6. #19098892C2semidirect
7. #19098886C2semidirect
8. #19098885C2semidirect
9. #19098880C2semidirect
10. #19098875C2semidirect
11. #19098601C2semidirect
12. #19098599C2semidirect
13. #19098559C2semidirect
14. C2×(C2×D79)⋊C8C2semidirect
15. #416×C79C2semidirect
36. #14579095C22semidirect
37. #14579095C22semidirect
38. #14579094C22semidirect
39. #14579094C22semidirect
40. #14579093C22semidirect
41. #14579093C22semidirect
42. #14579092C22semidirect
43. #14579092C22semidirect
44. #14579085C22semidirect
45. #14579085C22semidirect
46. #14579082C22semidirect
47. #14579082C22semidirect
55. #103×C79C22semidirect
56. #103×C79C22semidirect
57. #102×C79C22semidirect
58. #102×C79C22semidirect
183. C79#3091semidirect
197. #416D79semidirect
232. #103C2×D79semidirect
233. #103C2×D79semidirect
236. #102C2×D79semidirect
237. #102C2×D79semidirect