Finite Group Databasebeta

← #23773580

Subgroups — #23773580

Order 10112.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099178C211yesmaximal, characteristic, complemented
2#19099035C211yesmaximal, characteristic, complemented
3#19098906C211yesmaximal, characteristic, complemented
4#19098886C211yesmaximal, characteristic, complemented
5#19098851C211yesmaximal, characteristic, complemented
6#19098842C211yesmaximal, characteristic, complemented
7#19098777C211yesmaximal, characteristic, complemented
8#19098776C211yesmaximal, characteristic, complemented
9#19098715C211yesmaximal, characteristic, complemented
10#19098695C211yesmaximal, characteristic
11#19098673C211yesmaximal, characteristic, complemented
12#19098663C211yesmaximal, characteristic, complemented
13C4×#11929613C211yesmaximal, characteristic, complemented
14#19098622C211yesmaximal, characteristic, complemented
15C4×D8×C79C211yesmaximal, characteristic, complemented
16C2×D4×D79C2211yescharacteristic
17C2×#11929613C2211yescharacteristic
18C2×#11929612C2211yescharacteristic
19C2×#11929609C2211yescharacteristic
20#14579160C2211yescharacteristic, complemented
21#14579154—21no—
22#14579148C2211yescharacteristic, complemented
23#14579147—21no—
24#14579144—21no—
25#14579141C2211yescharacteristic
26#14579140—21no—
27#14579132C2211yescharacteristic
28C4×Dic158C2211yescharacteristic, complemented
29C4×D316C2211yescharacteristic
30D4×Dic79C2211yescharacteristic
31#14579123C2211yescharacteristic
32C4×C22⋊D79—21no—
33(C22⋊D79)⋊C4—21no—
34#14579119C2211yescharacteristic
35#14579118C2211yescharacteristic
36C2×(C2×D79)⋊C4—21no—
37C22⋊C4×D79—21no—
38#14579094C2211yescharacteristic, complemented
39#14579093C2211yescharacteristic, complemented
40#14579092C2211yescharacteristic, complemented
41Dic79⋊C8C2211yescharacteristic, complemented
42Dic79⋊C8C2211yescharacteristic, complemented
43#14579086C2211yescharacteristic, complemented
44#14579084C2211yescharacteristic, complemented
45#14579083C2211yescharacteristic
46#14579082C2211yescharacteristic
47#14579082C2211yescharacteristic, complemented
48#14579081C2211yescharacteristic
49(C2×D79)⋊C8C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic
51#14579072C2211yescharacteristic, complemented
52C2×D8×C79C2211yescharacteristic
53C4×D4×C79C2211yescharacteristic
54C4×D4×C79C2211yescharacteristic, complemented
55#107×C79C2211yescharacteristic, complemented
56#102×C79C2211yescharacteristic
57#102×C79C2211yescharacteristic, complemented
58C4×C8×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60C2×Dic158—21no—
61C2×Dic158C2311yescharacteristic
62C2×D316C2311yescharacteristic
63C2×C22⋊D79—21no—
64C2×C22⋊D79—21no—
65D4×D79—22no—
66D4×D79—22no—
67C22×Dic79—21no—
68C2×C4×D79—21no—
69C2×C4×D79—21no—
70C2×C4×D79C2311yescharacteristic
71#11929613—22no—
72#11929612—22no—
73#11929609—22no—
74C2×C79⋊C8C2311yescharacteristic
75C2×C79⋊C8C2311yescharacteristic
76C4⋊Dic79—21no—
77C4⋊Dic79C2311yescharacteristic
78C4⋊Dic79C2311yescharacteristic
79Dic79⋊C4—21no—
80Dic79⋊C4—21no—
81Dic79⋊C4D411yescharacteristic
82Dic79⋊C4D411yescharacteristic
83C22⋊Dic79—21no—
84C22⋊Dic79—21no—
85C22⋊Dic79—21no—
86C22⋊Dic79—21no—
87(C2×D79)⋊C4—21no—
88(C2×D79)⋊C4—21no—
89(C2×D79)⋊C4—21no—
90(C2×D79)⋊C4—21no—
91(C2×D79)⋊C4D411yescharacteristic
92(C2×D79)⋊C4D411yescharacteristic
93C4×Dic79—21no—
94C4×Dic79—21no—
95C4×Dic79C2311yescharacteristic
96C2×D4×C79C2311yescharacteristic
97C2×D4×C79C2311yescharacteristic
98C22×C4×C79—21no—
99C22×C4×C79—21no—
100D8×C79—22no—
101C2×C8×C79C2311yescharacteristic
102C2×C8×C79C2311yescharacteristic
103C4⋊C4×C79C2311yescharacteristic
104C4⋊C4×C79C2311yescharacteristic
105C22⋊C4×C79—21no—
106C22⋊C4×C79—21no—
107C42×C79C2311yescharacteristic
108C23×C79—21no—
109C23×C79—21no—
110C22×D79—21no—
111C22×D79—24no—
112C22×D79—81no—
113C22×D79—81no—
114C22×D79C2×D411yescharacteristic
115D4×C79—21no—
116D4×C79—21no—
117D4×C79—21no—
118D4×C79#4112yes—
119C2×C4×C79—21no—
120C2×C4×C79—21no—
121C2×C4×C79—81no—
122C2×C4×C79—81no—
123C2×C4×C79C2×D411yescharacteristic
124C2×C4×C79C2×D411yescharacteristic
125C2×C4×C79C2411yescharacteristic
126C22⋊D79—24no—
127C22⋊D79—81no—
128C2×Dic79—21no—
129C2×Dic79—21no—
130C2×Dic79—21no—
131C2×Dic79—81no—
132C2×Dic79C2×D411yescharacteristic
133C2×Dic79C2×D411yescharacteristic
134C2×Dic79C2×D411yescharacteristic
135D316—21no—
136D316#4112yes—
137C4×D79—21no—
138C4×D79—21no—
139C4×D79—81no—
140C4×D79—81no—
141Dic158—21no—
142Dic158—21no—
143Dic158—81no—
144C8×C79—21no—
145C8×C79—21no—
146C79⋊C8—21no—
147C79⋊C8—21no—
148C22×C79—22no—
149C22×C79—41no—
150C22×C79—41no—
151C22×C79—41no—
152C22×C79—41no—
153C22×C79—41no—
154C22×C79C22×D411yescharacteristic
155C2×D79—22no—
156C2×D79—21no—
157C2×D79—21no—
158C2×D79—21no—
159C2×D79—41no—
160C2×D79—41no—
161C2×D79—84no—
162C4×C79—21no—
163C4×C79—21no—
164C4×C79—41no—
165C4×C79—41no—
166C4×C79C2×#4111yescharacteristic
167C4×C79C2×#4111yescharacteristic
168Dic79—21no—
169Dic79—21no—
170Dic79—21no—
171Dic79—41no—
172Dic79—41no—
173Dic79—41no—
174C2×C79—42no—
175C2×C79—81no—
176C2×C79#52511yescharacteristic
177C2×C79#57611yescharacteristic
178C2×C79#57711yescharacteristic
179D79—41no—
180D79—42no—
181#3118—791nomaximal, Sylow
182C79#311811yescharacteristic, complemented, Sylow
183#542—791no—
184#518—791no—
185#485—791no—
186#482—791no—
187#476—791no—
188#474—791no—
189#463—791no—
190#463—791no—
191#450—791no—
192#447—791no—
193#442—791no—
194#440—791no—
195C4×SD16—791no—
196C4×D8D7911yescharacteristic, complemented
197#433—791no—
198C22×D4—791no—
199C2×SD16—791no—
200C2×SD16—791no—
201C2×D8—791no—
202C2×D8C2×D7911yescharacteristic
203C4⋊Q8—791no—
204#126—1581no—
205#124—791no—
206#124—1581no—
207#123—1581no—
208C22⋊Q8—791no—
209C22⋊Q8—1581no—
210#121—791no—
211C4×Q8—791no—
212C4×D4—791no—
213C4×D4—791no—
214C4×D4—791no—
215C4×D4—1581no—
216C4×D4—1581no—
217C4×D4C2×D7911yescharacteristic
218C4×D4C2×D7911yescharacteristic, complemented
219#117—791no—
220#117—791no—
221C2×C22⋊C4—1581no—
222C2×C22⋊C4—1581no—
223#107—791no—
224#107C2×D7911yescharacteristic, complemented
225#106—791no—
226#106—791no—
227C4⋊C8—791no—
228C4⋊C8—791no—
229#103—791no—
230#103—791no—
231#102—791no—
232#102—791no—
233#102—791no—
234#102—791no—
235#102C2×D7911yescharacteristic
236#102C2×D7911yescharacteristic, complemented
237C22⋊C8—791no—
238C22⋊C8—791no—
239#97—791no—
240C4×C8C2×D7911yescharacteristic, complemented
241C24—1581no—
242C2×Q8—791no—
243C2×Q8—1581no—
244C2×D4—791no—
245C2×D4—1581no—
246C2×D4—1582no—
247C2×D4—1581no—
248C2×D4—1582no—
249C2×D4C22×D7911yescharacteristic
250C2×D4C22×D7911yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—791no—
254C22×C4—1581no—
255C22×C4—1581no—
256C22×C4—1581no—
257SD16—1582no—
258SD16—1582no—
259D8—22no—
260D8—1582no—
261C2×C8—791no—
262C2×C8—791no—
263C2×C8C22×D7911yescharacteristic
264C2×C8C22×D7911yescharacteristic
265C4⋊C4—791no—
266C4⋊C4—791no—
267C4⋊C4—791no—
268C4⋊C4—791no—
269C4⋊C4—1581no—
270C4⋊C4—1581no—
271C4⋊C4—1581no—
272C4⋊C4C22×D7911yescharacteristic
273C4⋊C4C22×D7911yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—791no—
277C22⋊C4—791no—
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—791no—
287C42—1581no—
288C42—1581no—
289C42C22×D7911yescharacteristic
290C23—21no—
291C23—21no—
292C23—791no—
293C23—6321no—
294C23—6321no—
295C23—1584no—
296C23—1581no—
297Q8—6321no—
298Q8—1581no—
299Q8—1581no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—792no—
304D4—6321no—
305D4—1584no—
306D4—1581no—
307D4#1192962412yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—791no—
313C2×C4—791no—
314C2×C4—791no—
315C2×C4—6321no—
316C2×C4—6321no—
317C2×C4—6321no—
318C2×C4—1581no—
319C2×C4—1581no—
320C2×C4—1581no—
321C2×C4—1581no—
322C2×C4—1581no—
323C2×C4D4×D7911yescharacteristic
324C2×C4D4×D7911yescharacteristic
325C2×C4C23×D7911yescharacteristic
326C8—21no—
327C8—21no—
328C8—1581no—
329C8—1581no—
330C22—22no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—3161no—
337C22—3161no—
338C22—6324no—
339C22—1581no—
340C22—1582no—
341C22—1581no—
342C22—1581no—
343C22C2×D4×D7911yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—3161no—
349C4—3161no—
350C4—3161no—
351C4—1581no—
352C4—1581no—
353C4—1581no—
354C4#41×D7911yescharacteristic
355C4C2×#1192962411yescharacteristic
356C2—42no—
357C2—81no—
358C2—3162no—
359C2—3161no—
360C2#1909907211yescharacteristic
361C2#1909936411yescharacteristic
362C2#1909937011yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
FittingC4×D8×C79C2
socleC22×C79C22×D4
prime radical#19098695C2
hypercenterC4×D8D79
hypocenterC79#3118
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #19099178C2semidirect
2. #19099035C2semidirect
3. #19098906C2semidirect
4. #19098886C2semidirect
5. #19098851C2semidirect
6. #19098842C2semidirect
7. #19098777C2semidirect
8. #19098776C2semidirect
9. #19098715C2semidirect
11. #19098673C2semidirect
12. #19098663C2semidirect
13. C4×#11929613C2semidirect
14. #19098622C2semidirect
15. C4×D8×C79C2semidirect
20. #14579160C22semidirect
22. #14579148C22semidirect
28. C4×Dic158C22semidirect
38. #14579094C22semidirect
39. #14579093C22semidirect
40. #14579092C22semidirect
41. Dic79⋊C8C22semidirect
42. Dic79⋊C8C22semidirect
43. #14579086C22semidirect
44. #14579084C22semidirect
47. #14579082C22semidirect
51. #14579072C22semidirect
54. C4×D4×C79C22semidirect
55. #107×C79C22semidirect
57. #102×C79C22semidirect
58. C4×C8×C79C22semidirect
182. C79#3118semidirect
196. C4×D8D79semidirect
218. C4×D4C2×D79semidirect
224. #107C2×D79semidirect
236. #102C2×D79semidirect
240. C4×C8C2×D79semidirect