Finite Group Databasebeta

← #23773226

Subgroups — #23773226

Order 10112.

398 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099190C211yesmaximal, characteristic, complemented
2#19099035C211yesmaximal, characteristic
3#19098865C211yesmaximal, characteristic, complemented
4#19098864C211yesmaximal, characteristic, complemented
5#19098863C211yesmaximal, characteristic, complemented
6#19098862C211yesmaximal, characteristic, complemented
7#19098852C211yesmaximal, characteristic, complemented
8#19098841C211yesmaximal, characteristic, complemented
9#19098840C211yesmaximal, characteristic, complemented
10#19098602C211yesmaximal, characteristic, complemented
11#19098598C211yesmaximal, characteristic, complemented
12#19098588C211yesmaximal, characteristic, complemented
13#19098566C211yesmaximal, characteristic
14#102×D79C211yesmaximal, characteristic
15#476×C79C211yesmaximal, characteristic, complemented
16C2×D4×D79C2211yescharacteristic
17C2×#11929607C2211yescharacteristic
18C2×C8×D79C2211yescharacteristic
19#14579160C2211yescharacteristic, complemented
20#14579159—21no—
21#14579153C2211yescharacteristic, complemented
22#14579152C2211yescharacteristic, complemented
23#14579151—21no—
24#14579139—21no—
25#14579137—21no—
26C4×D316C2211yescharacteristic
27D4×Dic79C2211yescharacteristic
28#14579123C2211yescharacteristic
29C4×C22⋊D79—21no—
30(C22⋊D79)⋊C4—21no—
31#14579119C2211yescharacteristic
32#14579119C2211yescharacteristic
33#14579118C2211yescharacteristic
34C4⋊C4×D79C2211yescharacteristic
35C2×(C2×D79)⋊C4—21no—
36C22⋊C4×D79—21no—
37#14579095C2211yescharacteristic, complemented
38#14579094C2211yescharacteristic, complemented
39#14579094C2211yescharacteristic, complemented
40#14579094C2211yescharacteristic, complemented
41#14579093C2211yescharacteristic, complemented
42#14579092C2211yescharacteristic, complemented
43C4⋊(C79⋊C8)C2211yescharacteristic, complemented
44Dic79⋊C8C2211yescharacteristic, complemented
45Dic79⋊C8C2211yescharacteristic, complemented
46#14579083C2211yescharacteristic
47#14579083C2211yescharacteristic
48#14579082C2211yescharacteristic
49#14579082C2211yescharacteristic
50#14579081C2211yescharacteristic
51#14579081C2211yescharacteristic
52C4⋊Q8×C79C2211yescharacteristic, complemented
53C4×D4×C79C2211yescharacteristic
54#106×C79C2211yescharacteristic, complemented
55#106×C79C2211yescharacteristic, complemented
56C4⋊C8×C79C2211yescharacteristic, complemented
57#102×C79C2211yescharacteristic
58#102×C79C2211yescharacteristic
59C23×D79—21no—
60C2×Dic158—21no—
61C2×D316C2311yescharacteristic
62C2×C22⋊D79—21no—
63D4×D79—22no—
64D4×D79Q814yescomplemented
65C22×Dic79—21no—
66C2×C4×D79—21no—
67C2×C4×D79—21no—
68C2×C4×D79—21no—
69C2×C4×D79C2311yescharacteristic
70#11929607—22no—
71C2×C79⋊C8C2311yescharacteristic
72C2×C79⋊C8C2311yescharacteristic
73C8×D79—22no—
74C4⋊Dic79—21no—
75C4⋊Dic79C2311yescharacteristic
76C4⋊Dic79C2311yescharacteristic
77C4⋊Dic79C2311yescharacteristic
78Dic79⋊C4—21no—
79Dic79⋊C4—21no—
80Dic79⋊C4—21no—
81Dic79⋊C4—21no—
82Dic79⋊C4—21no—
83Dic79⋊C4D411yescharacteristic
84Dic79⋊C4D411yescharacteristic
85C22⋊Dic79—21no—
86(C2×D79)⋊C4—21no—
87(C2×D79)⋊C4—21no—
88(C2×D79)⋊C4—21no—
89(C2×D79)⋊C4—21no—
90(C2×D79)⋊C4D411yescharacteristic
91(C2×D79)⋊C4D411yescharacteristic
92C4×Dic79—21no—
93C4×Dic79—21no—
94C4×Dic79C2311yescharacteristic
95C2×Q8×C79—21no—
96C2×D4×C79C2311yescharacteristic
97C22×C4×C79—21no—
98C2×C8×C79C2311yescharacteristic
99C2×C8×C79C2311yescharacteristic
100C4⋊C4×C79—21no—
101C4⋊C4×C79C2311yescharacteristic
102C4⋊C4×C79C2311yescharacteristic
103C4⋊C4×C79C2311yescharacteristic
104C22⋊C4×C79—21no—
105C42×C79C2311yescharacteristic
106C23×C79—21no—
107C22×D79—21no—
108C22×D79—24no—
109C22×D79—81no—
110C22×D79—81no—
111C22×D79C2×D411yescharacteristic
112Q8×C79—81no—
113D4×C79—21no—
114D4×C79C2×Q812yes—
115C2×C4×C79—21no—
116C2×C4×C79—21no—
117C2×C4×C79—21no—
118C2×C4×C79—81no—
119C2×C4×C79C2×D411yescharacteristic
120C2×C4×C79C2×D411yescharacteristic
121C2×C4×C79C2411yescharacteristic
122C22⋊D79—24no—
123C2×Dic79—21no—
124C2×Dic79—21no—
125C2×Dic79—21no—
126C2×Dic79—81no—
127C2×Dic79C2×D411yescharacteristic
128C2×Dic79C2×D411yescharacteristic
129C2×Dic79C2×D411yescharacteristic
130D316—21no—
131D316C2×Q812yes—
132C4×D79—81no—
133C4×D79—81no—
134C4×D79—81no—
135C4×D79C2×Q812yes—
136C4×D79#4112yes—
137Dic158—81no—
138C8×C79—21no—
139C8×C79—21no—
140C79⋊C8—21no—
141C79⋊C8—21no—
142C22×C79—22no—
143C22×C79—41no—
144C22×C79—41no—
145C22×C79C22×D411yescharacteristic
146C2×D79—21no—
147C2×D79—21no—
148C2×D79—22no—
149C2×D79—41no—
150C2×D79—41no—
151C2×D79—84no—
152C2×D79C22⋊Q812yes—
153C4×C79—21no—
154C4×C79—21no—
155C4×C79—41no—
156C4×C79—41no—
157C4×C79—41no—
158C4×C79C22×Q811yescharacteristic
159C4×C79C2×#4111yescharacteristic
160Dic79—21no—
161Dic79—21no—
162Dic79—41no—
163Dic79—41no—
164Dic79—41no—
165Dic79C22⋊Q812yes—
166C2×C79—42no—
167C2×C79C2×C22⋊Q811yescharacteristic
168C2×C79#57611yescharacteristic
169C2×C79#57711yescharacteristic
170D79—22no—
171D79—42no—
172#3081—791nomaximal, Sylow
173C79#308111yescharacteristic, complemented, Sylow
174#544—791no—
175#518—791no—
176#478—791no—
177#478—791no—
178#478—791no—
179#478—791no—
180#476—791no—
181#476D7911yescharacteristic, complemented
182#474—791no—
183#474—791no—
184#428—791no—
185#427—791no—
186#424—791no—
187#418—791no—
188C2×#102—791no—
189C22×D4—791no—
190C2×M16—791no—
191C22×C8—791no—
192C4⋊Q8—791no—
193C4⋊Q8—1581no—
194C4⋊Q8C2×D7911yescharacteristic, complemented
195#125—791no—
196#125—791no—
197#125—1581no—
198C22⋊Q8—1581no—
199C22⋊Q8—1581no—
200C4×D4—791no—
201C4×D4—791no—
202C4×D4—791no—
203C4×D4—1581no—
204C4×D4—1581no—
205C4×D4C2×D7911yescharacteristic
206#117—791no—
207#117—791no—
208#117—791no—
209C2×C4⋊C4—791no—
210C2×C22⋊C4—1581no—
211C2×C22⋊C4—1581no—
212#107—791no—
213#107—791no—
214#107—791no—
215#107—791no—
216#106—791no—
217#106—791no—
218#106C2×D7911yescharacteristic, complemented
219#106C2×D7911yescharacteristic, complemented
220C4⋊C8—791no—
221C4⋊C8—791no—
222C4⋊C8—791no—
223C4⋊C8C2×D7911yescharacteristic, complemented
224#102—791no—
225#102—791no—
226#102—791no—
227#102—791no—
228#102—791no—
229#102—791no—
230#102C2×D7911yescharacteristic
231#102C2×D7911yescharacteristic
232C24—1581no—
233C2×Q8—21no—
234C2×Q8—1581no—
235C2×D4—794no—
236C2×D4—791no—
237C2×D4—1582no—
238C2×D4—1581no—
239C2×D4C22×D7911yescharacteristic
240C22×C4—21no—
241C22×C4—791no—
242C22×C4—1581no—
243C22×C4—1581no—
244C22×C4—1581no—
245C22×C4—1581no—
246M16—1582no—
247C2×C8—791no—
248C2×C8—791no—
249C2×C8—1582no—
250C2×C8C22×D7911yescharacteristic
251C2×C8C22×D7911yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—791no—
254C4⋊C4—791no—
255C4⋊C4—791no—
256C4⋊C4—791no—
257C4⋊C4—791no—
258C4⋊C4—1581no—
259C4⋊C4—1581no—
260C4⋊C4—1581no—
261C4⋊C4—1581no—
262C4⋊C4—1581no—
263C4⋊C4—1581no—
264C4⋊C4C22×D7911yescharacteristic
265C4⋊C4C22×D7911yescharacteristic
266C4⋊C4C22×D7911yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—791no—
269C22⋊C4—791no—
270C22⋊C4—1581no—
271C22⋊C4—1581no—
272C22⋊C4—1581no—
273C22⋊C4—1581no—
274C22⋊C4—1581no—
275C42—791no—
276C42—1581no—
277C42—1581no—
278C42C22×D7911yescharacteristic
279C23—21no—
280C23—791no—
281C23—6321no—
282C23—6321no—
283C23—1584no—
284C23—1581no—
285Q8—81no—
286Q8—6321no—
287D4—21no—
288D4—792no—
289D4—1584no—
290D4—1581no—
291D4Q8×D7912yes—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—81no—
296C2×C4—791no—
297C2×C4—792no—
298C2×C4—792no—
299C2×C4—791no—
300C2×C4—791no—
301C2×C4—6321no—
302C2×C4—6321no—
303C2×C4—6321no—
304C2×C4—6321no—
305C2×C4—1581no—
306C2×C4—1581no—
307C2×C4—1581no—
308C2×C4D4×D7911yescharacteristic
309C2×C4D4×D7911yescharacteristic
310C2×C4C23×D7911yescharacteristic
311C8—21no—
312C8—21no—
313C8—1581no—
314C8—1581no—
315C22—22no—
316C22—41no—
317C22—41no—
318C22—3161no—
319C22—3161no—
320C22—792no—
321C22—6324no—
322C22—1582no—
323C22—1581no—
324C22—1581no—
325C22C2×D4×D7911yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—3161no—
332C4—3161no—
333C4—3161no—
334C4—792no—
335C4—1581no—
336C4—1581no—
337C4C2×Q8×D7911yescharacteristic
338C4#41×D7911yescharacteristic
339C2—42no—
340C2—3162no—
341C2—1582no—
342C2C22⋊Q8×D7911yescharacteristic
343C2#1909936711yescharacteristic
344C2#1909936911yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#476×C79C2
socleC22×C79C22×D4
prime radicalC2×D4×D79C22
hypercenter#476D79
hypocenterC79#3081
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #19099190C2semidirect
3. #19098865C2semidirect
4. #19098864C2semidirect
5. #19098863C2semidirect
6. #19098862C2semidirect
7. #19098852C2semidirect
8. #19098841C2semidirect
9. #19098840C2semidirect
10. #19098602C2semidirect
11. #19098598C2semidirect
12. #19098588C2semidirect
15. #476×C79C2semidirect
19. #14579160C22semidirect
21. #14579153C22semidirect
22. #14579152C22semidirect
37. #14579095C22semidirect
38. #14579094C22semidirect
39. #14579094C22semidirect
40. #14579094C22semidirect
41. #14579093C22semidirect
42. #14579092C22semidirect
43. C4⋊(C79⋊C8)C22semidirect
44. Dic79⋊C8C22semidirect
45. Dic79⋊C8C22semidirect
52. C4⋊Q8×C79C22semidirect
54. #106×C79C22semidirect
55. #106×C79C22semidirect
56. C4⋊C8×C79C22semidirect
64. D4×D79Q8semidirect
173. C79#3081semidirect
181. #476D79semidirect
194. C4⋊Q8C2×D79semidirect
218. #106C2×D79semidirect
219. #106C2×D79semidirect
223. C4⋊C8C2×D79semidirect