Finite Group Databasebeta

← #23773654

Subgroups — #23773654

Order 10112.

394 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099176C211yesmaximal, characteristic, complemented
2#19099035C211yesmaximal, characteristic
3#19098907C211yesmaximal, characteristic, complemented
4#19098906C211yesmaximal, characteristic, complemented
5#19098860C211yesmaximal, characteristic, complemented
6#19098769C211yesmaximal, characteristic, complemented
7#19098768C211yesmaximal, characteristic, complemented
8#19098715C211yesmaximal, characteristic
9#19098715C211yesmaximal, characteristic
10#19098662C211yesmaximal, characteristic, complemented
11#19098660C211yesmaximal, characteristic, complemented
12#19098654C211yesmaximal, characteristic, complemented
13#19098650C211yesmaximal, characteristic, complemented
14#19098623C211yesmaximal, characteristic, complemented
15#478×C79C211yesmaximal, characteristic, complemented
16C2×D4×D79C2211yescharacteristic
17C2×#11929613C2211yescharacteristic
18C2×#11929613C2211yescharacteristic
19C2×#11929612C2211yescharacteristic
20C2×#11929612C2211yescharacteristic
21#14579161C2211yescharacteristic, complemented
22#14579156—21no—
23#14579156—21no—
24#14579152—21no—
25#14579152—21no—
26#14579141C2211yescharacteristic
27#14579141C2211yescharacteristic
28#14579126C2211yescharacteristic, complemented
29#14579126C2211yescharacteristic, complemented
30C4×D316C2211yescharacteristic
31D4×Dic79C2211yescharacteristic
32#14579123C2211yescharacteristic
33C4×C22⋊D79—21no—
34(C22⋊D79)⋊C4—21no—
35#14579119C2211yescharacteristic
36#14579118C2211yescharacteristic
37C2×(C2×D79)⋊C4—21no—
38C22⋊C4×D79—21no—
39#14579094C2211yescharacteristic, complemented
40#14579092C2211yescharacteristic, complemented
41C4⋊(C79⋊C8)C2211yescharacteristic, complemented
42#14579086C2211yescharacteristic, complemented
43#14579086C2211yescharacteristic, complemented
44#14579084C2211yescharacteristic, complemented
45#14579084C2211yescharacteristic, complemented
46#14579081C2211yescharacteristic
47#14579081C2211yescharacteristic
48(C2×D79)⋊C8C2211yescharacteristic
49(C2×D79)⋊C8C2211yescharacteristic
50#14579071C2211yescharacteristic, complemented
51C8×Dic79C2211yescharacteristic, complemented
52#125×C79C2211yescharacteristic, complemented
53C4×D4×C79C2211yescharacteristic
54#107×C79C2211yescharacteristic, complemented
55#106×C79C2211yescharacteristic, complemented
56C4⋊C8×C79C2211yescharacteristic, complemented
57#102×C79C2211yescharacteristic
58#102×C79C2211yescharacteristic
59C23×D79—21no—
60C2×Dic158C2311yescharacteristic
61C2×Dic158C2311yescharacteristic
62C2×D316C2311yescharacteristic
63C2×C22⋊D79—21no—
64D4×D79—22no—
65D4×D79—22no—
66C22×Dic79—21no—
67C2×C4×D79—21no—
68C2×C4×D79—21no—
69C2×C4×D79C2311yescharacteristic
70#11929613—22no—
71#11929613—22no—
72#11929612—22no—
73#11929612—22no—
74C2×C79⋊C8C2311yescharacteristic
75C2×C79⋊C8C2311yescharacteristic
76C4⋊Dic79—21no—
77C4⋊Dic79—21no—
78C4⋊Dic79—21no—
79C4⋊Dic79—21no—
80C4⋊Dic79C2311yescharacteristic
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)⋊C4—21no—
91(C2×D79)⋊C4D411yescharacteristic
92(C2×D79)⋊C4D411yescharacteristic
93C4×Dic79—21no—
94C4×Dic79—21no—
95C4×Dic79—21no—
96C4×Dic79C2311yescharacteristic
97C2×D4×C79C2311yescharacteristic
98C22×C4×C79—21no—
99C2×C8×C79C2311yescharacteristic
100C2×C8×C79C2311yescharacteristic
101C4⋊C4×C79—21no—
102C4⋊C4×C79—21no—
103C4⋊C4×C79C2311yescharacteristic
104C4⋊C4×C79C2311yescharacteristic
105C4⋊C4×C79C2311yescharacteristic
106C22⋊C4×C79—21no—
107C42×C79C2311yescharacteristic
108C23×C79—21no—
109C22×D79—21no—
110C22×D79—24no—
111C22×D79—81no—
112C22×D79—81no—
113C22×D79C2×D411yescharacteristic
114D4×C79—21no—
115D4×C79#4112yes—
116C2×C4×C79—21no—
117C2×C4×C79—21no—
118C2×C4×C79—21no—
119C2×C4×C79—81no—
120C2×C4×C79C2×D411yescharacteristic
121C2×C4×C79C2×D411yescharacteristic
122C2×C4×C79C2411yescharacteristic
123C22⋊D79—24no—
124C2×Dic79—21no—
125C2×Dic79—21no—
126C2×Dic79—21no—
127C2×Dic79—81no—
128C2×Dic79C2×D411yescharacteristic
129C2×Dic79C2×D411yescharacteristic
130C2×Dic79C2×D411yescharacteristic
131D316—21no—
132D316#4112yes—
133C4×D79—21no—
134C4×D79—21no—
135C4×D79—81no—
136C4×D79—81no—
137Dic158—21no—
138Dic158—21no—
139Dic158—21no—
140Dic158—21no—
141C8×C79—21no—
142C8×C79—21no—
143C79⋊C8—21no—
144C79⋊C8—21no—
145C22×C79—22no—
146C22×C79—41no—
147C22×C79—41no—
148C22×C79C22×D411yescharacteristic
149C2×D79—22no—
150C2×D79—21no—
151C2×D79—21no—
152C2×D79—21no—
153C2×D79—41no—
154C2×D79—41no—
155C2×D79—84no—
156C4×C79—21no—
157C4×C79—21no—
158C4×C79—41no—
159C4×C79—41no—
160C4×C79—41no—
161C4×C79C2×#4111yescharacteristic
162C4×C79C2×#4111yescharacteristic
163Dic79—21no—
164Dic79—21no—
165Dic79—21no—
166Dic79—41no—
167Dic79—41no—
168Dic79—41no—
169C2×C79—42no—
170C2×C79#52511yescharacteristic
171C2×C79#57711yescharacteristic
172C2×C79#57711yescharacteristic
173D79—41no—
174D79—42no—
175#3123—791nomaximal, Sylow
176C79#312311yescharacteristic, complemented, Sylow
177#541—791no—
178#518—791no—
179#485—791no—
180#485—791no—
181#478—791no—
182#478D7911yescharacteristic, complemented
183#461—791no—
184#461—791no—
185#450—791no—
186#450—791no—
187#440—791no—
188#440—791no—
189C4×SD16—791no—
190C4×SD16—791no—
191#433—791no—
192C22×D4—791no—
193C2×SD16—791no—
194C2×SD16—791no—
195C2×SD16—791no—
196C2×SD16—791no—
197C4⋊Q8—791no—
198#126—1581no—
199#126—1581no—
200#125—1581no—
201#125—1581no—
202#125C2×D7911yescharacteristic, complemented
203C22⋊Q8—791no—
204C22⋊Q8—791no—
205C4×Q8—791no—
206C4×Q8—791no—
207C4×D4—791no—
208C4×D4—791no—
209C4×D4—791no—
210C4×D4—1581no—
211C4×D4—1581no—
212C4×D4C2×D7911yescharacteristic
213#117—791no—
214#117—791no—
215C2×C22⋊C4—1581no—
216C2×C22⋊C4—1581no—
217#107—791no—
218#107C2×D7911yescharacteristic, complemented
219#106—791no—
220#106C2×D7911yescharacteristic, complemented
221C4⋊C8—791no—
222C4⋊C8C2×D7911yescharacteristic, complemented
223#103—791no—
224#103—791no—
225#103—791no—
226#103—791no—
227#102—791no—
228#102—791no—
229#102C2×D7911yescharacteristic
230#102C2×D7911yescharacteristic
231C22⋊C8—791no—
232C22⋊C8—791no—
233#97—791no—
234C4×C8—791no—
235C24—1581no—
236C2×Q8—791no—
237C2×Q8—791no—
238C2×D4—791no—
239C2×D4—1581no—
240C2×D4—1582no—
241C2×D4—1582no—
242C2×D4C22×D7911yescharacteristic
243C22×C4—21no—
244C22×C4—791no—
245C22×C4—1581no—
246C22×C4—1581no—
247C22×C4—1581no—
248SD16—1582no—
249SD16—1582no—
250SD16—1582no—
251SD16—1582no—
252C2×C8—791no—
253C2×C8—791no—
254C2×C8C22×D7911yescharacteristic
255C2×C8C22×D7911yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—791no—
259C4⋊C4—791no—
260C4⋊C4—791no—
261C4⋊C4—1581no—
262C4⋊C4—1581no—
263C4⋊C4—1581no—
264C4⋊C4—1581no—
265C4⋊C4—1581no—
266C4⋊C4—1581no—
267C4⋊C4C22×D7911yescharacteristic
268C4⋊C4C22×D7911yescharacteristic
269C4⋊C4C22×D7911yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—791no—
272C22⋊C4—791no—
273C22⋊C4—1581no—
274C22⋊C4—1581no—
275C22⋊C4—1581no—
276C22⋊C4—1581no—
277C22⋊C4—1581no—
278C22⋊C4—1581no—
279C42—791no—
280C42—1581no—
281C42—1581no—
282C42—1581no—
283C42C22×D7911yescharacteristic
284C23—21no—
285C23—791no—
286C23—6321no—
287C23—6321no—
288C23—1584no—
289C23—1581no—
290Q8—1581no—
291Q8—1581no—
292Q8—1581no—
293Q8—1581no—
294D4—21no—
295D4—792no—
296D4—1584no—
297D4—1581no—
298D4#1192962512yes—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—791no—
304C2×C4—791no—
305C2×C4—791no—
306C2×C4—6321no—
307C2×C4—6321no—
308C2×C4—6321no—
309C2×C4—1581no—
310C2×C4—1581no—
311C2×C4—1581no—
312C2×C4—1581no—
313C2×C4—1581no—
314C2×C4D4×D7911yescharacteristic
315C2×C4D4×D7911yescharacteristic
316C2×C4C23×D7911yescharacteristic
317C8—21no—
318C8—21no—
319C8—1581no—
320C8—1581no—
321C22—22no—
322C22—41no—
323C22—41no—
324C22—3161no—
325C22—3161no—
326C22—6324no—
327C22—1581no—
328C22—1582no—
329C22—1581no—
330C22—1581no—
331C22C2×D4×D7911yescharacteristic
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—3161no—
338C4—3161no—
339C4—3161no—
340C4—1581no—
341C4—1581no—
342C4—1581no—
343C4#41×D7911yescharacteristic
344C4C2×#1192962511yescharacteristic
345C2—42no—
346C2—3162no—
347C2—3161no—
348C2#1909907611yescharacteristic
349C2#1909937011yescharacteristic
350C2#1909937311yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#478×C79C2
socleC22×C79C22×D4
prime radicalC2×D4×D79C22
hypercenter#478D79
hypocenterC79#3123
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #19099176C2semidirect
3. #19098907C2semidirect
4. #19098906C2semidirect
5. #19098860C2semidirect
6. #19098769C2semidirect
7. #19098768C2semidirect
10. #19098662C2semidirect
11. #19098660C2semidirect
12. #19098654C2semidirect
13. #19098650C2semidirect
14. #19098623C2semidirect
15. #478×C79C2semidirect
21. #14579161C22semidirect
28. #14579126C22semidirect
29. #14579126C22semidirect
39. #14579094C22semidirect
40. #14579092C22semidirect
41. C4⋊(C79⋊C8)C22semidirect
42. #14579086C22semidirect
43. #14579086C22semidirect
44. #14579084C22semidirect
45. #14579084C22semidirect
50. #14579071C22semidirect
51. C8×Dic79C22semidirect
52. #125×C79C22semidirect
54. #107×C79C22semidirect
55. #106×C79C22semidirect
56. C4⋊C8×C79C22semidirect
176. C79#3123semidirect
182. #478D79semidirect
202. #125C2×D79semidirect
218. #107C2×D79semidirect
220. #106C2×D79semidirect
222. C4⋊C8C2×D79semidirect