Finite Group Databasebeta

← #23773648

Subgroups — #23773648

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#19099173C211yesmaximal, characteristic, complemented
2#19099037C211yesmaximal, characteristic
3#19098904C211yesmaximal, characteristic, complemented
4#19098866C211yesmaximal, characteristic, complemented
5#19098862C211yesmaximal, characteristic, complemented
6#19098767C211yesmaximal, characteristic, complemented
7#19098767C211yesmaximal, characteristic, complemented
8#19098716C211yesmaximal, characteristic
9#19098713C211yesmaximal, characteristic
10#19098666C211yesmaximal, characteristic, complemented
11#19098662C211yesmaximal, characteristic, complemented
12#19098650C211yesmaximal, characteristic, complemented
13#19098648C211yesmaximal, characteristic, complemented
14#19098621C211yesmaximal, characteristic, complemented
15#485×C79C211yesmaximal, characteristic, complemented
16C22×D316C2211yescharacteristic
17C2×#11929613C2211yescharacteristic
18C2×#11929613C2211yescharacteristic
19C2×#11929611C2211yescharacteristic
20C2×#11929611C2211yescharacteristic
21#14579159C2211yescharacteristic, complemented
22#14579154—21no—
23#14579154—21no—
24#14579152—21no—
25#14579152C2211yescharacteristic, complemented
26#14579151—21no—
27#14579140C2211yescharacteristic
28Q8×Dic79C2211yescharacteristic, complemented
29#14579126C2211yescharacteristic, complemented
30C4×D316—21no—
31C4×D316—21no—
32#14579123C2211yescharacteristic
33#14579123C2211yescharacteristic
34#14579123C2211yescharacteristic
35#14579123C2211yescharacteristic
36#14579120C2211yescharacteristic
37C22⋊C4×D79—21no—
38C22⋊C4×D79—21no—
39#14579094C2211yescharacteristic, complemented
40#14579092C2211yescharacteristic, complemented
41Dic79⋊C8C2211yescharacteristic, complemented
42Dic79⋊C8C2211yescharacteristic, complemented
43#14579084C2211yescharacteristic, complemented
44#14579084C2211yescharacteristic, complemented
45#14579083C2211yescharacteristic
46#14579083C2211yescharacteristic
47#14579081C2211yescharacteristic
48#14579081C2211yescharacteristic
49C22⋊(C79⋊C8)C2211yescharacteristic
50#14579071C2211yescharacteristic, complemented
51C8×Dic79C2211yescharacteristic, complemented
52C22⋊Q8×C79C2211yescharacteristic
53#117×C79C2211yescharacteristic
54#107×C79C2211yescharacteristic, complemented
55#106×C79C2211yescharacteristic, complemented
56#103×C79C2211yescharacteristic, complemented
57#103×C79C2211yescharacteristic, complemented
58C22⋊C8×C79C2211yescharacteristic
59C23×D79—21no—
60C2×Dic158C2311yescharacteristic
61C2×D316—22no—
62C2×D316—22no—
63C2×D316—21no—
64C2×D316C2311yescharacteristic
65C2×D316C2311yescharacteristic
66C2×C4×D79—21no—
67C2×C4×D79—21no—
68C2×C4×D79—21no—
69C2×C4×D79—21no—
70#11929613—22no—
71#11929613—22no—
72#11929611—22no—
73#11929611—22no—
74C2×C79⋊C8C2311yescharacteristic
75C2×C79⋊C8C2311yescharacteristic
76C4⋊Dic79—21no—
77C4⋊Dic79—21no—
78C4⋊Dic79D411yescharacteristic
79C4⋊Dic79D411yescharacteristic
80C4⋊Dic79C2311yescharacteristic
81Dic79⋊C4—21no—
82Dic79⋊C4—21no—
83Dic79⋊C4—21no—
84Dic79⋊C4—21no—
85Dic79⋊C4—21no—
86C22⋊Dic79—21no—
87C22⋊Dic79D411yescharacteristic
88C22⋊Dic79D411yescharacteristic
89(C2×D79)⋊C4—21no—
90(C2×D79)⋊C4—21no—
91(C2×D79)⋊C4—21no—
92(C2×D79)⋊C4—21no—
93C4×Dic79—21no—
94C4×Dic79—21no—
95C4×Dic79C2311yescharacteristic
96C4×Dic79C2311yescharacteristic
97C2×Q8×C79C2311yescharacteristic
98C22×C4×C79C2311yescharacteristic
99C2×C8×C79C2311yescharacteristic
100C2×C8×C79C2311yescharacteristic
101C4⋊C4×C79—21no—
102C4⋊C4×C79C2311yescharacteristic
103C4⋊C4×C79C2311yescharacteristic
104C4⋊C4×C79C2311yescharacteristic
105C22⋊C4×C79—21no—
106C22⋊C4×C79—21no—
107C42×C79—21no—
108C23×C79C2×D411yescharacteristic
109C22×D79—21no—
110C22×D79—21no—
111C22×D79—24no—
112C22×D79—81no—
113C22×D79—81no—
114Q8×C79—21no—
115Q8×C79—21no—
116C2×C4×C79—21no—
117C2×C4×C79—21no—
118C2×C4×C79—21no—
119C2×C4×C79—21no—
120C2×C4×C79—21no—
121C2×C4×C79—21no—
122C2×C4×C79C2×D411yescharacteristic
123C2×C4×C79C2411yescharacteristic
124C2×Dic79—21no—
125C2×Dic79—21no—
126C2×Dic79C2×D411yescharacteristic
127C2×Dic79C2×D411yescharacteristic
128C2×Dic79C2×D411yescharacteristic
129C2×Dic79C2×D411yescharacteristic
130D316—24no—
131D316—21no—
132D316—21no—
133D316#4112yes—
134D316#4112yes—
135C4×D79—81no—
136C4×D79—81no—
137C4×D79—81no—
138C4×D79—81no—
139Dic158—21no—
140Dic158—21no—
141C8×C79—21no—
142C8×C79—21no—
143C79⋊C8—21no—
144C79⋊C8—21no—
145C22×C79—21no—
146C22×C79—21no—
147C22×C79—21no—
148C22×C79C22×D411yescharacteristic
149C2×D79—22no—
150C2×D79—22no—
151C2×D79—41no—
152C2×D79—41no—
153C2×D79—41no—
154C2×D79—41no—
155C2×D79—84no—
156C4×C79—21no—
157C4×C79—41no—
158C4×C79—41no—
159C4×C79—41no—
160C4×C79—41no—
161C4×C79C2×#4111yescharacteristic
162C4×C79C2×#4111yescharacteristic
163Dic79—21no—
164Dic79—21no—
165Dic79—21no—
166Dic79—21no—
167Dic79—41no—
168Dic79—41no—
169C2×C79—41no—
170C2×C79#52511yescharacteristic
171C2×C79#57711yescharacteristic
172C2×C79#57711yescharacteristic
173D79—42no—
174D79—42no—
175#3123—791nomaximal, Sylow
176C79#312311yescharacteristic, complemented, Sylow
177#541—791no—
178#518—791no—
179#485—791no—
180#485D7911yescharacteristic, complemented
181#478—791no—
182#478—791no—
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—791no—
201#125—1581no—
202#125—1581no—
203C22⋊Q8—791no—
204C22⋊Q8C2×D7911yescharacteristic
205C4×Q8—791no—
206C4×Q8—791no—
207C4×D4—791no—
208C4×D4—791no—
209C4×D4—791no—
210C4×D4—791no—
211C4×D4—1581no—
212C4×D4—1581no—
213#117—791no—
214#117C2×D7911yescharacteristic
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⋊C8—791no—
223#103—791no—
224#103—791no—
225#103C2×D7911yescharacteristic, complemented
226#103C2×D7911yescharacteristic, complemented
227#102—791no—
228#102—791no—
229#102—791no—
230#102—791no—
231C22⋊C8—791no—
232C22⋊C8C2×D7911yescharacteristic
233#97—791no—
234C4×C8—791no—
235C24—1581no—
236C2×Q8—791no—
237C2×Q8C22×D7911yescharacteristic
238C2×D4—791no—
239C2×D4—791no—
240C2×D4—1582no—
241C2×D4—1582no—
242C2×D4—1581no—
243C22×C4—1581no—
244C22×C4—1581no—
245C22×C4—1581no—
246C22×C4—1581no—
247C22×C4C22×D7911yescharacteristic
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—791no—
258C4⋊C4—791no—
259C4⋊C4—791no—
260C4⋊C4—1581no—
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—21no—
272C22⋊C4—791no—
273C22⋊C4—791no—
274C22⋊C4—1581no—
275C22⋊C4—1581no—
276C22⋊C4—1581no—
277C22⋊C4—1581no—
278C22⋊C4—1581no—
279C42—21no—
280C42—791no—
281C42—791no—
282C42—1581no—
283C42—1581no—
284C23—6321no—
285C23—6321no—
286C23—1584no—
287C23—1581no—
288C23—1581no—
289C23D4×D7911yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—1581no—
293Q8—1581no—
294D4—792no—
295D4—792no—
296D4—1584no—
297D4—1581no—
298D4—1581no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—791no—
306C2×C4—791no—
307C2×C4—791no—
308C2×C4—791no—
309C2×C4—6321no—
310C2×C4—6321no—
311C2×C4—6321no—
312C2×C4—6321no—
313C2×C4—1581no—
314C2×C4—1581no—
315C2×C4D4×D7911yescharacteristic
316C2×C4C23×D7911yescharacteristic
317C8—21no—
318C8—21no—
319C8—1581no—
320C8—1581no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—3161no—
325C22—3161no—
326C22—3161no—
327C22—3161no—
328C22—6324no—
329C22—1582no—
330C22—1582no—
331C22C2×D4×D7911yescharacteristic
332C4—21no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—3161no—
338C4—3161no—
339C4—1581no—
340C4—1581no—
341C4—1581no—
342C4—1581no—
343C4#41×D7911yescharacteristic
344C4#41×D7911yescharacteristic
345C2—41no—
346C2—3162no—
347C2—3162no—
348C2#1909907111yescharacteristic
349C2#1909937011yescharacteristic
350C2#1909937211yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#485×C79C2
socleC22×C79C22×D4
prime radicalC22×D316C22
hypercenter#485D79
hypocenterC79#3123
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #19099173C2semidirect
3. #19098904C2semidirect
4. #19098866C2semidirect
5. #19098862C2semidirect
6. #19098767C2semidirect
7. #19098767C2semidirect
10. #19098666C2semidirect
11. #19098662C2semidirect
12. #19098650C2semidirect
13. #19098648C2semidirect
14. #19098621C2semidirect
15. #485×C79C2semidirect
21. #14579159C22semidirect
25. #14579152C22semidirect
28. Q8×Dic79C22semidirect
29. #14579126C22semidirect
39. #14579094C22semidirect
40. #14579092C22semidirect
41. Dic79⋊C8C22semidirect
42. Dic79⋊C8C22semidirect
43. #14579084C22semidirect
44. #14579084C22semidirect
50. #14579071C22semidirect
51. C8×Dic79C22semidirect
54. #107×C79C22semidirect
55. #106×C79C22semidirect
56. #103×C79C22semidirect
57. #103×C79C22semidirect
176. C79#3123semidirect
180. #485D79semidirect
218. #107C2×D79semidirect
220. #106C2×D79semidirect
225. #103C2×D79semidirect
226. #103C2×D79semidirect