Finite Group Databasebeta

← #23773672

Subgroups — #23773672

Order 10112.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099186C211yesmaximal, characteristic, complemented
2#19099044C211yesmaximal, characteristic, complemented
3#19098881C211yesmaximal, characteristic, complemented
4#19098852C211yesmaximal, characteristic, complemented
5#19098847C211yesmaximal, characteristic, complemented
6#19098788C211yesmaximal, characteristic, complemented
7#19098781C211yesmaximal, characteristic, complemented
8#19098723C211yesmaximal, characteristic, complemented
9#19098710C211yesmaximal, characteristic
10#19098674C211yesmaximal, characteristic, complemented
11#19098667C211yesmaximal, characteristic, complemented
12#19098650C211yesmaximal, characteristic, complemented
13#19098648C211yesmaximal, characteristic, complemented
14#19098621C211yesmaximal, characteristic, complemented
15#483×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C2×#11929614C2211yescharacteristic
18C2×#11929613C2211yescharacteristic
19C2×#11929611C2211yescharacteristic
20C2×D632C2211yescharacteristic
21#14579160C2211yescharacteristic
22#14579156—21no—
23#14579150C2211yescharacteristic
24#14579147—21no—
25#14579143—21no—
26#14579141—21no—
27#14579135C2211yescharacteristic
28Q8×Dic79C2211yescharacteristic
29#14579126C2211yescharacteristic
30#14579126C2211yescharacteristic
31#14579123C2211yescharacteristic
32#14579123C2211yescharacteristic
33#14579123C2211yescharacteristic
34C4×C22⋊D79—21no—
35C4×C22⋊D79—21no—
36#14579120C2211yescharacteristic
37#14579119—21no—
38C4⋊C4×D79—21no—
39#14579092C2211yescharacteristic
40#14579092C2211yescharacteristic
41Dic79⋊C8C2211yescharacteristic
42Dic79⋊C8C2211yescharacteristic
43#14579086C2211yescharacteristic
44#14579084C2211yescharacteristic
45#14579083C2211yescharacteristic
46#14579081C2211yescharacteristic
47#14579081C2211yescharacteristic
48#14579081C2211yescharacteristic
49C22⋊(C79⋊C8)C2211yescharacteristic
50#14579071C2211yescharacteristic
51C8×Dic79C2211yescharacteristic
52C22⋊Q8×C79C2211yescharacteristic
53C2×C4⋊C4×C79C2211yescharacteristic
54#106×C79C2211yescharacteristic
55#106×C79C2211yescharacteristic
56#103×C79C2211yescharacteristic
57#103×C79C2211yescharacteristic
58C22⋊C8×C79C2211yescharacteristic
59#11929624—22no—
60#11929624—22no—
61C2×Dic158—21no—
62C2×Dic158C2311yescharacteristic
63C2×D316C2311yescharacteristic
64C2×D316C2311yescharacteristic
65C2×C22⋊D79—21no—
66C2×C22⋊D79—21no—
67C2×C4×D79—21no—
68C2×C4×D79—21no—
69C2×C4×D79—21no—
70C2×C4×D79—21no—
71#11929614—22no—
72#11929613—22no—
73#11929611—22no—
74D632—22no—
75C2×C79⋊C8C2311yescharacteristic
76C2×C79⋊C8C2311yescharacteristic
77C4⋊Dic79—21no—
78C4⋊Dic79D411yescharacteristic
79C4⋊Dic79D411yescharacteristic
80C4⋊Dic79C2311yescharacteristic
81Dic79⋊C4—21no—
82Dic79⋊C4—21no—
83Dic79⋊C4—21no—
84C22⋊Dic79D411yescharacteristic
85C22⋊Dic79D411yescharacteristic
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)⋊C4—21no—
92C4×Dic79—21no—
93C4×Dic79—21no—
94C4×Dic79—21no—
95C4×Dic79C2311yescharacteristic
96C4×Dic79C2311yescharacteristic
97C2×Q8×C79C2311yescharacteristic
98C22×C4×C79—21no—
99C22×C4×C79C2311yescharacteristic
100C2×C8×C79C2311yescharacteristic
101C2×C8×C79C2311yescharacteristic
102C4⋊C4×C79—21no—
103C4⋊C4×C79—21no—
104C4⋊C4×C79C2311yescharacteristic
105C4⋊C4×C79C2311yescharacteristic
106C4⋊C4×C79C2311yescharacteristic
107C22⋊C4×C79—21no—
108C23×C79C2×D411yescharacteristic
109C22×D79—21no—
110C22×D79—21no—
111Q8×C79—21no—
112Q8×C79—21no—
113C2×C4×C79—21no—
114C2×C4×C79—21no—
115C2×C4×C79—21no—
116C2×C4×C79—21no—
117C2×C4×C79—21no—
118C2×C4×C79—21no—
119C2×C4×C79—81no—
120C2×C4×C79C2×D411yescharacteristic
121C2×C4×C79C2411yescharacteristic
122C22⋊D79—24no—
123C22⋊D79—81no—
124C2×Dic79—21no—
125C2×Dic79—21no—
126C2×Dic79C2×D411yescharacteristic
127C2×Dic79C2×D411yescharacteristic
128C2×Dic79C2×D411yescharacteristic
129C2×Dic79C2×D411yescharacteristic
130D316—21no—
131D316—21no—
132D316—21no—
133D316#4112yes—
134C4×D79—24no—
135C4×D79—81no—
136C4×D79—81no—
137C4×D79—81no—
138Dic158—21no—
139Dic158—81no—
140Dic158#4112yes—
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—41no—
151C2×D79—41no—
152C2×D79—41no—
153C2×D79—41no—
154C2×D79—41no—
155C4×C79—21no—
156C4×C79—41no—
157C4×C79—41no—
158C4×C79—41no—
159C4×C79—41no—
160C4×C79C2×#4111yescharacteristic
161C4×C79C2×#4111yescharacteristic
162Dic79—22no—
163Dic79—21no—
164Dic79—21no—
165Dic79—21no—
166Dic79—21no—
167Dic79—41no—
168C2×C79—41no—
169C2×C79#52511yescharacteristic
170C2×C79#57711yescharacteristic
171C2×C79#57711yescharacteristic
172D79—42no—
173D79—81no—
174#3125—791nomaximal, Sylow
175C79#312511yescharacteristic, complemented, Sylow
176#542—791no—
177#520—791no—
178#483D7911yescharacteristic, complemented
179#481—791no—
180#476—791no—
181#475—791no—
182#464—791no—
183#463—791no—
184#452—791no—
185#449—791no—
186#442—791no—
187#441—791no—
188C4×SD16—791no—
189C4×SD16—791no—
190#433—791no—
191C2×#41—791no—
192C2×Q16—791no—
193C2×SD16—791no—
194C2×SD16—791no—
195C2×D8—791no—
196C4⋊Q8—791no—
197#126—1581no—
198#124—791no—
199#124—1581no—
200#123—1581no—
201C22⋊Q8—1581no—
202C22⋊Q8C2×D7911yescharacteristic
203#121—791no—
204C4×Q8—791no—
205C4×Q8—791no—
206C4×Q8—791no—
207C4×D4—791no—
208C4×D4—791no—
209C4×D4—791no—
210C4×D4—1581no—
211C4×D4—1581no—
212#117—791no—
213#117—1581no—
214C2×C4⋊C4—1581no—
215C2×C4⋊C4C2×D7911yescharacteristic
216#106—791no—
217#106—791no—
218#106C2×D7911yescharacteristic
219#106C2×D7911yescharacteristic
220C4⋊C8—791no—
221C4⋊C8—791no—
222#103—791no—
223#103—791no—
224#103C2×D7911yescharacteristic
225#103C2×D7911yescharacteristic
226#102—791no—
227#102—791no—
228#102—791no—
229#102—791no—
230C22⋊C8—791no—
231C22⋊C8C2×D7911yescharacteristic
232#97—791no—
233C4×C8—791no—
234#41—1582no—
235#41—1582no—
236C2×Q8—791no—
237C2×Q8—1581no—
238C2×Q8C22×D7911yescharacteristic
239C2×D4—791no—
240C2×D4—791no—
241C2×D4—1581no—
242C2×D4—1581no—
243C22×C4—21no—
244C22×C4—1581no—
245C22×C4—1581no—
246C22×C4—1581no—
247C22×C4—1581no—
248C22×C4C22×D7911yescharacteristic
249Q16—1582no—
250SD16—1582no—
251SD16—1582no—
252D8—1582no—
253C2×C8—791no—
254C2×C8—791no—
255C2×C8C22×D7911yescharacteristic
256C2×C8C22×D7911yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—791no—
260C4⋊C4—791no—
261C4⋊C4—791no—
262C4⋊C4—1581no—
263C4⋊C4—1581no—
264C4⋊C4—1581no—
265C4⋊C4—1581no—
266C4⋊C4C22×D7911yescharacteristic
267C4⋊C4C22×D7911yescharacteristic
268C4⋊C4C22×D7911yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—791no—
271C22⋊C4—791no—
272C22⋊C4—1581no—
273C22⋊C4—1581no—
274C22⋊C4—1581no—
275C22⋊C4—1581no—
276C22⋊C4—1581no—
277C22⋊C4—1581no—
278C42—791no—
279C42—791no—
280C42—1581no—
281C42—1581no—
282C42—1581no—
283C23—1581no—
284C23—1581no—
285C23D4×D7911yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—792no—
289Q8—6321no—
290Q8—1581no—
291D4—792no—
292D4—6321no—
293D4—1584no—
294D4—1581no—
295D4—1581no—
296D4—1581no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—81no—
304C2×C4—791no—
305C2×C4—791no—
306C2×C4—791no—
307C2×C4—791no—
308C2×C4—6321no—
309C2×C4—6321no—
310C2×C4—6321no—
311C2×C4—1584no—
312C2×C4—1581no—
313C2×C4—1581no—
314C2×C4D4×D7911yescharacteristic
315C2×C4C23×D7911yescharacteristic
316C8—21no—
317C8—21no—
318C8—1581no—
319C8—1581no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—3161no—
324C22—3161no—
325C22—3161no—
326C22—3161no—
327C22—3161no—
328C22—1582no—
329C22C2×D4×D7911yescharacteristic
330C4—21no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—3161no—
336C4—1582no—
337C4—1581no—
338C4—1581no—
339C4—1581no—
340C4—1581no—
341C4#41×D7911yescharacteristic
342C4#41×D7911yescharacteristic
343C2—41no—
344C2—3162no—
345C2—6321no—
346C2#1909907111yescharacteristic
347C2#1909936911yescharacteristic
348C2#1909937211yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#483×C79C2
socleC22×C79C22×D4
prime radical#19098710C2
hypercenter#483D79
hypocenterC79#3125
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
1. #19099186C2semidirect
2. #19099044C2semidirect
3. #19098881C2semidirect
4. #19098852C2semidirect
5. #19098847C2semidirect
6. #19098788C2semidirect
7. #19098781C2semidirect
8. #19098723C2semidirect
10. #19098674C2semidirect
11. #19098667C2semidirect
12. #19098650C2semidirect
13. #19098648C2semidirect
14. #19098621C2semidirect
15. #483×C79C2semidirect
175. C79#3125semidirect
178. #483D79semidirect