Finite Group Databasebeta

← #23776472

Subgroups — #23776472

Order 10112.

368 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099295C211yesmaximal, characteristic, complemented
2#19099282C211yesmaximal, characteristic, complemented
3#19098956C211yesmaximal, characteristic, complemented
4#19098951C211yesmaximal, characteristic
5#19098783C211yesmaximal, characteristic, complemented
6#19098782C211yesmaximal, characteristic, complemented
7#19098780C211yesmaximal, characteristic, complemented
8#19098775C211yesmaximal, characteristic, complemented
9#19098766C211yesmaximal, characteristic, complemented
10#19098761C211yesmaximal, characteristic, complemented
11#19098693C211yesmaximal, characteristic, complemented
12#19098675C211yesmaximal, characteristic, complemented
13#19098670C211yesmaximal, characteristic, complemented
14C4×#11929613C211yesmaximal, characteristic, complemented
15#495×C79C211yesmaximal, characteristic, complemented
16C2×#11929614C2211yescharacteristic
17C2×#11929613C2211yescharacteristic
18C2×#11929612C2211yescharacteristic
19C2×#11929611C2211yescharacteristic
20C2×#11929609C2211yescharacteristic
21#14579159C2211yescharacteristic
22#14579157C2211yescharacteristic
23#14579154—21no—
24#14579154—21no—
25#14579150C2211yescharacteristic
26#14579148C2211yescharacteristic
27#14579147—21no—
28#14579145—21no—
29#14579143—21no—
30#14579138—21no—
31Q8×Dic79C2211yescharacteristic
32Q8×Dic79C2211yescharacteristic
33C4×Dic158C2211yescharacteristic
34C4×Dic158C2211yescharacteristic
35C4×D316C2211yescharacteristic
36D4×Dic79C2211yescharacteristic
37D4×Dic79C2211yescharacteristic
38(C22⋊D79)⋊C4—21no—
39#14579117—21no—
40#14579093C2211yescharacteristic
41C4⋊(C79⋊C8)C2211yescharacteristic
42Dic79⋊C8C2211yescharacteristic
43Dic79⋊C8C2211yescharacteristic
44#14579086C2211yescharacteristic
45#14579085C2211yescharacteristic
46#14579085C2211yescharacteristic
47#14579083C2211yescharacteristic
48#14579082C2211yescharacteristic
49#14579082C2211yescharacteristic
50#14579071C2211yescharacteristic
51#14579071C2211yescharacteristic
52C2×Q16×C79C2211yescharacteristic
53C2×SD16×C79C2211yescharacteristic
54C2×SD16×C79C2211yescharacteristic
55C2×D8×C79C2211yescharacteristic
56#124×C79C2211yescharacteristic
57#124×C79C2211yescharacteristic
58C4×C8×C79C2211yescharacteristic
59C2×Dic158D411yescharacteristic
60C2×Dic158C2311yescharacteristic
61C2×D316C2311yescharacteristic
62C2×C22⋊D79—21no—
63C2×C22⋊D79—21no—
64C22×Dic79—21no—
65C22×Dic79—21no—
66C2×C4×D79—21no—
67#11929614—41no—
68#11929613—22no—
69#11929612—41no—
70#11929611—41no—
71#11929609—41no—
72C2×C79⋊C8C2311yescharacteristic
73C2×C79⋊C8C2311yescharacteristic
74C4⋊Dic79—21no—
75C4⋊Dic79—21no—
76C4⋊Dic79D411yescharacteristic
77C4⋊Dic79C2311yescharacteristic
78C4⋊Dic79C2311yescharacteristic
79Dic79⋊C4—21no—
80Dic79⋊C4—21no—
81Dic79⋊C4—21no—
82Dic79⋊C4D411yescharacteristic
83Dic79⋊C4D411yescharacteristic
84C22⋊Dic79—21no—
85C22⋊Dic79—21no—
86C22⋊Dic79—21no—
87C22⋊Dic79—21no—
88(C2×D79)⋊C4—21no—
89(C2×D79)⋊C4—21no—
90(C2×D79)⋊C4—21no—
91C4×Dic79—21no—
92C4×Dic79—21no—
93C4×Dic79—21no—
94C4×Dic79C2311yescharacteristic
95C4×Dic79C2311yescharacteristic
96C2×Q8×C79C2311yescharacteristic
97C2×Q8×C79C2311yescharacteristic
98C2×D4×C79C2311yescharacteristic
99C2×D4×C79C2311yescharacteristic
100Q16×C79—22no—
101SD16×C79—41no—
102SD16×C79—41no—
103D8×C79—22no—
104C2×C8×C79C2311yescharacteristic
105C2×C8×C79C2311yescharacteristic
106C22⋊C4×C79—21no—
107C22⋊C4×C79—21no—
108C22⋊C4×C79—21no—
109C22⋊C4×C79—21no—
110C42×C79C2311yescharacteristic
111C23×C79—21no—
112C23×C79—21no—
113C22×D79—21no—
114Q8×C79—21no—
115Q8×C79—21no—
116Q8×C79—21no—
117Q8×C79—21no—
118D4×C79—21no—
119D4×C79—21no—
120D4×C79—21no—
121D4×C79—21no—
122C2×C4×C79—21no—
123C2×C4×C79—21no—
124C2×C4×C79C2×D411yescharacteristic
125C2×C4×C79C2×D411yescharacteristic
126C2×C4×C79C2411yescharacteristic
127C22⋊D79—42no—
128C22⋊D79—81no—
129C2×Dic79—21no—
130C2×Dic79—21no—
131C2×Dic79—21no—
132C2×Dic79—42no—
133C2×Dic79—81no—
134C2×Dic79C2×D411yescharacteristic
135C2×Dic79C2×D411yescharacteristic
136C2×Dic79C2×D411yescharacteristic
137C2×Dic79C2×D411yescharacteristic
138D316—21no—
139D316—21no—
140C4×D79—81no—
141Dic158—21no—
142Dic158—21no—
143Dic158—41no—
144C8×C79—21no—
145C8×C79#4112yes—
146C79⋊C8—21no—
147C79⋊C8—21no—
148C22×C79—41no—
149C22×C79—41no—
150C22×C79—41no—
151C22×C79—41no—
152C22×C79—41no—
153C22×C79—41no—
154C22×C79C22×D411yescharacteristic
155C2×D79—41no—
156C2×D79—41no—
157C2×D79—41no—
158C4×C79—21no—
159C4×C79—21no—
160C4×C79—41no—
161C4×C79—41no—
162C4×C79C2×#4111yescharacteristic
163C4×C79H(5,𝔽2)11yescharacteristic
164Dic79—21no—
165Dic79—21no—
166Dic79—21no—
167Dic79—21no—
168Dic79—41no—
169Dic79—41no—
170Dic79—41no—
171C2×C79—81no—
172C2×C79—81no—
173C2×C79#55011yescharacteristic
174C2×C79#57511yescharacteristic
175C2×C79#57711yescharacteristic
176D79—81no—
177#3401—791nomaximal, Sylow
178C79#340111yescharacteristic, complemented, Sylow
179#559—791no—
180#556—791no—
181#497—791no—
182#496—791no—
183#495D7911yescharacteristic, complemented
184#464—791no—
185#464—791no—
186#463—791no—
187#463—791no—
188#461—791no—
189#460—791no—
190#446—791no—
191#442—791no—
192#441—791no—
193C4×SD16—791no—
194C2×Q16—791no—
195C2×Q16C2×D7911yescharacteristic
196C2×SD16—791no—
197C2×SD16—791no—
198C2×SD16—791no—
199C2×SD16C2×D7911yescharacteristic
200C2×SD16C2×D7911yescharacteristic
201C2×D8—791no—
202C2×D8C2×D7911yescharacteristic
203C4⋊Q8—791no—
204#127—791no—
205#126—1581no—
206#126—1581no—
207#124—791no—
208#124—791no—
209#124—1581no—
210#124C2×D7911yescharacteristic
211#124C2×D7911yescharacteristic
212#123—1581no—
213#123—1581no—
214C22⋊Q8—1581no—
215C4×Q8—791no—
216C4×Q8—791no—
217C4×Q8—791no—
218C4×Q8—791no—
219C4×D4—791no—
220C4×D4—791no—
221C4×D4—791no—
222C4×D4—1581no—
223#117—1581no—
224#106—791no—
225C4⋊C8—791no—
226C4⋊C8—791no—
227C4⋊C8—791no—
228#103—791no—
229#103—791no—
230#103—791no—
231#102—791no—
232#102—791no—
233#102—791no—
234#97—791no—
235#97—791no—
236C4×C8C2×D7911yescharacteristic
237C2×Q8—791no—
238C2×Q8—791no—
239C2×Q8C22×D7911yescharacteristic
240C2×Q8C22×D7911yescharacteristic
241C2×D4—791no—
242C2×D4—1581no—
243C2×D4—1581no—
244C2×D4C22×D7911yescharacteristic
245C2×D4C22×D7911yescharacteristic
246C22×C4—1581no—
247C22×C4—1581no—
248C22×C4—1581no—
249Q16—22no—
250Q16—3161no—
251SD16—41no—
252SD16—41no—
253SD16—3161no—
254SD16—3161no—
255SD16—1582no—
256D8—22no—
257D8—3161no—
258C2×C8—791no—
259C2×C8—791no—
260C2×C8C22×D7911yescharacteristic
261C2×C8C22×D7911yescharacteristic
262C4⋊C4—791no—
263C4⋊C4—791no—
264C4⋊C4—791no—
265C4⋊C4—791no—
266C4⋊C4—791no—
267C4⋊C4—1581no—
268C4⋊C4—1581no—
269C4⋊C4—1581no—
270C4⋊C4—1581no—
271C4⋊C4—1581no—
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—1581no—
277C22⋊C4—1581no—
278C22⋊C4—1581no—
279C22⋊C4—1581no—
280C22⋊C4—1581no—
281C22⋊C4—1581no—
282C22⋊C4—1581no—
283C42—791no—
284C42—791no—
285C42—1581no—
286C42—1581no—
287C42—1581no—
288C42C22×D7911yescharacteristic
289C23—21no—
290C23—21no—
291C23—1581no—
292Q8—21no—
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—3161no—
297Q8—1581no—
298Q8—1581no—
299D4—21no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—3162no—
304D4—6321no—
305D4—1581no—
306D4—1581no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—3162no—
310C2×C4—791no—
311C2×C4—791no—
312C2×C4—791no—
313C2×C4—791no—
314C2×C4—6321no—
315C2×C4—6321no—
316C2×C4—1581no—
317C2×C4—1581no—
318C2×C4—1581no—
319C2×C4D4×D7911yescharacteristic
320C2×C4D4×D7911yescharacteristic
321C2×C4C23×D7911yescharacteristic
322C8—21no—
323C8—1581no—
324C8—1581no—
325C8#1192962312yes—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—3161no—
333C22—3161no—
334C22—3161no—
335C22C2×D4×D7911yescharacteristic
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—3161no—
341C4—3161no—
342C4—3161no—
343C4—1581no—
344C4—1581no—
345C4—1581no—
346C4—1581no—
347C4C2×#1192962311yescharacteristic
348C4#1457920611yescharacteristic
349C2—81no—
350C2—81no—
351C2—6321no—
352C2#1909923311yescharacteristic
353C2#1909936011yescharacteristic
354C2#1909937011yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#495×C79C2
socleC22×C79C22×D4
prime radical#19098951C2
hypercenter#495D79
hypocenterC79#3401
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #19099295C2semidirect
2. #19099282C2semidirect
3. #19098956C2semidirect
5. #19098783C2semidirect
6. #19098782C2semidirect
7. #19098780C2semidirect
8. #19098775C2semidirect
9. #19098766C2semidirect
10. #19098761C2semidirect
11. #19098693C2semidirect
12. #19098675C2semidirect
13. #19098670C2semidirect
14. C4×#11929613C2semidirect
15. #495×C79C2semidirect
178. C79#3401semidirect
183. #495D79semidirect