Finite Group Databasebeta

← #23774747

Subgroups — #23774747

Order 10112.

360 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#19099097C211yesmaximal, characteristic, complemented
2#19098870C211yesmaximal, characteristic, complemented
3#19098867C211yesmaximal, characteristic, complemented
4#19098863C211yesmaximal, characteristic, complemented
5#19098860C211yesmaximal, characteristic, complemented
6#19098802C211yesmaximal, characteristic, complemented
7#19098797C211yesmaximal, characteristic
8#19098794C211yesmaximal, characteristic, complemented
9#19098790C211yesmaximal, characteristic, complemented
10#19098785C211yesmaximal, characteristic, complemented
11#19098782C211yesmaximal, characteristic, complemented
12#19098778C211yesmaximal, characteristic, complemented
13#19098775C211yesmaximal, characteristic, complemented
14C2×C4⋊(C79⋊C8)C211yesmaximal, characteristic, complemented
15#529×C79C211yesmaximal, characteristic, complemented
16C2×#11929614C2211yescharacteristic
17C2×#11929612C2211yescharacteristic
18C2×#11929611C2211yescharacteristic
19C2×#11929609C2211yescharacteristic
20C22×C79⋊C8C2211yescharacteristic
21C22×C79⋊C8C2211yescharacteristic
22#14579155—21no—
23#14579153C2211yescharacteristic
24#14579149C2211yescharacteristic
25#14579144—21no—
26#14579140C2211yescharacteristic
27#14579135C2211yescharacteristic
28C4×Dic158C2211yescharacteristic
29C4×D316C2211yescharacteristic
30C4×C22⋊D79—21no—
31#14579118—21no—
32#14579094C2211yescharacteristic
33#14579094C2211yescharacteristic
34#14579092C2211yescharacteristic
35#14579092C2211yescharacteristic
36C4⋊(C79⋊C8)C2211yescharacteristic
37C4⋊(C79⋊C8)C2211yescharacteristic
38C4⋊(C79⋊C8)C2211yescharacteristic
39C4⋊(C79⋊C8)C2211yescharacteristic
40#14579085C2211yescharacteristic
41#14579085C2211yescharacteristic
42#14579084C2211yescharacteristic
43#14579084C2211yescharacteristic
44#14579082C2211yescharacteristic
45#14579082C2211yescharacteristic
46#14579081C2211yescharacteristic
47#14579081C2211yescharacteristic
48#126×C79—21no—
49#125×C79C2211yescharacteristic
50#124×C79C2211yescharacteristic
51#123×C79—21no—
52C22⋊Q8×C79C2211yescharacteristic
53#121×C79C2211yescharacteristic
54C4×Q8×C79C2211yescharacteristic
55C4×D4×C79—21no—
56C4×D4×C79C2211yescharacteristic
57#117×C79—21no—
58C2×C42×C79C2211yescharacteristic
59C2×Dic158C2311yescharacteristic
60C2×D316C2311yescharacteristic
61C2×C22⋊D79—21no—
62C2×C4×D79—21no—
63#11929614—41no—
64#11929612—41no—
65#11929611—41no—
66#11929609—41no—
67C2×C79⋊C8—41no—
68C2×C79⋊C8—41no—
69C2×C79⋊C8C2311yescharacteristic
70C2×C79⋊C8C2311yescharacteristic
71C2×C79⋊C8C2311yescharacteristic
72C2×C79⋊C8C2311yescharacteristic
73C4⋊Dic79C2311yescharacteristic
74C4⋊Dic79C2311yescharacteristic
75Dic79⋊C4—21no—
76Dic79⋊C4—21no—
77Dic79⋊C4—21no—
78Dic79⋊C4—21no—
79C22⋊Dic79—21no—
80(C2×D79)⋊C4—21no—
81(C2×D79)⋊C4—21no—
82(C2×D79)⋊C4—21no—
83(C2×D79)⋊C4—21no—
84C4×Dic79—21no—
85C2×Q8×C79C2311yescharacteristic
86C2×D4×C79—21no—
87C2×D4×C79C2311yescharacteristic
88C22×C4×C79—21no—
89C22×C4×C79D411yescharacteristic
90C22×C4×C79D411yescharacteristic
91C22×C4×C79C2311yescharacteristic
92C4⋊C4×C79—21no—
93C4⋊C4×C79—21no—
94C4⋊C4×C79—21no—
95C4⋊C4×C79—21no—
96C4⋊C4×C79C2311yescharacteristic
97C4⋊C4×C79C2311yescharacteristic
98C22⋊C4×C79—21no—
99C22⋊C4×C79—21no—
100C22⋊C4×C79—21no—
101C22⋊C4×C79—21no—
102C22⋊C4×C79—21no—
103C42×C79—21no—
104C42×C79D411yescharacteristic
105C42×C79D411yescharacteristic
106C42×C79C2311yescharacteristic
107C42×C79C2311yescharacteristic
108C23×C79—21no—
109C23×C79C2×D411yescharacteristic
110C22×D79—21no—
111Q8×C79—21no—
112Q8×C79—21no—
113D4×C79—21no—
114D4×C79—21no—
115D4×C79—42no—
116C2×C4×C79—22no—
117C2×C4×C79—21no—
118C2×C4×C79—21no—
119C2×C4×C79—21no—
120C2×C4×C79—21no—
121C2×C4×C79—21no—
122C2×C4×C79—41no—
123C2×C4×C79—42no—
124C2×C4×C79C2×D411yescharacteristic
125C2×C4×C79C2×D411yescharacteristic
126C2×C4×C79C2×D411yescharacteristic
127C2×C4×C79C2×D411yescharacteristic
128C2×C4×C79C2×D411yescharacteristic
129C2×C4×C79C2411yescharacteristic
130C22⋊D79—42no—
131C2×Dic79—21no—
132C2×Dic79—21no—
133C2×Dic79—21no—
134D316—21no—
135D316—21no—
136C4×D79—42no—
137Dic158—21no—
138Dic158—21no—
139C79⋊C8—21no—
140C79⋊C8—21no—
141C79⋊C8—21no—
142C79⋊C8—21no—
143C22×C79—21no—
144C22×C79—21no—
145C22×C79—41no—
146C22×C79—41no—
147C22×C79—41no—
148C22×C79#13512yes—
149C22×C79C22×D411yescharacteristic
150C2×D79—41no—
151C2×D79—41no—
152C2×D79—41no—
153C4×C79—21no—
154C4×C79—21no—
155C4×C79—21no—
156C4×C79—21no—
157C4×C79—21no—
158C4×C79—41no—
159C4×C79—41no—
160C4×C79—41no—
161C4×C79H(5,𝔽2)11yescharacteristic
162C4×C792−1+411yescharacteristic
163Dic79—41no—
164Dic79—41no—
165Dic79—41no—
166C2×C79—22no—
167C2×C79—81no—
168C2×C79#53711yescharacteristic
169C2×C79C2×#13511yescharacteristic
170C2×C79#57511yescharacteristic
171D79—81no—
172#3250—791nomaximal, Sylow
173C79#325011yescharacteristic, complemented, Sylow
174#529—791no—
175#529D7911yescharacteristic, complemented
176#479—791no—
177#479—791no—
178#478—791no—
179#478—791no—
180#467—791no—
181#466—791no—
182#465—791no—
183#465—791no—
184#464—791no—
185#464—791no—
186#463—791no—
187#463—791no—
188C2×C4⋊C8—791no—
189C2×Q16—791no—
190C2×SD16—791no—
191C2×SD16—791no—
192C2×D8—791no—
193C22×C8—791no—
194C22×C8—791no—
195#126—21no—
196#126—1581no—
197#125—791no—
198#125C2×D7911yescharacteristic
199#124—791no—
200#124C2×D7911yescharacteristic
201#123—21no—
202#123—1581no—
203C22⋊Q8—791no—
204C22⋊Q8C2×D7911yescharacteristic
205#121—791no—
206#121C2×D7911yescharacteristic
207C4×Q8—791no—
208C4×Q8C2×D7911yescharacteristic
209C4×D4—21no—
210C4×D4—791no—
211C4×D4—1581no—
212C4×D4C2×D7911yescharacteristic
213#117—21no—
214#117—1581no—
215C2×C42C2×D7911yescharacteristic
216#107—791no—
217#107—791no—
218#106—791no—
219#106—791no—
220C4⋊C8—791no—
221C4⋊C8—791no—
222C4⋊C8—791no—
223C4⋊C8—791no—
224#103—791no—
225#103—791no—
226#103—791no—
227#103—791no—
228#102—791no—
229#102—791no—
230#102—791no—
231#102—791no—
232C2×Q8—791no—
233C2×Q8C22×D7911yescharacteristic
234C2×D4—21no—
235C2×D4—791no—
236C2×D4—1581no—
237C2×D4C22×D7911yescharacteristic
238C22×C4—21no—
239C22×C4—1581no—
240C22×C4C22⋊D7911yescharacteristic
241C22×C4C22⋊D7911yescharacteristic
242C22×C4C22×D7911yescharacteristic
243Q16—3161no—
244SD16—3161no—
245SD16—3161no—
246D8—3161no—
247C2×C8—3161no—
248C2×C8—3161no—
249C2×C8—791no—
250C2×C8—791no—
251C2×C8—791no—
252C2×C8—791no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—791no—
258C4⋊C4—791no—
259C4⋊C4—1581no—
260C4⋊C4—1581no—
261C4⋊C4—1581no—
262C4⋊C4—1581no—
263C4⋊C4C22×D7911yescharacteristic
264C4⋊C4C22×D7911yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—1581no—
271C22⋊C4—1581no—
272C22⋊C4—1581no—
273C22⋊C4—1581no—
274C22⋊C4—1581no—
275C42—21no—
276C42—1581no—
277C42C22⋊D7911yescharacteristic
278C42C22⋊D7911yescharacteristic
279C42C22×D7911yescharacteristic
280C42C22×D7911yescharacteristic
281C23—21no—
282C23—1581no—
283C23C2×C22⋊D7911yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—1581no—
287Q8—1581no—
288D4—21no—
289D4—21no—
290D4—42no—
291D4—3162no—
292D4—1581no—
293D4—1581no—
294C2×C4—22no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—3162no—
303C2×C4—1581no—
304C2×C4—1581no—
305C2×C4—1581no—
306C2×C4C2×C22⋊D7911yescharacteristic
307C2×C4C2×C22⋊D7911yescharacteristic
308C2×C4C2×C22⋊D7911yescharacteristic
309C2×C4C2×C22⋊D7911yescharacteristic
310C2×C4C2×C22⋊D7911yescharacteristic
311C2×C4C23×D7911yescharacteristic
312C8—1581no—
313C8—1581no—
314C8—1581no—
315C8—1581no—
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—3161no—
322C22—3161no—
323C22—3161no—
324C22#1457918112yes—
325C22C22×C22⋊D7911yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—3161no—
335C4—3161no—
336C4—3161no—
337C4#1457920711yescharacteristic
338C4#1457920811yescharacteristic
339C2—22no—
340C2—81no—
341C2—6321no—
342C2#1909914111yescharacteristic
343C2C2×#1457918111yescharacteristic
344C2#1909936111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#529×C79C2
socleC22×C79C22×D4
prime radical#19098797C2
hypercenter#529D79
hypocenterC79#3250
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. #19099097C2semidirect
2. #19098870C2semidirect
3. #19098867C2semidirect
4. #19098863C2semidirect
5. #19098860C2semidirect
6. #19098802C2semidirect
8. #19098794C2semidirect
9. #19098790C2semidirect
10. #19098785C2semidirect
11. #19098782C2semidirect
12. #19098778C2semidirect
13. #19098775C2semidirect
14. C2×C4⋊(C79⋊C8)C2semidirect
15. #529×C79C2semidirect
173. C79#3250semidirect
175. #529D79semidirect