Finite Group Databasebeta

← #23775400

Subgroups — #23775400

Order 10112.

404 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099234C211yesmaximal, characteristic, complemented
2#19098929C211yesmaximal, characteristic, complemented
3#19098887C211yesmaximal, characteristic, complemented
4#19098876C211yesmaximal, characteristic, complemented
5#19098867C211yesmaximal, characteristic, complemented
6#19098814C211yesmaximal, characteristic, complemented
7#19098797C211yesmaximal, characteristic, complemented
8#19098758C211yesmaximal, characteristic, complemented
9#19098706C211yesmaximal, characteristic, complemented
10#19098706C211yesmaximal, characteristic, complemented
11#19098663C211yesmaximal, characteristic, complemented
12#19098635C211yesmaximal, characteristic, complemented
13#19098562C211yesmaximal, characteristic, complemented
14#19098557C211yesmaximal, characteristic, complemented
15#553×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C2×#11929624C2211yescharacteristic
18C2×#11929612C2211yescharacteristic
19C2×#11929609C2211yescharacteristic
20C2×#11929609C2211yescharacteristic
21C2×#11929608C2211yescharacteristic
22C22×C79⋊C8C2211yescharacteristic
23#14579158C2211yescharacteristic
24#14579157—21no—
25#14579135C2211yescharacteristic
26#14579135C2211yescharacteristic
27#14579134—21no—
28#14579134—21no—
29C4×Dic158C2211yescharacteristic
30#14579123—21no—
31#14579094C2211yescharacteristic
32#14579094C2211yescharacteristic
33#14579092C2211yescharacteristic
34C4⋊(C79⋊C8)C2211yescharacteristic
35#14579084C2211yescharacteristic
36#14579084C2211yescharacteristic
37#14579084C2211yescharacteristic
38#14579082C2211yescharacteristic
39#14579081C2211yescharacteristic
40#14579081C2211yescharacteristic
41#14579081C2211yescharacteristic
42#14579081C2211yescharacteristic
43#14579081C2211yescharacteristic
44#14579081C2211yescharacteristic
45C22⋊(C79⋊C8)C2211yescharacteristic
46C22⋊(C79⋊C8)C2211yescharacteristic
47#14579072C2211yescharacteristic
48#126×C79—21no—
49#125×C79C2211yescharacteristic
50#123×C79—21no—
51#121×C79—21no—
52#121×C79C2211yescharacteristic
53#121×C79C2211yescharacteristic
54C4×D4×C79—21no—
55C4×D4×C79C2211yescharacteristic
56C4×D4×C79C2211yescharacteristic
57#117×C79C2211yescharacteristic
58C2×C4⋊C4×C79C2211yescharacteristic
59#11929624—22no—
60#11929624—22no—
61#11929624—41no—
62#11929624—41no—
63C2×Dic158C2311yescharacteristic
64C2×D316—21no—
65C2×D316—21no—
66C2×D316C2311yescharacteristic
67C2×D316C2311yescharacteristic
68C2×C22⋊D79—21no—
69C2×C22⋊D79—21no—
70C2×C22⋊D79—21no—
71C2×C22⋊D79—21no—
72C2×C4×D79—21no—
73C2×C4×D79—21no—
74#11929612—22no—
75#11929609—41no—
76#11929609—41no—
77#11929608—41no—
78C2×C79⋊C8—41no—
79C2×C79⋊C8C2311yescharacteristic
80C2×C79⋊C8C2311yescharacteristic
81C2×C79⋊C8C2311yescharacteristic
82C2×C79⋊C8C2311yescharacteristic
83C4⋊Dic79C2311yescharacteristic
84Dic79⋊C4—21no—
85(C2×D79)⋊C4—21no—
86(C2×D79)⋊C4—21no—
87C4×Dic79—21no—
88C2×D4×C79—21no—
89C2×D4×C79—21no—
90C2×D4×C79D411yescharacteristic
91C2×D4×C79C2311yescharacteristic
92C22×C4×C79—21no—
93C22×C4×C79—21no—
94C22×C4×C79C2311yescharacteristic
95C22×C4×C79C2311yescharacteristic
96C4⋊C4×C79—21no—
97C4⋊C4×C79—21no—
98C4⋊C4×C79—21no—
99C4⋊C4×C79D411yescharacteristic
100C4⋊C4×C79C2311yescharacteristic
101C4⋊C4×C79C2311yescharacteristic
102C4⋊C4×C79C2311yescharacteristic
103C22⋊C4×C79—21no—
104C22⋊C4×C79—21no—
105C22⋊C4×C79—21no—
106C22⋊C4×C79—21no—
107C22⋊C4×C79D411yescharacteristic
108C22⋊C4×C79D411yescharacteristic
109C42×C79—21no—
110C42×C79C2311yescharacteristic
111C23×C79—21no—
112C23×C79C2×D411yescharacteristic
113C23×C79C2×D411yescharacteristic
114C22×D79—21no—
115C22×D79—21no—
116D4×C79—21no—
117D4×C79—21no—
118D4×C79—41no—
119D4×C79—42no—
120D4×C79—81no—
121C2×C4×C79—21no—
122C2×C4×C79—21no—
123C2×C4×C79—21no—
124C2×C4×C79—21no—
125C2×C4×C79—21no—
126C2×C4×C79—21no—
127C2×C4×C79—21no—
128C2×C4×C79—81no—
129C2×C4×C79—81no—
130C2×C4×C79C2×D411yescharacteristic
131C2×C4×C79C2×D411yescharacteristic
132C2×C4×C79C2×D411yescharacteristic
133C2×C4×C79C2×D411yescharacteristic
134C2×C4×C79C2411yescharacteristic
135C22⋊D79—42no—
136C22⋊D79—42no—
137C22⋊D79—81no—
138C22⋊D79—81no—
139C2×Dic79—21no—
140C2×Dic79—21no—
141D316—21no—
142D316—21no—
143D316—21no—
144D316—21no—
145D316—42no—
146D316—81no—
147C4×D79—42no—
148C4×D79—42no—
149Dic158—21no—
150Dic158#4112yes—
151C79⋊C8—21no—
152C79⋊C8—21no—
153C79⋊C8—21no—
154C79⋊C8—21no—
155C22×C79—21no—
156C22×C79—21no—
157C22×C79—21no—
158C22×C79—21no—
159C22×C79—21no—
160C22×C79—21no—
161C22×C79—41no—
162C22×C79—41no—
163C22×C79—41no—
164C22×C79C22×D411yescharacteristic
165C2×D79—41no—
166C2×D79—41no—
167C2×D79—41no—
168C2×D79—41no—
169C2×D79—41no—
170C2×D79—41no—
171C4×C79—21no—
172C4×C79—21no—
173C4×C79—21no—
174C4×C79—21no—
175C4×C79—41no—
176C4×C79—41no—
177C4×C79—41no—
178C4×C79C2×#4111yescharacteristic
179C4×C79H(5,𝔽2)11yescharacteristic
180Dic79—22no—
181Dic79—41no—
182C2×C79—41no—
183C2×C79—41no—
184C2×C79—81no—
185C2×C79#54611yescharacteristic
186C2×C79#57511yescharacteristic
187C2×C79#57611yescharacteristic
188D79—81no—
189D79—81no—
190#3309—791nomaximal, Sylow
191C79#330911yescharacteristic, complemented, Sylow
192#553D7911yescharacteristic, complemented
193#550—791no—
194#490—791no—
195#482—791no—
196#480—791no—
197#479—791no—
198#469—791no—
199#466—791no—
200#459—791no—
201#449—791no—
202#449—791no—
203#440—791no—
204#435—791no—
205#417—791no—
206#416—791no—
207C2×#41—791no—
208C2×#41—791no—
209C2×SD16—791no—
210C2×D8—791no—
211C2×D8—791no—
212C2×M16—791no—
213C22×C8—791no—
214#127—791no—
215#127—1581no—
216#126—21no—
217#125C2×D7911yescharacteristic
218#123—21no—
219#121—21no—
220#121—791no—
221#121—791no—
222#121—1581no—
223#121—1581no—
224#121C2×D7911yescharacteristic
225#121C2×D7911yescharacteristic
226C4×Q8—791no—
227C4×D4—21no—
228C4×D4—1581no—
229C4×D4C2×D7911yescharacteristic
230C4×D4C2×D7911yescharacteristic
231#117C2×D7911yescharacteristic
232C2×C4⋊C4C2×D7911yescharacteristic
233#107—791no—
234#107—791no—
235#106—791no—
236C4⋊C8—791no—
237#103—791no—
238#103—791no—
239#103—791no—
240#102—791no—
241#102—791no—
242#102—791no—
243#102—791no—
244#102—791no—
245#102—791no—
246#102—791no—
247C22⋊C8—791no—
248C22⋊C8—791no—
249#97—791no—
250#41—3161no—
251#41—3161no—
252#41—1582no—
253#41—1582no—
254C2×Q8—791no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—791no—
258C2×D4—791no—
259C2×D4—1581no—
260C2×D4—1581no—
261C2×D4—1581no—
262C2×D4—1581no—
263C2×D4—1581no—
264C2×D4—1581no—
265C2×D4C22⋊D7911yescharacteristic
266C2×D4C22×D7911yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—1581no—
270C22×C4—1581no—
271C22×C4C22×D7911yescharacteristic
272C22×C4C22×D7911yescharacteristic
273SD16—1582no—
274D8—3161no—
275D8—3161no—
276M16—3161no—
277C2×C8—3161no—
278C2×C8—791no—
279C2×C8—791no—
280C2×C8—791no—
281C2×C8—791no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—791no—
286C4⋊C4—1581no—
287C4⋊C4C22⋊D7911yescharacteristic
288C4⋊C4C22×D7911yescharacteristic
289C4⋊C4C22×D7911yescharacteristic
290C4⋊C4C22×D7911yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—1581no—
296C22⋊C4—1581no—
297C22⋊C4C22⋊D7911yescharacteristic
298C22⋊C4C22⋊D7911yescharacteristic
299C42—21no—
300C42—1581no—
301C42C22×D7911yescharacteristic
302C23—21no—
303C23—1581no—
304C23—1581no—
305C23C2×C22⋊D7911yescharacteristic
306C23C2×C22⋊D7911yescharacteristic
307Q8—792no—
308Q8—1581no—
309D4—21no—
310D4—21no—
311D4—41no—
312D4—42no—
313D4—81no—
314D4—3162no—
315D4—3162no—
316D4—3162no—
317D4—6321no—
318D4—6321no—
319D4—6321no—
320D4—1581no—
321D4—1581no—
322D4—1581no—
323D4—1581no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—3162no—
334C2×C4—3162no—
335C2×C4—1581no—
336C2×C4—1581no—
337C2×C4C2×C22⋊D7911yescharacteristic
338C2×C4C2×C22⋊D7911yescharacteristic
339C2×C4C2×C22⋊D7911yescharacteristic
340C2×C4C2×C22⋊D7911yescharacteristic
341C2×C4C23×D7911yescharacteristic
342C8—1581no—
343C8—1581no—
344C8—1581no—
345C8—1581no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—3161no—
356C22—3161no—
357C22—3161no—
358C22—3161no—
359C22—3161no—
360C22—3161no—
361C22C22×C22⋊D7911yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—3161no—
370C4—1582no—
371C4#41×D7911yescharacteristic
372C4#1457920711yescharacteristic
373C2—41no—
374C2—41no—
375C2—81no—
376C2—6321no—
377C2—6321no—
378C2#1909920111yescharacteristic
379C2#1909936111yescharacteristic
380C2#1909936611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#553×C79C2
socleC22×C79C22×D4
hypercenter#553D79
hypocenterC79#3309
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #19099234C2semidirect
2. #19098929C2semidirect
3. #19098887C2semidirect
4. #19098876C2semidirect
5. #19098867C2semidirect
6. #19098814C2semidirect
7. #19098797C2semidirect
8. #19098758C2semidirect
9. #19098706C2semidirect
10. #19098706C2semidirect
11. #19098663C2semidirect
12. #19098635C2semidirect
13. #19098562C2semidirect
14. #19098557C2semidirect
15. #553×C79C2semidirect
191. C79#3309semidirect
192. #553D79semidirect