Finite Group Databasebeta

← #23775580

Subgroups — #23775580

Order 10112.

392 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099222C211yesmaximal, characteristic, complemented
2#19098925C211yesmaximal, characteristic, complemented
3#19098904C211yesmaximal, characteristic, complemented
4#19098887C211yesmaximal, characteristic, complemented
5#19098845C211yesmaximal, characteristic, complemented
6#19098814C211yesmaximal, characteristic, complemented
7#19098790C211yesmaximal, characteristic, complemented
8#19098778C211yesmaximal, characteristic, complemented
9#19098706C211yesmaximal, characteristic, complemented
10#19098701C211yesmaximal, characteristic, complemented
11#19098663C211yesmaximal, characteristic, complemented
12#19098635C211yesmaximal, characteristic, complemented
13#19098571C211yesmaximal, characteristic, complemented
14#19098557C211yesmaximal, characteristic, complemented
15#555×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C22×Dic158C2211yescharacteristic
18C2×#11929612C2211yescharacteristic
19C2×#11929612C2211yescharacteristic
20C2×#11929609C2211yescharacteristic
21C2×#11929608C2211yescharacteristic
22C22×C79⋊C8C2211yescharacteristic
23#14579149C2211yescharacteristic
24#14579147—21no—
25#14579140C2211yescharacteristic
26#14579139—21no—
27#14579135C2211yescharacteristic
28#14579133—21no—
29C4×Dic158C2211yescharacteristic
30(C22⋊D79)⋊C4—21no—
31#14579094C2211yescharacteristic
32#14579092C2211yescharacteristic
33#14579092C2211yescharacteristic
34C4⋊(C79⋊C8)C2211yescharacteristic
35#14579084C2211yescharacteristic
36#14579084C2211yescharacteristic
37#14579084C2211yescharacteristic
38#14579084C2211yescharacteristic
39#14579084C2211yescharacteristic
40#14579084C2211yescharacteristic
41#14579082C2211yescharacteristic
42#14579081C2211yescharacteristic
43#14579081C2211yescharacteristic
44#14579081C2211yescharacteristic
45C22⋊(C79⋊C8)C2211yescharacteristic
46C22⋊(C79⋊C8)C2211yescharacteristic
47#14579072C2211yescharacteristic
48C4⋊Q8×C79C2211yescharacteristic
49#124×C79—21no—
50#124×C79—21no—
51#121×C79—21no—
52#121×C79C2211yescharacteristic
53#121×C79C2211yescharacteristic
54C4×D4×C79C2211yescharacteristic
55C4×D4×C79C2211yescharacteristic
56#117×C79—21no—
57#117×C79C2211yescharacteristic
58#117×C79C2211yescharacteristic
59#11929624—22no—
60#11929624—41no—
61C2×Dic158—22no—
62C2×Dic158—21no—
63C2×Dic158—41no—
64C2×Dic158C2311yescharacteristic
65C2×Dic158C2311yescharacteristic
66C2×D316C2311yescharacteristic
67C2×C22⋊D79—21no—
68C2×C22⋊D79—21no—
69C22×Dic79—21no—
70C2×C4×D79—21no—
71#11929612—22no—
72#11929612—41no—
73#11929609—41no—
74#11929608—41no—
75C2×C79⋊C8—41no—
76C2×C79⋊C8C2311yescharacteristic
77C2×C79⋊C8C2311yescharacteristic
78C2×C79⋊C8C2311yescharacteristic
79C2×C79⋊C8C2311yescharacteristic
80C4⋊Dic79C2311yescharacteristic
81Dic79⋊C4—21no—
82Dic79⋊C4—21no—
83C22⋊Dic79—21no—
84(C2×D79)⋊C4—21no—
85(C2×D79)⋊C4—21no—
86(C2×D79)⋊C4—21no—
87C4×Dic79—21no—
88C2×Q8×C79—21no—
89C2×D4×C79—21no—
90C2×D4×C79—21no—
91C2×D4×C79D411yescharacteristic
92C2×D4×C79C2311yescharacteristic
93C22×C4×C79—21no—
94C22×C4×C79C2311yescharacteristic
95C22×C4×C79C2311yescharacteristic
96C4⋊C4×C79—21no—
97C4⋊C4×C79D411yescharacteristic
98C4⋊C4×C79C2311yescharacteristic
99C4⋊C4×C79C2311yescharacteristic
100C4⋊C4×C79C2311yescharacteristic
101C22⋊C4×C79—21no—
102C22⋊C4×C79—21no—
103C22⋊C4×C79—21no—
104C22⋊C4×C79—21no—
105C22⋊C4×C79—21no—
106C22⋊C4×C79D411yescharacteristic
107C22⋊C4×C79D411yescharacteristic
108C42×C79—21no—
109C42×C79—21no—
110C42×C79C2311yescharacteristic
111C23×C79—21no—
112C23×C79C2×D411yescharacteristic
113C23×C79C2×D411yescharacteristic
114C22×D79—21no—
115Q8×C79—81no—
116D4×C79—21no—
117D4×C79—21no—
118D4×C79—41no—
119D4×C79—81no—
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—42no—
129C2×C4×C79C2×D411yescharacteristic
130C2×C4×C79C2×D411yescharacteristic
131C2×C4×C79C2×D411yescharacteristic
132C2×C4×C79C2×D411yescharacteristic
133C2×C4×C79C2411yescharacteristic
134C22⋊D79—42no—
135C22⋊D79—42no—
136C2×Dic79—21no—
137C2×Dic79—21no—
138C2×Dic79—21no—
139C2×Dic79—42no—
140D316—21no—
141D316—21no—
142C4×D79—42no—
143Dic158—21no—
144Dic158—21no—
145Dic158—21no—
146Dic158—42no—
147Dic158#4112yes—
148C79⋊C8—21no—
149C79⋊C8—21no—
150C79⋊C8—21no—
151C79⋊C8—21no—
152C22×C79—21no—
153C22×C79—21no—
154C22×C79—21no—
155C22×C79—21no—
156C22×C79—21no—
157C22×C79—21no—
158C22×C79—41no—
159C22×C79—41no—
160C22×C79—41no—
161C22×C79C22×D411yescharacteristic
162C2×D79—41no—
163C2×D79—41no—
164C2×D79—41no—
165C4×C79—21no—
166C4×C79—21no—
167C4×C79—21no—
168C4×C79—21no—
169C4×C79—41no—
170C4×C79—41no—
171C4×C79—41no—
172C4×C79C2×#4111yescharacteristic
173C4×C79H(5,𝔽2)11yescharacteristic
174Dic79—22no—
175Dic79—41no—
176Dic79—41no—
177C2×C79—41no—
178C2×C79—41no—
179C2×C79—81no—
180C2×C79#54611yescharacteristic
181C2×C79#57511yescharacteristic
182C2×C79#57711yescharacteristic
183D79—81no—
184#3321—791nomaximal, Sylow
185C79#332111yescharacteristic, complemented, Sylow
186#555D7911yescharacteristic, complemented
187#548—791no—
188#489—791no—
189#485—791no—
190#482—791no—
191#475—791no—
192#469—791no—
193#465—791no—
194#463—791no—
195#449—791no—
196#448—791no—
197#440—791no—
198#435—791no—
199#419—791no—
200#416—791no—
201C2×#41—791no—
202C22×Q8—791no—
203C2×SD16—791no—
204C2×SD16—791no—
205C2×D8—791no—
206C2×M16—791no—
207C22×C8—791no—
208C4⋊Q8C2×D7911yescharacteristic
209#124—21no—
210#124—21no—
211#124—791no—
212#124—1581no—
213C22⋊Q8—791no—
214C22⋊Q8—1581no—
215#121—21no—
216#121—791no—
217#121—1581no—
218#121C2×D7911yescharacteristic
219#121C2×D7911yescharacteristic
220C4×Q8—791no—
221C4×D4—1581no—
222C4×D4C2×D7911yescharacteristic
223C4×D4C2×D7911yescharacteristic
224#117—21no—
225#117C2×D7911yescharacteristic
226#117C2×D7911yescharacteristic
227#107—791no—
228#106—791no—
229#106—791no—
230C4⋊C8—791no—
231#103—791no—
232#103—791no—
233#103—791no—
234#103—791no—
235#103—791no—
236#103—791no—
237#102—791no—
238#102—791no—
239#102—791no—
240#102—791no—
241C22⋊C8—791no—
242C22⋊C8—791no—
243#97—791no—
244#41—3161no—
245#41—1582no—
246C2×Q8—21no—
247C2×Q8—3161no—
248C2×Q8—791no—
249C2×Q8—791no—
250C2×Q8—1582no—
251C2×Q8—1581no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—791no—
255C2×D4—1581no—
256C2×D4—1581no—
257C2×D4C22⋊D7911yescharacteristic
258C2×D4C22×D7911yescharacteristic
259C22×C4—21no—
260C22×C4—1581no—
261C22×C4—1581no—
262C22×C4C22×D7911yescharacteristic
263C22×C4C22×D7911yescharacteristic
264SD16—3161no—
265SD16—1582no—
266D8—3161no—
267M16—3161no—
268C2×C8—3161no—
269C2×C8—791no—
270C2×C8—791no—
271C2×C8—791no—
272C2×C8—791no—
273C4⋊C4—21no—
274C4⋊C4—791no—
275C4⋊C4—1581no—
276C4⋊C4—1581no—
277C4⋊C4C22⋊D7911yescharacteristic
278C4⋊C4C22×D7911yescharacteristic
279C4⋊C4C22×D7911yescharacteristic
280C4⋊C4C22×D7911yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—1581no—
287C22⋊C4—1581no—
288C22⋊C4—1581no—
289C22⋊C4—1581no—
290C22⋊C4C22⋊D7911yescharacteristic
291C22⋊C4C22⋊D7911yescharacteristic
292C42—21no—
293C42—21no—
294C42—1581no—
295C42C22×D7911yescharacteristic
296C23—21no—
297C23—1581no—
298C23C2×C22⋊D7911yescharacteristic
299C23C2×C22⋊D7911yescharacteristic
300Q8—81no—
301Q8—3162no—
302Q8—792no—
303Q8—1581no—
304Q8—1581no—
305Q8—1581no—
306D4—21no—
307D4—21no—
308D4—41no—
309D4—81no—
310D4—81no—
311D4—3162no—
312D4—3162no—
313D4—1581no—
314D4—1581no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—3162no—
324C2×C4—3162no—
325C2×C4—1581no—
326C2×C4—1581no—
327C2×C4—1581no—
328C2×C4C2×C22⋊D7911yescharacteristic
329C2×C4C2×C22⋊D7911yescharacteristic
330C2×C4C2×C22⋊D7911yescharacteristic
331C2×C4C2×C22⋊D7911yescharacteristic
332C2×C4C23×D7911yescharacteristic
333C8—1581no—
334C8—1581no—
335C8—1581no—
336C8—1581no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—3161no—
347C22—3161no—
348C22—3161no—
349C22C22×C22⋊D7911yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—3161no—
358C4—3161no—
359C4—1582no—
360C4#41×D7911yescharacteristic
361C4#1457920711yescharacteristic
362C2—41no—
363C2—41no—
364C2—81no—
365C2—6321no—
366C2#1909920111yescharacteristic
367C2#1909936111yescharacteristic
368C2#1909937411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#555×C79C2
socleC22×C79C22×D4
hypercenter#555D79
hypocenterC79#3321
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×D4 ◁ #555

Complements

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

NH ≅ G/Ntype
1. #19099222C2semidirect
2. #19098925C2semidirect
3. #19098904C2semidirect
4. #19098887C2semidirect
5. #19098845C2semidirect
6. #19098814C2semidirect
7. #19098790C2semidirect
8. #19098778C2semidirect
9. #19098706C2semidirect
10. #19098701C2semidirect
11. #19098663C2semidirect
12. #19098635C2semidirect
13. #19098571C2semidirect
14. #19098557C2semidirect
15. #555×C79C2semidirect
185. C79#3321semidirect
186. #555D79semidirect