Finite Group Databasebeta

← #23775370

Subgroups — #23775370

Order 10112.

394 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#19099218C211yesmaximal, characteristic, complemented
2#19098933C211yesmaximal, characteristic, complemented
3#19098904C211yesmaximal, characteristic, complemented
4#19098893C211yesmaximal, characteristic, complemented
5#19098860C211yesmaximal, characteristic, complemented
6#19098807C211yesmaximal, characteristic, complemented
7#19098790C211yesmaximal, characteristic, complemented
8#19098768C211yesmaximal, characteristic, complemented
9#19098706C211yesmaximal, characteristic, complemented
10#19098706C211yesmaximal, characteristic, complemented
11#19098673C211yesmaximal, 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×#11929612C2211yescharacteristic
20C2×#11929609C2211yescharacteristic
21C2×#11929608C2211yescharacteristic
22C22×C79⋊C8C2211yescharacteristic
23#14579161C2211yescharacteristic
24#14579143—21no—
25#14579143—21no—
26#14579140C2211yescharacteristic
27#14579140C2211yescharacteristic
28#14579132—21no—
29C4×D316C2211yescharacteristic
30C4⋊C4×D79—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
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×Dic158C2311yescharacteristic
65C2×D316C2311yescharacteristic
66C2×C22⋊D79—21no—
67C2×C22⋊D79—21no—
68C2×C4×D79—21no—
69C2×C4×D79—21no—
70C2×C4×D79—21no—
71#11929612—41no—
72#11929612—41no—
73#11929609—22no—
74#11929608—41no—
75C2×C79⋊C8—41no—
76C2×C79⋊C8C2311yescharacteristic
77C2×C79⋊C8C2311yescharacteristic
78C2×C79⋊C8C2311yescharacteristic
79C2×C79⋊C8C2311yescharacteristic
80C4⋊Dic79—21no—
81C4⋊Dic79—21no—
82C4⋊Dic79C2311yescharacteristic
83Dic79⋊C4—21no—
84Dic79⋊C4—21no—
85C22⋊Dic79—21no—
86C22⋊Dic79—21no—
87(C2×D79)⋊C4—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—
115D4×C79—21no—
116D4×C79—21no—
117D4×C79—41no—
118D4×C79—42no—
119D4×C79—81no—
120C2×C4×C79—21no—
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—81no—
128C2×C4×C79—81no—
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—
139D316—21no—
140D316#4112yes—
141C4×D79—42no—
142C4×D79—42no—
143C4×D79—42no—
144Dic158—21no—
145Dic158—21no—
146Dic158—21no—
147Dic158—21no—
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—22no—
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—41no—
175Dic79—41no—
176Dic79—41no—
177C2×C79—41no—
178C2×C79—41no—
179C2×C79—81no—
180C2×C79#54611yescharacteristic
181C2×C79#57511yescharacteristic
182C2×C79#57711yescharacteristic
183D79—42no—
184#3307—791nomaximal, Sylow
185C79#330711yescharacteristic, complemented, Sylow
186#553D7911yescharacteristic, complemented
187#547—791no—
188#491—791no—
189#485—791no—
190#483—791no—
191#478—791no—
192#468—791no—
193#465—791no—
194#461—791no—
195#449—791no—
196#449—791no—
197#442—791no—
198#435—791no—
199#417—791no—
200#416—791no—
201C2×#41—791no—
202C2×#41—791no—
203C2×SD16—791no—
204C2×SD16—791no—
205C2×D8—791no—
206C2×M16—791no—
207C22×C8—791no—
208C4⋊Q8—791no—
209#126—21no—
210#125C2×D7911yescharacteristic
211#123—21no—
212#123—1581no—
213#123—1581no—
214C22⋊Q8—791no—
215C22⋊Q8—791no—
216#121—21no—
217#121—1581no—
218#121C2×D7911yescharacteristic
219#121C2×D7911yescharacteristic
220C4×D4—21no—
221C4×D4—791no—
222C4×D4C2×D7911yescharacteristic
223C4×D4C2×D7911yescharacteristic
224#117C2×D7911yescharacteristic
225C2×C4⋊C4—1581no—
226C2×C4⋊C4C2×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—3161no—
246#41—1582no—
247#41—1582no—
248C2×Q8—791no—
249C2×Q8—791no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—791no—
253C2×D4—1581no—
254C2×D4—1581no—
255C2×D4C22⋊D7911yescharacteristic
256C2×D4C22×D7911yescharacteristic
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—1581no—
260C22×C4—1581no—
261C22×C4—1581no—
262C22×C4C22×D7911yescharacteristic
263C22×C4C22×D7911yescharacteristic
264SD16—3161no—
265SD16—3161no—
266D8—1582no—
267M16—3161no—
268C2×C8—3161no—
269C2×C8—791no—
270C2×C8—791no—
271C2×C8—791no—
272C2×C8—791no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—791no—
277C4⋊C4—1581no—
278C4⋊C4—1581no—
279C4⋊C4—1581no—
280C4⋊C4—1581no—
281C4⋊C4C22⋊D7911yescharacteristic
282C4⋊C4C22×D7911yescharacteristic
283C4⋊C4C22×D7911yescharacteristic
284C4⋊C4C22×D7911yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—1581no—
290C22⋊C4—1581no—
291C22⋊C4—1581no—
292C22⋊C4C22⋊D7911yescharacteristic
293C22⋊C4C22⋊D7911yescharacteristic
294C42—21no—
295C42C22×D7911yescharacteristic
296C23—21no—
297C23—1581no—
298C23C2×C22⋊D7911yescharacteristic
299C23C2×C22⋊D7911yescharacteristic
300Q8—1581no—
301Q8—1581no—
302Q8—1581no—
303Q8—1581no—
304D4—21no—
305D4—21no—
306D4—41no—
307D4—42no—
308D4—81no—
309D4—3162no—
310D4—3162no—
311D4—792no—
312D4—1581no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—3162no—
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—1582no—
349C22C22×C22⋊D7911yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—3161no—
358C4—3161no—
359C4—3161no—
360C4#41×D7911yescharacteristic
361C4#1457920711yescharacteristic
362C2—41no—
363C2—41no—
364C2—81no—
365C2—3162no—
366C2#1909920111yescharacteristic
367C2#1909936111yescharacteristic
368C2#1909937411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#553×C79C2
socleC22×C79C22×D4
hypercenter#553D79
hypocenterC79#3307
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. #19099218C2semidirect
2. #19098933C2semidirect
3. #19098904C2semidirect
4. #19098893C2semidirect
5. #19098860C2semidirect
6. #19098807C2semidirect
7. #19098790C2semidirect
8. #19098768C2semidirect
9. #19098706C2semidirect
10. #19098706C2semidirect
11. #19098673C2semidirect
12. #19098635C2semidirect
13. #19098562C2semidirect
14. #19098557C2semidirect
15. #553×C79C2semidirect
185. C79#3307semidirect
186. #553D79semidirect