Finite Group Databasebeta

← #23775511

Subgroups — #23775511

Order 10112.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099270C211yesmaximal, characteristic, complemented
2#19098922C211yesmaximal, characteristic, complemented
3#19098891C211yesmaximal, characteristic, complemented
4#19098879C211yesmaximal, characteristic, complemented
5#19098848C211yesmaximal, characteristic, complemented
6#19098819C211yesmaximal, characteristic, complemented
7#19098790C211yesmaximal, characteristic, complemented
8#19098782C211yesmaximal, characteristic, complemented
9#19098725C211yesmaximal, characteristic, complemented
10#19098719C211yesmaximal, characteristic, complemented
11#19098668C211yesmaximal, characteristic, complemented
12#19098635C211yesmaximal, characteristic, complemented
13#19098564C211yesmaximal, characteristic, complemented
14C2×#14579085C211yesmaximal, characteristic, complemented
15#548×C79C211yesmaximal, characteristic
16C2×#11929614C2211yescharacteristic
17C2×#11929614C2211yescharacteristic
18C2×#11929612C2211yescharacteristic
19C2×#11929608C2211yescharacteristic
20C22×C79⋊C8C2211yescharacteristic
21#14579161C2211yescharacteristic
22#14579152—21no—
23#14579140C2211yescharacteristic
24#14579140C2211yescharacteristic
25#14579138—21no—
26#14579138—21no—
27C4×Dic158C2211yescharacteristic
28D4×Dic79—21no—
29C2×C4⋊Dic79C2211yescharacteristic
30C2×C4⋊Dic79C2211yescharacteristic
31#14579092C2211yescharacteristic
32#14579092C2211yescharacteristic
33#14579092C2211yescharacteristic
34C4⋊(C79⋊C8)C2211yescharacteristic
35#14579085C2211yescharacteristic
36#14579085C2211yescharacteristic
37#14579085C2211yescharacteristic
38#14579085C2211yescharacteristic
39#14579085C2211yescharacteristic
40#14579085C2211yescharacteristic
41#14579084C2211yescharacteristic
42#14579082C2211yescharacteristic
43#14579082C2211yescharacteristic
44#14579082C2211yescharacteristic
45C22⋊(C79⋊C8)C2211yescharacteristic
46C22⋊(C79⋊C8)C2211yescharacteristic
47#14579072C2211yescharacteristic
48C2×#41×C79C2211yescharacteristic
49C22×Q8×C79C2211yescharacteristic
50#124×C79—21no—
51#124×C79C2211yescharacteristic
52C22⋊Q8×C79—21no—
53C22⋊Q8×C79C2211yescharacteristic
54#121×C79—21no—
55#121×C79C2211yescharacteristic
56C4×Q8×C79C2211yescharacteristic
57C4×D4×C79—21no—
58C4×D4×C79C2211yescharacteristic
59C2×Dic158—21no—
60C2×Dic158C2311yescharacteristic
61C22×Dic79—21no—
62C22×Dic79—21no—
63#11929614—22no—
64#11929614—41no—
65#11929612—41no—
66#11929608—41no—
67C2×C79⋊C8—41no—
68C2×C79⋊C8C2311yescharacteristic
69C2×C79⋊C8C2311yescharacteristic
70C2×C79⋊C8C2311yescharacteristic
71C2×C79⋊C8C2311yescharacteristic
72C4⋊Dic79—21no—
73C4⋊Dic79—21no—
74C4⋊Dic79—21no—
75C4⋊Dic79C2311yescharacteristic
76C4⋊Dic79C2311yescharacteristic
77C4⋊Dic79C2311yescharacteristic
78Dic79⋊C4—21no—
79Dic79⋊C4—21no—
80Dic79⋊C4—21no—
81C22⋊Dic79—21no—
82C22⋊Dic79—21no—
83C4×Dic79—21no—
84#41×C79—22no—
85#41×C79—41no—
86C2×Q8×C79—21no—
87C2×Q8×C79—22no—
88C2×Q8×C79—41no—
89C2×Q8×C79C2311yescharacteristic
90C2×Q8×C79C2311yescharacteristic
91C2×D4×C79—21no—
92C2×D4×C79—21no—
93C2×D4×C79D411yescharacteristic
94C2×D4×C79C2311yescharacteristic
95C22×C4×C79—21no—
96C22×C4×C79—21no—
97C22×C4×C79C2311yescharacteristic
98C22×C4×C79C2311yescharacteristic
99C4⋊C4×C79—21no—
100C4⋊C4×C79—21no—
101C4⋊C4×C79D411yescharacteristic
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
114Q8×C79—21no—
115Q8×C79—21no—
116Q8×C79—21no—
117Q8×C79—42no—
118Q8×C79#4112yes—
119D4×C79—22no—
120D4×C79—21no—
121D4×C79—21no—
122D4×C79—42no—
123D4×C79—42no—
124C2×C4×C79—21no—
125C2×C4×C79—21no—
126C2×C4×C79—21no—
127C2×C4×C79—21no—
128C2×C4×C79—21no—
129C2×C4×C79—21no—
130C2×C4×C79—21no—
131C2×C4×C79—42no—
132C2×C4×C79—42no—
133C2×C4×C79C2×D411yescharacteristic
134C2×C4×C79C2×D411yescharacteristic
135C2×C4×C79C2×D411yescharacteristic
136C2×C4×C79C2×D411yescharacteristic
137C2×C4×C79C2411yescharacteristic
138C2×Dic79—21no—
139C2×Dic79—21no—
140C2×Dic79—21no—
141C2×Dic79—21no—
142C2×Dic79—81no—
143C2×Dic79—81no—
144Dic158—21no—
145Dic158—21no—
146Dic158—81no—
147C79⋊C8—21no—
148C79⋊C8—21no—
149C79⋊C8—21no—
150C79⋊C8—21no—
151C22×C79—21no—
152C22×C79—21no—
153C22×C79—21no—
154C22×C79—21no—
155C22×C79—21no—
156C22×C79—41no—
157C22×C79—41no—
158C22×C79—41no—
159C22×C79#13712yes—
160C22×C79C22×D411yescharacteristic
161C4×C79—21no—
162C4×C79—21no—
163C4×C79—22no—
164C4×C79—21no—
165C4×C79—21no—
166C4×C79—41no—
167C4×C79—41no—
168C4×C79C2×#4111yescharacteristic
169C4×C79H(5,𝔽2)11yescharacteristic
170Dic79—41no—
171Dic79—41no—
172Dic79—41no—
173Dic79—41no—
174C2×C79—22no—
175C2×C79—41no—
176C2×C79—81no—
177C2×C79#54611yescharacteristic
178C2×C79C2×#13711yescharacteristic
179C2×C79#57711yescharacteristic
180#3316—791nomaximal, Sylow
181C79#331611yescharacteristic, complemented, Sylow
182#554—791no—
183#548D7911yescharacteristic
184#489—791no—
185#483—791no—
186#481—791no—
187#475—791no—
188#470—791no—
189#465—791no—
190#464—791no—
191#452—791no—
192#451—791no—
193#441—791no—
194#435—791no—
195#417—791no—
196C2×#103—791no—
197C2×#41C2×D7911yescharacteristic
198C22×Q8C2×D7911yescharacteristic
199C2×Q16—791no—
200C2×Q16—791no—
201C2×SD16—791no—
202C2×M16—791no—
203C22×C8—791no—
204C4⋊Q8—791no—
205#125—1581no—
206#124—21no—
207#124C2×D7911yescharacteristic
208C22⋊Q8—21no—
209C22⋊Q8—791no—
210C22⋊Q8—791no—
211C22⋊Q8—1581no—
212C22⋊Q8—1581no—
213C22⋊Q8C2×D7911yescharacteristic
214#121—21no—
215#121C2×D7911yescharacteristic
216C4×Q8—791no—
217C4×Q8C2×D7911yescharacteristic
218C4×D4—21no—
219C4×D4—1581no—
220C4×D4C2×D7911yescharacteristic
221C2×C4⋊C4—791no—
222C2×C4⋊C4—791no—
223#106—791no—
224#106—791no—
225#106—791no—
226C4⋊C8—791no—
227#103—791no—
228#103—791no—
229#103—791no—
230#103—791no—
231#103—791no—
232#103—791no—
233#103—791no—
234#102—791no—
235#102—791no—
236#102—791no—
237C22⋊C8—791no—
238C22⋊C8—791no—
239#97—791no—
240#41—22no—
241#41—41no—
242C2×Q8—21no—
243C2×Q8—22no—
244C2×Q8—41no—
245C2×Q8—791no—
246C2×Q8—1581no—
247C2×Q8C22×D7911yescharacteristic
248C2×Q8C22×D7911yescharacteristic
249C2×D4—21no—
250C2×D4—21no—
251C2×D4C22⋊D7911yescharacteristic
252C2×D4C22×D7911yescharacteristic
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—1581no—
256C22×C4—1581no—
257C22×C4C22×D7911yescharacteristic
258C22×C4C22×D7911yescharacteristic
259Q16—3161no—
260Q16—1582no—
261SD16—3161no—
262M16—3161no—
263C2×C8—3161no—
264C2×C8—791no—
265C2×C8—791no—
266C2×C8—791no—
267C2×C8—791no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—791no—
271C4⋊C4—791no—
272C4⋊C4—791no—
273C4⋊C4—1581no—
274C4⋊C4—1581no—
275C4⋊C4—1581no—
276C4⋊C4—1581no—
277C4⋊C4—1581no—
278C4⋊C4—1581no—
279C4⋊C4C22⋊D7911yescharacteristic
280C4⋊C4C22×D7911yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—1581no—
286C22⋊C4—1581no—
287C22⋊C4C22⋊D7911yescharacteristic
288C22⋊C4C22⋊D7911yescharacteristic
289C42—21no—
290C42—1581no—
291C42C22×D7911yescharacteristic
292C23—21no—
293C23C2×C22⋊D7911yescharacteristic
294C23C2×C22⋊D7911yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—42no—
299Q8—6321no—
300Q8—1581no—
301Q8—1581no—
302Q8#1192962312yes—
303D4—22no—
304D4—21no—
305D4—21no—
306D4—42no—
307D4—42no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—6321no—
318C2×C4—6321no—
319C2×C4—1581no—
320C2×C4—1581no—
321C2×C4—1581no—
322C2×C4—1581no—
323C2×C4C2×C22⋊D7911yescharacteristic
324C2×C4C2×C22⋊D7911yescharacteristic
325C2×C4C2×C22⋊D7911yescharacteristic
326C2×C4C2×C22⋊D7911yescharacteristic
327C2×C4C23×D7911yescharacteristic
328C8—1581no—
329C8—1581no—
330C8—1581no—
331C8—1581no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22#1457919112yes—
341C22C22×C22⋊D7911yescharacteristic
342C4—21no—
343C4—21no—
344C4—22no—
345C4—21no—
346C4—21no—
347C4—41no—
348C4—41no—
349C4—3161no—
350C4—3161no—
351C4—3161no—
352C4—3161no—
353C4C2×#1192962311yescharacteristic
354C4#1457920611yescharacteristic
355C2—22no—
356C2—41no—
357C2—81no—
358C2#1909920711yescharacteristic
359C2C2×#1457919111yescharacteristic
360C2#1909937111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting, prime radical#548×C79C2
socleC22×C79C22×D4
hypercenter#548D79
hypocenterC79#3316
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #19099270C2semidirect
2. #19098922C2semidirect
3. #19098891C2semidirect
4. #19098879C2semidirect
5. #19098848C2semidirect
6. #19098819C2semidirect
7. #19098790C2semidirect
8. #19098782C2semidirect
9. #19098725C2semidirect
10. #19098719C2semidirect
11. #19098668C2semidirect
12. #19098635C2semidirect
13. #19098564C2semidirect
14. C2×#14579085C2semidirect
181. C79#3316semidirect