Finite Group Databasebeta

← #23775260

Subgroups — #23775260

Order 10112.

420 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099226C211yesmaximal, characteristic, complemented
2#19099213C211yesmaximal, characteristic
3#19098912C211yesmaximal, characteristic, complemented
4#19098895C211yesmaximal, characteristic, complemented
5#19098891C211yesmaximal, characteristic, complemented
6#19098847C211yesmaximal, characteristic, complemented
7#19098791C211yesmaximal, characteristic, complemented
8#19098766C211yesmaximal, characteristic, complemented
9#19098701C211yesmaximal, characteristic, complemented
10#19098700C211yesmaximal, characteristic, complemented
11#19098654C211yesmaximal, characteristic, complemented
12C8×C22⋊D79C211yesmaximal, characteristic, complemented
13C2×#14579086C211yesmaximal, characteristic, complemented
14#103×D79C211yesmaximal, characteristic, complemented
15#465×C79C211yesmaximal, characteristic, complemented
16C2×#11929623—21no—
17C22×Dic158C2211yescharacteristic
18C2×Q8×D79C2211yescharacteristic
19C2×#11929612C2211yescharacteristic
20C2×#11929612C2211yescharacteristic
21C2×C8×D79C2211yescharacteristic
22#14579160—21no—
23#14579160C2211yescharacteristic
24#14579159C2211yescharacteristic
25#14579143—21no—
26#14579142—21no—
27#14579141C2211yescharacteristic
28#14579139—21no—
29#14579138—21no—
30#14579138—21no—
31#14579132C2211yescharacteristic
32#14579126C2211yescharacteristic
33D4×Dic79C2211yescharacteristic
34C4×C22⋊D79C2211yescharacteristic
35(C22⋊D79)⋊C4—21no—
36C2×C4⋊Dic79C2211yescharacteristic
37C4⋊C4×D79C2211yescharacteristic
38#14579092C2211yescharacteristic
39#14579092C2211yescharacteristic
40Dic79⋊C8C2211yescharacteristic
41#14579086C2211yescharacteristic
42#14579086C2211yescharacteristic
43#14579086C2211yescharacteristic
44#14579086C2211yescharacteristic
45#14579085C2211yescharacteristic
46#14579085C2211yescharacteristic
47#14579084C2211yescharacteristic
48#14579084C2211yescharacteristic
49C22⋊(C79⋊C8)C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic
51C8×Dic79C2211yescharacteristic
52C2×SD16×C79C2211yescharacteristic
53C22×C8×C79C2211yescharacteristic
54C22⋊Q8×C79C2211yescharacteristic
55#121×C79C2211yescharacteristic
56#106×C79C2211yescharacteristic
57#103×C79C2211yescharacteristic
58#102×C79C2211yescharacteristic
59#11929623—44no—
60C2×Dic158—22no—
61C2×Dic158—21no—
62C2×Dic158—21no—
63C2×Dic158—21no—
64C2×Dic158—41no—
65C2×Dic158C2311yescharacteristic
66C2×Dic158C2311yescharacteristic
67Q8×D79—22no—
68Q8×D79—41no—
69C2×C22⋊D79—21no—
70C2×C22⋊D79D411yescharacteristic
71C22×Dic79—21no—
72C22×Dic79—21no—
73C22×Dic79—21no—
74C2×C4×D79—21no—
75C2×C4×D79—21no—
76C2×C4×D79C2311yescharacteristic
77#11929612—22no—
78#11929612—41no—
79C2×C79⋊C8C2311yescharacteristic
80C2×C79⋊C8C2311yescharacteristic
81C8×D79—41no—
82C4⋊Dic79—21no—
83C4⋊Dic79—21no—
84C4⋊Dic79C2311yescharacteristic
85C4⋊Dic79C2311yescharacteristic
86Dic79⋊C4—21no—
87Dic79⋊C4—21no—
88Dic79⋊C4—21no—
89Dic79⋊C4—21no—
90Dic79⋊C4—21no—
91Dic79⋊C4D411yescharacteristic
92C22⋊Dic79—21no—
93C22⋊Dic79—21no—
94C22⋊Dic79D411yescharacteristic
95(C2×D79)⋊C4—21no—
96(C2×D79)⋊C4D411yescharacteristic
97C4×Dic79—21no—
98C4×Dic79C2311yescharacteristic
99C2×Q8×C79C2311yescharacteristic
100C2×D4×C79—21no—
101C2×D4×C79C2311yescharacteristic
102C22×C4×C79C2311yescharacteristic
103SD16×C79—41no—
104C2×C8×C79—41no—
105C2×C8×C79C2311yescharacteristic
106C2×C8×C79C2311yescharacteristic
107C4⋊C4×C79—21no—
108C4⋊C4×C79C2311yescharacteristic
109C4⋊C4×C79C2311yescharacteristic
110C22⋊C4×C79—21no—
111C22⋊C4×C79—21no—
112C23×C79—21no—
113C23×C79C2×D411yescharacteristic
114C22×D79C2×D411yescharacteristic
115Q8×C79—21no—
116Q8×C79—21no—
117D4×C79—21no—
118D4×C79—21no—
119D4×C79—42no—
120C2×C4×C79—21no—
121C2×C4×C79—21no—
122C2×C4×C79—21no—
123C2×C4×C79—21no—
124C2×C4×C79—21no—
125C2×C4×C79C2×D411yescharacteristic
126C2×C4×C79C2411yescharacteristic
127C22⋊D79—42no—
128C22⋊D79SD1614yescomplemented
129C2×Dic79—21no—
130C2×Dic79—21no—
131C2×Dic79—21no—
132C2×Dic79—21no—
133C2×Dic79—42no—
134C2×Dic79—42no—
135C2×Dic79—42no—
136C2×Dic79C2×D411yescharacteristic
137C2×Dic79C2×D411yescharacteristic
138C2×Dic79C2×D411yescharacteristic
139C4×D79—21no—
140C4×D79—21no—
141C4×D79—42no—
142C4×D79—42no—
143Dic158—21no—
144Dic158—21no—
145Dic158—21no—
146Dic158—42no—
147Dic158—42no—
148Dic158—42no—
149Dic158#4112yescomplemented
150C8×C79—21no—
151C8×C79—21no—
152C79⋊C8—21no—
153C79⋊C8—21no—
154C22×C79—21no—
155C22×C79—21no—
156C22×C79—41no—
157C22×C79—41no—
158C22×C79—41no—
159C22×C79C2×SD1612yes—
160C22×C79C22×D411yescharacteristic
161C2×D79—21no—
162C2×D79—21no—
163C2×D79C2×SD1612yes—
164C4×C79—21no—
165C4×C79—41no—
166C4×C79—41no—
167C4×C79—41no—
168C4×C79C2×#4111yescharacteristic
169C4×C79H(5,𝔽2)11yescharacteristic
170Dic79—22no—
171Dic79—21no—
172Dic79—21no—
173Dic79—41no—
174Dic79—41no—
175Dic79—41no—
176Dic79C2×SD1612yes—
177C2×C79—22no—
178C2×C79—81no—
179C2×C79#54611yescharacteristic
180C2×C79C22×SD1611yescharacteristic
181C2×C79#57811yescharacteristic
182D79—22no—
183#3298—791nomaximal, Sylow
184C79#329811yescharacteristic, complemented, Sylow
185D4×Q8—791no—
186#547—791no—
187#487—791no—
188#483—791no—
189#483—791no—
190#475—791no—
191#465—791no—
192#465D7911yescharacteristic, complemented
193#461—791no—
194#448—791no—
195#448—791no—
196C4×SD16—791no—
197C8×D4—791no—
198C2×#103—791no—
199C2×#103—791no—
200C2×#41—1581no—
201C22×Q8—791no—
202C22×Q8—791no—
203C2×SD16—791no—
204C2×SD16—791no—
205C2×SD16C2×D7911yescharacteristic
206C22×C8—791no—
207C22×C8C2×D7911yescharacteristic
208C4⋊Q8—791no—
209C4⋊Q8—791no—
210C4⋊Q8—1581no—
211#123—1581no—
212#123—1581no—
213C22⋊Q8—791no—
214C22⋊Q8—1581no—
215C22⋊Q8—1581no—
216C22⋊Q8—1581no—
217C22⋊Q8C2×D7911yescharacteristic
218#121—791no—
219#121C2×D7911yescharacteristic
220C4×Q8—791no—
221C4×D4—791no—
222C4×D4—791no—
223C4×D4—1581no—
224C2×C4⋊C4—791no—
225C2×C4⋊C4—791no—
226#106—791no—
227#106—791no—
228#106C2×D7911yescharacteristic
229C4⋊C8—791no—
230#103—791no—
231#103—791no—
232#103—791no—
233#103—791no—
234#103—791no—
235#103—791no—
236#103—791no—
237#103—791no—
238#103C2×D7911yescharacteristic
239#102C2×D7911yescharacteristic
240C22⋊C8—791no—
241C22⋊C8—791no—
242C4×C8—791no—
243#41—3164no—
244C2×Q8—3161no—
245C2×Q8—3161no—
246C2×Q8—791no—
247C2×Q8—791no—
248C2×Q8—1582no—
249C2×Q8—1581no—
250C2×Q8—1581no—
251C2×Q8—1582no—
252C2×Q8—1581no—
253C2×Q8C22×D7911yescharacteristic
254C2×D4—21no—
255C2×D4—791no—
256C2×D4—1581no—
257C2×D4C22×D7911yescharacteristic
258C22×C4—791no—
259C22×C4—1581no—
260C22×C4—1581no—
261C22×C4—1581no—
262C22×C4—1581no—
263C22×C4—1581no—
264C22×C4C22×D7911yescharacteristic
265SD16—41no—
266SD16—3161no—
267SD16—1582no—
268C2×C8—41no—
269C2×C8—3161no—
270C2×C8—791no—
271C2×C8—791no—
272C2×C8C22×D7911yescharacteristic
273C2×C8C22×D7911yescharacteristic
274C4⋊C4—21no—
275C4⋊C4—791no—
276C4⋊C4—791no—
277C4⋊C4—791no—
278C4⋊C4—1581no—
279C4⋊C4—1581no—
280C4⋊C4—1581no—
281C4⋊C4—1581no—
282C4⋊C4—1581no—
283C4⋊C4—1581no—
284C4⋊C4—1581no—
285C4⋊C4C22×D7911yescharacteristic
286C4⋊C4C22×D7911yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—791no—
290C22⋊C4—791no—
291C22⋊C4—1581no—
292C22⋊C4—1581no—
293C22⋊C4—1581no—
294C42—791no—
295C42—1581no—
296C23—21no—
297C23—791no—
298C23D4×D7911yescharacteristic
299Q8—21no—
300Q8—21no—
301Q8—3162no—
302Q8—3162no—
303Q8—3162no—
304Q8—792no—
305Q8—1581no—
306Q8—1581no—
307Q8—1581no—
308D4—21no—
309D4—21no—
310D4—42no—
311D4—3162no—
312D4—794no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—3162no—
319C2×C4—3162no—
320C2×C4—3162no—
321C2×C4—3162no—
322C2×C4—3162no—
323C2×C4—791no—
324C2×C4—791no—
325C2×C4—791no—
326C2×C4—1581no—
327C2×C4—1581no—
328C2×C4—1581no—
329C2×C4—1581no—
330C2×C4—1581no—
331C2×C4—1581no—
332C2×C4D4×D7911yescharacteristic
333C2×C4C23×D7911yescharacteristic
334C8—21no—
335C8—21no—
336C8—1581no—
337C8—1581no—
338C22—21no—
339C22—21no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—792no—
344C22—1581no—
345C22—1581no—
346C22SD16×D7912yes—
347C22C2×D4×D7911yescharacteristic
348C4—21no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—3161no—
353C4—3161no—
354C4—3161no—
355C4—792no—
356C4—1582no—
357C4—1581no—
358C4—1581no—
359C4#41×D7911yescharacteristic
360C4#1457920611yescharacteristic
361C2—22no—
362C2—81no—
363C2—1582no—
364C2#1909920211yescharacteristic
365C2C2×SD16×D7911yescharacteristic
366C2#1909937711yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#465×C79C2
socleC22×C79C22×D4
prime radical#19099213C2
hypercenter#465D79
hypocenterC79#3298
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #19099226C2semidirect
3. #19098912C2semidirect
4. #19098895C2semidirect
5. #19098891C2semidirect
6. #19098847C2semidirect
7. #19098791C2semidirect
8. #19098766C2semidirect
9. #19098701C2semidirect
10. #19098700C2semidirect
11. #19098654C2semidirect
12. C8×C22⋊D79C2semidirect
13. C2×#14579086C2semidirect
14. #103×D79C2semidirect
15. #465×C79C2semidirect
128. C22⋊D79SD16semidirect
149. Dic158#41semidirect
184. C79#3298semidirect
192. #465D79semidirect