Finite Group Databasebeta

← #23775577

Subgroups — #23775577

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#19099265C211yesmaximal, characteristic
2#19099226C211yesmaximal, characteristic, complemented
3#19098930C211yesmaximal, characteristic, complemented
4#19098907C211yesmaximal, characteristic, complemented
5#19098896C211yesmaximal, characteristic, complemented
6#19098873C211yesmaximal, characteristic, complemented
7#19098808C211yesmaximal, characteristic, complemented
8#19098766C211yesmaximal, characteristic, complemented
9#19098701C211yesmaximal, characteristic, complemented
10#19098700C211yesmaximal, characteristic, complemented
11#19098660C211yesmaximal, characteristic, complemented
12#19098634C211yesmaximal, characteristic, complemented
13#19098570C211yesmaximal, characteristic, complemented
14C2×#14579086C211yesmaximal, characteristic, complemented
15#465×C79C211yesmaximal, characteristic, complemented
16C22×Dic158C2211yescharacteristic
17C2×Q8×D79C2211yescharacteristic
18C2×#11929612C2211yescharacteristic
19C2×#11929612C2211yescharacteristic
20C2×#11929607C2211yescharacteristic
21#14579160—21no—
22#14579159C2211yescharacteristic
23#14579154—21no—
24#14579152C2211yescharacteristic
25#14579145—21no—
26#14579141C2211yescharacteristic
27#14579139—21no—
28#14579138—21no—
29#14579133—21no—
30#14579132C2211yescharacteristic
31#14579126C2211yescharacteristic
32D4×Dic79—21no—
33D4×Dic79C2211yescharacteristic
34C4×C22⋊D79C2211yescharacteristic
35(C22⋊D79)⋊C4—21no—
36#14579119C2211yescharacteristic
37C2×C4⋊Dic79C2211yescharacteristic
38#14579094C2211yescharacteristic
39#14579094C2211yescharacteristic
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
51#14579071C2211yescharacteristic
52C2×SD16×C79C2211yescharacteristic
53C22×C8×C79C2211yescharacteristic
54C22⋊Q8×C79C2211yescharacteristic
55#121×C79C2211yescharacteristic
56#106×C79C2211yescharacteristic
57#103×C79C2211yescharacteristic
58#102×C79C2211yescharacteristic
59C2×Dic158—22no—
60C2×Dic158—21no—
61C2×Dic158—21no—
62C2×Dic158—41no—
63C2×Dic158C2311yescharacteristic
64C2×Dic158C2311yescharacteristic
65Q8×D79—22no—
66Q8×D79—41no—
67C2×C22⋊D79—21no—
68C2×C22⋊D79D411yescharacteristic
69C22×Dic79—21no—
70C22×Dic79—21no—
71C22×Dic79—21no—
72C2×C4×D79—21no—
73C2×C4×D79C2311yescharacteristic
74#11929612—22no—
75#11929612—41no—
76#11929607—41no—
77C2×C79⋊C8C2311yescharacteristic
78C2×C79⋊C8C2311yescharacteristic
79C4⋊Dic79—21no—
80C4⋊Dic79—21no—
81C4⋊Dic79—21no—
82C4⋊Dic79C2311yescharacteristic
83C4⋊Dic79C2311yescharacteristic
84Dic79⋊C4—21no—
85Dic79⋊C4—21no—
86Dic79⋊C4—21no—
87Dic79⋊C4—21no—
88Dic79⋊C4D411yescharacteristic
89C22⋊Dic79—21no—
90C22⋊Dic79—21no—
91C22⋊Dic79D411yescharacteristic
92(C2×D79)⋊C4—21no—
93(C2×D79)⋊C4—21no—
94(C2×D79)⋊C4D411yescharacteristic
95C4×Dic79—21no—
96C4×Dic79—21no—
97C4×Dic79C2311yescharacteristic
98C2×Q8×C79C2311yescharacteristic
99C2×D4×C79—21no—
100C2×D4×C79C2311yescharacteristic
101C22×C4×C79C2311yescharacteristic
102SD16×C79—41no—
103C2×C8×C79—41no—
104C2×C8×C79C2311yescharacteristic
105C2×C8×C79C2311yescharacteristic
106C4⋊C4×C79—21no—
107C4⋊C4×C79C2311yescharacteristic
108C4⋊C4×C79C2311yescharacteristic
109C22⋊C4×C79—21no—
110C22⋊C4×C79—21no—
111C23×C79—21no—
112C23×C79C2×D411yescharacteristic
113C22×D79C2×D411yescharacteristic
114Q8×C79—21no—
115Q8×C79—21no—
116D4×C79—21no—
117D4×C79—21no—
118D4×C79—42no—
119C2×C4×C79—21no—
120C2×C4×C79—21no—
121C2×C4×C79—21no—
122C2×C4×C79—21no—
123C2×C4×C79—21no—
124C2×C4×C79C2×D411yescharacteristic
125C2×C4×C79C2411yescharacteristic
126C22⋊D79—22no—
127C22⋊D79—81no—
128C2×Dic79—21no—
129C2×Dic79—21no—
130C2×Dic79—21no—
131C2×Dic79—21no—
132C2×Dic79—42no—
133C2×Dic79—81no—
134C2×Dic79—81no—
135C2×Dic79C2×D411yescharacteristic
136C2×Dic79C2×D411yescharacteristic
137C2×Dic79C2×D411yescharacteristic
138C4×D79—21no—
139C4×D79—21no—
140C4×D79—42no—
141Dic158—21no—
142Dic158—21no—
143Dic158—21no—
144Dic158—42no—
145Dic158—42no—
146Dic158#4112yes—
147C8×C79—21no—
148C8×C79—21no—
149C79⋊C8—21no—
150C79⋊C8—21no—
151C22×C79—21no—
152C22×C79—21no—
153C22×C79—41no—
154C22×C79—41no—
155C22×C79—41no—
156C22×C79#13712yes—
157C22×C79C22×D411yescharacteristic
158C2×D79—21no—
159C2×D79—21no—
160C2×D79—21no—
161C4×C79—21no—
162C4×C79—41no—
163C4×C79—41no—
164C4×C79—41no—
165C4×C79C2×#4111yescharacteristic
166C4×C79H(5,𝔽2)11yescharacteristic
167Dic79—22no—
168Dic79—21no—
169Dic79—21no—
170Dic79—21no—
171Dic79—41no—
172Dic79—41no—
173Dic79—41no—
174C2×C79—22no—
175C2×C79—81no—
176C2×C79#54611yescharacteristic
177C2×C79C2×#13711yescharacteristic
178C2×C79#57711yescharacteristic
179D79—41no—
180#3320—791nomaximal, Sylow
181C79#332011yescharacteristic, complemented, Sylow
182#553—791no—
183D4×Q8—791no—
184#491—791no—
185#485—791no—
186#484—791no—
187#479—791no—
188#468—791no—
189#465D7911yescharacteristic, complemented
190#461—791no—
191#448—791no—
192#448—791no—
193#440—791no—
194#435—791no—
195#419—791no—
196C2×#103—791no—
197C22×Q8—791no—
198C22×Q8—791no—
199C2×SD16—791no—
200C2×SD16—791no—
201C2×SD16C2×D7911yescharacteristic
202C2×M16—791no—
203C22×C8C2×D7911yescharacteristic
204C4⋊Q8—791no—
205C4⋊Q8—1581no—
206#126—1581no—
207#125—791no—
208#123—1581no—
209C22⋊Q8—791no—
210C22⋊Q8—1581no—
211C22⋊Q8—1581no—
212C22⋊Q8C2×D7911yescharacteristic
213#121—791no—
214#121—1581no—
215#121C2×D7911yescharacteristic
216C4×Q8—791no—
217C4×D4—791no—
218C4×D4—791no—
219C4×D4—1581no—
220C4×D4—1581no—
221#117—791no—
222C2×C4⋊C4—791no—
223#107—791no—
224#107—791no—
225#106C2×D7911yescharacteristic
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#103—791no—
235#103C2×D7911yescharacteristic
236#102C2×D7911yescharacteristic
237C22⋊C8—791no—
238C22⋊C8—791no—
239#97—791no—
240C2×Q8—3161no—
241C2×Q8—3161no—
242C2×Q8—791no—
243C2×Q8—791no—
244C2×Q8—1582no—
245C2×Q8—1581no—
246C2×Q8—1582no—
247C2×Q8—1581no—
248C2×Q8C22×D7911yescharacteristic
249C2×D4—21no—
250C2×D4—791no—
251C2×D4—1581no—
252C2×D4C22×D7911yescharacteristic
253C22×C4—791no—
254C22×C4—1581no—
255C22×C4—1581no—
256C22×C4—1581no—
257C22×C4—1581no—
258C22×C4C22×D7911yescharacteristic
259SD16—41no—
260SD16—3161no—
261SD16—1582no—
262M16—3161no—
263C2×C8—41no—
264C2×C8—791no—
265C2×C8—791no—
266C2×C8C22×D7911yescharacteristic
267C2×C8C22×D7911yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—791no—
270C4⋊C4—791no—
271C4⋊C4—791no—
272C4⋊C4—1581no—
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—791no—
284C22⋊C4—791no—
285C22⋊C4—1581no—
286C22⋊C4—1581no—
287C22⋊C4—1581no—
288C22⋊C4—1581no—
289C42—791no—
290C42—1581no—
291C42—1581no—
292C23—21no—
293C23—791no—
294C23D4×D7911yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—3162no—
298Q8—3162no—
299Q8—792no—
300Q8—1581no—
301Q8—1581no—
302Q8—1581no—
303D4—21no—
304D4—21no—
305D4—42no—
306D4—6321no—
307D4—1582no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—3162no—
314C2×C4—3162no—
315C2×C4—791no—
316C2×C4—791no—
317C2×C4—791no—
318C2×C4—6321no—
319C2×C4—6321no—
320C2×C4—1581no—
321C2×C4—1581no—
322C2×C4—1581no—
323C2×C4—1581no—
324C2×C4—1581no—
325C2×C4—1581no—
326C2×C4D4×D7911yescharacteristic
327C2×C4C23×D7911yescharacteristic
328C8—21no—
329C8—21no—
330C8—1581no—
331C8—1581no—
332C22—21no—
333C22—21no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—1581no—
338C22—1581no—
339C22—1581no—
340C22#1457919012yes—
341C22C2×D4×D7911yescharacteristic
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—3161no—
347C4—3161no—
348C4—3161no—
349C4—1582no—
350C4—1581no—
351C4—1581no—
352C4—1581no—
353C4#41×D7911yescharacteristic
354C4#1457920611yescharacteristic
355C2—22no—
356C2—81no—
357C2—3161no—
358C2#1909920211yescharacteristic
359C2C2×#1457919011yescharacteristic
360C2#1909937011yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#465×C79C2
socleC22×C79C22×D4
prime radical#19099265C2
hypercenter#465D79
hypocenterC79#3320
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
2. #19099226C2semidirect
3. #19098930C2semidirect
4. #19098907C2semidirect
5. #19098896C2semidirect
6. #19098873C2semidirect
7. #19098808C2semidirect
8. #19098766C2semidirect
9. #19098701C2semidirect
10. #19098700C2semidirect
11. #19098660C2semidirect
12. #19098634C2semidirect
13. #19098570C2semidirect
14. C2×#14579086C2semidirect
15. #465×C79C2semidirect
181. C79#3320semidirect
189. #465D79semidirect