Finite Group Databasebeta

← #23773355

Subgroups — #23773355

Order 10112.

418 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099129C211yesmaximal, characteristic
2#19099043C211yesmaximal, characteristic, complemented
3#19098890C211yesmaximal, characteristic, complemented
4#19098887C211yesmaximal, characteristic, complemented
5#19098885C211yesmaximal, characteristic, complemented
6#19098883C211yesmaximal, characteristic, complemented
7#19098879C211yesmaximal, characteristic, complemented
8#19098877C211yesmaximal, characteristic, complemented
9#19098875C211yesmaximal, characteristic, complemented
10#19098602C211yesmaximal, characteristic, complemented
11#19098600C211yesmaximal, characteristic, complemented
12#19098566C211yesmaximal, characteristic, complemented
13#102×D79C211yesmaximal, characteristic, complemented
14#19098528C211yesmaximal, characteristic, complemented
15#482×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C2×D4×D79C2211yescharacteristic
18C2×#11929607C2211yescharacteristic
19C2×C8×D79C2211yescharacteristic
20#14579157—21no—
21#14579147—21no—
22#14579136C2211yescharacteristic
23#14579135C2211yescharacteristic
24#14579132C2211yescharacteristic
25#14579131—21no—
26#14579129—21no—
27C4×Dic158—21no—
28C4×D316—21no—
29(C22⋊D79)⋊C4—21no—
30(C22⋊D79)⋊C4—21no—
31#14579119C2211yescharacteristic
32#14579119C2211yescharacteristic
33#14579119C2211yescharacteristic, complemented
34C2×C4⋊Dic79C2211yescharacteristic, complemented
35C4⋊C4×D79C2211yescharacteristic
36C4⋊C4×D79C2211yescharacteristic, complemented
37#14579095C2211yescharacteristic, complemented
38#14579095C2211yescharacteristic, complemented
39#14579094C2211yescharacteristic, complemented
40#14579092C2211yescharacteristic, complemented
41#14579092C2211yescharacteristic, complemented
42#14579092C2211yescharacteristic, complemented
43#14579083C2211yescharacteristic
44#14579083C2211yescharacteristic
45#14579082C2211yescharacteristic
46#14579082C2211yescharacteristic
47#14579081C2211yescharacteristic
48#14579081C2211yescharacteristic
49C22⋊(C79⋊C8)C2211yescharacteristic, complemented
50(C2×D79)⋊C8C2211yescharacteristic, complemented
51(C2×D79)⋊C8C2211yescharacteristic, complemented
52#121×C79C2211yescharacteristic
53#117×C79C2211yescharacteristic, complemented
54#107×C79C2211yescharacteristic, complemented
55#106×C79C2211yescharacteristic, complemented
56#102×C79C2211yescharacteristic
57#102×C79C2211yescharacteristic
58C22⋊C8×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60#11929624—22no—
61#11929624—22no—
62C2×Dic158D411yescharacteristic
63C2×D316—21no—
64C2×D316D411yescharacteristic
65C2×D316C2311yescharacteristic
66C2×C22⋊D79—21no—
67C2×C22⋊D79—21no—
68C2×C22⋊D79—21no—
69C2×C22⋊D79D411yescharacteristic
70C2×C22⋊D79D411yescharacteristic
71D4×D79—22no—
72D4×D79—22no—
73C22×Dic79—21no—
74C2×C4×D79—21no—
75C2×C4×D79—21no—
76C2×C4×D79C2311yescharacteristic
77C2×C4×D79C2311yescharacteristic
78#11929607—22no—
79C2×C79⋊C8C2311yescharacteristic
80C2×C79⋊C8C2311yescharacteristic
81C8×D79—22no—
82C4⋊Dic79—21no—
83C4⋊Dic79C2311yescharacteristic
84C4⋊Dic79C2311yescharacteristic
85C4⋊Dic79C2311yescharacteristic
86Dic79⋊C4—21no—
87Dic79⋊C4—21no—
88C22⋊Dic79—21no—
89(C2×D79)⋊C4—21no—
90(C2×D79)⋊C4—21no—
91(C2×D79)⋊C4—21no—
92(C2×D79)⋊C4—21no—
93(C2×D79)⋊C4—21no—
94C4×Dic79—21no—
95C4×Dic79—21no—
96C4×Dic79—21no—
97C2×D4×C79—21no—
98C2×D4×C79C2311yescharacteristic
99C22×C4×C79C2311yescharacteristic
100C2×C8×C79C2311yescharacteristic
101C2×C8×C79C2311yescharacteristic
102C4⋊C4×C79C2311yescharacteristic
103C4⋊C4×C79C2311yescharacteristic
104C4⋊C4×C79C2311yescharacteristic
105C22⋊C4×C79—21no—
106C22⋊C4×C79—21no—
107C42×C79—21no—
108C23×C79—21no—
109C23×C79C2×D411yescharacteristic
110C22×D79—21no—
111C22×D79—42no—
112C22×D79—81no—
113C22×D79—81no—
114C22×D79C2×D411yescharacteristic
115C22×D79C2×D411yescharacteristic
116D4×C79—21no—
117D4×C79—21no—
118D4×C79—81no—
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—22no—
128C22⋊D79—42no—
129C22⋊D79—81no—
130C22⋊D79—81no—
131C2×Dic79—21no—
132C2×Dic79—21no—
133C2×Dic79—21no—
134C2×Dic79—81no—
135C2×Dic79C2×D411yescharacteristic
136C2×Dic79C2×D411yescharacteristic
137D316—22no—
138D316—21no—
139D316—21no—
140D316—81no—
141C4×D79—21no—
142C4×D79—21no—
143C4×D79—81no—
144C4×D79—81no—
145C4×D79#4112yes—
146C4×D79#4112yes—
147Dic158—22no—
148C8×C79—21no—
149C8×C79—21no—
150C79⋊C8—21no—
151C79⋊C8—21no—
152C22×C79—21no—
153C22×C79—21no—
154C22×C79—21no—
155C22×C79—41no—
156C22×C79—41no—
157C22×C79—41no—
158C22×C79C22×D411yescharacteristic
159C2×D79—21no—
160C2×D79—21no—
161C2×D79—21no—
162C2×D79—21no—
163C2×D79—21no—
164C2×D79—41no—
165C2×D79—41no—
166C2×D79—41no—
167C2×D79—84no—
168C2×D79#12312yes—
169C4×C79—21no—
170C4×C79—41no—
171C4×C79—41no—
172C4×C79—41no—
173C4×C79C2×#4111yescharacteristic
174C4×C79C2×#4111yescharacteristic
175Dic79—21no—
176Dic79—41no—
177Dic79—41no—
178Dic79—41no—
179Dic79#12312yes—
180C2×C79—41no—
181C2×C79—81no—
182C2×C79C2×#12311yescharacteristic
183C2×C79#57611yescharacteristic
184C2×C79#57711yescharacteristic
185D79—22no—
186D79—41no—
187D79—81no—
188#3096—791nomaximal, Sylow
189C79#309611yescharacteristic, complemented, Sylow
190#535—791no—
191#520—791no—
192#482—791no—
193#482—791no—
194#482—791no—
195#482D7911yescharacteristic, complemented
196#481—791no—
197#481—791no—
198#480—791no—
199#480—791no—
200#428—791no—
201#427—791no—
202#418—791no—
203C2×#102—791no—
204#408—791no—
205C2×#41—791no—
206C22×D4—791no—
207C2×M16—791no—
208C22×C8—791no—
209#127—1581no—
210#124—1581no—
211#121—791no—
212#121—791no—
213#121—791no—
214#121C2×D7911yescharacteristic
215#120—1581no—
216#120—1581no—
217C4×Q8—1581no—
218C4×D4—1581no—
219C4×D4—1581no—
220C4×D4—1581no—
221#117—791no—
222#117—791no—
223#117—791no—
224#117C2×D7911yescharacteristic, complemented
225C2×C4⋊C4—791no—
226C2×C4⋊C4—791no—
227C2×C4⋊C4—791no—
228#107—791no—
229#107—791no—
230#107—791no—
231#107C2×D7911yescharacteristic, complemented
232#106—791no—
233#106—791no—
234#106—791no—
235#106C2×D7911yescharacteristic, complemented
236#102—791no—
237#102—791no—
238#102—791no—
239#102—791no—
240#102—791no—
241#102—791no—
242#102C2×D7911yescharacteristic
243#102C2×D7911yescharacteristic
244C22⋊C8—791no—
245C22⋊C8—791no—
246C22⋊C8—791no—
247C22⋊C8C2×D7911yescharacteristic, complemented
248C24—1581no—
249#41—1582no—
250#41—1582no—
251C2×Q8—791no—
252C2×D4—21no—
253C2×D4—791no—
254C2×D4—791no—
255C2×D4—791no—
256C2×D4—791no—
257C2×D4—1581no—
258C2×D4—1582no—
259C2×D4—1582no—
260C2×D4—1581no—
261C2×D4—1581no—
262C2×D4—1581no—
263C2×D4C22×D7911yescharacteristic
264C22×C4—791no—
265C22×C4—791no—
266C22×C4—1581no—
267C22×C4—1581no—
268C22×C4—1581no—
269C22×C4C22×D7911yescharacteristic
270M16—1582no—
271C2×C8—791no—
272C2×C8—791no—
273C2×C8—1582no—
274C2×C8C22×D7911yescharacteristic
275C2×C8C22×D7911yescharacteristic
276C4⋊C4—791no—
277C4⋊C4—791no—
278C4⋊C4—791no—
279C4⋊C4—1581no—
280C4⋊C4—1581no—
281C4⋊C4—1581no—
282C4⋊C4C22×D7911yescharacteristic
283C4⋊C4C22×D7911yescharacteristic
284C4⋊C4C22×D7911yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—1581no—
288C22⋊C4—1581no—
289C22⋊C4—1581no—
290C22⋊C4—1581no—
291C22⋊C4—1581no—
292C22⋊C4—1581no—
293C42—21no—
294C42—1581no—
295C42—1581no—
296C42—1581no—
297C23—21no—
298C23—3162no—
299C23—791no—
300C23—791no—
301C23—6321no—
302C23—6321no—
303C23—1581no—
304C23D4×D7911yescharacteristic
305Q8—1582no—
306D4—21no—
307D4—21no—
308D4—81no—
309D4—3162no—
310D4—6321no—
311D4—6321no—
312D4—6321no—
313D4—1582no—
314D4—1582no—
315D4—1582no—
316D4—1581no—
317D4—1581no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—791no—
324C2×C4—792no—
325C2×C4—792no—
326C2×C4—791no—
327C2×C4—6321no—
328C2×C4—6321no—
329C2×C4—6321no—
330C2×C4—1581no—
331C2×C4—1581no—
332C2×C4—1581no—
333C2×C4—1581no—
334C2×C4—1581no—
335C2×C4D4×D7911yescharacteristic
336C2×C4C23×D7911yescharacteristic
337C8—21no—
338C8—21no—
339C8—1581no—
340C8—1581no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—3161no—
348C22—3161no—
349C22—3161no—
350C22—792no—
351C22—6324no—
352C22—1581no—
353C22—1581no—
354C22—1581no—
355C22—1581no—
356C22—1581no—
357C22C2×D4×D7911yescharacteristic
358C4—21no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—3161no—
363C4—3161no—
364C4—3161no—
365C4—792no—
366C4—1581no—
367C4#41×D7911yescharacteristic
368C4#41×D7911yescharacteristic
369C2—41no—
370C2—81no—
371C2—3161no—
372C2—6321no—
373C2—1582no—
374C2#123×D7911yescharacteristic
375C2#1909936511yescharacteristic
376C2#1909937311yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#482×C79C2
socleC22×C79C22×D4
prime radical#19099129C2
hypercenter#482D79
hypocenterC79#3096
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #19099043C2semidirect
3. #19098890C2semidirect
4. #19098887C2semidirect
5. #19098885C2semidirect
6. #19098883C2semidirect
7. #19098879C2semidirect
8. #19098877C2semidirect
9. #19098875C2semidirect
10. #19098602C2semidirect
11. #19098600C2semidirect
12. #19098566C2semidirect
13. #102×D79C2semidirect
14. #19098528C2semidirect
15. #482×C79C2semidirect
33. #14579119C22semidirect
34. C2×C4⋊Dic79C22semidirect
36. C4⋊C4×D79C22semidirect
37. #14579095C22semidirect
38. #14579095C22semidirect
39. #14579094C22semidirect
40. #14579092C22semidirect
41. #14579092C22semidirect
42. #14579092C22semidirect
49. C22⋊(C79⋊C8)C22semidirect
50. (C2×D79)⋊C8C22semidirect
51. (C2×D79)⋊C8C22semidirect
53. #117×C79C22semidirect
54. #107×C79C22semidirect
55. #106×C79C22semidirect
58. C22⋊C8×C79C22semidirect
189. C79#3096semidirect
195. #482D79semidirect
224. #117C2×D79semidirect
231. #107C2×D79semidirect
235. #106C2×D79semidirect
247. C22⋊C8C2×D79semidirect