Finite Group Databasebeta

← #23773317

Subgroups — #23773317

Order 10112.

420 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099075C211yesmaximal, characteristic
2#117×D79C211yesmaximal, characteristic, complemented
3#19098907C211yesmaximal, characteristic, complemented
4#19098906C211yesmaximal, characteristic, complemented
5#19098900C211yesmaximal, characteristic, complemented
6#19098895C211yesmaximal, characteristic, complemented
7#19098890C211yesmaximal, characteristic, complemented
8#19098889C211yesmaximal, characteristic, complemented
9#19098883C211yesmaximal, characteristic, complemented
10#19098878C211yesmaximal, characteristic, complemented
11#19098599C211yesmaximal, characteristic, complemented
12#19098560C211yesmaximal, characteristic, complemented
13#19098557C211yesmaximal, characteristic, complemented
14C2×(C2×D79)⋊C8C211yesmaximal, characteristic, complemented
15#427×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C22×C4×D79C2211yescharacteristic
18C22×C79⋊C8C2211yescharacteristic
19#14579145—21no—
20#14579141C2211yescharacteristic
21#14579141C2211yescharacteristic
22#14579136C2211yescharacteristic
23#14579136C2211yescharacteristic
24#14579131—21no—
25C4×D316—21no—
26C4×D316—21no—
27#14579120C2211yescharacteristic
28#14579119C2211yescharacteristic
29#14579119C2211yescharacteristic
30#14579118—21no—
31#14579117—21no—
32C4⋊C4×D79C2211yescharacteristic
33C4⋊C4×D79C2211yescharacteristic
34C22⋊C4×D79—21no—
35C42×D79—21no—
36#14579094C2211yescharacteristic, complemented
37#14579094C2211yescharacteristic, complemented
38#14579092C2211yescharacteristic, complemented
39#14579092C2211yescharacteristic, complemented
40#14579086C2211yescharacteristic, complemented
41#14579086C2211yescharacteristic, complemented
42#14579084C2211yescharacteristic, complemented
43#14579084C2211yescharacteristic, complemented
44#14579083C2211yescharacteristic, complemented
45#14579083C2211yescharacteristic, complemented
46#14579081C2211yescharacteristic, complemented
47#14579081C2211yescharacteristic, complemented
48(C2×D79)⋊C8C2211yescharacteristic
49(C2×D79)⋊C8C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic
51(C2×D79)⋊C8C2211yescharacteristic
52C22×C8×C79C2211yescharacteristic
53#117×C79C2211yescharacteristic
54#117×C79C2211yescharacteristic
55#107×C79C2211yescharacteristic, complemented
56#107×C79C2211yescharacteristic, complemented
57#106×C79C2211yescharacteristic, complemented
58#106×C79C2211yescharacteristic, complemented
59C23×D79D411yescharacteristic
60#11929624—22no—
61#11929624—22no—
62C2×Dic158C2311yescharacteristic
63C2×D316—21no—
64C2×D316—21no—
65C2×D316C2311yescharacteristic
66C2×C22⋊D79—21no—
67C22×Dic79D411yescharacteristic
68C2×C4×D79—21no—
69C2×C4×D79—21no—
70C2×C4×D79—21no—
71C2×C4×D79—22no—
72C2×C4×D79—22no—
73C2×C4×D79D411yescharacteristic
74C2×C4×D79D411yescharacteristic
75C2×C4×D79C2311yescharacteristic
76C2×C4×D79C2311yescharacteristic
77C2×C79⋊C8—22no—
78C2×C79⋊C8C2311yescharacteristic
79C2×C79⋊C8C2311yescharacteristic
80C4⋊Dic79—21no—
81C4⋊Dic79—21no—
82C4⋊Dic79C2311yescharacteristic
83C4⋊Dic79C2311yescharacteristic
84Dic79⋊C4—21no—
85Dic79⋊C4—21no—
86C22⋊Dic79—21no—
87(C2×D79)⋊C4—21no—
88(C2×D79)⋊C4—21no—
89(C2×D79)⋊C4—21no—
90(C2×D79)⋊C4—21no—
91(C2×D79)⋊C4—21no—
92(C2×D79)⋊C4—21no—
93C4×Dic79—21no—
94C4×Dic79—21no—
95C4×Dic79—21no—
96C22×C4×C79C2311yescharacteristic
97C2×C8×C79—22no—
98C2×C8×C79C2311yescharacteristic
99C2×C8×C79C2311yescharacteristic
100C4⋊C4×C79C2311yescharacteristic
101C4⋊C4×C79C2311yescharacteristic
102C4⋊C4×C79C2311yescharacteristic
103C4⋊C4×C79C2311yescharacteristic
104C22⋊C4×C79—21no—
105C22⋊C4×C79—21no—
106C42×C79—21no—
107C42×C79—21no—
108C23×C79C2×D411yescharacteristic
109C22×D79—22no—
110C22×D79—22no—
111C22×D79—21no—
112C22×D79—41no—
113C22×D79C2×D411yescharacteristic
114C22×D79C2×D411yescharacteristic
115C2×C4×C79—21no—
116C2×C4×C79—21no—
117C2×C4×C79—21no—
118C2×C4×C79—21no—
119C2×C4×C79C2×D411yescharacteristic
120C2×C4×C79#4112yes—
121C2×C4×C79#4112yes—
122C2×C4×C79C2411yescharacteristic
123C22⋊D79—42no—
124C2×Dic79—22no—
125C2×Dic79—21no—
126C2×Dic79—21no—
127C2×Dic79—21no—
128C2×Dic79C2×D411yescharacteristic
129C2×Dic79C2×D411yescharacteristic
130D316—21no—
131D316—21no—
132D316—42no—
133D316—42no—
134C4×D79—22no—
135C4×D79—22no—
136C4×D79—21no—
137C4×D79—21no—
138C4×D79—21no—
139C4×D79—21no—
140C4×D79—42no—
141C4×D79—42no—
142C4×D79—42no—
143Dic158—21no—
144Dic158—21no—
145C8×C79—21no—
146C8×C79—21no—
147C79⋊C8—21no—
148C79⋊C8—21no—
149C22×C79—21no—
150C22×C79—21no—
151C22×C79#12312yes—
152C22×C79C22×D411yescharacteristic
153C2×D79—21no—
154C2×D79—21no—
155C2×D79—21no—
156C2×D79—21no—
157C2×D79—21no—
158C2×D79—44no—
159C2×D79—41no—
160C2×D79—41no—
161C2×D79—41no—
162C2×D79#13512yes—
163C4×C79—41no—
164C4×C79—41no—
165C4×C79—41no—
166C4×C79—41no—
167C4×C79#12312yes—
168C4×C79C2×#4111yescharacteristic
169C4×C79C2×#4111yescharacteristic
170Dic79—21no—
171Dic79—21no—
172Dic79—41no—
173Dic79—41no—
174Dic79—41no—
175C2×C79—22no—
176C2×C79C2×#12311yescharacteristic
177C2×C79C2×#13511yescharacteristic
178C2×C79#57511yescharacteristic
179D79—22no—
180D79—41no—
181D79—81no—
182#3091—791nomaximal, Sylow
183C79#309111yescharacteristic, complemented, Sylow
184#525—791no—
185C2×#117—791no—
186#485—791no—
187#485—791no—
188#484—791no—
189#483—791no—
190#482—791no—
191#482—791no—
192#481—791no—
193#480—791no—
194#427—791no—
195#427D7911yescharacteristic, complemented
196#416—791no—
197#416—791no—
198C2×C22⋊C8—791no—
199C2×#41—791no—
200C23×C4—791no—
201C22×C8—791no—
202C22×C8C2×D7911yescharacteristic
203#123—1581no—
204C22⋊Q8—791no—
205C22⋊Q8—791no—
206#121—791no—
207#121—791no—
208#120—1581no—
209C4×D4—1581no—
210C4×D4—1581no—
211#117—791no—
212#117—791no—
213#117—791no—
214#117—1581no—
215#117—1581no—
216#117C2×D7911yescharacteristic
217#117C2×D7911yescharacteristic
218C2×C4⋊C4—791no—
219C2×C4⋊C4—791no—
220C2×C22⋊C4—1581no—
221C2×C42—1581no—
222#107—791no—
223#107—791no—
224#107C2×D7911yescharacteristic, complemented
225#107C2×D7911yescharacteristic, complemented
226#106—791no—
227#106—791no—
228#106C2×D7911yescharacteristic, complemented
229#106C2×D7911yescharacteristic, complemented
230#103—791no—
231#103—791no—
232#103—791no—
233#103—791no—
234#102—791no—
235#102—791no—
236#102—791no—
237#102—791no—
238C22⋊C8—791no—
239C22⋊C8—791no—
240C22⋊C8—791no—
241C22⋊C8—791no—
242C24—791no—
243#41—1582no—
244#41—1582no—
245C2×Q8—791no—
246C2×D4—791no—
247C2×D4—1581no—
248C2×D4—1581no—
249C2×D4—1581no—
250C22×C4—791no—
251C22×C4—791no—
252C22×C4—791no—
253C22×C4—791no—
254C22×C4—791no—
255C22×C4—1581no—
256C22×C4—1581no—
257C22×C4—1581no—
258C22×C4—1582no—
259C22×C4—1582no—
260C22×C4C22×D7911yescharacteristic
261C2×C8—22no—
262C2×C8—791no—
263C2×C8—791no—
264C2×C8—1582no—
265C2×C8C22×D7911yescharacteristic
266C2×C8C22×D7911yescharacteristic
267C4⋊C4—791no—
268C4⋊C4—791no—
269C4⋊C4—1581no—
270C4⋊C4—1581no—
271C4⋊C4—1581no—
272C4⋊C4—1581no—
273C4⋊C4C22×D7911yescharacteristic
274C4⋊C4C22×D7911yescharacteristic
275C4⋊C4C22×D7911yescharacteristic
276C4⋊C4C22×D7911yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—1581no—
280C22⋊C4—1581no—
281C22⋊C4—1581no—
282C22⋊C4—1581no—
283C22⋊C4—1581no—
284C22⋊C4—1581no—
285C22⋊C4—1581no—
286C42—21no—
287C42—21no—
288C42—1581no—
289C42—1581no—
290C42—1581no—
291C23—3161no—
292C23—791no—
293C23—791no—
294C23—1582no—
295C23—1581no—
296C23—1582no—
297C23D4×D7911yescharacteristic
298Q8—1581no—
299Q8—1581no—
300D4—3162no—
301D4—3162no—
302D4—3162no—
303D4—1581no—
304D4—1581no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—3162no—
310C2×C4—3162no—
311C2×C4—3162no—
312C2×C4—791no—
313C2×C4—791no—
314C2×C4—1581no—
315C2×C4—1581no—
316C2×C4—1581no—
317C2×C4—1582no—
318C2×C4—1581no—
319C2×C4—1581no—
320C2×C4—1581no—
321C2×C4—1581no—
322C2×C4—1582no—
323C2×C4—1582no—
324C2×C4D4×D7911yescharacteristic
325C2×C4#1192962412yes—
326C2×C4#1192962512yes—
327C2×C4C23×D7911yescharacteristic
328C8—21no—
329C8—21no—
330C8—1581no—
331C8—1581no—
332C22—21no—
333C22—21no—
334C22—3164no—
335C22—3161no—
336C22—3161no—
337C22—3161no—
338C22—792no—
339C22—1581no—
340C22—1581no—
341C22—1581no—
342C22—1581no—
343C22—1581no—
344C22#1457914612yes—
345C22C2×D4×D7911yescharacteristic
346C4—41no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—3161no—
351C4—3161no—
352C4—3161no—
353C4—1581no—
354C4—1581no—
355C4#1457914612yes—
356C4C2×#1192962411yescharacteristic
357C4C2×#1192962511yescharacteristic
358C2—22no—
359C2—3161no—
360C2—6321no—
361C2—1582no—
362C2C2×#1457914611yescharacteristic
363C2#135×D7911yescharacteristic
364C2#1909936011yescharacteristic
subgroupG/H
centerC2×C4D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#427×C79C2
socleC22×C79C22×D4
prime radical#19099075C2
hypercenter#427D79
hypocenterC79#3091
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #427

Complements

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

NH ≅ G/Ntype
2. #117×D79C2semidirect
3. #19098907C2semidirect
4. #19098906C2semidirect
5. #19098900C2semidirect
6. #19098895C2semidirect
7. #19098890C2semidirect
8. #19098889C2semidirect
9. #19098883C2semidirect
10. #19098878C2semidirect
11. #19098599C2semidirect
12. #19098560C2semidirect
13. #19098557C2semidirect
14. C2×(C2×D79)⋊C8C2semidirect
15. #427×C79C2semidirect
36. #14579094C22semidirect
37. #14579094C22semidirect
38. #14579092C22semidirect
39. #14579092C22semidirect
40. #14579086C22semidirect
41. #14579086C22semidirect
42. #14579084C22semidirect
43. #14579084C22semidirect
44. #14579083C22semidirect
45. #14579083C22semidirect
46. #14579081C22semidirect
47. #14579081C22semidirect
55. #107×C79C22semidirect
56. #107×C79C22semidirect
57. #106×C79C22semidirect
58. #106×C79C22semidirect
183. C79#3091semidirect
195. #427D79semidirect
224. #107C2×D79semidirect
225. #107C2×D79semidirect
228. #106C2×D79semidirect
229. #106C2×D79semidirect