Finite Group Databasebeta

← #23775366

Subgroups — #23775366

Order 10112.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099218C211yesmaximal, characteristic, complemented
2#19099208C211yesmaximal, characteristic, complemented
3#19098923C211yesmaximal, characteristic, complemented
4#19098895C211yesmaximal, characteristic, complemented
5#19098883C211yesmaximal, characteristic, complemented
6#19098853C211yesmaximal, characteristic, complemented
7#19098815C211yesmaximal, characteristic, complemented
8#19098791C211yesmaximal, characteristic, complemented
9#19098778C211yesmaximal, characteristic, complemented
10#19098705C211yesmaximal, characteristic, complemented
11#19098695C211yesmaximal, characteristic, complemented
12#19098636C211yesmaximal, characteristic, complemented
13#19098561C211yesmaximal, characteristic, complemented
14#102×D79C211yesmaximal, characteristic, complemented
15#442×C79C211yesmaximal, characteristic, complemented
16C2×#11929624—21no—
17C2×#11929623C2211yescharacteristic
18C2×D4×D79C2211yescharacteristic
19C2×#11929612C2211yescharacteristic, complemented
20C2×#11929609C2211yescharacteristic
21C2×#11929607C2211yescharacteristic, complemented
22C2×C8×D79C2211yescharacteristic
23#14579161C2211yescharacteristic, complemented
24#14579149C2211yescharacteristic
25#14579145—21no—
26#14579143—21no—
27#14579143—21no—
28#14579141C2211yescharacteristic
29#14579140—21no—
30#14579136C2211yescharacteristic
31#14579135—21no—
32#14579132C2211yescharacteristic
33#14579132C2211yescharacteristic, complemented
34#14579131—21no—
35C4×D316C2211yescharacteristic
36C4⋊C4×D79C2211yescharacteristic
37C4⋊C4×D79C2211yescharacteristic, complemented
38C2×(C2×D79)⋊C4—21no—
39#14579092C2211yescharacteristic, complemented
40#14579092C2211yescharacteristic, complemented
41C4⋊(C79⋊C8)C2211yescharacteristic, complemented
42#14579086C2211yescharacteristic, complemented
43#14579086C2211yescharacteristic, complemented
44#14579084C2211yescharacteristic, complemented
45#14579083C2211yescharacteristic
46#14579083C2211yescharacteristic
47#14579082C2211yescharacteristic
48#14579082C2211yescharacteristic
49#14579081C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic
51(C2×D79)⋊C8C2211yescharacteristic, complemented
52C2×D8×C79C2211yescharacteristic
53C4×D4×C79C2211yescharacteristic
54C4×D4×C79C2211yescharacteristic, complemented
55#106×C79C2211yescharacteristic, complemented
56#102×C79C2211yescharacteristic
57#102×C79C2211yescharacteristic, complemented
58#97×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60#11929624—44no—
61#11929623—22no—
62#11929623—41no—
63C2×Dic158—21no—
64C2×Dic158C2311yescharacteristic
65C2×D316—21no—
66C2×D316D411yescharacteristic
67C2×D316C2311yescharacteristic
68C2×C22⋊D79—21no—
69C2×C22⋊D79—21no—
70C2×C22⋊D79—21no—
71C2×C22⋊D79—21no—
72D4×D79—22no—
73D4×D79—41no—
74C22×Dic79—21no—
75C2×C4×D79—21no—
76C2×C4×D79—21no—
77C2×C4×D79C2311yescharacteristic
78C2×C4×D79C2311yescharacteristic
79#11929612—41no—
80#11929609—41no—
81#11929607—41no—
82C2×C79⋊C8C2311yescharacteristic
83C2×C79⋊C8C2311yescharacteristic
84C8×D79—41no—
85C4⋊Dic79—21no—
86C4⋊Dic79—21no—
87C4⋊Dic79D411yescharacteristic
88C4⋊Dic79C2311yescharacteristic
89C4⋊Dic79C2311yescharacteristic
90Dic79⋊C4—21no—
91Dic79⋊C4—21no—
92C22⋊Dic79—21no—
93C22⋊Dic79—21no—
94(C2×D79)⋊C4—21no—
95(C2×D79)⋊C4—21no—
96(C2×D79)⋊C4—21no—
97(C2×D79)⋊C4—21no—
98(C2×D79)⋊C4D411yescharacteristic
99(C2×D79)⋊C4D411yescharacteristic
100C2×D4×C79C2311yescharacteristic
101C2×D4×C79C2311yescharacteristic
102C22×C4×C79—21no—
103C22×C4×C79—21no—
104D8×C79—22no—
105C2×C8×C79C2311yescharacteristic
106C2×C8×C79C2311yescharacteristic
107C4⋊C4×C79C2311yescharacteristic
108C4⋊C4×C79C2311yescharacteristic
109C22⋊C4×C79—21no—
110C22⋊C4×C79—21no—
111C42×C79C2311yescharacteristic
112C23×C79—21no—
113C23×C79—21no—
114C22×D79—21no—
115C22×D79—42no—
116C22×D79—42no—
117C22×D79—81no—
118C22×D79C2×D411yescharacteristic
119C22×D79C2×D411yescharacteristic
120D4×C79—21no—
121D4×C79—21no—
122D4×C79—21no—
123D4×C79#4112yescomplemented
124C2×C4×C79—21no—
125C2×C4×C79—21no—
126C2×C4×C79—42no—
127C2×C4×C79—81no—
128C2×C4×C79C2×D411yescharacteristic
129C2×C4×C79C2×D411yescharacteristic
130C2×C4×C79C2411yescharacteristic
131C22⋊D79—42no—
132C22⋊D79—42no—
133C22⋊D79—42no—
134C22⋊D79—42no—
135C2×Dic79—21no—
136C2×Dic79—21no—
137C2×Dic79—21no—
138C2×Dic79—42no—
139C2×Dic79C2×D411yescharacteristic
140C2×Dic79C2×D411yescharacteristic
141D316—22no—
142D316—21no—
143D316—21no—
144D316—81no—
145C4×D79—21no—
146C4×D79—21no—
147C4×D79—21no—
148C4×D79—21no—
149C4×D79—42no—
150C4×D79—42no—
151Dic158—21no—
152Dic158—21no—
153Dic158—42no—
154C8×C79—21no—
155C8×C79—21no—
156C79⋊C8—21no—
157C79⋊C8—21no—
158C22×C79—22no—
159C22×C79—41no—
160C22×C79—41no—
161C22×C79—41no—
162C22×C79—41no—
163C22×C79—41no—
164C22×C79C22×D411yescharacteristic
165C2×D79—21no—
166C2×D79—21no—
167C2×D79—21no—
168C2×D79—21no—
169C2×D79—21no—
170C2×D79—41no—
171C2×D79—41no—
172C2×D79—41no—
173C2×D79—84no—
174C2×D79AGL(1,ℤ/8)12yes—
175C4×C79—21no—
176C4×C79—21no—
177C4×C79—41no—
178C4×C79—41no—
179C4×C79C2×#4111yescharacteristic
180C4×C79H(5,𝔽2)11yescharacteristic
181Dic79—21no—
182Dic79—21no—
183Dic79—41no—
184Dic79—41no—
185Dic79—41no—
186C2×C79—42no—
187C2×C79—81no—
188C2×C79#54611yescharacteristic
189C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
190C2×C79#57711yescharacteristic
191D79—22no—
192D79—41no—
193D79—81no—
194#3306—791nomaximal, Sylow
195C79#330611yescharacteristic, complemented, Sylow
196#547—791no—
197#546—791no—
198#489—791no—
199#483—791no—
200#481—791no—
201#476—791no—
202#469—791no—
203#465—791no—
204#463—791no—
205#449—791no—
206#447—791no—
207#442D7911yescharacteristic, complemented
208#435—791no—
209#417—791no—
210C2×#102—791no—
211C2×#41—791no—
212C2×#41—1581no—
213C22×D4—791no—
214C2×SD16—791no—
215C2×D8—791no—
216C2×D8C2×D7911yescharacteristic
217C2×M16—791no—
218C22×C8—791no—
219C4⋊Q8—791no—
220#124—791no—
221#123—1581no—
222#123—1581no—
223#123—1581no—
224C22⋊Q8—791no—
225C22⋊Q8—1581no—
226#121—791no—
227#121—791no—
228#121—791no—
229#121—1581no—
230#120—1581no—
231C4×D4—791no—
232C4×D4C2×D7911yescharacteristic
233C4×D4C2×D7911yescharacteristic, complemented
234C2×C4⋊C4—791no—
235C2×C4⋊C4—791no—
236C2×C22⋊C4—1581no—
237#106—791no—
238#106—791no—
239#106C2×D7911yescharacteristic, complemented
240C4⋊C8—791no—
241#103—791no—
242#103—791no—
243#103—791no—
244#102—791no—
245#102—791no—
246#102—791no—
247#102—791no—
248#102—791no—
249#102C2×D7911yescharacteristic
250#102C2×D7911yescharacteristic, complemented
251C22⋊C8—791no—
252C22⋊C8—791no—
253#97C2×D7911yescharacteristic, complemented
254C24—1581no—
255#41—3164no—
256#41—3161no—
257#41—1582no—
258C2×Q8—791no—
259C2×Q8—1581no—
260C2×D4—3161no—
261C2×D4—791no—
262C2×D4—791no—
263C2×D4—1581no—
264C2×D4—1581no—
265C2×D4—1581no—
266C2×D4—1581no—
267C2×D4—1581no—
268C2×D4—1582no—
269C2×D4C22×D7911yescharacteristic
270C2×D4C22×D7911yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—791no—
274C22×C4—791no—
275C22×C4—1581no—
276C22×C4—1581no—
277C22×C4—1581no—
278SD16—3161no—
279D8—22no—
280D8—3161no—
281M16—3161no—
282C2×C8—3161no—
283C2×C8—791no—
284C2×C8—791no—
285C2×C8C22×D7911yescharacteristic
286C2×C8C22×D7911yescharacteristic
287C4⋊C4—791no—
288C4⋊C4—791no—
289C4⋊C4—791no—
290C4⋊C4—1581no—
291C4⋊C4—1581no—
292C4⋊C4—1581no—
293C4⋊C4—1581no—
294C4⋊C4C22×D7911yescharacteristic
295C4⋊C4C22×D7911yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—791no—
299C22⋊C4—791no—
300C22⋊C4—1581no—
301C22⋊C4—1581no—
302C22⋊C4—1581no—
303C22⋊C4—1581no—
304C22⋊C4—1581no—
305C22⋊C4—1581no—
306C42C22×D7911yescharacteristic
307C23—21no—
308C23—21no—
309C23—3162no—
310C23—3162no—
311C23—791no—
312C23—791no—
313C23—6321no—
314C23—1581no—
315Q8—3162no—
316Q8—1581no—
317Q8—1581no—
318D4—21no—
319D4—21no—
320D4—21no—
321D4—3162no—
322D4—3162no—
323D4—3162no—
324D4—3162no—
325D4—6321no—
326D4—1582no—
327D4—1581no—
328D4—1581no—
329D4#1192962412yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—42no—
333C2×C4—81no—
334C2×C4—3162no—
335C2×C4—3162no—
336C2×C4—3162no—
337C2×C4—791no—
338C2×C4—791no—
339C2×C4—1581no—
340C2×C4—1581no—
341C2×C4—1581no—
342C2×C4—1581no—
343C2×C4—1581no—
344C2×C4—1581no—
345C2×C4—1581no—
346C2×C4D4×D7911yescharacteristic
347C2×C4D4×D7911yescharacteristic
348C2×C4C23×D7911yescharacteristic
349C8—21no—
350C8—21no—
351C8—1581no—
352C8—1581no—
353C22—22no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—3161no—
360C22—3161no—
361C22—3161no—
362C22—792no—
363C22—6324no—
364C22—1581no—
365C22—1581no—
366C22—1581no—
367C22—1581no—
368C22—1581no—
369C22C2×D4×D7911yescharacteristic
370C4—21no—
371C4—21no—
372C4—41no—
373C4—41no—
374C4—3161no—
375C4—3161no—
376C4—3161no—
377C4—1581no—
378C4—1581no—
379C4C2×#1192962411yescharacteristic
380C4#1457920711yescharacteristic
381C2—42no—
382C2—81no—
383C2—3161no—
384C2—6321no—
385C2—1582no—
386C2#1909920911yescharacteristic
387C2AGL(1,ℤ/8)×D7911yescharacteristic
388C2#1909937311yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#442×C79C2
socleC22×C79C22×D4
hypercenter#442D79
hypocenterC79#3306
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #19099218C2semidirect
2. #19099208C2semidirect
3. #19098923C2semidirect
4. #19098895C2semidirect
5. #19098883C2semidirect
6. #19098853C2semidirect
7. #19098815C2semidirect
8. #19098791C2semidirect
9. #19098778C2semidirect
10. #19098705C2semidirect
11. #19098695C2semidirect
12. #19098636C2semidirect
13. #19098561C2semidirect
14. #102×D79C2semidirect
15. #442×C79C2semidirect
19. C2×#11929612C22semidirect
21. C2×#11929607C22semidirect
23. #14579161C22semidirect
33. #14579132C22semidirect
37. C4⋊C4×D79C22semidirect
39. #14579092C22semidirect
40. #14579092C22semidirect
41. C4⋊(C79⋊C8)C22semidirect
42. #14579086C22semidirect
43. #14579086C22semidirect
44. #14579084C22semidirect
51. (C2×D79)⋊C8C22semidirect
54. C4×D4×C79C22semidirect
55. #106×C79C22semidirect
57. #102×C79C22semidirect
58. #97×C79C22semidirect
123. D4×C79#41semidirect
195. C79#3306semidirect
207. #442D79semidirect
233. C4×D4C2×D79semidirect
239. #106C2×D79semidirect
250. #102C2×D79semidirect
253. #97C2×D79semidirect
329. D4#11929624semidirect