Finite Group Databasebeta

← #23774496

Subgroups — #23774496

Order 10112.

408 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099184C211yesmaximal, characteristic, complemented
2#19099132C211yesmaximal, characteristic, complemented
3#19098952C211yesmaximal, characteristic, complemented
4#19098947C211yesmaximal, characteristic, complemented
5#19098923C211yesmaximal, characteristic, complemented
6#19098910C211yesmaximal, characteristic, complemented
7#19098786C211yesmaximal, characteristic, complemented
8#19098779C211yesmaximal, characteristic, complemented
9#19098764C211yesmaximal, characteristic, complemented
10#19098759C211yesmaximal, characteristic, complemented
11#19098727C211yesmaximal, characteristic, complemented
12#19098716C211yesmaximal, characteristic, complemented
13#19098710C211yesmaximal, characteristic, complemented
14#19098699C211yesmaximal, characteristic, complemented
15#433×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C22×D316C2211yescharacteristic
18C2×Dic316C2211yescharacteristic, complemented
19C2×#11929613C2211yescharacteristic
20C2×#11929613C2211yescharacteristic
21C2×#11929613C2211yescharacteristic, complemented
22C2×#11929613C2211yescharacteristic, complemented
23C2×D632C2211yescharacteristic
24C2×D632C2211yescharacteristic
25C2×D632C2211yescharacteristic, complemented
26#14579161C2211yescharacteristic, complemented
27#14579158C2211yescharacteristic
28#14579158C2211yescharacteristic
29#14579156—21no—
30#14579149C2211yescharacteristic
31#14579149C2211yescharacteristic
32#14579149C2211yescharacteristic, complemented
33#14579147—21no—
34#14579143—21no—
35#14579140C2211yescharacteristic
36#14579139—21no—
37#14579136—21no—
38#14579136—21no—
39#14579135C2211yescharacteristic
40#14579131—21no—
41#14579131—21no—
42C4×Dic158C2211yescharacteristic, complemented
43C4×D316C2211yescharacteristic, complemented
44#14579086C2211yescharacteristic, complemented
45#14579086C2211yescharacteristic, complemented
46#14579083C2211yescharacteristic
47#14579083C2211yescharacteristic
48#14579083C2211yescharacteristic
49#14579083C2211yescharacteristic
50#14579083C2211yescharacteristic, complemented
51#14579083C2211yescharacteristic, complemented
52#117×C79C2211yescharacteristic
53C4⋊C8×C79C2211yescharacteristic, complemented
54C4⋊C8×C79C2211yescharacteristic, complemented
55C22⋊C8×C79C2211yescharacteristic
56C22⋊C8×C79C2211yescharacteristic
57#97×C79C2211yescharacteristic, complemented
58C4×C8×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60#11929624—41no—
61#11929624—41no—
62C2×Dic158—21no—
63C2×Dic158C2311yescharacteristic
64C2×Dic158C2311yescharacteristic
65C2×D316—21no—
66C2×D316—21no—
67C2×D316—21no—
68C2×D316—21no—
69C2×D316—21no—
70C2×D316—41no—
71C2×D316—41no—
72C2×D316C2311yescharacteristic
73C2×D316C2311yescharacteristic
74C2×D316C2311yescharacteristic
75C2×D316C2311yescharacteristic
76C2×C22⋊D79—21no—
77C2×C22⋊D79—21no—
78C2×C4×D79—21no—
79C2×C4×D79—21no—
80Dic316—41no—
81#11929613—41no—
82#11929613—41no—
83#11929613—41no—
84#11929613—41no—
85D632—41no—
86D632—41no—
87D632—41no—
88C4⋊Dic79—21no—
89C4⋊Dic79C2311yescharacteristic
90C4⋊Dic79C2311yescharacteristic
91Dic79⋊C4—21no—
92Dic79⋊C4—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)⋊C4—21no—
99(C2×D79)⋊C4—21no—
100(C2×D79)⋊C4—21no—
101(C2×D79)⋊C4—21no—
102C4×Dic79—21no—
103C22×C4×C79C2311yescharacteristic
104C2×C8×C79C2311yescharacteristic
105C2×C8×C79C2311yescharacteristic
106C2×C8×C79C2311yescharacteristic
107C2×C8×C79C2311yescharacteristic
108C4⋊C4×C79D411yescharacteristic
109C4⋊C4×C79D411yescharacteristic
110C22⋊C4×C79D411yescharacteristic
111C22⋊C4×C79D411yescharacteristic
112C42×C79C2311yescharacteristic
113C42×C79C2311yescharacteristic
114C23×C79C2×D411yescharacteristic
115C22×D79—21no—
116C22×D79—21no—
117C22×D79—21no—
118C22×D79—21no—
119C22×D79—42no—
120C22×D79—81no—
121C22×D79—81no—
122C2×C4×C79—21no—
123C2×C4×C79—21no—
124C2×C4×C79C2×D411yescharacteristic
125C2×C4×C79C2×D411yescharacteristic
126C2×C4×C79C2×D411yescharacteristic
127C2×C4×C79C2×D411yescharacteristic
128C2×C4×C79C2×D411yescharacteristic
129C2×C4×C79C2411yescharacteristic
130C22⋊D79—42no—
131C22⋊D79—81no—
132C2×Dic79—21no—
133C2×Dic79—21no—
134C2×Dic79—21no—
135C2×Dic79—21no—
136D316—21no—
137D316—21no—
138D316—21no—
139D316—21no—
140D316—21no—
141D316—21no—
142D316—21no—
143D316—21no—
144D316—42no—
145D316—81no—
146D316—81no—
147D316—81no—
148D316—81no—
149C4×D79—42no—
150C4×D79—81no—
151Dic158—21no—
152Dic158—21no—
153Dic158—21no—
154Dic158—21no—
155Dic158—81no—
156C8×C79—21no—
157C8×C79—21no—
158C8×C79—21no—
159C8×C79—21no—
160C22×C79—21no—
161C22×C79—21no—
162C22×C79—21no—
163C22×C79C22×D411yescharacteristic
164C2×D79—41no—
165C2×D79—41no—
166C2×D79—41no—
167C2×D79—41no—
168C2×D79—41no—
169C2×D79—41no—
170C2×D79—41no—
171C2×D79—41no—
172C2×D79—41no—
173C2×D79—41no—
174C2×D79—41no—
175C2×D79—41no—
176C2×D79—84no—
177C4×C79—21no—
178C4×C79—21no—
179C4×C79—21no—
180C4×C79—21no—
181C4×C79—21no—
182C4×C79H(5,𝔽2)11yescharacteristic
183C4×C79H(5,𝔽2)11yescharacteristic
184Dic79—41no—
185Dic79—41no—
186Dic79—41no—
187Dic79—41no—
188C2×C79—41no—
189C2×C79#53511yescharacteristic
190C2×C79#57611yescharacteristic
191C2×C79#57711yescharacteristic
192D79—81no—
193D79—81no—
194D79—81no—
195D79—81no—
196#3224—791nomaximal, Sylow
197C79#322411yescharacteristic, complemented, Sylow
198#542—791no—
199#535—791no—
200#496—791no—
201#495—791no—
202#489—791no—
203#486—791no—
204#464—791no—
205#463—791no—
206#460—791no—
207#459—791no—
208#452—791no—
209#450—791no—
210#449—791no—
211#447—791no—
212#433D7911yescharacteristic, complemented
213C2×#41—791no—
214C22×D4—791no—
215C2×Q16—791no—
216C2×SD16—791no—
217C2×SD16—791no—
218C2×SD16—791no—
219C2×SD16—791no—
220C2×D8—791no—
221C2×D8—791no—
222C2×D8—791no—
223C4⋊Q8—791no—
224#127—791no—
225#127—791no—
226#126—1581no—
227#124—791no—
228#124—791no—
229#124—791no—
230#124—1581no—
231#123—1581no—
232C22⋊Q8—791no—
233C22⋊Q8—1581no—
234#121—791no—
235#121—1581no—
236#121—1581no—
237#120—1581no—
238#120—1581no—
239C4×Q8—791no—
240C4×D4—791no—
241#117C2×D7911yescharacteristic
242C4⋊C8C2×D7911yescharacteristic, complemented
243C4⋊C8C2×D7911yescharacteristic, complemented
244#103—791no—
245#103—791no—
246#102—791no—
247#102—791no—
248#102—791no—
249#102—791no—
250#102—791no—
251#102—791no—
252C22⋊C8C2×D7911yescharacteristic
253C22⋊C8C2×D7911yescharacteristic
254#97C2×D7911yescharacteristic, complemented
255C4×C8C2×D7911yescharacteristic, complemented
256C24—1581no—
257#41—3161no—
258#41—3161no—
259C2×Q8—791no—
260C2×Q8—791no—
261C2×Q8—1581no—
262C2×D4—3161no—
263C2×D4—3161no—
264C2×D4—791no—
265C2×D4—791no—
266C2×D4—791no—
267C2×D4—791no—
268C2×D4—1581no—
269C2×D4—1581no—
270C2×D4—1581no—
271C2×D4—1581no—
272C2×D4—1581no—
273C2×D4—1581no—
274C2×D4—1581no—
275C22×C4—1581no—
276C22×C4—1581no—
277C22×C4C22×D7911yescharacteristic
278Q16—3161no—
279SD16—3161no—
280SD16—3161no—
281SD16—3161no—
282SD16—3161no—
283D8—3161no—
284D8—3161no—
285D8—3161no—
286C2×C8C22×D7911yescharacteristic
287C2×C8C22×D7911yescharacteristic
288C2×C8C22×D7911yescharacteristic
289C2×C8C22×D7911yescharacteristic
290C4⋊C4—791no—
291C4⋊C4—791no—
292C4⋊C4—1581no—
293C4⋊C4—1581no—
294C4⋊C4—1581no—
295C4⋊C4D31611yescharacteristic
296C4⋊C4D31611yescharacteristic
297C22⋊C4—1581no—
298C22⋊C4—1581no—
299C22⋊C4—1581no—
300C22⋊C4—1581no—
301C22⋊C4—1581no—
302C22⋊C4—1581no—
303C22⋊C4—1581no—
304C22⋊C4—1581no—
305C22⋊C4—1581no—
306C22⋊C4D31611yescharacteristic
307C22⋊C4D31611yescharacteristic
308C42—1581no—
309C42C22×D7911yescharacteristic
310C42C22×D7911yescharacteristic
311C23—3162no—
312C23—6321no—
313C23—6321no—
314C23—1581no—
315C23—1581no—
316C23—1581no—
317C23—1581no—
318C23C2×D31611yescharacteristic
319Q8—6321no—
320Q8—1581no—
321Q8—1581no—
322Q8—1581no—
323Q8—1581no—
324D4—3162no—
325D4—3162no—
326D4—6321no—
327D4—6321no—
328D4—6321no—
329D4—6321no—
330D4—6321no—
331D4—1581no—
332D4—1581no—
333D4—1581no—
334D4—1581no—
335D4—1581no—
336D4—1581no—
337D4—1581no—
338D4—1581no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—3162no—
342C2×C4—6321no—
343C2×C4—1581no—
344C2×C4—1581no—
345C2×C4—1581no—
346C2×C4—1581no—
347C2×C4C2×D31611yescharacteristic
348C2×C4C2×D31611yescharacteristic
349C2×C4C2×D31611yescharacteristic
350C2×C4C2×D31611yescharacteristic
351C2×C4C2×D31611yescharacteristic
352C2×C4C23×D7911yescharacteristic
353C8—21no—
354C8—21no—
355C8—21no—
356C8—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—3161no—
361C22—3161no—
362C22—3161no—
363C22—3161no—
364C22—3161no—
365C22—3161no—
366C22—3161no—
367C22—3161no—
368C22—3161no—
369C22—3161no—
370C22—3161no—
371C22—3161no—
372C22—6324no—
373C22C22×D31611yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—3161no—
380C4—3161no—
381C4—3161no—
382C4—3161no—
383C4#1457920711yescharacteristic
384C4#1457920711yescharacteristic
385C2—41no—
386C2—6321no—
387C2—6321no—
388C2—6321no—
389C2—6321no—
390C2#1909913211yescharacteristic
391C2#1909936811yescharacteristic
392C2#1909937511yescharacteristic
subgroupG/H
centerC22C22×D316
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#433×C79C2
socleC22×C79C22×D4
hypercenter#433D79
hypocenterC79#3224
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #19099184C2semidirect
2. #19099132C2semidirect
3. #19098952C2semidirect
4. #19098947C2semidirect
5. #19098923C2semidirect
6. #19098910C2semidirect
7. #19098786C2semidirect
8. #19098779C2semidirect
9. #19098764C2semidirect
10. #19098759C2semidirect
11. #19098727C2semidirect
12. #19098716C2semidirect
13. #19098710C2semidirect
14. #19098699C2semidirect
15. #433×C79C2semidirect
18. C2×Dic316C22semidirect
21. C2×#11929613C22semidirect
22. C2×#11929613C22semidirect
25. C2×D632C22semidirect
26. #14579161C22semidirect
32. #14579149C22semidirect
42. C4×Dic158C22semidirect
43. C4×D316C22semidirect
44. #14579086C22semidirect
45. #14579086C22semidirect
50. #14579083C22semidirect
51. #14579083C22semidirect
53. C4⋊C8×C79C22semidirect
54. C4⋊C8×C79C22semidirect
57. #97×C79C22semidirect
58. C4×C8×C79C22semidirect
197. C79#3224semidirect
212. #433D79semidirect
242. C4⋊C8C2×D79semidirect
243. C4⋊C8C2×D79semidirect
254. #97C2×D79semidirect
255. C4×C8C2×D79semidirect