Finite Group Databasebeta

← #23773037

Subgroups — #23773037

Order 10112.

492 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D79C211yesmaximal, characteristic, complemented
2C2×#14579169C211yesmaximal, characteristic, complemented
3#19099136C211yesmaximal, characteristic, complemented
4#19099129C211yesmaximal, characteristic
5#19098810C211yesmaximal, characteristic, complemented
6#19098809C211yesmaximal, characteristic, complemented
7#19098806C211yesmaximal, characteristic, complemented
8#19098795C211yesmaximal, characteristic, complemented
9#19098794C211yesmaximal, characteristic, complemented
10#19098791C211yesmaximal, characteristic, complemented
11#19098790C211yesmaximal, characteristic, complemented
12#19098600C211yesmaximal, characteristic, complemented
13#19098570C211yesmaximal, characteristic, complemented
14#19098566C211yesmaximal, characteristic, complemented
15#468×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C2×Q8×D79C2211yescharacteristic
18C2×D4×D79C2211yescharacteristic
19C2×#11929613C2211yescharacteristic
20C2×#11929612C2211yescharacteristic
21C2×#11929611C2211yescharacteristic
22SD16×D79—24no—
23#14579169—24no—
24C2×#11929607C2211yescharacteristic
25C2×#11929607C2211yescharacteristic, complemented
26C22×C79⋊C8C2211yescharacteristic, complemented
27C2×C8×D79C2211yescharacteristic
28C2×C8×D79C2211yescharacteristic, complemented
29#14579160—21no—
30#14579157—21no—
31#14579147—21no—
32#14579147—21no—
33#14579146—21no—
34#14579143—21no—
35#14579141C2211yescharacteristic, complemented
36#14579140C2211yescharacteristic, complemented
37#14579137C2211yescharacteristic, complemented
38#14579136C2211yescharacteristic
39#14579135C2211yescharacteristic
40#14579132C2211yescharacteristic
41#14579131—21no—
42#14579129—21no—
43#14579119C2211yescharacteristic
44#14579119C2211yescharacteristic
45#14579095C2211yescharacteristic, complemented
46#14579092C2211yescharacteristic, complemented
47#14579092C2211yescharacteristic, complemented
48#14579086C2211yescharacteristic, complemented
49#14579085C2211yescharacteristic, complemented
50#14579084C2211yescharacteristic, complemented
51#14579083C2211yescharacteristic
52#14579082C2211yescharacteristic
53#14579081C2211yescharacteristic
54C2×SD16×C79C2211yescharacteristic
55C2×M16×C79C2211yescharacteristic, complemented
56C22⋊Q8×C79C2211yescharacteristic, complemented
57#121×C79C2211yescharacteristic
58#107×C79C2211yescharacteristic, complemented
59#103×C79C2211yescharacteristic, complemented
60#102×C79C2211yescharacteristic
61C23×D79—21no—
62#11929624—22no—
63#11929624—22no—
64C2×Dic158—21no—
65C2×Dic158D411yescharacteristic
66C2×Dic158C2311yescharacteristic
67Q8×D79—22no—
68Q8×D79—22no—
69C2×D316—21no—
70C2×D316D411yescharacteristic
71C2×D316C2311yescharacteristic
72C2×C22⋊D79—21no—
73C2×C22⋊D79—21no—
74C2×C22⋊D79—21no—
75C2×C22⋊D79D411yescharacteristic
76C2×C22⋊D79D411yescharacteristic
77D4×D79—22no—
78D4×D79—22no—
79C2×C4×D79—21no—
80C2×C4×D79C2311yescharacteristic
81C2×C4×D79C2311yescharacteristic
82#11929613—22no—
83#11929612—22no—
84#11929611—22no—
85#11929607—22no—
86#11929607—22no—
87C2×C79⋊C8—22no—
88C2×C79⋊C8C2311yescharacteristic
89C2×C79⋊C8C2311yescharacteristic
90C8×D79—22no—
91C8×D79D414yescomplemented
92C4⋊Dic79—21no—
93C4⋊Dic79C2311yescharacteristic
94C4⋊Dic79C2311yescharacteristic
95Dic79⋊C4—21no—
96Dic79⋊C4—21no—
97C22⋊Dic79—21no—
98C22⋊Dic79—21no—
99(C2×D79)⋊C4—21no—
100(C2×D79)⋊C4—21no—
101(C2×D79)⋊C4—21no—
102(C2×D79)⋊C4—21no—
103(C2×D79)⋊C4—21no—
104(C2×D79)⋊C4—21no—
105C4×Dic79—21no—
106C4×Dic79—21no—
107C2×Q8×C79C2311yescharacteristic
108C2×D4×C79—21no—
109C2×D4×C79C2311yescharacteristic
110C22×C4×C79C2311yescharacteristic
111SD16×C79—22no—
112M16×C79—22no—
113C2×C8×C79C2311yescharacteristic
114C2×C8×C79C2311yescharacteristic
115C4⋊C4×C79—21no—
116C4⋊C4×C79C2311yescharacteristic
117C4⋊C4×C79C2311yescharacteristic
118C22⋊C4×C79—21no—
119C22⋊C4×C79—21no—
120C23×C79—21no—
121C23×C79C2×D411yescharacteristic
122C22×D79—21no—
123C22×D79—42no—
124C22×D79—81no—
125C22×D79—81no—
126C22×D79C2×D411yescharacteristic
127C22×D79C2×D411yescharacteristic
128Q8×C79—21no—
129Q8×C79—21no—
130D4×C79—21no—
131D4×C79—21no—
132D4×C79—81no—
133C2×C4×C79—21no—
134C2×C4×C79—21no—
135C2×C4×C79—21no—
136C2×C4×C79—21no—
137C2×C4×C79—21no—
138C2×C4×C79C2×D411yescharacteristic
139C2×C4×C79C2411yescharacteristic
140C22⋊D79—22no—
141C22⋊D79—22no—
142C22⋊D79—42no—
143C22⋊D79—81no—
144C22⋊D79—81no—
145C2×Dic79—21no—
146C2×Dic79—21no—
147C2×Dic79—21no—
148C2×Dic79C2×D411yescharacteristic
149C2×Dic79C2×D411yescharacteristic
150D316—22no—
151D316—21no—
152D316—21no—
153D316—81no—
154C4×D79—21no—
155C4×D79—21no—
156C4×D79—42no—
157C4×D79C2×D412yes—
158C4×D79#4112yes—
159Dic158—22no—
160Dic158—21no—
161Dic158—21no—
162Dic158—42no—
163C8×C79—21no—
164C8×C79C2×D412yes—
165C79⋊C8—21no—
166C79⋊C8C2×D412yes—
167C22×C79—21no—
168C22×C79—21no—
169C22×C79—21no—
170C22×C79—41no—
171C22×C79—41no—
172C22×C79—41no—
173C22×C79C22×D411yescharacteristic
174C2×D79—21no—
175C2×D79—21no—
176C2×D79—21no—
177C2×D79—21no—
178C2×D79—21no—
179C2×D79—41no—
180C2×D79—41no—
181C2×D79—41no—
182C2×D79—84no—
183C2×D79#12112yes—
184C4×C79—21no—
185C4×C79—41no—
186C4×C79—41no—
187C4×C79—41no—
188C4×C79C22×D411yescharacteristic
189C4×C79C2×#4111yescharacteristic
190Dic79—21no—
191Dic79—41no—
192Dic79—41no—
193Dic79—41no—
194Dic79#12112yes—
195C2×C79—41no—
196C2×C79—81no—
197C2×C79C2×#12111yescharacteristic
198C2×C79#57711yescharacteristic
199C2×C79#57711yescharacteristic
200D79—22no—
201D79—41no—
202D79—81no—
203#3057—791nomaximal, Sylow
204C79#305711yescharacteristic, complemented, Sylow
205C22×SD16—791no—
206C2×#131—791no—
207#536—791no—
208#535—791no—
209#468—791no—
210#468—791no—
211#468—791no—
212#468D7911yescharacteristic, complemented
213#465—791no—
214#465—791no—
215#465—791no—
216#465—791no—
217#427—791no—
218#419—791no—
219#418—791no—
220C2×#41—791no—
221C22×Q8—791no—
222C22×D4—791no—
223C2×SD16—791no—
224C2×SD16—791no—
225C2×SD16—791no—
226C2×SD16—1584no—
227C2×SD16C2×D7911yescharacteristic
228#131—1584no—
229C2×M16—791no—
230C2×M16—791no—
231C2×M16C2×D7911yescharacteristic, complemented
232C22×C8—791no—
233C22×C8—791no—
234C22×C8—791no—
235C4⋊Q8—1581no—
236#127—1581no—
237#124—1581no—
238#124—1581no—
239#123—1581no—
240#123—1581no—
241C22⋊Q8—791no—
242C22⋊Q8—791no—
243C22⋊Q8—791no—
244C22⋊Q8C2×D7911yescharacteristic, complemented
245#121—791no—
246#121—791no—
247#121—791no—
248#121C2×D7911yescharacteristic
249#120—1581no—
250#120—1581no—
251#117—791no—
252#117—791no—
253#107—791no—
254#107C2×D7911yescharacteristic, complemented
255#106—791no—
256#106—791no—
257#103—791no—
258#103—791no—
259#103—791no—
260#103C2×D7911yescharacteristic, complemented
261#102—791no—
262#102—791no—
263#102—791no—
264#102C2×D7911yescharacteristic
265C24—1581no—
266#41—1582no—
267#41—1582no—
268C2×Q8—791no—
269C2×Q8—791no—
270C2×Q8—1581no—
271C2×Q8—1582no—
272C2×Q8—1582no—
273C2×Q8C22×D7911yescharacteristic
274C2×D4—21no—
275C2×D4—791no—
276C2×D4—791no—
277C2×D4—791no—
278C2×D4—791no—
279C2×D4—1581no—
280C2×D4—1582no—
281C2×D4—1582no—
282C2×D4—1581no—
283C2×D4—1581no—
284C2×D4—1581no—
285C2×D4C22×D7911yescharacteristic
286C22×C4—791no—
287C22×C4—791no—
288C22×C4—1581no—
289C22×C4C22×D7911yescharacteristic
290SD16—22no—
291SD16—1582no—
292SD16—1582no—
293SD16—1582no—
294M16—22no—
295M16—1582no—
296M16—1582no—
297C2×C8—791no—
298C2×C8—794no—
299C2×C8—791no—
300C2×C8—1582no—
301C2×C8—1582no—
302C2×C8C22×D7911yescharacteristic
303C2×C8C22×D7911yescharacteristic
304C4⋊C4—21no—
305C4⋊C4—791no—
306C4⋊C4—791no—
307C4⋊C4—1581no—
308C4⋊C4—1581no—
309C4⋊C4—1581no—
310C4⋊C4C22×D7911yescharacteristic
311C4⋊C4C22×D7911yescharacteristic
312C22⋊C4—21no—
313C22⋊C4—21no—
314C22⋊C4—1581no—
315C22⋊C4—1581no—
316C22⋊C4—1581no—
317C22⋊C4—1581no—
318C22⋊C4—1581no—
319C22⋊C4—1581no—
320C22⋊C4—1581no—
321C22⋊C4—1581no—
322C42—1581no—
323C42—1581no—
324C23—21no—
325C23—3162no—
326C23—791no—
327C23—791no—
328C23—6321no—
329C23—6321no—
330C23—1581no—
331C23D4×D7911yescharacteristic
332Q8—21no—
333Q8—21no—
334Q8—3162no—
335Q8—1582no—
336Q8—1581no—
337Q8—1581no—
338D4—21no—
339D4—21no—
340D4—81no—
341D4—3162no—
342D4—6321no—
343D4—6321no—
344D4—6321no—
345D4—1582no—
346D4—1582no—
347D4—1582no—
348D4—1581no—
349D4—1581no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—3162no—
356C2×C4—791no—
357C2×C4—792no—
358C2×C4—792no—
359C2×C4—791no—
360C2×C4—1581no—
361C2×C4—1581no—
362C2×C4—1581no—
363C2×C4—1581no—
364C2×C4—1581no—
365C2×C4D4×D7911yescharacteristic
366C2×C4C23×D7911yescharacteristic
367C8—21no—
368C8—792no—
369C8—1581no—
370C8D4×D7912yes—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—3161no—
378C22—3161no—
379C22—3161no—
380C22—792no—
381C22—6324no—
382C22—1581no—
383C22—1581no—
384C22—1581no—
385C22—1581no—
386C22—1581no—
387C22C2×D4×D7911yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—3161no—
393C4—3161no—
394C4—3161no—
395C4—792no—
396C4—1581no—
397C4C2×D4×D7911yescharacteristic
398C4#41×D7911yescharacteristic
399C2—41no—
400C2—81no—
401C2—3161no—
402C2—6321no—
403C2—1582no—
404C2#121×D7911yescharacteristic
405C2#1909937211yescharacteristic
406C2#1909937311yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#468×C79C2
socleC22×C79C22×D4
prime radical#19099129C2
hypercenter#468D79
hypocenterC79#3057
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D79C2semidirect
2. C2×#14579169C2semidirect
3. #19099136C2semidirect
5. #19098810C2semidirect
6. #19098809C2semidirect
7. #19098806C2semidirect
8. #19098795C2semidirect
9. #19098794C2semidirect
10. #19098791C2semidirect
11. #19098790C2semidirect
12. #19098600C2semidirect
13. #19098570C2semidirect
14. #19098566C2semidirect
15. #468×C79C2semidirect
25. C2×#11929607C22semidirect
26. C22×C79⋊C8C22semidirect
28. C2×C8×D79C22semidirect
35. #14579141C22semidirect
36. #14579140C22semidirect
37. #14579137C22semidirect
45. #14579095C22semidirect
46. #14579092C22semidirect
47. #14579092C22semidirect
48. #14579086C22semidirect
49. #14579085C22semidirect
50. #14579084C22semidirect
55. C2×M16×C79C22semidirect
56. C22⋊Q8×C79C22semidirect
58. #107×C79C22semidirect
59. #103×C79C22semidirect
91. C8×D79D4semidirect
204. C79#3057semidirect
212. #468D79semidirect
231. C2×M16C2×D79semidirect
244. C22⋊Q8C2×D79semidirect
254. #107C2×D79semidirect
260. #103C2×D79semidirect