Finite Group Databasebeta

← #23774201

Subgroups — #23774201

Order 10112.

462 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
1C22⋊Q8×D79C211yesmaximal, characteristic, complemented
2#121×D79C211yesmaximal, characteristic
3#19098900C211yesmaximal, characteristic, complemented
4#19098897C211yesmaximal, characteristic, complemented
5#19098878C211yesmaximal, characteristic, complemented
6#19098875C211yesmaximal, characteristic, complemented
7#19098811C211yesmaximal, characteristic, complemented
8#19098809C211yesmaximal, characteristic, complemented
9#19098807C211yesmaximal, characteristic, complemented
10#19098715C211yesmaximal, characteristic, complemented
11#19098712C211yesmaximal, characteristic, complemented
12#19098703C211yesmaximal, characteristic, complemented
13#19098700C211yesmaximal, characteristic, complemented
14#19098526C211yesmaximal, characteristic, complemented
15#468×C79C211yesmaximal, characteristic, complemented
16C2×Q8×D79C2211yescharacteristic, complemented
17C2×D4×D79—21no—
18C2×D4×D79C2211yescharacteristic
19C22×C4×D79C2211yescharacteristic
20C2×#11929613C2211yescharacteristic, complemented
21C2×#11929612C2211yescharacteristic, complemented
22C2×#11929611C2211yescharacteristic, complemented
23C2×#11929608C2211yescharacteristic, complemented
24#14579141C2211yescharacteristic
25#14579140C2211yescharacteristic, complemented
26#14579139—21no—
27#14579138—21no—
28#14579137C2211yescharacteristic
29#14579136C2211yescharacteristic
30#14579135C2211yescharacteristic
31#14579134—21no—
32#14579133—21no—
33#14579132C2211yescharacteristic
34C4⋊C4×D79—21no—
35C4⋊C4×D79C2211yescharacteristic
36C4⋊C4×D79C2211yescharacteristic, complemented
37C22⋊C4×D79—21no—
38C22⋊C4×D79—21no—
39#14579095C2211yescharacteristic, complemented
40#14579094C2211yescharacteristic, complemented
41#14579094C2211yescharacteristic, complemented
42#14579086C2211yescharacteristic, complemented
43#14579085C2211yescharacteristic, complemented
44#14579084C2211yescharacteristic, complemented
45#14579083C2211yescharacteristic, complemented
46#14579082C2211yescharacteristic, complemented
47#14579081C2211yescharacteristic, complemented
48(C2×D79)⋊C8C2211yescharacteristic
49(C2×D79)⋊C8C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic, complemented
51(C2×D79)⋊C8C2211yescharacteristic, complemented
52C2×SD16×C79C2211yescharacteristic, complemented
53C2×M16×C79C2211yescharacteristic, complemented
54C22⋊Q8×C79C2211yescharacteristic, complemented
55#121×C79C2211yescharacteristic
56#107×C79C2211yescharacteristic, complemented
57#103×C79C2211yescharacteristic, complemented
58#102×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60C23×D79D411yescharacteristic
61C2×Dic158—21no—
62C2×Dic158C2311yescharacteristic
63Q8×D79—41no—
64Q8×D79—41no—
65C2×D316—21no—
66C2×D316C2311yescharacteristic
67C2×C22⋊D79—21no—
68C2×C22⋊D79—21no—
69C2×C22⋊D79—21no—
70D4×D79—41no—
71D4×D79—41no—
72D4×D79—44no—
73C22×Dic79D411yescharacteristic
74C2×C4×D79—21no—
75C2×C4×D79—21no—
76C2×C4×D79—21no—
77C2×C4×D79—41no—
78C2×C4×D79—41no—
79C2×C4×D79D411yescharacteristic
80C2×C4×D79D411yescharacteristic
81C2×C4×D79C2311yescharacteristic
82C2×C4×D79C2311yescharacteristic
83#11929613—41no—
84#11929612—41no—
85#11929611—41no—
86#11929608—41no—
87C2×C79⋊C8C2311yescharacteristic
88C2×C79⋊C8C2311yescharacteristic
89C4⋊Dic79—21no—
90C4⋊Dic79C2311yescharacteristic
91C4⋊Dic79C2311yescharacteristic
92Dic79⋊C4—21no—
93Dic79⋊C4—21no—
94Dic79⋊C4—21no—
95Dic79⋊C4—21no—
96C22⋊Dic79—21no—
97C22⋊Dic79—21no—
98(C2×D79)⋊C4—21no—
99(C2×D79)⋊C4—21no—
100(C2×D79)⋊C4—21no—
101(C2×D79)⋊C4—21no—
102C2×Q8×C79C2311yescharacteristic
103C2×D4×C79—21no—
104C2×D4×C79C2311yescharacteristic
105C22×C4×C79C2311yescharacteristic
106SD16×C79—41no—
107M16×C79—41no—
108C2×C8×C79C2311yescharacteristic
109C2×C8×C79C2311yescharacteristic
110C4⋊C4×C79—21no—
111C4⋊C4×C79C2311yescharacteristic
112C4⋊C4×C79C2311yescharacteristic
113C22⋊C4×C79—21no—
114C22⋊C4×C79—21no—
115C23×C79—21no—
116C23×C79C2×D411yescharacteristic
117C22×D79—22no—
118C22×D79—22no—
119C22×D79—21no—
120C22×D79—41no—
121C22×D79—42no—
122C22×D79—42no—
123C22×D79—42no—
124C22×D79C2×D411yescharacteristic
125C22×D79C2×D411yescharacteristic
126Q8×C79—21no—
127Q8×C79—21no—
128D4×C79—21no—
129D4×C79—21no—
130D4×C79—42no—
131C2×C4×C79—21no—
132C2×C4×C79—21no—
133C2×C4×C79—21no—
134C2×C4×C79—21no—
135C2×C4×C79—21no—
136C2×C4×C79C2×D411yescharacteristic
137C2×C4×C79C2411yescharacteristic
138C22⋊D79—42no—
139C22⋊D79—42no—
140C22⋊D79—42no—
141C2×Dic79—21no—
142C2×Dic79—21no—
143C2×Dic79—21no—
144C2×Dic79—41no—
145C2×Dic79C2×D411yescharacteristic
146C2×Dic79C2×D411yescharacteristic
147D316—21no—
148D316—21no—
149D316—42no—
150C4×D79—21no—
151C4×D79—21no—
152C4×D79—21no—
153C4×D79—21no—
154C4×D79—41no—
155C4×D79—41no—
156C4×D79—42no—
157C4×D79—42no—
158C4×D79—42no—
159Dic158—21no—
160Dic158—21no—
161Dic158—42no—
162C8×C79—21no—
163C8×C79—21no—
164C79⋊C8—21no—
165C79⋊C8—21no—
166C22×C79—21no—
167C22×C79—21no—
168C22×C79—21no—
169C22×C79—41no—
170C22×C79—41no—
171C22×C79—41no—
172C22×C79C22×D411yescharacteristic
173C2×D79—21no—
174C2×D79—21no—
175C2×D79—21no—
176C2×D79—21no—
177C2×D79—44no—
178C2×D79—41no—
179C2×D79—41no—
180C2×D79—41no—
181C2×D79—84no—
182C2×D79AGL(1,ℤ/8)12yes—
183C2×D79#13712yes—
184C4×C79—21no—
185C4×C79—41no—
186C4×C79—41no—
187C4×C79—41no—
188C4×C79H(5,𝔽2)11yescharacteristic
189C4×C79H(5,𝔽2)11yescharacteristic
190Dic79—21no—
191Dic79—21no—
192Dic79—41no—
193Dic79—41no—
194Dic79—41no—
195C2×C79—41no—
196C2×C79—81no—
197C2×C79#53411yescharacteristic
198C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
199C2×C79C2×#13711yescharacteristic
200D79—22no—
201D79—22no—
202D79—81no—
203#3193—791nomaximal, Sylow
204C79#319311yescharacteristic, complemented, Sylow
205C2×C22⋊Q8—791no—
206C2×#121—791no—
207#484—791no—
208#484—791no—
209#480—791no—
210#480—791no—
211#468—791no—
212#468—791no—
213#468—791no—
214#468D7911yescharacteristic, complemented
215#450—791no—
216#450—791no—
217#448—791no—
218#448—791no—
219#407—791no—
220C22×Q8—791no—
221C22×D4—791no—
222C22×D4—1581no—
223C23×C4—791no—
224C2×SD16—791no—
225C2×SD16—791no—
226C2×SD16—791no—
227C2×SD16C2×D7911yescharacteristic, complemented
228C2×M16—791no—
229C2×M16C2×D7911yescharacteristic, complemented
230C22⋊Q8—791no—
231C22⋊Q8—791no—
232C22⋊Q8—791no—
233C22⋊Q8—1581no—
234C22⋊Q8—1581no—
235C22⋊Q8C2×D7911yescharacteristic, complemented
236#121—791no—
237#121—791no—
238#121—791no—
239#121—1581no—
240#121—1581no—
241#121C2×D7911yescharacteristic
242C2×C4⋊C4—791no—
243C2×C4⋊C4—791no—
244C2×C4⋊C4—1581no—
245C2×C22⋊C4—1581no—
246C2×C22⋊C4—1581no—
247#107—791no—
248#107—791no—
249#107—791no—
250#107C2×D7911yescharacteristic, complemented
251#103—791no—
252#103—791no—
253#103—791no—
254#103C2×D7911yescharacteristic, complemented
255#102—791no—
256#102—791no—
257#102—791no—
258#102C2×D7911yescharacteristic, complemented
259C22⋊C8—791no—
260C22⋊C8—791no—
261C22⋊C8—791no—
262C22⋊C8—791no—
263C24—791no—
264C24—1581no—
265C2×Q8—3161no—
266C2×Q8—3161no—
267C2×Q8—791no—
268C2×Q8—1581no—
269C2×Q8C22×D7911yescharacteristic
270C2×D4—21no—
271C2×D4—3164no—
272C2×D4—3161no—
273C2×D4—3161no—
274C2×D4—791no—
275C2×D4—1581no—
276C2×D4—1581no—
277C2×D4—1581no—
278C2×D4—1581no—
279C2×D4C22×D7911yescharacteristic
280C22×C4—3161no—
281C22×C4—3161no—
282C22×C4—791no—
283C22×C4—791no—
284C22×C4—791no—
285C22×C4—791no—
286C22×C4—791no—
287C22×C4—1581no—
288C22×C4—1581no—
289C22×C4—1581no—
290C22×C4C22×D7911yescharacteristic
291SD16—41no—
292SD16—3161no—
293SD16—3161no—
294SD16—3161no—
295M16—41no—
296M16—3161no—
297C2×C8—791no—
298C2×C8—791no—
299C2×C8C22×D7911yescharacteristic
300C2×C8C22×D7911yescharacteristic
301C4⋊C4—21no—
302C4⋊C4—791no—
303C4⋊C4—791no—
304C4⋊C4—1581no—
305C4⋊C4—1581no—
306C4⋊C4—1581no—
307C4⋊C4—1581no—
308C4⋊C4—1581no—
309C4⋊C4C22×D7911yescharacteristic
310C4⋊C4C22×D7911yescharacteristic
311C22⋊C4—21no—
312C22⋊C4—21no—
313C22⋊C4—1581no—
314C22⋊C4—1581no—
315C22⋊C4—1581no—
316C22⋊C4—1581no—
317C22⋊C4—1581no—
318C22⋊C4—1581no—
319C23—21no—
320C23—3161no—
321C23—3162no—
322C23—3162no—
323C23—3162no—
324C23—791no—
325C23—791no—
326C23—1582no—
327C23—1582no—
328C23—1581no—
329C23D4×D7911yescharacteristic
330Q8—21no—
331Q8—21no—
332Q8—3162no—
333Q8—1581no—
334Q8—1581no—
335D4—21no—
336D4—21no—
337D4—42no—
338D4—3162no—
339D4—3162no—
340D4—3162no—
341D4—3162no—
342D4—1581no—
343D4—1581no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—3161no—
350C2×C4—3161no—
351C2×C4—3162no—
352C2×C4—3162no—
353C2×C4—3162no—
354C2×C4—3161no—
355C2×C4—791no—
356C2×C4—791no—
357C2×C4—1581no—
358C2×C4—1581no—
359C2×C4—1581no—
360C2×C4—1581no—
361C2×C4—1581no—
362C2×C4—1581no—
363C2×C4—1581no—
364C2×C4D4×D7911yescharacteristic
365C2×C4C23×D7911yescharacteristic
366C8—21no—
367C8—21no—
368C8—1581no—
369C8—1581no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—3164no—
377C22—3161no—
378C22—3161no—
379C22—3161no—
380C22—792no—
381C22—792no—
382C22—6324no—
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—1581no—
396C4—1581no—
397C4#1457920611yescharacteristic
398C4#1457920711yescharacteristic
399C2—41no—
400C2—81no—
401C2—6321no—
402C2—1582no—
403C2—1582no—
404C2#1909912111yescharacteristic
405C2AGL(1,ℤ/8)×D7911yescharacteristic
406C2#137×D7911yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#468×C79C2
socleC22×C79C22×D4
prime radical#121×D79C2
hypercenter#468D79
hypocenterC79#3193
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. C22⋊Q8×D79C2semidirect
3. #19098900C2semidirect
4. #19098897C2semidirect
5. #19098878C2semidirect
6. #19098875C2semidirect
7. #19098811C2semidirect
8. #19098809C2semidirect
9. #19098807C2semidirect
10. #19098715C2semidirect
11. #19098712C2semidirect
12. #19098703C2semidirect
13. #19098700C2semidirect
14. #19098526C2semidirect
15. #468×C79C2semidirect
16. C2×Q8×D79C22semidirect
20. C2×#11929613C22semidirect
21. C2×#11929612C22semidirect
22. C2×#11929611C22semidirect
23. C2×#11929608C22semidirect
25. #14579140C22semidirect
36. C4⋊C4×D79C22semidirect
39. #14579095C22semidirect
40. #14579094C22semidirect
41. #14579094C22semidirect
42. #14579086C22semidirect
43. #14579085C22semidirect
44. #14579084C22semidirect
45. #14579083C22semidirect
46. #14579082C22semidirect
47. #14579081C22semidirect
50. (C2×D79)⋊C8C22semidirect
51. (C2×D79)⋊C8C22semidirect
52. C2×SD16×C79C22semidirect
53. C2×M16×C79C22semidirect
54. C22⋊Q8×C79C22semidirect
56. #107×C79C22semidirect
57. #103×C79C22semidirect
58. #102×C79C22semidirect
204. C79#3193semidirect
214. #468D79semidirect
227. C2×SD16C2×D79semidirect
229. C2×M16C2×D79semidirect
235. C22⋊Q8C2×D79semidirect
250. #107C2×D79semidirect
254. #103C2×D79semidirect
258. #102C2×D79semidirect