Finite Group Databasebeta

← #23772227

Subgroups — #23772227

Order 10112.

506 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579188C211yesmaximal, characteristic
2#19099045C211yesmaximal, characteristic, complemented
3#19099035C211yesmaximal, characteristic, complemented
4#19098674C211yesmaximal, characteristic, complemented
5#19098673C211yesmaximal, characteristic, complemented
6#19098664C211yesmaximal, characteristic, complemented
7#19098661C211yesmaximal, characteristic, complemented
8#19098648C211yesmaximal, characteristic, complemented
9C4×D632C211yesmaximal, characteristic, complemented
10#19098643C211yesmaximal, characteristic, complemented
11#19098602C211yesmaximal, characteristic, complemented
12#19098558C211yesmaximal, characteristic, complemented
13#102×D79C211yesmaximal, characteristic, complemented
14#19098517C211yesmaximal, characteristic, complemented
15C4×SD16×C79C211yesmaximal, characteristic, complemented
16C2×#11929625C2211yescharacteristic
17C2×D4×D79C2211yescharacteristic
18#14579188C418yescomplemented
19C2×#11929611C2211yescharacteristic
20C2×D632C2211yescharacteristic
21C2×#11929609C2211yescharacteristic
22C2×#11929607C2211yescharacteristic
23C2×C8×D79C2211yescharacteristic
24Q8×Dic79C2211yescharacteristic, complemented
25C4×D316—21no—
26C4×D316C2211yescharacteristic
27C4×D316C2211yescharacteristic, complemented
28D4×Dic79C2211yescharacteristic
29#14579123—21no—
30#14579123C2211yescharacteristic
31#14579123C2211yescharacteristic, complemented
32C4×C22⋊D79—21no—
33(C22⋊D79)⋊C4—21no—
34#14579119C2211yescharacteristic
35#14579118—21no—
36#14579118C2211yescharacteristic
37C4⋊C4×D79—21no—
38C4⋊C4×D79C2211yescharacteristic
39C2×(C2×D79)⋊C4—21no—
40C22⋊C4×D79—21no—
41#14579095C2211yescharacteristic, complemented
42#14579094C2211yescharacteristic, complemented
43#14579092C2211yescharacteristic, complemented
44#14579085C2211yescharacteristic, complemented
45#14579083C2211yescharacteristic
46#14579083C2211yescharacteristic, complemented
47#14579082C2211yescharacteristic
48#14579081C2211yescharacteristic
49#14579081C2211yescharacteristic, complemented
50#14579072C2211yescharacteristic, complemented
51#14579071C2211yescharacteristic, complemented
52C8×Dic79C2211yescharacteristic, complemented
53C2×SD16×C79C2211yescharacteristic
54C4×Q8×C79C2211yescharacteristic, complemented
55C4×D4×C79C2211yescharacteristic
56#106×C79C2211yescharacteristic, complemented
57#103×C79C2211yescharacteristic, complemented
58#102×C79C2211yescharacteristic
59C4×C8×C79C2211yescharacteristic, complemented
60C23×D79—21no—
61#11929625—22no—
62#11929625C2×C414yescomplemented
63C2×D316—21no—
64C2×D316C2311yescharacteristic
65C2×D316C2311yescharacteristic
66C2×C22⋊D79—21no—
67D4×D79—22no—
68D4×D79C2×C414yescomplemented
69C22×Dic79—21no—
70C2×C4×D79—21no—
71C2×C4×D79—21no—
72C2×C4×D79—21no—
73C2×C4×D79—21no—
74C2×C4×D79—21no—
75C2×C4×D79—21no—
76C2×C4×D79C2311yescharacteristic
77#11929611C2×C414yescomplemented
78D632C2×C414yescomplemented
79#11929609C2×C414yescomplemented
80#11929607C2×C414yescomplemented
81C2×C79⋊C8C2311yescharacteristic
82C2×C79⋊C8C2311yescharacteristic
83C8×D79—22no—
84C4⋊Dic79—21no—
85C4⋊Dic79C2311yescharacteristic
86C4⋊Dic79C2311yescharacteristic
87Dic79⋊C4—21no—
88Dic79⋊C4D411yescharacteristic
89Dic79⋊C4D411yescharacteristic
90C22⋊Dic79—21no—
91(C2×D79)⋊C4—21no—
92(C2×D79)⋊C4—21no—
93(C2×D79)⋊C4—21no—
94(C2×D79)⋊C4—21no—
95(C2×D79)⋊C4—21no—
96(C2×D79)⋊C4D411yescharacteristic
97(C2×D79)⋊C4D411yescharacteristic
98C4×Dic79—21no—
99C4×Dic79—21no—
100C4×Dic79C2311yescharacteristic
101C2×Q8×C79C2311yescharacteristic
102C2×D4×C79C2311yescharacteristic
103C22×C4×C79—21no—
104SD16×C79C2×C414yescomplemented
105C2×C8×C79C2311yescharacteristic
106C2×C8×C79C2311yescharacteristic
107C4⋊C4×C79—21no—
108C4⋊C4×C79C2311yescharacteristic
109C4⋊C4×C79C2311yescharacteristic
110C22⋊C4×C79—21no—
111C42×C79—21no—
112C42×C79C2311yescharacteristic
113C23×C79—21no—
114C22×D79—21no—
115C22×D79—21no—
116C22×D79—24no—
117C22×D79—81no—
118C22×D79—81no—
119C22×D79C2×D411yescharacteristic
120Q8×C79—21no—
121Q8×C79C22×C412yes—
122D4×C79—21no—
123D4×C79C22×C412yes—
124C2×C4×C79—21no—
125C2×C4×C79—21no—
126C2×C4×C79—21no—
127C2×C4×C79—81no—
128C2×C4×C79C2×D411yescharacteristic
129C2×C4×C79C2×D411yescharacteristic
130C2×C4×C79C2411yescharacteristic
131C22⋊D79—24no—
132C2×Dic79—21no—
133C2×Dic79—21no—
134C2×Dic79—81no—
135C2×Dic79C2×D411yescharacteristic
136C2×Dic79C2×D411yescharacteristic
137C2×Dic79C2×D411yescharacteristic
138D316—24no—
139D316—21no—
140D316—21no—
141D316C22×C412yes—
142D316C22×C412yes—
143C4×D79—24no—
144C4×D79—81no—
145C4×D79—81no—
146C4×D79—81no—
147C4×D79—81no—
148C4×D79—81no—
149C4×D79C22×C412yes—
150C4×D79#4112yes—
151C8×C79—21no—
152C8×C79C22×C412yes—
153C79⋊C8—21no—
154C79⋊C8C22×C412yes—
155C22×C79—22no—
156C22×C79—41no—
157C22×C79—41no—
158C22×C79C22×D411yescharacteristic
159C2×D79—21no—
160C2×D79—21no—
161C2×D79—22no—
162C2×D79—22no—
163C2×D79—41no—
164C2×D79—41no—
165C2×D79—41no—
166C2×D79—41no—
167C2×D79—84no—
168C2×D79C4×D412yes—
169C4×C79—22no—
170C4×C79—21no—
171C4×C79—21no—
172C4×C79—41no—
173C4×C79—41no—
174C4×C79C23×C411yescharacteristic
175C4×C79C2×#4111yescharacteristic
176Dic79—21no—
177Dic79—21no—
178Dic79—41no—
179Dic79—41no—
180Dic79C4×D412yes—
181C2×C79—42no—
182C2×C79C2×C4×D411yescharacteristic
183C2×C79#57611yescharacteristic
184C2×C79#57711yescharacteristic
185D79—22no—
186D79—42no—
187D79—42no—
188#2946—791nomaximal, Sylow
189C79#294611yescharacteristic, complemented, Sylow
190C2×AGL(1,ℤ/8)—791no—
191#520—791no—
192#518—791no—
193#442—791no—
194#442—791no—
195#440—791no—
196#440—791no—
197C4×SD16—791no—
198C4×SD16D7911yescharacteristic, complemented
199C4×D8—791no—
200C4×D8—791no—
201#428—791no—
202#416—791no—
203C2×#102—791no—
204#405—791no—
205C2×#41—791no—
206C22×D4—791no—
207AGL(1,ℤ/8)—798no—
208C2×SD16—791no—
209C2×SD16C2×D7911yescharacteristic
210C2×D8—791no—
211C2×D8—791no—
212C2×M16—791no—
213C22×C8—791no—
214C4×Q8—791no—
215C4×Q8C2×D7911yescharacteristic, complemented
216C4×D4—791no—
217C4×D4—791no—
218C4×D4—791no—
219C4×D4—791no—
220C4×D4—791no—
221C4×D4—1581no—
222C4×D4—1581no—
223C4×D4—1581no—
224C4×D4—1581no—
225C4×D4C2×D7911yescharacteristic
226#117—791no—
227#117—791no—
228#117—1581no—
229C2×C4⋊C4—791no—
230C2×C4⋊C4—1581no—
231C2×C22⋊C4—1581no—
232C2×C22⋊C4—1581no—
233#107—791no—
234#107—791no—
235#106—791no—
236#106C2×D7911yescharacteristic, complemented
237#103—791no—
238#103C2×D7911yescharacteristic, complemented
239#102—791no—
240#102—791no—
241#102—791no—
242#102—791no—
243#102—791no—
244#102C2×D7911yescharacteristic
245#97—791no—
246#97—791no—
247C4×C8—791no—
248C4×C8C2×D7911yescharacteristic, complemented
249C24—1581no—
250#41—794no—
251#41—1582no—
252C2×Q8C22×D7911yescharacteristic
253C2×D4—794no—
254C2×D4—791no—
255C2×D4—791no—
256C2×D4—1581no—
257C2×D4—1582no—
258C2×D4—1581no—
259C2×D4C22×D7911yescharacteristic
260C22×C4—21no—
261C22×C4—791no—
262C22×C4—1581no—
263C22×C4—1581no—
264C22×C4—1581no—
265C22×C4—1581no—
266C22×C4—1581no—
267C22×C4—1581no—
268C22×C4—1581no—
269SD16—794no—
270SD16C4×D7914yescomplemented
271D8—794no—
272D8—794no—
273M16—794no—
274C2×C8—791no—
275C2×C8—791no—
276C2×C8—1582no—
277C2×C8C22×D7911yescharacteristic
278C2×C8C22×D7911yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—791no—
281C4⋊C4—791no—
282C4⋊C4—791no—
283C4⋊C4—791no—
284C4⋊C4—1581no—
285C4⋊C4—1581no—
286C4⋊C4C22×D7911yescharacteristic
287C4⋊C4C22×D7911yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—791no—
290C22⋊C4—791no—
291C22⋊C4—1581no—
292C22⋊C4—1581no—
293C22⋊C4—1581no—
294C22⋊C4—1581no—
295C22⋊C4—1581no—
296C22⋊C4—1581no—
297C42—21no—
298C42—791no—
299C42—1581no—
300C42—1581no—
301C42C22×D7911yescharacteristic
302C23—21no—
303C23—791no—
304C23—6321no—
305C23—6321no—
306C23—1584no—
307C23—1581no—
308C23—1581no—
309Q8—21no—
310Q8C2×C4×D7912yes—
311D4—21no—
312D4—792no—
313D4—792no—
314D4—1584no—
315D4—1584no—
316D4—1581no—
317D4—1581no—
318D4C2×C4×D7912yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—81no—
323C2×C4—791no—
324C2×C4—792no—
325C2×C4—792no—
326C2×C4—791no—
327C2×C4—791no—
328C2×C4—6321no—
329C2×C4—6321no—
330C2×C4—6321no—
331C2×C4—6321no—
332C2×C4—6321no—
333C2×C4—6321no—
334C2×C4—1584no—
335C2×C4—1581no—
336C2×C4—1581no—
337C2×C4D4×D7911yescharacteristic
338C2×C4D4×D7911yescharacteristic
339C2×C4C23×D7911yescharacteristic
340C8—21no—
341C8—792no—
342C8—1581no—
343C8C2×C4×D7912yes—
344C22—22no—
345C22—41no—
346C22—41no—
347C22—3161no—
348C22—3161no—
349C22—3161no—
350C22—3161no—
351C22—792no—
352C22—6324no—
353C22—1582no—
354C22—1582no—
355C22—1581no—
356C22—1581no—
357C22C2×D4×D7911yescharacteristic
358C4—22no—
359C4—21no—
360C4—21no—
361C4—41no—
362C4—41no—
363C4—3161no—
364C4—3161no—
365C4—792no—
366C4—1581no—
367C4—1581no—
368C4C22×C4×D7911yescharacteristic
369C4#41×D7911yescharacteristic
370C2—42no—
371C2—3162no—
372C2—3162no—
373C2—1582no—
374C2C4×D4×D7911yescharacteristic
375C2#1909936511yescharacteristic
376C2#1909936911yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutatorC4×C79C23×C4
FrattiniC2×C4C23×D79
FittingC4×SD16×C79C2
socleC22×C79C22×D4
prime radicalC2×#14579188C2
cosocleC2×C4×C79C24
hypercenterC4×SD16D79
hypocenterC79#2946
LCSG ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. #19099045C2semidirect
3. #19099035C2semidirect
4. #19098674C2semidirect
5. #19098673C2semidirect
6. #19098664C2semidirect
7. #19098661C2semidirect
8. #19098648C2semidirect
9. C4×D632C2semidirect
10. #19098643C2semidirect
11. #19098602C2semidirect
12. #19098558C2semidirect
13. #102×D79C2semidirect
14. #19098517C2semidirect
15. C4×SD16×C79C2semidirect
18. #14579188C4semidirect
24. Q8×Dic79C22semidirect
27. C4×D316C22semidirect
31. #14579123C22semidirect
41. #14579095C22semidirect
42. #14579094C22semidirect
43. #14579092C22semidirect
44. #14579085C22semidirect
46. #14579083C22semidirect
49. #14579081C22semidirect
50. #14579072C22semidirect
51. #14579071C22semidirect
52. C8×Dic79C22semidirect
54. C4×Q8×C79C22semidirect
56. #106×C79C22semidirect
57. #103×C79C22semidirect
59. C4×C8×C79C22semidirect
62. #11929625C2×C4semidirect
68. D4×D79C2×C4semidirect
77. #11929611C2×C4semidirect
78. D632C2×C4semidirect
79. #11929609C2×C4semidirect
80. #11929607C2×C4semidirect
104. SD16×C79C2×C4semidirect
189. C79#2946semidirect
198. C4×SD16D79semidirect
215. C4×Q8C2×D79semidirect
236. #106C2×D79semidirect
238. #103C2×D79semidirect
248. C4×C8C2×D79semidirect
270. SD16C4×D79semidirect