Finite Group Databasebeta

← #23772225

Subgroups — #23772225

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×#14579185C211yesmaximal, characteristic
2#19099042C211yesmaximal, characteristic, complemented
3#19099035C211yesmaximal, characteristic, complemented
4#19098675C211yesmaximal, characteristic, complemented
5#19098673C211yesmaximal, characteristic, complemented
6#19098663C211yesmaximal, characteristic, complemented
7#19098662C211yesmaximal, characteristic, complemented
8#19098654C211yesmaximal, characteristic, complemented
9C4×#11929613C211yesmaximal, characteristic, complemented
10#19098643C211yesmaximal, characteristic, complemented
11#19098604C211yesmaximal, characteristic, complemented
12#19098556C211yesmaximal, characteristic, complemented
13#102×D79C211yesmaximal, characteristic, complemented
14#19098517C211yesmaximal, characteristic, complemented
15C4×D8×C79C211yesmaximal, characteristic, complemented
16C2×#11929623C2211yescharacteristic
17C2×D4×D79C2211yescharacteristic
18#14579185C418yescomplemented
19C2×#11929613C2211yescharacteristic
20C2×#11929612C2211yescharacteristic
21C2×#11929609C2211yescharacteristic
22C2×#11929607C2211yescharacteristic
23C2×C8×D79C2211yescharacteristic
24C4×Dic158C2211yescharacteristic, complemented
25#14579126C2211yescharacteristic, complemented
26C4×D316C2211yescharacteristic
27D4×Dic79C2211yescharacteristic
28D4×Dic79C2211yescharacteristic, complemented
29#14579123C2211yescharacteristic
30C4×C22⋊D79—21no—
31C4×C22⋊D79—21no—
32(C22⋊D79)⋊C4—21no—
33(C22⋊D79)⋊C4—21no—
34#14579119C2211yescharacteristic
35#14579118C2211yescharacteristic
36#14579117—21no—
37C2×Dic79⋊C4—21no—
38C4⋊C4×D79C2211yescharacteristic
39C2×(C2×D79)⋊C4—21no—
40C22⋊C4×D79—21no—
41#14579094C2211yescharacteristic, complemented
42#14579093C2211yescharacteristic, complemented
43#14579092C2211yescharacteristic, complemented
44#14579086C2211yescharacteristic, complemented
45#14579084C2211yescharacteristic, complemented
46#14579083C2211yescharacteristic
47#14579082C2211yescharacteristic
48#14579082C2211yescharacteristic, complemented
49#14579081C2211yescharacteristic
50#14579072C2211yescharacteristic, complemented
51#14579071C2211yescharacteristic, complemented
52C8×Dic79C2211yescharacteristic, complemented
53C2×D8×C79C2211yescharacteristic
54C4×D4×C79C2211yescharacteristic
55C4×D4×C79C2211yescharacteristic, complemented
56#107×C79C2211yescharacteristic, complemented
57#102×C79C2211yescharacteristic
58#102×C79C2211yescharacteristic, complemented
59C4×C8×C79C2211yescharacteristic, complemented
60C23×D79—21no—
61#11929623—22no—
62#11929623C2×C414yescomplemented
63C2×Dic158C2311yescharacteristic
64C2×D316C2311yescharacteristic
65C2×C22⋊D79—21no—
66C2×C22⋊D79—21no—
67D4×D79—22no—
68D4×D79C2×C414yescomplemented
69C22×Dic79—21no—
70C22×Dic79—21no—
71C22×Dic79—21no—
72C2×C4×D79—21no—
73C2×C4×D79—21no—
74C2×C4×D79—21no—
75C2×C4×D79C2311yescharacteristic
76#11929613C2×C414yescomplemented
77#11929612C2×C414yescomplemented
78#11929609C2×C414yescomplemented
79#11929607C2×C414yescomplemented
80C2×C79⋊C8C2311yescharacteristic
81C2×C79⋊C8C2311yescharacteristic
82C8×D79—22no—
83C4⋊Dic79C2311yescharacteristic
84C4⋊Dic79C2311yescharacteristic
85Dic79⋊C4—21no—
86Dic79⋊C4—21no—
87Dic79⋊C4—21no—
88Dic79⋊C4D411yescharacteristic
89Dic79⋊C4D411yescharacteristic
90C22⋊Dic79—21no—
91C22⋊Dic79—21no—
92(C2×D79)⋊C4—21no—
93(C2×D79)⋊C4—21no—
94(C2×D79)⋊C4—21no—
95(C2×D79)⋊C4D411yescharacteristic
96(C2×D79)⋊C4D411yescharacteristic
97C4×Dic79—21no—
98C4×Dic79—21no—
99C4×Dic79—21no—
100C4×Dic79C2311yescharacteristic
101C2×D4×C79C2311yescharacteristic
102C2×D4×C79C2311yescharacteristic
103C22×C4×C79—21no—
104C22×C4×C79—21no—
105D8×C79C2×C414yescomplemented
106C2×C8×C79C2311yescharacteristic
107C2×C8×C79C2311yescharacteristic
108C4⋊C4×C79C2311yescharacteristic
109C4⋊C4×C79C2311yescharacteristic
110C22⋊C4×C79—21no—
111C22⋊C4×C79—21no—
112C42×C79C2311yescharacteristic
113C23×C79—21no—
114C23×C79—21no—
115C22×D79—21no—
116C22×D79—24no—
117C22×D79—81no—
118C22×D79—81no—
119C22×D79C2×D411yescharacteristic
120D4×C79—21no—
121D4×C79—21no—
122D4×C79C22×C412yes—
123D4×C79C22×C412yes—
124C2×C4×C79—21no—
125C2×C4×C79—21no—
126C2×C4×C79—81no—
127C2×C4×C79—81no—
128C2×C4×C79C2×D411yescharacteristic
129C2×C4×C79C2×D411yescharacteristic
130C2×C4×C79C2411yescharacteristic
131C22⋊D79—24no—
132C22⋊D79—24no—
133C2×Dic79—21no—
134C2×Dic79—24no—
135C2×Dic79—21no—
136C2×Dic79—21no—
137C2×Dic79—81no—
138C2×Dic79—81no—
139C2×Dic79C2×D411yescharacteristic
140C2×Dic79C2×D411yescharacteristic
141C2×Dic79C2×D411yescharacteristic
142D316—21no—
143D316C22×C412yes—
144C4×D79—81no—
145C4×D79—81no—
146C4×D79—81no—
147C4×D79C22×C412yes—
148C4×D79#4112yes—
149Dic158—21no—
150Dic158C22×C412yes—
151C8×C79—21no—
152C8×C79C22×C412yes—
153C79⋊C8—21no—
154C79⋊C8C22×C412yes—
155C22×C79—22no—
156C22×C79—22no—
157C22×C79—41no—
158C22×C79—41no—
159C22×C79—41no—
160C22×C79—41no—
161C22×C79C22×D411yescharacteristic
162C2×D79—21no—
163C2×D79—21no—
164C2×D79—22no—
165C2×D79—41no—
166C2×D79—41no—
167C2×D79—84no—
168C2×D79C4×D412yes—
169C4×C79—21no—
170C4×C79—21no—
171C4×C79—41no—
172C4×C79—41no—
173C4×C79C23×C411yescharacteristic
174C4×C79C2×#4111yescharacteristic
175Dic79—22no—
176Dic79—21no—
177Dic79—21no—
178Dic79—41no—
179Dic79—41no—
180Dic79C4×D412yes—
181C2×C79—42no—
182C2×C79—42no—
183C2×C79C2×C4×D411yescharacteristic
184C2×C79#57611yescharacteristic
185C2×C79#57711yescharacteristic
186D79—22no—
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×SD16—791no—
199C4×D8—791no—
200C4×D8D7911yescharacteristic, complemented
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×SD16—791no—
210C2×D8—791no—
211C2×D8C2×D7911yescharacteristic
212C2×M16—791no—
213C22×C8—791no—
214C4×Q8—791no—
215C4×Q8—791no—
216C4×D4—791no—
217C4×D4—791no—
218C4×D4—791no—
219C4×D4—791no—
220C4×D4—1581no—
221C4×D4—1581no—
222C4×D4—1581no—
223C4×D4—1581no—
224C4×D4C2×D7911yescharacteristic
225C4×D4C2×D7911yescharacteristic, complemented
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#107C2×D7911yescharacteristic, complemented
235#106—791no—
236#106—791no—
237#103—791no—
238#103—791no—
239#102—791no—
240#102—791no—
241#102—791no—
242#102—791no—
243#102C2×D7911yescharacteristic
244#102C2×D7911yescharacteristic, complemented
245#97—791no—
246#97—791no—
247C4×C8—791no—
248C4×C8C2×D7911yescharacteristic, complemented
249C24—1581no—
250#41—794no—
251#41—1582no—
252C2×Q8—791no—
253C2×D4—794no—
254C2×D4—791no—
255C2×D4—1582no—
256C2×D4—1581no—
257C2×D4—1581no—
258C2×D4C22×D7911yescharacteristic
259C2×D4C22×D7911yescharacteristic
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—791no—
263C22×C4—1581no—
264C22×C4—1581no—
265C22×C4—1581no—
266C22×C4—1581no—
267C22×C4—1581no—
268C22×C4—1581no—
269SD16—794no—
270SD16—794no—
271D8—794no—
272D8C4×D7914yescomplemented
273M16—794no—
274C2×C8—791no—
275C2×C8—791no—
276C2×C8—1582no—
277C2×C8C22×D7911yescharacteristic
278C2×C8C22×D7911yescharacteristic
279C4⋊C4—791no—
280C4⋊C4—791no—
281C4⋊C4—791no—
282C4⋊C4—791no—
283C4⋊C4—1581no—
284C4⋊C4—1581no—
285C4⋊C4—1581no—
286C4⋊C4C22×D7911yescharacteristic
287C4⋊C4C22×D7911yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—791no—
291C22⋊C4—791no—
292C22⋊C4—1581no—
293C22⋊C4—1581no—
294C22⋊C4—1581no—
295C22⋊C4—1581no—
296C22⋊C4—1581no—
297C42—791no—
298C42—1581no—
299C42—1581no—
300C42—1581no—
301C42C22×D7911yescharacteristic
302C23—21no—
303C23—21no—
304C23—791no—
305C23—6321no—
306C23—6321no—
307C23—1584no—
308C23—1581no—
309Q8—792no—
310Q8—1581no—
311D4—21no—
312D4—21no—
313D4—792no—
314D4—1584no—
315D4—1584no—
316D4—1581no—
317D4C2×C4×D7912yes—
318D4C2×C4×D7912yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—81no—
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—1581no—
334C2×C4—1581no—
335C2×C4—1584no—
336C2×C4—1581no—
337C2×C4D4×D7911yescharacteristic
338C2×C4D4×D7911yescharacteristic
339C2×C4C23×D7911yescharacteristic
340C8—21no—
341C8—792no—
342C8—1581no—
343C8C2×C4×D7912yes—
344C22—22no—
345C22—22no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—3161no—
351C22—3161no—
352C22—792no—
353C22—6324no—
354C22—1582no—
355C22—1581no—
356C22—1581no—
357C22C2×D4×D7911yescharacteristic
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—3161no—
363C4—3161no—
364C4—792no—
365C4—1582no—
366C4—1581no—
367C4—1581no—
368C4C22×C4×D7911yescharacteristic
369C4#41×D7911yescharacteristic
370C2—42no—
371C2—42no—
372C2—3162no—
373C2—1582no—
374C2C4×D4×D7911yescharacteristic
375C2#1909936411yescharacteristic
376C2#1909937011yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutatorC4×C79C23×C4
FrattiniC2×C4C23×D79
FittingC4×D8×C79C2
socleC22×C79C22×D4
prime radicalC2×#14579185C2
cosocleC2×C4×C79C24
hypercenterC4×D8D79
hypocenterC79#2946
LCSG ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
2. #19099042C2semidirect
3. #19099035C2semidirect
4. #19098675C2semidirect
5. #19098673C2semidirect
6. #19098663C2semidirect
7. #19098662C2semidirect
8. #19098654C2semidirect
9. C4×#11929613C2semidirect
10. #19098643C2semidirect
11. #19098604C2semidirect
12. #19098556C2semidirect
13. #102×D79C2semidirect
14. #19098517C2semidirect
15. C4×D8×C79C2semidirect
18. #14579185C4semidirect
24. C4×Dic158C22semidirect
25. #14579126C22semidirect
28. D4×Dic79C22semidirect
41. #14579094C22semidirect
42. #14579093C22semidirect
43. #14579092C22semidirect
44. #14579086C22semidirect
45. #14579084C22semidirect
48. #14579082C22semidirect
50. #14579072C22semidirect
51. #14579071C22semidirect
52. C8×Dic79C22semidirect
55. C4×D4×C79C22semidirect
56. #107×C79C22semidirect
58. #102×C79C22semidirect
59. C4×C8×C79C22semidirect
62. #11929623C2×C4semidirect
68. D4×D79C2×C4semidirect
76. #11929613C2×C4semidirect
77. #11929612C2×C4semidirect
78. #11929609C2×C4semidirect
79. #11929607C2×C4semidirect
105. D8×C79C2×C4semidirect
189. C79#2946semidirect
200. C4×D8D79semidirect
225. C4×D4C2×D79semidirect
234. #107C2×D79semidirect
244. #102C2×D79semidirect
248. C4×C8C2×D79semidirect
272. D8C4×D79semidirect