Finite Group Databasebeta

← #482×D107 #28346341

Subgroups — #482×D107 #28346341

Order 13696.

468 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#121×D107C211yesmaximal, characteristic
2#117×D107C211yesmaximal, characteristic, complemented
3#20292954C211yesmaximal, characteristic, complemented
4#20292953C211yesmaximal, characteristic, complemented
5#20292952C211yesmaximal, characteristic, complemented
6#20292951C211yesmaximal, characteristic, complemented
7#20292950C211yesmaximal, characteristic, complemented
8#20292949C211yesmaximal, characteristic, complemented
9#20292948C211yesmaximal, characteristic, complemented
10#107×D107C211yesmaximal, characteristic, complemented
11#106×D107C211yesmaximal, characteristic, complemented
12#102×D107C211yesmaximal, characteristic, complemented
13#102×D107C211yesmaximal, characteristic, complemented
14C22⋊C8×D107C211yesmaximal, characteristic, complemented
15#482×C107C211yesmaximal, characteristic, complemented
16C2×D4×D107—21no—
17C2×D4×D107C2211yescharacteristic
18C22×C4×D107C2211yescharacteristic
19C2×C8×D107C2211yescharacteristic
20C2×C8×D107C2211yescharacteristic
21#16812084C2211yescharacteristic
22#16812083C2211yescharacteristic
23#16812082—21no—
24#16812081—21no—
25#16812080C2211yescharacteristic
26#16812068C2211yescharacteristic, complemented
27#16812067C2211yescharacteristic, complemented
28#16812067C2211yescharacteristic, complemented
29#16812066—21no—
30#16812065—21no—
31C4⋊C4×D107C2211yescharacteristic
32C4⋊C4×D107C2211yescharacteristic
33C4⋊C4×D107C2211yescharacteristic
34C22⋊C4×D107—21no—
35C22⋊C4×D107—21no—
36C42×D107—21no—
37#16812043C2211yescharacteristic, complemented
38#16812042C2211yescharacteristic, complemented
39#16812042C2211yescharacteristic, complemented
40#16812041C2211yescharacteristic, complemented
41#16812040C2211yescharacteristic, complemented
42#16812040C2211yescharacteristic, complemented
43#16812031C2211yescharacteristic, complemented
44#16812031C2211yescharacteristic, complemented
45#16812030C2211yescharacteristic, complemented
46#16812030C2211yescharacteristic, complemented
47#16812029C2211yescharacteristic, complemented
48#16812029C2211yescharacteristic, complemented
49C22⋊(C107⋊C8)C2211yescharacteristic, complemented
50(C2×D107)⋊C8C2211yescharacteristic, complemented
51(C2×D107)⋊C8C2211yescharacteristic, complemented
52#121×C107C2211yescharacteristic
53#117×C107C2211yescharacteristic, complemented
54#107×C107C2211yescharacteristic, complemented
55#106×C107C2211yescharacteristic, complemented
56#102×C107C2211yescharacteristic, complemented
57#102×C107C2211yescharacteristic, complemented
58C22⋊C8×C107C2211yescharacteristic, complemented
59C23×D107—21no—
60C23×D107D411yescharacteristic
61C2×D428—21no—
62C2×D428C2311yescharacteristic
63C2×C22⋊D107—21no—
64C2×C22⋊D107—21no—
65C2×C22⋊D107—21no—
66D4×D107—22no—
67D4×D107—22no—
68D4×D107—44no—
69C22×Dic107D411yescharacteristic
70C2×C4×D107—22no—
71C2×C4×D107—22no—
72C2×C4×D107—21no—
73C2×C4×D107—21no—
74C2×C4×D107—21no—
75C2×C4×D107D411yescharacteristic
76C2×C4×D107D411yescharacteristic
77C2×C4×D107C2311yescharacteristic
78C2×C4×D107C2311yescharacteristic
79C2×C107⋊C8C2311yescharacteristic
80C2×C107⋊C8C2311yescharacteristic
81C8×D107—22no—
82C8×D107—22no—
83C4⋊Dic107C2311yescharacteristic
84C4⋊Dic107C2311yescharacteristic
85C4⋊Dic107C2311yescharacteristic
86Dic107⋊C4—21no—
87Dic107⋊C4—21no—
88Dic107⋊C4—21no—
89C22⋊Dic107—21no—
90C22⋊Dic107—21no—
91(C2×D107)⋊C4—21no—
92(C2×D107)⋊C4—21no—
93(C2×D107)⋊C4—21no—
94(C2×D107)⋊C4—21no—
95C4×Dic107—21no—
96C4×Dic107—21no—
97C4×Dic107—21no—
98C2×D4×C107—21no—
99C2×D4×C107C2311yescharacteristic
100C22×C4×C107C2311yescharacteristic
101C2×C8×C107C2311yescharacteristic
102C2×C8×C107C2311yescharacteristic
103C4⋊C4×C107C2311yescharacteristic
104C4⋊C4×C107C2311yescharacteristic
105C4⋊C4×C107C2311yescharacteristic
106C22⋊C4×C107—21no—
107C22⋊C4×C107—21no—
108C42×C107—21no—
109C23×C107—21no—
110C23×C107C2×D411yescharacteristic
111C22×D107—22no—
112C22×D107—22no—
113C22×D107—22no—
114C22×D107—21no—
115C22×D107—42no—
116C22×D107—42no—
117C22×D107—42no—
118C22×D107C2×D411yescharacteristic
119C22×D107C2×D411yescharacteristic
120D4×C107—21no—
121D4×C107—21no—
122D4×C107—42no—
123C2×C4×C107—21no—
124C2×C4×C107—21no—
125C2×C4×C107—21no—
126C2×C4×C107—21no—
127C2×C4×C107—21no—
128C2×C4×C107C2×D411yescharacteristic
129C2×C4×C107C2411yescharacteristic
130C22⋊D107—42no—
131C22⋊D107—42no—
132C22⋊D107—42no—
133C2×Dic107—22no—
134C2×Dic107—21no—
135C2×Dic107—21no—
136C2×Dic107—21no—
137C2×Dic107C2×D411yescharacteristic
138C2×Dic107C2×D411yescharacteristic
139D428—21no—
140D428—21no—
141D428—42no—
142C4×D107—22no—
143C4×D107—21no—
144C4×D107—21no—
145C4×D107—22no—
146C4×D107—42no—
147C4×D107—42no—
148C4×D107—42no—
149C4×D107#4112yes—
150C4×D107#4112yes—
151C8×C107—21no—
152C8×C107—21no—
153C107⋊C8—21no—
154C107⋊C8—21no—
155C22×C107—21no—
156C22×C107—21no—
157C22×C107—21no—
158C22×C107—41no—
159C22×C107—41no—
160C22×C107—41no—
161C22×C107C22×D411yescharacteristic
162C2×D107—21no—
163C2×D107—21no—
164C2×D107—21no—
165C2×D107—44no—
166C2×D107—41no—
167C2×D107—41no—
168C2×D107—41no—
169C2×D107—84no—
170C2×D107#12312yes—
171C2×D107#13512yes—
172C2×D107AGL(1,ℤ/8)12yes—
173C4×C107—21no—
174C4×C107—41no—
175C4×C107—41no—
176C4×C107—41no—
177C4×C107C2×#4111yescharacteristic
178C4×C107C2×#4111yescharacteristic
179Dic107—21no—
180Dic107—41no—
181Dic107—41no—
182Dic107—41no—
183Dic107#12312yes—
184C2×C107—41no—
185C2×C107—81no—
186C2×C107C2×#12311yescharacteristic
187C2×C107C2×#13511yescharacteristic
188C2×C107C2×AGL(1,ℤ/8)11yescharacteristic
189D107—41no—
190D107—81no—
191D107#48214yesdirect product factor
192C2×#482—1071nomaximal, Sylow
193C107C2×#48211yescharacteristic, complemented, Sylow
194C2×#121—1071no—
195C2×#117—1071no—
196#482—1071no—
197#482—1071no—
198#482—1071no—
199#482—1071no—
200#482—1071no—
201#482—1071no—
202#482—1071no—
203#482D10711yescharacteristic, direct product factor
204C2×#107—1071no—
205C2×#106—1071no—
206C2×#102—1071no—
207C2×#102—1071no—
208C2×C22⋊C8—1071no—
209C22×D4—1071no—
210C22×D4—2141no—
211C23×C4—1071no—
212C22×C8—1071no—
213C22×C8—1071no—
214#121—1071no—
215#121—1071no—
216#121—1071no—
217#121—2141no—
218#121—2141no—
219#121C2×D10711yescharacteristic
220#117—1071no—
221#117—1071no—
222#117—1071no—
223#117—2141no—
224#117—2141no—
225#117C2×D10711yescharacteristic, complemented
226C2×C4⋊C4—1071no—
227C2×C4⋊C4—1071no—
228C2×C4⋊C4—1071no—
229C2×C22⋊C4—2141no—
230C2×C22⋊C4—2141no—
231C2×C42—2141no—
232#107—1071no—
233#107—1071no—
234#107—1071no—
235#107C2×D10711yescharacteristic, complemented
236#106—1071no—
237#106—1071no—
238#106—1071no—
239#106C2×D10711yescharacteristic, complemented
240#102—1071no—
241#102—1071no—
242#102—1071no—
243#102—1071no—
244#102—1071no—
245#102—1071no—
246#102C2×D10711yescharacteristic, complemented
247#102C2×D10711yescharacteristic, complemented
248C22⋊C8—1071no—
249C22⋊C8—1071no—
250C22⋊C8—1071no—
251C22⋊C8C2×D10711yescharacteristic, complemented
252C24—1071no—
253C24—2141no—
254C2×D4—21no—
255C2×D4—1071no—
256C2×D4—4284no—
257C2×D4—2141no—
258C2×D4—2142no—
259C2×D4—2142no—
260C2×D4—2141no—
261C2×D4—2141no—
262C2×D4—2141no—
263C2×D4C22×D10711yescharacteristic
264C22×C4—1071no—
265C22×C4—1071no—
266C22×C4—1071no—
267C22×C4—1071no—
268C22×C4—1071no—
269C22×C4—2142no—
270C22×C4—2142no—
271C22×C4—2141no—
272C22×C4—2141no—
273C22×C4—2141no—
274C22×C4C22×D10711yescharacteristic
275C2×C8—1071no—
276C2×C8—1071no—
277C2×C8—2142no—
278C2×C8—2142no—
279C2×C8C22×D10711yescharacteristic
280C2×C8C22×D10711yescharacteristic
281C4⋊C4—1071no—
282C4⋊C4—1071no—
283C4⋊C4—1071no—
284C4⋊C4—2141no—
285C4⋊C4—2141no—
286C4⋊C4—2141no—
287C4⋊C4C22×D10711yescharacteristic
288C4⋊C4C22×D10711yescharacteristic
289C4⋊C4C22×D10711yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—2141no—
293C22⋊C4—2141no—
294C22⋊C4—2141no—
295C22⋊C4—2141no—
296C22⋊C4—2141no—
297C22⋊C4—2141no—
298C42—21no—
299C42—2141no—
300C42—2141no—
301C42—2141no—
302C23—21no—
303C23—1071no—
304C23—1071no—
305C23—4282no—
306C23—4282no—
307C23—4282no—
308C23—2142no—
309C23—2142no—
310C23—2142no—
311C23—2141no—
312C23D4×D10711yescharacteristic
313D4—21no—
314D4—21no—
315D4—42no—
316D4—4282no—
317D4—4282no—
318D4—4282no—
319D4—4282no—
320D4—2141no—
321D4—2141no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—1071no—
328C2×C4—1072no—
329C2×C4—1072no—
330C2×C4—1071no—
331C2×C4—4282no—
332C2×C4—4282no—
333C2×C4—4282no—
334C2×C4—2142no—
335C2×C4—2142no—
336C2×C4—2142no—
337C2×C4—2141no—
338C2×C4—2141no—
339C2×C4—2141no—
340C2×C4—2141no—
341C2×C4—2141no—
342C2×C4D4×D10711yescharacteristic
343C2×C4C23×D10711yescharacteristic
344C8—21no—
345C8—21no—
346C8—2141no—
347C8—2141no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—8564no—
355C22—1072no—
356C22—1072no—
357C22—1072no—
358C22—4284no—
359C22—4281no—
360C22—4281no—
361C22—4281no—
362C22—2141no—
363C22—2141no—
364C22—2141no—
365C22C2×D4×D10711yescharacteristic
366C4—21no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—1072no—
371C4—4281no—
372C4—4281no—
373C4—4281no—
374C4—2141no—
375C4#41×D10711yescharacteristic
376C4#41×D10711yescharacteristic
377C2—41no—
378C2—81no—
379C2—8561no—
380C2—1074no—
381C2—4281no—
382C2#123×D10711yescharacteristic
383C2#135×D10711yescharacteristic
384C2AGL(1,ℤ/8)×D10711yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#482×C107C2
socleC22×C107C22×D4
prime radical#121×D107C2
hypercenter#482D107
hypocenterC107C2×#482
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #117×D107C2semidirect
3. #20292954C2semidirect
4. #20292953C2semidirect
5. #20292952C2semidirect
6. #20292951C2semidirect
7. #20292950C2semidirect
8. #20292949C2semidirect
9. #20292948C2semidirect
10. #107×D107C2semidirect
11. #106×D107C2semidirect
12. #102×D107C2semidirect
13. #102×D107C2semidirect
14. C22⋊C8×D107C2semidirect
15. #482×C107C2semidirect
26. #16812068C22semidirect
27. #16812067C22semidirect
28. #16812067C22semidirect
37. #16812043C22semidirect
38. #16812042C22semidirect
39. #16812042C22semidirect
40. #16812041C22semidirect
41. #16812040C22semidirect
42. #16812040C22semidirect
43. #16812031C22semidirect
44. #16812031C22semidirect
45. #16812030C22semidirect
46. #16812030C22semidirect
47. #16812029C22semidirect
48. #16812029C22semidirect
49. C22⋊(C107⋊C8)C22semidirect
50. (C2×D107)⋊C8C22semidirect
51. (C2×D107)⋊C8C22semidirect
53. #117×C107C22semidirect
54. #107×C107C22semidirect
55. #106×C107C22semidirect
56. #102×C107C22semidirect
57. #102×C107C22semidirect
58. C22⋊C8×C107C22semidirect
191. D107#482direct (N × H)
193. C107C2×#482semidirect
203. #482D107direct (N × H)
225. #117C2×D107semidirect
235. #107C2×D107semidirect
239. #106C2×D107semidirect
246. #102C2×D107semidirect
247. #102C2×D107semidirect
251. C22⋊C8C2×D107semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#121×D1072
#117×D1072
#202929542
#202929532
#202929522
#202929512
#202929502
#202929492
#202929482
#107×D1072
#106×D1072
#102×D1072
C22⋊C8×D1072
#482×C1072
C2×#482107