Finite Group Databasebeta

← #464×D107 #28345901

Subgroups — #464×D107 #28345901

Order 13696.

500 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q16×D107C211yesmaximal, characteristic, complemented
2C2×SD16×D107C211yesmaximal, characteristic
3#124×D107C211yesmaximal, characteristic
4C4×Q8×D107C211yesmaximal, characteristic, complemented
5#20292852C211yesmaximal, characteristic, complemented
6#20292851C211yesmaximal, characteristic, complemented
7#20292850C211yesmaximal, characteristic, complemented
8#20292849C211yesmaximal, characteristic, complemented
9#20292848C211yesmaximal, characteristic, complemented
10#20292847C211yesmaximal, characteristic, complemented
11#20292846C211yesmaximal, characteristic, complemented
12C4⋊C8×D107C211yesmaximal, characteristic, complemented
13#103×D107C211yesmaximal, characteristic, complemented
14#102×D107C211yesmaximal, characteristic
15#464×C107C211yesmaximal, characteristic, complemented
16C2×Q8×D107C2211yescharacteristic
17C2×Q8×D107C2211yescharacteristic
18C2×D4×D107C2211yescharacteristic
19C2×Dic428C2211yescharacteristic, complemented
20C2×#13133808C2211yescharacteristic, complemented
21C2×#13133808C2211yescharacteristic, complemented
22Q16×D107—24no—
23C2×#13133807C2211yescharacteristic
24C2×#13133806C2211yescharacteristic
25C2×#13133805C2211yescharacteristic
26SD16×D107—24no—
27C2×C8×D107C2211yescharacteristic
28C2×C8×D107C2211yescharacteristic
29#16812098C2211yescharacteristic
30#16812097C2211yescharacteristic
31#16812096C2211yescharacteristic
32#16812095—21no—
33#16812095—21no—
34Q8×Dic107C2211yescharacteristic, complemented
35C4×Dic214—21no—
36C4×Dic214C2211yescharacteristic, complemented
37#16812074—21no—
38#16812074C2211yescharacteristic, complemented
39C4⋊C4×D107—21no—
40C4⋊C4×D107C2211yescharacteristic
41C22⋊C4×D107—21no—
42C22⋊C4×D107—21no—
43C42×D107—21no—
44C42×D107C2211yescharacteristic
45C4⋊(C107⋊C8)C2211yescharacteristic, complemented
46Dic107⋊C8C2211yescharacteristic, complemented
47Dic107⋊C8C2211yescharacteristic, complemented
48#16812034C2211yescharacteristic, complemented
49#16812033C2211yescharacteristic, complemented
50#16812032C2211yescharacteristic, complemented
51#16812031C2211yescharacteristic
52#16812030C2211yescharacteristic
53#16812029C2211yescharacteristic
54C2×Q16×C107C2211yescharacteristic, complemented
55C2×SD16×C107C2211yescharacteristic
56#124×C107C2211yescharacteristic
57C4×Q8×C107C2211yescharacteristic, complemented
58C4⋊C8×C107C2211yescharacteristic, complemented
59#103×C107C2211yescharacteristic, complemented
60#102×C107C2211yescharacteristic
61C23×D107—21no—
62C2×Dic214—21no—
63C2×Dic214—21no—
64C2×Dic214C2311yescharacteristic
65C2×Dic214C2311yescharacteristic
66Q8×D107—22no—
67Q8×D107—22no—
68Q8×D107—22no—
69Q8×D107D414yes—
70C2×D428C2311yescharacteristic
71C2×C22⋊D107—21no—
72D4×D107—22no—
73D4×D107—22no—
74C2×C4×D107—21no—
75C2×C4×D107—21no—
76C2×C4×D107—21no—
77C2×C4×D107D411yescharacteristic
78C2×C4×D107D411yescharacteristic
79C2×C4×D107C2311yescharacteristic
80Dic428—22no—
81#13133808—22no—
82#13133808—22no—
83#13133807—22no—
84#13133806—22no—
85#13133805—22no—
86C2×C107⋊C8C2311yescharacteristic
87C2×C107⋊C8C2311yescharacteristic
88C8×D107—22no—
89C8×D107—22no—
90C4⋊Dic107—21no—
91C4⋊Dic107C2311yescharacteristic
92Dic107⋊C4—21no—
93Dic107⋊C4—21no—
94Dic107⋊C4—21no—
95C22⋊Dic107—21no—
96C22⋊Dic107—21no—
97(C2×D107)⋊C4—21no—
98(C2×D107)⋊C4—21no—
99(C2×D107)⋊C4—21no—
100(C2×D107)⋊C4—21no—
101C4×Dic107—21no—
102C4×Dic107—21no—
103C4×Dic107—21no—
104C4×Dic107D411yescharacteristic
105C4×Dic107D411yescharacteristic
106C4×Dic107C2311yescharacteristic
107C2×Q8×C107C2311yescharacteristic
108C2×Q8×C107C2311yescharacteristic
109C2×D4×C107C2311yescharacteristic
110Q16×C107—22no—
111SD16×C107—22no—
112C2×C8×C107C2311yescharacteristic
113C2×C8×C107C2311yescharacteristic
114C4⋊C4×C107—21no—
115C4⋊C4×C107C2311yescharacteristic
116C22⋊C4×C107—21no—
117C22⋊C4×C107—21no—
118C42×C107—21no—
119C42×C107C2311yescharacteristic
120C23×C107—21no—
121C22×D107—21no—
122C22×D107—42no—
123C22×D107—42no—
124C22×D107—42no—
125C22×D107C2×D411yescharacteristic
126Q8×C107—21no—
127Q8×C107—21no—
128Q8×C107—21no—
129Q8×C107C2×D412yes—
130D4×C107—21no—
131D4×C107—21no—
132C2×C4×C107—21no—
133C2×C4×C107—21no—
134C2×C4×C107—21no—
135C2×C4×C107C2×D411yescharacteristic
136C2×C4×C107C2×D411yescharacteristic
137C2×C4×C107C2411yescharacteristic
138C22⋊D107—42no—
139C2×Dic107—21no—
140C2×Dic107—21no—
141C2×Dic107—21no—
142C2×Dic107C2×D411yescharacteristic
143C2×Dic107C2×D411yescharacteristic
144C2×Dic107C2×D411yescharacteristic
145D428—21no—
146D428—21no—
147C4×D107—24no—
148C4×D107—22no—
149C4×D107—22no—
150C4×D107—42no—
151C4×D107—42no—
152C4×D107C2×D412yes—
153C4×D107#4112yes—
154Dic214—21no—
155Dic214—24no—
156Dic214—21no—
157Dic214—21no—
158Dic214—42no—
159Dic214C2×D412yes—
160C8×C107—21no—
161C8×C107—21no—
162C107⋊C8—21no—
163C107⋊C8—21no—
164C22×C107—41no—
165C22×C107—41no—
166C22×C107—41no—
167C22×C107C22×D411yescharacteristic
168C2×D107—41no—
169C2×D107—41no—
170C2×D107—41no—
171C2×D107—84no—
172C2×D107#12112yes—
173C2×D107#13512yes—
174C2×D107#13712yes—
175C4×C107—22no—
176C4×C107—21no—
177C4×C107—21no—
178C4×C107—41no—
179C4×C107—41no—
180C4×C107C22×D411yescharacteristic
181C4×C107C2×#4111yescharacteristic
182Dic107—22no—
183Dic107—21no—
184Dic107—21no—
185Dic107—41no—
186Dic107—41no—
187Dic107#12112yes—
188C2×C107—81no—
189C2×C107C2×#12111yescharacteristic
190C2×C107C2×#13511yescharacteristic
191C2×C107C2×#13711yescharacteristic
192D107—81no—
193D107#46414yesdirect product factor
194C2×#464—1071nomaximal, Sylow
195C107C2×#46411yescharacteristic, complemented, Sylow
196C22×Q16—1071no—
197C22×SD16—1071no—
198C2×#124—1071no—
199C2×C4×Q8—1071no—
200#464—1071no—
201#464—1071no—
202#464—1071no—
203#464—1071no—
204#464—1071no—
205#464—1071no—
206#464—1071no—
207#464D10711yescharacteristic, direct product factor
208C2×C4⋊C8—1071no—
209C2×#103—1071no—
210C2×#102—1071no—
211C22×Q8—1071no—
212C22×Q8—1071no—
213C22×D4—1071no—
214C2×Q16—1071no—
215C2×Q16—1071no—
216C2×Q16—1071no—
217C2×Q16—2144no—
218C2×Q16C2×D10711yescharacteristic, complemented
219C2×SD16—1071no—
220C2×SD16—1071no—
221C2×SD16—1071no—
222C2×SD16—2144no—
223C2×SD16C2×D10711yescharacteristic
224C22×C8—1071no—
225C22×C8—1071no—
226#124—1071no—
227#124—1071no—
228#124—1071no—
229#124—2141no—
230#124—2141no—
231#124C2×D10711yescharacteristic
232C4×Q8—1071no—
233C4×Q8—1071no—
234C4×Q8—1071no—
235C4×Q8—2141no—
236C4×Q8—2141no—
237C4×Q8C2×D10711yescharacteristic, complemented
238C2×C4⋊C4—1071no—
239C2×C4⋊C4—2141no—
240C2×C22⋊C4—2141no—
241C2×C22⋊C4—2141no—
242C2×C42—1071no—
243C2×C42—2141no—
244C4⋊C8—1071no—
245C4⋊C8—1071no—
246C4⋊C8—1071no—
247C4⋊C8C2×D10711yescharacteristic, complemented
248#103—1071no—
249#103—1071no—
250#103—1071no—
251#103C2×D10711yescharacteristic, complemented
252#102—1071no—
253#102—1071no—
254#102—1071no—
255#102C2×D10711yescharacteristic
256C24—2141no—
257C2×Q8—1074no—
258C2×Q8—1071no—
259C2×Q8—1071no—
260C2×Q8—2141no—
261C2×Q8—2141no—
262C2×Q8—2142no—
263C2×Q8—2142no—
264C2×Q8—2142no—
265C2×Q8C22×D10711yescharacteristic
266C2×Q8C22×D10711yescharacteristic
267C2×D4—1071no—
268C2×D4—2142no—
269C2×D4—2142no—
270C2×D4—2141no—
271C2×D4C22×D10711yescharacteristic
272C22×C4—1071no—
273C22×C4—1071no—
274C22×C4—1071no—
275C22×C4—2141no—
276C22×C4—2141no—
277C22×C4—2141no—
278Q16—22no—
279Q16—2142no—
280Q16—2142no—
281Q16—2142no—
282SD16—22no—
283SD16—2142no—
284SD16—2142no—
285SD16—2142no—
286C2×C8—1071no—
287C2×C8—1071no—
288C2×C8—2142no—
289C2×C8—2142no—
290C2×C8C22×D10711yescharacteristic
291C2×C8C22×D10711yescharacteristic
292C4⋊C4—21no—
293C4⋊C4—1071no—
294C4⋊C4—2141no—
295C4⋊C4—2141no—
296C4⋊C4—2141no—
297C4⋊C4—2141no—
298C4⋊C4C22×D10711yescharacteristic
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—2141no—
302C22⋊C4—2141no—
303C22⋊C4—2141no—
304C22⋊C4—2141no—
305C22⋊C4—2141no—
306C22⋊C4—2141no—
307C42—21no—
308C42—1071no—
309C42—1071no—
310C42—1071no—
311C42—2141no—
312C42—2141no—
313C42—2141no—
314C42C22×D10711yescharacteristic
315C23—21no—
316C23—1071no—
317C23—4282no—
318C23—4282no—
319C23—4282no—
320C23—2141no—
321Q8—21no—
322Q8—21no—
323Q8—21no—
324Q8—1072no—
325Q8—4282no—
326Q8—2144no—
327Q8—2141no—
328Q8—2141no—
329Q8—2141no—
330Q8D4×D10712yes—
331D4—21no—
332D4—21no—
333D4—4282no—
334D4—2141no—
335D4—2141no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—1071no—
340C2×C4—1072no—
341C2×C4—1072no—
342C2×C4—1071no—
343C2×C4—1071no—
344C2×C4—4282no—
345C2×C4—4282no—
346C2×C4—2142no—
347C2×C4—2142no—
348C2×C4—2144no—
349C2×C4—2141no—
350C2×C4—2141no—
351C2×C4—2141no—
352C2×C4D4×D10711yescharacteristic
353C2×C4D4×D10711yescharacteristic
354C2×C4C23×D10711yescharacteristic
355C8—21no—
356C8—21no—
357C8—2141no—
358C8—2141no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—8564no—
363C22—1072no—
364C22—1072no—
365C22—1072no—
366C22—4281no—
367C22—4281no—
368C22—4281no—
369C22C2×D4×D10711yescharacteristic
370C4—21no—
371C4—21no—
372C4—22no—
373C4—41no—
374C4—41no—
375C4—1072no—
376C4—4281no—
377C4—4281no—
378C4—2141no—
379C4—2141no—
380C4—2142no—
381C4C2×D4×D10711yescharacteristic
382C4#41×D10711yescharacteristic
383C2—81no—
384C2—8561no—
385C2—1074no—
386C2#121×D10711yescharacteristic
387C2#135×D10711yescharacteristic
388C2#137×D10711yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#464×C107C2
socleC22×C107C22×D4
prime radicalC2×D4×D107C22
hypercenter#464D107
hypocenterC107C2×#464
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. C2×Q16×D107C2semidirect
4. C4×Q8×D107C2semidirect
5. #20292852C2semidirect
6. #20292851C2semidirect
7. #20292850C2semidirect
8. #20292849C2semidirect
9. #20292848C2semidirect
10. #20292847C2semidirect
11. #20292846C2semidirect
12. C4⋊C8×D107C2semidirect
13. #103×D107C2semidirect
15. #464×C107C2semidirect
19. C2×Dic428C22semidirect
20. C2×#13133808C22semidirect
21. C2×#13133808C22semidirect
34. Q8×Dic107C22semidirect
36. C4×Dic214C22semidirect
38. #16812074C22semidirect
45. C4⋊(C107⋊C8)C22semidirect
46. Dic107⋊C8C22semidirect
47. Dic107⋊C8C22semidirect
48. #16812034C22semidirect
49. #16812033C22semidirect
50. #16812032C22semidirect
54. C2×Q16×C107C22semidirect
57. C4×Q8×C107C22semidirect
58. C4⋊C8×C107C22semidirect
59. #103×C107C22semidirect
193. D107#464direct (N × H)
195. C107C2×#464semidirect
207. #464D107direct (N × H)
218. C2×Q16C2×D107semidirect
237. C4×Q8C2×D107semidirect
247. C4⋊C8C2×D107semidirect
251. #103C2×D107semidirect

Maximal subgroups

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

subgroupindex
C2×Q16×D1072
C2×SD16×D1072
#124×D1072
C4×Q8×D1072
#202928522
#202928512
#202928502
#202928492
#202928482
#202928472
#202928462
C4⋊C8×D1072
#103×D1072
#102×D1072
#464×C1072
C2×#464107