Finite Group Databasebeta

← #28346638

Subgroups — #28346638

Order 13696.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20293244C211yesmaximal, characteristic, complemented
2#20293102C211yesmaximal, characteristic, complemented
3#20292969C211yesmaximal, characteristic, complemented
4#20292948C211yesmaximal, characteristic, complemented
5#20292915C211yesmaximal, characteristic, complemented
6#20292905C211yesmaximal, characteristic, complemented
7#20292840C211yesmaximal, characteristic, complemented
8#20292840C211yesmaximal, characteristic, complemented
9#20292778C211yesmaximal, characteristic, complemented
10#20292739C211yesmaximal, characteristic, complemented
11#20292724C211yesmaximal, characteristic, complemented
12#20292718C211yesmaximal, characteristic, complemented
13D8×Dic107C211yesmaximal, characteristic, complemented
14#20292685C211yesmaximal, characteristic, complemented
15#447×C107C211yesmaximal, characteristic
16C2×#13133806C2211yescharacteristic
17C2×#13133806C2211yescharacteristic
18#16812108C2211yescharacteristic, complemented
19#16812102—21no—
20#16812096—21no—
21#16812096C2211yescharacteristic, complemented
22#16812090—21no—
23#16812088C2211yescharacteristic
24#16812086—21no—
25#16812074C2211yescharacteristic, complemented
26D4×Dic107—21no—
27D4×Dic107—21no—
28D4×Dic107C2211yescharacteristic
29D4×Dic107C2211yescharacteristic
30D4×Dic107C2211yescharacteristic
31D4×Dic107C2211yescharacteristic
32D4×Dic107C2211yescharacteristic, complemented
33#16812068C2211yescharacteristic
34#16812068C2211yescharacteristic
35C2×C22⋊Dic107—21no—
36C2×C22⋊Dic107—21no—
37#16812043C2211yescharacteristic, complemented
38#16812042C2211yescharacteristic, complemented
39#16812041C2211yescharacteristic, complemented
40#16812040C2211yescharacteristic, complemented
41Dic107⋊C8C2211yescharacteristic, complemented
42Dic107⋊C8C2211yescharacteristic, complemented
43#16812034C2211yescharacteristic, complemented
44#16812034C2211yescharacteristic, complemented
45#16812030C2211yescharacteristic
46#16812030C2211yescharacteristic
47#16812030C2211yescharacteristic, complemented
48#16812030C2211yescharacteristic, complemented
49C22⋊(C107⋊C8)C2211yescharacteristic
50#16812019C2211yescharacteristic, complemented
51C8×Dic107C2211yescharacteristic, complemented
52C22×D4×C107C2211yescharacteristic
53C2×D8×C107C2211yescharacteristic
54C2×D8×C107C2211yescharacteristic
55#121×C107C2211yescharacteristic
56#102×C107C2211yescharacteristic
57#102×C107C2211yescharacteristic
58C22⋊C8×C107C2211yescharacteristic
59C2×Dic214—21no—
60C2×Dic214C2311yescharacteristic
61C22×Dic107—21no—
62C22×Dic107—21no—
63C22×Dic107—21no—
64C22×Dic107—21no—
65C22×Dic107—21no—
66#13133806—22no—
67#13133806—22no—
68C2×C107⋊C8C2311yescharacteristic
69C2×C107⋊C8C2311yescharacteristic
70C4⋊Dic107D411yescharacteristic
71C4⋊Dic107D411yescharacteristic
72C4⋊Dic107C2311yescharacteristic
73C4⋊Dic107C2311yescharacteristic
74C4⋊Dic107C2311yescharacteristic
75Dic107⋊C4—21no—
76Dic107⋊C4—21no—
77Dic107⋊C4—21no—
78C22⋊Dic107—21no—
79C22⋊Dic107—21no—
80C22⋊Dic107—21no—
81C22⋊Dic107—21no—
82C22⋊Dic107—21no—
83C22⋊Dic107—21no—
84C22⋊Dic107—21no—
85C22⋊Dic107—21no—
86C22⋊Dic107—21no—
87C22⋊Dic107D411yescharacteristic
88C22⋊Dic107D411yescharacteristic
89C4×Dic107—21no—
90C4×Dic107—21no—
91C4×Dic107C2311yescharacteristic
92C4×Dic107C2311yescharacteristic
93C24×C107—21no—
94C2×D4×C107—22no—
95C2×D4×C107—22no—
96C2×D4×C107—21no—
97C2×D4×C107—21no—
98C2×D4×C107C2311yescharacteristic
99C2×D4×C107C2311yescharacteristic
100C2×D4×C107C2311yescharacteristic
101C22×C4×C107C2311yescharacteristic
102D8×C107—22no—
103D8×C107—22no—
104C2×C8×C107C2311yescharacteristic
105C2×C8×C107C2311yescharacteristic
106C4⋊C4×C107C2311yescharacteristic
107C22⋊C4×C107—21no—
108C23×C107—24no—
109C23×C107—21no—
110C23×C107—21no—
111C23×C107—21no—
112C23×C107—81no—
113C23×C107—81no—
114C23×C107C2×D411yescharacteristic
115D4×C107—24no—
116D4×C107—21no—
117D4×C107—21no—
118D4×C107—21no—
119D4×C107—21no—
120D4×C107—81no—
121D4×C107#4112yes—
122D4×C107#4112yes—
123C2×C4×C107—21no—
124C2×C4×C107—21no—
125C2×C4×C107—21no—
126C2×C4×C107C2×D411yescharacteristic
127C2×C4×C107C2411yescharacteristic
128C2×Dic107—21no—
129C2×Dic107—21no—
130C2×Dic107—21no—
131C2×Dic107—21no—
132C2×Dic107—81no—
133C2×Dic107—81no—
134C2×Dic107—81no—
135C2×Dic107—81no—
136C2×Dic107—81no—
137C2×Dic107C2×D411yescharacteristic
138C2×Dic107C2×D411yescharacteristic
139C2×Dic107C2×D411yescharacteristic
140C2×Dic107C2×D411yescharacteristic
141Dic214—21no—
142Dic214—21no—
143Dic214—81no—
144C8×C107—21no—
145C8×C107—21no—
146C107⋊C8—21no—
147C107⋊C8—21no—
148C22×C107—21no—
149C22×C107—22no—
150C22×C107—22no—
151C22×C107—21no—
152C22×C107—21no—
153C22×C107—41no—
154C22×C107—41no—
155C22×C107—41no—
156C22×C107—41no—
157C22×C107—41no—
158C22×C107—41no—
159C22×C107—41no—
160C22×C107—84no—
161C22×C107C22×D411yescharacteristic
162C4×C107—21no—
163C4×C107—41no—
164C4×C107C2×#4111yescharacteristic
165C4×C107C2×#4111yescharacteristic
166Dic107—21no—
167Dic107—21no—
168Dic107—21no—
169Dic107—21no—
170Dic107—41no—
171Dic107—41no—
172Dic107—41no—
173Dic107—41no—
174C2×C107—41no—
175C2×C107—42no—
176C2×C107—42no—
177C2×C107—81no—
178C2×C107#52511yescharacteristic
179C2×C107#57611yescharacteristic
180C2×C107#57711yescharacteristic
181#3118—1071nomaximal, Sylow
182C107#311811yescharacteristic, complemented, Sylow
183#542—1071no—
184#518—1071no—
185#485—1071no—
186#482—1071no—
187#476—1071no—
188#474—1071no—
189#463—1071no—
190#463—1071no—
191#450—1071no—
192#447D10711yescharacteristic
193#442—1071no—
194#440—1071no—
195C4×SD16—1071no—
196C4×D8—1071no—
197#433—1071no—
198C22×D4C2×D10711yescharacteristic
199C2×SD16—1071no—
200C2×SD16—1071no—
201C2×D8C2×D10711yescharacteristic
202C2×D8C2×D10711yescharacteristic
203C4⋊Q8—1071no—
204#126—2141no—
205#124—1071no—
206#124—2141no—
207#123—2141no—
208C22⋊Q8—1071no—
209C22⋊Q8—2141no—
210#121C2×D10711yescharacteristic
211C4×Q8—1071no—
212C4×D4—1071no—
213C4×D4—1071no—
214C4×D4—1071no—
215C4×D4—1071no—
216C4×D4—1071no—
217C4×D4—2141no—
218C4×D4—2141no—
219#117—1071no—
220#117—1071no—
221C2×C22⋊C4—2141no—
222C2×C22⋊C4—2141no—
223#107—1071no—
224#107—1071no—
225#106—1071no—
226#106—1071no—
227C4⋊C8—1071no—
228C4⋊C8—1071no—
229#103—1071no—
230#103—1071no—
231#102—1071no—
232#102—1071no—
233#102—1071no—
234#102—1071no—
235#102C2×D10711yescharacteristic
236#102C2×D10711yescharacteristic
237C22⋊C8—1071no—
238C22⋊C8C2×D10711yescharacteristic
239#97—1071no—
240C4×C8—1071no—
241C24—21no—
242C2×Q8—1071no—
243C2×Q8—2141no—
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—21no—
247C2×D4—21no—
248C2×D4C22×D10711yescharacteristic
249C2×D4C22×D10711yescharacteristic
250C2×D4C22×D10711yescharacteristic
251C22×C4—2141no—
252C22×C4—2141no—
253C22×C4—2141no—
254C22×C4—2141no—
255C22×C4—2141no—
256C22×C4C22×D10711yescharacteristic
257SD16—2142no—
258SD16—2142no—
259D8—22no—
260D8—22no—
261C2×C8—1071no—
262C2×C8—1071no—
263C2×C8C22×D10711yescharacteristic
264C2×C8C22×D10711yescharacteristic
265C4⋊C4—1071no—
266C4⋊C4—1071no—
267C4⋊C4—1071no—
268C4⋊C4—1071no—
269C4⋊C4—1071no—
270C4⋊C4—2141no—
271C4⋊C4—2141no—
272C4⋊C4—2141no—
273C4⋊C4C22×D10711yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—1071no—
276C22⋊C4—1071no—
277C22⋊C4—2141no—
278C22⋊C4—2141no—
279C22⋊C4—2141no—
280C22⋊C4—2141no—
281C22⋊C4—2141no—
282C22⋊C4—2141no—
283C22⋊C4—2141no—
284C22⋊C4—2141no—
285C22⋊C4—2141no—
286C42—1071no—
287C42—1071no—
288C42—2141no—
289C42—2141no—
290C23—24no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—81no—
295C23—81no—
296C23D4×D10711yescharacteristic
297Q8—8561no—
298Q8—2141no—
299Q8—2141no—
300D4—24no—
301D4—21no—
302D4—21no—
303D4—21no—
304D4—21no—
305D4—81no—
306D4#1313381712yes—
307D4#1313381712yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—8561no—
312C2×C4—8561no—
313C2×C4—8561no—
314C2×C4—8561no—
315C2×C4—8561no—
316C2×C4—1071no—
317C2×C4—1071no—
318C2×C4—1071no—
319C2×C4—1071no—
320C2×C4—2141no—
321C2×C4—2141no—
322C2×C4—2141no—
323C2×C4—2141no—
324C2×C4D4×D10711yescharacteristic
325C2×C4C23×D10711yescharacteristic
326C8—21no—
327C8—21no—
328C8—2141no—
329C8—2141no—
330C22—21no—
331C22—22no—
332C22—22no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—84no—
343C22C2×D4×D10711yescharacteristic
344C4—21no—
345C4—41no—
346C4—4281no—
347C4—4281no—
348C4—4281no—
349C4—4281no—
350C4—2141no—
351C4—2141no—
352C4—2141no—
353C4—2141no—
354C4C2×#1313381711yescharacteristic
355C4C2×#1313381711yescharacteristic
356C2—41no—
357C2—42no—
358C2—42no—
359C2—81no—
360C2#2029313311yescharacteristic
361C2#2029342811yescharacteristic
362C2#2029343711yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting, prime radical#447×C107C2
socleC22×C107C22×D4
hypercenter#447D107
hypocenterC107#3118
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #20293244C2semidirect
2. #20293102C2semidirect
3. #20292969C2semidirect
4. #20292948C2semidirect
5. #20292915C2semidirect
6. #20292905C2semidirect
7. #20292840C2semidirect
8. #20292840C2semidirect
9. #20292778C2semidirect
10. #20292739C2semidirect
11. #20292724C2semidirect
12. #20292718C2semidirect
13. D8×Dic107C2semidirect
14. #20292685C2semidirect
18. #16812108C22semidirect
21. #16812096C22semidirect
25. #16812074C22semidirect
32. D4×Dic107C22semidirect
37. #16812043C22semidirect
38. #16812042C22semidirect
39. #16812041C22semidirect
40. #16812040C22semidirect
41. Dic107⋊C8C22semidirect
42. Dic107⋊C8C22semidirect
43. #16812034C22semidirect
44. #16812034C22semidirect
47. #16812030C22semidirect
48. #16812030C22semidirect
50. #16812019C22semidirect
51. C8×Dic107C22semidirect
182. C107#3118semidirect

Maximal subgroups

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

subgroupindex
#202932442
#202931022
#202929692
#202929482
#202929152
#202929052
#202928402
#202927782
#202927392
#202927242
#202927182
D8×Dic1072
#202926852
#447×C1072
#3118107