Finite Group Databasebeta

← #28346701

Subgroups — #28346701

Order 13696.

418 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20293228C211yesmaximal, characteristic, complemented
2#20293099C211yesmaximal, characteristic, complemented
3#20292954C211yesmaximal, characteristic, complemented
4#20292949C211yesmaximal, characteristic, complemented
5#20292930C211yesmaximal, characteristic, complemented
6#20292925C211yesmaximal, characteristic, complemented
7#20292821C211yesmaximal, characteristic, complemented
8#20292820C211yesmaximal, characteristic, complemented
9#20292762C211yesmaximal, characteristic, complemented
10#20292759C211yesmaximal, characteristic, complemented
11#20292737C211yesmaximal, characteristic, complemented
12#20292737C211yesmaximal, characteristic, complemented
13C4×D856C211yesmaximal, characteristic, complemented
14#20292686C211yesmaximal, characteristic, complemented
15C4×D8×C107C211yesmaximal, characteristic, complemented
16C2×D4×D107C2211yescharacteristic
17C2×D856C2211yescharacteristic
18C2×#13133803C2211yescharacteristic
19C2×#13133803C2211yescharacteristic
20#16812105C2211yescharacteristic, complemented
21#16812100C2211yescharacteristic, complemented
22#16812092—21no—
23#16812091—21no—
24#16812084C2211yescharacteristic
25#16812083—21no—
26#16812082—21no—
27#16812080C2211yescharacteristic
28C4×D428C2211yescharacteristic
29C4×D428C2211yescharacteristic, complemented
30D4×Dic107C2211yescharacteristic
31#16812071C2211yescharacteristic
32C4×C22⋊D107—21no—
33(C22⋊D107)⋊C4—21no—
34#16812067C2211yescharacteristic
35#16812066C2211yescharacteristic
36C2×(C2×D107)⋊C4—21no—
37C22⋊C4×D107—21no—
38#16812043C2211yescharacteristic, complemented
39#16812040C2211yescharacteristic, complemented
40#16812040C2211yescharacteristic, complemented
41Dic107⋊C8C2211yescharacteristic, complemented
42Dic107⋊C8C2211yescharacteristic, complemented
43#16812031C2211yescharacteristic
44#16812031C2211yescharacteristic, complemented
45#16812030C2211yescharacteristic
46#16812030C2211yescharacteristic, complemented
47#16812029C2211yescharacteristic
48#16812029C2211yescharacteristic, complemented
49(C2×D107)⋊C8C2211yescharacteristic
50(C2×D107)⋊C8C2211yescharacteristic
51#16812020C2211yescharacteristic, complemented
52C2×D8×C107C2211yescharacteristic
53C4×D4×C107C2211yescharacteristic
54C4×D4×C107C2211yescharacteristic, complemented
55#107×C107C2211yescharacteristic, complemented
56#102×C107C2211yescharacteristic
57#102×C107C2211yescharacteristic, complemented
58C4×C8×C107C2211yescharacteristic, complemented
59C23×D107—21no—
60C2×D428—21no—
61C2×D428C2311yescharacteristic
62C2×D428C2311yescharacteristic
63C2×C22⋊D107—21no—
64C2×C22⋊D107—21no—
65C2×C22⋊D107—21no—
66C2×C22⋊D107—21no—
67D4×D107—22no—
68D4×D107—22no—
69C22×Dic107—21no—
70C2×C4×D107—21no—
71C2×C4×D107—21no—
72C2×C4×D107—21no—
73C2×C4×D107C2311yescharacteristic
74D856—22no—
75#13133803—22no—
76#13133803—22no—
77C2×C107⋊C8C2311yescharacteristic
78C2×C107⋊C8C2311yescharacteristic
79C4⋊Dic107—21no—
80C4⋊Dic107C2311yescharacteristic
81C4⋊Dic107C2311yescharacteristic
82Dic107⋊C4—21no—
83Dic107⋊C4D411yescharacteristic
84Dic107⋊C4D411yescharacteristic
85C22⋊Dic107—21no—
86C22⋊Dic107—21no—
87(C2×D107)⋊C4—21no—
88(C2×D107)⋊C4—21no—
89(C2×D107)⋊C4—21no—
90(C2×D107)⋊C4—21no—
91(C2×D107)⋊C4—21no—
92(C2×D107)⋊C4D411yescharacteristic
93(C2×D107)⋊C4D411yescharacteristic
94C4×Dic107—21no—
95C4×Dic107C2311yescharacteristic
96C2×D4×C107C2311yescharacteristic
97C2×D4×C107C2311yescharacteristic
98C22×C4×C107—21no—
99C22×C4×C107—21no—
100D8×C107—22no—
101C2×C8×C107C2311yescharacteristic
102C2×C8×C107C2311yescharacteristic
103C4⋊C4×C107C2311yescharacteristic
104C4⋊C4×C107C2311yescharacteristic
105C22⋊C4×C107—21no—
106C22⋊C4×C107—21no—
107C42×C107C2311yescharacteristic
108C23×C107—21no—
109C23×C107—21no—
110C22×D107—21no—
111C22×D107—24no—
112C22×D107—21no—
113C22×D107—81no—
114C22×D107—81no—
115C22×D107C2×D411yescharacteristic
116D4×C107—21no—
117D4×C107—21no—
118D4×C107—21no—
119D4×C107#4112yes—
120C2×C4×C107—21no—
121C2×C4×C107—21no—
122C2×C4×C107—81no—
123C2×C4×C107—81no—
124C2×C4×C107C2×D411yescharacteristic
125C2×C4×C107C2×D411yescharacteristic
126C2×C4×C107C2411yescharacteristic
127C22⋊D107—24no—
128C22⋊D107—81no—
129C22⋊D107—81no—
130C22⋊D107—81no—
131C2×Dic107—21no—
132C2×Dic107—21no—
133C2×Dic107—81no—
134C2×Dic107C2×D411yescharacteristic
135C2×Dic107C2×D411yescharacteristic
136C2×Dic107C2×D411yescharacteristic
137D428—21no—
138D428—21no—
139D428—21no—
140D428—81no—
141D428#4112yes—
142C4×D107—21no—
143C4×D107—21no—
144C4×D107—81no—
145C4×D107—81no—
146C4×D107—81no—
147C8×C107—21no—
148C8×C107—21no—
149C107⋊C8—21no—
150C107⋊C8—21no—
151C22×C107—22no—
152C22×C107—41no—
153C22×C107—41no—
154C22×C107—41no—
155C22×C107—41no—
156C22×C107—41no—
157C22×C107C22×D411yescharacteristic
158C2×D107—21no—
159C2×D107—22no—
160C2×D107—21no—
161C2×D107—21no—
162C2×D107—41no—
163C2×D107—41no—
164C2×D107—41no—
165C2×D107—41no—
166C2×D107—41no—
167C2×D107—84no—
168C4×C107—21no—
169C4×C107—21no—
170C4×C107—41no—
171C4×C107—41no—
172C4×C107C2×#4111yescharacteristic
173C4×C107C2×#4111yescharacteristic
174Dic107—21no—
175Dic107—21no—
176Dic107—21no—
177Dic107—41no—
178Dic107—41no—
179C2×C107—42no—
180C2×C107—81no—
181C2×C107#52511yescharacteristic
182C2×C107#57611yescharacteristic
183C2×C107#57611yescharacteristic
184D107—41no—
185D107—42no—
186D107—81no—
187#3122—1071nomaximal, Sylow
188C107#312211yescharacteristic, complemented, Sylow
189#540—1071no—
190#518—1071no—
191#482—1071no—
192#482—1071no—
193#478—1071no—
194#478—1071no—
195#459—1071no—
196#459—1071no—
197#447—1071no—
198#447—1071no—
199#442—1071no—
200#442—1071no—
201C4×D8—1071no—
202C4×D8D10711yescharacteristic, complemented
203#433—1071no—
204C22×D4—1071no—
205C2×D8—1071no—
206C2×D8—1071no—
207C2×D8—1071no—
208C2×D8C2×D10711yescharacteristic
209#127—1071no—
210#125—1071no—
211#123—2141no—
212#123—2141no—
213#121—1071no—
214#121—1071no—
215#121—2141no—
216#121—2141no—
217C4×D4—1071no—
218C4×D4—1071no—
219C4×D4—1071no—
220C4×D4—1071no—
221C4×D4—2141no—
222C4×D4—2141no—
223C4×D4C2×D10711yescharacteristic
224C4×D4C2×D10711yescharacteristic, complemented
225#117—1071no—
226#117—1071no—
227C2×C22⋊C4—2141no—
228C2×C22⋊C4—2141no—
229#107—1071no—
230#107C2×D10711yescharacteristic, complemented
231#106—1071no—
232#106—1071no—
233C4⋊C8—1071no—
234C4⋊C8—1071no—
235#102—1071no—
236#102—1071no—
237#102—1071no—
238#102—1071no—
239#102—1071no—
240#102—1071no—
241#102C2×D10711yescharacteristic
242#102C2×D10711yescharacteristic, complemented
243C22⋊C8—1071no—
244C22⋊C8—1071no—
245#97—1071no—
246C4×C8C2×D10711yescharacteristic, complemented
247C24—2141no—
248C2×D4—1071no—
249C2×D4—1071no—
250C2×D4—2141no—
251C2×D4—2141no—
252C2×D4—2141no—
253C2×D4—2141no—
254C2×D4—2142no—
255C2×D4—2141no—
256C2×D4—2142no—
257C2×D4C22×D10711yescharacteristic
258C2×D4C22×D10711yescharacteristic
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—1071no—
262C22×C4—2141no—
263C22×C4—2141no—
264C22×C4—2141no—
265C22×C4—2141no—
266D8—22no—
267D8—2142no—
268D8—2142no—
269D8—2142no—
270C2×C8—1071no—
271C2×C8—1071no—
272C2×C8C22×D10711yescharacteristic
273C2×C8C22×D10711yescharacteristic
274C4⋊C4—1071no—
275C4⋊C4—1071no—
276C4⋊C4—1071no—
277C4⋊C4—1071no—
278C4⋊C4—2141no—
279C4⋊C4—2141no—
280C4⋊C4C22×D10711yescharacteristic
281C4⋊C4C22×D10711yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—1071no—
285C22⋊C4—1071no—
286C22⋊C4—2141no—
287C22⋊C4—2141no—
288C22⋊C4—2141no—
289C22⋊C4—2141no—
290C22⋊C4—2141no—
291C22⋊C4—2141no—
292C22⋊C4—2141no—
293C42—1071no—
294C42—2141no—
295C42C22×D10711yescharacteristic
296C23—21no—
297C23—21no—
298C23—8561no—
299C23—8561no—
300C23—1071no—
301C23—2144no—
302C23—2141no—
303C23—2141no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—8561no—
308D4—8561no—
309D4—8561no—
310D4—8561no—
311D4—1072no—
312D4—2144no—
313D4—2141no—
314D4—2141no—
315D4—2141no—
316D4#1313381812yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—8561no—
322C2×C4—8561no—
323C2×C4—8561no—
324C2×C4—8561no—
325C2×C4—1071no—
326C2×C4—1071no—
327C2×C4—1071no—
328C2×C4—2141no—
329C2×C4—2141no—
330C2×C4—2141no—
331C2×C4—2141no—
332C2×C4D4×D10711yescharacteristic
333C2×C4D4×D10711yescharacteristic
334C2×C4C23×D10711yescharacteristic
335C8—21no—
336C8—21no—
337C8—2141no—
338C8—2141no—
339C22—22no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—8564no—
346C22—4281no—
347C22—4281no—
348C22—4281no—
349C22—4281no—
350C22—4281no—
351C22—2141no—
352C22—2142no—
353C22—2141no—
354C22—2141no—
355C22C2×D4×D10711yescharacteristic
356C4—21no—
357C4—21no—
358C4—41no—
359C4—41no—
360C4—4281no—
361C4—4281no—
362C4—2141no—
363C4—2141no—
364C4—2141no—
365C4#41×D10711yescharacteristic
366C4C2×#1313381811yescharacteristic
367C2—42no—
368C2—81no—
369C2—8561no—
370C2—4281no—
371C2—4282no—
372C2#2029313611yescharacteristic
373C2#2029342811yescharacteristic
374C2#2029342911yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
FittingC4×D8×C107C2
socleC22×C107C22×D4
hypercenterC4×D8D107
hypocenterC107#3122
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #20293228C2semidirect
2. #20293099C2semidirect
3. #20292954C2semidirect
4. #20292949C2semidirect
5. #20292930C2semidirect
6. #20292925C2semidirect
7. #20292821C2semidirect
8. #20292820C2semidirect
9. #20292762C2semidirect
10. #20292759C2semidirect
11. #20292737C2semidirect
12. #20292737C2semidirect
13. C4×D856C2semidirect
14. #20292686C2semidirect
15. C4×D8×C107C2semidirect
20. #16812105C22semidirect
21. #16812100C22semidirect
29. C4×D428C22semidirect
38. #16812043C22semidirect
39. #16812040C22semidirect
40. #16812040C22semidirect
41. Dic107⋊C8C22semidirect
42. Dic107⋊C8C22semidirect
44. #16812031C22semidirect
46. #16812030C22semidirect
48. #16812029C22semidirect
51. #16812020C22semidirect
54. C4×D4×C107C22semidirect
55. #107×C107C22semidirect
57. #102×C107C22semidirect
58. C4×C8×C107C22semidirect
188. C107#3122semidirect
202. C4×D8D107semidirect
224. C4×D4C2×D107semidirect
230. #107C2×D107semidirect
242. #102C2×D107semidirect
246. C4×C8C2×D107semidirect

Maximal subgroups

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

subgroupindex
#202932282
#202930992
#202929542
#202929492
#202929302
#202929252
#202928212
#202928202
#202927622
#202927592
#202927372
C4×D8562
#202926862
C4×D8×C1072
#3122107