Finite Group Databasebeta

← #28345288

Subgroups — #28345288

Order 13696.

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×#16812136C211yesmaximal, characteristic
2#20293109C211yesmaximal, characteristic, complemented
3#20293099C211yesmaximal, characteristic, complemented
4#20292738C211yesmaximal, characteristic, complemented
5#20292737C211yesmaximal, characteristic, complemented
6#20292728C211yesmaximal, characteristic, complemented
7#20292725C211yesmaximal, characteristic, complemented
8#20292712C211yesmaximal, characteristic, complemented
9C4×D856C211yesmaximal, characteristic, complemented
10#20292707C211yesmaximal, characteristic, complemented
11#20292666C211yesmaximal, characteristic, complemented
12#20292622C211yesmaximal, characteristic, complemented
13#102×D107C211yesmaximal, characteristic, complemented
14#20292581C211yesmaximal, characteristic, complemented
15C4×SD16×C107C211yesmaximal, characteristic, complemented
16C2×#13133819C2211yescharacteristic
17C2×D4×D107C2211yescharacteristic
18#16812136C418yescomplemented
19C2×#13133805C2211yescharacteristic
20C2×D856C2211yescharacteristic
21C2×#13133803C2211yescharacteristic
22C2×#13133801C2211yescharacteristic
23C2×C8×D107C2211yescharacteristic
24Q8×Dic107C2211yescharacteristic, complemented
25C4×D428—21no—
26C4×D428C2211yescharacteristic
27C4×D428C2211yescharacteristic, complemented
28D4×Dic107C2211yescharacteristic
29#16812071—21no—
30#16812071C2211yescharacteristic
31#16812071C2211yescharacteristic, complemented
32C4×C22⋊D107—21no—
33(C22⋊D107)⋊C4—21no—
34#16812067C2211yescharacteristic
35#16812066—21no—
36#16812066C2211yescharacteristic
37C4⋊C4×D107—21no—
38C4⋊C4×D107C2211yescharacteristic
39C2×(C2×D107)⋊C4—21no—
40C22⋊C4×D107—21no—
41#16812043C2211yescharacteristic, complemented
42#16812042C2211yescharacteristic, complemented
43#16812040C2211yescharacteristic, complemented
44#16812033C2211yescharacteristic, complemented
45#16812031C2211yescharacteristic
46#16812031C2211yescharacteristic, complemented
47#16812030C2211yescharacteristic
48#16812029C2211yescharacteristic
49#16812029C2211yescharacteristic, complemented
50#16812020C2211yescharacteristic, complemented
51#16812019C2211yescharacteristic, complemented
52C8×Dic107C2211yescharacteristic, complemented
53C2×SD16×C107C2211yescharacteristic
54C4×Q8×C107C2211yescharacteristic, complemented
55C4×D4×C107C2211yescharacteristic
56#106×C107C2211yescharacteristic, complemented
57#103×C107C2211yescharacteristic, complemented
58#102×C107C2211yescharacteristic
59C4×C8×C107C2211yescharacteristic, complemented
60C23×D107—21no—
61#13133819—22no—
62#13133819C2×C414yescomplemented
63C2×D428—21no—
64C2×D428C2311yescharacteristic
65C2×D428C2311yescharacteristic
66C2×C22⋊D107—21no—
67D4×D107—22no—
68D4×D107C2×C414yescomplemented
69C22×Dic107—21no—
70C2×C4×D107—21no—
71C2×C4×D107—21no—
72C2×C4×D107—21no—
73C2×C4×D107—21no—
74C2×C4×D107—21no—
75C2×C4×D107—21no—
76C2×C4×D107C2311yescharacteristic
77#13133805C2×C414yescomplemented
78D856C2×C414yescomplemented
79#13133803C2×C414yescomplemented
80#13133801C2×C414yescomplemented
81C2×C107⋊C8C2311yescharacteristic
82C2×C107⋊C8C2311yescharacteristic
83C8×D107—22no—
84C4⋊Dic107—21no—
85C4⋊Dic107C2311yescharacteristic
86C4⋊Dic107C2311yescharacteristic
87Dic107⋊C4—21no—
88Dic107⋊C4D411yescharacteristic
89Dic107⋊C4D411yescharacteristic
90C22⋊Dic107—21no—
91(C2×D107)⋊C4—21no—
92(C2×D107)⋊C4—21no—
93(C2×D107)⋊C4—21no—
94(C2×D107)⋊C4—21no—
95(C2×D107)⋊C4—21no—
96(C2×D107)⋊C4D411yescharacteristic
97(C2×D107)⋊C4D411yescharacteristic
98C4×Dic107—21no—
99C4×Dic107—21no—
100C4×Dic107C2311yescharacteristic
101C2×Q8×C107C2311yescharacteristic
102C2×D4×C107C2311yescharacteristic
103C22×C4×C107—21no—
104SD16×C107C2×C414yescomplemented
105C2×C8×C107C2311yescharacteristic
106C2×C8×C107C2311yescharacteristic
107C4⋊C4×C107—21no—
108C4⋊C4×C107C2311yescharacteristic
109C4⋊C4×C107C2311yescharacteristic
110C22⋊C4×C107—21no—
111C42×C107—21no—
112C42×C107C2311yescharacteristic
113C23×C107—21no—
114C22×D107—21no—
115C22×D107—21no—
116C22×D107—24no—
117C22×D107—81no—
118C22×D107—81no—
119C22×D107C2×D411yescharacteristic
120Q8×C107—21no—
121Q8×C107C22×C412yes—
122D4×C107—21no—
123D4×C107C22×C412yes—
124C2×C4×C107—21no—
125C2×C4×C107—21no—
126C2×C4×C107—21no—
127C2×C4×C107—81no—
128C2×C4×C107C2×D411yescharacteristic
129C2×C4×C107C2×D411yescharacteristic
130C2×C4×C107C2411yescharacteristic
131C22⋊D107—24no—
132C2×Dic107—21no—
133C2×Dic107—21no—
134C2×Dic107—81no—
135C2×Dic107C2×D411yescharacteristic
136C2×Dic107C2×D411yescharacteristic
137C2×Dic107C2×D411yescharacteristic
138D428—24no—
139D428—21no—
140D428—21no—
141D428C22×C412yes—
142D428C22×C412yes—
143C4×D107—24no—
144C4×D107—81no—
145C4×D107—81no—
146C4×D107—81no—
147C4×D107—81no—
148C4×D107—81no—
149C4×D107C22×C412yes—
150C4×D107#4112yes—
151C8×C107—21no—
152C8×C107C22×C412yes—
153C107⋊C8—21no—
154C107⋊C8C22×C412yes—
155C22×C107—22no—
156C22×C107—41no—
157C22×C107—41no—
158C22×C107C22×D411yescharacteristic
159C2×D107—21no—
160C2×D107—21no—
161C2×D107—22no—
162C2×D107—22no—
163C2×D107—41no—
164C2×D107—41no—
165C2×D107—41no—
166C2×D107—41no—
167C2×D107—84no—
168C2×D107C4×D412yes—
169C4×C107—22no—
170C4×C107—21no—
171C4×C107—21no—
172C4×C107—41no—
173C4×C107—41no—
174C4×C107C23×C411yescharacteristic
175C4×C107C2×#4111yescharacteristic
176Dic107—21no—
177Dic107—21no—
178Dic107—41no—
179Dic107—41no—
180Dic107C4×D412yes—
181C2×C107—42no—
182C2×C107C2×C4×D411yescharacteristic
183C2×C107#57611yescharacteristic
184C2×C107#57711yescharacteristic
185D107—22no—
186D107—42no—
187D107—42no—
188#2946—1071nomaximal, Sylow
189C107#294611yescharacteristic, complemented, Sylow
190C2×AGL(1,ℤ/8)—1071no—
191#520—1071no—
192#518—1071no—
193#442—1071no—
194#442—1071no—
195#440—1071no—
196#440—1071no—
197C4×SD16—1071no—
198C4×SD16D10711yescharacteristic, complemented
199C4×D8—1071no—
200C4×D8—1071no—
201#428—1071no—
202#416—1071no—
203C2×#102—1071no—
204#405—1071no—
205C2×#41—1071no—
206C22×D4—1071no—
207AGL(1,ℤ/8)—1078no—
208C2×SD16—1071no—
209C2×SD16C2×D10711yescharacteristic
210C2×D8—1071no—
211C2×D8—1071no—
212C2×M16—1071no—
213C22×C8—1071no—
214C4×Q8—1071no—
215C4×Q8C2×D10711yescharacteristic, complemented
216C4×D4—1071no—
217C4×D4—1071no—
218C4×D4—1071no—
219C4×D4—1071no—
220C4×D4—1071no—
221C4×D4—2141no—
222C4×D4—2141no—
223C4×D4—2141no—
224C4×D4—2141no—
225C4×D4C2×D10711yescharacteristic
226#117—1071no—
227#117—1071no—
228#117—2141no—
229C2×C4⋊C4—1071no—
230C2×C4⋊C4—2141no—
231C2×C22⋊C4—2141no—
232C2×C22⋊C4—2141no—
233#107—1071no—
234#107—1071no—
235#106—1071no—
236#106C2×D10711yescharacteristic, complemented
237#103—1071no—
238#103C2×D10711yescharacteristic, complemented
239#102—1071no—
240#102—1071no—
241#102—1071no—
242#102—1071no—
243#102—1071no—
244#102C2×D10711yescharacteristic
245#97—1071no—
246#97—1071no—
247C4×C8—1071no—
248C4×C8C2×D10711yescharacteristic, complemented
249C24—2141no—
250#41—1074no—
251#41—2142no—
252C2×Q8C22×D10711yescharacteristic
253C2×D4—1074no—
254C2×D4—1071no—
255C2×D4—1071no—
256C2×D4—2141no—
257C2×D4—2142no—
258C2×D4—2141no—
259C2×D4C22×D10711yescharacteristic
260C22×C4—21no—
261C22×C4—1071no—
262C22×C4—2141no—
263C22×C4—2141no—
264C22×C4—2141no—
265C22×C4—2141no—
266C22×C4—2141no—
267C22×C4—2141no—
268C22×C4—2141no—
269SD16—1074no—
270SD16C4×D10714yescomplemented
271D8—1074no—
272D8—1074no—
273M16—1074no—
274C2×C8—1071no—
275C2×C8—1071no—
276C2×C8—2142no—
277C2×C8C22×D10711yescharacteristic
278C2×C8C22×D10711yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—1071no—
281C4⋊C4—1071no—
282C4⋊C4—1071no—
283C4⋊C4—1071no—
284C4⋊C4—2141no—
285C4⋊C4—2141no—
286C4⋊C4C22×D10711yescharacteristic
287C4⋊C4C22×D10711yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—1071no—
290C22⋊C4—1071no—
291C22⋊C4—2141no—
292C22⋊C4—2141no—
293C22⋊C4—2141no—
294C22⋊C4—2141no—
295C22⋊C4—2141no—
296C22⋊C4—2141no—
297C42—21no—
298C42—1071no—
299C42—2141no—
300C42—2141no—
301C42C22×D10711yescharacteristic
302C23—21no—
303C23—8561no—
304C23—8561no—
305C23—1071no—
306C23—2144no—
307C23—2141no—
308C23—2141no—
309Q8—21no—
310Q8C2×C4×D10712yes—
311D4—21no—
312D4—1072no—
313D4—1072no—
314D4—2144no—
315D4—2144no—
316D4—2141no—
317D4—2141no—
318D4C2×C4×D10712yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—81no—
323C2×C4—8561no—
324C2×C4—8561no—
325C2×C4—8561no—
326C2×C4—8561no—
327C2×C4—8561no—
328C2×C4—8561no—
329C2×C4—1071no—
330C2×C4—1072no—
331C2×C4—1072no—
332C2×C4—1071no—
333C2×C4—1071no—
334C2×C4—2144no—
335C2×C4—2141no—
336C2×C4—2141no—
337C2×C4D4×D10711yescharacteristic
338C2×C4D4×D10711yescharacteristic
339C2×C4C23×D10711yescharacteristic
340C8—21no—
341C8—1072no—
342C8—2141no—
343C8C2×C4×D10712yes—
344C22—22no—
345C22—41no—
346C22—41no—
347C22—8564no—
348C22—1072no—
349C22—4281no—
350C22—4281no—
351C22—4281no—
352C22—4281no—
353C22—2142no—
354C22—2142no—
355C22—2141no—
356C22—2141no—
357C22C2×D4×D10711yescharacteristic
358C4—21no—
359C4—21no—
360C4—22no—
361C4—41no—
362C4—41no—
363C4—1072no—
364C4—4281no—
365C4—4281no—
366C4—2141no—
367C4—2141no—
368C4C22×C4×D10711yescharacteristic
369C4#41×D10711yescharacteristic
370C2—42no—
371C2—4282no—
372C2—4282no—
373C2—2142no—
374C2C4×D4×D10711yescharacteristic
375C2#2029342911yescharacteristic
376C2#2029343311yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutatorC4×C107C23×C4
FrattiniC2×C4C23×D107
FittingC4×SD16×C107C2
socleC22×C107C22×D4
prime radicalC2×#16812136C2
cosocleC2×C4×C107C24
hypercenterC4×SD16D107
hypocenterC107#2946
LCSG ▷ C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. #20293109C2semidirect
3. #20293099C2semidirect
4. #20292738C2semidirect
5. #20292737C2semidirect
6. #20292728C2semidirect
7. #20292725C2semidirect
8. #20292712C2semidirect
9. C4×D856C2semidirect
10. #20292707C2semidirect
11. #20292666C2semidirect
12. #20292622C2semidirect
13. #102×D107C2semidirect
14. #20292581C2semidirect
15. C4×SD16×C107C2semidirect
18. #16812136C4semidirect
24. Q8×Dic107C22semidirect
27. C4×D428C22semidirect
31. #16812071C22semidirect
41. #16812043C22semidirect
42. #16812042C22semidirect
43. #16812040C22semidirect
44. #16812033C22semidirect
46. #16812031C22semidirect
49. #16812029C22semidirect
50. #16812020C22semidirect
51. #16812019C22semidirect
52. C8×Dic107C22semidirect
54. C4×Q8×C107C22semidirect
56. #106×C107C22semidirect
57. #103×C107C22semidirect
59. C4×C8×C107C22semidirect
62. #13133819C2×C4semidirect
68. D4×D107C2×C4semidirect
77. #13133805C2×C4semidirect
78. D856C2×C4semidirect
79. #13133803C2×C4semidirect
80. #13133801C2×C4semidirect
104. SD16×C107C2×C4semidirect
189. C107#2946semidirect
198. C4×SD16D107semidirect
215. C4×Q8C2×D107semidirect
236. #106C2×D107semidirect
238. #103C2×D107semidirect
248. C4×C8C2×D107semidirect
270. SD16C4×D107semidirect

Maximal subgroups

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

subgroupindex
C2×#168121362
#202931092
#202930992
#202927382
#202927372
#202927282
#202927252
#202927122
C4×D8562
#202927072
#202926662
#202926222
#102×D1072
#202925812
C4×SD16×C1072
#2946107