Finite Group Databasebeta

← #28346003

Subgroups — #28346003

Order 13696.

504 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16812136C211yesmaximal, characteristic, complemented
2C2×#16812132C211yesmaximal, characteristic, complemented
3#20293195C211yesmaximal, characteristic, complemented
4#20293109C211yesmaximal, characteristic, complemented
5#20292851C211yesmaximal, characteristic, complemented
6#20292845C211yesmaximal, characteristic, complemented
7#20292839C211yesmaximal, characteristic, complemented
8#20292827C211yesmaximal, characteristic, complemented
9#20292825C211yesmaximal, characteristic, complemented
10#20292823C211yesmaximal, characteristic, complemented
11#20292821C211yesmaximal, characteristic, complemented
12#20292652C211yesmaximal, characteristic, complemented
13#20292627C211yesmaximal, characteristic, complemented
14#102×D107C211yesmaximal, characteristic, complemented
15#464×C107C211yesmaximal, characteristic, complemented
16C2×#13133819C2211yescharacteristic
17C2×#13133819C2211yescharacteristic
18C2×D4×D107C2211yescharacteristic
19#16812136—24no—
20#16812132—24no—
21C2×#13133805C2211yescharacteristic
22C2×#13133805C2211yescharacteristic, complemented
23C2×#13133805C2211yescharacteristic, complemented
24C2×D856C2211yescharacteristic
25C2×D856C2211yescharacteristic, complemented
26C2×#13133803C2211yescharacteristic
27C2×#13133801C2211yescharacteristic
28C2×C8×D107C2211yescharacteristic
29#16812106C2211yescharacteristic
30#16812105C2211yescharacteristic
31#16812098C2211yescharacteristic
32#16812082—21no—
33#16812082—21no—
34#16812079—21no—
35#16812079—21no—
36Q8×Dic107C2211yescharacteristic, complemented
37C4×D428—21no—
38C4×D428C2211yescharacteristic, complemented
39#16812071—21no—
40#16812071C2211yescharacteristic, complemented
41#16812066—21no—
42#16812066C2211yescharacteristic
43C4⋊C4×D107—21no—
44C4⋊C4×D107C2211yescharacteristic
45C4⋊(C107⋊C8)C2211yescharacteristic, complemented
46Dic107⋊C8C2211yescharacteristic, complemented
47Dic107⋊C8C2211yescharacteristic, complemented
48#16812033C2211yescharacteristic, complemented
49#16812031C2211yescharacteristic
50#16812031C2211yescharacteristic, complemented
51#16812030C2211yescharacteristic
52#16812029C2211yescharacteristic
53#16812029C2211yescharacteristic, complemented
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—
62#13133819—22no—
63#13133819—22no—
64#13133819—22no—
65#13133819D414yescomplemented
66C2×D428—21no—
67C2×D428—21no—
68C2×D428—21no—
69C2×D428—21no—
70C2×D428C2311yescharacteristic
71C2×D428C2311yescharacteristic
72C2×D428C2311yescharacteristic
73C2×C22⋊D107—21no—
74C2×C22⋊D107—21no—
75C2×C22⋊D107—21no—
76D4×D107—22no—
77D4×D107—22no—
78C2×C4×D107—21no—
79C2×C4×D107—21no—
80C2×C4×D107—21no—
81C2×C4×D107—21no—
82C2×C4×D107—21no—
83C2×C4×D107C2311yescharacteristic
84#13133805—22no—
85#13133805—22no—
86#13133805—22no—
87D856—22no—
88D856—22no—
89#13133803—22no—
90#13133801—22no—
91C2×C107⋊C8C2311yescharacteristic
92C2×C107⋊C8C2311yescharacteristic
93C8×D107—22no—
94C4⋊Dic107—21no—
95C4⋊Dic107C2311yescharacteristic
96Dic107⋊C4—21no—
97Dic107⋊C4D411yescharacteristic
98Dic107⋊C4D411yescharacteristic
99(C2×D107)⋊C4—21no—
100(C2×D107)⋊C4—21no—
101(C2×D107)⋊C4—21no—
102(C2×D107)⋊C4—21no—
103(C2×D107)⋊C4D411yescharacteristic
104(C2×D107)⋊C4D411yescharacteristic
105C4×Dic107—21no—
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—21no—
123C22×D107—21no—
124C22×D107—42no—
125C22×D107—81no—
126C22×D107—81no—
127C22×D107C2×D411yescharacteristic
128Q8×C107—21no—
129Q8×C107—21no—
130Q8×C107—21no—
131Q8×C107C2×D412yes—
132D4×C107—21no—
133D4×C107—21no—
134C2×C4×C107—21no—
135C2×C4×C107—21no—
136C2×C4×C107—21no—
137C2×C4×C107C2×D411yescharacteristic
138C2×C4×C107C2×D411yescharacteristic
139C2×C4×C107C2411yescharacteristic
140C22⋊D107—42no—
141C22⋊D107—81no—
142C22⋊D107—81no—
143C2×Dic107—21no—
144C2×Dic107C2×D411yescharacteristic
145C2×Dic107C2×D411yescharacteristic
146C2×Dic107C2×D411yescharacteristic
147D428—24no—
148D428—21no—
149D428—21no—
150D428—21no—
151D428—21no—
152D428—21no—
153D428—42no—
154D428—81no—
155D428—81no—
156D428C2×D412yes—
157C4×D107—24no—
158C4×D107—42no—
159C4×D107—81no—
160C4×D107—81no—
161C4×D107—81no—
162C4×D107C2×D412yes—
163C4×D107#4112yes—
164C8×C107—21no—
165C8×C107—21no—
166C107⋊C8—21no—
167C107⋊C8—21no—
168C22×C107—41no—
169C22×C107—41no—
170C22×C107—41no—
171C22×C107C22×D411yescharacteristic
172C2×D107—21no—
173C2×D107—21no—
174C2×D107—22no—
175C2×D107—41no—
176C2×D107—41no—
177C2×D107—41no—
178C2×D107—41no—
179C2×D107—41no—
180C2×D107—41no—
181C2×D107—41no—
182C2×D107—41no—
183C2×D107—84no—
184C2×D107#12112yes—
185C4×C107—22no—
186C4×C107—21no—
187C4×C107—21no—
188C4×C107—41no—
189C4×C107—41no—
190C4×C107C22×D411yescharacteristic
191C4×C107C2×#4111yescharacteristic
192Dic107—21no—
193Dic107—21no—
194Dic107—41no—
195Dic107#12112yes—
196C2×C107—81no—
197C2×C107C2×#12111yescharacteristic
198C2×C107#57611yescharacteristic
199C2×C107#57711yescharacteristic
200D107—22no—
201D107—42no—
202D107—81no—
203D107—81no—
204#3045—1071nomaximal, Sylow
205C107#304511yescharacteristic, complemented, Sylow
206C2×AGL(1,ℤ/8)—1071no—
207C2×#135—1071no—
208#535—1071no—
209#520—1071no—
210#464—1071no—
211#464D10711yescharacteristic, complemented
212#463—1071no—
213#463—1071no—
214#460—1071no—
215#460—1071no—
216#459—1071no—
217#459—1071no—
218#424—1071no—
219#417—1071no—
220C2×#102—1071no—
221C2×#41—1071no—
222C2×#41—1071no—
223C22×D4—1071no—
224AGL(1,ℤ/8)—2144no—
225#135—2144no—
226C2×Q16C2×D10711yescharacteristic, complemented
227C2×SD16—1071no—
228C2×SD16—1071no—
229C2×SD16—1071no—
230C2×SD16C2×D10711yescharacteristic
231C2×D8—1071no—
232C2×D8—1071no—
233C2×D8—1071no—
234C2×M16—1071no—
235C22×C8—1071no—
236#127—1071no—
237#127—1071no—
238#124—1071no—
239#124C2×D10711yescharacteristic
240#121—2141no—
241#121—2141no—
242#120—2141no—
243#120—2141no—
244C4×Q8—1071no—
245C4×Q8C2×D10711yescharacteristic, complemented
246C4×D4—1071no—
247C4×D4—1071no—
248C4×D4—2141no—
249C4×D4—2141no—
250#117—1071no—
251#117—2141no—
252C2×C4⋊C4—1071no—
253C2×C4⋊C4—2141no—
254C4⋊C8—1071no—
255C4⋊C8—1071no—
256C4⋊C8—1071no—
257C4⋊C8C2×D10711yescharacteristic, complemented
258#103—1071no—
259#103C2×D10711yescharacteristic, complemented
260#102—1071no—
261#102—1071no—
262#102—1071no—
263#102—1071no—
264#102—1071no—
265#102C2×D10711yescharacteristic
266C24—2141no—
267#41—1074no—
268#41—2142no—
269#41—2142no—
270#41—2142no—
271C2×Q8C22×D10711yescharacteristic
272C2×Q8C22×D10711yescharacteristic
273C2×D4—1071no—
274C2×D4—1071no—
275C2×D4—1071no—
276C2×D4—2141no—
277C2×D4—2141no—
278C2×D4—2142no—
279C2×D4—2142no—
280C2×D4—2141no—
281C2×D4—2141no—
282C2×D4—2141no—
283C2×D4—2141no—
284C2×D4—2141no—
285C2×D4C22×D10711yescharacteristic
286C22×C4—1071no—
287C22×C4—2141no—
288C22×C4—2141no—
289C22×C4—2141no—
290C22×C4—2141no—
291C22×C4—2141no—
292Q16—22no—
293SD16—22no—
294SD16—2142no—
295SD16—2142no—
296SD16—2142no—
297D8—2142no—
298D8—2142no—
299D8—2142no—
300M16—2142no—
301C2×C8—1071no—
302C2×C8—1071no—
303C2×C8—2142no—
304C2×C8C22×D10711yescharacteristic
305C2×C8C22×D10711yescharacteristic
306C4⋊C4—21no—
307C4⋊C4—1071no—
308C4⋊C4—1071no—
309C4⋊C4—1071no—
310C4⋊C4—2141no—
311C4⋊C4—2141no—
312C4⋊C4C22×D10711yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—1071no—
316C22⋊C4—1071no—
317C22⋊C4—2141no—
318C22⋊C4—2141no—
319C22⋊C4—2141no—
320C22⋊C4—2141no—
321C42—21no—
322C42—1071no—
323C42—2141no—
324C42C22×D10711yescharacteristic
325C23—21no—
326C23—8561no—
327C23—8561no—
328C23—1071no—
329C23—4282no—
330C23—2141no—
331C23—2141no—
332C23—2141no—
333Q8—21no—
334Q8—21no—
335Q8—21no—
336Q8D4×D10712yes—
337D4—21no—
338D4—21no—
339D4—8561no—
340D4—8561no—
341D4—8561no—
342D4—8561no—
343D4—1072no—
344D4—4282no—
345D4—4282no—
346D4—2144no—
347D4—2141no—
348D4—2141no—
349D4—2141no—
350D4—2141no—
351D4—2141no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—8561no—
356C2×C4—8561no—
357C2×C4—8561no—
358C2×C4—1071no—
359C2×C4—1072no—
360C2×C4—1072no—
361C2×C4—1071no—
362C2×C4—1071no—
363C2×C4—4282no—
364C2×C4—2144no—
365C2×C4—2141no—
366C2×C4D4×D10711yescharacteristic
367C2×C4D4×D10711yescharacteristic
368C2×C4C23×D10711yescharacteristic
369C8—21no—
370C8—21no—
371C8—2141no—
372C8—2141no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—8564no—
377C22—1072no—
378C22—4281no—
379C22—4281no—
380C22—4281no—
381C22—4281no—
382C22—4281no—
383C22—4281no—
384C22—4281no—
385C22—4281no—
386C22—2142no—
387C22—2141no—
388C22—2141no—
389C22C2×D4×D10711yescharacteristic
390C4—21no—
391C4—21no—
392C4—22no—
393C4—41no—
394C4—41no—
395C4—1072no—
396C4—4281no—
397C4—2141no—
398C4—2141no—
399C4C2×D4×D10711yescharacteristic
400C4#41×D10711yescharacteristic
401C2—81no—
402C2—8561no—
403C2—8561no—
404C2—4282no—
405C2—2142no—
406C2#121×D10711yescharacteristic
407C2#2029342911yescharacteristic
408C2#2029343611yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#464×C107C2
socleC22×C107C22×D4
hypercenter#464D107
hypocenterC107#3045
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×#16812136C2semidirect
2. C2×#16812132C2semidirect
3. #20293195C2semidirect
4. #20293109C2semidirect
5. #20292851C2semidirect
6. #20292845C2semidirect
7. #20292839C2semidirect
8. #20292827C2semidirect
9. #20292825C2semidirect
10. #20292823C2semidirect
11. #20292821C2semidirect
12. #20292652C2semidirect
13. #20292627C2semidirect
14. #102×D107C2semidirect
15. #464×C107C2semidirect
22. C2×#13133805C22semidirect
23. C2×#13133805C22semidirect
25. C2×D856C22semidirect
36. Q8×Dic107C22semidirect
38. C4×D428C22semidirect
40. #16812071C22semidirect
45. C4⋊(C107⋊C8)C22semidirect
46. Dic107⋊C8C22semidirect
47. Dic107⋊C8C22semidirect
48. #16812033C22semidirect
50. #16812031C22semidirect
53. #16812029C22semidirect
54. C2×Q16×C107C22semidirect
57. C4×Q8×C107C22semidirect
58. C4⋊C8×C107C22semidirect
59. #103×C107C22semidirect
65. #13133819D4semidirect
205. C107#3045semidirect
211. #464D107semidirect
226. C2×Q16C2×D107semidirect
245. C4×Q8C2×D107semidirect
257. C4⋊C8C2×D107semidirect
259. #103C2×D107semidirect

Maximal subgroups

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

subgroupindex
C2×#168121362
C2×#168121322
#202931952
#202931092
#202928512
#202928452
#202928392
#202928272
#202928252
#202928232
#202928212
#202926522
#202926272
#102×D1072
#464×C1072
#3045107