Finite Group Databasebeta

← SD16×C22⋊D107 #28348151

Subgroups — SD16×C22⋊D107 #28348151

Order 13696.

546 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D107C211yesmaximal, characteristic, complemented
2Q8×C22⋊D107C211yesmaximal, characteristic, complemented
3D4×C22⋊D107C211yesmaximal, characteristic
4#20292998C211yesmaximal, characteristic, complemented
5#20292856C211yesmaximal, characteristic, complemented
6#20292853C211yesmaximal, characteristic, complemented
7#20292830C211yesmaximal, characteristic, complemented
8#20292825C211yesmaximal, characteristic, complemented
9#20292778C211yesmaximal, characteristic, complemented
10#20292776C211yesmaximal, characteristic, complemented
11#20292766C211yesmaximal, characteristic, complemented
12#20292764C211yesmaximal, characteristic, complemented
13SD16×Dic107C211yesmaximal, characteristic, complemented
14C8×C22⋊D107C211yesmaximal, characteristic, complemented
15C22×SD16×C107C211yesmaximal, characteristic, complemented
16C2×Q8×D107C2211yescharacteristic, complemented
17C22×C22⋊D107—21no—
18C2×D4×D107C2211yescharacteristic
19C2×#13133807C2211yescharacteristic, complemented
20C2×#13133806C2211yescharacteristic
21C2×#13133806C2211yescharacteristic, complemented
22C2×#13133805C2211yescharacteristic, complemented
23C2×#13133805C2211yescharacteristic, complemented
24SD16×D107—24no—
25C2×C8×D107C2211yescharacteristic, complemented
26#16812107—21no—
27#16812107C2211yescharacteristic, complemented
28#16812105C2211yescharacteristic
29#16812088—21no—
30#16812088C2211yescharacteristic, complemented
31#16812085—21no—
32#16812085C2211yescharacteristic, complemented
33#16812083C2211yescharacteristic
34#16812081—21no—
35#16812080C2211yescharacteristic
36#16812078—21no—
37#16812077—21no—
38Q8×Dic107C2211yescharacteristic, complemented
39D4×Dic107C2211yescharacteristic
40C4×C22⋊D107—21no—
41C4×C22⋊D107C2211yescharacteristic
42#16812041C2211yescharacteristic, complemented
43Dic107⋊C8C2211yescharacteristic, complemented
44#16812034C2211yescharacteristic, complemented
45#16812033C2211yescharacteristic, complemented
46#16812033C2211yescharacteristic, complemented
47#16812031C2211yescharacteristic, complemented
48#16812030C2211yescharacteristic
49#16812030C2211yescharacteristic, complemented
50C22⋊(C107⋊C8)C2211yescharacteristic, complemented
51(C2×D107)⋊C8C2211yescharacteristic, complemented
52C8×Dic107C2211yescharacteristic, complemented
53C22×Q8×C107C2211yescharacteristic, complemented
54C22×D4×C107C2211yescharacteristic
55C2×SD16×C107—24no—
56C2×SD16×C107C2211yescharacteristic
57C2×SD16×C107C2211yescharacteristic
58C2×SD16×C107C2211yescharacteristic, complemented
59C2×SD16×C107C2211yescharacteristic, complemented
60C22×C8×C107C2211yescharacteristic, complemented
61C23×D107—21no—
62C2×Dic214—21no—
63C2×Dic214C2311yescharacteristic
64Q8×D107—22no—
65Q8×D107—41no—
66C2×D428C2311yescharacteristic
67C2×C22⋊D107—21no—
68C2×C22⋊D107—21no—
69C2×C22⋊D107—21no—
70C2×C22⋊D107—21no—
71C2×C22⋊D107—21no—
72C2×C22⋊D107—44no—
73C2×C22⋊D107D411yescharacteristic
74D4×D107—22no—
75D4×D107—41no—
76C22×Dic107—21no—
77C2×C4×D107—21no—
78C2×C4×D107C2311yescharacteristic
79#13133807—22no—
80#13133806—22no—
81#13133806—41no—
82#13133805—22no—
83#13133805—41no—
84C2×C107⋊C8C2311yescharacteristic
85C2×C107⋊C8C2311yescharacteristic
86C8×D107—22no—
87C4⋊Dic107—21no—
88C4⋊Dic107C2311yescharacteristic
89C4⋊Dic107C2311yescharacteristic
90Dic107⋊C4—21no—
91Dic107⋊C4—21no—
92Dic107⋊C4—21no—
93Dic107⋊C4—21no—
94Dic107⋊C4D411yescharacteristic
95C22⋊Dic107—21no—
96C22⋊Dic107—21no—
97C22⋊Dic107—21no—
98C22⋊Dic107D411yescharacteristic
99(C2×D107)⋊C4—21no—
100(C2×D107)⋊C4—21no—
101(C2×D107)⋊C4D411yescharacteristic
102C4×Dic107—21no—
103C4×Dic107C2311yescharacteristic
104C24×C107—21no—
105C2×Q8×C107—21no—
106C2×Q8×C107—22no—
107C2×Q8×C107—41no—
108C2×Q8×C107C2311yescharacteristic
109C2×Q8×C107C2311yescharacteristic
110C2×D4×C107—22no—
111C2×D4×C107—21no—
112C2×D4×C107—41no—
113C2×D4×C107C2311yescharacteristic
114C2×D4×C107C2311yescharacteristic
115C22×C4×C107—21no—
116C22×C4×C107C2311yescharacteristic
117SD16×C107—22no—
118SD16×C107—22no—
119SD16×C107—22no—
120SD16×C107D414yescomplemented
121C2×C8×C107—22no—
122C2×C8×C107C2311yescharacteristic
123C2×C8×C107C2311yescharacteristic
124C23×C107—21no—
125C23×C107—21no—
126C23×C107—42no—
127C23×C107—42no—
128C23×C107—81no—
129C23×C107C2×D411yescharacteristic
130C22×D107—21no—
131C22×D107—42no—
132C22×D107—42no—
133C22×D107—81no—
134C22×D107C2×D411yescharacteristic
135Q8×C107—21no—
136Q8×C107—21no—
137Q8×C107—21no—
138Q8×C107—42no—
139Q8×C107C2×D412yescomplemented
140D4×C107—21no—
141D4×C107—21no—
142D4×C107—21no—
143D4×C107—42no—
144D4×C107C2×D412yes—
145C2×C4×C107—21no—
146C2×C4×C107—21no—
147C2×C4×C107—21no—
148C2×C4×C107—21no—
149C2×C4×C107—42no—
150C2×C4×C107C2×D411yescharacteristic
151C2×C4×C107C2411yescharacteristic
152C22⋊D107—42no—
153C22⋊D107—42no—
154C22⋊D107—42no—
155C22⋊D107—42no—
156C22⋊D107—81no—
157C22⋊D107SD1614yesdirect product factor
158C2×Dic107—21no—
159C2×Dic107—21no—
160C2×Dic107—21no—
161C2×Dic107—42no—
162C2×Dic107C2×D411yescharacteristic
163C2×Dic107C2×D411yescharacteristic
164C2×Dic107C2×D411yescharacteristic
165D428—21no—
166D428—21no—
167C4×D107—21no—
168C4×D107—21no—
169C4×D107—42no—
170Dic214—21no—
171Dic214—21no—
172Dic214—42no—
173C8×C107—21no—
174C8×C107C2×D412yescomplemented
175C107⋊C8—21no—
176C107⋊C8—21no—
177C22×C107—21no—
178C22×C107—21no—
179C22×C107—22no—
180C22×C107—41no—
181C22×C107—41no—
182C22×C107—41no—
183C22×C107—41no—
184C22×C107—41no—
185C22×C107—84no—
186C22×C107C2×SD1612yescomplemented
187C22×C107C22×D411yescharacteristic
188C2×D107—21no—
189C2×D107—21no—
190C2×D107—41no—
191C2×D107—41no—
192C2×D107—41no—
193C2×D107—84no—
194C2×D107C2×SD1612yescomplemented
195C4×C107—22no—
196C4×C107—21no—
197C4×C107—41no—
198C4×C107C22×D411yescharacteristic
199C4×C107H(5,𝔽2)11yescharacteristic
200Dic107—21no—
201Dic107—21no—
202Dic107—41no—
203Dic107—41no—
204Dic107—41no—
205Dic107C2×SD1612yescomplemented
206C2×C107—22no—
207C2×C107—42no—
208C2×C107—81no—
209C2×C107D4211yescharacteristic
210C2×C107C22×SD1611yescharacteristic
211C2×C107#57711yescharacteristic
212D107—22no—
213D107—81no—
214D4×SD16—1071nomaximal, Sylow
215C107D4×SD1611yescharacteristic, complemented, Sylow
216C22×SD16—1071no—
217C22×SD16D10711yescharacteristic, complemented
218D4×Q8—1071no—
219D42—1071no—
220#492—1071no—
221#465—1071no—
222#465—1071no—
223#461—1071no—
224#460—1071no—
225#450—1071no—
226#450—1071no—
227#448—1071no—
228#448—1071no—
229C4×SD16—1071no—
230C8×D4—1071no—
231C22×Q8—1071no—
232C22×Q8C2×D10711yescharacteristic, complemented
233C22×D4—1071no—
234C22×D4—2141no—
235C22×D4C2×D10711yescharacteristic
236C2×SD16—24no—
237C2×SD16—1071no—
238C2×SD16—1071no—
239C2×SD16—1071no—
240C2×SD16—1071no—
241C2×SD16—1071no—
242C2×SD16—2144no—
243C2×SD16C2×D10711yescharacteristic
244C2×SD16C2×D10711yescharacteristic
245C2×SD16C2×D10711yescharacteristic, complemented
246C2×SD16C2×D10711yescharacteristic, complemented
247C22×C8—1071no—
248C22×C8C2×D10711yescharacteristic, complemented
249C4⋊Q8—1071no—
250C4⋊Q8—2141no—
251#127—1071no—
252C22⋊Q8—1071no—
253C22⋊Q8—1071no—
254C22⋊Q8—2141no—
255C22⋊Q8—2141no—
256#121—1071no—
257#121—1071no—
258#121—2141no—
259#120—2141no—
260#120—2141no—
261C4×Q8—1071no—
262C4×D4—1071no—
263C4×D4—1071no—
264C4×D4—2141no—
265#106—1071no—
266C4⋊C8—1071no—
267#103—1071no—
268#103—1071no—
269#103—1071no—
270#102—1071no—
271#102—1071no—
272#102—1071no—
273C22⋊C8—1071no—
274C22⋊C8—1071no—
275C4×C8—1071no—
276C24—21no—
277C24—2141no—
278C2×Q8—21no—
279C2×Q8—22no—
280C2×Q8—41no—
281C2×Q8—1071no—
282C2×Q8—4281no—
283C2×Q8—2141no—
284C2×Q8—2142no—
285C2×Q8C22×D10711yescharacteristic
286C2×Q8C22×D10711yescharacteristic
287C2×D4—22no—
288C2×D4—21no—
289C2×D4—41no—
290C2×D4—1071no—
291C2×D4—1071no—
292C2×D4—4284no—
293C2×D4—4281no—
294C2×D4—2141no—
295C2×D4—2141no—
296C2×D4—2141no—
297C2×D4—2141no—
298C2×D4—2141no—
299C2×D4—2142no—
300C2×D4C22×D10711yescharacteristic
301C2×D4C22×D10711yescharacteristic
302C22×C4—21no—
303C22×C4—1071no—
304C22×C4—2141no—
305C22×C4—2141no—
306C22×C4C22×D10711yescharacteristic
307SD16—22no—
308SD16—22no—
309SD16—22no—
310SD16—4281no—
311SD16—4281no—
312SD16—2142no—
313SD16—2142no—
314SD16—2142no—
315SD16C22⋊D10714yesdirect product factor
316C2×C8—22no—
317C2×C8—1071no—
318C2×C8—1071no—
319C2×C8—2142no—
320C2×C8C22×D10711yescharacteristic
321C2×C8C22×D10711yescharacteristic
322C4⋊C4—1071no—
323C4⋊C4—1071no—
324C4⋊C4—1071no—
325C4⋊C4—2141no—
326C4⋊C4—2141no—
327C4⋊C4—2141no—
328C4⋊C4—2141no—
329C4⋊C4—2141no—
330C22⋊C4—1071no—
331C22⋊C4—1071no—
332C22⋊C4—2141no—
333C22⋊C4—2141no—
334C22⋊C4—2141no—
335C22⋊C4—2141no—
336C22⋊C4—2141no—
337C42—1071no—
338C42—2141no—
339C23—21no—
340C23—21no—
341C23—42no—
342C23—42no—
343C23—81no—
344C23—8561no—
345C23—1071no—
346C23—4282no—
347C23—4282no—
348C23—2141no—
349C23D4×D10711yescharacteristic
350Q8—21no—
351Q8—21no—
352Q8—21no—
353Q8—42no—
354Q8—4282no—
355Q8—2141no—
356Q8—2141no—
357Q8C2×C22⋊D10712yescomplemented
358D4—21no—
359D4—21no—
360D4—21no—
361D4—42no—
362D4—8561no—
363D4—1074no—
364D4—4282no—
365D4—4282no—
366D4—4282no—
367D4—4282no—
368D4—2141no—
369D4—2141no—
370D4C2×C22⋊D10712yes—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—42no—
376C2×C4—1071no—
377C2×C4—1071no—
378C2×C4—1071no—
379C2×C4—4282no—
380C2×C4—4282no—
381C2×C4—2141no—
382C2×C4—2141no—
383C2×C4—2141no—
384C2×C4—2141no—
385C2×C4—2141no—
386C2×C4D4×D10711yescharacteristic
387C2×C4C23×D10711yescharacteristic
388C8—21no—
389C8—2141no—
390C8—2141no—
391C8C2×C22⋊D10712yescomplemented
392C22—21no—
393C22—21no—
394C22—22no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—84no—
401C22—8564no—
402C22—1072no—
403C22—4281no—
404C22—4281no—
405C22—4281no—
406C22—2141no—
407C22—2141no—
408C22SD16×D10712yescomplemented
409C22C2×D4×D10711yescharacteristic
410C4—21no—
411C4—22no—
412C4—41no—
413C4—1072no—
414C4—4281no—
415C4—4281no—
416C4—4281no—
417C4—2141no—
418C4—2141no—
419C4C22×C22⋊D10711yescharacteristic
420C4#1681215411yescharacteristic
421C2—22no—
422C2—42no—
423C2—81no—
424C2—8561no—
425C2—2142no—
426C2D4×C22⋊D10711yescharacteristic
427C2C2×SD16×D10711yescharacteristic
428C2#2029343311yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
FittingC22×SD16×C107C2
socleC22×C107C22×D4
prime radicalD4×C22⋊D107C2
hypercenterC22×SD16D107
hypocenterC107D4×SD16
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D107C2semidirect
2. Q8×C22⋊D107C2semidirect
4. #20292998C2semidirect
5. #20292856C2semidirect
6. #20292853C2semidirect
7. #20292830C2semidirect
8. #20292825C2semidirect
9. #20292778C2semidirect
10. #20292776C2semidirect
11. #20292766C2semidirect
12. #20292764C2semidirect
13. SD16×Dic107C2semidirect
14. C8×C22⋊D107C2semidirect
15. C22×SD16×C107C2semidirect
16. C2×Q8×D107C22semidirect
19. C2×#13133807C22semidirect
21. C2×#13133806C22semidirect
22. C2×#13133805C22semidirect
23. C2×#13133805C22semidirect
25. C2×C8×D107C22semidirect
27. #16812107C22semidirect
30. #16812088C22semidirect
32. #16812085C22semidirect
38. Q8×Dic107C22semidirect
42. #16812041C22semidirect
43. Dic107⋊C8C22semidirect
44. #16812034C22semidirect
45. #16812033C22semidirect
46. #16812033C22semidirect
47. #16812031C22semidirect
49. #16812030C22semidirect
50. C22⋊(C107⋊C8)C22semidirect
51. (C2×D107)⋊C8C22semidirect
52. C8×Dic107C22semidirect
53. C22×Q8×C107C22semidirect
58. C2×SD16×C107C22semidirect
59. C2×SD16×C107C22semidirect
60. C22×C8×C107C22semidirect
120. SD16×C107D4semidirect
139. Q8×C107C2×D4semidirect
157. C22⋊D107SD16direct (N × H)
174. C8×C107C2×D4semidirect
186. C22×C107C2×SD16semidirect
194. C2×D107C2×SD16semidirect
205. Dic107C2×SD16semidirect
215. C107D4×SD16semidirect
217. C22×SD16D107semidirect
232. C22×Q8C2×D107semidirect
245. C2×SD16C2×D107semidirect
246. C2×SD16C2×D107semidirect
248. C22×C8C2×D107semidirect
315. SD16C22⋊D107direct (N × H)
357. Q8C2×C22⋊D107semidirect
391. C8C2×C22⋊D107semidirect
408. C22SD16×D107semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D1072
Q8×C22⋊D1072
D4×C22⋊D1072
#202929982
#202928562
#202928532
#202928302
#202928252
#202927782
#202927762
#202927662
#202927642
SD16×Dic1072
C8×C22⋊D1072
C22×SD16×C1072
D4×SD16107