Finite Group Databasebeta

← #15683112

Subgroups — #15683112

Order 2944.

452 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13093216C211yesmaximal, characteristic, complemented
2#13093213C211yesmaximal, characteristic, complemented
3C2×#10625087C211yesmaximal, characteristic, complemented
4#131×D23C211yesmaximal, characteristic, complemented
5#13092691C211yesmaximal, characteristic, complemented
6#13092690C211yesmaximal, characteristic, complemented
7#13092686C211yesmaximal, characteristic, complemented
8#13092685C211yesmaximal, characteristic, complemented
9#13092681C211yesmaximal, characteristic, complemented
10#13092680C211yesmaximal, characteristic, complemented
11#13092677C211yesmaximal, characteristic, complemented
12#108×D23C211yesmaximal, characteristic, complemented
13#13092400C211yesmaximal, characteristic, complemented
14#13092398C211yesmaximal, characteristic, complemented
15C23×#471C211yesmaximal, characteristic, complemented
16#41×D23C2211yescharacteristic
17C2×#67292C2211yescharacteristic
18C2×#67290C2211yescharacteristic
19C23×#137C2211yescharacteristic
20C23×AGL(1,ℤ/8)C2211yescharacteristic
21C2×SD16×C23C2211yescharacteristic, complemented
22C23×#131C2211yescharacteristic
23#10625122C2211yescharacteristic
24#10625120C2211yescharacteristic
25#10625119C2211yescharacteristic
26C2×#67275C2211yescharacteristic, complemented
27#10625113C2211yescharacteristic
28#10625103C2211yescharacteristic
29C2×#67272C2211yescharacteristic, complemented
30#10625090—21no—
31#10625089—21no—
32#10625087—21no—
33#10625087—21no—
34#10625087—21no—
35#10625087—21no—
36#10625087—21no—
37#10625087—21no—
38#10625086—21no—
39#10625085—21no—
40#10625083—21no—
41#10625082—21no—
42#10625080C2211yescharacteristic
43#10625079C2211yescharacteristic
44#10625078—21no—
45#10625078C2211yescharacteristic
46M16×D23—21no—
47M16×D23C2211yescharacteristic
48M16×D23C2211yescharacteristic
49M16×D23C2211yescharacteristic
50C2×#67263C2211yescharacteristic, complemented
51#10625072—21no—
52#10625072C2211yescharacteristic
53C2×C8×D23—21no—
54C2×C8×D23C2211yescharacteristic
55C23×#108C2211yescharacteristic, complemented
56C23×#101C2211yescharacteristic, complemented
57C23×#100C2211yescharacteristic, complemented
58#10625018C2211yescharacteristic, complemented
59#10625015C2211yescharacteristic, complemented
60#10625006C2211yescharacteristic, complemented
61#10625006C2211yescharacteristic, complemented
62#10625005C2211yescharacteristic, complemented
63#10625005C2211yescharacteristic, complemented
64#10625004C2211yescharacteristic, complemented
65#10625004C2211yescharacteristic, complemented
66#10625001C2211yescharacteristic, complemented
67#41×C23C2311yescharacteristic
68C2×Q8×C23C2311yescharacteristic
69C2×D4×C23C2311yescharacteristic
70C2×C22⋊D23—21no—
71C22×Dic23—21no—
72#67292—21no—
73#67292—21no—
74#67292—21no—
75#67292—21no—
76#67292D411yescharacteristic
77Q8×D23D411yescharacteristic
78#67290—21no—
79#67290—21no—
80#67290—21no—
81#67290—21no—
82#67290—21no—
83#67290D411yescharacteristic
84D4×D23—21no—
85D4×D23D411yescharacteristic
86#67288—21no—
87#67288C2311yescharacteristic
88C2×D92—21no—
89C2×D92C2311yescharacteristic
90C2×C4×D23—21no—
91C2×C4×D23—21no—
92C2×C4×D23C2311yescharacteristic
93C2×Dic46C2311yescharacteristic
94Q16×C23—21no—
95SD16×C23—21no—
96SD16×C23—21no—
97SD16×C23—21no—
98SD16×C23—21no—
99D8×C23—21no—
100M16×C23—21no—
101M16×C23C2311yescharacteristic
102M16×C23C2311yescharacteristic
103M16×C23C2311yescharacteristic
104C2×C8×C23—21no—
105C2×C8×C23C2311yescharacteristic
106#67275—21no—
107#67275—21no—
108#67275—21no—
109#67275—21no—
110#67274—21no—
111#67274—21no—
112#67273—21no—
113#67273—21no—
114#67272—21no—
115#67272—21no—
116#67272—21no—
117#67272—21no—
118#67267—21no—
119#67267C2311yescharacteristic
120#67267C2311yescharacteristic
121#67267C2311yescharacteristic
122C2×C23⋊C8—21no—
123C2×C23⋊C8C2311yescharacteristic
124Dic92—21no—
125D184—21no—
126#67263—21no—
127#67263—21no—
128#67263—21no—
129#67263—21no—
130#67262—21no—
131#67262—21no—
132#67262—21no—
133#67262—21no—
134#67262—21no—
135C8×D23—21no—
136C8×D23—21no—
137C8×D23—21no—
138C8×D23—21no—
139C8×D23—21no—
140C8×D23D411yescharacteristic
141C8×D23D411yescharacteristic
142C8×D23D411yescharacteristic
143C8×D23D411yescharacteristic
144C23×C23—21no—
145C22×D23—21no—
146C22×D23—21no—
147C22×D23#4111yescharacteristic
148Q8×C23—21no—
149Q8×C23—21no—
150Q8×C23C2×D411yescharacteristic
151D4×C23—21no—
152D4×C23—21no—
153D4×C23—21no—
154D4×C23C2×D411yescharacteristic
155C2×C4×C23—21no—
156C2×C4×C23—21no—
157C2×C4×C23C2411yescharacteristic
158C22⋊D23—21no—
159C22⋊D23—21no—
160C22⋊D23—21no—
161C22⋊D23—41no—
162C22⋊D23—41no—
163C2×Dic23—21no—
164C2×Dic23—21no—
165C2×Dic23—41no—
166C2×Dic23—41no—
167C2×Dic23#4111yescharacteristic
168D92—21no—
169D92—21no—
170D92—21no—
171D92—41no—
172D92—41no—
173D92C2×D411yescharacteristic
174C4×D23—21no—
175C4×D23—21no—
176C4×D23—21no—
177C4×D23—41no—
178C4×D23—41no—
179C4×D23C2×D411yescharacteristic
180C4×D23C2×D411yescharacteristic
181C4×D23C2×D411yescharacteristic
182C4×D23C2×D411yescharacteristic
183Dic46—21no—
184Dic46—21no—
185Dic46—21no—
186Dic46C2×D411yescharacteristic
187C8×C23—21no—
188C8×C23—21no—
189C8×C23—21no—
190C8×C23C2×D411yescharacteristic
191C8×C23C2×D411yescharacteristic
192C23⋊C8—21no—
193C23⋊C8—21no—
194C23⋊C8—21no—
195C23⋊C8C2×D411yescharacteristic
196C23⋊C8C2×D411yescharacteristic
197#3067—231nomaximal, Sylow
198C22×C23—21no—
199C22×C23—41no—
200C22×C23—81no—
201C22×C23C2×#4111yescharacteristic
202C2×D23—21no—
203C2×D23—41no—
204C2×D23—42no—
205C2×D23—41no—
206C2×D23—81no—
207C2×D23#12111yescharacteristic
208C2×D23#12111yescharacteristic
209C4×C23—21no—
210C4×C23—41no—
211C4×C23C22×D411yescharacteristic
212C4×C23C22×D411yescharacteristic
213Dic23—21no—
214Dic23—41no—
215Dic23#12111yescharacteristic
216Dic23#12111yescharacteristic
217#575—231no—
218#575—231no—
219C2×#135—231no—
220C2×#131—231no—
221#473—231no—
222#473—231no—
223#472—231no—
224#472—231no—
225#471—231no—
226#471—231no—
227#471—231no—
228#471D2311yescharacteristic, complemented
229C2×#108—231no—
230#413—231no—
231#413—231no—
232C2×C23—21no—
233C2×C23—41no—
234C2×C23—81no—
235C2×C23C2×#12111yescharacteristic
236D23—21no—
237D23—21no—
238D23—41no—
239D23—81no—
240C2×#41—231no—
241C2×#41—231no—
242C2×#41—231no—
243#137—231no—
244#137—231no—
245#137—231no—
246#137—461no—
247#137—461no—
248#137C2×D2311yescharacteristic
249AGL(1,ℤ/8)—231no—
250AGL(1,ℤ/8)—231no—
251AGL(1,ℤ/8)—231no—
252AGL(1,ℤ/8)—461no—
253AGL(1,ℤ/8)—461no—
254AGL(1,ℤ/8)C2×D2311yescharacteristic
255#135—461no—
256#135—461no—
257#135—461no—
258#135—461no—
259#135—461no—
260#135—461no—
261#135—461no—
262#135—461no—
263C2×Q16—231no—
264C2×SD16—231no—
265C2×SD16C2×D2311yescharacteristic, complemented
266C2×D8—231no—
267#131—231no—
268#131—231no—
269#131—231no—
270#131—461no—
271#131—461no—
272#131C2×D2311yescharacteristic
273C2×M16—231no—
274C2×M16—231no—
275C2×M16—231no—
276C2×M16—461no—
277C22×C8—231no—
278C22×C8—461no—
279#108—231no—
280#108—231no—
281#108—231no—
282#108C2×D2311yescharacteristic, complemented
283#101—231no—
284#101—231no—
285#101—231no—
286#101C2×D2311yescharacteristic, complemented
287#100—231no—
288#100—231no—
289#100—231no—
290#100C2×D2311yescharacteristic, complemented
291C23#306711yescharacteristic, complemented, Sylow
292#41—231no—
293#41—231no—
294#41—231no—
295#41—461no—
296#41—461no—
297#41—461no—
298#41—461no—
299#41—461no—
300#41—461no—
301#41—461no—
302#41—461no—
303#41—461no—
304#41—461no—
305#41C22×D2311yescharacteristic
306C2×Q8—231no—
307C2×Q8—231no—
308C2×Q8C22×D2311yescharacteristic
309C2×D4—231no—
310C2×D4—231no—
311C2×D4—461no—
312C2×D4—461no—
313C2×D4—461no—
314C2×D4C22×D2311yescharacteristic
315C22×C4—231no—
316C22×C4—461no—
317C22×C4—461no—
318C22×C4—461no—
319Q16—21no—
320Q16—461no—
321Q16—461no—
322Q16—461no—
323Q16—461no—
324Q16—461no—
325SD16—21no—
326SD16—21no—
327SD16—21no—
328SD16—21no—
329SD16—461no—
330SD16—461no—
331SD16—461no—
332SD16—461no—
333SD16—461no—
334SD16—461no—
335SD16—461no—
336SD16—461no—
337D8—21no—
338D8—461no—
339D8—461no—
340D8—461no—
341D8—461no—
342D8—461no—
343M16—21no—
344M16—231no—
345M16—231no—
346M16—231no—
347M16—461no—
348M16—461no—
349M16—461no—
350M16—461no—
351M16—461no—
352M16—461no—
353M16C22×D2311yescharacteristic
354M16C22×D2311yescharacteristic
355M16C22×D2311yescharacteristic
356C2×C8—21no—
357C2×C8—231no—
358C2×C8—231no—
359C2×C8—231no—
360C2×C8—231no—
361C2×C8—231no—
362C2×C8—461no—
363C2×C8—461no—
364C2×C8—461no—
365C2×C8—461no—
366C2×C8—461no—
367C2×C8—461no—
368C2×C8C22×D2311yescharacteristic
369C23—21no—
370C23—231no—
371C23—461no—
372C23—461no—
373Q8—21no—
374Q8—21no—
375Q8—231no—
376Q8—461no—
377Q8—461no—
378Q8—461no—
379Q8D4×D2311yescharacteristic
380D4—21no—
381D4—21no—
382D4—21no—
383D4—231no—
384D4—461no—
385D4—461no—
386D4—461no—
387D4—461no—
388D4—461no—
389D4—461no—
390D4—921no—
391D4—921no—
392D4—921no—
393D4—921no—
394D4D4×D2311yescharacteristic
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—231no—
398C2×C4—231no—
399C2×C4—231no—
400C2×C4—231no—
401C2×C4—231no—
402C2×C4—461no—
403C2×C4—461no—
404C2×C4—461no—
405C2×C4—461no—
406C2×C4—461no—
407C2×C4—921no—
408C2×C4—921no—
409C2×C4—921no—
410C2×C4—921no—
411C2×C4C23×D2311yescharacteristic
412C8—21no—
413C8—21no—
414C8—21no—
415C8—231no—
416C8—231no—
417C8—461no—
418C8—461no—
419C8—461no—
420C8D4×D2311yescharacteristic
421C8D4×D2311yescharacteristic
422C22—21no—
423C22—41no—
424C22—81no—
425C22—231no—
426C22—231no—
427C22—461no—
428C22—921no—
429C22—922no—
430C22—921no—
431C22—1841no—
432C22#41×D2311yescharacteristic
433C4—21no—
434C4—41no—
435C4—231no—
436C4—231no—
437C4—461no—
438C4—921no—
439C4C2×D4×D2311yescharacteristic
440C4C2×D4×D2311yescharacteristic
441C2—21no—
442C2—41no—
443C2—81no—
444C2—461no—
445C2—461no—
446C2—921no—
447C2—1841no—
448C2#121×D2311yescharacteristic
subgroupG/H
centerC2#121×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#471C2
socleC2×C23C2×#121
hypercenter#471D23
hypocenterC23#3067
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ #471

Complements

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

NH ≅ G/Ntype
1. #13093216C2semidirect
2. #13093213C2semidirect
3. C2×#10625087C2semidirect
4. #131×D23C2semidirect
5. #13092691C2semidirect
6. #13092690C2semidirect
7. #13092686C2semidirect
8. #13092685C2semidirect
9. #13092681C2semidirect
10. #13092680C2semidirect
11. #13092677C2semidirect
12. #108×D23C2semidirect
13. #13092400C2semidirect
14. #13092398C2semidirect
15. C23×#471C2semidirect
21. C2×SD16×C23C22semidirect
26. C2×#67275C22semidirect
29. C2×#67272C22semidirect
50. C2×#67263C22semidirect
55. C23×#108C22semidirect
56. C23×#101C22semidirect
57. C23×#100C22semidirect
58. #10625018C22semidirect
59. #10625015C22semidirect
60. #10625006C22semidirect
61. #10625006C22semidirect
62. #10625005C22semidirect
63. #10625005C22semidirect
64. #10625004C22semidirect
65. #10625004C22semidirect
66. #10625001C22semidirect
228. #471D23semidirect
265. C2×SD16C2×D23semidirect
282. #108C2×D23semidirect
286. #101C2×D23semidirect
290. #100C2×D23semidirect
291. C23#3067semidirect

Maximal subgroups

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

subgroupindex
#130932162
#130932132
C2×#106250872
#131×D232
#130926912
#130926902
#130926862
#130926852
#130926812
#130926802
#130926772
#108×D232
#130924002
#130923982
C23×#4712
#306723