Finite Group Databasebeta

← #15683132

Subgroups — #15683132

Order 2944.

446 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13093216C211yesmaximal, characteristic
2C2×#10625089C211yesmaximal, characteristic, complemented
3#137×D23C211yesmaximal, characteristic, complemented
4#13093182C211yesmaximal, characteristic, complemented
5#13092691C211yesmaximal, characteristic, complemented
6#13092690C211yesmaximal, characteristic, complemented
7#13092689C211yesmaximal, characteristic, complemented
8#13092683C211yesmaximal, characteristic, complemented
9#13092682C211yesmaximal, characteristic, complemented
10#13092681C211yesmaximal, characteristic, complemented
11#13092680C211yesmaximal, characteristic, complemented
12#13092464C211yesmaximal, characteristic, complemented
13#13092400C211yesmaximal, characteristic, complemented
14#101×D23C211yesmaximal, characteristic, complemented
15C23×#473C211yesmaximal, characteristic, complemented
16#41×D23C2211yescharacteristic
17C2×#67292C2211yescharacteristic
18C2×Q8×D23C2211yescharacteristic
19C23×#137C2211yescharacteristic
20C23×#137C2211yescharacteristic
21C2×Q16×C23C2211yescharacteristic, complemented
22C23×#131C2211yescharacteristic
23#10625122C2211yescharacteristic
24#10625120C2211yescharacteristic
25#10625119C2211yescharacteristic
26C2×#67275C2211yescharacteristic, complemented
27#10625113C2211yescharacteristic
28#10625113C2211yescharacteristic
29C2×#67274C2211yescharacteristic, complemented
30#10625090—21no—
31#10625089—21no—
32#10625089—21no—
33#10625089—21no—
34#10625089—21no—
35#10625089—21no—
36#10625089—21no—
37Q16×D23—21no—
38#10625087—21no—
39#10625086—21no—
40#10625085—21no—
41SD16×D23—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×#67262—21no—
54C2×#67262C2211yescharacteristic
55C23×#108C2211yescharacteristic, complemented
56C23×#101C2211yescharacteristic, complemented
57C23×#101C2211yescharacteristic, complemented
58#10625018C2211yescharacteristic, complemented
59#10625018C2211yescharacteristic, 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×Q8×C23C2311yescharacteristic
70#67292—21no—
71#67292—21no—
72#67292—21no—
73#67292—21no—
74#67292D411yescharacteristic
75Q8×D23—21no—
76Q8×D23—21no—
77Q8×D23—21no—
78Q8×D23—21no—
79Q8×D23D411yescharacteristic
80#67290—21no—
81#67290D411yescharacteristic
82D4×D23—21no—
83D4×D23D411yescharacteristic
84#67288—21no—
85#67288C2311yescharacteristic
86C2×D92—21no—
87C2×D92C2311yescharacteristic
88C2×C4×D23—21no—
89C2×C4×D23—21no—
90C2×C4×D23—21no—
91C2×C4×D23C2311yescharacteristic
92C2×Dic46—21no—
93C2×Dic46C2311yescharacteristic
94Q16×C23—21no—
95Q16×C23—21no—
96Q16×C23—21no—
97Q16×C23—21no—
98SD16×C23—21no—
99SD16×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#67275—21no—
111#67274—21no—
112#67274—21no—
113#67274—21no—
114#67274—21no—
115#67274—21no—
116#67273—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—
135#67262D411yescharacteristic
136#67262D411yescharacteristic
137#67262D411yescharacteristic
138#67262D411yescharacteristic
139C8×D23—21no—
140C8×D23—21no—
141C8×D23—21no—
142C8×D23—21no—
143C8×D23—21no—
144C22×D23—21no—
145C22×D23—21no—
146C22×D23#4111yescharacteristic
147Q8×C23—21no—
148Q8×C23—21no—
149Q8×C23—21no—
150Q8×C23—21no—
151Q8×C23C2×D411yescharacteristic
152D4×C23—21no—
153D4×C23C2×D411yescharacteristic
154C2×C4×C23—21no—
155C2×C4×C23—21no—
156C2×C4×C23—21no—
157C2×C4×C23C2411yescharacteristic
158C22⋊D23—21no—
159C22⋊D23—21no—
160C22⋊D23—21no—
161C2×Dic23—21no—
162C2×Dic23—21no—
163C2×Dic23#4111yescharacteristic
164D92—21no—
165D92—21no—
166D92—21no—
167D92—41no—
168D92—41no—
169D92C2×D411yescharacteristic
170C4×D23—21no—
171C4×D23—21no—
172C4×D23—21no—
173C4×D23—41no—
174C4×D23—41no—
175C4×D23—41no—
176C4×D23—41no—
177C4×D23C2×D411yescharacteristic
178C4×D23C2×D411yescharacteristic
179C4×D23C2×D411yescharacteristic
180C4×D23C2×D411yescharacteristic
181Dic46—21no—
182Dic46—21no—
183Dic46—21no—
184Dic46—41no—
185Dic46—41no—
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#3069—231nomaximal, Sylow
198C22×C23—21no—
199C22×C23C2×#4111yescharacteristic
200C2×D23—21no—
201C2×D23—41no—
202C2×D23—41no—
203C2×D23—81no—
204C2×D23—81no—
205C2×D23#12111yescharacteristic
206C2×D23#12111yescharacteristic
207C4×C23—21no—
208C4×C23—41no—
209C4×C23—41no—
210C4×C23C22×D411yescharacteristic
211C4×C23C22×D411yescharacteristic
212Dic23—21no—
213Dic23—41no—
214Dic23#12111yescharacteristic
215Dic23#12111yescharacteristic
216#575—231no—
217C2×#137—231no—
218C2×#137—231no—
219#568—231no—
220#473—231no—
221#473—231no—
222#473—231no—
223#473D2311yescharacteristic, complemented
224#471—231no—
225#471—231no—
226#471—231no—
227#471—231no—
228#430—231no—
229#413—231no—
230C2×#101—231no—
231C2×C23—21no—
232C2×C23—41no—
233C2×C23C2×#12111yescharacteristic
234D23—21no—
235D23—21no—
236D23—41no—
237D23—81no—
238C2×#41—231no—
239C2×#41—231no—
240C22×Q8—231no—
241#137—231no—
242#137—231no—
243#137—231no—
244#137—231no—
245#137—461no—
246#137—461no—
247#137—461no—
248#137—461no—
249#137—461no—
250#137—461no—
251#137—461no—
252#137C2×D2311yescharacteristic
253#137C2×D2311yescharacteristic
254AGL(1,ℤ/8)—231no—
255AGL(1,ℤ/8)—231no—
256AGL(1,ℤ/8)—461no—
257#135—461no—
258#135—461no—
259C2×Q16—231no—
260C2×Q16—461no—
261C2×Q16C2×D2311yescharacteristic, complemented
262C2×SD16—231no—
263C2×SD16—231no—
264C2×SD16—461no—
265#131—231no—
266#131—231no—
267#131—231no—
268#131—461no—
269#131—461no—
270#131C2×D2311yescharacteristic
271C2×M16—231no—
272C2×M16—231no—
273C2×M16—231no—
274C2×M16—231no—
275C2×M16—461no—
276C2×M16—461no—
277#108—231no—
278#108—231no—
279#108—231no—
280#108C2×D2311yescharacteristic, complemented
281#101—231no—
282#101—231no—
283#101—231no—
284#101—231no—
285#101C2×D2311yescharacteristic, complemented
286#101C2×D2311yescharacteristic, complemented
287#100—231no—
288#100—231no—
289C23#306911yescharacteristic, complemented, Sylow
290#41—231no—
291#41—231no—
292#41—231no—
293#41—461no—
294#41—461no—
295#41—461no—
296#41—461no—
297#41—461no—
298#41—461no—
299#41C22×D2311yescharacteristic
300C2×Q8—231no—
301C2×Q8—231no—
302C2×Q8—461no—
303C2×Q8—461no—
304C2×Q8—461no—
305C2×Q8—461no—
306C2×Q8—461no—
307C2×Q8C22×D2311yescharacteristic
308C2×Q8C22×D2311yescharacteristic
309C2×D4—231no—
310C2×D4—231no—
311C2×D4—461no—
312C2×D4—461no—
313C22×C4—231no—
314C22×C4—461no—
315C22×C4—461no—
316C22×C4—461no—
317Q16—21no—
318Q16—21no—
319Q16—21no—
320Q16—21no—
321Q16—461no—
322Q16—461no—
323Q16—461no—
324Q16—461no—
325Q16—461no—
326Q16—461no—
327SD16—21no—
328SD16—21no—
329SD16—461no—
330SD16—461no—
331SD16—461no—
332SD16—461no—
333SD16—461no—
334SD16—461no—
335SD16—461no—
336SD16—461no—
337SD16—461no—
338SD16—461no—
339D8—461no—
340D8—461no—
341M16—21no—
342M16—231no—
343M16—231no—
344M16—231no—
345M16—231no—
346M16—231no—
347M16—231no—
348M16—231no—
349M16—461no—
350M16—461no—
351M16—461no—
352M16—461no—
353M16—461no—
354M16—461no—
355M16C22×D2311yescharacteristic
356M16C22×D2311yescharacteristic
357M16C22×D2311yescharacteristic
358C2×C8—21no—
359C2×C8—231no—
360C2×C8—461no—
361C2×C8—461no—
362C2×C8—461no—
363C2×C8—461no—
364C2×C8—461no—
365C2×C8—461no—
366C2×C8C22×D2311yescharacteristic
367C23—231no—
368C23—461no—
369C23—461no—
370Q8—21no—
371Q8—21no—
372Q8—21no—
373Q8—21no—
374Q8—231no—
375Q8—461no—
376Q8—461no—
377Q8—461no—
378Q8—921no—
379Q8—921no—
380Q8D4×D2311yescharacteristic
381D4—21no—
382D4—231no—
383D4—461no—
384D4—461no—
385D4—461no—
386D4—461no—
387D4—461no—
388D4—461no—
389D4—921no—
390D4—921no—
391D4D4×D2311yescharacteristic
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—231no—
396C2×C4—231no—
397C2×C4—231no—
398C2×C4—231no—
399C2×C4—231no—
400C2×C4—461no—
401C2×C4—461no—
402C2×C4—461no—
403C2×C4—461no—
404C2×C4—461no—
405C2×C4—921no—
406C2×C4—921no—
407C2×C4—921no—
408C2×C4—921no—
409C2×C4C23×D2311yescharacteristic
410C8—21no—
411C8—21no—
412C8—21no—
413C8—231no—
414C8—231no—
415C8—461no—
416C8—461no—
417C8—461no—
418C8D4×D2311yescharacteristic
419C8D4×D2311yescharacteristic
420C22—21no—
421C22—231no—
422C22—231no—
423C22—461no—
424C22—921no—
425C22—921no—
426C22—1841no—
427C22—1841no—
428C22#41×D2311yescharacteristic
429C4—21no—
430C4—41no—
431C4—41no—
432C4—231no—
433C4—231no—
434C4—461no—
435C4—921no—
436C4C2×D4×D2311yescharacteristic
437C4C2×D4×D2311yescharacteristic
438C2—21no—
439C2—41no—
440C2—461no—
441C2—461no—
442C2—921no—
443C2—1841no—
444C2#121×D2311yescharacteristic
subgroupG/H
centerC2#121×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#473C2
socleC2×C23C2×#121
prime radical#13093216C2
hypercenter#473D23
hypocenterC23#3069
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ #473

Complements

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

NH ≅ G/Ntype
2. C2×#10625089C2semidirect
3. #137×D23C2semidirect
4. #13093182C2semidirect
5. #13092691C2semidirect
6. #13092690C2semidirect
7. #13092689C2semidirect
8. #13092683C2semidirect
9. #13092682C2semidirect
10. #13092681C2semidirect
11. #13092680C2semidirect
12. #13092464C2semidirect
13. #13092400C2semidirect
14. #101×D23C2semidirect
15. C23×#473C2semidirect
21. C2×Q16×C23C22semidirect
26. C2×#67275C22semidirect
29. C2×#67274C22semidirect
50. C2×#67263C22semidirect
55. C23×#108C22semidirect
56. C23×#101C22semidirect
57. C23×#101C22semidirect
58. #10625018C22semidirect
59. #10625018C22semidirect
60. #10625006C22semidirect
61. #10625006C22semidirect
62. #10625005C22semidirect
63. #10625005C22semidirect
64. #10625004C22semidirect
65. #10625004C22semidirect
66. #10625001C22semidirect
223. #473D23semidirect
261. C2×Q16C2×D23semidirect
280. #108C2×D23semidirect
285. #101C2×D23semidirect
286. #101C2×D23semidirect
289. C23#3069semidirect

Maximal subgroups

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

subgroupindex
#130932162
C2×#106250892
#137×D232
#130931822
#130926912
#130926902
#130926892
#130926832
#130926822
#130926812
#130926802
#130924642
#130924002
#101×D232
C23×#4732
#306923