Finite Group Databasebeta

← #15685169

Subgroups — #15685169

Order 2944.

448 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13093234C211yesmaximal, characteristic, complemented
2#13093233C211yesmaximal, characteristic, complemented
3#13093227C211yesmaximal, characteristic, complemented
4#13093223C211yesmaximal, characteristic, complemented
5#13092808C211yesmaximal, characteristic, complemented
6#13092693C211yesmaximal, characteristic, complemented
7#13092691C211yesmaximal, characteristic, complemented
8#13092679C211yesmaximal, characteristic, complemented
9#13092602C211yesmaximal, characteristic, complemented
10#13092598C211yesmaximal, characteristic, complemented
11#13092597C211yesmaximal, characteristic, complemented
12#13092588C211yesmaximal, characteristic, complemented
13#13092538C211yesmaximal, characteristic, complemented
14#13092537C211yesmaximal, characteristic, complemented
15C23×#471C211yesmaximal, characteristic, complemented
16#10625161C2211yescharacteristic
17#10625161C2211yescharacteristic, complemented
18#10625158C2211yescharacteristic
19#10625155C2211yescharacteristic
20C23×#137C2211yescharacteristic, complemented
21C23×AGL(1,ℤ/8)C2211yescharacteristic
22C2×SD16×C23C2211yescharacteristic
23C23×#131C2211yescharacteristic, complemented
24#10625121C2211yescharacteristic
25#10625115C2211yescharacteristic, complemented
26C2×#67275C2211yescharacteristic, complemented
27#10625113C2211yescharacteristic
28#10625107C2211yescharacteristic
29C2×#67273C2211yescharacteristic
30#10625103C2211yescharacteristic
31#10625089—21no—
32Q16×D23—21no—
33#10625087—21no—
34#10625087—21no—
35#10625086—21no—
36#10625086—21no—
37#10625086—21no—
38#10625085—21no—
39SD16×D23—21no—
40SD16×D23—21no—
41#10625083—21no—
42#10625082—21no—
43#10625080—21no—
44#10625080—21no—
45#10625080C2211yescharacteristic
46#10625080C2211yescharacteristic
47#10625080C2211yescharacteristic
48#10625080C2211yescharacteristic, complemented
49#10625078C2211yescharacteristic
50#10625078C2211yescharacteristic, complemented
51C2×Dic92—21no—
52C2×Dic92C2211yescharacteristic, complemented
53#10625075—21no—
54#10625075C2211yescharacteristic
55#10625072C2211yescharacteristic
56C23×#108C2211yescharacteristic, complemented
57C23×#101C2211yescharacteristic, complemented
58C23×#100C2211yescharacteristic
59#10625019C2211yescharacteristic, complemented
60#10625007C2211yescharacteristic
61#10625007C2211yescharacteristic
62#10625007C2211yescharacteristic, complemented
63#10625006C2211yescharacteristic, complemented
64#10625006C2211yescharacteristic, complemented
65#10625004C2211yescharacteristic, complemented
66#10624997C2211yescharacteristic, complemented
67#41×C23C2311yescharacteristic
68C2×Q8×C23C2311yescharacteristic
69C2×D4×C23C2311yescharacteristic
70C2×C22⋊D23—41no—
71#67292—21no—
72#67292—21no—
73Q8×D23—21no—
74Q8×D23—21no—
75Q8×D23—21no—
76Q8×D23—21no—
77#67290—21no—
78#67290—21no—
79#67290—21no—
80#67290—21no—
81#67290—41no—
82#67290—41no—
83D4×D23—21no—
84D4×D23—21no—
85#67288—21no—
86#67288—21no—
87#67288—41no—
88#67288C2311yescharacteristic
89#67288C2311yescharacteristic
90#67288C2311yescharacteristic
91C2×Dic46—21no—
92C2×Dic46—21no—
93C2×Dic46C2311yescharacteristic
94C2×Dic46C2311yescharacteristic
95Q16×C23—21no—
96SD16×C23—21no—
97SD16×C23—21no—
98SD16×C23—21no—
99SD16×C23—21no—
100D8×C23—21no—
101M16×C23—21no—
102M16×C23C2311yescharacteristic
103M16×C23C2311yescharacteristic
104M16×C23C2311yescharacteristic
105C2×C8×C23—21no—
106C2×C8×C23C2311yescharacteristic
107C22⋊Dic23—41no—
108#67275—21no—
109#67275—21no—
110#67275—21no—
111#67275D411yescharacteristic
112#67274—21no—
113#67274D411yescharacteristic
114#67273—21no—
115#67273—21no—
116#67273—21no—
117#67273D411yescharacteristic
118#67272—21no—
119#67272D411yescharacteristic
120Dic23⋊C4—41no—
121C4×Dic23C2311yescharacteristic
122#67267C2311yescharacteristic
123C2×C23⋊C8C2311yescharacteristic
124Dic92—21no—
125Dic92—21no—
126Dic92—21no—
127Dic92—21no—
128Dic92—21no—
129Dic92—21no—
130Dic92D411yescharacteristic
131D184D411yescharacteristic
132#67263—21no—
133#67263—21no—
134#67263—21no—
135#67263—21no—
136#67263D411yescharacteristic
137#67263D411yescharacteristic
138#67262—21no—
139#67262—21no—
140#67262—21no—
141C8×D23—21no—
142C8×D23—21no—
143C8×D23—21no—
144C23×C23—21no—
145C22×D23—41no—
146Q8×C23—21no—
147Q8×C23—21no—
148Q8×C23C2×D411yescharacteristic
149D4×C23—21no—
150D4×C23—21no—
151D4×C23—21no—
152D4×C23C2×D411yescharacteristic
153C2×C4×C23—21no—
154C2×C4×C23—21no—
155C2×C4×C23C2411yescharacteristic
156C22⋊D23—21no—
157C22⋊D23—21no—
158C22⋊D23—21no—
159C22⋊D23—41no—
160C22⋊D23—41no—
161C22⋊D23—41no—
162C22⋊D23—41no—
163C2×Dic23—21no—
164C2×Dic23—21no—
165C2×Dic23—21no—
166C2×Dic23—41no—
167C2×Dic23—41no—
168C2×Dic23—41no—
169D92—41no—
170D92C2×D411yescharacteristic
171D92C2×D411yescharacteristic
172D92C2×D411yescharacteristic
173C4×D23—21no—
174C4×D23—21no—
175C4×D23—21no—
176C4×D23—41no—
177C4×D23—41no—
178C4×D23—41no—
179C4×D23—41no—
180Dic46—21no—
181Dic46—21no—
182Dic46—21no—
183Dic46—21no—
184Dic46—41no—
185Dic46—41no—
186Dic46—41no—
187Dic46C2×D411yescharacteristic
188Dic46C2×D411yescharacteristic
189Dic46C2×D411yescharacteristic
190C8×C23—21no—
191C8×C23—21no—
192C8×C23—21no—
193C8×C23C2×D411yescharacteristic
194C8×C23C2×D411yescharacteristic
195C23⋊C8—21no—
196C23⋊C8C2×D411yescharacteristic
197C23⋊C8C2×D411yescharacteristic
198#3289—231nomaximal, Sylow
199C22×C23—21no—
200C22×C23—41no—
201C22×C23—81no—
202C22×C23H(5,𝔽2)11yescharacteristic
203C2×D23—21no—
204C2×D23—21no—
205C2×D23—21no—
206C2×D23—161no—
207C4×C23—21no—
208C4×C23—41no—
209C4×C23C22×D411yescharacteristic
210C4×C23C22×D411yescharacteristic
211Dic23—21no—
212Dic23—21no—
213Dic23—21no—
214Dic23—41no—
215Dic23—41no—
216Dic23—41no—
217#578—231no—
218#578—231no—
219#577—231no—
220#577—231no—
221#497—231no—
222#473—231no—
223#473—231no—
224#471—231no—
225#471D2311yescharacteristic, complemented
226#456—231no—
227#456—231no—
228#455—231no—
229#454—231no—
230#444—231no—
231#444—231no—
232C2×C23—21no—
233C2×C23—41no—
234C2×C23—81no—
235C2×C23D4211yescharacteristic
236D23—41no—
237D23—41no—
238D23—41no—
2392−1+4—231no—
2402−1+4—231no—
2412−1+4—231no—
242H(5,𝔽2)—231no—
243#137—231no—
244#137—231no—
245#137—231no—
246#137—231no—
247#137—231no—
248#137—461no—
249#137—461no—
250#137—461no—
251#137—461no—
252#137—461no—
253#137—461no—
254#137C2×D2311yescharacteristic, complemented
255AGL(1,ℤ/8)—231no—
256AGL(1,ℤ/8)—461no—
257AGL(1,ℤ/8)—461no—
258AGL(1,ℤ/8)C2×D2311yescharacteristic
259#135—231no—
260#135—231no—
261#135—461no—
262#135—461no—
263#135—461no—
264#135—461no—
265C2×Q16—231no—
266C2×Q16—231no—
267C2×Q16—461no—
268C2×Q16—461no—
269C2×SD16—231no—
270C2×SD16—461no—
271C2×SD16—461no—
272C2×SD16C2×D2311yescharacteristic
273#131—231no—
274#131—231no—
275#131—231no—
276#131C2×D2311yescharacteristic, complemented
277C4⋊Q8—231no—
278#124—231no—
279#108—231no—
280#108C2×D2311yescharacteristic, complemented
281#104—231no—
282#104—231no—
283#104—231no—
284#104—231no—
285#101—231no—
286#101—231no—
287#101C2×D2311yescharacteristic, complemented
288#100C2×D2311yescharacteristic
289#97—231no—
290C23#328911yescharacteristic, complemented, Sylow
291#41—231no—
292#41—231no—
293#41—231no—
294#41—461no—
295#41—461no—
296#41—461no—
297#41—461no—
298#41—461no—
299#41—461no—
300#41—461no—
301#41—461no—
302#41—921no—
303#41—921no—
304#41—921no—
305#41C22×D2311yescharacteristic
306C2×Q8—231no—
307C2×Q8—231no—
308C2×Q8—461no—
309C2×Q8—461no—
310C2×Q8—461no—
311C2×Q8—461no—
312C2×Q8—461no—
313C2×Q8—461no—
314C2×Q8C22×D2311yescharacteristic
315C2×D4—461no—
316C2×D4—461no—
317C2×D4—921no—
318C2×D4C22×D2311yescharacteristic
319Q16—21no—
320Q16—231no—
321Q16—231no—
322Q16—461no—
323Q16—461no—
324Q16—461no—
325Q16—461no—
326Q16—461no—
327Q16—461no—
328Q16—461no—
329Q16—461no—
330Q16—461no—
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—21no—
335SD16—231no—
336SD16—231no—
337SD16—231no—
338SD16—231no—
339SD16—461no—
340SD16—461no—
341SD16—461no—
342SD16—461no—
343SD16—461no—
344SD16—461no—
345SD16—461no—
346SD16—461no—
347D8—21no—
348D8—231no—
349D8—231no—
350D8—461no—
351M16—21no—
352M16—231no—
353M16—461no—
354M16—461no—
355M16—461no—
356M16C22×D2311yescharacteristic
357M16C22×D2311yescharacteristic
358M16C22×D2311yescharacteristic
359C2×C8—21no—
360C2×C8—231no—
361C2×C8—461no—
362C2×C8—461no—
363C2×C8—461no—
364C2×C8C22×D2311yescharacteristic
365C4⋊C4—921no—
366C22⋊C4—921no—
367C42—231no—
368C23—21no—
369C23—921no—
370Q8—21no—
371Q8—21no—
372Q8—231no—
373Q8—231no—
374Q8—231no—
375Q8—461no—
376Q8—461no—
377Q8—461no—
378Q8—461no—
379Q8—921no—
380Q8—921no—
381Q8—921no—
382Q8D4×D2311yescharacteristic
383D4—21no—
384D4—21no—
385D4—21no—
386D4—231no—
387D4—231no—
388D4—231no—
389D4—461no—
390D4—461no—
391D4—461no—
392D4—921no—
393D4—921no—
394D4—921no—
395D4—921no—
396D4—921no—
397D4D4×D2311yescharacteristic
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—461no—
401C2×C4—461no—
402C2×C4—461no—
403C2×C4—461no—
404C2×C4—461no—
405C2×C4—461no—
406C2×C4—921no—
407C2×C4—921no—
408C2×C4—921no—
409C2×C4—921no—
410C2×C4—921no—
411C2×C4—921no—
412C2×C4—921no—
413C2×C4C23×D2311yescharacteristic
414C8—21no—
415C8—21no—
416C8—21no—
417C8—231no—
418C8—231no—
419C8—461no—
420C8D4×D2311yescharacteristic
421C8D4×D2311yescharacteristic
422C22—21no—
423C22—41no—
424C22—81no—
425C22—461no—
426C22—461no—
427C22—461no—
428C22—3681no—
429C22#1062516011yescharacteristic
430C4—21no—
431C4—41no—
432C4—461no—
433C4—461no—
434C4—461no—
435C4—921no—
436C4—921no—
437C4—921no—
438C4C2×D4×D2311yescharacteristic
439C4C2×D4×D2311yescharacteristic
440C2—21no—
441C2—41no—
442C2—81no—
443C2—921no—
444C2—921no—
445C2—921no—
446C2#1309305111yescharacteristic
subgroupG/H
centerC2#13093051
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#471C2
socleC2×C23D42
hypercenter#471D23
hypocenterC23#3289
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. #13093234C2semidirect
2. #13093233C2semidirect
3. #13093227C2semidirect
4. #13093223C2semidirect
5. #13092808C2semidirect
6. #13092693C2semidirect
7. #13092691C2semidirect
8. #13092679C2semidirect
9. #13092602C2semidirect
10. #13092598C2semidirect
11. #13092597C2semidirect
12. #13092588C2semidirect
13. #13092538C2semidirect
14. #13092537C2semidirect
15. C23×#471C2semidirect
17. #10625161C22semidirect
20. C23×#137C22semidirect
23. C23×#131C22semidirect
25. #10625115C22semidirect
26. C2×#67275C22semidirect
48. #10625080C22semidirect
50. #10625078C22semidirect
52. C2×Dic92C22semidirect
56. C23×#108C22semidirect
57. C23×#101C22semidirect
59. #10625019C22semidirect
62. #10625007C22semidirect
63. #10625006C22semidirect
64. #10625006C22semidirect
65. #10625004C22semidirect
66. #10624997C22semidirect
225. #471D23semidirect
254. #137C2×D23semidirect
276. #131C2×D23semidirect
280. #108C2×D23semidirect
287. #101C2×D23semidirect
290. C23#3289semidirect

Maximal subgroups

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

subgroupindex
#130932342
#130932332
#130932272
#130932232
#130928082
#130926932
#130926912
#130926792
#130926022
#130925982
#130925972
#130925882
#130925382
#130925372
C23×#4712
#328923