Finite Group Databasebeta

← #15685173

Subgroups — #15685173

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#13093231C211yesmaximal, characteristic, complemented
3#13093229C211yesmaximal, characteristic, complemented
4#13093224C211yesmaximal, characteristic, complemented
5#13092811C211yesmaximal, characteristic, complemented
6#13092693C211yesmaximal, characteristic, complemented
7#13092692C211yesmaximal, characteristic, complemented
8#13092681C211yesmaximal, characteristic, complemented
9#13092680C211yesmaximal, characteristic, complemented
10#13092601C211yesmaximal, characteristic, complemented
11#13092601C211yesmaximal, characteristic, complemented
12#13092596C211yesmaximal, characteristic, complemented
13#13092591C211yesmaximal, characteristic, complemented
14#13092540C211yesmaximal, characteristic, complemented
15C23×#444C211yesmaximal, characteristic, complemented
16#10625161C2211yescharacteristic
17#10625161C2211yescharacteristic
18#10625161C2211yescharacteristic, complemented
19#10625160C2211yescharacteristic
20C23×#135C2211yescharacteristic
21C23×#131C2211yescharacteristic
22C23×#131C2211yescharacteristic, complemented
23#10625122C2211yescharacteristic
24#10625122C2211yescharacteristic
25#10625122C2211yescharacteristic, complemented
26#10625120C2211yescharacteristic
27#10625089—21no—
28Q16×D23—21no—
29#10625087—21no—
30#10625086—21no—
31#10625086—21no—
32SD16×D23—21no—
33#10625083—21no—
34#10625082—21no—
35#10625080—21no—
36#10625080—21no—
37#10625080—21no—
38#10625080C2211yescharacteristic
39#10625080C2211yescharacteristic
40#10625080C2211yescharacteristic, complemented
41#10625079—21no—
42#10625079C2211yescharacteristic
43C2×Dic92—21no—
44C2×Dic92C2211yescharacteristic, complemented
45C2×Dic92C2211yescharacteristic, complemented
46#10625075—21no—
47#10625075—21no—
48#10625075C2211yescharacteristic
49C2×#67263—21no—
50C2×#67263C2211yescharacteristic
51C2×#67263C2211yescharacteristic
52#10625072C2211yescharacteristic
53#10625072C2211yescharacteristic, complemented
54#10625046C2211yescharacteristic
55#10625040C2211yescharacteristic, complemented
56C23×#108C2211yescharacteristic, complemented
57C23×#104C2211yescharacteristic
58C23×#104C2211yescharacteristic, complemented
59C23×#97C2211yescharacteristic, complemented
60#10625006C2211yescharacteristic, complemented
61#10625006C2211yescharacteristic, complemented
62#10625006C2211yescharacteristic, complemented
63#10625005C2211yescharacteristic
64#10625001C2211yescharacteristic, complemented
65#10624987C2211yescharacteristic
66#10624987C2211yescharacteristic, complemented
67#41×C23C2311yescharacteristic
68#41×C23C2311yescharacteristic
69#67292—21no—
70Q8×D23—21no—
71Q8×D23—21no—
72Q8×D23—21no—
73#67290—21no—
74#67290—21no—
75#67290—21no—
76#67290—41no—
77#67290—41no—
78#67290—41no—
79D4×D23—21no—
80D4×D23—41no—
81#67288—21no—
82#67288—21no—
83#67288—21no—
84#67288—21no—
85#67288C2311yescharacteristic
86#67288C2311yescharacteristic
87C2×D92—21no—
88C2×D92C2311yescharacteristic
89C2×Dic46—21no—
90C2×Dic46—21no—
91C2×Dic46—21no—
92C2×Dic46C2311yescharacteristic
93C2×Dic46C2311yescharacteristic
94C2×Dic46C2311yescharacteristic
95Q16×C23D411yescharacteristic
96SD16×C23D411yescharacteristic
97SD16×C23D411yescharacteristic
98D8×C23D411yescharacteristic
99M16×C23—21no—
100M16×C23—21no—
101M16×C23C2311yescharacteristic
102M16×C23C2311yescharacteristic
103C2×C8×C23—21no—
104C2×C8×C23—21no—
105C2×C8×C23C2311yescharacteristic
106C2×C8×C23C2311yescharacteristic
107C42×C23C2311yescharacteristic
108#67275—21no—
109#67275—21no—
110#67275—21no—
111#67274—21no—
112#67273—21no—
113#67273—21no—
114#67273—21no—
115#67272—21no—
116(C2×D23)⋊C4—41no—
117C4⋊Dic23—41no—
118#67267C2311yescharacteristic
119#67267C2311yescharacteristic
120Dic92—21no—
121Dic92—21no—
122Dic92—21no—
123Dic92—21no—
124Dic92—21no—
125Dic92—21no—
126Dic92—21no—
127Dic92D411yescharacteristic
128D184—21no—
129D184D411yescharacteristic
130#67263—21no—
131#67263—21no—
132#67263—21no—
133#67263—21no—
134#67263—21no—
135#67263—21no—
136#67263—21no—
137#67263—21no—
138#67263D411yescharacteristic
139#67263D411yescharacteristic
140#67262—21no—
141#67262—21no—
142C8×D23—21no—
143C8×D23—21no—
144C22×D23—21no—
145C22×D23—41no—
146Q8×C23C2×D411yescharacteristic
147Q8×C23C2×D411yescharacteristic
148D4×C23—21no—
149D4×C23—21no—
150D4×C23C2×D411yescharacteristic
151D4×C23C2×D411yescharacteristic
152C2×C4×C23—21no—
153C2×C4×C23—21no—
154C2×C4×C23—21no—
155C2×C4×C23C2411yescharacteristic
156C22⋊D23—21no—
157C22⋊D23—21no—
158C22⋊D23—41no—
159C22⋊D23—41no—
160C22⋊D23—41no—
161C22⋊D23—41no—
162C2×Dic23—21no—
163C2×Dic23—21no—
164C2×Dic23—21no—
165C2×Dic23—41no—
166C2×Dic23—41no—
167C2×Dic23—41no—
168D92—21no—
169D92—21no—
170D92—41no—
171D92C2×D411yescharacteristic
172D92C2×D411yescharacteristic
173C4×D23—21no—
174C4×D23—21no—
175C4×D23—41no—
176C4×D23—41no—
177C4×D23—41no—
178C4×D23—41no—
179Dic46—21no—
180Dic46—21no—
181Dic46—21no—
182Dic46—21no—
183Dic46—21no—
184Dic46—21no—
185Dic46—41no—
186Dic46—41no—
187Dic46—41no—
188Dic46C2×D411yescharacteristic
189Dic46C2×D411yescharacteristic
190C8×C23—21no—
191C8×C23—21no—
192C8×C23C2×D411yescharacteristic
193C8×C23C2×D411yescharacteristic
194C8×C23C2×D411yescharacteristic
195C8×C23C2×D411yescharacteristic
196C23⋊C8—21no—
197C23⋊C8—21no—
198#3289—231nomaximal, Sylow
199C22×C23—21no—
200C22×C23—21no—
201C22×C23H(5,𝔽2)11yescharacteristic
202C2×D23—21no—
203C2×D23—21no—
204C2×D23—41no—
205C2×D23—81no—
206C2×D23—161no—
207C4×C23—21no—
208C4×C23—21no—
209C4×C23—41no—
210C4×C23C22×D411yescharacteristic
211C4×C23C22×D411yescharacteristic
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#471—231no—
226#456—231no—
227#456—231no—
228#455—231no—
229#454—231no—
230#444—231no—
231#444D2311yescharacteristic, complemented
232C2×C23—21no—
233C2×C23—41no—
234C2×C23—41no—
235C2×C23D4211yescharacteristic
236D23—41no—
237D23—41no—
238D23—81no—
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—231no—
249#137—461no—
250#137—461no—
251#137—461no—
252#137—461no—
253#137—461no—
254#137—461no—
255AGL(1,ℤ/8)—231no—
256AGL(1,ℤ/8)—231no—
257AGL(1,ℤ/8)—461no—
258AGL(1,ℤ/8)—461no—
259#135—231no—
260#135—461no—
261#135—461no—
262#135—461no—
263#135—461no—
264#135C2×D2311yescharacteristic
265C2×Q16—231no—
266C2×Q16—231no—
267C2×Q16—461no—
268C2×Q16—461no—
269C2×SD16—231no—
270C2×SD16—231no—
271C2×SD16—461no—
272C2×SD16—461no—
273#131—231no—
274#131—231no—
275#131C2×D2311yescharacteristic
276#131C2×D2311yescharacteristic, complemented
277C4⋊Q8—231no—
278#124—231no—
279#108—231no—
280#108C2×D2311yescharacteristic, complemented
281#104—231no—
282#104—231no—
283#104C2×D2311yescharacteristic
284#104C2×D2311yescharacteristic, complemented
285#101—231no—
286#101—231no—
287#101—231no—
288#100—231no—
289#97C2×D2311yescharacteristic, complemented
290C23#328911yescharacteristic, complemented, Sylow
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#41—461no—
300#41—461no—
301#41—921no—
302#41—921no—
303#41—921no—
304#41C22×D2311yescharacteristic
305#41C22×D2311yescharacteristic
306C2×Q8—231no—
307C2×Q8—231no—
308C2×Q8—231no—
309C2×Q8—461no—
310C2×Q8—461no—
311C2×Q8—461no—
312C2×Q8—461no—
313C2×Q8—461no—
314C2×Q8—461no—
315C2×D4—231no—
316C2×D4—461no—
317C2×D4—461no—
318C2×D4—921no—
319Q16—231no—
320Q16—461no—
321Q16—461no—
322Q16—461no—
323Q16—461no—
324Q16—461no—
325Q16—461no—
326Q16—461no—
327Q16—461no—
328Q16—461no—
329Q16—461no—
330Q16D9211yescharacteristic
331SD16—231no—
332SD16—231no—
333SD16—461no—
334SD16—461no—
335SD16—461no—
336SD16—461no—
337SD16—461no—
338SD16—461no—
339SD16—461no—
340SD16—461no—
341SD16—461no—
342SD16—461no—
343SD16—461no—
344SD16—461no—
345SD16D9211yescharacteristic
346SD16D9211yescharacteristic
347D8—231no—
348D8—461no—
349D8—461no—
350D8D9211yescharacteristic
351M16—21no—
352M16—21no—
353M16—231no—
354M16—231no—
355M16—461no—
356M16—461no—
357M16C22×D2311yescharacteristic
358M16C22×D2311yescharacteristic
359C2×C8—21no—
360C2×C8—21no—
361C2×C8—461no—
362C2×C8—461no—
363C2×C8C22×D2311yescharacteristic
364C2×C8C22×D2311yescharacteristic
365C4⋊C4—921no—
366C22⋊C4—921no—
367C42C22×D2311yescharacteristic
368C23—461no—
369C23—921no—
370Q8—231no—
371Q8—231no—
372Q8—461no—
373Q8—461no—
374Q8—461no—
375Q8—461no—
376Q8—461no—
377Q8—461no—
378Q8—921no—
379Q8—921no—
380Q8—921no—
381Q8C2×D9211yescharacteristic
382Q8C2×D9211yescharacteristic
383D4—21no—
384D4—21no—
385D4—231no—
386D4—231no—
387D4—461no—
388D4—461no—
389D4—461no—
390D4—461no—
391D4—921no—
392D4—921no—
393D4—921no—
394D4—921no—
395D4—921no—
396D4C2×D9211yescharacteristic
397D4C2×D9211yescharacteristic
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
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—461no—
417C8—461no—
418C8C2×D9211yescharacteristic
419C8C2×D9211yescharacteristic
420C8D4×D2311yescharacteristic
421C8D4×D2311yescharacteristic
422C22—21no—
423C22—21no—
424C22—461no—
425C22—461no—
426C22—921no—
427C22—3681no—
428C22—1841no—
429C22#1062516011yescharacteristic
430C4—21no—
431C4—21no—
432C4—41no—
433C4—461no—
434C4—461no—
435C4—921no—
436C4—921no—
437C4—921no—
438C4C22×D9211yescharacteristic
439C4C2×D4×D2311yescharacteristic
440C2—21no—
441C2—41no—
442C2—41no—
443C2—921no—
444C2—921no—
445C2—1841no—
446C2D4×D9211yescharacteristic
subgroupG/H
centerC2D4×D92
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#444C2
socleC2×C23D42
hypercenter#444D23
hypocenterC23#3289
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ #444

Complements

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

NH ≅ G/Ntype
1. #13093234C2semidirect
2. #13093231C2semidirect
3. #13093229C2semidirect
4. #13093224C2semidirect
5. #13092811C2semidirect
6. #13092693C2semidirect
7. #13092692C2semidirect
8. #13092681C2semidirect
9. #13092680C2semidirect
10. #13092601C2semidirect
11. #13092601C2semidirect
12. #13092596C2semidirect
13. #13092591C2semidirect
14. #13092540C2semidirect
15. C23×#444C2semidirect
18. #10625161C22semidirect
22. C23×#131C22semidirect
25. #10625122C22semidirect
40. #10625080C22semidirect
44. C2×Dic92C22semidirect
45. C2×Dic92C22semidirect
53. #10625072C22semidirect
55. #10625040C22semidirect
56. C23×#108C22semidirect
58. C23×#104C22semidirect
59. C23×#97C22semidirect
60. #10625006C22semidirect
61. #10625006C22semidirect
62. #10625006C22semidirect
64. #10625001C22semidirect
66. #10624987C22semidirect
231. #444D23semidirect
276. #131C2×D23semidirect
280. #108C2×D23semidirect
284. #104C2×D23semidirect
289. #97C2×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
#130932312
#130932292
#130932242
#130928112
#130926932
#130926922
#130926812
#130926802
#130926012
#130925962
#130925912
#130925402
C23×#4442
#328923