Finite Group Databasebeta

← #15685167

Subgroups — #15685167

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#13093233C211yesmaximal, characteristic, complemented
2#13093232C211yesmaximal, characteristic, complemented
3#13093226C211yesmaximal, characteristic, complemented
4#13093225C211yesmaximal, characteristic, complemented
5#13092809C211yesmaximal, characteristic, complemented
6#13092691C211yesmaximal, characteristic, complemented
7#13092690C211yesmaximal, characteristic, complemented
8#13092683C211yesmaximal, characteristic, complemented
9#13092682C211yesmaximal, characteristic, complemented
10#13092599C211yesmaximal, characteristic, complemented
11#13092596C211yesmaximal, characteristic, complemented
12#13092591C211yesmaximal, characteristic, complemented
13#13092536C211yesmaximal, characteristic, complemented
14#13092536C211yesmaximal, characteristic, complemented
15C23×#456C211yesmaximal, characteristic, complemented
16C23×2−1+4C2211yescharacteristic
17#10625161C2211yescharacteristic, complemented
18#10625160C2211yescharacteristic
19#10625158C2211yescharacteristic
20C23×#137C2211yescharacteristic
21C23×#137C2211yescharacteristic, complemented
22C23×C4⋊Q8C2211yescharacteristic, complemented
23#10625122—21no—
24#10625122C2211yescharacteristic
25#10625121—21no—
26#10625121—21no—
27#10625121C2211yescharacteristic
28#10625121C2211yescharacteristic
29#10625120—21no—
30#10625120C2211yescharacteristic
31#10625119C2211yescharacteristic
32#10625119C2211yescharacteristic, complemented
33C2×#67275—21no—
34C2×#67275C2211yescharacteristic, complemented
35C2×#67275C2211yescharacteristic, complemented
36#10625113—21no—
37#10625113—21no—
38#10625113C2211yescharacteristic
39#10625113C2211yescharacteristic, complemented
40C2×#67274—21no—
41C2×#67274C2211yescharacteristic
42C2×#67274C2211yescharacteristic
43#10625090—21no—
44#10625089—21no—
45#10625089—21no—
46Q16×D23—21no—
47#10625087—21no—
48#10625086—21no—
49#10625085—21no—
50SD16×D23—21no—
51#10625080C2211yescharacteristic
52#10625079C2211yescharacteristic
53#10625078C2211yescharacteristic
54#10625078C2211yescharacteristic, complemented
55#10625046C2211yescharacteristic
56C23×#104C2211yescharacteristic
57C23×#104C2211yescharacteristic, complemented
58C23×#101C2211yescharacteristic, complemented
59#10625018C2211yescharacteristic, complemented
60#10625006C2211yescharacteristic, complemented
61#10625005C2211yescharacteristic
62#10625004C2211yescharacteristic, complemented
63#10625004C2211yescharacteristic, complemented
64#10624987C2211yescharacteristic
65#10624987C2211yescharacteristic, complemented
66#10624985C2211yescharacteristic, complemented
67#41×C23—21no—
68#41×C23—21no—
69#41×C23—41no—
70#41×C23C2311yescharacteristic
71#41×C23C2311yescharacteristic
72C2×Q8×C23—21no—
73C2×Q8×C23—21no—
74C2×Q8×C23C2311yescharacteristic
75C2×Q8×C23C2311yescharacteristic
76#67292—21no—
77#67292—21no—
78#67292—21no—
79Q8×D23—21no—
80Q8×D23—21no—
81Q8×D23—21no—
82#67290—21no—
83#67290—41no—
84D4×D23—21no—
85D4×D23—41no—
86#67288—21no—
87#67288—21no—
88#67288—41no—
89#67288C2311yescharacteristic
90#67288C2311yescharacteristic
91C2×D92—21no—
92C2×D92C2311yescharacteristic
93C2×Dic46—21no—
94C2×Dic46C2311yescharacteristic
95Q16×C23—21no—
96Q16×C23—21no—
97SD16×C23—21no—
98SD16×C23—21no—
99M16×C23C2311yescharacteristic
100M16×C23C2311yescharacteristic
101C4⋊C4×C23—41no—
102C42×C23C2311yescharacteristic
103#67275—21no—
104#67275—21no—
105#67275—21no—
106#67275—21no—
107#67275—21no—
108#67275—21no—
109#67275—21no—
110#67275D411yescharacteristic
111#67275D411yescharacteristic
112#67274—21no—
113#67274—21no—
114#67274—21no—
115#67274—21no—
116#67274—21no—
117#67274—21no—
118#67274—21no—
119#67274D411yescharacteristic
120#67274D411yescharacteristic
121#67273—21no—
122#67273D411yescharacteristic
123#67273D411yescharacteristic
124#67272—21no—
125#67272D411yescharacteristic
126#67272D411yescharacteristic
127(C2×D23)⋊C4—41no—
128#67267—21no—
129#67267—21no—
130#67267C2311yescharacteristic
131#67267C2311yescharacteristic
132C2×C23⋊C8—21no—
133C2×C23⋊C8—21no—
134C2×C23⋊C8C2311yescharacteristic
135C2×C23⋊C8C2311yescharacteristic
136Dic92—21no—
137D184—21no—
138#67263—21no—
139#67263—21no—
140#67262—21no—
141#67262—21no—
142C8×D23—21no—
143C8×D23—21no—
144C22×D23—21no—
145C22×D23—41no—
146Q8×C23—21no—
147Q8×C23—21no—
148Q8×C23—21no—
149Q8×C23—21no—
150Q8×C23—41no—
151Q8×C23C2×D411yescharacteristic
152Q8×C23C2×D411yescharacteristic
153D4×C23—21no—
154D4×C23—21no—
155D4×C23—41no—
156D4×C23C2×D411yescharacteristic
157D4×C23C2×D411yescharacteristic
158C2×C4×C23—21no—
159C2×C4×C23—21no—
160C2×C4×C23—21no—
161C2×C4×C23—21no—
162C2×C4×C23—21no—
163C2×C4×C23—41no—
164C2×C4×C23—41no—
165C2×C4×C23C2411yescharacteristic
166C22⋊D23—21no—
167C22⋊D23—21no—
168C22⋊D23—41no—
169C22⋊D23—41no—
170C2×Dic23—21no—
171C2×Dic23—41no—
172D92—21no—
173D92—21no—
174D92—41no—
175D92—41no—
176D92C2×D411yescharacteristic
177D92C2×D411yescharacteristic
178C4×D23—21no—
179C4×D23—21no—
180C4×D23—41no—
181C4×D23—41no—
182C4×D23—41no—
183C4×D23—41no—
184Dic46—21no—
185Dic46—21no—
186Dic46—41no—
187Dic46—41no—
188Dic46C2×D411yescharacteristic
189Dic46C2×D411yescharacteristic
190C8×C23—21no—
191C8×C23—21no—
192C23⋊C8—21no—
193C23⋊C8—21no—
194C23⋊C8C2×D411yescharacteristic
195C23⋊C8C2×D411yescharacteristic
196C23⋊C8C2×D411yescharacteristic
197C23⋊C8C2×D411yescharacteristic
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×C23—41no—
211C4×C23—41no—
212C4×C23C22×D411yescharacteristic
213C4×C23C22×D411yescharacteristic
214Dic23—21no—
215Dic23—21no—
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#456D2311yescharacteristic, complemented
228#455—231no—
229#454—231no—
230#444—231no—
231#444—231no—
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+4C2×D2311yescharacteristic
242H(5,𝔽2)—231no—
243#137—231no—
244#137—231no—
245#137—231no—
246#137—231no—
247#137—461no—
248#137—461no—
249#137—461no—
250#137—461no—
251#137—461no—
252#137—461no—
253#137C2×D2311yescharacteristic
254#137C2×D2311yescharacteristic, complemented
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—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—231no—
271C2×SD16—461no—
272C2×SD16—461no—
273#131—231no—
274#131—231no—
275#131—231no—
276#131—231no—
277C4⋊Q8C2×D2311yescharacteristic, complemented
278#124—231no—
279#108—231no—
280#108—231no—
281#104—231no—
282#104—231no—
283#104C2×D2311yescharacteristic
284#104C2×D2311yescharacteristic, complemented
285#101—231no—
286#101—231no—
287#101C2×D2311yescharacteristic, complemented
288#100—231no—
289#97—231no—
290C23#328911yescharacteristic, complemented, Sylow
291#41—21no—
292#41—21no—
293#41—41no—
294#41—231no—
295#41—231no—
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#41C22×D2311yescharacteristic
305#41C22×D2311yescharacteristic
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—231no—
309C2×Q8—461no—
310C2×Q8—461no—
311C2×Q8—461no—
312C2×Q8—461no—
313C2×Q8C22×D2311yescharacteristic
314C2×Q8C22×D2311yescharacteristic
315C2×D4—231no—
316C2×D4—461no—
317C2×D4—461no—
318C2×D4—921no—
319Q16—21no—
320Q16—21no—
321Q16—231no—
322Q16—231no—
323Q16—461no—
324Q16—461no—
325Q16—461no—
326Q16—461no—
327Q16—461no—
328Q16—461no—
329Q16—461no—
330Q16—461no—
331SD16—21no—
332SD16—21no—
333SD16—231no—
334SD16—231no—
335SD16—231no—
336SD16—231no—
337SD16—461no—
338SD16—461no—
339SD16—461no—
340SD16—461no—
341SD16—461no—
342SD16—461no—
343SD16—461no—
344SD16—461no—
345SD16—461no—
346SD16—461no—
347D8—231no—
348D8—231no—
349D8—461no—
350D8—461no—
351M16—231no—
352M16—231no—
353M16—461no—
354M16—461no—
355M16—461no—
356M16—461no—
357M16C22×D2311yescharacteristic
358M16C22×D2311yescharacteristic
359C2×C8—231no—
360C2×C8—231no—
361C2×C8—461no—
362C2×C8—461no—
363C2×C8—461no—
364C2×C8—461no—
365C4⋊C4—41no—
366C22⋊C4—921no—
367C42C22×D2311yescharacteristic
368C23—461no—
369C23—921no—
370Q8—21no—
371Q8—21no—
372Q8—21no—
373Q8—21no—
374Q8—41no—
375Q8—231no—
376Q8—231no—
377Q8—461no—
378Q8—461no—
379Q8—921no—
380Q8—921no—
381Q8D4×D2311yescharacteristic
382Q8D4×D2311yescharacteristic
383D4—21no—
384D4—21no—
385D4—41no—
386D4—231no—
387D4—231no—
388D4—461no—
389D4—461no—
390D4—461no—
391D4—461no—
392D4—921no—
393D4—921no—
394D4—921no—
395D4—921no—
396D4D4×D2311yescharacteristic
397D4D4×D2311yescharacteristic
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—461no—
406C2×C4—461no—
407C2×C4—461no—
408C2×C4—921no—
409C2×C4—921no—
410C2×C4—921no—
411C2×C4—921no—
412C2×C4—921no—
413C2×C4C23×D2311yescharacteristic
414C8—21no—
415C8—21no—
416C8—231no—
417C8—231no—
418C8—231no—
419C8—231no—
420C8—461no—
421C8—461no—
422C22—21no—
423C22—21no—
424C22—461no—
425C22—461no—
426C22—921no—
427C22—3681no—
428C22—1841no—
429C22#1062515511yescharacteristic
430C4—21no—
431C4—21no—
432C4—41no—
433C4—41no—
434C4—41no—
435C4—461no—
436C4—461no—
437C4—921no—
438C4C2×D4×D2311yescharacteristic
439C4C2×D4×D2311yescharacteristic
440C2—21no—
441C2—41no—
442C2—41no—
443C2—921no—
444C2—921no—
445C2—1841no—
446C2#1309304911yescharacteristic
subgroupG/H
centerC2#13093049
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#456C2
socleC2×C23D42
hypercenter#456D23
hypocenterC23#3289
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ #456

Complements

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

NH ≅ G/Ntype
1. #13093233C2semidirect
2. #13093232C2semidirect
3. #13093226C2semidirect
4. #13093225C2semidirect
5. #13092809C2semidirect
6. #13092691C2semidirect
7. #13092690C2semidirect
8. #13092683C2semidirect
9. #13092682C2semidirect
10. #13092599C2semidirect
11. #13092596C2semidirect
12. #13092591C2semidirect
13. #13092536C2semidirect
14. #13092536C2semidirect
15. C23×#456C2semidirect
17. #10625161C22semidirect
21. C23×#137C22semidirect
22. C23×C4⋊Q8C22semidirect
32. #10625119C22semidirect
34. C2×#67275C22semidirect
35. C2×#67275C22semidirect
39. #10625113C22semidirect
54. #10625078C22semidirect
57. C23×#104C22semidirect
58. C23×#101C22semidirect
59. #10625018C22semidirect
60. #10625006C22semidirect
62. #10625004C22semidirect
63. #10625004C22semidirect
65. #10624987C22semidirect
66. #10624985C22semidirect
227. #456D23semidirect
254. #137C2×D23semidirect
277. C4⋊Q8C2×D23semidirect
284. #104C2×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
#130932332
#130932322
#130932262
#130932252
#130928092
#130926912
#130926902
#130926832
#130926822
#130925992
#130925962
#130925912
#130925362
C23×#4562
#328923