Finite Group Databasebeta

← #15685170

Subgroups — #15685170

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#13093232C211yesmaximal, characteristic, complemented
2#13093231C211yesmaximal, characteristic, complemented
3#13093228C211yesmaximal, characteristic, complemented
4#13092808C211yesmaximal, characteristic, complemented
5#13092692C211yesmaximal, characteristic, complemented
6#13092690C211yesmaximal, characteristic, complemented
7#13092678C211yesmaximal, characteristic, complemented
8#13092677C211yesmaximal, characteristic, complemented
9#13092600C211yesmaximal, characteristic, complemented
10#13092598C211yesmaximal, characteristic, complemented
11#13092595C211yesmaximal, characteristic, complemented
12#13092588C211yesmaximal, characteristic, complemented
13#13092539C211yesmaximal, characteristic, complemented
14#13092537C211yesmaximal, characteristic, complemented
15C23×#577C211yesmaximal, characteristic, complemented
16C23×2−1+4C2211yescharacteristic
17C23×H(5,𝔽2)C2211yescharacteristic
18#10625161C2211yescharacteristic
19#10625161C2211yescharacteristic, complemented
20C23×#137—21no—
21C23×#137C2211yescharacteristic
22C23×AGL(1,ℤ/8)—21no—
23C23×AGL(1,ℤ/8)C2211yescharacteristic
24C23×#135—21no—
25C23×#135C2211yescharacteristic
26C2×SD16×C23—21no—
27C2×SD16×C23C2211yescharacteristic
28C23×#131C2211yescharacteristic
29#10625122—21no—
30#10625122—21no—
31#10625122C2211yescharacteristic
32#10625122C2211yescharacteristic
33#10625122C2211yescharacteristic
34#10625122C2211yescharacteristic, complemented
35#10625121—21no—
36#10625121—21no—
37#10625121C2211yescharacteristic
38#10625119C2211yescharacteristic
39#10625119C2211yescharacteristic, complemented
40#10625115C2211yescharacteristic, complemented
41C2×#67275—21no—
42C2×#67275C2211yescharacteristic, complemented
43#10625113—21no—
44#10625113C2211yescharacteristic, complemented
45#10625107C2211yescharacteristic
46C2×#67273—21no—
47C2×#67273C2211yescharacteristic
48#10625103—21no—
49#10625103C2211yescharacteristic
50Q16×D23—21no—
51#10625086—21no—
52#10625086—21no—
53#10625083—21no—
54C2×Dic92C2211yescharacteristic, complemented
55#10625072C2211yescharacteristic, complemented
56#10625019C2211yescharacteristic
57#10625019C2211yescharacteristic
58#10625019C2211yescharacteristic, complemented
59#10625018C2211yescharacteristic, complemented
60#10625015C2211yescharacteristic
61#10625007C2211yescharacteristic, complemented
62#10625006C2211yescharacteristic, complemented
63#10625006C2211yescharacteristic, complemented
64#10625004C2211yescharacteristic, complemented
65#10625001C2211yescharacteristic, complemented
66#10624997C2211yescharacteristic, complemented
67#41×C23—21no—
68#41×C23—21no—
69#41×C23—21no—
70#41×C23—21no—
71#41×C23—41no—
72#41×C23C2311yescharacteristic
73#41×C23C2311yescharacteristic
74#41×C23C2311yescharacteristic
75C2×Q8×C23—21no—
76C2×Q8×C23—21no—
77C2×Q8×C23C2311yescharacteristic
78C2×D4×C23—21no—
79C2×D4×C23—21no—
80C2×D4×C23—41no—
81C2×D4×C23C2311yescharacteristic
82Q8×D23—21no—
83Q8×D23—21no—
84#67290—21no—
85#67290—21no—
86#67290—41no—
87#67290—41no—
88#67288—21no—
89#67288—21no—
90#67288C2311yescharacteristic
91C2×Dic46—21no—
92C2×Dic46—21no—
93C2×Dic46C2311yescharacteristic
94C2×Dic46C2311yescharacteristic
95Q16×C23—21no—
96Q16×C23D411yescharacteristic
97SD16×C23—21no—
98SD16×C23—21no—
99SD16×C23—21no—
100SD16×C23—21no—
101SD16×C23D411yescharacteristic
102SD16×C23D411yescharacteristic
103D8×C23—21no—
104D8×C23D411yescharacteristic
105M16×C23—21no—
106M16×C23C2311yescharacteristic
107C2×C8×C23—21no—
108C2×C8×C23C2311yescharacteristic
109C22⋊Dic23—41no—
110#67275—21no—
111#67275—21no—
112#67275—21no—
113#67275—21no—
114#67275—21no—
115#67275—21no—
116#67275—21no—
117#67275D411yescharacteristic
118#67274—21no—
119#67274D411yescharacteristic
120#67273—21no—
121#67273—21no—
122#67273—21no—
123#67273—21no—
124#67273—21no—
125#67273—21no—
126#67273—21no—
127#67273D411yescharacteristic
128#67272—21no—
129#67272D411yescharacteristic
130Dic23⋊C4—41no—
131C4×Dic23C2311yescharacteristic
132#67267—21no—
133#67267—21no—
134#67267C2311yescharacteristic
135#67267C2311yescharacteristic
136#67267C2311yescharacteristic
137C2×C23⋊C8—21no—
138C2×C23⋊C8—21no—
139C2×C23⋊C8C2311yescharacteristic
140Dic92—21no—
141Dic92—21no—
142#67262—21no—
143C8×D23—21no—
144C23×C23—21no—
145C23×C23—41no—
146Q8×C23—21no—
147Q8×C23—21no—
148Q8×C23—41no—
149Q8×C23C2×D411yescharacteristic
150Q8×C23C2×D411yescharacteristic
151Q8×C23C2×D411yescharacteristic
152D4×C23—21no—
153D4×C23—21no—
154D4×C23—21no—
155D4×C23—21no—
156D4×C23—21no—
157D4×C23—41no—
158D4×C23—41no—
159D4×C23—41no—
160D4×C23C2×D411yescharacteristic
161D4×C23C2×D411yescharacteristic
162D4×C23C2×D411yescharacteristic
163C2×C4×C23—21no—
164C2×C4×C23—21no—
165C2×C4×C23—21no—
166C2×C4×C23—21no—
167C2×C4×C23—41no—
168C2×C4×C23—41no—
169C2×C4×C23—41no—
170C2×C4×C23C2411yescharacteristic
171C22⋊D23—21no—
172C22⋊D23—41no—
173C22⋊D23—41no—
174C2×Dic23—21no—
175C2×Dic23—21no—
176C2×Dic23—21no—
177C2×Dic23—41no—
178C2×Dic23—41no—
179D92C2×D411yescharacteristic
180C4×D23—21no—
181C4×D23—41no—
182C4×D23—41no—
183Dic46—21no—
184Dic46—21no—
185Dic46—21no—
186Dic46—21no—
187Dic46—41no—
188Dic46—41no—
189Dic46C2×D411yescharacteristic
190C8×C23—21no—
191C8×C23C2×D411yescharacteristic
192C8×C23C2×D411yescharacteristic
193C23⋊C8—21no—
194C23⋊C8—21no—
195C23⋊C8—21no—
196C23⋊C8C2×D411yescharacteristic
197C23⋊C8C2×D411yescharacteristic
198#3289—231nomaximal, Sylow
199C22×C23—21no—
200C22×C23—21no—
201C22×C23—21no—
202C22×C23—41no—
203C22×C23—81no—
204C22×C23—161no—
205C22×C23H(5,𝔽2)11yescharacteristic
206C2×D23—21no—
207C4×C23—21no—
208C4×C23—21no—
209C4×C23—21no—
210C4×C23—41no—
211C4×C23C22×D411yescharacteristic
212C4×C23C22×D411yescharacteristic
213Dic23—21no—
214Dic23—41no—
215Dic23—41no—
216Dic23—41no—
217#578—231no—
218#578—231no—
219#577—231no—
220#577D2311yescharacteristic, complemented
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#444—231no—
232C2×C23—21no—
233C2×C23—41no—
234C2×C23—41no—
235C2×C23—41no—
236C2×C23—81no—
237C2×C23D4211yescharacteristic
238D23—41no—
2392−1+4—231no—
2402−1+4—231no—
2412−1+4C2×D2311yescharacteristic
242H(5,𝔽2)C2×D2311yescharacteristic
243#137—21no—
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#137C2×D2311yescharacteristic
255AGL(1,ℤ/8)—21no—
256AGL(1,ℤ/8)—231no—
257AGL(1,ℤ/8)—461no—
258AGL(1,ℤ/8)C2×D2311yescharacteristic
259#135—21no—
260#135—231no—
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—21no—
270C2×SD16—231no—
271C2×SD16—461no—
272C2×SD16C2×D2311yescharacteristic
273#131—231no—
274#131—231no—
275#131—231no—
276#131C2×D2311yescharacteristic
277C4⋊Q8—231no—
278#124—231no—
279#108—231no—
280#108—231no—
281#104—231no—
282#104—231no—
283#104—231no—
284#104—231no—
285#101—231no—
286#101—231no—
287#101—231no—
288#100—231no—
289#97—231no—
290C23#328911yescharacteristic, complemented, Sylow
291#41—21no—
292#41—21no—
293#41—21no—
294#41—21no—
295#41—41no—
296#41—231no—
297#41—461no—
298#41—461no—
299#41—461no—
300#41—461no—
301#41—921no—
302#41—921no—
303#41C22×D2311yescharacteristic
304#41C22×D2311yescharacteristic
305#41C22×D2311yescharacteristic
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—231no—
309C2×Q8—231no—
310C2×Q8—461no—
311C2×Q8—461no—
312C2×Q8—461no—
313C2×Q8—461no—
314C2×Q8C22×D2311yescharacteristic
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—41no—
318C2×D4C22×D2311yescharacteristic
319Q16—21no—
320Q16—231no—
321Q16—461no—
322Q16—461no—
323Q16—461no—
324Q16—461no—
325Q16—461no—
326Q16—461no—
327Q16—461no—
328Q16—461no—
329Q16—461no—
330Q16C22⋊D2311yescharacteristic
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—21no—
335SD16—231no—
336SD16—231no—
337SD16—461no—
338SD16—461no—
339SD16—461no—
340SD16—461no—
341SD16—461no—
342SD16—461no—
343SD16—461no—
344SD16—461no—
345SD16C22⋊D2311yescharacteristic
346SD16C22⋊D2311yescharacteristic
347D8—21no—
348D8—231no—
349D8—461no—
350D8C22⋊D2311yescharacteristic
351M16—21no—
352M16—231no—
353M16—231no—
354M16—231no—
355M16—461no—
356M16—461no—
357M16—461no—
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—41no—
370Q8—21no—
371Q8—21no—
372Q8—41no—
373Q8—231no—
374Q8—461no—
375Q8—461no—
376Q8—461no—
377Q8—461no—
378Q8—921no—
379Q8—921no—
380Q8D4×D2311yescharacteristic
381Q8C2×C22⋊D2311yescharacteristic
382Q8C2×C22⋊D2311yescharacteristic
383D4—21no—
384D4—21no—
385D4—21no—
386D4—21no—
387D4—21no—
388D4—41no—
389D4—41no—
390D4—41no—
391D4—231no—
392D4—461no—
393D4—921no—
394D4—921no—
395D4D4×D2311yescharacteristic
396D4C2×C22⋊D2311yescharacteristic
397D4C2×C22⋊D2311yescharacteristic
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—461no—
406C2×C4—461no—
407C2×C4—461no—
408C2×C4—461no—
409C2×C4—921no—
410C2×C4—921no—
411C2×C4—921no—
412C2×C4—921no—
413C2×C4C23×D2311yescharacteristic
414C8—21no—
415C8—231no—
416C8—231no—
417C8—461no—
418C8—461no—
419C8—461no—
420C8C2×C22⋊D2311yescharacteristic
421C8C2×C22⋊D2311yescharacteristic
422C22—21no—
423C22—21no—
424C22—21no—
425C22—41no—
426C22—81no—
427C22—161no—
428C22—461no—
429C22#1062515511yescharacteristic
430C4—21no—
431C4—21no—
432C4—21no—
433C4—41no—
434C4—461no—
435C4—921no—
436C4—921no—
437C4—921no—
438C4C2×D4×D2311yescharacteristic
439C4C22×C22⋊D2311yescharacteristic
440C2—21no—
441C2—41no—
442C2—41no—
443C2—41no—
444C2—81no—
445C2—921no—
446C2D4×C22⋊D2311yescharacteristic
subgroupG/H
centerC2D4×C22⋊D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#577C2
socleC2×C23D42
hypercenter#577D23
hypocenterC23#3289
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ #577

Complements

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

NH ≅ G/Ntype
1. #13093232C2semidirect
2. #13093231C2semidirect
3. #13093228C2semidirect
4. #13092808C2semidirect
5. #13092692C2semidirect
6. #13092690C2semidirect
7. #13092678C2semidirect
8. #13092677C2semidirect
9. #13092600C2semidirect
10. #13092598C2semidirect
11. #13092595C2semidirect
12. #13092588C2semidirect
13. #13092539C2semidirect
14. #13092537C2semidirect
15. C23×#577C2semidirect
19. #10625161C22semidirect
34. #10625122C22semidirect
39. #10625119C22semidirect
40. #10625115C22semidirect
42. C2×#67275C22semidirect
44. #10625113C22semidirect
54. C2×Dic92C22semidirect
55. #10625072C22semidirect
58. #10625019C22semidirect
59. #10625018C22semidirect
61. #10625007C22semidirect
62. #10625006C22semidirect
63. #10625006C22semidirect
64. #10625004C22semidirect
65. #10625001C22semidirect
66. #10624997C22semidirect
220. #577D23semidirect
290. C23#3289semidirect

Maximal subgroups

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

subgroupindex
#130932322
#130932312
#130932282
#130928082
#130926922
#130926902
#130926782
#130926772
#130926002
#130925982
#130925952
#130925882
#130925392
#130925372
C23×#5772
#328923