Finite Group Databasebeta

← #15684937

Subgroups — #15684937

Order 2944.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10625085C211yesmaximal, characteristic, complemented
2#13093086C211yesmaximal, characteristic, complemented
3#13093055C211yesmaximal, characteristic, complemented
4#13092803C211yesmaximal, characteristic, complemented
5#13092660C211yesmaximal, characteristic, complemented
6#13092653C211yesmaximal, characteristic, complemented
7#13092641C211yesmaximal, characteristic, complemented
8#13092610C211yesmaximal, characteristic, complemented
9#13092578C211yesmaximal, characteristic, complemented
10#13092562C211yesmaximal, characteristic, complemented
11#13092562C211yesmaximal, characteristic, complemented
12#13092549C211yesmaximal, characteristic, complemented
13#13092518C211yesmaximal, characteristic, complemented
14#13092488C211yesmaximal, characteristic, complemented
15C2×C23×#135C211yesmaximal, characteristic, complemented
16C2×#41×C23C2211yescharacteristic
17C2×#41×C23C2211yescharacteristic, complemented
18C2×#67292C2211yescharacteristic
19C2×D4×D23C2211yescharacteristic
20C23×#135—24no—
21C2×Q16×C23C2211yescharacteristic, complemented
22C2×SD16×C23C2211yescharacteristic
23C2×SD16×C23C2211yescharacteristic, complemented
24C2×D8×C23C2211yescharacteristic
25C22×C8×C23C2211yescharacteristic, complemented
26#10625118C2211yescharacteristic
27#10625117C2211yescharacteristic
28Q8×Dic23C2211yescharacteristic, complemented
29C2×#67274C2211yescharacteristic
30C2×#67274C2211yescharacteristic, complemented
31#10625111—21no—
32#10625111C2211yescharacteristic, complemented
33#10625110—21no—
34#10625109—21no—
35#10625109C2211yescharacteristic
36#10625108—21no—
37D4×Dic23C2211yescharacteristic
38C2×#67272C2211yescharacteristic
39C2×#67272C2211yescharacteristic
40#10625101—21no—
41#10625101C2211yescharacteristic
42#10625101C2211yescharacteristic, complemented
43#10625100—21no—
44C4×C22⋊D23—21no—
45C4×C22⋊D23C2211yescharacteristic
46C2×(C2×D23)⋊C4—21no—
47#10625085—24no—
48C2×D184C2211yescharacteristic
49C2×#67262C2211yescharacteristic
50#10625017C2211yescharacteristic, complemented
51#10625017C2211yescharacteristic, complemented
52#10625014C2211yescharacteristic
53#10625014C2211yescharacteristic, complemented
54C22⋊(C23⋊C8)C2211yescharacteristic, complemented
55#10625003C2211yescharacteristic
56#10625003C2211yescharacteristic, complemented
57(C2×D23)⋊C8C2211yescharacteristic
58#10625000C2211yescharacteristic, complemented
59#10624997C2211yescharacteristic, complemented
60Dic23⋊C8C2211yescharacteristic, complemented
61C23×D23—21no—
62#41×C23—22no—
63#41×C23—22no—
64#41×C23—41no—
65#41×C23—41no—
66C2×Q8×C23C2311yescharacteristic
67C2×Q8×C23C2311yescharacteristic
68C2×D4×C23—21no—
69C2×D4×C23—21no—
70C2×D4×C23C2311yescharacteristic
71C2×D4×C23C2311yescharacteristic
72C22×C4×C23—21no—
73C22×C4×C23—21no—
74C22×C4×C23C2311yescharacteristic
75C2×C22⋊D23—21no—
76C2×C22⋊D23—21no—
77C2×C22⋊D23—21no—
78C2×C22⋊D23—21no—
79C2×C22⋊D23—21no—
80C2×C22⋊D23—21no—
81C2×C22⋊D23D411yescharacteristic
82C22×Dic23—21no—
83#67292—22no—
84#67292—41no—
85D4×D23—22no—
86D4×D23—41no—
87C2×D92—21no—
88C2×D92C2311yescharacteristic
89C2×D92C2311yescharacteristic
90C2×C4×D23—21no—
91C2×C4×D23C2311yescharacteristic
92Q16×C23—22no—
93SD16×C23—22no—
94SD16×C23D414yescomplemented
95D8×C23—22no—
96C2×C8×C23—22no—
97C2×C8×C23C2311yescharacteristic
98C2×C8×C23C2311yescharacteristic
99C22⋊Dic23—21no—
100C22⋊Dic23—21no—
101C22⋊Dic23D411yescharacteristic
102#67274—22no—
103#67274—41no—
104#67272—22no—
105#67272—41no—
106(C2×D23)⋊C4—21no—
107(C2×D23)⋊C4—21no—
108(C2×D23)⋊C4—21no—
109(C2×D23)⋊C4—21no—
110(C2×D23)⋊C4—21no—
111(C2×D23)⋊C4D411yescharacteristic
112C4⋊Dic23—21no—
113C4⋊Dic23C2311yescharacteristic
114C4⋊Dic23C2311yescharacteristic
115Dic23⋊C4—21no—
116Dic23⋊C4D411yescharacteristic
117C4×Dic23—21no—
118C4×Dic23C2311yescharacteristic
119C2×C23⋊C8C2311yescharacteristic
120C2×C23⋊C8C2311yescharacteristic
121D184—22no—
122#67262—22no—
123C23×C23—21no—
124C23×C23—21no—
125C23×C23C2×D411yescharacteristic
126C22×D23—21no—
127C22×D23—21no—
128C22×D23—42no—
129C22×D23—42no—
130C22×D23—81no—
131C22×D23C2×D411yescharacteristic
132Q8×C23—21no—
133Q8×C23—21no—
134Q8×C23—21no—
135Q8×C23C2×D412yes—
136D4×C23—21no—
137D4×C23—21no—
138D4×C23—21no—
139D4×C23—42no—
140D4×C23—42no—
141D4×C23C2×D412yes—
142C2×C4×C23—21no—
143C2×C4×C23—21no—
144C2×C4×C23—21no—
145C2×C4×C23—21no—
146C2×C4×C23—42no—
147C2×C4×C23—42no—
148C2×C4×C23C2×D411yescharacteristic
149C2×C4×C23C2411yescharacteristic
150C22⋊D23—41no—
151C22⋊D23—42no—
152C22⋊D23—42no—
153C22⋊D23—81no—
154C22⋊D23—81no—
155C22⋊D23—81no—
156C22⋊D23—81no—
157C2×Dic23—21no—
158C2×Dic23—21no—
159C2×Dic23—81no—
160C2×Dic23C2×D411yescharacteristic
161C2×Dic23C2×D411yescharacteristic
162C2×Dic23C2×D411yescharacteristic
163D92—21no—
164D92—21no—
165D92—21no—
166D92—21no—
167D92—42no—
168C4×D23—21no—
169C4×D23—21no—
170C4×D23—42no—
171C8×C23—21no—
172C8×C23C2×D412yes—
173C23⋊C8—21no—
174C23⋊C8—21no—
175#3268—231nomaximal, Sylow
176C22×C23—22no—
177C22×C23—21no—
178C22×C23—21no—
179C22×C23—21no—
180C22×C23—41no—
181C22×C23—41no—
182C22×C23—41no—
183C22×C23—41no—
184C22×C23—41no—
185C22×C23C22×D411yescharacteristic
186C2×D23—21no—
187C2×D23—21no—
188C2×D23—21no—
189C2×D23—41no—
190C2×D23—41no—
191C2×D23—41no—
192C2×D23—41no—
193C2×D23—41no—
194C2×D23—41no—
195C2×D23—84no—
196C4×C23—22no—
197C4×C23—21no—
198C4×C23—41no—
199C4×C23C22×D411yescharacteristic
200C4×C23H(5,𝔽2)11yescharacteristic
201Dic23—21no—
202Dic23—21no—
203Dic23—21no—
204Dic23—41no—
205Dic23—41no—
206C2×AGL(1,ℤ/8)—231no—
207C2×#135D2311yescharacteristic, complemented
208#550—231no—
209#546—231no—
210#496—231no—
211#468—231no—
212#466—231no—
213#464—231no—
214#459—231no—
215#452—231no—
216#449—231no—
217#449—231no—
218#447—231no—
219#440—231no—
220#435—231no—
221C2×C23—42no—
222C2×C23—41no—
223C2×C23—81no—
224C2×C23D4211yescharacteristic
225C2×C23#57511yescharacteristic
226C2×C23#57611yescharacteristic
227D23—41no—
228D23—81no—
229D23—81no—
230C2×#41—231no—
231C2×#41C2×D2311yescharacteristic
232C2×#41C2×D2311yescharacteristic, complemented
233C22×D4—231no—
234AGL(1,ℤ/8)—464no—
235#135—24no—
236C2×Q16C2×D2311yescharacteristic, complemented
237C2×SD16—231no—
238C2×SD16—231no—
239C2×SD16C2×D2311yescharacteristic
240C2×SD16C2×D2311yescharacteristic, complemented
241C2×D8—231no—
242C2×D8—231no—
243C2×D8—231no—
244C2×D8C2×D2311yescharacteristic
245C2×M16—231no—
246C22×C8C2×D2311yescharacteristic, complemented
247#127—231no—
248#127—461no—
249#124—231no—
250#123—461no—
251C22⋊Q8—231no—
252#121—231no—
253#121—231no—
254#121—231no—
255#121—461no—
256#121—461no—
257#121—461no—
258#120—461no—
259C4×Q8—231no—
260C4×D4—231no—
261C4×D4—231no—
262C4×D4—461no—
263C2×C22⋊C4—461no—
264#107—231no—
265C4⋊C8—231no—
266#103—231no—
267#103—231no—
268#102—231no—
269#102—231no—
270#102—231no—
271#102—231no—
272C22⋊C8—231no—
273C22⋊C8—231no—
274#97—231no—
275C23#326811yescharacteristic, complemented, Sylow
276C24—461no—
277#41—22no—
278#41—22no—
279#41—41no—
280#41—41no—
281#41—462no—
282#41—921no—
283C2×Q8C22×D2311yescharacteristic
284C2×Q8C22×D2311yescharacteristic
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—231no—
288C2×D4—231no—
289C2×D4—231no—
290C2×D4—461no—
291C2×D4—461no—
292C2×D4—461no—
293C2×D4—461no—
294C2×D4—462no—
295C2×D4—461no—
296C2×D4—461no—
297C2×D4—461no—
298C2×D4—921no—
299C2×D4C22×D2311yescharacteristic
300C2×D4C22×D2311yescharacteristic
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—231no—
304C22×C4—461no—
305C22×C4—461no—
306C22×C4C22×D2311yescharacteristic
307Q16—22no—
308SD16—22no—
309SD16—462no—
310SD16—921no—
311SD16C22⋊D2314yescomplemented
312D8—22no—
313D8—462no—
314D8—462no—
315D8—921no—
316M16—462no—
317C2×C8—22no—
318C2×C8—231no—
319C2×C8—231no—
320C2×C8C22×D2311yescharacteristic
321C2×C8C22×D2311yescharacteristic
322C4⋊C4—231no—
323C4⋊C4—231no—
324C4⋊C4—231no—
325C4⋊C4—461no—
326C4⋊C4—461no—
327C22⋊C4—231no—
328C22⋊C4—231no—
329C22⋊C4—461no—
330C22⋊C4—461no—
331C22⋊C4—461no—
332C22⋊C4—461no—
333C22⋊C4—461no—
334C22⋊C4—461no—
335C22⋊C4—461no—
336C42—231no—
337C42—461no—
338C23—21no—
339C23—21no—
340C23—231no—
341C23—461no—
342C23—461no—
343C23—922no—
344C23—922no—
345C23—1841no—
346C23D4×D2311yescharacteristic
347Q8—21no—
348Q8—21no—
349Q8—21no—
350Q8C2×C22⋊D2312yes—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—42no—
355D4—42no—
356D4—461no—
357D4—461no—
358D4—461no—
359D4—461no—
360D4—922no—
361D4—921no—
362D4—922no—
363D4—922no—
364D4—1841no—
365D4—1841no—
366D4—1841no—
367D4—1841no—
368D4C2×C22⋊D2312yes—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—231no—
376C2×C4—231no—
377C2×C4—231no—
378C2×C4—461no—
379C2×C4—461no—
380C2×C4—461no—
381C2×C4—461no—
382C2×C4—922no—
383C2×C4—1841no—
384C2×C4D4×D2311yescharacteristic
385C2×C4C23×D2311yescharacteristic
386C8—21no—
387C8—461no—
388C8—461no—
389C8C2×C22⋊D2312yes—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—22no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—461no—
400C22—461no—
401C22—461no—
402C22—921no—
403C22—921no—
404C22—921no—
405C22—921no—
406C22—921no—
407C22—921no—
408C22—1844no—
409C22C2×D4×D2311yescharacteristic
410C4—21no—
411C4—22no—
412C4—41no—
413C4—461no—
414C4—461no—
415C4—461no—
416C4—921no—
417C4—921no—
418C4#1062515511yescharacteristic
419C4C22×C22⋊D2311yescharacteristic
420C2—41no—
421C2—42no—
422C2—81no—
423C2—921no—
424C2—1841no—
425C2—1841no—
426C2D4×C22⋊D2311yescharacteristic
427C2#1309321411yescharacteristic
428C2#1309321911yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC2×C23×#135C2
socleC22×C23C22×D4
hypercenterC2×#135D23
hypocenterC23#3268
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#10625085C2semidirect
2. #13093086C2semidirect
3. #13093055C2semidirect
4. #13092803C2semidirect
5. #13092660C2semidirect
6. #13092653C2semidirect
7. #13092641C2semidirect
8. #13092610C2semidirect
9. #13092578C2semidirect
10. #13092562C2semidirect
11. #13092562C2semidirect
12. #13092549C2semidirect
13. #13092518C2semidirect
14. #13092488C2semidirect
15. C2×C23×#135C2semidirect
17. C2×#41×C23C22semidirect
21. C2×Q16×C23C22semidirect
23. C2×SD16×C23C22semidirect
25. C22×C8×C23C22semidirect
28. Q8×Dic23C22semidirect
30. C2×#67274C22semidirect
32. #10625111C22semidirect
42. #10625101C22semidirect
50. #10625017C22semidirect
51. #10625017C22semidirect
53. #10625014C22semidirect
54. C22⋊(C23⋊C8)C22semidirect
56. #10625003C22semidirect
58. #10625000C22semidirect
59. #10624997C22semidirect
60. Dic23⋊C8C22semidirect
94. SD16×C23D4semidirect
207. C2×#135D23semidirect
232. C2×#41C2×D23semidirect
236. C2×Q16C2×D23semidirect
240. C2×SD16C2×D23semidirect
246. C22×C8C2×D23semidirect
275. C23#3268semidirect
311. SD16C22⋊D23semidirect

Maximal subgroups

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

subgroupindex
C2×#106250852
#130930862
#130930552
#130928032
#130926602
#130926532
#130926412
#130926102
#130925782
#130925622
#130925492
#130925182
#130924882
C2×C23×#1352
#326823