Finite Group Databasebeta

← #15684936

Subgroups — #15684936

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×#10625082C211yesmaximal, characteristic, complemented
2C2×#10625087C211yesmaximal, characteristic, complemented
3#13093087C211yesmaximal, characteristic, complemented
4#13093060C211yesmaximal, characteristic, complemented
5#13092660C211yesmaximal, characteristic, complemented
6#13092650C211yesmaximal, characteristic, complemented
7#13092636C211yesmaximal, characteristic, complemented
8#13092609C211yesmaximal, characteristic, complemented
9#13092576C211yesmaximal, characteristic, complemented
10#13092561C211yesmaximal, characteristic, complemented
11#13092559C211yesmaximal, characteristic, complemented
12#13092549C211yesmaximal, characteristic, complemented
13#13092519C211yesmaximal, characteristic, complemented
14#13092490C211yesmaximal, characteristic, complemented
15C23×#496C211yesmaximal, characteristic, complemented
16C2×#67292C2211yescharacteristic
17C2×#67290C2211yescharacteristic
18C2×#67290C2211yescharacteristic, complemented
19C2×D4×D23C2211yescharacteristic
20C2×SD16×C23C2211yescharacteristic, complemented
21C2×SD16×C23C2211yescharacteristic, complemented
22C2×D8×C23C2211yescharacteristic
23C2×D8×C23C2211yescharacteristic
24C23×#127C2211yescharacteristic, complemented
25C23×#124C2211yescharacteristic
26#10625117C2211yescharacteristic
27C2×#67275C2211yescharacteristic, complemented
28#10625111—21no—
29#10625110—21no—
30#10625110—21no—
31#10625109C2211yescharacteristic
32#10625109C2211yescharacteristic
33#10625109C2211yescharacteristic, complemented
34D4×Dic23—21no—
35C2×#67273C2211yescharacteristic
36C2×#67272C2211yescharacteristic
37C2×#67272C2211yescharacteristic
38#10625087—24no—
39#10625082—24no—
40C2×#67263C2211yescharacteristic
41C2×#67262C2211yescharacteristic
42C2×C8×D23C2211yescharacteristic, complemented
43#10625055—21no—
44#10625054—21no—
45#10625053—21no—
46C22⋊C4×D23—21no—
47C4×D92C2211yescharacteristic
48C4×D92C2211yescharacteristic
49C4×Dic46C2211yescharacteristic, complemented
50C23×#97C2211yescharacteristic, complemented
51#10625017C2211yescharacteristic, complemented
52#10625014C2211yescharacteristic
53#10625014C2211yescharacteristic, complemented
54#10625014C2211yescharacteristic, complemented
55#10625003C2211yescharacteristic
56(C2×D23)⋊C8C2211yescharacteristic
57(C2×D23)⋊C8C2211yescharacteristic, complemented
58#10625000C2211yescharacteristic, complemented
59#10624998C2211yescharacteristic, complemented
60C4⋊(C23⋊C8)C2211yescharacteristic, complemented
61C23×D23—21no—
62C2×Q8×C23C2311yescharacteristic
63C2×D4×C23—21no—
64C2×D4×C23—21no—
65C2×D4×C23C2311yescharacteristic
66C2×D4×C23C2311yescharacteristic
67C2×D4×C23C2311yescharacteristic
68C2×C22⋊D23—21no—
69C2×C22⋊D23—21no—
70C2×C22⋊D23—21no—
71C2×C22⋊D23—21no—
72C2×C22⋊D23—21no—
73C2×C22⋊D23—21no—
74C22×Dic23—21no—
75C22×Dic23—21no—
76#67292—22no—
77#67292—41no—
78#67290—22no—
79#67290—22no—
80#67290—41no—
81#67290—41no—
82D4×D23—22no—
83D4×D23—41no—
84C2×D92—21no—
85C2×D92D411yescharacteristic
86C2×D92C2311yescharacteristic
87C2×C4×D23—21no—
88C2×C4×D23—21no—
89C2×C4×D23C2311yescharacteristic
90C2×C4×D23C2311yescharacteristic
91C2×Dic46C2311yescharacteristic
92SD16×C23—22no—
93SD16×C23—41no—
94D8×C23—22no—
95D8×C23—41no—
96C2×C8×C23C2311yescharacteristic
97C2×C8×C23C2311yescharacteristic
98C22⋊C4×C23—21no—
99C22⋊C4×C23—21no—
100C42×C23C2311yescharacteristic
101C22⋊Dic23—21no—
102C22⋊Dic23—21no—
103C22⋊Dic23—21no—
104#67275—22no—
105#67273—22no—
106#67272—22no—
107#67272—22no—
108(C2×D23)⋊C4—21no—
109(C2×D23)⋊C4—21no—
110(C2×D23)⋊C4D411yescharacteristic
111(C2×D23)⋊C4D411yescharacteristic
112C4⋊Dic23D411yescharacteristic
113C4⋊Dic23C2311yescharacteristic
114C4⋊Dic23C2311yescharacteristic
115Dic23⋊C4—21no—
116Dic23⋊C4—21no—
117C4×Dic23—21no—
118C2×C23⋊C8C2311yescharacteristic
119C2×C23⋊C8C2311yescharacteristic
120#67263D414yescomplemented
121#67262—22no—
122C8×D23—22no—
123C23×C23—21no—
124C23×C23—21no—
125C23×C23—21no—
126C22×D23—21no—
127C22×D23—42no—
128C22×D23—42no—
129C22×D23—81no—
130C22×D23C2×D411yescharacteristic
131C22×D23C2×D411yescharacteristic
132Q8×C23—21no—
133Q8×C23—21no—
134D4×C23—21no—
135D4×C23—21no—
136D4×C23—21no—
137D4×C23—21no—
138D4×C23—21no—
139D4×C23—21no—
140D4×C23—42no—
141D4×C23—81no—
142C2×C4×C23—21no—
143C2×C4×C23C2×D411yescharacteristic
144C2×C4×C23C2×D411yescharacteristic
145C2×C4×C23C2411yescharacteristic
146C22⋊D23—42no—
147C22⋊D23—42no—
148C22⋊D23—42no—
149C22⋊D23—81no—
150C22⋊D23—81no—
151C22⋊D23—81no—
152C2×Dic23—21no—
153C2×Dic23—21no—
154C2×Dic23—21no—
155C2×Dic23—42no—
156C2×Dic23—42no—
157C2×Dic23C2×D411yescharacteristic
158C2×Dic23C2×D411yescharacteristic
159D92—21no—
160D92—41no—
161D92—42no—
162D92C2×D412yes—
163C4×D23—21no—
164C4×D23—21no—
165C4×D23—21no—
166C4×D23—21no—
167C4×D23—42no—
168C4×D23—81no—
169Dic46—21no—
170Dic46C2×D412yes—
171C8×C23—21no—
172C8×C23C2×D412yes—
173C23⋊C8—21no—
174C23⋊C8—21no—
175#3268—231nomaximal, Sylow
176C22×C23—41no—
177C22×C23—41no—
178C22×C23—41no—
179C22×C23—41no—
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—22no—
189C2×D23—21no—
190C2×D23—21no—
191C2×D23—21no—
192C2×D23—21no—
193C2×D23—41no—
194C2×D23—41no—
195C2×D23—84no—
196C4×C23—21no—
197C4×C23—21no—
198C4×C23—41no—
199C4×C23C22×D411yescharacteristic
200C4×C23H(5,𝔽2)11yescharacteristic
201Dic23—22no—
202Dic23—21no—
203Dic23—21no—
204Dic23—41no—
205Dic23—41no—
206C2×AGL(1,ℤ/8)—231no—
207C2×#135—231no—
208#550—231no—
209#546—231no—
210#496D2311yescharacteristic, complemented
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—81no—
222C2×C23—81no—
223C2×C23—81no—
224C2×C23D4211yescharacteristic
225C2×C23#57511yescharacteristic
226C2×C23#57611yescharacteristic
227D23—41no—
228D23—41no—
229D23—42no—
230C2×#41—231no—
231C2×#41—231no—
232C2×#41—231no—
233C22×D4—231no—
234AGL(1,ℤ/8)—464no—
235#135—464no—
236C2×Q16—231no—
237C2×SD16—231no—
238C2×SD16—231no—
239C2×SD16C2×D2311yescharacteristic, complemented
240C2×SD16C2×D2311yescharacteristic, complemented
241C2×D8—231no—
242C2×D8—231no—
243C2×D8C2×D2311yescharacteristic
244C2×D8C2×D2311yescharacteristic
245C2×M16—231no—
246C22×C8—231no—
247#127—461no—
248#127C2×D2311yescharacteristic, complemented
249#124C2×D2311yescharacteristic
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#97C2×D2311yescharacteristic, complemented
275C23#326811yescharacteristic, complemented, Sylow
276C24—461no—
277#41—462no—
278#41—462no—
279#41—462no—
280#41—921no—
281#41—921no—
282#41—921no—
283C2×Q8—231no—
284C2×Q8C22×D2311yescharacteristic
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—231no—
288C2×D4—231no—
289C2×D4—461no—
290C2×D4—461no—
291C2×D4—462no—
292C2×D4—461no—
293C2×D4—461no—
294C2×D4—461no—
295C2×D4—461no—
296C2×D4—461no—
297C2×D4—921no—
298C2×D4C22×D2311yescharacteristic
299C2×D4C22×D2311yescharacteristic
300C2×D4C22×D2311yescharacteristic
301C22×C4—231no—
302C22×C4—231no—
303C22×C4—461no—
304C22×C4—461no—
305C22×C4—461no—
306C22×C4—461no—
307Q16—462no—
308SD16—22no—
309SD16—41no—
310SD16—234no—
311SD16—462no—
312D8—22no—
313D8—41no—
314D8—462no—
315D8—462no—
316M16—462no—
317C2×C8—231no—
318C2×C8—231no—
319C2×C8—462no—
320C2×C8C22×D2311yescharacteristic
321C2×C8C22×D2311yescharacteristic
322C4⋊C4—231no—
323C4⋊C4—231no—
324C4⋊C4—231no—
325C4⋊C4—461no—
326C4⋊C4—461no—
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—231no—
330C22⋊C4—231no—
331C22⋊C4—461no—
332C22⋊C4—461no—
333C22⋊C4—461no—
334C22⋊C4—461no—
335C22⋊C4—461no—
336C42—461no—
337C42C22×D2311yescharacteristic
338C23—21no—
339C23—21no—
340C23—21no—
341C23—231no—
342C23—231no—
343C23—461no—
344C23—922no—
345C23—922no—
346C23—1841no—
347Q8—21no—
348Q8—21no—
349Q8—232no—
350Q8—461no—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—21no—
355D4—21no—
356D4—21no—
357D4—42no—
358D4—81no—
359D4—232no—
360D4—461no—
361D4—921no—
362D4—922no—
363D4—922no—
364D4—922no—
365D4—922no—
366D4—1841no—
367D4—1841no—
368D4—1841no—
369C2×C4—21no—
370C2×C4—231no—
371C2×C4—231no—
372C2×C4—461no—
373C2×C4—461no—
374C2×C4—461no—
375C2×C4—461no—
376C2×C4—461no—
377C2×C4—461no—
378C2×C4—461no—
379C2×C4—922no—
380C2×C4—922no—
381C2×C4—922no—
382C2×C4—1841no—
383C2×C4D4×D2311yescharacteristic
384C2×C4D4×D2311yescharacteristic
385C2×C4C23×D2311yescharacteristic
386C8—21no—
387C8—461no—
388C8—461no—
389C8D4×D2312yes—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—461no—
400C22—461no—
401C22—461no—
402C22—461no—
403C22—461no—
404C22—461no—
405C22—462no—
406C22—921no—
407C22—921no—
408C22—1844no—
409C22C2×D4×D2311yescharacteristic
410C4—21no—
411C4—21no—
412C4—41no—
413C4—461no—
414C4—461no—
415C4—462no—
416C4—921no—
417C4—921no—
418C4C2×D4×D2311yescharacteristic
419C4#1062515511yescharacteristic
420C2—81no—
421C2—81no—
422C2—81no—
423C2—921no—
424C2—921no—
425C2—922no—
426C2#1309305211yescharacteristic
427C2#1309321311yescharacteristic
428C2#1309322111yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#496C2
socleC22×C23C22×D4
hypercenter#496D23
hypocenterC23#3268
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. C2×#10625082C2semidirect
2. C2×#10625087C2semidirect
3. #13093087C2semidirect
4. #13093060C2semidirect
5. #13092660C2semidirect
6. #13092650C2semidirect
7. #13092636C2semidirect
8. #13092609C2semidirect
9. #13092576C2semidirect
10. #13092561C2semidirect
11. #13092559C2semidirect
12. #13092549C2semidirect
13. #13092519C2semidirect
14. #13092490C2semidirect
15. C23×#496C2semidirect
18. C2×#67290C22semidirect
20. C2×SD16×C23C22semidirect
21. C2×SD16×C23C22semidirect
24. C23×#127C22semidirect
27. C2×#67275C22semidirect
33. #10625109C22semidirect
42. C2×C8×D23C22semidirect
49. C4×Dic46C22semidirect
50. C23×#97C22semidirect
51. #10625017C22semidirect
53. #10625014C22semidirect
54. #10625014C22semidirect
57. (C2×D23)⋊C8C22semidirect
58. #10625000C22semidirect
59. #10624998C22semidirect
60. C4⋊(C23⋊C8)C22semidirect
120. #67263D4semidirect
210. #496D23semidirect
239. C2×SD16C2×D23semidirect
240. C2×SD16C2×D23semidirect
248. #127C2×D23semidirect
274. #97C2×D23semidirect
275. C23#3268semidirect

Maximal subgroups

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

subgroupindex
C2×#106250822
C2×#106250872
#130930872
#130930602
#130926602
#130926502
#130926362
#130926092
#130925762
#130925612
#130925592
#130925492
#130925192
#130924902
C23×#4962
#326823