Finite Group Databasebeta

← #11858173

Subgroups — #11858173

Order 1152.

1107 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593139C211yesmaximal, characteristic
2#10589847C211yesmaximal, characteristic, complemented
3C4×#3697C211yesmaximal, characteristic, complemented
4C2×C9×#104C211yesmaximal, characteristic, complemented
5#10588914C211yesmaximal, characteristic, complemented
6#10588819C211yesmaximal, characteristic, complemented
7C2×#63364C211yesmaximal, characteristic, complemented
8#10588501C214yesmaximal, complemented
9D9×#104C214yesmaximal, complemented
10#78983—31nomaximal
11C2×C9×#41C2211yescharacteristic
12#63716—21no—
13#63716C412yescomplemented
14#63715—21no—
15#63715C412yescomplemented
16#41×D9—22no—
17#41×D9C2214yes—
18#63713C412yescomplemented
19#63710—22no—
20#63710C412yescomplemented
21C2×#3697—22no—
22C2×#3697C2211yescharacteristic
23C2×#3697C2211yescharacteristic
24C2×C9×M16C2211yescharacteristic, complemented
25C2×C42×C9C2211yescharacteristic, complemented
26C4×#611—22no—
27#63488C2211yescharacteristic, complemented
28C2×#3667C2211yescharacteristic, complemented
29#63469—22no—
30M16×D9C2214yescomplemented
31#63464—22no—
32C4×D36—21no—
33#63434C2212yescomplemented
34C42×D9C2212yescomplemented
35C4×Dic18—21no—
36C9×#104C2212yescomplemented
37C9×#104C2212yescomplemented
38#63396C2214yescomplemented
39#63384C2214yescomplemented
40#63364C2212yescomplemented
41#63364C2212yescomplemented
42#5964—31no—
43#5745—31no—
44C4×#235—31no—
45C2×C3×#104D311yescharacteristic
46#5236—31no—
47#5139—31no—
48C2×#805—31no—
49#4821—34no—
50D3×#104—34no—
51C9×#41—21no—
52C9×#41—21no—
53C9×#41C2×C412yescomplemented
54C9×#41C2312yes—
55C2×Q8×C9C2×C411yescharacteristic, complemented
56C2×D4×C9—21no—
57C2×D4×C9C2×C411yescharacteristic, complemented
58C22×C4×C9—21no—
59C22×C4×C9—21no—
60C22×C4×C9C2311yescharacteristic
61C2×#611—21no—
62C2×#611—24no—
63C2×#611D412yes—
64#3701—22no—
65#3701C2×C414yescomplemented
66Q8×D9—22no—
67Q8×D9C2×C414yescomplemented
68#3699—24no—
69#3699—24no—
70#3699—22no—
71#3699C2×C414yescomplemented
72D4×D9—24no—
73D4×D9—24no—
74D4×D9—22no—
75D4×D9C2×C414yescomplemented
76#3697—21no—
77#3697—21no—
78#3697—24no—
79#3697—22no—
80#3697—24no—
81#3697—22no—
82#3697C2×C412yes—
83#3697C2×C412yes—
84#3697C2×C412yescomplemented
85#3697D412yes—
86#3697D412yes—
87#3697C2312yes—
88C2×D36—22no—
89C2×D36C2×C411yescharacteristic, complemented
90C2×D36D411yescharacteristic
91C2×C4×D9—21no—
92C2×C4×D9—24no—
93C2×C4×D9—22no—
94C2×C4×D9C2312yes—
95C2×Dic18—22no—
96C2×Dic18C2×C411yescharacteristic, complemented
97C2×Dic18D411yescharacteristic
98C9×M16—21no—
99C9×M16C2312yes—
100C2×C8×C9—21no—
101C42×C9—21no—
102C42×C9C2311yescharacteristic
103C42×C9C2311yescharacteristic
104#3676—21no—
105(C2×D9)⋊C4—22no—
106C4⋊Dic9—21no—
107Dic9⋊C4—22no—
108C4×Dic9—22no—
109C4×Dic9C2312yes—
110#3667—21no—
111#3667C2312yes—
112C2×C9⋊C8—21no—
113#3663—24no—
114C8×D9—24no—
115#2901—91noSylow
116C2×C3×#41C2×D311yescharacteristic
117#1010—32no—
118#1010—61no—
119#1009—32no—
120#1009—61no—
121D3×#41—34no—
122D3×#41—62no—
123#1007—32no—
124#1004—32no—
125#1004—62no—
126C2×#235—31no—
127C2×#235—31no—
128C2×#235—62no—
129C2×C3×M16C2×D311yescharacteristic
130C2×C3×C42C2×D311yescharacteristic
131C4×#67—62no—
132#926—31no—
133C2×#208—31no—
134#907—62no—
135D3×M16—34no—
136#901—62no—
137C4×D12—61no—
138#872—32no—
139C42×D3—32no—
140C4×Dic6—61no—
141C3×#104C2×D312yes—
142C3×#104C2×D312yes—
143#837—34no—
144#825—34no—
145#805—32no—
146#805—32no—
147C23×C9—21no—
148C23×C9C2×D411yescharacteristic
149C22×D9—21no—
150C22×D9—24no—
151C22×D9C2×D412yes—
152Q8×C9—21no—
153Q8×C9C22×C412yes—
154D4×C9—22no—
155D4×C9—22no—
156D4×C9—21no—
157D4×C9C22×C412yes—
158C2×C4×C9—21no—
159C2×C4×C9—21no—
160C2×C4×C9—22no—
161C2×C4×C9—22no—
162C2×C4×C9—21no—
163C2×C4×C9—42no—
164C2×C4×C9C22×C411yescharacteristic
165C2×C4×C9C22×C411yescharacteristic
166C2×C4×C9C2×D411yescharacteristic
167C2×C4×C9C2×D411yescharacteristic
168C2×C4×C9C2×D411yescharacteristic
169C2×C4×C9C2411yescharacteristic
170#611—22no—
171#611—22no—
172#611—24no—
173#611—24no—
174#611C22⋊C414yes—
175#611C22⋊C414yes—
176C2×Dic9—21no—
177C2×Dic9—24no—
178C2×Dic9—22no—
179C2×Dic9C2×D412yes—
180D36—24no—
181D36—21no—
182D36C22⋊C412yes—
183D36C22⋊C412yes—
184D36C22×C412yes—
185C4×D9—24no—
186C4×D9—22no—
187C4×D9—22no—
188C4×D9—24no—
189C4×D9—44no—
190C4×D9C22×C414yes—
191C4×D9C2×D414yes—
192Dic18—21no—
193Dic18—24no—
194Dic18C22⋊C412yes—
195Dic18C22⋊C412yes—
196Dic18C22×C412yes—
197C8×C9—22no—
198C9⋊C8—22no—
199#585—91no—
200#568—91no—
201C4×#41—91no—
202#421—91no—
203#421—91no—
204#421—94no—
205C2×#104—91no—
206C2×#104—94no—
207C2×#104D911yescharacteristic, complemented
208C3×#41—21no—
209C3×#41—21no—
210C3×#41C4×D312yes—
211C3×#41C22×D312yes—
212C2×C3×Q8C4×D311yescharacteristic
213C2×C3×D4—21no—
214C2×C3×D4C4×D311yescharacteristic
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4C22×D311yescharacteristic
218C2×#67—32no—
219C2×#67—64no—
220C2×#67—61no—
221#239—34no—
222#239—62no—
223D3×Q8—34no—
224D3×Q8—62no—
225#237—34no—
226#237—62no—
227#237—64no—
228#237—64no—
229D3×D4—34no—
230D3×D4—62no—
231D3×D4—64no—
232D3×D4—64no—
233#235—32no—
234#235—32no—
235#235—32no—
236#235—32no—
237#235—32no—
238#235—32no—
239#235—62no—
240#235—64no—
241#235—62no—
242#235—64no—
243#235—61no—
244#235—61no—
245C2×D12—31no—
246C2×D12—31no—
247C2×D12—62no—
248C2×C4×D3—32no—
249C2×C4×D3—64no—
250C2×C4×D3—61no—
251C2×C4×D3—62no—
252C2×Dic6—31no—
253C2×Dic6—31no—
254C2×Dic6—62no—
255C3×M16—21no—
256C3×M16C22×D312yes—
257C2×C3×C8—21no—
258C3×C42—21no—
259C3×C42C22×D311yescharacteristic
260C3×C42C22×D311yescharacteristic
261#217—61no—
262(C2×D3)⋊C4—62no—
263C4⋊Dic3—61no—
264Dic3⋊C4—62no—
265C4×Dic3—32no—
266C4×Dic3—62no—
267#208—32no—
268#208—61no—
269C2×C3⋊C8—61no—
270ΓL(1,𝔽25)—64no—
271D3×C8—64no—
272C22×C9—22no—
273C22×C9—41no—
274C22×C9—81no—
275C22×C9C2×C22⋊C411yescharacteristic
276C22×C9C2×C22⋊C411yescharacteristic
277C22×C9C22×D411yescharacteristic
278C2×D9—22no—
279C2×D9—42no—
280C2×D9—84no—
281C2×D9—81no—
282C2×D9C2×C22⋊C414yes—
283C4×C9—22no—
284C4×C9—22no—
285C4×C9—41no—
286C4×C9C2×C22⋊C411yescharacteristic
287C4×C9C2×C22⋊C411yescharacteristic
288C4×C9C23×C411yescharacteristic
289C4×C9C22×D411yescharacteristic
290Dic9—22no—
291Dic9—42no—
292Dic9C2×C22⋊C414yes—
2932−1+4—92no—
2942−1+4—92no—
2952−1+4—181no—
296H(5,𝔽2)—92no—
297H(5,𝔽2)—92no—
298H(5,𝔽2)—182no—
299H(5,𝔽2)—181no—
300C2×#41—91no—
301C2×#41—94no—
302C2×#41—91no—
303C2×#41—182no—
304C2×#41—182no—
305C2×#41C2×D911yescharacteristic
306#131—182no—
307#131—182no—
308C2×M16—91no—
309C2×M16—94no—
310C2×M16C2×D911yescharacteristic, complemented
311C4×Q8—181no—
312C4×D4—181no—
313C4×D4—182no—
314#117—91no—
315#117—92no—
316C2×C42—92no—
317C2×C42C2×D911yescharacteristic, complemented
318#104—94no—
319#104—94no—
320#104—92no—
321#104—92no—
322#104C2×D912yescomplemented
323#104C2×D912yescomplemented
324C23×C3—21no—
325C23×C3D3×D411yescharacteristic
326C22×D3—32no—
327C22×D3—64no—
328C22×D3—61no—
329C3×Q8—21no—
330C3×Q8C2×C4×D312yes—
331C3×D4—22no—
332C3×D4—22no—
333C3×D4—21no—
334C3×D4C2×C4×D312yes—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—21no—
340C2×C3×C4—42no—
341C2×C3×C4C2×C4×D311yescharacteristic
342C2×C3×C4C2×C4×D311yescharacteristic
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4C23×D311yescharacteristic
347#67—34no—
348#67—34no—
349#67—64no—
350#67—64no—
351#67—62no—
352#67—62no—
353C2×Dic3—32no—
354C2×Dic3—64no—
355C2×Dic3—61no—
356C2×Dic3—62no—
357D12—32no—
358D12—32no—
359D12—32no—
360D12—64no—
361D12—61no—
362C4×D3—34no—
363C4×D3—34no—
364C4×D3—64no—
365C4×D3—64no—
366C4×D3—62no—
367C4×D3—62no—
368C4×D3—124no—
369Dic6—32no—
370Dic6—32no—
371Dic6—32no—
372Dic6—64no—
373Dic6—61no—
374C3×C8—22no—
375C3⋊C8—62no—
376C2×C9—21no—
377C2×C9—21no—
378C2×C9—21no—
379C2×C9—42no—
380C2×C9C22×C22⋊C411yescharacteristic
381D9—24no—
382D9—42no—
383#41—21no—
384#41—21no—
385#41—92no—
386#41—92no—
387#41—92no—
388#41—92no—
389#41—94no—
390#41—94no—
391#41—92no—
392#41—92no—
393#41—184no—
394#41—184no—
395#41—182no—
396#41—182no—
397#41—184no—
398#41—184no—
399#41—182no—
400#41—182no—
401#41—181no—
402#41—181no—
403#41C4×D912yescomplemented
404#41C22×D912yes—
405C2×Q8—91no—
406C2×Q8—94no—
407C2×Q8—91no—
408C2×Q8—182no—
409C2×Q8—182no—
410C2×Q8C4×D911yescharacteristic, complemented
411C2×D4—21no—
412C2×D4—92no—
413C2×D4—94no—
414C2×D4—91no—
415C2×D4—91no—
416C2×D4—182no—
417C2×D4—184no—
418C2×D4—182no—
419C2×D4—184no—
420C2×D4—184no—
421C2×D4—181no—
422C2×D4C4×D911yescharacteristic, complemented
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—92no—
426C22×C4—184no—
427C22×C4—182no—
428C22×C4—181no—
429C22×C4C22×D911yescharacteristic
430M16—21no—
431M16—92no—
432M16—184no—
433M16—181no—
434M16C22×D912yes—
435C2×C8—21no—
436C2×C8—184no—
437C2×C8—181no—
438C4⋊C4—182no—
439C4⋊C4—181no—
440C22⋊C4—182no—
441C22⋊C4—181no—
442C42—21no—
443C42—92no—
444C42—182no—
445C42C22×D911yescharacteristic
446C42C22×D911yescharacteristic
447C22×C3—22no—
448C22×C3—41no—
449C22×C3—81no—
450C22×C3D3×C22⋊C411yescharacteristic
451C22×C3D3×C22⋊C411yescharacteristic
452C22×C3C2×D3×D411yescharacteristic
453C2×D3—34no—
454C2×D3—62no—
455C2×D3—122no—
456C2×D3—244no—
457C2×D3—241no—
458C3×C4—22no—
459C3×C4—22no—
460C3×C4—41no—
461C3×C4D3×C22⋊C411yescharacteristic
462C3×C4D3×C22⋊C411yescharacteristic
463C3×C4C22×C4×D311yescharacteristic
464C3×C4C2×D3×D411yescharacteristic
465Dic3—34no—
466Dic3—62no—
467Dic3—122no—
468C9#290111yescharacteristic, complemented, Sylow
469C23—21no—
470C23—92no—
471C23—184no—
472C23—181no—
473C23D4×D911yescharacteristic
474Q8—21no—
475Q8—92no—
476Q8—92no—
477Q8—92no—
478Q8—184no—
479Q8—181no—
480Q8C2×C4×D912yes—
481D4—22no—
482D4—22no—
483D4—21no—
484D4—94no—
485D4—94no—
486D4—92no—
487D4—92no—
488D4—92no—
489D4—184no—
490D4—184no—
491D4—184no—
492D4—182no—
493D4—182no—
494D4—181no—
495D4C2×C4×D912yes—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—21no—
501C2×C4—42no—
502C2×C4—92no—
503C2×C4—94no—
504C2×C4—94no—
505C2×C4—184no—
506C2×C4—184no—
507C2×C4—184no—
508C2×C4—181no—
509C2×C4—182no—
510C2×C4—182no—
511C2×C4—182no—
512C2×C4—364no—
513C2×C4C2×C4×D911yescharacteristic
514C2×C4C2×C4×D911yescharacteristic
515C2×C4D4×D911yescharacteristic
516C2×C4D4×D911yescharacteristic
517C2×C4D4×D911yescharacteristic
518C2×C4C23×D911yescharacteristic
519C8—22no—
520C8—182no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—21no—
524C2×C3—42no—
525C2×C3C2×D3×C22⋊C411yescharacteristic
526D3—64no—
527D3—122no—
528C22—22no—
529C22—41no—
530C22—81no—
531C22—94no—
532C22—182no—
533C22—362no—
534C22—721no—
535C22—724no—
536C22C22⋊C4×D911yescharacteristic
537C22C22⋊C4×D911yescharacteristic
538C22C2×D4×D911yescharacteristic
539C4—22no—
540C4—22no—
541C4—41no—
542C4—94no—
543C4—182no—
544C4—362no—
545C4C22⋊C4×D911yescharacteristic
546C4C22⋊C4×D911yescharacteristic
547C4C22×C4×D911yescharacteristic
548C4C2×D4×D911yescharacteristic
549C3#7898311yescharacteristic
550C2—21no—
551C2—21no—
552C2—21no—
553C2—42no—
554C2—184no—
555C2—362no—
556C2C2×C22⋊C4×D911yescharacteristic
subgroupG/H
centerC4C2×D4×D9
commutatorC4×C9C23×C4
FrattiniC2×C3×C4C23×D3
FittingC2×C9×#104C2
socleC2×C3C2×D3×C22⋊C4
prime radical#10593139C2
cosocleC2×C4×C9C24
hypercenterC2×#104D9
hypocenterC9#2901
LCSG ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. #10589847C2semidirect
3. C4×#3697C2semidirect
4. C2×C9×#104C2semidirect
5. #10588914C2semidirect
6. #10588819C2semidirect
7. C2×#63364C2semidirect
8. #10588501C2semidirect
9. D9×#104C2semidirect
13. #63716C4semidirect
15. #63715C4semidirect
18. #63713C4semidirect
20. #63710C4semidirect
24. C2×C9×M16C22semidirect
25. C2×C42×C9C22semidirect
27. #63488C22semidirect
28. C2×#3667C22semidirect
30. M16×D9C22semidirect
33. #63434C22semidirect
34. C42×D9C22semidirect
36. C9×#104C22semidirect
37. C9×#104C22semidirect
38. #63396C22semidirect
39. #63384C22semidirect
40. #63364C22semidirect
41. #63364C22semidirect
53. C9×#41C2×C4semidirect
55. C2×Q8×C9C2×C4semidirect
57. C2×D4×C9C2×C4semidirect
65. #3701C2×C4semidirect
67. Q8×D9C2×C4semidirect
71. #3699C2×C4semidirect
75. D4×D9C2×C4semidirect
84. #3697C2×C4semidirect
89. C2×D36C2×C4semidirect
96. C2×Dic18C2×C4semidirect
207. C2×#104D9semidirect
310. C2×M16C2×D9semidirect
317. C2×C42C2×D9semidirect
322. #104C2×D9semidirect
323. #104C2×D9semidirect
403. #41C4×D9semidirect
410. C2×Q8C4×D9semidirect
422. C2×D4C4×D9semidirect
468. C9#2901semidirect

Maximal subgroups

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

subgroupindex
#105931392
#105898472
C4×#36972
C2×C9×#1042
#105889142
#105888192
C2×#633642
#105885012
D9×#1042
#789833