Finite Group Databasebeta

← #11860556

Subgroups — #11860556

Order 1152.

705 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63477C211yesmaximal, characteristic
2#10589674C211yesmaximal, characteristic, complemented
3#10589648C211yesmaximal, characteristic
4C4×C9×SD16C211yesmaximal, characteristic, complemented
5#10588844C211yesmaximal, characteristic, complemented
6#10588706C211yesmaximal, characteristic, complemented
7#10588694C211yesmaximal, characteristic, complemented
8#10588541C211yesmaximal, characteristic, complemented
9#10588533C211yesmaximal, characteristic, complemented
10D9×#103C211yesmaximal, characteristic, complemented
11#10588470C211yesmaximal, characteristic, complemented
12#10588452C211yesmaximal, characteristic
13#10588438C211yesmaximal, characteristic, complemented
14#10588371C211yesmaximal, characteristic, complemented
15C4×Dic36C211yesmaximal, characteristic, complemented
16#79648—31nomaximal
17C2×Q8×D9C2211yescharacteristic
18C2×#3699C2211yescharacteristic
19C2×C9×SD16C2211yescharacteristic
20C4×Q8×C9C2211yescharacteristic
21C4×D4×C9C2211yescharacteristic
22Q8×Dic9C2211yescharacteristic
23C2×#3674C2211yescharacteristic
24D4×Dic9C2211yescharacteristic
25C2×#3672C2211yescharacteristic
26C4×#611—21no—
27C2×Dic9⋊C4—21no—
28#63477C418yescomplemented
29C2×#3663C2211yescharacteristic
30C2×C8×D9C2211yescharacteristic
31C2×Dic36C2211yescharacteristic
32#63454—21no—
33#63454C2211yescharacteristic
34C4⋊C4×D9C2211yescharacteristic
35#63449—21no—
36#63449C2211yescharacteristic
37#63449C2211yescharacteristic
38#611⋊C4—21no—
39#63439—21no—
40#63434—21no—
41#63434C2211yescharacteristic
42C4×Dic18—21no—
43C4×Dic18C2211yescharacteristic
44C4×Dic18C2211yescharacteristic
45C9×#106C2211yescharacteristic
46C9×#103C2211yescharacteristic
47C9×#102C2211yescharacteristic
48C4×C8×C9C2211yescharacteristic
49#63395C2211yescharacteristic
50#63392C2211yescharacteristic
51#63378C2211yescharacteristic
52#63376C2211yescharacteristic
53#63376C2211yescharacteristic
54#63375C2211yescharacteristic
55C8×Dic9C2211yescharacteristic
56#63368C2211yescharacteristic
57#63368C2211yescharacteristic
58#63367C2211yescharacteristic
59#63366C2211yescharacteristic
60#63362C2211yescharacteristic
61C2×#915—31no—
62#5572—31no—
63#5546—31no—
64C3×C4×SD16D311yescharacteristic
65#5164—31no—
66#5030—31no—
67#5018—31no—
68#4861—31no—
69#4853—31no—
70D3×#103—31no—
71#4790—31no—
72#4772—31no—
73#4758—31no—
74C4×Dic12—31no—
75#4689—31no—
76C2×Q8×C9C2311yescharacteristic
77C2×D4×C9C2311yescharacteristic
78C22×C4×C9—21no—
79C2×#611—21no—
80C22×Dic9—21no—
81C22×Dic9—21no—
82Q8×D9—22no—
83Q8×D9C2×C414yescomplemented
84#3699—22no—
85#3699C2×C414yes—
86C2×C4×D9—21no—
87C2×C4×D9—21no—
88C2×C4×D9C2311yescharacteristic
89C2×Dic18—21no—
90C2×Dic18C2311yescharacteristic
91C2×Dic18C2311yescharacteristic
92C9×SD16C2×C414yescomplemented
93C2×C8×C9C2311yescharacteristic
94C2×C8×C9C2311yescharacteristic
95C9×C4⋊C4—21no—
96C9×C4⋊C4C2311yescharacteristic
97C9×C4⋊C4C2311yescharacteristic
98C9×C22⋊C4—21no—
99C42×C9—21no—
100C42×C9C2311yescharacteristic
101#3676—21no—
102#3674C2×C414yescomplemented
103#3672C2×C414yescomplemented
104(C2×D9)⋊C4—21no—
105(C2×D9)⋊C4D411yescharacteristic
106(C2×D9)⋊C4D411yescharacteristic
107C4⋊Dic9—21no—
108C4⋊Dic9C2311yescharacteristic
109C4⋊Dic9C2311yescharacteristic
110Dic9⋊C4—21no—
111Dic9⋊C4—21no—
112Dic9⋊C4—21no—
113Dic9⋊C4—21no—
114Dic9⋊C4—21no—
115Dic9⋊C4D411yescharacteristic
116Dic9⋊C4D411yescharacteristic
117C4×Dic9—21no—
118C4×Dic9—21no—
119C4×Dic9—21no—
120C4×Dic9—21no—
121C4×Dic9—21no—
122C4×Dic9—21no—
123C4×Dic9C2311yescharacteristic
124C2×C9⋊C8C2311yescharacteristic
125C2×C9⋊C8C2311yescharacteristic
126#3663C2×C414yescomplemented
127C8×D9—22no—
128Dic36C2×C414yescomplemented
129#2947—91noSylow
130C2×D3×Q8—31no—
131C2×#237—31no—
132C2×C3×SD16C2×D311yescharacteristic
133C3×C4×Q8C2×D311yescharacteristic
134C3×C4×D4C2×D311yescharacteristic
135Q8×Dic3—31no—
136C2×#216—31no—
137D4×Dic3—31no—
138C2×#214—31no—
139C4×#67—61no—
140C2×Dic3⋊C4—61no—
141#915—38no—
142C2×Dic12—31no—
143C2×ΓL(1,𝔽25)—31no—
144C2×D3×C8—31no—
145#892—31no—
146#892—61no—
147D3×C4⋊C4—31no—
148#887—31no—
149#887—31no—
150#887—61no—
151#67⋊C4—61no—
152#877—61no—
153#872—31no—
154#872—61no—
155C4×Dic6—31no—
156C4×Dic6—31no—
157C4×Dic6—61no—
158C3×#106C2×D311yescharacteristic
159C3×#103C2×D311yescharacteristic
160C3×#102C2×D311yescharacteristic
161C3×C4×C8C2×D311yescharacteristic
162#835—31no—
163#832—31no—
164#818—31no—
165#816—31no—
166#816—31no—
167#815—31no—
168C8×Dic3—31no—
169#810—31no—
170#810—31no—
171#808—31no—
172#807—31no—
173#803—31no—
174C23×C9—21no—
175C22×D9C2×D411yescharacteristic
176Q8×C9—21no—
177Q8×C9C22×C412yes—
178D4×C9—21no—
179D4×C9C22×C412yes—
180C2×C4×C9—21no—
181C2×C4×C9—21no—
182C2×C4×C9—21no—
183C2×C4×C9—81no—
184C2×C4×C9C2×D411yescharacteristic
185C2×C4×C9C2×D411yescharacteristic
186C2×C4×C9C2411yescharacteristic
187#611—24no—
188C2×Dic9—21no—
189C2×Dic9—21no—
190C2×Dic9—24no—
191C2×Dic9—21no—
192C2×Dic9—21no—
193C2×Dic9—81no—
194C2×Dic9C2×D411yescharacteristic
195C2×Dic9C2×D411yescharacteristic
196C2×Dic9C2×D411yescharacteristic
197C4×D9—24no—
198C4×D9—81no—
199C4×D9C22×C412yes—
200C4×D9#4112yes—
201Dic18—21no—
202Dic18—21no—
203Dic18—24no—
204Dic18C22×C412yes—
205Dic18C22×C412yes—
206C8×C9—21no—
207C8×C9C22×C412yes—
208C9⋊C8—21no—
209C9⋊C8C22×C412yes—
210C2×#137—91no—
211#520—91no—
212#519—91no—
213#441—91no—
214#441—91no—
215#440—91no—
216#440—91no—
217C4×Q16—91no—
218C4×Q16—91no—
219C4×SD16—91no—
220C4×SD16D911yescharacteristic, complemented
221#428—91no—
222#416—91no—
223C2×#103—91no—
224#405—91no—
225C2×C3×Q8C22×D311yescharacteristic
226C2×C3×D4C22×D311yescharacteristic
227C22×C3×C4—21no—
228C2×#67—61no—
229C22×Dic3—61no—
230C22×Dic3—61no—
231D3×Q8—34no—
232D3×Q8—62no—
233#237—34no—
234#237—62no—
235C2×C4×D3—31no—
236C2×C4×D3—61no—
237C2×C4×D3—61no—
238C2×Dic6—31no—
239C2×Dic6—31no—
240C2×Dic6—61no—
241C3×SD16C4×D314yes—
242C2×C3×C8C22×D311yescharacteristic
243C2×C3×C8C22×D311yescharacteristic
244C3×C4⋊C4—21no—
245C3×C4⋊C4C22×D311yescharacteristic
246C3×C4⋊C4C22×D311yescharacteristic
247C3×C22⋊C4—21no—
248C3×C42—21no—
249C3×C42C22×D311yescharacteristic
250#217—61no—
251#216—34no—
252#214—34no—
253(C2×D3)⋊C4—31no—
254(C2×D3)⋊C4—31no—
255(C2×D3)⋊C4—61no—
256C4⋊Dic3—31no—
257C4⋊Dic3—31no—
258C4⋊Dic3—61no—
259Dic3⋊C4—31no—
260Dic3⋊C4—31no—
261Dic3⋊C4—61no—
262Dic3⋊C4—61no—
263Dic3⋊C4—61no—
264Dic3⋊C4—61no—
265Dic3⋊C4—61no—
266C4×Dic3—31no—
267C4×Dic3—61no—
268C4×Dic3—61no—
269C4×Dic3—61no—
270C4×Dic3—61no—
271C4×Dic3—61no—
272C4×Dic3—61no—
273C2×C3⋊C8—31no—
274C2×C3⋊C8—31no—
275Dic12—34no—
276ΓL(1,𝔽25)—34no—
277D3×C8—62no—
278C22×C9—22no—
279C22×C9—41no—
280C22×C9—41no—
281C22×C9C22×D411yescharacteristic
282C2×D9—21no—
283C2×D9—21no—
284C2×D9C4×D412yes—
285C4×C9—22no—
286C4×C9—21no—
287C4×C9—21no—
288C4×C9—41no—
289C4×C9—41no—
290C4×C9C23×C411yescharacteristic
291C4×C9C2×#4111yescharacteristic
292Dic9—22no—
293Dic9—22no—
294Dic9—21no—
295Dic9—21no—
296Dic9—41no—
297Dic9—41no—
298Dic9C4×D412yes—
299C2×#41—91no—
300C22×Q8—91no—
301#137—98no—
302C2×Q16—91no—
303C2×Q16—91no—
304C2×SD16—91no—
305C2×SD16C2×D911yescharacteristic
306C2×M16—91no—
307C22×C8—91no—
308C4×Q8—91no—
309C4×Q8—91no—
310C4×Q8—91no—
311C4×Q8—91no—
312C4×Q8—91no—
313C4×Q8—181no—
314C4×Q8—181no—
315C4×Q8C2×D911yescharacteristic
316C4×D4—91no—
317C4×D4—181no—
318C4×D4—181no—
319C4×D4C2×D911yescharacteristic
320#117—91no—
321#117—91no—
322#117—181no—
323#117—181no—
324#117—181no—
325C2×C4⋊C4—91no—
326C2×C4⋊C4—181no—
327#107—91no—
328#107—91no—
329#106—91no—
330#106C2×D911yescharacteristic
331#103—91no—
332#103—91no—
333#103—91no—
334#103—91no—
335#103—91no—
336#103C2×D911yescharacteristic
337#102—91no—
338#102C2×D911yescharacteristic
339#97—91no—
340#97—91no—
341C4×C8—91no—
342C4×C8C2×D911yescharacteristic
343C23×C3—21no—
344C22×D3—31no—
345C3×Q8—21no—
346C3×Q8C2×C4×D312yes—
347C3×D4—21no—
348C3×D4C2×C4×D312yes—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—81no—
353C2×C3×C4D3×D411yescharacteristic
354C2×C3×C4D3×D411yescharacteristic
355C2×C3×C4C23×D311yescharacteristic
356#67—64no—
357C2×Dic3—31no—
358C2×Dic3—31no—
359C2×Dic3—31no—
360C2×Dic3—64no—
361C2×Dic3—61no—
362C2×Dic3—61no—
363C2×Dic3—61no—
364C2×Dic3—61no—
365C2×Dic3—241no—
366C4×D3—32no—
367C4×D3—32no—
368C4×D3—64no—
369C4×D3—241no—
370Dic6—32no—
371Dic6—32no—
372Dic6—64no—
373Dic6—61no—
374Dic6—61no—
375C3×C8—21no—
376C3×C8C2×C4×D312yes—
377C3⋊C8—32no—
378C3⋊C8—61no—
379C2×C9—42no—
380C2×C9C2×C4×D411yescharacteristic
381C2×C9#57711yescharacteristic
382C2×C9#57811yescharacteristic
383D9—22no—
384#41—94no—
385#41—182no—
386C2×Q8—94no—
387C2×Q8—91no—
388C2×Q8—91no—
389C2×Q8—181no—
390C2×Q8—182no—
391C2×Q8C22×D911yescharacteristic
392C2×D4—181no—
393C2×D4C22×D911yescharacteristic
394C22×C4—21no—
395C22×C4—91no—
396C22×C4—181no—
397C22×C4—181no—
398C22×C4—181no—
399C22×C4—181no—
400Q16—94no—
401Q16—94no—
402SD16—94no—
403SD16C4×D914yescomplemented
404M16—94no—
405C2×C8—91no—
406C2×C8—91no—
407C2×C8—182no—
408C2×C8C22×D911yescharacteristic
409C2×C8C22×D911yescharacteristic
410C4⋊C4—21no—
411C4⋊C4—91no—
412C4⋊C4—91no—
413C4⋊C4—91no—
414C4⋊C4—91no—
415C4⋊C4—181no—
416C4⋊C4—181no—
417C4⋊C4—181no—
418C4⋊C4—181no—
419C4⋊C4—181no—
420C4⋊C4—181no—
421C4⋊C4C22×D911yescharacteristic
422C4⋊C4C22×D911yescharacteristic
423C22⋊C4—21no—
424C22⋊C4—91no—
425C22⋊C4—91no—
426C22⋊C4—181no—
427C22⋊C4—181no—
428C42—21no—
429C42—91no—
430C42—181no—
431C42—181no—
432C42—181no—
433C42—181no—
434C42—181no—
435C42—181no—
436C42C22×D911yescharacteristic
437C22×C3—22no—
438C22×C3—41no—
439C22×C3—41no—
440C22×C3C2×D3×D411yescharacteristic
441C2×D3—32no—
442C2×D3—61no—
443C2×D3—61no—
444C3×C4—21no—
445C3×C4—21no—
446C3×C4—22no—
447C3×C4—41no—
448C3×C4—41no—
449C3×C4C22×C4×D311yescharacteristic
450C3×C4D3×#4111yescharacteristic
451Dic3—32no—
452Dic3—61no—
453Dic3—61no—
454Dic3—62no—
455Dic3—62no—
456Dic3—121no—
457Dic3—121no—
458C9#294711yescharacteristic, complemented, Sylow
459C23—21no—
460C23—91no—
461Q8—21no—
462Q8—92no—
463Q8—92no—
464Q8—184no—
465Q8—181no—
466Q8—181no—
467Q8C2×C4×D912yes—
468D4—21no—
469D4—184no—
470D4C2×C4×D912yes—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—81no—
475C2×C4—91no—
476C2×C4—92no—
477C2×C4—92no—
478C2×C4—91no—
479C2×C4—91no—
480C2×C4—184no—
481C2×C4—184no—
482C2×C4—181no—
483C2×C4—181no—
484C2×C4—181no—
485C2×C4—181no—
486C2×C4—721no—
487C2×C4—721no—
488C2×C4D4×D911yescharacteristic
489C2×C4D4×D911yescharacteristic
490C2×C4C23×D911yescharacteristic
491C8—21no—
492C8—92no—
493C8—181no—
494C8C2×C4×D912yes—
495C2×C3—42no—
496C2×C3C4×D3×D411yescharacteristic
497C2×C3#576211yescharacteristic
498C2×C3#577111yescharacteristic
499D3—62no—
500C22—22no—
501C22—41no—
502C22—41no—
503C22—92no—
504C22—181no—
505C22—181no—
506C22C2×D4×D911yescharacteristic
507C4—21no—
508C4—21no—
509C4—22no—
510C4—41no—
511C4—41no—
512C4—92no—
513C4—181no—
514C4—181no—
515C4—182no—
516C4—182no—
517C4—361no—
518C4—361no—
519C4C22×C4×D911yescharacteristic
520C4#41×D911yescharacteristic
521C3#7964811yescharacteristic
522C2—42no—
523C2—182no—
524C2C4×D4×D911yescharacteristic
525C2#1058986411yescharacteristic
526C2#1058987311yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutatorC4×C9C23×C4
FrattiniC2×C3×C4C23×D3
FittingC4×C9×SD16C2
socleC22×C3C2×D3×D4
prime radicalC2×#3699C22
cosocleC2×C4×C9C24
hypercenterC4×SD16D9
hypocenterC9#2947
LCSG ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. #10589674C2semidirect
4. C4×C9×SD16C2semidirect
5. #10588844C2semidirect
6. #10588706C2semidirect
7. #10588694C2semidirect
8. #10588541C2semidirect
9. #10588533C2semidirect
10. D9×#103C2semidirect
11. #10588470C2semidirect
13. #10588438C2semidirect
14. #10588371C2semidirect
15. C4×Dic36C2semidirect
28. #63477C4semidirect
83. Q8×D9C2×C4semidirect
92. C9×SD16C2×C4semidirect
102. #3674C2×C4semidirect
103. #3672C2×C4semidirect
126. #3663C2×C4semidirect
128. Dic36C2×C4semidirect
220. C4×SD16D9semidirect
403. SD16C4×D9semidirect
458. C9#2947semidirect

Maximal subgroups

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

subgroupindex
C2×#634772
#105896742
#105896482
C4×C9×SD162
#105888442
#105887062
#105886942
#105885412
#105885332
D9×#1032
#105884702
#105884522
#105884382
#105883712
C4×Dic362
#796483