Finite Group Databasebeta

← #11869014

Subgroups — #11869014

Order 1152.

543 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10589831C211yesmaximal, characteristic
2#10589674C211yesmaximal, characteristic
3C9×#475C211yesmaximal, characteristic, complemented
4#10588764C211yesmaximal, characteristic, complemented
5#10588704C211yesmaximal, characteristic, complemented
6#10588541C211yesmaximal, characteristic
7#10588540C211yesmaximal, characteristic
8#10588537C211yesmaximal, characteristic, complemented
9#10588534C211yesmaximal, characteristic, complemented
10#10588523C211yesmaximal, characteristic
11#10588511C211yesmaximal, characteristic, complemented
12#10588482C211yesmaximal, characteristic
13D9×#103C211yesmaximal, characteristic
14#10588479C211yesmaximal, characteristic, complemented
15#10588473C211yesmaximal, characteristic, complemented
16#81013—31nomaximal
17C2×Q8×D9C2211yescharacteristic
18C9×C4⋊Q8C2211yescharacteristic
19C4×Q8×C9C2211yescharacteristic
20#63508—21no—
21Q8×Dic9C2211yescharacteristic
22#63506—21no—
23C2×#3663C2211yescharacteristic
24C2×C8×D9C2211yescharacteristic
25#63458—21no—
26#63454—21no—
27#63454C2211yescharacteristic
28#63454C2211yescharacteristic
29C4⋊C4×D9C2211yescharacteristic
30#63452C2211yescharacteristic
31#63451—21no—
32#63450C2211yescharacteristic
33#63449—21no—
34#63449C2211yescharacteristic
35#63434—21no—
36#63434C2211yescharacteristic
37#63432C2211yescharacteristic
38C4×Dic18—21no—
39C4×Dic18C2211yescharacteristic
40C9×#106C2211yescharacteristic
41C9×#106C2211yescharacteristic
42C9×C4⋊C8C2211yescharacteristic
43C9×#103C2211yescharacteristic
44C9×#103C2211yescharacteristic
45#63395C2211yescharacteristic
46#63395C2211yescharacteristic
47#63378C2211yescharacteristic
48#63377C2211yescharacteristic
49#63376C2211yescharacteristic
50#63376C2211yescharacteristic
51Dic9⋊C8C2211yescharacteristic
52Dic9⋊C8C2211yescharacteristic
53#63368C2211yescharacteristic
54#63368C2211yescharacteristic
55#63367C2211yescharacteristic
56#63366C2211yescharacteristic
57#63366C2211yescharacteristic
58#63366C2211yescharacteristic
59C4⋊(C9⋊C8)C2211yescharacteristic
60#5729—31no—
61#5572—31no—
62C3×#475D311yescharacteristic
63#5091—31no—
64#5022—31no—
65#4861—31no—
66#4860—31no—
67#4857—31no—
68#4854—31no—
69#4839—31no—
70#4829—31no—
71#4802—31no—
72D3×#103—31no—
73#4799—31no—
74#4793—31no—
75C2×Q8×C9—21no—
76C2×Q8×C9C2311yescharacteristic
77Q8×D9—22no—
78Q8×D9Q814yescomplemented
79C2×C4×D9—21no—
80C2×C4×D9—21no—
81C2×C4×D9C2311yescharacteristic
82C2×Dic18—21no—
83C2×Dic18—21no—
84C2×Dic18C2311yescharacteristic
85C2×C8×C9C2311yescharacteristic
86C2×C8×C9C2311yescharacteristic
87C9×C4⋊C4—21no—
88C9×C4⋊C4—21no—
89C9×C4⋊C4C2311yescharacteristic
90C9×C4⋊C4C2311yescharacteristic
91C9×C4⋊C4C2311yescharacteristic
92C42×C9—21no—
93C42×C9C2311yescharacteristic
94(C2×D9)⋊C4—21no—
95(C2×D9)⋊C4—21no—
96(C2×D9)⋊C4D411yescharacteristic
97(C2×D9)⋊C4D411yescharacteristic
98C4⋊Dic9—21no—
99C4⋊Dic9—21no—
100C4⋊Dic9C2311yescharacteristic
101C4⋊Dic9C2311yescharacteristic
102C4⋊Dic9C2311yescharacteristic
103Dic9⋊C4—21no—
104Dic9⋊C4—21no—
105Dic9⋊C4—21no—
106Dic9⋊C4—21no—
107Dic9⋊C4—21no—
108Dic9⋊C4—21no—
109Dic9⋊C4—21no—
110Dic9⋊C4D411yescharacteristic
111Dic9⋊C4D411yescharacteristic
112C4×Dic9—21no—
113C4×Dic9—21no—
114C4×Dic9—21no—
115C4×Dic9—21no—
116C4×Dic9—21no—
117C4×Dic9C2311yescharacteristic
118C2×C9⋊C8C2311yescharacteristic
119C2×C9⋊C8C2311yescharacteristic
120#3663—22no—
121C8×D9—22no—
122#3082—91noSylow
123C2×D3×Q8—31no—
124C3×C4⋊Q8C2×D311yescharacteristic
125C3×C4×Q8C2×D311yescharacteristic
126#946—61no—
127Q8×Dic3—31no—
128#944—61no—
129C2×ΓL(1,𝔽25)—31no—
130C2×D3×C8—31no—
131#896—61no—
132#892—31no—
133#892—31no—
134#892—61no—
135D3×C4⋊C4—31no—
136#890—31no—
137#889—61no—
138#888—31no—
139#887—31no—
140#887—61no—
141#872—31no—
142#872—61no—
143#870—31no—
144C4×Dic6—31no—
145C4×Dic6—61no—
146C3×#106C2×D311yescharacteristic
147C3×#106C2×D311yescharacteristic
148C3×C4⋊C8C2×D311yescharacteristic
149C3×#103C2×D311yescharacteristic
150C3×#103C2×D311yescharacteristic
151#835—31no—
152#835—31no—
153#818—31no—
154#817—31no—
155#816—31no—
156#816—31no—
157Dic3⋊C8—31no—
158Dic3⋊C8—31no—
159#810—31no—
160#810—31no—
161#808—31no—
162#807—31no—
163#807—31no—
164#807—31no—
165C4⋊(C3⋊C8)—31no—
166C22×D9C2×D411yescharacteristic
167Q8×C9—21no—
168Q8×C9—81no—
169Q8×C9C2×Q812yes—
170C2×C4×C9—21no—
171C2×C4×C9—21no—
172C2×C4×C9—21no—
173C2×C4×C9—21no—
174C2×C4×C9C2×D411yescharacteristic
175C2×C4×C9C2×D411yescharacteristic
176C2×C4×C9C2411yescharacteristic
177C2×Dic9—21no—
178C2×Dic9—21no—
179C2×Dic9—21no—
180C2×Dic9—21no—
181C2×Dic9C2×D411yescharacteristic
182C2×Dic9C2×D411yescharacteristic
183C2×Dic9C2×D411yescharacteristic
184C4×D9—24no—
185C4×D9—81no—
186C4×D9C2×Q812yes—
187C4×D9#4112yes—
188Dic18—21no—
189Dic18—24no—
190Dic18—81no—
191Dic18C2×Q812yes—
192C8×C9—21no—
193C8×C9—21no—
194C9⋊C8—21no—
195C9⋊C8—21no—
196#544—91no—
197#519—91no—
198#479—91no—
199#479—91no—
200#479—91no—
201#479—91no—
202#477—91no—
203#477—91no—
204#475—91no—
205#475D911yescharacteristic, complemented
206#428—91no—
207#427—91no—
208#424—91no—
209#419—91no—
210C2×#103—91no—
211C2×C3×Q8—21no—
212C2×C3×Q8C22×D311yescharacteristic
213D3×Q8—34no—
214D3×Q8—62no—
215C2×C4×D3—31no—
216C2×C4×D3—61no—
217C2×C4×D3—61no—
218C2×Dic6—31no—
219C2×Dic6—61no—
220C2×Dic6—61no—
221C2×C3×C8C22×D311yescharacteristic
222C2×C3×C8C22×D311yescharacteristic
223C3×C4⋊C4—21no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4C22×D311yescharacteristic
226C3×C4⋊C4C22×D311yescharacteristic
227C3×C4⋊C4C22×D311yescharacteristic
228C3×C42—21no—
229C3×C42C22×D311yescharacteristic
230(C2×D3)⋊C4—31no—
231(C2×D3)⋊C4—31no—
232(C2×D3)⋊C4—61no—
233(C2×D3)⋊C4—61no—
234C4⋊Dic3—31no—
235C4⋊Dic3—31no—
236C4⋊Dic3—31no—
237C4⋊Dic3—61no—
238C4⋊Dic3—61no—
239Dic3⋊C4—31no—
240Dic3⋊C4—31no—
241Dic3⋊C4—61no—
242Dic3⋊C4—61no—
243Dic3⋊C4—61no—
244Dic3⋊C4—61no—
245Dic3⋊C4—61no—
246Dic3⋊C4—61no—
247Dic3⋊C4—61no—
248C4×Dic3—31no—
249C4×Dic3—61no—
250C4×Dic3—61no—
251C4×Dic3—61no—
252C4×Dic3—61no—
253C4×Dic3—61no—
254C2×C3⋊C8—31no—
255C2×C3⋊C8—31no—
256ΓL(1,𝔽25)—62no—
257D3×C8—62no—
258C22×C9C22×D411yescharacteristic
259C2×D9—21no—
260C2×D9—21no—
261C2×D9C22⋊Q812yes—
262C4×C9—22no—
263C4×C9—21no—
264C4×C9—21no—
265C4×C9—41no—
266C4×C9—41no—
267C4×C9—41no—
268C4×C9C22×Q811yescharacteristic
269C4×C9C2×#4111yescharacteristic
270Dic9—22no—
271Dic9—21no—
272Dic9—21no—
273Dic9—41no—
274Dic9—41no—
275Dic9—41no—
276Dic9C22⋊Q812yes—
277C22×Q8—91no—
278C2×M16—91no—
279C22×C8—91no—
280C4⋊Q8—91no—
281C4⋊Q8—181no—
282C4⋊Q8C2×D911yescharacteristic
283#125—91no—
284#125—91no—
285#125—181no—
286C22⋊Q8—181no—
287C22⋊Q8—181no—
288C4×Q8—91no—
289C4×Q8—91no—
290C4×Q8—91no—
291C4×Q8—181no—
292C4×Q8—181no—
293C4×Q8C2×D911yescharacteristic
294#117—91no—
295#117—91no—
296#117—91no—
297#117—181no—
298#117—181no—
299C2×C4⋊C4—91no—
300#107—91no—
301#107—91no—
302#107—91no—
303#107—91no—
304#106—91no—
305#106—91no—
306#106C2×D911yescharacteristic
307#106C2×D911yescharacteristic
308C4⋊C8—91no—
309C4⋊C8—91no—
310C4⋊C8—91no—
311C4⋊C8C2×D911yescharacteristic
312#103—91no—
313#103—91no—
314#103—91no—
315#103—91no—
316#103—91no—
317#103—91no—
318#103C2×D911yescharacteristic
319#103C2×D911yescharacteristic
320C22×D3—31no—
321C3×Q8—21no—
322C3×Q8—81no—
323C3×Q8D3×Q812yes—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4D3×D411yescharacteristic
329C2×C3×C4D3×D411yescharacteristic
330C2×C3×C4C23×D311yescharacteristic
331C2×Dic3—31no—
332C2×Dic3—31no—
333C2×Dic3—31no—
334C2×Dic3—61no—
335C2×Dic3—61no—
336C2×Dic3—61no—
337C2×Dic3—61no—
338C4×D3—32no—
339C4×D3—32no—
340C4×D3—64no—
341C4×D3—241no—
342Dic6—32no—
343Dic6—64no—
344Dic6—61no—
345Dic6—241no—
346C3×C8—21no—
347C3×C8—21no—
348C3⋊C8—61no—
349C3⋊C8—61no—
350C2×C9C2×C22⋊Q811yescharacteristic
351C2×C9#57711yescharacteristic
352C2×C9#57811yescharacteristic
353D9—22no—
354C2×Q8—21no—
355C2×Q8—94no—
356C2×Q8—91no—
357C2×Q8—181no—
358C2×Q8—181no—
359C2×Q8—182no—
360C2×Q8C22×D911yescharacteristic
361C22×C4—91no—
362C22×C4—181no—
363C22×C4—181no—
364M16—182no—
365C2×C8—91no—
366C2×C8—91no—
367C2×C8—182no—
368C2×C8C22×D911yescharacteristic
369C2×C8C22×D911yescharacteristic
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—91no—
373C4⋊C4—91no—
374C4⋊C4—91no—
375C4⋊C4—91no—
376C4⋊C4—91no—
377C4⋊C4—181no—
378C4⋊C4—181no—
379C4⋊C4—181no—
380C4⋊C4—181no—
381C4⋊C4—181no—
382C4⋊C4—181no—
383C4⋊C4—181no—
384C4⋊C4—181no—
385C4⋊C4—181no—
386C4⋊C4C22×D911yescharacteristic
387C4⋊C4C22×D911yescharacteristic
388C4⋊C4C22×D911yescharacteristic
389C22⋊C4—91no—
390C22⋊C4—91no—
391C22⋊C4—181no—
392C22⋊C4—181no—
393C42—21no—
394C42—91no—
395C42—181no—
396C42—181no—
397C42—181no—
398C42—181no—
399C42—181no—
400C42C22×D911yescharacteristic
401C22×C3C2×D3×D411yescharacteristic
402C2×D3—32no—
403C2×D3—61no—
404C2×D3—61no—
405C3×C4—21no—
406C3×C4—21no—
407C3×C4—22no—
408C3×C4—41no—
409C3×C4—41no—
410C3×C4—41no—
411C3×C4C2×D3×Q811yescharacteristic
412C3×C4D3×#4111yescharacteristic
413Dic3—32no—
414Dic3—61no—
415Dic3—61no—
416Dic3—62no—
417Dic3—121no—
418Dic3—121no—
419Dic3—121no—
420C9#308211yescharacteristic, complemented, Sylow
421C23—91no—
422Q8—21no—
423Q8—81no—
424Q8—92no—
425Q8—184no—
426Q8—181no—
427Q8—721no—
428Q8Q8×D912yes—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—91no—
434C2×C4—92no—
435C2×C4—92no—
436C2×C4—91no—
437C2×C4—91no—
438C2×C4—184no—
439C2×C4—181no—
440C2×C4—181no—
441C2×C4—181no—
442C2×C4—181no—
443C2×C4—721no—
444C2×C4D4×D911yescharacteristic
445C2×C4D4×D911yescharacteristic
446C2×C4C23×D911yescharacteristic
447C8—21no—
448C8—21no—
449C8—181no—
450C8—181no—
451C2×C3D3×C22⋊Q811yescharacteristic
452C2×C3#576211yescharacteristic
453C2×C3#577911yescharacteristic
454D3—62no—
455C22—92no—
456C22—181no—
457C22—181no—
458C22C2×D4×D911yescharacteristic
459C4—22no—
460C4—21no—
461C4—21no—
462C4—41no—
463C4—41no—
464C4—41no—
465C4—92no—
466C4—182no—
467C4—181no—
468C4—181no—
469C4—361no—
470C4—361no—
471C4—361no—
472C4C2×Q8×D911yescharacteristic
473C4#41×D911yescharacteristic
474C3#8101311yescharacteristic
475C2—182no—
476C2D9×C22⋊Q811yescharacteristic
477C2#1058986411yescharacteristic
478C2#1058988111yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#475C2
socleC22×C3C2×D3×D4
prime radicalC22×D9C2×D4
hypercenter#475D9
hypocenterC9#3082
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
3. C9×#475C2semidirect
4. #10588764C2semidirect
5. #10588704C2semidirect
8. #10588537C2semidirect
9. #10588534C2semidirect
11. #10588511C2semidirect
14. #10588479C2semidirect
15. #10588473C2semidirect
78. Q8×D9Q8semidirect
205. #475D9semidirect
420. C9#3082semidirect

Maximal subgroups

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

subgroupindex
#105898312
#105896742
C9×#4752
#105887642
#105887042
#105885412
#105885402
#105885372
#105885342
#105885232
#105885112
#105884822
D9×#1032
#105884792
#105884732
#810133