Finite Group Databasebeta

← #11868635

Subgroups — #11868635

Order 1152.

660 conjugacy classes of subgroups.

The subgroup lattice has 435 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10589830C211yesmaximal, characteristic, complemented
2C4×D4×D9C211yesmaximal, characteristic
3C9×#474C211yesmaximal, characteristic, complemented
4#10588772C211yesmaximal, characteristic, complemented
5#10588691C211yesmaximal, characteristic, complemented
6#10588571C212yesmaximal, complemented
7#10588561C212yesmaximal, complemented
8#10588526C211yesmaximal, characteristic, complemented
9#10588521C211yesmaximal, characteristic, complemented
10#10588450C212yesmaximal
11#10588443C212yesmaximal, complemented
12#80965—31nomaximal
13C2×D4×D9C2211yescharacteristic
14C22×C4×D9—21no—
15C9×C4⋊Q8C2211yescharacteristic, complemented
16C4×D4×C9C2211yescharacteristic
17#63508—21no—
18Q8×Dic9—21no—
19D4×Dic9C2211yescharacteristic
20C4×#611—21no—
21C2×#3663C2212yes—
22#63459—21no—
23#63455C2211yescharacteristic
24#63454C2212yes—
25C4⋊C4×D9C2211yescharacteristic
26#63452C2212yescomplemented
27#63449—21no—
28#611⋊C4—21no—
29C22⋊C4×D9—21no—
30C4×D36C2211yescharacteristic
31C42×D9C2211yescharacteristic
32#63431C2211yescharacteristic, complemented
33C9×#107C2212yescomplemented
34C9×C4⋊C8C2211yescharacteristic, complemented
35C9×#102C2212yes—
36#63392C2212yes—
37#63380C2212yes—
38#63377C2212yescomplemented
39Dic9⋊C8C2212yescomplemented
40#63369C2212yes—
41#63367C2212yescomplemented
42#63366C2212yescomplemented
43C4⋊(C9⋊C8)C2211yescharacteristic, complemented
44#5728—31no—
45C4×D3×D4—31no—
46C3×#474D311yescharacteristic
47#5087—31no—
48#5008—31no—
49#4891—32no—
50#4881—32no—
51#4842—31no—
52#4837—31no—
53#4770—32no—
54#4763—32no—
55C23×D9—21no—
56C2×Q8×C9—21no—
57C2×D4×C9C2311yescharacteristic
58C22×C4×C9—21no—
59C2×#611—21no—
60C22×Dic9—21no—
61D4×D9—22no—
62D4×D9Q814yescomplemented
63C2×D36C2311yescharacteristic
64C2×C4×D9—21no—
65C2×C4×D9—21no—
66C2×C4×D9—21no—
67C2×C4×D9—44no—
68C2×C4×D9D411yescharacteristic
69C2×C4×D9D411yescharacteristic
70C2×C4×D9C2311yescharacteristic
71C2×Dic18—21no—
72C2×C8×C9C2312yes—
73C9×C4⋊C4—21no—
74C9×C4⋊C4C2311yescharacteristic
75C9×C4⋊C4C2312yes—
76C9×C22⋊C4—21no—
77C42×C9C2311yescharacteristic
78#3676—21no—
79(C2×D9)⋊C4—22no—
80(C2×D9)⋊C4—21no—
81(C2×D9)⋊C4—21no—
82C4⋊Dic9—21no—
83C4⋊Dic9—22no—
84C4⋊Dic9C2311yescharacteristic
85C4⋊Dic9C2312yes—
86Dic9⋊C4—21no—
87Dic9⋊C4—22no—
88C4×Dic9—22no—
89C4×Dic9D411yescharacteristic
90C4×Dic9D411yescharacteristic
91C4×Dic9C2311yescharacteristic
92C2×C9⋊C8C2312yes—
93#3663—24no—
94#3077—91noSylow
95C2×D3×D4—31no—
96C22×C4×D3—61no—
97C3×C4⋊Q8C2×D311yescharacteristic
98C3×C4×D4C2×D311yescharacteristic
99#946—61no—
100Q8×Dic3—61no—
101D4×Dic3—31no—
102C4×#67—61no—
103C2×ΓL(1,𝔽25)—32no—
104#897—61no—
105#893—31no—
106#892—32no—
107D3×C4⋊C4—31no—
108#890—32no—
109#887—61no—
110#67⋊C4—61no—
111D3×C22⋊C4—61no—
112C4×D12—31no—
113C42×D3—31no—
114#869—31no—
115C3×#107C2×D312yes—
116C3×C4⋊C8C2×D311yescharacteristic
117C3×#102C2×D312yes—
118#832—32no—
119#821—32no—
120#817—32no—
121Dic3⋊C8—32no—
122#809—32no—
123#808—32no—
124#807—32no—
125C4⋊(C3⋊C8)—31no—
126C23×C9—21no—
127C22×D9—21no—
128C22×D9—24no—
129C22×D9—42no—
130C22×D9—42no—
131C22×D9C2×D411yescharacteristic
132Q8×C9—42no—
133D4×C9—21no—
134D4×C9C2×Q812yes—
135C2×C4×C9—22no—
136C2×C4×C9—21no—
137C2×C4×C9—42no—
138C2×C4×C9C2×D411yescharacteristic
139C2×C4×C9C2×D411yescharacteristic
140C2×C4×C9C2411yescharacteristic
141#611—24no—
142C2×Dic9—22no—
143C2×Dic9—21no—
144C2×Dic9—42no—
145C2×Dic9C2×D411yescharacteristic
146C2×Dic9C2×D411yescharacteristic
147C2×Dic9C2×D411yescharacteristic
148D36—21no—
149D36C2×Q812yes—
150C4×D9—22no—
151C4×D9—41no—
152C4×D9—42no—
153C4×D9—42no—
154C4×D9—42no—
155C4×D9C2×Q812yes—
156C4×D9#4112yes—
157Dic18—42no—
158C8×C9—22no—
159C9⋊C8—22no—
160#533—91no—
161C2×C4×D4—91no—
162#478—92no—
163#478—92no—
164#476—91no—
165#476—91no—
166#474—91no—
167#474D911yescharacteristic, complemented
168#428—92no—
169#423—91no—
170#418—92no—
171C23×D3—61no—
172C2×C3×Q8—21no—
173C2×C3×D4C22×D311yescharacteristic
174C22×C3×C4—21no—
175C2×#67—61no—
176C22×Dic3—61no—
177D3×D4—34no—
178D3×D4—62no—
179C2×D12—31no—
180C2×C4×D3—31no—
181C2×C4×D3—31no—
182C2×C4×D3—31no—
183C2×C4×D3—61no—
184C2×C4×D3—61no—
185C2×C4×D3—61no—
186C2×C4×D3—124no—
187C2×Dic6—61no—
188C2×C3×C8C22×D312yes—
189C3×C4⋊C4—21no—
190C3×C4⋊C4C22×D312yes—
191C3×C4⋊C4C22×D311yescharacteristic
192C3×C22⋊C4—21no—
193C3×C42C22×D311yescharacteristic
194#217—61no—
195(C2×D3)⋊C4—61no—
196(C2×D3)⋊C4—62no—
197(C2×D3)⋊C4—61no—
198C4⋊Dic3—31no—
199C4⋊Dic3—32no—
200C4⋊Dic3—62no—
201C4⋊Dic3—61no—
202Dic3⋊C4—61no—
203Dic3⋊C4—62no—
204C4×Dic3—31no—
205C4×Dic3—31no—
206C4×Dic3—31no—
207C4×Dic3—62no—
208C2×C3⋊C8—32no—
209ΓL(1,𝔽25)—64no—
210C22×C9—22no—
211C22×C9—41no—
212C22×C9—41no—
213C22×C9C22×D411yescharacteristic
214C2×D9—21no—
215C2×D9—21no—
216C2×D9—22no—
217C2×D9—48no—
218C2×D9—41no—
219C2×D9—41no—
220C2×D9C22⋊Q812yes—
221C4×C9—21no—
222C4×C9—41no—
223C4×C9—42no—
224C4×C9AGL(1,ℤ/8)12yes—
225C4×C9C22×Q811yescharacteristic
226C4×C9C2×#4111yescharacteristic
227Dic9—21no—
228Dic9—21no—
229Dic9—41no—
230Dic9—42no—
231Dic9C22⋊Q812yes—
232C22×D4—91no—
233C23×C4—181no—
234C2×M16—92no—
235C4⋊Q8—91no—
236C4⋊Q8C2×D911yescharacteristic, complemented
237#125—92no—
238C22⋊Q8—181no—
239C22⋊Q8—181no—
240C4×Q8—181no—
241C4×Q8—181no—
242C4×D4—91no—
243C4×D4—91no—
244C4×D4—91no—
245C4×D4—181no—
246C4×D4—181no—
247C4×D4C2×D911yescharacteristic
248#117—92no—
249C2×C4⋊C4—91no—
250C2×C22⋊C4—181no—
251C2×C42—91no—
252#107—92no—
253#107C2×D912yescomplemented
254#106—92no—
255#106—92no—
256C4⋊C8—92no—
257C4⋊C8—91no—
258C4⋊C8C2×D911yescharacteristic, complemented
259#102—92no—
260#102—92no—
261#102—92no—
262#102C2×D912yes—
263C23×C3—21no—
264C22×D3—31no—
265C22×D3—64no—
266C22×D3—61no—
267C22×D3—122no—
268C22×D3—122no—
269C3×Q8—42no—
270C3×D4—21no—
271C3×D4D3×Q812yes—
272C2×C3×C4—22no—
273C2×C3×C4—21no—
274C2×C3×C4—42no—
275C2×C3×C4D3×D411yescharacteristic
276C2×C3×C4D3×D411yescharacteristic
277C2×C3×C4C23×D311yescharacteristic
278#67—64no—
279C2×Dic3—31no—
280C2×Dic3—31no—
281C2×Dic3—31no—
282C2×Dic3—62no—
283C2×Dic3—61no—
284C2×Dic3—122no—
285D12—32no—
286D12—61no—
287C4×D3—32no—
288C4×D3—32no—
289C4×D3—62no—
290C4×D3—121no—
291C4×D3—122no—
292C4×D3—122no—
293C4×D3—122no—
294Dic6—122no—
295C3×C8—22no—
296C3⋊C8—62no—
297C2×C9—42no—
298C2×C9C2×C22⋊Q811yescharacteristic
299C2×C9C2×AGL(1,ℤ/8)11yescharacteristic
300C2×C9#57511yescharacteristic
301D9—22no—
302D9—42no—
303C24—181no—
304C2×Q8—21no—
305C2×Q8—181no—
306C2×D4—94no—
307C2×D4—91no—
308C2×D4—182no—
309C2×D4—181no—
310C2×D4C22×D911yescharacteristic
311C22×C4—21no—
312C22×C4—91no—
313C22×C4—91no—
314C22×C4—91no—
315C22×C4—181no—
316C22×C4—181no—
317C22×C4—181no—
318C22×C4—181no—
319C22×C4—364no—
320M16—184no—
321C2×C8—92no—
322C2×C8C22×D912yes—
323C4⋊C4—21no—
324C4⋊C4—92no—
325C4⋊C4—91no—
326C4⋊C4—181no—
327C4⋊C4—182no—
328C4⋊C4—182no—
329C4⋊C4—181no—
330C4⋊C4C22×D912yes—
331C4⋊C4C22×D911yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—181no—
334C22⋊C4—182no—
335C22⋊C4—181no—
336C22⋊C4—181no—
337C42—91no—
338C42—91no—
339C42—91no—
340C42—182no—
341C42C22×D911yescharacteristic
342C22×C3—22no—
343C22×C3—41no—
344C22×C3—41no—
345C22×C3C2×D3×D411yescharacteristic
346C2×D3—32no—
347C2×D3—61no—
348C2×D3—61no—
349C2×D3—62no—
350C2×D3—128no—
351C2×D3—121no—
352C2×D3—121no—
353C3×C4—21no—
354C3×C4—41no—
355C3×C4—42no—
356C3×C4#91112yes—
357C3×C4C2×D3×Q811yescharacteristic
358C3×C4D3×#4111yescharacteristic
359Dic3—32no—
360Dic3—61no—
361Dic3—61no—
362Dic3—121no—
363Dic3—122no—
364C9#307711yescharacteristic, complemented, Sylow
365C23—21no—
366C23—91no—
367C23—184no—
368C23—181no—
369C23—362no—
370C23—362no—
371Q8—42no—
372Q8—362no—
373D4—21no—
374D4—92no—
375D4—184no—
376D4—181no—
377D4Q8×D912yes—
378C2×C4—22no—
379C2×C4—21no—
380C2×C4—42no—
381C2×C4—91no—
382C2×C4—92no—
383C2×C4—92no—
384C2×C4—91no—
385C2×C4—91no—
386C2×C4—182no—
387C2×C4—182no—
388C2×C4—181no—
389C2×C4—361no—
390C2×C4—362no—
391C2×C4—362no—
392C2×C4—362no—
393C2×C4—362no—
394C2×C4D4×D911yescharacteristic
395C2×C4D4×D911yescharacteristic
396C2×C4C23×D911yescharacteristic
397C8—22no—
398C8—182no—
399C2×C3—42no—
400C2×C3D3×C22⋊Q811yescharacteristic
401C2×C3C2×#91111yescharacteristic
402C2×C3#577711yescharacteristic
403D3—62no—
404D3—122no—
405C22—22no—
406C22—41no—
407C22—41no—
408C22—92no—
409C22—181no—
410C22—181no—
411C22—182no—
412C22—368no—
413C22—361no—
414C22—361no—
415C22C2×D4×D911yescharacteristic
416C4—21no—
417C4—41no—
418C4—42no—
419C4—92no—
420C4—181no—
421C4—181no—
422C4—361no—
423C4—362no—
424C4#6347312yes—
425C4C2×Q8×D911yescharacteristic
426C4#41×D911yescharacteristic
427C3#8096511yescharacteristic
428C2—42no—
429C2—182no—
430C2—362no—
431C2D9×C22⋊Q811yescharacteristic
432C2C2×#6347311yescharacteristic
433C2#1058987911yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#474C2
socleC22×C3C2×D3×D4
prime radicalC2×D4×D9C22
hypercenter#474D9
hypocenterC9#3077
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #10589830C2semidirect
3. C9×#474C2semidirect
4. #10588772C2semidirect
5. #10588691C2semidirect
6. #10588571C2semidirect
7. #10588561C2semidirect
8. #10588526C2semidirect
9. #10588521C2semidirect
11. #10588443C2semidirect
15. C9×C4⋊Q8C22semidirect
26. #63452C22semidirect
32. #63431C22semidirect
33. C9×#107C22semidirect
34. C9×C4⋊C8C22semidirect
38. #63377C22semidirect
39. Dic9⋊C8C22semidirect
41. #63367C22semidirect
42. #63366C22semidirect
43. C4⋊(C9⋊C8)C22semidirect
62. D4×D9Q8semidirect
167. #474D9semidirect
236. C4⋊Q8C2×D9semidirect
253. #107C2×D9semidirect
258. C4⋊C8C2×D9semidirect
364. C9#3077semidirect

Maximal subgroups

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

subgroupindex
#105898302
C4×D4×D92
C9×#4742
#105887722
#105886912
#105885712
#105885612
#105885262
#105885212
#105884502
#105884432
#809653