Finite Group Databasebeta

← #11868641

Subgroups — #11868641

Order 1152.

660 conjugacy classes of subgroups.

The subgroup lattice has 417 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic9C211yesmaximal, characteristic
2#10589619C211yesmaximal, characteristic, complemented
3C9×#418C211yesmaximal, characteristic
4#10588896C211yesmaximal, characteristic
5#10588805C211yesmaximal, characteristic, complemented
6#10588802C211yesmaximal, characteristic, complemented
7#10588679C211yesmaximal, characteristic, complemented
8#10588446C212yesmaximal, complemented
9#10588443C212yesmaximal, complemented
10#10588441C212yesmaximal, complemented
11#10588439C212yesmaximal, complemented
12#78917—31nomaximal
13C22×D4×C9C2211yescharacteristic
14C23×Dic9—21no—
15C2×C9×M16C2211yescharacteristic
16C9×#117C2211yescharacteristic
17C2×#3676—21no—
18D4×Dic9—21no—
19D4×Dic9—21no—
20D4×Dic9C2212yes—
21D4×Dic9C2212yes—
22#63488C2211yescharacteristic
23C2×C4⋊Dic9C2211yescharacteristic
24C2×C4×Dic9C2211yescharacteristic
25C2×#3667C2211yescharacteristic
26#63452C2211yescharacteristic, complemented
27#63452C2211yescharacteristic, complemented
28#63450C2211yescharacteristic, complemented
29#63450C2211yescharacteristic, complemented
30#63440—21no—
31#63440—21no—
32C4×Dic18—21no—
33C4×Dic18—21no—
34C9×#102C2212yes—
35C9×#102C2212yes—
36#63392C2212yes—
37#63392C2212yes—
38#63378C2212yescomplemented
39#63377C2212yescomplemented
40Dic9⋊C8C2212yescomplemented
41Dic9⋊C8C2212yescomplemented
42#63367C2212yescomplemented
43#63366C2212yescomplemented
44C2×D4×Dic3—31no—
45#5517—31no—
46C3×#418D311yescharacteristic
47#5215—31no—
48#5121—31no—
49#5118—31no—
50#4995—31no—
51#4766—32no—
52#4763—32no—
53#4761—32no—
54#4759—32no—
55C24×C9—21no—
56C2×D4×C9—21no—
57C2×D4×C9—22no—
58C2×D4×C9Q814yescomplemented
59C2×D4×C9C2312yes—
60C22×C4×C9C2311yescharacteristic
61C22×Dic9—21no—
62C22×Dic9—22no—
63C22×Dic9—22no—
64C22×Dic9—44no—
65C22×Dic9D411yescharacteristic
66C22×Dic9D411yescharacteristic
67C2×Dic18—21no—
68C2×Dic18—21no—
69C9×M16—22no—
70C2×C8×C9C2312yes—
71C9×C4⋊C4C2311yescharacteristic
72C9×C4⋊C4C2311yescharacteristic
73C9×C22⋊C4—21no—
74C42×C9—21no—
75#3676—21no—
76#3676—22no—
77#3676—22no—
78C4⋊Dic9—21no—
79C4⋊Dic9—21no—
80C4⋊Dic9—21no—
81C4⋊Dic9C2311yescharacteristic
82C4⋊Dic9C2311yescharacteristic
83C4⋊Dic9C2312yes—
84Dic9⋊C4—21no—
85Dic9⋊C4—21no—
86Dic9⋊C4—21no—
87Dic9⋊C4—21no—
88C4×Dic9—21no—
89C4×Dic9D411yescharacteristic
90C4×Dic9D411yescharacteristic
91C4×Dic9C2311yescharacteristic
92C4×Dic9C2311yescharacteristic
93#3667—22no—
94C2×C9⋊C8C2312yes—
95#3077—91noSylow
96C22×C3×D4C2×D311yescharacteristic
97C23×Dic3—61no—
98C2×C3×M16C2×D311yescharacteristic
99C3×#117C2×D311yescharacteristic
100C2×#217—61no—
101D4×Dic3—32no—
102D4×Dic3—32no—
103D4×Dic3—61no—
104D4×Dic3—61no—
105#926—31no—
106C2×C4⋊Dic3—31no—
107C2×C4×Dic3—31no—
108C2×#208—31no—
109#890—31no—
110#890—31no—
111#888—31no—
112#888—31no—
113#878—61no—
114#878—61no—
115C4×Dic6—61no—
116C4×Dic6—61no—
117C3×#102C2×D312yes—
118C3×#102C2×D312yes—
119#832—32no—
120#832—32no—
121#818—32no—
122#817—32no—
123Dic3⋊C8—32no—
124Dic3⋊C8—32no—
125#808—32no—
126#807—32no—
127C23×C9—24no—
128C23×C9—22no—
129C23×C9—42no—
130C23×C9—42no—
131C23×C9C2×D411yescharacteristic
132D4×C9—24no—
133D4×C9—22no—
134D4×C9C2×Q814yes—
135C2×C4×C9—21no—
136C2×C4×C9—21no—
137C2×C4×C9C2×D411yescharacteristic
138C2×C4×C9C2×Q812yes—
139C2×C4×C9#4112yes—
140C2×C4×C9C2411yescharacteristic
141C2×Dic9—22no—
142C2×Dic9—21no—
143C2×Dic9—21no—
144C2×Dic9—22no—
145C2×Dic9—41no—
146C2×Dic9—44no—
147C2×Dic9—42no—
148C2×Dic9—44no—
149C2×Dic9C2×D411yescharacteristic
150C2×Dic9C2×D411yescharacteristic
151C2×Dic9C2×D411yescharacteristic
152C2×Dic9C2×D411yescharacteristic
153Dic18—42no—
154Dic18—42no—
155C8×C9—22no—
156C9⋊C8—22no—
157#533—91no—
158C2×C4×D4—91no—
159#478—92no—
160#478—92no—
161#476—92no—
162#474—92no—
163#428—91no—
164#428—91no—
165#423—91no—
166#418—91no—
167#418D911yescharacteristic
168C24×C3—21no—
169C2×C3×D4—21no—
170C2×C3×D4—22no—
171C2×C3×D4Dic614yes—
172C2×C3×D4C22×D312yes—
173C22×C3×C4C22×D311yescharacteristic
174C22×Dic3—31no—
175C22×Dic3—31no—
176C22×Dic3—62no—
177C22×Dic3—62no—
178C22×Dic3—61no—
179C22×Dic3—124no—
180C2×Dic6—61no—
181C2×Dic6—61no—
182C3×M16—22no—
183C2×C3×C8C22×D312yes—
184C3×C4⋊C4C22×D311yescharacteristic
185C3×C4⋊C4C22×D311yescharacteristic
186C3×C22⋊C4—21no—
187C3×C42—21no—
188#217—62no—
189#217—62no—
190#217—61no—
191C4⋊Dic3—32no—
192C4⋊Dic3—31no—
193C4⋊Dic3—31no—
194C4⋊Dic3—61no—
195C4⋊Dic3—61no—
196C4⋊Dic3—61no—
197Dic3⋊C4—61no—
198Dic3⋊C4—61no—
199Dic3⋊C4—61no—
200Dic3⋊C4—61no—
201C4×Dic3—31no—
202C4×Dic3—31no—
203C4×Dic3—31no—
204C4×Dic3—31no—
205C4×Dic3—61no—
206#208—62no—
207C2×C3⋊C8—32no—
208C22×C9—21no—
209C22×C9—21no—
210C22×C9—24no—
211C22×C9—48no—
212C22×C9—42no—
213C22×C9—42no—
214C22×C9C22⋊Q812yes—
215C22×C9C22×D411yescharacteristic
216C4×C9—41no—
217C4×C9—41no—
218C4×C9C22⋊Q812yes—
219C4×C9C22×Q811yescharacteristic
220C4×C9C2×#4111yescharacteristic
221Dic9—21no—
222Dic9—21no—
223Dic9—21no—
224Dic9—41no—
225Dic9—42no—
226Dic9—41no—
227Dic9AGL(1,ℤ/8)12yes—
228C22×D4C2×D911yescharacteristic
229C23×C4—181no—
230C2×M16—91no—
231C2×M16C2×D911yescharacteristic
232C4⋊Q8—91no—
233C4⋊Q8—91no—
234#125—91no—
235#125—91no—
236C22⋊Q8—181no—
237C22⋊Q8—181no—
238C4×Q8—181no—
239C4×Q8—181no—
240C4×D4—92no—
241C4×D4—92no—
242C4×D4—181no—
243C4×D4—181no—
244#117—91no—
245#117C2×D911yescharacteristic
246C2×C4⋊C4—91no—
247C2×C22⋊C4—181no—
248C2×C42—91no—
249#107—92no—
250#107—92no—
251#106—92no—
252#106—92no—
253C4⋊C8—92no—
254C4⋊C8—92no—
255#102—92no—
256#102—92no—
257#102C2×D912yes—
258#102C2×D912yes—
259C23×C3—24no—
260C23×C3—22no—
261C23×C3—42no—
262C23×C3—42no—
263C23×C3D3×D411yescharacteristic
264C3×D4—24no—
265C3×D4—22no—
266C3×D4C2×Dic614yes—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4C2×Dic612yes—
270C2×C3×C4D3×D411yescharacteristic
271C2×C3×C4#23712yes—
272C2×C3×C4C23×D311yescharacteristic
273C2×Dic3—31no—
274C2×Dic3—31no—
275C2×Dic3—31no—
276C2×Dic3—31no—
277C2×Dic3—62no—
278C2×Dic3—61no—
279C2×Dic3—61no—
280C2×Dic3—62no—
281C2×Dic3—124no—
282C2×Dic3—121no—
283C2×Dic3—124no—
284C2×Dic3—122no—
285Dic6—122no—
286Dic6—122no—
287C3×C8—22no—
288C3⋊C8—62no—
289C2×C9—22no—
290C2×C9—44no—
291C2×C9C2×C22⋊Q811yescharacteristic
292C2×C9C2×AGL(1,ℤ/8)11yescharacteristic
293C2×C9#57511yescharacteristic
294C24—21no—
295C2×Q8—181no—
296C2×Q8—181no—
297C2×D4—21no—
298C2×D4—22no—
299C2×D4Dic1814yescomplemented
300C2×D4C22×D912yes—
301C22×C4—91no—
302C22×C4—91no—
303C22×C4—182no—
304C22×C4—182no—
305C22×C4—181no—
306C22×C4—364no—
307C22×C4C22×D911yescharacteristic
308M16—22no—
309M16—182no—
310C2×C8—92no—
311C2×C8C22×D912yes—
312C4⋊C4—91no—
313C4⋊C4—91no—
314C4⋊C4—92no—
315C4⋊C4—181no—
316C4⋊C4—181no—
317C4⋊C4—181no—
318C4⋊C4—181no—
319C4⋊C4—181no—
320C4⋊C4—181no—
321C4⋊C4—181no—
322C4⋊C4C22×D911yescharacteristic
323C4⋊C4C22×D911yescharacteristic
324C22⋊C4—21no—
325C22⋊C4—182no—
326C22⋊C4—182no—
327C22⋊C4—181no—
328C42—21no—
329C42—91no—
330C42—91no—
331C42—91no—
332C42—91no—
333C42—181no—
334C22×C3—21no—
335C22×C3—21no—
336C22×C3—24no—
337C22×C3—48no—
338C22×C3—42no—
339C22×C3—42no—
340C22×C3#87812yes—
341C22×C3C2×D3×D411yescharacteristic
342C3×C4—41no—
343C3×C4—41no—
344C3×C4#87812yes—
345C3×C4C22×Dic611yescharacteristic
346C3×C4C2×#23711yescharacteristic
347Dic3—32no—
348Dic3—61no—
349Dic3—61no—
350Dic3—61no—
351Dic3—121no—
352Dic3—122no—
353Dic3—121no—
354C9#307711yescharacteristic, complemented, Sylow
355C23—24no—
356C23—22no—
357C23—42no—
358C23—42no—
359C23D4×D911yescharacteristic
360Q8—362no—
361Q8—362no—
362D4—24no—
363D4—22no—
364D4C2×Dic1814yes—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—91no—
368C2×C4—91no—
369C2×C4—91no—
370C2×C4—91no—
371C2×C4—182no—
372C2×C4—181no—
373C2×C4—181no—
374C2×C4—182no—
375C2×C4—364no—
376C2×C4—361no—
377C2×C4—364no—
378C2×C4—362no—
379C2×C4C2×Dic1812yes—
380C2×C4D4×D911yescharacteristic
381C2×C4#369912yes—
382C2×C4C23×D911yescharacteristic
383C8—22no—
384C8—182no—
385C2×C3—22no—
386C2×C3—44no—
387C2×C3C2×#87811yescharacteristic
388C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
389C2×C3#577311yescharacteristic
390C22—21no—
391C22—21no—
392C22—24no—
393C22—48no—
394C22—42no—
395C22—42no—
396C22#6344012yes—
397C22C2×D4×D911yescharacteristic
398C4—41no—
399C4—41no—
400C4—92no—
401C4—181no—
402C4—181no—
403C4—181no—
404C4—362no—
405C4—361no—
406C4—361no—
407C4#6344012yes—
408C4C22×Dic1811yescharacteristic
409C4C2×#369911yescharacteristic
410C3#7891711yescharacteristic
411C2—22no—
412C2—44no—
413C2C2×#6344011yescharacteristic
414C2D9×AGL(1,ℤ/8)11yescharacteristic
415C2#1058987511yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#418C2
socleC22×C3C2×D3×D4
prime radicalC22×C3×D4C2×D3
hypercenter#418D9
hypocenterC9#3077
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
2. #10589619C2semidirect
5. #10588805C2semidirect
6. #10588802C2semidirect
7. #10588679C2semidirect
8. #10588446C2semidirect
9. #10588443C2semidirect
10. #10588441C2semidirect
11. #10588439C2semidirect
26. #63452C22semidirect
27. #63452C22semidirect
28. #63450C22semidirect
29. #63450C22semidirect
38. #63378C22semidirect
39. #63377C22semidirect
40. Dic9⋊C8C22semidirect
41. Dic9⋊C8C22semidirect
42. #63367C22semidirect
43. #63366C22semidirect
58. C2×D4×C9Q8semidirect
299. C2×D4Dic18semidirect
354. C9#3077semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic92
#105896192
C9×#4182
#105888962
#105888052
#105888022
#105886792
#105884462
#105884432
#105884412
#105884392
#789173