Finite Group Databasebeta

← #11868647

Subgroups — #11868647

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
1#10589619C211yesmaximal, characteristic, complemented
2C2×#63455C211yesmaximal, characteristic
3C9×#428C211yesmaximal, characteristic, complemented
4#10588813C211yesmaximal, characteristic
5#10588802C211yesmaximal, characteristic, complemented
6#10588682C211yesmaximal, characteristic
7#10588644C211yesmaximal, characteristic, complemented
8#10588571C212yesmaximal, complemented
9#10588570C212yesmaximal, complemented
10#10588551C212yesmaximal, complemented
11#10588550C212yesmaximal, complemented
12#79239—31nomaximal
13C22×D36C2211yescharacteristic
14C22×C4×D9—21no—
15C2×C9×M16C2211yescharacteristic
16C9×#117C2211yescharacteristic
17C2×C9×C4⋊C4C2211yescharacteristic
18C2×(C2×D9)⋊C4—21no—
19#63488C2211yescharacteristic
20C2×C4×Dic9C2211yescharacteristic
21C2×#3667C2211yescharacteristic
22#63455—21no—
23#63455—21no—
24#63455C2212yes—
25#63455C2212yes—
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×#107C2212yescomplemented
35C9×#106C2212yescomplemented
36#63380C2212yes—
37#63380C2212yes—
38Dic9⋊C8C2212yescomplemented
39Dic9⋊C8C2212yescomplemented
40#63369C2212yes—
41#63369C2212yes—
42#63367C2212yescomplemented
43#63366C2212yescomplemented
44#5517—31no—
45C2×#893—31no—
46C3×#428D311yescharacteristic
47#5131—31no—
48#5118—31no—
49#5001—31no—
50#4964—31no—
51#4891—32no—
52#4890—32no—
53#4871—32no—
54#4870—32no—
55C23×D9—21no—
56C22×C4×C9—21no—
57C22×C4×C9C2311yescharacteristic
58C22×Dic9D411yescharacteristic
59C22×Dic9D411yescharacteristic
60C2×D36—21no—
61C2×D36—22no—
62C2×D36Q814yescomplemented
63C2×D36C2312yes—
64C2×C4×D9—22no—
65C2×C4×D9—22no—
66C2×C4×D9—44no—
67C2×Dic18—21no—
68C2×Dic18—21no—
69C9×M16—22no—
70C2×C8×C9C2312yes—
71C9×C4⋊C4—21no—
72C9×C4⋊C4C2312yes—
73C9×C4⋊C4C2311yescharacteristic
74C9×C4⋊C4C2311yescharacteristic
75C9×C22⋊C4—21no—
76C42×C9—21no—
77#3676—21no—
78(C2×D9)⋊C4—22no—
79(C2×D9)⋊C4—22no—
80C4⋊Dic9—21no—
81C4⋊Dic9—21no—
82C4⋊Dic9C2311yescharacteristic
83C4⋊Dic9C2311yescharacteristic
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×D12—31no—
97C22×C4×D3—61no—
98C2×C3×M16C2×D311yescharacteristic
99C3×#117C2×D311yescharacteristic
100C2×C3×C4⋊C4C2×D311yescharacteristic
101C2×(C2×D3)⋊C4—61no—
102#926—31no—
103C2×C4×Dic3—31no—
104C2×#208—31no—
105#893—32no—
106#893—32no—
107#893—61no—
108#893—61no—
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×#107C2×D312yes—
118C3×#106C2×D312yes—
119#821—32no—
120#821—32no—
121Dic3⋊C8—32no—
122Dic3⋊C8—32no—
123#809—32no—
124#809—32no—
125#808—32no—
126#807—32no—
127C23×C9C2×D411yescharacteristic
128C22×D9—24no—
129C22×D9—22no—
130C22×D9—42no—
131C22×D9—42no—
132C2×C4×C9—21no—
133C2×C4×C9—21no—
134C2×C4×C9—22no—
135C2×C4×C9—42no—
136C2×C4×C9C2×D411yescharacteristic
137C2×C4×C9C2×Q812yes—
138C2×C4×C9#4112yes—
139C2×C4×C9C2411yescharacteristic
140C2×Dic9—22no—
141C2×Dic9—21no—
142C2×Dic9—21no—
143C2×Dic9—41no—
144C2×Dic9C2×D411yescharacteristic
145C2×Dic9C2×D411yescharacteristic
146C2×Dic9C2×D411yescharacteristic
147C2×Dic9C2×D411yescharacteristic
148D36—24no—
149D36—22no—
150D36C2×Q814yes—
151C4×D9—44no—
152C4×D9—44no—
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#428D911yescharacteristic, complemented
165#423—91no—
166#418—91no—
167#418—91no—
168C23×D3—61no—
169C22×C3×C4—21no—
170C22×C3×C4C22×D311yescharacteristic
171C22×Dic3—31no—
172C22×Dic3—31no—
173C2×D12—34no—
174C2×D12—32no—
175C2×D12—62no—
176C2×D12—61no—
177C2×C4×D3—62no—
178C2×C4×D3—62no—
179C2×C4×D3—124no—
180C2×Dic6—61no—
181C2×Dic6—61no—
182C3×M16—22no—
183C2×C3×C8C22×D312yes—
184C3×C4⋊C4—21no—
185C3×C4⋊C4C22×D312yes—
186C3×C4⋊C4C22×D311yescharacteristic
187C3×C4⋊C4C22×D311yescharacteristic
188C3×C22⋊C4—21no—
189C3×C42—21no—
190#217—61no—
191(C2×D3)⋊C4—62no—
192(C2×D3)⋊C4—62no—
193C4⋊Dic3—31no—
194C4⋊Dic3—31no—
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×C9C22⋊Q812yes—
211C22×C9C22×D411yescharacteristic
212C2×D9—24no—
213C2×D9—48no—
214C2×D9—42no—
215C2×D9—42no—
216C4×C9—41no—
217C4×C9—42no—
218C4×C9—41no—
219C4×C9C22⋊Q812yes—
220C4×C9C22×Q811yescharacteristic
221C4×C9C2×#4111yescharacteristic
222Dic9—21no—
223Dic9—21no—
224Dic9—21no—
225Dic9—41no—
226Dic9—41no—
227Dic9AGL(1,ℤ/8)12yes—
228C22×D4—91no—
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⋊C4C2×D911yescharacteristic
247C2×C22⋊C4—181no—
248C2×C42—91no—
249#107—92no—
250#107C2×D912yescomplemented
251#106—92no—
252#106C2×D912yescomplemented
253C4⋊C8—92no—
254C4⋊C8—92no—
255#102—92no—
256#102—92no—
257#102—92no—
258#102—92no—
259C23×C3D3×D411yescharacteristic
260C22×D3—64no—
261C22×D3—62no—
262C22×D3—122no—
263C22×D3—122no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—22no—
267C2×C3×C4—42no—
268C2×C3×C4#23512yes—
269C2×C3×C4D3×D411yescharacteristic
270C2×C3×C4D3×Q812yes—
271C2×C3×C4C23×D311yescharacteristic
272C2×Dic3—31no—
273C2×Dic3—31no—
274C2×Dic3—31no—
275C2×Dic3—31no—
276C2×Dic3—62no—
277C2×Dic3—61no—
278C2×Dic3—61no—
279C2×Dic3—121no—
280D12—34no—
281D12—64no—
282D12—62no—
283C4×D3—124no—
284C4×D3—124no—
285Dic6—122no—
286Dic6—122no—
287C3×C8—22no—
288C3⋊C8—62no—
289C2×C9—22no—
290C2×C9C2×C22⋊Q811yescharacteristic
291C2×C9C2×AGL(1,ℤ/8)11yescharacteristic
292C2×C9#57511yescharacteristic
293D9—44no—
294C24—181no—
295C2×Q8—181no—
296C2×Q8—181no—
297C2×D4—94no—
298C2×D4—92no—
299C2×D4—182no—
300C2×D4—181no—
301C22×C4—21no—
302C22×C4—91no—
303C22×C4—91no—
304C22×C4—182no—
305C22×C4—182no—
306C22×C4—364no—
307C22×C4C22×D911yescharacteristic
308M16—22no—
309M16—182no—
310C2×C8—92no—
311C2×C8C22×D912yes—
312C4⋊C4—21no—
313C4⋊C4—91no—
314C4⋊C4—91no—
315C4⋊C4—181no—
316C4⋊C4—181no—
317C4⋊C4—181no—
318C4⋊C4—181no—
319C4⋊C4—181no—
320C4⋊C4—181no—
321C4⋊C4C22×D911yescharacteristic
322C4⋊C4C22×D911yescharacteristic
323C4⋊C4C22×D912yes—
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#89612yes—
337C22×C3C2×D3×D411yescharacteristic
338C2×D3—64no—
339C2×D3—128no—
340C2×D3—122no—
341C2×D3—122no—
342C3×C4—41no—
343C3×C4—42no—
344C3×C4—41no—
345C3×C4#89612yes—
346C3×C4C2×#23511yescharacteristic
347C3×C4C2×D3×Q811yescharacteristic
348Dic3—32no—
349Dic3—61no—
350Dic3—61no—
351Dic3—61no—
352Dic3—121no—
353Dic3—121no—
354C9#307711yescharacteristic, complemented, Sylow
355C23—182no—
356C23—184no—
357C23—362no—
358C23—362no—
359C23D4×D911yescharacteristic
360Q8—362no—
361Q8—362no—
362D4—94no—
363D4—182no—
364D4—184no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—22no—
368C2×C4—42no—
369C2×C4—91no—
370C2×C4—91no—
371C2×C4—91no—
372C2×C4—91no—
373C2×C4—182no—
374C2×C4—181no—
375C2×C4—181no—
376C2×C4—364no—
377C2×C4—364no—
378C2×C4—361no—
379C2×C4#369712yes—
380C2×C4D4×D911yescharacteristic
381C2×C4Q8×D912yes—
382C2×C4C23×D911yescharacteristic
383C8—22no—
384C8—182no—
385C2×C3—22no—
386C2×C3C2×#89611yescharacteristic
387C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
388C2×C3#577711yescharacteristic
389D3—124no—
390C22—21no—
391C22—21no—
392C22—184no—
393C22—368no—
394C22—362no—
395C22—362no—
396C22#6345812yes—
397C22C2×D4×D911yescharacteristic
398C4—42no—
399C4—41no—
400C4—41no—
401C4—92no—
402C4—181no—
403C4—181no—
404C4—181no—
405C4—361no—
406C4—361no—
407C4#6345812yes—
408C4C2×#369711yescharacteristic
409C4C2×Q8×D911yescharacteristic
410C3#7923911yescharacteristic
411C2—22no—
412C2—364no—
413C2C2×#6345811yescharacteristic
414C2D9×AGL(1,ℤ/8)11yescharacteristic
415C2#1058987911yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#428C2
socleC22×C3C2×D3×D4
prime radicalC22×D36C22
hypercenter#428D9
hypocenterC9#3077
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
1. #10589619C2semidirect
3. C9×#428C2semidirect
5. #10588802C2semidirect
7. #10588644C2semidirect
8. #10588571C2semidirect
9. #10588570C2semidirect
10. #10588551C2semidirect
11. #10588550C2semidirect
26. #63452C22semidirect
27. #63452C22semidirect
28. #63450C22semidirect
29. #63450C22semidirect
34. C9×#107C22semidirect
35. C9×#106C22semidirect
38. Dic9⋊C8C22semidirect
39. Dic9⋊C8C22semidirect
42. #63367C22semidirect
43. #63366C22semidirect
62. C2×D36Q8semidirect
164. #428D9semidirect
250. #107C2×D9semidirect
252. #106C2×D9semidirect
354. C9#3077semidirect

Maximal subgroups

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

subgroupindex
#105896192
C2×#634552
C9×#4282
#105888132
#105888022
#105886822
#105886442
#105885712
#105885702
#105885512
#105885502
#792393