Finite Group Databasebeta

← #11901758

Subgroups — #11901758

Order 1152.

1560 conjugacy classes of subgroups.

The subgroup lattice has 411 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#533C211yesmaximal, characteristic, complemented
2#10589835C214yesmaximal, complemented
3#10589800C212yesmaximal, complemented
4#10589799C212yesmaximal, complemented
5#10589747C214yesmaximal, complemented
6#10589746C214yesmaximal, complemented
7#10589682C218yesmaximal, complemented
8#10589626C212yesmaximal, complemented
9#10589624C212yesmaximal, complemented
10#10589579C211yesmaximal, characteristic, complemented
11C2×#63434C211yesmaximal, characteristic, complemented
12#86273—31nomaximal
13C2×#3697C2212yes—
14C22×C4×D9C2211yescharacteristic
15C9×C4⋊Q8C2212yescomplemented
16C9×#125C2212yescomplemented
17C9×C22⋊Q8C2214yes—
18C4×Q8×C9C2214yescomplemented
19C9×#117C2212yes—
20C2×C42×C9C2211yescharacteristic
21#63509C2218yes—
22#63508C2218yescomplemented
23#63492C2214yes—
24C2×(C2×D9)⋊C4C2212yes—
25C2×Dic9⋊C4C2212yes—
26C2×C4×Dic9C2211yescharacteristic
27#63460C2218yes—
28#63460C2218yescomplemented
29#63459C2214yes—
30#63457C2218yes—
31#63457C2214yes—
32#63456C2218yes—
33#63456C2218yescomplemented
34#63455C2214yescomplemented
35#63452C2218yescomplemented
36#63449C2214yescomplemented
37#63448C2214yes—
38#63444C2214yes—
39#611⋊C4C2218yes—
40#63437C2212yescomplemented
41#63436C2211yescharacteristic, complemented
42C4×D36C2218yes—
43C4×D36C2214yescomplemented
44#63434C2212yes—
45#63434C2212yes—
46#63434C2214yes—
47#63434C2214yescomplemented
48C42×D9C2214yescomplemented
49#63431C2211yescharacteristic, complemented
50C3×#533D311yescharacteristic
51#5733—34no—
52#5698—32no—
53#5697—32no—
54#5645—34no—
55#5644—34no—
56#5580—38no—
57#5524—32no—
58#5522—32no—
59#5477—31no—
60C2×#872—31no—
61C23×D9C2311yescharacteristic
62C2×Q8×C9C2314yes—
63C22×C4×C9C2312yes—
64C22×C4×C9C2311yescharacteristic
65C2×#611C2314yes—
66C22×Dic9C2311yescharacteristic
67C22×Dic9C2312yes—
68#3697—28no—
69C2×D36C2312yes—
70C2×D36C2314yes—
71C2×D36C2318yes—
72C2×C4×D9—24no—
73C2×C4×D9C2314yes—
74C2×C4×D9C2312yes—
75C2×C4×D9C2312yes—
76C2×C4×D9C2318yes—
77C2×Dic18C2312yes—
78C9×C4⋊C4C2314yes—
79C9×C4⋊C4C2318yes—
80C9×C4⋊C4C2314yes—
81C9×C22⋊C4C2314yes—
82C42×C9C2312yes—
83C42×C9C2311yescharacteristic
84C42×C9C2311yescharacteristic
85C42×C9C2314yes—
86(C2×D9)⋊C4C2314yes—
87(C2×D9)⋊C4C2314yes—
88(C2×D9)⋊C4C2318yes—
89(C2×D9)⋊C4C2318yes—
90(C2×D9)⋊C4C2318yes—
91(C2×D9)⋊C4C2318yes—
92C4⋊Dic9C2314yes—
93C4⋊Dic9C2318yes—
94Dic9⋊C4C2314yes—
95Dic9⋊C4C2318yes—
96Dic9⋊C4C2314yes—
97C4×Dic9C2318yes—
98C4×Dic9C2312yes—
99C4×Dic9C2312yes—
100#3455—91noSylow
101C2×#235—32no—
102C22×C4×D3—31no—
103C3×C4⋊Q8C2×D312yes—
104C3×#125C2×D312yes—
105C3×C22⋊Q8C2×D314yes—
106C3×C4×Q8C2×D314yes—
107C3×#117C2×D312yes—
108C2×C3×C42C2×D311yescharacteristic
109#947—38no—
110#946—38no—
111#930—34no—
112C2×(C2×D3)⋊C4—32no—
113C2×Dic3⋊C4—32no—
114C2×C4×Dic3—31no—
115#898—38no—
116#898—38no—
117#897—34no—
118#895—38no—
119#895—34no—
120#894—38no—
121#894—38no—
122#893—34no—
123#890—38no—
124#887—34no—
125#886—34no—
126#882—34no—
127#67⋊C4—38no—
128#875—32no—
129#874—31no—
130C4×D12—34no—
131C4×D12—38no—
132#872—32no—
133#872—32no—
134#872—34no—
135#872—34no—
136C42×D3—34no—
137#869—31no—
138C23×C9C2411yescharacteristic
139C22×D9—22no—
140C22×D9—42no—
141C22×D9C2412yes—
142C22×D9C2414yes—
143Q8×C9—44no—
144C2×C4×C9—42no—
145C2×C4×C9#4114yes—
146C2×C4×C9C2418yes—
147C2×C4×C9C2412yes—
148C2×C4×C9C2412yes—
149C2×C4×C9C2411yescharacteristic
150C2×C4×C9C2411yescharacteristic
151#611—28no—
152C2×Dic9—22no—
153C2×Dic9—42no—
154C2×Dic9C2414yes—
155C2×Dic9C2414yes—
156C2×Dic9C2412yes—
157D36—24no—
158D36—48no—
159D36—44no—
160C4×D9—24no—
161C4×D9—24no—
162C4×D9—28no—
163C4×D9—48no—
164Dic18—24no—
165#542—94no—
166#541—92no—
167#540—92no—
168#539—94no—
169#538—94no—
170#533D911yescharacteristic, complemented
171#532—91no—
172#529—98no—
173#525—92no—
174C4×#41—92no—
175C2×#117—91no—
176C23×D3—31no—
177C2×C3×Q8C22×D314yes—
178C22×C3×C4C22×D312yes—
179C22×C3×C4C22×D311yescharacteristic
180C2×#67—34no—
181C22×Dic3—31no—
182C22×Dic3—32no—
183#235—68no—
184C2×D12—32no—
185C2×D12—34no—
186C2×D12—38no—
187C2×C4×D3—34no—
188C2×C4×D3—32no—
189C2×C4×D3—32no—
190C2×C4×D3—38no—
191C2×C4×D3—64no—
192C2×Dic6—32no—
193C3×C4⋊C4C22×D314yes—
194C3×C4⋊C4C22×D318yes—
195C3×C4⋊C4C22×D314yes—
196C3×C22⋊C4C22×D314yes—
197C3×C42C22×D311yescharacteristic
198C3×C42C22×D314yes—
199C3×C42C22×D312yes—
200C3×C42C22×D311yescharacteristic
201(C2×D3)⋊C4—34no—
202(C2×D3)⋊C4—34no—
203(C2×D3)⋊C4—38no—
204(C2×D3)⋊C4—38no—
205(C2×D3)⋊C4—38no—
206(C2×D3)⋊C4—38no—
207C4⋊Dic3—34no—
208C4⋊Dic3—38no—
209Dic3⋊C4—34no—
210Dic3⋊C4—34no—
211Dic3⋊C4—38no—
212C4×Dic3—32no—
213C4×Dic3—38no—
214C4×Dic3—32no—
215C22×C9—22no—
216C22×C9C2×#4112yes—
217C22×C9C2511yescharacteristic
218C2×D9—22no—
219C2×D9—24no—
220C2×D9—28no—
221C2×D9—24no—
222C2×D9—44no—
223C4×C9—28no—
224C4×C9—22no—
225C4×C9—22no—
226C4×C9C2×#4112yes—
227C4×C9C2×#4112yes—
228Dic9—24no—
229Dic9—22no—
230Dic9—24no—
231C2×#41—92no—
232C23×C4—91no—
233C4⋊Q8—91no—
234C4⋊Q8C2×D912yescomplemented
235#127—91no—
236#126—98no—
237#126—98no—
238#125—98no—
239#125C2×D912yescomplemented
240#124—98no—
241#124—92no—
242#123—98no—
243#123—98no—
244#123—94no—
245C22⋊Q8—98no—
246C22⋊Q8—94no—
247C22⋊Q8C2×D914yes—
248#121—94no—
249#121—94no—
250#121—98no—
251#120—94no—
252C4×Q8—94no—
253C4×Q8C2×D914yescomplemented
254C4×D4—94no—
255C4×D4—98no—
256C4×D4—98no—
257C4×D4—94no—
258#117—94no—
259#117—92no—
260#117—92no—
261#117—94no—
262#117C2×D912yes—
263C2×C4⋊C4—92no—
264C2×C22⋊C4—92no—
265C2×C42—91no—
266C2×C42—94no—
267C2×C42C2×D911yescharacteristic
268C23×C3C23×D311yescharacteristic
269C22×D3—32no—
270C22×D3—34no—
271C22×D3—62no—
272C22×D3—122no—
273C3×Q8—44no—
274C2×C3×C4—42no—
275C2×C3×C4#23914yes—
276C2×C3×C4C23×D318yes—
277C2×C3×C4C23×D312yes—
278C2×C3×C4C23×D312yes—
279C2×C3×C4C23×D311yescharacteristic
280C2×C3×C4C23×D311yescharacteristic
281#67—68no—
282C2×Dic3—34no—
283C2×Dic3—34no—
284C2×Dic3—32no—
285C2×Dic3—62no—
286C2×Dic3—122no—
287D12—64no—
288D12—128no—
289D12—124no—
290C4×D3—64no—
291C4×D3—64no—
292C4×D3—68no—
293C4×D3—128no—
294Dic6—64no—
295C2×C9—22no—
296C2×C9C22×#4111yescharacteristic
297C2×C9#58512yes—
298D9—44no—
299D9—42no—
300C24—91no—
301#41—188no—
302C2×Q8—92no—
303C2×Q8C22×D914yes—
304C2×D4—94no—
305C2×D4—92no—
306C2×D4—98no—
307C2×D4—94no—
308C22×C4—91no—
309C22×C4—92no—
310C22×C4—92no—
311C22×C4—94no—
312C22×C4—92no—
313C22×C4—98no—
314C22×C4—184no—
315C22×C4C22×D912yes—
316C22×C4C22×D911yescharacteristic
317C4⋊C4—94no—
318C4⋊C4—94no—
319C4⋊C4—98no—
320C4⋊C4—94no—
321C4⋊C4—98no—
322C4⋊C4C22×D914yes—
323C4⋊C4C22×D918yes—
324C4⋊C4C22×D914yes—
325C22⋊C4—94no—
326C22⋊C4—94no—
327C22⋊C4—98no—
328C22⋊C4—98no—
329C22⋊C4—98no—
330C22⋊C4—98no—
331C22⋊C4C22×D914yes—
332C42—92no—
333C42—98no—
334C42—92no—
335C42C22×D911yescharacteristic
336C42C22×D911yescharacteristic
337C42C22×D914yes—
338C42C22×D912yes—
339C22×C3—22no—
340C22×C3C2×#23912yes—
341C22×C3C24×D311yescharacteristic
342C2×D3—62no—
343C2×D3—64no—
344C2×D3—68no—
345C2×D3—64no—
346C2×D3—124no—
347C3×C4—28no—
348C3×C4—22no—
349C3×C4—22no—
350C3×C4C2×#23912yes—
351C3×C4C2×#23912yes—
352Dic3—64no—
353Dic3—62no—
354Dic3—64no—
355C9#345511yescharacteristic, complemented, Sylow
356C23—92no—
357C23—94no—
358C23—182no—
359C23—362no—
360C23C23×D911yescharacteristic
361Q8—44no—
362Q8—184no—
363D4—188no—
364D4—184no—
365D4—364no—
366D4—368no—
367C2×C4—42no—
368C2×C4—94no—
369C2×C4—94no—
370C2×C4—92no—
371C2×C4—182no—
372C2×C4—184no—
373C2×C4—184no—
374C2×C4—188no—
375C2×C4—368no—
376C2×C4—362no—
377C2×C4#370114yes—
378C2×C4C23×D918yes—
379C2×C4C23×D912yes—
380C2×C4C23×D912yes—
381C2×C4C23×D911yescharacteristic
382C2×C4C23×D911yescharacteristic
383C2×C3—22no—
384C2×C3C22×#23911yescharacteristic
385C2×C3#596412yes—
386D3—122no—
387D3—124no—
388C22—22no—
389C22—182no—
390C22—184no—
391C22—188no—
392C22—184no—
393C22—364no—
394C22C2×#370112yes—
395C22C24×D911yescharacteristic
396C4—22no—
397C4—22no—
398C4—28no—
399C4—182no—
400C4—184no—
401C4—184no—
402C4C2×#370112yes—
403C4C2×#370112yes—
404C3#8627311yescharacteristic
405C2—22no—
406C2—362no—
407C2—364no—
408C2C22×#370111yescharacteristic
409C2#1059313912yes—
subgroupG/H
centerC2×C4C23×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingC9×#533C2
hypercenter#533D9
hypocenterC9#3455
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C2×C4 ◁ #533

Complements

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

NH ≅ G/Ntype
1. C9×#533C2semidirect
2. #10589835C2semidirect
3. #10589800C2semidirect
4. #10589799C2semidirect
5. #10589747C2semidirect
6. #10589746C2semidirect
7. #10589682C2semidirect
8. #10589626C2semidirect
9. #10589624C2semidirect
10. #10589579C2semidirect
11. C2×#63434C2semidirect
15. C9×C4⋊Q8C22semidirect
16. C9×#125C22semidirect
18. C4×Q8×C9C22semidirect
22. #63508C22semidirect
28. #63460C22semidirect
33. #63456C22semidirect
34. #63455C22semidirect
35. #63452C22semidirect
36. #63449C22semidirect
40. #63437C22semidirect
41. #63436C22semidirect
43. C4×D36C22semidirect
47. #63434C22semidirect
48. C42×D9C22semidirect
49. #63431C22semidirect
170. #533D9semidirect
234. C4⋊Q8C2×D9semidirect
239. #125C2×D9semidirect
253. C4×Q8C2×D9semidirect
355. C9#3455semidirect

Maximal subgroups

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

subgroupindex
C9×#5332
#105898352
#105898002
#105897992
#105897472
#105897462
#105896822
#105896262
#105896242
#105895792
C2×#634342
#862733