Finite Group Databasebeta

← #11901749

Subgroups — #11901749

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×#532C211yesmaximal, characteristic, complemented
2#10589930C212yesmaximal, complemented
3#41×Dic9C212yesmaximal, complemented
4#10589833C212yesmaximal, complemented
5#10589821C212yesmaximal, complemented
6#10589784C214yesmaximal, complemented
7#10589719C214yesmaximal, complemented
8#10589704C214yesmaximal, complemented
9#10589640C218yesmaximal, complemented
10C2×#63434C211yesmaximal, characteristic, complemented
11#10589572C211yesmaximal, characteristic, complemented
12#86236—31nomaximal
13C2×C9×#41C2212yes—
14C22×C4×D9C2211yescharacteristic
15C9×C4⋊Q8C2211yescharacteristic, complemented
16C9×#127C2211yescharacteristic, complemented
17C9×#124C2212yescomplemented
18C9×#121C2214yes—
19C4×D4×C9C2214yescomplemented
20C2×C42×C9C2211yescharacteristic
21#63508C2214yes—
22Q8×Dic9C2214yescomplemented
23#63501C2218yes—
24#63500C2214yes—
25#63499C2214yes—
26#63497C2214yes—
27#63497C2218yescomplemented
28D4×Dic9C2218yes—
29D4×Dic9C2214yescomplemented
30C4×#611C2218yes—
31C2×(C2×D9)⋊C4C2212yes—
32#63488C2212yes—
33#63488C2214yescomplemented
34#63486C2214yes—
35C2×Dic9⋊C4C2212yes—
36C2×C4×Dic9C2211yescharacteristic
37C2×C4×Dic9C2214yescomplemented
38#63460C2218yes—
39#63451C2218yescomplemented
40#63448C2218yes—
41#63447C2218yes—
42#63441C2218yescomplemented
43#63440C2218yescomplemented
44#63434C2212yes—
45#63434C2212yes—
46#63434C2214yes—
47#63432C2212yescomplemented
48#63431C2212yescomplemented
49C4×Dic18C2214yescomplemented
50C3×#532D311yescharacteristic
51#5828—32no—
52Dic3×#41—32no—
53#5731—32no—
54#5719—32no—
55#5682—34no—
56#5617—34no—
57#5602—34no—
58#5538—38no—
59C2×#872—31no—
60#5470—31no—
61C23×D9C2311yescharacteristic
62C9×#41—28no—
63C2×Q8×C9C2312yes—
64C2×D4×C9C2314yes—
65C2×D4×C9C2312yes—
66C2×D4×C9C2314yes—
67C22×C4×C9C2314yes—
68C22×C4×C9C2312yes—
69C22×C4×C9C2311yescharacteristic
70C2×#611C2318yes—
71C22×Dic9C2311yescharacteristic
72C22×Dic9C2312yes—
73C22×Dic9C2318yes—
74C2×C4×D9—24no—
75C2×C4×D9C2312yes—
76C2×C4×D9C2312yes—
77C2×Dic18C2314yes—
78C9×C4⋊C4C2314yes—
79C9×C22⋊C4C2318yes—
80C42×C9C2312yes—
81C42×C9C2311yescharacteristic
82C42×C9C2311yescharacteristic
83#3676C2314yes—
84#3676C2318yes—
85#3676C2318yes—
86(C2×D9)⋊C4C2314yes—
87(C2×D9)⋊C4C2314yes—
88(C2×D9)⋊C4C2318yes—
89C4⋊Dic9C2314yes—
90C4⋊Dic9C2318yes—
91C4⋊Dic9C2314yes—
92Dic9⋊C4C2318yes—
93Dic9⋊C4C2314yes—
94Dic9⋊C4C2318yes—
95Dic9⋊C4C2314yes—
96C4×Dic9C2314yes—
97C4×Dic9C2312yes—
98C4×Dic9C2318yes—
99C4×Dic9C2312yes—
100#3455—91noSylow
101C2×C3×#41C2×D312yes—
102C22×C4×D3—31no—
103C3×C4⋊Q8C2×D311yescharacteristic
104C3×#127C2×D311yescharacteristic
105C3×#124C2×D312yes—
106C3×#121C2×D314yes—
107C3×C4×D4C2×D314yes—
108C2×C3×C42C2×D311yescharacteristic
109#946—34no—
110Q8×Dic3—34no—
111#939—38no—
112#938—34no—
113#937—34no—
114#935—34no—
115#935—38no—
116D4×Dic3—38no—
117D4×Dic3—34no—
118C4×#67—38no—
119C2×(C2×D3)⋊C4—32no—
120#926—32no—
121#926—34no—
122#924—34no—
123C2×Dic3⋊C4—32no—
124C2×C4×Dic3—31no—
125C2×C4×Dic3—34no—
126#898—38no—
127#889—38no—
128#886—38no—
129#885—38no—
130#879—38no—
131#878—38no—
132#872—32no—
133#872—32no—
134#872—34no—
135#870—32no—
136#869—32no—
137C4×Dic6—34no—
138C23×C9C2414yes—
139C23×C9C2411yescharacteristic
140C22×D9—22no—
141C22×D9—42no—
142C22×D9C2412yes—
143Q8×C9—24no—
144D4×C9—28no—
145D4×C9—24no—
146D4×C9—44no—
147C2×C4×C9—28no—
148C2×C4×C9—42no—
149C2×C4×C9#4114yes—
150C2×C4×C9C2414yes—
151C2×C4×C9C2412yes—
152C2×C4×C9C2412yes—
153C2×C4×C9C2411yescharacteristic
154C2×C4×C9C2411yescharacteristic
155#611—48no—
156C2×Dic9—22no—
157C2×Dic9—48no—
158C2×Dic9—42no—
159C2×Dic9C2414yes—
160C2×Dic9C2418yes—
161C2×Dic9C2412yes—
162C4×D9—24no—
163C4×D9—24no—
164Dic18—44no—
165#542—94no—
166#541—92no—
167#540—92no—
168#539—94no—
169#538—94no—
170#533—91no—
171#532D911yescharacteristic, complemented
172#529—98no—
173#525—92no—
174C4×#41—92no—
175C2×#117—91no—
176C23×D3—31no—
177C3×#41—28no—
178C2×C3×Q8C22×D312yes—
179C2×C3×D4C22×D314yes—
180C2×C3×D4C22×D312yes—
181C2×C3×D4C22×D314yes—
182C22×C3×C4C22×D314yes—
183C22×C3×C4C22×D312yes—
184C22×C3×C4C22×D311yescharacteristic
185C2×#67—38no—
186C22×Dic3—31no—
187C22×Dic3—38no—
188C22×Dic3—32no—
189C2×C4×D3—32no—
190C2×C4×D3—32no—
191C2×C4×D3—64no—
192C2×Dic6—34no—
193C3×C4⋊C4C22×D314yes—
194C3×C22⋊C4C22×D318yes—
195C3×C42C22×D312yes—
196C3×C42C22×D311yescharacteristic
197C3×C42C22×D311yescharacteristic
198#217—38no—
199#217—38no—
200#217—34no—
201(C2×D3)⋊C4—34no—
202(C2×D3)⋊C4—34no—
203(C2×D3)⋊C4—38no—
204C4⋊Dic3—34no—
205C4⋊Dic3—34no—
206C4⋊Dic3—38no—
207Dic3⋊C4—38no—
208Dic3⋊C4—34no—
209Dic3⋊C4—34no—
210Dic3⋊C4—38no—
211C4×Dic3—34no—
212C4×Dic3—32no—
213C4×Dic3—32no—
214C4×Dic3—38no—
215C22×C9—22no—
216C22×C9—24no—
217C22×C9—28no—
218C22×C9C2×#4112yes—
219C22×C9C2511yescharacteristic
220C2×D9—22no—
221C2×D9—24no—
222C2×D9—44no—
223C4×C9—24no—
224C4×C9—22no—
225C4×C9—22no—
226C4×C9C2×#4112yes—
227C4×C9C2×#4112yes—
228Dic9—22no—
229Dic9—28no—
230Dic9—24no—
231C2×#41C2×D912yes—
232C23×C4—91no—
233C4⋊Q8—92no—
234C4⋊Q8C2×D911yescharacteristic, complemented
235#127C2×D911yescharacteristic, complemented
236#126—98no—
237#126—98no—
238#125—98no—
239#125—92no—
240#124—98no—
241#124C2×D912yescomplemented
242#123—94no—
243#123—98no—
244#123—98no—
245C22⋊Q8—94no—
246C22⋊Q8—94no—
247C22⋊Q8—98no—
248#121—94no—
249#121—98no—
250#121C2×D914yes—
251#120—94no—
252C4×Q8—94no—
253C4×Q8—94no—
254C4×D4—98no—
255C4×D4—94no—
256C4×D4—98no—
257C4×D4C2×D914yescomplemented
258#117—92no—
259#117—94no—
260#117—94no—
261#117—92no—
262#117—92no—
263C2×C4⋊C4—92no—
264C2×C22⋊C4—92no—
265C2×C42—91no—
266C2×C42—94no—
267C2×C42C2×D911yescharacteristic
268C23×C3C23×D314yes—
269C23×C3C23×D311yescharacteristic
270C22×D3—32no—
271C22×D3—62no—
272C22×D3—122no—
273C3×Q8—24no—
274C3×D4—28no—
275C3×D4—24no—
276C3×D4—44no—
277C2×C3×C4—28no—
278C2×C3×C4—42no—
279C2×C3×C4#23714yes—
280C2×C3×C4C23×D314yes—
281C2×C3×C4C23×D312yes—
282C2×C3×C4C23×D312yes—
283C2×C3×C4C23×D311yescharacteristic
284C2×C3×C4C23×D311yescharacteristic
285#67—128no—
286C2×Dic3—34no—
287C2×Dic3—38no—
288C2×Dic3—32no—
289C2×Dic3—62no—
290C2×Dic3—128no—
291C2×Dic3—122no—
292C4×D3—64no—
293C4×D3—64no—
294Dic6—124no—
295C2×C9—22no—
296C2×C9—44no—
297C2×C9C22×#4111yescharacteristic
298C2×C9#58512yes—
299D9—42no—
300C24—91no—
301#41—28no—
302C2×Q8—94no—
303C2×Q8C22×D912yes—
304C2×D4—98no—
305C2×D4C22×D914yes—
306C2×D4C22×D912yes—
307C2×D4C22×D914yes—
308C22×C4—91no—
309C22×C4—92no—
310C22×C4—98no—
311C22×C4—92no—
312C22×C4—92no—
313C22×C4—184no—
314C22×C4C22×D914yes—
315C22×C4C22×D912yes—
316C22×C4C22×D911yescharacteristic
317C4⋊C4—94no—
318C4⋊C4—94no—
319C4⋊C4—94no—
320C4⋊C4—98no—
321C4⋊C4—98no—
322C4⋊C4—98no—
323C4⋊C4—94no—
324C4⋊C4C22×D914yes—
325C22⋊C4—94no—
326C22⋊C4—98no—
327C22⋊C4—98no—
328C22⋊C4—94no—
329C22⋊C4—94no—
330C22⋊C4—98no—
331C22⋊C4C22×D918yes—
332C42—92no—
333C42—98no—
334C42—92no—
335C42—94no—
336C42C22×D911yescharacteristic
337C42C22×D911yescharacteristic
338C42C22×D912yes—
339C22×C3—22no—
340C22×C3—24no—
341C22×C3—28no—
342C22×C3C2×#23712yes—
343C22×C3C24×D311yescharacteristic
344C2×D3—62no—
345C2×D3—64no—
346C2×D3—124no—
347C3×C4—24no—
348C3×C4—22no—
349C3×C4—22no—
350C3×C4C2×#23712yes—
351C3×C4C2×#23712yes—
352Dic3—62no—
353Dic3—68no—
354Dic3—64no—
355C9#345511yescharacteristic, complemented, Sylow
356C23—92no—
357C23—182no—
358C23—362no—
359C23C23×D914yes—
360C23C23×D911yescharacteristic
361Q8—24no—
362Q8—364no—
363D4—28no—
364D4—24no—
365D4—44no—
366D4—368no—
367C2×C4—28no—
368C2×C4—42no—
369C2×C4—94no—
370C2×C4—98no—
371C2×C4—92no—
372C2×C4—182no—
373C2×C4—184no—
374C2×C4—184no—
375C2×C4—362no—
376C2×C4—368no—
377C2×C4#369914yes—
378C2×C4C23×D914yes—
379C2×C4C23×D912yes—
380C2×C4C23×D912yes—
381C2×C4C23×D911yescharacteristic
382C2×C4C23×D911yescharacteristic
383C2×C3—22no—
384C2×C3—44no—
385C2×C3C22×#23711yescharacteristic
386C2×C3#596412yes—
387D3—122no—
388C22—22no—
389C22—24no—
390C22—28no—
391C22—182no—
392C22—184no—
393C22—364no—
394C22C2×#369912yes—
395C22C24×D911yescharacteristic
396C4—24no—
397C4—22no—
398C4—22no—
399C4—182no—
400C4—184no—
401C4—188no—
402C4C2×#369912yes—
403C4C2×#369912yes—
404C3#8623611yescharacteristic
405C2—22no—
406C2—44no—
407C2—362no—
408C2C22×#369911yescharacteristic
409C2#1059313912yes—
subgroupG/H
centerC2×C4C23×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingC9×#532C2
hypercenter#532D9
hypocenterC9#3455
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C2×C4 ◁ #532

Complements

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

NH ≅ G/Ntype
1. C9×#532C2semidirect
2. #10589930C2semidirect
3. #41×Dic9C2semidirect
4. #10589833C2semidirect
5. #10589821C2semidirect
6. #10589784C2semidirect
7. #10589719C2semidirect
8. #10589704C2semidirect
9. #10589640C2semidirect
10. C2×#63434C2semidirect
11. #10589572C2semidirect
15. C9×C4⋊Q8C22semidirect
16. C9×#127C22semidirect
17. C9×#124C22semidirect
19. C4×D4×C9C22semidirect
22. Q8×Dic9C22semidirect
27. #63497C22semidirect
29. D4×Dic9C22semidirect
33. #63488C22semidirect
37. C2×C4×Dic9C22semidirect
39. #63451C22semidirect
42. #63441C22semidirect
43. #63440C22semidirect
47. #63432C22semidirect
48. #63431C22semidirect
49. C4×Dic18C22semidirect
171. #532D9semidirect
234. C4⋊Q8C2×D9semidirect
235. #127C2×D9semidirect
241. #124C2×D9semidirect
257. C4×D4C2×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×#5322
#105899302
#41×Dic92
#105898332
#105898212
#105897842
#105897192
#105897042
#105896402
C2×#634342
#105895722
#862363