Finite Group Databasebeta

← #11904372

Subgroups — #11904372

Order 1152.

2340 conjugacy classes of subgroups.

The subgroup lattice has 399 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C9×H(5,𝔽2)C211yesmaximal, characteristic, complemented
2C22×#3699C211yesmaximal, characteristic, complemented
3#10589930C212yesmaximal, complemented
4#10589927C212yesmaximal, complemented
5#10589926C218yesmaximal, complemented
6#10589908C218yesmaximal, complemented
7#10589906C214yesmaximal, complemented
8#10589900C211yesmaximal, characteristic, complemented
9C2×#63497C214yesmaximal, complemented
10#87280—31nomaximal
11C9×H(5,𝔽2)—28no—
12C2×C9×#41C2212yes—
13C2×C9×#41C2214yescomplemented
14C22×D4×C9C2214yes—
15C22×D4×C9C2211yescharacteristic
16C22×D4×C9C2214yescomplemented
17C22×#611C2212yescomplemented
18C23×Dic9C2212yescomplemented
19C2×#3699—28no—
20C2×#3699C2218yescomplemented
21C22×C4×D9C2211yescharacteristic, complemented
22C22×Dic18C2211yescharacteristic, complemented
23#63515C2218yescomplemented
24C2×#3676C2214yescomplemented
25C2×#3676C2218yescomplemented
26#63508C2214yescomplemented
27#63506C2214yescomplemented
28#63501C22116yescomplemented
29#63500C2214yescomplemented
30#63499C2214yescomplemented
31#63498C2214yescomplemented
32#63497C2214yescomplemented
33#63497C2218yescomplemented
34#63497C22116yescomplemented
35D4×Dic9C2218yescomplemented
36#63491C2218yescomplemented
37C4×#611C2218yescomplemented
38#63488C2212yescomplemented
39#63486C2218yescomplemented
40C2×Dic9⋊C4C2218yescomplemented
41C2×C3×H(5,𝔽2)D311yescharacteristic
42C22×#237—31no—
43#5828—32no—
44#5825—32no—
45#5824—38no—
46#5806—38no—
47#5804—34no—
48#5798—31no—
49C2×#935—34no—
50C24×C9C2314yes—
51C24×C9C2312yes—
52C23×D9C2311yescharacteristic
53C9×#41—216no—
54C9×#41—28no—
55C2×Q8×C9C2312yes—
56C2×D4×C9—216no—
57C2×D4×C9—216no—
58C2×D4×C9D418yescomplemented
59C2×D4×C9C2314yes—
60C2×D4×C9C2318yes—
61C2×D4×C9C2312yes—
62C2×D4×C9C2314yes—
63C22×C4×C9C2314yes—
64C22×C4×C9C2314yes—
65C22×C4×C9C2311yescharacteristic
66C2×#611—28no—
67C2×#611C2318yes—
68C2×#611C2318yes—
69C22×Dic9—28no—
70C22×Dic9C2312yes—
71C22×Dic9C2311yescharacteristic
72C22×Dic9C2318yes—
73C22×Dic9C2318yes—
74#3699—232no—
75C2×C4×D9—24no—
76C2×C4×D9C2314yes—
77C2×Dic18—24no—
78C2×Dic18C2314yes—
79#3676C2314yes—
80#3676C2318yes—
81#3676C2318yes—
82#3676C23116yes—
83(C2×D9)⋊C4C2318yes—
84C4⋊Dic9C2314yes—
85Dic9⋊C4C2318yes—
86Dic9⋊C4C23116yes—
87C4×Dic9C2314yes—
88#3485—91noSylow
89C3×H(5,𝔽2)—28no—
90C2×C3×#41C2×D312yes—
91C2×C3×#41C2×D314yes—
92C22×C3×D4C2×D314yes—
93C22×C3×D4C2×D311yescharacteristic
94C22×C3×D4C2×D314yes—
95C22×#67—32no—
96C23×Dic3—32no—
97C2×#237—38no—
98C2×#237—68no—
99C22×C4×D3—31no—
100C22×Dic6—31no—
101#953—38no—
102C2×#217—34no—
103C2×#217—38no—
104#946—34no—
105#944—34no—
106#939—316no—
107#938—34no—
108#937—34no—
109#936—34no—
110#935—34no—
111#935—38no—
112#935—316no—
113D4×Dic3—38no—
114#929—38no—
115C4×#67—38no—
116#926—32no—
117#924—38no—
118C2×Dic3⋊C4—38no—
119C23×C9—28no—
120C23×C9—44no—
121C23×C9—48no—
122C23×C9C2×D418yes—
123C23×C9C2414yes—
124C23×C9C2411yescharacteristic
125C23×C9C2414yes—
126C22×D9—22no—
127C22×D9—42no—
128C22×D9C2412yes—
129Q8×C9—24no—
130D4×C9—28no—
131D4×C9—216no—
132D4×C9—24no—
133D4×C9C2×D4116yes—
134C2×C4×C9—28no—
135C2×C4×C9—28no—
136C2×C4×C9C2×D414yes—
137C2×C4×C9C2414yes—
138C2×C4×C9C2412yes—
139#611—216no—
140#611—48no—
141C2×Dic9—24no—
142C2×Dic9—22no—
143C2×Dic9—216no—
144C2×Dic9—48no—
145C2×Dic9C2418yes—
146C2×Dic9C2414yes—
147C2×Dic9C2412yes—
148C4×D9—28no—
149Dic18—28no—
150C2×H(5,𝔽2)D911yescharacteristic, complemented
151C22×#41—91no—
152#547—98no—
153#546—98no—
154#536—92no—
155#534—94no—
156#525—92no—
157C2×#123—94no—
158#518—91no—
159C24×C3C22×D314yes—
160C24×C3C22×D312yes—
161C23×D3—31no—
162C3×#41—216no—
163C3×#41—28no—
164C2×C3×Q8C22×D312yes—
165C2×C3×D4—216no—
166C2×C3×D4—216no—
167C2×C3×D4#6718yes—
168C2×C3×D4C22×D314yes—
169C2×C3×D4C22×D318yes—
170C2×C3×D4C22×D312yes—
171C2×C3×D4C22×D314yes—
172C22×C3×C4C22×D314yes—
173C22×C3×C4C22×D314yes—
174C22×C3×C4C22×D311yescharacteristic
175C2×#67—38no—
176C2×#67—38no—
177C2×#67—68no—
178C22×Dic3—38no—
179C22×Dic3—32no—
180C22×Dic3—31no—
181C22×Dic3—38no—
182C22×Dic3—68no—
183#237—632no—
184C2×C4×D3—34no—
185C2×C4×D3—64no—
186C2×Dic6—34no—
187C2×Dic6—64no—
188#217—316no—
189#217—34no—
190#217—38no—
191#217—38no—
192(C2×D3)⋊C4—38no—
193C4⋊Dic3—34no—
194Dic3⋊C4—38no—
195Dic3⋊C4—316no—
196C4×Dic3—34no—
197C22×C9—28no—
198C22×C9—22no—
199C22×C9—24no—
200C22×C9—28no—
201C22×C9—48no—
202C22×C9—88no—
203C22×C9C22×D412yes—
204C22×C9C22×D418yes—
205C22×C9C2511yescharacteristic
206C2×D9—22no—
207C2×D9—24no—
208C2×D9—44no—
209C4×C9—24no—
210C4×C9C22×D414yes—
211Dic9—24no—
212Dic9—22no—
213Dic9—28no—
214H(5,𝔽2)—28no—
215C2×#41—98no—
216C2×#41—188no—
217C2×#41C2×D912yes—
218C2×#41C2×D914yescomplemented
219C22×Q8—91no—
220C22×D4—92no—
221C22×D4C2×D914yes—
222C22×D4C2×D911yescharacteristic
223C22×D4C2×D914yescomplemented
224C23×C4—92no—
225C23×C4—91no—
226C4⋊Q8—94no—
227#124—94no—
228#123—94no—
229#123—98no—
230#123—916no—
231#123—98no—
232C22⋊Q8—94no—
233C22⋊Q8—98no—
234#121—94no—
235#121—916no—
236#120—98no—
237#120—94no—
238C4×D4—98no—
239C4×D4—98no—
240#117—92no—
241C2×C4⋊C4—98no—
242C2×C22⋊C4—94no—
243C2×C22⋊C4—98no—
244C23×C3—28no—
245C23×C3—44no—
246C23×C3—48no—
247C23×C3C2×#6718yes—
248C23×C3C23×D314yes—
249C23×C3C23×D311yescharacteristic
250C23×C3C23×D314yes—
251C22×D3—32no—
252C22×D3—62no—
253C22×D3—122no—
254C3×Q8—24no—
255C3×D4—28no—
256C3×D4—216no—
257C3×D4—24no—
258C3×D4C2×#67116yes—
259C2×C3×C4—28no—
260C2×C3×C4—28no—
261C2×C3×C4C2×#6714yes—
262C2×C3×C4C23×D314yes—
263C2×C3×C4C23×D312yes—
264#67—616no—
265#67—128no—
266C2×Dic3—38no—
267C2×Dic3—34no—
268C2×Dic3—32no—
269C2×Dic3—64no—
270C2×Dic3—62no—
271C2×Dic3—616no—
272C2×Dic3—128no—
273C4×D3—68no—
274Dic6—68no—
275C2×C9—22no—
276C2×C9—28no—
277C2×C9—44no—
278C2×C9C23×D411yescharacteristic
279C2×C9#58512yes—
280D9—42no—
281C24—91no—
282C24C22×D914yes—
283C24C22×D912yes—
284#41—216no—
285#41—28no—
286#41—1832no—
287C2×Q8—94no—
288C2×Q8—184no—
289C2×Q8C22×D912yes—
290C2×D4—216no—
291C2×D4—216no—
292C2×D4—98no—
293C2×D4—98no—
294C2×D4—188no—
295C2×D4#61118yescomplemented
296C2×D4C22×D914yes—
297C2×D4C22×D918yes—
298C2×D4C22×D912yes—
299C2×D4C22×D914yes—
300C22×C4—98no—
301C22×C4—91no—
302C22×C4—92no—
303C22×C4—98no—
304C22×C4—94no—
305C22×C4—188no—
306C22×C4—184no—
307C22×C4C22×D914yes—
308C22×C4C22×D914yes—
309C22×C4C22×D911yescharacteristic
310C4⋊C4—98no—
311C4⋊C4—916no—
312C4⋊C4—94no—
313C22⋊C4—94no—
314C22⋊C4—98no—
315C22⋊C4—98no—
316C22⋊C4—916no—
317C22⋊C4—98no—
318C42—94no—
319C22×C3—28no—
320C22×C3—22no—
321C22×C3—28no—
322C22×C3—24no—
323C22×C3—48no—
324C22×C3—88no—
325C22×C3C22×#6712yes—
326C22×C3C22×#6718yes—
327C22×C3C24×D311yescharacteristic
328C2×D3—64no—
329C2×D3—62no—
330C2×D3—124no—
331C3×C4—24no—
332C3×C4C22×#6714yes—
333Dic3—68no—
334Dic3—64no—
335Dic3—62no—
336C9#348511yescharacteristic, complemented, Sylow
337C23—28no—
338C23—44no—
339C23—48no—
340C23—92no—
341C23—182no—
342C23—362no—
343C23C2×#61118yes—
344C23C23×D914yes—
345C23C23×D911yescharacteristic
346C23C23×D914yes—
347Q8—24no—
348Q8—188no—
349D4—216no—
350D4—28no—
351D4—24no—
352D4—1816no—
353D4—368no—
354D4C2×#611116yes—
355C2×C4—28no—
356C2×C4—28no—
357C2×C4—98no—
358C2×C4—92no—
359C2×C4—94no—
360C2×C4—182no—
361C2×C4—184no—
362C2×C4—1816no—
363C2×C4—188no—
364C2×C4—368no—
365C2×C4C2×#61114yes—
366C2×C4C23×D914yes—
367C2×C4C23×D912yes—
368C2×C3—22no—
369C2×C3—28no—
370C2×C3—44no—
371C2×C3#596612yes—
372C2×C3C23×#6711yescharacteristic
373D3—122no—
374C22—28no—
375C22—22no—
376C22—28no—
377C22—24no—
378C22—48no—
379C22—88no—
380C22—184no—
381C22—182no—
382C22—364no—
383C22C22×#61118yes—
384C22C22×#61112yes—
385C22C24×D911yescharacteristic
386C4—24no—
387C4—188no—
388C4—182no—
389C4—184no—
390C4C22×#61114yes—
391C3#8728011yescharacteristic
392C2—22no—
393C2—28no—
394C2—44no—
395C2—362no—
396C2#1059314112yes—
397C2C23×#61111yescharacteristic
subgroupG/H
centerC22C24×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingC2×C9×H(5,𝔽2)C2
hypercenterC2×H(5,𝔽2)D9
hypocenterC9#3485
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C2×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. C2×C9×H(5,𝔽2)C2semidirect
2. C22×#3699C2semidirect
3. #10589930C2semidirect
4. #10589927C2semidirect
5. #10589926C2semidirect
6. #10589908C2semidirect
7. #10589906C2semidirect
8. #10589900C2semidirect
9. C2×#63497C2semidirect
13. C2×C9×#41C22semidirect
16. C22×D4×C9C22semidirect
17. C22×#611C22semidirect
18. C23×Dic9C22semidirect
20. C2×#3699C22semidirect
21. C22×C4×D9C22semidirect
22. C22×Dic18C22semidirect
23. #63515C22semidirect
24. C2×#3676C22semidirect
25. C2×#3676C22semidirect
26. #63508C22semidirect
27. #63506C22semidirect
28. #63501C22semidirect
29. #63500C22semidirect
30. #63499C22semidirect
31. #63498C22semidirect
32. #63497C22semidirect
33. #63497C22semidirect
34. #63497C22semidirect
35. D4×Dic9C22semidirect
36. #63491C22semidirect
37. C4×#611C22semidirect
38. #63488C22semidirect
39. #63486C22semidirect
40. C2×Dic9⋊C4C22semidirect
58. C2×D4×C9D4semidirect
150. C2×H(5,𝔽2)D9semidirect
218. C2×#41C2×D9semidirect
223. C22×D4C2×D9semidirect
295. C2×D4#611semidirect
336. C9#3485semidirect

Maximal subgroups

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

subgroupindex
C2×C9×H(5,𝔽2)2
C22×#36992
#105899302
#105899272
#105899262
#105899082
#105899062
#105899002
C2×#634972
#872803