Finite Group Databasebeta

← #11808539

Subgroups — #11808539

Order 1152.

840 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C9×#117C211yesmaximal, characteristic, complemented
2C2×C4×#611C211yesmaximal, characteristic
3C4×#3676C211yesmaximal, characteristic, complemented
4#10588673C211yesmaximal, characteristic, complemented
5#10588672C211yesmaximal, characteristic, complemented
6#10588665C211yesmaximal, characteristic, complemented
7#10588663C211yesmaximal, characteristic, complemented
8#10588639C212yesmaximal
9#10588632C212yesmaximal, complemented
10C4×(C2×D9)⋊C4C212yesmaximal, complemented
11C4×Dic9⋊C4C212yesmaximal, complemented
12#82274—31nomaximal
13C23×C4×C9C2211yescharacteristic
14C22×#611C2211yescharacteristic
15C22×C4×D9C2211yescharacteristic
16C9×#117—24no—
17C2×C9×C4⋊C4C2211yescharacteristic
18C2×C9×C4⋊C4C2211yescharacteristic
19C2×C9×C22⋊C4C2212yes—
20C2×C42×C9C2212yes—
21C2×#3676C2211yescharacteristic
22C2×#3676C2212yes—
23C4×#611—24no—
24C2×(C2×D9)⋊C4C2211yescharacteristic
25C2×(C2×D9)⋊C4C2212yes—
26C2×(C2×D9)⋊C4C2212yes—
27C2×Dic9⋊C4C2212yes—
28C2×Dic9⋊C4C2211yescharacteristic
29C2×Dic9⋊C4C2212yes—
30C2×C4×Dic9C2211yescharacteristic
31C2×C4×Dic9C2212yes—
32C9⋊#95C2212yes—
33C9⋊#95C2211yescharacteristic
34C9⋊#95C2211yescharacteristic
35C9⋊#95C2212yes—
36C9⋊#95C2212yes—
37C9⋊#95C2212yes—
38C2×C3×#117D311yescharacteristic
39C2×C4×#67—31no—
40C4×#217—31no—
41#4993—31no—
42#4992—31no—
43#4985—31no—
44#4983—31no—
45#4959—32no—
46#4952—32no—
47C4×(C2×D3)⋊C4—32no—
48C4×Dic3⋊C4—32no—
49C24×C9C2311yescharacteristic
50C23×D9C2311yescharacteristic
51C22×C4×C9—24no—
52C22×C4×C9D414yes—
53C22×C4×C9C2312yes—
54C22×C4×C9C2312yes—
55C22×C4×C9C2311yescharacteristic
56C22×C4×C9C2311yescharacteristic
57C2×#611—22no—
58C2×#611—22no—
59C2×#611—22no—
60C22×Dic9C2312yes—
61C22×Dic9C2311yescharacteristic
62C22×Dic9C2311yescharacteristic
63C22×Dic9C2312yes—
64C22×Dic9C2311yescharacteristic
65C2×C4×D9—22no—
66C2×C4×D9—24no—
67C9×C4⋊C4—22no—
68C9×C4⋊C4—22no—
69C9×C22⋊C4—24no—
70C42×C9—24no—
71#3676—22no—
72#3676—24no—
73(C2×D9)⋊C4—24no—
74(C2×D9)⋊C4—22no—
75(C2×D9)⋊C4—24no—
76Dic9⋊C4—22no—
77Dic9⋊C4—24no—
78Dic9⋊C4—24no—
79C4×Dic9—22no—
80C4×Dic9—24no—
81#2395—91noSylow
82C23×C3×C4C2×D311yescharacteristic
83C22×#67—31no—
84C22×C4×D3—31no—
85C3×#117—24no—
86C2×C3×C4⋊C4C2×D311yescharacteristic
87C2×C3×C4⋊C4C2×D311yescharacteristic
88C2×C3×C22⋊C4C2×D312yes—
89C2×C3×C42C2×D312yes—
90C2×#217—31no—
91C2×#217—32no—
92C4×#67—64no—
93C2×(C2×D3)⋊C4—32no—
94C2×(C2×D3)⋊C4—32no—
95C2×(C2×D3)⋊C4—31no—
96C2×Dic3⋊C4—32no—
97C2×Dic3⋊C4—32no—
98C2×Dic3⋊C4—31no—
99C2×C4×Dic3—31no—
100C2×C4×Dic3—32no—
101C3⋊#95—32no—
102C3⋊#95—32no—
103C3⋊#95—32no—
104C3⋊#95—32no—
105C3⋊#95—31no—
106C3⋊#95—31no—
107C23×C9—22no—
108C23×C9—21no—
109C23×C9—21no—
110C23×C9—22no—
111C23×C9C2×D412yes—
112C23×C9C2411yescharacteristic
113C22×D9—21no—
114C22×D9—22no—
115C22×D9—22no—
116C22×D9—21no—
117C22×D9#4112yes—
118C2×C4×C9—22no—
119C2×C4×C9—28no—
120C2×C4×C9—22no—
121C2×C4×C9—22no—
122C2×C4×C9—22no—
123C2×C4×C9—22no—
124C2×C4×C9—22no—
125C2×C4×C9—22no—
126C2×C4×C9C2×D412yes—
127C2×C4×C9C2×D412yes—
128C2×C4×C9#4114yes—
129#611—28no—
130C2×Dic9—21no—
131C2×Dic9—22no—
132C2×Dic9—22no—
133C2×Dic9—21no—
134C2×Dic9—21no—
135C2×Dic9—21no—
136C2×Dic9—22no—
137C2×Dic9—22no—
138C2×Dic9—22no—
139C2×Dic9—22no—
140C2×Dic9—22no—
141C2×Dic9#4112yes—
142C2×Dic9#4114yes—
143C4×D9—44no—
144C2×C4×D4—91no—
145C2×#117D911yescharacteristic, complemented
146#400—91no—
147#399—91no—
148#398—91no—
149#397—91no—
150#397—92no—
151#394—92no—
152C4×C4⋊C4—92no—
153C4×C22⋊C4—91no—
154C4×C22⋊C4—92no—
155C24×C3C22×D311yescharacteristic
156C23×D3—31no—
157C22×C3×C4—24no—
158C22×C3×C4#6714yes—
159C22×C3×C4C22×D312yes—
160C22×C3×C4C22×D312yes—
161C22×C3×C4C22×D311yescharacteristic
162C22×C3×C4C22×D311yescharacteristic
163C2×#67—62no—
164C2×#67—62no—
165C2×#67—62no—
166C22×Dic3—31no—
167C22×Dic3—32no—
168C22×Dic3—32no—
169C22×Dic3—31no—
170C22×Dic3—31no—
171C2×C4×D3—64no—
172C2×C4×D3—62no—
173C3×C4⋊C4—22no—
174C3×C4⋊C4—22no—
175C3×C22⋊C4—24no—
176C3×C42—24no—
177#217—64no—
178#217—62no—
179(C2×D3)⋊C4—64no—
180(C2×D3)⋊C4—64no—
181(C2×D3)⋊C4—62no—
182Dic3⋊C4—64no—
183Dic3⋊C4—64no—
184Dic3⋊C4—62no—
185C4×Dic3—64no—
186C4×Dic3—62no—
187C22×C9—22no—
188C22×C9—22no—
189C22×C9—22no—
190C22×C9—42no—
191C22×C9—42no—
192C22×C9C22×D411yescharacteristic
193C22×C9C2×#4112yes—
194C22×C9C2×#4111yescharacteristic
195C22×C9C2×#4111yescharacteristic
196C22×C9C2×#4112yes—
197C2×D9—22no—
198C2×D9—24no—
199C2×D9—41no—
200C2×D9—42no—
201C2×D9—41no—
202C4×C9—22no—
203C4×C9—42no—
204C4×C9—42no—
205C4×C9#12314yes—
206Dic9—22no—
207Dic9—24no—
208Dic9—41no—
209Dic9—42no—
210Dic9—41no—
211C22×D4—91no—
212C23×C4—91no—
213C23×C4C2×D911yescharacteristic
214C4×D4—184no—
215#117—24no—
216C2×C4⋊C4—91no—
217C2×C4⋊C4—92no—
218C2×C4⋊C4—92no—
219C2×C4⋊C4C2×D911yescharacteristic
220C2×C4⋊C4C2×D911yescharacteristic
221C2×C22⋊C4—91no—
222C2×C22⋊C4—92no—
223C2×C22⋊C4—91no—
224C2×C22⋊C4—92no—
225C2×C22⋊C4—92no—
226C2×C22⋊C4C2×D912yes—
227C2×C42—91no—
228C2×C42—92no—
229C2×C42C2×D912yes—
230#95—92no—
231#95—91no—
232#95—92no—
233#95—91no—
234#95—92no—
235#95—92no—
236C23×C3—22no—
237C23×C3—22no—
238C23×C3—21no—
239C23×C3—21no—
240C23×C3C2×#6712yes—
241C23×C3C23×D311yescharacteristic
242C22×D3—32no—
243C22×D3—62no—
244C22×D3—62no—
245C22×D3—61no—
246C22×D3—61no—
247C2×C3×C4—22no—
248C2×C3×C4—28no—
249C2×C3×C4—22no—
250C2×C3×C4—22no—
251C2×C3×C4—22no—
252C2×C3×C4—22no—
253C2×C3×C4—22no—
254C2×C3×C4—22no—
255C2×C3×C4#23514yes—
256C2×C3×C4C2×#6712yes—
257C2×C3×C4C2×#6712yes—
258#67—68no—
259C2×Dic3—32no—
260C2×Dic3—34no—
261C2×Dic3—62no—
262C2×Dic3—62no—
263C2×Dic3—61no—
264C2×Dic3—61no—
265C2×Dic3—62no—
266C2×Dic3—62no—
267C2×Dic3—62no—
268C2×Dic3—62no—
269C2×Dic3—62no—
270C2×Dic3—61no—
271C2×Dic3—61no—
272C4×D3—124no—
273C2×C9—42no—
274C2×C9C2×#12311yescharacteristic
275C2×C9#52511yescharacteristic
276C2×C9#52912yes—
277C2×C9#52912yes—
278C2×C9#53211yescharacteristic
279D9—42no—
280C24—91no—
281C24C22×D911yescharacteristic
282C2×D4—182no—
283C2×D4—182no—
284C2×D4—182no—
285C22×C4—24no—
286C22×C4—92no—
287C22×C4—91no—
288C22×C4—92no—
289C22×C4—91no—
290C22×C4—91no—
291C22×C4—184no—
292C22×C4—182no—
293C22×C4#61114yes—
294C22×C4C22×D912yes—
295C22×C4C22×D912yes—
296C22×C4C22×D911yescharacteristic
297C22×C4C22×D911yescharacteristic
298C4⋊C4—22no—
299C4⋊C4—22no—
300C4⋊C4—184no—
301C4⋊C4—184no—
302C4⋊C4—182no—
303C22⋊C4—24no—
304C22⋊C4—184no—
305C22⋊C4—184no—
306C22⋊C4—184no—
307C22⋊C4—182no—
308C22⋊C4—182no—
309C42—24no—
310C42—184no—
311C42—182no—
312C22×C3—22no—
313C22×C3—22no—
314C22×C3—22no—
315C22×C3—42no—
316C22×C3—42no—
317C22×C3C2×#23512yes—
318C22×C3D3×#4111yescharacteristic
319C22×C3D3×#4111yescharacteristic
320C22×C3D3×#4112yes—
321C22×C3C22×#6711yescharacteristic
322C2×D3—64no—
323C2×D3—62no—
324C2×D3—122no—
325C2×D3—121no—
326C2×D3—121no—
327C3×C4—22no—
328C3×C4—42no—
329C3×C4—42no—
330C3×C4#92914yes—
331Dic3—64no—
332Dic3—62no—
333Dic3—122no—
334Dic3—121no—
335Dic3—121no—
336C9#239511yescharacteristic, complemented, Sylow
337C23—22no—
338C23—22no—
339C23—21no—
340C23—21no—
341C23—92no—
342C23—182no—
343C23—182no—
344C23—181no—
345C23—181no—
346C23C2×#61112yes—
347C23C23×D911yescharacteristic
348D4—188no—
349C2×C4—22no—
350C2×C4—28no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—94no—
358C2×C4—92no—
359C2×C4—182no—
360C2×C4—182no—
361C2×C4—181no—
362C2×C4—181no—
363C2×C4—182no—
364C2×C4—182no—
365C2×C4—182no—
366C2×C4—182no—
367C2×C4—182no—
368C2×C4—181no—
369C2×C4—181no—
370C2×C4—364no—
371C2×C4#369714yes—
372C2×C4C2×#61112yes—
373C2×C4C2×#61112yes—
374C2×C3—42no—
375C2×C3#552812yes—
376C2×C3#552812yes—
377C2×C3C2×#92911yescharacteristic
378C2×C3#582811yescharacteristic
379C2×C3#583211yescharacteristic
380D3—122no—
381C22—22no—
382C22—22no—
383C22—22no—
384C22—42no—
385C22—42no—
386C22—184no—
387C22—182no—
388C22—362no—
389C22—361no—
390C22—361no—
391C22C2×#369712yes—
392C22#41×D911yescharacteristic
393C22#41×D911yescharacteristic
394C22#41×D912yes—
395C22C22×#61111yescharacteristic
396C4—22no—
397C4—42no—
398C4—42no—
399C4—184no—
400C4—182no—
401C4—362no—
402C4—361no—
403C4—361no—
404C4#6349114yes—
405C3#8227411yescharacteristic
406C2—42no—
407C2—362no—
408C2#1058963012yes—
409C2#1058963012yes—
410C2C2×#6349111yescharacteristic
411C2#1058993011yescharacteristic
412C2#1058993411yescharacteristic
subgroupG/H
centerC22×C4C22×D9
commutator, cosocleC23×C9C24
Frattini, socleC23×C3C23×D3
FittingC2×C9×#117C2
prime radicalC22×#611C22
hypercenterC2×#117D9
hypocenterC9#2395
LCSG ▷ C23×C9 ▷ C9
UCSC1 ◁ C22×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. C2×C9×#117C2semidirect
3. C4×#3676C2semidirect
4. #10588673C2semidirect
5. #10588672C2semidirect
6. #10588665C2semidirect
7. #10588663C2semidirect
9. #10588632C2semidirect
10. C4×(C2×D9)⋊C4C2semidirect
11. C4×Dic9⋊C4C2semidirect
145. C2×#117D9semidirect
336. C9#2395semidirect

Maximal subgroups

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

subgroupindex
C2×C9×#1172
C2×C4×#6112
C4×#36762
#105886732
#105886722
#105886652
#105886632
#105886392
#105886322
C4×(C2×D9)⋊C42
C4×Dic9⋊C42
#822743