Finite Group Databasebeta

← #11873465

Subgroups — #11873465

Order 1152.

600 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10589934C211yesmaximal, characteristic
2#10589619C211yesmaximal, characteristic, complemented
3C9×#416C211yesmaximal, characteristic, complemented
4#10588917C211yesmaximal, characteristic, complemented
5#10588794C211yesmaximal, characteristic, complemented
6C2×C8×Dic9C211yesmaximal, characteristic, complemented
7#10588683C211yesmaximal, characteristic, complemented
8#10588480C212yesmaximal, complemented
9#10588472C212yesmaximal, complemented
10#10588448C212yesmaximal, complemented
11#10588440C212yesmaximal, complemented
12#78825—31nomaximal
13C2×C9×#41C2211yescharacteristic
14C2×#3697C2211yescharacteristic
15C22×C8×C9C2211yescharacteristic
16C9×#117C2211yescharacteristic
17#63509C2211yescharacteristic
18#63506C2211yescharacteristic
19#63502C2211yescharacteristic
20#63501—22no—
21#63498C2211yescharacteristic
22C4×#611—22no—
23#63488C2211yescharacteristic
24C2×C4×Dic9C2211yescharacteristic
25C22×C9⋊C8C2211yescharacteristic
26#63452C2212yes—
27#63450C2212yes—
28#63440—22no—
29C4×Dic18—22no—
30C9×#103C2212yes—
31C9×#102C2212yes—
32#63395C2212yes—
33#63392C2212yes—
34#63380C2212yes—
35#63376C2212yes—
36C8×Dic9C2212yes—
37C8×Dic9C2212yes—
38#63369C2212yes—
39#63368C2212yes—
40#5832—31no—
41#5517—31no—
42C3×#416D311yescharacteristic
43#5233—31no—
44#5113—31no—
45C2×C8×Dic3—31no—
46#5002—31no—
47#4800—32no—
48#4792—32no—
49#4768—32no—
50#4760—32no—
51C9×#41—22no—
52C9×#41—22no—
53C2×Q8×C9C2311yescharacteristic
54C2×D4×C9—21no—
55C2×D4×C9C2311yescharacteristic
56C22×C4×C9—21no—
57C22×C4×C9C2311yescharacteristic
58C2×#611—21no—
59C2×#611—22no—
60C22×Dic9D412yes—
61#3697—22no—
62#3697—22no—
63C2×D36C2311yescharacteristic
64C2×C4×D9—21no—
65C2×Dic18—22no—
66C2×Dic18C2311yescharacteristic
67C2×C8×C9—22no—
68C2×C8×C9C2312yes—
69C9×C4⋊C4C2312yes—
70C9×C22⋊C4—21no—
71C42×C9—21no—
72#3676—21no—
73#3676—22no—
74(C2×D9)⋊C4—22no—
75C4⋊Dic9—22no—
76C4⋊Dic9C2312yes—
77Dic9⋊C4—22no—
78Dic9⋊C4—22no—
79Dic9⋊C4—22no—
80C4×Dic9—21no—
81C4×Dic9D412yes—
82C4×Dic9C2311yescharacteristic
83C4×Dic9C2311yescharacteristic
84C2×C9⋊C8—22no—
85C2×C9⋊C8C2312yes—
86#3131—91noSylow
87C2×C3×#41C2×D311yescharacteristic
88C2×#235—31no—
89C22×C3×C8C2×D311yescharacteristic
90C3×#117C2×D311yescharacteristic
91#947—31no—
92#944—31no—
93#940—31no—
94#939—62no—
95#936—31no—
96C4×#67—62no—
97#926—31no—
98C2×C4×Dic3—31no—
99C22×C3⋊C8—31no—
100#890—32no—
101#888—32no—
102#878—62no—
103C4×Dic6—62no—
104C3×#103C2×D312yes—
105C3×#102C2×D312yes—
106#835—32no—
107#832—32no—
108#821—32no—
109#816—32no—
110C8×Dic3—32no—
111C8×Dic3—32no—
112#810—32no—
113#809—32no—
114C23×C9—21no—
115C23×C9C2×D411yescharacteristic
116C22×D9—21no—
117Q8×C9—21no—
118Q8×C9—21no—
119D4×C9—21no—
120D4×C9—21no—
121D4×C9—42no—
122C2×C4×C9—22no—
123C2×C4×C9—21no—
124C2×C4×C9—42no—
125C2×C4×C9C2×D411yescharacteristic
126C2×C4×C9#4112yes—
127C2×C4×C9#4112yes—
128C2×C4×C9C2411yescharacteristic
129#611—42no—
130#611—44no—
131C2×Dic9—24no—
132C2×Dic9—22no—
133C2×Dic9—21no—
134C2×Dic9C2×D412yes—
135C2×Dic9C2×D412yes—
136D36—21no—
137D36—21no—
138C4×D9—42no—
139Dic18—21no—
140Dic18—21no—
141Dic18—44no—
142C8×C9—22no—
143C9⋊C8—22no—
144#533—91no—
145#532—91no—
146#488—92no—
147#488—92no—
148#487—92no—
149#486—92no—
150#416—91no—
151#416—91no—
152#416—91no—
153#416D911yescharacteristic, complemented
154C2×C4×C8—91no—
155C3×#41—22no—
156C3×#41—22no—
157C2×C3×Q8C22×D311yescharacteristic
158C2×C3×D4—21no—
159C2×C3×D4C22×D311yescharacteristic
160C22×C3×C4—21no—
161C22×C3×C4C22×D311yescharacteristic
162C2×#67—62no—
163C2×#67—61no—
164C22×Dic3—32no—
165#235—62no—
166#235—62no—
167C2×D12—31no—
168C2×C4×D3—61no—
169C2×Dic6—31no—
170C2×Dic6—62no—
171C2×C3×C8—22no—
172C2×C3×C8C22×D312yes—
173C3×C4⋊C4C22×D312yes—
174C3×C22⋊C4—21no—
175C3×C42—21no—
176#217—62no—
177#217—61no—
178(C2×D3)⋊C4—62no—
179C4⋊Dic3—32no—
180C4⋊Dic3—62no—
181Dic3⋊C4—62no—
182Dic3⋊C4—62no—
183Dic3⋊C4—62no—
184C4×Dic3—32no—
185C4×Dic3—31no—
186C4×Dic3—31no—
187C4×Dic3—61no—
188C2×C3⋊C8—32no—
189C2×C3⋊C8—62no—
190C22×C9—22no—
191C22×C9—41no—
192C22×C9—42no—
193C22×C9#12412yes—
194C22×C9C22×D411yescharacteristic
195C2×D9—41no—
196C2×D9—42no—
197C4×C9—41no—
198C4×C9—42no—
199C4×C9#12412yes—
200C4×C9C2×#4111yescharacteristic
201C4×C9C2×#4111yescharacteristic
202Dic9—22no—
203Dic9—41no—
204Dic9—42no—
205Dic9#13514yes—
206C2×#41—91no—
207C2×#41C2×D911yescharacteristic
208C22×C8—91no—
209C22×C8C2×D911yescharacteristic
210C4⋊Q8—92no—
211C4⋊Q8—91no—
212#127—91no—
213#125—92no—
214#124—91no—
215#124—91no—
216C22⋊Q8—182no—
217#121—182no—
218C4×Q8—182no—
219C4×D4—182no—
220#117—91no—
221#117C2×D911yescharacteristic
222C2×C42—91no—
223#103—92no—
224#103—92no—
225#103—92no—
226#103C2×D912yes—
227#102—92no—
228#102—92no—
229#102—92no—
230#102C2×D912yes—
231C4×C8—92no—
232C4×C8—92no—
233C23×C3—21no—
234C23×C3D3×D411yescharacteristic
235C22×D3—61no—
236C3×Q8—21no—
237C3×Q8—21no—
238C3×D4—21no—
239C3×D4—21no—
240C3×D4—42no—
241C2×C3×C4—22no—
242C2×C3×C4—21no—
243C2×C3×C4—42no—
244C2×C3×C4#23512yes—
245C2×C3×C4D3×D411yescharacteristic
246C2×C3×C4#23712yes—
247C2×C3×C4C23×D311yescharacteristic
248#67—124no—
249#67—122no—
250C2×Dic3—32no—
251C2×Dic3—32no—
252C2×Dic3—64no—
253C2×Dic3—62no—
254C2×Dic3—61no—
255D12—61no—
256D12—61no—
257C4×D3—122no—
258Dic6—61no—
259Dic6—61no—
260Dic6—124no—
261C3×C8—22no—
262C3⋊C8—62no—
263C2×C9—22no—
264C2×C9—81no—
265C2×C9C2×#12411yescharacteristic
266C2×C9C2×#13512yes—
267D9—81no—
268#41—22no—
269#41—22no—
270#41—182no—
271#41—182no—
272C2×Q8—91no—
273C2×Q8—182no—
274C2×Q8C22×D911yescharacteristic
275C2×D4—21no—
276C2×D4—91no—
277C2×D4—182no—
278C2×D4—181no—
279C2×D4C22×D911yescharacteristic
280C22×C4—21no—
281C22×C4—92no—
282C22×C4—181no—
283C22×C4C22×D911yescharacteristic
284C2×C8—22no—
285C2×C8—92no—
286C2×C8—182no—
287C2×C8C22×D912yes—
288C4⋊C4—92no—
289C4⋊C4—182no—
290C4⋊C4—182no—
291C4⋊C4—182no—
292C4⋊C4—182no—
293C4⋊C4C22×D912yes—
294C22⋊C4—21no—
295C22⋊C4—182no—
296C22⋊C4—182no—
297C22⋊C4—181no—
298C42—21no—
299C42—92no—
300C42—91no—
301C42—91no—
302C42—181no—
303C22×C3—22no—
304C22×C3—41no—
305C22×C3—42no—
306C22×C3#88512yes—
307C22×C3C2×D3×D411yescharacteristic
308C2×D3—121no—
309C2×D3—122no—
310C3×C4—41no—
311C3×C4—42no—
312C3×C4#88512yes—
313C3×C4C2×#23511yescharacteristic
314C3×C4C2×#23711yescharacteristic
315Dic3—34no—
316Dic3—62no—
317Dic3—121no—
318Dic3—122no—
319C9#313111yescharacteristic, complemented, Sylow
320C23—21no—
321C23—181no—
322C23D4×D911yescharacteristic
323Q8—21no—
324Q8—21no—
325Q8—181no—
326Q8—181no—
327Q8—364no—
328D4—21no—
329D4—21no—
330D4—42no—
331D4—181no—
332D4—181no—
333D4—364no—
334D4—362no—
335C2×C4—22no—
336C2×C4—21no—
337C2×C4—42no—
338C2×C4—92no—
339C2×C4—92no—
340C2×C4—184no—
341C2×C4—182no—
342C2×C4—181no—
343C2×C4—362no—
344C2×C4#369712yes—
345C2×C4D4×D911yescharacteristic
346C2×C4#369912yes—
347C2×C4C23×D911yescharacteristic
348C8—22no—
349C8—182no—
350C2×C3—22no—
351C2×C3—81no—
352C2×C3C2×#88511yescharacteristic
353C2×C3D3×#13512yes—
354D3—241no—
355C22—22no—
356C22—41no—
357C22—42no—
358C22—361no—
359C22—362no—
360C22#6344712yes—
361C22C2×D4×D911yescharacteristic
362C4—41no—
363C4—42no—
364C4—94no—
365C4—182no—
366C4—361no—
367C4—362no—
368C4#6344712yes—
369C4C2×#369711yescharacteristic
370C4C2×#369911yescharacteristic
371C3#7882511yescharacteristic
372C2—22no—
373C2—81no—
374C2—721no—
375C2C2×#6344711yescharacteristic
376C2D9×#13512yes—
subgroupG/H
centerC2×C4D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#416C2
socleC22×C3C2×D3×D4
prime radical#10589934C2
hypercenter#416D9
hypocenterC9#3131
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
2. #10589619C2semidirect
3. C9×#416C2semidirect
4. #10588917C2semidirect
5. #10588794C2semidirect
6. C2×C8×Dic9C2semidirect
7. #10588683C2semidirect
8. #10588480C2semidirect
9. #10588472C2semidirect
10. #10588448C2semidirect
11. #10588440C2semidirect
153. #416D9semidirect
319. C9#3131semidirect

Maximal subgroups

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

subgroupindex
#105899342
#105896192
C9×#4162
#105889172
#105887942
C2×C8×Dic92
#105886832
#105884802
#105884722
#105884482
#105884402
#788253