Finite Group Databasebeta

← #11888016

Subgroups — #11888016

Order 1152.

579 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
1C9×#547C211yesmaximal, characteristic
2#10589644C211yesmaximal, characteristic, complemented
3#10588918C212yesmaximal, complemented
4#10588917C212yesmaximal, complemented
5#10588763C211yesmaximal, characteristic, complemented
6#10588759C211yesmaximal, characteristic, complemented
7#10588727C212yesmaximal, complemented
8#10588725C212yesmaximal, complemented
9C4×#3672C211yesmaximal, characteristic, complemented
10#10588690C211yesmaximal, characteristic, complemented
11D4×C9⋊C8C211yesmaximal, characteristic, complemented
12#83510—31nomaximal
13C2×C9×#41C2212yes—
14C9×C4⋊Q8C2211yescharacteristic
15C9×#123—22no—
16C9×C22⋊Q8C2212yes—
17C9×#121—21no—
18C4×D4×C9C2211yescharacteristic
19C4×D4×C9C2211yescharacteristic
20C2×C9×C4⋊C4—21no—
21C2×#3674C2212yes—
22#63498—21no—
23C2×#3672C2211yescharacteristic
24#63488C2212yes—
25#63486C2212yes—
26C22×C9⋊C8C2212yes—
27#63449—21no—
28#63441—22no—
29#63431C2211yescharacteristic
30C4×Dic18C2211yescharacteristic
31#63395C2212yes—
32#63395C2212yes—
33#63395C2212yes—
34#63392C2212yes—
35#63392C2211yescharacteristic
36#63389C2212yes—
37#63368C2211yescharacteristic
38#63367C2211yescharacteristic
39#63366C2212yes—
40C4⋊(C9⋊C8)C2211yescharacteristic
41C4×C9⋊C8C2211yescharacteristic
42C3×#547D311yescharacteristic
43#5542—31no—
44#5239—32no—
45#5233—32no—
46#5090—31no—
47#5079—31no—
48#5051—32no—
49#5045—32no—
50C4×#214—31no—
51D4×C3⋊C8—31no—
52#5007—31no—
53C9×#41—24no—
54C9×#41—42no—
55C2×Q8×C9C2312yes—
56C2×D4×C9—22no—
57C2×D4×C9D411yescharacteristic
58C2×D4×C9C2311yescharacteristic
59C22×C4×C9—21no—
60C22×C4×C9—22no—
61C22×C4×C9C2312yes—
62C2×Dic18—21no—
63C2×Dic18C2311yescharacteristic
64C9×C4⋊C4—21no—
65C9×C4⋊C4—22no—
66C9×C4⋊C4—21no—
67C9×C4⋊C4D411yescharacteristic
68C9×C4⋊C4C2311yescharacteristic
69C9×C22⋊C4—22no—
70C9×C22⋊C4—21no—
71C9×C22⋊C4D412yes—
72C42×C9C2311yescharacteristic
73#3676—22no—
74#3676—22no—
75#3674—42no—
76#3672—22no—
77C4⋊Dic9—21no—
78C4⋊Dic9C2311yescharacteristic
79C4⋊Dic9C2312yes—
80Dic9⋊C4—21no—
81Dic9⋊C4—22no—
82C4×Dic9—22no—
83C4×Dic9—21no—
84C2×C9⋊C8—42no—
85C2×C9⋊C8C2311yescharacteristic
86C2×C9⋊C8C2312yes—
87C2×C9⋊C8C2311yescharacteristic
88#3302—91noSylow
89C2×C3×#41C2×D312yes—
90C3×C4⋊Q8C2×D311yescharacteristic
91C3×#123—22no—
92C3×C22⋊Q8C2×D312yes—
93C3×#121—21no—
94C3×C4×D4C2×D311yescharacteristic
95C3×C4×D4C2×D311yescharacteristic
96C2×C3×C4⋊C4—21no—
97C2×#216—32no—
98#936—61no—
99C2×#214—31no—
100#926—32no—
101#924—32no—
102C22×C3⋊C8—32no—
103#887—61no—
104#879—62no—
105#869—31no—
106C4×Dic6—31no—
107#835—32no—
108#835—32no—
109#835—32no—
110#832—31no—
111#832—32no—
112#830—32no—
113#810—31no—
114#808—31no—
115#807—32no—
116C4⋊(C3⋊C8)—31no—
117C4×C3⋊C8—31no—
118C23×C9—21no—
119C23×C9C2×D412yes—
120Q8×C9—22no—
121Q8×C9—22no—
122D4×C9—22no—
123D4×C9—21no—
124D4×C9—44no—
125D4×C9#4112yes—
126C2×C4×C9—22no—
127C2×C4×C9—22no—
128C2×C4×C9—21no—
129C2×C4×C9—22no—
130C2×C4×C9—44no—
131C2×C4×C9—42no—
132C2×C4×C9C2×D412yes—
133C2×C4×C9C2×D411yescharacteristic
134C2×C4×C9C2×D411yescharacteristic
135C2×C4×C9C2411yescharacteristic
136C2×Dic9—21no—
137C2×Dic9—21no—
138C2×Dic9—22no—
139Dic18—21no—
140Dic18—21no—
141Dic18—42no—
142C9⋊C8—21no—
143C9⋊C8—21no—
144C9⋊C8—22no—
145#556—91no—
146#547D911yescharacteristic
147#487—91no—
148#485—92no—
149#474—91no—
150#467—92no—
151#462—91no—
152#452—92no—
153C4×SD16—91no—
154C8×D4—91no—
155#416—92no—
156C3×#41—24no—
157C3×#41—42no—
158C2×C3×Q8C22×D312yes—
159C2×C3×D4—22no—
160C2×C3×D4#6711yescharacteristic
161C2×C3×D4C22×D311yescharacteristic
162C22×C3×C4—21no—
163C22×C3×C4—22no—
164C22×C3×C4C22×D312yes—
165C2×Dic6—31no—
166C2×Dic6—61no—
167C3×C4⋊C4—21no—
168C3×C4⋊C4—22no—
169C3×C4⋊C4—21no—
170C3×C4⋊C4#6711yescharacteristic
171C3×C4⋊C4C22×D311yescharacteristic
172C3×C22⋊C4—22no—
173C3×C22⋊C4—21no—
174C3×C22⋊C4#6712yes—
175C3×C42C22×D311yescharacteristic
176#217—62no—
177#217—62no—
178#216—122no—
179#214—62no—
180C4⋊Dic3—32no—
181C4⋊Dic3—31no—
182C4⋊Dic3—61no—
183Dic3⋊C4—61no—
184Dic3⋊C4—62no—
185C4×Dic3—61no—
186C4×Dic3—62no—
187C2×C3⋊C8—31no—
188C2×C3⋊C8—31no—
189C2×C3⋊C8—32no—
190C2×C3⋊C8—122no—
191C22×C9—22no—
192C22×C9—22no—
193C22×C9—22no—
194C22×C9—22no—
195C22×C9—41no—
196C22×C9—41no—
197C22×C9C22×D411yescharacteristic
198C4×C9—22no—
199C4×C9—21no—
200C4×C9—42no—
201C4×C9—41no—
202C4×C9#13512yes—
203C4×C9C2×#4111yescharacteristic
204C4×C9H(5,𝔽2)11yescharacteristic
205Dic9—41no—
206Dic9—42no—
207Dic9—41no—
208C2×#41C2×D912yes—
209C2×Q16—92no—
210C2×SD16—91no—
211C22×C8—92no—
212C4⋊Q8—91no—
213C4⋊Q8C2×D911yescharacteristic
214#126—182no—
215#124—181no—
216#123—22no—
217C22⋊Q8—92no—
218C22⋊Q8C2×D912yes—
219#121—21no—
220C4×Q8—91no—
221C4×Q8—181no—
222C4×D4C2×D911yescharacteristic
223C4×D4C2×D911yescharacteristic
224#117—92no—
225C2×C4⋊C4—21no—
226#107—92no—
227#106—91no—
228C4⋊C8—91no—
229#103—92no—
230#103—92no—
231#103—92no—
232#103—91no—
233#102—91no—
234#102—92no—
235C22⋊C8—92no—
236C4×C8—91no—
237C23×C3—21no—
238C23×C3C2×#6712yes—
239C3×Q8—22no—
240C3×Q8—22no—
241C3×D4—22no—
242C3×D4—21no—
243C3×D4—44no—
244C3×D4#23712yes—
245C2×C3×C4—22no—
246C2×C3×C4—22no—
247C2×C3×C4—21no—
248C2×C3×C4—22no—
249C2×C3×C4—44no—
250C2×C3×C4—42no—
251C2×C3×C4C2×#6712yes—
252C2×C3×C4C2×#6711yescharacteristic
253C2×C3×C4C2×#6711yescharacteristic
254C2×C3×C4C23×D311yescharacteristic
255C2×Dic3—61no—
256C2×Dic3—61no—
257C2×Dic3—62no—
258Dic6—61no—
259Dic6—61no—
260Dic6—122no—
261C3⋊C8—61no—
262C3⋊C8—61no—
263C3⋊C8—62no—
264C2×C9—42no—
265C2×C9—42no—
266C2×C9#54611yescharacteristic
267C2×C9C2×#13511yescharacteristic
268C2×C9#57811yescharacteristic
269#41—24no—
270#41—42no—
271C2×Q8—91no—
272C2×Q8—181no—
273C2×Q8C22×D912yes—
274C2×D4—22no—
275C2×D4#61111yescharacteristic
276C2×D4C22×D911yescharacteristic
277C22×C4—21no—
278C22×C4—22no—
279C22×C4C22×D912yes—
280Q16—362no—
281SD16—182no—
282C2×C8—91no—
283C2×C8—91no—
284C2×C8—92no—
285C2×C8—362no—
286C4⋊C4—21no—
287C4⋊C4—22no—
288C4⋊C4—21no—
289C4⋊C4—91no—
290C4⋊C4—92no—
291C4⋊C4—181no—
292C4⋊C4—182no—
293C4⋊C4—181no—
294C4⋊C4#61111yescharacteristic
295C4⋊C4C22×D911yescharacteristic
296C22⋊C4—22no—
297C22⋊C4—21no—
298C22⋊C4—182no—
299C22⋊C4—182no—
300C22⋊C4#61112yes—
301C42—182no—
302C42—181no—
303C42C22×D911yescharacteristic
304C22×C3—22no—
305C22×C3—22no—
306C22×C3—22no—
307C22×C3—22no—
308C22×C3—41no—
309C22×C3—41no—
310C22×C3C22×#6711yescharacteristic
311C3×C4—22no—
312C3×C4—21no—
313C3×C4—42no—
314C3×C4—41no—
315C3×C4#95012yes—
316C3×C4C2×#23711yescharacteristic
317C3×C4#100411yescharacteristic
318Dic3—121no—
319Dic3—122no—
320Dic3—121no—
321C9#330211yescharacteristic, complemented, Sylow
322C23—21no—
323C23C2×#61112yes—
324Q8—22no—
325Q8—22no—
326Q8—181no—
327Q8—181no—
328Q8—362no—
329D4—22no—
330D4—21no—
331D4—44no—
332D4#369912yes—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—21no—
336C2×C4—22no—
337C2×C4—44no—
338C2×C4—42no—
339C2×C4—181no—
340C2×C4—182no—
341C2×C4—181no—
342C2×C4C2×#61112yes—
343C2×C4C2×#61111yescharacteristic
344C2×C4C2×#61111yescharacteristic
345C2×C4C23×D911yescharacteristic
346C8—181no—
347C8—181no—
348C8—182no—
349C2×C3—42no—
350C2×C3—42no—
351C2×C3#580611yescharacteristic
352C2×C3C2×#95011yescharacteristic
353C2×C3#583811yescharacteristic
354C22—22no—
355C22—22no—
356C22—22no—
357C22—22no—
358C22—41no—
359C22—41no—
360C22C22×#61111yescharacteristic
361C4—22no—
362C4—21no—
363C4—42no—
364C4—41no—
365C4—361no—
366C4—362no—
367C4—361no—
368C4#6351312yes—
369C4C2×#369911yescharacteristic
370C4#6371011yescharacteristic
371C3#8351011yescharacteristic
372C2—42no—
373C2—42no—
374C2#1058990811yescharacteristic
375C2C2×#6351311yescharacteristic
376C2#1058994011yescharacteristic
subgroupG/H
centerC22C22×#611
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#547C2
socleC22×C3C22×#67
prime radicalC3×#547D3
hypercenter#547D9
hypocenterC9#3302
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
2. #10589644C2semidirect
3. #10588918C2semidirect
4. #10588917C2semidirect
5. #10588763C2semidirect
6. #10588759C2semidirect
7. #10588727C2semidirect
8. #10588725C2semidirect
9. C4×#3672C2semidirect
10. #10588690C2semidirect
11. D4×C9⋊C8C2semidirect
321. C9#3302semidirect

Maximal subgroups

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

subgroupindex
C9×#5472
#105896442
#105889182
#105889172
#105887632
#105887592
#105887272
#105887252
C4×#36722
#105886902
D4×C9⋊C82
#835103