Finite Group Databasebeta

← #11895507

Subgroups — #11895507

Order 1152.

504 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#556C211yesmaximal, characteristic
2#10589669C211yesmaximal, characteristic, complemented
3#10588763C211yesmaximal, characteristic, complemented
4#10588759C211yesmaximal, characteristic, complemented
5#10588736C212yesmaximal
6#10588735C212yesmaximal
7C4×#3674C212yesmaximal, complemented
8#10588704C212yesmaximal, complemented
9Q8×C9⋊C8C211yesmaximal, characteristic, complemented
10C4×#3672C211yesmaximal, characteristic
11#10588690C211yesmaximal, characteristic
12#83676—31nomaximal
13C9×C4⋊Q8C2211yescharacteristic
14C9×#126—22no—
15C9×#124C2212yes—
16C9×C22⋊Q8—21no—
17C4×Q8×C9C2212yes—
18C4×Q8×C9C2211yescharacteristic
19C4×D4×C9C2211yescharacteristic
20C9×#117—21no—
21#63506—21no—
22C2×#3674C2212yes—
23C2×#3672C2211yescharacteristic
24#63451—22no—
25#63449—21no—
26#63432C2212yes—
27#63431C2211yescharacteristic
28C4×Dic18C2211yescharacteristic
29C4×Dic18C2212yes—
30#63395C2212yes—
31#63395C2212yes—
32#63395C2212yes—
33#63392C2212yes—
34#63392C2211yescharacteristic
35#63368C2211yescharacteristic
36#63367C2211yescharacteristic
37#63366C2212yes—
38C4⋊(C9⋊C8)C2211yescharacteristic
39C4⋊(C9⋊C8)C2212yes—
40C4×C9⋊C8C2211yescharacteristic
41C4×C9⋊C8C2212yes—
42C3×#556D311yescharacteristic
43#5567—31no—
44#5090—31no—
45#5079—31no—
46#5056—32no—
47#5054—32no—
48C4×#216—32no—
49Q8×C3⋊C8—31no—
50#5022—32no—
51C4×#214—31no—
52#5007—31no—
53C2×Q8×C9D411yescharacteristic
54C2×Q8×C9C2312yes—
55C2×D4×C9C2311yescharacteristic
56C22×C4×C9—21no—
57C2×Dic18—21no—
58C2×Dic18C2311yescharacteristic
59C9×C4⋊C4—21no—
60C9×C4⋊C4—22no—
61C9×C4⋊C4—21no—
62C9×C4⋊C4D411yescharacteristic
63C9×C4⋊C4D412yes—
64C9×C4⋊C4C2311yescharacteristic
65C9×C22⋊C4—22no—
66C9×C22⋊C4—21no—
67C9×C22⋊C4—22no—
68C42×C9—22no—
69C42×C9C2311yescharacteristic
70C42×C9C2312yes—
71#3674—24no—
72#3672—22no—
73C4⋊Dic9—21no—
74C4⋊Dic9C2312yes—
75C4⋊Dic9C2311yescharacteristic
76Dic9⋊C4—22no—
77Dic9⋊C4—22no—
78Dic9⋊C4—21no—
79Dic9⋊C4—22no—
80C4×Dic9—21no—
81C4×Dic9—22no—
82C2×C9⋊C8C2311yescharacteristic
83C2×C9⋊C8C2312yes—
84C2×C9⋊C8C2311yescharacteristic
85#3364—91noSylow
86C3×C4⋊Q8C2×D311yescharacteristic
87C3×#126—22no—
88C3×#124C2×D312yes—
89C3×C22⋊Q8—21no—
90C3×C4×Q8C2×D312yes—
91C3×C4×Q8C2×D311yescharacteristic
92C3×C4×D4C2×D311yescharacteristic
93C3×#117—21no—
94#944—61no—
95C2×#216—32no—
96C2×#214—31no—
97#889—62no—
98#887—61no—
99#870—32no—
100#869—31no—
101C4×Dic6—31no—
102C4×Dic6—32no—
103#835—32no—
104#835—32no—
105#835—32no—
106#832—32no—
107#832—31no—
108#810—31no—
109#808—31no—
110#807—32no—
111C4⋊(C3⋊C8)—31no—
112C4⋊(C3⋊C8)—32no—
113C4×C3⋊C8—31no—
114C4×C3⋊C8—32no—
115C23×C9—21no—
116Q8×C9—22no—
117Q8×C9—22no—
118Q8×C9—22no—
119D4×C9—21no—
120D4×C9—21no—
121C2×C4×C9—21no—
122C2×C4×C9—22no—
123C2×C4×C9—42no—
124C2×C4×C9C2×D412yes—
125C2×C4×C9C2×D412yes—
126C2×C4×C9C2×D411yescharacteristic
127C2×C4×C9C2×D411yescharacteristic
128C2×C4×C9C2411yescharacteristic
129C2×Dic9—21no—
130C2×Dic9—21no—
131C2×Dic9—22no—
132Dic18—21no—
133Dic18—42no—
134Dic18#4112yes—
135C9⋊C8—21no—
136C9⋊C8—22no—
137C9⋊C8—21no—
138#557—91no—
139#556D911yescharacteristic
140#488—92no—
141#487—91no—
142#479—92no—
143#474—91no—
144#464—92no—
145#462—91no—
146C8×Q8—91no—
147C4×Q16—92no—
148C4×SD16—91no—
149C2×C3×Q8#6711yescharacteristic
150C2×C3×Q8C22×D312yes—
151C2×C3×D4C22×D311yescharacteristic
152C22×C3×C4—21no—
153C2×Dic6—31no—
154C2×Dic6—61no—
155C3×C4⋊C4—21no—
156C3×C4⋊C4—22no—
157C3×C4⋊C4—21no—
158C3×C4⋊C4#6711yescharacteristic
159C3×C4⋊C4#6712yes—
160C3×C4⋊C4C22×D311yescharacteristic
161C3×C22⋊C4—22no—
162C3×C22⋊C4—21no—
163C3×C22⋊C4—22no—
164C3×C42—22no—
165C3×C42C22×D311yescharacteristic
166C3×C42C22×D312yes—
167#216—64no—
168#214—62no—
169C4⋊Dic3—32no—
170C4⋊Dic3—31no—
171C4⋊Dic3—61no—
172Dic3⋊C4—61no—
173Dic3⋊C4—62no—
174Dic3⋊C4—62no—
175Dic3⋊C4—62no—
176C4×Dic3—62no—
177C4×Dic3—61no—
178C2×C3⋊C8—31no—
179C2×C3⋊C8—32no—
180C2×C3⋊C8—31no—
181C22×C9—41no—
182C22×C9—41no—
183C22×C9—41no—
184C22×C9C22×D411yescharacteristic
185C4×C9—22no—
186C4×C9—22no—
187C4×C9—21no—
188C4×C9—42no—
189C4×C9—41no—
190C4×C9#13512yes—
191C4×C9C2×#4111yescharacteristic
192C4×C92−1+411yescharacteristic
193Dic9—22no—
194Dic9—42no—
195Dic9—41no—
196C2×Q16—92no—
197C2×SD16—91no—
198C4⋊Q8—91no—
199C4⋊Q8—181no—
200C4⋊Q8C2×D911yescharacteristic
201#126—22no—
202#125—92no—
203#125—182no—
204#124C2×D912yes—
205C22⋊Q8—21no—
206C4×Q8—91no—
207C4×Q8—92no—
208C4×Q8—181no—
209C4×Q8C2×D912yes—
210C4×Q8C2×D911yescharacteristic
211C4×D4C2×D911yescharacteristic
212#117—21no—
213#107—92no—
214#106—91no—
215C4⋊C8—91no—
216C4⋊C8—92no—
217#103—92no—
218#103—92no—
219#103—92no—
220#103—91no—
221#102—91no—
222#102—92no—
223C4×C8—91no—
224C4×C8—92no—
225C23×C3—21no—
226C3×Q8—22no—
227C3×Q8—22no—
228C3×Q8—22no—
229C3×D4—21no—
230C3×D4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—22no—
233C2×C3×C4—42no—
234C2×C3×C4C2×#6712yes—
235C2×C3×C4C2×#6712yes—
236C2×C3×C4C2×#6711yescharacteristic
237C2×C3×C4C2×#6711yescharacteristic
238C2×C3×C4C23×D311yescharacteristic
239C2×Dic3—61no—
240C2×Dic3—61no—
241C2×Dic3—62no—
242Dic6—32no—
243Dic6—61no—
244Dic6—122no—
245C3⋊C8—61no—
246C3⋊C8—62no—
247C3⋊C8—61no—
248C2×C9—81no—
249C2×C9#54811yescharacteristic
250C2×C9C2×#13511yescharacteristic
251C2×C9#57811yescharacteristic
252C2×Q8—91no—
253C2×Q8—181no—
254C2×Q8#61111yescharacteristic
255C2×Q8C22×D912yes—
256C2×D4C22×D911yescharacteristic
257C22×C4—21no—
258Q16—184no—
259SD16—182no—
260C2×C8—91no—
261C2×C8—92no—
262C2×C8—91no—
263C4⋊C4—21no—
264C4⋊C4—22no—
265C4⋊C4—21no—
266C4⋊C4—91no—
267C4⋊C4—92no—
268C4⋊C4—181no—
269C4⋊C4—182no—
270C4⋊C4—182no—
271C4⋊C4—182no—
272C4⋊C4—181no—
273C4⋊C4#61111yescharacteristic
274C4⋊C4#61112yes—
275C4⋊C4C22×D911yescharacteristic
276C22⋊C4—22no—
277C22⋊C4—21no—
278C22⋊C4—22no—
279C42—22no—
280C42—182no—
281C42—181no—
282C42C22×D911yescharacteristic
283C42C22×D912yes—
284C22×C3—41no—
285C22×C3—41no—
286C22×C3—41no—
287C22×C3C22×#6711yescharacteristic
288C3×C4—22no—
289C3×C4—22no—
290C3×C4—21no—
291C3×C4—41no—
292C3×C4—42no—
293C3×C4#95012yes—
294C3×C4D3×#4111yescharacteristic
295C3×C4#101011yescharacteristic
296Dic3—62no—
297Dic3—122no—
298Dic3—121no—
299C9#336411yescharacteristic, complemented, Sylow
300C23—21no—
301Q8—22no—
302Q8—22no—
303Q8—22no—
304Q8—92no—
305Q8—181no—
306Q8—362no—
307D4—21no—
308D4—21no—
309C2×C4—21no—
310C2×C4—22no—
311C2×C4—42no—
312C2×C4—181no—
313C2×C4—181no—
314C2×C4—182no—
315C2×C4C2×#61112yes—
316C2×C4C2×#61111yescharacteristic
317C2×C4C2×#61112yes—
318C2×C4C2×#61111yescharacteristic
319C2×C4C23×D911yescharacteristic
320C8—181no—
321C8—182no—
322C8—181no—
323C2×C3—81no—
324C2×C3C2×#95011yescharacteristic
325C2×C3#583111yescharacteristic
326C2×C3#583811yescharacteristic
327C22—41no—
328C22—41no—
329C22—41no—
330C22C22×#61111yescharacteristic
331C4—22no—
332C4—22no—
333C4—21no—
334C4—41no—
335C4—42no—
336C4—182no—
337C4—362no—
338C4—361no—
339C4#6351312yes—
340C4#41×D911yescharacteristic
341C4#6371611yescharacteristic
342C3#8367611yescharacteristic
343C2—81no—
344C2C2×#6351311yescharacteristic
345C2#1058993311yescharacteristic
346C2#1058994011yescharacteristic
subgroupG/H
centerC22C22×#611
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#556C2
socleC22×C3C22×#67
prime radicalC2×C3×D4C22×D3
hypercenter#556D9
hypocenterC9#3364
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #556

Complements

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

NH ≅ G/Ntype
2. #10589669C2semidirect
3. #10588763C2semidirect
4. #10588759C2semidirect
7. C4×#3674C2semidirect
8. #10588704C2semidirect
9. Q8×C9⋊C8C2semidirect
299. C9#3364semidirect

Maximal subgroups

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

subgroupindex
C9×#5562
#105896692
#105887632
#105887592
#105887362
#105887352
C4×#36742
#105887042
Q8×C9⋊C82
C4×#36722
#105886902
#836763