Finite Group Databasebeta

← #11869035

Subgroups — #11869035

Order 1152.

543 conjugacy classes of subgroups.

The subgroup lattice has 351 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#519C211yesmaximal, characteristic
2#10589621C211yesmaximal, characteristic
3#10588906C211yesmaximal, characteristic
4C2×#63395C211yesmaximal, characteristic
5#10588704C212yesmaximal, complemented
6#10588704C212yesmaximal, complemented
7#10588703C212yesmaximal, complemented
8#10588702C212yesmaximal, complemented
9#10588679C211yesmaximal, characteristic
10#10588677C211yesmaximal, characteristic
11#10588676C211yesmaximal, characteristic
12#82550—31nomaximal
13C22×Q8×C9C2211yescharacteristic
14C4×Q8×C9—21no—
15C4×Q8×C9—21no—
16C4×Q8×C9C2212yes—
17C4×Q8×C9C2212yes—
18C9×#117—22no—
19C9×#117C2211yescharacteristic
20C9×#117C2211yescharacteristic
21#63488C2211yescharacteristic
22C2×C4⋊Dic9C2211yescharacteristic
23C2×#3667C2211yescharacteristic
24C22×C9⋊C8C2211yescharacteristic
25#63452—21no—
26#63450—21no—
27#63440—22no—
28#63432C2212yes—
29#63431C2212yes—
30#63395C2212yes—
31#63395C2212yes—
32#63395C2212yes—
33#63395C2212yes—
34#63367C2211yescharacteristic
35#63367C2211yescharacteristic
36#63367C2212yes—
37#63366C2211yescharacteristic
38#63366C2211yescharacteristic
39#63366C2212yes—
40C4⋊(C9⋊C8)C2212yes—
41C4⋊(C9⋊C8)C2212yes—
42C3×#519D311yescharacteristic
43#5519—31no—
44#5225—31no—
45C2×#835—31no—
46#5022—32no—
47#5022—32no—
48#5021—32no—
49#5020—32no—
50#4999—31no—
51#4998—31no—
52#4995—31no—
53C2×Q8×C9—21no—
54C2×Q8×C9—22no—
55C2×Q8×C9Q814yescomplemented
56C2×Q8×C9C2312yes—
57C22×C4×C9—21no—
58C22×C4×C9C2311yescharacteristic
59C22×Dic9—21no—
60C2×Dic18—22no—
61C9×C4⋊C4—22no—
62C9×C4⋊C4—22no—
63C9×C4⋊C4D411yescharacteristic
64C9×C4⋊C4D411yescharacteristic
65C9×C4⋊C4C2311yescharacteristic
66C9×C4⋊C4C2311yescharacteristic
67C9×C22⋊C4—21no—
68C9×C22⋊C4D412yes—
69C42×C9—22no—
70C42×C9—22no—
71C42×C9—21no—
72C42×C9C2312yes—
73#3676—21no—
74C4⋊Dic9—22no—
75C4⋊Dic9—21no—
76C4⋊Dic9C2311yescharacteristic
77C4⋊Dic9C2311yescharacteristic
78C4⋊Dic9C2312yes—
79Dic9⋊C4—22no—
80Dic9⋊C4—22no—
81C4×Dic9—21no—
82#3667—22no—
83C2×C9⋊C8—22no—
84C2×C9⋊C8C2311yescharacteristic
85C2×C9⋊C8C2312yes—
86C2×C9⋊C8C2311yescharacteristic
87#3082—91noSylow
88C22×C3×Q8C2×D311yescharacteristic
89C3×C4×Q8—21no—
90C3×C4×Q8—21no—
91C3×C4×Q8C2×D312yes—
92C3×C4×Q8C2×D312yes—
93C3×#117—22no—
94C3×#117C2×D311yescharacteristic
95C3×#117C2×D311yescharacteristic
96#926—31no—
97C2×C4⋊Dic3—31no—
98C2×#208—31no—
99C22×C3⋊C8—31no—
100#890—61no—
101#888—61no—
102#878—62no—
103#870—32no—
104#869—32no—
105#835—32no—
106#835—32no—
107#835—32no—
108#835—32no—
109#808—32no—
110#808—31no—
111#808—31no—
112#807—32no—
113#807—31no—
114#807—31no—
115C4⋊(C3⋊C8)—32no—
116C4⋊(C3⋊C8)—32no—
117C23×C9C2×D411yescharacteristic
118Q8×C9—24no—
119Q8×C9—22no—
120Q8×C9C2×Q814yes—
121C2×C4×C9—24no—
122C2×C4×C9—22no—
123C2×C4×C9—21no—
124C2×C4×C9—21no—
125C2×C4×C9C2×D412yes—
126C2×C4×C9C2×D412yes—
127C2×C4×C9C2×D411yescharacteristic
128C2×C4×C9C2×Q812yes—
129C2×C4×C9#4112yes—
130C2×C4×C9C2411yescharacteristic
131C2×Dic9—21no—
132C2×Dic9—21no—
133C2×Dic9—22no—
134C2×Dic9—81no—
135Dic18—82no—
136C9⋊C8—21no—
137C9⋊C8—21no—
138C9⋊C8—22no—
139#544—91no—
140#519D911yescharacteristic
141#479—92no—
142#479—92no—
143#477—92no—
144#475—92no—
145#428—91no—
146#427—91no—
147#424—91no—
148#419—91no—
149C2×#103—91no—
150C2×C3×Q8—22no—
151C2×C3×Q8—21no—
152C2×C3×Q8Dic614yes—
153C2×C3×Q8C22×D312yes—
154C22×C3×C4—21no—
155C22×C3×C4C22×D311yescharacteristic
156C22×Dic3—61no—
157C2×Dic6—62no—
158C3×C4⋊C4—22no—
159C3×C4⋊C4—22no—
160C3×C4⋊C4#6711yescharacteristic
161C3×C4⋊C4#6711yescharacteristic
162C3×C4⋊C4C22×D311yescharacteristic
163C3×C4⋊C4C22×D311yescharacteristic
164C3×C22⋊C4—21no—
165C3×C22⋊C4#6712yes—
166C3×C42—22no—
167C3×C42—22no—
168C3×C42—21no—
169C3×C42C22×D312yes—
170#217—61no—
171C4⋊Dic3—31no—
172C4⋊Dic3—32no—
173C4⋊Dic3—31no—
174C4⋊Dic3—62no—
175C4⋊Dic3—61no—
176Dic3⋊C4—62no—
177Dic3⋊C4—62no—
178C4×Dic3—61no—
179#208—62no—
180C2×C3⋊C8—31no—
181C2×C3⋊C8—32no—
182C2×C3⋊C8—31no—
183C2×C3⋊C8—62no—
184C22×C9—21no—
185C22×C9—21no—
186C22×C9C22⋊Q812yes—
187C22×C9C22×D411yescharacteristic
188C4×C9—24no—
189C4×C9—22no—
190C4×C9—22no—
191C4×C9—41no—
192C4×C9—41no—
193C4×C9C22⋊Q812yes—
194C4×C9C22×Q811yescharacteristic
195C4×C9C2×#4111yescharacteristic
196Dic9—41no—
197Dic9—42no—
198Dic9—41no—
199C22×Q8C2×D911yescharacteristic
200C2×M16—91no—
201C22×C8—91no—
202C4⋊Q8—92no—
203C4⋊Q8—181no—
204#125—92no—
205#125—181no—
206C22⋊Q8—182no—
207C4×Q8—21no—
208C4×Q8—21no—
209C4×Q8C2×D912yes—
210C4×Q8C2×D912yes—
211#117—22no—
212#117—91no—
213#117C2×D911yescharacteristic
214#117C2×D911yescharacteristic
215C2×C4⋊C4—91no—
216#107—91no—
217#107—91no—
218#107—92no—
219#106—91no—
220#106—91no—
221#106—92no—
222C4⋊C8—92no—
223C4⋊C8—92no—
224#103—92no—
225#103—92no—
226#103—92no—
227#103—92no—
228C23×C3C2×#6711yescharacteristic
229C3×Q8—24no—
230C3×Q8—22no—
231C3×Q8C2×Dic614yes—
232C2×C3×C4—24no—
233C2×C3×C4—22no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4C2×Dic612yes—
237C2×C3×C4#23512yes—
238C2×C3×C4C2×#6712yes—
239C2×C3×C4C2×#6712yes—
240C2×C3×C4C2×#6711yescharacteristic
241C2×C3×C4C23×D311yescharacteristic
242C2×Dic3—61no—
243C2×Dic3—61no—
244C2×Dic3—62no—
245C2×Dic3—241no—
246Dic6—242no—
247C3⋊C8—61no—
248C3⋊C8—61no—
249C3⋊C8—62no—
250C2×C9—22no—
251C2×C9C2×C22⋊Q811yescharacteristic
252C2×C9#57711yescharacteristic
253C2×C9#57811yescharacteristic
254C2×Q8—22no—
255C2×Q8—21no—
256C2×Q8—182no—
257C2×Q8Dic1814yescomplemented
258C2×Q8C22×D912yes—
259C22×C4—21no—
260C22×C4—181no—
261C22×C4C22×D911yescharacteristic
262M16—182no—
263C2×C8—91no—
264C2×C8—92no—
265C2×C8—91no—
266C2×C8—182no—
267C4⋊C4—22no—
268C4⋊C4—22no—
269C4⋊C4—92no—
270C4⋊C4—91no—
271C4⋊C4—91no—
272C4⋊C4—181no—
273C4⋊C4—182no—
274C4⋊C4—182no—
275C4⋊C4—182no—
276C4⋊C4#61111yescharacteristic
277C4⋊C4#61111yescharacteristic
278C4⋊C4C22×D911yescharacteristic
279C4⋊C4C22×D911yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—181no—
282C22⋊C4#61112yes—
283C42—22no—
284C42—22no—
285C42—21no—
286C42—181no—
287C42C22×D912yes—
288C22×C3—21no—
289C22×C3—21no—
290C22×C3#92412yes—
291C22×C3C22×#6711yescharacteristic
292C3×C4—24no—
293C3×C4—22no—
294C3×C4—22no—
295C3×C4—41no—
296C3×C4—41no—
297C3×C4#92412yes—
298C3×C4C22×Dic611yescharacteristic
299C3×C4C2×#23511yescharacteristic
300Dic3—121no—
301Dic3—122no—
302Dic3—121no—
303C9#308211yescharacteristic, complemented, Sylow
304C23C2×#61111yescharacteristic
305Q8—22no—
306Q8—24no—
307Q8—722no—
308Q8C2×Dic1814yes—
309C2×C4—22no—
310C2×C4—24no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—181no—
314C2×C4—181no—
315C2×C4—182no—
316C2×C4—721no—
317C2×C4C2×Dic1812yes—
318C2×C4#369712yes—
319C2×C4C2×#61112yes—
320C2×C4C2×#61112yes—
321C2×C4C2×#61111yescharacteristic
322C2×C4C23×D911yescharacteristic
323C8—181no—
324C8—181no—
325C8—182no—
326C2×C3—22no—
327C2×C3C2×#92411yescharacteristic
328C2×C3#583711yescharacteristic
329C2×C3#583811yescharacteristic
330C22—21no—
331C22—21no—
332C22#6348612yes—
333C22C22×#61111yescharacteristic
334C4—24no—
335C4—22no—
336C4—22no—
337C4—41no—
338C4—41no—
339C4—362no—
340C4—361no—
341C4—361no—
342C4#6348612yes—
343C4C22×Dic1811yescharacteristic
344C4C2×#369711yescharacteristic
345C3#8255011yescharacteristic
346C2—22no—
347C2C2×#6348611yescharacteristic
348C2#1058993911yescharacteristic
349C2#1058994011yescharacteristic
subgroupG/H
centerC22C22×#611
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#519C2
socleC22×C3C22×#67
prime radicalC23×C3C2×#67
hypercenter#519D9
hypocenterC9#3082
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ #117 ◁ #519

Complements

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

NH ≅ G/Ntype
5. #10588704C2semidirect
6. #10588704C2semidirect
7. #10588703C2semidirect
8. #10588702C2semidirect
55. C2×Q8×C9Q8semidirect
257. C2×Q8Dic18semidirect
303. C9#3082semidirect

Maximal subgroups

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

subgroupindex
C9×#5192
#105896212
#105889062
C2×#633952
#105887042
#105887032
#105887022
#105886792
#105886772
#105886762
#825503