Finite Group Databasebeta

← #11869029

Subgroups — #11869029

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
1#10589618C211yesmaximal, characteristic
2#10589602C211yesmaximal, characteristic
3C9×#428C211yesmaximal, characteristic
4#10588804C211yesmaximal, characteristic
5#10588803C211yesmaximal, characteristic
6#10588676C211yesmaximal, characteristic
7C2×#63368C211yesmaximal, characteristic
8#10588557C212yesmaximal, complemented
9#10588555C212yesmaximal, complemented
10#10588537C212yesmaximal, complemented
11#10588534C212yesmaximal, complemented
12#79246—31nomaximal
13C22×Dic18C2211yescharacteristic
14C2×C9×M16C2211yescharacteristic
15C9×#117C2211yescharacteristic
16C2×C9×C4⋊C4C2211yescharacteristic
17#63488C2211yescharacteristic
18#63488C2211yescharacteristic
19#63486—22no—
20C22×C9⋊C8C2211yescharacteristic
21#63452—21no—
22#63452C2212yes—
23#63450—21no—
24#63450C2212yes—
25#63449C2212yes—
26#63449C2212yes—
27#63439—22no—
28C4×Dic18—21no—
29C4×Dic18—21no—
30C9×#107C2212yes—
31C9×#106C2212yes—
32#63376C2212yes—
33#63376C2212yes—
34Dic9⋊C8C2212yes—
35Dic9⋊C8C2212yes—
36#63368C2212yes—
37#63368C2212yes—
38#63367C2211yescharacteristic
39#63367C2211yescharacteristic
40#63366C2211yescharacteristic
41#63366C2211yescharacteristic
42#5516—31no—
43#5500—31no—
44C3×#428D311yescharacteristic
45#5120—31no—
46#5119—31no—
47#4998—31no—
48C2×#810—31no—
49#4877—32no—
50#4875—32no—
51#4857—32no—
52#4854—32no—
53C22×C4×C9—21no—
54C22×C4×C9C2311yescharacteristic
55C22×Dic9—21no—
56C2×Dic18—21no—
57C2×Dic18—22no—
58C2×Dic18—22no—
59C2×Dic18Q814yescomplemented
60C2×Dic18C2312yes—
61C9×M16—22no—
62C2×C8×C9C2312yes—
63C9×C4⋊C4—21no—
64C9×C4⋊C4C2312yes—
65C9×C4⋊C4C2311yescharacteristic
66C9×C4⋊C4C2311yescharacteristic
67C9×C22⋊C4—21no—
68C42×C9—21no—
69#3676—21no—
70#3676D412yes—
71C4⋊Dic9—22no—
72C4⋊Dic9D411yescharacteristic
73C4⋊Dic9D411yescharacteristic
74C4⋊Dic9C2311yescharacteristic
75C4⋊Dic9C2311yescharacteristic
76Dic9⋊C4—22no—
77Dic9⋊C4—22no—
78Dic9⋊C4—22no—
79Dic9⋊C4—22no—
80C4×Dic9—21no—
81C4×Dic9—22no—
82C4×Dic9—22no—
83C4×Dic9C2312yes—
84C2×C9⋊C8—22no—
85C2×C9⋊C8C2311yescharacteristic
86C2×C9⋊C8C2311yescharacteristic
87#3082—91noSylow
88C22×Dic6—31no—
89C2×C3×M16C2×D311yescharacteristic
90C3×#117C2×D311yescharacteristic
91C2×C3×C4⋊C4C2×D311yescharacteristic
92#926—31no—
93#926—31no—
94#924—62no—
95C22×C3⋊C8—31no—
96#890—32no—
97#890—61no—
98#888—32no—
99#888—61no—
100#887—32no—
101#887—32no—
102#877—62no—
103C4×Dic6—61no—
104C4×Dic6—61no—
105C3×#107C2×D312yes—
106C3×#106C2×D312yes—
107#816—32no—
108#816—32no—
109Dic3⋊C8—32no—
110Dic3⋊C8—32no—
111#810—32no—
112#810—32no—
113#808—31no—
114#808—31no—
115#807—31no—
116#807—31no—
117C23×C9C2×D411yescharacteristic
118C2×C4×C9—21no—
119C2×C4×C9—21no—
120C2×C4×C9—22no—
121C2×C4×C9—81no—
122C2×C4×C9C2×D411yescharacteristic
123C2×C4×C9C2×Q812yes—
124C2×C4×C9#4112yes—
125C2×C4×C9C2411yescharacteristic
126C2×Dic9—24no—
127C2×Dic9—22no—
128C2×Dic9—21no—
129C2×Dic9—21no—
130C2×Dic9C2×D412yes—
131C2×Dic9C2×D412yes—
132Dic18—24no—
133Dic18—22no—
134Dic18—82no—
135Dic18C2×Q814yes—
136C8×C9—22no—
137C9⋊C8—21no—
138C9⋊C8—21no—
139#544—91no—
140#519—91no—
141#479—92no—
142#479—92no—
143#477—92no—
144#475—92no—
145#428D911yescharacteristic
146#427—91no—
147#424—91no—
148#419—91no—
149C2×#103—91no—
150C22×C3×C4—21no—
151C22×C3×C4C22×D311yescharacteristic
152C22×Dic3—61no—
153C2×Dic6—34no—
154C2×Dic6—32no—
155C2×Dic6—62no—
156C2×Dic6—61no—
157C2×Dic6—62no—
158C3×M16—22no—
159C2×C3×C8C22×D312yes—
160C3×C4⋊C4—21no—
161C3×C4⋊C4C22×D311yescharacteristic
162C3×C4⋊C4C22×D311yescharacteristic
163C3×C4⋊C4C22×D312yes—
164C3×C22⋊C4—21no—
165C3×C42—21no—
166#217—32no—
167#217—61no—
168C4⋊Dic3—31no—
169C4⋊Dic3—31no—
170C4⋊Dic3—31no—
171C4⋊Dic3—31no—
172C4⋊Dic3—62no—
173Dic3⋊C4—62no—
174Dic3⋊C4—62no—
175Dic3⋊C4—62no—
176Dic3⋊C4—62no—
177C4×Dic3—32no—
178C4×Dic3—62no—
179C4×Dic3—62no—
180C4×Dic3—61no—
181C2×C3⋊C8—31no—
182C2×C3⋊C8—31no—
183C2×C3⋊C8—62no—
184C22×C9—21no—
185C22×C9—21no—
186C22×C9C22⋊Q812yes—
187C22×C9C22×D411yescharacteristic
188C4×C9—42no—
189C4×C9—41no—
190C4×C9—41no—
191C4×C9C22⋊Q812yes—
192C4×C9C22×Q811yescharacteristic
193C4×C9C2×#4111yescharacteristic
194Dic9—24no—
195Dic9—22no—
196Dic9—22no—
197Dic9—41no—
198Dic9—41no—
199C22×Q8—91no—
200C2×M16C2×D911yescharacteristic
201C22×C8—91no—
202C4⋊Q8—92no—
203C4⋊Q8—181no—
204#125—92no—
205#125—181no—
206C22⋊Q8—182no—
207C4×Q8—92no—
208C4×Q8—92no—
209C4×Q8—181no—
210C4×Q8—181no—
211#117—91no—
212#117—91no—
213#117—182no—
214#117C2×D911yescharacteristic
215C2×C4⋊C4C2×D911yescharacteristic
216#107—91no—
217#107—91no—
218#107C2×D912yes—
219#106—91no—
220#106—91no—
221#106C2×D912yes—
222C4⋊C8—92no—
223C4⋊C8—92no—
224#103—92no—
225#103—92no—
226#103—92no—
227#103—92no—
228C23×C3D3×D411yescharacteristic
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—22no—
232C2×C3×C4—81no—
233C2×C3×C4#23512yes—
234C2×C3×C4D3×D411yescharacteristic
235C2×C3×C4D3×Q812yes—
236C2×C3×C4C23×D311yescharacteristic
237C2×Dic3—32no—
238C2×Dic3—32no—
239C2×Dic3—64no—
240C2×Dic3—62no—
241C2×Dic3—61no—
242C2×Dic3—61no—
243Dic6—34no—
244Dic6—64no—
245Dic6—62no—
246Dic6—242no—
247C3×C8—22no—
248C3⋊C8—61no—
249C3⋊C8—61no—
250C2×C9—22no—
251C2×C9C2×C22⋊Q811yescharacteristic
252C2×C9#57711yescharacteristic
253C2×C9#57811yescharacteristic
254C2×Q8—94no—
255C2×Q8—92no—
256C2×Q8—182no—
257C2×Q8—182no—
258C2×Q8—181no—
259C22×C4—21no—
260C22×C4—181no—
261C22×C4C22×D911yescharacteristic
262M16—22no—
263C2×C8—91no—
264C2×C8—91no—
265C2×C8—182no—
266C2×C8C22×D912yes—
267C4⋊C4—21no—
268C4⋊C4—91no—
269C4⋊C4—91no—
270C4⋊C4—91no—
271C4⋊C4—91no—
272C4⋊C4—182no—
273C4⋊C4—182no—
274C4⋊C4—182no—
275C4⋊C4—182no—
276C4⋊C4—182no—
277C4⋊C4C22×D912yes—
278C4⋊C4C22×D911yescharacteristic
279C4⋊C4C22×D911yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—92no—
282C22⋊C4—181no—
283C42—21no—
284C42—92no—
285C42—182no—
286C42—182no—
287C42—181no—
288C22×C3—21no—
289C22×C3—21no—
290C22×C3#89612yes—
291C22×C3C2×D3×D411yescharacteristic
292C3×C4—42no—
293C3×C4—41no—
294C3×C4—41no—
295C3×C4#89612yes—
296C3×C4C2×#23511yescharacteristic
297C3×C4C2×D3×Q811yescharacteristic
298Dic3—64no—
299Dic3—62no—
300Dic3—62no—
301Dic3—121no—
302Dic3—121no—
303C9#308211yescharacteristic, complemented, Sylow
304C23D4×D911yescharacteristic
305Q8—94no—
306Q8—182no—
307Q8—184no—
308Q8—722no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—22no—
312C2×C4—81no—
313C2×C4—92no—
314C2×C4—92no—
315C2×C4—182no—
316C2×C4—184no—
317C2×C4—181no—
318C2×C4—181no—
319C2×C4#369712yes—
320C2×C4D4×D911yescharacteristic
321C2×C4Q8×D912yes—
322C2×C4C23×D911yescharacteristic
323C8—22no—
324C8—181no—
325C8—181no—
326C2×C3—22no—
327C2×C3C2×#89611yescharacteristic
328C2×C3#577511yescharacteristic
329C2×C3#577911yescharacteristic
330C22—21no—
331C22—21no—
332C22#6345812yes—
333C22C2×D4×D911yescharacteristic
334C4—42no—
335C4—41no—
336C4—41no—
337C4—184no—
338C4—182no—
339C4—182no—
340C4—361no—
341C4—361no—
342C4#6345812yes—
343C4C2×#369711yescharacteristic
344C4C2×Q8×D911yescharacteristic
345C3#7924611yescharacteristic
346C2—22no—
347C2C2×#6345811yescharacteristic
348C2#1058987711yescharacteristic
349C2#1058988111yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#428C2
socleC22×C3C2×D3×D4
prime radicalC23×C3D3×D4
hypercenter#428D9
hypocenterC9#3082
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
8. #10588557C2semidirect
9. #10588555C2semidirect
10. #10588537C2semidirect
11. #10588534C2semidirect
59. C2×Dic18Q8semidirect
303. C9#3082semidirect

Maximal subgroups

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

subgroupindex
#105896182
#105896022
C9×#4282
#105888042
#105888032
#105886762
C2×#633682
#105885572
#105885552
#105885372
#105885342
#792463