Finite Group Databasebeta

← #11869044

Subgroups — #11869044

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#10589621C211yesmaximal, characteristic
2#10589618C211yesmaximal, characteristic
3C9×#427C211yesmaximal, characteristic
4C2×#63376C211yesmaximal, characteristic
5#10588783C211yesmaximal, characteristic
6#10588681C211yesmaximal, characteristic
7#10588679C211yesmaximal, characteristic
8#10588557C212yesmaximal, complemented
9#10588555C212yesmaximal, complemented
10#10588537C212yesmaximal, complemented
11#10588534C212yesmaximal, complemented
12#79198—31nomaximal
13C22×Dic18C2211yescharacteristic
14C22×C8×C9C2211yescharacteristic
15C9×#117C2211yescharacteristic
16C9×#117C2211yescharacteristic
17#63488C2211yescharacteristic
18C2×C4⋊Dic9C2211yescharacteristic
19C2×#3667C2211yescharacteristic
20#63452C2212yes—
21#63450C2212yes—
22#63449C2212yes—
23#63449C2212yes—
24#63440—22no—
25#63439—22no—
26#63432—21no—
27#63431—21no—
28C4×Dic18—21no—
29C4×Dic18—21no—
30C9×#107C2211yescharacteristic
31C9×#107C2211yescharacteristic
32C9×#106C2211yescharacteristic
33C9×#106C2211yescharacteristic
34#63376C2212yes—
35#63376C2212yes—
36Dic9⋊C8C2212yes—
37Dic9⋊C8C2212yes—
38#63368C2212yes—
39#63368C2212yes—
40#63367C2212yes—
41#63366C2212yes—
42#5519—31no—
43#5516—31no—
44C3×#427D311yescharacteristic
45C2×#816—31no—
46#5102—31no—
47#5004—31no—
48#4995—31no—
49#4877—32no—
50#4875—32no—
51#4857—32no—
52#4854—32no—
53C22×C4×C9C2311yescharacteristic
54C22×Dic9—21no—
55C22×Dic9—21no—
56C2×Dic18—21no—
57C2×Dic18—22no—
58C2×Dic18—22no—
59C2×Dic18Q814yescomplemented
60C2×Dic18C2312yes—
61C2×C8×C9—22no—
62C2×C8×C9C2311yescharacteristic
63C2×C8×C9C2311yescharacteristic
64C9×C4⋊C4C2311yescharacteristic
65C9×C4⋊C4C2311yescharacteristic
66C9×C4⋊C4C2311yescharacteristic
67C9×C4⋊C4C2311yescharacteristic
68C9×C22⋊C4—21no—
69C9×C22⋊C4—21no—
70C42×C9—21no—
71C42×C9—21no—
72#3676D412yes—
73C4⋊Dic9—21no—
74C4⋊Dic9—22no—
75C4⋊Dic9D411yescharacteristic
76C4⋊Dic9D411yescharacteristic
77C4⋊Dic9C2312yes—
78Dic9⋊C4—22no—
79Dic9⋊C4—22no—
80Dic9⋊C4—22no—
81Dic9⋊C4—22no—
82C4×Dic9—22no—
83C4×Dic9—22no—
84C4×Dic9C2312yes—
85#3667—22no—
86C2×C9⋊C8C2312yes—
87#3082—91noSylow
88C22×Dic6—31no—
89C22×C3×C8C2×D311yescharacteristic
90C3×#117C2×D311yescharacteristic
91C3×#117C2×D311yescharacteristic
92#926—31no—
93C2×C4⋊Dic3—31no—
94C2×#208—31no—
95#890—32no—
96#888—32no—
97#887—32no—
98#887—32no—
99#878—62no—
100#877—62no—
101#870—61no—
102#869—61no—
103C4×Dic6—61no—
104C4×Dic6—61no—
105C3×#107C2×D311yescharacteristic
106C3×#107C2×D311yescharacteristic
107C3×#106C2×D311yescharacteristic
108C3×#106C2×D311yescharacteristic
109#816—32no—
110#816—32no—
111Dic3⋊C8—32no—
112Dic3⋊C8—32no—
113#810—32no—
114#810—32no—
115#808—32no—
116#807—32no—
117C23×C9C2×D411yescharacteristic
118C2×C4×C9—21no—
119C2×C4×C9—21no—
120C2×C4×C9—21no—
121C2×C4×C9—21no—
122C2×C4×C9C2×D411yescharacteristic
123C2×C4×C9C2×Q812yes—
124C2×C4×C9#4112yes—
125C2×C4×C9C2411yescharacteristic
126C2×Dic9—24no—
127C2×Dic9—22no—
128C2×Dic9—22no—
129C2×Dic9—81no—
130C2×Dic9C2×D412yes—
131C2×Dic9C2×D412yes—
132Dic18—24no—
133Dic18—22no—
134Dic18—82no—
135Dic18C2×Q814yes—
136C8×C9—21no—
137C8×C9—21no—
138C9⋊C8—22no—
139#544—91no—
140#519—91no—
141#479—92no—
142#479—92no—
143#477—92no—
144#475—92no—
145#428—91no—
146#427D911yescharacteristic
147#424—91no—
148#419—91no—
149C2×#103—91no—
150C22×C3×C4C22×D311yescharacteristic
151C22×Dic3—61no—
152C22×Dic3—61no—
153C2×Dic6—34no—
154C2×Dic6—32no—
155C2×Dic6—62no—
156C2×Dic6—61no—
157C2×Dic6—62no—
158C2×C3×C8—22no—
159C2×C3×C8C22×D311yescharacteristic
160C2×C3×C8C22×D311yescharacteristic
161C3×C4⋊C4C22×D311yescharacteristic
162C3×C4⋊C4C22×D311yescharacteristic
163C3×C4⋊C4C22×D311yescharacteristic
164C3×C4⋊C4C22×D311yescharacteristic
165C3×C22⋊C4—21no—
166C3×C22⋊C4—21no—
167C3×C42—21no—
168C3×C42—21no—
169#217—32no—
170C4⋊Dic3—31no—
171C4⋊Dic3—31no—
172C4⋊Dic3—32no—
173C4⋊Dic3—62no—
174C4⋊Dic3—61no—
175Dic3⋊C4—62no—
176Dic3⋊C4—62no—
177Dic3⋊C4—62no—
178Dic3⋊C4—62no—
179C4×Dic3—32no—
180C4×Dic3—62no—
181C4×Dic3—62no—
182#208—62no—
183C2×C3⋊C8—32no—
184C22×C9—21no—
185C22×C9—21no—
186C22×C9C22⋊Q812yes—
187C22×C9C22×D411yescharacteristic
188C4×C9—41no—
189C4×C9—41no—
190C4×C9—41no—
191C4×C9—41no—
192C4×C9C22⋊Q812yes—
193C4×C9C22×Q811yescharacteristic
194C4×C9C2×#4111yescharacteristic
195Dic9—24no—
196Dic9—22no—
197Dic9—22no—
198Dic9—42no—
199C22×Q8—91no—
200C2×M16—91no—
201C22×C8C2×D911yescharacteristic
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—182no—
213#117C2×D911yescharacteristic
214#117C2×D911yescharacteristic
215C2×C4⋊C4—91no—
216#107—92no—
217#107C2×D911yescharacteristic
218#107C2×D911yescharacteristic
219#106—92no—
220#106C2×D911yescharacteristic
221#106C2×D911yescharacteristic
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—21no—
232C2×C3×C4—21no—
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—62no—
242C2×Dic3—241no—
243Dic6—34no—
244Dic6—64no—
245Dic6—62no—
246Dic6—242no—
247C3×C8—21no—
248C3×C8—21no—
249C3⋊C8—62no—
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—181no—
260C22×C4—181no—
261C22×C4C22×D911yescharacteristic
262M16—182no—
263C2×C8—22no—
264C2×C8—92no—
265C2×C8C22×D911yescharacteristic
266C2×C8C22×D911yescharacteristic
267C4⋊C4—91no—
268C4⋊C4—91no—
269C4⋊C4—92no—
270C4⋊C4—182no—
271C4⋊C4—182no—
272C4⋊C4—182no—
273C4⋊C4—182no—
274C4⋊C4—182no—
275C4⋊C4—181no—
276C4⋊C4C22×D911yescharacteristic
277C4⋊C4C22×D911yescharacteristic
278C4⋊C4C22×D911yescharacteristic
279C4⋊C4C22×D911yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—92no—
283C42—21no—
284C42—21no—
285C42—92no—
286C42—182no—
287C42—182no—
288C22×C3—21no—
289C22×C3—21no—
290C22×C3#89612yes—
291C22×C3C2×D3×D411yescharacteristic
292C3×C4—41no—
293C3×C4—41no—
294C3×C4—41no—
295C3×C4—41no—
296C3×C4#89612yes—
297C3×C4C2×#23511yescharacteristic
298C3×C4C2×D3×Q811yescharacteristic
299Dic3—64no—
300Dic3—62no—
301Dic3—62no—
302Dic3—122no—
303C9#308211yescharacteristic, complemented, Sylow
304C23D4×D911yescharacteristic
305Q8—94no—
306Q8—182no—
307Q8—184no—
308Q8—722no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—92no—
314C2×C4—92no—
315C2×C4—182no—
316C2×C4—184no—
317C2×C4—182no—
318C2×C4—721no—
319C2×C4#369712yes—
320C2×C4D4×D911yescharacteristic
321C2×C4Q8×D912yes—
322C2×C4C23×D911yescharacteristic
323C8—21no—
324C8—21no—
325C8—182no—
326C2×C3—22no—
327C2×C3C2×#89611yescharacteristic
328C2×C3#577011yescharacteristic
329C2×C3#577111yescharacteristic
330C22—21no—
331C22—21no—
332C22#6345812yes—
333C22C2×D4×D911yescharacteristic
334C4—41no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—184no—
339C4—182no—
340C4—182no—
341C4—362no—
342C4#6345812yes—
343C4C2×#369711yescharacteristic
344C4C2×Q8×D911yescharacteristic
345C3#7919811yescharacteristic
346C2—22no—
347C2C2×#6345811yescharacteristic
348C2#1058987211yescharacteristic
349C2#1058987311yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#427C2
socleC22×C3C2×D3×D4
prime radicalC23×C3D3×D4
hypercenter#427D9
hypocenterC9#3082
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #427

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
#105896212
#105896182
C9×#4272
C2×#633762
#105887832
#105886812
#105886792
#105885572
#105885552
#105885372
#105885342
#791983