Finite Group Databasebeta

← #11896036

Subgroups — #11896036

Order 1152.

507 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#10589834C211yesmaximal, characteristic
2Q8×Dic18C211yesmaximal, characteristic, complemented
3C9×#462C211yesmaximal, characteristic, complemented
4#10588865C212yesmaximal
5#10588864C212yesmaximal, complemented
6#10588759C211yesmaximal, characteristic, complemented
7C4×#3675C211yesmaximal, characteristic
8#10588526C211yesmaximal, characteristic
9#10588509C211yesmaximal, characteristic, complemented
10#10588474C212yesmaximal
11#10588471C212yesmaximal, complemented
12#80464—31nomaximal
13C2×C9×Q16C2212yes—
14C9×C4⋊Q8C2211yescharacteristic
15C4×Q8×C9C2211yescharacteristic
16#63509C2212yes—
17Q8×Dic9C2212yes—
18Q8×Dic9C2212yes—
19C2×#3675C2211yescharacteristic
20#63460—22no—
21#63459—21no—
22#63454—21no—
23#63450—22no—
24#63450C2212yes—
25C4×D36C2211yescharacteristic
26#63431—21no—
27#63431C2211yescharacteristic
28C4×Dic18—21no—
29C4×Dic18C2211yescharacteristic
30C9×C4⋊C8C2211yescharacteristic
31C9×#103C2212yes—
32#63395C2211yescharacteristic
33#63395C2212yes—
34#63395C2212yes—
35#63380C2212yes—
36#63377C2212yes—
37#63375C2212yes—
38Dic9⋊C8C2212yes—
39#63369C2211yescharacteristic
40#63367C2211yescharacteristic
41C4×C9⋊C8C2211yescharacteristic
42#5732—31no—
43Q8×Dic6—31no—
44C3×#462D311yescharacteristic
45#5185—32no—
46#5184—32no—
47#5079—31no—
48C4×#215—31no—
49#4842—31no—
50#4831—31no—
51#4794—32no—
52#4791—32no—
53C2×Q8×C9C2312yes—
54C2×Q8×C9C2311yescharacteristic
55C2×D36C2311yescharacteristic
56C2×C4×D9—21no—
57C2×Dic18—21no—
58C2×Dic18—22no—
59C2×Dic18D411yescharacteristic
60C9×Q16—24no—
61C2×C8×C9C2312yes—
62C9×C4⋊C4—21no—
63C9×C4⋊C4—21no—
64C9×C4⋊C4—21no—
65C9×C4⋊C4C2311yescharacteristic
66C42×C9—21no—
67C42×C9C2311yescharacteristic
68#3675—22no—
69(C2×D9)⋊C4—21no—
70(C2×D9)⋊C4—22no—
71(C2×D9)⋊C4—22no—
72C4⋊Dic9—21no—
73C4⋊Dic9—22no—
74C4⋊Dic9—22no—
75C4⋊Dic9D411yescharacteristic
76C4⋊Dic9C2311yescharacteristic
77C4⋊Dic9C2312yes—
78Dic9⋊C4—22no—
79Dic9⋊C4D412yes—
80C4×Dic9—22no—
81C4×Dic9—22no—
82C4×Dic9C2312yes—
83C2×C9⋊C8C2311yescharacteristic
84C2×C9⋊C8C2311yescharacteristic
85#3369—91noSylow
86C2×C3×Q16C2×D312yes—
87C3×C4⋊Q8C2×D311yescharacteristic
88C3×C4×Q8C2×D311yescharacteristic
89#947—32no—
90Q8×Dic3—32no—
91Q8×Dic3—32no—
92C2×#215—31no—
93#898—62no—
94#897—61no—
95#892—61no—
96#888—32no—
97#888—62no—
98C4×D12—31no—
99#869—31no—
100#869—61no—
101C4×Dic6—31no—
102C4×Dic6—61no—
103C3×C4⋊C8C2×D311yescharacteristic
104C3×#103C2×D312yes—
105#835—31no—
106#835—32no—
107#835—32no—
108#821—32no—
109#817—32no—
110#815—32no—
111Dic3⋊C8—32no—
112#809—31no—
113#808—31no—
114C4×C3⋊C8—31no—
115C22×D9—21no—
116Q8×C9—21no—
117Q8×C9—22no—
118Q8×C9—22no—
119Q8×C9#4112yes—
120C2×C4×C9—21no—
121C2×C4×C9—22no—
122C2×C4×C9—21no—
123C2×C4×C9C2×D411yescharacteristic
124C2×C4×C9C2×D411yescharacteristic
125C2×C4×C9C2411yescharacteristic
126C2×Dic9—21no—
127C2×Dic9—22no—
128C2×Dic9C2×D412yes—
129C2×Dic9C2×D412yes—
130D36—21no—
131D36—21no—
132C4×D9—42no—
133Dic18—22no—
134Dic18—82no—
135Dic18—81no—
136C8×C9—22no—
137C9⋊C8—21no—
138C9⋊C8—21no—
139Q82—91no—
140#556—91no—
141#489—92no—
142#487—91no—
143#476—91no—
144#475—92no—
145#464—92no—
146#462D911yescharacteristic, complemented
147#446—91no—
148#441—92no—
149C4×SD16—91no—
150C2×C3×Q8C22×D312yes—
151C2×C3×Q8C22×D311yescharacteristic
152C2×D12—31no—
153C2×C4×D3—61no—
154C2×Dic6—31no—
155C2×Dic6—62no—
156C2×Dic6—61no—
157C3×Q16—24no—
158C2×C3×C8C22×D312yes—
159C3×C4⋊C4—21no—
160C3×C4⋊C4—21no—
161C3×C4⋊C4—21no—
162C3×C4⋊C4C22×D311yescharacteristic
163C3×C42—21no—
164C3×C42C22×D311yescharacteristic
165#215—62no—
166(C2×D3)⋊C4—62no—
167(C2×D3)⋊C4—62no—
168(C2×D3)⋊C4—61no—
169C4⋊Dic3—31no—
170C4⋊Dic3—31no—
171C4⋊Dic3—32no—
172C4⋊Dic3—62no—
173C4⋊Dic3—62no—
174C4⋊Dic3—61no—
175Dic3⋊C4—32no—
176Dic3⋊C4—62no—
177C4×Dic3—32no—
178C4×Dic3—62no—
179C4×Dic3—62no—
180C2×C3⋊C8—31no—
181C2×C3⋊C8—31no—
182C22×C9C22×D411yescharacteristic
183C2×D9—41no—
184C2×D9—41no—
185C2×D9—41no—
186C4×C9—22no—
187C4×C9—21no—
188C4×C9—42no—
189C4×C9—41no—
190C4×C9#13712yes—
191C4×C9C2×#4111yescharacteristic
192C4×C92−1+411yescharacteristic
193Dic9—22no—
194Dic9—22no—
195Dic9—41no—
196Dic9—42no—
197C2×Q16C2×D912yes—
198C2×SD16—91no—
199C4⋊Q8—92no—
200C4⋊Q8—91no—
201C4⋊Q8—181no—
202C4⋊Q8—182no—
203C4⋊Q8C2×D911yescharacteristic
204#126—182no—
205#124—92no—
206C22⋊Q8—181no—
207C4×Q8—91no—
208C4×Q8—92no—
209C4×Q8—92no—
210C4×Q8—181no—
211C4×Q8C2×D911yescharacteristic
212C4×D4—91no—
213#117—181no—
214#106—92no—
215#106—91no—
216C4⋊C8—92no—
217C4⋊C8C2×D911yescharacteristic
218#103—91no—
219#103—92no—
220#103—92no—
221#103C2×D912yes—
222#102—92no—
223#102—91no—
224#97—92no—
225C4×C8—91no—
226C22×D3—61no—
227C3×Q8—21no—
228C3×Q8—22no—
229C3×Q8—22no—
230C3×Q8#23712yes—
231C2×C3×C4—21no—
232C2×C3×C4—22no—
233C2×C3×C4—21no—
234C2×C3×C4D3×D411yescharacteristic
235C2×C3×C4D3×D411yescharacteristic
236C2×C3×C4C23×D311yescharacteristic
237C2×Dic3—32no—
238C2×Dic3—32no—
239C2×Dic3—61no—
240C2×Dic3—62no—
241D12—61no—
242D12—61no—
243C4×D3—122no—
244Dic6—62no—
245Dic6—242no—
246Dic6—241no—
247C3×C8—22no—
248C3⋊C8—61no—
249C3⋊C8—61no—
250C2×C9#54811yescharacteristic
251C2×C9C2×#13711yescharacteristic
252C2×C9#57711yescharacteristic
253D9—81no—
254C2×Q8—91no—
255C2×Q8—182no—
256C2×Q8—181no—
257C2×Q8C22×D912yes—
258C2×Q8C22×D911yescharacteristic
259C2×D4—91no—
260C22×C4—181no—
261Q16—24no—
262SD16—182no—
263C2×C8—91no—
264C2×C8—91no—
265C2×C8C22×D912yes—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—91no—
270C4⋊C4—92no—
271C4⋊C4—92no—
272C4⋊C4—91no—
273C4⋊C4—182no—
274C4⋊C4—182no—
275C4⋊C4—182no—
276C4⋊C4—181no—
277C4⋊C4C22×D911yescharacteristic
278C22⋊C4—182no—
279C22⋊C4—182no—
280C22⋊C4—181no—
281C42—21no—
282C42—92no—
283C42—182no—
284C42—182no—
285C42C22×D911yescharacteristic
286C22×C3C2×D3×D411yescharacteristic
287C2×D3—121no—
288C2×D3—121no—
289C2×D3—121no—
290C3×C4—21no—
291C3×C4—22no—
292C3×C4—41no—
293C3×C4—42no—
294C3×C4#91812yes—
295C3×C4C2×#23711yescharacteristic
296C3×C4#101011yescharacteristic
297Dic3—62no—
298Dic3—62no—
299Dic3—121no—
300Dic3—122no—
301C9#336911yescharacteristic, complemented, Sylow
302C23—181no—
303Q8—21no—
304Q8—22no—
305Q8—22no—
306Q8—182no—
307Q8—721no—
308Q8—722no—
309Q8#369912yes—
310D4—181no—
311D4—181no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—22no—
315C2×C4—92no—
316C2×C4—92no—
317C2×C4—181no—
318C2×C4—182no—
319C2×C4—362no—
320C2×C4D4×D911yescharacteristic
321C2×C4D4×D911yescharacteristic
322C2×C4C23×D911yescharacteristic
323C8—22no—
324C8—181no—
325C8—181no—
326C2×C3#559811yescharacteristic
327C2×C3C2×#91811yescharacteristic
328C2×C3#577811yescharacteristic
329D3—241no—
330C22—361no—
331C22—361no—
332C22—361no—
333C22C2×D4×D911yescharacteristic
334C4—22no—
335C4—21no—
336C4—42no—
337C4—41no—
338C4—182no—
339C4—182no—
340C4—361no—
341C4—362no—
342C4#6348012yes—
343C4C2×#369911yescharacteristic
344C4#6371611yescharacteristic
345C3#8046411yescharacteristic
346C2—721no—
347C2#1058970011yescharacteristic
348C2C2×#6348011yescharacteristic
349C2#1058988011yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#462C2
socleC22×C3C2×D3×D4
prime radicalC2×D36C23
hypercenter#462D9
hypocenterC9#3369
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
2. Q8×Dic18C2semidirect
3. C9×#462C2semidirect
5. #10588864C2semidirect
6. #10588759C2semidirect
9. #10588509C2semidirect
11. #10588471C2semidirect
146. #462D9semidirect
301. C9#3369semidirect

Maximal subgroups

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

subgroupindex
#105898342
Q8×Dic182
C9×#4622
#105888652
#105888642
#105887592
C4×#36752
#105885262
#105885092
#105884742
#105884712
#804643