Finite Group Databasebeta

← #11895306

Subgroups — #11895306

Order 1152.

543 conjugacy classes of subgroups.

The subgroup lattice has 369 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10589832C211yesmaximal, characteristic, complemented
2#10589687C211yesmaximal, characteristic, complemented
3C9×#477C211yesmaximal, characteristic, complemented
4#10588773C211yesmaximal, characteristic, complemented
5C4×#3675C211yesmaximal, characteristic, complemented
6#10588571C212yesmaximal, complemented
7#10588552C212yesmaximal, complemented
8#10588527C211yesmaximal, characteristic
9#10588508C211yesmaximal, characteristic, complemented
10#10588499C212yesmaximal, complemented
11#10588480C212yesmaximal, complemented
12#81134—31nomaximal
13C9×C4⋊Q8C2211yescharacteristic
14C4×Q8×C9C2211yescharacteristic
15#63509C2212yes—
16#63508—22no—
17C2×#3675C2211yescharacteristic
18C2×D72C2212yes—
19#63459—21no—
20#63456—22no—
21#63455C2212yes—
22#63455C2212yes—
23C4⋊C4×D9—21no—
24#63452C2212yes—
25#63437—21no—
26#63436C2211yescharacteristic
27C4×D36—21no—
28C4×D36C2211yescharacteristic
29C4×Dic18C2211yescharacteristic
30C9×#107C2212yes—
31C9×C4⋊C8C2211yescharacteristic
32C9×#103C2212yes—
33#63395C2211yescharacteristic
34#63380C2212yes—
35Dic9⋊C8C2212yes—
36C8×Dic9C2212yes—
37#63369C2211yescharacteristic
38#63369C2212yes—
39#63369C2212yes—
40#63367C2211yescharacteristic
41C4×C9⋊C8C2211yescharacteristic
42#5730—31no—
43#5585—31no—
44C3×#477D311yescharacteristic
45#5088—31no—
46C4×#215—31no—
47#4891—32no—
48#4872—32no—
49#4843—31no—
50#4830—31no—
51#4819—32no—
52#4800—32no—
53C2×Q8×C9—21no—
54C2×Q8×C9C2311yescharacteristic
55C2×D36—21no—
56C2×D36—21no—
57C2×D36C2312yes—
58C2×D36C2311yescharacteristic
59C2×C4×D9—21no—
60C2×C4×D9—22no—
61C2×C4×D9—22no—
62C2×Dic18D411yescharacteristic
63C2×C8×C9C2312yes—
64C9×C4⋊C4—21no—
65C9×C4⋊C4—21no—
66C9×C4⋊C4C2311yescharacteristic
67C9×C4⋊C4C2312yes—
68C42×C9—21no—
69C42×C9C2311yescharacteristic
70#3675—22no—
71(C2×D9)⋊C4—21no—
72(C2×D9)⋊C4—22no—
73(C2×D9)⋊C4—22no—
74(C2×D9)⋊C4—22no—
75(C2×D9)⋊C4—22no—
76C4⋊Dic9—22no—
77C4⋊Dic9D411yescharacteristic
78C4⋊Dic9C2311yescharacteristic
79Dic9⋊C4—22no—
80Dic9⋊C4D412yes—
81C4×Dic9C2312yes—
82C2×C9⋊C8C2311yescharacteristic
83C2×C9⋊C8C2311yescharacteristic
84D72—24no—
85#3361—91noSylow
86C3×C4⋊Q8C2×D311yescharacteristic
87C3×C4×Q8C2×D311yescharacteristic
88#947—32no—
89#946—62no—
90C2×#215—31no—
91C2×D24—32no—
92#897—61no—
93#894—62no—
94#893—32no—
95#893—32no—
96D3×C4⋊C4—61no—
97#890—32no—
98#875—61no—
99#874—31no—
100C4×D12—31no—
101C4×D12—61no—
102C4×Dic6—31no—
103C3×#107C2×D312yes—
104C3×C4⋊C8C2×D311yescharacteristic
105C3×#103C2×D312yes—
106#835—31no—
107#821—32no—
108Dic3⋊C8—32no—
109C8×Dic3—32no—
110#809—31no—
111#809—32no—
112#809—32no—
113#808—31no—
114C4×C3⋊C8—31no—
115C22×D9—21no—
116C22×D9—22no—
117Q8×C9—21no—
118Q8×C9—21no—
119Q8×C9—81no—
120C2×C4×C9—22no—
121C2×C4×C9—21no—
122C2×C4×C9—21no—
123C2×C4×C9C2×D411yescharacteristic
124C2×C4×C9C2×D411yescharacteristic
125C2×C4×C9C2411yescharacteristic
126C2×Dic9—21no—
127C2×Dic9C2×D412yes—
128C2×Dic9C2×D412yes—
129D36—22no—
130D36—21no—
131D36—22no—
132D36—42no—
133D36—81no—
134D36#4112yes—
135C4×D9—42no—
136C4×D9—82no—
137C4×D9—82no—
138Dic18—22no—
139C8×C9—22no—
140C9⋊C8—21no—
141C9⋊C8—21no—
142#559—91no—
143#554—91no—
144#488—92no—
145#486—91no—
146#478—92no—
147#477D911yescharacteristic, complemented
148#463—92no—
149#459—91no—
150C8×Q8—91no—
151C4×SD16—91no—
152C4×D8—92no—
153C2×C3×Q8—21no—
154C2×C3×Q8C22×D311yescharacteristic
155C2×D12—31no—
156C2×D12—32no—
157C2×D12—61no—
158C2×D12—61no—
159C2×C4×D3—61no—
160C2×C4×D3—62no—
161C2×C4×D3—62no—
162C2×Dic6—31no—
163C2×C3×C8C22×D312yes—
164C3×C4⋊C4—21no—
165C3×C4⋊C4—21no—
166C3×C4⋊C4C22×D311yescharacteristic
167C3×C4⋊C4C22×D312yes—
168C3×C42—21no—
169C3×C42C22×D311yescharacteristic
170#215—62no—
171(C2×D3)⋊C4—62no—
172(C2×D3)⋊C4—62no—
173(C2×D3)⋊C4—62no—
174(C2×D3)⋊C4—62no—
175(C2×D3)⋊C4—61no—
176C4⋊Dic3—31no—
177C4⋊Dic3—31no—
178C4⋊Dic3—62no—
179Dic3⋊C4—32no—
180Dic3⋊C4—62no—
181C4×Dic3—32no—
182C2×C3⋊C8—31no—
183C2×C3⋊C8—31no—
184D24—64no—
185C22×C9C22×D411yescharacteristic
186C2×D9—22no—
187C2×D9—41no—
188C2×D9—41no—
189C2×D9—42no—
190C2×D9—42no—
191C2×D9—42no—
192C4×C9—21no—
193C4×C9—41no—
194C4×C9—41no—
195C4×C9—42no—
196C4×C9#13512yes—
197C4×C9C2×#4111yescharacteristic
198C4×C92−1+411yescharacteristic
199Dic9—22no—
200Dic9—22no—
201Dic9—41no—
202C2×SD16—91no—
203C2×D8—92no—
204C4⋊Q8C2×D911yescharacteristic
205#127—91no—
206#125—92no—
207#124—92no—
208#124—181no—
209#123—182no—
210C22⋊Q8—181no—
211C22⋊Q8—182no—
212C4×Q8—91no—
213C4×Q8C2×D911yescharacteristic
214C4×D4—92no—
215C4×D4—92no—
216C4×D4—91no—
217C4×D4—181no—
218C2×C4⋊C4—181no—
219#107C2×D912yes—
220#106—91no—
221C4⋊C8—92no—
222C4⋊C8C2×D911yescharacteristic
223#103—91no—
224#103C2×D912yes—
225#102—92no—
226#102—91no—
227#102—92no—
228#102—92no—
229C4×C8—92no—
230C4×C8—91no—
231C22×D3—61no—
232C22×D3—62no—
233C3×Q8—21no—
234C3×Q8—21no—
235C3×Q8—81no—
236C2×C3×C4—22no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4D3×D411yescharacteristic
240C2×C3×C4D3×D411yescharacteristic
241C2×C3×C4C23×D311yescharacteristic
242C2×Dic3—32no—
243C2×Dic3—32no—
244C2×Dic3—61no—
245D12—32no—
246D12—61no—
247D12—62no—
248D12—62no—
249D12—122no—
250D12—241no—
251C4×D3—122no—
252C4×D3—242no—
253C4×D3—242no—
254Dic6—62no—
255C3×C8—22no—
256C3⋊C8—61no—
257C3⋊C8—61no—
258C2×C9#54811yescharacteristic
259C2×C9C2×#13511yescharacteristic
260C2×C9#57611yescharacteristic
261D9—42no—
262D9—82no—
263C2×Q8—21no—
264C2×Q8—91no—
265C2×Q8C22×D911yescharacteristic
266C2×D4—91no—
267C2×D4—92no—
268C2×D4—181no—
269C2×D4—181no—
270C22×C4—182no—
271C22×C4—182no—
272C22×C4—181no—
273SD16—182no—
274D8—184no—
275C2×C8—91no—
276C2×C8—91no—
277C2×C8C22×D912yes—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—91no—
281C4⋊C4—92no—
282C4⋊C4—91no—
283C4⋊C4—182no—
284C4⋊C4—182no—
285C4⋊C4C22×D912yes—
286C4⋊C4C22×D911yescharacteristic
287C22⋊C4—182no—
288C22⋊C4—182no—
289C22⋊C4—182no—
290C22⋊C4—182no—
291C22⋊C4—181no—
292C42—21no—
293C42—92no—
294C42C22×D911yescharacteristic
295C22×C3C2×D3×D411yescharacteristic
296C2×D3—62no—
297C2×D3—121no—
298C2×D3—121no—
299C2×D3—122no—
300C2×D3—122no—
301C2×D3—122no—
302C3×C4—21no—
303C3×C4—41no—
304C3×C4—41no—
305C3×C4—42no—
306C3×C4#91912yes—
307C3×C4#100711yescharacteristic
308C3×C4D3×#4111yescharacteristic
309Dic3—62no—
310Dic3—62no—
311Dic3—121no—
312C9#336111yescharacteristic, complemented, Sylow
313C23—181no—
314C23—182no—
315Q8—21no—
316Q8—21no—
317Q8—81no—
318Q8—182no—
319D4—92no—
320D4—181no—
321D4—182no—
322D4—182no—
323D4—362no—
324D4—721no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—22no—
328C2×C4—92no—
329C2×C4—92no—
330C2×C4—181no—
331C2×C4—362no—
332C2×C4—722no—
333C2×C4—722no—
334C2×C4D4×D911yescharacteristic
335C2×C4D4×D911yescharacteristic
336C2×C4C23×D911yescharacteristic
337C8—22no—
338C8—181no—
339C8—181no—
340C2×C3#563311yescharacteristic
341C2×C3C2×#91911yescharacteristic
342C2×C3#577411yescharacteristic
343D3—122no—
344D3—242no—
345C22—182no—
346C22—361no—
347C22—361no—
348C22—362no—
349C22—362no—
350C22—362no—
351C22C2×D4×D911yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—42no—
356C4—182no—
357C4—182no—
358C4—361no—
359C4#6348112yes—
360C4#6371311yescharacteristic
361C4#41×D911yescharacteristic
362C3#8113411yescharacteristic
363C2—362no—
364C2—722no—
365C2#1058973511yescharacteristic
366C2C2×#6348111yescharacteristic
367C2#1058987611yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#477C2
socleC22×C3C2×D3×D4
prime radical#10588527C2
hypercenter#477D9
hypocenterC9#3361
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
1. #10589832C2semidirect
2. #10589687C2semidirect
3. C9×#477C2semidirect
4. #10588773C2semidirect
5. C4×#3675C2semidirect
6. #10588571C2semidirect
7. #10588552C2semidirect
9. #10588508C2semidirect
10. #10588499C2semidirect
11. #10588480C2semidirect
147. #477D9semidirect
312. C9#3361semidirect

Maximal subgroups

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

subgroupindex
#105898322
#105896872
C9×#4772
#105887732
C4×#36752
#105885712
#105885522
#105885272
#105885082
#105884992
#105884802
#811343