Finite Group Databasebeta

← #11796230

Subgroups — #11796230

Order 1152.

420 conjugacy classes of subgroups.

The subgroup lattice has 381 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#534C211yesmaximal, characteristic
2C2×#63393C211yesmaximal, characteristic, complemented
3C2×#63391C211yesmaximal, characteristic, complemented
4#10588216C212yesmaximal, complemented
5#10588213C212yesmaximal, complemented
6#71847—31nomaximal
7C22×D4×C9C411yescharacteristic, complemented
8C22×D4×C9C2211yescharacteristic
9C9×#123—21no—
10C9×#123C411yescharacteristic, complemented
11C9×#123C2211yescharacteristic
12C9×#121—21no—
13C9×#121—21no—
14C9×#120—21no—
15C9×#120C411yescharacteristic, complemented
16C9×#120C2211yescharacteristic
17C2×C9×C22⋊C4C411yescharacteristic, complemented
18C2×#3676—21no—
19C2×#3667—21no—
20#63393—21no—
21#63393C2212yes—
22#63391—21no—
23#63391C2212yes—
24C3×#534D311yescharacteristic
25C2×#834—31no—
26C2×#833—31no—
27#4539—32no—
28#4536—32no—
29C24×C9C2×C411yescharacteristic
30C24×C9C2×C411yescharacteristic, complemented
31C24×C9D411yescharacteristic
32C2×D4×C9—21no—
33C2×D4×C9—21no—
34C2×D4×C9—21no—
35C2×D4×C9—21no—
36C2×D4×C9—41no—
37C2×D4×C9—41no—
38C2×D4×C9—41no—
39C2×D4×C9—41no—
40C2×D4×C9C2×C411yescharacteristic
41C2×D4×C9D411yescharacteristic
42C2×D4×C9D411yescharacteristic
43C2×D4×C9C2311yescharacteristic
44C22×C4×C9—21no—
45C22×C4×C9C2×C411yescharacteristic, complemented
46C22×C4×C9D411yescharacteristic
47C22×Dic9—41no—
48C9×C4⋊C4—21no—
49C9×C4⋊C4—21no—
50C9×C22⋊C4—21no—
51C9×C22⋊C4—21no—
52C9×C22⋊C4—21no—
53C9×C22⋊C4—21no—
54C9×C22⋊C4—21no—
55C9×C22⋊C4C2×C411yescharacteristic, complemented
56C9×C22⋊C4C2×C411yescharacteristic, complemented
57#3676—22no—
58#3676—41no—
59#3667—22no—
60#3667—41no—
61C2×C9⋊C8—41no—
62#2121—91noSylow
63C22×C3×D4Dic311yescharacteristic
64C22×C3×D4C2×D311yescharacteristic
65C3×#123—21no—
66C3×#123Dic311yescharacteristic
67C3×#123C2×D311yescharacteristic
68C3×#121—21no—
69C3×#121—21no—
70C3×#120—21no—
71C3×#120Dic311yescharacteristic
72C3×#120C2×D311yescharacteristic
73C2×C3×C22⋊C4Dic311yescharacteristic
74C2×#217—61no—
75C2×#208—61no—
76#834—32no—
77#834—61no—
78#833—32no—
79#833—61no—
80C23×C9—21no—
81C23×C9—21no—
82C23×C9—21no—
83C23×C9—21no—
84C23×C9—21no—
85C23×C9—41no—
86C23×C9—81no—
87C23×C9—81no—
88C23×C9—81no—
89C23×C9C22⋊C411yescharacteristic
90C23×C9C22⋊C411yescharacteristic
91C23×C9C22⋊C411yescharacteristic
92C23×C9C22×C411yescharacteristic
93C23×C9C2×D411yescharacteristic
94D4×C9—41no—
95D4×C9—41no—
96D4×C9—41no—
97D4×C9—41no—
98D4×C9—42no—
99D4×C9—41no—
100D4×C9—41no—
101D4×C9—81no—
102D4×C9—81no—
103C2×C4×C9—21no—
104C2×C4×C9—21no—
105C2×C4×C9—21no—
106C2×C4×C9—21no—
107C2×C4×C9—21no—
108C2×C4×C9—41no—
109C2×C4×C9—81no—
110C2×C4×C9C22⋊C411yescharacteristic
111C2×C4×C9C2×D411yescharacteristic
112C2×Dic9—42no—
113C2×Dic9—82no—
114C9⋊C8—42no—
115#534D911yescharacteristic
116C2×#100—91no—
117C2×#99—91no—
118#352—92no—
119AΣL(1,𝔽16)—92no—
120C24×C3C2×Dic311yescharacteristic
121C24×C3C2×Dic311yescharacteristic
122C24×C3#6711yescharacteristic
123C2×C3×D4—21no—
124C2×C3×D4—21no—
125C2×C3×D4—21no—
126C2×C3×D4—21no—
127C2×C3×D4—41no—
128C2×C3×D4—41no—
129C2×C3×D4—41no—
130C2×C3×D4—41no—
131C2×C3×D4C2×Dic311yescharacteristic
132C2×C3×D4#6711yescharacteristic
133C2×C3×D4#6711yescharacteristic
134C2×C3×D4C22×D311yescharacteristic
135C22×C3×C4—21no—
136C22×C3×C4C2×Dic311yescharacteristic
137C22×C3×C4#6711yescharacteristic
138C22×Dic3—121no—
139C3×C4⋊C4—21no—
140C3×C4⋊C4—21no—
141C3×C22⋊C4—21no—
142C3×C22⋊C4—21no—
143C3×C22⋊C4—21no—
144C3×C22⋊C4—21no—
145C3×C22⋊C4—21no—
146C3×C22⋊C4C2×Dic311yescharacteristic
147C3×C22⋊C4C2×Dic311yescharacteristic
148#217—62no—
149#217—121no—
150#208—62no—
151#208—121no—
152C2×C3⋊C8—121no—
153C22×C9—21no—
154C22×C9—21no—
155C22×C9—21no—
156C22×C9—21no—
157C22×C9—41no—
158C22×C9—41no—
159C22×C9—41no—
160C22×C9—41no—
161C22×C9—41no—
162C22×C9—42no—
163C22×C9—41no—
164C22×C9—41no—
165C22×C9—41no—
166C22×C9—81no—
167C22×C9—81no—
168C22×C9—81no—
169C22×C9—82no—
170C22×C9#9911yescharacteristic
171C22×C9#9911yescharacteristic
172C22×C9C2×C22⋊C411yescharacteristic
173C4×C9—21no—
174C4×C9—21no—
175C4×C9—41no—
176C4×C9—41no—
177C4×C9—41no—
178Dic9—82no—
179C22×D4Dic911yescharacteristic, complemented
180C22×D4C2×D911yescharacteristic
181C2×M16—181no—
182#123—21no—
183#123Dic911yescharacteristic, complemented
184#123C2×D911yescharacteristic
185#121—21no—
186#121—21no—
187#120—21no—
188#120Dic911yescharacteristic, complemented
189#120C2×D911yescharacteristic
190C2×C22⋊C4—181no—
191C2×C22⋊C4Dic911yescharacteristic, complemented
192#100—92no—
193#100—181no—
194#99—92no—
195#99—181no—
196C23×C3—21no—
197C23×C3—21no—
198C23×C3—21no—
199C23×C3—21no—
200C23×C3—21no—
201C23×C3—41no—
202C23×C3—81no—
203C23×C3—81no—
204C23×C3—81no—
205C23×C3#21711yescharacteristic
206C23×C3#21711yescharacteristic
207C23×C3#21711yescharacteristic
208C23×C3C22×Dic311yescharacteristic
209C23×C3C2×#6711yescharacteristic
210C3×D4—41no—
211C3×D4—41no—
212C3×D4—41no—
213C3×D4—41no—
214C3×D4—42no—
215C3×D4—41no—
216C3×D4—41no—
217C3×D4—81no—
218C3×D4—81no—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4—21no—
224C2×C3×C4—41no—
225C2×C3×C4—81no—
226C2×C3×C4#21711yescharacteristic
227C2×C3×C4C2×#6711yescharacteristic
228C2×Dic3—122no—
229C2×Dic3—242no—
230C3⋊C8—122no—
231C2×C9—21no—
232C2×C9—21no—
233C2×C9—21no—
234C2×C9—41no—
235C2×C9—41no—
236C2×C9—41no—
237C2×C9—41no—
238C2×C9—81no—
239C2×C9C2×#9911yescharacteristic
240C24C2×Dic911yescharacteristic
241C24C2×Dic911yescharacteristic, complemented
242C24#61111yescharacteristic
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—41no—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4—41no—
251C2×D4C2×Dic911yescharacteristic
252C2×D4#61111yescharacteristic
253C2×D4#61111yescharacteristic
254C2×D4C22×D911yescharacteristic
255C22×C4—21no—
256C22×C4—361no—
257C22×C4C2×Dic911yescharacteristic, complemented
258C22×C4#61111yescharacteristic
259M16—182no—
260M16—361no—
261C2×C8—361no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—182no—
270C22⋊C4—361no—
271C22⋊C4C2×Dic911yescharacteristic, complemented
272C22⋊C4C2×Dic911yescharacteristic, complemented
273C22×C3—21no—
274C22×C3—21no—
275C22×C3—21no—
276C22×C3—21no—
277C22×C3—41no—
278C22×C3—41no—
279C22×C3—41no—
280C22×C3—41no—
281C22×C3—41no—
282C22×C3—42no—
283C22×C3—41no—
284C22×C3—41no—
285C22×C3—41no—
286C22×C3—81no—
287C22×C3—81no—
288C22×C3—81no—
289C22×C3—82no—
290C22×C3#83411yescharacteristic
291C22×C3#83411yescharacteristic
292C22×C3C2×#21711yescharacteristic
293C3×C4—21no—
294C3×C4—21no—
295C3×C4—41no—
296C3×C4—41no—
297C3×C4—41no—
298Dic3—242no—
299C9#212111yescharacteristic, complemented, Sylow
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—41no—
306C23—81no—
307C23—81no—
308C23—81no—
309C23#367611yescharacteristic
310C23#367611yescharacteristic
311C23#367611yescharacteristic
312C23C22×Dic911yescharacteristic
313C23C2×#61111yescharacteristic
314D4—41no—
315D4—41no—
316D4—41no—
317D4—41no—
318D4—42no—
319D4—41no—
320D4—41no—
321D4—81no—
322D4—81no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—41no—
329C2×C4—81no—
330C2×C4—362no—
331C2×C4—722no—
332C2×C4#367611yescharacteristic
333C2×C4C2×#61111yescharacteristic
334C8—362no—
335C2×C3—21no—
336C2×C3—21no—
337C2×C3—21no—
338C2×C3—41no—
339C2×C3—41no—
340C2×C3—41no—
341C2×C3—41no—
342C2×C3—81no—
343C2×C3C2×#83411yescharacteristic
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—42no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22—82no—
361C22#6339311yescharacteristic
362C22#6339311yescharacteristic
363C22C2×#367611yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—722no—
370C3#7184711yescharacteristic
371C2—21no—
372C2—21no—
373C2—21no—
374C2—41no—
375C2—41no—
376C2—41no—
377C2—41no—
378C2—81no—
379C2C2×#6339311yescharacteristic
subgroupG/H
centerC2C2×#63393
commutatorC23×C9C22×C4
FrattiniC2×C3×D4C22×D3
FittingC9×#534C2
socleC2×C3C2×#834
prime radicalC3×#534D3
cosocleC2×D4×C9C23
hypercenter#534D9
hypocenterC9#2121
LCSG ▷ C23×C9 ▷ C22×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2 ◁ C23 ◁ C22×D4 ◁ #534

Complements

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

NH ≅ G/Ntype
2. C2×#63393C2semidirect
3. C2×#63391C2semidirect
4. #10588216C2semidirect
5. #10588213C2semidirect
7. C22×D4×C9C4semidirect
10. C9×#123C4semidirect
15. C9×#120C4semidirect
17. C2×C9×C22⋊C4C4semidirect
30. C24×C9C2×C4semidirect
45. C22×C4×C9C2×C4semidirect
55. C9×C22⋊C4C2×C4semidirect
56. C9×C22⋊C4C2×C4semidirect
179. C22×D4Dic9semidirect
183. #123Dic9semidirect
188. #120Dic9semidirect
191. C2×C22⋊C4Dic9semidirect
241. C24C2×Dic9semidirect
257. C22×C4C2×Dic9semidirect
271. C22⋊C4C2×Dic9semidirect
272. C22⋊C4C2×Dic9semidirect
299. C9#2121semidirect

Maximal subgroups

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

subgroupindex
C9×#5342
C2×#633932
C2×#633912
#105882162
#105882132
#718473