Finite Group Databasebeta

← #11796231

Subgroups — #11796231

Order 1152.

840 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
1C32×#534C211yesmaximal, characteristic
2C2×#63661C211yesmaximal, characteristic, complemented
3C2×#63660C211yesmaximal, characteristic, complemented
4#10589405C212yesmaximal, complemented
5#10589402C212yesmaximal, complemented
6#71847—34nomaximal
7C22×C32×D4C411yescharacteristic, complemented
8C22×C32×D4C2211yescharacteristic
9C32×#123—21no—
10C32×#123C411yescharacteristic, complemented
11C32×#123C2211yescharacteristic
12C32×#121—21no—
13C32×#121—21no—
14C32×#120—21no—
15C32×#120C411yescharacteristic, complemented
16C32×#120C2211yescharacteristic
17C2×C32×C22⋊C4C411yescharacteristic, complemented
18C2×#3757—21no—
19C2×#3748—21no—
20#63661—21no—
21#63661C2212yes—
22#63660—21no—
23#63660C2212yes—
24C3×#534D314yes—
25C2×#834—34no—
26C2×#833—34no—
27#4539—38no—
28#4536—38no—
29C24×C32C2×C411yescharacteristic
30C24×C32C2×C411yescharacteristic, complemented
31C24×C32D411yescharacteristic
32C2×C32×D4—21no—
33C2×C32×D4—21no—
34C2×C32×D4—21no—
35C2×C32×D4—21no—
36C2×C32×D4—41no—
37C2×C32×D4—41no—
38C2×C32×D4—41no—
39C2×C32×D4—41no—
40C2×C32×D4C2×C411yescharacteristic
41C2×C32×D4D411yescharacteristic
42C2×C32×D4D411yescharacteristic
43C2×C32×D4C2311yescharacteristic
44C22×C32×C4—21no—
45C22×C32×C4C2×C411yescharacteristic, complemented
46C22×C32×C4D411yescharacteristic
47C22×C3⋊Dic3—41no—
48C32×C4⋊C4—21no—
49C32×C4⋊C4—21no—
50C32×C22⋊C4—21no—
51C32×C22⋊C4—21no—
52C32×C22⋊C4—21no—
53C32×C22⋊C4—21no—
54C32×C22⋊C4—21no—
55C32×C22⋊C4C2×C411yescharacteristic, complemented
56C32×C22⋊C4C2×C411yescharacteristic, complemented
57#3757—22no—
58#3757—41no—
59#3748—22no—
60#3748—41no—
61C2×C3⋊(C3⋊C8)—41no—
62#2121—91noSylow
63C22×C3×D4Dic314yescomplemented
64C22×C3×D4C2×D314yes—
65C3×#123—24no—
66C3×#123Dic314yescomplemented
67C3×#123C2×D314yes—
68C3×#121—24no—
69C3×#121—24no—
70C3×#120—24no—
71C3×#120Dic314yescomplemented
72C3×#120C2×D314yes—
73C2×C3×C22⋊C4Dic314yescomplemented
74C2×#217—64no—
75C2×#208—64no—
76#834—38no—
77#834—64no—
78#833—38no—
79#833—64no—
80C23×C32—21no—
81C23×C32—21no—
82C23×C32—21no—
83C23×C32—21no—
84C23×C32—21no—
85C23×C32—41no—
86C23×C32—81no—
87C23×C32—81no—
88C23×C32—81no—
89C23×C32C22⋊C411yescharacteristic
90C23×C32C22⋊C411yescharacteristic
91C23×C32C22⋊C411yescharacteristic
92C23×C32C22×C411yescharacteristic
93C23×C32C2×D411yescharacteristic
94C32×D4—41no—
95C32×D4—41no—
96C32×D4—41no—
97C32×D4—41no—
98C32×D4—42no—
99C32×D4—41no—
100C32×D4—41no—
101C32×D4—81no—
102C32×D4—81no—
103C2×C32×C4—21no—
104C2×C32×C4—21no—
105C2×C32×C4—21no—
106C2×C32×C4—21no—
107C2×C32×C4—21no—
108C2×C32×C4—41no—
109C2×C32×C4—81no—
110C2×C32×C4C22⋊C411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C3⋊Dic3—42no—
113C2×C3⋊Dic3—82no—
114C3⋊(C3⋊C8)—42no—
115#534C3⋊D311yescharacteristic
116C2×#100—91no—
117C2×#99—91no—
118#352—92no—
119AΣL(1,𝔽16)—92no—
120C24×C3C2×Dic314yes—
121C24×C3C2×Dic314yescomplemented
122C24×C3#6714yes—
123C2×C3×D4—24no—
124C2×C3×D4—24no—
125C2×C3×D4—24no—
126C2×C3×D4—24no—
127C2×C3×D4—44no—
128C2×C3×D4—44no—
129C2×C3×D4—44no—
130C2×C3×D4—44no—
131C2×C3×D4C2×Dic314yes—
132C2×C3×D4#6714yes—
133C2×C3×D4#6714yes—
134C2×C3×D4C22×D314yes—
135C22×C3×C4—24no—
136C22×C3×C4C2×Dic314yescomplemented
137C22×C3×C4#6714yes—
138C22×Dic3—124no—
139C3×C4⋊C4—24no—
140C3×C4⋊C4—24no—
141C3×C22⋊C4—24no—
142C3×C22⋊C4—24no—
143C3×C22⋊C4—24no—
144C3×C22⋊C4—24no—
145C3×C22⋊C4—24no—
146C3×C22⋊C4C2×Dic314yescomplemented
147C3×C22⋊C4C2×Dic314yescomplemented
148#217—68no—
149#217—124no—
150#208—68no—
151#208—124no—
152C2×C3⋊C8—124no—
153C22×C32—21no—
154C22×C32—21no—
155C22×C32—21no—
156C22×C32—21no—
157C22×C32—41no—
158C22×C32—41no—
159C22×C32—41no—
160C22×C32—41no—
161C22×C32—41no—
162C22×C32—42no—
163C22×C32—41no—
164C22×C32—41no—
165C22×C32—41no—
166C22×C32—81no—
167C22×C32—81no—
168C22×C32—81no—
169C22×C32—82no—
170C22×C32#9911yescharacteristic
171C22×C32#9911yescharacteristic
172C22×C32C2×C22⋊C411yescharacteristic
173C32×C4—21no—
174C32×C4—21no—
175C32×C4—41no—
176C32×C4—41no—
177C32×C4—41no—
178C3⋊Dic3—82no—
179C22×D4C3⋊Dic311yescharacteristic, complemented
180C22×D4C2×C3⋊D311yescharacteristic
181C2×M16—181no—
182#123—21no—
183#123C3⋊Dic311yescharacteristic, complemented
184#123C2×C3⋊D311yescharacteristic
185#121—21no—
186#121—21no—
187#120—21no—
188#120C3⋊Dic311yescharacteristic, complemented
189#120C2×C3⋊D311yescharacteristic
190C2×C22⋊C4—181no—
191C2×C22⋊C4C3⋊Dic311yescharacteristic, complemented
192#100—92no—
193#100—181no—
194#99—92no—
195#99—181no—
196C23×C3—24no—
197C23×C3—24no—
198C23×C3—24no—
199C23×C3—24no—
200C23×C3—24no—
201C23×C3—44no—
202C23×C3—84no—
203C23×C3—84no—
204C23×C3—84no—
205C23×C3#21714yes—
206C23×C3#21714yes—
207C23×C3#21714yes—
208C23×C3C22×Dic314yes—
209C23×C3C2×#6714yes—
210C3×D4—44no—
211C3×D4—44no—
212C3×D4—44no—
213C3×D4—44no—
214C3×D4—48no—
215C3×D4—44no—
216C3×D4—44no—
217C3×D4—84no—
218C3×D4—84no—
219C2×C3×C4—24no—
220C2×C3×C4—24no—
221C2×C3×C4—24no—
222C2×C3×C4—24no—
223C2×C3×C4—24no—
224C2×C3×C4—44no—
225C2×C3×C4—84no—
226C2×C3×C4#21714yes—
227C2×C3×C4C2×#6714yes—
228C2×Dic3—128no—
229C2×Dic3—248no—
230C3⋊C8—128no—
231C2×C32—21no—
232C2×C32—21no—
233C2×C32—21no—
234C2×C32—41no—
235C2×C32—41no—
236C2×C32—41no—
237C2×C32—41no—
238C2×C32—81no—
239C2×C32C2×#9911yescharacteristic
240C24C2×C3⋊Dic311yescharacteristic
241C24C2×C3⋊Dic311yescharacteristic, complemented
242C24#63811yescharacteristic
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×C3⋊Dic311yescharacteristic
252C2×D4#63811yescharacteristic
253C2×D4#63811yescharacteristic
254C2×D4C22×C3⋊D311yescharacteristic
255C22×C4—21no—
256C22×C4—361no—
257C22×C4C2×C3⋊Dic311yescharacteristic, complemented
258C22×C4#63811yescharacteristic
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×C3⋊Dic311yescharacteristic, complemented
272C22⋊C4C2×C3⋊Dic311yescharacteristic, complemented
273C22×C3—24no—
274C22×C3—24no—
275C22×C3—24no—
276C22×C3—24no—
277C22×C3—44no—
278C22×C3—44no—
279C22×C3—44no—
280C22×C3—44no—
281C22×C3—44no—
282C22×C3—48no—
283C22×C3—44no—
284C22×C3—44no—
285C22×C3—44no—
286C22×C3—84no—
287C22×C3—84no—
288C22×C3—84no—
289C22×C3—88no—
290C22×C3#83414yes—
291C22×C3#83414yes—
292C22×C3C2×#21714yes—
293C3×C4—24no—
294C3×C4—24no—
295C3×C4—44no—
296C3×C4—44no—
297C3×C4—44no—
298Dic3—248no—
299C32#212111yescharacteristic, complemented, Sylow
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—41no—
306C23—81no—
307C23—81no—
308C23—81no—
309C23#375711yescharacteristic
310C23#375711yescharacteristic
311C23#375711yescharacteristic
312C23C22×C3⋊Dic311yescharacteristic
313C23C2×#63811yescharacteristic
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#375711yescharacteristic
333C2×C4C2×#63811yescharacteristic
334C8—362no—
335C2×C3—24no—
336C2×C3—24no—
337C2×C3—24no—
338C2×C3—44no—
339C2×C3—44no—
340C2×C3—44no—
341C2×C3—44no—
342C2×C3—84no—
343C2×C3C2×#83414yes—
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#6366111yescharacteristic
362C22#6366111yescharacteristic
363C22C2×#375711yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—722no—
370C3#7184714yescomplemented
371C2—21no—
372C2—21no—
373C2—21no—
374C2—41no—
375C2—41no—
376C2—41no—
377C2—41no—
378C2—81no—
379C2C2×#6366111yescharacteristic
subgroupG/H
centerC2C2×#63661
commutatorC23×C32C22×C4
FrattiniC2×D4C22×C3⋊D3
Fitting, prime radicalC32×#534C2
socleC2×C32C2×#99
cosocleC2×C32×D4C23
hypercenter#534C3⋊D3
hypocenterC32#2121
LCSG ▷ C23×C32 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C23 ◁ C22×D4 ◁ #534

Complements

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

NH ≅ G/Ntype
2. C2×#63661C2semidirect
3. C2×#63660C2semidirect
4. #10589405C2semidirect
5. #10589402C2semidirect
7. C22×C32×D4C4semidirect
10. C32×#123C4semidirect
15. C32×#120C4semidirect
17. C2×C32×C22⋊C4C4semidirect
30. C24×C32C2×C4semidirect
45. C22×C32×C4C2×C4semidirect
55. C32×C22⋊C4C2×C4semidirect
56. C32×C22⋊C4C2×C4semidirect
63. C22×C3×D4Dic3semidirect
66. C3×#123Dic3semidirect
71. C3×#120Dic3semidirect
73. C2×C3×C22⋊C4Dic3semidirect
121. C24×C3C2×Dic3semidirect
136. C22×C3×C4C2×Dic3semidirect
146. C3×C22⋊C4C2×Dic3semidirect
147. C3×C22⋊C4C2×Dic3semidirect
179. C22×D4C3⋊Dic3semidirect
183. #123C3⋊Dic3semidirect
188. #120C3⋊Dic3semidirect
191. C2×C22⋊C4C3⋊Dic3semidirect
241. C24C2×C3⋊Dic3semidirect
257. C22×C4C2×C3⋊Dic3semidirect
271. C22⋊C4C2×C3⋊Dic3semidirect
272. C22⋊C4C2×C3⋊Dic3semidirect
299. C32#2121semidirect
370. C3#71847semidirect

Maximal subgroups

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

subgroupindex
C32×#5342
C2×#636612
C2×#636602
#105894052
#105894022
#718473