Finite Group Databasebeta

← #11775157

Subgroups — #11775157

Order 1152.

599 conjugacy classes of subgroups.

The subgroup lattice has 375 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5477C211yesmaximal, characteristic
2#10592625C211yesmaximal, characteristic, complemented
3C3×#4932C211yesmaximal, characteristic, complemented
4#10589149C214yesmaximal, complemented
5#71812—31nomaximal
6#69432—31nomaximal
7C2×C3×#235—21no—
8C2×C32×C42C2211yescharacteristic
9C3×#930—21no—
10C3×#930C2212yes—
11C2×C3×C4×Dic3—21no—
12C3×#875—21no—
13C3×#874C411yescharacteristic, complemented
14C3×C4×D12—21no—
15C3×C4×D12C412yescomplemented
16C3×#869C411yescharacteristic, complemented
17#63657C2212yes—
18C4⋊(C3⋊(C3⋊C8))—21no—
19#63630—21no—
20C3×C3⋊#95—21no—
21C3×C3⋊#95C2212yes—
22C3×#532—31no—
23#5477D311yescharacteristic
24C3×#376—31no—
25#4932D311yescharacteristic, complemented
26#4926—31no—
27#4926—31no—
28#4926—61no—
29#4537—34no—
30#4451—34no—
31C22×C32×C4D411yescharacteristic
32C22×C32×C4D411yescharacteristic
33C22×C32×C4C2311yescharacteristic
34C2×C3×#67—22no—
35C22×C3×Dic3—22no—
36C3×#235—44no—
37C2×C3×D12—21no—
38C2×C3×D12—21no—
39C2×C3×D12C2×C412yes—
40C2×C3×C4×D3—22no—
41C2×C3×Dic6—21no—
42C32×C42C2×C411yescharacteristic
43C32×C42C2×C411yescharacteristic
44C32×C42D411yescharacteristic
45C32×C42D411yescharacteristic
46C2×C3⋊(C3⋊C8)—22no—
47C3×(C2×D3)⋊C4—22no—
48C3×(C2×D3)⋊C4—22no—
49C3×C4⋊Dic3—21no—
50C3×C4⋊Dic3C2×C412yes—
51C3×C4×Dic3—24no—
52#1505—91noSylow
53C2×C3×#41—61no—
54C2×#235—21no—
55C3×C4⋊Q8—31no—
56C3×#127—31no—
57C3×#124—61no—
58C3×#121—32no—
59C3×#121—61no—
60C3×C4×D4—32no—
61C3×C4×D4—61no—
62C2×C3×C42—21no—
63C2×C3×C42—61no—
64C2×C3×C42C2×D311yescharacteristic
65C2×C3×C42C2×D311yescharacteristic
66#930—21no—
67#930C2×D312yes—
68C2×C4×Dic3—21no—
69#875—21no—
70#874Dic311yescharacteristic, complemented
71C4×D12—21no—
72C4×D12Dic312yescomplemented
73#869Dic311yescharacteristic, complemented
74C3×#95—32no—
75C3×#95—61no—
76C3⋊#95—21no—
77C3⋊#95C2×D312yes—
78#830—32no—
79#830—32no—
80#830—62no—
81C4⋊(C3⋊C8)—62no—
82C4⋊(C3⋊C8)—61no—
83C4⋊(C3⋊C8)—61no—
84#803—62no—
85#803—61no—
86#803—61no—
87C23×C32C2×D411yescharacteristic
88C22×C3×D3—22no—
89C2×C32×C4—22no—
90C2×C32×C4—22no—
91C2×C32×C4—41no—
92C2×C32×C4C22⋊C411yescharacteristic
93C2×C32×C4C22⋊C411yescharacteristic
94C2×C32×C4C22⋊C411yescharacteristic
95C2×C32×C4C22⋊C411yescharacteristic
96C2×C32×C4C22×C411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C3×#67—44no—
99C2×C3×Dic3—24no—
100C2×C3×Dic3—22no—
101C2×C3×Dic3—42no—
102C2×C3×Dic3—42no—
103C3×D12—42no—
104C3×D12—42no—
105C3×D12—42no—
106C3×C4×D3—44no—
107C3×Dic6—42no—
108C3⋊(C3⋊C8)—42no—
109#532—31no—
110#432—91no—
111#376—31no—
112#327—94no—
113C3×#41—124no—
114C2×C3×Q8—61no—
115C2×C3×D4—32no—
116C2×C3×D4—62no—
117C2×C3×D4—61no—
118C2×C3×D4—61no—
119C22×C3×C4—21no—
120C22×C3×C4—21no—
121C22×C3×C4—21no—
122C22×C3×C4—62no—
123C22×C3×C4—62no—
124C22×C3×C4#6711yescharacteristic
125C22×C3×C4#6711yescharacteristic
126C22×C3×C4#6711yescharacteristic
127C22×C3×C4#6711yescharacteristic
128C22×C3×C4C22×D311yescharacteristic
129C22×C3×C4C22×D311yescharacteristic
130C2×#67—22no—
131C22×Dic3—22no—
132#235—44no—
133C2×D12—21no—
134C2×D12—21no—
135C2×D12C2×Dic312yes—
136C2×C4×D3—22no—
137C2×Dic6—21no—
138C3×C4⋊C4—32no—
139C3×C4⋊C4—61no—
140C3×C22⋊C4—62no—
141C3×C22⋊C4—62no—
142C3×C42—21no—
143C3×C42—21no—
144C3×C42—21no—
145C3×C42—21no—
146C3×C42—64no—
147C3×C42C4×D311yescharacteristic
148C3×C42C4×D311yescharacteristic
149C3×C42D1211yescharacteristic
150C3×C42D1211yescharacteristic
151C3×C42C2×Dic311yescharacteristic
152C3×C42C2×Dic311yescharacteristic
153C3×C42#6711yescharacteristic
154C3×C42#6711yescharacteristic
155(C2×D3)⋊C4—22no—
156(C2×D3)⋊C4—22no—
157C4⋊Dic3—21no—
158C4⋊Dic3C2×Dic312yes—
159C4×Dic3—24no—
160C2×C3⋊C8—64no—
161C2×C3⋊C8—62no—
162C2×C3⋊C8—62no—
163C22×C32—21no—
164C22×C32—21no—
165C22×C32C2×C22⋊C411yescharacteristic
166C22×C32AGL(1,ℤ/8)12yes—
167C2×C3×D3—42no—
168C2×C3×D3—42no—
169C2×C3×D3—42no—
170C32×C4—21no—
171C32×C4—21no—
172C32×C4—21no—
173C32×C4—21no—
174C32×C4—21no—
175C32×C4#10412yes—
176C3×Dic3—44no—
177C3×Dic3—42no—
178C2×#41—61no—
179C4⋊Q8—31no—
180#127—31no—
181#124—61no—
182#121—32no—
183#121—61no—
184C4×D4—32no—
185C4×D4—61no—
186C2×C42—61no—
187C2×C42D3211yescharacteristic
188C4⋊C8—181no—
189C22⋊C8—92no—
190#97—181no—
191#95—32no—
192#95—61no—
193C23×C3—21no—
194C23×C3—62no—
195C23×C3C2×#6711yescharacteristic
196C23×C3C2×#6711yescharacteristic
197C22×D3—22no—
198C3×Q8—122no—
199C3×D4—122no—
200C3×D4—122no—
201C3×D4—124no—
202C3×D4—122no—
203C2×C3×C4—22no—
204C2×C3×C4—22no—
205C2×C3×C4—22no—
206C2×C3×C4—22no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—42no—
214C2×C3×C4—42no—
215C2×C3×C4—41no—
216C2×C3×C4—41no—
217C2×C3×C4—42no—
218C2×C3×C4—64no—
219C2×C3×C4—62no—
220C2×C3×C4—124no—
221C2×C3×C4—122no—
222C2×C3×C4—122no—
223C2×C3×C4(C2×D3)⋊C411yescharacteristic
224C2×C3×C4(C2×D3)⋊C411yescharacteristic
225C2×C3×C4(C2×D3)⋊C411yescharacteristic
226C2×C3×C4(C2×D3)⋊C411yescharacteristic
227C2×C3×C4#21711yescharacteristic
228C2×C3×C4#21711yescharacteristic
229C2×C3×C4#21711yescharacteristic
230C2×C3×C4#21711yescharacteristic
231C2×C3×C4C2×C4×D311yescharacteristic
232C2×C3×C4C2×D1211yescharacteristic
233C2×C3×C4C22×Dic311yescharacteristic
234C2×C3×C4C2×#6711yescharacteristic
235#67—44no—
236C2×Dic3—24no—
237C2×Dic3—22no—
238C2×Dic3—42no—
239C2×Dic3—42no—
240D12—42no—
241D12—42no—
242D12—42no—
243C4×D3—44no—
244Dic6—42no—
245C3⋊C8—124no—
246C3⋊C8—122no—
247C3⋊C8—122no—
248C2×C32—22no—
249C2×C32#41011yescharacteristic
250C2×C32#41811yescharacteristic
251C2×C32C2×#10411yescharacteristic
252C3×D3—82no—
253#41—124no—
254C2×Q8—61no—
255C2×D4—32no—
256C2×D4—62no—
257C2×D4—61no—
258C2×D4—61no—
259C22×C4—62no—
260C22×C4—62no—
261C22×C4#62511yescharacteristic
262C22×C4#62511yescharacteristic
263C22×C4C2×D3211yescharacteristic
264C2×C8—182no—
265C4⋊C4—32no—
266C4⋊C4—61no—
267C22⋊C4—62no—
268C22⋊C4—62no—
269C42—64no—
270C42D3×Dic311yescharacteristic
271C42D3×Dic311yescharacteristic
272C42#62611yescharacteristic
273C42#62611yescharacteristic
274C22×C3—21no—
275C22×C3—21no—
276C22×C3—21no—
277C22×C3—21no—
278C22×C3—22no—
279C22×C3—21no—
280C22×C3—41no—
281C22×C3—41no—
282C22×C3—122no—
283C22×C3—122no—
284C22×C3—122no—
285C22×C3C2×(C2×D3)⋊C411yescharacteristic
286C22×C3#93212yes—
287C22×C3#94912yes—
288C22×C3C2×#21711yescharacteristic
289C2×D3—42no—
290C2×D3—42no—
291C2×D3—42no—
292C3×C4—22no—
293C3×C4—21no—
294C3×C4—21no—
295C3×C4—21no—
296C3×C4—21no—
297C3×C4—21no—
298C3×C4—21no—
299C3×C4—21no—
300C3×C4—21no—
301C3×C4—21no—
302C3×C4—21no—
303C3×C4—22no—
304C3×C4—41no—
305C3×C4—41no—
306C3×C4—41no—
307C3×C4—41no—
308C3×C4—124no—
309C3×C4—122no—
310C3×C4#80512yes—
311C3×C4#83712yes—
312Dic3—44no—
313Dic3—42no—
314C32#150511yescharacteristic, complemented, Sylow
315C23—62no—
316C23C2×#62511yescharacteristic
317Q8—122no—
318D4—122no—
319D4—122no—
320D4—124no—
321D4—122no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—41no—
325C2×C4—64no—
326C2×C4—62no—
327C2×C4—124no—
328C2×C4—122no—
329C2×C4—122no—
330C2×C4(C2×D3)⋊Dic311yescharacteristic
331C2×C4(C2×D3)⋊Dic311yescharacteristic
332C2×C4(C2×D3)⋊Dic311yescharacteristic
333C2×C4(C2×D3)⋊Dic311yescharacteristic
334C2×C4C2×D3×Dic311yescharacteristic
335C2×C4C2×#62611yescharacteristic
336C8—362no—
337C2×C3—22no—
338C2×C3—22no—
339C2×C3—21no—
340C2×C3—21no—
341C2×C3—21no—
342C2×C3—42no—
343C2×C3—242no—
344C2×C3C2×#80511yescharacteristic
345C2×C3#500111yescharacteristic
346C2×C3#500611yescharacteristic
347C2×C3#521511yescharacteristic
348C2×C3C2×#83711yescharacteristic
349C2×C3#524011yescharacteristic
350D3—82no—
351C22—21no—
352C22—21no—
353C22—122no—
354C22—122no—
355C22—122no—
356C22#6382312yes—
357C22C2×(C2×D3)⋊Dic311yescharacteristic
358C4—21no—
359C4—21no—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—124no—
364C4—122no—
365C4#6356912yes—
366C3—21no—
367C3#6943211yescharacteristic, complemented
368C3#7181211yescharacteristic, complemented
369C2—22no—
370C2—242no—
371C2#1059108511yescharacteristic
372C2C2×#6356911yescharacteristic
373C2#1059123111yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊Dic3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
prime radicalC3×#5477C2
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1505
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #10592625C2semidirect
3. C3×#4932C2semidirect
4. #10589149C2semidirect
13. C3×#874C4semidirect
15. C3×C4×D12C4semidirect
16. C3×#869C4semidirect
25. #4932D3semidirect
70. #874Dic3semidirect
72. C4×D12Dic3semidirect
73. #869Dic3semidirect
314. C32#1505semidirect
367. C3#69432semidirect
368. C3#71812semidirect

Maximal subgroups

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

subgroupindex
C3×#54772
#105926252
C3×#49322
#105891492
#718123
#694323