Finite Group Databasebeta

← #11775155

Subgroups — #11775155

Order 1152.

633 conjugacy classes of subgroups.

The subgroup lattice has 379 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5477C211yesmaximal, characteristic
2#10592631C211yesmaximal, characteristic, complemented
3C3×#4926C211yesmaximal, characteristic, complemented
4#10589150C214yesmaximal, complemented
5#71812—31nomaximal
6#70832—31nomaximal
7C2×C3×#235—21no—
8C2×C32×C42C2211yescharacteristic
9C2×C4×C3⋊Dic3—21no—
10C3×#930—21no—
11C3×#930C2212yes—
12C3×#875—21no—
13C3×#874C411yescharacteristic, complemented
14C3×C4×D12—21no—
15C3×C4×D12C412yescomplemented
16C3×#869C411yescharacteristic, complemented
17#63658—21no—
18#63658C2212yes—
19C3×#830C2212yes—
20C3×C4⋊(C3⋊C8)—21no—
21C3×#803—21no—
22C3×#532—31no—
23#5477D311yescharacteristic
24C3×#432—31no—
25#4932—31no—
26#4932—31no—
27#4932—61no—
28#4926D311yescharacteristic, complemented
29#4537—34no—
30#4470—34no—
31C22×C32×C4D411yescharacteristic
32C22×C32×C4D411yescharacteristic
33C22×C32×C4C2311yescharacteristic
34C22×C3⋊Dic3—22no—
35C2×C3×#67—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
46C4×C3⋊Dic3—24no—
47C3×(C2×D3)⋊C4—22no—
48C3×(C2×D3)⋊C4—22no—
49C3×C4⋊Dic3—21no—
50C3×C4⋊Dic3C2×C412yes—
51C2×C3×C3⋊C8—22no—
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×C42C2×D311yescharacteristic
64C2×C3×C42C2×D311yescharacteristic
65#930—21no—
66#930C2×D312yes—
67C2×C4×Dic3—62no—
68C2×C4×Dic3—61no—
69C2×C4×Dic3—61no—
70#875—21no—
71#874Dic311yescharacteristic, complemented
72C4×D12—21no—
73C4×D12Dic312yescomplemented
74#869Dic311yescharacteristic, complemented
75C3×C4⋊C8—61no—
76C3×C22⋊C8—32no—
77C3×#97—61no—
78C3⋊#95—32no—
79C3⋊#95—32no—
80C3⋊#95—62no—
81C3⋊#95—62no—
82C3⋊#95—61no—
83C3⋊#95—61no—
84#830C2×D312yes—
85C4⋊(C3⋊C8)—21no—
86#803—21no—
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
98C2×C3⋊Dic3—24no—
99C2×C3⋊Dic3—42no—
100C2×C3⋊Dic3—42no—
101C3×#67—44no—
102C2×C3×Dic3—22no—
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—31no—
111#376—91no—
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×C4D1211yescharacteristic
124C22×C3×C4D1211yescharacteristic
125C22×C3×C4#6711yescharacteristic
126C22×C3×C4#6711yescharacteristic
127C22×C3×C4C22×D311yescharacteristic
128C22×C3×C4C22×D311yescharacteristic
129C2×#67—22no—
130C22×Dic3—64no—
131C22×Dic3—62no—
132C22×Dic3—62no—
133#235—44no—
134C2×D12—21no—
135C2×D12—21no—
136C2×D12C2×Dic312yes—
137C2×C4×D3—22no—
138C2×Dic6—21no—
139C2×C3×C8—62no—
140C3×C4⋊C4—32no—
141C3×C4⋊C4—61no—
142C3×C22⋊C4—62no—
143C3×C22⋊C4—62no—
144C3×C42—21no—
145C3×C42—21no—
146C3×C42—21no—
147C3×C42—21no—
148C3×C42C4×D311yescharacteristic
149C3×C42C4×D311yescharacteristic
150C3×C42C2×Dic311yescharacteristic
151C3×C42C2×Dic311yescharacteristic
152C3×C42#6711yescharacteristic
153C3×C42#6711yescharacteristic
154C3×C42#6711yescharacteristic
155C3×C42#6711yescharacteristic
156(C2×D3)⋊C4—22no—
157(C2×D3)⋊C4—22no—
158C4⋊Dic3—21no—
159C4⋊Dic3C2×Dic312yes—
160C4×Dic3—68no—
161C4×Dic3—64no—
162C4×Dic3—64no—
163C2×C3⋊C8—22no—
164C22×C32—21no—
165C22×C32—21no—
166C22×C32C2×C22⋊C411yescharacteristic
167C22×C32AGL(1,ℤ/8)12yes—
168C2×C3×D3—42no—
169C2×C3×D3—42no—
170C2×C3×D3—42no—
171C32×C4—21no—
172C32×C4—21no—
173C32×C4—21no—
174C32×C4—21no—
175C32×C4—21no—
176C32×C4#10412yes—
177C3⋊Dic3—44no—
178C3×Dic3—42no—
179C2×#41—61no—
180C4⋊Q8—31no—
181#127—31no—
182#124—61no—
183#121—32no—
184#121—61no—
185C4×D4—32no—
186C4×D4—61no—
187C2×C42—181no—
188C2×C42D3211yescharacteristic
189C4⋊C8—61no—
190C22⋊C8—32no—
191#97—61no—
192#95—92no—
193#95—181no—
194C23×C3—21no—
195C23×C3—62no—
196C23×C3C2×D1211yescharacteristic
197C23×C3C2×#6711yescharacteristic
198C22×D3—22no—
199C3×Q8—122no—
200C3×D4—122no—
201C3×D4—122no—
202C3×D4—124no—
203C3×D4—122no—
204C2×C3×C4—24no—
205C2×C3×C4—22no—
206C2×C3×C4—22no—
207C2×C3×C4—22no—
208C2×C3×C4—22no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—42no—
216C2×C3×C4—41no—
217C2×C3×C4—41no—
218C2×C3×C4—42no—
219C2×C3×C4—62no—
220C2×C3×C4—124no—
221C2×C3×C4(C2×D3)⋊C411yescharacteristic
222C2×C3×C4(C2×D3)⋊C411yescharacteristic
223C2×C3×C4(C2×D3)⋊C411yescharacteristic
224C2×C3×C4(C2×D3)⋊C411yescharacteristic
225C2×C3×C4#21711yescharacteristic
226C2×C3×C4#21711yescharacteristic
227C2×C3×C4#21711yescharacteristic
228C2×C3×C4#21711yescharacteristic
229C2×C3×C4C2×C4×D311yescharacteristic
230C2×C3×C4C22×Dic311yescharacteristic
231C2×C3×C4C2×#6711yescharacteristic
232C2×C3×C4C2×#6711yescharacteristic
233#67—44no—
234C2×Dic3—22no—
235C2×Dic3—68no—
236C2×Dic3—64no—
237C2×Dic3—64no—
238C2×Dic3—124no—
239C2×Dic3—122no—
240C2×Dic3—122no—
241C2×Dic3—124no—
242C2×Dic3—122no—
243C2×Dic3—122no—
244D12—42no—
245D12—42no—
246D12—42no—
247C4×D3—44no—
248Dic6—42no—
249C3×C8—122no—
250C3⋊C8—42no—
251C2×C32—22no—
252C2×C32#41011yescharacteristic
253C2×C32#41811yescharacteristic
254C2×C32C2×#10411yescharacteristic
255C3×D3—82no—
256#41—124no—
257C2×Q8—61no—
258C2×D4—32no—
259C2×D4—62no—
260C2×D4—61no—
261C2×D4—61no—
262C22×C4—62no—
263C22×C4—182no—
264C22×C4#62611yescharacteristic
265C22×C4#62611yescharacteristic
266C22×C4C2×D3211yescharacteristic
267C2×C8—62no—
268C4⋊C4—32no—
269C4⋊C4—61no—
270C22⋊C4—62no—
271C22⋊C4—62no—
272C42—184no—
273C42D3×Dic311yescharacteristic
274C42D3×Dic311yescharacteristic
275C42#62511yescharacteristic
276C42#62511yescharacteristic
277C22×C3—22no—
278C22×C3—22no—
279C22×C3—21no—
280C22×C3—21no—
281C22×C3—21no—
282C22×C3—21no—
283C22×C3—22no—
284C22×C3—21no—
285C22×C3—122no—
286C22×C3—122no—
287C22×C3—122no—
288C22×C3#90812yes—
289C22×C3C2×(C2×D3)⋊C411yescharacteristic
290C22×C3#93212yes—
291C22×C3C2×#21711yescharacteristic
292C2×D3—42no—
293C2×D3—42no—
294C2×D3—42no—
295C3×C4—22no—
296C3×C4—21no—
297C3×C4—21no—
298C3×C4—21no—
299C3×C4—21no—
300C3×C4—21no—
301C3×C4—21no—
302C3×C4—21no—
303C3×C4—21no—
304C3×C4—21no—
305C3×C4—21no—
306C3×C4—22no—
307C3×C4—41no—
308C3×C4—41no—
309C3×C4—41no—
310C3×C4—41no—
311C3×C4—122no—
312C3×C4#82512yes—
313C3×C4#83712yes—
314Dic3—42no—
315Dic3—128no—
316Dic3—124no—
317Dic3—124no—
318C32#150511yescharacteristic, complemented, Sylow
319C23—62no—
320C23C2×#62611yescharacteristic
321Q8—122no—
322D4—122no—
323D4—122no—
324D4—124no—
325D4—122no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4—62no—
330C2×C4—124no—
331C2×C4—184no—
332C2×C4—362no—
333C2×C4—362no—
334C2×C4(C2×D3)⋊Dic311yescharacteristic
335C2×C4(C2×D3)⋊Dic311yescharacteristic
336C2×C4(C2×D3)⋊Dic311yescharacteristic
337C2×C4(C2×D3)⋊Dic311yescharacteristic
338C2×C4C2×D3×Dic311yescharacteristic
339C2×C4C2×#62511yescharacteristic
340C8—122no—
341C2×C3—24no—
342C2×C3—22no—
343C2×C3—22no—
344C2×C3—21no—
345C2×C3—21no—
346C2×C3—21no—
347C2×C3—242no—
348C2×C3#500611yescharacteristic
349C2×C3#513111yescharacteristic
350C2×C3C2×#82511yescharacteristic
351C2×C3#521511yescharacteristic
352C2×C3C2×#83711yescharacteristic
353C2×C3#524011yescharacteristic
354D3—82no—
355C22—21no—
356C22—21no—
357C22—122no—
358C22—122no—
359C22—122no—
360C22#6383012yes—
361C22C2×(C2×D3)⋊Dic311yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—122no—
368C4—364no—
369C4#6356812yes—
370C3—21no—
371C3#7083211yescharacteristic, complemented
372C3#7181211yescharacteristic, complemented
373C2—22no—
374C2—242no—
375C2#1059108611yescharacteristic
376C2C2×#6356811yescharacteristic
377C2#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. #10592631C2semidirect
3. C3×#4926C2semidirect
4. #10589150C2semidirect
13. C3×#874C4semidirect
15. C3×C4×D12C4semidirect
16. C3×#869C4semidirect
28. #4926D3semidirect
71. #874Dic3semidirect
73. C4×D12Dic3semidirect
74. #869Dic3semidirect
318. C32#1505semidirect
371. C3#70832semidirect
372. C3#71812semidirect

Maximal subgroups

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

subgroupindex
C3×#54772
#105926312
C3×#49262
#105891502
#718123
#708323