Finite Group Databasebeta

← #11802864

Subgroups — #11802864

Order 1152.

1133 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
1C2×#64081C211yesmaximal, characteristic
2C3×C4×C4⋊Dic3C212yesmaximal, complemented
3#10591359C211yesmaximal, characteristic, complemented
4#10591325C212yesmaximal
5#10591230C211yesmaximal, characteristic, complemented
6#10591202C214yesmaximal
7#10591197C214yesmaximal, complemented
8#73760—32nomaximal
9C22×C4×C3⋊D3C2211yescharacteristic
10C2×C32×C42C2211yescharacteristic
11C2×#3752C2212yes—
12C2×#3750C2212yes—
13C2×C4×C3⋊Dic3C2211yescharacteristic
14#64081C418yescomplemented
15C2×C3×C4⋊Dic3C2212yes—
16C2×C3×C4⋊Dic3C2212yes—
17C2×C3×C4×Dic3C2214yes—
18C2×#3724C2214yes—
19C2×#3722C2214yes—
20C3×C3⋊#95C2214yes—
21#63579C2214yes—
22#63579C2214yes—
23C2×#872—32no—
24C2×#872—61no—
25C3×C4×C4⋊C4—32no—
26#4987—32no—
27#4987—32no—
28#4977—32no—
29#4975—32no—
30#4940—34no—
31C4×C4⋊Dic3D312yescomplemented
32#4933—34no—
33#4669—34no—
34#4652—34no—
35C23×C3⋊D3C2311yescharacteristic
36C22×C32×C4C2312yes—
37C22×C32×C4C2311yescharacteristic
38C22×C3⋊Dic3C2311yescharacteristic
39C22×C3⋊Dic3C2312yes—
40C2×C4×C3⋊D3—22no—
41C2×C4×C3⋊D3—22no—
42C2×C4×C3⋊D3C2×C414yes—
43C22×C3×Dic3C2314yes—
44C22×C3×Dic3C2314yes—
45C32×C42C2×C414yes—
46#3752C2×C418yes—
47#3750C2×C418yes—
48C4×C3⋊Dic3C2×C414yes—
49C3×C4⋊Dic3—24no—
50C3×C4⋊Dic3—24no—
51C3×C4×Dic3—44no—
52#3724—44no—
53#3722—44no—
54#2314—91noSylow
55C22×C4×D3—32no—
56C22×C4×D3—61no—
57C2×C3×C4⋊C4—32no—
58C2×C3×C4⋊C4—32no—
59C2×C3×C42—21no—
60C2×C3×C42—34no—
61C2×C3×C42C2×D312yes—
62C2×(C2×D3)⋊C4—32no—
63C2×(C2×D3)⋊C4—32no—
64C2×(C2×D3)⋊C4—34no—
65C2×(C2×D3)⋊C4—34no—
66C2×(C2×D3)⋊C4—62no—
67C2×C4⋊Dic3C2×D312yes—
68C2×C4⋊Dic3C2×D312yes—
69C2×Dic3⋊C4—32no—
70C2×Dic3⋊C4—32no—
71C2×Dic3⋊C4—34no—
72C2×Dic3⋊C4—34no—
73C2×Dic3⋊C4—62no—
74C2×C4×Dic3—32no—
75C2×C4×Dic3—61no—
76C2×C4×Dic3C2×D314yes—
77#872—316no—
78#872—68no—
79C3×#95—34no—
80C3⋊#95—34no—
81C3⋊#95—34no—
82C3⋊#95—34no—
83C3⋊#95—34no—
84C3⋊#95C2×D314yes—
85C23×C32C2411yescharacteristic
86C22×C3⋊D3—21no—
87C22×C3⋊D3—21no—
88C22×C3⋊D3—22no—
89C22×C3⋊D3—22no—
90C22×C3⋊D3C22×C412yes—
91C2×C32×C4—22no—
92C2×C32×C4—22no—
93C2×C32×C4C22×C414yes—
94C2×C32×C4C22×C412yes—
95C2×C32×C4#4112yes—
96C2×C32×C4#4112yes—
97C2×C3⋊Dic3—21no—
98C2×C3⋊Dic3—21no—
99C2×C3⋊Dic3—22no—
100C2×C3⋊Dic3—22no—
101C2×C3⋊Dic3C22×C414yes—
102C2×C3⋊Dic3C22×C412yes—
103C4×C3⋊D3—28no—
104C2×C3×Dic3—24no—
105C2×C3×Dic3—24no—
106C2×C3×Dic3—24no—
107C2×C3×Dic3—24no—
108C2×C3×Dic3—24no—
109C2×C3×Dic3—24no—
110C2×#117—91no—
111#388—94no—
112#387—94no—
113#384—91no—
114#382—91no—
115#380—92no—
116C4×C4⋊C4—32no—
117C23×D3—32no—
118C23×D3—61no—
119C22×C3×C4—21no—
120C22×C3×C4—22no—
121C22×C3×C4—34no—
122C22×C3×C4—34no—
123C22×C3×C4C22×D312yes—
124C22×C3×C4C22×D312yes—
125C22×C3×C4C22×D312yes—
126C22×Dic3—32no—
127C22×Dic3—32no—
128C22×Dic3—32no—
129C22×Dic3—61no—
130C22×Dic3—62no—
131C22×Dic3C22×D314yes—
132C22×Dic3C22×D314yes—
133C2×C4×D3—38no—
134C2×C4×D3—64no—
135C2×C4×D3—64no—
136C2×C4×D3—64no—
137C2×C4×D3—64no—
138C2×C4×D3—64no—
139C3×C4⋊C4—64no—
140C3×C4⋊C4—64no—
141C3×C42—24no—
142C3×C42—124no—
143C3×C42C4×D318yes—
144(C2×D3)⋊C4—38no—
145(C2×D3)⋊C4—38no—
146(C2×D3)⋊C4—68no—
147(C2×D3)⋊C4—124no—
148(C2×D3)⋊C4—124no—
149C4⋊Dic3—24no—
150C4⋊Dic3—24no—
151Dic3⋊C4—38no—
152Dic3⋊C4—38no—
153Dic3⋊C4—68no—
154Dic3⋊C4—124no—
155Dic3⋊C4—124no—
156C4×Dic3—38no—
157C4×Dic3—44no—
158C4×Dic3—64no—
159C22×C32C23×C411yescharacteristic
160C22×C32C2×#4111yescharacteristic
161C22×C32C2×#4111yescharacteristic
162C22×C32H(5,𝔽2)12yes—
163C22×C322−1+412yes—
164C2×C3⋊D3—22no—
165C2×C3⋊D3—24no—
166C2×C3⋊D3—41no—
167C2×C3⋊D3—41no—
168C2×C3⋊D3—42no—
169C32×C4—24no—
170C32×C4#11714yes—
171C3⋊Dic3—22no—
172C3⋊Dic3—24no—
173C3×Dic3—44no—
174C3×Dic3—44no—
175C23×C4—91no—
176#117—98no—
177C2×C4⋊C4—32no—
178C2×C4⋊C4—32no—
179C2×C4⋊C4—92no—
180C2×C4⋊C4—94no—
181C2×C22⋊C4—92no—
182C2×C22⋊C4—94no—
183C2×C42—34no—
184C2×C42—91no—
185C2×C42D3211yescharacteristic
186#95—34no—
187#95—94no—
188#95—94no—
189C23×C3—21no—
190C23×C3C23×D312yes—
191C22×D3—34no—
192C22×D3—62no—
193C22×D3—62no—
194C22×D3—62no—
195C22×D3—62no—
196C22×D3—62no—
197C22×D3—62no—
198C22×D3—62no—
199C22×D3—62no—
200C22×D3—62no—
201C22×D3—122no—
202C22×D3—122no—
203C2×C3×C4—22no—
204C2×C3×C4—22no—
205C2×C3×C4—22no—
206C2×C3×C4—22no—
207C2×C3×C4—22no—
208C2×C3×C4—22no—
209C2×C3×C4—22no—
210C2×C3×C4—24no—
211C2×C3×C4—42no—
212C2×C3×C4—42no—
213C2×C3×C4—64no—
214C2×C3×C4—64no—
215C2×C3×C4—64no—
216C2×C3×C4—64no—
217C2×C3×C4—64no—
218C2×C3×C4—64no—
219C2×C3×C4C2×C4×D314yes—
220C2×C3×C4C2×C4×D314yes—
221C2×C3×C4C2×C4×D314yes—
222C2×C3×C4#23514yes—
223C2×C3×C4#23514yes—
224C2×Dic3—24no—
225C2×Dic3—24no—
226C2×Dic3—24no—
227C2×Dic3—24no—
228C2×Dic3—24no—
229C2×Dic3—24no—
230C2×Dic3—34no—
231C2×Dic3—34no—
232C2×Dic3—34no—
233C2×Dic3—62no—
234C2×Dic3—64no—
235C2×Dic3—62no—
236C2×Dic3—62no—
237C2×Dic3—62no—
238C2×Dic3—62no—
239C2×Dic3—62no—
240C2×Dic3—62no—
241C2×Dic3—62no—
242C2×Dic3—62no—
243C2×Dic3—122no—
244C2×Dic3—122no—
245C4×D3—616no—
246C4×D3—616no—
247C2×C32C2×#11711yescharacteristic
248C2×C32#52012yes—
249C2×C32#54011yescharacteristic
250C2×C32#54111yescharacteristic
251C2×C32#54212yes—
252C3⋊D3—42no—
253C24—91no—
254C22×C4—34no—
255C22×C4—34no—
256C22×C4—91no—
257C22×C4—92no—
258C22×C4—94no—
259C22×C4—182no—
260C22×C4—182no—
261C22×C4C2×D3212yes—
262C22×C4C2×D3211yescharacteristic
263C4⋊C4—64no—
264C4⋊C4—64no—
265C4⋊C4—98no—
266C4⋊C4—364no—
267C22⋊C4—98no—
268C22⋊C4—364no—
269C42—94no—
270C42—124no—
271C42#62414yes—
272C22×C3—22no—
273C22×C3—21no—
274C22×C3—21no—
275C22×C3—22no—
276C22×C3—21no—
277C22×C3C22×C4×D312yes—
278C22×C3C2×#23512yes—
279C22×C3C2×#23512yes—
280C22×C3#100412yes—
281C22×C3#100712yes—
282C22×C3#100912yes—
283C22×C3#101012yes—
284C2×D3—64no—
285C2×D3—64no—
286C2×D3—64no—
287C2×D3—64no—
288C2×D3—124no—
289C2×D3—124no—
290C2×D3—122no—
291C2×D3—122no—
292C2×D3—122no—
293C2×D3—122no—
294C2×D3—122no—
295C2×D3—122no—
296C3×C4—24no—
297C3×C4—24no—
298C3×C4—24no—
299C3×C4—44no—
300C3×C4—124no—
301C3×C4—124no—
302C3×C4#87218yes—
303Dic3—44no—
304Dic3—44no—
305Dic3—64no—
306Dic3—64no—
307Dic3—64no—
308Dic3—64no—
309Dic3—124no—
310C32#231411yescharacteristic, complemented, Sylow
311C23—92no—
312C23—182no—
313C23—181no—
314C23—181no—
315C23—182no—
316C23C22×D3211yescharacteristic
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—64no—
320C2×C4—64no—
321C2×C4—64no—
322C2×C4—64no—
323C2×C4—64no—
324C2×C4—64no—
325C2×C4—94no—
326C2×C4—92no—
327C2×C4—182no—
328C2×C4—181no—
329C2×C4—181no—
330C2×C4—182no—
331C2×C4—188no—
332C2×C4#379812yes—
333C2×C4#379812yes—
334C2×C4C2×#62414yes—
335C2×C4C2×#62412yes—
336C2×C3—21no—
337C2×C3—22no—
338C2×C3—21no—
339C2×C3—22no—
340C2×C3—21no—
341C2×C3C2×#87212yes—
342C2×C3#550412yes—
343C2×C3#552312yes—
344C2×C3#556112yes—
345C2×C3#556212yes—
346C2×C3#558212yes—
347C2×C3#558312yes—
348D3—124no—
349D3—124no—
350C22—182no—
351C22—184no—
352C22—362no—
353C22—361no—
354C22—361no—
355C22#6429712yes—
356C22C2×#379811yescharacteristic
357C22C2×#379811yescharacteristic
358C22#6430712yes—
359C22C22×#62411yescharacteristic
360C4—24no—
361C4—124no—
362C4—124no—
363C4—182no—
364C4—184no—
365C4#6387414yes—
366C3—21no—
367C3#7376012yescomplemented
368C2—362no—
369C2#1059387612yes—
370C2#1059388311yescharacteristic
371C2#1059398411yescharacteristic
372C2C2×#6387411yescharacteristic
373C2#1059499012yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC2×C42D32
hypocenterC32#2314
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C3×C4×C4⋊Dic3C2semidirect
3. #10591359C2semidirect
5. #10591230C2semidirect
7. #10591197C2semidirect
14. #64081C4semidirect
31. C4×C4⋊Dic3D3semidirect
310. C32#2314semidirect
367. C3#73760semidirect

Maximal subgroups

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

subgroupindex
C2×#640812
C3×C4×C4⋊Dic32
#105913592
#105913252
#105912302
#105912022
#105911972
#737603