Finite Group Databasebeta

← #11801915

Subgroups — #11801915

Order 1152.

1572 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64081C211yesmaximal, characteristic
2C32×C4×C4⋊C4C211yesmaximal, characteristic, complemented
3#10592689C212yesmaximal
4#10592677C212yesmaximal, complemented
5C4×#3752C211yesmaximal, characteristic
6C4×#3752C211yesmaximal, characteristic
7C4×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
8#10592631C211yesmaximal, characteristic, complemented
9C42×C3⋊Dic3C211yesmaximal, characteristic, complemented
10#10592369C212yesmaximal
11#10592354C212yesmaximal, complemented
12#73620—34nomaximal
13C22×C4×C3⋊D3C2211yescharacteristic
14C2×C32×C4⋊C4C2212yes—
15C2×C32×C42C2211yescharacteristic
16C2×C32×C42C2211yescharacteristic
17C2×C32×C42C2211yescharacteristic
18C2×#3752C2212yes—
19C2×#3752C2212yes—
20C2×#3752C2211yescharacteristic
21C2×#3752C2211yescharacteristic
22C2×C4⋊(C3⋊Dic3)C2212yes—
23C2×#3750C2211yescharacteristic
24C2×#3750C2211yescharacteristic
25C2×C4×C3⋊Dic3C2212yes—
26C2×C4×C3⋊Dic3C2212yes—
27C2×C4×C3⋊Dic3C2211yescharacteristic
28C2×C4×C3⋊Dic3C2211yescharacteristic
29C2×C4×C3⋊Dic3C2211yescharacteristic
30#64081C418yescomplemented
31C32×#95C2212yes—
32#63658C2212yes—
33#63658C2212yes—
34#63658C2212yes—
35#63658C2212yes—
36#63658C2212yes—
37C2×#872—34no—
38C3×C4×C4⋊C4D314yescomplemented
39#4990—38no—
40#4978—38no—
41C4×(C2×D3)⋊C4—34no—
42C4×(C2×D3)⋊C4—34no—
43C4×C4⋊Dic3—34no—
44#4932—34no—
45C42×Dic3—34no—
46#4670—38no—
47#4655—38no—
48C23×C3⋊D3C2311yescharacteristic
49C22×C32×C4C2312yes—
50C22×C32×C4C2311yescharacteristic
51C22×C32×C4C2311yescharacteristic
52C22×C32×C4C2312yes—
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3C2312yes—
55C22×C3⋊Dic3C2311yescharacteristic
56C22×C3⋊Dic3C2311yescharacteristic
57C22×C3⋊Dic3C2311yescharacteristic
58C22×C3⋊Dic3C2312yes—
59C2×C4×C3⋊D3—22no—
60C2×C4×C3⋊D3—22no—
61C2×C4×C3⋊D3C2×C414yes—
62C32×C4⋊C4—24no—
63C32×C42—22no—
64C32×C42—22no—
65C32×C42C2×C414yes—
66#3752—24no—
67#3752—24no—
68#3752C2×C414yes—
69#3752C2×C414yes—
70C4⋊(C3⋊Dic3)—24no—
71#3750C2×C414yes—
72#3750C2×C414yes—
73C4×C3⋊Dic3—24no—
74C4×C3⋊Dic3—22no—
75C4×C3⋊Dic3—22no—
76C4×C3⋊Dic3—24no—
77C4×C3⋊Dic3C2×C414yes—
78#2298—91noSylow
79C22×C4×D3—34no—
80C2×C3×C4⋊C4C2×D318yes—
81C2×C3×C42C2×D314yes—
82C2×C3×C42C2×D314yes—
83C2×C3×C42C2×D314yes—
84C2×(C2×D3)⋊C4—34no—
85C2×(C2×D3)⋊C4—34no—
86C2×(C2×D3)⋊C4—38no—
87C2×(C2×D3)⋊C4—38no—
88C2×C4⋊Dic3—38no—
89C2×Dic3⋊C4—34no—
90C2×Dic3⋊C4—34no—
91C2×C4×Dic3—34no—
92C2×C4×Dic3—38no—
93C2×C4×Dic3—38no—
94C2×C4×Dic3—34no—
95C2×C4×Dic3—34no—
96#872—332no—
97C3×#95C2×D318yes—
98C3⋊#95—38no—
99C3⋊#95—38no—
100C3⋊#95—38no—
101C3⋊#95—38no—
102C3⋊#95—38no—
103C23×C32C2411yescharacteristic
104C22×C3⋊D3—22no—
105C22×C3⋊D3—22no—
106C22×C3⋊D3—21no—
107C22×C3⋊D3—21no—
108C22×C3⋊D3C22×C412yes—
109C2×C32×C4—22no—
110C2×C32×C4—22no—
111C2×C32×C4—22no—
112C2×C32×C4—22no—
113C2×C32×C4—22no—
114C2×C32×C4—22no—
115C2×C32×C4—22no—
116C2×C32×C4C22×C412yes—
117C2×C32×C4C22×C412yes—
118C2×C32×C4C22×C412yes—
119C2×C32×C4#4114yes—
120C2×C32×C4#4112yes—
121C2×C32×C4#4112yes—
122C2×C3⋊Dic3—22no—
123C2×C3⋊Dic3—22no—
124C2×C3⋊Dic3—22no—
125C2×C3⋊Dic3—22no—
126C2×C3⋊Dic3—21no—
127C2×C3⋊Dic3—21no—
128C2×C3⋊Dic3—22no—
129C2×C3⋊Dic3—22no—
130C2×C3⋊Dic3—22no—
131C2×C3⋊Dic3C22×C412yes—
132C2×C3⋊Dic3C22×C412yes—
133C2×C3⋊Dic3C22×C412yes—
134C2×C3⋊Dic3#4114yes—
135C4×C3⋊D3—28no—
136C2×#117—91no—
137#388—92no—
138#388—92no—
139#387—92no—
140#387—92no—
141C4×C4⋊C4—91no—
142C4×C4⋊C4C3⋊D311yescharacteristic, complemented
143C4×C22⋊C4—91no—
144C4×C22⋊C4—91no—
145#376—91no—
146C43—91no—
147C23×D3—34no—
148C22×C3×C4C22×D318yes—
149C22×C3×C4C22×D314yes—
150C22×C3×C4C22×D314yes—
151C22×C3×C4C22×D318yes—
152C22×C3×C4C22×D314yes—
153C22×Dic3—34no—
154C22×Dic3—34no—
155C22×Dic3—34no—
156C22×Dic3—38no—
157C22×Dic3—38no—
158C2×C4×D3—316no—
159C2×C4×D3—68no—
160C2×C4×D3—68no—
161C3×C4⋊C4—216no—
162C3×C42—28no—
163C3×C42—28no—
164C3×C42C4×D3116yes—
165(C2×D3)⋊C4—316no—
166(C2×D3)⋊C4—316no—
167(C2×D3)⋊C4—616no—
168(C2×D3)⋊C4—616no—
169C4⋊Dic3—616no—
170Dic3⋊C4—316no—
171Dic3⋊C4—316no—
172C4×Dic3—316no—
173C4×Dic3—616no—
174C4×Dic3—616no—
175C4×Dic3—68no—
176C4×Dic3—68no—
177C22×C32C23×C411yescharacteristic
178C22×C32C2×#4112yes—
179C22×C32C2×#4111yescharacteristic
180C22×C32C2×#4111yescharacteristic
181C22×C32C2×#4112yes—
182C2×C3⋊D3—22no—
183C2×C3⋊D3—22no—
184C2×C3⋊D3—22no—
185C2×C3⋊D3—42no—
186C2×C3⋊D3—42no—
187C32×C4—22no—
188C32×C4—22no—
189C32×C4—24no—
190C32×C4—42no—
191C32×C4#11714yes—
192C3⋊Dic3—22no—
193C3⋊Dic3—22no—
194C3⋊Dic3—22no—
195C3⋊Dic3—24no—
196C3⋊Dic3—42no—
197C23×C4—91no—
198#117—98no—
199C2×C4⋊C4—91no—
200C2×C4⋊C4—91no—
201C2×C4⋊C4—92no—
202C2×C4⋊C4C2×C3⋊D312yes—
203C2×C22⋊C4—91no—
204C2×C22⋊C4—91no—
205C2×C22⋊C4—92no—
206C2×C22⋊C4—92no—
207C2×C42—91no—
208C2×C42—92no—
209C2×C42—92no—
210C2×C42—91no—
211C2×C42—91no—
212C2×C42C2×C3⋊D311yescharacteristic
213C2×C42C2×C3⋊D311yescharacteristic
214C2×C42C2×C3⋊D311yescharacteristic
215#95—92no—
216#95—92no—
217#95—92no—
218#95—92no—
219#95—92no—
220#95C2×C3⋊D312yes—
221C23×C3C23×D314yes—
222C22×D3—38no—
223C22×D3—68no—
224C22×D3—64no—
225C22×D3—64no—
226C22×D3—68no—
227C2×C3×C4—28no—
228C2×C3×C4—28no—
229C2×C3×C4—28no—
230C2×C3×C4—28no—
231C2×C3×C4—28no—
232C2×C3×C4—28no—
233C2×C3×C4—28no—
234C2×C3×C4C2×C4×D318yes—
235C2×C3×C4C2×C4×D318yes—
236C2×C3×C4C2×C4×D318yes—
237C2×C3×C4#235116yes—
238C2×C3×C4#23718yes—
239C2×C3×C4#23918yes—
240C2×Dic3—38no—
241C2×Dic3—38no—
242C2×Dic3—38no—
243C2×Dic3—316no—
244C2×Dic3—68no—
245C2×Dic3—68no—
246C2×Dic3—64no—
247C2×Dic3—68no—
248C2×Dic3—64no—
249C2×Dic3—68no—
250C2×Dic3—68no—
251C2×Dic3—68no—
252C2×Dic3—68no—
253C4×D3—632no—
254C2×C32C2×#11711yescharacteristic
255C2×C32C4×#4111yescharacteristic
256C2×C32C4×#4111yescharacteristic
257C2×C32#52912yes—
258C2×C32#52912yes—
259C3⋊D3—42no—
260C24—91no—
261C22×C4—91no—
262C22×C4—91no—
263C22×C4—91no—
264C22×C4—92no—
265C22×C4—94no—
266C22×C4—92no—
267C22×C4—182no—
268C22×C4—182no—
269C22×C4C22×C3⋊D312yes—
270C22×C4C22×C3⋊D311yescharacteristic
271C22×C4C22×C3⋊D311yescharacteristic
272C22×C4C22×C3⋊D312yes—
273C22×C4C22×C3⋊D311yescharacteristic
274C4⋊C4—24no—
275C4⋊C4—94no—
276C4⋊C4—94no—
277C4⋊C4—184no—
278C22⋊C4—94no—
279C22⋊C4—94no—
280C22⋊C4—184no—
281C22⋊C4—184no—
282C42—22no—
283C42—22no—
284C42—94no—
285C42—184no—
286C42—184no—
287C42—182no—
288C42—182no—
289C42C4×C3⋊D314yes—
290C22×C3C22×C4×D314yes—
291C22×C3C2×#23518yes—
292C22×C3C2×#23714yes—
293C22×C3C2×#23914yes—
294C22×C3D3×#4118yes—
295C2×D3—68no—
296C2×D3—68no—
297C2×D3—68no—
298C2×D3—128no—
299C2×D3—128no—
300C3×C4—28no—
301C3×C4—28no—
302C3×C4—216no—
303C3×C4—48no—
304C3×C4#892116yes—
305Dic3—68no—
306Dic3—68no—
307Dic3—68no—
308Dic3—616no—
309Dic3—128no—
310C32#229811yescharacteristic, complemented, Sylow
311C23—92no—
312C23—182no—
313C23—181no—
314C23—181no—
315C23—182no—
316C23C23×C3⋊D311yescharacteristic
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—92no—
325C2×C4—92no—
326C2×C4—92no—
327C2×C4—94no—
328C2×C4—182no—
329C2×C4—182no—
330C2×C4—181no—
331C2×C4—182no—
332C2×C4—181no—
333C2×C4—182no—
334C2×C4—188no—
335C2×C4—182no—
336C2×C4—182no—
337C2×C4—182no—
338C2×C4C2×C4×C3⋊D312yes—
339C2×C4C2×C4×C3⋊D312yes—
340C2×C4C2×C4×C3⋊D312yes—
341C2×C4#382814yes—
342C2×C4#383012yes—
343C2×C4#383212yes—
344C2×C3C4×#23514yes—
345C2×C3C2×#89214yes—
346C2×C3#552214yes—
347C2×C3#553818yes—
348C2×C3#558018yes—
349D3—128no—
350C22—182no—
351C22—182no—
352C22—182no—
353C22—362no—
354C22—362no—
355C22C22×C4×C3⋊D311yescharacteristic
356C22C2×#382812yes—
357C22C2×#383011yescharacteristic
358C22C2×#383211yescharacteristic
359C22#41×C3⋊D312yes—
360C4—22no—
361C4—22no—
362C4—24no—
363C4—42no—
364C4—182no—
365C4—182no—
366C4—182no—
367C4—184no—
368C4—362no—
369C4#6410114yes—
370C3#7362014yescomplemented
371C2—362no—
372C2C4×#382811yescharacteristic
373C2C2×#6410111yescharacteristic
374C2#1059599311yescharacteristic
375C2#1059600912yes—
376C2#1059605112yes—
subgroupG/H
centerC22×C4C22×C3⋊D3
commutatorC22×C32C23×C4
FrattiniC23C23×C3⋊D3
FittingC32×C4×C4⋊C4C2
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC4×C4⋊C4C3⋊D3
hypocenterC32#2298
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C32×C4×C4⋊C4C2semidirect
4. #10592677C2semidirect
7. C4×C4⋊(C3⋊Dic3)C2semidirect
8. #10592631C2semidirect
9. C42×C3⋊Dic3C2semidirect
11. #10592354C2semidirect
30. #64081C4semidirect
38. C3×C4×C4⋊C4D3semidirect
142. C4×C4⋊C4C3⋊D3semidirect
310. C32#2298semidirect
370. C3#73620semidirect

Maximal subgroups

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

subgroupindex
C2×#640812
C32×C4×C4⋊C42
#105926892
#105926772
C4×#37522
C4×C4⋊(C3⋊Dic3)2
#105926312
C42×C3⋊Dic32
#105923692
#105923542
#736203