Finite Group Databasebeta

← #11922836

Subgroups — #11922836

Order 1152.

854 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 854 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C3⋊S4C211yesmaximal, characteristic
2C3×C42×A4C211yesmaximal, characteristic, complemented
3#10593647C212yesmaximal
4#10593645C212yesmaximal, complemented
5C4×C3⋊SL(2,ℤ/4)C211yesmaximal, characteristic, complemented
6#85287—33nomaximal
7#82065—31nomaximal
8C22×C3⋊S4C2211yescharacteristic
9C2×C3×C4×A4C2212yes—
10C2×C3×C4×A4C2211yescharacteristic
11C2×C3⋊SL(2,ℤ/4)C2212yes—
12C2×C3⋊SL(2,ℤ/4)C2211yescharacteristic
13C4×C3⋊S4C414yescomplemented
14#64081—41nomaximal
15C2×C4×S4—33no—
16C22×C3×C42D311yescharacteristic, complemented
17C2×C4×#67—31no—
18C2×#872—31no—
19C42×A4D313yescomplemented
20(C2×S4)⋊C4—36no—
21SL(2,ℤ/4)⋊C4—36no—
22C4×SL(2,ℤ/4)—33no—
23#5213—32no—
24#5210—32no—
25C4×#217—31no—
26#4940—32no—
27C4×(C2×D3)⋊C4—31no—
28#4933—32no—
29#4932—31no—
30C4×Dic3⋊C4—31no—
31C22×C3×A4C2311yescharacteristic
32C2×C3⋊S4—22no—
33C2×C3⋊S4C2×C412yes—
34C2×C4×C3⋊D3—41no—
35C3×C4×A4—22no—
36C3×C4×A4C2×C412yes—
37C3⋊SL(2,ℤ/4)—22no—
38C3⋊SL(2,ℤ/4)C2×C412yes—
39C32×C42—41no—
40#3752—42no—
41#3750—42no—
42C4×C3⋊Dic3—41no—
43#2290—91noSylow
44C22×S4—33no—
45C23×C3×C4C2×D312yes—
46C23×C3×C4C2×D311yescharacteristic
47C22×#67—31no—
48C22×C4×D3—31no—
49C2×C4×A4C2×D316yes—
50C2×C4×A4C2×D313yes—
51C2×SL(2,ℤ/4)—33no—
52C2×SL(2,ℤ/4)—36no—
53C4×S4—312no—
54C2×C3×C42—31no—
55C2×C3×C42—31no—
56C2×C3×C42—32no—
57C2×#217—31no—
58C2×#217—32no—
59C4×#67—34no—
60C4×#67—34no—
61C2×(C2×D3)⋊C4—31no—
62C2×(C2×D3)⋊C4—32no—
63C2×(C2×D3)⋊C4—32no—
64C2×Dic3⋊C4—31no—
65C2×Dic3⋊C4—32no—
66C2×Dic3⋊C4—32no—
67C2×C4×Dic3—31no—
68C2×C4×Dic3—31no—
69C2×C4×Dic3—31no—
70#872—62no—
71#872—61no—
72#872—61no—
73#872—123no—
74C3⋊#95—32no—
75C3⋊#95—32no—
76C3⋊#95—32no—
77C3⋊#95—32no—
78C3⋊#95—32no—
79C22×C3⋊D3—41no—
80C2×C3×A4C22×C411yescharacteristic
81C2×C3×A4#4112yes—
82C3⋊S4—22no—
83C2×C32×C4—41no—
84C2×C32×C4—42no—
85C2×C3⋊Dic3—41no—
86C2×C3⋊Dic3—42no—
87C4×C3⋊D3—44no—
88C2×C4×D4—91no—
89C2×#117—91no—
90C22×C42C3⋊D311yescharacteristic, complemented
91#388—92no—
92#387—92no—
93#386—92no—
94#385—92no—
95C4×C4⋊C4—91no—
96C4×C22⋊C4—91no—
97C4×C22⋊C4—91no—
98#376—91no—
99C24×C3C22×D311yescharacteristic
100C23×D3—31no—
101C22×A4C22×D313yes—
102C2×S4—36no—
103C2×S4—66no—
104C22×C3×C4—22no—
105C22×C3×C4—31no—
106C22×C3×C4—31no—
107C22×C3×C4—32no—
108C22×C3×C4—32no—
109C22×C3×C4—32no—
110C22×C3×C4—62no—
111C22×C3×C4C4×D312yes—
112C2×#67—32no—
113C2×#67—32no—
114C2×#67—62no—
115C2×#67—62no—
116C22×Dic3—31no—
117C22×Dic3—31no—
118C22×Dic3—31no—
119C22×Dic3—32no—
120C22×Dic3—32no—
121C2×C4×D3—34no—
122C2×C4×D3—61no—
123C2×C4×D3—62no—
124C2×C4×D3—61no—
125C2×C4×D3—123no—
126C4×A4—26no—
127C4×A4C4×D316yes—
128SL(2,ℤ/4)—36no—
129SL(2,ℤ/4)—66no—
130C3×C42—32no—
131C3×C42—31no—
132C3×C42—43no—
133C3×C42—61no—
134C3×C42S411yescharacteristic, complemented
135#217—32no—
136#217—32no—
137#217—62no—
138#217—62no—
139(C2×D3)⋊C4—34no—
140(C2×D3)⋊C4—62no—
141(C2×D3)⋊C4—64no—
142(C2×D3)⋊C4—62no—
143(C2×D3)⋊C4—126no—
144Dic3⋊C4—34no—
145Dic3⋊C4—62no—
146Dic3⋊C4—64no—
147Dic3⋊C4—62no—
148Dic3⋊C4—126no—
149C4×Dic3—34no—
150C4×Dic3—61no—
151C4×Dic3—62no—
152C4×Dic3—61no—
153C4×Dic3—123no—
154C22×C32—41no—
155C2×C3⋊D3—42no—
156C2×C3⋊D3—82no—
157C3×A4#11711yescharacteristic, complemented
158C32×C4—42no—
159C32×C4—82no—
160C3⋊Dic3—42no—
161C3⋊Dic3—82no—
162C22×D4—91no—
163C23×C4—91no—
164C23×C4C2×C3⋊D312yes—
165C23×C4C2×C3⋊D311yescharacteristic
166C4×D4—94no—
167C4×D4—94no—
168#117—182no—
169#117—181no—
170#117—181no—
171C2×C4⋊C4—91no—
172C2×C4⋊C4—92no—
173C2×C4⋊C4—92no—
174C2×C22⋊C4—91no—
175C2×C22⋊C4—91no—
176C2×C22⋊C4—92no—
177C2×C22⋊C4—92no—
178C2×C22⋊C4—92no—
179C2×C42—31no—
180C2×C42—31no—
181C2×C42—32no—
182C2×C42—91no—
183C2×C42—91no—
184C2×C42—91no—
185#95—92no—
186#95—92no—
187#95—92no—
188#95—92no—
189#95—92no—
190C23×C3—31no—
191C23×C3—31no—
192C23×C3—32no—
193C23×C3C2×C4×D311yescharacteristic
194C23×C3#23512yes—
195C22×D3—32no—
196C22×D3—62no—
197C22×D3—61no—
198C22×D3—62no—
199C22×D3—61no—
200C22×D3—123no—
201C2×A4C2×C4×D313yes—
202C2×A4#23516yes—
203S4—66no—
204C2×C3×C4—31no—
205C2×C3×C4—32no—
206C2×C3×C4—32no—
207C2×C3×C4—32no—
208C2×C3×C4—34no—
209C2×C3×C4—32no—
210C2×C3×C4—46no—
211C2×C3×C4—43no—
212C2×C3×C4—62no—
213C2×C3×C4—62no—
214C2×C3×C4—61no—
215C2×C3×C4—62no—
216C2×C3×C4C2×S412yes—
217C2×C3×C4C2×S411yescharacteristic
218#67—62no—
219#67—64no—
220#67—62no—
221C2×Dic3—32no—
222C2×Dic3—32no—
223C2×Dic3—32no—
224C2×Dic3—62no—
225C2×Dic3—61no—
226C2×Dic3—62no—
227C2×Dic3—61no—
228C2×Dic3—62no—
229C2×Dic3—62no—
230C2×Dic3—62no—
231C2×Dic3—62no—
232C2×Dic3—62no—
233C2×Dic3—62no—
234C2×Dic3—123no—
235C2×Dic3—126no—
236C4×D3—64no—
237C4×D3—64no—
238C4×D3—1212no—
239C2×C32—41no—
240C2×C32—42no—
241C3⋊D3—82no—
242C24—91no—
243C24C22×C3⋊D311yescharacteristic
244C2×D4—92no—
245C2×D4—92no—
246C2×D4—182no—
247C2×D4—182no—
248C22×C4—22no—
249C22×C4—31no—
250C22×C4—31no—
251C22×C4—32no—
252C22×C4—32no—
253C22×C4—32no—
254C22×C4—62no—
255C22×C4—94no—
256C22×C4—91no—
257C22×C4—91no—
258C22×C4—91no—
259C22×C4—92no—
260C22×C4—92no—
261C22×C4—181no—
262C22×C4—182no—
263C22×C4—181no—
264C22×C4C4×C3⋊D312yes—
265C4⋊C4—94no—
266C4⋊C4—182no—
267C4⋊C4—184no—
268C4⋊C4—182no—
269C22⋊C4—94no—
270C22⋊C4—92no—
271C22⋊C4—92no—
272C22⋊C4—182no—
273C22⋊C4—184no—
274C22⋊C4—182no—
275C22⋊C4—182no—
276C22⋊C4—182no—
277C42—32no—
278C42—31no—
279C42—61no—
280C42—94no—
281C42—181no—
282C42—182no—
283C42—181no—
284C42C3⋊S411yescharacteristic, complemented
285C22×C3—31no—
286C22×C3—32no—
287C22×C3—31no—
288C22×C3—31no—
289C22×C3—32no—
290C22×C3—32no—
291C22×C3—43no—
292C22×C3—61no—
293C22×C3#87211yescharacteristic, complemented
294C22×C3C22×S411yescharacteristic
295C2×D3—62no—
296C2×D3—62no—
297C2×D3—62no—
298C2×D3—126no—
299C2×D3—122no—
300C2×D3—122no—
301C2×D3—246no—
302A4#87213yescomplemented
303C3×C4—22no—
304C3×C4—32no—
305C3×C4—46no—
306C3×C4—62no—
307C3×C4—86no—
308C3×C4C4×S412yes—
309Dic3—62no—
310Dic3—62no—
311Dic3—62no—
312Dic3—126no—
313Dic3—122no—
314Dic3—122no—
315Dic3—246no—
316C32—41noSylow
317C23—31no—
318C23—31no—
319C23—32no—
320C23—92no—
321C23—182no—
322C23—181no—
323C23—182no—
324C23—181no—
325C23C2×C4×C3⋊D311yescharacteristic
326C23#382812yes—
327D4—182no—
328D4—184no—
329D4—182no—
330C2×C4—31no—
331C2×C4—32no—
332C2×C4—32no—
333C2×C4—32no—
334C2×C4—34no—
335C2×C4—32no—
336C2×C4—62no—
337C2×C4—62no—
338C2×C4—61no—
339C2×C4—62no—
340C2×C4—92no—
341C2×C4—92no—
342C2×C4—92no—
343C2×C4—184no—
344C2×C4—182no—
345C2×C4—181no—
346C2×C4—182no—
347C2×C4—181no—
348C2×C4—184no—
349C2×C4—182no—
350C2×C4—182no—
351C2×C4—182no—
352C2×C4—182no—
353C2×C4—182no—
354C2×C4—182no—
355C2×C4C2×C3⋊S412yes—
356C2×C4C2×C3⋊S411yescharacteristic
357C2×C3—31no—
358C2×C3—31no—
359C2×C3—32no—
360C2×C3—43no—
361C2×C3—46no—
362C2×C3C2×C4×S411yescharacteristic
363C2×C3#591212yes—
364D3—122no—
365D3—246no—
366C22—31no—
367C22—32no—
368C22—31no—
369C22—31no—
370C22—32no—
371C22—32no—
372C22—61no—
373C22—182no—
374C22—182no—
375C22—182no—
376C22—362no—
377C22—362no—
378C22#6408111yescharacteristic, complemented
379C22C22×C3⋊S411yescharacteristic
380C4—22no—
381C4—32no—
382C4—62no—
383C4—182no—
384C4—182no—
385C4—182no—
386C4—362no—
387C4—362no—
388C4C4×C3⋊S412yes—
389C3—43no—
390C3#8528711yescharacteristic, complemented
391C2—31no—
392C2—31no—
393C2—32no—
394C2—362no—
395C2C2×C4×C3⋊S411yescharacteristic
396C2#1059657512yes—
subgroupG/H
centerC2×C4C2×C3⋊S4
commutatorC2×C3×A4C22×C4
FrattiniC22C22×C3⋊S4
FittingC22×C3×C42D3
socleC24×C3C22×D3
prime radicalC22×C3⋊S4C22
cosocleC22×C3×A4C23
hypercenterC42C3⋊S4
hypocenterC3×A4#117
LCSG ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C3×C42×A4C2semidirect
4. #10593645C2semidirect
5. C4×C3⋊SL(2,ℤ/4)C2semidirect
13. C4×C3⋊S4C4semidirect
16. C22×C3×C42D3semidirect
19. C42×A4D3semidirect
90. C22×C42C3⋊D3semidirect
134. C3×C42S4semidirect
157. C3×A4#117semidirect
284. C42C3⋊S4semidirect
293. C22×C3#872semidirect
302. A4#872semidirect
378. C22#64081semidirect
390. C3#85287semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C3⋊S42
C3×C42×A42
#105936472
#105936452
C4×C3⋊SL(2,ℤ/4)2
#852873
#820653
#640814