Finite Group Databasebeta

← #11923031

Subgroups — #11923031

Order 1152.

974 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 974 conjugacy classes of subgroups — too many to draw. Only its 163 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
1C22×C3×C4×A4C211yesmaximal, characteristic
2#10593666C212yesmaximal
3C4⋊(C3⋊SL(2,ℤ/4))C212yesmaximal, complemented
4C4×C3⋊SL(2,ℤ/4)C212yesmaximal, complemented
5#85482—33nomaximal
6#84027—31nomaximal
7C23×C3×A4C2211yescharacteristic
8C2×C3×C4×A4C414yescomplemented
9C2×C3×C4×A4C2211yescharacteristic
10C2×C3×C4×A4C2211yescharacteristic
11C2×C3⋊SL(2,ℤ/4)C2214yes—
12#64135—41nomaximal
13C24×C3×C4D311yescharacteristic
14C22×C4×A4D313yes—
15C2×#926—31no—
16C2×#926—31no—
17#5432—36no—
18C4⋊SL(2,ℤ/4)—36no—
19C4×SL(2,ℤ/4)—36no—
20#5247—32no—
21#5212—32no—
22#5212—32no—
23#5211—32no—
24C4×#217—32no—
25C4×#217—32no—
26C22×C3×A4—22no—
27C22×C3×A4C2×C412yes—
28C22×C3×A4C2311yescharacteristic
29C22×C32×C4—41no—
30C3×C4×A4C2×C412yes—
31C3×C4×A4C2×C412yes—
32C3⋊SL(2,ℤ/4)—24no—
33#3757—42no—
34C4⋊(C3⋊Dic3)—42no—
35C4×C3⋊Dic3—42no—
36#2280—91noSylow
37C25×C3C2×D311yescharacteristic
38C23×A4C2×D313yes—
39C23×C3×C4—31no—
40C23×C3×C4—34no—
41C23×C3×C4—31no—
42C23×C3×C4—31no—
43C23×C3×C4—31no—
44C23×C3×C4Dic314yescomplemented
45C23×C3×C4C2×D311yescharacteristic
46C23×C3×C4C2×D311yescharacteristic
47C2×C4×A4Dic3112yescomplemented
48C2×C4×A4C2×D313yes—
49C2×C4×A4C2×D313yes—
50C2×SL(2,ℤ/4)—312no—
51C2×#217—34no—
52C2×#217—32no—
53C2×#217—32no—
54C2×#217—34no—
55#926—64no—
56#926—61no—
57#926—61no—
58#926—61no—
59#926—61no—
60#926—123no—
61C2×C4⋊Dic3—32no—
62C2×C4⋊Dic3—32no—
63C2×C4×Dic3—32no—
64C2×C4×Dic3—32no—
65C3⋊#95—34no—
66C3⋊#95—34no—
67C23×C32—41no—
68C2×C3×A4—22no—
69C2×C3×A4C22×C411yescharacteristic
70C2×C3×A4#4112yes—
71C2×C32×C4—44no—
72C2×C32×C4—41no—
73C2×C32×C4—41no—
74C2×C3⋊Dic3—44no—
75C24×C4C3⋊D311yescharacteristic
76C2×#117—91no—
77C2×#117—91no—
78#381—92no—
79#380—92no—
80#380—92no—
81#379—92no—
82C4×C22⋊C4—92no—
83C4×C22⋊C4—92no—
84C24×C3—22no—
85C24×C3—31no—
86C24×C3—31no—
87C24×C3—32no—
88C24×C3—62no—
89C24×C3C2×Dic312yes—
90C24×C3C22×D311yescharacteristic
91C22×A4—26no—
92C22×A4C2×Dic316yes—
93C22×A4C22×D313yes—
94C22×C3×C4—31no—
95C22×C3×C4—34no—
96C22×C3×C4—34no—
97C22×C3×C4—31no—
98C22×C3×C4—31no—
99C22×C3×C4—31no—
100C22×C3×C4—31no—
101C22×C3×C4—31no—
102C22×C3×C4—31no—
103C22×C3×C4—34no—
104C22×C3×C4—34no—
105C22×C3×C4—34no—
106C22×C3×C4—32no—
107C22×C3×C4—32no—
108C22×C3×C4—43no—
109C22×C3×C4—62no—
110C22×C3×C4—62no—
111C22×C3×C4—62no—
112C22×C3×C4—61no—
113C22×C3×C4C2×Dic312yes—
114C22×C3×C4C2×Dic312yes—
115C22×C3×C4S411yescharacteristic
116C22×Dic3—34no—
117C22×Dic3—34no—
118C4×A4C2×Dic316yes—
119C4×A4C2×Dic316yes—
120SL(2,ℤ/4)—612no—
121#217—64no—
122#217—62no—
123#217—64no—
124#217—68no—
125#217—64no—
126#217—62no—
127#217—126no—
128C4⋊Dic3—64no—
129C4⋊Dic3—62no—
130C4⋊Dic3—62no—
131C4⋊Dic3—126no—
132C4×Dic3—64no—
133C4×Dic3—62no—
134C4×Dic3—62no—
135C4×Dic3—126no—
136C22×C32—42no—
137C22×C32—41no—
138C22×C32—82no—
139C3×A4#11711yescharacteristic, complemented
140C32×C4—42no—
141C32×C4—42no—
142C3⋊Dic3—84no—
143C25C2×C3⋊D311yescharacteristic
144C23×C4—31no—
145C23×C4—31no—
146C23×C4—31no—
147C23×C4—31no—
148C23×C4—34no—
149C23×C4C3⋊Dic314yescomplemented
150C23×C4C2×C3⋊D311yescharacteristic
151C23×C4C2×C3⋊D311yescharacteristic
152#117—184no—
153#117—181no—
154#117—181no—
155#117—181no—
156#117—181no—
157C2×C4⋊C4—92no—
158C2×C4⋊C4—92no—
159C2×C22⋊C4—92no—
160C2×C22⋊C4—92no—
161C2×C22⋊C4—94no—
162C2×C22⋊C4—94no—
163C2×C42—92no—
164C2×C42—92no—
165#95—94no—
166#95—94no—
167C23×C3—22no—
168C23×C3—31no—
169C23×C3—32no—
170C23×C3—32no—
171C23×C3—31no—
172C23×C3—34no—
173C23×C3—32no—
174C23×C3—32no—
175C23×C3—31no—
176C23×C3—43no—
177C23×C3—62no—
178C23×C3—62no—
179C23×C3—62no—
180C23×C3—61no—
181C23×C3—64no—
182C23×C3—62no—
183C23×C3—64no—
184C23×C3#23512yes—
185C23×C3C22×Dic311yescharacteristic
186C23×C3C2×S411yescharacteristic
187C2×A4—26no—
188C2×A4#23516yes—
189C2×A4C22×Dic313yes—
190C2×C3×C4—34no—
191C2×C3×C4—31no—
192C2×C3×C4—31no—
193C2×C3×C4—32no—
194C2×C3×C4—32no—
195C2×C3×C4—32no—
196C2×C3×C4—32no—
197C2×C3×C4—34no—
198C2×C3×C4—34no—
199C2×C3×C4—32no—
200C2×C3×C4—32no—
201C2×C3×C4—43no—
202C2×C3×C4—43no—
203C2×C3×C4—412no—
204C2×C3×C4—61no—
205C2×C3×C4—61no—
206C2×C3×C4—64no—
207C2×C3×C4SL(2,ℤ/4)14yescomplemented
208C2×C3×C4C2×S411yescharacteristic
209C2×C3×C4C2×S411yescharacteristic
210C2×Dic3—64no—
211C2×Dic3—64no—
212C2×Dic3—64no—
213C2×Dic3—64no—
214C2×Dic3—64no—
215C2×Dic3—64no—
216C2×Dic3—1212no—
217C2×C32—42no—
218C2×C32—41no—
219C2×C32—82no—
220C24—22no—
221C24—31no—
222C24—31no—
223C24—32no—
224C24—62no—
225C24C2×C3⋊Dic312yes—
226C24C22×C3⋊D311yescharacteristic
227C22×C4—31no—
228C22×C4—31no—
229C22×C4—31no—
230C22×C4—31no—
231C22×C4—31no—
232C22×C4—34no—
233C22×C4—34no—
234C22×C4—31no—
235C22×C4—31no—
236C22×C4—34no—
237C22×C4—34no—
238C22×C4—34no—
239C22×C4—32no—
240C22×C4—32no—
241C22×C4—62no—
242C22×C4—62no—
243C22×C4—62no—
244C22×C4—61no—
245C22×C4—94no—
246C22×C4—94no—
247C22×C4C2×C3⋊Dic312yes—
248C22×C4C2×C3⋊Dic312yes—
249C22×C4C3⋊S411yescharacteristic
250C4⋊C4—182no—
251C4⋊C4—184no—
252C4⋊C4—182no—
253C22⋊C4—184no—
254C22⋊C4—182no—
255C22⋊C4—184no—
256C22⋊C4—188no—
257C22⋊C4—182no—
258C22⋊C4—184no—
259C42—182no—
260C42—184no—
261C42—182no—
262C22×C3—22no—
263C22×C3—32no—
264C22×C3—31no—
265C22×C3—32no—
266C22×C3—32no—
267C22×C3—31no—
268C22×C3—31no—
269C22×C3—34no—
270C22×C3—32no—
271C22×C3—46no—
272C22×C3—43no—
273C22×C3—62no—
274C22×C3—64no—
275C22×C3—62no—
276C22×C3—61no—
277C22×C3—62no—
278C22×C3—64no—
279C22×C3—62no—
280C22×C3—86no—
281C22×C3#92611yescharacteristic, complemented
282C22×C3C2×SL(2,ℤ/4)12yes—
283C22×C3C22×S411yescharacteristic
284A4#92613yescomplemented
285C3×C4—32no—
286C3×C4—32no—
287C3×C4—46no—
288C3×C4—46no—
289C3×C4C2×SL(2,ℤ/4)12yes—
290C3×C4C2×SL(2,ℤ/4)12yes—
291Dic3—124no—
292Dic3—124no—
293Dic3—2412no—
294C32—41noSylow
295C23—22no—
296C23—31no—
297C23—32no—
298C23—32no—
299C23—31no—
300C23—34no—
301C23—32no—
302C23—32no—
303C23—31no—
304C23—62no—
305C23—62no—
306C23—62no—
307C23—61no—
308C23—64no—
309C23—62no—
310C23—64no—
311C23#382812yes—
312C23C22×C3⋊Dic311yescharacteristic
313C23C2×C3⋊S411yescharacteristic
314C2×C4—34no—
315C2×C4—31no—
316C2×C4—31no—
317C2×C4—32no—
318C2×C4—32no—
319C2×C4—32no—
320C2×C4—32no—
321C2×C4—34no—
322C2×C4—34no—
323C2×C4—32no—
324C2×C4—32no—
325C2×C4—61no—
326C2×C4—61no—
327C2×C4—64no—
328C2×C4—184no—
329C2×C4—184no—
330C2×C4—184no—
331C2×C4—184no—
332C2×C4—184no—
333C2×C4—184no—
334C2×C4C3⋊SL(2,ℤ/4)14yescomplemented
335C2×C4C2×C3⋊S411yescharacteristic
336C2×C4C2×C3⋊S411yescharacteristic
337C2×C3—22no—
338C2×C3—32no—
339C2×C3—31no—
340C2×C3—31no—
341C2×C3—46no—
342C2×C3—43no—
343C2×C3—62no—
344C2×C3—86no—
345C2×C3#591212yes—
346C2×C3C22×SL(2,ℤ/4)11yescharacteristic
347C22—22no—
348C22—32no—
349C22—31no—
350C22—32no—
351C22—32no—
352C22—31no—
353C22—31no—
354C22—34no—
355C22—32no—
356C22—62no—
357C22—64no—
358C22—62no—
359C22—61no—
360C22—62no—
361C22—64no—
362C22—62no—
363C22#6413511yescharacteristic, complemented
364C22C2×C3⋊SL(2,ℤ/4)12yes—
365C22C22×C3⋊S411yescharacteristic
366C4—32no—
367C4—32no—
368C4—364no—
369C4—364no—
370C4C2×C3⋊SL(2,ℤ/4)12yes—
371C4C2×C3⋊SL(2,ℤ/4)12yes—
372C3—43no—
373C3#8548211yescharacteristic, complemented
374C2—22no—
375C2—32no—
376C2—31no—
377C2—31no—
378C2—62no—
379C2#1059657512yes—
380C2C22×C3⋊SL(2,ℤ/4)11yescharacteristic
subgroupG/H
centerC2×C4C2×C3⋊S4
commutatorC2×C3×A4C22×C4
FrattiniC22C22×C3⋊S4
FittingC24×C3×C4D3
socleC24×C3C22×D3
prime radicalC23×C3×A4C22
cosocleC22×C3×A4C23
hypercenterC22×C4C3⋊S4
hypocenterC3×A4#117
LCSG ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
3. C4⋊(C3⋊SL(2,ℤ/4))C2semidirect
4. C4×C3⋊SL(2,ℤ/4)C2semidirect
8. C2×C3×C4×A4C4semidirect
44. C23×C3×C4Dic3semidirect
47. C2×C4×A4Dic3semidirect
139. C3×A4#117semidirect
149. C23×C4C3⋊Dic3semidirect
207. C2×C3×C4SL(2,ℤ/4)semidirect
281. C22×C3#926semidirect
284. A4#926semidirect
334. C2×C4C3⋊SL(2,ℤ/4)semidirect
363. C22#64135semidirect
373. C3#85482semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C4×A42
#105936662
C4⋊(C3⋊SL(2,ℤ/4))2
C4×C3⋊SL(2,ℤ/4)2
#854823
#840273
#641354