Finite Group Databasebeta

← #11922855

Subgroups — #11922855

Order 1152.

622 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 622 conjugacy classes of subgroups — too many to draw. Only its 99 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
1C3×A4×C4⋊C4C211yesmaximal, characteristic
2C4⋊(C3⋊SL(2,ℤ/4))C212yesmaximal
3C4⋊(C3⋊SL(2,ℤ/4))C211yesmaximal, characteristic
4#10593645C212yesmaximal
5C4×C3⋊SL(2,ℤ/4)C211yesmaximal, characteristic
6#85305—33nomaximal
7#82172—31nomaximal
8C2×C3×C4×A4C2212yes—
9C2×C3×C4×A4C2211yescharacteristic
10C2×C3⋊SL(2,ℤ/4)C2211yescharacteristic
11C2×C3⋊SL(2,ℤ/4)C2211yescharacteristic
12C2×C3⋊SL(2,ℤ/4)C2212yes—
13#64099—41nomaximal
14C22×C3×C4⋊C4D311yescharacteristic
15C2×#890—31no—
16A4×C4⋊C4D313yes—
17C4⋊SL(2,ℤ/4)—36no—
18C4⋊SL(2,ℤ/4)—33no—
19SL(2,ℤ/4)⋊C4—36no—
20C4×SL(2,ℤ/4)—33no—
21#5212—32no—
22#5212—31no—
23#5210—32no—
24C4×#217—31no—
25#4986—32no—
26#4984—31no—
27#4982—32no—
28#4977—31no—
29#4972—31no—
30C22×C3×A4C2311yescharacteristic
31C3×C4×A4—22no—
32C3×C4×A4Q812yes—
33C3⋊SL(2,ℤ/4)—21no—
34C3⋊SL(2,ℤ/4)—21no—
35C3⋊SL(2,ℤ/4)—22no—
36C32×C4⋊C4—41no—
37C4⋊(C3⋊Dic3)—42no—
38C4⋊(C3⋊Dic3)—41no—
39#3750—42no—
40C4×C3⋊Dic3—41no—
41#2442—91noSylow
42C23×C3×C4C2×D312yes—
43C23×C3×C4C2×D311yescharacteristic
44C2×C4×A4C2×D316yes—
45C2×C4×A4C2×D313yes—
46C2×SL(2,ℤ/4)—33no—
47C2×SL(2,ℤ/4)—33no—
48C2×SL(2,ℤ/4)—36no—
49C2×C3×C4⋊C4—31no—
50C2×C3×C4⋊C4—31no—
51C2×C3×C4⋊C4—32no—
52C2×#217—31no—
53C2×#217—31no—
54C2×#217—32no—
55C2×C4⋊Dic3—31no—
56C2×C4⋊Dic3—31no—
57C2×C4⋊Dic3—32no—
58C2×C4⋊Dic3—32no—
59C2×Dic3⋊C4—32no—
60C2×Dic3⋊C4—32no—
61C2×C4×Dic3—31no—
62C2×C4×Dic3—31no—
63#890—62no—
64#890—61no—
65#890—61no—
66#890—123no—
67C3⋊#95—31no—
68C3⋊#95—31no—
69C3⋊#95—32no—
70C3⋊#95—32no—
71C3⋊#95—32no—
72C3⋊#95—32no—
73C3⋊#95—32no—
74C2×C3×A4C2×Q811yescharacteristic
75C2×C3×A4#4111yescharacteristic
76C2×C3×A4#4111yescharacteristic
77C2×C32×C4—41no—
78C2×C32×C4—42no—
79C2×C3⋊Dic3—41no—
80C2×C3⋊Dic3—41no—
81C2×C3⋊Dic3—42no—
82C2×#125—91no—
83C22×C4⋊C4C3⋊D311yescharacteristic
84#400—92no—
85#398—92no—
86#389—91no—
87#389—91no—
88#385—92no—
89#382—91no—
90#380—92no—
91#380—91no—
92C4×C22⋊C4—91no—
93C24×C3C22×D311yescharacteristic
94C22×A4C22×D313yes—
95C22×C3×C4—22no—
96C22×C3×C4—31no—
97C22×C3×C4—31no—
98C22×C3×C4—32no—
99C22×C3×C4—32no—
100C22×C3×C4—32no—
101C22×C3×C4—62no—
102C22×C3×C4Dic612yes—
103C22×Dic3—31no—
104C22×Dic3—31no—
105C22×Dic3—31no—
106C22×Dic3—32no—
107C22×Dic3—32no—
108C22×Dic3—31no—
109C4×A4—26no—
110C4×A4Dic616yes—
111SL(2,ℤ/4)—63no—
112SL(2,ℤ/4)—63no—
113SL(2,ℤ/4)—66no—
114C3×C4⋊C4—32no—
115C3×C4⋊C4—31no—
116C3×C4⋊C4—43no—
117C3×C4⋊C4—61no—
118C3×C4⋊C4S411yescharacteristic
119#217—61no—
120#217—62no—
121#217—61no—
122#217—61no—
123#217—61no—
124#217—62no—
125C4⋊Dic3—62no—
126C4⋊Dic3—61no—
127C4⋊Dic3—62no—
128C4⋊Dic3—62no—
129C4⋊Dic3—61no—
130C4⋊Dic3—126no—
131C4⋊Dic3—123no—
132C4⋊Dic3—122no—
133Dic3⋊C4—62no—
134Dic3⋊C4—62no—
135Dic3⋊C4—126no—
136Dic3⋊C4—122no—
137C4×Dic3—61no—
138C4×Dic3—62no—
139C4×Dic3—61no—
140C4×Dic3—123no—
141C22×C32—41no—
142C3×A4#12511yescharacteristic, complemented
143C32×C4—42no—
144C32×C4—82no—
145C3⋊Dic3—81no—
146C3⋊Dic3—81no—
147C3⋊Dic3—82no—
148C23×C4C2×C3⋊D312yes—
149C23×C4C2×C3⋊D311yescharacteristic
150#125—182no—
151#125—181no—
152#125—181no—
153C2×C4⋊C4—31no—
154C2×C4⋊C4—31no—
155C2×C4⋊C4—32no—
156C2×C4⋊C4—91no—
157C2×C4⋊C4—92no—
158C2×C4⋊C4—92no—
159C2×C4⋊C4—91no—
160C2×C4⋊C4—92no—
161C2×C4⋊C4—92no—
162C2×C22⋊C4—91no—
163C2×C22⋊C4—91no—
164C2×C22⋊C4—92no—
165C2×C42—91no—
166C2×C42—91no—
167#95—91no—
168#95—91no—
169#95—92no—
170#95—92no—
171#95—92no—
172#95—92no—
173#95—92no—
174C23×C3—31no—
175C23×C3—31no—
176C23×C3—31no—
177C23×C3—31no—
178C23×C3C2×Dic611yescharacteristic
179C23×C3#23711yescharacteristic
180C23×C3#23911yescharacteristic
181C2×A4C2×Dic613yes—
182C2×A4#23713yes—
183C2×A4#23913yes—
184C2×C3×C4—31no—
185C2×C3×C4—32no—
186C2×C3×C4—32no—
187C2×C3×C4—32no—
188C2×C3×C4—32no—
189C2×C3×C4—43no—
190C2×C3×C4—46no—
191C2×C3×C4—62no—
192C2×C3×C4—62no—
193C2×C3×C4—61no—
194C2×C3×C4—62no—
195C2×C3×C4—62no—
196C2×C3×C4C2×S412yes—
197C2×C3×C4C2×S411yescharacteristic
198C2×Dic3—61no—
199C2×Dic3—61no—
200C2×Dic3—61no—
201C2×Dic3—62no—
202C2×Dic3—62no—
203C2×Dic3—61no—
204C2×Dic3—61no—
205C2×Dic3—61no—
206C2×Dic3—62no—
207C2×Dic3—61no—
208C2×Dic3—61no—
209C2×Dic3—62no—
210C2×Dic3—61no—
211C2×Dic3—61no—
212C2×Dic3—62no—
213C2×Dic3—61no—
214C2×Dic3—61no—
215C2×Dic3—62no—
216C2×Dic3—123no—
217C2×Dic3—123no—
218C2×Dic3—126no—
219C2×C32—41no—
220C2×C32—41no—
221C2×C32—41no—
222C24C22×C3⋊D311yescharacteristic
223C22×C4—22no—
224C22×C4—31no—
225C22×C4—31no—
226C22×C4—32no—
227C22×C4—32no—
228C22×C4—32no—
229C22×C4—62no—
230C22×C4—91no—
231C22×C4—91no—
232C22×C4—91no—
233C22×C4—92no—
234C22×C4—92no—
235C22×C4—91no—
236C22×C4#63412yes—
237C4⋊C4—32no—
238C4⋊C4—31no—
239C4⋊C4—61no—
240C4⋊C4—182no—
241C4⋊C4—181no—
242C4⋊C4—182no—
243C4⋊C4—182no—
244C4⋊C4—182no—
245C4⋊C4—182no—
246C4⋊C4—181no—
247C4⋊C4—362no—
248C4⋊C4—362no—
249C4⋊C4C3⋊S411yescharacteristic
250C22⋊C4—181no—
251C22⋊C4—182no—
252C22⋊C4—181no—
253C22⋊C4—181no—
254C22⋊C4—181no—
255C22⋊C4—182no—
256C42—181no—
257C42—182no—
258C42—181no—
259C22×C3—31no—
260C22×C3—31no—
261C22×C3—31no—
262C22×C3—31no—
263C22×C3—31no—
264C22×C3—31no—
265C22×C3—31no—
266C22×C3—31no—
267C22×C3—31no—
268C22×C3—43no—
269C22×C3—61no—
270C22×C3#89011yescharacteristic, complemented
271C22×C3C22×S411yescharacteristic
272A4#89013yescomplemented
273C3×C4—22no—
274C3×C4—32no—
275C3×C4—46no—
276C3×C4—62no—
277C3×C4—86no—
278C3×C4A4⋊Q812yes—
279Dic3—121no—
280Dic3—122no—
281Dic3—121no—
282Dic3—121no—
283Dic3—121no—
284Dic3—122no—
285Dic3—243no—
286Dic3—243no—
287Dic3—246no—
288C32—41noSylow
289C23—31no—
290C23—31no—
291C23—31no—
292C23—31no—
293C23C2×#63411yescharacteristic
294C23#383011yescharacteristic
295C23#383211yescharacteristic
296C2×C4—31no—
297C2×C4—32no—
298C2×C4—32no—
299C2×C4—32no—
300C2×C4—32no—
301C2×C4—62no—
302C2×C4—62no—
303C2×C4—61no—
304C2×C4—62no—
305C2×C4—62no—
306C2×C4—181no—
307C2×C4—181no—
308C2×C4—181no—
309C2×C4—181no—
310C2×C4—182no—
311C2×C4—181no—
312C2×C4—181no—
313C2×C4—182no—
314C2×C4—182no—
315C2×C4—182no—
316C2×C4—181no—
317C2×C4—181no—
318C2×C4—181no—
319C2×C4—181no—
320C2×C4—182no—
321C2×C4—181no—
322C2×C4—181no—
323C2×C4—182no—
324C2×C4C2×C3⋊S412yes—
325C2×C4C2×C3⋊S411yescharacteristic
326C2×C3—31no—
327C2×C3—31no—
328C2×C3—31no—
329C2×C3—31no—
330C2×C3—43no—
331C2×C3—43no—
332C2×C3—43no—
333C2×C3C2×A4⋊Q811yescharacteristic
334C2×C3#591411yescharacteristic
335C2×C3#591911yescharacteristic
336C22—31no—
337C22—31no—
338C22—31no—
339C22—31no—
340C22—31no—
341C22—31no—
342C22—31no—
343C22—31no—
344C22—31no—
345C22—61no—
346C22#6409911yescharacteristic, complemented
347C22C22×C3⋊S411yescharacteristic
348C4—22no—
349C4—32no—
350C4—62no—
351C4—361no—
352C4—362no—
353C4—361no—
354C4—361no—
355C4—361no—
356C4—362no—
357C4#6425912yes—
358C3—43no—
359C3#8530511yescharacteristic, complemented
360C2—31no—
361C2—31no—
362C2—31no—
363C2—31no—
364C2C2×#6425911yescharacteristic
365C2#1059657711yescharacteristic
366C2#1059658211yescharacteristic
subgroupG/H
center, FrattiniC22C22×C3⋊S4
commutator, prime radical, cosocleC22×C3×A4C23
FittingC22×C3×C4⋊C4D3
socleC24×C3C22×D3
hypercenterC4⋊C4C3⋊S4
hypocenterC3×A4#125
LCSG ▷ C22×C3×A4 ▷ C3×A4
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
142. C3×A4#125semidirect
270. C22×C3#890semidirect
272. A4#890semidirect
346. C22#64099semidirect
359. C3#85305semidirect

Maximal subgroups

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

subgroupindex
C3×A4×C4⋊C42
C4⋊(C3⋊SL(2,ℤ/4))2
#105936452
C4×C3⋊SL(2,ℤ/4)2
#853053
#821723
#640994