Finite Group Databasebeta

← #11921003

Subgroups — #11921003

Order 1152.

472 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 61 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
1#10596575C211yesmaximal, characteristic
2C3×C42×A4C211yesmaximal, characteristic, complemented
3#10593643C211yesmaximal, characteristic, complemented
4#73046—33nomaximal
5#71532—31nomaximal
6C2×C3×C4×A4—21no—
7C2×C3×C4×A4C2211yescharacteristic
8#64269—21no—
9C4⋊(C3⋊S4)C411yescharacteristic, complemented
10C4×C3⋊S4—21no—
11#64259C411yescharacteristic, complemented
12C3⋊(A4⋊C8)—21no—
13#63632—41nomaximal
14#5912—33no—
15C22×C3×C42D311yescharacteristic, complemented
16#5791—31no—
17C42×A4D313yescomplemented
18#5409—33no—
19#5207—31no—
20C2×#805—31no—
21C2×#805—31no—
22#4523—31no—
23#4523—31no—
24C22×C3×A4D411yescharacteristic
25C2×C3⋊S4—21no—
26#3828—41no—
27C3×C4×A4—22no—
28C3×C4×A4C2×C411yescharacteristic
29C3×C4×A4D411yescharacteristic
30C3⋊SL(2,ℤ/4)—21no—
31C32×C42—41no—
32#3748—41no—
33#1896—91noSylow
34C23×C3×C4—21no—
35C23×C3×C4C2×D311yescharacteristic
36C2×#235—31no—
37C2×C4×A4—23no—
38C2×C4×A4C2×D313yes—
39GL(2,ℤ/4)—63no—
40C4⋊S4—33no—
41C4×S4—63no—
42A4⋊Q8—33no—
43C2×C3×C42—31no—
44C2×C3×C42—31no—
45C2×C3×C42—61no—
46#953—61no—
47#930—31no—
48#930—31no—
49#929—61no—
50C4×#67—61no—
51C4×#67—61no—
52#926—31no—
53#924—31no—
54#924—31no—
55C2×#208—31no—
56C2×#208—31no—
57A4⋊C8—63no—
58#830—61no—
59#830—61no—
60#805—62no—
61#805—61no—
62#805—61no—
63#805—123no—
64C2×C3×A4—21no—
65C2×C3×A4C22⋊C411yescharacteristic
66C3⋊S4—41no—
67C2×C32×C4—41no—
68C2×C32×C4—81no—
69#638—81no—
70C4⋊(C3⋊D3)—41no—
71C4×C3⋊D3—81no—
72#634—41no—
73C3⋊(C3⋊C8)—81no—
74#525—91no—
75C22×C42C3⋊D311yescharacteristic, complemented
76C2×#104—91no—
77C2×#104—91no—
78#407—91no—
79#339—91no—
80#339—91no—
81C24×C3#6711yescharacteristic
82C22×A4#6713yes—
83C2×S4—63no—
84C22×C3×C4—22no—
85C22×C3×C4—31no—
86C22×C3×C4—31no—
87C22×C3×C4—31no—
88C22×C3×C4—31no—
89C22×C3×C4—61no—
90C22×C3×C4—61no—
91C22×C3×C4—62no—
92C22×C3×C4C4×D311yescharacteristic
93C22×C3×C4D1211yescharacteristic
94C2×#67—61no—
95C2×#67—61no—
96C2×#67—61no—
97#235—61no—
98#235—61no—
99#235—61no—
100#235—61no—
101#235—123no—
102C2×D12—31no—
103C2×C4×D3—61no—
104C2×Dic6—31no—
105C4×A4—26no—
106C4×A4C4×D313yes—
107C4×A4D1213yes—
108SL(2,ℤ/4)—63no—
109C3×C42—32no—
110C3×C42—31no—
111C3×C42—43no—
112C3×C42—61no—
113C3×C42S411yescharacteristic, complemented
114#217—61no—
115#217—61no—
116#217—61no—
117(C2×D3)⋊C4—61no—
118(C2×D3)⋊C4—61no—
119C4⋊Dic3—31no—
120C4⋊Dic3—31no—
121Dic3⋊C4—61no—
122Dic3⋊C4—61no—
123C4×Dic3—61no—
124#208—61no—
125#208—61no—
126#208—61no—
127#208—61no—
128#208—123no—
129C2×C3⋊C8—61no—
130C2×C3⋊C8—61no—
131C22×C32—41no—
132C2×C3⋊D3—81no—
133C3×A4#10411yescharacteristic, complemented
134C32×C4—41no—
135C32×C4—41no—
136C32×C4—82no—
137C3⋊Dic3—81no—
138C2×#41—91no—
139C23×C4—21no—
140C23×C4C2×C3⋊D311yescharacteristic
141C2×M16—91no—
142C2×M16—91no—
143#123—181no—
144C22⋊Q8—91no—
145C22⋊Q8—91no—
146#121—91no—
147#121—91no—
148#120—181no—
149C4×D4—181no—
150C4×D4—181no—
151#117—91no—
152C2×C42—31no—
153C2×C42—31no—
154C2×C42—61no—
155#104—182no—
156#104—181no—
157#104—181no—
158C22⋊C8—181no—
159C22⋊C8—181no—
160C23×C3—21no—
161C23×C3—31no—
162C23×C3—31no—
163C23×C3—61no—
164C23×C3(C2×D3)⋊C411yescharacteristic
165C22×D3—61no—
166C2×A4—23no—
167C2×A4(C2×D3)⋊C413yes—
168S4—123no—
169C2×C3×C4—21no—
170C2×C3×C4—31no—
171C2×C3×C4—31no—
172C2×C3×C4—31no—
173C2×C3×C4—31no—
174C2×C3×C4—31no—
175C2×C3×C4—31no—
176C2×C3×C4—31no—
177C2×C3×C4—43no—
178C2×C3×C4—62no—
179C2×C3×C4—62no—
180C2×C3×C4—61no—
181C2×C3×C4—62no—
182C2×C3×C4—61no—
183C2×C3×C4—62no—
184C2×C3×C4—83no—
185C2×C3×C4C2×S411yescharacteristic
186#67—121no—
187#67—121no—
188#67—122no—
189#67—121no—
190#67—121no—
191#67—243no—
192C2×Dic3—61no—
193C2×Dic3—61no—
194C2×Dic3—61no—
195D12—61no—
196D12—61no—
197D12—123no—
198C4×D3—121no—
199C4×D3—121no—
200C4×D3—243no—
201Dic6—61no—
202Dic6—61no—
203Dic6—123no—
204C3⋊C8—121no—
205C3⋊C8—121no—
206C3⋊C8—243no—
207C2×C32—41no—
208C2×C32—81no—
209C3⋊D3—161no—
210C24#63811yescharacteristic
211#41—181no—
212#41—181no—
213#41—181no—
214#41—181no—
215C2×Q8—91no—
216C2×D4—91no—
217C2×D4—181no—
218C2×D4—181no—
219C2×D4—181no—
220C22×C4—22no—
221C22×C4—31no—
222C22×C4—31no—
223C22×C4—31no—
224C22×C4—31no—
225C22×C4—61no—
226C22×C4—61no—
227C22×C4—62no—
228C22×C4—181no—
229C22×C4C4×C3⋊D311yescharacteristic
230C22×C4C4⋊(C3⋊D3)11yescharacteristic
231M16—181no—
232M16—181no—
233M16—181no—
234M16—181no—
235C2×C8—181no—
236C2×C8—181no—
237C4⋊C4—91no—
238C4⋊C4—91no—
239C4⋊C4—181no—
240C4⋊C4—181no—
241C22⋊C4—181no—
242C22⋊C4—181no—
243C22⋊C4—181no—
244C22⋊C4—181no—
245C22⋊C4—181no—
246C42—32no—
247C42—31no—
248C42—61no—
249C42—181no—
250C42C3⋊S411yescharacteristic, complemented
251C22×C3—31no—
252C22×C3—31no—
253C22×C3—32no—
254C22×C3—31no—
255C22×C3—43no—
256C22×C3—61no—
257C22×C3—61no—
258C22×C3—61no—
259C22×C3#80511yescharacteristic, complemented
260C22×C3GL(2,ℤ/4)11yescharacteristic
261C2×D3—121no—
262C2×D3—121no—
263C2×D3—121no—
264C2×D3—243no—
265A4#80513yescomplemented
266C3×C4—22no—
267C3×C4—31no—
268C3×C4—31no—
269C3×C4—43no—
270C3×C4—43no—
271C3×C4—62no—
272C3×C4—86no—
273C3×C4C4×S411yescharacteristic
274C3×C4C4⋊S411yescharacteristic
275Dic3—121no—
276Dic3—121no—
277Dic3—121no—
278Dic3—243no—
279C32—41noSylow
280C23—21no—
281C23—31no—
282C23—31no—
283C23—61no—
284C23—181no—
285C23#375211yescharacteristic
286Q8—181no—
287Q8—181no—
288D4—181no—
289D4—181no—
290D4—361no—
291D4—361no—
292D4—362no—
293D4—361no—
294D4—361no—
295C2×C4—21no—
296C2×C4—31no—
297C2×C4—31no—
298C2×C4—31no—
299C2×C4—31no—
300C2×C4—31no—
301C2×C4—31no—
302C2×C4—31no—
303C2×C4—62no—
304C2×C4—62no—
305C2×C4—61no—
306C2×C4—62no—
307C2×C4—61no—
308C2×C4—62no—
309C2×C4—181no—
310C2×C4—181no—
311C2×C4—181no—
312C2×C4—361no—
313C2×C4—361no—
314C2×C4C2×C3⋊S411yescharacteristic
315C8—361no—
316C8—361no—
317C2×C3—21no—
318C2×C3—31no—
319C2×C3—31no—
320C2×C3—43no—
321C2×C3—61no—
322C2×C3—83no—
323C2×C3(C2×S4)⋊C411yescharacteristic
324D3—241no—
325D3—483no—
326C22—31no—
327C22—31no—
328C22—32no—
329C22—31no—
330C22—61no—
331C22—61no—
332C22—61no—
333C22—361no—
334C22—361no—
335C22—361no—
336C22#6363211yescharacteristic, complemented
337C22#6426911yescharacteristic
338C4—22no—
339C4—31no—
340C4—31no—
341C4—62no—
342C4—361no—
343C4—361no—
344C4—361no—
345C4C4×C3⋊S411yescharacteristic
346C4C4⋊(C3⋊S4)11yescharacteristic
347C3—43no—
348C3#7304611yescharacteristic, complemented
349C2—21no—
350C2—31no—
351C2—31no—
352C2—61no—
353C2—721no—
354C2#1059364711yescharacteristic
subgroupG/H
centerC4C4⋊(C3⋊S4)
commutatorC3×C4×A4C2×C4
FrattiniC2×C4C2×C3⋊S4
FittingC22×C3×C42D3
socleC23×C3(C2×D3)⋊C4
prime radical#10596575C2
cosocleC2×C3×C4×A4C22
hypercenterC42C3⋊S4
hypocenterC3×A4#104
LCSG ▷ C3×C4×A4 ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C4 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C3×C42×A4C2semidirect
3. #10593643C2semidirect
9. C4⋊(C3⋊S4)C4semidirect
11. #64259C4semidirect
15. C22×C3×C42D3semidirect
17. C42×A4D3semidirect
75. C22×C42C3⋊D3semidirect
113. C3×C42S4semidirect
133. C3×A4#104semidirect
250. C42C3⋊S4semidirect
259. C22×C3#805semidirect
265. A4#805semidirect
336. C22#63632semidirect
348. C3#73046semidirect

Maximal subgroups

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

subgroupindex
#105965752
C3×C42×A42
#105936432
#730463
#715323
#636324