Finite Group Databasebeta

← #11921073

Subgroups — #11921073

Order 1152.

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

normal subgroups only

This group has 466 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×A4×M16C211yesmaximal, characteristic, complemented
3C4×C3⋊SL(2,ℤ/4)C211yesmaximal, characteristic, complemented
4#73117—33nomaximal
5#71984—31nomaximal
6C2×C3×C4×A4C2211yescharacteristic
7#64269—21no—
8C2×C3⋊SL(2,ℤ/4)—21no—
9C4⋊(C3⋊S4)C411yescharacteristic, complemented
10C4×C3⋊S4—21no—
11#64259C411yescharacteristic, complemented
12C3×C8×A4—21no—
13#63652—41nomaximal
14#5912—33no—
15C22×C3×M16D311yescharacteristic, complemented
16#5791—31no—
17A4×M16D313yescomplemented
18C4×SL(2,ℤ/4)—33no—
19C4×#217—31no—
20C2×#825—31no—
21C2×#825—31no—
22#4555—31no—
23#4555—31no—
24C22×C3×A4D411yescharacteristic
25C2×C3⋊S4—21no—
26#3828—41no—
27C3×C4×A4C2×C411yescharacteristic
28C3×C4×A4D411yescharacteristic
29C3⋊SL(2,ℤ/4)—22no—
30C3⋊SL(2,ℤ/4)—21no—
31C32×M16—41no—
32C4×C3⋊Dic3—41no—
33#1871—91noSylow
34C23×C3×C4C2×D311yescharacteristic
35C2×#235—31no—
36C2×C4×A4C2×D313yes—
37GL(2,ℤ/4)—63no—
38C2×SL(2,ℤ/4)—63no—
39C4⋊S4—33no—
40C4×S4—63no—
41A4⋊Q8—33no—
42C2×C3×M16—31no—
43C2×C3×M16—31no—
44C2×C3×M16—61no—
45C22×C3×C8—21no—
46#953—61no—
47C2×#217—61no—
48#930—31no—
49#930—31no—
50#929—61no—
51C4×#67—61no—
52C4×#67—61no—
53#926—31no—
54#924—31no—
55#924—31no—
56C2×C4×Dic3—31no—
57C2×C4×Dic3—31no—
58C8×A4—23no—
59C3⋊#95—61no—
60#825—62no—
61#825—61no—
62#825—61no—
63#825—123no—
64C2×C3×A4—21no—
65C2×C3×A4C22⋊C411yescharacteristic
66C3⋊S4—41no—
67C2×C32×C4—41no—
68#638—81no—
69C2×C3⋊Dic3—81no—
70C4⋊(C3⋊D3)—41no—
71C4×C3⋊D3—81no—
72#634—41no—
73C32×C8—81no—
74C22×M16C3⋊D311yescharacteristic, complemented
75#525—91no—
76C2×#104—91no—
77C2×#104—91no—
78C4×C22⋊C4—91no—
79#339—91no—
80#339—91no—
81C24×C3D1211yescharacteristic
82C22×A4D1213yes—
83C2×S4—63no—
84C22×C3×C4—31no—
85C22×C3×C4—31no—
86C22×C3×C4—31no—
87C22×C3×C4—31no—
88C22×C3×C4C4×D311yescharacteristic
89C22×C3×C4#6711yescharacteristic
90C2×#67—61no—
91C2×#67—61no—
92C2×#67—61no—
93C22×Dic3—61no—
94C22×Dic3—61no—
95#235—61no—
96#235—61no—
97#235—61no—
98#235—61no—
99#235—123no—
100C2×D12—31no—
101C2×C4×D3—61no—
102C2×Dic6—31no—
103C4×A4C4×D313yes—
104C4×A4#6713yes—
105SL(2,ℤ/4)—66no—
106SL(2,ℤ/4)—63no—
107C3×M16—32no—
108C3×M16—31no—
109C3×M16—43no—
110C3×M16—61no—
111C3×M16S411yescharacteristic, complemented
112C2×C3×C8—61no—
113C2×C3×C8—61no—
114#217—62no—
115#217—61no—
116#217—61no—
117#217—62no—
118#217—61no—
119(C2×D3)⋊C4—61no—
120(C2×D3)⋊C4—61no—
121C4⋊Dic3—31no—
122C4⋊Dic3—31no—
123Dic3⋊C4—61no—
124Dic3⋊C4—61no—
125C4×Dic3—61no—
126C4×Dic3—61no—
127C4×Dic3—61no—
128C4×Dic3—61no—
129C4×Dic3—61no—
130C4×Dic3—123no—
131C22×C32—41no—
132C2×C3⋊D3—81no—
133C3×A4#10411yescharacteristic, complemented
134C32×C4—41no—
135C32×C4—41no—
136C3⋊Dic3—81no—
137C3⋊Dic3—82no—
138C2×#41—91no—
139C23×C4C2×C3⋊D311yescharacteristic
140C2×M16—31no—
141C2×M16—31no—
142C2×M16—61no—
143C22×C8—21no—
144#123—181no—
145C22⋊Q8—91no—
146C22⋊Q8—91no—
147#121—91no—
148#121—91no—
149#120—181no—
150C4×D4—181no—
151C4×D4—181no—
152#117—91no—
153C2×C22⋊C4—181no—
154C2×C42—91no—
155C2×C42—91no—
156#104—182no—
157#104—181no—
158#104—181no—
159#95—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—31no—
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—43no—
177C2×C3×C4—61no—
178C2×C3×C4C2×S411yescharacteristic
179#67—121no—
180#67—121no—
181#67—122no—
182#67—121no—
183#67—121no—
184#67—243no—
185C2×Dic3—61no—
186C2×Dic3—61no—
187C2×Dic3—61no—
188C2×Dic3—62no—
189C2×Dic3—62no—
190C2×Dic3—121no—
191C2×Dic3—121no—
192C2×Dic3—121no—
193C2×Dic3—121no—
194C2×Dic3—243no—
195D12—61no—
196D12—61no—
197D12—123no—
198C4×D3—121no—
199C4×D3—121no—
200C4×D3—243no—
201Dic6—61no—
202Dic6—61no—
203Dic6—123no—
204C3×C8—21no—
205C3×C8—61no—
206C3×C8—83no—
207C2×C32—41no—
208C2×C32—81no—
209C3⋊D3—161no—
210C24C4⋊(C3⋊D3)11yescharacteristic
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—31no—
221C22×C4—31no—
222C22×C4—31no—
223C22×C4—31no—
224C22×C4—181no—
225C22×C4—181no—
226C22×C4—181no—
227C22×C4C4×C3⋊D311yescharacteristic
228C22×C4#63811yescharacteristic
229M16—32no—
230M16—31no—
231M16—61no—
232M16C3⋊S411yescharacteristic, complemented
233C2×C8—61no—
234C2×C8—61no—
235C4⋊C4—91no—
236C4⋊C4—91no—
237C4⋊C4—181no—
238C4⋊C4—181no—
239C22⋊C4—181no—
240C22⋊C4—181no—
241C22⋊C4—182no—
242C22⋊C4—181no—
243C22⋊C4—181no—
244C22⋊C4—182no—
245C22⋊C4—181no—
246C42—181no—
247C42—181no—
248C42—181no—
249C42—181no—
250C42—181no—
251C22×C3—31no—
252C22×C3—31no—
253C22×C3—31no—
254C22×C3—43no—
255C22×C3—61no—
256C22×C3—61no—
257C22×C3—61no—
258C22×C3—61no—
259C22×C3#82511yescharacteristic, complemented
260C22×C3C4⋊S411yescharacteristic
261C2×D3—121no—
262C2×D3—121no—
263C2×D3—121no—
264C2×D3—243no—
265A4#82513yescomplemented
266C3×C4—31no—
267C3×C4—31no—
268C3×C4—43no—
269C3×C4—43no—
270C3×C4C4×S411yescharacteristic
271C3×C4GL(2,ℤ/4)11yescharacteristic
272Dic3—122no—
273Dic3—121no—
274Dic3—121no—
275Dic3—122no—
276Dic3—121no—
277Dic3—243no—
278Dic3—246no—
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—31no—
296C2×C4—31no—
297C2×C4—31no—
298C2×C4—31no—
299C2×C4—31no—
300C2×C4—31no—
301C2×C4—31no—
302C2×C4—61no—
303C2×C4—181no—
304C2×C4—181no—
305C2×C4—181no—
306C2×C4—182no—
307C2×C4—182no—
308C2×C4—361no—
309C2×C4—361no—
310C2×C4—361no—
311C2×C4—361no—
312C2×C4—361no—
313C2×C4—361no—
314C2×C4C2×C3⋊S411yescharacteristic
315C8—21no—
316C8—61no—
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—31no—
329C22—61no—
330C22—61no—
331C22—61no—
332C22—61no—
333C22—361no—
334C22—361no—
335C22—361no—
336C22#6365211yescharacteristic, complemented
337C22C4⋊(C3⋊S4)11yescharacteristic
338C4—31no—
339C4—31no—
340C4—362no—
341C4—361no—
342C4—361no—
343C4—362no—
344C4—361no—
345C4C4×C3⋊S411yescharacteristic
346C4#6426911yescharacteristic
347C3—43no—
348C3#7311711yescharacteristic, complemented
349C2—21no—
350C2—31no—
351C2—31no—
352C2—61no—
353C2—721no—
354C2#1059364711yescharacteristic
subgroupG/H
centerC4#64269
commutatorC3×C4×A4C2×C4
FrattiniC2×C4C2×C3⋊S4
FittingC22×C3×M16D3
socleC23×C3(C2×D3)⋊C4
prime radical#10596575C2
cosocleC2×C3×C4×A4C22
hypercenterM16C3⋊S4
hypocenterC3×A4#104
LCSG ▷ C3×C4×A4 ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C4 ◁ C2×C4 ◁ M16

Complements

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

NH ≅ G/Ntype
2. C3×A4×M16C2semidirect
3. C4×C3⋊SL(2,ℤ/4)C2semidirect
9. C4⋊(C3⋊S4)C4semidirect
11. #64259C4semidirect
15. C22×C3×M16D3semidirect
17. A4×M16D3semidirect
74. C22×M16C3⋊D3semidirect
111. C3×M16S4semidirect
133. C3×A4#104semidirect
232. M16C3⋊S4semidirect
259. C22×C3#825semidirect
265. A4#825semidirect
336. C22#63652semidirect
348. C3#73117semidirect

Maximal subgroups

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

subgroupindex
#105965752
C3×A4×M162
C4×C3⋊SL(2,ℤ/4)2
#731173
#719843
#636524