Finite Group Databasebeta

← #11920630

Subgroups — #11920630

Order 1152.

392 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 59 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×C3×A4⋊Q8C211yesmaximal, characteristic
2C2×A4×C3⋊C8C211yesmaximal, characteristic
3C4⋊(C3⋊SL(2,ℤ/4))C211yesmaximal, characteristic
4#73109—31nomaximal
5#71696—31nomaximal
6C2×C3×C4×A4C2211yescharacteristic
7C2×C3⋊SL(2,ℤ/4)—21no—
8C2×C3×SL(2,ℤ/4)—21no—
9C3×A4⋊Q8—21no—
10C3×A4⋊Q8C412yescomplemented
11A4×C3⋊C8—21no—
12#63566—41nomaximal
13C2×A4⋊Q8D311yescharacteristic
14C2×C3×C22⋊Q8—31no—
15C23×C3⋊C8D311yescharacteristic
16C2×C8×A4—31no—
17C4⋊SL(2,ℤ/4)—31no—
18C4⋊SL(2,ℤ/4)—61no—
19C2×#835—31no—
20C2×#835—31no—
21#5212—31no—
22#4529—31no—
23#4529—31no—
24C22×C3×A4D411yescharacteristic
25C2×C3×Dic6—41no—
26C3×C4×A4C2×C411yescharacteristic
27C3×C4×A4D411yescharacteristic
28C3⋊SL(2,ℤ/4)—41no—
29C3×SL(2,ℤ/4)—22no—
30C4⋊(C3⋊Dic3)—41no—
31C2×C3×C3⋊C8—41no—
32#1892—91noSylow
33C22×C3×Q8—31no—
34C23×C3×C4C2×D311yescharacteristic
35C2×C4×A4—21no—
36C2×C4×A4C2×D311yescharacteristic
37C2×SL(2,ℤ/4)—21no—
38C2×SL(2,ℤ/4)—62no—
39C2×SL(2,ℤ/4)—61no—
40A4⋊Q8—21no—
41A4⋊Q8Dic312yescomplemented
42C3×C22⋊Q8—32no—
43C3×C22⋊Q8—32no—
44C3×C22⋊Q8—61no—
45C3×C22⋊Q8—61no—
46C2×C3×C4⋊C4—31no—
47C2×C3×C4⋊C4—61no—
48C2×C3×C22⋊C4—61no—
49C2×#217—61no—
50C2×C4⋊Dic3—31no—
51C2×C4⋊Dic3—31no—
52C22×C3⋊C8—21no—
53C22×C3⋊C8—31no—
54C22×C3⋊C8—31no—
55C22×C3⋊C8—61no—
56C8×A4—61no—
57#835—62no—
58#835—61no—
59#835—61no—
60C3⋊#95—61no—
61#816—121no—
62C2×C3×A4C22⋊C411yescharacteristic
63C2×C3×A4SD1611yescharacteristic
64C2×C3×A4Q1611yescharacteristic
65C2×C32×C4—41no—
66C2×C3⋊Dic3—81no—
67C2×C3×Dic3—81no—
68C3×Dic6—42no—
69C3×Dic6—81no—
70C3×C3⋊C8—81no—
71C23×C8—31no—
72C2×C22⋊Q8—31no—
73C2×#103—91no—
74C2×#103—91no—
75#380—91no—
76#340—91no—
77#340—91no—
78C24×C3D1211yescharacteristic
79C22×A4—21no—
80C22×A4#6711yescharacteristic
81C2×C3×Q8—32no—
82C2×C3×Q8—61no—
83C2×C3×Q8—61no—
84C2×C3×Q8—61no—
85C2×C3×Q8—61no—
86C2×C3×Q8—61no—
87C22×C3×C4—31no—
88C22×C3×C4—31no—
89C22×C3×C4—31no—
90C22×C3×C4—31no—
91C22×C3×C4—61no—
92C22×C3×C4—61no—
93C22×C3×C4C4×D311yescharacteristic
94C22×C3×C4#6711yescharacteristic
95C22×Dic3—61no—
96C22×Dic3—61no—
97C2×Dic6—41no—
98C4×A4—21no—
99C4×A4—21no—
100C4×A4C2×Dic311yescharacteristic
101C4×A4#6711yescharacteristic
102SL(2,ℤ/4)—22no—
103SL(2,ℤ/4)—122no—
104SL(2,ℤ/4)—121no—
105C2×C3×C8—121no—
106C3×C4⋊C4—32no—
107C3×C4⋊C4—61no—
108C3×C4⋊C4—62no—
109C3×C4⋊C4—62no—
110C3×C22⋊C4—62no—
111C3×C22⋊C4—62no—
112#217—121no—
113#217—121no—
114C4⋊Dic3—61no—
115C4⋊Dic3—61no—
116C4⋊Dic3—61no—
117C4⋊Dic3—61no—
118C4⋊Dic3—121no—
119C4⋊Dic3—241no—
120C2×C3⋊C8—32no—
121C2×C3⋊C8—31no—
122C2×C3⋊C8—61no—
123C2×C3⋊C8—61no—
124C2×C3⋊C8—61no—
125C2×C3⋊C8S411yescharacteristic
126C22×C32—41no—
127C3×A4#10311yescharacteristic, complemented
128C32×C4—41no—
129C32×C4—41no—
130C3⋊Dic3—161no—
131C3×Dic3—82no—
132C22×Q8—31no—
133C23×C4D3211yescharacteristic
134C22×C8—61no—
135C22×C8—91no—
136C22×C8—91no—
137C22×C8—181no—
138C22⋊Q8—32no—
139C22⋊Q8—32no—
140C22⋊Q8—61no—
141C22⋊Q8—61no—
142C2×C4⋊C4—31no—
143C2×C4⋊C4—61no—
144C2×C4⋊C4—91no—
145C2×C4⋊C4—91no—
146C2×C22⋊C4—61no—
147C2×C22⋊C4—181no—
148#103—181no—
149#103—182no—
150#103—181no—
151#95—181no—
152C23×C3—31no—
153C23×C3—31no—
154C23×C3—31no—
155C23×C3—31no—
156C23×C3#20411yescharacteristic
157C23×C3Dic1211yescharacteristic
158C23×C3(C2×D3)⋊C411yescharacteristic
159C2×A4—21no—
160C2×A4—21no—
161C2×A4—21no—
162C2×A4#21511yescharacteristic
163C2×A4#21611yescharacteristic
164C2×A4#21711yescharacteristic
165C3×Q8—62no—
166C3×Q8—62no—
167C3×Q8—121no—
168C3×Q8—121no—
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—41no—
177C2×C3×C4—61no—
178C2×C3×C4—62no—
179C2×C3×C4—62no—
180C2×C3×C4—81no—
181C2×C3×C4—121no—
182C2×C3×C4—121no—
183C2×C3×C4—121no—
184C2×C3×C4—121no—
185C2×C3×C4C2×S411yescharacteristic
186C2×Dic3—81no—
187C2×Dic3—121no—
188C2×Dic3—121no—
189C2×Dic3—121no—
190C2×Dic3—121no—
191C2×Dic3—121no—
192C2×Dic3—121no—
193C2×Dic3—241no—
194C2×Dic3—242no—
195Dic6—42no—
196Dic6—81no—
197C3×C8—241no—
198C3⋊C8—21no—
199C3⋊C8—61no—
200C2×C32—41no—
201C2×C32—41no—
202C2×C32—41no—
203C24#62611yescharacteristic
204C2×Q8—32no—
205C2×Q8—61no—
206C2×Q8—61no—
207C2×Q8—61no—
208C2×Q8—61no—
209C2×Q8—61no—
210C22×C4—31no—
211C22×C4—31no—
212C22×C4—31no—
213C22×C4—31no—
214C22×C4—61no—
215C22×C4—61no—
216C22×C4—181no—
217C22×C4—181no—
218C22×C4D3×Dic311yescharacteristic
219C22×C4#62511yescharacteristic
220C2×C8—31no—
221C2×C8—92no—
222C2×C8—91no—
223C2×C8—181no—
224C2×C8—181no—
225C2×C8—181no—
226C4⋊C4—32no—
227C4⋊C4—61no—
228C4⋊C4—62no—
229C4⋊C4—62no—
230C4⋊C4—181no—
231C4⋊C4—181no—
232C4⋊C4—181no—
233C4⋊C4—181no—
234C22⋊C4—62no—
235C22⋊C4—62no—
236C22⋊C4—361no—
237C22⋊C4—361no—
238C22×C3—31no—
239C22×C3—31no—
240C22×C3—31no—
241C22×C3—31no—
242C22×C3—31no—
243C22×C3—31no—
244C22×C3—31no—
245C22×C3—31no—
246C22×C3—31no—
247C22×C3—41no—
248C22×C3—61no—
249C22×C3—81no—
250C22×C3#81611yescharacteristic, complemented
251C22×C3C4⋊S411yescharacteristic
252A4—21no—
253A4#83511yescharacteristic, complemented
254C3×C4—31no—
255C3×C4—31no—
256C3×C4—41no—
257C3×C4—41no—
258C3×C4—81no—
259C3×C4—81no—
260C3×C4—122no—
261C3×C4—122no—
262C3×C4C4×S411yescharacteristic
263C3×C4GL(2,ℤ/4)11yescharacteristic
264Dic3—82no—
265Dic3—241no—
266Dic3—241no—
267Dic3—481no—
268Dic3—482no—
269C32—41noSylow
270C23—31no—
271C23—31no—
272C23—31no—
273C23—31no—
274C23#371711yescharacteristic
275C23#371911yescharacteristic
276C23(C2×D3)⋊Dic311yescharacteristic
277Q8—62no—
278Q8—62no—
279Q8—121no—
280Q8—121no—
281C2×C4—31no—
282C2×C4—31no—
283C2×C4—31no—
284C2×C4—31no—
285C2×C4—31no—
286C2×C4—31no—
287C2×C4—31no—
288C2×C4—61no—
289C2×C4—62no—
290C2×C4—62no—
291C2×C4—121no—
292C2×C4—121no—
293C2×C4—121no—
294C2×C4—121no—
295C2×C4—361no—
296C2×C4—361no—
297C2×C4—361no—
298C2×C4—361no—
299C2×C4—361no—
300C2×C4—361no—
301C2×C4D3×S411yescharacteristic
302C8—61no—
303C8—181no—
304C2×C3—31no—
305C2×C3—31no—
306C2×C3—31no—
307C2×C3—31no—
308C2×C3—41no—
309C2×C3—41no—
310C2×C3—41no—
311C2×C3—81no—
312C2×C3—81no—
313C2×C3—81no—
314C2×C3#539811yescharacteristic
315C2×C3#540111yescharacteristic
316C2×C3(C2×S4)⋊C411yescharacteristic
317C22—31no—
318C22—31no—
319C22—31no—
320C22—31no—
321C22—31no—
322C22—31no—
323C22—31no—
324C22—31no—
325C22—31no—
326C22—61no—
327C22#6356611yescharacteristic, complemented
328C22#6420711yescharacteristic
329C4—31no—
330C4—31no—
331C4—122no—
332C4—122no—
333C4—721no—
334C4—721no—
335C4Dic3×S411yescharacteristic
336C4#6420911yescharacteristic
337C3—41no—
338C3—81no—
339C3#7310911yescharacteristic, complemented
340C2—31no—
341C2—31no—
342C2—31no—
343C2—31no—
344C2#1059317811yescharacteristic
345C2#1059318011yescharacteristic
346C2(C2×S4)⋊Dic311yescharacteristic
subgroupG/H
centerC22#64207
commutatorC3×C4×A4C2×C4
Frattini, hypercenterC2×C4D3×S4
FittingC23×C3×C4C2×D3
socleC24×C3D12
prime radicalC22×C3×A4D4
cosocleC2×C3×C4×A4C22
hypocenterC3×A4#103
LCSG ▷ C3×C4×A4 ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
10. C3×A4⋊Q8C4semidirect
41. A4⋊Q8Dic3semidirect
127. C3×A4#103semidirect
250. C22×C3#816semidirect
253. A4#835semidirect
327. C22#63566semidirect
339. C3#73109semidirect

Maximal subgroups

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

subgroupindex
C2×C3×A4⋊Q82
C2×A4×C3⋊C82
C4⋊(C3⋊SL(2,ℤ/4))2
#731093
#716963
#635664