Finite Group Databasebeta

← #11920631

Subgroups — #11920631

Order 1152.

404 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 57 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×#64259C211yesmaximal, characteristic
2C2×A4×C3⋊C8C211yesmaximal, characteristic
3C3×C4⋊SL(2,ℤ/4)C211yesmaximal, characteristic
4#73109—31nomaximal
5#69514—31nomaximal
6C2×C3×C4×A4C2211yescharacteristic
7C2×C3⋊SL(2,ℤ/4)—21no—
8#64259—21no—
9#64259C412yescomplemented
10C2×C3×SL(2,ℤ/4)—21no—
11A4×C3⋊C8—21no—
12#63567—41nomaximal
13C2×A4⋊Q8—31no—
14C2×A4⋊Q8—61no—
15C2×#924—31no—
16C23×C3⋊C8D311yescharacteristic
17C2×C8×A4—31no—
18C4⋊SL(2,ℤ/4)D311yescharacteristic
19C3×#380—31no—
20C2×#810—31no—
21C2×#810—31no—
22#4529—31no—
23#4529—31no—
24C22×C3×A4D411yescharacteristic
25C2×#634—41no—
26C3×C4×A4C2×C411yescharacteristic
27C3×C4×A4D411yescharacteristic
28C3⋊SL(2,ℤ/4)—22no—
29C3×SL(2,ℤ/4)—41no—
30C3×C4⋊Dic3—41no—
31C2×C3×C3⋊C8—41no—
32#1892—91noSylow
33C23×C3×C4C2×D311yescharacteristic
34C22×Dic6—31no—
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—32no—
41A4⋊Q8—62no—
42A4⋊Q8—62no—
43A4⋊Q8—61no—
44C2×C3×C4⋊C4—31no—
45C2×C3×C4⋊C4—31no—
46C2×C3×C22⋊C4—61no—
47C2×#217—61no—
48C2×C4⋊Dic3—31no—
49#924—32no—
50#924—32no—
51#924—61no—
52#924—61no—
53C2×Dic3⋊C4—61no—
54C22×C3⋊C8—21no—
55C22×C3⋊C8—31no—
56C22×C3⋊C8—31no—
57C22×C3⋊C8—61no—
58C8×A4—61no—
59C3×#95—61no—
60#816—121no—
61#810—62no—
62#810—61no—
63#810—61no—
64C2×C3×A4C22⋊C411yescharacteristic
65C2×C3×A4SD1611yescharacteristic
66C2×C3×A4Q1611yescharacteristic
67C2×C32×C4—41no—
68C2×C3⋊Dic3—81no—
69#634—42no—
70#634—81no—
71C2×C3×Dic3—81no—
72C3×C3⋊C8—81no—
73C23×C8—31no—
74C2×C22⋊Q8—91no—
75C2×#103—91no—
76C2×#103—91no—
77#380—31no—
78#340—91no—
79#340—91no—
80C24×C3D1211yescharacteristic
81C22×A4—21no—
82C22×A4#6711yescharacteristic
83C22×C3×C4—31no—
84C22×C3×C4—31no—
85C22×C3×C4—31no—
86C22×C3×C4—31no—
87C22×C3×C4—61no—
88C22×C3×C4—61no—
89C22×C3×C4C4×D311yescharacteristic
90C22×C3×C4#6711yescharacteristic
91C22×Dic3—61no—
92C22×Dic3—61no—
93C2×Dic6—32no—
94C2×Dic6—61no—
95C2×Dic6—61no—
96C2×Dic6—61no—
97C2×Dic6—61no—
98C2×Dic6—61no—
99C2×Dic6—121no—
100C2×Dic6—241no—
101C4×A4—21no—
102C4×A4—21no—
103C4×A4C4×D311yescharacteristic
104C4×A4D1211yescharacteristic
105SL(2,ℤ/4)—41no—
106SL(2,ℤ/4)—64no—
107SL(2,ℤ/4)—62no—
108C2×C3×C8—121no—
109C3×C4⋊C4—61no—
110C3×C4⋊C4—61no—
111C3×C4⋊C4—61no—
112C3×C4⋊C4—61no—
113C3×C22⋊C4—121no—
114C3×C22⋊C4—121no—
115#217—62no—
116#217—62no—
117C4⋊Dic3—32no—
118C4⋊Dic3—41no—
119C4⋊Dic3—61no—
120Dic3⋊C4—62no—
121Dic3⋊C4—62no—
122C2×C3⋊C8—32no—
123C2×C3⋊C8—31no—
124C2×C3⋊C8—61no—
125C2×C3⋊C8—61no—
126C2×C3⋊C8—61no—
127C2×C3⋊C8S411yescharacteristic
128C22×C32—41no—
129C3×A4#10311yescharacteristic, complemented
130C32×C4—41no—
131C32×C4—41no—
132C3⋊Dic3—82no—
133C3×Dic3—161no—
134C22×Q8—91no—
135C23×C4D3211yescharacteristic
136C22×C8—61no—
137C22×C8—91no—
138C22×C8—91no—
139C22×C8—181no—
140C22⋊Q8—92no—
141C22⋊Q8—92no—
142C22⋊Q8—181no—
143C22⋊Q8—181no—
144C2×C4⋊C4—31no—
145C2×C4⋊C4—31no—
146C2×C4⋊C4—91no—
147C2×C4⋊C4—181no—
148C2×C22⋊C4—61no—
149C2×C22⋊C4—181no—
150#103—181no—
151#103—182no—
152#103—181no—
153#95—61no—
154C23×C3—31no—
155C23×C3—31no—
156C23×C3—31no—
157C23×C3—31no—
158C23×C3#20411yescharacteristic
159C23×C3Dic1211yescharacteristic
160C23×C3(C2×D3)⋊C411yescharacteristic
161C2×A4—21no—
162C2×A4—21no—
163C2×A4—21no—
164C2×A4(C2×D3)⋊C411yescharacteristic
165C2×A4#21411yescharacteristic
166C2×A4#21611yescharacteristic
167C2×C3×C4—31no—
168C2×C3×C4—31no—
169C2×C3×C4—31no—
170C2×C3×C4—31no—
171C2×C3×C4—31no—
172C2×C3×C4—31no—
173C2×C3×C4—31no—
174C2×C3×C4—41no—
175C2×C3×C4—61no—
176C2×C3×C4—81no—
177C2×C3×C4—121no—
178C2×C3×C4—121no—
179C2×C3×C4—121no—
180C2×C3×C4—121no—
181C2×C3×C4—121no—
182C2×C3×C4—121no—
183C2×C3×C4C2×S411yescharacteristic
184C2×Dic3—62no—
185C2×Dic3—62no—
186C2×Dic3—81no—
187C2×Dic3—121no—
188C2×Dic3—121no—
189C2×Dic3—121no—
190C2×Dic3—121no—
191C2×Dic3—241no—
192C2×Dic3—242no—
193Dic6—62no—
194Dic6—62no—
195Dic6—122no—
196Dic6—121no—
197Dic6—121no—
198Dic6—242no—
199Dic6—241no—
200Dic6—242no—
201C3×C8—241no—
202C3⋊C8—21no—
203C3⋊C8—61no—
204C2×C32—41no—
205C2×C32—41no—
206C2×C32—41no—
207C24#62611yescharacteristic
208C2×Q8—92no—
209C2×Q8—181no—
210C2×Q8—181no—
211C2×Q8—181no—
212C2×Q8—181no—
213C2×Q8—181no—
214C22×C4—31no—
215C22×C4—31no—
216C22×C4—31no—
217C22×C4—31no—
218C22×C4—61no—
219C22×C4—61no—
220C22×C4—181no—
221C22×C4—181no—
222C22×C4#62411yescharacteristic
223C22×C4#62611yescharacteristic
224C2×C8—31no—
225C2×C8—92no—
226C2×C8—91no—
227C2×C8—181no—
228C2×C8—181no—
229C2×C8—181no—
230C4⋊C4—61no—
231C4⋊C4—61no—
232C4⋊C4—61no—
233C4⋊C4—61no—
234C4⋊C4—92no—
235C4⋊C4—181no—
236C4⋊C4—182no—
237C4⋊C4—182no—
238C22⋊C4—121no—
239C22⋊C4—121no—
240C22⋊C4—182no—
241C22⋊C4—182no—
242C22×C3—31no—
243C22×C3—31no—
244C22×C3—31no—
245C22×C3—31no—
246C22×C3—31no—
247C22×C3—31no—
248C22×C3—31no—
249C22×C3—31no—
250C22×C3—31no—
251C22×C3—41no—
252C22×C3—61no—
253C22×C3—81no—
254C22×C3#81611yescharacteristic, complemented
255C22×C3C4⋊S411yescharacteristic
256A4—21no—
257A4#81011yescharacteristic, complemented
258C3×C4—31no—
259C3×C4—31no—
260C3×C4—41no—
261C3×C4—41no—
262C3×C4—81no—
263C3×C4—81no—
264C3×C4—241no—
265C3×C4—241no—
266C3×C4C4×S411yescharacteristic
267C3×C4GL(2,ℤ/4)11yescharacteristic
268Dic3—122no—
269Dic3—122no—
270Dic3—161no—
271Dic3—242no—
272Dic3—244no—
273C32—41noSylow
274C23—31no—
275C23—31no—
276C23—31no—
277C23—31no—
278C23#371611yescharacteristic
279C23#371911yescharacteristic
280C23#372211yescharacteristic
281Q8—182no—
282Q8—182no—
283Q8—361no—
284Q8—361no—
285C2×C4—31no—
286C2×C4—31no—
287C2×C4—31no—
288C2×C4—31no—
289C2×C4—31no—
290C2×C4—31no—
291C2×C4—31no—
292C2×C4—61no—
293C2×C4—121no—
294C2×C4—121no—
295C2×C4—121no—
296C2×C4—121no—
297C2×C4—121no—
298C2×C4—121no—
299C2×C4—182no—
300C2×C4—182no—
301C2×C4—361no—
302C2×C4—361no—
303C2×C4—361no—
304C2×C4—361no—
305C2×C4D3×S411yescharacteristic
306C8—61no—
307C8—181no—
308C2×C3—31no—
309C2×C3—31no—
310C2×C3—31no—
311C2×C3—31no—
312C2×C3—41no—
313C2×C3—41no—
314C2×C3—41no—
315C2×C3—81no—
316C2×C3—81no—
317C2×C3—81no—
318C2×C3#539811yescharacteristic
319C2×C3#540111yescharacteristic
320C2×C3(C2×S4)⋊C411yescharacteristic
321C22—31no—
322C22—31no—
323C22—31no—
324C22—31no—
325C22—31no—
326C22—31no—
327C22—31no—
328C22—31no—
329C22—31no—
330C22—61no—
331C22#6356711yescharacteristic, complemented
332C22#6420711yescharacteristic
333C4—31no—
334C4—31no—
335C4—241no—
336C4—241no—
337C4—362no—
338C4—362no—
339C4(C3⋊S4)⋊C411yescharacteristic
340C4#6421011yescharacteristic
341C3—41no—
342C3—81no—
343C3#7310911yescharacteristic, complemented
344C2—31no—
345C2—31no—
346C2—31no—
347C2—31no—
348C2#1059317711yescharacteristic
349C2#1059318011yescharacteristic
350C2#1059324211yescharacteristic
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
9. #64259C4semidirect
129. C3×A4#103semidirect
254. C22×C3#816semidirect
257. A4#810semidirect
331. C22#63567semidirect
343. C3#73109semidirect

Maximal subgroups

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

subgroupindex
C2×#642592
C2×A4×C3⋊C82
C3×C4⋊SL(2,ℤ/4)2
#731093
#695143
#635674