Finite Group Databasebeta

← #11920652

Subgroups — #11920652

Order 1152.

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

normal subgroups only

This group has 444 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
1C2×A4×Dic6C211yesmaximal, characteristic
2C4⋊(C3⋊SL(2,ℤ/4))C211yesmaximal, characteristic
3C2×C3×A4⋊C8C211yesmaximal, characteristic
4#73147—31nomaximal
5#69963—31nomaximal
6C2×C3×C4×A4C2211yescharacteristic
7C2×Dic3×A4—21no—
8A4×Dic6—21no—
9A4×Dic6C412yescomplemented
10C2×C3⋊SL(2,ℤ/4)—21no—
11C3×A4⋊C8—21no—
12#63566—41nomaximal
13C23×Dic6D311yescharacteristic
14C2×Q8×A4—31no—
15C4⋊SL(2,ℤ/4)—31no—
16C4⋊SL(2,ℤ/4)—61no—
17C2×A4⋊C8D311yescharacteristic
18C2×C3×C22⋊C8—31no—
19#5212—31no—
20C2×#816—31no—
21C2×#816—31no—
22C2×#816—31no—
23C2×#816—31no—
24C22×C3×A4D411yescharacteristic
25C2×C3×Dic6—41no—
26C3×C4×A4C2×C411yescharacteristic
27C3×C4×A4D411yescharacteristic
28Dic3×A4—22no—
29C3⋊SL(2,ℤ/4)—41no—
30C4⋊(C3⋊Dic3)—41no—
31C2×C3×C3⋊C8—41no—
32#1787—91noSylow
33C23×C3×C4C2×D311yescharacteristic
34C23×Dic3—21no—
35C22×Dic6—21no—
36C22×Dic6—31no—
37C22×Dic6—31no—
38C22×Dic6—32no—
39C22×Dic6—61no—
40C22×Dic6—61no—
41C22×Dic6Dic312yescomplemented
42Q8×A4—32no—
43Q8×A4—61no—
44C2×C4×A4—21no—
45C2×C4×A4—61no—
46C2×C4×A4C2×D311yescharacteristic
47C2×SL(2,ℤ/4)—62no—
48C2×SL(2,ℤ/4)—61no—
49C22×C3×C8—31no—
50C22×C3×C8—31no—
51C2×#217—61no—
52C2×C4⋊Dic3—31no—
53C2×C4⋊Dic3—31no—
54A4⋊C8—21no—
55C3×C22⋊C8—61no—
56C3×C22⋊C8—61no—
57#835—121no—
58C3⋊#95—61no—
59#816—62no—
60#816—62no—
61#816—62no—
62#816—61no—
63#816—61no—
64C2×C3×A4C22⋊C411yescharacteristic
65C2×C3×A4SD1611yescharacteristic
66C2×C3×A4Q1611yescharacteristic
67C2×C32×C4—41no—
68C2×C3⋊Dic3—81no—
69C2×C3×Dic3—81no—
70C3×Dic6—42no—
71C3×Dic6—81no—
72C3×C3⋊C8—81no—
73C23×Q8—31no—
74C2×#103—91no—
75C2×#103—91no—
76C2×#103—91no—
77C2×#103—91no—
78C2×C22⋊C8—31no—
79#380—91no—
80C24×C3#6711yescharacteristic
81C22×A4—21no—
82C22×A4D1211yescharacteristic
83C2×C3×Q8—121no—
84C22×C3×C4—31no—
85C22×C3×C4—31no—
86C22×C3×C4—31no—
87C22×C3×C4—31no—
88C22×C3×C4C2×Dic311yescharacteristic
89C22×C3×C4#6711yescharacteristic
90C22×Dic3—22no—
91C22×Dic3—61no—
92C22×Dic3—62no—
93C22×Dic3—61no—
94C22×Dic3—61no—
95C22×Dic3—61no—
96C2×Dic6—32no—
97C2×Dic6—32no—
98C2×Dic6—32no—
99C2×Dic6—31no—
100C2×Dic6—32no—
101C2×Dic6—32no—
102C2×Dic6—61no—
103C2×Dic6—61no—
104C2×Dic6—61no—
105C2×Dic6—62no—
106C2×Dic6—64no—
107C2×Dic6—61no—
108C2×Dic6—62no—
109C2×Dic6—61no—
110C2×Dic6S411yescharacteristic
111C4×A4—21no—
112C4×A4—21no—
113C4×A4—62no—
114C4×A4C4×D311yescharacteristic
115C4×A4#6711yescharacteristic
116SL(2,ℤ/4)—122no—
117SL(2,ℤ/4)—121no—
118C2×C3×C8—61no—
119C2×C3×C8—61no—
120C2×C3×C8—61no—
121C2×C3×C8—61no—
122C2×C3×C8—61no—
123C2×C3×C8—61no—
124#217—121no—
125#217—121no—
126C4⋊Dic3—61no—
127C4⋊Dic3—61no—
128C4⋊Dic3—61no—
129C4⋊Dic3—61no—
130C4⋊Dic3—121no—
131C4⋊Dic3—241no—
132C2×C3⋊C8—41no—
133C22×C32—41no—
134C3×A4#10311yescharacteristic, complemented
135C32×C4—41no—
136C32×C4—41no—
137C3⋊Dic3—161no—
138C3×Dic3—82no—
139C22×Q8—32no—
140C22×Q8—61no—
141C22×Q8—91no—
142C22×Q8—91no—
143C22×Q8—92no—
144C22×Q8—181no—
145C22×Q8—181no—
146C23×C4—61no—
147C23×C4D3211yescharacteristic
148C22×C8—31no—
149C22×C8—31no—
150C2×C4⋊C4—91no—
151C2×C4⋊C4—91no—
152C2×C22⋊C4—181no—
153#103—181no—
154#103—182no—
155#103—182no—
156#103—182no—
157#103—181no—
158C22⋊C8—61no—
159C22⋊C8—61no—
160#95—181no—
161C23×C3—31no—
162C23×C3—31no—
163C23×C3—31no—
164C23×C3—31no—
165C23×C3#21511yescharacteristic
166C23×C3#21611yescharacteristic
167C23×C3#21711yescharacteristic
168C2×A4—21no—
169C2×A4—21no—
170C2×A4—21no—
171C2×A4#20411yescharacteristic
172C2×A4Dic1211yescharacteristic
173C2×A4(C2×D3)⋊C411yescharacteristic
174C3×Q8—122no—
175C3×Q8—241no—
176C2×C3×C4—31no—
177C2×C3×C4—31no—
178C2×C3×C4—31no—
179C2×C3×C4—31no—
180C2×C3×C4—31no—
181C2×C3×C4—31no—
182C2×C3×C4—31no—
183C2×C3×C4—41no—
184C2×C3×C4—61no—
185C2×C3×C4—81no—
186C2×C3×C4—241no—
187C2×C3×C4C2×S411yescharacteristic
188C2×Dic3—21no—
189C2×Dic3—62no—
190C2×Dic3—62no—
191C2×Dic3—62no—
192C2×Dic3—61no—
193C2×Dic3—62no—
194C2×Dic3—121no—
195C2×Dic3—121no—
196C2×Dic3—121no—
197C2×Dic3—121no—
198C2×Dic3—121no—
199C2×Dic3—121no—
200C2×Dic3—241no—
201C2×Dic3—242no—
202Dic6—21no—
203Dic6—34no—
204Dic6—32no—
205Dic6—62no—
206Dic6—62no—
207Dic6—62no—
208Dic6—61no—
209Dic6SL(2,ℤ/4)12yescomplemented
210C3×C8—121no—
211C3×C8—121no—
212C3⋊C8—81no—
213C2×C32—41no—
214C2×C32—41no—
215C2×C32—41no—
216C24#62611yescharacteristic
217C2×Q8—31no—
218C2×Q8—92no—
219C2×Q8—92no—
220C2×Q8—92no—
221C2×Q8—92no—
222C2×Q8—92no—
223C2×Q8—91no—
224C2×Q8—181no—
225C2×Q8—181no—
226C2×Q8—181no—
227C2×Q8—182no—
228C2×Q8—181no—
229C2×Q8—181no—
230C2×Q8—182no—
231C2×Q8—184no—
232C22×C4—31no—
233C22×C4—31no—
234C22×C4—31no—
235C22×C4—31no—
236C22×C4—62no—
237C22×C4—181no—
238C22×C4—182no—
239C22×C4—181no—
240C22×C4—181no—
241C22×C4—181no—
242C22×C4D3×Dic311yescharacteristic
243C22×C4#62511yescharacteristic
244C2×C8—61no—
245C2×C8—61no—
246C2×C8—61no—
247C2×C8—61no—
248C2×C8—61no—
249C2×C8—61no—
250C4⋊C4—181no—
251C4⋊C4—181no—
252C4⋊C4—181no—
253C4⋊C4—181no—
254C22⋊C4—361no—
255C22⋊C4—361no—
256C22×C3—31no—
257C22×C3—31no—
258C22×C3—31no—
259C22×C3—31no—
260C22×C3—31no—
261C22×C3—31no—
262C22×C3—31no—
263C22×C3—31no—
264C22×C3—31no—
265C22×C3—41no—
266C22×C3—61no—
267C22×C3—81no—
268C22×C3#83511yescharacteristic, complemented
269C22×C3GL(2,ℤ/4)11yescharacteristic
270A4—21no—
271A4#81611yescharacteristic, complemented
272C3×C4—31no—
273C3×C4—31no—
274C3×C4—41no—
275C3×C4—41no—
276C3×C4—81no—
277C3×C4—81no—
278C3×C4—242no—
279C3×C4C2×SL(2,ℤ/4)11yescharacteristic
280C3×C4GL(2,ℤ/4)11yescharacteristic
281Dic3—22no—
282Dic3—62no—
283Dic3—241no—
284Dic3—241no—
285Dic3—481no—
286Dic3—482no—
287C32—41noSylow
288C23—31no—
289C23—31no—
290C23—31no—
291C23—31no—
292C23#371711yescharacteristic
293C23#371911yescharacteristic
294C23(C2×D3)⋊Dic311yescharacteristic
295Q8—32no—
296Q8—61no—
297Q8—94no—
298Q8—92no—
299Q8—182no—
300Q8—182no—
301Q8—182no—
302Q8—181no—
303C2×C4—31no—
304C2×C4—31no—
305C2×C4—31no—
306C2×C4—31no—
307C2×C4—31no—
308C2×C4—31no—
309C2×C4—31no—
310C2×C4—61no—
311C2×C4—61no—
312C2×C4—182no—
313C2×C4—182no—
314C2×C4—182no—
315C2×C4—181no—
316C2×C4—182no—
317C2×C4—361no—
318C2×C4—361no—
319C2×C4—361no—
320C2×C4—361no—
321C2×C4—361no—
322C2×C4—361no—
323C2×C4D3×S411yescharacteristic
324C8—121no—
325C8—121no—
326C2×C3—31no—
327C2×C3—31no—
328C2×C3—31no—
329C2×C3—31no—
330C2×C3—41no—
331C2×C3—41no—
332C2×C3—41no—
333C2×C3—81no—
334C2×C3—81no—
335C2×C3—81no—
336C2×C3#541611yescharacteristic
337C2×C3#541711yescharacteristic
338C2×C3#543211yescharacteristic
339C22—31no—
340C22—31no—
341C22—31no—
342C22—31no—
343C22—31no—
344C22—31no—
345C22—31no—
346C22—31no—
347C22—31no—
348C22—61no—
349C22#6356611yescharacteristic, complemented
350C22#6421011yescharacteristic
351C4—31no—
352C4—31no—
353C4—62no—
354C4—182no—
355C4—721no—
356C4—721no—
357C4D3×SL(2,ℤ/4)11yescharacteristic
358C4#6420911yescharacteristic
359C3—41no—
360C3—81no—
361C3#7314711yescharacteristic, complemented
362C2—31no—
363C2—31no—
364C2—31no—
365C2—31no—
366C2#1059318811yescharacteristic
367C2#1059319011yescharacteristic
368C2(C2×D3)⋊SL(2,ℤ/4)11yescharacteristic
subgroupG/H
centerC22#64210
commutatorC3×C4×A4C2×C4
Frattini, hypercenterC2×C4D3×S4
FittingC23×C3×C4C2×D3
socleC24×C3#67
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. A4×Dic6C4semidirect
41. C22×Dic6Dic3semidirect
134. C3×A4#103semidirect
209. Dic6SL(2,ℤ/4)semidirect
268. C22×C3#835semidirect
271. A4#816semidirect
349. C22#63566semidirect
361. C3#73147semidirect

Maximal subgroups

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

subgroupindex
C2×A4×Dic62
C4⋊(C3⋊SL(2,ℤ/4))2
C2×C3×A4⋊C82
#731473
#699633
#635664