Finite Group Databasebeta

← #11921106

Subgroups — #11921106

Order 1152.

524 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C3×A4×#41C211yesmaximal, characteristic
2C4×C3⋊SL(2,ℤ/4)C211yesmaximal, characteristic, complemented
3#10593643C211yesmaximal, characteristic, complemented
4#73150—33nomaximal
5#72138—31nomaximal
6C3×Q8×A4C411yescharacteristic, complemented
7C3×D4×A4—21no—
8C3×D4×A4C411yescharacteristic, complemented
9C2×C3×C4×A4—21no—
10C2×C3×C4×A4C2211yescharacteristic
11C2×C3⋊SL(2,ℤ/4)—21no—
12C3⋊(A4⋊C8)—21no—
13#63664—41nomaximal
14C22×C3×#41D311yescharacteristic
15A4×#41D313yes—
16C4×SL(2,ℤ/4)—33no—
17#5409—33no—
18C2×#837—31no—
19C2×#837—31no—
20C2×#837—31no—
21C2×#837—31no—
22C4×#217—31no—
23#5207—31no—
24C22×C3×A4—21no—
25C22×C3×A4D411yescharacteristic
26C32×#41—41no—
27C3×C4×A4—21no—
28C3×C4×A4C2×C411yescharacteristic
29C3×C4×A4D411yescharacteristic
30C3⋊SL(2,ℤ/4)—22no—
31C4×C3⋊Dic3—41no—
32#3748—41no—
33#1789—91noSylow
34C2×C3×#41—31no—
35C2×C3×#41—31no—
36C2×C3×#41—31no—
37C2×C3×#41—31no—
38C2×C3×#41—61no—
39C2×C3×#41—61no—
40C22×C3×Q8Dic311yescharacteristic, complemented
41C22×C3×D4—21no—
42C22×C3×D4Dic311yescharacteristic, complemented
43C23×C3×C4—21no—
44C23×C3×C4C2×D311yescharacteristic
45Q8×A4Dic313yescomplemented
46D4×A4—23no—
47D4×A4Dic313yescomplemented
48C2×C4×A4—23no—
49C2×C4×A4C2×D313yes—
50C2×SL(2,ℤ/4)—63no—
51C2×#217—61no—
52C2×C4×Dic3—31no—
53C2×C4×Dic3—31no—
54C2×#208—31no—
55C2×#208—31no—
56A4⋊C8—63no—
57#837—62no—
58#837—62no—
59#837—61no—
60#837—61no—
61#837—61no—
62#837—61no—
63#837—123no—
64C3⋊#95—61no—
65#830—61no—
66#830—61no—
67C2×C3×A4—21no—
68C2×C3×A4—41no—
69C2×C3×A4C22⋊C411yescharacteristic
70C32×Q8—41no—
71C32×D4—41no—
72C32×D4—81no—
73C2×C32×C4—41no—
74C2×C32×C4—81no—
75C2×C3⋊Dic3—81no—
76C3⋊(C3⋊C8)—81no—
77C22×#41C3⋊D311yescharacteristic
78C2×#104—91no—
79C2×#104—91no—
80C2×#104—91no—
81C2×#104—91no—
82#407—91no—
83C4×C22⋊C4—91no—
84C24×C3—21no—
85C24×C3#6711yescharacteristic
86C22×A4—23no—
87C22×A4#6713yes—
88C3×#41—32no—
89C3×#41—32no—
90C3×#41—31no—
91C3×#41—31no—
92C3×#41—31no—
93C3×#41—43no—
94C3×#41—61no—
95C3×#41—61no—
96C3×#41—61no—
97C3×#41—62no—
98C3×#41—62no—
99C3×#41S411yescharacteristic
100C2×C3×Q8—31no—
101C2×C3×Q8—31no—
102C2×C3×Q8—61no—
103C2×C3×D4—31no—
104C2×C3×D4—31no—
105C2×C3×D4—61no—
106C2×C3×D4—61no—
107C2×C3×D4—61no—
108C2×C3×D4—61no—
109C2×C3×D4—61no—
110C22×C3×C4—21no—
111C22×C3×C4—31no—
112C22×C3×C4—31no—
113C22×C3×C4—31no—
114C22×C3×C4—31no—
115C22×C3×C4—61no—
116C22×C3×C4—61no—
117C22×C3×C4—61no—
118C22×C3×C4—61no—
119C22×C3×C4C2×Dic311yescharacteristic
120C22×C3×C4#6711yescharacteristic
121C22×Dic3—61no—
122C22×Dic3—61no—
123C4×A4—23no—
124C4×A4C2×Dic313yes—
125C4×A4#6713yes—
126SL(2,ℤ/4)—66no—
127#217—62no—
128#217—62no—
129C4×Dic3—61no—
130C4×Dic3—61no—
131C4×Dic3—61no—
132C4×Dic3—61no—
133C4×Dic3—123no—
134#208—61no—
135#208—61no—
136#208—61no—
137#208—61no—
138#208—123no—
139C2×C3⋊C8—61no—
140C2×C3⋊C8—61no—
141C22×C32—41no—
142C22×C32—81no—
143C3×A4#10411yescharacteristic, complemented
144C32×C4—41no—
145C32×C4—41no—
146C32×C4—81no—
147C3⋊Dic3—82no—
148C2×#41—31no—
149C2×#41—31no—
150C2×#41—31no—
151C2×#41—31no—
152C2×#41—61no—
153C2×#41—61no—
154C22×Q8C3⋊Dic311yescharacteristic, complemented
155C22×D4—21no—
156C22×D4C3⋊Dic311yescharacteristic, complemented
157C23×C4—21no—
158C23×C4C2×C3⋊D311yescharacteristic
159C2×M16—91no—
160C2×M16—91no—
161C2×C22⋊C4—181no—
162C2×C42—91no—
163C2×C42—91no—
164#104—182no—
165#104—182no—
166#104—181no—
167#104—181no—
168#104—181no—
169#104—181no—
170C22⋊C8—181no—
171C22⋊C8—181no—
172#95—181no—
173C23×C3—21no—
174C23×C3—31no—
175C23×C3—31no—
176C23×C3—41no—
177C23×C3—61no—
178C23×C3—61no—
179C23×C3—61no—
180C23×C3—121no—
181C23×C3#21711yescharacteristic
182C2×A4—23no—
183C2×A4—43no—
184C2×A4#21713yes—
185C3×Q8—32no—
186C3×Q8—31no—
187C3×Q8—43no—
188C3×Q8—61no—
189C3×Q8SL(2,ℤ/4)11yescharacteristic, complemented
190C3×D4—21no—
191C3×D4—32no—
192C3×D4—31no—
193C3×D4—43no—
194C3×D4—61no—
195C3×D4—61no—
196C3×D4—61no—
197C3×D4—62no—
198C3×D4—61no—
199C3×D4—83no—
200C3×D4SL(2,ℤ/4)11yescharacteristic, complemented
201C2×C3×C4—21no—
202C2×C3×C4—31no—
203C2×C3×C4—31no—
204C2×C3×C4—31no—
205C2×C3×C4—31no—
206C2×C3×C4—31no—
207C2×C3×C4—31no—
208C2×C3×C4—31no—
209C2×C3×C4—43no—
210C2×C3×C4—61no—
211C2×C3×C4—61no—
212C2×C3×C4—61no—
213C2×C3×C4—61no—
214C2×C3×C4—62no—
215C2×C3×C4—61no—
216C2×C3×C4—61no—
217C2×C3×C4—83no—
218C2×C3×C4C2×S411yescharacteristic
219C2×Dic3—62no—
220C2×Dic3—62no—
221C2×Dic3—121no—
222C2×Dic3—121no—
223C2×Dic3—121no—
224C2×Dic3—121no—
225C2×Dic3—243no—
226C3⋊C8—121no—
227C3⋊C8—121no—
228C3⋊C8—243no—
229C2×C32—41no—
230C2×C32—81no—
231C2×C32—161no—
232C24—21no—
233C24#63811yescharacteristic
234#41—32no—
235#41—32no—
236#41—31no—
237#41—31no—
238#41—31no—
239#41—61no—
240#41—61no—
241#41—61no—
242#41—62no—
243#41—62no—
244#41C3⋊S411yescharacteristic
245C2×Q8—31no—
246C2×Q8—31no—
247C2×Q8—61no—
248C2×D4—31no—
249C2×D4—31no—
250C2×D4—61no—
251C2×D4—61no—
252C2×D4—61no—
253C2×D4—61no—
254C2×D4—61no—
255C22×C4—21no—
256C22×C4—31no—
257C22×C4—31no—
258C22×C4—31no—
259C22×C4—31no—
260C22×C4—61no—
261C22×C4—61no—
262C22×C4—61no—
263C22×C4—61no—
264C22×C4—181no—
265C22×C4—181no—
266C22×C4C2×C3⋊Dic311yescharacteristic
267C22×C4#63811yescharacteristic
268M16—181no—
269M16—181no—
270M16—181no—
271M16—181no—
272C2×C8—181no—
273C2×C8—181no—
274C22⋊C4—182no—
275C22⋊C4—182no—
276C42—181no—
277C42—181no—
278C42—181no—
279C42—181no—
280C22×C3—21no—
281C22×C3—31no—
282C22×C3—31no—
283C22×C3—31no—
284C22×C3—43no—
285C22×C3—61no—
286C22×C3—61no—
287C22×C3—61no—
288C22×C3—61no—
289C22×C3—61no—
290C22×C3—83no—
291C22×C3—121no—
292C22×C3—121no—
293C22×C3—121no—
294C22×C3—121no—
295C22×C3#83711yescharacteristic, complemented
296C22×C3GL(2,ℤ/4)11yescharacteristic
297A4#83713yescomplemented
298C3×C4—21no—
299C3×C4—31no—
300C3×C4—31no—
301C3×C4—43no—
302C3×C4—43no—
303C3×C4—61no—
304C3×C4—83no—
305C3×C4C2×SL(2,ℤ/4)11yescharacteristic
306C3×C4GL(2,ℤ/4)11yescharacteristic
307Dic3—122no—
308Dic3—122no—
309Dic3—246no—
310C32—41noSylow
311C23—21no—
312C23—31no—
313C23—31no—
314C23—41no—
315C23—61no—
316C23—61no—
317C23—61no—
318C23—121no—
319C23#375711yescharacteristic
320Q8—32no—
321Q8—31no—
322Q8—61no—
323Q8C3⋊SL(2,ℤ/4)11yescharacteristic, complemented
324D4—21no—
325D4—32no—
326D4—31no—
327D4—61no—
328D4—61no—
329D4—61no—
330D4—62no—
331D4—61no—
332D4C3⋊SL(2,ℤ/4)11yescharacteristic, complemented
333C2×C4—21no—
334C2×C4—31no—
335C2×C4—31no—
336C2×C4—31no—
337C2×C4—31no—
338C2×C4—31no—
339C2×C4—31no—
340C2×C4—31no—
341C2×C4—61no—
342C2×C4—61no—
343C2×C4—61no—
344C2×C4—61no—
345C2×C4—62no—
346C2×C4—61no—
347C2×C4—61no—
348C2×C4—182no—
349C2×C4—182no—
350C2×C4—361no—
351C2×C4—361no—
352C2×C4—361no—
353C2×C4—361no—
354C2×C4C2×C3⋊S411yescharacteristic
355C8—361no—
356C8—361no—
357C2×C3—21no—
358C2×C3—31no—
359C2×C3—31no—
360C2×C3—41no—
361C2×C3—43no—
362C2×C3—61no—
363C2×C3—83no—
364C2×C3—121no—
365C2×C3—163no—
366C2×C3#543211yescharacteristic
367C22—21no—
368C22—31no—
369C22—31no—
370C22—31no—
371C22—61no—
372C22—61no—
373C22—61no—
374C22—61no—
375C22—61no—
376C22—121no—
377C22—121no—
378C22—121no—
379C22—121no—
380C22#6366411yescharacteristic, complemented
381C22#6426911yescharacteristic
382C4—21no—
383C4—31no—
384C4—31no—
385C4—61no—
386C4—362no—
387C4—362no—
388C4C2×C3⋊SL(2,ℤ/4)11yescharacteristic
389C4#6426911yescharacteristic
390C3—43no—
391C3#7315011yescharacteristic, complemented
392C2—21no—
393C2—31no—
394C2—31no—
395C2—41no—
396C2—61no—
397C2—121no—
398C2#1059366611yescharacteristic
subgroupG/H
centerC4#64269
commutatorC3×C4×A4C2×C4
FrattiniC2×C4C2×C3⋊S4
FittingC22×C3×#41D3
socleC23×C3#217
prime radicalC3×A4×#41C2
cosocleC2×C3×C4×A4C22
hypercenter#41C3⋊S4
hypocenterC3×A4#104
LCSG ▷ C3×C4×A4 ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C4 ◁ C2×C4 ◁ #41

Complements

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

NH ≅ G/Ntype
2. C4×C3⋊SL(2,ℤ/4)C2semidirect
3. #10593643C2semidirect
6. C3×Q8×A4C4semidirect
8. C3×D4×A4C4semidirect
40. C22×C3×Q8Dic3semidirect
42. C22×C3×D4Dic3semidirect
45. Q8×A4Dic3semidirect
47. D4×A4Dic3semidirect
143. C3×A4#104semidirect
154. C22×Q8C3⋊Dic3semidirect
156. C22×D4C3⋊Dic3semidirect
189. C3×Q8SL(2,ℤ/4)semidirect
200. C3×D4SL(2,ℤ/4)semidirect
295. C22×C3#837semidirect
297. A4#837semidirect
323. Q8C3⋊SL(2,ℤ/4)semidirect
332. D4C3⋊SL(2,ℤ/4)semidirect
380. C22#63664semidirect
391. C3#73150semidirect

Maximal subgroups

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

subgroupindex
C3×A4×#412
C4×C3⋊SL(2,ℤ/4)2
#105936432
#731503
#721383
#636644