Finite Group Databasebeta

← C3×A4×#104 #11919548

Subgroups — C3×A4×#104 #11919548

Order 1152.

520 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 96 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
2C3×A4×M16C211yesmaximal, characteristic, complemented
3C3×C42×A4C211yesmaximal, characteristic, complemented
4C22×C3×#104C311yesmaximal, characteristic, complemented
5A4×#104C313yesmaximal, direct product factor
6C3×Q8×A4C411yescharacteristic, complemented
7C3×D4×A4—21no—
8C3×D4×A4C411yescharacteristic, complemented
9C2×C3×C4×A4—21no—
10C2×C3×C4×A4—21no—
11C2×C3×C4×A4C2211yescharacteristic
12C3×C8×A4—21no—
13C32×#104—41nomaximal
14C22×C3×#41C2×C311yescharacteristic
15A4×#41C2×C313yes—
16C22×C3×M16C2×C311yescharacteristic, complemented
17C22×C3×C42C2×C311yescharacteristic, complemented
18A4×M16C2×C313yescomplemented
19C42×A4C2×C313yescomplemented
20C2×C3×#104—31no—
21C2×C3×#104—31no—
22C2×C3×#104—31no—
23C2×C3×#104—31no—
24C22×C3×A4—21no—
25C22×C3×A4D411yescharacteristic
26C32×#41—41no—
27C3×C4×A4—22no—
28C3×C4×A4—21no—
29C3×C4×A4C2×C411yescharacteristic
30C3×C4×A4D411yescharacteristic
31C32×M16—41no—
32C32×C42—41no—
33C22×#104C3211yescharacteristic, complemented, Sylow
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×Q8C3×C411yescharacteristic, complemented
41C22×C3×D4—21no—
42C22×C3×D4C3×C411yescharacteristic, complemented
43C23×C3×C4—21no—
44C23×C3×C4—21no—
45C23×C3×C4C22×C311yescharacteristic
46Q8×A4C3×C413yescomplemented
47D4×A4—23no—
48D4×A4C3×C413yescomplemented
49C2×C4×A4—23no—
50C2×C4×A4—23no—
51C2×C4×A4C22×C313yes—
52C2×C3×M16—31no—
53C2×C3×M16—31no—
54C2×C3×M16—61no—
55C22×C3×C8—21no—
56C2×C3×C42—31no—
57C2×C3×C42—31no—
58C2×C3×C42—61no—
59C8×A4—23no—
60C3×#104—32no—
61C3×#104—31no—
62C3×#104—31no—
63C3×#104—31no—
64C3×#104—43no—
65C3×#104A411yescharacteristic, direct product factor
66C2×C3×A4—21no—
67C2×C3×A4—41no—
68C2×C3×A4C22⋊C411yescharacteristic
69C32×Q8—41no—
70C32×D4—41no—
71C32×D4—81no—
72C2×C32×C4—41no—
73C2×C32×C4—81no—
74C2×C32×C4—81no—
75C32×C8—81no—
76C22×#41C2×C3211yescharacteristic
77C22×M16C2×C3211yescharacteristic, complemented
78C22×C42C2×C3211yescharacteristic, complemented
79C2×#104—31no—
80C2×#104—31no—
81C2×#104—31no—
82C2×#104—31no—
83C24×C3—21no—
84C24×C3C3×D411yescharacteristic
85C22×A4—23no—
86C22×A4C3×D413yes—
87C3×#41—32no—
88C3×#41—31no—
89C3×#41—31no—
90C3×#41—31no—
91C3×#41—43no—
92C3×#41—61no—
93C3×#41—61no—
94C3×#41—62no—
95C3×#41—62no—
96C3×#41—61no—
97C3×#41—61no—
98C3×#41C2×A411yescharacteristic
99C2×C3×Q8—31no—
100C2×C3×Q8—31no—
101C2×C3×Q8—61no—
102C2×C3×D4—31no—
103C2×C3×D4—31no—
104C2×C3×D4—61no—
105C2×C3×D4—61no—
106C2×C3×D4—61no—
107C2×C3×D4—61no—
108C2×C3×D4—61no—
109C22×C3×C4—22no—
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×C4—61no—
120C22×C3×C4—61no—
121C22×C3×C4—62no—
122C22×C3×C4C2×C3×C411yescharacteristic
123C22×C3×C4C3×D411yescharacteristic
124C4×A4—26no—
125C4×A4—23no—
126C4×A4C2×C3×C413yes—
127C4×A4C3×D413yes—
128C3×M16—31no—
129C3×M16—43no—
130C3×M16—61no—
131C3×M16—61no—
132C3×M16C2×A411yescharacteristic, complemented
133C2×C3×C8—61no—
134C2×C3×C8—61no—
135C3×C42—31no—
136C3×C42—43no—
137C3×C42—61no—
138C3×C42—61no—
139C3×C42C2×A411yescharacteristic, complemented
140C22×C32—41no—
141C22×C32—81no—
142C3×A4#10411yescharacteristic, direct product factor
143C32×C4—41no—
144C32×C4—41no—
145C32×C4—81no—
146C32×C4—82no—
147C2×#41—31no—
148C2×#41—31no—
149C2×#41—31no—
150C2×#41—31no—
151C2×#41—61no—
152C2×#41—61no—
153C22×Q8C32×C411yescharacteristic, complemented
154C22×D4—21no—
155C22×D4C32×C411yescharacteristic, complemented
156C23×C4—21no—
157C23×C4—21no—
158C23×C4C22×C3211yescharacteristic
159C2×M16—31no—
160C2×M16—31no—
161C2×M16—61no—
162C22×C8—21no—
163C2×C42—31no—
164C2×C42—31no—
165C2×C42—61no—
166#104—32no—
167#104—31no—
168#104—31no—
169#104—31no—
170#104C3×A411yescharacteristic, direct product factor
171C23×C3—21no—
172C23×C3—31no—
173C23×C3—31no—
174C23×C3—41no—
175C23×C3—61no—
176C23×C3—61no—
177C23×C3—61no—
178C23×C3—121no—
179C23×C3C3×C22⋊C411yescharacteristic
180C2×A4—23no—
181C2×A4—43no—
182C2×A4C3×C22⋊C413yes—
183C3×Q8—31no—
184C3×Q8—43no—
185C3×Q8—61no—
186C3×Q8—61no—
187C3×Q8C4×A411yescharacteristic, complemented
188C3×D4—21no—
189C3×D4—31no—
190C3×D4—43no—
191C3×D4—61no—
192C3×D4—61no—
193C3×D4—61no—
194C3×D4—61no—
195C3×D4—62no—
196C3×D4—61no—
197C3×D4—83no—
198C3×D4C4×A411yescharacteristic, complemented
199C2×C3×C4—21no—
200C2×C3×C4—21no—
201C2×C3×C4—32no—
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—62no—
213C2×C3×C4—62no—
214C2×C3×C4—61no—
215C2×C3×C4—62no—
216C2×C3×C4—62no—
217C2×C3×C4—61no—
218C2×C3×C4—61no—
219C2×C3×C4—61no—
220C2×C3×C4—62no—
221C2×C3×C4—83no—
222C2×C3×C4—83no—
223C2×C3×C4C22×A411yescharacteristic
224C3×C8—21no—
225C3×C8—61no—
226C3×C8—83no—
227C2×C32—41no—
228C2×C32—81no—
229C2×C32—161no—
230C24—21no—
231C24C32×D411yescharacteristic
232#41—32no—
233#41—31no—
234#41—31no—
235#41—31no—
236#41—61no—
237#41—61no—
238#41—62no—
239#41—62no—
240#41—61no—
241#41—61no—
242#41C2×C3×A411yescharacteristic
243C2×Q8—31no—
244C2×Q8—31no—
245C2×Q8—61no—
246C2×D4—31no—
247C2×D4—31no—
248C2×D4—61no—
249C2×D4—61no—
250C2×D4—61no—
251C2×D4—61no—
252C2×D4—61no—
253C22×C4—22no—
254C22×C4—21no—
255C22×C4—31no—
256C22×C4—31no—
257C22×C4—31no—
258C22×C4—31no—
259C22×C4—61no—
260C22×C4—61no—
261C22×C4—61no—
262C22×C4—61no—
263C22×C4—61no—
264C22×C4—61no—
265C22×C4—62no—
266C22×C4C2×C32×C411yescharacteristic
267C22×C4C32×D411yescharacteristic
268M16—31no—
269M16—61no—
270M16—61no—
271M16C2×C3×A411yescharacteristic, complemented
272C2×C8—61no—
273C2×C8—61no—
274C42—31no—
275C42—61no—
276C42—61no—
277C42C2×C3×A411yescharacteristic, complemented
278C22×C3—21no—
279C22×C3—31no—
280C22×C3—31no—
281C22×C3—31no—
282C22×C3—43no—
283C22×C3—61no—
284C22×C3—61no—
285C22×C3—61no—
286C22×C3—61no—
287C22×C3—61no—
288C22×C3—83no—
289C22×C3—121no—
290C22×C3—121no—
291C22×C3—121no—
292C22×C3—121no—
293C22×C3C3×#10411yescharacteristic, complemented
294C22×C3D4×A411yescharacteristic
295A4C3×#10413yesdirect product factor
296C3×C4—22no—
297C3×C4—21no—
298C3×C4—31no—
299C3×C4—31no—
300C3×C4—43no—
301C3×C4—43no—
302C3×C4—62no—
303C3×C4—61no—
304C3×C4—83no—
305C3×C4—86no—
306C3×C4C2×C4×A411yescharacteristic
307C3×C4D4×A411yescharacteristic
308C32—41noSylow
309C23—21no—
310C23—31no—
311C23—31no—
312C23—41no—
313C23—61no—
314C23—61no—
315C23—61no—
316C23—121no—
317C23C32×C22⋊C411yescharacteristic
318Q8—31no—
319Q8—61no—
320Q8—61no—
321Q8C3×C4×A411yescharacteristic, complemented
322D4—21no—
323D4—31no—
324D4—61no—
325D4—61no—
326D4—61no—
327D4—61no—
328D4—62no—
329D4—61no—
330D4C3×C4×A411yescharacteristic, complemented
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—32no—
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—62no—
344C2×C4—62no—
345C2×C4—61no—
346C2×C4—62no—
347C2×C4—62no—
348C2×C4—61no—
349C2×C4—61no—
350C2×C4—61no—
351C2×C4—62no—
352C2×C4C22×C3×A411yescharacteristic
353C8—21no—
354C8—61no—
355C2×C3—21no—
356C2×C3—31no—
357C2×C3—31no—
358C2×C3—41no—
359C2×C3—43no—
360C2×C3—61no—
361C2×C3—83no—
362C2×C3—121no—
363C2×C3—163no—
364C2×C3A4×C22⋊C411yescharacteristic
365C22—21no—
366C22—31no—
367C22—31no—
368C22—31no—
369C22—61no—
370C22—61no—
371C22—61no—
372C22—61no—
373C22—61no—
374C22—121no—
375C22—121no—
376C22—121no—
377C22—121no—
378C22C32×#10411yescharacteristic, complemented
379C22C3×D4×A411yescharacteristic
380C4—22no—
381C4—21no—
382C4—31no—
383C4—31no—
384C4—62no—
385C4—61no—
386C4C2×C3×C4×A411yescharacteristic
387C4C3×D4×A411yescharacteristic
388C3—43no—
389C3A4×#10411yescharacteristic, direct product factor
390C2—21no—
391C2—31no—
392C2—31no—
393C2—41no—
394C2—61no—
395C2—121no—
396C2C3×A4×C22⋊C411yescharacteristic
subgroupG/H
centerC3×C4D4×A4
commutatorC22×C4C2×C32×C4
FrattiniC2×C4C22×C3×A4
FittingC22×C3×#104C3
socleC23×C3C3×C22⋊C4
prime radicalC3×A4×#41C2
cosocleC23×C4C22×C32
hypercenterC3×#104A4
hypocenterC22C32×#104
LCSG ▷ C22×C4 ▷ C23 ▷ C22
UCSC1 ◁ C3×C4 ◁ C2×C3×C4 ◁ C3×#104

Complements

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

NH ≅ G/Ntype
2. C3×A4×M16C2semidirect
3. C3×C42×A4C2semidirect
4. C22×C3×#104C3semidirect
5. A4×#104C3direct (N × H)
6. C3×Q8×A4C4semidirect
8. C3×D4×A4C4semidirect
16. C22×C3×M16C2×C3semidirect
17. C22×C3×C42C2×C3semidirect
18. A4×M16C2×C3semidirect
19. C42×A4C2×C3semidirect
33. C22×#104C32semidirect
40. C22×C3×Q8C3×C4semidirect
42. C22×C3×D4C3×C4semidirect
46. Q8×A4C3×C4semidirect
48. D4×A4C3×C4semidirect
65. C3×#104A4direct (N × H)
77. C22×M16C2×C32semidirect
78. C22×C42C2×C32semidirect
132. C3×M16C2×A4semidirect
139. C3×C42C2×A4semidirect
142. C3×A4#104direct (N × H)
153. C22×Q8C32×C4semidirect
155. C22×D4C32×C4semidirect
170. #104C3×A4direct (N × H)
187. C3×Q8C4×A4semidirect
198. C3×D4C4×A4semidirect
271. M16C2×C3×A4semidirect
277. C42C2×C3×A4semidirect
293. C22×C3C3×#104semidirect
295. A4C3×#104direct (N × H)
321. Q8C3×C4×A4semidirect
330. D4C3×C4×A4semidirect
378. C22C32×#104semidirect
389. C3A4×#104direct (N × H)

Maximal subgroups

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

subgroupindex
C3×A4×#412
C3×A4×M162
C3×C42×A42
C22×C3×#1043
A4×#1043
C32×#1044