Finite Group Databasebeta

← C3×#73150 #11920928

Subgroups — C3×#73150 #11920928

Order 1152.

476 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 60 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×C4×SL(2,ℤ/4)C211yesmaximal, characteristic, complemented
3C3×#5409C211yesmaximal, characteristic, complemented
4#73150C311yesmaximal, characteristic, direct product factor
5C3×#1789—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—
13C3×#837—41nomaximal
14C22×C3×#41D311yescharacteristic
15A4×#41—21no—
16A4×#41C2×C311yescharacteristic
17C4×SL(2,ℤ/4)C2×C311yescharacteristic, complemented
18#5409C2×C311yescharacteristic, complemented
19C2×C3×#104—31no—
20C2×C3×#104—31no—
21C2×C3×#104—31no—
22C2×C3×#104—31no—
23C3×#407—31no—
24C3×C4×C22⋊C4—31no—
25C22×C3×A4—21no—
26C22×C3×A4D411yescharacteristic
27C32×#41—41no—
28C3×C4×A4—21no—
29C3×C4×A4C2×C411yescharacteristic
30C3×C4×A4D411yescharacteristic
31C3×SL(2,ℤ/4)—22no—
32C3×C4×Dic3—41no—
33C3×#208—41no—
34#1789—31noSylow
35C2×C3×#41—31no—
36C2×C3×#41—31no—
37C2×C3×#41—31no—
38C2×C3×#41—31no—
39C2×C3×#41—61no—
40C2×C3×#41—61no—
41C22×C3×Q8Dic311yescharacteristic, complemented
42C22×C3×D4—21no—
43C22×C3×D4Dic311yescharacteristic, complemented
44C23×C3×C4—21no—
45C23×C3×C4C2×D311yescharacteristic
46Q8×A4—21no—
47Q8×A4C3×C411yescharacteristic, complemented
48D4×A4—22no—
49D4×A4—21no—
50D4×A4—21no—
51D4×A4C3×C411yescharacteristic, complemented
52C2×C4×A4—22no—
53C2×C4×A4—21no—
54C2×C4×A4—21no—
55C2×C4×A4C22×C311yescharacteristic
56C2×SL(2,ℤ/4)—21no—
57C2×C3×M16—31no—
58C2×C3×M16—31no—
59C2×C3×C22⋊C4—61no—
60C2×C3×C42—31no—
61C2×C3×C42—31no—
62A4⋊C8—21no—
63C3×#104—62no—
64C3×#104—62no—
65C3×#104—61no—
66C3×#104—61no—
67C3×#104—61no—
68C3×#104—61no—
69C3×C22⋊C8—61no—
70C3×C22⋊C8—61no—
71C3×#95—61no—
72#837—41no—
73C2×C3×A4—21no—
74C2×C3×A4—41no—
75C2×C3×A4C22⋊C411yescharacteristic
76C32×Q8—41no—
77C32×D4—41no—
78C32×D4—81no—
79C2×C32×C4—41no—
80C2×C32×C4—81no—
81C2×C3×Dic3—81no—
82C3×C3⋊C8—81no—
83C22×#41C3×D311yescharacteristic
84C2×#104—31no—
85C2×#104—31no—
86C2×#104—31no—
87C2×#104—31no—
88#407—31no—
89C4×C22⋊C4—31no—
90C24×C3—21no—
91C24×C3#6711yescharacteristic
92C22×A4—22no—
93C22×A4—21no—
94C22×A4—21no—
95C22×A4C3×D411yescharacteristic
96C3×#41—32no—
97C3×#41—32no—
98C3×#41—31no—
99C3×#41—31no—
100C3×#41—31no—
101C3×#41—41no—
102C3×#41—61no—
103C3×#41—61no—
104C3×#41—61no—
105C3×#41—62no—
106C3×#41—62no—
107C3×#41—81no—
108C3×#41S411yescharacteristic
109C2×C3×Q8—31no—
110C2×C3×Q8—31no—
111C2×C3×Q8—61no—
112C2×C3×D4—31no—
113C2×C3×D4—31no—
114C2×C3×D4—61no—
115C2×C3×D4—61no—
116C2×C3×D4—61no—
117C2×C3×D4—61no—
118C2×C3×D4—61no—
119C22×C3×C4—21no—
120C22×C3×C4—31no—
121C22×C3×C4—31no—
122C22×C3×C4—31no—
123C22×C3×C4—31no—
124C22×C3×C4—61no—
125C22×C3×C4—61no—
126C22×C3×C4—61no—
127C22×C3×C4—61no—
128C22×C3×C4—61no—
129C22×C3×C4—61no—
130C22×C3×C4C2×Dic311yescharacteristic
131C22×C3×C4#6711yescharacteristic
132C4×A4—22no—
133C4×A4—21no—
134C4×A4—21no—
135C4×A4—21no—
136C4×A4C2×C3×C411yescharacteristic
137C4×A4C3×D411yescharacteristic
138SL(2,ℤ/4)—22no—
139C3×M16—61no—
140C3×M16—61no—
141C3×M16—61no—
142C3×M16—61no—
143C2×C3×C8—61no—
144C2×C3×C8—61no—
145C3×C22⋊C4—62no—
146C3×C22⋊C4—62no—
147C3×C42—61no—
148C3×C42—61no—
149C3×C42—61no—
150C3×C42—61no—
151C4×Dic3—41no—
152#208—41no—
153C22×C32—41no—
154C22×C32—81no—
155C3×A4#10411yescharacteristic, complemented
156C32×C4—41no—
157C32×C4—41no—
158C32×C4—81no—
159C3×Dic3—82no—
160C2×#41—31no—
161C2×#41—31no—
162C2×#41—31no—
163C2×#41—31no—
164C2×#41—61no—
165C2×#41—61no—
166C22×Q8C3×Dic311yescharacteristic, complemented
167C22×D4—21no—
168C22×D4C3×Dic311yescharacteristic, complemented
169C23×C4—21no—
170C23×C4C2×C3×D311yescharacteristic
171C2×M16—31no—
172C2×M16—31no—
173C2×C22⋊C4—61no—
174C2×C42—31no—
175C2×C42—31no—
176#104—62no—
177#104—62no—
178#104—61no—
179#104—61no—
180#104—61no—
181#104—61no—
182C22⋊C8—61no—
183C22⋊C8—61no—
184#95—61no—
185C23×C3—21no—
186C23×C3—31no—
187C23×C3—31no—
188C23×C3—41no—
189C23×C3—61no—
190C23×C3—61no—
191C23×C3—61no—
192C23×C3—121no—
193C23×C3#21711yescharacteristic
194C2×A4—21no—
195C2×A4—21no—
196C2×A4—41no—
197C2×A4—42no—
198C2×A4—41no—
199C2×A4C3×C22⋊C411yescharacteristic
200C3×Q8—32no—
201C3×Q8—31no—
202C3×Q8—41no—
203C3×Q8—61no—
204C3×Q8—81no—
205C3×Q8SL(2,ℤ/4)11yescharacteristic, complemented
206C3×D4—21no—
207C3×D4—32no—
208C3×D4—31no—
209C3×D4—41no—
210C3×D4—61no—
211C3×D4—61no—
212C3×D4—61no—
213C3×D4—62no—
214C3×D4—61no—
215C3×D4—81no—
216C3×D4—82no—
217C3×D4—81no—
218C3×D4SL(2,ℤ/4)11yescharacteristic, complemented
219C2×C3×C4—21no—
220C2×C3×C4—31no—
221C2×C3×C4—31no—
222C2×C3×C4—31no—
223C2×C3×C4—31no—
224C2×C3×C4—31no—
225C2×C3×C4—31no—
226C2×C3×C4—31no—
227C2×C3×C4—41no—
228C2×C3×C4—61no—
229C2×C3×C4—61no—
230C2×C3×C4—61no—
231C2×C3×C4—61no—
232C2×C3×C4—62no—
233C2×C3×C4—61no—
234C2×C3×C4—61no—
235C2×C3×C4—62no—
236C2×C3×C4—62no—
237C2×C3×C4—81no—
238C2×C3×C4—82no—
239C2×C3×C4—81no—
240C2×C3×C4—121no—
241C2×C3×C4—121no—
242C2×C3×C4—121no—
243C2×C3×C4—121no—
244C2×C3×C4C2×S411yescharacteristic
245C2×Dic3—81no—
246C3×C8—121no—
247C3×C8—121no—
248C3⋊C8—81no—
249C2×C32—41no—
250C2×C32—81no—
251C2×C32—161no—
252C24—21no—
253C24C3×#6711yescharacteristic
254#41—32no—
255#41—32no—
256#41—31no—
257#41—31no—
258#41—31no—
259#41—61no—
260#41—61no—
261#41—61no—
262#41—62no—
263#41—62no—
264#41C3×S411yescharacteristic
265C2×Q8—31no—
266C2×Q8—31no—
267C2×Q8—61no—
268C2×D4—31no—
269C2×D4—31no—
270C2×D4—61no—
271C2×D4—61no—
272C2×D4—61no—
273C2×D4—61no—
274C2×D4—61no—
275C22×C4—21no—
276C22×C4—31no—
277C22×C4—31no—
278C22×C4—31no—
279C22×C4—31no—
280C22×C4—61no—
281C22×C4—61no—
282C22×C4—61no—
283C22×C4—61no—
284C22×C4—61no—
285C22×C4—61no—
286C22×C4C2×C3×Dic311yescharacteristic
287C22×C4C3×#6711yescharacteristic
288M16—61no—
289M16—61no—
290M16—61no—
291M16—61no—
292C2×C8—61no—
293C2×C8—61no—
294C22⋊C4—62no—
295C22⋊C4—62no—
296C42—61no—
297C42—61no—
298C42—61no—
299C42—61no—
300C22×C3—21no—
301C22×C3—31no—
302C22×C3—31no—
303C22×C3—31no—
304C22×C3—41no—
305C22×C3—61no—
306C22×C3—61no—
307C22×C3—61no—
308C22×C3—61no—
309C22×C3—61no—
310C22×C3—81no—
311C22×C3—82no—
312C22×C3—81no—
313C22×C3—121no—
314C22×C3—121no—
315C22×C3—121no—
316C22×C3—121no—
317C22×C3#83711yescharacteristic, complemented
318C22×C3GL(2,ℤ/4)11yescharacteristic
319A4—21no—
320A4C3×#10411yescharacteristic, complemented
321C3×C4—21no—
322C3×C4—31no—
323C3×C4—31no—
324C3×C4—41no—
325C3×C4—41no—
326C3×C4—61no—
327C3×C4—81no—
328C3×C4—82no—
329C3×C4—81no—
330C3×C4—81no—
331C3×C4—122no—
332C3×C4—122no—
333C3×C4C2×SL(2,ℤ/4)11yescharacteristic
334C3×C4GL(2,ℤ/4)11yescharacteristic
335Dic3—82no—
336C32—41noSylow
337C23—21no—
338C23—31no—
339C23—31no—
340C23—41no—
341C23—61no—
342C23—61no—
343C23—61no—
344C23—121no—
345C23C3×#21711yescharacteristic
346Q8—32no—
347Q8—31no—
348Q8—61no—
349Q8C3×SL(2,ℤ/4)11yescharacteristic, complemented
350D4—21no—
351D4—32no—
352D4—31no—
353D4—61no—
354D4—61no—
355D4—61no—
356D4—62no—
357D4—61no—
358D4C3×SL(2,ℤ/4)11yescharacteristic, complemented
359C2×C4—21no—
360C2×C4—31no—
361C2×C4—31no—
362C2×C4—31no—
363C2×C4—31no—
364C2×C4—31no—
365C2×C4—31no—
366C2×C4—31no—
367C2×C4—61no—
368C2×C4—61no—
369C2×C4—61no—
370C2×C4—61no—
371C2×C4—62no—
372C2×C4—61no—
373C2×C4—61no—
374C2×C4—62no—
375C2×C4—62no—
376C2×C4—121no—
377C2×C4—121no—
378C2×C4—121no—
379C2×C4—121no—
380C2×C4C2×C3×S411yescharacteristic
381C8—121no—
382C8—121no—
383C2×C3—21no—
384C2×C3—31no—
385C2×C3—31no—
386C2×C3—41no—
387C2×C3—41no—
388C2×C3—61no—
389C2×C3—81no—
390C2×C3—81no—
391C2×C3—121no—
392C2×C3—161no—
393C2×C3—161no—
394C2×C3—162no—
395C2×C3#543211yescharacteristic
396C22—21no—
397C22—31no—
398C22—31no—
399C22—31no—
400C22—61no—
401C22—61no—
402C22—61no—
403C22—61no—
404C22—61no—
405C22—121no—
406C22—121no—
407C22—121no—
408C22—121no—
409C22C3×#83711yescharacteristic, complemented
410C22C3×GL(2,ℤ/4)11yescharacteristic
411C4—21no—
412C4—31no—
413C4—31no—
414C4—61no—
415C4—122no—
416C4—122no—
417C4C2×C3×SL(2,ℤ/4)11yescharacteristic
418C4C3×GL(2,ℤ/4)11yescharacteristic
419C3—41no—
420C3—81no—
421C3#7315011yescharacteristic, direct product factor
422C2—21no—
423C2—31no—
424C2—31no—
425C2—41no—
426C2—61no—
427C2—121no—
428C2C3×#543211yescharacteristic
subgroupG/H
centerC3×C4GL(2,ℤ/4)
commutatorC4×A4C2×C3×C4
FrattiniC2×C4C2×C3×S4
FittingC22×C3×#41D3
socleC23×C3#217
prime radicalC3×A4×#41C2
cosocleC2×C4×A4C22×C3
hypercenterC3×#41S4
hypocenterA4C3×#104
LCSG ▷ C4×A4 ▷ C2×A4 ▷ A4
UCSC1 ◁ C3×C4 ◁ C2×C3×C4 ◁ C3×#41

Complements

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

NH ≅ G/Ntype
2. C3×C4×SL(2,ℤ/4)C2semidirect
3. C3×#5409C2semidirect
4. #73150C3direct (N × H)
6. C3×Q8×A4C4semidirect
8. C3×D4×A4C4semidirect
17. C4×SL(2,ℤ/4)C2×C3semidirect
18. #5409C2×C3semidirect
41. C22×C3×Q8Dic3semidirect
43. C22×C3×D4Dic3semidirect
47. Q8×A4C3×C4semidirect
51. D4×A4C3×C4semidirect
155. C3×A4#104semidirect
166. C22×Q8C3×Dic3semidirect
168. C22×D4C3×Dic3semidirect
205. C3×Q8SL(2,ℤ/4)semidirect
218. C3×D4SL(2,ℤ/4)semidirect
317. C22×C3#837semidirect
320. A4C3×#104semidirect
349. Q8C3×SL(2,ℤ/4)semidirect
358. D4C3×SL(2,ℤ/4)semidirect
409. C22C3×#837semidirect
421. C3#73150direct (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×C4×SL(2,ℤ/4)2
C3×#54092
#731503
C3×#17893
C3×#8374