Finite Group Databasebeta

← C3×#73144 #11920922

Subgroups — C3×#73144 #11920922

Order 1152.

584 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 72 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×C3×D4×A4C211yesmaximal, characteristic
2C3×C4⋊SL(2,ℤ/4)C211yesmaximal, characteristic, complemented
3C2×C3×A4⋊C8C211yesmaximal, characteristic, complemented
4#73144C311yesmaximal, characteristic, direct product factor
5C3×#1786—31nomaximal
6C23×C3×A4—21no—
7C3×D4×A4—21no—
8C3×D4×A4C412yescomplemented
9C2×C3×C4×A4C2211yescharacteristic
10C2×C3×SL(2,ℤ/4)—21no—
11C3×A4⋊C8—21no—
12C3×#832—41nomaximal
13C23×C3×D4D311yescharacteristic
14C2×D4×A4—21no—
15C2×D4×A4C2×C311yescharacteristic
16C4⋊SL(2,ℤ/4)C2×C311yescharacteristic, complemented
17C2×A4⋊C8C2×C311yescharacteristic, complemented
18C2×C3×#102—31no—
19C2×C3×#102—31no—
20C2×C3×#102—31no—
21C2×C3×#102—31no—
22C2×C3×C22⋊C8—31no—
23C3×#380—31no—
24C22×C3×A4—22no—
25C22×C3×A4—41no—
26C22×C3×A4—41no—
27C22×C3×A4D411yescharacteristic
28C2×C32×D4—41no—
29C3×C4×A4C2×C411yescharacteristic
30C3×C4×A4D411yescharacteristic
31C3×SL(2,ℤ/4)—41no—
32C3×C4⋊Dic3—41no—
33C2×C3×C3⋊C8—41no—
34#1786—31noSylow
35C25×C3—21no—
36C23×A4—22no—
37C23×A4—21no—
38C22×C3×D4—21no—
39C22×C3×D4—31no—
40C22×C3×D4—31no—
41C22×C3×D4—32no—
42C22×C3×D4—61no—
43C22×C3×D4—61no—
44C22×C3×D4Dic312yescomplemented
45C23×C3×C4C2×D311yescharacteristic
46D4×A4—22no—
47D4×A4—21no—
48D4×A4—22no—
49D4×A4C3×C412yescomplemented
50C2×C4×A4—21no—
51C2×C4×A4C22×C311yescharacteristic
52C2×SL(2,ℤ/4)—21no—
53C22×C3×C8—31no—
54C22×C3×C8—31no—
55C2×C3×C4⋊C4—31no—
56C2×C3×C4⋊C4—31no—
57C2×C3×C22⋊C4—61no—
58A4⋊C8—21no—
59C3×#102—62no—
60C3×#102—62no—
61C3×#102—62no—
62C3×#102—61no—
63C3×#102—61no—
64C3×C22⋊C8—61no—
65C3×C22⋊C8—61no—
66C3×#95—61no—
67#832—41no—
68C23×C32—81no—
69C2×C3×A4—42no—
70C2×C3×A4C22⋊C411yescharacteristic
71C2×C3×A4D811yescharacteristic
72C2×C3×A4SD1611yescharacteristic
73C32×D4—42no—
74C32×D4—81no—
75C2×C32×C4—41no—
76C2×C3×Dic3—81no—
77C3×C3⋊C8—81no—
78C23×D4C3×D311yescharacteristic
79C2×#102—31no—
80C2×#102—31no—
81C2×#102—31no—
82C2×#102—31no—
83C2×C22⋊C8—31no—
84#380—31no—
85C24×C3—22no—
86C24×C3—41no—
87C24×C3—41no—
88C24×C3—61no—
89C24×C3—61no—
90C24×C3—62no—
91C24×C3—121no—
92C24×C3—121no—
93C24×C3#6711yescharacteristic
94C22×A4—24no—
95C22×A4—22no—
96C22×A4—21no—
97C22×A4—42no—
98C22×A4—42no—
99C22×A4—41no—
100C22×A4—41no—
101C22×A4C3×D411yescharacteristic
102C2×C3×D4—32no—
103C2×C3×D4—32no—
104C2×C3×D4—32no—
105C2×C3×D4—32no—
106C2×C3×D4—32no—
107C2×C3×D4—31no—
108C2×C3×D4—41no—
109C2×C3×D4—61no—
110C2×C3×D4—61no—
111C2×C3×D4—61no—
112C2×C3×D4—62no—
113C2×C3×D4—61no—
114C2×C3×D4—61no—
115C2×C3×D4—62no—
116C2×C3×D4—64no—
117C2×C3×D4—81no—
118C2×C3×D4S411yescharacteristic
119C22×C3×C4—31no—
120C22×C3×C4—31no—
121C22×C3×C4—31no—
122C22×C3×C4—31no—
123C22×C3×C4—61no—
124C22×C3×C4—61no—
125C22×C3×C4C2×Dic311yescharacteristic
126C22×C3×C4#6711yescharacteristic
127C4×A4—21no—
128C4×A4—21no—
129C4×A4C2×C3×C411yescharacteristic
130C4×A4C3×D411yescharacteristic
131SL(2,ℤ/4)—41no—
132C2×C3×C8—61no—
133C2×C3×C8—61no—
134C2×C3×C8—61no—
135C2×C3×C8—61no—
136C2×C3×C8—61no—
137C2×C3×C8—61no—
138C3×C4⋊C4—61no—
139C3×C4⋊C4—61no—
140C3×C4⋊C4—61no—
141C3×C4⋊C4—61no—
142C3×C22⋊C4—121no—
143C3×C22⋊C4—121no—
144C4⋊Dic3—41no—
145C2×C3⋊C8—41no—
146C22×C32—41no—
147C22×C32—82no—
148C22×C32—161no—
149C22×C32—161no—
150C3×A4#10211yescharacteristic, complemented
151C32×C4—41no—
152C32×C4—41no—
153C3×Dic3—161no—
154C25—21no—
155C22×D4—21no—
156C22×D4—31no—
157C22×D4—31no—
158C22×D4—32no—
159C22×D4—61no—
160C22×D4—61no—
161C22×D4C3×Dic312yescomplemented
162C23×C4C2×C3×D311yescharacteristic
163C22×C8—31no—
164C22×C8—31no—
165C2×C4⋊C4—31no—
166C2×C4⋊C4—31no—
167C2×C22⋊C4—61no—
168#102—62no—
169#102—62no—
170#102—62no—
171#102—61no—
172#102—61no—
173C22⋊C8—61no—
174C22⋊C8—61no—
175#95—61no—
176C23×C3—21no—
177C23×C3—31no—
178C23×C3—31no—
179C23×C3—31no—
180C23×C3—31no—
181C23×C3—42no—
182C23×C3—62no—
183C23×C3—62no—
184C23×C3—62no—
185C23×C3—62no—
186C23×C3—61no—
187C23×C3—81no—
188C23×C3—82no—
189C23×C3—121no—
190C23×C3—121no—
191C23×C3—121no—
192C23×C3—121no—
193C23×C3—122no—
194C23×C3—122no—
195C23×C3—122no—
196C23×C3—121no—
197C23×C3—121no—
198C23×C3—121no—
199C23×C3—121no—
200C23×C3—124no—
201C23×C3#21311yescharacteristic
202C23×C3#21411yescharacteristic
203C23×C3#21711yescharacteristic
204C2×A4—21no—
205C2×A4—21no—
206C2×A4—21no—
207C2×A4—44no—
208C2×A4—42no—
209C2×A4C3×C22⋊C411yescharacteristic
210C2×A4C3×D811yescharacteristic
211C2×A4C3×SD1611yescharacteristic
212C3×D4—21no—
213C3×D4—34no—
214C3×D4—32no—
215C3×D4—42no—
216C3×D4—62no—
217C3×D4—62no—
218C3×D4—62no—
219C3×D4—61no—
220C3×D4—81no—
221C3×D4—82no—
222C3×D4—82no—
223C3×D4SL(2,ℤ/4)12yescomplemented
224C2×C3×C4—31no—
225C2×C3×C4—31no—
226C2×C3×C4—31no—
227C2×C3×C4—31no—
228C2×C3×C4—31no—
229C2×C3×C4—31no—
230C2×C3×C4—31no—
231C2×C3×C4—41no—
232C2×C3×C4—61no—
233C2×C3×C4—81no—
234C2×C3×C4—121no—
235C2×C3×C4—121no—
236C2×C3×C4—121no—
237C2×C3×C4—121no—
238C2×C3×C4—121no—
239C2×C3×C4—121no—
240C2×C3×C4C2×S411yescharacteristic
241C2×Dic3—81no—
242C3×C8—121no—
243C3×C8—121no—
244C3⋊C8—81no—
245C2×C32—41no—
246C2×C32—41no—
247C2×C32—41no—
248C2×C32—162no—
249C24—22no—
250C24—41no—
251C24—41no—
252C24—61no—
253C24—61no—
254C24—62no—
255C24—121no—
256C24—121no—
257C24C3×#6711yescharacteristic
258C2×D4—32no—
259C2×D4—32no—
260C2×D4—32no—
261C2×D4—32no—
262C2×D4—32no—
263C2×D4—31no—
264C2×D4—61no—
265C2×D4—61no—
266C2×D4—61no—
267C2×D4—62no—
268C2×D4—61no—
269C2×D4—61no—
270C2×D4—62no—
271C2×D4—64no—
272C2×D4C3×S411yescharacteristic
273C22×C4—31no—
274C22×C4—31no—
275C22×C4—31no—
276C22×C4—31no—
277C22×C4—61no—
278C22×C4—61no—
279C22×C4C2×C3×Dic311yescharacteristic
280C22×C4C3×#6711yescharacteristic
281C2×C8—61no—
282C2×C8—61no—
283C2×C8—61no—
284C2×C8—61no—
285C2×C8—61no—
286C2×C8—61no—
287C4⋊C4—61no—
288C4⋊C4—61no—
289C4⋊C4—61no—
290C4⋊C4—61no—
291C22⋊C4—121no—
292C22⋊C4—121no—
293C22×C3—22no—
294C22×C3—31no—
295C22×C3—31no—
296C22×C3—31no—
297C22×C3—31no—
298C22×C3—31no—
299C22×C3—31no—
300C22×C3—31no—
301C22×C3—31no—
302C22×C3—31no—
303C22×C3—41no—
304C22×C3—41no—
305C22×C3—41no—
306C22×C3—61no—
307C22×C3—62no—
308C22×C3—82no—
309C22×C3—84no—
310C22×C3—81no—
311C22×C3—122no—
312C22×C3—122no—
313C22×C3—122no—
314C22×C3—122no—
315C22×C3—122no—
316C22×C3—122no—
317C22×C3—122no—
318C22×C3—122no—
319C22×C3—121no—
320C22×C3—121no—
321C22×C3—161no—
322C22×C3—161no—
323C22×C3—162no—
324C22×C3—162no—
325C22×C3#83211yescharacteristic, complemented
326C22×C3GL(2,ℤ/4)11yescharacteristic
327A4—21no—
328A4C3×#10211yescharacteristic, complemented
329C3×C4—31no—
330C3×C4—31no—
331C3×C4—41no—
332C3×C4—41no—
333C3×C4—81no—
334C3×C4—81no—
335C3×C4—241no—
336C3×C4—241no—
337C3×C4C2×SL(2,ℤ/4)11yescharacteristic
338C3×C4GL(2,ℤ/4)11yescharacteristic
339Dic3—161no—
340C32—41noSylow
341C23—21no—
342C23—31no—
343C23—31no—
344C23—31no—
345C23—31no—
346C23—42no—
347C23—62no—
348C23—62no—
349C23—62no—
350C23—62no—
351C23—61no—
352C23—121no—
353C23—121no—
354C23—121no—
355C23—121no—
356C23—122no—
357C23—122no—
358C23—122no—
359C23—121no—
360C23—121no—
361C23—121no—
362C23—121no—
363C23—124no—
364C23C3×#21311yescharacteristic
365C23C3×#21411yescharacteristic
366C23C3×#21711yescharacteristic
367D4—21no—
368D4—34no—
369D4—32no—
370D4—62no—
371D4—62no—
372D4—62no—
373D4—61no—
374D4C3×SL(2,ℤ/4)12yescomplemented
375C2×C4—31no—
376C2×C4—31no—
377C2×C4—31no—
378C2×C4—31no—
379C2×C4—31no—
380C2×C4—31no—
381C2×C4—31no—
382C2×C4—61no—
383C2×C4—121no—
384C2×C4—121no—
385C2×C4—121no—
386C2×C4—121no—
387C2×C4—121no—
388C2×C4—121no—
389C2×C4C2×C3×S411yescharacteristic
390C8—121no—
391C8—121no—
392C2×C3—31no—
393C2×C3—31no—
394C2×C3—31no—
395C2×C3—31no—
396C2×C3—42no—
397C2×C3—41no—
398C2×C3—41no—
399C2×C3—41no—
400C2×C3—81no—
401C2×C3—81no—
402C2×C3—81no—
403C2×C3—122no—
404C2×C3—162no—
405C2×C3—164no—
406C2×C3#541411yescharacteristic
407C2×C3#541511yescharacteristic
408C2×C3#543211yescharacteristic
409C22—22no—
410C22—31no—
411C22—31no—
412C22—31no—
413C22—31no—
414C22—31no—
415C22—31no—
416C22—31no—
417C22—31no—
418C22—31no—
419C22—41no—
420C22—41no—
421C22—61no—
422C22—62no—
423C22—122no—
424C22—122no—
425C22—122no—
426C22—122no—
427C22—122no—
428C22—122no—
429C22—122no—
430C22—122no—
431C22—121no—
432C22—121no—
433C22C3×#83211yescharacteristic, complemented
434C22C3×GL(2,ℤ/4)11yescharacteristic
435C4—31no—
436C4—31no—
437C4—241no—
438C4—241no—
439C4C2×C3×SL(2,ℤ/4)11yescharacteristic
440C4C3×GL(2,ℤ/4)11yescharacteristic
441C3—41no—
442C3—81no—
443C3#7314411yescharacteristic, direct product factor
444C2—31no—
445C2—31no—
446C2—31no—
447C2—31no—
448C2—42no—
449C2—122no—
450C2C3×#541411yescharacteristic
451C2C3×#541511yescharacteristic
452C2C3×#543211yescharacteristic
subgroupG/H
centerC22×C3GL(2,ℤ/4)
commutatorC4×A4C2×C3×C4
FrattiniC2×C4C2×C3×S4
FittingC23×C3×D4D3
socleC24×C3#67
prime radicalC2×C3×D4×A4C2
cosocleC2×C4×A4C22×C3
hypercenterC2×C3×D4S4
hypocenterA4C3×#102
LCSG ▷ C4×A4 ▷ C2×A4 ▷ A4
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
2. C3×C4⋊SL(2,ℤ/4)C2semidirect
3. C2×C3×A4⋊C8C2semidirect
4. #73144C3direct (N × H)
8. C3×D4×A4C4semidirect
16. C4⋊SL(2,ℤ/4)C2×C3semidirect
17. C2×A4⋊C8C2×C3semidirect
44. C22×C3×D4Dic3semidirect
49. D4×A4C3×C4semidirect
150. C3×A4#102semidirect
161. C22×D4C3×Dic3semidirect
223. C3×D4SL(2,ℤ/4)semidirect
325. C22×C3#832semidirect
328. A4C3×#102semidirect
374. D4C3×SL(2,ℤ/4)semidirect
433. C22C3×#832semidirect
443. C3#73144direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D4×A42
C3×C4⋊SL(2,ℤ/4)2
C2×C3×A4⋊C82
#731443
C3×#17863
C3×#8324