Finite Group Databasebeta

← C3×#73145 #11920923

Subgroups — C3×#73145 #11920923

Order 1152.

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

normal subgroups only

This group has 620 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
1C2×C3×D4×A4C211yesmaximal, characteristic
2C3×#5432C212yesmaximal, complemented
3#73145C311yesmaximal, characteristic, direct product factor
4C3×#1781—31nomaximal
5C23×C3×A4C411yescharacteristic, complemented
6C23×C3×A4C2211yescharacteristic
7C3×D4×A4—22no—
8C2×C3×C4×A4C411yescharacteristic, complemented
9C2×C3×SL(2,ℤ/4)—22no—
10C3×#834—41nomaximal
11C23×C3×D4D311yescharacteristic
12C2×D4×A4—21no—
13C2×D4×A4C2×C311yescharacteristic
14#5432C2×C312yescomplemented
15C2×C3×#99—32no—
16C2×C3×#99—31no—
17C2×C3×#99—31no—
18C3×#379—32no—
19C22×C3×A4—21no—
20C22×C3×A4—41no—
21C22×C3×A4—41no—
22C22×C3×A4C2×C411yescharacteristic
23C22×C3×A4D412yes—
24C2×C32×D4—41no—
25C3×C4×A4—21no—
26C3×SL(2,ℤ/4)—42no—
27C3×#217—42no—
28#1781—31noSylow
29C25×C3Dic311yescharacteristic, complemented
30C25×C3C2×D311yescharacteristic
31C23×A4—21no—
32C23×A4—21no—
33C23×A4C3×C411yescharacteristic, complemented
34C23×A4C22×C311yescharacteristic
35C22×C3×D4—22no—
36C22×C3×D4—31no—
37C22×C3×D4—31no—
38C22×C3×D4—31no—
39C22×C3×D4—31no—
40C22×C3×D4—62no—
41C23×C3×C4Dic311yescharacteristic, complemented
42D4×A4—24no—
43D4×A4—22no—
44C2×C4×A4—21no—
45C2×C4×A4C3×C411yescharacteristic, complemented
46C2×SL(2,ℤ/4)—22no—
47C2×C3×C22⋊C4—32no—
48C2×C3×C22⋊C4—32no—
49C2×C3×C22⋊C4—62no—
50C2×C3×C22⋊C4—62no—
51C3×#99—64no—
52C3×#99—61no—
53C3×#99—61no—
54C3×#99—61no—
55C3×#99—61no—
56#834—41no—
57C23×C32—41no—
58C23×C32—41no—
59C2×C3×A4—21no—
60C2×C3×A4—22no—
61C2×C3×A4—41no—
62C2×C3×A4C22⋊C411yescharacteristic
63C32×D4—82no—
64C2×C32×C4—41no—
65C2×C3×Dic3—82no—
66C23×D4C3×D311yescharacteristic
67C2×#99—32no—
68C2×#99—31no—
69C2×#99—31no—
70#379—32no—
71C24×C3—21no—
72C24×C3—31no—
73C24×C3—32no—
74C24×C3—31no—
75C24×C3—31no—
76C24×C3—31no—
77C24×C3—41no—
78C24×C3—41no—
79C24×C3—61no—
80C24×C3—121no—
81C24×C3—121no—
82C24×C3C2×Dic311yescharacteristic
83C24×C3#6712yes—
84C22×A4—22no—
85C22×A4—21no—
86C22×A4—21no—
87C22×A4—22no—
88C22×A4—41no—
89C22×A4—41no—
90C22×A4—42no—
91C22×A4—42no—
92C22×A4C2×C3×C411yescharacteristic
93C22×A4C3×D412yes—
94C2×C3×D4—34no—
95C2×C3×D4—31no—
96C2×C3×D4—31no—
97C2×C3×D4—31no—
98C2×C3×D4—41no—
99C2×C3×D4—61no—
100C2×C3×D4—62no—
101C2×C3×D4—62no—
102C2×C3×D4—62no—
103C2×C3×D4—62no—
104C2×C3×D4—62no—
105C2×C3×D4—62no—
106C2×C3×D4—62no—
107C2×C3×D4—81no—
108C2×C3×D4S411yescharacteristic
109C22×C3×C4—21no—
110C22×C3×C4—31no—
111C22×C3×C4—31no—
112C22×C3×C4—61no—
113C22×C3×C4—62no—
114C22×C3×C4—62no—
115C4×A4—22no—
116C4×A4—21no—
117SL(2,ℤ/4)—42no—
118C3×C22⋊C4—62no—
119C3×C22⋊C4—62no—
120C3×C22⋊C4—62no—
121C3×C22⋊C4—62no—
122C3×C22⋊C4—122no—
123C3×C22⋊C4—122no—
124C3×C22⋊C4—124no—
125#217—42no—
126C22×C32—41no—
127C22×C32—42no—
128C22×C32—81no—
129C22×C32—161no—
130C22×C32—161no—
131C3×A4#9911yescharacteristic, complemented
132C32×C4—81no—
133C3×Dic3—162no—
134C25C3×Dic311yescharacteristic, complemented
135C25C2×C3×D311yescharacteristic
136C22×D4—22no—
137C22×D4—31no—
138C22×D4—31no—
139C22×D4—31no—
140C22×D4—31no—
141C22×D4—62no—
142C23×C4C3×Dic311yescharacteristic, complemented
143C2×C22⋊C4—32no—
144C2×C22⋊C4—32no—
145C2×C22⋊C4—62no—
146C2×C22⋊C4—62no—
147#99—64no—
148#99—61no—
149#99—61no—
150#99—61no—
151#99—61no—
152C23×C3—22no—
153C23×C3—21no—
154C23×C3—31no—
155C23×C3—32no—
156C23×C3—31no—
157C23×C3—32no—
158C23×C3—31no—
159C23×C3—32no—
160C23×C3—32no—
161C23×C3—31no—
162C23×C3—41no—
163C23×C3—41no—
164C23×C3—41no—
165C23×C3—61no—
166C23×C3—61no—
167C23×C3—61no—
168C23×C3—61no—
169C23×C3—62no—
170C23×C3—64no—
171C23×C3—61no—
172C23×C3—81no—
173C23×C3—81no—
174C23×C3—121no—
175C23×C3—122no—
176C23×C3—121no—
177C23×C3—121no—
178C23×C3—121no—
179C23×C3—121no—
180C23×C3—122no—
181C23×C3—121no—
182C23×C3—121no—
183C23×C3—121no—
184C23×C3—121no—
185C23×C3—122no—
186C23×C3#21711yescharacteristic
187C23×C3SL(2,ℤ/4)11yescharacteristic, complemented
188C23×C3C2×S411yescharacteristic
189C2×A4—22no—
190C2×A4—22no—
191C2×A4—21no—
192C2×A4—21no—
193C2×A4—42no—
194C2×A4—42no—
195C2×A4—41no—
196C2×A4C3×C22⋊C411yescharacteristic
197C3×D4—22no—
198C3×D4—62no—
199C3×D4—62no—
200C3×D4—64no—
201C3×D4—62no—
202C3×D4—82no—
203C3×D4—84no—
204C2×C3×C4—32no—
205C2×C3×C4—31no—
206C2×C3×C4—41no—
207C2×C3×C4—61no—
208C2×C3×C4—61no—
209C2×C3×C4—61no—
210C2×C3×C4—81no—
211C2×C3×C4—122no—
212C2×C3×C4—122no—
213C2×C3×C4—122no—
214C2×C3×C4—122no—
215C2×C3×C4—122no—
216C2×C3×C4—122no—
217C2×C3×C4SL(2,ℤ/4)11yescharacteristic, complemented
218C2×Dic3—82no—
219C2×C32—41no—
220C2×C32—81no—
221C2×C32—82no—
222C2×C32—161no—
223C24—21no—
224C24—31no—
225C24—32no—
226C24—31no—
227C24—31no—
228C24—31no—
229C24—41no—
230C24—41no—
231C24—61no—
232C24—121no—
233C24—121no—
234C24C2×C3×Dic311yescharacteristic
235C24C3×#6712yes—
236C2×D4—34no—
237C2×D4—31no—
238C2×D4—31no—
239C2×D4—31no—
240C2×D4—61no—
241C2×D4—62no—
242C2×D4—62no—
243C2×D4—62no—
244C2×D4—62no—
245C2×D4—62no—
246C2×D4—62no—
247C2×D4—62no—
248C2×D4C3×S411yescharacteristic
249C22×C4—21no—
250C22×C4—31no—
251C22×C4—31no—
252C22×C4—61no—
253C22×C4—62no—
254C22×C4—62no—
255C22⋊C4—62no—
256C22⋊C4—62no—
257C22⋊C4—62no—
258C22⋊C4—62no—
259C22⋊C4—122no—
260C22⋊C4—122no—
261C22⋊C4—124no—
262C22×C3—21no—
263C22×C3—31no—
264C22×C3—31no—
265C22×C3—32no—
266C22×C3—31no—
267C22×C3—32no—
268C22×C3—41no—
269C22×C3—41no—
270C22×C3—41no—
271C22×C3—42no—
272C22×C3—62no—
273C22×C3—62no—
274C22×C3—61no—
275C22×C3—61no—
276C22×C3—62no—
277C22×C3—61no—
278C22×C3—62no—
279C22×C3—61no—
280C22×C3—81no—
281C22×C3—82no—
282C22×C3—81no—
283C22×C3—82no—
284C22×C3—122no—
285C22×C3—121no—
286C22×C3—121no—
287C22×C3—121no—
288C22×C3—121no—
289C22×C3—121no—
290C22×C3—121no—
291C22×C3—122no—
292C22×C3—122no—
293C22×C3—122no—
294C22×C3—161no—
295C22×C3—161no—
296C22×C3—162no—
297C22×C3—162no—
298C22×C3#83411yescharacteristic, complemented
299C22×C3C2×SL(2,ℤ/4)11yescharacteristic
300C22×C3GL(2,ℤ/4)12yes—
301A4—21no—
302A4C3×#9911yescharacteristic, complemented
303C3×C4—21no—
304C3×C4—61no—
305C3×C4—81no—
306C3×C4—82no—
307C3×C4—242no—
308C3×C4—242no—
309Dic3—162no—
310C32—41noSylow
311C23—22no—
312C23—21no—
313C23—31no—
314C23—32no—
315C23—31no—
316C23—32no—
317C23—31no—
318C23—32no—
319C23—32no—
320C23—31no—
321C23—41no—
322C23—61no—
323C23—61no—
324C23—61no—
325C23—61no—
326C23—62no—
327C23—64no—
328C23—61no—
329C23—121no—
330C23—122no—
331C23—121no—
332C23—121no—
333C23—121no—
334C23—121no—
335C23—122no—
336C23—121no—
337C23—121no—
338C23—121no—
339C23—121no—
340C23—122no—
341C23C3×#21711yescharacteristic
342C23C3×SL(2,ℤ/4)11yescharacteristic, complemented
343C23C2×C3×S411yescharacteristic
344D4—22no—
345D4—62no—
346D4—62no—
347D4—64no—
348D4—62no—
349C2×C4—32no—
350C2×C4—31no—
351C2×C4—61no—
352C2×C4—61no—
353C2×C4—61no—
354C2×C4—122no—
355C2×C4—122no—
356C2×C4—122no—
357C2×C4—122no—
358C2×C4—122no—
359C2×C4—122no—
360C2×C4C3×SL(2,ℤ/4)11yescharacteristic, complemented
361C2×C3—22no—
362C2×C3—21no—
363C2×C3—31no—
364C2×C3—31no—
365C2×C3—41no—
366C2×C3—41no—
367C2×C3—62no—
368C2×C3—61no—
369C2×C3—82no—
370C2×C3—81no—
371C2×C3—82no—
372C2×C3—81no—
373C2×C3—121no—
374C2×C3—162no—
375C2×C3—161no—
376C2×C3—162no—
377C2×C3#543211yescharacteristic
378C22—21no—
379C22—31no—
380C22—31no—
381C22—32no—
382C22—31no—
383C22—32no—
384C22—41no—
385C22—41no—
386C22—62no—
387C22—62no—
388C22—61no—
389C22—61no—
390C22—61no—
391C22—62no—
392C22—62no—
393C22—61no—
394C22—122no—
395C22—121no—
396C22—121no—
397C22—121no—
398C22—121no—
399C22—121no—
400C22—121no—
401C22—122no—
402C22—122no—
403C22—122no—
404C22C3×#83411yescharacteristic, complemented
405C22C2×C3×SL(2,ℤ/4)11yescharacteristic
406C22C3×GL(2,ℤ/4)12yes—
407C4—21no—
408C4—61no—
409C4—242no—
410C4—242no—
411C3—41no—
412C3—81no—
413C3#7314511yescharacteristic, direct product factor
414C2—22no—
415C2—21no—
416C2—31no—
417C2—31no—
418C2—41no—
419C2—62no—
420C2—61no—
421C2—121no—
422C2C3×#543211yescharacteristic
subgroupG/H
centerC2×C3#5432
commutatorC22×A4C2×C3×C4
FrattiniC23C2×C3×S4
FittingC23×C3×D4D3
socleC23×C3#217
prime radicalC2×C3×D4×A4C2
cosocleC23×A4C22×C3
hypercenterC2×C3×D4S4
hypocenterA4C3×#99
LCSG ▷ C22×A4 ▷ C2×A4 ▷ A4
UCSC1 ◁ C2×C3 ◁ C23×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
2. C3×#5432C2semidirect
3. #73145C3direct (N × H)
5. C23×C3×A4C4semidirect
8. C2×C3×C4×A4C4semidirect
14. #5432C2×C3semidirect
29. C25×C3Dic3semidirect
33. C23×A4C3×C4semidirect
41. C23×C3×C4Dic3semidirect
45. C2×C4×A4C3×C4semidirect
131. C3×A4#99semidirect
134. C25C3×Dic3semidirect
142. C23×C4C3×Dic3semidirect
187. C23×C3SL(2,ℤ/4)semidirect
217. C2×C3×C4SL(2,ℤ/4)semidirect
298. C22×C3#834semidirect
302. A4C3×#99semidirect
342. C23C3×SL(2,ℤ/4)semidirect
360. C2×C4C3×SL(2,ℤ/4)semidirect
404. C22C3×#834semidirect
413. C3#73145direct (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×#54322
#731453
C3×#17813
C3×#8344