Finite Group Databasebeta

← C3×#85305 #11922590

Subgroups — C3×#85305 #11922590

Order 1152.

536 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 88 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×C4⋊C4C211yesmaximal, characteristic
2C3×C4⋊SL(2,ℤ/4)C212yesmaximal
3C3×C4⋊SL(2,ℤ/4)C211yesmaximal, characteristic
4C3×SL(2,ℤ/4)⋊C4C212yesmaximal
5C3×C4×SL(2,ℤ/4)C211yesmaximal, characteristic
6#85305C311yesmaximal, characteristic, direct product factor
7C3×#2442—31nomaximal
8C2×C3×C4×A4C2212yes—
9C2×C3×C4×A4C2211yescharacteristic
10C2×C3×SL(2,ℤ/4)C2211yescharacteristic
11C2×C3×SL(2,ℤ/4)C2211yescharacteristic
12C2×C3×SL(2,ℤ/4)C2212yes—
13C3×#890—41nomaximal
14C2×C3×#125—31no—
15C22×C3×C4⋊C4D311yescharacteristic
16A4×C4⋊C4—21no—
17A4×C4⋊C4C2×C311yescharacteristic
18C4⋊SL(2,ℤ/4)C2×C312yes—
19C4⋊SL(2,ℤ/4)C2×C311yescharacteristic
20SL(2,ℤ/4)⋊C4C2×C312yes—
21C4×SL(2,ℤ/4)C2×C311yescharacteristic
22C3×#400—32no—
23C3×#398—32no—
24C3×#389—31no—
25C3×#389—31no—
26C3×#385—32no—
27C3×#382—31no—
28C3×#380—32no—
29C3×#380—31no—
30C3×C4×C22⋊C4—31no—
31C22×C3×A4C2311yescharacteristic
32C3×C4×A4—22no—
33C3×C4×A4Q812yes—
34C3×SL(2,ℤ/4)—21no—
35C3×SL(2,ℤ/4)—21no—
36C3×SL(2,ℤ/4)—22no—
37C32×C4⋊C4—41no—
38C3×C4⋊Dic3—42no—
39C3×C4⋊Dic3—41no—
40C3×Dic3⋊C4—42no—
41C3×C4×Dic3—41no—
42#2442—31noSylow
43C23×C3×C4C2×D312yes—
44C23×C3×C4C2×D311yescharacteristic
45C2×C4×A4—21no—
46C2×C4×A4—22no—
47C2×C4×A4C22×C312yes—
48C2×C4×A4C22×C311yescharacteristic
49C2×SL(2,ℤ/4)C22×C311yescharacteristic
50C2×SL(2,ℤ/4)C22×C311yescharacteristic
51C2×SL(2,ℤ/4)C22×C312yes—
52C3×#125—62no—
53C3×#125—61no—
54C3×#125—61no—
55C2×C3×C4⋊C4—31no—
56C2×C3×C4⋊C4—31no—
57C2×C3×C4⋊C4—32no—
58C2×C3×C4⋊C4—31no—
59C2×C3×C4⋊C4—31no—
60C2×C3×C4⋊C4—32no—
61C2×C3×C4⋊C4—32no—
62C2×C3×C4⋊C4—32no—
63C2×C3×C4⋊C4—32no—
64C2×C3×C22⋊C4—31no—
65C2×C3×C22⋊C4—31no—
66C2×C3×C22⋊C4—32no—
67C2×C3×C42—31no—
68C2×C3×C42—31no—
69#890—41no—
70C3×#95—31no—
71C3×#95—31no—
72C3×#95—32no—
73C3×#95—32no—
74C3×#95—32no—
75C3×#95—32no—
76C3×#95—32no—
77C2×C3×A4C2×Q811yescharacteristic
78C2×C3×A4#4111yescharacteristic
79C2×C3×A4#4111yescharacteristic
80C2×C32×C4—41no—
81C2×C32×C4—42no—
82C2×C3×Dic3—41no—
83C2×C3×Dic3—41no—
84C2×C3×Dic3—42no—
85C2×#125—31no—
86C22×C4⋊C4C3×D311yescharacteristic
87#400—32no—
88#398—32no—
89#389—31no—
90#389—31no—
91#385—32no—
92#382—31no—
93#380—32no—
94#380—31no—
95C4×C22⋊C4—31no—
96C24×C3C22×D311yescharacteristic
97C22×A4—21no—
98C22×A4C23×C311yescharacteristic
99C22×C3×C4—22no—
100C22×C3×C4—31no—
101C22×C3×C4—31no—
102C22×C3×C4—32no—
103C22×C3×C4—32no—
104C22×C3×C4—32no—
105C22×C3×C4—31no—
106C22×C3×C4—31no—
107C22×C3×C4—31no—
108C22×C3×C4—32no—
109C22×C3×C4—32no—
110C22×C3×C4—31no—
111C22×C3×C4—62no—
112C22×C3×C4Dic612yes—
113C4×A4—22no—
114C4×A4—22no—
115C4×A4—42no—
116C4×A4C3×Q812yes—
117SL(2,ℤ/4)—21no—
118SL(2,ℤ/4)—21no—
119SL(2,ℤ/4)—22no—
120C3×C4⋊C4—32no—
121C3×C4⋊C4—31no—
122C3×C4⋊C4—41no—
123C3×C4⋊C4—61no—
124C3×C4⋊C4—62no—
125C3×C4⋊C4—61no—
126C3×C4⋊C4—62no—
127C3×C4⋊C4—62no—
128C3×C4⋊C4—62no—
129C3×C4⋊C4—62no—
130C3×C4⋊C4—61no—
131C3×C4⋊C4—81no—
132C3×C4⋊C4—122no—
133C3×C4⋊C4—122no—
134C3×C4⋊C4S411yescharacteristic
135C3×C22⋊C4—61no—
136C3×C22⋊C4—62no—
137C3×C22⋊C4—61no—
138C3×C22⋊C4—61no—
139C3×C22⋊C4—61no—
140C3×C22⋊C4—62no—
141C3×C42—62no—
142C3×C42—61no—
143C3×C42—61no—
144C4⋊Dic3—42no—
145C4⋊Dic3—41no—
146Dic3⋊C4—42no—
147C4×Dic3—41no—
148C22×C32—41no—
149C3×A4#12511yescharacteristic, complemented
150C32×C4—42no—
151C32×C4—82no—
152C3×Dic3—81no—
153C3×Dic3—81no—
154C3×Dic3—82no—
155C23×C4C2×C3×D312yes—
156C23×C4C2×C3×D311yescharacteristic
157#125—62no—
158#125—61no—
159#125—61no—
160C2×C4⋊C4—31no—
161C2×C4⋊C4—31no—
162C2×C4⋊C4—32no—
163C2×C4⋊C4—31no—
164C2×C4⋊C4—32no—
165C2×C4⋊C4—32no—
166C2×C4⋊C4—31no—
167C2×C4⋊C4—32no—
168C2×C4⋊C4—32no—
169C2×C22⋊C4—31no—
170C2×C22⋊C4—31no—
171C2×C22⋊C4—32no—
172C2×C42—31no—
173C2×C42—31no—
174#95—31no—
175#95—31no—
176#95—32no—
177#95—32no—
178#95—32no—
179#95—32no—
180#95—32no—
181C23×C3—31no—
182C23×C3—31no—
183C23×C3—31no—
184C23×C3—31no—
185C23×C3C2×Dic611yescharacteristic
186C23×C3#23711yescharacteristic
187C23×C3#23911yescharacteristic
188C2×A4—21no—
189C2×A4—21no—
190C2×A4—21no—
191C2×A4C2×C3×Q811yescharacteristic
192C2×A4C3×#4111yescharacteristic
193C2×A4C3×#4111yescharacteristic
194C2×C3×C4—31no—
195C2×C3×C4—32no—
196C2×C3×C4—32no—
197C2×C3×C4—32no—
198C2×C3×C4—32no—
199C2×C3×C4—41no—
200C2×C3×C4—42no—
201C2×C3×C4—62no—
202C2×C3×C4—62no—
203C2×C3×C4—61no—
204C2×C3×C4—62no—
205C2×C3×C4—62no—
206C2×C3×C4—61no—
207C2×C3×C4—61no—
208C2×C3×C4—61no—
209C2×C3×C4—61no—
210C2×C3×C4—62no—
211C2×C3×C4—61no—
212C2×C3×C4—61no—
213C2×C3×C4—62no—
214C2×C3×C4—62no—
215C2×C3×C4—61no—
216C2×C3×C4—62no—
217C2×C3×C4—61no—
218C2×C3×C4—61no—
219C2×C3×C4—61no—
220C2×C3×C4—62no—
221C2×C3×C4—61no—
222C2×C3×C4—61no—
223C2×C3×C4—62no—
224C2×C3×C4—81no—
225C2×C3×C4—82no—
226C2×C3×C4C2×S412yes—
227C2×C3×C4C2×S411yescharacteristic
228C2×Dic3—41no—
229C2×Dic3—41no—
230C2×Dic3—42no—
231C2×C32—41no—
232C2×C32—41no—
233C2×C32—41no—
234C24C22×C3×D311yescharacteristic
235C22×C4—22no—
236C22×C4—31no—
237C22×C4—31no—
238C22×C4—32no—
239C22×C4—32no—
240C22×C4—32no—
241C22×C4—31no—
242C22×C4—31no—
243C22×C4—31no—
244C22×C4—32no—
245C22×C4—32no—
246C22×C4—31no—
247C22×C4—62no—
248C22×C4C3×Dic612yes—
249C4⋊C4—32no—
250C4⋊C4—31no—
251C4⋊C4—61no—
252C4⋊C4—61no—
253C4⋊C4—62no—
254C4⋊C4—62no—
255C4⋊C4—62no—
256C4⋊C4—62no—
257C4⋊C4—62no—
258C4⋊C4—61no—
259C4⋊C4—122no—
260C4⋊C4—122no—
261C4⋊C4C3×S411yescharacteristic
262C22⋊C4—61no—
263C22⋊C4—62no—
264C22⋊C4—61no—
265C22⋊C4—61no—
266C22⋊C4—61no—
267C22⋊C4—62no—
268C42—61no—
269C42—62no—
270C42—61no—
271C22×C3—31no—
272C22×C3—31no—
273C22×C3—31no—
274C22×C3—31no—
275C22×C3—31no—
276C22×C3—31no—
277C22×C3—31no—
278C22×C3—31no—
279C22×C3—31no—
280C22×C3—41no—
281C22×C3—61no—
282C22×C3—81no—
283C22×C3#89011yescharacteristic, complemented
284C22×C3C22×S411yescharacteristic
285A4—21no—
286A4C3×#12511yescharacteristic, complemented
287C3×C4—22no—
288C3×C4—32no—
289C3×C4—42no—
290C3×C4—62no—
291C3×C4—82no—
292C3×C4—82no—
293C3×C4—121no—
294C3×C4—122no—
295C3×C4—121no—
296C3×C4—121no—
297C3×C4—121no—
298C3×C4—122no—
299C3×C4—162no—
300C3×C4A4⋊Q812yes—
301Dic3—81no—
302Dic3—81no—
303Dic3—82no—
304C32—41noSylow
305C23—31no—
306C23—31no—
307C23—31no—
308C23—31no—
309C23C2×C3×Dic611yescharacteristic
310C23C3×#23711yescharacteristic
311C23C3×#23911yescharacteristic
312C2×C4—31no—
313C2×C4—32no—
314C2×C4—32no—
315C2×C4—32no—
316C2×C4—32no—
317C2×C4—62no—
318C2×C4—62no—
319C2×C4—61no—
320C2×C4—62no—
321C2×C4—62no—
322C2×C4—61no—
323C2×C4—61no—
324C2×C4—61no—
325C2×C4—61no—
326C2×C4—62no—
327C2×C4—61no—
328C2×C4—61no—
329C2×C4—62no—
330C2×C4—62no—
331C2×C4—61no—
332C2×C4—62no—
333C2×C4—61no—
334C2×C4—61no—
335C2×C4—61no—
336C2×C4—62no—
337C2×C4—61no—
338C2×C4—61no—
339C2×C4—62no—
340C2×C4C2×C3×S412yes—
341C2×C4C2×C3×S411yescharacteristic
342C2×C3—31no—
343C2×C3—31no—
344C2×C3—31no—
345C2×C3—31no—
346C2×C3—41no—
347C2×C3—41no—
348C2×C3—41no—
349C2×C3—81no—
350C2×C3—81no—
351C2×C3—81no—
352C2×C3C2×A4⋊Q811yescharacteristic
353C2×C3#591411yescharacteristic
354C2×C3#591911yescharacteristic
355C22—31no—
356C22—31no—
357C22—31no—
358C22—31no—
359C22—31no—
360C22—31no—
361C22—31no—
362C22—31no—
363C22—31no—
364C22—61no—
365C22C3×#89011yescharacteristic, complemented
366C22C22×C3×S411yescharacteristic
367C4—22no—
368C4—32no—
369C4—62no—
370C4—121no—
371C4—122no—
372C4—121no—
373C4—121no—
374C4—121no—
375C4—122no—
376C4C3×A4⋊Q812yes—
377C3—41no—
378C3—81no—
379C3#8530511yescharacteristic, direct product factor
380C2—31no—
381C2—31no—
382C2—31no—
383C2—31no—
384C2C2×C3×A4⋊Q811yescharacteristic
385C2C3×#591411yescharacteristic
386C2C3×#591911yescharacteristic
subgroupG/H
centerC22×C3C22×S4
commutator, cosocleC22×A4C23×C3
FrattiniC22C22×C3×S4
FittingC22×C3×C4⋊C4D3
socleC24×C3C22×D3
prime radicalC22×C3×A4C23
hypercenterC3×C4⋊C4S4
hypocenterA4C3×#125
LCSG ▷ C22×A4 ▷ A4
UCSC1 ◁ C22×C3 ◁ C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
6. #85305C3direct (N × H)
149. C3×A4#125semidirect
283. C22×C3#890semidirect
286. A4C3×#125semidirect
365. C22C3×#890semidirect
379. C3#85305direct (N × H)

Maximal subgroups

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

subgroupindex
C3×A4×C4⋊C42
C3×C4⋊SL(2,ℤ/4)2
C3×SL(2,ℤ/4)⋊C42
C3×C4×SL(2,ℤ/4)2
#853053
C3×#24423
C3×#8904