Finite Group Databasebeta

← C3×#85303 #11922588

Subgroups — C3×#85303 #11922588

Order 1152.

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

normal subgroups only

This group has 648 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
1C2×C3×A4⋊Q8C212yesmaximal
2C3×A4×C4⋊C4C211yesmaximal, characteristic
3C3×C4⋊SL(2,ℤ/4)C211yesmaximal, characteristic
4C3×SL(2,ℤ/4)⋊C4C212yesmaximal
5C3×C4×SL(2,ℤ/4)C211yesmaximal, characteristic
6#85303C311yesmaximal, characteristic, direct product factor
7C3×#2440—31nomaximal
8C2×C3×C4×A4C2212yes—
9C2×C3×C4×A4C2211yescharacteristic
10C2×C3×SL(2,ℤ/4)C2212yes—
11C2×C3×SL(2,ℤ/4)C2211yescharacteristic
12C2×C3×SL(2,ℤ/4)C2211yescharacteristic
13C3×A4⋊Q8—24no—
14C3×#888—41nomaximal
15C2×A4⋊Q8C2×C312yes—
16C2×C3×C4⋊Q8—31no—
17C2×C3×C22⋊Q8—32no—
18C22×C3×C4⋊C4D311yescharacteristic
19A4×C4⋊C4—21no—
20A4×C4⋊C4C2×C311yescharacteristic
21C4⋊SL(2,ℤ/4)C2×C311yescharacteristic
22SL(2,ℤ/4)⋊C4C2×C312yes—
23C4×SL(2,ℤ/4)C2×C311yescharacteristic
24C3×#398—32no—
25C3×#395—32no—
26C3×#389—31no—
27C3×#389—31no—
28C3×#385—32no—
29C3×#384—31no—
30C3×#380—31no—
31C3×C4×C22⋊C4—31no—
32C22×C3×A4C2311yescharacteristic
33C2×C3×Dic6—42no—
34C3×C4×A4—22no—
35C3×C4×A4Q812yescomplemented
36C3×SL(2,ℤ/4)—22no—
37C3×SL(2,ℤ/4)D412yes—
38C3×SL(2,ℤ/4)Q812yescomplemented
39C32×C4⋊C4—41no—
40C3×C4⋊Dic3—41no—
41C3×Dic3⋊C4—42no—
42C3×C4×Dic3—41no—
43#2440—31noSylow
44C22×C3×Q8—32no—
45C23×C3×C4C2×D312yes—
46C23×C3×C4C2×D311yescharacteristic
47C2×C4×A4—21no—
48C2×C4×A4—22no—
49C2×C4×A4C22×C312yes—
50C2×C4×A4C22×C311yescharacteristic
51C2×SL(2,ℤ/4)C22×C312yes—
52C2×SL(2,ℤ/4)C22×C311yescharacteristic
53C2×SL(2,ℤ/4)C22×C311yescharacteristic
54A4⋊Q8—24no—
55C3×C4⋊Q8—62no—
56C3×C4⋊Q8—61no—
57C3×C4⋊Q8—61no—
58C3×C22⋊Q8—64no—
59C3×C22⋊Q8—64no—
60C2×C3×C4⋊C4—31no—
61C2×C3×C4⋊C4—31no—
62C2×C3×C4⋊C4—32no—
63C2×C3×C4⋊C4—31no—
64C2×C3×C4⋊C4—31no—
65C2×C3×C4⋊C4—32no—
66C2×C3×C4⋊C4—32no—
67C2×C3×C4⋊C4—32no—
68C2×C3×C4⋊C4—32no—
69C2×C3×C4⋊C4—32no—
70C2×C3×C22⋊C4—31no—
71C2×C3×C22⋊C4—31no—
72C2×C3×C22⋊C4—32no—
73C2×C3×C42—31no—
74C2×C3×C42—31no—
75#888—41no—
76C3×#95—31no—
77C3×#95—31no—
78C3×#95—32no—
79C3×#95—32no—
80C3×#95—32no—
81C2×C3×A4C2×D411yescharacteristic
82C2×C3×A4C2×Q811yescharacteristic
83C2×C3×A4C2×Q811yescharacteristic
84C2×C32×C4—41no—
85C2×C32×C4—42no—
86C2×C3×Dic3—41no—
87C2×C3×Dic3—41no—
88C2×C3×Dic3—42no—
89C3×Dic6—84no—
90C2×C4⋊Q8—31no—
91C2×C22⋊Q8—32no—
92C22×C4⋊C4C3×D311yescharacteristic
93#398—32no—
94#395—32no—
95#389—31no—
96#389—31no—
97#385—32no—
98#384—31no—
99#380—31no—
100C4×C22⋊C4—31no—
101C24×C3C22×D311yescharacteristic
102C22×A4—21no—
103C22×A4C23×C311yescharacteristic
104C2×C3×Q8—64no—
105C2×C3×Q8—62no—
106C2×C3×Q8—62no—
107C2×C3×Q8—122no—
108C22×C3×C4—22no—
109C22×C3×C4—31no—
110C22×C3×C4—31no—
111C22×C3×C4—32no—
112C22×C3×C4—31no—
113C22×C3×C4—31no—
114C22×C3×C4—31no—
115C22×C3×C4—31no—
116C22×C3×C4—32no—
117C22×C3×C4—32no—
118C22×C3×C4—32no—
119C22×C3×C4—32no—
120C22×C3×C4—62no—
121C22×C3×C4Dic612yescomplemented
122C2×Dic6—42no—
123C4×A4—22no—
124C4×A4—22no—
125C4×A4—42no—
126C4×A4C3×Q812yescomplemented
127SL(2,ℤ/4)—22no—
128SL(2,ℤ/4)C3×D412yes—
129SL(2,ℤ/4)C3×Q812yescomplemented
130C3×C4⋊C4—32no—
131C3×C4⋊C4—31no—
132C3×C4⋊C4—41no—
133C3×C4⋊C4—61no—
134C3×C4⋊C4—62no—
135C3×C4⋊C4—64no—
136C3×C4⋊C4—64no—
137C3×C4⋊C4—64no—
138C3×C4⋊C4—61no—
139C3×C4⋊C4—62no—
140C3×C4⋊C4—62no—
141C3×C4⋊C4—61no—
142C3×C4⋊C4—81no—
143C3×C4⋊C4—122no—
144C3×C4⋊C4S411yescharacteristic
145C3×C22⋊C4—32no—
146C3×C22⋊C4—32no—
147C3×C22⋊C4—32no—
148C3×C22⋊C4—32no—
149C3×C22⋊C4—62no—
150C3×C22⋊C4—62no—
151C3×C42—62no—
152C3×C42—61no—
153C3×C42—61no—
154C4⋊Dic3—41no—
155Dic3⋊C4—42no—
156C4×Dic3—41no—
157C22×C32—41no—
158C3×A4C4⋊Q811yescharacteristic, complemented
159C32×C4—42no—
160C32×C4—82no—
161C3×Dic3—42no—
162C3×Dic3—42no—
163C3×Dic3—82no—
164C22×Q8—32no—
165C23×C4C2×C3×D312yes—
166C23×C4C2×C3×D311yescharacteristic
167C4⋊Q8—62no—
168C4⋊Q8—61no—
169C4⋊Q8—61no—
170C22⋊Q8—64no—
171C22⋊Q8—64no—
172C2×C4⋊C4—31no—
173C2×C4⋊C4—31no—
174C2×C4⋊C4—32no—
175C2×C4⋊C4—32no—
176C2×C4⋊C4—32no—
177C2×C4⋊C4—32no—
178C2×C4⋊C4—31no—
179C2×C4⋊C4—32no—
180C2×C4⋊C4—31no—
181C2×C4⋊C4—32no—
182C2×C22⋊C4—31no—
183C2×C22⋊C4—31no—
184C2×C22⋊C4—32no—
185C2×C42—31no—
186C2×C42—31no—
187#95—31no—
188#95—31no—
189#95—32no—
190#95—32no—
191#95—32no—
192C23×C3—31no—
193C23×C3—31no—
194C23×C3—31no—
195C23×C3—31no—
196C23×C3C2×Dic611yescharacteristic
197C23×C3D3×D411yescharacteristic
198C23×C3D3×Q811yescharacteristic
199C2×A4—21no—
200C2×A4—21no—
201C2×A4—21no—
202C2×A4C2×C3×D411yescharacteristic
203C2×A4C2×C3×Q811yescharacteristic
204C2×A4C2×C3×Q811yescharacteristic
205C3×Q8—124no—
206C3×Q8—124no—
207C2×C3×C4—31no—
208C2×C3×C4—32no—
209C2×C3×C4—32no—
210C2×C3×C4—32no—
211C2×C3×C4—32no—
212C2×C3×C4—32no—
213C2×C3×C4—32no—
214C2×C3×C4—32no—
215C2×C3×C4—32no—
216C2×C3×C4—41no—
217C2×C3×C4—42no—
218C2×C3×C4—62no—
219C2×C3×C4—62no—
220C2×C3×C4—61no—
221C2×C3×C4—61no—
222C2×C3×C4—61no—
223C2×C3×C4—61no—
224C2×C3×C4—61no—
225C2×C3×C4—61no—
226C2×C3×C4—61no—
227C2×C3×C4—61no—
228C2×C3×C4—61no—
229C2×C3×C4—62no—
230C2×C3×C4—62no—
231C2×C3×C4—62no—
232C2×C3×C4—62no—
233C2×C3×C4—62no—
234C2×C3×C4—62no—
235C2×C3×C4—62no—
236C2×C3×C4—62no—
237C2×C3×C4—81no—
238C2×C3×C4—82no—
239C2×C3×C4C2×S412yes—
240C2×C3×C4C2×S411yescharacteristic
241C2×Dic3—41no—
242C2×Dic3—41no—
243C2×Dic3—42no—
244Dic6—84no—
245C2×C32—41no—
246C2×C32—41no—
247C2×C32—41no—
248C24C22×C3×D311yescharacteristic
249C2×Q8—64no—
250C2×Q8—62no—
251C2×Q8—62no—
252C2×Q8—122no—
253C22×C4—22no—
254C22×C4—31no—
255C22×C4—31no—
256C22×C4—32no—
257C22×C4—31no—
258C22×C4—31no—
259C22×C4—31no—
260C22×C4—31no—
261C22×C4—32no—
262C22×C4—32no—
263C22×C4—32no—
264C22×C4—32no—
265C22×C4—62no—
266C22×C4C3×Dic612yescomplemented
267C4⋊C4—32no—
268C4⋊C4—31no—
269C4⋊C4—61no—
270C4⋊C4—64no—
271C4⋊C4—64no—
272C4⋊C4—64no—
273C4⋊C4—61no—
274C4⋊C4—62no—
275C4⋊C4—62no—
276C4⋊C4—62no—
277C4⋊C4—61no—
278C4⋊C4—122no—
279C4⋊C4C3×S411yescharacteristic
280C22⋊C4—32no—
281C22⋊C4—32no—
282C22⋊C4—32no—
283C22⋊C4—32no—
284C22⋊C4—62no—
285C22⋊C4—62no—
286C42—61no—
287C42—62no—
288C42—61no—
289C22×C3—31no—
290C22×C3—31no—
291C22×C3—31no—
292C22×C3—31no—
293C22×C3—31no—
294C22×C3—31no—
295C22×C3—31no—
296C22×C3—31no—
297C22×C3—31no—
298C22×C3—41no—
299C22×C3—61no—
300C22×C3—81no—
301C22×C3#88811yescharacteristic, complemented
302C22×C3C22×S411yescharacteristic
303A4—21no—
304A4C3×C4⋊Q811yescharacteristic, complemented
305C3×C4—22no—
306C3×C4—32no—
307C3×C4—42no—
308C3×C4—62no—
309C3×C4—62no—
310C3×C4—62no—
311C3×C4—62no—
312C3×C4—62no—
313C3×C4—82no—
314C3×C4—82no—
315C3×C4—122no—
316C3×C4—122no—
317C3×C4—162no—
318C3×C4A4⋊Q812yescomplemented
319Dic3—42no—
320Dic3—42no—
321Dic3—82no—
322C32—41noSylow
323C23—31no—
324C23—31no—
325C23—31no—
326C23—31no—
327C23C2×C3×Dic611yescharacteristic
328C23C3×D3×D411yescharacteristic
329C23C3×D3×Q811yescharacteristic
330Q8—124no—
331Q8—124no—
332C2×C4—31no—
333C2×C4—32no—
334C2×C4—32no—
335C2×C4—32no—
336C2×C4—32no—
337C2×C4—32no—
338C2×C4—32no—
339C2×C4—32no—
340C2×C4—32no—
341C2×C4—62no—
342C2×C4—62no—
343C2×C4—61no—
344C2×C4—61no—
345C2×C4—61no—
346C2×C4—61no—
347C2×C4—61no—
348C2×C4—61no—
349C2×C4—61no—
350C2×C4—61no—
351C2×C4—61no—
352C2×C4—62no—
353C2×C4—62no—
354C2×C4—62no—
355C2×C4—62no—
356C2×C4—62no—
357C2×C4—62no—
358C2×C4—62no—
359C2×C4—62no—
360C2×C4C2×C3×S412yes—
361C2×C4C2×C3×S411yescharacteristic
362C2×C3—31no—
363C2×C3—31no—
364C2×C3—31no—
365C2×C3—31no—
366C2×C3—41no—
367C2×C3—41no—
368C2×C3—41no—
369C2×C3—81no—
370C2×C3—81no—
371C2×C3—81no—
372C2×C3C2×A4⋊Q811yescharacteristic
373C2×C3D4×S411yescharacteristic
374C2×C3Q8×S411yescharacteristic
375C22—31no—
376C22—31no—
377C22—31no—
378C22—31no—
379C22—31no—
380C22—31no—
381C22—31no—
382C22—31no—
383C22—31no—
384C22—61no—
385C22C3×#88811yescharacteristic, complemented
386C22C22×C3×S411yescharacteristic
387C4—22no—
388C4—32no—
389C4—62no—
390C4—62no—
391C4—62no—
392C4—62no—
393C4—62no—
394C4—122no—
395C4—122no—
396C4C3×A4⋊Q812yescomplemented
397C3—41no—
398C3—81no—
399C3#8530311yescharacteristic, direct product factor
400C2—31no—
401C2—31no—
402C2—31no—
403C2—31no—
404C2C2×C3×A4⋊Q811yescharacteristic
405C2C3×D4×S411yescharacteristic
406C2C3×Q8×S411yescharacteristic
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×C4⋊Q8
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. #85303C3direct (N × H)
35. C3×C4×A4Q8semidirect
38. C3×SL(2,ℤ/4)Q8semidirect
121. C22×C3×C4Dic6semidirect
126. C4×A4C3×Q8semidirect
129. SL(2,ℤ/4)C3×Q8semidirect
158. C3×A4C4⋊Q8semidirect
266. C22×C4C3×Dic6semidirect
301. C22×C3#888semidirect
304. A4C3×C4⋊Q8semidirect
318. C3×C4A4⋊Q8semidirect
385. C22C3×#888semidirect
396. C4C3×A4⋊Q8semidirect
399. C3#85303direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×A4⋊Q82
C3×A4×C4⋊C42
C3×C4⋊SL(2,ℤ/4)2
C3×SL(2,ℤ/4)⋊C42
C3×C4×SL(2,ℤ/4)2
#853033
C3×#24403
C3×#8884