Finite Group Databasebeta

← C3×#3482⋊C3 #11919732

Subgroups — C3×#3482⋊C3 #11919732

Order 1152.

722 conjugacy classes of subgroups; only the 166 normal subgroups are shown.

normal subgroups only

This group has 722 conjugacy classes of subgroups — too many to draw. Only its 166 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×#557⋊C3C211yesmaximal, characteristic, complemented
2C3×D4×SL(2,𝔽3)C211yesmaximal, characteristic, complemented
3C3×#548⋊C3C212yesmaximal, complemented
4C3×C4×#41⋊C3C211yesmaximal, characteristic, complemented
5C2×C3×C4×SL(2,𝔽3)C212yesmaximal, complemented
6C3×#3482C311yesmaximal, characteristic, complemented
7#3482⋊C3C313yesmaximal, direct product factor
8C2×C3×#41⋊C3C2211yescharacteristic
9C22×C3×SL(2,𝔽3)C2212yes—
10C32×C4×D4—41nomaximal
11C3×C4×SL(2,𝔽3)C2211yescharacteristic
12C3×C4×SL(2,𝔽3)C2212yes—
13C3×C4×SL(2,𝔽3)C2211yescharacteristic
14C3×#557C2×C311yescharacteristic, complemented
15C3×#556—31no—
16C3×#552—32no—
17C3×D4×Q8C2×C311yescharacteristic
18C3×#548C2×C312yescomplemented
19C3×#547—31no—
20C3×#533—31no—
21C3×#529—32no—
22C3×C4×#41—31no—
23C3×C4×#41C2×C311yescharacteristic, complemented
24C2×C3×C4×Q8C2×C312yescomplemented
25#557⋊C3C2×C313yescomplemented
26D4×SL(2,𝔽3)C2×C313yescomplemented
27#548⋊C3C2×C316yescomplemented
28C4×#41⋊C3C2×C313yescomplemented
29C2×C4×SL(2,𝔽3)C2×C316yescomplemented
30C2×C32×D4—41no—
31C22×C32×C4—42no—
32C3×#41⋊C3—21no—
33C2×C3×SL(2,𝔽3)—22no—
34C2×C3×SL(2,𝔽3)C2311yescharacteristic
35C32×C4⋊C4—41no—
36C32×C22⋊C4—42no—
37C32×C42—41no—
38#3482C3211yescharacteristic, complemented, Sylow
39C2×C3×#41—31no—
40C2×C3×#41C22×C311yescharacteristic
41C22×C3×Q8C22×C312yes—
42C2×#41⋊C3C22×C313yes—
43C22×SL(2,𝔽3)C22×C316yes—
44C3×C4⋊Q8—31no—
45C3×C4⋊Q8—31no—
46C3×#126—34no—
47C3×#125—32no—
48C3×#125—32no—
49C3×#124—32no—
50C3×#123—34no—
51C3×C22⋊Q8—32no—
52C3×C22⋊Q8—32no—
53C3×C22⋊Q8—32no—
54C3×#121—32no—
55C3×C4×Q8—31no—
56C3×C4×Q8—31no—
57C3×C4×Q8—32no—
58C3×C4×Q8—32no—
59C3×C4×Q8C22×C311yescharacteristic
60C3×C4×Q8C22×C312yes—
61C3×C4×Q8C22×C311yescharacteristic
62C3×C4×D4—31no—
63C3×C4×D4—32no—
64C3×C4×D4—31no—
65C3×C4×D4—31no—
66C3×C4×D4—32no—
67C3×C4×D4—43no—
68C3×C4×D4A411yescharacteristic
69C3×#117—32no—
70C3×#117—31no—
71C3×#117—32no—
72C3×#117—31no—
73C2×C3×C4⋊C4—32no—
74C2×C3×C42—32no—
75C2×C3×C42—31no—
76C4×SL(2,𝔽3)C22×C313yes—
77C4×SL(2,𝔽3)C22×C316yes—
78C4×SL(2,𝔽3)C22×C313yes—
79C23×C32—42no—
80C32×D4—44no—
81C2×C32×C4—41no—
82C2×C32×C4—41no—
83C2×C32×C4—42no—
84C2×C32×C4—41no—
85C2×C32×C4—84no—
86C3×SL(2,𝔽3)#4111yescharacteristic, complemented
87#557C2×C3211yescharacteristic, complemented
88#556—31no—
89#552—32no—
90D4×Q8C2×C3211yescharacteristic
91#548C2×C3212yescomplemented
92#547—31no—
93#533—31no—
94#529—32no—
95C4×#41—31no—
96C4×#41C2×C3211yescharacteristic, complemented
97C2×C4×Q8C2×C3212yescomplemented
98C3×#41—21no—
99C3×#41—64no—
100C3×#41—61no—
101C2×C3×Q8—22no—
102C2×C3×Q8—31no—
103C2×C3×Q8—32no—
104C2×C3×Q8—62no—
105C2×C3×Q8C23×C311yescharacteristic
106C2×C3×D4—31no—
107C2×C3×D4—32no—
108C2×C3×D4—43no—
109C2×C3×D4C2×A411yescharacteristic
110C22×C3×C4—32no—
111C22×C3×C4—32no—
112C22×C3×C4—31no—
113C22×C3×C4—31no—
114C22×C3×C4—31no—
115C22×C3×C4—46no—
116C22×C3×C4C2×A412yes—
117#41⋊C3—23no—
118C2×SL(2,𝔽3)—26no—
119C2×SL(2,𝔽3)C23×C313yes—
120C3×C4⋊C4—31no—
121C3×C4⋊C4—32no—
122C3×C4⋊C4—31no—
123C3×C4⋊C4—34no—
124C3×C4⋊C4—32no—
125C3×C4⋊C4—32no—
126C3×C4⋊C4—31no—
127C3×C4⋊C4—32no—
128C3×C4⋊C4—32no—
129C3×C4⋊C4—43no—
130C3×C4⋊C4C2×A411yescharacteristic
131C3×C22⋊C4—32no—
132C3×C22⋊C4—34no—
133C3×C22⋊C4—32no—
134C3×C22⋊C4—32no—
135C3×C22⋊C4—46no—
136C3×C22⋊C4C2×A412yes—
137C3×C42—31no—
138C3×C42—32no—
139C3×C42—31no—
140C3×C42—32no—
141C3×C42—31no—
142C3×C42—32no—
143C3×C42—43no—
144C3×C42C2×A411yescharacteristic
145C22×C32—44no—
146C22×C32—41no—
147C22×C32—82no—
148C22×C32—82no—
149C32×C4—42no—
150C32×C4—42no—
151C32×C4—82no—
152C32×C4—81no—
153C2×#41—31no—
154C2×#41C22×C3211yescharacteristic
155C22×Q8C22×C3212yes—
156C4⋊Q8—31no—
157C4⋊Q8—31no—
158#126—34no—
159#125—32no—
160#125—32no—
161#124—32no—
162#123—34no—
163C22⋊Q8—32no—
164C22⋊Q8—32no—
165C22⋊Q8—32no—
166#121—32no—
167C4×Q8—31no—
168C4×Q8—31no—
169C4×Q8—32no—
170C4×Q8—32no—
171C4×Q8C22×C3211yescharacteristic
172C4×Q8C22×C3212yes—
173C4×Q8C22×C3211yescharacteristic
174C4×D4—31no—
175C4×D4—32no—
176C4×D4—31no—
177C4×D4—31no—
178C4×D4—32no—
179C4×D4C3×A411yescharacteristic
180#117—32no—
181#117—31no—
182#117—32no—
183#117—31no—
184C2×C4⋊C4—32no—
185C2×C42—32no—
186C2×C42—31no—
187C23×C3—31no—
188C23×C3—46no—
189C23×C3C22×A412yes—
190C3×Q8—31no—
191C3×Q8—62no—
192C3×Q8—62no—
193C3×Q8—62no—
194C3×Q8C3×#4111yescharacteristic
195C3×D4—412no—
196C3×D4—61no—
197C3×D4—61no—
198C3×D4—64no—
199C3×D4#41⋊C314yescomplemented
200C2×C3×C4—24no—
201C2×C3×C4—31no—
202C2×C3×C4—31no—
203C2×C3×C4—31no—
204C2×C3×C4—32no—
205C2×C3×C4—32no—
206C2×C3×C4—43no—
207C2×C3×C4—43no—
208C2×C3×C4—46no—
209C2×C3×C4—43no—
210C2×C3×C4—61no—
211C2×C3×C4—61no—
212C2×C3×C4—62no—
213C2×C3×C4—62no—
214C2×C3×C4—64no—
215C2×C3×C4—62no—
216C2×C3×C4—62no—
217C2×C3×C4—812no—
218C2×C3×C4C22×A412yes—
219C2×C3×C4C22×A411yescharacteristic
220C2×C3×C4C22×A411yescharacteristic
221C2×C3×C4C22×A411yescharacteristic
222SL(2,𝔽3)C3×#4113yescomplemented
223C2×C32—41no—
224C2×C32—41no—
225C2×C32—41no—
226C2×C32—84no—
227#41—21no—
228#41—64no—
229#41—61no—
230C2×Q8—22no—
231C2×Q8—31no—
232C2×Q8—32no—
233C2×Q8—62no—
234C2×Q8C23×C3211yescharacteristic
235C2×D4—31no—
236C2×D4—32no—
237C2×D4C2×C3×A411yescharacteristic
238C22×C4—32no—
239C22×C4—32no—
240C22×C4—31no—
241C22×C4—31no—
242C22×C4—31no—
243C22×C4C2×C3×A412yes—
244C4⋊C4—31no—
245C4⋊C4—32no—
246C4⋊C4—31no—
247C4⋊C4—34no—
248C4⋊C4—32no—
249C4⋊C4—32no—
250C4⋊C4—31no—
251C4⋊C4—32no—
252C4⋊C4—32no—
253C4⋊C4C2×C3×A411yescharacteristic
254C22⋊C4—32no—
255C22⋊C4—34no—
256C22⋊C4—32no—
257C22⋊C4—32no—
258C22⋊C4C2×C3×A412yes—
259C42—31no—
260C42—31no—
261C42—32no—
262C42—32no—
263C42—31no—
264C42—32no—
265C42C2×C3×A411yescharacteristic
266C22×C3—22no—
267C22×C3—22no—
268C22×C3—412no—
269C22×C3—43no—
270C22×C3—61no—
271C22×C3—61no—
272C22×C3—61no—
273C22×C3—86no—
274C22×C3—86no—
275C22×C3C2×#41⋊C314yes—
276C22×C3C23×A411yescharacteristic
277C3×C4—21no—
278C3×C4—22no—
279C3×C4—31no—
280C3×C4—31no—
281C3×C4—46no—
282C3×C4—46no—
283C3×C4—61no—
284C3×C4—62no—
285C3×C4—62no—
286C3×C4—61no—
287C3×C4—86no—
288C3×C4—83no—
289C3×C4C2×#41⋊C312yes—
290C3×C42−1+4⋊C312yes—
291C32—41noSylow
292C23—31no—
293C23C22×C3×A412yes—
294Q8—31no—
295Q8—62no—
296Q8—62no—
297Q8—62no—
298Q8C32×#4111yescharacteristic
299D4—61no—
300D4—61no—
301D4—64no—
302D4C3×#41⋊C314yescomplemented
303C2×C4—24no—
304C2×C4—31no—
305C2×C4—31no—
306C2×C4—31no—
307C2×C4—32no—
308C2×C4—32no—
309C2×C4—61no—
310C2×C4—61no—
311C2×C4—62no—
312C2×C4—62no—
313C2×C4—64no—
314C2×C4—62no—
315C2×C4—62no—
316C2×C4C22×C3×A412yes—
317C2×C4C22×C3×A411yescharacteristic
318C2×C4C22×C3×A411yescharacteristic
319C2×C4C22×C3×A411yescharacteristic
320C2×C3—24no—
321C2×C3—43no—
322C2×C3—43no—
323C2×C3—43no—
324C2×C3—812no—
325C2×C3—121no—
326C2×C3C22×#41⋊C311yescharacteristic
327C2×C3A4×#4111yescharacteristic
328C2×C3C2×2−1+4⋊C311yescharacteristic
329C22—22no—
330C22—22no—
331C22—61no—
332C22—61no—
333C22—61no—
334C22C2×C3×#41⋊C314yes—
335C22C23×C3×A411yescharacteristic
336C4—21no—
337C4—22no—
338C4—31no—
339C4—31no—
340C4—61no—
341C4—62no—
342C4—62no—
343C4—61no—
344C4C2×C3×#41⋊C312yes—
345C4C3×2−1+4⋊C312yes—
346C3—43no—
347C3#3482⋊C311yescharacteristic, direct product factor
348C2—24no—
349C2—121no—
350C2C22×C3×#41⋊C311yescharacteristic
351C2C3×A4×#4111yescharacteristic
352C2C2×C3×2−1+4⋊C311yescharacteristic
subgroupG/H
centerC2×C3×C4C22×A4
commutator, cosocleC2×Q8C23×C32
FrattiniC22C23×C3×A4
FittingC3×#3482C3
socleC22×C3C23×A4
hypercenterC3×C4×D4A4
hypocenterQ8C32×#41
LCSG ▷ C2×Q8 ▷ Q8
UCSC1 ◁ C2×C3×C4 ◁ C3×C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×#557⋊C3C2semidirect
2. C3×D4×SL(2,𝔽3)C2semidirect
3. C3×#548⋊C3C2semidirect
4. C3×C4×#41⋊C3C2semidirect
5. C2×C3×C4×SL(2,𝔽3)C2semidirect
6. C3×#3482C3semidirect
7. #3482⋊C3C3direct (N × H)
14. C3×#557C2×C3semidirect
18. C3×#548C2×C3semidirect
23. C3×C4×#41C2×C3semidirect
24. C2×C3×C4×Q8C2×C3semidirect
25. #557⋊C3C2×C3semidirect
26. D4×SL(2,𝔽3)C2×C3semidirect
27. #548⋊C3C2×C3semidirect
28. C4×#41⋊C3C2×C3semidirect
29. C2×C4×SL(2,𝔽3)C2×C3semidirect
38. #3482C32semidirect
86. C3×SL(2,𝔽3)#41semidirect
87. #557C2×C32semidirect
91. #548C2×C32semidirect
96. C4×#41C2×C32semidirect
97. C2×C4×Q8C2×C32semidirect
199. C3×D4#41⋊C3semidirect
222. SL(2,𝔽3)C3×#41semidirect
302. D4C3×#41⋊C3semidirect
347. C3#3482⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#557⋊C32
C3×D4×SL(2,𝔽3)2
C3×#548⋊C32
C3×C4×#41⋊C32
C2×C3×C4×SL(2,𝔽3)2
C3×#34823
#3482⋊C33
C32×C4×D44