Finite Group Databasebeta

← C3×#73157 #11920935

Subgroups — C3×#73157 #11920935

Order 1152.

416 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 56 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×#5945C211yesmaximal, characteristic
2C3×#5424C211yesmaximal, characteristic, complemented
3C3×#5423C211yesmaximal, characteristic, complemented
4#73157C311yesmaximal, characteristic, direct product factor
5C3×#1794—31nomaximal
6C3×2−1+4⋊C3—21no—
7C3×2−1+4⋊C3C411yescharacteristic, complemented
8C3×#994C411yescharacteristic, complemented
9C2×C3×#41⋊C3—21no—
10C2×C3×#41⋊C3C2211yescharacteristic
11C3×GU(2,𝔽3)—21no—
12C3×#859—21no—
13C3×#837—41nomaximal
14C3×#585D311yescharacteristic
15#5945—21no—
16#5945C2×C311yescharacteristic
17#5424C2×C311yescharacteristic, complemented
18#5423C2×C311yescharacteristic, complemented
19C3×#421—31no—
20C3×#421—31no—
21C3×#416—31no—
22C3×#416—31no—
23C3×#410—31no—
24C3×#408—31no—
25C32×#41—41no—
26C3×#41⋊C3—21no—
27C3×#41⋊C3C2×C411yescharacteristic
28C3×#41⋊C3D411yescharacteristic
29C2×C3×SL(2,𝔽3)—21no—
30C2×C3×SL(2,𝔽3)D411yescharacteristic
31C3×C4×Dic3—41no—
32C3×#208—41no—
33#1794—31noSylow
34C3×2−1+4—21no—
35C3×2−1+4—31no—
36C3×2−1+4Dic311yescharacteristic, complemented
37C3×H(5,𝔽2)—31no—
38C3×H(5,𝔽2)—61no—
39C3×H(5,𝔽2)Dic311yescharacteristic, complemented
40C2×C3×#41—21no—
41C2×C3×#41—31no—
42C2×C3×#41—31no—
43C2×C3×#41—61no—
44C2×C3×#41C2×D311yescharacteristic
452−1+4⋊C3—22no—
462−1+4⋊C3—21no—
472−1+4⋊C3—21no—
482−1+4⋊C3C3×C411yescharacteristic, complemented
49#994—21no—
50#994C3×C411yescharacteristic, complemented
51C2×#41⋊C3—22no—
52C2×#41⋊C3—21no—
53C2×#41⋊C3—21no—
54C2×#41⋊C3C22×C311yescharacteristic
55C2×C3×M16—31no—
56C22×C3×C8—31no—
57C3×#117—31no—
58C3×#117—31no—
59GU(2,𝔽3)—21no—
60#859—21no—
61C3×#104—61no—
62C3×#104—61no—
63C3×#104—61no—
64C3×#104—61no—
65C3×#103—61no—
66C3×#103—61no—
67C3×#102—61no—
68C3×#102—61no—
69C3×#99—62no—
70C3×C22⋊C8—62no—
71#837—41no—
72C32×Q8—41no—
73C32×D4—41no—
74C32×D4—81no—
75C2×C32×C4—41no—
76C2×C32×C4—81no—
77C2×C3×Dic3—81no—
78C3×SL(2,𝔽3)C22⋊C411yescharacteristic
79C3×C3⋊C8—81no—
80#585C3×D311yescharacteristic
81#421—31no—
82#421—31no—
83#416—31no—
84#416—31no—
85#410—31no—
86#408—31no—
87C3×#41—21no—
88C3×#41—31no—
89C3×#41—31no—
90C3×#41—31no—
91C3×#41—31no—
92C3×#41—31no—
93C3×#41—41no—
94C3×#41—61no—
95C3×#41—61no—
96C3×#41—61no—
97C3×#41—61no—
98C3×#41—62no—
99C3×#41—61no—
100C3×#41—61no—
101C3×#41—61no—
102C3×#41—61no—
103C3×#41—81no—
104C3×#41C2×Dic311yescharacteristic
105C3×#41#6711yescharacteristic
106C3×#41S411yescharacteristic
107C2×C3×Q8—21no—
108C2×C3×Q8—31no—
109C2×C3×Q8—31no—
110C2×C3×Q8—61no—
111C2×C3×Q8#6711yescharacteristic
112C2×C3×D4—31no—
113C2×C3×D4—31no—
114C2×C3×D4—31no—
115C2×C3×D4—32no—
116C2×C3×D4—61no—
117C2×C3×D4—61no—
118C2×C3×D4—61no—
119C2×C3×D4—62no—
120C22×C3×C4—31no—
121C22×C3×C4—32no—
122C22×C3×C4—61no—
123#41⋊C3—22no—
124#41⋊C3—21no—
125#41⋊C3—21no—
126#41⋊C3—21no—
127#41⋊C3C2×C3×C411yescharacteristic
128#41⋊C3C3×D411yescharacteristic
129C2×SL(2,𝔽3)—22no—
130C2×SL(2,𝔽3)—21no—
131C2×SL(2,𝔽3)—21no—
132C2×SL(2,𝔽3)C3×D411yescharacteristic
133C3×M16—61no—
134C3×M16—61no—
135C2×C3×C8—61no—
136C2×C3×C8—61no—
137C2×C3×C8—61no—
138C2×C3×C8—61no—
139C3×C4⋊C4—61no—
140C3×C4⋊C4—61no—
141C3×C22⋊C4—61no—
142C3×C22⋊C4—61no—
143C3×C42—61no—
144C3×C42—61no—
145C4×Dic3—41no—
146#208—41no—
147C22×C32—41no—
148C22×C32—81no—
149C32×C4—41no—
150C32×C4—41no—
151C32×C4—81no—
152C3×Dic3—82no—
1532−1+4—21no—
1542−1+4—31no—
1552−1+4C3×Dic311yescharacteristic, complemented
156H(5,𝔽2)—31no—
157H(5,𝔽2)—61no—
158H(5,𝔽2)C3×Dic311yescharacteristic, complemented
159C2×#41—21no—
160C2×#41—31no—
161C2×#41—31no—
162C2×#41—61no—
163C2×#41C2×C3×D311yescharacteristic
164C2×M16—31no—
165C22×C8—31no—
166#117—31no—
167#117—31no—
168#104—61no—
169#104—61no—
170#104—61no—
171#104—61no—
172#103—61no—
173#103—61no—
174#102—61no—
175#102—61no—
176#99—62no—
177C22⋊C8—62no—
178C23×C3—31no—
179C23×C3—32no—
180C23×C3—61no—
181C3×Q8—31no—
182C3×Q8—31no—
183C3×Q8—41no—
184C3×Q8—61no—
185C3×Q8—61no—
186C3×Q8—81no—
187C3×Q8#21711yescharacteristic
188C3×Q8SL(2,ℤ/4)11yescharacteristic
189C3×D4—21no—
190C3×D4—31no—
191C3×D4—31no—
192C3×D4—31no—
193C3×D4—41no—
194C3×D4—61no—
195C3×D4—61no—
196C3×D4—61no—
197C3×D4—61no—
198C3×D4—61no—
199C3×D4—62no—
200C3×D4—61no—
201C3×D4—81no—
202C3×D4—82no—
203C3×D4—81no—
204C3×D4SL(2,ℤ/4)11yescharacteristic
205C2×C3×C4—21no—
206C2×C3×C4—31no—
207C2×C3×C4—31no—
208C2×C3×C4—31no—
209C2×C3×C4—31no—
210C2×C3×C4—31no—
211C2×C3×C4—32no—
212C2×C3×C4—41no—
213C2×C3×C4—61no—
214C2×C3×C4—61no—
215C2×C3×C4—61no—
216C2×C3×C4—62no—
217C2×C3×C4—61no—
218C2×C3×C4—81no—
219C2×C3×C4—82no—
220C2×C3×C4—81no—
221C2×C3×C4—121no—
222C2×C3×C4—121no—
223C2×C3×C4C2×S411yescharacteristic
224C2×Dic3—81no—
225SL(2,𝔽3)—21no—
226SL(2,𝔽3)C3×C22⋊C411yescharacteristic
227C3×C8—121no—
228C3×C8—121no—
229C3⋊C8—81no—
230C2×C32—41no—
231C2×C32—81no—
232C2×C32—161no—
233#41—21no—
234#41—31no—
235#41—31no—
236#41—31no—
237#41—31no—
238#41—31no—
239#41—61no—
240#41—61no—
241#41—61no—
242#41—61no—
243#41—62no—
244#41—61no—
245#41—61no—
246#41—61no—
247#41—61no—
248#41C2×C3×Dic311yescharacteristic
249#41C3×#6711yescharacteristic
250#41C3×S411yescharacteristic
251C2×Q8—21no—
252C2×Q8—31no—
253C2×Q8—31no—
254C2×Q8—61no—
255C2×Q8C3×#6711yescharacteristic
256C2×D4—31no—
257C2×D4—31no—
258C2×D4—31no—
259C2×D4—32no—
260C2×D4—61no—
261C2×D4—61no—
262C2×D4—61no—
263C2×D4—62no—
264C22×C4—31no—
265C22×C4—32no—
266C22×C4—61no—
267M16—61no—
268M16—61no—
269C2×C8—61no—
270C2×C8—61no—
271C2×C8—61no—
272C2×C8—61no—
273C4⋊C4—61no—
274C4⋊C4—61no—
275C22⋊C4—61no—
276C22⋊C4—61no—
277C42—61no—
278C42—61no—
279C22×C3—21no—
280C22×C3—31no—
281C22×C3—31no—
282C22×C3—41no—
283C22×C3—61no—
284C22×C3—81no—
285C22×C3—82no—
286C22×C3—81no—
287C22×C3—121no—
288C22×C3—122no—
289C22×C3—241no—
290C22×C3GL(2,ℤ/4)11yescharacteristic
291C3×C4—21no—
292C3×C4—31no—
293C3×C4—31no—
294C3×C4—41no—
295C3×C4—41no—
296C3×C4—61no—
297C3×C4—81no—
298C3×C4—82no—
299C3×C4—81no—
300C3×C4—81no—
301C3×C4—241no—
302C3×C4—241no—
303C3×C4C2×SL(2,ℤ/4)11yescharacteristic
304C3×C4GL(2,ℤ/4)11yescharacteristic
305Dic3—82no—
306C32—41noSylow
307C23—31no—
308C23—32no—
309C23—61no—
310Q8—31no—
311Q8—31no—
312Q8—61no—
313Q8—61no—
314Q8C3×#21711yescharacteristic
315Q8C3×SL(2,ℤ/4)11yescharacteristic
316D4—21no—
317D4—31no—
318D4—31no—
319D4—31no—
320D4—61no—
321D4—61no—
322D4—61no—
323D4—61no—
324D4—61no—
325D4—62no—
326D4—61no—
327D4C3×SL(2,ℤ/4)11yescharacteristic
328C2×C4—21no—
329C2×C4—31no—
330C2×C4—31no—
331C2×C4—31no—
332C2×C4—31no—
333C2×C4—31no—
334C2×C4—32no—
335C2×C4—61no—
336C2×C4—61no—
337C2×C4—61no—
338C2×C4—62no—
339C2×C4—61no—
340C2×C4—121no—
341C2×C4—121no—
342C2×C4C2×C3×S411yescharacteristic
343C8—121no—
344C8—121no—
345C2×C3—21no—
346C2×C3—41no—
347C2×C3—41no—
348C2×C3—61no—
349C2×C3—61no—
350C2×C3—81no—
351C2×C3—81no—
352C2×C3—121no—
353C2×C3—161no—
354C2×C3—161no—
355C2×C3—162no—
356C2×C3#543211yescharacteristic
357C22—21no—
358C22—31no—
359C22—31no—
360C22—61no—
361C22—121no—
362C22—122no—
363C22—241no—
364C22C3×GL(2,ℤ/4)11yescharacteristic
365C4—21no—
366C4—31no—
367C4—31no—
368C4—61no—
369C4—241no—
370C4—241no—
371C4C2×C3×SL(2,ℤ/4)11yescharacteristic
372C4C3×GL(2,ℤ/4)11yescharacteristic
373C3—41no—
374C3—81no—
375C3#7315711yescharacteristic, direct product factor
376C2—21no—
377C2—41no—
378C2—61no—
379C2—61no—
380C2—121no—
381C2C3×#543211yescharacteristic
subgroupG/H
centerC3×C4GL(2,ℤ/4)
commutator#41⋊C3C2×C3×C4
FrattiniC2×C4C2×C3×S4
FittingC3×#585D3
socleC2×C3#5432
prime radicalC3×#5945C2
cosocleC2×#41⋊C3C22×C3
hypercenterC3×#41S4
hypocenterSL(2,𝔽3)C3×C22⋊C4
LCSG ▷ #41⋊C3 ▷ SL(2,𝔽3)
UCSC1 ◁ C3×C4 ◁ C2×C3×C4 ◁ C3×#41

Complements

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

NH ≅ G/Ntype
2. C3×#5424C2semidirect
3. C3×#5423C2semidirect
4. #73157C3direct (N × H)
7. C3×2−1+4⋊C3C4semidirect
8. C3×#994C4semidirect
17. #5424C2×C3semidirect
18. #5423C2×C3semidirect
36. C3×2−1+4Dic3semidirect
39. C3×H(5,𝔽2)Dic3semidirect
48. 2−1+4⋊C3C3×C4semidirect
50. #994C3×C4semidirect
155. 2−1+4C3×Dic3semidirect
158. H(5,𝔽2)C3×Dic3semidirect
375. C3#73157direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#59452
C3×#54242
C3×#54232
#731573
C3×#17943
C3×#8374