Finite Group Databasebeta

← C3×#3487⋊C3 #11919738

Subgroups — C3×#3487⋊C3 #11919738

Order 1152.

864 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 864 conjugacy classes of subgroups — too many to draw. Only its 158 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×C3×2−1+4⋊C3C211yesmaximal, characteristic, complemented
2C22×C3×#41⋊C3C211yesmaximal, characteristic, complemented
3C3×C4⋊(#41⋊C3)C212yesmaximal, complemented
4C3×#548⋊C3C212yesmaximal, complemented
5C3×#519⋊C3C211yesmaximal, characteristic, complemented
6C3×#3487C311yesmaximal, characteristic, complemented
7#3487⋊C3C313yesmaximal, direct product factor
8C3×2−1+4⋊C3—22no—
9C2×C3×#41⋊C3—22no—
10C2×C3×#41⋊C3C2212yes—
11C2×C3×#41⋊C3C2211yescharacteristic, complemented
12C22×C3×SL(2,𝔽3)C2211yescharacteristic
13C22×C3×SL(2,𝔽3)C2211yescharacteristic, complemented
14C32×#123—41nomaximal
15C3×C4×SL(2,𝔽3)C2212yescomplemented
16C2×C3×2−1+4C2×C311yescharacteristic
17C22×C3×#41C2×C311yescharacteristic, complemented
18C2×2−1+4⋊C3C2×C313yescomplemented
19C22×#41⋊C3C2×C313yescomplemented
20C3×#550—32no—
21C3×#550C2×C312yescomplemented
22C3×#548—32no—
23C3×#548C2×C312yescomplemented
24C3×#535—31no—
25C3×#535—31no—
26C3×#525—31no—
27C3×#525—31no—
28C3×#519C2×C311yescharacteristic, complemented
29C4⋊(#41⋊C3)C2×C316yescomplemented
30#548⋊C3C2×C316yescomplemented
31#519⋊C3C2×C313yescomplemented
32C2×C32×D4—41no—
33C22×C32×C4—41no—
34C3×#41⋊C3—22no—
35C3×#41⋊C3—21no—
36C2×C3×SL(2,𝔽3)—21no—
37C2×C3×SL(2,𝔽3)D412yescomplemented
38C2×C3×SL(2,𝔽3)C2311yescharacteristic
39C32×C4⋊C4—42no—
40C32×C22⋊C4—41no—
41C32×C22⋊C4—42no—
42#3487C3211yescharacteristic, complemented, Sylow
43C3×2−1+4—22no—
44C3×2−1+4—62no—
45C2×C3×#41—22no—
46C2×C3×#41—31no—
47C2×C3×#41—31no—
48C2×C3×#41—31no—
49C2×C3×#41—32no—
50C2×C3×#41—62no—
51C2×C3×#41C22×C312yes—
52C2×C3×#41C22×C311yescharacteristic
53C22×C3×Q8—31no—
54C22×C3×Q8C22×C311yescharacteristic
55C22×C3×Q8C22×C311yescharacteristic
56C22×C3×D4—31no—
57C23×C3×C4—31no—
582−1+4⋊C3—26no—
59C2×#41⋊C3—26no—
60C2×#41⋊C3C22×C316yes—
61C2×#41⋊C3C22×C313yescomplemented
62C22×SL(2,𝔽3)C22×C313yes—
63C22×SL(2,𝔽3)C22×C313yescomplemented
64C3×#127—32no—
65C3×#127—32no—
66C3×#124—32no—
67C3×#124—32no—
68C3×#123—31no—
69C3×#123—43no—
70C3×#123A411yescharacteristic
71C3×C22⋊Q8—32no—
72C3×C22⋊Q8—32no—
73C3×#121—32no—
74C3×#121—34no—
75C3×#121—32no—
76C3×#121—32no—
77C3×#121—32no—
78C3×#120—32no—
79C3×#120—31no—
80C3×#120—31no—
81C3×C4×Q8—32no—
82C3×C4×Q8C22×C312yes—
83C3×C4×D4—34no—
84C3×C4×D4—32no—
85C3×C4×D4—32no—
86C3×#117—31no—
87C3×#117—31no—
88C4×SL(2,𝔽3)C22×C316yescomplemented
89C23×C32—41no—
90C23×C32—41no—
91C32×D4—82no—
92C2×C32×C4—42no—
93C2×C32×C4—41no—
94C2×C32×C4—42no—
95C2×C32×C4—82no—
96C3×SL(2,𝔽3)C2×D411yescharacteristic
97C2×2−1+4C2×C3211yescharacteristic
98C22×#41C2×C3211yescharacteristic, complemented
99#550—32no—
100#550C2×C3212yescomplemented
101#548—32no—
102#548C2×C3212yescomplemented
103#535—31no—
104#535—31no—
105#525—31no—
106#525—31no—
107#519C2×C3211yescharacteristic, complemented
108C24×C3—31no—
109C3×#41—22no—
110C3×#41—21no—
111C3×#41—62no—
112C3×#41—62no—
113C3×#41—62no—
114C3×#41—62no—
115C3×#41—64no—
116C3×#41—62no—
117C3×#41—62no—
118C3×#41—64no—
119C3×#41—62no—
120C3×#41—61no—
121C2×C3×Q8—21no—
122C2×C3×Q8—31no—
123C2×C3×Q8—31no—
124C2×C3×Q8—32no—
125C2×C3×Q8—31no—
126C2×C3×Q8—62no—
127C2×C3×Q8—62no—
128C2×C3×Q8—61no—
129C2×C3×Q8C3×D412yes—
130C2×C3×Q8C23×C311yescharacteristic
131C2×C3×D4—32no—
132C2×C3×D4—31no—
133C2×C3×D4—32no—
134C2×C3×D4—31no—
135C2×C3×D4—31no—
136C2×C3×D4—34no—
137C2×C3×D4—32no—
138C2×C3×D4—32no—
139C2×C3×D4—43no—
140C2×C3×D4—62no—
141C2×C3×D4—62no—
142C2×C3×D4C2×A411yescharacteristic
143C22×C3×C4—31no—
144C22×C3×C4—32no—
145C22×C3×C4—31no—
146C22×C3×C4—31no—
147C22×C3×C4—32no—
148C22×C3×C4—32no—
149C22×C3×C4—43no—
150C22×C3×C4—62no—
151C22×C3×C4—62no—
152C22×C3×C4C2×A411yescharacteristic
153#41⋊C3—26no—
154#41⋊C3—23no—
155C2×SL(2,𝔽3)—23no—
156C2×SL(2,𝔽3)C3×D416yescomplemented
157C2×SL(2,𝔽3)C23×C313yes—
158C3×C4⋊C4—32no—
159C3×C4⋊C4—32no—
160C3×C4⋊C4—32no—
161C3×C4⋊C4—46no—
162C3×C4⋊C4C2×A412yes—
163C3×C22⋊C4—34no—
164C3×C22⋊C4—31no—
165C3×C22⋊C4—32no—
166C3×C22⋊C4—32no—
167C3×C22⋊C4—32no—
168C3×C22⋊C4—43no—
169C3×C22⋊C4—46no—
170C3×C22⋊C4C2×A411yescharacteristic
171C3×C22⋊C4C2×A412yes—
172C3×C42—32no—
173C3×C42—32no—
174C22×C32—42no—
175C22×C32—41no—
176C22×C32—82no—
177C22×C32—81no—
178C22×C32—82no—
179C32×C4—82no—
180C32×C4—82no—
181C32×C4—81no—
1822−1+4—22no—
1832−1+4—62no—
184C2×#41—22no—
185C2×#41—31no—
186C2×#41—31no—
187C2×#41—31no—
188C2×#41—32no—
189C2×#41—62no—
190C2×#41C22×C3212yes—
191C2×#41C22×C3211yescharacteristic
192C22×Q8—31no—
193C22×Q8C22×C3211yescharacteristic
194C22×Q8C22×C3211yescharacteristic
195C22×D4—31no—
196C23×C4—31no—
197#127—32no—
198#127—32no—
199#124—32no—
200#124—32no—
201#123—31no—
202#123C3×A411yescharacteristic
203C22⋊Q8—32no—
204C22⋊Q8—32no—
205#121—32no—
206#121—34no—
207#121—32no—
208#121—32no—
209#121—32no—
210#120—32no—
211#120—31no—
212#120—31no—
213C4×Q8—32no—
214C4×Q8C22×C3212yes—
215C4×D4—34no—
216C4×D4—32no—
217C4×D4—32no—
218#117—31no—
219#117—31no—
220C23×C3—32no—
221C23×C3—31no—
222C23×C3—43no—
223C23×C3—43no—
224C23×C3—62no—
225C23×C3—122no—
226C23×C3C22×A411yescharacteristic
227C23×C3C22×A411yescharacteristic
228C3×Q8—32no—
229C3×Q8—31no—
230C3×Q8—32no—
231C3×Q8—62no—
232C3×Q8—61no—
233C3×Q8—61no—
234C3×Q8C2×C3×D411yescharacteristic
235C3×D4—22no—
236C3×D4—62no—
237C3×D4—62no—
238C3×D4—62no—
239C3×D4—61no—
240C3×D4—61no—
241C3×D4—64no—
242C3×D4—62no—
243C3×D4—86no—
244C3×D4—122no—
245C3×D4—122no—
246C3×D4—124no—
247C2×C3×C4—22no—
248C2×C3×C4—32no—
249C2×C3×C4—32no—
250C2×C3×C4—31no—
251C2×C3×C4—31no—
252C2×C3×C4—32no—
253C2×C3×C4—31no—
254C2×C3×C4—46no—
255C2×C3×C4—46no—
256C2×C3×C4—43no—
257C2×C3×C4—62no—
258C2×C3×C4—64no—
259C2×C3×C4—62no—
260C2×C3×C4—61no—
261C2×C3×C4—61no—
262C2×C3×C4—61no—
263C2×C3×C4—61no—
264C2×C3×C4—64no—
265C2×C3×C4—86no—
266C2×C3×C4C22×A412yes—
267C2×C3×C4C22×A411yescharacteristic
268C2×C3×C4C22×A412yes—
269SL(2,𝔽3)C2×C3×D413yes—
270C2×C32—41no—
271C2×C32—42no—
272C2×C32—82no—
273C2×C32—161no—
274C24—31no—
275#41—22no—
276#41—21no—
277#41—62no—
278#41—62no—
279#41—62no—
280#41—62no—
281#41—64no—
282#41—62no—
283#41—62no—
284#41—64no—
285#41—62no—
286#41—61no—
287C2×Q8—21no—
288C2×Q8—31no—
289C2×Q8—31no—
290C2×Q8—32no—
291C2×Q8—31no—
292C2×Q8—62no—
293C2×Q8—62no—
294C2×Q8—61no—
295C2×Q8C32×D412yes—
296C2×Q8C23×C3211yescharacteristic
297C2×D4—32no—
298C2×D4—31no—
299C2×D4—32no—
300C2×D4—31no—
301C2×D4—31no—
302C2×D4—34no—
303C2×D4—32no—
304C2×D4—32no—
305C2×D4—62no—
306C2×D4—62no—
307C2×D4C2×C3×A411yescharacteristic
308C22×C4—31no—
309C22×C4—32no—
310C22×C4—31no—
311C22×C4—31no—
312C22×C4—32no—
313C22×C4—32no—
314C22×C4—62no—
315C22×C4—62no—
316C22×C4C2×C3×A411yescharacteristic
317C4⋊C4—32no—
318C4⋊C4—32no—
319C4⋊C4—32no—
320C4⋊C4C2×C3×A412yes—
321C22⋊C4—34no—
322C22⋊C4—31no—
323C22⋊C4—32no—
324C22⋊C4—32no—
325C22⋊C4—32no—
326C22⋊C4C2×C3×A411yescharacteristic
327C22⋊C4C2×C3×A412yes—
328C42—32no—
329C42—32no—
330C22×C3—22no—
331C22×C3—21no—
332C22×C3—22no—
333C22×C3—46no—
334C22×C3—43no—
335C22×C3—61no—
336C22×C3—62no—
337C22×C3—62no—
338C22×C3—62no—
339C22×C3—62no—
340C22×C3—86no—
341C22×C3—83no—
342C22×C3—86no—
343C22×C3—124no—
344C22×C3D4×A412yes—
345C22×C3C23×A411yescharacteristic
346C3×C4—22no—
347C3×C4—21no—
348C3×C4—22no—
349C3×C4—32no—
350C3×C4—31no—
351C3×C4—31no—
352C3×C4—61no—
353C3×C4—62no—
354C3×C4—86no—
355C3×C4—83no—
356C3×C4—86no—
357C32—41noSylow
358C23—32no—
359C23—31no—
360C23—62no—
361C23—122no—
362C23C22×C3×A411yescharacteristic
363C23C22×C3×A411yescharacteristic
364Q8—32no—
365Q8—31no—
366Q8—32no—
367Q8—62no—
368Q8—61no—
369Q8—61no—
370Q8C2×C32×D411yescharacteristic
371D4—22no—
372D4—62no—
373D4—62no—
374D4—62no—
375D4—61no—
376D4—61no—
377D4—64no—
378D4—62no—
379D4—122no—
380D4—122no—
381D4—124no—
382C2×C4—22no—
383C2×C4—32no—
384C2×C4—32no—
385C2×C4—31no—
386C2×C4—31no—
387C2×C4—32no—
388C2×C4—31no—
389C2×C4—62no—
390C2×C4—62no—
391C2×C4—64no—
392C2×C4—61no—
393C2×C4—61no—
394C2×C4—61no—
395C2×C4—61no—
396C2×C4—64no—
397C2×C4C22×C3×A412yes—
398C2×C4C22×C3×A411yescharacteristic
399C2×C4C22×C3×A412yes—
400C2×C3—22no—
401C2×C3—41no—
402C2×C3—43no—
403C2×C3—46no—
404C2×C3—86no—
405C2×C3—121no—
406C2×C3—122no—
407C2×C3—163no—
408C2×C3C2×D4×A411yescharacteristic
409C2×C3#594512yes—
410C22—22no—
411C22—21no—
412C22—22no—
413C22—61no—
414C22—62no—
415C22—62no—
416C22—62no—
417C22—62no—
418C22—124no—
419C22C3×D4×A412yes—
420C22C23×C3×A411yescharacteristic
421C4—22no—
422C4—21no—
423C4—22no—
424C4—31no—
425C4—32no—
426C4—31no—
427C4—61no—
428C4—62no—
429C3—43no—
430C3#3487⋊C311yescharacteristic, direct product factor
431C2—22no—
432C2—41no—
433C2—122no—
434C2—121no—
435C2C2×C3×D4×A411yescharacteristic
436C2C3×#594512yes—
subgroupG/H
center, socleC22×C3C23×A4
commutator, cosocleC2×Q8C23×C32
FrattiniC22C23×C3×A4
FittingC3×#3487C3
hypercenterC3×#123A4
hypocenterQ8C2×C32×D4
LCSG ▷ C2×Q8 ▷ Q8
UCSC1 ◁ C22×C3 ◁ C3×#123

Complements

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

NH ≅ G/Ntype
1. C2×C3×2−1+4⋊C3C2semidirect
2. C22×C3×#41⋊C3C2semidirect
3. C3×C4⋊(#41⋊C3)C2semidirect
4. C3×#548⋊C3C2semidirect
5. C3×#519⋊C3C2semidirect
6. C3×#3487C3semidirect
7. #3487⋊C3C3direct (N × H)
11. C2×C3×#41⋊C3C22semidirect
13. C22×C3×SL(2,𝔽3)C22semidirect
15. C3×C4×SL(2,𝔽3)C22semidirect
17. C22×C3×#41C2×C3semidirect
18. C2×2−1+4⋊C3C2×C3semidirect
19. C22×#41⋊C3C2×C3semidirect
21. C3×#550C2×C3semidirect
23. C3×#548C2×C3semidirect
28. C3×#519C2×C3semidirect
29. C4⋊(#41⋊C3)C2×C3semidirect
30. #548⋊C3C2×C3semidirect
31. #519⋊C3C2×C3semidirect
37. C2×C3×SL(2,𝔽3)D4semidirect
42. #3487C32semidirect
61. C2×#41⋊C3C22×C3semidirect
63. C22×SL(2,𝔽3)C22×C3semidirect
88. C4×SL(2,𝔽3)C22×C3semidirect
98. C22×#41C2×C32semidirect
100. #550C2×C32semidirect
102. #548C2×C32semidirect
107. #519C2×C32semidirect
156. C2×SL(2,𝔽3)C3×D4semidirect
430. C3#3487⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×2−1+4⋊C32
C22×C3×#41⋊C32
C3×C4⋊(#41⋊C3)2
C3×#548⋊C32
C3×#519⋊C32
C3×#34873
#3487⋊C33
C32×#1234