Finite Group Databasebeta

← C3×#6290⋊C3 #14518624

Subgroups — C3×#6290⋊C3 #14518624

Order 1944.

801 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 801 conjugacy classes of subgroups — too many to draw. Only its 94 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×D3×H(3,𝔽3)C211yesmaximal, characteristic, complemented
2C2×C32×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
3C3×C3⋊((C3⋊Dic3)⋊C3)C211yesmaximal, characteristic, complemented
4C3×#6290C311yesmaximal, characteristic, complemented
5C32×#625—31nomaximal
6C3×#638⋊C3—31nomaximal
7#6290⋊C3C313yesmaximal, direct product factor
8C2×C32×H(3,𝔽3)C2211yescharacteristic
9C3×D3×H(3,𝔽3)—21no—
10C32×(C3⋊D3)⋊C3—21no—
11C2×C32×C3⋊D3C2×C311yescharacteristic, complemented
12C2×C33×D3—21no—
13C2×C33×D3—31no—
14C2×C33×D3D311yescharacteristic, complemented
15C2×C33×D3C2×C311yescharacteristic, complemented
16C3×C3⋊(C3⋊Dic3)C2×C311yescharacteristic, complemented
17C32×C3⋊Dic3—31no—
18C22×C3×H(3,𝔽3)—31no—
19C2×D3×H(3,𝔽3)—23no—
20C2×D3×H(3,𝔽3)C2×C313yescomplemented
21C2×C3×(C3⋊D3)⋊C3—21no—
22C2×C3×(C3⋊D3)⋊C3—23no—
23C2×C3×(C3⋊D3)⋊C3D311yescharacteristic, complemented
24C2×C3×(C3⋊D3)⋊C3C2×C313yescomplemented
25C3⋊((C3⋊Dic3)⋊C3)C2×C313yescomplemented
26C3×(C3⋊Dic3)⋊C3—31no—
27C3×(C3⋊Dic3)⋊C3—61no—
28C32×H(3,𝔽3)D411yescharacteristic, complemented, Sylow
29C3×#638—31no—
30C32×#67—91no—
31C32×#67—91no—
32#6290C3211yescharacteristic, complemented
33C3×#625—31no—
34C3×#625—33no—
35C3×#625—91no—
36#638⋊C3—33no—
37C2×C34—21no—
38C2×C34C2×D311yescharacteristic
39C2×C34C22×C311yescharacteristic
40C32×C3⋊D3—21no—
41C33×D3—22no—
42C33×D3—21no—
43C33×D3—21no—
44C33×D3—61no—
45C2×C3×H(3,𝔽3)—21no—
46C2×C3×H(3,𝔽3)—21no—
47C2×C3×H(3,𝔽3)—23no—
48C2×C3×H(3,𝔽3)—23no—
49C2×C3×H(3,𝔽3)—43no—
50C2×C3×H(3,𝔽3)—41no—
51C2×C3×H(3,𝔽3)—61no—
52C2×C3×H(3,𝔽3)C2×D311yescharacteristic
53C2×C3×H(3,𝔽3)C22×C313yes—
54D3×H(3,𝔽3)—26no—
55D3×H(3,𝔽3)—23no—
56C3×(C3⋊D3)⋊C3—22no—
57C3×(C3⋊D3)⋊C3—26no—
58C3×(C3⋊D3)⋊C3—21no—
59C3×(C3⋊D3)⋊C3—23no—
60C22×C33—31no—
61C22×C33—31no—
62C22×C33—61no—
63C22×C33—91no—
64C2×C3×C3⋊D3—21no—
65C2×C3×C3⋊D3C3×D311yescharacteristic, complemented
66C2×C3×C3⋊D3C2×C3211yescharacteristic, complemented
67C2×C32×D3—21no—
68C2×C32×D3—23no—
69C2×C32×D3—31no—
70C2×C32×D3—31no—
71C2×C32×D3—31no—
72C2×C32×D3—33no—
73C2×C32×D3—31no—
74C2×C32×D3—63no—
75C2×C32×D3—61no—
76C2×C32×D3—61no—
77C2×C32×D3—61no—
78C2×C32×D3—62no—
79C2×C32×D3—61no—
80C2×C32×D3—91no—
81C2×C32×D3C3×D311yescharacteristic
82C2×C32×D3C3×D313yescomplemented
83C2×C32×D3C2×C3211yescharacteristic, complemented
84C3⋊(C3⋊Dic3)C2×C3211yescharacteristic, complemented
85C3×C3⋊Dic3—33no—
86C3×C3⋊Dic3—31no—
87C3×C3⋊Dic3—31no—
88C3×C3⋊Dic3—61no—
89C3×C3⋊Dic3—91no—
90C3×C3⋊Dic3—181no—
91C32×Dic3—91no—
92C32×Dic3—91no—
93C32×Dic3—181no—
94C22×H(3,𝔽3)—33no—
95C22×H(3,𝔽3)—63no—
96C2×(C3⋊D3)⋊C3—23no—
97C2×(C3⋊D3)⋊C3C3×D313yescomplemented
98(C3⋊Dic3)⋊C3—33no—
99(C3⋊Dic3)⋊C3—63no—
100C34—21no—
101C34#6711yescharacteristic, complemented
102C34C3×D411yescharacteristic, complemented
103C3×H(3,𝔽3)—21no—
104C3×H(3,𝔽3)—21no—
105C3×H(3,𝔽3)—23no—
106C3×H(3,𝔽3)—23no—
107C3×H(3,𝔽3)—43no—
108C3×H(3,𝔽3)—41no—
109C3×H(3,𝔽3)#6711yescharacteristic, complemented
110C3×H(3,𝔽3)C3×D413yescomplemented
111C32×D4—271no—
112#638—31no—
113C3×#67—93no—
114C3×#67—91no—
115C3×#67—93no—
116C3×#67—91no—
117C3×#67—271no—
118#625—31no—
119#625—91no—
120C2×C33—21no—
121C2×C33—23no—
122C2×C33—21no—
123C2×C33—21no—
124C2×C33—21no—
125C2×C33—23no—
126C2×C33—21no—
127C2×C33—31no—
128C2×C33—31no—
129C2×C33—41no—
130C2×C33—43no—
131C2×C33—41no—
132C2×C33—61no—
133C2×C33—61no—
134C2×C33—61no—
135C2×C33—61no—
136C2×C33—62no—
137C2×C33—61no—
138C2×C33—62no—
139C2×C33—61no—
140C2×C33—61no—
141C2×C33—121no—
142C2×C33—121no—
143C2×C33—121no—
144C2×C33—122no—
145C2×C33—181no—
146C2×C33D3211yescharacteristic
147C2×C33C2×C3×D311yescharacteristic
148C2×C33C2×C3×D313yes—
149C2×C33C2×C3×D311yescharacteristic
150C2×C33C22×C3211yescharacteristic
151C3×C3⋊D3—22no—
152C3×C3⋊D3—21no—
153C3×C3⋊D3—21no—
154C32×D3—21no—
155C32×D3—22no—
156C32×D3—26no—
157C32×D3—23no—
158C32×D3—21no—
159C32×D3—61no—
160C32×D3—61no—
161C32×D3—62no—
162C32×D3—62no—
163C32×D3—64no—
164C32×D3—62no—
165C32×D3—62no—
166C32×D3—66no—
167C32×D3—61no—
168C32×D3—61no—
169C32×D3—63no—
170C32×D3—181no—
171C2×H(3,𝔽3)—23no—
172C2×H(3,𝔽3)—23no—
173C2×H(3,𝔽3)—23no—
174C2×H(3,𝔽3)—43no—
175C2×H(3,𝔽3)—43no—
176C2×H(3,𝔽3)—46no—
177C2×H(3,𝔽3)—43no—
178C2×H(3,𝔽3)—66no—
179C2×H(3,𝔽3)—63no—
180C2×H(3,𝔽3)C2×C3×D313yes—
181(C3⋊D3)⋊C3—26no—
182(C3⋊D3)⋊C3—23no—
183C22×C32—31no—
184C22×C32—33no—
185C22×C32—31no—
186C22×C32—63no—
187C22×C32—61no—
188C22×C32—91no—
189C22×C32—91no—
190C22×C32—91no—
191C22×C32—93no—
192C22×C32—91no—
193C22×C32—181no—
194C22×C32—181no—
195C22×C32—181no—
196C22×C32—182no—
197C22×C32—183no—
198C22×C32—181no—
199C2×C3⋊D3C32×D311yescharacteristic, complemented
200C2×C3×D3—21no—
201C2×C3×D3—33no—
202C2×C3×D3—31no—
203C2×C3×D3—31no—
204C2×C3×D3—33no—
205C2×C3×D3—31no—
206C2×C3×D3—63no—
207C2×C3×D3—61no—
208C2×C3×D3—61no—
209C2×C3×D3—63no—
210C2×C3×D3—91no—
211C2×C3×D3—91no—
212C2×C3×D3—181no—
213C2×C3×D3(C3⋊D3)⋊C311yescharacteristic, complemented
214C2×C3×D3C32×D311yescharacteristic
215C32×C4—271no—
216C3⋊Dic3—31no—
217C3⋊Dic3—31no—
218C3⋊Dic3—61no—
219C3⋊Dic3—91no—
220C3⋊Dic3—181no—
221C3×Dic3—93no—
222C3×Dic3—91no—
223C3×Dic3—93no—
224C3×Dic3—91no—
225C3×Dic3—181no—
226C3×Dic3—183no—
227C3×Dic3—271no—
228C3×Dic3—541no—
229C33—21no—
230C33—21no—
231C33—23no—
232C33—21no—
233C33—21no—
234C33—23no—
235C33—21no—
236C33—31no—
237C33—31no—
238C33—41no—
239C33—43no—
240C33—41no—
241C33—61no—
242C33—61no—
243C33—61no—
244C33—61no—
245C33—62no—
246C33—61no—
247C33—121no—
248C33—121no—
249C33—121no—
250C33—122no—
251C33#62511yescharacteristic, complemented
252C33C3×#6711yescharacteristic
253C33C3×#6711yescharacteristic, complemented
254C33C3×#6713yescomplemented
255C33C32×D411yescharacteristic, complemented
256H(3,𝔽3)—23no—
257H(3,𝔽3)—23no—
258H(3,𝔽3)—23no—
259H(3,𝔽3)—43no—
260H(3,𝔽3)—43no—
261H(3,𝔽3)—46no—
262H(3,𝔽3)—43no—
263H(3,𝔽3)C3×#6713yescomplemented
264C3×D4—271no—
265C3×D4—273no—
266#67—91no—
267#67—91no—
268#67—271no—
269C2×C32—21no—
270C2×C32—21no—
271C2×C32—21no—
272C2×C32—21no—
273C2×C32—21no—
274C2×C32—23no—
275C2×C32—23no—
276C2×C32—31no—
277C2×C32—31no—
278C2×C32—33no—
279C2×C32—31no—
280C2×C32—41no—
281C2×C32—43no—
282C2×C32—41no—
283C2×C32—61no—
284C2×C32—63no—
285C2×C32—63no—
286C2×C32—61no—
287C2×C32—61no—
288C2×C32—61no—
289C2×C32—62no—
290C2×C32—61no—
291C2×C32—61no—
292C2×C32—61no—
293C2×C32—61no—
294C2×C32—61no—
295C2×C32—63no—
296C2×C32—62no—
297C2×C32—66no—
298C2×C32—63no—
299C2×C32—61no—
300C2×C32—121no—
301C2×C32—121no—
302C2×C32—123no—
303C2×C32—121no—
304C2×C32—121no—
305C2×C32—123no—
306C2×C32—122no—
307C2×C32—123no—
308C2×C32—121no—
309C2×C32—122no—
310C2×C32—126no—
311C2×C32—121no—
312C2×C32—181no—
313C2×C32—181no—
314C2×C32—182no—
315C2×C32—182no—
316C2×C32—184no—
317C2×C32—182no—
318C2×C32—181no—
319C2×C32—183no—
320C2×C32—186no—
321C2×C32—182no—
322C2×C32—181no—
323C2×C32C2×(C3⋊D3)⋊C311yescharacteristic
324C2×C32C3×D3211yescharacteristic
325C2×C32C3×D3213yes—
326C2×C32C2×C32×D311yescharacteristic
327C2×C32C2×C32×D311yescharacteristic
328C3⋊D3—21no—
329C3×D3—22no—
330C3×D3—21no—
331C3×D3—21no—
332C3×D3—61no—
333C3×D3—63no—
334C3×D3—62no—
335C3×D3—66no—
336C3×D3—66no—
337C3×D3—62no—
338C3×D3—61no—
339C3×D3—63no—
340C3×D3—61no—
341C3×D3—181no—
342C3×D3—181no—
343C3×D3—182no—
344C22×C3—31no—
345C22×C3—31no—
346C22×C3—61no—
347C22×C3—91no—
348C22×C3—93no—
349C22×C3—93no—
350C22×C3—91no—
351C22×C3—91no—
352C22×C3—181no—
353C22×C3—183no—
354C22×C3—181no—
355C22×C3—183no—
356C2×D3—31no—
357C2×D3—91no—
358C2×D3C3×(C3⋊D3)⋊C311yescharacteristic, complemented
359C3×C4—273no—
360C3×C4—271no—
361Dic3—91no—
362Dic3—91no—
363Dic3—181no—
364Dic3—271no—
365Dic3—541no—
366C32—21no—
367C32—21no—
368C32—21no—
369C32—23no—
370C32—21no—
371C32—23no—
372C32—21no—
373C32—31no—
374C32—31no—
375C32—33no—
376C32—31no—
377C32—41no—
378C32—43no—
379C32—41no—
380C32—61no—
381C32—61no—
382C32—63no—
383C32—61no—
384C32—63no—
385C32—61no—
386C32—62no—
387C32—61no—
388C32—61no—
389C32—61no—
390C32—63no—
391C32—61no—
392C32—121no—
393C32—121no—
394C32—121no—
395C32—121no—
396C32—123no—
397C32—123no—
398C32—122no—
399C32—123no—
400C32—121no—
401C32—122no—
402C32—126no—
403C32—121no—
404C32#638⋊C311yescharacteristic, complemented
405C32C3×#62511yescharacteristic
406C32C3×#62513yescomplemented
407C32C32×#6711yescharacteristic
408C32C32×#6711yescharacteristic, complemented
409D4—271noSylow
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3—31no—
414C2×C3—33no—
415C2×C3—41no—
416C2×C3—62no—
417C2×C3—61no—
418C2×C3—61no—
419C2×C3—61no—
420C2×C3—63no—
421C2×C3—61no—
422C2×C3—63no—
423C2×C3—121no—
424C2×C3—123no—
425C2×C3—181no—
426C2×C3—183no—
427C2×C3—182no—
428C2×C3—186no—
429C2×C3—182no—
430C2×C3—183no—
431C2×C3—186no—
432C2×C3—181no—
433C2×C3—181no—
434C2×C3D3×(C3⋊D3)⋊C311yescharacteristic
435C2×C3C2×C3×(C3⋊D3)⋊C311yescharacteristic
436C2×C3C32×D3211yescharacteristic
437D3—21no—
438D3—61no—
439D3—181no—
440C22—31no—
441C22—91no—
442C4—271no—
443C3—21no—
444C3—21no—
445C3—21no—
446C3—31no—
447C3—33no—
448C3—41no—
449C3—63no—
450C3—61no—
451C3—63no—
452C3—61no—
453C3—121no—
454C3—123no—
455C3#6290⋊C311yescharacteristic, direct product factor
456C3C3×#638⋊C311yescharacteristic, complemented
457C3C32×#62511yescharacteristic
458C2—61no—
459C2—181no—
460C2C3×D3×(C3⋊D3)⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2×C3D3×(C3⋊D3)⋊C3
commutator, cosocleC2×C33C22×C32
FrattiniC2×C3C32×D32
FittingC2×C32×H(3,𝔽3)C22
socleC2×C33C2×C3×D3
hypocenterC33C32×D4
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×H(3,𝔽3)C2semidirect
2. C2×C32×(C3⋊D3)⋊C3C2semidirect
3. C3×C3⋊((C3⋊Dic3)⋊C3)C2semidirect
4. C3×#6290C3semidirect
7. #6290⋊C3C3direct (N × H)
11. C2×C32×C3⋊D3C2×C3semidirect
14. C2×C33×D3D3semidirect
15. C2×C33×D3C2×C3semidirect
16. C3×C3⋊(C3⋊Dic3)C2×C3semidirect
20. C2×D3×H(3,𝔽3)C2×C3semidirect
23. C2×C3×(C3⋊D3)⋊C3D3semidirect
24. C2×C3×(C3⋊D3)⋊C3C2×C3semidirect
25. C3⋊((C3⋊Dic3)⋊C3)C2×C3semidirect
28. C32×H(3,𝔽3)D4semidirect
32. #6290C32semidirect
65. C2×C3×C3⋊D3C3×D3semidirect
66. C2×C3×C3⋊D3C2×C32semidirect
82. C2×C32×D3C3×D3semidirect
83. C2×C32×D3C2×C32semidirect
84. C3⋊(C3⋊Dic3)C2×C32semidirect
97. C2×(C3⋊D3)⋊C3C3×D3semidirect
101. C34#67semidirect
102. C34C3×D4semidirect
109. C3×H(3,𝔽3)#67semidirect
110. C3×H(3,𝔽3)C3×D4semidirect
199. C2×C3⋊D3C32×D3semidirect
213. C2×C3×D3(C3⋊D3)⋊C3semidirect
251. C33#625semidirect
253. C33C3×#67semidirect
254. C33C3×#67semidirect
255. C33C32×D4semidirect
263. H(3,𝔽3)C3×#67semidirect
358. C2×D3C3×(C3⋊D3)⋊C3semidirect
404. C32#638⋊C3semidirect
406. C32C3×#625semidirect
408. C32C32×#67semidirect
455. C3#6290⋊C3direct (N × H)
456. C3C3×#638⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×H(3,𝔽3)2
C2×C32×(C3⋊D3)⋊C32
C3×C3⋊((C3⋊Dic3)⋊C3)2
C3×#62903
C32×#6253
C3×#638⋊C33
#6290⋊C33