Finite Group Databasebeta

← C3×#10619886 #14518685

Subgroups — C3×#10619886 #14518685

Order 1944.

833 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 833 conjugacy classes of subgroups — too many to draw. Only its 76 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×C3⋊#272C211yesmaximal, characteristic, complemented
2C2×C32×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
3C3×C3⋊((C3⋊Dic3)⋊C3)C211yesmaximal, characteristic, complemented
4C3×#6295—31nomaximal
5C3×#6290—31nomaximal
6#10619886C311yesmaximal, characteristic, direct product factor
7C3×#6200—33nomaximal
8C2×C32×H(3,𝔽3)C2211yescharacteristic
9C3×C3⋊#272—21no—
10C32×(C3⋊D3)⋊C3—21no—
11C2×C32×C3⋊D3—31no—
12C2×C32×C3⋊D3—31no—
13C2×C32×C3⋊D3—61no—
14C2×C32×C3⋊D3D311yescharacteristic, complemented
15C2×C33×D3—31no—
16C3×C3⋊(C3⋊Dic3)D311yescharacteristic, complemented
17C32×C3⋊Dic3—31no—
18C2×C3⋊#272C2×C311yescharacteristic, complemented
19C2×C3×#272—33no—
20C2×C3×#272—63no—
21C2×C3×(C3⋊D3)⋊C3—21no—
22C2×C3×(C3⋊D3)⋊C3—23no—
23C2×C3×(C3⋊D3)⋊C3D313yescomplemented
24C2×C3×(C3⋊D3)⋊C3C2×C311yescharacteristic, complemented
25C3⋊((C3⋊Dic3)⋊C3)—21no—
26C3⋊((C3⋊Dic3)⋊C3)C2×C311yescharacteristic, complemented
27C3×(C3⋊Dic3)⋊C3—33no—
28C32×H(3,𝔽3)D411yescharacteristic, complemented, Sylow
29C3×#638—91no—
30#6295—31no—
31#6290—31no—
32C3×#626—91no—
33C3×#626—91no—
34C3×#625—93no—
35C3×#625—91no—
36#6200—33no—
37C2×C34—21no—
38C2×C34C2×D311yescharacteristic
39C2×C34C2×D311yescharacteristic
40C32×C3⋊D3—21no—
41C32×C3⋊D3—62no—
42C32×C3⋊D3—61no—
43C32×C3⋊D3—61no—
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)C2×D313yes—
52C2×C3×H(3,𝔽3)C22×C311yescharacteristic
53C3⋊#272—21no—
54C3×#272—66no—
55C3×#272—63no—
56C3×(C3⋊D3)⋊C3—22no—
57C3×(C3⋊D3)⋊C3—26no—
58C3×(C3⋊D3)⋊C3—23no—
59C3×(C3⋊D3)⋊C3—21no—
60C22×C33—91no—
61C2×C3×C3⋊D3—21no—
62C2×C3×C3⋊D3—31no—
63C2×C3×C3⋊D3—31no—
64C2×C3×C3⋊D3—31no—
65C2×C3×C3⋊D3—31no—
66C2×C3×C3⋊D3—61no—
67C2×C3×C3⋊D3—61no—
68C2×C3×C3⋊D3—61no—
69C2×C3×C3⋊D3—61no—
70C2×C3×C3⋊D3—62no—
71C2×C3×C3⋊D3C3×D311yescharacteristic, complemented
72C2×C3×C3⋊D3C3⋊D311yescharacteristic, complemented
73C2×C32×D3—33no—
74C2×C32×D3—31no—
75C2×C32×D3—31no—
76C2×C32×D3—63no—
77C2×C32×D3—61no—
78C2×C32×D3—91no—
79C2×C32×D3—93no—
80C2×C32×D3—91no—
81C2×C32×D3—91no—
82C2×C32×D3—183no—
83C2×C32×D3—181no—
84C3⋊(C3⋊Dic3)C3×D311yescharacteristic, complemented
85C3×C3⋊Dic3—31no—
86C3×C3⋊Dic3—33no—
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—
94C2×#272—33no—
95C2×#272—63no—
96C2×(C3⋊D3)⋊C3—23no—
97C2×(C3⋊D3)⋊C3C3×D313yescomplemented
98(C3⋊Dic3)⋊C3—33no—
99(C3⋊Dic3)⋊C3—63no—
100C34—21no—
101C34D1211yescharacteristic, complemented
102C34#6711yescharacteristic, 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)#6713yescomplemented
110C3×H(3,𝔽3)C3×D411yescharacteristic, complemented
111#638—91no—
112C3×#67—271no—
113C3×#67—271no—
114C3×#67—273no—
115C3×D12—271no—
116#626—91no—
117#626—91no—
118#625—93no—
119#625—91no—
120C2×C33—23no—
121C2×C33—21no—
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—121no—
139C2×C33—121no—
140C2×C33—121no—
141C2×C33—122no—
142C2×C33—181no—
143C2×C33D3211yescharacteristic
144C2×C33D3213yes—
145C2×C33C2×C3×D311yescharacteristic
146C2×C33C2×C3×D311yescharacteristic
147C2×C33C2×C3⋊D311yescharacteristic
148C3×C3⋊D3—22no—
149C3×C3⋊D3—21no—
150C3×C3⋊D3—21no—
151C3×C3⋊D3—62no—
152C3×C3⋊D3—61no—
153C3×C3⋊D3—61no—
154C3×C3⋊D3—62no—
155C3×C3⋊D3—62no—
156C3×C3⋊D3—64no—
157C3×C3⋊D3—62no—
158C3×C3⋊D3—61no—
159C3×C3⋊D3—61no—
160C32×D3—62no—
161C32×D3—66no—
162C32×D3—61no—
163C32×D3—63no—
164C32×D3—61no—
165C32×D3—181no—
166C32×D3—182no—
167C32×D3—186no—
168C32×D3—181no—
169C32×D3—183no—
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)C2×C3×D313yes—
179#272—66no—
180#272—63no—
181(C3⋊D3)⋊C3—26no—
182(C3⋊D3)⋊C3—23no—
183C22×C32—91no—
184C22×C32—93no—
185C22×C32—91no—
186C22×C32—183no—
187C22×C32—181no—
188C22×C32—271no—
189C2×C3⋊D3—31no—
190C2×C3⋊D3—31no—
191C2×C3⋊D3—61no—
192C2×C3⋊D3C3×C3⋊D311yescharacteristic, complemented
193C2×C3×D3—33no—
194C2×C3×D3—31no—
195C2×C3×D3—31no—
196C2×C3×D3—63no—
197C2×C3×D3—61no—
198C2×C3×D3—91no—
199C2×C3×D3—91no—
200C2×C3×D3—91no—
201C2×C3×D3—93no—
202C2×C3×D3—91no—
203C2×C3×D3—93no—
204C2×C3×D3—91no—
205C2×C3×D3—91no—
206C2×C3×D3—181no—
207C2×C3×D3—181no—
208C2×C3×D3—181no—
209C2×C3×D3—183no—
210C2×C3×D3—183no—
211C2×C3×D3—181no—
212C2×C3×D3—181no—
213C2×C3×D3—183no—
214C2×C3×D3—182no—
215C2×C3×D3—186no—
216C32×C4—271no—
217C3⋊Dic3—31no—
218C3⋊Dic3—33no—
219C3⋊Dic3—91no—
220C3⋊Dic3—181no—
221C3×Dic3—91no—
222C3×Dic3—91no—
223C3×Dic3—91no—
224C3×Dic3—91no—
225C3×Dic3—181no—
226C3×Dic3—181no—
227C3×Dic3—181no—
228C3×Dic3—181no—
229C3×Dic3—182no—
230C3×Dic3—273no—
231C33—21no—
232C33—21no—
233C33—23no—
234C33—21no—
235C33—21no—
236C33—23no—
237C33—21no—
238C33—31no—
239C33—31no—
240C33—41no—
241C33—43no—
242C33—41no—
243C33—61no—
244C33—61no—
245C33—61no—
246C33—61no—
247C33—62no—
248C33—61no—
249C33—121no—
250C33—121no—
251C33—121no—
252C33—122no—
253C33#62611yescharacteristic
254C33#62613yescomplemented
255C33C3×D1211yescharacteristic, complemented
256C33C3×#6711yescharacteristic, complemented
257C33#63811yescharacteristic, complemented
258H(3,𝔽3)—23no—
259H(3,𝔽3)—23no—
260H(3,𝔽3)—23no—
261H(3,𝔽3)—43no—
262H(3,𝔽3)—43no—
263H(3,𝔽3)—46no—
264H(3,𝔽3)—43no—
265H(3,𝔽3)C3×#6713yescomplemented
266C3×D4—811no—
267#67—271no—
268#67—271no—
269#67—273no—
270D12—271no—
271C2×C32—21no—
272C2×C32—21no—
273C2×C32—21no—
274C2×C32—21no—
275C2×C32—21no—
276C2×C32—23no—
277C2×C32—23no—
278C2×C32—31no—
279C2×C32—31no—
280C2×C32—33no—
281C2×C32—31no—
282C2×C32—41no—
283C2×C32—43no—
284C2×C32—41no—
285C2×C32—61no—
286C2×C32—63no—
287C2×C32—63no—
288C2×C32—61no—
289C2×C32—61no—
290C2×C32—61no—
291C2×C32—62no—
292C2×C32—62no—
293C2×C32—66no—
294C2×C32—61no—
295C2×C32—61no—
296C2×C32—61no—
297C2×C32—61no—
298C2×C32—63no—
299C2×C32—121no—
300C2×C32—121no—
301C2×C32—121no—
302C2×C32—123no—
303C2×C32—122no—
304C2×C32—123no—
305C2×C32—121no—
306C2×C32—122no—
307C2×C32—126no—
308C2×C32—121no—
309C2×C32—181no—
310C2×C32—183no—
311C2×C32—186no—
312C2×C32—182no—
313C2×C32—181no—
314C2×C32—541no—
315C2×C32((C3⋊D3)⋊C3)⋊C211yescharacteristic
316C2×C32C3×D3211yescharacteristic
317C2×C32C3×D3213yes—
318C2×C32D3×C3⋊D311yescharacteristic
319C2×C32C2×C3×C3⋊D311yescharacteristic
320C3⋊D3—21no—
321C3⋊D3—61no—
322C3⋊D3—61no—
323C3⋊D3—62no—
324C3×D3—66no—
325C3×D3—62no—
326C3×D3—61no—
327C3×D3—63no—
328C3×D3—61no—
329C3×D3—181no—
330C3×D3—181no—
331C3×D3—182no—
332C3×D3—182no—
333C3×D3—186no—
334C3×D3—182no—
335C3×D3—181no—
336C3×D3—183no—
337C3×D3—186no—
338C3×D3—182no—
339C3×D3—184no—
340C3×D3—1812no—
341C3×D3—182no—
342C3×D3—186no—
343C3×D3—181no—
344C3×D3—181no—
345C3×D3—183no—
346C3×D3—181no—
347C22×C3—93no—
348C22×C3—91no—
349C22×C3—91no—
350C22×C3—181no—
351C22×C3—183no—
352C22×C3—271no—
353C22×C3—271no—
354C22×C3—541no—
355C2×D3—31no—
356C2×D3—91no—
357C2×D3—91no—
358C2×D3—93no—
359C2×D3—91no—
360C2×D3—181no—
361C2×D3—183no—
362C3×C4—271no—
363C3×C4—271no—
364C3×C4—541no—
365Dic3—91no—
366Dic3—91no—
367Dic3—181no—
368Dic3—273no—
369C32—21no—
370C32—21no—
371C32—21no—
372C32—23no—
373C32—21no—
374C32—23no—
375C32—21no—
376C32—31no—
377C32—31no—
378C32—31no—
379C32—33no—
380C32—41no—
381C32—43no—
382C32—41no—
383C32—61no—
384C32—63no—
385C32—61no—
386C32—61no—
387C32—63no—
388C32—61no—
389C32—62no—
390C32—66no—
391C32—62no—
392C32—61no—
393C32—61no—
394C32—61no—
395C32—61no—
396C32—63no—
397C32—121no—
398C32—121no—
399C32—121no—
400C32—123no—
401C32—122no—
402C32—123no—
403C32—121no—
404C32—122no—
405C32—126no—
406C32—121no—
407C32#620011yescharacteristic, complemented
408C32C3×#62611yescharacteristic
409C32C3×#62613yescomplemented
410C32#629111yescharacteristic
411C32C3×#63811yescharacteristic, complemented
412D4—811noSylow
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—33no—
417C2×C3—31no—
418C2×C3—41no—
419C2×C3—61no—
420C2×C3—61no—
421C2×C3—63no—
422C2×C3—63no—
423C2×C3—121no—
424C2×C3—123no—
425C2×C3—182no—
426C2×C3—183no—
427C2×C3—186no—
428C2×C3—181no—
429C2×C3—181no—
430C2×C3—542no—
431C2×C3—541no—
432C2×C3—541no—
433C2×C3C3×((C3⋊D3)⋊C3)⋊C211yescharacteristic
434C2×C3((C3⋊D3)⋊C3)⋊D311yescharacteristic
435C2×C3C3×D3×C3⋊D311yescharacteristic
436D3—61no—
437D3—181no—
438D3—181no—
439D3—183no—
440D3—182no—
441D3—186no—
442D3—181no—
443C22—91no—
444C22—271no—
445C4—271no—
446C3—21no—
447C3—21no—
448C3—21no—
449C3—31no—
450C3—33no—
451C3—41no—
452C3—61no—
453C3—63no—
454C3—63no—
455C3—61no—
456C3—121no—
457C3—123no—
458C3C3×#620011yescharacteristic, complemented
459C3#1061988611yescharacteristic, direct product factor
460C3C3×#629111yescharacteristic
461C2—181no—
462C2—541no—
463C2C3×((C3⋊D3)⋊C3)⋊D311yescharacteristic
subgroupG/H
center, hypercenterC2×C3((C3⋊D3)⋊C3)⋊D3
commutator, cosocleC2×C3×H(3,𝔽3)C22×C3
FrattiniC2×C3C3×D3×C3⋊D3
FittingC2×C32×H(3,𝔽3)C22
socleC2×C33D32
hypocenterC3×H(3,𝔽3)C3×D4
LCSG ▷ C2×C3×H(3,𝔽3) ▷ C3×H(3,𝔽3)
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. C2×C3×C3⋊#272C2semidirect
2. C2×C32×(C3⋊D3)⋊C3C2semidirect
3. C3×C3⋊((C3⋊Dic3)⋊C3)C2semidirect
6. #10619886C3direct (N × H)
14. C2×C32×C3⋊D3D3semidirect
16. C3×C3⋊(C3⋊Dic3)D3semidirect
18. C2×C3⋊#272C2×C3semidirect
23. C2×C3×(C3⋊D3)⋊C3D3semidirect
24. C2×C3×(C3⋊D3)⋊C3C2×C3semidirect
26. C3⋊((C3⋊Dic3)⋊C3)C2×C3semidirect
28. C32×H(3,𝔽3)D4semidirect
71. C2×C3×C3⋊D3C3×D3semidirect
72. C2×C3×C3⋊D3C3⋊D3semidirect
84. C3⋊(C3⋊Dic3)C3×D3semidirect
97. C2×(C3⋊D3)⋊C3C3×D3semidirect
101. C34D12semidirect
102. C34#67semidirect
109. C3×H(3,𝔽3)#67semidirect
110. C3×H(3,𝔽3)C3×D4semidirect
192. C2×C3⋊D3C3×C3⋊D3semidirect
254. C33#626semidirect
255. C33C3×D12semidirect
256. C33C3×#67semidirect
257. C33#638semidirect
265. H(3,𝔽3)C3×#67semidirect
407. C32#6200semidirect
409. C32C3×#626semidirect
411. C32C3×#638semidirect
458. C3C3×#6200semidirect
459. C3#10619886direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C3⋊#2722
C2×C32×(C3⋊D3)⋊C32
C3×C3⋊((C3⋊Dic3)⋊C3)2
C3×#62953
C3×#62903
#106198863
C3×#62003