Finite Group Databasebeta

← C3×#10619884 #14518674

Subgroups — C3×#10619884 #14518674

Order 1944.

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

normal subgroups only

This group has 777 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⋊((C3⋊D3)⋊C3)C211yesmaximal, characteristic, complemented
2C2×C32×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
3C3×C3⋊#1084C211yesmaximal, characteristic, complemented
4C3×#6295—31nomaximal
5C3×#6291—31nomaximal
6#10619884C311yesmaximal, characteristic, direct product factor
7C3×#6198—33nomaximal
8C2×C32×H(3,𝔽3)C2211yescharacteristic
9C3×C3⋊((C3⋊D3)⋊C3)—21no—
10C32×(C3⋊D3)⋊C3—21no—
11C2×C3×C3⋊(C3⋊D3)D311yescharacteristic, complemented
12C2×C32×C3⋊D3—31no—
13C2×C32×C3⋊D3D311yescharacteristic, complemented
14C2×C33×D3—31no—
15C32×C3⋊Dic3—31no—
16C32×C3⋊Dic3—31no—
17C32×C3⋊Dic3—61no—
18C2×C3⋊((C3⋊D3)⋊C3)—21no—
19C2×C3⋊((C3⋊D3)⋊C3)C2×C311yescharacteristic, complemented
20C2×C3×(C3⋊D3)⋊C3—21no—
21C2×C3×(C3⋊D3)⋊C3—23no—
22C2×C3×(C3⋊D3)⋊C3—33no—
23C2×C3×(C3⋊D3)⋊C3D313yescomplemented
24C2×C3×(C3⋊D3)⋊C3C2×C311yescharacteristic, complemented
25C3⋊#1084C2×C311yescharacteristic, complemented
26C3×#1084—33no—
27C3×#1084—63no—
28C32×H(3,𝔽3)D411yescharacteristic, complemented, Sylow
29C3×#638—91no—
30#6295—31no—
31#6291—31no—
32C3×#626—93no—
33C3×#626—91no—
34C3×#626—91no—
35C3×#625—91no—
36#6198—33no—
37C2×C34—21no—
38C2×C34C2×D311yescharacteristic
39C2×C34C2×D311yescharacteristic
40C3×C3⋊(C3⋊D3)—21no—
41C32×C3⋊D3—21no—
42C32×C3⋊D3—61no—
43C33×D3—61no—
44C2×C3×H(3,𝔽3)—21no—
45C2×C3×H(3,𝔽3)—21no—
46C2×C3×H(3,𝔽3)—23no—
47C2×C3×H(3,𝔽3)—23no—
48C2×C3×H(3,𝔽3)—43no—
49C2×C3×H(3,𝔽3)—41no—
50C2×C3×H(3,𝔽3)C2×D313yes—
51C2×C3×H(3,𝔽3)C22×C311yescharacteristic
52C3⋊((C3⋊D3)⋊C3)—22no—
53C3⋊((C3⋊D3)⋊C3)—21no—
54C3×(C3⋊D3)⋊C3—22no—
55C3×(C3⋊D3)⋊C3—26no—
56C3×(C3⋊D3)⋊C3—23no—
57C3×(C3⋊D3)⋊C3—21no—
58C3×(C3⋊D3)⋊C3—63no—
59C22×C33—91no—
60C2×C3⋊(C3⋊D3)C3×D311yescharacteristic, complemented
61C2×C3×C3⋊D3—21no—
62C2×C3×C3⋊D3—31no—
63C2×C3×C3⋊D3—33no—
64C2×C3×C3⋊D3—31no—
65C2×C3×C3⋊D3—61no—
66C2×C3×C3⋊D3—91no—
67C2×C3×C3⋊D3—181no—
68C2×C3×C3⋊D3C3×D311yescharacteristic, complemented
69C2×C3×C3⋊D3C3⋊D311yescharacteristic, complemented
70C2×C32×D3—33no—
71C2×C32×D3—31no—
72C2×C32×D3—31no—
73C2×C32×D3—63no—
74C2×C32×D3—61no—
75C2×C32×D3—91no—
76C2×C32×D3—91no—
77C2×C32×D3—91no—
78C2×C32×D3—181no—
79C3×C3⋊Dic3—31no—
80C3×C3⋊Dic3—31no—
81C3×C3⋊Dic3—31no—
82C3×C3⋊Dic3—31no—
83C3×C3⋊Dic3—61no—
84C3×C3⋊Dic3—61no—
85C3×C3⋊Dic3—61no—
86C3×C3⋊Dic3—61no—
87C3×C3⋊Dic3—62no—
88C32×Dic3—93no—
89C32×Dic3—91no—
90C32×Dic3—91no—
91C32×Dic3—183no—
92C32×Dic3—181no—
93C2×(C3⋊D3)⋊C3—23no—
94C2×(C3⋊D3)⋊C3—33no—
95C2×(C3⋊D3)⋊C3—63no—
96C2×(C3⋊D3)⋊C3C3×D313yescomplemented
97#1084—33no—
98#1084—63no—
99C34—21no—
100C34#6711yescharacteristic, complemented
101C34#6711yescharacteristic, complemented
102C3×H(3,𝔽3)—21no—
103C3×H(3,𝔽3)—21no—
104C3×H(3,𝔽3)—23no—
105C3×H(3,𝔽3)—23no—
106C3×H(3,𝔽3)—43no—
107C3×H(3,𝔽3)—41no—
108C3×H(3,𝔽3)#6713yescomplemented
109C3×H(3,𝔽3)C3×D411yescharacteristic, complemented
110#638—91no—
111C3×#67—271no—
112C3×#67—271no—
113C3×#67—273no—
114C3×D12—271no—
115#626—93no—
116#626—91no—
117#626—91no—
118#625—91no—
119C2×C33—21no—
120C2×C33—23no—
121C2×C33—21no—
122C2×C33—21no—
123C2×C33—21no—
124C2×C33—23no—
125C2×C33—21no—
126C2×C33—31no—
127C2×C33—31no—
128C2×C33—41no—
129C2×C33—43no—
130C2×C33—41no—
131C2×C33—61no—
132C2×C33—61no—
133C2×C33—61no—
134C2×C33—61no—
135C2×C33—62no—
136C2×C33—61no—
137C2×C33—121no—
138C2×C33—121no—
139C2×C33—121no—
140C2×C33—122no—
141C2×C33—181no—
142C2×C33D3211yescharacteristic
143C2×C33D3213yes—
144C2×C33C2×C3×D311yescharacteristic
145C2×C33C2×C3×D311yescharacteristic
146C2×C33C2×C3⋊D311yescharacteristic
147C3⋊(C3⋊D3)—21no—
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—63no—
155C3×C3⋊D3—181no—
156C3×C3⋊D3—182no—
157C32×D3—62no—
158C32×D3—66no—
159C32×D3—61no—
160C32×D3—63no—
161C32×D3—61no—
162C32×D3—181no—
163C32×D3—181no—
164C32×D3—182no—
165C32×D3—181no—
166C2×H(3,𝔽3)—23no—
167C2×H(3,𝔽3)—23no—
168C2×H(3,𝔽3)—23no—
169C2×H(3,𝔽3)—43no—
170C2×H(3,𝔽3)—43no—
171C2×H(3,𝔽3)—46no—
172C2×H(3,𝔽3)—43no—
173C2×H(3,𝔽3)C2×C3×D313yes—
174(C3⋊D3)⋊C3—26no—
175(C3⋊D3)⋊C3—23no—
176(C3⋊D3)⋊C3—66no—
177(C3⋊D3)⋊C3—63no—
178C22×C32—91no—
179C22×C32—93no—
180C22×C32—91no—
181C22×C32—183no—
182C22×C32—181no—
183C22×C32—271no—
184C2×C3⋊D3—31no—
185C2×C3⋊D3—33no—
186C2×C3⋊D3—91no—
187C2×C3⋊D3—181no—
188C2×C3⋊D3C3×C3⋊D311yescharacteristic, complemented
189C2×C3×D3—33no—
190C2×C3×D3—31no—
191C2×C3×D3—31no—
192C2×C3×D3—63no—
193C2×C3×D3—61no—
194C2×C3×D3—91no—
195C2×C3×D3—91no—
196C2×C3×D3—91no—
197C2×C3×D3—91no—
198C2×C3×D3—91no—
199C2×C3×D3—91no—
200C2×C3×D3—181no—
201C2×C3×D3—181no—
202C2×C3×D3—181no—
203C2×C3×D3—181no—
204C2×C3×D3—181no—
205C2×C3×D3—182no—
206C2×C3×D3—273no—
207C32×C4—271no—
208C3⋊Dic3—31no—
209C3⋊Dic3—31no—
210C3⋊Dic3—61no—
211C3×Dic3—93no—
212C3×Dic3—91no—
213C3×Dic3—91no—
214C3×Dic3—93no—
215C3×Dic3—91no—
216C3×Dic3—91no—
217C3×Dic3—181no—
218C3×Dic3—183no—
219C3×Dic3—181no—
220C3×Dic3—183no—
221C3×Dic3—181no—
222C3×Dic3—181no—
223C3×Dic3—183no—
224C3×Dic3—182no—
225C3×Dic3—186no—
226C33—21no—
227C33—21no—
228C33—23no—
229C33—21no—
230C33—21no—
231C33—23no—
232C33—21no—
233C33—31no—
234C33—31no—
235C33—41no—
236C33—43no—
237C33—41no—
238C33—61no—
239C33—61no—
240C33—61no—
241C33—61no—
242C33—62no—
243C33—61no—
244C33—121no—
245C33—121no—
246C33—121no—
247C33—122no—
248C33#62511yescharacteristic
249C33#62513yescomplemented
250C33C3×#6711yescharacteristic, complemented
251C33C3×#6711yescharacteristic, complemented
252C33#63811yescharacteristic, complemented
253H(3,𝔽3)—23no—
254H(3,𝔽3)—23no—
255H(3,𝔽3)—23no—
256H(3,𝔽3)—43no—
257H(3,𝔽3)—43no—
258H(3,𝔽3)—46no—
259H(3,𝔽3)—43no—
260H(3,𝔽3)C3×#6713yescomplemented
261C3×D4—811no—
262#67—271no—
263#67—271no—
264#67—273no—
265D12—271no—
266C2×C32—21no—
267C2×C32—21no—
268C2×C32—21no—
269C2×C32—21no—
270C2×C32—21no—
271C2×C32—23no—
272C2×C32—23no—
273C2×C32—31no—
274C2×C32—31no—
275C2×C32—33no—
276C2×C32—31no—
277C2×C32—41no—
278C2×C32—43no—
279C2×C32—41no—
280C2×C32—61no—
281C2×C32—63no—
282C2×C32—63no—
283C2×C32—61no—
284C2×C32—61no—
285C2×C32—61no—
286C2×C32—62no—
287C2×C32—66no—
288C2×C32—62no—
289C2×C32—61no—
290C2×C32—61no—
291C2×C32—61no—
292C2×C32—61no—
293C2×C32—63no—
294C2×C32—121no—
295C2×C32—121no—
296C2×C32—121no—
297C2×C32—123no—
298C2×C32—122no—
299C2×C32—123no—
300C2×C32—121no—
301C2×C32—122no—
302C2×C32—126no—
303C2×C32—121no—
304C2×C32—181no—
305C2×C32—183no—
306C2×C32—186no—
307C2×C32—182no—
308C2×C32—181no—
309C2×C32—541no—
310C2×C32((C3⋊D3)⋊C3)⋊C211yescharacteristic
311C2×C32C3×D3211yescharacteristic
312C2×C32C3×D3213yes—
313C2×C32D3×C3⋊D311yescharacteristic
314C2×C32C2×C3×C3⋊D311yescharacteristic
315C3⋊D3—21no—
316C3⋊D3—61no—
317C3⋊D3—63no—
318C3⋊D3—181no—
319C3⋊D3—182no—
320C3×D3—66no—
321C3×D3—62no—
322C3×D3—61no—
323C3×D3—63no—
324C3×D3—61no—
325C3×D3—181no—
326C3×D3—181no—
327C3×D3—182no—
328C3×D3—182no—
329C3×D3—182no—
330C3×D3—181no—
331C3×D3—182no—
332C3×D3—184no—
333C3×D3—182no—
334C3×D3—181no—
335C3×D3—181no—
336C3×D3—181no—
337C3×D3—543no—
338C22×C3—93no—
339C22×C3—91no—
340C22×C3—91no—
341C22×C3—181no—
342C22×C3—183no—
343C22×C3—271no—
344C22×C3—271no—
345C22×C3—541no—
346C2×D3—31no—
347C2×D3—91no—
348C2×D3—91no—
349C2×D3—91no—
350C2×D3—181no—
351C2×D3—273no—
352C3×C4—271no—
353C3×C4—271no—
354C3×C4—541no—
355Dic3—91no—
356Dic3—93no—
357Dic3—91no—
358Dic3—181no—
359Dic3—183no—
360C32—21no—
361C32—21no—
362C32—21no—
363C32—23no—
364C32—21no—
365C32—21no—
366C32—23no—
367C32—31no—
368C32—31no—
369C32—31no—
370C32—33no—
371C32—41no—
372C32—43no—
373C32—41no—
374C32—61no—
375C32—61no—
376C32—63no—
377C32—61no—
378C32—63no—
379C32—61no—
380C32—62no—
381C32—62no—
382C32—66no—
383C32—61no—
384C32—61no—
385C32—61no—
386C32—61no—
387C32—63no—
388C32—121no—
389C32—121no—
390C32—121no—
391C32—123no—
392C32—122no—
393C32—123no—
394C32—121no—
395C32—122no—
396C32—126no—
397C32—121no—
398C32#619811yescharacteristic, complemented
399C32C3×#62511yescharacteristic
400C32C3×#62513yescomplemented
401C32#629011yescharacteristic
402C32C3×#63811yescharacteristic, complemented
403D4—811noSylow
404C2×C3—21no—
405C2×C3—21no—
406C2×C3—21no—
407C2×C3—31no—
408C2×C3—33no—
409C2×C3—41no—
410C2×C3—61no—
411C2×C3—63no—
412C2×C3—63no—
413C2×C3—61no—
414C2×C3—121no—
415C2×C3—123no—
416C2×C3—182no—
417C2×C3—183no—
418C2×C3—186no—
419C2×C3—181no—
420C2×C3—181no—
421C2×C3—541no—
422C2×C3—542no—
423C2×C3—541no—
424C2×C3C3×((C3⋊D3)⋊C3)⋊C211yescharacteristic
425C2×C3((C3⋊D3)⋊C3)⋊D311yescharacteristic
426C2×C3C3×D3×C3⋊D311yescharacteristic
427D3—61no—
428D3—181no—
429D3—182no—
430D3—181no—
431D3—181no—
432D3—543no—
433C22—91no—
434C22—271no—
435C4—271no—
436C3—21no—
437C3—21no—
438C3—21no—
439C3—31no—
440C3—33no—
441C3—41no—
442C3—63no—
443C3—61no—
444C3—61no—
445C3—63no—
446C3—121no—
447C3—123no—
448C3C3×#619811yescharacteristic, complemented
449C3#1061988411yescharacteristic, direct product factor
450C3C3×#629011yescharacteristic
451C2—181no—
452C2—541no—
453C2C3×((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⋊((C3⋊D3)⋊C3)C2semidirect
2. C2×C32×(C3⋊D3)⋊C3C2semidirect
3. C3×C3⋊#1084C2semidirect
6. #10619884C3direct (N × H)
11. C2×C3×C3⋊(C3⋊D3)D3semidirect
13. C2×C32×C3⋊D3D3semidirect
19. C2×C3⋊((C3⋊D3)⋊C3)C2×C3semidirect
23. C2×C3×(C3⋊D3)⋊C3D3semidirect
24. C2×C3×(C3⋊D3)⋊C3C2×C3semidirect
25. C3⋊#1084C2×C3semidirect
28. C32×H(3,𝔽3)D4semidirect
60. C2×C3⋊(C3⋊D3)C3×D3semidirect
68. C2×C3×C3⋊D3C3×D3semidirect
69. C2×C3×C3⋊D3C3⋊D3semidirect
96. C2×(C3⋊D3)⋊C3C3×D3semidirect
100. C34#67semidirect
101. C34#67semidirect
108. C3×H(3,𝔽3)#67semidirect
109. C3×H(3,𝔽3)C3×D4semidirect
188. C2×C3⋊D3C3×C3⋊D3semidirect
249. C33#625semidirect
250. C33C3×#67semidirect
251. C33C3×#67semidirect
252. C33#638semidirect
260. H(3,𝔽3)C3×#67semidirect
398. C32#6198semidirect
400. C32C3×#625semidirect
402. C32C3×#638semidirect
448. C3C3×#6198semidirect
449. C3#10619884direct (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⋊((C3⋊D3)⋊C3)2
C2×C32×(C3⋊D3)⋊C32
C3×C3⋊#10842
C3×#62953
C3×#62913
#106198843
C3×#61983