Finite Group Databasebeta

← C3×#10619885 #14518679

Subgroups — C3×#10619885 #14518679

Order 1944.

783 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 783 conjugacy classes of subgroups — too many to draw. Only its 80 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
2C3×C3⋊((C3⋊Dic3)⋊C3)C211yesmaximal, characteristic, complemented
3C32×(C3⋊Dic3)⋊C3C211yesmaximal, characteristic, complemented
4C3×#6294—31nomaximal
5C3×Dic3×C3⋊D3—31nomaximal
6#10619885C311yesmaximal, characteristic, direct product factor
7C3×#6199—33nomaximal
8C2×C32×H(3,𝔽3)C2211yescharacteristic
9C3×C3⋊#272C412yescomplemented
10C2×C32×C3⋊D3—31no—
11C2×C32×C3⋊D3—31no—
12C2×C32×C3⋊D3—61no—
13C3×C3⋊(C3⋊Dic3)D311yescharacteristic, complemented
14C32×C3⋊Dic3—31no—
15C32×C3⋊Dic3D311yescharacteristic, complemented
16C33×Dic3—31no—
17C2×C3⋊#272C2×C311yescharacteristic
18C2×C3×#272—33no—
19C2×C3×#272—63no—
20C3⋊((C3⋊Dic3)⋊C3)—21no—
21C3⋊((C3⋊Dic3)⋊C3)C2×C311yescharacteristic, complemented
22C3×(C3⋊Dic3)⋊C3—21no—
23C3×(C3⋊Dic3)⋊C3—23no—
24C3×(C3⋊Dic3)⋊C3—33no—
25C3×(C3⋊Dic3)⋊C3D313yescomplemented
26C3×(C3⋊Dic3)⋊C3C2×C311yescharacteristic, complemented
27C32×H(3,𝔽3)C2×C411yescharacteristic, complemented, Sylow
28C3×C4×C3⋊D3—91no—
29#6294—31no—
30Dic3×C3⋊D3—31no—
31C3×#624—91no—
32C3×D3×Dic3—93no—
33C3×D3×Dic3—91no—
34C3×D3×Dic3—91no—
35#6199—33no—
36C2×C34—21no—
37C2×C34C2×D311yescharacteristic
38C2×C34C2×D311yescharacteristic
39C32×C3⋊D3—32no—
40C32×C3⋊D3—32no—
41C32×C3⋊D3—62no—
42C2×C3×H(3,𝔽3)—21no—
43C2×C3×H(3,𝔽3)—21no—
44C2×C3×H(3,𝔽3)—23no—
45C2×C3×H(3,𝔽3)—23no—
46C2×C3×H(3,𝔽3)—43no—
47C2×C3×H(3,𝔽3)—41no—
48C2×C3×H(3,𝔽3)C2×D313yes—
49C2×C3×H(3,𝔽3)C22×C311yescharacteristic
50C3⋊#272C3×C412yescomplemented
51C3×#272—36no—
52C3×#272—66no—
53C2×C3×C3⋊D3—31no—
54C2×C3×C3⋊D3—31no—
55C2×C3×C3⋊D3—31no—
56C2×C3×C3⋊D3—31no—
57C2×C3×C3⋊D3—61no—
58C2×C3×C3⋊D3—61no—
59C2×C3×C3⋊D3—61no—
60C2×C3×C3⋊D3—61no—
61C2×C3×C3⋊D3—62no—
62C2×C32×D3—93no—
63C2×C32×D3—91no—
64C2×C32×D3—91no—
65C2×C32×D3—183no—
66C2×C32×D3—181no—
67C33×C4—91no—
68C3⋊(C3⋊Dic3)C3×D311yescharacteristic, complemented
69C3×C3⋊Dic3—21no—
70C3×C3⋊Dic3—31no—
71C3×C3⋊Dic3—33no—
72C3×C3⋊Dic3—31no—
73C3×C3⋊Dic3—61no—
74C3×C3⋊Dic3—91no—
75C3×C3⋊Dic3—181no—
76C3×C3⋊Dic3C3×D311yescharacteristic, complemented
77C3×C3⋊Dic3C3⋊D311yescharacteristic, complemented
78C32×Dic3—33no—
79C32×Dic3—31no—
80C32×Dic3—31no—
81C32×Dic3—63no—
82C32×Dic3—61no—
83C32×Dic3—91no—
84C32×Dic3—91no—
85C32×Dic3—91no—
86C32×Dic3—181no—
87C2×#272—33no—
88C2×#272—63no—
89(C3⋊Dic3)⋊C3—23no—
90(C3⋊Dic3)⋊C3—33no—
91(C3⋊Dic3)⋊C3—63no—
92(C3⋊Dic3)⋊C3C3×D313yescomplemented
93C34—21no—
94C34C4×D311yescharacteristic, complemented
95C34C4×D311yescharacteristic, complemented
96C3×H(3,𝔽3)—21no—
97C3×H(3,𝔽3)—21no—
98C3×H(3,𝔽3)—23no—
99C3×H(3,𝔽3)—23no—
100C3×H(3,𝔽3)—43no—
101C3×H(3,𝔽3)—41no—
102C3×H(3,𝔽3)C4×D313yescomplemented
103C3×H(3,𝔽3)C2×C3×C411yescharacteristic, complemented
104C4×C3⋊D3—91no—
105C2×C3×Dic3—271no—
106C3×C4×D3—271no—
107C3×C4×D3—271no—
108C3×C4×D3—273no—
109#624—91no—
110D3×Dic3—93no—
111D3×Dic3—91no—
112D3×Dic3—91no—
113C2×C33—23no—
114C2×C33—21no—
115C2×C33—21no—
116C2×C33—21no—
117C2×C33—21no—
118C2×C33—23no—
119C2×C33—21no—
120C2×C33—31no—
121C2×C33—31no—
122C2×C33—41no—
123C2×C33—43no—
124C2×C33—41no—
125C2×C33—61no—
126C2×C33—61no—
127C2×C33—61no—
128C2×C33—61no—
129C2×C33—62no—
130C2×C33—61no—
131C2×C33—121no—
132C2×C33—121no—
133C2×C33—121no—
134C2×C33—122no—
135C2×C33D3211yescharacteristic
136C2×C33D3213yes—
137C2×C33C2×C3×D311yescharacteristic
138C2×C33C2×C3×D311yescharacteristic
139C2×C33C2×C3⋊D311yescharacteristic
140C3×C3⋊D3—32no—
141C3×C3⋊D3—32no—
142C3×C3⋊D3—32no—
143C3×C3⋊D3—32no—
144C3×C3⋊D3—62no—
145C3×C3⋊D3—62no—
146C3×C3⋊D3—62no—
147C3×C3⋊D3—62no—
148C3×C3⋊D3—64no—
149C32×D3—92no—
150C32×D3—96no—
151C32×D3—92no—
152C32×D3—186no—
153C32×D3—182no—
154C2×H(3,𝔽3)—23no—
155C2×H(3,𝔽3)—23no—
156C2×H(3,𝔽3)—23no—
157C2×H(3,𝔽3)—43no—
158C2×H(3,𝔽3)—43no—
159C2×H(3,𝔽3)—46no—
160C2×H(3,𝔽3)—43no—
161C2×H(3,𝔽3)C2×C3×D313yes—
162#272—36no—
163#272—66no—
164C22×C32—271no—
165C2×C3⋊D3—31no—
166C2×C3⋊D3—31no—
167C2×C3⋊D3—61no—
168C2×C3×D3—93no—
169C2×C3×D3—91no—
170C2×C3×D3—91no—
171C2×C3×D3—93no—
172C2×C3×D3—91no—
173C2×C3×D3—91no—
174C2×C3×D3—181no—
175C2×C3×D3—183no—
176C2×C3×D3—181no—
177C2×C3×D3—183no—
178C2×C3×D3—181no—
179C2×C3×D3—181no—
180C2×C3×D3—183no—
181C2×C3×D3—182no—
182C2×C3×D3—186no—
183C32×C4—91no—
184C32×C4—93no—
185C32×C4—91no—
186C32×C4—183no—
187C32×C4—181no—
188C32×C4—271no—
189C3⋊Dic3—31no—
190C3⋊Dic3—33no—
191C3⋊Dic3—91no—
192C3⋊Dic3—181no—
193C3⋊Dic3C3×C3⋊D311yescharacteristic, complemented
194C3×Dic3—33no—
195C3×Dic3—31no—
196C3×Dic3—31no—
197C3×Dic3—63no—
198C3×Dic3—61no—
199C3×Dic3—91no—
200C3×Dic3—91no—
201C3×Dic3—91no—
202C3×Dic3—91no—
203C3×Dic3—91no—
204C3×Dic3—91no—
205C3×Dic3—181no—
206C3×Dic3—181no—
207C3×Dic3—181no—
208C3×Dic3—181no—
209C3×Dic3—181no—
210C3×Dic3—182no—
211C3×Dic3—273no—
212C33—21no—
213C33—21no—
214C33—23no—
215C33—21no—
216C33—21no—
217C33—23no—
218C33—21no—
219C33—31no—
220C33—31no—
221C33—41no—
222C33—43no—
223C33—41no—
224C33—61no—
225C33—61no—
226C33—61no—
227C33—61no—
228C33—62no—
229C33—61no—
230C33—121no—
231C33—121no—
232C33—121no—
233C33—122no—
234C33#62411yescharacteristic
235C33#62413yescomplemented
236C33C3×C4×D311yescharacteristic, complemented
237C33C3×C4×D311yescharacteristic, complemented
238C33C4×C3⋊D311yescharacteristic, complemented
239H(3,𝔽3)—23no—
240H(3,𝔽3)—23no—
241H(3,𝔽3)—23no—
242H(3,𝔽3)—43no—
243H(3,𝔽3)—43no—
244H(3,𝔽3)—46no—
245H(3,𝔽3)—43no—
246H(3,𝔽3)C3×C4×D313yescomplemented
247C2×C3×C4—811no—
248C2×Dic3—271no—
249C4×D3—271no—
250C4×D3—271no—
251C4×D3—273no—
252C2×C32—21no—
253C2×C32—21no—
254C2×C32—21no—
255C2×C32—21no—
256C2×C32—21no—
257C2×C32—23no—
258C2×C32—23no—
259C2×C32—31no—
260C2×C32—31no—
261C2×C32—33no—
262C2×C32—31no—
263C2×C32—41no—
264C2×C32—43no—
265C2×C32—41no—
266C2×C32—61no—
267C2×C32—63no—
268C2×C32—63no—
269C2×C32—61no—
270C2×C32—61no—
271C2×C32—61no—
272C2×C32—62no—
273C2×C32—62no—
274C2×C32—66no—
275C2×C32—61no—
276C2×C32—61no—
277C2×C32—61no—
278C2×C32—61no—
279C2×C32—63no—
280C2×C32—121no—
281C2×C32—121no—
282C2×C32—121no—
283C2×C32—123no—
284C2×C32—122no—
285C2×C32—123no—
286C2×C32—121no—
287C2×C32—122no—
288C2×C32—126no—
289C2×C32—121no—
290C2×C32—272no—
291C2×C32((C3⋊D3)⋊C3)⋊C211yescharacteristic
292C2×C32C3×D3211yescharacteristic
293C2×C32C3×D3213yes—
294C2×C32D3×C3⋊D311yescharacteristic
295C2×C32C2×C3×C3⋊D311yescharacteristic
296C3⋊D3—32no—
297C3⋊D3—32no—
298C3⋊D3—62no—
299C3×D3—96no—
300C3×D3—92no—
301C3×D3—92no—
302C3×D3—92no—
303C3×D3—96no—
304C3×D3—92no—
305C3×D3—182no—
306C3×D3—186no—
307C3×D3—182no—
308C3×D3—186no—
309C3×D3—182no—
310C3×D3—182no—
311C3×D3—186no—
312C3×D3—184no—
313C3×D3—1812no—
314C22×C3—271no—
315C22×C3—271no—
316C22×C3—541no—
317C2×D3—91no—
318C2×D3—93no—
319C2×D3—91no—
320C2×D3—181no—
321C2×D3—183no—
322C3×C4—93no—
323C3×C4—91no—
324C3×C4—91no—
325C3×C4—181no—
326C3×C4—183no—
327C3×C4—271no—
328C3×C4—271no—
329C3×C4—541no—
330Dic3—31no—
331Dic3—91no—
332Dic3—91no—
333Dic3—91no—
334Dic3—181no—
335Dic3—273no—
336C32—21no—
337C32—21no—
338C32—21no—
339C32—21no—
340C32—23no—
341C32—21no—
342C32—23no—
343C32—31no—
344C32—31no—
345C32—33no—
346C32—31no—
347C32—41no—
348C32—43no—
349C32—41no—
350C32—61no—
351C32—63no—
352C32—61no—
353C32—61no—
354C32—63no—
355C32—61no—
356C32—62no—
357C32—66no—
358C32—62no—
359C32—61no—
360C32—61no—
361C32—61no—
362C32—61no—
363C32—63no—
364C32—121no—
365C32—121no—
366C32—121no—
367C32—123no—
368C32—122no—
369C32—123no—
370C32—121no—
371C32—122no—
372C32—126no—
373C32—121no—
374C32#619911yescharacteristic, complemented
375C32C3×#62411yescharacteristic
376C32C3×#62413yescomplemented
377C32#628911yescharacteristic
378C32C3×C4×C3⋊D311yescharacteristic, complemented
379C2×C4—811noSylow
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—21no—
383C2×C3—31no—
384C2×C3—33no—
385C2×C3—41no—
386C2×C3—63no—
387C2×C3—61no—
388C2×C3—61no—
389C2×C3—63no—
390C2×C3—121no—
391C2×C3—123no—
392C2×C3—272no—
393C2×C3—272no—
394C2×C3—542no—
395C2×C3C3×((C3⋊D3)⋊C3)⋊C211yescharacteristic
396C2×C3((C3⋊D3)⋊C3)⋊D311yescharacteristic
397C2×C3C3×D3×C3⋊D311yescharacteristic
398D3—96no—
399D3—92no—
400D3—92no—
401D3—182no—
402D3—186no—
403C22—271no—
404C4—91no—
405C4—271no—
406C3—21no—
407C3—21no—
408C3—21no—
409C3—33no—
410C3—31no—
411C3—41no—
412C3—61no—
413C3—63no—
414C3—63no—
415C3—61no—
416C3—121no—
417C3—123no—
418C3C3×#619911yescharacteristic, complemented
419C3#1061988511yescharacteristic, direct product factor
420C3C3×#628911yescharacteristic
421C2—272no—
422C2C3×((C3⋊D3)⋊C3)⋊D311yescharacteristic
subgroupG/H
center, hypercenterC2×C3((C3⋊D3)⋊C3)⋊D3
commutator, hypocenterC3×H(3,𝔽3)C2×C3×C4
FrattiniC2×C3C3×D3×C3⋊D3
FittingC2×C32×H(3,𝔽3)C22
socleC2×C33D32
prime radicalC2×C3×C3⋊#272C2
cosocleC2×C3×H(3,𝔽3)C22×C3
LCSG ▷ C3×H(3,𝔽3)
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
2. C3×C3⋊((C3⋊Dic3)⋊C3)C2semidirect
3. C32×(C3⋊Dic3)⋊C3C2semidirect
6. #10619885C3direct (N × H)
9. C3×C3⋊#272C4semidirect
13. C3×C3⋊(C3⋊Dic3)D3semidirect
15. C32×C3⋊Dic3D3semidirect
21. C3⋊((C3⋊Dic3)⋊C3)C2×C3semidirect
25. C3×(C3⋊Dic3)⋊C3D3semidirect
26. C3×(C3⋊Dic3)⋊C3C2×C3semidirect
27. C32×H(3,𝔽3)C2×C4semidirect
50. C3⋊#272C3×C4semidirect
68. C3⋊(C3⋊Dic3)C3×D3semidirect
76. C3×C3⋊Dic3C3×D3semidirect
77. C3×C3⋊Dic3C3⋊D3semidirect
92. (C3⋊Dic3)⋊C3C3×D3semidirect
94. C34C4×D3semidirect
95. C34C4×D3semidirect
102. C3×H(3,𝔽3)C4×D3semidirect
103. C3×H(3,𝔽3)C2×C3×C4semidirect
193. C3⋊Dic3C3×C3⋊D3semidirect
235. C33#624semidirect
236. C33C3×C4×D3semidirect
237. C33C3×C4×D3semidirect
238. C33C4×C3⋊D3semidirect
246. H(3,𝔽3)C3×C4×D3semidirect
374. C32#6199semidirect
376. C32C3×#624semidirect
378. C32C3×C4×C3⋊D3semidirect
418. C3C3×#6199semidirect
419. C3#10619885direct (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
C3×C3⋊((C3⋊Dic3)⋊C3)2
C32×(C3⋊Dic3)⋊C32
C3×#62943
C3×Dic3×C3⋊D33
#106198853
C3×#61993