Finite Group Databasebeta

← C3×#10619883 #14518671

Subgroups — C3×#10619883 #14518671

Order 1944.

727 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 727 conjugacy classes of subgroups — too many to draw. Only its 84 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
2C3×C3⋊#1084C211yesmaximal, characteristic, complemented
3C32×(C3⋊Dic3)⋊C3C211yesmaximal, characteristic, complemented
4C3×#6294—31nomaximal
5C3×#6289—31nomaximal
6#10619883C311yesmaximal, characteristic, direct product factor
7C3×((C3⋊D3)⋊C3)⋊C4—33nomaximal
8C2×C32×H(3,𝔽3)C2211yescharacteristic
9C3×C3⋊((C3⋊D3)⋊C3)C412yescomplemented
10C2×C3×C3⋊(C3⋊D3)D311yescharacteristic
11C2×C32×C3⋊D3—31no—
12C32×C3⋊Dic3—31no—
13C32×C3⋊Dic3—31no—
14C32×C3⋊Dic3—61no—
15C32×C3⋊Dic3D311yescharacteristic, complemented
16C33×Dic3—31no—
17C2×C3⋊((C3⋊D3)⋊C3)—21no—
18C2×C3⋊((C3⋊D3)⋊C3)C2×C311yescharacteristic
19C2×C3×(C3⋊D3)⋊C3—33no—
20C3⋊#1084C2×C311yescharacteristic, complemented
21C3×#1084—33no—
22C3×#1084—63no—
23C3×(C3⋊Dic3)⋊C3—21no—
24C3×(C3⋊Dic3)⋊C3—23no—
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—
30#6289—31no—
31C3×#624—93no—
32C3×#624—91no—
33C3×D3×Dic3—91no—
34C3×D3×Dic3—91no—
35((C3⋊D3)⋊C3)⋊C4—33no—
36C2×C34—21no—
37C2×C34C2×D311yescharacteristic
38C2×C34C2×D311yescharacteristic
39C3×C3⋊(C3⋊D3)Dic312yescomplemented
40C32×C3⋊D3—32no—
41C2×C3×H(3,𝔽3)—21no—
42C2×C3×H(3,𝔽3)—21no—
43C2×C3×H(3,𝔽3)—23no—
44C2×C3×H(3,𝔽3)—23no—
45C2×C3×H(3,𝔽3)—43no—
46C2×C3×H(3,𝔽3)—41no—
47C2×C3×H(3,𝔽3)C2×D313yes—
48C2×C3×H(3,𝔽3)C22×C311yescharacteristic
49C3⋊((C3⋊D3)⋊C3)—22no—
50C3⋊((C3⋊D3)⋊C3)C3×C412yescomplemented
51C3×(C3⋊D3)⋊C3—36no—
52C2×C3⋊(C3⋊D3)C3×D311yescharacteristic
53C2×C3×C3⋊D3—31no—
54C2×C3×C3⋊D3—33no—
55C2×C3×C3⋊D3—31no—
56C2×C3×C3⋊D3—61no—
57C2×C3×C3⋊D3—91no—
58C2×C3×C3⋊D3—181no—
59C2×C32×D3—91no—
60C2×C32×D3—91no—
61C2×C32×D3—181no—
62C33×C4—91no—
63C3×C3⋊Dic3—21no—
64C3×C3⋊Dic3—31no—
65C3×C3⋊Dic3—31no—
66C3×C3⋊Dic3—31no—
67C3×C3⋊Dic3—31no—
68C3×C3⋊Dic3—61no—
69C3×C3⋊Dic3—61no—
70C3×C3⋊Dic3—61no—
71C3×C3⋊Dic3—61no—
72C3×C3⋊Dic3—62no—
73C3×C3⋊Dic3C3×D311yescharacteristic, complemented
74C3×C3⋊Dic3C3⋊D311yescharacteristic, complemented
75C32×Dic3—33no—
76C32×Dic3—31no—
77C32×Dic3—31no—
78C32×Dic3—63no—
79C32×Dic3—61no—
80C32×Dic3—91no—
81C32×Dic3—93no—
82C32×Dic3—91no—
83C32×Dic3—91no—
84C32×Dic3—183no—
85C32×Dic3—181no—
86C2×(C3⋊D3)⋊C3—33no—
87C2×(C3⋊D3)⋊C3—63no—
88#1084—33no—
89#1084—63no—
90(C3⋊Dic3)⋊C3—23no—
91(C3⋊Dic3)⋊C3C3×D313yescomplemented
92C34—21no—
93C34C4×D311yescharacteristic, complemented
94C34C2×Dic311yescharacteristic, complemented
95C3×H(3,𝔽3)—21no—
96C3×H(3,𝔽3)—21no—
97C3×H(3,𝔽3)—23no—
98C3×H(3,𝔽3)—23no—
99C3×H(3,𝔽3)—43no—
100C3×H(3,𝔽3)—41no—
101C3×H(3,𝔽3)C4×D313yescomplemented
102C3×H(3,𝔽3)C2×C3×C411yescharacteristic, complemented
103C4×C3⋊D3—91no—
104C2×C3×Dic3—271no—
105C3×C4×D3—271no—
106C3×C4×D3—271no—
107C3×C4×D3—273no—
108#624—93no—
109#624—91no—
110D3×Dic3—91no—
111D3×Dic3—91no—
112C2×C33—23no—
113C2×C33—21no—
114C2×C33—21no—
115C2×C33—21no—
116C2×C33—21no—
117C2×C33—23no—
118C2×C33—21no—
119C2×C33—31no—
120C2×C33—31no—
121C2×C33—41no—
122C2×C33—43no—
123C2×C33—41no—
124C2×C33—61no—
125C2×C33—61no—
126C2×C33—61no—
127C2×C33—61no—
128C2×C33—62no—
129C2×C33—61no—
130C2×C33—121no—
131C2×C33—121no—
132C2×C33—121no—
133C2×C33—122no—
134C2×C33D3211yescharacteristic
135C2×C33D3213yes—
136C2×C33C2×C3×D311yescharacteristic
137C2×C33C2×C3×D311yescharacteristic
138C2×C33C2×C3⋊D311yescharacteristic
139C3⋊(C3⋊D3)C3×Dic312yescomplemented
140C3×C3⋊D3—32no—
141C3×C3⋊D3—32no—
142C3×C3⋊D3—36no—
143C3×C3⋊D3—62no—
144C3×C3⋊D3—92no—
145C3×C3⋊D3—182no—
146C32×D3—92no—
147C32×D3—92no—
148C32×D3—182no—
149C2×H(3,𝔽3)—23no—
150C2×H(3,𝔽3)—23no—
151C2×H(3,𝔽3)—23no—
152C2×H(3,𝔽3)—43no—
153C2×H(3,𝔽3)—43no—
154C2×H(3,𝔽3)—46no—
155C2×H(3,𝔽3)—43no—
156C2×H(3,𝔽3)C2×C3×D313yes—
157(C3⋊D3)⋊C3—36no—
158(C3⋊D3)⋊C3—66no—
159C22×C32—271no—
160C2×C3⋊D3—31no—
161C2×C3⋊D3—33no—
162C2×C3⋊D3—91no—
163C2×C3⋊D3—181no—
164C2×C3×D3—91no—
165C2×C3×D3—91no—
166C2×C3×D3—91no—
167C2×C3×D3—91no—
168C2×C3×D3—181no—
169C2×C3×D3—181no—
170C2×C3×D3—181no—
171C2×C3×D3—181no—
172C2×C3×D3—182no—
173C2×C3×D3—273no—
174C32×C4—91no—
175C32×C4—93no—
176C32×C4—91no—
177C32×C4—183no—
178C32×C4—181no—
179C32×C4—271no—
180C3⋊Dic3—31no—
181C3⋊Dic3—31no—
182C3⋊Dic3—61no—
183C3⋊Dic3C3×C3⋊D311yescharacteristic, complemented
184C3×Dic3—33no—
185C3×Dic3—31no—
186C3×Dic3—31no—
187C3×Dic3—63no—
188C3×Dic3—61no—
189C3×Dic3—91no—
190C3×Dic3—91no—
191C3×Dic3—93no—
192C3×Dic3—91no—
193C3×Dic3—91no—
194C3×Dic3—93no—
195C3×Dic3—91no—
196C3×Dic3—91no—
197C3×Dic3—181no—
198C3×Dic3—181no—
199C3×Dic3—183no—
200C3×Dic3—181no—
201C3×Dic3—183no—
202C3×Dic3—181no—
203C3×Dic3—181no—
204C3×Dic3—183no—
205C3×Dic3—182no—
206C3×Dic3—186no—
207C33—21no—
208C33—21no—
209C33—23no—
210C33—21no—
211C33—21no—
212C33—23no—
213C33—21no—
214C33—31no—
215C33—31no—
216C33—41no—
217C33—43no—
218C33—41no—
219C33—61no—
220C33—61no—
221C33—61no—
222C33—61no—
223C33—62no—
224C33—61no—
225C33—121no—
226C33—121no—
227C33—121no—
228C33—122no—
229C33D3×Dic311yescharacteristic
230C33D3×Dic313yescomplemented
231C33C3×C4×D311yescharacteristic, complemented
232C33C2×C3×Dic311yescharacteristic, complemented
233C33C4×C3⋊D311yescharacteristic, complemented
234H(3,𝔽3)—23no—
235H(3,𝔽3)—23no—
236H(3,𝔽3)—23no—
237H(3,𝔽3)—43no—
238H(3,𝔽3)—43no—
239H(3,𝔽3)—46no—
240H(3,𝔽3)—43no—
241H(3,𝔽3)C3×C4×D313yescomplemented
242C2×C3×C4—811no—
243C2×Dic3—271no—
244C4×D3—271no—
245C4×D3—271no—
246C4×D3—273no—
247C2×C32—21no—
248C2×C32—21no—
249C2×C32—21no—
250C2×C32—21no—
251C2×C32—21no—
252C2×C32—23no—
253C2×C32—23no—
254C2×C32—31no—
255C2×C32—31no—
256C2×C32—33no—
257C2×C32—31no—
258C2×C32—41no—
259C2×C32—43no—
260C2×C32—41no—
261C2×C32—61no—
262C2×C32—63no—
263C2×C32—63no—
264C2×C32—61no—
265C2×C32—61no—
266C2×C32—61no—
267C2×C32—62no—
268C2×C32—66no—
269C2×C32—62no—
270C2×C32—61no—
271C2×C32—61no—
272C2×C32—61no—
273C2×C32—61no—
274C2×C32—63no—
275C2×C32—121no—
276C2×C32—121no—
277C2×C32—121no—
278C2×C32—123no—
279C2×C32—122no—
280C2×C32—123no—
281C2×C32—121no—
282C2×C32—122no—
283C2×C32—126no—
284C2×C32—121no—
285C2×C32—272no—
286C2×C32((C3⋊D3)⋊C3)⋊C211yescharacteristic
287C2×C32C3×D3211yescharacteristic
288C2×C32C3×D3213yes—
289C2×C32D3×C3⋊D311yescharacteristic
290C2×C32C2×C3×C3⋊D311yescharacteristic
291C3⋊D3—32no—
292C3⋊D3—36no—
293C3⋊D3—92no—
294C3⋊D3—182no—
295C3×D3—92no—
296C3×D3—92no—
297C3×D3—92no—
298C3×D3—92no—
299C3×D3—182no—
300C3×D3—182no—
301C3×D3—182no—
302C3×D3—182no—
303C3×D3—184no—
304C3×D3—276no—
305C22×C3—271no—
306C22×C3—271no—
307C22×C3—541no—
308C2×D3—91no—
309C2×D3—91no—
310C2×D3—181no—
311C2×D3—273no—
312C3×C4—93no—
313C3×C4—91no—
314C3×C4—91no—
315C3×C4—181no—
316C3×C4—183no—
317C3×C4—271no—
318C3×C4—271no—
319C3×C4—541no—
320Dic3—31no—
321Dic3—91no—
322Dic3—93no—
323Dic3—91no—
324Dic3—91no—
325Dic3—181no—
326Dic3—183no—
327C32—21no—
328C32—21no—
329C32—21no—
330C32—21no—
331C32—21no—
332C32—23no—
333C32—23no—
334C32—31no—
335C32—31no—
336C32—33no—
337C32—31no—
338C32—41no—
339C32—43no—
340C32—41no—
341C32—61no—
342C32—61no—
343C32—63no—
344C32—61no—
345C32—63no—
346C32—61no—
347C32—62no—
348C32—62no—
349C32—66no—
350C32—61no—
351C32—61no—
352C32—61no—
353C32—61no—
354C32—63no—
355C32—121no—
356C32—121no—
357C32—121no—
358C32—123no—
359C32—122no—
360C32—123no—
361C32—121no—
362C32—122no—
363C32—126no—
364C32—121no—
365C32((C3⋊D3)⋊C3)⋊C411yescharacteristic, complemented
366C32C3×D3×Dic311yescharacteristic
367C32C3×D3×Dic313yescomplemented
368C32Dic3×C3⋊D311yescharacteristic
369C32C3×C4×C3⋊D311yescharacteristic, complemented
370C2×C4—811noSylow
371C2×C3—21no—
372C2×C3—21no—
373C2×C3—21no—
374C2×C3—31no—
375C2×C3—33no—
376C2×C3—41no—
377C2×C3—61no—
378C2×C3—63no—
379C2×C3—63no—
380C2×C3—61no—
381C2×C3—121no—
382C2×C3—123no—
383C2×C3—272no—
384C2×C3—272no—
385C2×C3—542no—
386C2×C3C3×((C3⋊D3)⋊C3)⋊C211yescharacteristic
387C2×C3((C3⋊D3)⋊C3)⋊D311yescharacteristic
388C2×C3C3×D3×C3⋊D311yescharacteristic
389D3—92no—
390D3—92no—
391D3—182no—
392D3—276no—
393C22—271no—
394C4—91no—
395C4—271no—
396C3—21no—
397C3—21no—
398C3—21no—
399C3—33no—
400C3—31no—
401C3—41no—
402C3—61no—
403C3—61no—
404C3—63no—
405C3—63no—
406C3—121no—
407C3—123no—
408C3C3×((C3⋊D3)⋊C3)⋊C411yescharacteristic, complemented
409C3#1061988311yescharacteristic, direct product factor
410C3C3×Dic3×C3⋊D311yescharacteristic
411C2—272no—
412C2C3×((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⋊((C3⋊D3)⋊C3)C2
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⋊#1084C2semidirect
3. C32×(C3⋊Dic3)⋊C3C2semidirect
6. #10619883C3direct (N × H)
9. C3×C3⋊((C3⋊D3)⋊C3)C4semidirect
15. C32×C3⋊Dic3D3semidirect
20. C3⋊#1084C2×C3semidirect
25. C3×(C3⋊Dic3)⋊C3D3semidirect
26. C3×(C3⋊Dic3)⋊C3C2×C3semidirect
27. C32×H(3,𝔽3)C2×C4semidirect
39. C3×C3⋊(C3⋊D3)Dic3semidirect
50. C3⋊((C3⋊D3)⋊C3)C3×C4semidirect
73. C3×C3⋊Dic3C3×D3semidirect
74. C3×C3⋊Dic3C3⋊D3semidirect
91. (C3⋊Dic3)⋊C3C3×D3semidirect
93. C34C4×D3semidirect
94. C34C2×Dic3semidirect
101. C3×H(3,𝔽3)C4×D3semidirect
102. C3×H(3,𝔽3)C2×C3×C4semidirect
139. C3⋊(C3⋊D3)C3×Dic3semidirect
183. C3⋊Dic3C3×C3⋊D3semidirect
230. C33D3×Dic3semidirect
231. C33C3×C4×D3semidirect
232. C33C2×C3×Dic3semidirect
233. C33C4×C3⋊D3semidirect
241. H(3,𝔽3)C3×C4×D3semidirect
365. C32((C3⋊D3)⋊C3)⋊C4semidirect
367. C32C3×D3×Dic3semidirect
369. C32C3×C4×C3⋊D3semidirect
408. C3C3×((C3⋊D3)⋊C3)⋊C4semidirect
409. C3#10619883direct (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
C3×C3⋊#10842
C32×(C3⋊Dic3)⋊C32
C3×#62943
C3×#62893
#106198833
C3×((C3⋊D3)⋊C3)⋊C43