Finite Group Databasebeta

← #14518673

Subgroups — #14518673

Order 1944.

899 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 899 conjugacy classes of subgroups — too many to draw. Only its 92 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⋊((C3⋊Dic3)⋊C3)C211yesmaximal, characteristic, complemented
3C3×Dic3×H(3,𝔽3)C211yesmaximal, characteristic, complemented
4#10620144C311yesmaximal, characteristic, complemented
5C3×#6289—31nomaximal
6C4×C3⋊((C3⋊D3)⋊C3)—31nomaximal
7#6289⋊C3—33nomaximal
8C2×C32×H(3,𝔽3)C2211yescharacteristic
9C3⋊(C3⋊((C3⋊D3)⋊C3))C412yescomplemented
10C2×C3⋊(C3⋊(C3⋊D3))C2×C311yescharacteristic
11C2×C3×C3⋊(C3⋊D3)—31no—
12C3×C3⋊(C3⋊Dic3)C2×C311yescharacteristic, complemented
13C32×C3⋊Dic3—31no—
14C33×Dic3—21no—
15C33×Dic3D311yescharacteristic, complemented
16C33×Dic3C2×C311yescharacteristic, complemented
17C2×C3⋊((C3⋊D3)⋊C3)—31no—
18C2×C3⋊((C3⋊D3)⋊C3)—33no—
19C2×C3⋊((C3⋊D3)⋊C3)—63no—
20C2×C3⋊((C3⋊D3)⋊C3)—61no—
21C3×C4×H(3,𝔽3)—31no—
22C3⋊((C3⋊Dic3)⋊C3)—21no—
23C3⋊((C3⋊Dic3)⋊C3)D311yescharacteristic, complemented
24Dic3×H(3,𝔽3)—23no—
25Dic3×H(3,𝔽3)D313yescomplemented
26C3×(C3⋊Dic3)⋊C3—33no—
27C32×H(3,𝔽3)C2×C411yescharacteristic, complemented, Sylow
28C4×C3⋊(C3⋊D3)—31no—
29C3×C4×C3⋊D3—91no—
30#6289—31no—
31#6289—33no—
32#6289—93no—
33C3×#624—93no—
34C3×#624—91no—
35C4×(C3⋊D3)⋊C3—93no—
36C2×C34—21no—
37C2×C34C2×D311yescharacteristic
38C2×C34C22×C311yescharacteristic
39C3⋊(C3⋊(C3⋊D3))C3×C412yescomplemented
40C3×C3⋊(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×D311yescharacteristic
48C2×C3×H(3,𝔽3)C2×D313yes—
49C3⋊((C3⋊D3)⋊C3)—32no—
50C3⋊((C3⋊D3)⋊C3)—36no—
51C3⋊((C3⋊D3)⋊C3)—66no—
52C3⋊((C3⋊D3)⋊C3)—62no—
53C2×C3⋊(C3⋊D3)—31no—
54C2×C3⋊(C3⋊D3)—31no—
55C2×C3⋊(C3⋊D3)—33no—
56C2×C3⋊(C3⋊D3)—61no—
57C2×C3⋊(C3⋊D3)—63no—
58C2×C3⋊(C3⋊D3)—93no—
59C2×C3⋊(C3⋊D3)—183no—
60C2×C3×C3⋊D3—93no—
61C2×C3×C3⋊D3—91no—
62C2×C3×C3⋊D3—91no—
63C2×C3×C3⋊D3—181no—
64C2×C3×C3⋊D3—183no—
65C33×C4—31no—
66C33×C4—31no—
67C33×C4—61no—
68C3⋊(C3⋊Dic3)C3×D311yescharacteristic, complemented
69C3×C3⋊Dic3—31no—
70C3×C3⋊Dic3—31no—
71C3×C3⋊Dic3—33no—
72C3×C3⋊Dic3—61no—
73C3×C3⋊Dic3—93no—
74C32×Dic3—21no—
75C32×Dic3—23no—
76C32×Dic3—33no—
77C32×Dic3—33no—
78C32×Dic3—63no—
79C32×Dic3—93no—
80C32×Dic3—91no—
81C32×Dic3C3×D311yescharacteristic
82C32×Dic3C3×D313yescomplemented
83C32×Dic3C3⋊D311yescharacteristic, complemented
84C2×(C3⋊D3)⋊C3—93no—
85C2×(C3⋊D3)⋊C3—183no—
86C4×H(3,𝔽3)—33no—
87C4×H(3,𝔽3)—63no—
88(C3⋊Dic3)⋊C3—33no—
89(C3⋊Dic3)⋊C3—63no—
90C34—21no—
91C34C4×D311yescharacteristic, complemented
92C34C2×C3×C411yescharacteristic, complemented
93C3×H(3,𝔽3)—21no—
94C3×H(3,𝔽3)—21no—
95C3×H(3,𝔽3)—23no—
96C3×H(3,𝔽3)—23no—
97C3×H(3,𝔽3)—43no—
98C3×H(3,𝔽3)—41no—
99C3×H(3,𝔽3)C4×D311yescharacteristic, complemented
100C3×H(3,𝔽3)C4×D313yescomplemented
101C4×C3⋊D3—91no—
102C4×C3⋊D3—93no—
103C4×C3⋊D3—273no—
104C3×C4×D3—271no—
105C3×C4×D3—271no—
106C3×C4×D3—273no—
107#624—93no—
108#624—91no—
109#624—273no—
110C2×C33—21no—
111C2×C33—23no—
112C2×C33—21no—
113C2×C33—21no—
114C2×C33—21no—
115C2×C33—21no—
116C2×C33—23no—
117C2×C33—33no—
118C2×C33—33no—
119C2×C33—41no—
120C2×C33—43no—
121C2×C33—41no—
122C2×C33—63no—
123C2×C33—63no—
124C2×C33—63no—
125C2×C33—123no—
126C2×C33D3211yescharacteristic
127C2×C33C2×C3×D311yescharacteristic
128C2×C33C2×C3×D313yes—
129C2×C33C2×C3×D311yescharacteristic
130C2×C33C2×C3⋊D311yescharacteristic
131C3⋊(C3⋊D3)—32no—
132C3⋊(C3⋊D3)—32no—
133C3⋊(C3⋊D3)—36no—
134C3⋊(C3⋊D3)—62no—
135C3⋊(C3⋊D3)—66no—
136C3⋊(C3⋊D3)—96no—
137C3⋊(C3⋊D3)—186no—
138C3×C3⋊D3—92no—
139C3×C3⋊D3—96no—
140C3×C3⋊D3—92no—
141C3×C3⋊D3—182no—
142C3×C3⋊D3—186no—
143C2×H(3,𝔽3)—23no—
144C2×H(3,𝔽3)—23no—
145C2×H(3,𝔽3)—23no—
146C2×H(3,𝔽3)—43no—
147C2×H(3,𝔽3)—43no—
148C2×H(3,𝔽3)—46no—
149C2×H(3,𝔽3)—43no—
150C2×H(3,𝔽3)D3213yes—
151(C3⋊D3)⋊C3—96no—
152(C3⋊D3)⋊C3—186no—
153C2×C3⋊D3—91no—
154C2×C3⋊D3—93no—
155C2×C3⋊D3—91no—
156C2×C3⋊D3—93no—
157C2×C3⋊D3—181no—
158C2×C3⋊D3—183no—
159C2×C3⋊D3—183no—
160C2×C3⋊D3—273no—
161C2×C3⋊D3—273no—
162C2×C3⋊D3—543no—
163C2×C3⋊D3—549no—
164C2×C3⋊D3—543no—
165C2×C3×D3—271no—
166C2×C3×D3—273no—
167C2×C3×D3—271no—
168C2×C3×D3—541no—
169C2×C3×D3—543no—
170C32×C4—31no—
171C32×C4—33no—
172C32×C4—31no—
173C32×C4—63no—
174C32×C4—61no—
175C32×C4—93no—
176C32×C4—93no—
177C32×C4—183no—
178C32×C4—271no—
179C3⋊Dic3—31no—
180C3⋊Dic3—33no—
181C3⋊Dic3—93no—
182C3×Dic3—33no—
183C3×Dic3—31no—
184C3×Dic3—61no—
185C3×Dic3—63no—
186C3×Dic3—93no—
187C3×Dic3—93no—
188C3×Dic3—91no—
189C3×Dic3—91no—
190C3×Dic3—181no—
191C3×Dic3—183no—
192C3×Dic3—273no—
193C3×Dic3(C3⋊D3)⋊C313yescomplemented
194C3×Dic3C3×C3⋊D311yescharacteristic
195C33—21no—
196C33—21no—
197C33—23no—
198C33—21no—
199C33—21no—
200C33—21no—
201C33—23no—
202C33—33no—
203C33—33no—
204C33—41no—
205C33—43no—
206C33—41no—
207C33—63no—
208C33—63no—
209C33—63no—
210C33—123no—
211C33#62411yescharacteristic, complemented
212C33C3×C4×D311yescharacteristic
213C33C3×C4×D313yescomplemented
214C33C3×C4×D311yescharacteristic, complemented
215C33C4×C3⋊D311yescharacteristic, complemented
216H(3,𝔽3)—23no—
217H(3,𝔽3)—23no—
218H(3,𝔽3)—23no—
219H(3,𝔽3)—43no—
220H(3,𝔽3)—43no—
221H(3,𝔽3)—46no—
222H(3,𝔽3)—43no—
223H(3,𝔽3)#62413yescomplemented
224C2×C3×C4—811no—
225C4×D3—271no—
226C4×D3—273no—
227C4×D3—271no—
228C4×D3—813no—
229C2×C32—23no—
230C2×C32—21no—
231C2×C32—21no—
232C2×C32—21no—
233C2×C32—23no—
234C2×C32—23no—
235C2×C32—33no—
236C2×C32—33no—
237C2×C32—33no—
238C2×C32—31no—
239C2×C32—43no—
240C2×C32—41no—
241C2×C32—69no—
242C2×C32—63no—
243C2×C32—61no—
244C2×C32—63no—
245C2×C32—63no—
246C2×C32—63no—
247C2×C32—63no—
248C2×C32—61no—
249C2×C32—63no—
250C2×C32—123no—
251C2×C32—129no—
252C2×C32—121no—
253C2×C32—123no—
254C2×C32—123no—
255C2×C32C2×(C3⋊D3)⋊C313yes—
256C2×C32C3×D3213yes—
257C2×C32C3×D3211yescharacteristic
258C2×C32D3×C3⋊D311yescharacteristic
259C2×C32C2×C3×C3⋊D311yescharacteristic
260C3⋊D3—92no—
261C3⋊D3—96no—
262C3⋊D3—92no—
263C3⋊D3—96no—
264C3⋊D3—182no—
265C3⋊D3—186no—
266C3⋊D3—186no—
267C3⋊D3—276no—
268C3⋊D3—276no—
269C3⋊D3—546no—
270C3⋊D3—5418no—
271C3⋊D3—546no—
272C3×D3—272no—
273C3×D3—276no—
274C3×D3—272no—
275C3×D3—542no—
276C3×D3—546no—
277C22×C3—811no—
278C2×D3—273no—
279C2×D3—271no—
280C2×D3—271no—
281C2×D3—543no—
282C2×D3—541no—
283C2×D3—813no—
284C2×D3—1623no—
285C3×C4—33no—
286C3×C4—31no—
287C3×C4—93no—
288C3×C4—91no—
289C3×C4—181no—
290C3×C4—183no—
291C3×C4—271no—
292C3×C4—271no—
293C3×C4—541no—
294Dic3—93no—
295Dic3—91no—
296Dic3—273no—
297Dic3C3⋊((C3⋊D3)⋊C3)11yescharacteristic, complemented
298C32—23no—
299C32—21no—
300C32—23no—
301C32—21no—
302C32—21no—
303C32—23no—
304C32—33no—
305C32—31no—
306C32—33no—
307C32—33no—
308C32—43no—
309C32—41no—
310C32—61no—
311C32—63no—
312C32—69no—
313C32—63no—
314C32—63no—
315C32—63no—
316C32—61no—
317C32—63no—
318C32—63no—
319C32—123no—
320C32—121no—
321C32—123no—
322C32—129no—
323C32—123no—
324C32C4×(C3⋊D3)⋊C313yescomplemented
325C32C3×#62411yescharacteristic
326C32C3×#62413yescomplemented
327C32#628911yescharacteristic, complemented
328C32C3×C4×C3⋊D311yescharacteristic
329C2×C4—811noSylow
330C2×C3—23no—
331C2×C3—21no—
332C2×C3—33no—
333C2×C3—31no—
334C2×C3—61no—
335C2×C3—63no—
336C2×C3—61no—
337C2×C3—63no—
338C2×C3—121no—
339C2×C3—123no—
340C2×C3—812no—
341C2×C3D3×(C3⋊D3)⋊C313yes—
342C2×C3C2×C3⋊((C3⋊D3)⋊C3)11yescharacteristic
343C2×C3C3×D3×C3⋊D311yescharacteristic
344D3—272no—
345D3—276no—
346D3—272no—
347D3—546no—
348D3—542no—
349D3—816no—
350D3—1626no—
351C22—811no—
352C4—31no—
353C4—271no—
354C3—23no—
355C3—21no—
356C3—33no—
357C3—31no—
358C3—63no—
359C3—61no—
360C3—61no—
361C3—63no—
362C3—121no—
363C3—123no—
364C3#6289⋊C313yescomplemented
365C3C4×C3⋊((C3⋊D3)⋊C3)11yescharacteristic, complemented
366C3C3×#628911yescharacteristic
367C2—812no—
368C2D3×C3⋊((C3⋊D3)⋊C3)11yescharacteristic
subgroupG/H
center, hypercenterC2D3×C3⋊((C3⋊D3)⋊C3)
commutator, hypocenterC34C2×C3×C4
FrattiniC2×C3C3×D3×C3⋊D3
FittingC2×C32×H(3,𝔽3)C22
socleC2×C33C2×C3×D3
prime radicalC2×C3⋊(C3⋊((C3⋊D3)⋊C3))C2
cosocleC2×C34C22×C3
LCSG ▷ C34
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C3×C3⋊((C3⋊Dic3)⋊C3)C2semidirect
3. C3×Dic3×H(3,𝔽3)C2semidirect
4. #10620144C3semidirect
9. C3⋊(C3⋊((C3⋊D3)⋊C3))C4semidirect
12. C3×C3⋊(C3⋊Dic3)C2×C3semidirect
15. C33×Dic3D3semidirect
16. C33×Dic3C2×C3semidirect
23. C3⋊((C3⋊Dic3)⋊C3)D3semidirect
25. Dic3×H(3,𝔽3)D3semidirect
27. C32×H(3,𝔽3)C2×C4semidirect
39. C3⋊(C3⋊(C3⋊D3))C3×C4semidirect
68. C3⋊(C3⋊Dic3)C3×D3semidirect
82. C32×Dic3C3×D3semidirect
83. C32×Dic3C3⋊D3semidirect
91. C34C4×D3semidirect
92. C34C2×C3×C4semidirect
99. C3×H(3,𝔽3)C4×D3semidirect
100. C3×H(3,𝔽3)C4×D3semidirect
193. C3×Dic3(C3⋊D3)⋊C3semidirect
211. C33#624semidirect
213. C33C3×C4×D3semidirect
214. C33C3×C4×D3semidirect
215. C33C4×C3⋊D3semidirect
223. H(3,𝔽3)#624semidirect
297. Dic3C3⋊((C3⋊D3)⋊C3)semidirect
324. C32C4×(C3⋊D3)⋊C3semidirect
326. C32C3×#624semidirect
327. C32#6289semidirect
364. C3#6289⋊C3semidirect
365. C3C4×C3⋊((C3⋊D3)⋊C3)semidirect

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⋊((C3⋊Dic3)⋊C3)2
C3×Dic3×H(3,𝔽3)2
#106201443
C3×#62893
C4×C3⋊((C3⋊D3)⋊C3)3
#6289⋊C33