Finite Group Databasebeta

← #14518795

Subgroups — #14518795

Order 1944.

943 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 943 conjugacy classes of subgroups — too many to draw. Only its 106 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⋊#1084)C211yesmaximal, characteristic, complemented
3C3×C3⋊((C3⋊Dic3)⋊C3)C211yesmaximal, characteristic, complemented
4#10620155—31nomaximal
5#10620154—31nomaximal
6#10619883—33nomaximal
7((C3⋊D3)⋊C3)⋊Dic3—33nomaximal
8C2×C32×H(3,𝔽3)C2211yescharacteristic
9C3×C3⋊((C3⋊D3)⋊C3)C412yescomplemented
10C2×C3×C3⋊(C3⋊D3)D311yescharacteristic
11C2×C32×C3⋊D3—31no—
12C3×C3⋊(C3⋊Dic3)—31no—
13C3×C3⋊(C3⋊Dic3)—31no—
14C3×C3⋊(C3⋊Dic3)—61no—
15C3×C3⋊(C3⋊Dic3)D311yescharacteristic, complemented
16C32×C3⋊Dic3—31no—
17C2×C3⋊((C3⋊D3)⋊C3)D313yes—
18C2×C3×(C3⋊D3)⋊C3—33no—
19C3⋊#1084—33no—
20C3⋊#1084—33no—
21C3⋊#1084—69no—
22C3⋊#1084—63no—
23C3⋊#1084—63no—
24C3⋊((C3⋊Dic3)⋊C3)D313yescomplemented
25C3×(C3⋊Dic3)⋊C3—33no—
26C32×H(3,𝔽3)C2×C411yescharacteristic, complemented, Sylow
27#6294—93no—
28#6294—93no—
29#6294—91no—
30#6289—91no—
31Dic3×C3⋊D3—91no—
32D3×C3⋊Dic3—91no—
33D3×C3⋊Dic3—91no—
34((C3⋊D3)⋊C3)⋊C4—99no—
35C2×C34—21no—
36C2×C34C2×D311yescharacteristic
37C2×C34C2×D311yescharacteristic
38C3×C3⋊(C3⋊D3)Dic312yescomplemented
39C32×C3⋊D3—32no—
40C2×C3×H(3,𝔽3)—23no—
41C2×C3×H(3,𝔽3)—23no—
42C2×C3×H(3,𝔽3)—29no—
43C2×C3×H(3,𝔽3)C2×D313yes—
44C2×C3×H(3,𝔽3)C2×D313yes—
45C3⋊((C3⋊D3)⋊C3)Dic316yescomplemented
46C3×(C3⋊D3)⋊C3—36no—
47C2×C3⋊(C3⋊D3)C3⋊D311yescharacteristic
48C2×C3×C3⋊D3—33no—
49C2×C3×C3⋊D3—31no—
50C2×C3×C3⋊D3—33no—
51C2×C3×C3⋊D3—91no—
52C2×C3×C3⋊D3—181no—
53C2×C32×D3—91no—
54C2×C32×D3—91no—
55C2×C32×D3—181no—
56C3⋊(C3⋊Dic3)—31no—
57C3⋊(C3⋊Dic3)—31no—
58C3⋊(C3⋊Dic3)—61no—
59C3⋊(C3⋊Dic3)C3⋊D311yescharacteristic, complemented
60C3×C3⋊Dic3—33no—
61C3×C3⋊Dic3—31no—
62C3×C3⋊Dic3—33no—
63C3×C3⋊Dic3—91no—
64C3×C3⋊Dic3—93no—
65C3×C3⋊Dic3—93no—
66C3×C3⋊Dic3—91no—
67C3×C3⋊Dic3—91no—
68C3×C3⋊Dic3—91no—
69C3×C3⋊Dic3—183no—
70C3×C3⋊Dic3—183no—
71C3×C3⋊Dic3—183no—
72C3×C3⋊Dic3—183no—
73C3×C3⋊Dic3—181no—
74C3×C3⋊Dic3—181no—
75C3×C3⋊Dic3—186no—
76C3×C3⋊Dic3—181no—
77C32×Dic3—91no—
78C32×Dic3—91no—
79C32×Dic3—181no—
80C2×(C3⋊D3)⋊C3—39no—
81#1084—99no—
82#1084—189no—
83#1084—189no—
84#1084—1818no—
85(C3⋊Dic3)⋊C3—39no—
86C34—21no—
87C34C4×D311yescharacteristic, complemented
88C34C2×Dic311yescharacteristic, complemented
89C3×H(3,𝔽3)—23no—
90C3×H(3,𝔽3)—23no—
91C3×H(3,𝔽3)—29no—
92C3×H(3,𝔽3)C4×D313yescomplemented
93C3×H(3,𝔽3)C2×Dic313yescomplemented
94C2×C3⋊Dic3—271no—
95C4×C3⋊D3—271no—
96#624—273no—
97#624—271no—
98D3×Dic3—271no—
99D3×Dic3—273no—
100D3×Dic3—273no—
101D3×Dic3—271no—
102D3×Dic3—273no—
103C2×C33—26no—
104C2×C33—23no—
105C2×C33—23no—
106C2×C33—21no—
107C2×C33—21no—
108C2×C33—23no—
109C2×C33—23no—
110C2×C33—31no—
111C2×C33—31no—
112C2×C33—61no—
113C2×C33—61no—
114C2×C33—61no—
115C2×C33—61no—
116C2×C33—61no—
117C2×C33—121no—
118C2×C33—121no—
119C2×C33—121no—
120C2×C33—121no—
121C2×C33—122no—
122C2×C33D3211yescharacteristic
123C2×C33D3213yes—
124C2×C33D3213yes—
125C2×C33C2×C3⋊D311yescharacteristic
126C2×C33C2×C3⋊D311yescharacteristic
127C3⋊(C3⋊D3)C3⋊Dic312yescomplemented
128C3×C3⋊D3—32no—
129C3×C3⋊D3—36no—
130C3×C3⋊D3—36no—
131C3×C3⋊D3—92no—
132C3×C3⋊D3—182no—
133C32×D3—92no—
134C32×D3—92no—
135C32×D3—182no—
136C2×H(3,𝔽3)—218no—
137C2×H(3,𝔽3)—29no—
138C2×H(3,𝔽3)—29no—
139C2×H(3,𝔽3)D3219yes—
140(C3⋊D3)⋊C3—318no—
141C22×C32—271no—
142C2×C3⋊D3—31no—
143C2×C3⋊D3—33no—
144C2×C3⋊D3—91no—
145C2×C3⋊D3—181no—
146C2×C3×D3—93no—
147C2×C3×D3—91no—
148C2×C3×D3—93no—
149C2×C3×D3—91no—
150C2×C3×D3—181no—
151C2×C3×D3—183no—
152C2×C3×D3—273no—
153C32×C4—271no—
154C3⋊Dic3—31no—
155C3⋊Dic3—33no—
156C3⋊Dic3—91no—
157C3⋊Dic3—91no—
158C3⋊Dic3—91no—
159C3⋊Dic3—93no—
160C3⋊Dic3—93no—
161C3⋊Dic3—91no—
162C3⋊Dic3—181no—
163C3⋊Dic3—183no—
164C3⋊Dic3—183no—
165C3⋊Dic3—181no—
166C3⋊Dic3—181no—
167C3⋊Dic3—183no—
168C3⋊Dic3—183no—
169C3⋊Dic3—186no—
170C3×Dic3—93no—
171C3×Dic3—91no—
172C3×Dic3—93no—
173C3×Dic3—91no—
174C3×Dic3—181no—
175C3×Dic3—183no—
176C3×Dic3—273no—
177C3×Dic3—273no—
178C3×Dic3—273no—
179C3×Dic3—271no—
180C3×Dic3—271no—
181C3×Dic3—549no—
182C3×Dic3—543no—
183C3×Dic3—543no—
184C3×Dic3—541no—
185C33—26no—
186C33—21no—
187C33—23no—
188C33—23no—
189C33—21no—
190C33—23no—
191C33—23no—
192C33—31no—
193C33—31no—
194C33—61no—
195C33—61no—
196C33—61no—
197C33—61no—
198C33—61no—
199C33—121no—
200C33—121no—
201C33—121no—
202C33—121no—
203C33—122no—
204C33D3×Dic311yescharacteristic
205C33D3×Dic313yescomplemented
206C33D3×Dic313yescomplemented
207C33C4×C3⋊D311yescharacteristic, complemented
208C33C2×C3⋊Dic311yescharacteristic, complemented
209H(3,𝔽3)—218no—
210H(3,𝔽3)—29no—
211H(3,𝔽3)—29no—
212H(3,𝔽3)D3×Dic319yescomplemented
213C2×Dic3—811no—
214C2×Dic3—813no—
215C4×D3—811no—
216C4×D3—811no—
217C4×D3—813no—
218C2×C32—21no—
219C2×C32—21no—
220C2×C32—21no—
221C2×C32—23no—
222C2×C32—23no—
223C2×C32—29no—
224C2×C32—31no—
225C2×C32—31no—
226C2×C32—33no—
227C2×C32—33no—
228C2×C32—41no—
229C2×C32—61no—
230C2×C32—61no—
231C2×C32—63no—
232C2×C32—63no—
233C2×C32—63no—
234C2×C32—63no—
235C2×C32—66no—
236C2×C32—61no—
237C2×C32—61no—
238C2×C32—63no—
239C2×C32—63no—
240C2×C32—121no—
241C2×C32—121no—
242C2×C32—123no—
243C2×C32—123no—
244C2×C32—123no—
245C2×C32—123no—
246C2×C32—126no—
247C2×C32—272no—
248C2×C32((C3⋊D3)⋊C3)⋊C211yescharacteristic
249C2×C32D3×C3⋊D311yescharacteristic
250C2×C32D3×C3⋊D311yescharacteristic
251C2×C32D3×C3⋊D313yes—
252C2×C32D3×C3⋊D313yes—
253C3⋊D3—32no—
254C3⋊D3—36no—
255C3⋊D3—92no—
256C3⋊D3—182no—
257C3×D3—96no—
258C3×D3—92no—
259C3×D3—92no—
260C3×D3—96no—
261C3×D3—182no—
262C3×D3—186no—
263C3×D3—276no—
264C22×C3—273no—
265C22×C3—271no—
266C2×D3—91no—
267C2×D3—91no—
268C2×D3—181no—
269C2×D3—273no—
270C3×C4—273no—
271C3×C4—271no—
272C3×C4—811no—
273Dic3—91no—
274Dic3—91no—
275Dic3—181no—
276Dic3—273no—
277Dic3—273no—
278Dic3—273no—
279Dic3—271no—
280Dic3—271no—
281Dic3—541no—
282Dic3—543no—
283Dic3—543no—
284Dic3—549no—
285C32—21no—
286C32—21no—
287C32—21no—
288C32—23no—
289C32—23no—
290C32—29no—
291C32—31no—
292C32—31no—
293C32—33no—
294C32—33no—
295C32—41no—
296C32—61no—
297C32—61no—
298C32—63no—
299C32—63no—
300C32—63no—
301C32—63no—
302C32—66no—
303C32—61no—
304C32—63no—
305C32—61no—
306C32—63no—
307C32—121no—
308C32—121no—
309C32—123no—
310C32—123no—
311C32—123no—
312C32—123no—
313C32—126no—
314C32((C3⋊D3)⋊C3)⋊C411yescharacteristic, complemented
315C32D3×C3⋊Dic311yescharacteristic
316C32D3×C3⋊Dic313yescomplemented
317C32Dic3×C3⋊D311yescharacteristic
318C32Dic3×C3⋊D313yescomplemented
319C2×C4—2431noSylow
320C2×C3—21no—
321C2×C3—21no—
322C2×C3—21no—
323C2×C3—33no—
324C2×C3—33no—
325C2×C3—41no—
326C2×C3—63no—
327C2×C3—63no—
328C2×C3—69no—
329C2×C3—276no—
330C2×C3—272no—
331C2×C3((C3⋊D3)⋊C3)⋊D311yescharacteristic
332C2×C3((C3⋊D3)⋊C3)⋊D311yescharacteristic
333C2×C3C3⋊D3211yescharacteristic
334D3—92no—
335D3—92no—
336D3—182no—
337D3—276no—
338C22—271no—
339C4—271no—
340C4—811no—
341C3—21no—
342C3—21no—
343C3—21no—
344C3—33no—
345C3—33no—
346C3—41no—
347C3—63no—
348C3—63no—
349C3—69no—
350C3((C3⋊D3)⋊C3)⋊Dic311yescharacteristic, complemented
351C3#1061988311yescharacteristic, complemented
352C3C3⋊D3×C3⋊Dic311yescharacteristic
353C2—272no—
354C2#1175808411yescharacteristic
subgroupG/H
center, hypercenterC2#11758084
commutator, hypocenterC32×H(3,𝔽3)C2×C4
FrattiniC2×C3C3⋊D32
Fitting, cosocleC2×C32×H(3,𝔽3)C22
socleC2×C33D32
prime radicalC2×C3×C3⋊((C3⋊D3)⋊C3)C2
LCSG ▷ C32×H(3,𝔽3)
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C3⋊(C3⋊#1084)C2semidirect
3. C3×C3⋊((C3⋊Dic3)⋊C3)C2semidirect
9. C3×C3⋊((C3⋊D3)⋊C3)C4semidirect
15. C3×C3⋊(C3⋊Dic3)D3semidirect
24. C3⋊((C3⋊Dic3)⋊C3)D3semidirect
26. C32×H(3,𝔽3)C2×C4semidirect
38. C3×C3⋊(C3⋊D3)Dic3semidirect
45. C3⋊((C3⋊D3)⋊C3)Dic3semidirect
59. C3⋊(C3⋊Dic3)C3⋊D3semidirect
87. C34C4×D3semidirect
88. C34C2×Dic3semidirect
92. C3×H(3,𝔽3)C4×D3semidirect
93. C3×H(3,𝔽3)C2×Dic3semidirect
127. C3⋊(C3⋊D3)C3⋊Dic3semidirect
205. C33D3×Dic3semidirect
206. C33D3×Dic3semidirect
207. C33C4×C3⋊D3semidirect
208. C33C2×C3⋊Dic3semidirect
212. H(3,𝔽3)D3×Dic3semidirect
314. C32((C3⋊D3)⋊C3)⋊C4semidirect
316. C32D3×C3⋊Dic3semidirect
318. C32Dic3×C3⋊D3semidirect
350. C3((C3⋊D3)⋊C3)⋊Dic3semidirect
351. C3#10619883semidirect

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⋊#1084)2
C3×C3⋊((C3⋊Dic3)⋊C3)2
#106201553
#106201543
#106198833
((C3⋊D3)⋊C3)⋊Dic33