Finite Group Databasebeta

← #14518832

Subgroups — #14518832

Order 1944.

847 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 847 conjugacy classes of subgroups — too many to draw. Only its 87 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
3C3⋊(C3⋊((C3⋊Dic3)⋊C3))C211yesmaximal, characteristic, complemented
4#10620154—31nomaximal
5C3⋊D3×C3⋊Dic3—31nomaximal
6#10619901—33nomaximal
7((C3⋊D3)⋊C3)⋊Dic3—31nomaximal
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))D311yescharacteristic, complemented
13C3×C3⋊(C3⋊Dic3)—31no—
14C32×C3⋊Dic3—31no—
15C32×C3⋊Dic3—31no—
16C32×C3⋊Dic3—61no—
17C2×C3⋊((C3⋊D3)⋊C3)D313yes—
18C2×C3×(C3⋊D3)⋊C3—31no—
19C2×C3×(C3⋊D3)⋊C3—61no—
20C3⋊#1084D311yescharacteristic, complemented
21C3×#1084—33no—
22C3×#1084—63no—
23C3⋊((C3⋊Dic3)⋊C3)—31no—
24C3⋊((C3⋊Dic3)⋊C3)—33no—
25C3⋊((C3⋊Dic3)⋊C3)—63no—
26C3⋊((C3⋊Dic3)⋊C3)—61no—
27C32×H(3,𝔽3)C2×C411yescharacteristic, complemented, Sylow
28#6294—91no—
29#6294—93no—
30#6289—91no—
31Dic3×C3⋊D3—91no—
32Dic3×C3⋊D3—93no—
33D3×C3⋊Dic3—91no—
34D3×C3⋊Dic3—93no—
35((C3⋊D3)⋊C3)⋊C4—93no—
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×D311yescharacteristic
48C2×C3×H(3,𝔽3)C2×D313yes—
49C3⋊((C3⋊D3)⋊C3)Dic316yescomplemented
50C3×(C3⋊D3)⋊C3—32no—
51C3×(C3⋊D3)⋊C3—62no—
52C2×C3⋊(C3⋊D3)C3⋊D311yescharacteristic
53C2×C3×C3⋊D3—33no—
54C2×C3×C3⋊D3—31no—
55C2×C3×C3⋊D3—31no—
56C2×C3×C3⋊D3—61no—
57C2×C3×C3⋊D3—93no—
58C2×C32×D3—93no—
59C2×C32×D3—91no—
60C3⋊(C3⋊Dic3)—31no—
61C3⋊(C3⋊Dic3)—31no—
62C3⋊(C3⋊Dic3)—33no—
63C3⋊(C3⋊Dic3)—61no—
64C3⋊(C3⋊Dic3)—63no—
65C3⋊(C3⋊Dic3)—93no—
66C3⋊(C3⋊Dic3)—183no—
67C3×C3⋊Dic3—33no—
68C3×C3⋊Dic3—33no—
69C3×C3⋊Dic3—31no—
70C3×C3⋊Dic3—31no—
71C3×C3⋊Dic3—61no—
72C3×C3⋊Dic3—63no—
73C3×C3⋊Dic3—93no—
74C3×C3⋊Dic3—91no—
75C3×C3⋊Dic3—91no—
76C3×C3⋊Dic3—181no—
77C3×C3⋊Dic3—183no—
78C32×Dic3—93no—
79C32×Dic3—91no—
80C32×Dic3—91no—
81C32×Dic3—183no—
82C32×Dic3—181no—
83C2×(C3⋊D3)⋊C3—33no—
84C2×(C3⋊D3)⋊C3—63no—
85#1084—33no—
86#1084—63no—
87(C3⋊Dic3)⋊C3—93no—
88(C3⋊Dic3)⋊C3—183no—
89C34—21no—
90C34C4×D311yescharacteristic, complemented
91C34C2×Dic311yescharacteristic, complemented
92C3×H(3,𝔽3)—21no—
93C3×H(3,𝔽3)—21no—
94C3×H(3,𝔽3)—23no—
95C3×H(3,𝔽3)—23no—
96C3×H(3,𝔽3)—43no—
97C3×H(3,𝔽3)—41no—
98C3×H(3,𝔽3)C4×D311yescharacteristic, complemented
99C3×H(3,𝔽3)C2×Dic313yescomplemented
100C2×C3⋊Dic3—271no—
101C4×C3⋊D3—271no—
102#624—271no—
103#624—273no—
104D3×Dic3—273no—
105D3×Dic3—273no—
106D3×Dic3—271no—
107D3×Dic3—279no—
108D3×Dic3—271no—
109C2×C33—23no—
110C2×C33—21no—
111C2×C33—21no—
112C2×C33—21no—
113C2×C33—23no—
114C2×C33—21no—
115C2×C33—21no—
116C2×C33—33no—
117C2×C33—33no—
118C2×C33—41no—
119C2×C33—43no—
120C2×C33—41no—
121C2×C33—63no—
122C2×C33—63no—
123C2×C33—63no—
124C2×C33—123no—
125C2×C33D3211yescharacteristic
126C2×C33D3213yes—
127C2×C33D3211yescharacteristic
128C2×C33D3211yescharacteristic
129C2×C33C2×C3⋊D311yescharacteristic
130C3⋊(C3⋊D3)C3⋊Dic312yescomplemented
131C3×C3⋊D3—32no—
132C3×C3⋊D3—36no—
133C3×C3⋊D3—32no—
134C3×C3⋊D3—62no—
135C3×C3⋊D3—96no—
136C32×D3—96no—
137C32×D3—92no—
138C2×H(3,𝔽3)—23no—
139C2×H(3,𝔽3)—23no—
140C2×H(3,𝔽3)—23no—
141C2×H(3,𝔽3)—43no—
142C2×H(3,𝔽3)—43no—
143C2×H(3,𝔽3)—46no—
144C2×H(3,𝔽3)—43no—
145C2×H(3,𝔽3)D3213yes—
146(C3⋊D3)⋊C3—36no—
147(C3⋊D3)⋊C3—66no—
148C22×C32—271no—
149C2×C3⋊D3—31no—
150C2×C3⋊D3—31no—
151C2×C3⋊D3—61no—
152C2×C3⋊D3—93no—
153C2×C3×D3—99no—
154C2×C3×D3—93no—
155C2×C3×D3—93no—
156C2×C3×D3—91no—
157C2×C3×D3—271no—
158C2×C3×D3—541no—
159C32×C4—271no—
160C3⋊Dic3—31no—
161C3⋊Dic3—31no—
162C3⋊Dic3—61no—
163C3⋊Dic3—91no—
164C3⋊Dic3—93no—
165C3⋊Dic3—91no—
166C3⋊Dic3—93no—
167C3⋊Dic3—181no—
168C3⋊Dic3—183no—
169C3⋊Dic3—183no—
170C3⋊Dic3—271no—
171C3⋊Dic3—279no—
172C3⋊Dic3—541no—
173C3⋊Dic3—541no—
174C3⋊Dic3—549no—
175C3⋊Dic3—542no—
176C3×Dic3—99no—
177C3×Dic3—93no—
178C3×Dic3—93no—
179C3×Dic3—91no—
180C3×Dic3—93no—
181C3×Dic3—91no—
182C3×Dic3—183no—
183C3×Dic3—181no—
184C3×Dic3—183no—
185C3×Dic3—189no—
186C3×Dic3—271no—
187C3×Dic3—273no—
188C3×Dic3—271no—
189C3×Dic3—541no—
190C3×Dic3—543no—
191C33—21no—
192C33—23no—
193C33—21no—
194C33—21no—
195C33—23no—
196C33—21no—
197C33—21no—
198C33—33no—
199C33—33no—
200C33—41no—
201C33—43no—
202C33—41no—
203C33—63no—
204C33—63no—
205C33—63no—
206C33—123no—
207C33D3×Dic311yescharacteristic
208C33D3×Dic313yescomplemented
209C33D3×Dic311yescharacteristic, complemented
210C33#62411yescharacteristic, complemented
211C33C2×C3⋊Dic311yescharacteristic, complemented
212H(3,𝔽3)—23no—
213H(3,𝔽3)—23no—
214H(3,𝔽3)—23no—
215H(3,𝔽3)—43no—
216H(3,𝔽3)—43no—
217H(3,𝔽3)—46no—
218H(3,𝔽3)—43no—
219H(3,𝔽3)D3×Dic313yescomplemented
220C2×Dic3—811no—
221C2×Dic3—813no—
222C4×D3—811no—
223C4×D3—813no—
224C4×D3—811no—
225C2×C32—23no—
226C2×C32—21no—
227C2×C32—21no—
228C2×C32—21no—
229C2×C32—23no—
230C2×C32—23no—
231C2×C32—31no—
232C2×C32—39no—
233C2×C32—33no—
234C2×C32—31no—
235C2×C32—43no—
236C2×C32—41no—
237C2×C32—61no—
238C2×C32—69no—
239C2×C32—61no—
240C2×C32—63no—
241C2×C32—62no—
242C2×C32—61no—
243C2×C32—61no—
244C2×C32—63no—
245C2×C32—69no—
246C2×C32—61no—
247C2×C32—121no—
248C2×C32—123no—
249C2×C32—129no—
250C2×C32—121no—
251C2×C32—122no—
252C2×C32—121no—
253C2×C32—272no—
254C2×C32((C3⋊D3)⋊C3)⋊C213yes—
255C2×C32D3×C3⋊D311yescharacteristic
256C2×C32D3×C3⋊D311yescharacteristic
257C2×C32#111311yescharacteristic
258C2×C32#111313yes—
259C3⋊D3—32no—
260C3⋊D3—32no—
261C3⋊D3—62no—
262C3⋊D3—96no—
263C3×D3—918no—
264C3×D3—96no—
265C3×D3—92no—
266C3×D3—96no—
267C3×D3—272no—
268C3×D3—542no—
269C22×C3—273no—
270C22×C3—271no—
271C2×D3—93no—
272C2×D3—91no—
273C2×D3—271no—
274C2×D3—541no—
275C3×C4—273no—
276C3×C4—271no—
277C3×C4—811no—
278Dic3—91no—
279Dic3—93no—
280Dic3—91no—
281Dic3—181no—
282Dic3—183no—
283Dic3—273no—
284Dic3—271no—
285Dic3—271no—
286Dic3—543no—
287Dic3—541no—
288Dic3—813no—
289Dic3—1623no—
290C32—23no—
291C32—21no—
292C32—21no—
293C32—21no—
294C32—23no—
295C32—23no—
296C32—31no—
297C32—39no—
298C32—33no—
299C32—31no—
300C32—43no—
301C32—41no—
302C32—61no—
303C32—61no—
304C32—69no—
305C32—63no—
306C32—62no—
307C32—61no—
308C32—61no—
309C32—63no—
310C32—69no—
311C32—61no—
312C32—121no—
313C32—123no—
314C32—121no—
315C32—129no—
316C32—122no—
317C32—121no—
318C32((C3⋊D3)⋊C3)⋊C413yescomplemented
319C32D3×C3⋊Dic311yescharacteristic
320C32D3×C3⋊Dic311yescharacteristic, complemented
321C32#629411yescharacteristic
322C32#629413yescomplemented
323C2×C4—2431noSylow
324C2×C3—23no—
325C2×C3—21no—
326C2×C3—33no—
327C2×C3—31no—
328C2×C3—61no—
329C2×C3—63no—
330C2×C3—63no—
331C2×C3—61no—
332C2×C3—121no—
333C2×C3—123no—
334C2×C3—276no—
335C2×C3—272no—
336C2×C3((C3⋊D3)⋊C3)⋊D313yes—
337C2×C3#6643211yescharacteristic
338C2×C3C3⋊#111311yescharacteristic
339D3—96no—
340D3—92no—
341D3—272no—
342D3—542no—
343C22—271no—
344C4—271no—
345C4—811no—
346C3—23no—
347C3—21no—
348C3—31no—
349C3—33no—
350C3—61no—
351C3—63no—
352C3—61no—
353C3—63no—
354C3—121no—
355C3—123no—
356C3((C3⋊D3)⋊C3)⋊Dic313yescomplemented
357C3#1061990111yescharacteristic, complemented
358C3#1062015511yescharacteristic
359C2—272no—
360C2#1175809011yescharacteristic
subgroupG/H
center, hypercenterC2#11758090
commutator, hypocenterC32×H(3,𝔽3)C2×C4
FrattiniC2×C3C3⋊#1113
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⋊#1084C2semidirect
3. C3⋊(C3⋊((C3⋊Dic3)⋊C3))C2semidirect
9. C3×C3⋊((C3⋊D3)⋊C3)C4semidirect
12. C3⋊(C3⋊(C3⋊Dic3))D3semidirect
20. C3⋊#1084D3semidirect
27. C32×H(3,𝔽3)C2×C4semidirect
39. C3×C3⋊(C3⋊D3)Dic3semidirect
49. C3⋊((C3⋊D3)⋊C3)Dic3semidirect
90. C34C4×D3semidirect
91. C34C2×Dic3semidirect
98. C3×H(3,𝔽3)C4×D3semidirect
99. C3×H(3,𝔽3)C2×Dic3semidirect
130. C3⋊(C3⋊D3)C3⋊Dic3semidirect
208. C33D3×Dic3semidirect
209. C33D3×Dic3semidirect
210. C33#624semidirect
211. C33C2×C3⋊Dic3semidirect
219. H(3,𝔽3)D3×Dic3semidirect
318. C32((C3⋊D3)⋊C3)⋊C4semidirect
320. C32D3×C3⋊Dic3semidirect
322. C32#6294semidirect
356. C3((C3⋊D3)⋊C3)⋊Dic3semidirect
357. C3#10619901semidirect

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
C3⋊(C3⋊((C3⋊Dic3)⋊C3))2
#106201543
C3⋊D3×C3⋊Dic33
#106199013
((C3⋊D3)⋊C3)⋊Dic33