Finite Group Databasebeta

← #14518713

Subgroups — #14518713

Order 1944.

511 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 511 conjugacy classes of subgroups — too many to draw. Only its 73 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⋊#4207C211yesmaximal, characteristic, complemented
2C2×D3×#737C211yesmaximal, characteristic, complemented
3C3×#66409C211yesmaximal, characteristic, complemented
4#10619983—31nomaximal
5#10619880C311yesmaximal, characteristic, complemented
6#6195⋊C3—32nomaximal
7#6291⋊C3—31nomaximal
8C3×#6195—31nomaximal
9C2×C3×#737C2211yescharacteristic
10C3⋊#4207—21no—
11D3×#737—21no—
12C22×#737—31no—
13C2×C3⋊(C3⋊D9)C2×C311yescharacteristic, complemented
14C2×#4207—31no—
15C2×#4207—61no—
16C2×#4207—61no—
17C2×#4207—62no—
18C2×C3⋊AGL(1,ℤ/9)—32no—
19C2×C3⋊((C3⋊D3)⋊C3)—31no—
20C2×C3×C3⋊D9—31no—
21C2×D3×3−1+2—21no—
22C2×D3×3−1+2—22no—
23C2×D3×3−1+2D312yescomplemented
24C2×D3×H(3,𝔽3)D311yescharacteristic
25C2×C3×D3×C9—21no—
26C2×C3×D3×C9D311yescharacteristic, complemented
27C2×C3×D3×C9C2×C311yescharacteristic, complemented
28#66409—21no—
29#66409D311yescharacteristic, complemented
30C3×C3⋊Dic9C2×C311yescharacteristic, complemented
31C3×3−1+2⋊C4—32no—
32C3×(C3⋊Dic3)⋊C3—31no—
33C32×Dic9—31no—
34C3×#737D411yescharacteristic, complemented, Sylow
35#6291—31no—
36C3×#626—91no—
37#6233—31no—
38#611⋊C3—92no—
39#638⋊C3—91no—
40C3×#611—91no—
41#6195—31no—
42#6195—32no—
43C2×#737—22no—
44C2×#737—21no—
45C2×#737—21no—
46C2×#737—21no—
47C2×#737—41no—
48C2×#737—41no—
49C2×#737—42no—
50C2×#737—61no—
51C2×#737C2×D311yescharacteristic
52C2×C3×3−1+2—21no—
53C2×C3×3−1+2—22no—
54C2×C3×3−1+2C2×D312yes—
55C2×C3×H(3,𝔽3)C2×D311yescharacteristic
56C2×C32×C9—21no—
57C2×C32×C9C2×D311yescharacteristic
58C2×C32×C9C22×C311yescharacteristic
59C3⋊(C3⋊D9)—21no—
60#4207—64no—
61#4207—62no—
62#4207—62no—
63#4207—61no—
64C3⋊AGL(1,ℤ/9)—62no—
65C3⋊((C3⋊D3)⋊C3)—61no—
66C3×C3⋊D9—61no—
67D3×3−1+2—22no—
68D3×3−1+2—24no—
69D3×3−1+2—22no—
70D3×H(3,𝔽3)—21no—
71C3×D3×C9—22no—
72C3×D3×C9—21no—
73C3×D3×C9—21no—
74C2×C3⋊(C3⋊D3)—31no—
75C2×C3×C3⋊D3—91no—
76C2×C32×D3—21no—
77C2×C32×D3C3×D311yescharacteristic
78C2×C32×D3C3⋊D311yescharacteristic
79C3×C3⋊Dic3—31no—
80C32×Dic3—91no—
81C22×3−1+2—32no—
82C22×3−1+2—62no—
83C22×3−1+2—61no—
84C22×H(3,𝔽3)—31no—
85C22×C3×C9—31no—
86C22×C3×C9—31no—
87C22×C3×C9—61no—
88C2×C3⋊D9—31no—
89C2×C3⋊D9—31no—
90C2×C3⋊D9—32no—
91C2×C3⋊D9—61no—
92C2×C3⋊D9—62no—
93C2×C3⋊D9—61no—
94C2×AGL(1,ℤ/9)—92no—
95C2×AGL(1,ℤ/9)—182no—
96C2×(C3⋊D3)⋊C3—91no—
97C2×(C3⋊D3)⋊C3—181no—
98C2×D3×C9—22no—
99C2×D3×C9—21no—
100C2×D3×C9C3×D311yescharacteristic
101C2×D3×C9C3×D312yes—
102C2×C3×D9—91no—
103C2×C3×D9—181no—
104C3⋊Dic9C3×D311yescharacteristic, complemented
1053−1+2⋊C4—32no—
1063−1+2⋊C4—62no—
107(C3⋊Dic3)⋊C3—31no—
108(C3⋊Dic3)⋊C3—61no—
109C3×Dic9—31no—
110C3×Dic9—31no—
111C3×Dic9—32no—
112C3×Dic9—61no—
113#737—22no—
114#737—21no—
115#737—21no—
116#737—21no—
117#737—41no—
118#737—41no—
119#737—42no—
120#737D1211yescharacteristic, complemented
121C3×3−1+2—21no—
122C3×3−1+2—22no—
123C3×3−1+2#6712yescomplemented
124C3×H(3,𝔽3)#6711yescharacteristic
125C32×C9—21no—
126C32×C9#6711yescharacteristic, complemented
127C32×C9C3×D411yescharacteristic, complemented
128#638—91no—
129C3×#67—271no—
130C3×D12—271no—
131#626—91no—
132#626—271no—
133#611—91no—
134#611—92no—
135C2×C33—21no—
136C2×C33C2×C3×D311yescharacteristic
137C2×C33C2×C3⋊D311yescharacteristic
138C3⋊(C3⋊D3)—61no—
139C3×C3⋊D3—181no—
140C32×D3—22no—
141C32×D3—21no—
142C32×D3—21no—
143C2×3−1+2—21no—
144C2×3−1+2—22no—
145C2×3−1+2—22no—
146C2×3−1+2—22no—
147C2×3−1+2—42no—
148C2×3−1+2—42no—
149C2×3−1+2—42no—
150C2×3−1+2—42no—
151C2×3−1+2—42no—
152C2×3−1+2—41no—
153C2×3−1+2—41no—
154C2×3−1+2—42no—
155C2×3−1+2—62no—
156C2×3−1+2—64no—
157C2×3−1+2—62no—
158C2×3−1+2D3212yes—
159C2×H(3,𝔽3)—21no—
160C2×H(3,𝔽3)—21no—
161C2×H(3,𝔽3)—41no—
162C2×H(3,𝔽3)—61no—
163C2×H(3,𝔽3)D3211yescharacteristic
164C2×C3×C9—21no—
165C2×C3×C9—22no—
166C2×C3×C9—21no—
167C2×C3×C9—21no—
168C2×C3×C9—21no—
169C2×C3×C9—22no—
170C2×C3×C9—21no—
171C2×C3×C9—21no—
172C2×C3×C9—41no—
173C2×C3×C9—42no—
174C2×C3×C9—41no—
175C2×C3×C9—41no—
176C2×C3×C9—62no—
177C2×C3×C9—61no—
178C2×C3×C9—61no—
179C2×C3×C9D3211yescharacteristic
180C2×C3×C9C2×C3×D311yescharacteristic
181C2×C3×C9C2×C3×D312yes—
182C2×C3×C9C2×C3×D311yescharacteristic
183C3⋊D9—62no—
184C3⋊D9—64no—
185C3⋊D9—62no—
186C3⋊D9—61no—
187C3⋊D9—61no—
188C3⋊D9—62no—
189AGL(1,ℤ/9)—184no—
190AGL(1,ℤ/9)—182no—
191(C3⋊D3)⋊C3—182no—
192(C3⋊D3)⋊C3—181no—
193D3×C9—24no—
194D3×C9—22no—
195D3×C9—21no—
196D3×C9—22no—
197C3×D9—182no—
198C3×D9—181no—
199C22×C32—31no—
200C22×C32—31no—
201C22×C32—61no—
202C2×C3⋊D3—91no—
203C2×C3⋊D3—91no—
204C2×C3⋊D3—181no—
205C2×C3⋊D3—271no—
206C2×C3⋊D3—541no—
207C2×C3×D3—31no—
208C2×C3×D3—31no—
209C2×C3×D3—61no—
210C2×C3×D3—271no—
211C2×C3×D3—271no—
212C2×C3×D3—541no—
213C2×C3×D3C3×C3⋊D311yescharacteristic
214C32×C4—271no—
215C3⋊Dic3—31no—
216C3×Dic3—91no—
217C3×Dic3—91no—
218C3×Dic3—181no—
219C3×Dic3—271no—
220C22×C9—31no—
221C22×C9—32no—
222C22×C9—61no—
223C22×C9—62no—
224C2×D9—91no—
225C2×D9—92no—
226C2×D9—181no—
227C2×D9—182no—
228Dic9—31no—
229Dic9—32no—
230C33—21no—
231C33C3×#6711yescharacteristic
232C33#63811yescharacteristic
2333−1+2—21no—
2343−1+2—22no—
2353−1+2—22no—
2363−1+2—22no—
2373−1+2—42no—
2383−1+2—42no—
2393−1+2—42no—
2403−1+2—42no—
2413−1+2—42no—
2423−1+2—41no—
2433−1+2—41no—
2443−1+2—42no—
2453−1+2#62612yescomplemented
246H(3,𝔽3)—21no—
247H(3,𝔽3)—21no—
248H(3,𝔽3)—41no—
249H(3,𝔽3)#62611yescharacteristic
250C3×C9—21no—
251C3×C9—22no—
252C3×C9—21no—
253C3×C9—21no—
254C3×C9—21no—
255C3×C9—22no—
256C3×C9—21no—
257C3×C9—21no—
258C3×C9—41no—
259C3×C9—42no—
260C3×C9—41no—
261C3×C9—41no—
262C3×C9#62611yescharacteristic, complemented
263C3×C9C3×D1211yescharacteristic, complemented
264C3×C9C3×#6711yescharacteristic
265C3×C9C3×#6712yes—
266C3×D4—811no—
267#67—271no—
268#67—811no—
269D12—271no—
270C2×C32—21no—
271C2×C32—21no—
272C2×C32—21no—
273C2×C32—31no—
274C2×C32—31no—
275C2×C32—41no—
276C2×C32—61no—
277C2×C32—61no—
278C2×C32—61no—
279C2×C32—62no—
280C2×C32—61no—
281C2×C32—61no—
282C2×C32—121no—
283C2×C32C3×D3211yescharacteristic
284C2×C32D3×C3⋊D311yescharacteristic
285C2×C32C2×C3×C3⋊D311yescharacteristic
286C3⋊D3—181no—
287C3⋊D3—182no—
288C3⋊D3—181no—
289C3⋊D3—541no—
290C3⋊D3—542no—
291C3×D3—21no—
292C3×D3—61no—
293C3×D3—61no—
294C3×D3—62no—
295C3×D3—541no—
296C3×D3—542no—
297C3×D3—541no—
298C2×C9—21no—
299C2×C9—22no—
300C2×C9—22no—
301C2×C9—21no—
302C2×C9—41no—
303C2×C9—42no—
304C2×C9—64no—
305C2×C9—62no—
306C2×C9—61no—
307C2×C9—62no—
308C2×C9C3×D3211yescharacteristic
309C2×C9C3×D3212yes—
310D9—182no—
311D9—184no—
312D9—181no—
313D9—182no—
314C22×C3—31no—
315C22×C3—91no—
316C22×C3—91no—
317C22×C3—181no—
318C22×C3—811no—
319C2×D3—271no—
320C2×D3—271no—
321C2×D3—541no—
322C2×D3—811no—
323C2×D3—1621no—
324C2×D3#420711yescharacteristic, complemented
325C3×C4—271no—
326C3×C4—271no—
327C3×C4—541no—
328Dic3—91no—
329Dic3—271no—
330C32—21no—
331C32—21no—
332C32—21no—
333C32—31no—
334C32—31no—
335C32—41no—
336C32—61no—
337C32—61no—
338C32—61no—
339C32—121no—
340C32C3×#62611yescharacteristic
341C32#629111yescharacteristic
342C32C3×#63811yescharacteristic
343C9—21no—
344C9—22no—
345C9—22no—
346C9—21no—
347C9—41no—
348C9—42no—
349C9C3×#62611yescharacteristic
350C9C3×#62612yes—
351D4—811noSylow
352C2×C3—21no—
353C2×C3—31no—
354C2×C3—31no—
355C2×C3—61no—
356C2×C3—61no—
357C2×C3—61no—
358C2×C3—61no—
359C2×C3—121no—
360C2×C3—181no—
361C2×C3—181no—
362C2×C3—182no—
363C2×C3—1621no—
364C2×C3C2×#420711yescharacteristic
365C2×C3C3×D3×C3⋊D311yescharacteristic
366D3—21no—
367D3—542no—
368D3—541no—
369D3—541no—
370D3—1621no—
371D3—1622no—
372C22—31no—
373C22—811no—
374C4—271no—
375C3—21no—
376C3—31no—
377C3—31no—
378C3—61no—
379C3—61no—
380C3—61no—
381C3—121no—
382C3#1061998311yescharacteristic, complemented
383C3C3×#629111yescharacteristic
384C2—61no—
385C2—1621no—
386C2D3×#420711yescharacteristic
subgroupG/H
center, hypercenterC2D3×#4207
commutator, cosocleC2×C32×C9C22×C3
FrattiniC2×C3C3×D3×C3⋊D3
FittingC2×C3×#737C22
socleC2×C32C2×C3×C3⋊D3
hypocenterC32×C9C3×D4
LCSG ▷ C2×C32×C9 ▷ C32×C9
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C3⋊#4207C2semidirect
2. C2×D3×#737C2semidirect
3. C3×#66409C2semidirect
5. #10619880C3semidirect
13. C2×C3⋊(C3⋊D9)C2×C3semidirect
23. C2×D3×3−1+2D3semidirect
26. C2×C3×D3×C9D3semidirect
27. C2×C3×D3×C9C2×C3semidirect
29. #66409D3semidirect
30. C3×C3⋊Dic9C2×C3semidirect
34. C3×#737D4semidirect
104. C3⋊Dic9C3×D3semidirect
120. #737D12semidirect
123. C3×3−1+2#67semidirect
126. C32×C9#67semidirect
127. C32×C9C3×D4semidirect
245. 3−1+2#626semidirect
262. C3×C9#626semidirect
263. C3×C9C3×D12semidirect
324. C2×D3#4207semidirect
382. C3#10619983semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C3⋊#42072
C2×D3×#7372
C3×#664092
#106199833
#106198803
#6195⋊C33
#6291⋊C33
C3×#61953