Finite Group Databasebeta

← #14518676

Subgroups — #14518676

Order 1944.

919 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 919 conjugacy classes of subgroups — too many to draw. Only its 88 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, complemented
2C2×C3×C3⋊((C3⋊D3)⋊C3)C211yesmaximal, characteristic, complemented
3C3×Dic3×H(3,𝔽3)C211yesmaximal, characteristic, complemented
4#10620147C311yesmaximal, characteristic, complemented
5C3×#6292—31nomaximal
6C4⋊(C3⋊((C3⋊D3)⋊C3))—31nomaximal
7#6292⋊C3—33nomaximal
8C2×C32×H(3,𝔽3)C2211yescharacteristic
9C3⋊(C3⋊((C3⋊D3)⋊C3))—21no—
10C3×C3⋊((C3⋊D3)⋊C3)—21no—
11C2×C3⋊(C3⋊(C3⋊D3))C2×C311yescharacteristic, complemented
12C2×C3×C3⋊(C3⋊D3)—31no—
13C2×C3×C3⋊(C3⋊D3)C2×C311yescharacteristic, complemented
14C2×C32×C3⋊D3—31no—
15C33×Dic3—21no—
16C33×Dic3D311yescharacteristic, complemented
17C33×Dic3C2×C311yescharacteristic, complemented
18C2×C3⋊((C3⋊D3)⋊C3)—21no—
19C2×C3⋊((C3⋊D3)⋊C3)—31no—
20C2×C3⋊((C3⋊D3)⋊C3)—33no—
21C2×C3⋊((C3⋊D3)⋊C3)—63no—
22C2×C3⋊((C3⋊D3)⋊C3)—61no—
23C2×C3⋊((C3⋊D3)⋊C3)D311yescharacteristic, complemented
24C2×C3×(C3⋊D3)⋊C3—33no—
25C3×C4×H(3,𝔽3)—31no—
26Dic3×H(3,𝔽3)—23no—
27Dic3×H(3,𝔽3)D313yescomplemented
28C32×H(3,𝔽3)D411yescharacteristic, complemented, Sylow
29C4⋊(C3⋊(C3⋊D3))—31no—
30C3×C4⋊(C3⋊D3)—91no—
31#6292—31no—
32#6292—33no—
33#6292—93no—
34C3×#626—93no—
35C3×#626—91no—
36C4⋊((C3⋊D3)⋊C3)—93no—
37C2×C34—21no—
38C2×C34C2×D311yescharacteristic
39C2×C34C22×C311yescharacteristic
40C3⋊(C3⋊(C3⋊D3))—21no—
41C3×C3⋊(C3⋊D3)—21no—
42C3×C3⋊(C3⋊D3)—61no—
43C32×C3⋊D3—61no—
44C2×C3×H(3,𝔽3)—21no—
45C2×C3×H(3,𝔽3)—21no—
46C2×C3×H(3,𝔽3)—23no—
47C2×C3×H(3,𝔽3)—23no—
48C2×C3×H(3,𝔽3)—43no—
49C2×C3×H(3,𝔽3)—41no—
50C2×C3×H(3,𝔽3)C2×D311yescharacteristic
51C2×C3×H(3,𝔽3)C2×D313yes—
52C3⋊((C3⋊D3)⋊C3)—22no—
53C3⋊((C3⋊D3)⋊C3)—21no—
54C3⋊((C3⋊D3)⋊C3)—62no—
55C3⋊((C3⋊D3)⋊C3)—66no—
56C3⋊((C3⋊D3)⋊C3)—63no—
57C3⋊((C3⋊D3)⋊C3)—61no—
58C3×(C3⋊D3)⋊C3—63no—
59C2×C3⋊(C3⋊D3)—31no—
60C2×C3⋊(C3⋊D3)—31no—
61C2×C3⋊(C3⋊D3)—33no—
62C2×C3⋊(C3⋊D3)—61no—
63C2×C3⋊(C3⋊D3)—63no—
64C2×C3⋊(C3⋊D3)—93no—
65C2×C3⋊(C3⋊D3)—183no—
66C2×C3⋊(C3⋊D3)C3×D311yescharacteristic, complemented
67C2×C3×C3⋊D3—31no—
68C2×C3×C3⋊D3—31no—
69C2×C3×C3⋊D3—33no—
70C2×C3×C3⋊D3—61no—
71C2×C3×C3⋊D3—93no—
72C2×C3×C3⋊D3—93no—
73C2×C3×C3⋊D3—91no—
74C2×C3×C3⋊D3—91no—
75C2×C3×C3⋊D3—181no—
76C2×C3×C3⋊D3—183no—
77C2×C32×D3—93no—
78C2×C32×D3—91no—
79C33×C4—31no—
80C33×C4—31no—
81C33×C4—61no—
82C32×Dic3—21no—
83C32×Dic3—23no—
84C32×Dic3—33no—
85C32×Dic3—33no—
86C32×Dic3—63no—
87C32×Dic3C3×D311yescharacteristic
88C32×Dic3C3×D313yescomplemented
89C32×Dic3C3⋊D311yescharacteristic, complemented
90C2×(C3⋊D3)⋊C3—33no—
91C2×(C3⋊D3)⋊C3—63no—
92C2×(C3⋊D3)⋊C3—93no—
93C2×(C3⋊D3)⋊C3—183no—
94C4×H(3,𝔽3)—33no—
95C4×H(3,𝔽3)—63no—
96C34—21no—
97C34D1211yescharacteristic, complemented
98C34C3×D411yescharacteristic, complemented
99C3×H(3,𝔽3)—21no—
100C3×H(3,𝔽3)—21no—
101C3×H(3,𝔽3)—23no—
102C3×H(3,𝔽3)—23no—
103C3×H(3,𝔽3)—43no—
104C3×H(3,𝔽3)—41no—
105C3×H(3,𝔽3)D1213yescomplemented
106C3×H(3,𝔽3)#6711yescharacteristic, complemented
107C4⋊(C3⋊D3)—91no—
108C4⋊(C3⋊D3)—93no—
109C4⋊(C3⋊D3)—273no—
110C3×#67—271no—
111C3×D12—271no—
112C3×D12—273no—
113#626—93no—
114#626—91no—
115#626—273no—
116C2×C33—21no—
117C2×C33—23no—
118C2×C33—21no—
119C2×C33—21no—
120C2×C33—21no—
121C2×C33—21no—
122C2×C33—23no—
123C2×C33—33no—
124C2×C33—33no—
125C2×C33—41no—
126C2×C33—43no—
127C2×C33—41no—
128C2×C33—63no—
129C2×C33—63no—
130C2×C33—63no—
131C2×C33—123no—
132C2×C33D3211yescharacteristic
133C2×C33C2×C3×D311yescharacteristic
134C2×C33C2×C3×D313yes—
135C2×C33C2×C3×D311yescharacteristic
136C2×C33C2×C3⋊D311yescharacteristic
137C3⋊(C3⋊D3)—21no—
138C3⋊(C3⋊D3)—61no—
139C3⋊(C3⋊D3)—66no—
140C3⋊(C3⋊D3)—62no—
141C3⋊(C3⋊D3)—63no—
142C3⋊(C3⋊D3)—61no—
143C3⋊(C3⋊D3)—183no—
144C3⋊(C3⋊D3)—186no—
145C3×C3⋊D3—62no—
146C3×C3⋊D3—61no—
147C3×C3⋊D3—61no—
148C3×C3⋊D3—63no—
149C3×C3⋊D3—183no—
150C3×C3⋊D3—182no—
151C3×C3⋊D3—183no—
152C3×C3⋊D3—186no—
153C3×C3⋊D3—181no—
154C3×C3⋊D3—181no—
155C32×D3—183no—
156C32×D3—181no—
157C2×H(3,𝔽3)—23no—
158C2×H(3,𝔽3)—23no—
159C2×H(3,𝔽3)—23no—
160C2×H(3,𝔽3)—43no—
161C2×H(3,𝔽3)—43no—
162C2×H(3,𝔽3)—46no—
163C2×H(3,𝔽3)—43no—
164C2×H(3,𝔽3)D3213yes—
165(C3⋊D3)⋊C3—66no—
166(C3⋊D3)⋊C3—63no—
167(C3⋊D3)⋊C3—186no—
168(C3⋊D3)⋊C3—183no—
169C22×C32—271no—
170C2×C3⋊D3—31no—
171C2×C3⋊D3—33no—
172C2×C3⋊D3—93no—
173C2×C3⋊D3—91no—
174C2×C3⋊D3—93no—
175C2×C3⋊D3—91no—
176C2×C3⋊D3—93no—
177C2×C3⋊D3—181no—
178C2×C3⋊D3—183no—
179C2×C3⋊D3—183no—
180C2×C3⋊D3—273no—
181C2×C3⋊D3—273no—
182C2×C3⋊D3—543no—
183C2×C3⋊D3—549no—
184C2×C3⋊D3—543no—
185C2×C3×D3—93no—
186C2×C3×D3—93no—
187C2×C3×D3—91no—
188C2×C3×D3—91no—
189C2×C3×D3—181no—
190C2×C3×D3—183no—
191C2×C3×D3—273no—
192C2×C3×D3—271no—
193C2×C3×D3—273no—
194C2×C3×D3—271no—
195C2×C3×D3—541no—
196C2×C3×D3—543no—
197C32×C4—31no—
198C32×C4—33no—
199C32×C4—31no—
200C32×C4—63no—
201C32×C4—61no—
202C32×C4—93no—
203C32×C4—93no—
204C32×C4—183no—
205C3×Dic3—33no—
206C3×Dic3—31no—
207C3×Dic3—61no—
208C3×Dic3—63no—
209C3×Dic3(C3⋊D3)⋊C313yescomplemented
210C3×Dic3C3×C3⋊D311yescharacteristic
211C33—21no—
212C33—21no—
213C33—23no—
214C33—21no—
215C33—21no—
216C33—21no—
217C33—23no—
218C33—33no—
219C33—33no—
220C33—41no—
221C33—43no—
222C33—41no—
223C33—63no—
224C33—63no—
225C33—63no—
226C33—123no—
227C33#62611yescharacteristic, complemented
228C33C3×D1211yescharacteristic
229C33C3×D1213yescomplemented
230C33C3×#6711yescharacteristic, complemented
231C33C4⋊(C3⋊D3)11yescharacteristic, complemented
232H(3,𝔽3)—23no—
233H(3,𝔽3)—23no—
234H(3,𝔽3)—23no—
235H(3,𝔽3)—43no—
236H(3,𝔽3)—43no—
237H(3,𝔽3)—46no—
238H(3,𝔽3)—43no—
239H(3,𝔽3)#62613yescomplemented
240C3×D4—811no—
241#67—271no—
242D12—271no—
243D12—273no—
244D12—813no—
245C2×C32—23no—
246C2×C32—21no—
247C2×C32—21no—
248C2×C32—21no—
249C2×C32—23no—
250C2×C32—23no—
251C2×C32—33no—
252C2×C32—33no—
253C2×C32—33no—
254C2×C32—31no—
255C2×C32—43no—
256C2×C32—41no—
257C2×C32—69no—
258C2×C32—63no—
259C2×C32—61no—
260C2×C32—63no—
261C2×C32—63no—
262C2×C32—63no—
263C2×C32—63no—
264C2×C32—61no—
265C2×C32—63no—
266C2×C32—123no—
267C2×C32—129no—
268C2×C32—121no—
269C2×C32—123no—
270C2×C32—123no—
271C2×C32—541no—
272C2×C32C2×(C3⋊D3)⋊C313yes—
273C2×C32C3×D3213yes—
274C2×C32C3×D3211yescharacteristic
275C2×C32D3×C3⋊D311yescharacteristic
276C2×C32C2×C3×C3⋊D311yescharacteristic
277C3⋊D3—61no—
278C3⋊D3—63no—
279C3⋊D3—183no—
280C3⋊D3—182no—
281C3⋊D3—186no—
282C3⋊D3—183no—
283C3⋊D3—181no—
284C3⋊D3—181no—
285C3⋊D3—186no—
286C3⋊D3—183no—
287C3⋊D3—543no—
288C3⋊D3—543no—
289C3⋊D3—546no—
290C3⋊D3—5418no—
291C3⋊D3—546no—
292C3×D3—182no—
293C3×D3—183no—
294C3×D3—186no—
295C3×D3—183no—
296C3×D3—181no—
297C3×D3—181no—
298C3×D3—543no—
299C3×D3—541no—
300C3×D3—543no—
301C3×D3—542no—
302C3×D3—546no—
303C3×D3—541no—
304C22×C3—271no—
305C22×C3—271no—
306C22×C3—541no—
307C22×C3—811no—
308C2×D3—93no—
309C2×D3—91no—
310C2×D3—273no—
311C2×D3—273no—
312C2×D3—271no—
313C2×D3—271no—
314C2×D3—543no—
315C2×D3—541no—
316C2×D3—813no—
317C2×D3—1623no—
318C3×C4—33no—
319C3×C4—31no—
320C3×C4—93no—
321C3×C4—91no—
322C3×C4—181no—
323C3×C4—183no—
324Dic3C3⋊((C3⋊D3)⋊C3)11yescharacteristic, complemented
325C32—23no—
326C32—21no—
327C32—21no—
328C32—23no—
329C32—21no—
330C32—23no—
331C32—33no—
332C32—33no—
333C32—31no—
334C32—33no—
335C32—43no—
336C32—41no—
337C32—61no—
338C32—63no—
339C32—69no—
340C32—63no—
341C32—63no—
342C32—63no—
343C32—61no—
344C32—63no—
345C32—63no—
346C32—123no—
347C32—121no—
348C32—123no—
349C32—129no—
350C32—123no—
351C32C4⋊((C3⋊D3)⋊C3)13yescomplemented
352C32C3×#62611yescharacteristic
353C32C3×#62613yescomplemented
354C32#629211yescharacteristic, complemented
355C32C3×C4⋊(C3⋊D3)11yescharacteristic
356D4—811noSylow
357C2×C3—23no—
358C2×C3—21no—
359C2×C3—33no—
360C2×C3—31no—
361C2×C3—61no—
362C2×C3—63no—
363C2×C3—63no—
364C2×C3—61no—
365C2×C3—121no—
366C2×C3—123no—
367C2×C3—541no—
368C2×C3—542no—
369C2×C3—541no—
370C2×C3—1621no—
371C2×C3D3×(C3⋊D3)⋊C313yes—
372C2×C3C2×C3⋊((C3⋊D3)⋊C3)11yescharacteristic
373C2×C3C3×D3×C3⋊D311yescharacteristic
374D3—183no—
375D3—181no—
376D3—543no—
377D3—546no—
378D3—542no—
379D3—541no—
380D3—543no—
381D3—541no—
382D3—1623no—
383D3—1626no—
384C22—271no—
385C22—811no—
386C4—31no—
387C3—23no—
388C3—21no—
389C3—33no—
390C3—31no—
391C3—63no—
392C3—61no—
393C3—61no—
394C3—63no—
395C3—121no—
396C3—123no—
397C3#6292⋊C313yescomplemented
398C3C4⋊(C3⋊((C3⋊D3)⋊C3))11yescharacteristic, complemented
399C3C3×#629211yescharacteristic
400C2—541no—
401C2—1621no—
402C2D3×C3⋊((C3⋊D3)⋊C3)11yescharacteristic
subgroupG/H
center, hypercenterC2D3×C3⋊((C3⋊D3)⋊C3)
commutator, cosocleC2×C34C22×C3
FrattiniC2×C3C3×D3×C3⋊D3
FittingC2×C32×H(3,𝔽3)C22
socleC2×C33C2×C3×D3
hypocenterC34C3×D4
LCSG ▷ C2×C34 ▷ C34
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C3⋊(C3⋊((C3⋊D3)⋊C3))C2semidirect
2. C2×C3×C3⋊((C3⋊D3)⋊C3)C2semidirect
3. C3×Dic3×H(3,𝔽3)C2semidirect
4. #10620147C3semidirect
11. C2×C3⋊(C3⋊(C3⋊D3))C2×C3semidirect
13. C2×C3×C3⋊(C3⋊D3)C2×C3semidirect
16. C33×Dic3D3semidirect
17. C33×Dic3C2×C3semidirect
23. C2×C3⋊((C3⋊D3)⋊C3)D3semidirect
27. Dic3×H(3,𝔽3)D3semidirect
28. C32×H(3,𝔽3)D4semidirect
66. C2×C3⋊(C3⋊D3)C3×D3semidirect
88. C32×Dic3C3×D3semidirect
89. C32×Dic3C3⋊D3semidirect
97. C34D12semidirect
98. C34C3×D4semidirect
105. C3×H(3,𝔽3)D12semidirect
106. C3×H(3,𝔽3)#67semidirect
209. C3×Dic3(C3⋊D3)⋊C3semidirect
227. C33#626semidirect
229. C33C3×D12semidirect
230. C33C3×#67semidirect
231. C33C4⋊(C3⋊D3)semidirect
239. H(3,𝔽3)#626semidirect
324. Dic3C3⋊((C3⋊D3)⋊C3)semidirect
351. C32C4⋊((C3⋊D3)⋊C3)semidirect
353. C32C3×#626semidirect
354. C32#6292semidirect
397. C3#6292⋊C3semidirect
398. 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
C2×C3×C3⋊((C3⋊D3)⋊C3)2
C3×Dic3×H(3,𝔽3)2
#106201473
C3×#62923
C4⋊(C3⋊((C3⋊D3)⋊C3))3
#6292⋊C33