Finite Group Databasebeta

← #13156734

Subgroups — #13156734

Order 1728.

930 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Dic3×C3⋊Dic3C211yesmaximal, characteristic
2C2×C3×Dic3⋊Dic3C212yesmaximal
3#11722082C211yesmaximal, characteristic
4#11722061C212yesmaximal
5C3×#63579C211yesmaximal, characteristic
6#10591245—32nomaximal
7#10591230—31nomaximal
8C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
9C22×C3×C3⋊Dic3C2212yes—
10C22×C3×C3⋊Dic3C2211yescharacteristic
11C22×C32×Dic3C2212yes—
12C22×C32×Dic3C2211yescharacteristic
13Dic3×C3⋊Dic3C414yescomplemented
14C3×Dic3⋊Dic3—24no—
15C2×C4×C3⋊Dic3—31no—
16C2×C3×C4⋊Dic3—32no—
17C2×C3×Dic3⋊C4—32no—
18C2×Dic3⋊Dic3D312yes—
19C2×Dic32—32no—
20C2×Dic32—61no—
21#63658—32no—
22C3×C3⋊#95—32no—
23#63579—32no—
24#63579—31no—
25#63579—32no—
26#63579—32no—
27#63579—62no—
28#63579D311yescharacteristic
29C23×C33C2311yescharacteristic
30C2×C3⋊(C3⋊Dic3)—22no—
31C2×C3⋊(C3⋊Dic3)C2×C412yes—
32C2×C3×C3⋊Dic3—22no—
33C2×C3×C3⋊Dic3—22no—
34C2×C3×C3⋊Dic3—22no—
35C2×C3×C3⋊Dic3—22no—
36C2×C3×C3⋊Dic3C2×C412yes—
37C2×C32×Dic3—22no—
38C2×C32×Dic3—22no—
39C2×C32×Dic3—22no—
40C2×C32×Dic3C2×C412yes—
41C2×C32×Dic3D412yes—
42C2×C32×Dic3Q812yes—
43#4977—92no—
44#4650—91no—
45C22×C32×C4—31no—
46C22×C32×C4—32no—
47C22×C3⋊Dic3—31no—
48C22×C3⋊Dic3—32no—
49C22×C3⋊Dic3—61no—
50C22×C3⋊Dic3—62no—
51C22×C3⋊Dic3—121no—
52C22×C3⋊Dic3C2×D312yes—
53C22×C3⋊Dic3C2×D311yescharacteristic
54C22×C3×Dic3—21no—
55C22×C3×Dic3—22no—
56C22×C3×Dic3—32no—
57C22×C3×Dic3—32no—
58C22×C3×Dic3—32no—
59C22×C3×Dic3—61no—
60C22×C3×Dic3—62no—
61C22×C3×Dic3C2×D312yes—
62C22×C3×Dic3C2×D312yes—
63C22×C3×Dic3C2×D312yes—
64C4×C3⋊Dic3—34no—
65C3×C4⋊Dic3—64no—
66C3×Dic3⋊C4—64no—
67Dic3⋊Dic3—24no—
68Dic32—38no—
69Dic32—64no—
70C22×C33C22×C411yescharacteristic
71C22×C33C2×D411yescharacteristic
72C22×C33C2×Q811yescharacteristic
73C22×C33#4112yes—
74C22×C33#4112yes—
75C3⋊(C3⋊Dic3)—22no—
76C3×C3⋊Dic3—22no—
77C3×C3⋊Dic3—42no—
78C32×Dic3—42no—
79C32×Dic3C4⋊C414yes—
80C2×C3×C4⋊C4—92no—
81C2×C4⋊Dic3—32no—
82C2×Dic3⋊C4—32no—
83C2×C4×Dic3—92no—
84C2×C4×Dic3—91no—
85C2×C4×Dic3—181no—
86C3×#95—91no—
87C3⋊#95—32no—
88C3⋊#95—91no—
89C3⋊#95—92no—
90C3⋊#95—92no—
91C3⋊#95—92no—
92C3⋊#95—92no—
93C3⋊#95—182no—
94C23×C32—22no—
95C23×C32—21no—
96C23×C32—41no—
97C23×C32C22×D312yes—
98C23×C32C22×D311yescharacteristic
99C2×C32×C4—32no—
100C2×C32×C4—32no—
101C2×C32×C4—32no—
102C2×C32×C4—62no—
103C2×C32×C4—62no—
104C2×C32×C4—62no—
105C2×C3⋊Dic3—22no—
106C2×C3⋊Dic3—22no—
107C2×C3⋊Dic3—22no—
108C2×C3⋊Dic3—22no—
109C2×C3⋊Dic3—34no—
110C2×C3⋊Dic3—32no—
111C2×C3⋊Dic3—62no—
112C2×C3⋊Dic3—64no—
113C2×C3⋊Dic3—62no—
114C2×C3⋊Dic3—64no—
115C2×C3⋊Dic3—62no—
116C2×C3⋊Dic3—62no—
117C2×C3⋊Dic3—122no—
118C2×C3⋊Dic3—122no—
119C2×C3⋊Dic3—122no—
120C2×C3⋊Dic3—124no—
121C2×C3⋊Dic3C4×D312yes—
122C2×C3×Dic3—24no—
123C2×C3×Dic3—22no—
124C2×C3×Dic3—22no—
125C2×C3×Dic3—22no—
126C2×C3×Dic3—22no—
127C2×C3×Dic3—22no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3—22no—
130C2×C3×Dic3—22no—
131C2×C3×Dic3—22no—
132C2×C3×Dic3—34no—
133C2×C3×Dic3—42no—
134C2×C3×Dic3—42no—
135C2×C3×Dic3—62no—
136C2×C3×Dic3—64no—
137C2×C3×Dic3—62no—
138C2×C3×Dic3—62no—
139C2×C3×Dic3—64no—
140C2×C3×Dic3—62no—
141C2×C3×Dic3—62no—
142C2×C3×Dic3—62no—
143C2×C3×Dic3—62no—
144C2×C3×Dic3—62no—
145C2×C3×Dic3—62no—
146C2×C3×Dic3—122no—
147C2×C3×Dic3—122no—
148C2×C3×Dic3Dic614yes—
149C2×C3×Dic3C4×D314yes—
150C2×C3×Dic3#6714yes—
151#382—271noSylow
152C2×C33C2×C4⋊C411yescharacteristic
153C2×C33#11711yescharacteristic
154C2×C33#11711yescharacteristic
155C2×C33#12412yes—
156C2×C33#12512yes—
157C22×C3×C4—32no—
158C22×C3×C4—32no—
159C22×C3×C4—32no—
160C22×C3×C4—61no—
161C22×C3×C4—62no—
162C22×C3×C4—91no—
163C22×C3×C4—92no—
164C22×Dic3—32no—
165C22×Dic3—32no—
166C22×Dic3—32no—
167C22×Dic3—61no—
168C22×Dic3—62no—
169C22×Dic3—92no—
170C22×Dic3—91no—
171C22×Dic3—181no—
172C22×Dic3—182no—
173C22×Dic3—361no—
174C22×Dic3D3212yes—
175C22×Dic3D3211yescharacteristic
176C3×C4⋊C4—184no—
177C4⋊Dic3—64no—
178Dic3⋊C4—64no—
179C4×Dic3—98no—
180C4×Dic3—94no—
181C4×Dic3—184no—
182C22×C32—22no—
183C22×C32—22no—
184C22×C32—22no—
185C22×C32—22no—
186C22×C32—22no—
187C22×C32—22no—
188C22×C32—22no—
189C22×C32—22no—
190C22×C32—21no—
191C22×C32—21no—
192C22×C32—21no—
193C22×C32—22no—
194C22×C32—41no—
195C22×C32—41no—
196C22×C32—41no—
197C22×C32—42no—
198C22×C32—42no—
199C22×C32C2×Dic612yes—
200C22×C32C2×C4×D311yescharacteristic
201C22×C32C2×C4×D312yes—
202C22×C32#23512yes—
203C22×C32D3×D411yescharacteristic
204C22×C32#23712yes—
205C22×C32#23712yes—
206C22×C32#23712yes—
207C22×C32D3×Q811yescharacteristic
208C22×C32#23912yes—
209C22×C32#23912yes—
210C22×C32C2×#6712yes—
211C32×C4—34no—
212C32×C4—122no—
213C3⋊Dic3—22no—
214C3⋊Dic3—42no—
215C3⋊Dic3—62no—
216C3⋊Dic3—64no—
217C3⋊Dic3—64no—
218C3⋊Dic3—124no—
219C3⋊Dic3—124no—
220C3×Dic3—24no—
221C3×Dic3—44no—
222C3×Dic3—42no—
223C3×Dic3—42no—
224C3×Dic3—64no—
225C3×Dic3—64no—
226C3×Dic3—124no—
227C3×Dic3—122no—
228C3×Dic3—122no—
229C3×Dic3Dic3⋊C418yes—
230C2×C4⋊C4—92no—
231C2×C42—271no—
232#95—91no—
233#95—272no—
234#95—271no—
235C33#38211yescharacteristic, complemented, Sylow
236C23×C3—21no—
237C23×C3—22no—
238C23×C3—41no—
239C23×C3C2×D3212yes—
240C23×C3C2×D3211yescharacteristic
241C2×C3×C4—34no—
242C2×C3×C4—34no—
243C2×C3×C4—34no—
244C2×C3×C4—62no—
245C2×C3×C4—62no—
246C2×C3×C4—62no—
247C2×C3×C4—64no—
248C2×C3×C4—62no—
249C2×C3×C4—62no—
250C2×C3×C4—62no—
251C2×C3×C4—62no—
252C2×C3×C4—62no—
253C2×C3×C4—62no—
254C2×C3×C4—92no—
255C2×C3×C4—122no—
256C2×C3×C4—122no—
257C2×C3×C4—182no—
258C2×C3×C4—182no—
259C2×C3×C4—182no—
260C2×C3×C4—182no—
261C2×Dic3—22no—
262C2×Dic3—22no—
263C2×Dic3—22no—
264C2×Dic3—34no—
265C2×Dic3—62no—
266C2×Dic3—64no—
267C2×Dic3—62no—
268C2×Dic3—62no—
269C2×Dic3—64no—
270C2×Dic3—62no—
271C2×Dic3—62no—
272C2×Dic3—62no—
273C2×Dic3—62no—
274C2×Dic3—62no—
275C2×Dic3—62no—
276C2×Dic3—94no—
277C2×Dic3—92no—
278C2×Dic3—122no—
279C2×Dic3—122no—
280C2×Dic3—182no—
281C2×Dic3—184no—
282C2×Dic3—184no—
283C2×Dic3—182no—
284C2×Dic3—182no—
285C2×Dic3—182no—
286C2×Dic3—362no—
287C2×Dic3—362no—
288C2×Dic3—362no—
289C2×Dic3—364no—
290C2×Dic3#62412yes—
291C2×Dic3#62512yes—
292C2×Dic3#62712yes—
293C2×C32—22no—
294C2×C32—22no—
295C2×C32—22no—
296C2×C32—21no—
297C2×C32—21no—
298C2×C32—22no—
299C2×C32—22no—
300C2×C32—22no—
301C2×C32—22no—
302C2×C32—22no—
303C2×C32—22no—
304C2×C32—21no—
305C2×C32—41no—
306C2×C32—41no—
307C2×C32—41no—
308C2×C32—42no—
309C2×C32—42no—
310C2×C32#87211yescharacteristic
311C2×C32#87711yescharacteristic
312C2×C32#88512yes—
313C2×C32#88912yes—
314C2×C32#89012yes—
315C2×C32#89012yes—
316C2×C32D3×C4⋊C411yescharacteristic
317C2×C32#89212yes—
318C2×C32#89212yes—
319C2×C32C2×Dic3⋊C412yes—
320C2×C32#93612yes—
321C2×C32#94712yes—
322C22×C4—31no—
323C22×C4—32no—
324C22×C4—91no—
325C22×C4—92no—
326C22×C4—271no—
327C4⋊C4—184no—
328C42—274no—
329C22×C3—21no—
330C22×C3—22no—
331C22×C3—22no—
332C22×C3—21no—
333C22×C3—21no—
334C22×C3—22no—
335C22×C3—22no—
336C22×C3—22no—
337C22×C3—22no—
338C22×C3—22no—
339C22×C3—22no—
340C22×C3—22no—
341C22×C3—41no—
342C22×C3—41no—
343C22×C3—41no—
344C22×C3—42no—
345C22×C3—42no—
346C22×C3D3×Dic612yes—
347C22×C3#379612yes—
348C22×C3#379612yes—
349C22×C3#379612yes—
350C22×C3#379912yes—
351C22×C3C4×D3212yes—
352C22×C3#380412yes—
353C22×C3#380512yes—
354C22×C3C2×#62411yescharacteristic
355C22×C3C2×#62511yescharacteristic
356C22×C3C2×#62711yescharacteristic
357C22×C3D3×#6712yes—
358C3×C4—38no—
359C3×C4—64no—
360C3×C4—124no—
361C3×C4—122no—
362C3×C4—122no—
363C3×C4—182no—
364C3×C4—362no—
365Dic3—42no—
366Dic3—64no—
367Dic3—64no—
368Dic3—124no—
369Dic3—122no—
370Dic3—122no—
371Dic3—184no—
372Dic3—184no—
373Dic3—182no—
374Dic3—364no—
375Dic3—364no—
376Dic3#372414yes—
377C32—22no—
378C32—21no—
379C32—41no—
380C32#465011yescharacteristic, complemented
381C32#497712yescomplemented
382C23D3311yescharacteristic
383C2×C4—32no—
384C2×C4—32no—
385C2×C4—32no—
386C2×C4—62no—
387C2×C4—62no—
388C2×C4—62no—
389C2×C4—92no—
390C2×C4—182no—
391C2×C4—182no—
392C2×C4—182no—
393C2×C4—182no—
394C2×C4—272no—
395C2×C4—542no—
396C2×C3—22no—
397C2×C3—22no—
398C2×C3—22no—
399C2×C3—21no—
400C2×C3—22no—
401C2×C3—21no—
402C2×C3—22no—
403C2×C3—21no—
404C2×C3—22no—
405C2×C3—22no—
406C2×C3—22no—
407C2×C3—22no—
408C2×C3—42no—
409C2×C3—41no—
410C2×C3—41no—
411C2×C3—41no—
412C2×C3—42no—
413C2×C3#6383612yes—
414C2×C3#6384512yes—
415C2×C3#6384612yes—
416C2×C3#6384911yescharacteristic
417C2×C3#6384911yescharacteristic
418C2×C3#6386312yes—
419C2×C3#6387212yes—
420C2×C3D3×Dic3⋊C412yes—
421C2×C3#6387812yes—
422C2×C3#6390712yes—
423C2×C3#6395912yes—
424C2×C3C2×#372411yescharacteristic
425C22D3×#62411yescharacteristic
426C22D3×#62511yescharacteristic
427C22D3×#62711yescharacteristic
428C22#8896212yes—
429C22#8896412yes—
430C4—34no—
431C4—122no—
432C4—182no—
433C4—362no—
434C4—542no—
435C3—21no—
436C3—22no—
437C3—41no—
438C3#1059123011yescharacteristic, complemented
439C3#1059124512yescomplemented
440C2D3×#372411yescharacteristic
441C2#1172292011yescharacteristic
442C2#1172292111yescharacteristic
443C2#1172300112yes—
444C2#1172301312yes—
subgroupG/H
center, Frattini, hypercenterC23D33
commutatorC22×C33C22×C4
Fitting, socle, prime radical, cosocleC23×C33C23
hypocenterC33#382
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C23

Complements

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

NH ≅ G/Ntype
13. Dic3×C3⋊Dic3C4semidirect
235. C33#382semidirect
380. C32#4650semidirect
381. C32#4977semidirect
438. C3#10591230semidirect
439. C3#10591245semidirect

Maximal subgroups

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

subgroupindex
C2×Dic3×C3⋊Dic32
C2×C3×Dic3⋊Dic32
#117220822
#117220612
C3×#635792
#105912453
#105912303