Finite Group Databasebeta

← C2×#10591324 #11808485

Subgroups — C2×#10591324 #11808485

Order 1152.

1981 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×(C2×D3)⋊C4C211yesmaximal, characteristic
2C22×C3×C4⋊Dic3C211yesmaximal, characteristic, complemented
3C22×#3724C212yesmaximal, complemented
4C22×(C2×D3)⋊Dic3C212yesmaximal
5C2×#63658C211yesmaximal, characteristic, complemented
6#10591324C218yesmaximal, direct product factor
7C2×#4993—31nomaximal
8C2×#4949—31nomaximal
9C24×C3×D3C2211yescharacteristic
10C23×C32×C4C2211yescharacteristic
11C23×C3⋊Dic3C2212yes—
12C23×C3×Dic3C2212yes—
13C23×C3×Dic3C2211yescharacteristic
14C2×C3×(C2×D3)⋊C4—24no—
15C2×C3×(C2×D3)⋊C4C2214yes—
16C2×C3×C4⋊Dic3—24no—
17C2×C3×C4⋊Dic3C2214yescomplemented
18C2×#3724—28no—
19C2×#3724C2218yescomplemented
20C2×(C2×D3)⋊Dic3—28no—
21C2×(C2×D3)⋊Dic3C2218yes—
22#63658C2214yescomplemented
23C22×C3×C4⋊C4—31no—
24C22×C3×C22⋊C4—31no—
25C22×#217—32no—
26C22×(C2×D3)⋊C4—32no—
27C22×(C2×D3)⋊C4D311yescharacteristic
28C22×C4⋊Dic3D311yescharacteristic, complemented
29C22×Dic3⋊C4—32no—
30C22×Dic3⋊C4—32no—
31C2×C3⋊#95—31no—
32C2×C3⋊#95—31no—
33C2×C3⋊#95—61no—
34#4993—38no—
35#4949—38no—
36C24×C32C2311yescharacteristic
37C23×C3×D3—22no—
38C23×C3×D3—24no—
39C23×C3×D3—24no—
40C23×C3×D3—22no—
41C23×C3×D3Q814yes—
42C23×C3×D3C2312yes—
43C22×C32×C4—24no—
44C22×C32×C4D414yes—
45C22×C32×C4C2312yes—
46C22×C3⋊Dic3—24no—
47C22×C3⋊Dic3—24no—
48C22×C3⋊Dic3D418yes—
49C22×C3⋊Dic3C2314yes—
50C22×C3×Dic3—24no—
51C22×C3×Dic3—22no—
52C22×C3×Dic3—24no—
53C22×C3×Dic3—24no—
54C22×C3×Dic3—24no—
55C22×C3×Dic3C2314yes—
56C22×C3×Dic3C2312yes—
57C3×(C2×D3)⋊C4—28no—
58C3×C4⋊Dic3—28no—
59#3724—216no—
60(C2×D3)⋊Dic3—216no—
61C2×#399—91noSylow
62C25×C3—31no—
63C24×D3C2×D311yescharacteristic
64C23×C3×C4—21no—
65C23×C3×C4—31no—
66C23×C3×C4—32no—
67C23×C3×C4C2×D311yescharacteristic
68C23×C3×C4C2×D311yescharacteristic
69C23×Dic3—32no—
70C23×Dic3—32no—
71C23×Dic3—62no—
72C23×Dic3C2×D311yescharacteristic
73C23×Dic3C2×D312yes—
74C2×C3×C4⋊C4—34no—
75C2×C3×C4⋊C4—64no—
76C2×C3×C22⋊C4—34no—
77C2×C3×C22⋊C4—64no—
78C2×#217—38no—
79C2×#217—68no—
80C2×(C2×D3)⋊C4—24no—
81C2×(C2×D3)⋊C4—38no—
82C2×(C2×D3)⋊C4—68no—
83C2×(C2×D3)⋊C4C2×D314yes—
84C2×C4⋊Dic3—24no—
85C2×C4⋊Dic3C2×D314yescomplemented
86C2×Dic3⋊C4—38no—
87C2×Dic3⋊C4—38no—
88C2×Dic3⋊C4—68no—
89C2×Dic3⋊C4—68no—
90C3⋊#95—34no—
91C3⋊#95—34no—
92C3⋊#95—64no—
93C23×C32C2×D414yes—
94C23×C32C2×D412yes—
95C23×C32C2×Q812yes—
96C23×C32#4114yes—
97C23×C32#4112yes—
98C23×C32C2411yescharacteristic
99C22×C3×D3—216no—
100C22×C3×D3—28no—
101C22×C3×D3—24no—
102C22×C3×D3—22no—
103C22×C3×D3—22no—
104C22×C3×D3—24no—
105C22×C3×D3—48no—
106C22×C3×D3—44no—
107C22×C3×D3—44no—
108C22×C3×D3C2×Q814yes—
109C2×C32×C4—28no—
110C2×C32×C4—24no—
111C2×C32×C4C2×D414yes—
112C2×C3⋊Dic3—216no—
113C2×C3⋊Dic3—24no—
114C2×C3⋊Dic3—24no—
115C2×C3⋊Dic3C2×D418yes—
116C2×C3×Dic3—24no—
117C2×C3×Dic3—24no—
118C2×C3×Dic3—24no—
119C2×C3×Dic3—24no—
120C2×C3×Dic3—22no—
121C2×C3×Dic3—48no—
122C2×C3×Dic3—44no—
123C22×C4⋊C4—31no—
124C22×C4⋊C4—92no—
125C22×C22⋊C4—31no—
126C22×C22⋊C4—92no—
127#399—98no—
128C2×#95—91no—
129C24×C3—21no—
130C24×C3—34no—
131C24×C3—32no—
132C24×C3—64no—
133C24×C3—64no—
134C24×C3—62no—
135C24×C3—62no—
136C24×C3C22×D311yescharacteristic
137C24×C3C22×D311yescharacteristic
138C23×D3—22no—
139C23×D3—24no—
140C23×D3—24no—
141C23×D3—22no—
142C23×D3Dic614yes—
143C23×D3C22×D312yes—
144C22×C3×C4—24no—
145C22×C3×C4—24no—
146C22×C3×C4—24no—
147C22×C3×C4—22no—
148C22×C3×C4—32no—
149C22×C3×C4—34no—
150C22×C3×C4—44no—
151C22×C3×C4—64no—
152C22×C3×C4—64no—
153C22×C3×C4—64no—
154C22×C3×C4—62no—
155C22×C3×C4—64no—
156C22×C3×C4#6714yes—
157C22×C3×C4#6714yes—
158C22×C3×C4C22×D312yes—
159C22×C3×C4C22×D312yes—
160C22×Dic3—24no—
161C22×Dic3—24no—
162C22×Dic3—24no—
163C22×Dic3—24no—
164C22×Dic3—22no—
165C22×Dic3—38no—
166C22×Dic3—38no—
167C22×Dic3—34no—
168C22×Dic3—34no—
169C22×Dic3—64no—
170C22×Dic3—68no—
171C22×Dic3—64no—
172C22×Dic3—64no—
173C22×Dic3—64no—
174C22×Dic3—64no—
175C22×Dic3—124no—
176C22×Dic3—124no—
177C22×Dic3C22×D312yes—
178C22×Dic3C22×D314yes—
179C3×C4⋊C4—68no—
180C3×C22⋊C4—68no—
181#217—616no—
182(C2×D3)⋊C4—28no—
183(C2×D3)⋊C4—616no—
184C4⋊Dic3—28no—
185Dic3⋊C4—616no—
186Dic3⋊C4—616no—
187C22×C32C22⋊Q818yes—
188C22×C32C22⋊Q814yes—
189C22×C32#12318yes—
190C22×C32#12314yes—
191C22×C32#12714yes—
192C22×C32C22×D412yes—
193C22×C32C22×D411yescharacteristic
194C22×C32C22×Q811yescharacteristic
195C22×C32C2×#4112yes—
196C22×C32C2×#4111yescharacteristic
197C2×C3×D3—28no—
198C2×C3×D3—24no—
199C2×C3×D3—44no—
200C2×C3×D3—42no—
201C2×C3×D3—42no—
202C2×C3×D3—416no—
203C32×C4—24no—
204C3⋊Dic3—28no—
205C3×Dic3—44no—
206C3×Dic3—42no—
207C25—31no—
208C23×C4—31no—
209C23×C4—32no—
210C23×C4—92no—
211C23×C4D3211yescharacteristic
212C2×C4⋊C4—34no—
213C2×C4⋊C4—64no—
214C2×C4⋊C4—98no—
215C2×C4⋊C4—188no—
216C2×C22⋊C4—34no—
217C2×C22⋊C4—64no—
218C2×C22⋊C4—98no—
219C2×C22⋊C4—188no—
220#95—94no—
221C23×C3—21no—
222C23×C3—22no—
223C23×C3—22no—
224C23×C3—24no—
225C23×C3—24no—
226C23×C3—22no—
227C23×C3—34no—
228C23×C3—616no—
229C23×C3—68no—
230C23×C3—64no—
231C23×C3—64no—
232C23×C3—62no—
233C23×C3—62no—
234C23×C3—128no—
235C23×C3—124no—
236C23×C3—124no—
237C23×C3C2×Dic612yes—
238C23×C3#23512yes—
239C23×C3#23514yes—
240C23×C3D3×D414yes—
241C23×C3D3×D414yes—
242C23×C3#23714yes—
243C23×C3D3×Q812yes—
244C23×C3#23912yes—
245C23×C3C2×#6712yes—
246C23×C3C2×#6712yes—
247C23×C3C23×D311yescharacteristic
248C23×C3C23×D311yescharacteristic
249C22×D3—216no—
250C22×D3—28no—
251C22×D3—22no—
252C22×D3—24no—
253C22×D3—24no—
254C22×D3—22no—
255C22×D3—48no—
256C22×D3—44no—
257C22×D3—44no—
258C22×D3C2×Dic614yes—
259C2×C3×C4—28no—
260C2×C3×C4—28no—
261C2×C3×C4—24no—
262C2×C3×C4—24no—
263C2×C3×C4—24no—
264C2×C3×C4—44no—
265C2×C3×C4—48no—
266C2×C3×C4—64no—
267C2×C3×C4—64no—
268C2×C3×C4—64no—
269C2×C3×C4—62no—
270C2×C3×C4—64no—
271C2×C3×C4—128no—
272C2×C3×C4—124no—
273C2×C3×C4C2×#6714yes—
274C2×C3×C4C2×#6714yes—
275C2×Dic3—24no—
276C2×Dic3—24no—
277C2×Dic3—24no—
278C2×Dic3—24no—
279C2×Dic3—22no—
280C2×Dic3—38no—
281C2×Dic3—38no—
282C2×Dic3—44no—
283C2×Dic3—48no—
284C2×Dic3—68no—
285C2×Dic3—616no—
286C2×Dic3—616no—
287C2×Dic3—64no—
288C2×Dic3—64no—
289C2×Dic3—64no—
290C2×Dic3—64no—
291C2×Dic3—124no—
292C2×Dic3—124no—
293C2×Dic3—1216no—
294C2×C32#39918yescomplemented
295C2×C32C2×C22⋊Q812yes—
296C2×C32C2×C22⋊Q811yescharacteristic
297C2×C32C2×#12312yes—
298C2×C32C2×#12311yescharacteristic
299C2×C32C2×#12711yescharacteristic
300C3×D3—44no—
301C24—32no—
302C24—34no—
303C24—62no—
304C24—64no—
305C24—64no—
306C24—62no—
307C24C2×D3211yescharacteristic
308C22×C4—24no—
309C22×C4—32no—
310C22×C4—34no—
311C22×C4—64no—
312C22×C4—64no—
313C22×C4—64no—
314C22×C4—62no—
315C22×C4—64no—
316C22×C4—94no—
317C22×C4—98no—
318C22×C4—184no—
319C22×C4—184no—
320C22×C4#62514yes—
321C22×C4C2×D3212yes—
322C4⋊C4—68no—
323C4⋊C4—1816no—
324C22⋊C4—68no—
325C22⋊C4—1816no—
326C22×C3—21no—
327C22×C3—21no—
328C22×C3—22no—
329C22×C3—22no—
330C22×C3—21no—
331C22×C3—28no—
332C22×C3—24no—
333C22×C3—28no—
334C22×C3—24no—
335C22×C3—24no—
336C22×C3—68no—
337C22×C3—64no—
338C22×C3—1216no—
339C22×C3—124no—
340C22×C3—122no—
341C22×C3—122no—
342C22×C3#87818yes—
343C22×C3#88318yes—
344C22×C3#89418yes—
345C22×C3#89618yes—
346C22×C3#92414yes—
347C22×C3#92914yes—
348C22×C3#93514yes—
349C22×C3#94014yes—
350C22×C3#94014yes—
351C22×C3#94614yes—
352C22×C3C22×Dic611yescharacteristic
353C22×C3C2×#23511yescharacteristic
354C22×C3C2×#23512yes—
355C22×C3C2×D3×D412yes—
356C22×C3C2×D3×D412yes—
357C22×C3C2×#23712yes—
358C22×C3C2×D3×Q811yescharacteristic
359C22×C3C2×#23911yescharacteristic
360C22×C3C22×#6711yescharacteristic
361C22×C3C22×#6711yescharacteristic
362C2×D3—28no—
363C2×D3—24no—
364C2×D3—416no—
365C2×D3—44no—
366C2×D3—42no—
367C2×D3—42no—
368C3×C4—24no—
369C3×C4—24no—
370C3×C4—44no—
371C3×C4—122no—
372C3×C4—124no—
373Dic3—44no—
374Dic3—42no—
375Dic3—68no—
376Dic3—68no—
377Dic3—128no—
378C32C2×#39911yescharacteristic, complemented, Sylow
379C23—34no—
380C23—62no—
381C23—64no—
382C23—64no—
383C23—62no—
384C23—68no—
385C23—616no—
386C23—128no—
387C23—124no—
388C23—124no—
389C23D3×Dic612yes—
390C23#379912yes—
391C23#380214yes—
392C23#380414yes—
393C23C2×#62512yes—
394C23C22×D3211yescharacteristic
395C2×C4—24no—
396C2×C4—28no—
397C2×C4—64no—
398C2×C4—64no—
399C2×C4—64no—
400C2×C4—62no—
401C2×C4—64no—
402C2×C4—98no—
403C2×C4—128no—
404C2×C4—124no—
405C2×C4—184no—
406C2×C4—184no—
407C2×C4—1816no—
408C2×C4C2×#62514yes—
409C2×C3—22no—
410C2×C3—21no—
411C2×C3—28no—
412C2×C3—22no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—124no—
416C2×C3#494918yescomplemented
417C2×C3#499318yescomplemented
418C2×C3C2×#87812yes—
419C2×C3C2×#88312yes—
420C2×C3C2×#89412yes—
421C2×C3C2×#89612yes—
422C2×C3C2×#92411yescharacteristic
423C2×C3C2×#92911yescharacteristic
424C2×C3C2×#93511yescharacteristic
425C2×C3C2×#94011yescharacteristic
426C2×C3C2×#94011yescharacteristic
427C2×C3C2×#94611yescharacteristic
428D3—44no—
429C22—64no—
430C22—68no—
431C22—124no—
432C22—1216no—
433C22—122no—
434C22—122no—
435C22#6385418yes—
436C22#6385614yes—
437C22#6389918yes—
438C22#6391414yes—
439C22#6396114yes—
440C22C2×D3×Dic611yescharacteristic
441C22C2×#379911yescharacteristic
442C22C2×#380212yes—
443C22C2×#380412yes—
444C22C22×#62511yescharacteristic
445C4—24no—
446C4—124no—
447C4—122no—
448C4—188no—
449C3—21no—
450C3C2×#494911yescharacteristic, complemented
451C3C2×#499311yescharacteristic, complemented
452C2—124no—
453C2#1059132418yesdirect product factor
454C2C2×#6385412yes—
455C2C2×#6385611yescharacteristic
456C2C2×#6389912yes—
457C2C2×#6391411yescharacteristic
458C2C2×#6396111yescharacteristic
subgroupG/H
centerC24C2×D32
commutator, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC23×C32×C4C22
socleC24×C32C23
prime radicalC24×C3×D3C22
hypercenterC23×C4D32
hypocenterC32C2×#399
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×C3×C4⋊Dic3C2semidirect
3. C22×#3724C2semidirect
5. C2×#63658C2semidirect
6. #10591324C2direct (N × H)
17. C2×C3×C4⋊Dic3C22semidirect
19. C2×#3724C22semidirect
22. #63658C22semidirect
28. C22×C4⋊Dic3D3semidirect
85. C2×C4⋊Dic3C2×D3semidirect
294. C2×C32#399semidirect
378. C32C2×#399semidirect
416. C2×C3#4949semidirect
417. C2×C3#4993semidirect
450. C3C2×#4949semidirect
451. C3C2×#4993semidirect
453. C2#10591324direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×(C2×D3)⋊C42
C22×C3×C4⋊Dic32
C22×#37242
C22×(C2×D3)⋊Dic32
C2×#636582
#105913242
C2×#49933
C2×#49493