Finite Group Databasebeta

← C2×#10591304 #11808124

Subgroups — C2×#10591304 #11808124

Order 1152.

2237 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×Dic6C211yesmaximal, characteristic, complemented
2C22×C3×(C2×D3)⋊C4C211yesmaximal, characteristic
3C22×(C2×D3)⋊Dic3C212yesmaximal
4C2×#63658C211yesmaximal, characteristic, complemented
5C2×#63579C212yesmaximal, complemented
6#10591304C218yesmaximal, direct product factor
7C2×#5231—31nomaximal
8C2×#4947—31nomaximal
9C24×C3×D3C2211yescharacteristic
10C23×C32×C4C2211yescharacteristic
11C23×C3⋊Dic3C2212yes—
12C23×C3×Dic3C2211yescharacteristic
13C23×C3×Dic3C2212yes—
14C22×C3×Dic6—24no—
15C22×C3×Dic6—28no—
16C22×C3×Dic6C2214yescomplemented
17C2×C3×(C2×D3)⋊C4—24no—
18C2×C3×(C2×D3)⋊C4C2214yes—
19C2×(C2×D3)⋊Dic3—28no—
20C2×(C2×D3)⋊Dic3C2218yes—
21#63658C2214yescomplemented
22#63579C2218yescomplemented
23C23×C3×Q8—31no—
24C23×Dic6D311yescharacteristic, complemented
25C22×C3×C22⋊C4—31no—
26C22×#217—32no—
27C22×(C2×D3)⋊C4—32no—
28C22×(C2×D3)⋊C4D311yescharacteristic
29#5231—38no—
30C2×C3⋊#95—31no—
31C2×C3⋊#95—31no—
32C2×C3⋊#95—32no—
33C2×C3⋊#95—32no—
34C2×C3⋊#95—61no—
35#4947—38no—
36C24×C32C2311yescharacteristic
37C23×C3×D3—22no—
38C23×C3×D3—24no—
39C23×C3×D3—22no—
40C23×C3×D3—24no—
41C23×C3×D3Q814yescomplemented
42C23×C3×D3C2312yes—
43C22×C32×C4—24no—
44C22×C32×C4D414yes—
45C22×C32×C4C2312yes—
46C22×C3⋊Dic3—24no—
47C22×C3⋊Dic3—24no—
48C22×C3⋊Dic3—24no—
49C22×C3⋊Dic3C2314yes—
50C22×C3×Dic3—24no—
51C22×C3×Dic3—24no—
52C22×C3×Dic3—22no—
53C22×C3×Dic3—24no—
54C22×C3×Dic3D418yes—
55C22×C3×Dic3C2312yes—
56C22×C3×Dic3C2314yes—
57C2×C3×Dic6—232no—
58C2×C3×Dic6—28no—
59C2×C3×Dic6—216no—
60C3×(C2×D3)⋊C4—28no—
61(C2×D3)⋊Dic3—216no—
62C2×#393—91noSylow
63C25×C3—31no—
64C24×D3C2×D311yescharacteristic
65C22×C3×Q8—34no—
66C22×C3×Q8—68no—
67C22×C3×Q8—64no—
68C23×C3×C4—21no—
69C23×C3×C4—32no—
70C23×C3×C4—31no—
71C23×C3×C4C2×D311yescharacteristic
72C23×C3×C4C2×D311yescharacteristic
73C23×Dic3—32no—
74C23×Dic3—32no—
75C23×Dic3—62no—
76C23×Dic3C2×D311yescharacteristic
77C23×Dic3C2×D312yes—
78C22×Dic6—24no—
79C22×Dic6—28no—
80C22×Dic6C2×D314yescomplemented
81C2×C3×C22⋊C4—34no—
82C2×C3×C22⋊C4—64no—
83C2×#217—38no—
84C2×#217—68no—
85C2×(C2×D3)⋊C4—24no—
86C2×(C2×D3)⋊C4—38no—
87C2×(C2×D3)⋊C4—68no—
88C2×(C2×D3)⋊C4C2×D314yes—
89C3⋊#95—34no—
90C3⋊#95—34no—
91C3⋊#95—38no—
92C3⋊#95—38no—
93C3⋊#95—64no—
94C23×C32C2×D414yes—
95C23×C32C2×D412yes—
96C23×C32C2×Q812yes—
97C23×C32#4112yes—
98C23×C32#4114yes—
99C23×C32C2411yescharacteristic
100C22×C3×D3—216no—
101C22×C3×D3—28no—
102C22×C3×D3—24no—
103C22×C3×D3—22no—
104C22×C3×D3—22no—
105C22×C3×D3—24no—
106C22×C3×D3—44no—
107C22×C3×D3—48no—
108C22×C3×D3—44no—
109C22×C3×D3C2×Q814yescomplemented
110C2×C32×C4—28no—
111C2×C32×C4—24no—
112C2×C32×C4C2×D414yes—
113C2×C3⋊Dic3—24no—
114C2×C3⋊Dic3—24no—
115C2×C3⋊Dic3—24no—
116C2×C3⋊Dic3—48no—
117C2×C3×Dic3—216no—
118C2×C3×Dic3—24no—
119C2×C3×Dic3—24no—
120C2×C3×Dic3—22no—
121C2×C3×Dic3—24no—
122C2×C3×Dic3—44no—
123C2×C3×Dic3C2×D418yes—
124C3×Dic6—232no—
125C23×Q8—31no—
126C22×C22⋊C4—31no—
127C22×C22⋊C4—92no—
128#393—98no—
129C2×#95—92no—
130C2×#95—91no—
131C24×C3—21no—
132C24×C3—34no—
133C24×C3—32no—
134C24×C3—64no—
135C24×C3—62no—
136C24×C3—64no—
137C24×C3—62no—
138C24×C3C22×D311yescharacteristic
139C24×C3C22×D311yescharacteristic
140C23×D3—22no—
141C23×D3—24no—
142C23×D3—24no—
143C23×D3—22no—
144C23×D3Dic614yescomplemented
145C23×D3C22×D312yes—
146C2×C3×Q8—616no—
147C2×C3×Q8—632no—
148C2×C3×Q8—68no—
149C22×C3×C4—24no—
150C22×C3×C4—24no—
151C22×C3×C4—24no—
152C22×C3×C4—22no—
153C22×C3×C4—38no—
154C22×C3×C4—34no—
155C22×C3×C4—32no—
156C22×C3×C4—44no—
157C22×C3×C4—64no—
158C22×C3×C4—64no—
159C22×C3×C4—64no—
160C22×C3×C4—62no—
161C22×C3×C4#6714yes—
162C22×C3×C4#6714yes—
163C22×C3×C4C22×D312yes—
164C22×C3×C4C22×D312yes—
165C22×Dic3—24no—
166C22×Dic3—24no—
167C22×Dic3—24no—
168C22×Dic3—22no—
169C22×Dic3—34no—
170C22×Dic3—34no—
171C22×Dic3—64no—
172C22×Dic3—68no—
173C22×Dic3—64no—
174C22×Dic3—64no—
175C22×Dic3—64no—
176C22×Dic3—64no—
177C22×Dic3—64no—
178C22×Dic3—64no—
179C22×Dic3—124no—
180C22×Dic3—124no—
181C22×Dic3#6718yes—
182C22×Dic3C22×D312yes—
183C22×Dic3C22×D314yes—
184C2×Dic6—232no—
185C2×Dic6—28no—
186C2×Dic6—216no—
187C3×C22⋊C4—68no—
188#217—616no—
189(C2×D3)⋊C4—28no—
190(C2×D3)⋊C4—616no—
191C22×C32#12014yes—
192C22×C32C22⋊Q818yes—
193C22×C32C22⋊Q814yes—
194C22×C32#12418yes—
195C22×C32#12414yes—
196C22×C32C22×D412yes—
197C22×C32C22×D411yescharacteristic
198C22×C32C22×Q811yescharacteristic
199C22×C32C2×#4111yescharacteristic
200C22×C32C2×#4112yes—
201C2×C3×D3—28no—
202C2×C3×D3—24no—
203C2×C3×D3—42no—
204C2×C3×D3—44no—
205C2×C3×D3—42no—
206C2×C3×D3—416no—
207C32×C4—24no—
208C3⋊Dic3—44no—
209C3×Dic3—28no—
210C3×Dic3—42no—
211C25—31no—
212C22×Q8—34no—
213C22×Q8—68no—
214C22×Q8—64no—
215C23×C4—32no—
216C23×C4—31no—
217C23×C4—92no—
218C23×C4D3211yescharacteristic
219C2×C22⋊C4—34no—
220C2×C22⋊C4—64no—
221C2×C22⋊C4—98no—
222C2×C22⋊C4—188no—
223#95—98no—
224#95—94no—
225C23×C3—21no—
226C23×C3—22no—
227C23×C3—24no—
228C23×C3—22no—
229C23×C3—22no—
230C23×C3—24no—
231C23×C3—34no—
232C23×C3—68no—
233C23×C3—616no—
234C23×C3—64no—
235C23×C3—62no—
236C23×C3—64no—
237C23×C3—62no—
238C23×C3—124no—
239C23×C3—128no—
240C23×C3—124no—
241C23×C3C2×Dic612yes—
242C23×C3#23512yes—
243C23×C3D3×D414yes—
244C23×C3#23714yes—
245C23×C3D3×Q812yes—
246C23×C3#23914yes—
247C23×C3#23912yes—
248C23×C3C2×#6712yes—
249C23×C3C2×#6712yes—
250C23×C3C2×#6714yes—
251C23×C3C23×D311yescharacteristic
252C23×C3C23×D311yescharacteristic
253C22×D3—216no—
254C22×D3—28no—
255C22×D3—22no—
256C22×D3—24no—
257C22×D3—24no—
258C22×D3—22no—
259C22×D3—48no—
260C22×D3—44no—
261C22×D3—44no—
262C22×D3C2×Dic614yescomplemented
263C3×Q8—632no—
264C2×C3×C4—28no—
265C2×C3×C4—28no—
266C2×C3×C4—24no—
267C2×C3×C4—24no—
268C2×C3×C4—24no—
269C2×C3×C4—38no—
270C2×C3×C4—44no—
271C2×C3×C4—48no—
272C2×C3×C4—616no—
273C2×C3×C4—64no—
274C2×C3×C4—64no—
275C2×C3×C4—64no—
276C2×C3×C4—62no—
277C2×C3×C4—124no—
278C2×C3×C4C2×#6714yes—
279C2×C3×C4C2×#6714yes—
280C2×Dic3—216no—
281C2×Dic3—24no—
282C2×Dic3—24no—
283C2×Dic3—24no—
284C2×Dic3—22no—
285C2×Dic3—44no—
286C2×Dic3—68no—
287C2×Dic3—64no—
288C2×Dic3—64no—
289C2×Dic3—64no—
290C2×Dic3—64no—
291C2×Dic3—64no—
292C2×Dic3—64no—
293C2×Dic3—124no—
294C2×Dic3—124no—
295C2×Dic3—1216no—
296C2×Dic3—128no—
297C2×Dic3—128no—
298C2×Dic3C2×#6718yes—
299Dic6—232no—
300C2×C32#39318yescomplemented
301C2×C32C2×#12011yescharacteristic
302C2×C32C2×C22⋊Q812yes—
303C2×C32C2×C22⋊Q811yescharacteristic
304C2×C32C2×#12412yes—
305C2×C32C2×#12411yescharacteristic
306C3×D3—44no—
307C24—32no—
308C24—34no—
309C24—64no—
310C24—62no—
311C24—62no—
312C24—64no—
313C24C2×D3211yescharacteristic
314C2×Q8—616no—
315C2×Q8—632no—
316C2×Q8—68no—
317C22×C4—24no—
318C22×C4—34no—
319C22×C4—38no—
320C22×C4—32no—
321C22×C4—64no—
322C22×C4—64no—
323C22×C4—64no—
324C22×C4—62no—
325C22×C4—94no—
326C22×C4—184no—
327C22×C4—184no—
328C22×C4—184no—
329C22×C4#62514yes—
330C22×C4C2×D3212yes—
331C22⋊C4—68no—
332C22⋊C4—1816no—
333C22×C3—21no—
334C22×C3—22no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—22no—
338C22×C3—24no—
339C22×C3—24no—
340C22×C3—28no—
341C22×C3—28no—
342C22×C3—24no—
343C22×C3—64no—
344C22×C3—68no—
345C22×C3—1216no—
346C22×C3—122no—
347C22×C3—124no—
348C22×C3—122no—
349C22×C3#87818yes—
350C22×C3#88518yes—
351C22×C3#92414yes—
352C22×C3#93614yes—
353C22×C3#93714yes—
354C22×C3#94614yes—
355C22×C3#94618yes—
356C22×C3#94714yes—
357C22×C3#94718yes—
358C22×C3#95314yes—
359C22×C3C22×Dic611yescharacteristic
360C22×C3C2×#23511yescharacteristic
361C22×C3C2×D3×D412yes—
362C22×C3C2×#23712yes—
363C22×C3C2×D3×Q811yescharacteristic
364C22×C3C2×#23912yes—
365C22×C3C2×#23911yescharacteristic
366C22×C3C22×#6711yescharacteristic
367C22×C3C22×#6711yescharacteristic
368C22×C3C22×#6712yes—
369C2×D3—28no—
370C2×D3—24no—
371C2×D3—416no—
372C2×D3—44no—
373C2×D3—42no—
374C2×D3—42no—
375C3×C4—24no—
376C3×C4—24no—
377C3×C4—44no—
378C3×C4—68no—
379C3×C4—122no—
380Dic3—28no—
381Dic3—42no—
382Dic3—128no—
383Dic3—124no—
384Dic3—124no—
385C32C2×#39311yescharacteristic, complemented, Sylow
386C23—34no—
387C23—64no—
388C23—62no—
389C23—62no—
390C23—64no—
391C23—68no—
392C23—616no—
393C23—124no—
394C23—128no—
395C23—124no—
396C23D3×Dic612yes—
397C23#379614yes—
398C23#379912yes—
399C23C2×#62512yes—
400C23D3×#6714yes—
401C23C22×D3211yescharacteristic
402Q8—632no—
403C2×C4—24no—
404C2×C4—28no—
405C2×C4—38no—
406C2×C4—64no—
407C2×C4—64no—
408C2×C4—616no—
409C2×C4—64no—
410C2×C4—62no—
411C2×C4—124no—
412C2×C4—184no—
413C2×C4—184no—
414C2×C4—184no—
415C2×C4—368no—
416C2×C4C2×#62514yes—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—28no—
420C2×C3—22no—
421C2×C3—21no—
422C2×C3—22no—
423C2×C3—124no—
424C2×C3#494718yescomplemented
425C2×C3#523118yescomplemented
426C2×C3C2×#87812yes—
427C2×C3C2×#88512yes—
428C2×C3C2×#92411yescharacteristic
429C2×C3C2×#93611yescharacteristic
430C2×C3C2×#93711yescharacteristic
431C2×C3C2×#94611yescharacteristic
432C2×C3C2×#94612yes—
433C2×C3C2×#94711yescharacteristic
434C2×C3C2×#94712yes—
435C2×C3C2×#95311yescharacteristic
436D3—44no—
437C22—64no—
438C22—68no—
439C22—122no—
440C22—1216no—
441C22—122no—
442C22—124no—
443C22#6385614yes—
444C22#6386314yes—
445C22#6388718yes—
446C22#6390718yes—
447C22#6397614yes—
448C22C2×D3×Dic611yescharacteristic
449C22C2×#379612yes—
450C22C2×#379911yescharacteristic
451C22C22×#62511yescharacteristic
452C22C2×D3×#6712yes—
453C4—24no—
454C4—68no—
455C4—122no—
456C4—364no—
457C3—21no—
458C3C2×#494711yescharacteristic, complemented
459C3C2×#523111yescharacteristic, complemented
460C2—124no—
461C2#1059130418yesdirect product factor
462C2C2×#6385611yescharacteristic
463C2C2×#6386311yescharacteristic
464C2C2×#6388712yes—
465C2C2×#6390712yes—
466C2C2×#6397611yescharacteristic
subgroupG/H
centerC24C2×D32
commutator, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC23×C32×C4C22
socleC24×C32C23
prime radicalC24×C3×D3C22
hypercenterC23×C4D32
hypocenterC32C2×#393
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C23×C3×Dic6C2semidirect
4. C2×#63658C2semidirect
5. C2×#63579C2semidirect
6. #10591304C2direct (N × H)
16. C22×C3×Dic6C22semidirect
21. #63658C22semidirect
22. #63579C22semidirect
24. C23×Dic6D3semidirect
41. C23×C3×D3Q8semidirect
80. C22×Dic6C2×D3semidirect
109. C22×C3×D3C2×Q8semidirect
144. C23×D3Dic6semidirect
262. C22×D3C2×Dic6semidirect
300. C2×C32#393semidirect
385. C32C2×#393semidirect
424. C2×C3#4947semidirect
425. C2×C3#5231semidirect
458. C3C2×#4947semidirect
459. C3C2×#5231semidirect
461. C2#10591304direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×Dic62
C22×C3×(C2×D3)⋊C42
C22×(C2×D3)⋊Dic32
C2×#636582
C2×#635792
#105913042
C2×#52313
C2×#49473