Finite Group Databasebeta

← C2×#10591314 #11808308

Subgroups — C2×#10591314 #11808308

Order 1152.

1805 conjugacy classes of subgroups.

The subgroup lattice has 452 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×(C2×D3)⋊Dic3C212yesmaximal
4C2×#63658C211yesmaximal, characteristic, complemented
5C2×#63579C212yesmaximal, complemented
6#10591314C218yesmaximal, direct product factor
7C2×#4992—31nomaximal
8C2×#4953—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×(C2×D3)⋊Dic3—28no—
19C2×(C2×D3)⋊Dic3C2218yes—
20#63658C2214yescomplemented
21#63579C2218yescomplemented
22C22×C3×C4⋊C4—31no—
23C22×C3×C22⋊C4—31no—
24C22×#217—32no—
25C22×(C2×D3)⋊C4—32no—
26C22×(C2×D3)⋊C4D311yescharacteristic
27C22×C4⋊Dic3D311yescharacteristic, complemented
28C2×C3⋊#95—31no—
29C2×C3⋊#95—31no—
30C2×C3⋊#95—32no—
31C2×C3⋊#95—32no—
32C2×C3⋊#95—61no—
33#4992—38no—
34#4953—38no—
35C24×C32C2311yescharacteristic
36C23×C3×D3—22no—
37C23×C3×D3—22no—
38C23×C3×D3—24no—
39C23×C3×D3—24no—
40C23×C3×D3D414yes—
41C23×C3×D3C2312yes—
42C22×C32×C4—24no—
43C22×C32×C4D414yes—
44C22×C32×C4C2312yes—
45C22×C3⋊Dic3—24no—
46C22×C3⋊Dic3—24no—
47C22×C3⋊Dic3—24no—
48C22×C3⋊Dic3C2314yes—
49C22×C3×Dic3—24no—
50C22×C3×Dic3—22no—
51C22×C3×Dic3—24no—
52C22×C3×Dic3—24no—
53C22×C3×Dic3—24no—
54C22×C3×Dic3C2314yes—
55C22×C3×Dic3C2312yes—
56C3×(C2×D3)⋊C4—28no—
57C3×C4⋊Dic3—28no—
58(C2×D3)⋊Dic3—216no—
59C2×#397—91noSylow
60C25×C3—31no—
61C24×D3C2×D311yescharacteristic
62C23×C3×C4—21no—
63C23×C3×C4—31no—
64C23×C3×C4—32no—
65C23×C3×C4C2×D311yescharacteristic
66C23×C3×C4C2×D311yescharacteristic
67C23×Dic3—32no—
68C23×Dic3—32no—
69C23×Dic3—62no—
70C23×Dic3C2×D311yescharacteristic
71C23×Dic3C2×D312yes—
72C2×C3×C4⋊C4—34no—
73C2×C3×C4⋊C4—64no—
74C2×C3×C22⋊C4—34no—
75C2×C3×C22⋊C4—64no—
76C2×#217—38no—
77C2×#217—68no—
78C2×(C2×D3)⋊C4—24no—
79C2×(C2×D3)⋊C4—38no—
80C2×(C2×D3)⋊C4—68no—
81C2×(C2×D3)⋊C4C2×D314yes—
82C2×C4⋊Dic3—24no—
83C2×C4⋊Dic3C2×D314yescomplemented
84C3⋊#95—34no—
85C3⋊#95—34no—
86C3⋊#95—38no—
87C3⋊#95—38no—
88C3⋊#95—64no—
89C23×C32C2×D412yes—
90C23×C32C2×D412yes—
91C23×C32#4112yes—
92C23×C32#4114yes—
93C23×C32#4114yes—
94C23×C32C2411yescharacteristic
95C22×C3×D3—28no—
96C22×C3×D3—216no—
97C22×C3×D3—22no—
98C22×C3×D3—22no—
99C22×C3×D3—24no—
100C22×C3×D3—24no—
101C22×C3×D3—44no—
102C22×C3×D3—44no—
103C22×C3×D3—48no—
104C22×C3×D3C2×D414yes—
105C2×C32×C4—28no—
106C2×C32×C4—24no—
107C2×C32×C4C2×D414yes—
108C2×C3⋊Dic3—24no—
109C2×C3⋊Dic3—24no—
110C2×C3⋊Dic3—24no—
111C2×C3⋊Dic3—48no—
112C2×C3×Dic3—24no—
113C2×C3×Dic3—24no—
114C2×C3×Dic3—22no—
115C2×C3×Dic3—24no—
116C2×C3×Dic3—24no—
117C2×C3×Dic3—48no—
118C2×C3×Dic3—44no—
119C22×C4⋊C4—31no—
120C22×C22⋊C4—31no—
121C22×C22⋊C4—92no—
122#397—98no—
123C2×#95—92no—
124C2×#95—91no—
125C24×C3—21no—
126C24×C3—34no—
127C24×C3—32no—
128C24×C3—64no—
129C24×C3—62no—
130C24×C3—64no—
131C24×C3—62no—
132C24×C3C22×D311yescharacteristic
133C24×C3C22×D311yescharacteristic
134C23×D3—22no—
135C23×D3—24no—
136C23×D3—24no—
137C23×D3—22no—
138C23×D3D1214yes—
139C23×D3C22×D312yes—
140C22×C3×C4—24no—
141C22×C3×C4—24no—
142C22×C3×C4—24no—
143C22×C3×C4—22no—
144C22×C3×C4—32no—
145C22×C3×C4—34no—
146C22×C3×C4—44no—
147C22×C3×C4—64no—
148C22×C3×C4—64no—
149C22×C3×C4—64no—
150C22×C3×C4—62no—
151C22×C3×C4—64no—
152C22×C3×C4#6714yes—
153C22×C3×C4#6714yes—
154C22×C3×C4C22×D312yes—
155C22×C3×C4C22×D312yes—
156C22×Dic3—24no—
157C22×Dic3—24no—
158C22×Dic3—24no—
159C22×Dic3—24no—
160C22×Dic3—22no—
161C22×Dic3—34no—
162C22×Dic3—34no—
163C22×Dic3—64no—
164C22×Dic3—68no—
165C22×Dic3—64no—
166C22×Dic3—64no—
167C22×Dic3—64no—
168C22×Dic3—64no—
169C22×Dic3—64no—
170C22×Dic3—64no—
171C22×Dic3—124no—
172C22×Dic3—124no—
173C22×Dic3C22×D312yes—
174C22×Dic3C22×D314yes—
175C3×C4⋊C4—68no—
176C3×C22⋊C4—68no—
177#217—616no—
178(C2×D3)⋊C4—28no—
179(C2×D3)⋊C4—616no—
180C4⋊Dic3—28no—
181C22×C32#12114yes—
182C22×C32#12318yes—
183C22×C32#12314yes—
184C22×C32#12414yes—
185C22×C32#12618yes—
186C22×C32C22×D411yescharacteristic
187C22×C32C22×D411yescharacteristic
188C22×C32C2×#4111yescharacteristic
189C22×C32C2×#4112yes—
190C22×C32C2×#4112yes—
191C2×C3×D3—24no—
192C2×C3×D3—28no—
193C2×C3×D3—42no—
194C2×C3×D3—42no—
195C2×C3×D3—44no—
196C2×C3×D3—416no—
197C32×C4—24no—
198C3⋊Dic3—44no—
199C3×Dic3—44no—
200C3×Dic3—42no—
201C25—31no—
202C23×C4—31no—
203C23×C4—32no—
204C23×C4—92no—
205C23×C4D3211yescharacteristic
206C2×C4⋊C4—34no—
207C2×C4⋊C4—64no—
208C2×C22⋊C4—34no—
209C2×C22⋊C4—64no—
210C2×C22⋊C4—98no—
211C2×C22⋊C4—188no—
212#95—98no—
213#95—94no—
214C23×C3—21no—
215C23×C3—22no—
216C23×C3—24no—
217C23×C3—22no—
218C23×C3—24no—
219C23×C3—22no—
220C23×C3—34no—
221C23×C3—616no—
222C23×C3—68no—
223C23×C3—64no—
224C23×C3—62no—
225C23×C3—64no—
226C23×C3—62no—
227C23×C3—128no—
228C23×C3—124no—
229C23×C3—124no—
230C23×C3C2×D1212yes—
231C23×C3#23512yes—
232C23×C3#23514yes—
233C23×C3D3×D412yes—
234C23×C3#23712yes—
235C23×C3#23714yes—
236C23×C3#23714yes—
237C23×C3#23914yes—
238C23×C3C2×#6712yes—
239C23×C3C2×#6712yes—
240C23×C3C23×D311yescharacteristic
241C23×C3C23×D311yescharacteristic
242C22×D3—216no—
243C22×D3—28no—
244C22×D3—22no—
245C22×D3—24no—
246C22×D3—24no—
247C22×D3—22no—
248C22×D3—48no—
249C22×D3—44no—
250C22×D3—44no—
251C22×D3C2×D1214yes—
252C2×C3×C4—28no—
253C2×C3×C4—28no—
254C2×C3×C4—24no—
255C2×C3×C4—24no—
256C2×C3×C4—24no—
257C2×C3×C4—44no—
258C2×C3×C4—48no—
259C2×C3×C4—64no—
260C2×C3×C4—64no—
261C2×C3×C4—64no—
262C2×C3×C4—62no—
263C2×C3×C4—64no—
264C2×C3×C4—128no—
265C2×C3×C4—124no—
266C2×C3×C4C2×#6714yes—
267C2×C3×C4C2×#6714yes—
268C2×Dic3—24no—
269C2×Dic3—24no—
270C2×Dic3—24no—
271C2×Dic3—24no—
272C2×Dic3—22no—
273C2×Dic3—44no—
274C2×Dic3—48no—
275C2×Dic3—68no—
276C2×Dic3—64no—
277C2×Dic3—64no—
278C2×Dic3—64no—
279C2×Dic3—64no—
280C2×Dic3—64no—
281C2×Dic3—64no—
282C2×Dic3—124no—
283C2×Dic3—124no—
284C2×Dic3—1216no—
285C2×Dic3—128no—
286C2×Dic3—128no—
287C2×C32#39718yescomplemented
288C2×C32C2×#12111yescharacteristic
289C2×C32C2×#12312yes—
290C2×C32C2×#12311yescharacteristic
291C2×C32C2×#12411yescharacteristic
292C2×C32C2×#12612yes—
293C3×D3—44no—
294C24—32no—
295C24—34no—
296C24—62no—
297C24—64no—
298C24—64no—
299C24—62no—
300C24C2×D3211yescharacteristic
301C22×C4—24no—
302C22×C4—32no—
303C22×C4—34no—
304C22×C4—64no—
305C22×C4—64no—
306C22×C4—64no—
307C22×C4—62no—
308C22×C4—64no—
309C22×C4—94no—
310C22×C4—184no—
311C22×C4—184no—
312C22×C4—184no—
313C22×C4#62514yes—
314C22×C4C2×D3212yes—
315C4⋊C4—68no—
316C22⋊C4—68no—
317C22⋊C4—1816no—
318C22×C3—21no—
319C22×C3—22no—
320C22×C3—21no—
321C22×C3—22no—
322C22×C3—21no—
323C22×C3—28no—
324C22×C3—24no—
325C22×C3—28no—
326C22×C3—24no—
327C22×C3—24no—
328C22×C3—68no—
329C22×C3—64no—
330C22×C3—1216no—
331C22×C3—124no—
332C22×C3—122no—
333C22×C3—122no—
334C22×C3#87918yes—
335C22×C3#88618yes—
336C22×C3#89418yes—
337C22×C3#89818yes—
338C22×C3#92914yes—
339C22×C3#93014yes—
340C22×C3#93514yes—
341C22×C3#93614yes—
342C22×C3#93814yes—
343C22×C3#94714yes—
344C22×C3C22×D1211yescharacteristic
345C22×C3C2×#23511yescharacteristic
346C22×C3C2×#23512yes—
347C22×C3C2×D3×D411yescharacteristic
348C22×C3C2×#23711yescharacteristic
349C22×C3C2×#23712yes—
350C22×C3C2×#23712yes—
351C22×C3C2×#23912yes—
352C22×C3C22×#6711yescharacteristic
353C22×C3C22×#6711yescharacteristic
354C2×D3—28no—
355C2×D3—24no—
356C2×D3—416no—
357C2×D3—44no—
358C2×D3—42no—
359C2×D3—42no—
360C3×C4—24no—
361C3×C4—24no—
362C3×C4—44no—
363C3×C4—124no—
364C3×C4—122no—
365Dic3—42no—
366Dic3—44no—
367Dic3—128no—
368Dic3—124no—
369Dic3—124no—
370C32C2×#39711yescharacteristic, complemented, Sylow
371C23—34no—
372C23—62no—
373C23—64no—
374C23—64no—
375C23—62no—
376C23—616no—
377C23—68no—
378C23—128no—
379C23—124no—
380C23—124no—
381C23#379512yes—
382C23#379614yes—
383C23D3×D1212yes—
384C23#380414yes—
385C23C2×#62512yes—
386C23C22×D3211yescharacteristic
387C2×C4—24no—
388C2×C4—28no—
389C2×C4—64no—
390C2×C4—64no—
391C2×C4—64no—
392C2×C4—62no—
393C2×C4—64no—
394C2×C4—124no—
395C2×C4—128no—
396C2×C4—184no—
397C2×C4—184no—
398C2×C4—184no—
399C2×C4—368no—
400C2×C4C2×#62514yes—
401C2×C3—22no—
402C2×C3—21no—
403C2×C3—28no—
404C2×C3—22no—
405C2×C3—21no—
406C2×C3—21no—
407C2×C3—124no—
408C2×C3#495318yescomplemented
409C2×C3#499218yescomplemented
410C2×C3C2×#87912yes—
411C2×C3C2×#88612yes—
412C2×C3C2×#89412yes—
413C2×C3C2×#89812yes—
414C2×C3C2×#92911yescharacteristic
415C2×C3C2×#93011yescharacteristic
416C2×C3C2×#93511yescharacteristic
417C2×C3C2×#93611yescharacteristic
418C2×C3C2×#93811yescharacteristic
419C2×C3C2×#94711yescharacteristic
420D3—44no—
421C22—68no—
422C22—64no—
423C22—124no—
424C22—122no—
425C22—1216no—
426C22—122no—
427C22#6385818yes—
428C22#6386314yes—
429C22#6389018yes—
430C22#6390814yes—
431C22#6396114yes—
432C22C2×#379511yescharacteristic
433C22C2×#379612yes—
434C22C2×D3×D1211yescharacteristic
435C22C2×#380412yes—
436C22C22×#62511yescharacteristic
437C4—24no—
438C4—122no—
439C4—124no—
440C4—364no—
441C3—21no—
442C3C2×#495311yescharacteristic, complemented
443C3C2×#499211yescharacteristic, complemented
444C2—124no—
445C2#1059131418yesdirect product factor
446C2C2×#6385812yes—
447C2C2×#6386311yescharacteristic
448C2C2×#6389012yes—
449C2C2×#6390811yescharacteristic
450C2C2×#6396111yescharacteristic
subgroupG/H
centerC24C2×D32
commutator, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC23×C32×C4C22
socleC24×C32C23
prime radicalC24×C3×D3C22
hypercenterC23×C4D32
hypocenterC32C2×#397
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
4. C2×#63658C2semidirect
5. C2×#63579C2semidirect
6. #10591314C2direct (N × H)
17. C2×C3×C4⋊Dic3C22semidirect
20. #63658C22semidirect
21. #63579C22semidirect
27. C22×C4⋊Dic3D3semidirect
83. C2×C4⋊Dic3C2×D3semidirect
287. C2×C32#397semidirect
370. C32C2×#397semidirect
408. C2×C3#4953semidirect
409. C2×C3#4992semidirect
442. C3C2×#4953semidirect
443. C3C2×#4992semidirect
445. C2#10591314direct (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×(C2×D3)⋊Dic32
C2×#636582
C2×#635792
#105913142
C2×#49923
C2×#49533