Finite Group Databasebeta

← C2×#10591315 #11808307

Subgroups — C2×#10591315 #11808307

Order 1152.

1849 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
2C22×C3×(C2×D3)⋊C4C211yesmaximal, characteristic
3C22×(C2×D3)⋊Dic3C212yesmaximal
4C2×C3×C3⋊#95C211yesmaximal, characteristic, complemented
5C2×#63579C212yesmaximal, complemented
6#10591315C218yesmaximal, direct product factor
7C2×#4953—31nomaximal
8C2×#4674—31nomaximal
9C24×C3×D3C2211yescharacteristic
10C23×C32×C4C2211yescharacteristic
11C23×C3⋊Dic3C2212yes—
12C23×C3×Dic3C2211yescharacteristic
13C23×C3×Dic3C2212yes—
14C2×C4⋊(C3⋊Dic3)—24no—
15C2×C4⋊(C3⋊Dic3)C2214yescomplemented
16C2×C3×(C2×D3)⋊C4—24no—
17C2×C3×(C2×D3)⋊C4C2214yes—
18C2×(C2×D3)⋊Dic3—28no—
19C2×(C2×D3)⋊Dic3C2218yes—
20C3×C3⋊#95C2214yescomplemented
21#63579C2218yescomplemented
22C22×C3×C22⋊C4—31no—
23C22×#217—32no—
24C22×(C2×D3)⋊C4—32no—
25C22×(C2×D3)⋊C4D311yescharacteristic
26C22×C4⋊Dic3—31no—
27C22×C4⋊Dic3—31no—
28C22×C4⋊Dic3—61no—
29C2×C3×#95—31no—
30C2×C3⋊#95—32no—
31C2×C3⋊#95—32no—
32C2×C3⋊#95D311yescharacteristic, complemented
33#4953—38no—
34#4674—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—22no—
50C22×C3×Dic3—24no—
51C22×C3×Dic3—24no—
52C22×C3×Dic3—24no—
53C22×C3×Dic3—24no—
54C22×C3×Dic3C2312yes—
55C22×C3×Dic3C2314yes—
56C4⋊(C3⋊Dic3)—28no—
57C3×(C2×D3)⋊C4—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×C22⋊C4—34no—
73C2×C3×C22⋊C4—64no—
74C2×#217—38no—
75C2×#217—68no—
76C2×(C2×D3)⋊C4—24no—
77C2×(C2×D3)⋊C4—38no—
78C2×(C2×D3)⋊C4—68no—
79C2×(C2×D3)⋊C4C2×D314yes—
80C2×C4⋊Dic3—34no—
81C2×C4⋊Dic3—34no—
82C2×C4⋊Dic3—64no—
83C2×C4⋊Dic3—68no—
84C2×C4⋊Dic3—64no—
85C2×C4⋊Dic3—64no—
86C3×#95—34no—
87C3⋊#95—38no—
88C3⋊#95—38no—
89C3⋊#95C2×D314yescomplemented
90C23×C32C2×D412yes—
91C23×C32C2×D412yes—
92C23×C32#4114yes—
93C23×C32#4112yes—
94C23×C32#4114yes—
95C23×C32C2411yescharacteristic
96C22×C3×D3—28no—
97C22×C3×D3—216no—
98C22×C3×D3—22no—
99C22×C3×D3—22no—
100C22×C3×D3—24no—
101C22×C3×D3—24no—
102C22×C3×D3—44no—
103C22×C3×D3—44no—
104C22×C3×D3—48no—
105C22×C3×D3C2×D414yes—
106C2×C32×C4—28no—
107C2×C32×C4—24no—
108C2×C32×C4C2×D414yes—
109C2×C3⋊Dic3—24no—
110C2×C3⋊Dic3—24no—
111C2×C3⋊Dic3—24no—
112C2×C3⋊Dic3—48no—
113C2×C3×Dic3—24no—
114C2×C3×Dic3—22no—
115C2×C3×Dic3—24no—
116C2×C3×Dic3—24no—
117C2×C3×Dic3—24no—
118C2×C3×Dic3—48no—
119C2×C3×Dic3—44no—
120C22×C4⋊C4—91no—
121C22×C22⋊C4—31no—
122C22×C22⋊C4—92no—
123#397—98no—
124C2×#95—31no—
125C2×#95—92no—
126C24×C3—21no—
127C24×C3—34no—
128C24×C3—32no—
129C24×C3—62no—
130C24×C3—64no—
131C24×C3—64no—
132C24×C3—62no—
133C24×C3C22×D311yescharacteristic
134C24×C3C22×D311yescharacteristic
135C23×D3—22no—
136C23×D3—24no—
137C23×D3—24no—
138C23×D3—22no—
139C23×D3D1214yes—
140C23×D3C22×D312yes—
141C22×C3×C4—28no—
142C22×C3×C4—24no—
143C22×C3×C4—24no—
144C22×C3×C4—24no—
145C22×C3×C4—22no—
146C22×C3×C4—32no—
147C22×C3×C4—34no—
148C22×C3×C4—64no—
149C22×C3×C4—62no—
150C22×C3×C4—64no—
151C22×C3×C4—64no—
152C22×C3×C4—64no—
153C22×C3×C4D1214yes—
154C22×C3×C4#6714yes—
155C22×C3×C4C22×D312yes—
156C22×C3×C4C22×D312yes—
157C22×Dic3—24no—
158C22×Dic3—24no—
159C22×Dic3—24no—
160C22×Dic3—24no—
161C22×Dic3—22no—
162C22×Dic3—34no—
163C22×Dic3—34no—
164C22×Dic3—64no—
165C22×Dic3—68no—
166C22×Dic3—64no—
167C22×Dic3—64no—
168C22×Dic3—64no—
169C22×Dic3—64no—
170C22×Dic3—64no—
171C22×Dic3—64no—
172C22×Dic3—124no—
173C22×Dic3—124no—
174C22×Dic3C22×D312yes—
175C22×Dic3C22×D314yes—
176C3×C22⋊C4—68no—
177#217—616no—
178(C2×D3)⋊C4—28no—
179(C2×D3)⋊C4—616no—
180C4⋊Dic3—616no—
181C4⋊Dic3—68no—
182C4⋊Dic3—68no—
183C22×C32#12114yes—
184C22×C32#12318yes—
185C22×C32#12314yes—
186C22×C32#12414yes—
187C22×C32#12618yes—
188C22×C32C22×D411yescharacteristic
189C22×C32C22×D411yescharacteristic
190C22×C32C2×#4112yes—
191C22×C32C2×#4111yescharacteristic
192C22×C32C2×#4112yes—
193C2×C3×D3—24no—
194C2×C3×D3—28no—
195C2×C3×D3—42no—
196C2×C3×D3—42no—
197C2×C3×D3—44no—
198C2×C3×D3—416no—
199C32×C4—24no—
200C3⋊Dic3—44no—
201C3×Dic3—44no—
202C3×Dic3—42no—
203C25—31no—
204C23×C4—31no—
205C23×C4—32no—
206C23×C4—92no—
207C23×C4D3211yescharacteristic
208C2×C4⋊C4—94no—
209C2×C4⋊C4—184no—
210C2×C22⋊C4—34no—
211C2×C22⋊C4—64no—
212C2×C22⋊C4—98no—
213C2×C22⋊C4—188no—
214#95—34no—
215#95—98no—
216C23×C3—21no—
217C23×C3—24no—
218C23×C3—22no—
219C23×C3—22no—
220C23×C3—24no—
221C23×C3—22no—
222C23×C3—34no—
223C23×C3—616no—
224C23×C3—68no—
225C23×C3—62no—
226C23×C3—64no—
227C23×C3—64no—
228C23×C3—62no—
229C23×C3—124no—
230C23×C3—124no—
231C23×C3—128no—
232C23×C3C2×D1212yes—
233C23×C3C2×D1212yes—
234C23×C3#23514yes—
235C23×C3#23512yes—
236C23×C3D3×D412yes—
237C23×C3#23714yes—
238C23×C3#23714yes—
239C23×C3#23714yes—
240C23×C3#23912yes—
241C23×C3C2×#6712yes—
242C23×C3C23×D311yescharacteristic
243C23×C3C23×D311yescharacteristic
244C22×D3—216no—
245C22×D3—28no—
246C22×D3—22no—
247C22×D3—24no—
248C22×D3—24no—
249C22×D3—22no—
250C22×D3—48no—
251C22×D3—44no—
252C22×D3—44no—
253C22×D3C2×D1214yes—
254C2×C3×C4—28no—
255C2×C3×C4—216no—
256C2×C3×C4—28no—
257C2×C3×C4—28no—
258C2×C3×C4—24no—
259C2×C3×C4—24no—
260C2×C3×C4—24no—
261C2×C3×C4—64no—
262C2×C3×C4—62no—
263C2×C3×C4—64no—
264C2×C3×C4—64no—
265C2×C3×C4—64no—
266C2×C3×C4—124no—
267C2×C3×C4—128no—
268C2×C3×C4C2×D1214yes—
269C2×C3×C4C2×#6714yes—
270C2×Dic3—24no—
271C2×Dic3—24no—
272C2×Dic3—24no—
273C2×Dic3—24no—
274C2×Dic3—22no—
275C2×Dic3—48no—
276C2×Dic3—44no—
277C2×Dic3—68no—
278C2×Dic3—64no—
279C2×Dic3—64no—
280C2×Dic3—64no—
281C2×Dic3—64no—
282C2×Dic3—64no—
283C2×Dic3—64no—
284C2×Dic3—124no—
285C2×Dic3—124no—
286C2×Dic3—1216no—
287C2×Dic3—128no—
288C2×Dic3—128no—
289C2×C32#39718yescomplemented
290C2×C32C2×#12111yescharacteristic
291C2×C32C2×#12312yes—
292C2×C32C2×#12311yescharacteristic
293C2×C32C2×#12411yescharacteristic
294C2×C32C2×#12612yes—
295C3×D3—44no—
296C24—32no—
297C24—34no—
298C24—64no—
299C24—62no—
300C24—64no—
301C24—62no—
302C24C2×D3211yescharacteristic
303C22×C4—24no—
304C22×C4—34no—
305C22×C4—32no—
306C22×C4—64no—
307C22×C4—64no—
308C22×C4—64no—
309C22×C4—64no—
310C22×C4—62no—
311C22×C4—94no—
312C22×C4—184no—
313C22×C4—184no—
314C22×C4—184no—
315C22×C4#62614yes—
316C22×C4C2×D3212yes—
317C4⋊C4—188no—
318C22⋊C4—68no—
319C22⋊C4—1816no—
320C22×C3—22no—
321C22×C3—21no—
322C22×C3—21no—
323C22×C3—22no—
324C22×C3—21no—
325C22×C3—24no—
326C22×C3—28no—
327C22×C3—28no—
328C22×C3—24no—
329C22×C3—24no—
330C22×C3—68no—
331C22×C3—64no—
332C22×C3—1216no—
333C22×C3—122no—
334C22×C3—122no—
335C22×C3—124no—
336C22×C3#87514yes—
337C22×C3#87918yes—
338C22×C3#88318yes—
339C22×C3#88618yes—
340C22×C3#88614yes—
341C22×C3#89514yes—
342C22×C3#89818yes—
343C22×C3#93014yes—
344C22×C3#93514yes—
345C22×C3#93614yes—
346C22×C3C22×D1211yescharacteristic
347C22×C3C22×D1211yescharacteristic
348C22×C3C2×#23512yes—
349C22×C3C2×#23511yescharacteristic
350C22×C3C2×D3×D411yescharacteristic
351C22×C3C2×#23712yes—
352C22×C3C2×#23712yes—
353C22×C3C2×#23712yes—
354C22×C3C2×#23911yescharacteristic
355C22×C3C22×#6711yescharacteristic
356C2×D3—28no—
357C2×D3—24no—
358C2×D3—416no—
359C2×D3—44no—
360C2×D3—42no—
361C2×D3—42no—
362C3×C4—28no—
363C3×C4—24no—
364C3×C4—24no—
365C3×C4—122no—
366C3×C4—124no—
367Dic3—44no—
368Dic3—42no—
369Dic3—128no—
370Dic3—124no—
371Dic3—124no—
372C32C2×#39711yescharacteristic, complemented, Sylow
373C23—34no—
374C23—64no—
375C23—62no—
376C23—64no—
377C23—62no—
378C23—616no—
379C23—68no—
380C23—124no—
381C23—128no—
382C23—124no—
383C23#379514yes—
384C23#379912yes—
385C23D3×D1212yes—
386C23#380514yes—
387C23C2×#62612yes—
388C23C22×D3211yescharacteristic
389C2×C4—24no—
390C2×C4—28no—
391C2×C4—64no—
392C2×C4—64no—
393C2×C4—64no—
394C2×C4—64no—
395C2×C4—62no—
396C2×C4—124no—
397C2×C4—128no—
398C2×C4—184no—
399C2×C4—184no—
400C2×C4—184no—
401C2×C4—368no—
402C2×C4C2×#62614yes—
403C2×C3—21no—
404C2×C3—22no—
405C2×C3—28no—
406C2×C3—22no—
407C2×C3—21no—
408C2×C3—21no—
409C2×C3—124no—
410C2×C3#467418yescomplemented
411C2×C3#495318yescomplemented
412C2×C3C2×#87511yescharacteristic
413C2×C3C2×#87912yes—
414C2×C3C2×#88312yes—
415C2×C3C2×#88612yes—
416C2×C3C2×#88611yescharacteristic
417C2×C3C2×#89511yescharacteristic
418C2×C3C2×#89812yes—
419C2×C3C2×#93011yescharacteristic
420C2×C3C2×#93511yescharacteristic
421C2×C3C2×#93611yescharacteristic
422D3—44no—
423C22—68no—
424C22—64no—
425C22—122no—
426C22—124no—
427C22—1216no—
428C22—122no—
429C22#6386014yes—
430C22#6386118yes—
431C22#6389118yes—
432C22#6390914yes—
433C22#6396214yes—
434C22C2×#379512yes—
435C22C2×#379911yescharacteristic
436C22C2×D3×D1211yescharacteristic
437C22C2×#380512yes—
438C22C22×#62611yescharacteristic
439C4—24no—
440C4—122no—
441C4—124no—
442C4—364no—
443C3—21no—
444C3C2×#467411yescharacteristic, complemented
445C3C2×#495311yescharacteristic, complemented
446C2—124no—
447C2#1059131518yesdirect product factor
448C2C2×#6386011yescharacteristic
449C2C2×#6386112yes—
450C2C2×#6389112yes—
451C2C2×#6390911yescharacteristic
452C2C2×#6396211yescharacteristic
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
1. C22×C4⋊(C3⋊Dic3)C2semidirect
4. C2×C3×C3⋊#95C2semidirect
5. C2×#63579C2semidirect
6. #10591315C2direct (N × H)
15. C2×C4⋊(C3⋊Dic3)C22semidirect
20. C3×C3⋊#95C22semidirect
21. #63579C22semidirect
32. C2×C3⋊#95D3semidirect
89. C3⋊#95C2×D3semidirect
289. C2×C32#397semidirect
372. C32C2×#397semidirect
410. C2×C3#4674semidirect
411. C2×C3#4953semidirect
444. C3C2×#4674semidirect
445. C3C2×#4953semidirect
447. C2#10591315direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4⋊(C3⋊Dic3)2
C22×C3×(C2×D3)⋊C42
C22×(C2×D3)⋊Dic32
C2×C3×C3⋊#952
C2×#635792
#105913152
C2×#49533
C2×#46743