Finite Group Databasebeta

← C2×#10590270 #11868354

Subgroups — C2×#10590270 #11868354

Order 1152.

965 conjugacy classes of subgroups.

The subgroup lattice has 455 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×D12C211yesmaximal, characteristic
2C2×C3×#870C211yesmaximal, characteristic, complemented
3C2×C4⋊(C3⋊(C3⋊C8))C211yesmaximal, characteristic, complemented
4C2×#63576C211yesmaximal, characteristic, complemented
5C2×#63574C211yesmaximal, characteristic, complemented
6C2×#63562C211yesmaximal, characteristic
7C2×#63562C211yesmaximal, characteristic
8#10590270C218yesmaximal, direct product factor
9C2×#5066—31nomaximal
10C2×#5009—31nomaximal
11C22×C3×D12C2211yescharacteristic
12C22×C3×C4×D3—21no—
13C2×C32×C42C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C2×C3×(C2×D3)⋊C4—21no—
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×Dic3⋊C4—21no—
21C2×C3×Dic3⋊C4—21no—
22C3×C4×D12—22no—
23C3×C4×D12C2214yes—
24C3×#870—22no—
25C3×#870C2214yescomplemented
26C4⋊(C3⋊(C3⋊C8))C2214yescomplemented
27#63576C2214yescomplemented
28#63574C2214yescomplemented
29#63562C2214yes—
30#63562C2214yes—
31C2×C3×#125—31no—
32C2×C3×C4×D4—31no—
33C2×C4×D12D311yescharacteristic
34C2×#870D311yescharacteristic, complemented
35C2×#832—31no—
36C2×#832—31no—
37#5066—38no—
38#5009—38no—
39C2×#809—31no—
40C2×#809—31no—
41C2×#808—31no—
42C2×#808—31no—
43C2×#807—31no—
44C2×#807—31no—
45C2×C4⋊(C3⋊C8)—31no—
46C2×C4⋊(C3⋊C8)—31no—
47C2×C4⋊(C3⋊C8)—61no—
48C23×C3×D3—21no—
49C22×C32×C4D411yescharacteristic
50C22×C32×C4D411yescharacteristic
51C22×C32×C4C2311yescharacteristic
52C22×C3×Dic3—21no—
53C22×C3×Dic3—21no—
54C22×C3×Dic3—21no—
55C2×C3×D12—21no—
56C2×C3×D12—22no—
57C2×C3×D12Q814yes—
58C2×C3×D12C2312yes—
59C2×C3×C4×D3—24no—
60C2×C3×C4×D3—44no—
61C32×C42D412yes—
62C32×C42C2312yes—
63C2×C3⋊(C3⋊C8)—22no—
64C2×C3⋊(C3⋊C8)—22no—
65C2×C3⋊(C3⋊C8)C2312yes—
66C2×C3⋊(C3⋊C8)C2312yes—
67C3×(C2×D3)⋊C4—24no—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3C2312yes—
72C3×C4⋊Dic3C2312yes—
73C3×C4⋊Dic3C2312yes—
74C3×Dic3⋊C4—24no—
75C3×Dic3⋊C4—24no—
76C2×#478—91noSylow
77C22×C3×D4—31no—
78C23×C3×C4—61no—
79C22×D12C2×D311yescharacteristic
80C22×C4×D3—21no—
81C3×#125—34no—
82C3×#125—62no—
83C3×C4×D4—34no—
84C3×C4×D4—62no—
85C2×C3×C4⋊C4—31no—
86C2×C3×C4⋊C4—31no—
87C2×C3×C4⋊C4—31no—
88C2×C3×C4⋊C4—61no—
89C2×C3×C4⋊C4—61no—
90C2×C3×C22⋊C4—61no—
91C2×C3×C42—21no—
92C2×C3×C42C2×D311yescharacteristic
93C2×C3×C42C2×D311yescharacteristic
94C2×(C2×D3)⋊C4—21no—
95C2×C4⋊Dic3C2×D311yescharacteristic
96C2×C4⋊Dic3C2×D311yescharacteristic
97C2×C4⋊Dic3C2×D311yescharacteristic
98C2×Dic3⋊C4—21no—
99C2×Dic3⋊C4—21no—
100C22×C3⋊C8—31no—
101C22×C3⋊C8—31no—
102C22×C3⋊C8—31no—
103C22×C3⋊C8—31no—
104C22×C3⋊C8—61no—
105C22×C3⋊C8—61no—
106C4×D12—22no—
107C4×D12C2×D314yes—
108#870—22no—
109#870C2×D314yescomplemented
110#832—34no—
111#832—34no—
112#809—34no—
113#809—34no—
114#808—34no—
115#808—34no—
116#807—34no—
117#807—34no—
118C4⋊(C3⋊C8)—34no—
119C4⋊(C3⋊C8)—34no—
120C4⋊(C3⋊C8)—64no—
121C23×C32C2×D411yescharacteristic
122C22×C3×D3—24no—
123C22×C3×D3—22no—
124C22×C3×D3—42no—
125C22×C3×D3—42no—
126C2×C32×C4—22no—
127C2×C32×C4—22no—
128C2×C32×C4C2×D412yes—
129C2×C32×C4C2×D412yes—
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×Q812yes—
132C2×C32×C4#4112yes—
133C2×C32×C4C2411yescharacteristic
134C2×C3×Dic3—22no—
135C2×C3×Dic3—22no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—42no—
138C2×C3×Dic3—42no—
139C2×C3×Dic3—42no—
140C3×D12—24no—
141C3×D12—22no—
142C3×D12C2×Q814yes—
143C3×C4×D3—48no—
144C3⋊(C3⋊C8)—22no—
145C3⋊(C3⋊C8)—22no—
146C2×#125—31no—
147C2×C4×D4—31no—
148#478—98no—
149C2×#107—91no—
150C2×#106—91no—
151C2×C4⋊C8—91no—
152C2×#102—91no—
153C2×#102—91no—
154C24×C3—61no—
155C23×D3—21no—
156C2×C3×D4—34no—
157C2×C3×D4—32no—
158C2×C3×D4—62no—
159C2×C3×D4—61no—
160C22×C3×C4—21no—
161C22×C3×C4—21no—
162C22×C3×C4—21no—
163C22×C3×C4—61no—
164C22×C3×C4—61no—
165C22×C3×C4—61no—
166C22×C3×C4—64no—
167C22×C3×C4—124no—
168C22×C3×C4#6711yescharacteristic
169C22×C3×C4#6711yescharacteristic
170C22×C3×C4#6711yescharacteristic
171C22×C3×C4#6711yescharacteristic
172C22×C3×C4C22×D311yescharacteristic
173C22×C3×C4C22×D311yescharacteristic
174C22×Dic3—21no—
175C22×Dic3—21no—
176C22×Dic3—21no—
177C2×D12—22no—
178C2×D12—21no—
179C2×D12Dic614yes—
180C2×D12C22×D312yes—
181C2×C4×D3—24no—
182C2×C4×D3—44no—
183C3×C4⋊C4—32no—
184C3×C4⋊C4—32no—
185C3×C4⋊C4—32no—
186C3×C4⋊C4—64no—
187C3×C4⋊C4—64no—
188C3×C4⋊C4—61no—
189C3×C4⋊C4—61no—
190C3×C4⋊C4—61no—
191C3×C22⋊C4—64no—
192C3×C42—22no—
193C3×C42—22no—
194C3×C42#6712yes—
195C3×C42#6712yes—
196C3×C42C22×D312yes—
197C3×C42C22×D312yes—
198(C2×D3)⋊C4—24no—
199C4⋊Dic3—21no—
200C4⋊Dic3—21no—
201C4⋊Dic3—21no—
202C4⋊Dic3C22×D312yes—
203C4⋊Dic3C22×D312yes—
204C4⋊Dic3C22×D312yes—
205Dic3⋊C4—24no—
206Dic3⋊C4—24no—
207C2×C3⋊C8—32no—
208C2×C3⋊C8—32no—
209C2×C3⋊C8—32no—
210C2×C3⋊C8—32no—
211C2×C3⋊C8—62no—
212C2×C3⋊C8—62no—
213C2×C3⋊C8—62no—
214C2×C3⋊C8—62no—
215C2×C3⋊C8—62no—
216C2×C3⋊C8—62no—
217C2×C3⋊C8—122no—
218C2×C3⋊C8—122no—
219C22×C32C22⋊Q812yes—
220C22×C32#13512yes—
221C22×C32AGL(1,ℤ/8)12yes—
222C22×C32C22×D411yescharacteristic
223C2×C3×D3—24no—
224C2×C3×D3—42no—
225C2×C3×D3—42no—
226C2×C3×D3—48no—
227C32×C4—22no—
228C32×C4—22no—
229C32×C4C22⋊Q812yes—
230C32×C4C22×Q811yescharacteristic
231C32×C4C2×#4111yescharacteristic
232C3×Dic3—42no—
233C3×Dic3—42no—
234C3×Dic3—42no—
235C22×D4—31no—
236C23×C4—61no—
237C22×C8—91no—
238C22×C8—91no—
239#125—34no—
240#125—62no—
241C4×D4—34no—
242C4×D4—62no—
243C2×C4⋊C4—31no—
244C2×C4⋊C4—31no—
245C2×C4⋊C4—31no—
246C2×C4⋊C4—61no—
247C2×C4⋊C4—61no—
248C2×C22⋊C4—61no—
249C2×C42D3211yescharacteristic
250#107—94no—
251#106—94no—
252C4⋊C8—94no—
253#102—94no—
254#102—94no—
255C23×C3—21no—
256C23×C3—64no—
257C23×C3—62no—
258C23×C3—122no—
259C23×C3—122no—
260C23×C3C2×#6711yescharacteristic
261C23×C3C2×#6711yescharacteristic
262C22×D3—24no—
263C22×D3—22no—
264C22×D3—42no—
265C22×D3—42no—
266C3×D4—34no—
267C3×D4—64no—
268C3×D4—62no—
269C2×C3×C4—24no—
270C2×C3×C4—22no—
271C2×C3×C4—22no—
272C2×C3×C4—22no—
273C2×C3×C4—22no—
274C2×C3×C4—21no—
275C2×C3×C4—22no—
276C2×C3×C4—22no—
277C2×C3×C4—22no—
278C2×C3×C4—21no—
279C2×C3×C4—22no—
280C2×C3×C4—42no—
281C2×C3×C4—62no—
282C2×C3×C4—62no—
283C2×C3×C4—62no—
284C2×C3×C4—128no—
285C2×C3×C4—122no—
286C2×C3×C4—122no—
287C2×C3×C4—122no—
288C2×C3×C4C2×Dic612yes—
289C2×C3×C4#23512yes—
290C2×C3×C4D3×Q812yes—
291C2×C3×C4#23912yes—
292C2×C3×C4C2×#6712yes—
293C2×C3×C4C2×#6712yes—
294C2×C3×C4C2×#6712yes—
295C2×C3×C4C2×#6712yes—
296C2×C3×C4C2×#6711yescharacteristic
297C2×C3×C4C2×#6711yescharacteristic
298C2×C3×C4C23×D311yescharacteristic
299C2×C3×C4C23×D311yescharacteristic
300C2×Dic3—22no—
301C2×Dic3—22no—
302C2×Dic3—22no—
303C2×Dic3—42no—
304C2×Dic3—42no—
305C2×Dic3—42no—
306D12—24no—
307D12—22no—
308D12C2×Dic614yes—
309C4×D3—48no—
310C3⋊C8—62no—
311C3⋊C8—62no—
312C3⋊C8—62no—
313C3⋊C8—62no—
314C3⋊C8—122no—
315C3⋊C8—122no—
316C2×C32#47814yescomplemented
317C2×C32C2×C22⋊Q811yescharacteristic
318C2×C32C2×#13511yescharacteristic
319C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
320C3×D3—44no—
321C24—61no—
322C2×D4—32no—
323C2×D4—34no—
324C2×D4—62no—
325C2×D4—61no—
326C22×C4—61no—
327C22×C4—61no—
328C22×C4—61no—
329C22×C4—64no—
330C22×C4—124no—
331C22×C4#62511yescharacteristic
332C22×C4#62511yescharacteristic
333C22×C4C2×D3211yescharacteristic
334C2×C8—92no—
335C2×C8—92no—
336C2×C8—182no—
337C2×C8—182no—
338C4⋊C4—32no—
339C4⋊C4—32no—
340C4⋊C4—32no—
341C4⋊C4—61no—
342C4⋊C4—61no—
343C4⋊C4—61no—
344C4⋊C4—64no—
345C4⋊C4—64no—
346C22⋊C4—64no—
347C42#62512yes—
348C42C2×D3212yes—
349C22×C3—21no—
350C22×C3—22no—
351C22×C3—22no—
352C22×C3—22no—
353C22×C3—64no—
354C22×C3—122no—
355C22×C3—122no—
356C22×C3—128no—
357C22×C3#92412yes—
358C22×C3#93212yes—
359C22×C3#94612yes—
360C22×C3#94912yes—
361C22×C3#95012yes—
362C22×C3#95012yes—
363C22×C3C22×#6711yescharacteristic
364C22×C3C22×#6711yescharacteristic
365C2×D3—24no—
366C2×D3—48no—
367C2×D3—42no—
368C2×D3—42no—
369C3×C4—24no—
370C3×C4—22no—
371C3×C4—22no—
372C3×C4—22no—
373C3×C4—22no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—22no—
377C3×C4—42no—
378C3×C4—122no—
379C3×C4—122no—
380C3×C4—122no—
381C3×C4#92412yes—
382C3×C4#94612yes—
383C3×C4C22×Dic611yescharacteristic
384C3×C4C2×#23511yescharacteristic
385C3×C4C2×D3×Q811yescharacteristic
386C3×C4C2×#23911yescharacteristic
387Dic3—42no—
388Dic3—42no—
389Dic3—42no—
390C32C2×#47811yescharacteristic, complemented, Sylow
391C23—62no—
392C23—64no—
393C23—122no—
394C23—122no—
395C23C2×#62511yescharacteristic
396D4—34no—
397D4—62no—
398D4—64no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—62no—
402C2×C4—62no—
403C2×C4—62no—
404C2×C4—128no—
405C2×C4—122no—
406C2×C4—122no—
407C2×C4—122no—
408C2×C4D3×Dic612yes—
409C2×C4#379912yes—
410C2×C4C2×#62512yes—
411C2×C4C2×#62512yes—
412C2×C4C2×#62511yescharacteristic
413C2×C4C22×D3211yescharacteristic
414C8—182no—
415C8—182no—
416C2×C3—21no—
417C2×C3—24no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—124no—
421C2×C3#500914yescomplemented
422C2×C3#506614yescomplemented
423C2×C3C2×#92411yescharacteristic
424C2×C3C2×#93211yescharacteristic
425C2×C3C2×#94611yescharacteristic
426C2×C3C2×#94911yescharacteristic
427C2×C3C2×#95011yescharacteristic
428C2×C3C2×#95011yescharacteristic
429D3—44no—
430C22—64no—
431C22—128no—
432C22—122no—
433C22—122no—
434C22#6382212yes—
435C22#6382312yes—
436C22#6385612yes—
437C22C22×#62511yescharacteristic
438C4—22no—
439C4—22no—
440C4—122no—
441C4—122no—
442C4—122no—
443C4#6385612yes—
444C4C2×D3×Dic611yescharacteristic
445C4C2×#379911yescharacteristic
446C3—21no—
447C3C2×#500911yescharacteristic, complemented
448C3C2×#506611yescharacteristic, complemented
449C2—124no—
450C2#1059027014yesdirect product factor
451C2C2×#6382211yescharacteristic
452C2C2×#6382311yescharacteristic
453C2C2×#6385611yescharacteristic
subgroupG/H
centerC23C2×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC2×C42D32
hypocenterC32C2×#478
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×C3×#870C2semidirect
3. C2×C4⋊(C3⋊(C3⋊C8))C2semidirect
4. C2×#63576C2semidirect
5. C2×#63574C2semidirect
8. #10590270C2direct (N × H)
25. C3×#870C22semidirect
26. C4⋊(C3⋊(C3⋊C8))C22semidirect
27. #63576C22semidirect
28. #63574C22semidirect
34. C2×#870D3semidirect
109. #870C2×D3semidirect
316. C2×C32#478semidirect
390. C32C2×#478semidirect
421. C2×C3#5009semidirect
422. C2×C3#5066semidirect
447. C3C2×#5009semidirect
448. C3C2×#5066semidirect
450. C2#10590270direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C4×D122
C2×C3×#8702
C2×C4⋊(C3⋊(C3⋊C8))2
C2×#635762
C2×#635742
C2×#635622
#105902702
C2×#50663
C2×#50093