Finite Group Databasebeta

← C2×#10590468 #11868359

Subgroups — C2×#10590468 #11868359

Order 1152.

997 conjugacy classes of subgroups.

The subgroup lattice has 465 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#890C211yesmaximal, characteristic, complemented
2C2×#63894C211yesmaximal, characteristic
3C2×#63636C211yesmaximal, characteristic
4C2×C3×#807C211yesmaximal, characteristic, complemented
5C2×#63574C211yesmaximal, characteristic, complemented
6C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
7C2×#63564C211yesmaximal, characteristic
8#10590468C218yesmaximal, direct product factor
9C2×#5066—31nomaximal
10C2×#4891—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×#624—21no—
13C2×C32×C4⋊C4C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C2×C3×C4⋊Dic3—21no—
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×Dic3⋊C4—21no—
19C2×C3×C4×Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C3×#890—22no—
22C3×#890C2214yescomplemented
23C2×#3722—21no—
24#63894—22no—
25#63894C2214yes—
26#63636C2214yes—
27C3×#807C2214yescomplemented
28#63574C2214yescomplemented
29Dic3⋊(C3⋊C8)C2214yescomplemented
30#63564C2214yes—
31C2×C3×#125—31no—
32C2×#893—31no—
33C2×#890D311yescharacteristic, complemented
34C2×C4×D12—31no—
35C2×C3×#107—31no—
36C2×#821—31no—
37C2×Dic3⋊C8—31no—
38#5066—38no—
39C2×#809—31no—
40C2×#809—31no—
41C2×#809—31no—
42C2×#809—61no—
43C2×#808—31no—
44C2×#808—31no—
45C2×#807D311yescharacteristic, complemented
46C2×C4⋊(C3⋊C8)—31no—
47#4891—38no—
48C23×C3⋊D3—21no—
49C22×C32×C4—21no—
50C22×C32×C4C2311yescharacteristic
51C2×C4⋊(C3⋊D3)—21no—
52C2×C4⋊(C3⋊D3)—22no—
53C2×C4⋊(C3⋊D3)Q814yes—
54C2×C4⋊(C3⋊D3)C2312yes—
55C22×C3×Dic3—21no—
56C22×C3×Dic3—21no—
57C22×C3×Dic3D411yescharacteristic
58C22×C3×Dic3D411yescharacteristic
59C2×#624—24no—
60C2×#624—44no—
61C32×C4⋊C4—21no—
62C32×C4⋊C4C2312yes—
63C2×C3⋊(C3⋊C8)—22no—
64C2×C3⋊(C3⋊C8)C2312yes—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—24no—
68C3×C4⋊Dic3C2312yes—
69C3×C4⋊Dic3C2312yes—
70C3×Dic3⋊C4—24no—
71C3×C4×Dic3D412yes—
72C3×C4×Dic3C2312yes—
73C2×C3×C3⋊C8—22no—
74C2×C3×C3⋊C8C2312yes—
75#3722—24no—
76C2×#478—91noSylow
77C22×D12—31no—
78C22×D12—31no—
79C22×D12—61no—
80C22×C4×D3—61no—
81C22×C4×D3—61no—
82C22×C3×C8—31no—
83C3×#125—34no—
84C3×#125—62no—
85C2×C3×C4⋊C4—21no—
86C2×C3×C4⋊C4—31no—
87C2×C3×C4⋊C4—31no—
88C2×C3×C4⋊C4—61no—
89C2×C3×C4⋊C4—61no—
90C2×C3×C4⋊C4C2×D311yescharacteristic
91C2×C3×C4⋊C4C2×D311yescharacteristic
92C2×C3×C42—31no—
93C2×(C2×D3)⋊C4—61no—
94C2×(C2×D3)⋊C4—61no—
95C2×C4⋊Dic3—21no—
96C2×C4⋊Dic3C2×D311yescharacteristic
97C2×C4⋊Dic3C2×D311yescharacteristic
98C2×Dic3⋊C4—21no—
99C2×C4×Dic3C2×D311yescharacteristic
100C22×C3⋊C8—31no—
101C22×C3⋊C8—31no—
102C22×C3⋊C8—61no—
103C22×C3⋊C8C2×D311yescharacteristic
104#893—34no—
105#893—62no—
106#890—22no—
107#890C2×D314yescomplemented
108C4×D12—34no—
109C4×D12—62no—
110C3×#107—34no—
111#821—34no—
112Dic3⋊C8—34no—
113#809—34no—
114#809—34no—
115#809—34no—
116#809—64no—
117#808—34no—
118#808—34no—
119#807C2×D314yescomplemented
120C4⋊(C3⋊C8)—34no—
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—42no—
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×Q812yes—
130C2×C32×C4#4112yes—
131C2×C32×C4C2411yescharacteristic
132C4⋊(C3⋊D3)—24no—
133C4⋊(C3⋊D3)—22no—
134C4⋊(C3⋊D3)C2×Q814yes—
135C2×C3×Dic3—22no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—42no—
140C2×C3×Dic3—42no—
141C2×C3×Dic3C2×D412yes—
142C2×C3×Dic3C2×D412yes—
143#624—48no—
144C3⋊(C3⋊C8)—22no—
145C3×C3⋊C8—22no—
146C2×#125—31no—
147C2×C4×D4—91no—
148#478—98no—
149C2×#107—31no—
150C2×#106—91no—
151C2×C4⋊C8—91no—
152C2×#102—91no—
153C2×#102—91no—
154C23×D3—61no—
155C23×D3—61no—
156C23×D3—121no—
157C22×C3×C4—21no—
158C22×C3×C4—21no—
159C22×C3×C4—21no—
160C22×C3×C4—31no—
161C22×C3×C4—31no—
162C22×C3×C4—41no—
163C22×C3×C4—61no—
164C22×C3×C4—61no—
165C22×C3×C4C22×D311yescharacteristic
166C22×C3×C4C22×D311yescharacteristic
167C22×Dic3—21no—
168C22×Dic3—21no—
169C22×Dic3#6711yescharacteristic
170C22×Dic3#6711yescharacteristic
171C2×D12—34no—
172C2×D12—34no—
173C2×D12—32no—
174C2×D12—32no—
175C2×D12—62no—
176C2×D12—64no—
177C2×D12—62no—
178C2×D12—61no—
179C2×D12—62no—
180C2×D12—61no—
181C2×D12—122no—
182C2×D12—121no—
183C2×C4×D3—64no—
184C2×C4×D3—64no—
185C2×C4×D3—124no—
186C2×C4×D3—124no—
187C2×C3×C8—32no—
188C2×C3×C8—62no—
189C3×C4⋊C4—21no—
190C3×C4⋊C4—21no—
191C3×C4⋊C4—22no—
192C3×C4⋊C4—32no—
193C3×C4⋊C4—32no—
194C3×C4⋊C4—41no—
195C3×C4⋊C4—64no—
196C3×C4⋊C4—64no—
197C3×C4⋊C4—61no—
198C3×C4⋊C4—61no—
199C3×C4⋊C4C22×D312yes—
200C3×C4⋊C4C22×D312yes—
201C3×C42—32no—
202C3×C42—32no—
203(C2×D3)⋊C4—64no—
204(C2×D3)⋊C4—64no—
205C4⋊Dic3—21no—
206C4⋊Dic3—21no—
207C4⋊Dic3—24no—
208C4⋊Dic3C22×D312yes—
209C4⋊Dic3C22×D312yes—
210Dic3⋊C4—24no—
211C4×Dic3#6712yes—
212C4×Dic3C22×D312yes—
213C2×C3⋊C8—22no—
214C2×C3⋊C8—32no—
215C2×C3⋊C8—32no—
216C2×C3⋊C8—62no—
217C2×C3⋊C8—62no—
218C2×C3⋊C8—62no—
219C2×C3⋊C8—122no—
220C2×C3⋊C8C22×D312yes—
221C22×C32C22⋊Q812yes—
222C22×C32#13512yes—
223C22×C32AGL(1,ℤ/8)12yes—
224C22×C32C22×D411yescharacteristic
225C2×C3⋊D3—24no—
226C2×C3⋊D3—42no—
227C2×C3⋊D3—42no—
228C2×C3⋊D3—48no—
229C32×C4—42no—
230C32×C4C22⋊Q812yes—
231C32×C4C22×Q811yescharacteristic
232C32×C4C2×#4111yescharacteristic
233C3×Dic3—22no—
234C3×Dic3—22no—
235C3×Dic3—42no—
236C3×Dic3—42no—
237C22×D4—91no—
238C23×C4—181no—
239C22×C8—31no—
240C22×C8—91no—
241#125—34no—
242#125—62no—
243C4×D4—94no—
244C4×D4—182no—
245C2×C4⋊C4—31no—
246C2×C4⋊C4—31no—
247C2×C4⋊C4—61no—
248C2×C4⋊C4—61no—
249C2×C4⋊C4D3211yescharacteristic
250C2×C22⋊C4—181no—
251C2×C42—31no—
252#107—34no—
253#106—94no—
254C4⋊C8—94no—
255#102—94no—
256#102—94no—
257C23×C3—21no—
258C23×C3D3×D411yescharacteristic
259C23×C3C2×#6711yescharacteristic
260C22×D3—64no—
261C22×D3—64no—
262C22×D3—62no—
263C22×D3—62no—
264C22×D3—122no—
265C22×D3—124no—
266C22×D3—122no—
267C22×D3—122no—
268C22×D3—122no—
269C22×D3—122no—
270C22×D3—242no—
271C22×D3—242no—
272C2×C3×C4—22no—
273C2×C3×C4—22no—
274C2×C3×C4—21no—
275C2×C3×C4—22no—
276C2×C3×C4—22no—
277C2×C3×C4—21no—
278C2×C3×C4—32no—
279C2×C3×C4—32no—
280C2×C3×C4—42no—
281C2×C3×C4—42no—
282C2×C3×C4—42no—
283C2×C3×C4—62no—
284C2×C3×C4—62no—
285C2×C3×C4—62no—
286C2×C3×C4—62no—
287C2×C3×C4—82no—
288C2×C3×C4—122no—
289C2×C3×C4—122no—
290C2×C3×C4#23512yes—
291C2×C3×C4D3×D411yescharacteristic
292C2×C3×C4D3×Q812yes—
293C2×C3×C4D3×Q812yes—
294C2×C3×C4#23912yes—
295C2×C3×C4C2×#6711yescharacteristic
296C2×C3×C4C23×D311yescharacteristic
297C2×C3×C4C23×D311yescharacteristic
298C2×Dic3—22no—
299C2×Dic3—22no—
300C2×Dic3—22no—
301C2×Dic3—22no—
302C2×Dic3—42no—
303C2×Dic3—42no—
304C2×Dic3C2×#6712yes—
305C2×Dic3C2×#6712yes—
306D12—34no—
307D12—34no—
308D12—64no—
309D12—64no—
310D12—64no—
311D12—62no—
312D12—62no—
313D12—122no—
314D12—124no—
315C4×D3—128no—
316C4×D3—128no—
317C3×C8—62no—
318C3⋊C8—22no—
319C3⋊C8—62no—
320C3⋊C8—62no—
321C3⋊C8—122no—
322C2×C32#47814yescomplemented
323C2×C32C2×C22⋊Q811yescharacteristic
324C2×C32C2×#13511yescharacteristic
325C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
326C3⋊D3—44no—
327C24—181no—
328C2×D4—92no—
329C2×D4—94no—
330C2×D4—182no—
331C2×D4—181no—
332C22×C4—21no—
333C22×C4—31no—
334C22×C4—31no—
335C22×C4—61no—
336C22×C4—61no—
337C22×C4—184no—
338C22×C4—364no—
339C22×C4C2×D3211yescharacteristic
340C2×C8—32no—
341C2×C8—62no—
342C2×C8—92no—
343C2×C8—182no—
344C4⋊C4—21no—
345C4⋊C4—32no—
346C4⋊C4—32no—
347C4⋊C4—64no—
348C4⋊C4—64no—
349C4⋊C4—61no—
350C4⋊C4—61no—
351C4⋊C4C2×D3212yes—
352C22⋊C4—184no—
353C42—32no—
354C42—32no—
355C22×C3—21no—
356C22×C3—22no—
357C22×C3—22no—
358C22×C3—22no—
359C22×C3#89612yes—
360C22×C3#91112yes—
361C22×C3#91912yes—
362C22×C3#94612yes—
363C22×C3#94912yes—
364C22×C3#95012yes—
365C22×C3C2×D3×D411yescharacteristic
366C22×C3C22×#6711yescharacteristic
367C2×D3—64no—
368C2×D3—64no—
369C2×D3—124no—
370C2×D3—128no—
371C2×D3—122no—
372C2×D3—122no—
373C2×D3—122no—
374C2×D3—122no—
375C2×D3—128no—
376C2×D3—248no—
377C2×D3—242no—
378C2×D3—242no—
379C3×C4—21no—
380C3×C4—21no—
381C3×C4—22no—
382C3×C4—42no—
383C3×C4—42no—
384C3×C4—62no—
385C3×C4—62no—
386C3×C4—82no—
387C3×C4—122no—
388C3×C4—122no—
389C3×C4#89612yes—
390C3×C4#94612yes—
391C3×C4C2×#23511yescharacteristic
392C3×C4C2×D3×Q811yescharacteristic
393C3×C4C2×D3×Q811yescharacteristic
394C3×C4C2×#23911yescharacteristic
395Dic3—22no—
396Dic3—22no—
397Dic3—42no—
398Dic3—42no—
399C32C2×#47811yescharacteristic, complemented, Sylow
400C23—182no—
401C23—184no—
402C23—362no—
403C23—362no—
404C23D3×#6711yescharacteristic
405D4—94no—
406D4—182no—
407D4—184no—
408C2×C4—22no—
409C2×C4—32no—
410C2×C4—32no—
411C2×C4—42no—
412C2×C4—62no—
413C2×C4—62no—
414C2×C4—62no—
415C2×C4—62no—
416C2×C4—122no—
417C2×C4—122no—
418C2×C4—368no—
419C2×C4#379712yes—
420C2×C4#379912yes—
421C2×C4D3×#6711yescharacteristic
422C2×C4C22×D3211yescharacteristic
423C8—62no—
424C8—182no—
425C2×C3—24no—
426C2×C3—21no—
427C2×C3—21no—
428C2×C3—21no—
429C2×C3#489114yescomplemented
430C2×C3#506614yescomplemented
431C2×C3C2×#89611yescharacteristic
432C2×C3C2×#91111yescharacteristic
433C2×C3C2×#91911yescharacteristic
434C2×C3C2×#94611yescharacteristic
435C2×C3C2×#94911yescharacteristic
436C2×C3C2×#95011yescharacteristic
437D3—124no—
438D3—124no—
439D3—244no—
440C22—184no—
441C22—368no—
442C22—362no—
443C22—362no—
444C22#6388812yes—
445C22#6392512yes—
446C22#6394912yes—
447C22C2×D3×#6711yescharacteristic
448C4—42no—
449C4—62no—
450C4—62no—
451C4—122no—
452C4—122no—
453C4#6388812yes—
454C4C2×#379711yescharacteristic
455C4C2×#379911yescharacteristic
456C3—21no—
457C3C2×#489111yescharacteristic, complemented
458C3C2×#506611yescharacteristic, complemented
459C2—364no—
460C2#1059046814yesdirect product factor
461C2C2×#6388811yescharacteristic
462C2C2×#6392511yescharacteristic
463C2C2×#6394911yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#478
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#890C2semidirect
4. C2×C3×#807C2semidirect
5. C2×#63574C2semidirect
6. C2×Dic3⋊(C3⋊C8)C2semidirect
8. #10590468C2direct (N × H)
22. C3×#890C22semidirect
27. C3×#807C22semidirect
28. #63574C22semidirect
29. Dic3⋊(C3⋊C8)C22semidirect
33. C2×#890D3semidirect
45. C2×#807D3semidirect
107. #890C2×D3semidirect
119. #807C2×D3semidirect
322. C2×C32#478semidirect
399. C32C2×#478semidirect
429. C2×C3#4891semidirect
430. C2×C3#5066semidirect
457. C3C2×#4891semidirect
458. C3C2×#5066semidirect
460. C2#10590468direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#8902
C2×#638942
C2×#636362
C2×C3×#8072
C2×#635742
C2×Dic3⋊(C3⋊C8)2
C2×#635642
#105904682
C2×#50663
C2×#48913