Finite Group Databasebeta

← C2×#10591090 #11869448

Subgroups — C2×#10591090 #11869448

Order 1152.

1037 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#930C211yesmaximal, characteristic
2C2×C3×#926C211yesmaximal, characteristic, complemented
3C2×#63657C211yesmaximal, characteristic, complemented
4C2×#63576C211yesmaximal, characteristic, complemented
5C2×#63574C211yesmaximal, characteristic, complemented
6#10591090C218yesmaximal, direct product factor
7C2×#63562C211yesmaximal, characteristic, complemented
8C2×#63562C211yesmaximal, characteristic, complemented
9C2×#5035—31nomaximal
10C2×#5003—31nomaximal
11C23×C32×C4C2211yescharacteristic
12C22×C3×#67—21no—
13C22×C3×D12C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C2×C3×#217—21no—
17C3×#930—22no—
18C3×#930C2214yes—
19C2×C3×(C2×D3)⋊C4—21no—
20C3×#926—22no—
21C3×#926C2214yescomplemented
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×C4×Dic3—21no—
26#63657C2214yescomplemented
27#63576C2214yescomplemented
28#63574C2214yescomplemented
29#63562C2214yescomplemented
30#63562C2214yescomplemented
31C2×C3×#121—31no—
32C2×C3×#117—31no—
33C2×#930D311yescharacteristic
34C2×#926D311yescharacteristic, complemented
35C2×#832—31no—
36C2×#832—31no—
37C2×#830—31no—
38C2×#830—31no—
39C2×#830—61no—
40#5035—38no—
41#5003—38no—
42C2×#809—31no—
43C2×#809—31no—
44C2×#808—31no—
45C2×#808—31no—
46C2×#807—31no—
47C2×#807—31no—
48C24×C32D411yescharacteristic
49C23×C3×D3—21no—
50C22×C32×C4—22no—
51C22×C32×C4—22no—
52C22×C32×C4D411yescharacteristic
53C22×C32×C4D412yes—
54C22×C32×C4C2312yes—
55C22×C32×C4C2311yescharacteristic
56C2×C3×#67—24no—
57C2×C3×#67—44no—
58C22×C3×Dic3—21no—
59C22×C3×Dic3—21no—
60C22×C3×Dic3—21no—
61C2×C3×D12—22no—
62C2×C3×D12—22no—
63C2×C3×D12—21no—
64C2×C3×D12C2312yes—
65C2×C3⋊(C3⋊C8)—22no—
66C2×C3⋊(C3⋊C8)—22no—
67C2×C3⋊(C3⋊C8)C2312yes—
68C2×C3⋊(C3⋊C8)C2312yes—
69C3×#217—24no—
70C3×(C2×D3)⋊C4—24no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3—21no—
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3C2312yes—
75C3×C4⋊Dic3C2312yes—
76C3×C4⋊Dic3C2312yes—
77C3×C4×Dic3—24no—
78C2×#482—91noSylow
79C22×C3×D4—31no—
80C22×C3×D4—61no—
81C23×C3×C4—21no—
82C23×C3×C4C2×D311yescharacteristic
83C23×C3×C4C2×D311yescharacteristic
84C22×#67—21no—
85C22×D12C2×D311yescharacteristic
86C3×#121—34no—
87C3×#121—62no—
88C3×#117—34no—
89C3×#117—62no—
90C2×C3×C4⋊C4—31no—
91C2×C3×C4⋊C4—31no—
92C2×C3×C4⋊C4—31no—
93C2×C3×C22⋊C4—61no—
94C2×C3×C22⋊C4—61no—
95C2×C3×C42—61no—
96C2×#217—21no—
97#930—22no—
98#930C2×D314yes—
99C2×(C2×D3)⋊C4—21no—
100#926—22no—
101#926C2×D314yescomplemented
102C2×C4⋊Dic3C2×D311yescharacteristic
103C2×C4⋊Dic3C2×D311yescharacteristic
104C2×C4⋊Dic3C2×D311yescharacteristic
105C2×C4×Dic3—21no—
106C22×C3⋊C8—31no—
107C22×C3⋊C8—31no—
108C22×C3⋊C8—31no—
109C22×C3⋊C8—31no—
110C22×C3⋊C8—61no—
111C22×C3⋊C8—61no—
112#832—34no—
113#832—34no—
114#830—34no—
115#830—34no—
116#830—64no—
117#809—34no—
118#809—34no—
119#808—34no—
120#808—34no—
121#807—34no—
122#807—34no—
123C23×C32—22no—
124C23×C32—22no—
125C23×C32—22no—
126C23×C32C2×D412yes—
127C23×C32C2×D411yescharacteristic
128C22×C3×D3—22no—
129C22×C3×D3—42no—
130C22×C3×D3—42no—
131C22×C3×D3—42no—
132C2×C32×C4—22no—
133C2×C32×C4—24no—
134C2×C32×C4—22no—
135C2×C32×C4—22no—
136C2×C32×C4C2×D412yes—
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4#4112yes—
139C2×C32×C4#4112yes—
140C2×C32×C4C2411yescharacteristic
141C3×#67—48no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—42no—
146C2×C3×Dic3—42no—
147C2×C3×Dic3—42no—
148C3×D12—22no—
149C3×D12—22no—
150C3×D12—42no—
151C3⋊(C3⋊C8)—22no—
152C3⋊(C3⋊C8)—22no—
153C2×#121—31no—
154C2×#117—31no—
155#482—98no—
156C2×#107—91no—
157C2×#106—91no—
158C2×#102—91no—
159C2×#102—91no—
160C2×C22⋊C8—91no—
161C24×C3—21no—
162C24×C3—61no—
163C24×C3#6711yescharacteristic
164C24×C3#6711yescharacteristic
165C23×D3—21no—
166C2×C3×D4—32no—
167C2×C3×D4—64no—
168C2×C3×D4—62no—
169C2×C3×D4—62no—
170C2×C3×D4—61no—
171C2×C3×D4—124no—
172C22×C3×C4—22no—
173C22×C3×C4—22no—
174C22×C3×C4—22no—
175C22×C3×C4—22no—
176C22×C3×C4—22no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—22no—
180C22×C3×C4—42no—
181C22×C3×C4—42no—
182C22×C3×C4—61no—
183C22×C3×C4—61no—
184C22×C3×C4—61no—
185C22×C3×C4#6711yescharacteristic
186C22×C3×C4#6712yes—
187C22×C3×C4#6711yescharacteristic
188C22×C3×C4#6712yes—
189C22×C3×C4C22×D312yes—
190C22×C3×C4C22×D312yes—
191C22×C3×C4C22×D311yescharacteristic
192C22×C3×C4C22×D311yescharacteristic
193C2×#67—24no—
194C2×#67—44no—
195C22×Dic3—21no—
196C22×Dic3—21no—
197C22×Dic3—21no—
198C2×D12—22no—
199C2×D12—22no—
200C2×D12—21no—
201C2×D12C22×D312yes—
202C3×C4⋊C4—32no—
203C3×C4⋊C4—32no—
204C3×C4⋊C4—32no—
205C3×C4⋊C4—61no—
206C3×C4⋊C4—61no—
207C3×C4⋊C4—61no—
208C3×C22⋊C4—64no—
209C3×C22⋊C4—64no—
210C3×C42—64no—
211#217—24no—
212(C2×D3)⋊C4—24no—
213C4⋊Dic3—21no—
214C4⋊Dic3—21no—
215C4⋊Dic3—21no—
216C4⋊Dic3C22×D312yes—
217C4⋊Dic3C22×D312yes—
218C4⋊Dic3C22×D312yes—
219C4×Dic3—24no—
220C2×C3⋊C8—32no—
221C2×C3⋊C8—32no—
222C2×C3⋊C8—32no—
223C2×C3⋊C8—32no—
224C2×C3⋊C8—62no—
225C2×C3⋊C8—62no—
226C2×C3⋊C8—62no—
227C2×C3⋊C8—62no—
228C2×C3⋊C8—62no—
229C2×C3⋊C8—62no—
230C2×C3⋊C8—122no—
231C2×C3⋊C8—122no—
232C22×C32—22no—
233C22×C32—22no—
234C22×C32—22no—
235C22×C32—44no—
236C22×C32#12312yes—
237C22×C32#13512yes—
238C22×C32AGL(1,ℤ/8)12yes—
239C22×C32C22×D411yescharacteristic
240C2×C3×D3—42no—
241C2×C3×D3—42no—
242C2×C3×D3—42no—
243C2×C3×D3—84no—
244C32×C4—22no—
245C32×C4#12312yes—
246C32×C4C2×#4111yescharacteristic
247C32×C4C2×#4111yescharacteristic
248C3×Dic3—42no—
249C3×Dic3—42no—
250C3×Dic3—42no—
251C22×D4—31no—
252C22×D4—61no—
253C23×C4D3211yescharacteristic
254C22×C8—91no—
255C22×C8—91no—
256#121—34no—
257#121—62no—
258#117—34no—
259#117—62no—
260C2×C4⋊C4—31no—
261C2×C4⋊C4—31no—
262C2×C4⋊C4—31no—
263C2×C22⋊C4—61no—
264C2×C22⋊C4—61no—
265C2×C42—61no—
266#107—94no—
267#106—94no—
268#102—94no—
269#102—94no—
270C22⋊C8—94no—
271C23×C3—24no—
272C23×C3—22no—
273C23×C3—22no—
274C23×C3—22no—
275C23×C3—22no—
276C23×C3—22no—
277C23×C3—22no—
278C23×C3—22no—
279C23×C3—21no—
280C23×C3—42no—
281C23×C3—42no—
282C23×C3—62no—
283C23×C3—122no—
284C23×C3—122no—
285C23×C3—122no—
286C23×C3C2×#6712yes—
287C23×C3C2×#6712yes—
288C23×C3C2×#6711yescharacteristic
289C23×C3C2×#6711yescharacteristic
290C22×D3—22no—
291C22×D3—42no—
292C22×D3—42no—
293C22×D3—42no—
294C3×D4—62no—
295C3×D4—62no—
296C3×D4—128no—
297C3×D4—122no—
298C2×C3×C4—22no—
299C2×C3×C4—22no—
300C2×C3×C4—24no—
301C2×C3×C4—24no—
302C2×C3×C4—22no—
303C2×C3×C4—22no—
304C2×C3×C4—22no—
305C2×C3×C4—22no—
306C2×C3×C4—21no—
307C2×C3×C4—22no—
308C2×C3×C4—22no—
309C2×C3×C4—21no—
310C2×C3×C4—22no—
311C2×C3×C4—42no—
312C2×C3×C4—42no—
313C2×C3×C4—44no—
314C2×C3×C4—42no—
315C2×C3×C4—62no—
316C2×C3×C4—62no—
317C2×C3×C4—62no—
318C2×C3×C4—122no—
319C2×C3×C4—122no—
320C2×C3×C4—122no—
321C2×C3×C4#23512yes—
322C2×C3×C4#23512yes—
323C2×C3×C4#23712yes—
324C2×C3×C4#23712yes—
325C2×C3×C4C2×#6712yes—
326C2×C3×C4C2×#6712yes—
327C2×C3×C4C2×#6711yescharacteristic
328C2×C3×C4C2×#6711yescharacteristic
329C2×C3×C4C23×D311yescharacteristic
330C2×C3×C4C23×D311yescharacteristic
331#67—48no—
332C2×Dic3—22no—
333C2×Dic3—22no—
334C2×Dic3—22no—
335C2×Dic3—42no—
336C2×Dic3—42no—
337C2×Dic3—42no—
338D12—22no—
339D12—22no—
340D12—42no—
341C3⋊C8—62no—
342C3⋊C8—62no—
343C3⋊C8—62no—
344C3⋊C8—62no—
345C3⋊C8—122no—
346C3⋊C8—122no—
347C2×C32—42no—
348C2×C32#48214yescomplemented
349C2×C32C2×#12311yescharacteristic
350C2×C32C2×#13511yescharacteristic
351C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
352C3×D3—82no—
353C24—61no—
354C24#62511yescharacteristic
355C2×D4—32no—
356C2×D4—64no—
357C2×D4—62no—
358C2×D4—62no—
359C2×D4—61no—
360C2×D4—124no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—61no—
364C22×C4—61no—
365C22×C4—61no—
366C22×C4#62512yes—
367C22×C4#62511yescharacteristic
368C22×C4C2×D3212yes—
369C22×C4C2×D3211yescharacteristic
370C2×C8—92no—
371C2×C8—92no—
372C2×C8—182no—
373C2×C8—182no—
374C4⋊C4—32no—
375C4⋊C4—32no—
376C4⋊C4—32no—
377C4⋊C4—61no—
378C4⋊C4—61no—
379C4⋊C4—61no—
380C22⋊C4—64no—
381C22⋊C4—64no—
382C42—64no—
383C22×C3—24no—
384C22×C3—22no—
385C22×C3—22no—
386C22×C3—22no—
387C22×C3—22no—
388C22×C3—22no—
389C22×C3—22no—
390C22×C3—21no—
391C22×C3—22no—
392C22×C3—22no—
393C22×C3—22no—
394C22×C3—42no—
395C22×C3—42no—
396C22×C3—48no—
397C22×C3—44no—
398C22×C3—44no—
399C22×C3—122no—
400C22×C3—122no—
401C22×C3—122no—
402C22×C3—244no—
403C22×C3#92912yes—
404C22×C3#93212yes—
405C22×C3#93512yes—
406C22×C3#94912yes—
407C22×C3#95012yes—
408C22×C3#95012yes—
409C22×C3C22×#6711yescharacteristic
410C22×C3C22×#6711yescharacteristic
411C2×D3—42no—
412C2×D3—42no—
413C2×D3—42no—
414C2×D3—84no—
415C3×C4—22no—
416C3×C4—22no—
417C3×C4—21no—
418C3×C4—21no—
419C3×C4—22no—
420C3×C4—42no—
421C3×C4—122no—
422C3×C4—122no—
423C3×C4—122no—
424C3×C4#92912yes—
425C3×C4#93512yes—
426C3×C4C2×#23511yescharacteristic
427C3×C4C2×#23511yescharacteristic
428C3×C4C2×#23711yescharacteristic
429C3×C4C2×#23711yescharacteristic
430Dic3—42no—
431Dic3—42no—
432Dic3—42no—
433C32C2×#48211yescharacteristic, complemented, Sylow
434C23—22no—
435C23—22no—
436C23—22no—
437C23—62no—
438C23—122no—
439C23—122no—
440C23—122no—
441C23C2×#62512yes—
442C23C2×#62511yescharacteristic
443D4—62no—
444D4—62no—
445D4—128no—
446D4—122no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—24no—
451C2×C4—62no—
452C2×C4—62no—
453C2×C4—62no—
454C2×C4—122no—
455C2×C4—122no—
456C2×C4—122no—
457C2×C4#380412yes—
458C2×C4#380412yes—
459C2×C4C2×#62512yes—
460C2×C4C2×#62511yescharacteristic
461C2×C4C22×D3211yescharacteristic
462C8—182no—
463C8—182no—
464C2×C3—24no—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—21no—
468C2×C3—44no—
469C2×C3—42no—
470C2×C3—42no—
471C2×C3—242no—
472C2×C3#500314yescomplemented
473C2×C3#503514yescomplemented
474C2×C3C2×#92911yescharacteristic
475C2×C3C2×#93211yescharacteristic
476C2×C3C2×#93511yescharacteristic
477C2×C3C2×#94911yescharacteristic
478C2×C3C2×#95011yescharacteristic
479C2×C3C2×#95011yescharacteristic
480D3—82no—
481C22—22no—
482C22—22no—
483C22—22no—
484C22—44no—
485C22—122no—
486C22—122no—
487C22—122no—
488C22—244no—
489C22#6382212yes—
490C22#6382312yes—
491C22#6396112yes—
492C22C22×#62511yescharacteristic
493C4—22no—
494C4—122no—
495C4—122no—
496C4—122no—
497C4#6396112yes—
498C4C2×#380411yescharacteristic
499C4C2×#380411yescharacteristic
500C3—21no—
501C3C2×#500311yescharacteristic, complemented
502C3C2×#503511yescharacteristic, complemented
503C2—42no—
504C2—242no—
505C2#1059109014yesdirect product factor
506C2C2×#6382211yescharacteristic
507C2C2×#6382311yescharacteristic
508C2C2×#6396111yescharacteristic
subgroupG/H
centerC23C2×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC23×C32C2×D4
prime radicalC2×C3×#930C2
hypercenterC23×C4D32
hypocenterC32C2×#482
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#926C2semidirect
3. C2×#63657C2semidirect
4. C2×#63576C2semidirect
5. C2×#63574C2semidirect
6. #10591090C2direct (N × H)
7. C2×#63562C2semidirect
8. C2×#63562C2semidirect
21. C3×#926C22semidirect
26. #63657C22semidirect
27. #63576C22semidirect
28. #63574C22semidirect
29. #63562C22semidirect
30. #63562C22semidirect
34. C2×#926D3semidirect
101. #926C2×D3semidirect
348. C2×C32#482semidirect
433. C32C2×#482semidirect
472. C2×C3#5003semidirect
473. C2×C3#5035semidirect
501. C3C2×#5003semidirect
502. C3C2×#5035semidirect
505. C2#10591090direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9302
C2×C3×#9262
C2×#636572
C2×#635762
C2×#635742
#105910902
C2×#635622
C2×#50353
C2×#50033