Finite Group Databasebeta

← C2×#10591487 #11873366

Subgroups — C2×#10591487 #11873366

Order 1152.

1157 conjugacy classes of subgroups.

The subgroup lattice has 525 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#940C211yesmaximal, characteristic
2C2×#63918C211yesmaximal, characteristic, complemented
3C2×#63659C211yesmaximal, characteristic, complemented
4C2×C3×#832C211yesmaximal, characteristic, complemented
5#10591487C218yesmaximal, direct product factor
6C2×#63563C211yesmaximal, characteristic, complemented
7C2×#63562C211yesmaximal, characteristic, complemented
8C2×Dic3×C3⋊C8C211yesmaximal, characteristic, complemented
9C2×#5070—31nomaximal
10C2×#4760—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C22×C3×#67—21no—
13C22×C3×#67—21no—
14C22×C3×D12C2211yescharacteristic
15C22×#627—21no—
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#940—22no—
19C3×#940C2214yes—
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4×Dic3C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C2×Dic3⋊Dic3—21no—
24#63918—22no—
25#63918C2214yescomplemented
26#63659C2214yescomplemented
27C3×#832C2214yescomplemented
28#63563C2214yescomplemented
29#63562C2214yescomplemented
30Dic3×C3⋊C8C2214yescomplemented
31C2×C3×#127—31no—
32C2×#940D311yescharacteristic
33C2×#888—31no—
34C2×#869—31no—
35C2×C3×#102—31no—
36C2×#832—31no—
37C2×#832—31no—
38C2×#832—31no—
39C2×#832—31no—
40C2×#832—61no—
41C2×#832D311yescharacteristic, complemented
42C2×#821—31no—
43C2×C8×Dic3—31no—
44#5070—38no—
45C2×#809—31no—
46C2×C4×C3⋊C8—31no—
47#4760—38no—
48C24×C32—21no—
49C23×C3×D3—21no—
50C2×C32×D4—21no—
51C2×C32×D4—22no—
52C2×C32×D4—22no—
53C2×C32×D4C2312yes—
54C22×C32×C4C2311yescharacteristic
55C22×C3⋊Dic3—21no—
56C2×C3×#67—24no—
57C2×C3×#67—24no—
58C2×C3×#67—44no—
59C2×C3×#67—44no—
60C22×C3×Dic3—21no—
61C22×C3×Dic3D411yescharacteristic
62C22×C3×Dic3D411yescharacteristic
63C2×C3×D12—22no—
64C2×C3×D12—22no—
65C2×C3×D12—21no—
66C2×C3×D12C2312yes—
67C2×#627—24no—
68C2×#627—44no—
69C4⋊(C3⋊Dic3)—21no—
70C4⋊(C3⋊Dic3)C2312yes—
71C2×C3⋊(C3⋊C8)—22no—
72C2×C3⋊(C3⋊C8)C2312yes—
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3C2312yes—
75C3×C4×Dic3D412yes—
76C3×C4×Dic3C2312yes—
77C2×C3×C3⋊C8—22no—
78C2×C3×C3⋊C8C2312yes—
79Dic3⋊Dic3—24no—
80C2×#486—91noSylow
81C22×C3×D4—21no—
82C22×C3×D4—31no—
83C22×C3×D4—61no—
84C22×C3×D4—61no—
85C22×C3×D4C2×D311yescharacteristic
86C22×C3×D4C2×D311yescharacteristic
87C22×#67—21no—
88C22×#67—21no—
89C22×D12C2×D311yescharacteristic
90C22×Dic6—61no—
91C22×Dic6—61no—
92C22×C3×C8—31no—
93C3×#127—34no—
94C3×#127—62no—
95C2×C3×C4⋊C4—31no—
96C2×C3×C42—31no—
97#940—22no—
98#940C2×D314yes—
99C2×C4⋊Dic3—31no—
100C2×C4⋊Dic3—31no—
101C2×C4⋊Dic3—61no—
102C2×C4⋊Dic3—61no—
103C2×C4⋊Dic3C2×D311yescharacteristic
104C2×Dic3⋊C4—61no—
105C2×C4×Dic3C2×D311yescharacteristic
106C22×C3⋊C8—31no—
107C22×C3⋊C8—31no—
108C22×C3⋊C8—61no—
109C22×C3⋊C8C2×D311yescharacteristic
110#888—34no—
111#888—62no—
112#869—34no—
113#869—62no—
114C3×#102—34no—
115#832—34no—
116#832—34no—
117#832—34no—
118#832—34no—
119#832—64no—
120#832C2×D314yescomplemented
121#821—34no—
122C8×Dic3—34no—
123#809—34no—
124C4×C3⋊C8—34no—
125C23×C32—22no—
126C23×C32—42no—
127C23×C32—42no—
128C23×C32—42no—
129C23×C32C2×D411yescharacteristic
130C22×C3×D3—22no—
131C22×C3×D3—42no—
132C22×C3×D3—42no—
133C22×C3×D3—42no—
134C32×D4—22no—
135C32×D4—22no—
136C32×D4—42no—
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4#4112yes—
139C2×C32×C4#4112yes—
140C2×C32×C4C2411yescharacteristic
141C2×C3⋊Dic3—22no—
142C2×C3⋊Dic3—42no—
143C3×#67—48no—
144C3×#67—48no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—42no—
147C2×C3×Dic3D814yes—
148C2×C3×Dic3SD1614yes—
149C2×C3×Dic3C2×D412yes—
150C2×C3×Dic3C2×D412yes—
151C3×D12—22no—
152C3×D12—22no—
153C3×D12—42no—
154#627—48no—
155C3⋊(C3⋊C8)—22no—
156C3×C3⋊C8—22no—
157C2×C4⋊Q8—91no—
158C2×#127—31no—
159#486—98no—
160C2×#102—31no—
161C2×#102—91no—
162C2×#102—91no—
163C2×#102—91no—
164C2×C4×C8—91no—
165C24×C3—21no—
166C24×C3—21no—
167C24×C3—41no—
168C24×C3—61no—
169C23×D3—21no—
170C2×C3×D4—24no—
171C2×C3×D4—22no—
172C2×C3×D4—21no—
173C2×C3×D4—22no—
174C2×C3×D4—22no—
175C2×C3×D4—22no—
176C2×C3×D4—21no—
177C2×C3×D4—22no—
178C2×C3×D4—32no—
179C2×C3×D4—42no—
180C2×C3×D4—41no—
181C2×C3×D4—64no—
182C2×C3×D4—64no—
183C2×C3×D4—62no—
184C2×C3×D4—61no—
185C2×C3×D4—62no—
186C2×C3×D4—124no—
187C2×C3×D4—124no—
188C2×C3×D4C22×D312yes—
189C2×C3×D4C22×D312yes—
190C22×C3×C4—21no—
191C22×C3×C4—31no—
192C22×C3×C4—31no—
193C22×C3×C4—61no—
194C22×C3×C4C22×D311yescharacteristic
195C22×C3×C4C22×D311yescharacteristic
196C2×#67—24no—
197C2×#67—24no—
198C2×#67—44no—
199C2×#67—44no—
200C22×Dic3—21no—
201C22×Dic3—61no—
202C22×Dic3—61no—
203C22×Dic3—121no—
204C22×Dic3#6711yescharacteristic
205C22×Dic3#6711yescharacteristic
206C2×D12—22no—
207C2×D12—22no—
208C2×D12—21no—
209C2×D12C22×D312yes—
210C2×Dic6—64no—
211C2×Dic6—64no—
212C2×Dic6—124no—
213C2×Dic6—124no—
214C2×C3×C8—32no—
215C2×C3×C8—62no—
216C3×C4⋊C4—32no—
217C3×C4⋊C4—61no—
218C3×C42—32no—
219C3×C42—32no—
220C4⋊Dic3—21no—
221C4⋊Dic3—32no—
222C4⋊Dic3—32no—
223C4⋊Dic3—62no—
224C4⋊Dic3—64no—
225C4⋊Dic3—61no—
226C4⋊Dic3—61no—
227C4⋊Dic3—121no—
228C4⋊Dic3C22×D312yes—
229Dic3⋊C4—64no—
230C4×Dic3#6712yes—
231C4×Dic3C22×D312yes—
232C2×C3⋊C8—22no—
233C2×C3⋊C8—32no—
234C2×C3⋊C8—32no—
235C2×C3⋊C8—62no—
236C2×C3⋊C8—62no—
237C2×C3⋊C8—62no—
238C2×C3⋊C8—122no—
239C2×C3⋊C8C22×D312yes—
240C22×C32—42no—
241C22×C32—42no—
242C22×C32—42no—
243C22×C32—84no—
244C22×C32#12412yes—
245C22×C32C2×D812yes—
246C22×C32C2×SD1612yes—
247C22×C32C22×D411yescharacteristic
248C2×C3×D3—42no—
249C2×C3×D3—42no—
250C2×C3×D3—42no—
251C2×C3×D3—84no—
252C32×C4#12412yes—
253C32×C4C2×#4111yescharacteristic
254C32×C4C2×#4111yescharacteristic
255C3⋊Dic3—42no—
256C3×Dic3—42no—
257C3×Dic3C2×D814yes—
258C3×Dic3C2×SD1614yes—
259C22×Q8—181no—
260C22×D4—31no—
261C22×D4—61no—
262C22×D4—61no—
263C22×D4D3211yescharacteristic
264C22×C8—31no—
265C22×C8—91no—
266C4⋊Q8—94no—
267C4⋊Q8—182no—
268#127—34no—
269#127—62no—
270C2×C4⋊C4—31no—
271C2×C4⋊C4—91no—
272C2×C4⋊C4—181no—
273C2×C42—31no—
274#102—34no—
275#102—94no—
276#102—94no—
277#102—94no—
278C4×C8—94no—
279C23×C3—22no—
280C23×C3—22no—
281C23×C3—21no—
282C23×C3—42no—
283C23×C3—44no—
284C23×C3—42no—
285C23×C3—42no—
286C23×C3—42no—
287C23×C3—42no—
288C23×C3—42no—
289C23×C3—42no—
290C23×C3—62no—
291C23×C3—82no—
292C23×C3—82no—
293C23×C3—122no—
294C23×C3—122no—
295C23×C3—122no—
296C23×C3D3×D411yescharacteristic
297C23×C3C2×#6711yescharacteristic
298C22×D3—22no—
299C22×D3—42no—
300C22×D3—42no—
301C22×D3—42no—
302C3×D4—24no—
303C3×D4—22no—
304C3×D4—22no—
305C3×D4—22no—
306C3×D4—22no—
307C3×D4—42no—
308C3×D4—44no—
309C3×D4—42no—
310C3×D4—42no—
311C3×D4—62no—
312C3×D4—62no—
313C3×D4—128no—
314C3×D4—128no—
315C3×D4—122no—
316C2×C3×C4—21no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—21no—
320C2×C3×C4—34no—
321C2×C3×C4—34no—
322C2×C3×C4—32no—
323C2×C3×C4—32no—
324C2×C3×C4—62no—
325C2×C3×C4—122no—
326C2×C3×C4#23512yes—
327C2×C3×C4D3×D411yescharacteristic
328C2×C3×C4#23712yes—
329C2×C3×C4#23712yes—
330C2×C3×C4#23712yes—
331C2×C3×C4C2×#6711yescharacteristic
332C2×C3×C4C23×D311yescharacteristic
333C2×C3×C4C23×D311yescharacteristic
334#67—48no—
335#67—48no—
336C2×Dic3—22no—
337C2×Dic3—42no—
338C2×Dic3—62no—
339C2×Dic3—62no—
340C2×Dic3—122no—
341C2×Dic3—122no—
342C2×Dic3—122no—
343C2×Dic3—242no—
344C2×Dic3#21314yes—
345C2×Dic3#21414yes—
346C2×Dic3C2×#6712yes—
347C2×Dic3C2×#6712yes—
348D12—22no—
349D12—22no—
350D12—42no—
351Dic6—128no—
352Dic6—128no—
353C3×C8—62no—
354C3⋊C8—22no—
355C3⋊C8—62no—
356C3⋊C8—62no—
357C3⋊C8—122no—
358C2×C32—82no—
359C2×C32#48614yescomplemented
360C2×C32C2×#12411yescharacteristic
361C2×C32C22×D811yescharacteristic
362C2×C32C22×SD1611yescharacteristic
363C3×D3—82no—
364C24—21no—
365C24—61no—
366C2×Q8—184no—
367C2×Q8—364no—
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—21no—
371C2×D4—32no—
372C2×D4—64no—
373C2×D4—64no—
374C2×D4—62no—
375C2×D4—62no—
376C2×D4—61no—
377C2×D4—124no—
378C2×D4—124no—
379C2×D4C2×D3212yes—
380C22×C4—31no—
381C22×C4—31no—
382C22×C4—61no—
383C22×C4—181no—
384C22×C4C2×D3211yescharacteristic
385C2×C8—32no—
386C2×C8—62no—
387C2×C8—92no—
388C2×C8—182no—
389C4⋊C4—32no—
390C4⋊C4—61no—
391C4⋊C4—92no—
392C4⋊C4—184no—
393C4⋊C4—181no—
394C42—32no—
395C42—32no—
396C22×C3—21no—
397C22×C3—22no—
398C22×C3—22no—
399C22×C3—22no—
400C22×C3—44no—
401C22×C3—42no—
402C22×C3—42no—
403C22×C3—42no—
404C22×C3—42no—
405C22×C3—42no—
406C22×C3—42no—
407C22×C3—82no—
408C22×C3—82no—
409C22×C3—88no—
410C22×C3—84no—
411C22×C3—84no—
412C22×C3—122no—
413C22×C3—122no—
414C22×C3—122no—
415C22×C3—244no—
416C22×C3#88512yes—
417C22×C3D3×D812yes—
418C22×C3D3×SD1612yes—
419C22×C3C2×#21312yes—
420C22×C3C2×#21412yes—
421C22×C3#93612yes—
422C22×C3C2×D3×D411yescharacteristic
423C22×C3C22×#6711yescharacteristic
424C2×D3—42no—
425C2×D3—42no—
426C2×D3—42no—
427C2×D3—84no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—22no—
431C3×C4—34no—
432C3×C4—34no—
433C3×C4—122no—
434C3×C4#88512yes—
435C3×C4#93612yes—
436C3×C4C2×#23511yescharacteristic
437C3×C4C2×#23711yescharacteristic
438C3×C4C2×#23711yescharacteristic
439C3×C4C2×#23711yescharacteristic
440Dic3—42no—
441Dic3—122no—
442Dic3—122no—
443Dic3—242no—
444Dic3C2×#21314yes—
445Dic3C2×#21414yes—
446C32C2×#48611yescharacteristic, complemented, Sylow
447C23—22no—
448C23—42no—
449C23—42no—
450C23—42no—
451C23—62no—
452C23—122no—
453C23—122no—
454C23—122no—
455C23D3×#6711yescharacteristic
456Q8—368no—
457D4—22no—
458D4—22no—
459D4—42no—
460D4—62no—
461D4—62no—
462D4—128no—
463D4—128no—
464D4—122no—
465C2×C4—32no—
466C2×C4—32no—
467C2×C4—34no—
468C2×C4—34no—
469C2×C4—62no—
470C2×C4—122no—
471C2×C4—182no—
472C2×C4—362no—
473C2×C4#380412yes—
474C2×C4#380512yes—
475C2×C4D3×#6711yescharacteristic
476C2×C4C22×D3211yescharacteristic
477C8—62no—
478C8—182no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—24no—
483C2×C3—84no—
484C2×C3—82no—
485C2×C3—82no—
486C2×C3—242no—
487C2×C3#476014yescomplemented
488C2×C3#507014yescomplemented
489C2×C3C2×#88511yescharacteristic
490C2×C3C2×D3×D811yescharacteristic
491C2×C3C2×D3×SD1611yescharacteristic
492C2×C3C22×#21311yescharacteristic
493C2×C3C22×#21411yescharacteristic
494C2×C3C2×#93611yescharacteristic
495D3—82no—
496C22—42no—
497C22—42no—
498C22—42no—
499C22—84no—
500C22—122no—
501C22—122no—
502C22—122no—
503C22—244no—
504C22D3×#21312yes—
505C22D3×#21412yes—
506C22#6395912yes—
507C22C2×D3×#6711yescharacteristic
508C4—34no—
509C4—34no—
510C4—122no—
511C4—362no—
512C4#6395912yes—
513C4C2×#380411yescharacteristic
514C4C2×#380511yescharacteristic
515C3—21no—
516C3C2×#476011yescharacteristic, complemented
517C3C2×#507011yescharacteristic, complemented
518C2—82no—
519C2—242no—
520C2#1059148714yesdirect product factor
521C2C2×D3×#21311yescharacteristic
522C2C2×D3×#21411yescharacteristic
523C2C2×#6395911yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
prime radicalC2×C3×#940C2
hypercenterC22×D4D32
hypocenterC32C2×#486
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#63918C2semidirect
3. C2×#63659C2semidirect
4. C2×C3×#832C2semidirect
5. #10591487C2direct (N × H)
6. C2×#63563C2semidirect
7. C2×#63562C2semidirect
8. C2×Dic3×C3⋊C8C2semidirect
25. #63918C22semidirect
26. #63659C22semidirect
27. C3×#832C22semidirect
28. #63563C22semidirect
29. #63562C22semidirect
30. Dic3×C3⋊C8C22semidirect
41. C2×#832D3semidirect
120. #832C2×D3semidirect
359. C2×C32#486semidirect
446. C32C2×#486semidirect
487. C2×C3#4760semidirect
488. C2×C3#5070semidirect
516. C3C2×#4760semidirect
517. C3C2×#5070semidirect
520. C2#10591487direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9402
C2×#639182
C2×#636592
C2×C3×#8322
#105914872
C2×#635632
C2×#635622
C2×Dic3×C3⋊C82
C2×#50703
C2×#47603