Finite Group Databasebeta

← C2×#10591400 #11859838

Subgroups — C2×#10591400 #11859838

Order 1152.

1401 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3753C211yesmaximal, characteristic
2C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
3C2×#63894C211yesmaximal, characteristic, complemented
4C2×C3×#832C211yesmaximal, characteristic, complemented
5#10591400C218yesmaximal, direct product factor
6C2×#63576C211yesmaximal, characteristic, complemented
7C2×#63564C211yesmaximal, characteristic, complemented
8C2×Dic3×C3⋊C8C211yesmaximal, characteristic, complemented
9C2×C4×#213—31nomaximal
10C2×#4756—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C23×C3×Dic3—21no—
14C22×#624—21no—
15C2×#3753C418yescomplemented
16C2×#3753C2214yes—
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C2×C3×#217—21no—
19C3×D4×Dic3—22no—
20C3×D4×Dic3C2214yescomplemented
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4×Dic3C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C2×#3722—21no—
26#63894—22no—
27#63894C2214yescomplemented
28C3×#832C2214yescomplemented
29#63576C2214yescomplemented
30#63564C2214yescomplemented
31Dic3×C3⋊C8C2214yescomplemented
32C2×C3×C4×D4—31no—
33C2×D4×Dic3D311yescharacteristic, complemented
34C22×#213—31no—
35C22×#213—31no—
36C22×#213—61no—
37C2×#893—31no—
38C2×C4×D12—31no—
39C2×C3×#102—31no—
40C2×#832D311yescharacteristic, complemented
41C2×#821—31no—
42C2×C8×Dic3—31no—
43C4×#213—38no—
44C2×#809—31no—
45C2×#807—31no—
46C2×#807—31no—
47C2×C4×C3⋊C8—31no—
48#4756—38no—
49C24×C32—21no—
50C23×C3⋊D3—21no—
51C2×C32×D4—21no—
52C2×C32×D4—22no—
53C2×C32×D4C2×C414yescomplemented
54C2×C32×D4C2312yes—
55C22×C32×C4C2311yescharacteristic
56C2×C4⋊(C3⋊D3)—21no—
57C2×C4⋊(C3⋊D3)—22no—
58C2×C4⋊(C3⋊D3)C2×C414yescomplemented
59C2×C4⋊(C3⋊D3)C2312yes—
60C22×C3×Dic3—21no—
61C22×C3×Dic3—21no—
62C22×C3×Dic3—24no—
63C22×C3×Dic3—44no—
64C22×C3×Dic3D411yescharacteristic
65C22×C3×Dic3D411yescharacteristic
66C2×#624—24no—
67C2×#624—44no—
68#3753C2×C4116yescomplemented
69C2×C3⋊(C3⋊C8)C2×C414yescomplemented
70C2×C3⋊(C3⋊C8)C2312yes—
71C3×#217—24no—
72C3×C4⋊Dic3—21no—
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3C2312yes—
75C3×C4⋊Dic3C2312yes—
76C3×C4×Dic3D412yes—
77C3×C4×Dic3C2312yes—
78C2×C3×C3⋊C8—22no—
79C2×C3×C3⋊C8C2312yes—
80#3722—24no—
81C2×C4×D8—91noSylow
82C22×C3×D4—21no—
83C22×C3×D4C2×D311yescharacteristic
84C22×C3×D4C2×D311yescharacteristic
85C23×C3×C4—61no—
86C23×Dic3—21no—
87C22×D12—31no—
88C22×D12—31no—
89C22×D12—61no—
90C22×C4×D3—61no—
91C22×C4×D3—61no—
92C22×C3×C8—31no—
93C3×C4×D4—34no—
94C3×C4×D4—62no—
95C2×C3×C4⋊C4—31no—
96C2×C3×C4⋊C4—31no—
97C2×C3×C22⋊C4—61no—
98C2×C3×C42—31no—
99C2×#217—21no—
100D4×Dic3—22no—
101D4×Dic3C2×D314yescomplemented
102C2×#213—38no—
103C2×#213—38no—
104C2×#213—34no—
105C2×#213—34no—
106C2×#213—68no—
107C2×#213—64no—
108C2×(C2×D3)⋊C4—61no—
109C2×(C2×D3)⋊C4—61no—
110C2×C4⋊Dic3C2×D311yescharacteristic
111C2×C4⋊Dic3C2×D311yescharacteristic
112C2×C4×Dic3C2×D311yescharacteristic
113C22×C3⋊C8—31no—
114C22×C3⋊C8—31no—
115C22×C3⋊C8—61no—
116C22×C3⋊C8C2×D311yescharacteristic
117#893—34no—
118#893—62no—
119C4×D12—34no—
120C4×D12—62no—
121C3×#102—34no—
122#832C2×D314yescomplemented
123#821—34no—
124C8×Dic3—34no—
125#809—34no—
126#807—34no—
127#807—34no—
128C4×C3⋊C8—34no—
129C23×C32—24no—
130C23×C32—22no—
131C23×C32—42no—
132C23×C32—42no—
133C23×C32C2×D411yescharacteristic
134C22×C3⋊D3—24no—
135C22×C3⋊D3—22no—
136C22×C3⋊D3—42no—
137C22×C3⋊D3—42no—
138C32×D4—24no—
139C32×D4—22no—
140C32×D4C22×C414yescomplemented
141C2×C32×C4C22×C412yes—
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4#4112yes—
144C2×C32×C4C2411yescharacteristic
145C4⋊(C3⋊D3)—24no—
146C4⋊(C3⋊D3)—22no—
147C4⋊(C3⋊D3)C22×C414yescomplemented
148C2×C3×Dic3—22no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—42no—
152C2×C3×Dic3—42no—
153C2×C3×Dic3—48no—
154C2×C3×Dic3D814yescomplemented
155C2×C3×Dic3C2×D412yes—
156C2×C3×Dic3C2×D412yes—
157#624—48no—
158C3⋊(C3⋊C8)C22×C414yescomplemented
159C3×C3⋊C8—22no—
160C22×D8—91no—
161C2×C4×D4—31no—
162C2×C4×D4—91no—
163C4×D8—98no—
164C2×#107—91no—
165C2×#102—31no—
166C2×#102—91no—
167C2×C4×C8—91no—
168C24×C3—21no—
169C24×C3—21no—
170C24×C3—41no—
171C23×D3—61no—
172C23×D3—61no—
173C23×D3—121no—
174C2×C3×D4—22no—
175C2×C3×D4—21no—
176C2×C3×D4—22no—
177C2×C3×D4—21no—
178C2×C3×D4—24no—
179C2×C3×D4—22no—
180C2×C3×D4—42no—
181C2×C3×D4—41no—
182C2×C3×D4C4×D314yescomplemented
183C2×C3×D4C4×D314yescomplemented
184C2×C3×D4C22×D312yes—
185C2×C3×D4C22×D312yes—
186C22×C3×C4—21no—
187C22×C3×C4—31no—
188C22×C3×C4—31no—
189C22×C3×C4—64no—
190C22×C3×C4—61no—
191C22×C3×C4—61no—
192C22×C3×C4—124no—
193C22×C3×C4C22×D311yescharacteristic
194C22×C3×C4C22×D311yescharacteristic
195C22×Dic3—21no—
196C22×Dic3—21no—
197C22×Dic3—24no—
198C22×Dic3—44no—
199C22×Dic3#6711yescharacteristic
200C22×Dic3#6711yescharacteristic
201C2×D12—34no—
202C2×D12—34no—
203C2×D12—32no—
204C2×D12—32no—
205C2×D12—64no—
206C2×D12—62no—
207C2×D12—62no—
208C2×D12—61no—
209C2×D12—62no—
210C2×D12—61no—
211C2×D12—122no—
212C2×D12—121no—
213C2×C4×D3—64no—
214C2×C4×D3—64no—
215C2×C4×D3—124no—
216C2×C4×D3—124no—
217C2×C3×C8—32no—
218C2×C3×C8—62no—
219C3×C4⋊C4—32no—
220C3×C4⋊C4—32no—
221C3×C4⋊C4—61no—
222C3×C4⋊C4—61no—
223C3×C22⋊C4—64no—
224C3×C42—32no—
225C3×C42—32no—
226#217—24no—
227#213—316no—
228#213—316no—
229#213—616no—
230(C2×D3)⋊C4—64no—
231(C2×D3)⋊C4—64no—
232C4⋊Dic3—21no—
233C4⋊Dic3—21no—
234C4⋊Dic3C22×D312yes—
235C4⋊Dic3C22×D312yes—
236C4×Dic3#6712yes—
237C4×Dic3C22×D312yes—
238C2×C3⋊C8—22no—
239C2×C3⋊C8—34no—
240C2×C3⋊C8—34no—
241C2×C3⋊C8—32no—
242C2×C3⋊C8—32no—
243C2×C3⋊C8—64no—
244C2×C3⋊C8—62no—
245C2×C3⋊C8C22×D312yes—
246C22×C32—24no—
247C22×C32—42no—
248C22×C32—42no—
249C22×C32—48no—
250C22×C32C4×D412yes—
251C22×C32C2×D812yes—
252C22×C32#13512yes—
253C22×C32C22×D411yescharacteristic
254C2×C3⋊D3—24no—
255C2×C3⋊D3—42no—
256C2×C3⋊D3—42no—
257C2×C3⋊D3—48no—
258C32×C4C4×D412yes—
259C32×C4C23×C411yescharacteristic
260C32×C4C2×#4111yescharacteristic
261C3×Dic3—22no—
262C3×Dic3—42no—
263C3×Dic3—42no—
264C3×Dic3C2×D814yescomplemented
265C22×D4—91no—
266C22×D4D3211yescharacteristic
267C23×C4—61no—
268C23×C4—181no—
269C2×D8—98no—
270C2×D8—94no—
271C22×C8—31no—
272C22×C8—91no—
273C4×D4—34no—
274C4×D4—62no—
275C4×D4—94no—
276C4×D4—182no—
277C2×C4⋊C4—31no—
278C2×C4⋊C4—31no—
279C2×C22⋊C4—61no—
280C2×C22⋊C4—181no—
281C2×C42—31no—
282#107—94no—
283#102—34no—
284#102—94no—
285C4×C8—94no—
286C23×C3—24no—
287C23×C3—24no—
288C23×C3—22no—
289C23×C3—22no—
290C23×C3—21no—
291C23×C3—42no—
292C23×C3—44no—
293C23×C3—42no—
294C23×C3—42no—
295C23×C3—42no—
296C23×C3—42no—
297C23×C3—82no—
298C23×C3—82no—
299C23×C3D3×D411yescharacteristic
300C23×C3C2×#6711yescharacteristic
301C22×D3—64no—
302C22×D3—64no—
303C22×D3—62no—
304C22×D3—62no—
305C22×D3—122no—
306C22×D3—124no—
307C22×D3—122no—
308C22×D3—122no—
309C22×D3—122no—
310C22×D3—122no—
311C22×D3—242no—
312C22×D3—242no—
313C3×D4—24no—
314C3×D4—24no—
315C3×D4—22no—
316C3×D4—22no—
317C3×D4—24no—
318C3×D4—42no—
319C3×D4—44no—
320C3×D4C2×C4×D314yescomplemented
321C3×D4C2×C4×D314yescomplemented
322C2×C3×C4—21no—
323C2×C3×C4—22no—
324C2×C3×C4—22no—
325C2×C3×C4—21no—
326C2×C3×C4—34no—
327C2×C3×C4—32no—
328C2×C3×C4—32no—
329C2×C3×C4—62no—
330C2×C3×C4—62no—
331C2×C3×C4—62no—
332C2×C3×C4—128no—
333C2×C3×C4—122no—
334C2×C3×C4—122no—
335C2×C3×C4C2×C4×D312yes—
336C2×C3×C4C2×C4×D312yes—
337C2×C3×C4#23512yes—
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4#23712yes—
340C2×C3×C4C2×#6711yescharacteristic
341C2×C3×C4C23×D311yescharacteristic
342C2×C3×C4C23×D311yescharacteristic
343C2×Dic3—22no—
344C2×Dic3—22no—
345C2×Dic3—22no—
346C2×Dic3—42no—
347C2×Dic3—42no—
348C2×Dic3—48no—
349C2×Dic3#21314yescomplemented
350C2×Dic3C2×#6712yes—
351C2×Dic3C2×#6712yes—
352D12—34no—
353D12—34no—
354D12—64no—
355D12—64no—
356D12—64no—
357D12—62no—
358D12—62no—
359D12—122no—
360D12—124no—
361C4×D3—128no—
362C4×D3—128no—
363C3×C8—62no—
364C3⋊C8—22no—
365C3⋊C8—34no—
366C3⋊C8—34no—
367C3⋊C8—64no—
368C2×C32—44no—
369C2×C32C4×D814yescomplemented
370C2×C32C2×C4×D411yescharacteristic
371C2×C32C22×D811yescharacteristic
372C2×C32C2×#13511yescharacteristic
373C3⋊D3—44no—
374C24—21no—
375C24—181no—
376C2×D4—22no—
377C2×D4—21no—
378C2×D4—92no—
379C2×D4—94no—
380C2×D4—182no—
381C2×D4—181no—
382C2×D4#62414yescomplemented
383C2×D4C2×D3212yes—
384C22×C4—31no—
385C22×C4—31no—
386C22×C4—64no—
387C22×C4—61no—
388C22×C4—61no—
389C22×C4—124no—
390C22×C4—184no—
391C22×C4—364no—
392C22×C4C2×D3211yescharacteristic
393D8—916no—
394C2×C8—32no—
395C2×C8—62no—
396C2×C8—92no—
397C2×C8—94no—
398C4⋊C4—32no—
399C4⋊C4—32no—
400C4⋊C4—61no—
401C4⋊C4—61no—
402C22⋊C4—64no—
403C22⋊C4—184no—
404C42—32no—
405C42—32no—
406C22×C3—24no—
407C22×C3—24no—
408C22×C3—21no—
409C22×C3—22no—
410C22×C3—22no—
411C22×C3—22no—
412C22×C3—44no—
413C22×C3—42no—
414C22×C3—42no—
415C22×C3—48no—
416C22×C3—48no—
417C22×C3—42no—
418C22×C3—42no—
419C22×C3—82no—
420C22×C3—82no—
421C22×C3—88no—
422C22×C3#67⋊C412yes—
423C22×C3D3×D812yes—
424C22×C3#91612yes—
425C22×C3C4×#6712yes—
426C22×C3C2×#21312yes—
427C22×C3#95012yes—
428C22×C3C2×D3×D411yescharacteristic
429C22×C3C22×#6711yescharacteristic
430C2×D3—64no—
431C2×D3—64no—
432C2×D3—124no—
433C2×D3—122no—
434C2×D3—122no—
435C2×D3—128no—
436C2×D3—128no—
437C2×D3—122no—
438C2×D3—122no—
439C2×D3—242no—
440C2×D3—242no—
441C2×D3—248no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—22no—
445C3×C4—34no—
446C3×C4—62no—
447C3×C4—122no—
448C3×C4—122no—
449C3×C4#67⋊C412yes—
450C3×C4C4×#6712yes—
451C3×C4C22×C4×D311yescharacteristic
452C3×C4C22×C4×D311yescharacteristic
453C3×C4C2×#23511yescharacteristic
454C3×C4C2×#23711yescharacteristic
455Dic3—22no—
456Dic3—42no—
457Dic3—42no—
458Dic3C2×#21314yescomplemented
459C32C2×C4×D811yescharacteristic, complemented, Sylow
460C23—22no—
461C23—24no—
462C23—42no—
463C23—42no—
464C23—182no—
465C23—184no—
466C23—362no—
467C23—362no—
468C23D3×#6711yescharacteristic
469D4—22no—
470D4—24no—
471D4—94no—
472D4—182no—
473D4—184no—
474D4C2×#62414yescomplemented
475C2×C4—32no—
476C2×C4—34no—
477C2×C4—32no—
478C2×C4—62no—
479C2×C4—62no—
480C2×C4—62no—
481C2×C4—128no—
482C2×C4—122no—
483C2×C4—122no—
484C2×C4—368no—
485C2×C4#380412yes—
486C2×C4C2×#62412yes—
487C2×C4D3×#6711yescharacteristic
488C2×C4C22×D3211yescharacteristic
489C8—62no—
490C8—94no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—24no—
495C2×C3—44no—
496C2×C3—44no—
497C2×C3—84no—
498C2×C3#475614yescomplemented
499C2×C3C4×#21314yescomplemented
500C2×C3C2×#67⋊C411yescharacteristic
501C2×C3C2×D3×D811yescharacteristic
502C2×C3C2×#91611yescharacteristic
503C2×C3C2×C4×#6711yescharacteristic
504C2×C3C22×#21311yescharacteristic
505C2×C3C2×#95011yescharacteristic
506D3—124no—
507D3—124no—
508D3—244no—
509C22—24no—
510C22—42no—
511C22—42no—
512C22—48no—
513C22—184no—
514C22—362no—
515C22—362no—
516C22—368no—
517C22D3×#21312yes—
518C22#6393512yes—
519C22#6395212yes—
520C22C2×D3×#6711yescharacteristic
521C4—34no—
522C4—62no—
523C4—122no—
524C4—122no—
525C4#6395212yes—
526C4C2×#380411yescharacteristic
527C4C22×#62411yescharacteristic
528C3—21no—
529C3C2×#475611yescharacteristic, complemented
530C3C2×C4×#21311yescharacteristic, complemented
531C2—44no—
532C2—364no—
533C2#1059140014yesdirect product factor
534C2C2×D3×#21311yescharacteristic
535C2C2×#6393511yescharacteristic
536C2C2×#6395211yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
prime radicalC22×#3753C2
cosocleC2×C32×C4C24
hypercenterC22×D4D32
hypocenterC32C2×C4×D8
LCSG ▷ 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×C3×D4×Dic3C2semidirect
3. C2×#63894C2semidirect
4. C2×C3×#832C2semidirect
5. #10591400C2direct (N × H)
6. C2×#63576C2semidirect
7. C2×#63564C2semidirect
8. C2×Dic3×C3⋊C8C2semidirect
15. C2×#3753C4semidirect
20. C3×D4×Dic3C22semidirect
27. #63894C22semidirect
28. C3×#832C22semidirect
29. #63576C22semidirect
30. #63564C22semidirect
31. Dic3×C3⋊C8C22semidirect
33. C2×D4×Dic3D3semidirect
40. C2×#832D3semidirect
53. C2×C32×D4C2×C4semidirect
58. C2×C4⋊(C3⋊D3)C2×C4semidirect
68. #3753C2×C4semidirect
69. C2×C3⋊(C3⋊C8)C2×C4semidirect
101. D4×Dic3C2×D3semidirect
122. #832C2×D3semidirect
140. C32×D4C22×C4semidirect
147. C4⋊(C3⋊D3)C22×C4semidirect
154. C2×C3×Dic3D8semidirect
158. C3⋊(C3⋊C8)C22×C4semidirect
182. C2×C3×D4C4×D3semidirect
183. C2×C3×D4C4×D3semidirect
264. C3×Dic3C2×D8semidirect
320. C3×D4C2×C4×D3semidirect
321. C3×D4C2×C4×D3semidirect
349. C2×Dic3#213semidirect
369. C2×C32C4×D8semidirect
382. C2×D4#624semidirect
458. Dic3C2×#213semidirect
459. C32C2×C4×D8semidirect
474. D4C2×#624semidirect
498. C2×C3#4756semidirect
499. C2×C3C4×#213semidirect
529. C3C2×#4756semidirect
530. C3C2×C4×#213semidirect
533. C2#10591400direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37532
C2×C3×D4×Dic32
C2×#638942
C2×C3×#8322
#105914002
C2×#635762
C2×#635642
C2×Dic3×C3⋊C82
C2×C4×#2133
C2×#47563