Finite Group Databasebeta

← C2×#10591439 #11865598

Subgroups — C2×#10591439 #11865598

Order 1152.

1317 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3754C211yesmaximal, characteristic, complemented
2C2×C3×#940C211yesmaximal, characteristic
3C2×#63844C211yesmaximal, characteristic, complemented
4C22×#3716C211yesmaximal, characteristic, complemented
5C2×C3×#832C211yesmaximal, characteristic, complemented
6#10591439C218yesmaximal, direct product factor
7C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8C2×#63562C211yesmaximal, characteristic, complemented
9C2×#5075—31nomaximal
10C2×#4762—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C22×C3×#67—21no—
14C22×C3×#67—21no—
15C22×C3×D12C2211yescharacteristic
16C2×#3754—24no—
17C2×#3754C2214yescomplemented
18C22×C3⋊(C3⋊C8)C2211yescharacteristic
19C3×#940—22no—
20C3×#940C2214yes—
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4×Dic3C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C2×#3724—21no—
25C2×Dic32—21no—
26#63844—22no—
27#63844C2214yescomplemented
28C2×#3716—24no—
29C2×#3716C2214yescomplemented
30C3×#832C2214yescomplemented
31Dic3⋊(C3⋊C8)C2214yescomplemented
32#63562C2214yescomplemented
33C2×C3×#127—31no—
34C2×#940D311yescharacteristic
35C22×#214—31no—
36C22×#214—31no—
37C22×#214—31no—
38C22×#214—61no—
39C22×#204—31no—
40C2×#887—31no—
41C2×C4×Dic6—31no—
42C2×C3×#102—31no—
43C2×#832—31no—
44C2×#832D311yescharacteristic, complemented
45C2×Dic3⋊C8—31no—
46#5075—38no—
47C2×#809—31no—
48C2×C4⋊(C3⋊C8)—31no—
49#4762—38no—
50C24×C32—21no—
51C23×C3×D3—21no—
52C2×C32×D4—22no—
53C2×C32×D4—21no—
54C2×C32×D4—22no—
55C2×C32×D4C2312yes—
56C22×C32×C4C2311yescharacteristic
57C22×C3⋊Dic3—21no—
58C2×#634—21no—
59C2×#634—22no—
60C2×#634D414yescomplemented
61C2×#634C2312yes—
62C2×C3×#67—24no—
63C2×C3×#67—24no—
64C2×C3×#67—44no—
65C2×C3×#67—44no—
66C22×C3×Dic3—21no—
67C22×C3×Dic3D411yescharacteristic
68C22×C3×Dic3D411yescharacteristic
69C2×C3×D12—22no—
70C2×C3×D12—22no—
71C2×C3×D12—21no—
72C2×C3×D12C2312yes—
73#3754—28no—
74C2×C3⋊(C3⋊C8)—22no—
75C2×C3⋊(C3⋊C8)C2312yes—
76C3×C4⋊Dic3—21no—
77C3×C4⋊Dic3C2312yes—
78C3×C4×Dic3D412yes—
79C3×C4×Dic3C2312yes—
80C2×C3×C3⋊C8—22no—
81C2×C3×C3⋊C8C2312yes—
82#3724—24no—
83Dic32—24no—
84#3716—28no—
85C2×#460—91noSylow
86C22×C3×D4—21no—
87C22×C3×D4—31no—
88C22×C3×D4—61no—
89C22×C3×D4—61no—
90C22×C3×D4C2×D311yescharacteristic
91C22×C3×D4C2×D311yescharacteristic
92C22×#67—21no—
93C22×#67—21no—
94C22×D12C2×D311yescharacteristic
95C22×Dic6—31no—
96C22×Dic6—31no—
97C22×Dic6—61no—
98C22×C3×C8—31no—
99C3×#127—34no—
100C3×#127—62no—
101C2×C3×C4⋊C4—31no—
102C2×C3×C42—31no—
103#940—22no—
104#940C2×D314yes—
105C2×#214—34no—
106C2×#214—34no—
107C2×#214—34no—
108C2×#214—64no—
109C2×#214—64no—
110C2×#214—64no—
111C2×#214—64no—
112C2×#214—68no—
113C2×C4⋊Dic3C2×D311yescharacteristic
114C2×Dic3⋊C4—61no—
115C2×Dic3⋊C4—61no—
116C2×C4×Dic3—61no—
117C2×C4×Dic3—61no—
118C2×C4×Dic3C2×D311yescharacteristic
119C22×C3⋊C8—31no—
120C22×C3⋊C8—31no—
121C22×C3⋊C8—61no—
122C22×C3⋊C8C2×D311yescharacteristic
123C2×#204—34no—
124C2×#204—64no—
125#887—34no—
126#887—62no—
127C4×Dic6—34no—
128C4×Dic6—62no—
129C3×#102—34no—
130#832—34no—
131#832C2×D314yescomplemented
132Dic3⋊C8—34no—
133#809—34no—
134C4⋊(C3⋊C8)—34no—
135C23×C32—22no—
136C23×C32—42no—
137C23×C32—42no—
138C23×C32—42no—
139C23×C32C2×D411yescharacteristic
140C22×C3×D3—22no—
141C22×C3×D3—42no—
142C22×C3×D3—42no—
143C22×C3×D3—42no—
144C32×D4—22no—
145C32×D4—22no—
146C32×D4—42no—
147C2×C32×C4C2×D412yes—
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4#4112yes—
150C2×C32×C4C2411yescharacteristic
151C2×C3⋊Dic3—24no—
152C2×C3⋊Dic3—22no—
153#634—24no—
154#634—22no—
155#634C2×D414yescomplemented
156C3×#67—48no—
157C3×#67—48no—
158C2×C3×Dic3—22no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—42no—
161C2×C3×Dic3SD1614yescomplemented
162C2×C3×Dic3C2×D412yes—
163C2×C3×Dic3C2×D412yes—
164C3×D12—22no—
165C3×D12—22no—
166C3×D12—42no—
167C3⋊(C3⋊C8)—22no—
168C3×C3⋊C8—22no—
169C22×SD16—91no—
170C22×SD16—91no—
171C2×#127—31no—
172C2×C4×Q8—91no—
173#460—98no—
174C2×C4⋊C8—91no—
175C2×#102—31no—
176C2×#102—91no—
177C24×C3—21no—
178C24×C3—21no—
179C24×C3—41no—
180C24×C3—61no—
181C23×D3—21no—
182C2×C3×D4—24no—
183C2×C3×D4—22no—
184C2×C3×D4—22no—
185C2×C3×D4—22no—
186C2×C3×D4—21no—
187C2×C3×D4—22no—
188C2×C3×D4—21no—
189C2×C3×D4—22no—
190C2×C3×D4—32no—
191C2×C3×D4—42no—
192C2×C3×D4—41no—
193C2×C3×D4—64no—
194C2×C3×D4—64no—
195C2×C3×D4—62no—
196C2×C3×D4—62no—
197C2×C3×D4—61no—
198C2×C3×D4—124no—
199C2×C3×D4—124no—
200C2×C3×D4C22×D312yes—
201C2×C3×D4C22×D312yes—
202C22×C3×C4—21no—
203C22×C3×C4—31no—
204C22×C3×C4—31no—
205C22×C3×C4—61no—
206C22×C3×C4C22×D311yescharacteristic
207C22×C3×C4C22×D311yescharacteristic
208C2×#67—24no—
209C2×#67—24no—
210C2×#67—44no—
211C2×#67—44no—
212C22×Dic3—21no—
213C22×Dic3—61no—
214C22×Dic3—61no—
215C22×Dic3—121no—
216C22×Dic3#6711yescharacteristic
217C22×Dic3#6711yescharacteristic
218C2×D12—22no—
219C2×D12—22no—
220C2×D12—21no—
221C2×D12C22×D312yes—
222C2×Dic6—34no—
223C2×Dic6—34no—
224C2×Dic6—32no—
225C2×Dic6—32no—
226C2×Dic6—64no—
227C2×Dic6—62no—
228C2×Dic6—62no—
229C2×Dic6—61no—
230C2×Dic6—62no—
231C2×Dic6—61no—
232C2×Dic6—122no—
233C2×Dic6—121no—
234C2×C3×C8—32no—
235C2×C3×C8—62no—
236C3×C4⋊C4—32no—
237C3×C4⋊C4—61no—
238C3×C42—32no—
239C3×C42—32no—
240#214—68no—
241#214—68no—
242#214—68no—
243#214—616no—
244C4⋊Dic3—21no—
245C4⋊Dic3C22×D312yes—
246Dic3⋊C4—64no—
247Dic3⋊C4—64no—
248C4×Dic3—64no—
249C4×Dic3—64no—
250C4×Dic3#6712yes—
251C4×Dic3C22×D312yes—
252C2×C3⋊C8—22no—
253C2×C3⋊C8—32no—
254C2×C3⋊C8—32no—
255C2×C3⋊C8—62no—
256C2×C3⋊C8—64no—
257C2×C3⋊C8—62no—
258C2×C3⋊C8—62no—
259C2×C3⋊C8C22×D312yes—
260#204—68no—
261C22×C32—42no—
262C22×C32—42no—
263C22×C32—42no—
264C22×C32—84no—
265C22×C32#12112yes—
266C22×C32C2×SD1612yes—
267C22×C32AGL(1,ℤ/8)12yes—
268C22×C32C22×D411yescharacteristic
269C2×C3×D3—42no—
270C2×C3×D3—42no—
271C2×C3×D3—42no—
272C2×C3×D3—84no—
273C32×C4#12112yes—
274C32×C4C22×D411yescharacteristic
275C32×C4C2×#4111yescharacteristic
276C3⋊Dic3—24no—
277C3×Dic3—22no—
278C3×Dic3—42no—
279C3×Dic3C2×SD1614yescomplemented
280C22×Q8—91no—
281C22×D4—31no—
282C22×D4—61no—
283C22×D4—61no—
284C22×D4D3211yescharacteristic
285C2×SD16—94no—
286C2×SD16—94no—
287C2×SD16—184no—
288C2×SD16—184no—
289C22×C8—31no—
290C22×C8—91no—
291#127—34no—
292#127—62no—
293C4×Q8—94no—
294C4×Q8—182no—
295C2×C4⋊C4—31no—
296C2×C4⋊C4—181no—
297C2×C42—31no—
298C2×C42—181no—
299C4⋊C8—94no—
300#102—34no—
301#102—94no—
302C23×C3—22no—
303C23×C3—22no—
304C23×C3—21no—
305C23×C3—42no—
306C23×C3—44no—
307C23×C3—42no—
308C23×C3—42no—
309C23×C3—42no—
310C23×C3—42no—
311C23×C3—42no—
312C23×C3—42no—
313C23×C3—62no—
314C23×C3—82no—
315C23×C3—82no—
316C23×C3—122no—
317C23×C3—122no—
318C23×C3—122no—
319C23×C3D3×D411yescharacteristic
320C23×C3C2×#6711yescharacteristic
321C22×D3—22no—
322C22×D3—42no—
323C22×D3—42no—
324C22×D3—42no—
325C3×D4—24no—
326C3×D4—22no—
327C3×D4—22no—
328C3×D4—22no—
329C3×D4—22no—
330C3×D4—42no—
331C3×D4—44no—
332C3×D4—42no—
333C3×D4—42no—
334C3×D4—62no—
335C3×D4—62no—
336C3×D4—128no—
337C3×D4—128no—
338C3×D4—122no—
339C2×C3×C4—21no—
340C2×C3×C4—22no—
341C2×C3×C4—21no—
342C2×C3×C4—22no—
343C2×C3×C4—34no—
344C2×C3×C4—32no—
345C2×C3×C4—32no—
346C2×C3×C4—62no—
347C2×C3×C4—62no—
348C2×C3×C4—122no—
349C2×C3×C4#23512yes—
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4D3×D412yes—
352C2×C3×C4D3×D412yes—
353C2×C3×C4#23712yes—
354C2×C3×C4C2×#6711yescharacteristic
355C2×C3×C4C23×D311yescharacteristic
356C2×C3×C4C23×D311yescharacteristic
357#67—48no—
358#67—48no—
359C2×Dic3—22no—
360C2×Dic3—22no—
361C2×Dic3—42no—
362C2×Dic3—64no—
363C2×Dic3—64no—
364C2×Dic3—62no—
365C2×Dic3—62no—
366C2×Dic3—122no—
367C2×Dic3—124no—
368C2×Dic3#21414yescomplemented
369C2×Dic3C2×#6712yes—
370C2×Dic3C2×#6712yes—
371D12—22no—
372D12—22no—
373D12—42no—
374Dic6—34no—
375Dic6—34no—
376Dic6—64no—
377Dic6—64no—
378Dic6—64no—
379Dic6—62no—
380Dic6—62no—
381Dic6—122no—
382Dic6—124no—
383C3×C8—62no—
384C3⋊C8—22no—
385C3⋊C8—64no—
386C3⋊C8—62no—
387C3⋊C8—62no—
388C2×C32—82no—
389C2×C32#46014yescomplemented
390C2×C32C2×#12111yescharacteristic
391C2×C32C22×SD1611yescharacteristic
392C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
393C3×D3—82no—
394C24—21no—
395C24—61no—
396C2×Q8—92no—
397C2×Q8—94no—
398C2×Q8—182no—
399C2×Q8—181no—
400C2×D4—22no—
401C2×D4—21no—
402C2×D4—22no—
403C2×D4—32no—
404C2×D4—64no—
405C2×D4—64no—
406C2×D4—62no—
407C2×D4—61no—
408C2×D4—62no—
409C2×D4—124no—
410C2×D4—124no—
411C2×D4C2×D3212yes—
412C22×C4—31no—
413C22×C4—31no—
414C22×C4—61no—
415C22×C4—181no—
416C22×C4C2×D3211yescharacteristic
417SD16—188no—
418SD16—188no—
419C2×C8—32no—
420C2×C8—62no—
421C2×C8—92no—
422C2×C8—182no—
423C4⋊C4—32no—
424C4⋊C4—61no—
425C4⋊C4—184no—
426C42—32no—
427C42—32no—
428C42—184no—
429C22×C3—21no—
430C22×C3—22no—
431C22×C3—22no—
432C22×C3—22no—
433C22×C3—44no—
434C22×C3—42no—
435C22×C3—42no—
436C22×C3—42no—
437C22×C3—42no—
438C22×C3—42no—
439C22×C3—42no—
440C22×C3—82no—
441C22×C3—82no—
442C22×C3—88no—
443C22×C3—84no—
444C22×C3—84no—
445C22×C3—122no—
446C22×C3—122no—
447C22×C3—122no—
448C22×C3—244no—
449C22×C3#88412yes—
450C22×C3#91112yes—
451C22×C3D3×SD1612yes—
452C22×C3#93212yes—
453C22×C3C2×#21412yes—
454C22×C3#93812yes—
455C22×C3C2×D3×D411yescharacteristic
456C22×C3C22×#6711yescharacteristic
457C2×D3—42no—
458C2×D3—42no—
459C2×D3—42no—
460C2×D3—84no—
461C3×C4—21no—
462C3×C4—21no—
463C3×C4—22no—
464C3×C4—34no—
465C3×C4—62no—
466C3×C4—122no—
467C3×C4#88412yes—
468C3×C4#93812yes—
469C3×C4C2×#23511yescharacteristic
470C3×C4C2×D3×D411yescharacteristic
471C3×C4C2×D3×D411yescharacteristic
472C3×C4C2×#23711yescharacteristic
473Dic3—22no—
474Dic3—42no—
475Dic3—64no—
476Dic3—64no—
477Dic3—124no—
478Dic3C2×#21414yescomplemented
479C32C2×#46011yescharacteristic, complemented, Sylow
480C23—22no—
481C23—42no—
482C23—42no—
483C23—42no—
484C23—62no—
485C23—122no—
486C23—122no—
487C23—122no—
488C23D3×#6711yescharacteristic
489Q8—94no—
490Q8—182no—
491Q8—184no—
492D4—22no—
493D4—22no—
494D4—42no—
495D4—62no—
496D4—62no—
497D4—128no—
498D4—128no—
499D4—122no—
500C2×C4—32no—
501C2×C4—34no—
502C2×C4—32no—
503C2×C4—62no—
504C2×C4—62no—
505C2×C4—122no—
506C2×C4—182no—
507C2×C4—184no—
508C2×C4#380412yes—
509C2×C4D3×#6711yescharacteristic
510C2×C4#381112yes—
511C2×C4C22×D3211yescharacteristic
512C8—62no—
513C8—182no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—24no—
518C2×C3—84no—
519C2×C3—82no—
520C2×C3—82no—
521C2×C3—242no—
522C2×C3#476214yescomplemented
523C2×C3#507514yescomplemented
524C2×C3C2×#88411yescharacteristic
525C2×C3C2×#91111yescharacteristic
526C2×C3C2×D3×SD1611yescharacteristic
527C2×C3C2×#93211yescharacteristic
528C2×C3C22×#21411yescharacteristic
529C2×C3C2×#93811yescharacteristic
530D3—82no—
531C22—42no—
532C22—42no—
533C22—42no—
534C22—84no—
535C22—122no—
536C22—122no—
537C22—122no—
538C22—244no—
539C22D3×#21412yes—
540C22#6393212yes—
541C22#6395812yes—
542C22C2×D3×#6711yescharacteristic
543C4—34no—
544C4—62no—
545C4—122no—
546C4—184no—
547C4#6395812yes—
548C4C2×#380411yescharacteristic
549C4C2×#381111yescharacteristic
550C3—21no—
551C3C2×#476211yescharacteristic, complemented
552C3C2×#507511yescharacteristic, complemented
553C2—82no—
554C2—242no—
555C2#1059143914yesdirect product factor
556C2C2×D3×#21411yescharacteristic
557C2C2×#6393211yescharacteristic
558C2C2×#6395811yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
prime radicalC2×C3×#940C2
hypercenterC22×D4D32
hypocenterC32C2×#460
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
1. C22×#3754C2semidirect
3. C2×#63844C2semidirect
4. C22×#3716C2semidirect
5. C2×C3×#832C2semidirect
6. #10591439C2direct (N × H)
7. C2×Dic3⋊(C3⋊C8)C2semidirect
8. C2×#63562C2semidirect
17. C2×#3754C22semidirect
27. #63844C22semidirect
29. C2×#3716C22semidirect
30. C3×#832C22semidirect
31. Dic3⋊(C3⋊C8)C22semidirect
32. #63562C22semidirect
44. C2×#832D3semidirect
60. C2×#634D4semidirect
131. #832C2×D3semidirect
155. #634C2×D4semidirect
161. C2×C3×Dic3SD16semidirect
279. C3×Dic3C2×SD16semidirect
368. C2×Dic3#214semidirect
389. C2×C32#460semidirect
478. Dic3C2×#214semidirect
479. C32C2×#460semidirect
522. C2×C3#4762semidirect
523. C2×C3#5075semidirect
551. C3C2×#4762semidirect
552. C3C2×#5075semidirect
555. C2#10591439direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37542
C2×C3×#9402
C2×#638442
C22×#37162
C2×C3×#8322
#105914392
C2×Dic3⋊(C3⋊C8)2
C2×#635622
C2×#50753
C2×#47623