Finite Group Databasebeta

← C2×#10591482 #11874190

Subgroups — C2×#10591482 #11874190

Order 1152.

1689 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3753C211yesmaximal, characteristic, complemented
2C2×C3×#940C211yesmaximal, characteristic, complemented
3C22×C3×#213C211yesmaximal, characteristic, complemented
4C2×#63911C211yesmaximal, characteristic, complemented
5C22×#3714C211yesmaximal, characteristic, complemented
6C22×#3713C211yesmaximal, characteristic, complemented
7#10591482C218yesmaximal, direct product factor
8C2×Dic3×C3⋊C8C211yesmaximal, characteristic, complemented
9C2×#5151—31nomaximal
10C2×#5073—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C3×#67—22no—
14C22×C3×D12C2211yescharacteristic
15C22×C3×D12C2211yescharacteristic
16C22×#626—22no—
17C2×#3753—24no—
18C2×#3753C2214yescomplemented
19C22×C3⋊(C3⋊C8)C2211yescharacteristic
20C3×#940—22no—
21C3×#940C2214yescomplemented
22C2×C3×#213—24no—
23C2×C3×#213C2214yescomplemented
24C2×C3×C4×Dic3C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26#63911—22no—
27#63911C2214yescomplemented
28C2×#3714—24no—
29C2×#3714C2214yescomplemented
30C2×#3713—24no—
31C2×#3713C2214yescomplemented
32Dic3×C3⋊C8C2214yescomplemented
33C22×C3×D8—31no—
34C2×C3×#127—31no—
35C2×#940—31no—
36C2×#940D311yescharacteristic, complemented
37C22×#213—31no—
38C22×#213—31no—
39C22×#213—31no—
40C22×#213—31no—
41C22×#213—31no—
42C22×#213—61no—
43C22×#213D311yescharacteristic, complemented
44C22×D24—31no—
45C2×#874—31no—
46#5151—38no—
47C2×C8×Dic3—31no—
48#5073—38no—
49C2×C4×C3⋊C8—31no—
50C24×C32—21no—
51C23×C3⋊D3—21no—
52C23×C3×D3—21no—
53C23×C3×D3—21no—
54C2×C32×D4—22no—
55C2×C32×D4—22no—
56C2×C32×D4—21no—
57C2×C32×D4C2312yes—
58C22×C32×C4C2311yescharacteristic
59C2×C4⋊(C3⋊D3)—22no—
60C2×C4⋊(C3⋊D3)—22no—
61C2×C4⋊(C3⋊D3)—21no—
62C2×C4⋊(C3⋊D3)C2312yes—
63C2×C3×#67—28no—
64C2×C3×#67—48no—
65C22×C3×Dic3D412yes—
66C2×C3×D12—22no—
67C2×C3×D12—22no—
68C2×C3×D12—22no—
69C2×C3×D12—22no—
70C2×C3×D12—21no—
71C2×C3×D12—21no—
72C2×C3×D12C2312yes—
73C2×C3×D12C2312yes—
74C2×#626—28no—
75C2×#626—48no—
76#3753—28no—
77C2×C3⋊(C3⋊C8)D414yescomplemented
78C2×C3⋊(C3⋊C8)C2312yes—
79C3×#213—28no—
80C3×C4×Dic3D412yes—
81C3×C4×Dic3C2312yes—
82C2×C3×C3⋊C8D414yescomplemented
83C2×C3×C3⋊C8C2312yes—
84#3714—28no—
85#3713—28no—
86C2×#493—91noSylow
87C22×C3×D4—21no—
88C22×C3×D4—31no—
89C22×C3×D4—31no—
90C22×C3×D4—62no—
91C22×C3×D4C2×D311yescharacteristic
92C22×C3×D4C2×D311yescharacteristic
93C22×#67—22no—
94C22×#67—62no—
95C22×D12—31no—
96C22×D12—31no—
97C22×D12—61no—
98C22×D12—62no—
99C22×D12C2×D311yescharacteristic
100C22×D12C2×D311yescharacteristic
101C2×C3×D8—34no—
102C2×C3×D8—64no—
103C22×C3×C8—31no—
104C3×#127—34no—
105C3×#127—62no—
106C2×C3×C42—31no—
107#940—22no—
108#940—34no—
109#940—62no—
110#940C2×D314yescomplemented
111C2×#213—24no—
112C2×#213—34no—
113C2×#213—34no—
114C2×#213—34no—
115C2×#213—34no—
116C2×#213—34no—
117C2×#213—64no—
118C2×#213—64no—
119C2×#213—64no—
120C2×#213—64no—
121C2×#213—64no—
122C2×#213—68no—
123C2×#213—64no—
124C2×#213C2×D314yescomplemented
125C2×C4×Dic3C2×D311yescharacteristic
126C22×C3⋊C8—31no—
127C22×C3⋊C8—31no—
128C22×C3⋊C8—61no—
129C22×C3⋊C8C2×D311yescharacteristic
130C2×D24—34no—
131C2×D24—64no—
132#874—34no—
133#874—62no—
134C8×Dic3—34no—
135C4×C3⋊C8—34no—
136C23×C32—22no—
137C23×C32—42no—
138C23×C32—44no—
139C23×C32C2×D411yescharacteristic
140C22×C3⋊D3—22no—
141C22×C3⋊D3—42no—
142C22×C3⋊D3—44no—
143C22×C3×D3—22no—
144C22×C3×D3—22no—
145C22×C3×D3—42no—
146C22×C3×D3—42no—
147C22×C3×D3—44no—
148C22×C3×D3—44no—
149C32×D4—22no—
150C32×D4—22no—
151C32×D4—42no—
152C2×C32×C4C2×D412yes—
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4C2×D412yes—
155C2×C32×C4C2411yescharacteristic
156C4⋊(C3⋊D3)—22no—
157C4⋊(C3⋊D3)—22no—
158C4⋊(C3⋊D3)—42no—
159C3×#67—416no—
160C2×C3×Dic3D818yescomplemented
161C2×C3×Dic3C2×D414yes—
162C3×D12—22no—
163C3×D12—22no—
164C3×D12—22no—
165C3×D12—22no—
166C3×D12—42no—
167C3×D12—42no—
168#626—416no—
169C3⋊(C3⋊C8)C2×D414yescomplemented
170C3×C3⋊C8C2×D414yescomplemented
171C22×D8—31no—
172C22×D8—91no—
173C22×D8—91no—
174C22×D8—91no—
175C2×#127—31no—
176C2×#127—91no—
177#493—98no—
178C2×C4×C8—91no—
179C24×C3—21no—
180C24×C3—21no—
181C24×C3—41no—
182C24×C3—61no—
183C24×C3—61no—
184C23×D3—21no—
185C23×D3—21no—
186C23×D3—61no—
187C23×D3—61no—
188C23×D3—121no—
189C2×C3×D4—24no—
190C2×C3×D4—22no—
191C2×C3×D4—22no—
192C2×C3×D4—22no—
193C2×C3×D4—21no—
194C2×C3×D4—22no—
195C2×C3×D4—21no—
196C2×C3×D4—22no—
197C2×C3×D4—32no—
198C2×C3×D4—32no—
199C2×C3×D4—42no—
200C2×C3×D4—41no—
201C2×C3×D4—68no—
202C2×C3×D4—62no—
203C2×C3×D4—62no—
204C2×C3×D4—62no—
205C2×C3×D4—61no—
206C2×C3×D4—62no—
207C2×C3×D4—61no—
208C2×C3×D4—128no—
209C2×C3×D4C22×D312yes—
210C2×C3×D4C22×D312yes—
211C22×C3×C4—21no—
212C22×C3×C4—32no—
213C22×C3×C4C22×D311yescharacteristic
214C22×C3×C4C22×D311yescharacteristic
215C2×#67—28no—
216C2×#67—48no—
217C2×#67—68no—
218C2×#67—128no—
219C22×Dic3#6712yes—
220C2×D12—22no—
221C2×D12—22no—
222C2×D12—22no—
223C2×D12—22no—
224C2×D12—21no—
225C2×D12—21no—
226C2×D12—32no—
227C2×D12—32no—
228C2×D12—62no—
229C2×D12—64no—
230C2×D12—62no—
231C2×D12—62no—
232C2×D12—62no—
233C2×D12—62no—
234C2×D12—68no—
235C2×D12—61no—
236C2×D12—61no—
237C2×D12—122no—
238C2×D12—121no—
239C2×D12—128no—
240C2×D12C22×D312yes—
241C2×D12C22×D312yes—
242C3×D8—68no—
243C2×C3×C8—34no—
244C2×C3×C8—32no—
245C3×C42—32no—
246C3×C42—32no—
247#213—28no—
248#213—68no—
249#213—68no—
250#213—68no—
251#213—68no—
252#213—616no—
253#213—68no—
254C4×Dic3#6712yes—
255C4×Dic3C22×D312yes—
256C2×C3⋊C8—34no—
257C2×C3⋊C8—34no—
258C2×C3⋊C8—32no—
259C2×C3⋊C8—32no—
260C2×C3⋊C8—64no—
261C2×C3⋊C8—62no—
262C2×C3⋊C8#6714yescomplemented
263C2×C3⋊C8C22×D312yes—
264D24—68no—
265C22×C32—42no—
266C22×C32—44no—
267C22×C32—84no—
268C22×C32#12712yes—
269C22×C32C2×D814yes—
270C22×C32C22×D411yescharacteristic
271C2×C3⋊D3—42no—
272C2×C3⋊D3—44no—
273C2×C3⋊D3—84no—
274C2×C3×D3—42no—
275C2×C3×D3—42no—
276C2×C3×D3—44no—
277C2×C3×D3—44no—
278C2×C3×D3—84no—
279C2×C3×D3—84no—
280C32×C4#12712yes—
281C32×C4C22×D411yescharacteristic
282C32×C4C22×D411yescharacteristic
283C3×Dic3C2×D818yescomplemented
284C22×D4—31no—
285C22×D4—31no—
286C22×D4—62no—
287C22×D4—91no—
288C22×D4—182no—
289C22×D4D3211yescharacteristic
290C2×D8—34no—
291C2×D8—64no—
292C2×D8—94no—
293C2×D8—94no—
294C2×D8—94no—
295C2×D8—184no—
296C2×D8—184no—
297C2×D8—184no—
298C22×C8—31no—
299C22×C8—91no—
300#127—34no—
301#127—62no—
302#127—94no—
303#127—182no—
304C2×C42—31no—
305C4×C8—94no—
306C23×C3—22no—
307C23×C3—22no—
308C23×C3—21no—
309C23×C3—42no—
310C23×C3—44no—
311C23×C3—44no—
312C23×C3—44no—
313C23×C3—42no—
314C23×C3—42no—
315C23×C3—62no—
316C23×C3—62no—
317C23×C3—84no—
318C23×C3—124no—
319C23×C3—124no—
320C23×C3—122no—
321C23×C3—122no—
322C23×C3D3×D411yescharacteristic
323C23×C3C2×#6711yescharacteristic
324C22×D3—22no—
325C22×D3—22no—
326C22×D3—44no—
327C22×D3—44no—
328C22×D3—42no—
329C22×D3—42no—
330C22×D3—62no—
331C22×D3—62no—
332C22×D3—122no—
333C22×D3—124no—
334C22×D3—124no—
335C22×D3—124no—
336C22×D3—122no—
337C22×D3—122no—
338C22×D3—244no—
339C3×D4—24no—
340C3×D4—22no—
341C3×D4—22no—
342C3×D4—22no—
343C3×D4—22no—
344C3×D4—42no—
345C3×D4—44no—
346C3×D4—42no—
347C3×D4—42no—
348C3×D4—62no—
349C3×D4—62no—
350C3×D4—62no—
351C3×D4—62no—
352C3×D4—1216no—
353C3×D4—122no—
354C3×D4—122no—
355C2×C3×C4—21no—
356C2×C3×C4—22no—
357C2×C3×C4—21no—
358C2×C3×C4—22no—
359C2×C3×C4—38no—
360C2×C3×C4—34no—
361C2×C3×C4D3×D411yescharacteristic
362C2×C3×C4D3×D412yes—
363C2×C3×C4D3×D412yes—
364C2×C3×C4D3×D412yes—
365C2×C3×C4C2×#6711yescharacteristic
366C2×C3×C4C2×#6712yes—
367C2×C3×C4C23×D311yescharacteristic
368C2×C3×C4C23×D311yescharacteristic
369#67—416no—
370#67—1216no—
371C2×Dic3#21318yescomplemented
372C2×Dic3C2×#6714yes—
373D12—22no—
374D12—22no—
375D12—22no—
376D12—22no—
377D12—42no—
378D12—42no—
379D12—64no—
380D12—62no—
381D12—62no—
382D12—62no—
383D12—62no—
384D12—122no—
385D12—124no—
386D12—1216no—
387D12—122no—
388D12—122no—
389C3×C8—34no—
390C3⋊C8—34no—
391C3⋊C8—34no—
392C3⋊C8—64no—
393C3⋊C8C2×#6714yescomplemented
394C2×C32—82no—
395C2×C32#49314yescomplemented
396C2×C32C2×#12711yescharacteristic
397C2×C32C22×D812yes—
398C3⋊D3—82no—
399C3×D3—82no—
400C3×D3—82no—
401C24—21no—
402C24—61no—
403C24—61no—
404C24—181no—
405C2×D4—22no—
406C2×D4—21no—
407C2×D4—22no—
408C2×D4—32no—
409C2×D4—32no—
410C2×D4—68no—
411C2×D4—62no—
412C2×D4—62no—
413C2×D4—61no—
414C2×D4—61no—
415C2×D4—62no—
416C2×D4—62no—
417C2×D4—92no—
418C2×D4—128no—
419C2×D4—188no—
420C2×D4—182no—
421C2×D4—181no—
422C2×D4—182no—
423C2×D4—368no—
424C2×D4C2×D3212yes—
425C22×C4—32no—
426C22×C4C2×D3211yescharacteristic
427D8—68no—
428D8—188no—
429D8—188no—
430D8—188no—
431C2×C8—32no—
432C2×C8—34no—
433C2×C8—92no—
434C2×C8—94no—
435C42—32no—
436C42—32no—
437C22×C3—21no—
438C22×C3—24no—
439C22×C3—22no—
440C22×C3—44no—
441C22×C3—44no—
442C22×C3—44no—
443C22×C3—42no—
444C22×C3—42no—
445C22×C3—84no—
446C22×C3—88no—
447C22×C3—84no—
448C22×C3—84no—
449C22×C3—124no—
450C22×C3—124no—
451C22×C3—122no—
452C22×C3—122no—
453C22×C3—244no—
454C22×C3—244no—
455C22×C3D3×D814yes—
456C22×C3C2×#21314yes—
457C22×C3#94012yes—
458C22×C3#94012yes—
459C22×C3C2×D3×D411yescharacteristic
460C22×C3C22×#6711yescharacteristic
461C2×D3—44no—
462C2×D3—44no—
463C2×D3—42no—
464C2×D3—42no—
465C2×D3—84no—
466C2×D3—84no—
467C2×D3—124no—
468C2×D3—124no—
469C2×D3—124no—
470C2×D3—122no—
471C2×D3—122no—
472C2×D3—244no—
473C2×D3—248no—
474C2×D3—244no—
475C2×D3—244no—
476C3×C4—21no—
477C3×C4—21no—
478C3×C4—22no—
479C3×C4—38no—
480C3×C4#94012yes—
481C3×C4#94012yes—
482C3×C4C2×D3×D411yescharacteristic
483C3×C4C2×D3×D411yescharacteristic
484C3×C4C2×D3×D411yescharacteristic
485C3×C4C22×#6711yescharacteristic
486Dic3C2×#21318yescomplemented
487C32C2×#49311yescharacteristic, complemented, Sylow
488C23—22no—
489C23—44no—
490C23—42no—
491C23—62no—
492C23—62no—
493C23—124no—
494C23—124no—
495C23—122no—
496C23—122no—
497C23—182no—
498C23—364no—
499C23—362no—
500C23D3×#6711yescharacteristic
501D4—22no—
502D4—22no—
503D4—42no—
504D4—62no—
505D4—62no—
506D4—62no—
507D4—62no—
508D4—1216no—
509D4—122no—
510D4—122no—
511D4—182no—
512D4—182no—
513D4—3616no—
514D4—362no—
515C2×C4—34no—
516C2×C4—38no—
517C2×C4D3×#6712yes—
518C2×C4D3×#6711yescharacteristic
519C2×C4#381112yes—
520C2×C4C22×D3211yescharacteristic
521C8—34no—
522C8—94no—
523C2×C3—22no—
524C2×C3—21no—
525C2×C3—24no—
526C2×C3—84no—
527C2×C3—82no—
528C2×C3—82no—
529C2×C3—242no—
530C2×C3—242no—
531C2×C3#507314yescomplemented
532C2×C3#515114yescomplemented
533C2×C3C2×D3×D812yes—
534C2×C3C22×#21312yes—
535C2×C3C2×#94011yescharacteristic
536C2×C3C2×#94011yescharacteristic
537D3—82no—
538D3—82no—
539D3—244no—
540D3—242no—
541D3—242no—
542C22—44no—
543C22—42no—
544C22—84no—
545C22—124no—
546C22—124no—
547C22—122no—
548C22—122no—
549C22—244no—
550C22—244no—
551C22—364no—
552C22—362no—
553C22—724no—
554C22D3×#21314yes—
555C22#6397912yes—
556C22C2×D3×#6711yescharacteristic
557C4—38no—
558C4#6397912yes—
559C4C2×D3×#6711yescharacteristic
560C4C2×#381111yescharacteristic
561C3—21no—
562C3C2×#507311yescharacteristic, complemented
563C3C2×#515111yescharacteristic, complemented
564C2—82no—
565C2—242no—
566C2—242no—
567C2—722no—
568C2#1059148214yesdirect product factor
569C2C2×D3×#21312yes—
570C2C2×#6397911yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
hypercenterC22×D4D32
hypocenterC32C2×#493
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×#3753C2semidirect
2. C2×C3×#940C2semidirect
3. C22×C3×#213C2semidirect
4. C2×#63911C2semidirect
5. C22×#3714C2semidirect
6. C22×#3713C2semidirect
7. #10591482C2direct (N × H)
8. C2×Dic3×C3⋊C8C2semidirect
18. C2×#3753C22semidirect
21. C3×#940C22semidirect
23. C2×C3×#213C22semidirect
27. #63911C22semidirect
29. C2×#3714C22semidirect
31. C2×#3713C22semidirect
32. Dic3×C3⋊C8C22semidirect
36. C2×#940D3semidirect
43. C22×#213D3semidirect
77. C2×C3⋊(C3⋊C8)D4semidirect
82. C2×C3×C3⋊C8D4semidirect
110. #940C2×D3semidirect
124. C2×#213C2×D3semidirect
160. C2×C3×Dic3D8semidirect
169. C3⋊(C3⋊C8)C2×D4semidirect
170. C3×C3⋊C8C2×D4semidirect
262. C2×C3⋊C8#67semidirect
283. C3×Dic3C2×D8semidirect
371. C2×Dic3#213semidirect
393. C3⋊C8C2×#67semidirect
395. C2×C32#493semidirect
486. Dic3C2×#213semidirect
487. C32C2×#493semidirect
531. C2×C3#5073semidirect
532. C2×C3#5151semidirect
562. C3C2×#5073semidirect
563. C3C2×#5151semidirect
568. C2#10591482direct (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×#9402
C22×C3×#2132
C2×#639112
C22×#37142
C22×#37132
#105914822
C2×Dic3×C3⋊C82
C2×#51513
C2×#50733