Finite Group Databasebeta

← C2×#10591498 #11866750

Subgroups — C2×#10591498 #11866750

Order 1152.

1333 conjugacy classes of subgroups.

The subgroup lattice has 577 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#938C211yesmaximal, characteristic, complemented
2C22×C3×#213C211yesmaximal, characteristic, complemented
3C2×#63908C211yesmaximal, characteristic, complemented
4C22×D3×C3⋊C8C211yesmaximal, characteristic, complemented
5C2×#63659C211yesmaximal, characteristic, complemented
6#10591498C218yesmaximal, direct product factor
7C2×#63575C211yesmaximal, characteristic, complemented
8C2×#63562C211yesmaximal, characteristic, complemented
9C2×#5157—31nomaximal
10C2×#5038—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C22×C3×#67—21no—
13C22×C3×D12C2211yescharacteristic
14C22×C3×C4×D3C2211yescharacteristic
15C22×#625—21no—
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C2×C3×#217—21no—
19C3×#938—22no—
20C3×#938C2214yescomplemented
21C2×C3×#213—24no—
22C2×C3×#213C2214yescomplemented
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C2×(C2×D3)⋊Dic3—21no—
26#63908—22no—
27#63908C2214yescomplemented
28C2×D3×C3⋊C8—24no—
29C2×D3×C3⋊C8C2214yescomplemented
30#63659C2214yescomplemented
31#63575C2214yescomplemented
32#63562C2214yescomplemented
33C22×C3×D8—31no—
34C2×C3×#121—31no—
35C2×#938—31no—
36C2×#938D311yescharacteristic, complemented
37C22×#213D311yescharacteristic, complemented
38C2×#930—31no—
39C23×C3⋊C8—31no—
40C22×D3×C8—31no—
41C2×#832—31no—
42C2×#832—31no—
43C2×#832—31no—
44C2×#832—61no—
45#5157—38no—
46C2×#818—31no—
47#5038—38no—
48C2×#809—31no—
49C2×#807—31no—
50C24×C32—21no—
51C23×C3×D3—21no—
52C23×C3×D3D411yescharacteristic
53C2×C32×D4—22no—
54C2×C32×D4—21no—
55C2×C32×D4—22no—
56C2×C32×D4C2312yes—
57C22×C32×C4C2311yescharacteristic
58C22×C3⋊Dic3—21no—
59C2×C3×#67—24no—
60C2×C3×#67—44no—
61C22×C3×Dic3—21no—
62C22×C3×Dic3D411yescharacteristic
63C2×C3×D12—22no—
64C2×C3×D12—22no—
65C2×C3×D12—21no—
66C2×C3×D12C2312yes—
67C2×C3×C4×D3—22no—
68C2×C3×C4×D3—22no—
69C2×C3×C4×D3D412yes—
70C2×C3×C4×D3C2312yes—
71C2×#625—24no—
72C2×#625—44no—
73C4⋊(C3⋊Dic3)—21no—
74C4⋊(C3⋊Dic3)C2312yes—
75C2×C3⋊(C3⋊C8)—22no—
76C2×C3⋊(C3⋊C8)C2312yes—
77C3×#217—24no—
78C3×#213—28no—
79C3×C4⋊Dic3—21no—
80C3×C4⋊Dic3C2312yes—
81C2×C3×C3⋊C8D414yescomplemented
82C2×C3×C3⋊C8C2312yes—
83(C2×D3)⋊Dic3—24no—
84D3×C3⋊C8—28no—
85C2×#466—91noSylow
86C22×C3×D4—21no—
87C22×C3×D4—31no—
88C22×C3×D4—61no—
89C22×C3×D4C2×D311yescharacteristic
90C22×C3×D4C2×D311yescharacteristic
91C23×C3×C4—31no—
92C22×#67—21no—
93C22×#67—61no—
94C22×#67—61no—
95C22×D12C2×D311yescharacteristic
96C22×C4×D3C2×D311yescharacteristic
97C2×C3×D8—34no—
98C2×C3×D8—64no—
99C22×C3×C8—31no—
100C3×#121—34no—
101C3×#121—62no—
102C2×C3×C4⋊C4—31no—
103C2×C3×C22⋊C4—61no—
104C2×#217—21no—
105C2×#217—61no—
106#938—22no—
107#938—34no—
108#938—62no—
109#938C2×D314yescomplemented
110C2×#213—24no—
111C2×#213C2×D314yescomplemented
112#930—34no—
113#930—62no—
114C2×(C2×D3)⋊C4—61no—
115C2×C4⋊Dic3—31no—
116C2×C4⋊Dic3—31no—
117C2×C4⋊Dic3—61no—
118C2×C4⋊Dic3C2×D311yescharacteristic
119C22×C3⋊C8—31no—
120C22×C3⋊C8—31no—
121C22×C3⋊C8—34no—
122C22×C3⋊C8—61no—
123C22×C3⋊C8—64no—
124C22×C3⋊C8C2×D311yescharacteristic
125C2×D3×C8—34no—
126C2×D3×C8—64no—
127#832—34no—
128#832—34no—
129#832—34no—
130#832—64no—
131#818—34no—
132#809—34no—
133#807—34no—
134C23×C32—22no—
135C23×C32—42no—
136C23×C32—42no—
137C23×C32—42no—
138C23×C32C2×D411yescharacteristic
139C22×C3×D3—22no—
140C22×C3×D3—22no—
141C22×C3×D3—22no—
142C22×C3×D3—42no—
143C22×C3×D3—42no—
144C22×C3×D3—42no—
145C22×C3×D3D814yescomplemented
146C22×C3×D3C2×D412yes—
147C32×D4—22no—
148C32×D4—22no—
149C32×D4—42no—
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2×D412yes—
152C2×C32×C4#4112yes—
153C2×C32×C4C2411yescharacteristic
154C2×C3⋊Dic3—22no—
155C2×C3⋊Dic3—42no—
156C3×#67—48no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—22no—
159C2×C3×Dic3—42no—
160C2×C3×Dic3C2×D412yes—
161C3×D12—22no—
162C3×D12—22no—
163C3×D12—42no—
164C3×C4×D3—24no—
165C3×C4×D3—22no—
166C3×C4×D3—22no—
167#625—48no—
168C3⋊(C3⋊C8)—22no—
169C3×C3⋊C8C2×D414yescomplemented
170C22×D8—31no—
171C23×C8—91no—
172C2×#121—31no—
173C2×#121—91no—
174#466—98no—
175C2×#107—91no—
176C2×#102—91no—
177C2×#102—91no—
178C24×C3—21no—
179C24×C3—21no—
180C24×C3—31no—
181C24×C3—41no—
182C24×C3—61no—
183C23×D3—21no—
184C23×D3#6711yescharacteristic
185C2×C3×D4—24no—
186C2×C3×D4—22no—
187C2×C3×D4—21no—
188C2×C3×D4—22no—
189C2×C3×D4—22no—
190C2×C3×D4—22no—
191C2×C3×D4—21no—
192C2×C3×D4—22no—
193C2×C3×D4—32no—
194C2×C3×D4—42no—
195C2×C3×D4—41no—
196C2×C3×D4—64no—
197C2×C3×D4—62no—
198C2×C3×D4—62no—
199C2×C3×D4—61no—
200C2×C3×D4—124no—
201C2×C3×D4C22×D312yes—
202C2×C3×D4C22×D312yes—
203C22×C3×C4—21no—
204C22×C3×C4—31no—
205C22×C3×C4—32no—
206C22×C3×C4—32no—
207C22×C3×C4—62no—
208C22×C3×C4—62no—
209C22×C3×C4—61no—
210C22×C3×C4C22×D311yescharacteristic
211C22×C3×C4C22×D311yescharacteristic
212C2×#67—24no—
213C2×#67—44no—
214C2×#67—64no—
215C2×#67—64no—
216C2×#67—124no—
217C2×#67—124no—
218C22×Dic3—21no—
219C22×Dic3—61no—
220C22×Dic3—61no—
221C22×Dic3—121no—
222C22×Dic3#6711yescharacteristic
223C2×D12—22no—
224C2×D12—22no—
225C2×D12—21no—
226C2×D12C22×D312yes—
227C2×C4×D3—22no—
228C2×C4×D3—22no—
229C2×C4×D3#6712yes—
230C2×C4×D3C22×D312yes—
231C3×D8—68no—
232C2×C3×C8—34no—
233C2×C3×C8—32no—
234C3×C4⋊C4—32no—
235C3×C4⋊C4—61no—
236C3×C22⋊C4—64no—
237#217—24no—
238#217—64no—
239#213—28no—
240(C2×D3)⋊C4—64no—
241C4⋊Dic3—21no—
242C4⋊Dic3—32no—
243C4⋊Dic3—32no—
244C4⋊Dic3—62no—
245C4⋊Dic3—61no—
246C4⋊Dic3—61no—
247C4⋊Dic3—121no—
248C4⋊Dic3C22×D312yes—
249C2×C3⋊C8—32no—
250C2×C3⋊C8—32no—
251C2×C3⋊C8—62no—
252C2×C3⋊C8—62no—
253C2×C3⋊C8—62no—
254C2×C3⋊C8—68no—
255C2×C3⋊C8—122no—
256C2×C3⋊C8#6714yescomplemented
257C2×C3⋊C8C22×D312yes—
258D3×C8—68no—
259C22×C32—42no—
260C22×C32—42no—
261C22×C32—42no—
262C22×C32—84no—
263C22×C32#12112yes—
264C22×C32C2×D812yes—
265C22×C32#13512yes—
266C22×C32C22×D411yescharacteristic
267C2×C3×D3—22no—
268C2×C3×D3—22no—
269C2×C3×D3—28no—
270C2×C3×D3—42no—
271C2×C3×D3—42no—
272C2×C3×D3—42no—
273C2×C3×D3—84no—
274C2×C3×D3C2×D814yescomplemented
275C32×C4#12112yes—
276C32×C4C22×D411yescharacteristic
277C32×C4C2×#4111yescharacteristic
278C3⋊Dic3—42no—
279C3×Dic3—22no—
280C3×Dic3—42no—
281C22×D4—31no—
282C22×D4—61no—
283C22×D4—181no—
284C22×D4D3211yescharacteristic
285C23×C4—31no—
286C2×D8—34no—
287C2×D8—64no—
288C22×C8—31no—
289C22×C8—94no—
290C22×C8—91no—
291C22×C8—184no—
292#121—34no—
293#121—62no—
294#121—94no—
295#121—182no—
296C2×C4⋊C4—31no—
297C2×C4⋊C4—91no—
298C2×C22⋊C4—61no—
299C2×C22⋊C4—181no—
300#107—94no—
301#102—94no—
302#102—94no—
303C23×C3—22no—
304C23×C3—22no—
305C23×C3—21no—
306C23×C3—34no—
307C23×C3—32no—
308C23×C3—42no—
309C23×C3—44no—
310C23×C3—42no—
311C23×C3—42no—
312C23×C3—42no—
313C23×C3—42no—
314C23×C3—42no—
315C23×C3—42no—
316C23×C3—62no—
317C23×C3—62no—
318C23×C3—62no—
319C23×C3—82no—
320C23×C3—82no—
321C23×C3—122no—
322C23×C3—122no—
323C23×C3—122no—
324C23×C3D3×D411yescharacteristic
325C23×C3C2×#6711yescharacteristic
326C22×D3—22no—
327C22×D3—22no—
328C22×D3—22no—
329C22×D3—42no—
330C22×D3—42no—
331C22×D3—42no—
332C22×D3#21314yescomplemented
333C22×D3C2×#6712yes—
334C3×D4—24no—
335C3×D4—22no—
336C3×D4—22no—
337C3×D4—22no—
338C3×D4—22no—
339C3×D4—42no—
340C3×D4—44no—
341C3×D4—42no—
342C3×D4—42no—
343C3×D4—62no—
344C3×D4—62no—
345C3×D4—128no—
346C3×D4—122no—
347C2×C3×C4—21no—
348C2×C3×C4—22no—
349C2×C3×C4—22no—
350C2×C3×C4—21no—
351C2×C3×C4—32no—
352C2×C3×C4—62no—
353C2×C3×C4—64no—
354C2×C3×C4—62no—
355C2×C3×C4—62no—
356C2×C3×C4—62no—
357C2×C3×C4—122no—
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4D3×D412yes—
360C2×C3×C4#23712yes—
361C2×C3×C4#23712yes—
362C2×C3×C4C2×#6712yes—
363C2×C3×C4C2×#6711yescharacteristic
364C2×C3×C4C23×D311yescharacteristic
365C2×C3×C4C23×D311yescharacteristic
366#67—48no—
367#67—128no—
368#67—128no—
369C2×Dic3—22no—
370C2×Dic3—22no—
371C2×Dic3—42no—
372C2×Dic3—62no—
373C2×Dic3—62no—
374C2×Dic3—122no—
375C2×Dic3—122no—
376C2×Dic3—122no—
377C2×Dic3—242no—
378C2×Dic3C2×#6712yes—
379D12—22no—
380D12—22no—
381D12—42no—
382C4×D3—24no—
383C4×D3—22no—
384C4×D3—22no—
385C3×C8—34no—
386C3⋊C8—62no—
387C3⋊C8—62no—
388C3⋊C8—122no—
389C3⋊C8C2×#6714yescomplemented
390C2×C32—82no—
391C2×C32#46614yescomplemented
392C2×C32C2×#12111yescharacteristic
393C2×C32C22×D811yescharacteristic
394C2×C32C2×#13511yescharacteristic
395C3×D3—24no—
396C3×D3—82no—
397C24—21no—
398C24—31no—
399C24—61no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—21no—
403C2×D4—32no—
404C2×D4—64no—
405C2×D4—62no—
406C2×D4—62no—
407C2×D4—61no—
408C2×D4—124no—
409C2×D4—184no—
410C2×D4—364no—
411C2×D4C2×D3212yes—
412C22×C4—31no—
413C22×C4—32no—
414C22×C4—32no—
415C22×C4—62no—
416C22×C4—62no—
417C22×C4—61no—
418C22×C4—181no—
419C22×C4C2×D3211yescharacteristic
420D8—68no—
421C2×C8—32no—
422C2×C8—34no—
423C2×C8—92no—
424C2×C8—188no—
425C2×C8—182no—
426C4⋊C4—32no—
427C4⋊C4—61no—
428C4⋊C4—92no—
429C4⋊C4—181no—
430C22⋊C4—64no—
431C22⋊C4—184no—
432C22×C3—21no—
433C22×C3—22no—
434C22×C3—22no—
435C22×C3—22no—
436C22×C3—34no—
437C22×C3—44no—
438C22×C3—42no—
439C22×C3—42no—
440C22×C3—42no—
441C22×C3—42no—
442C22×C3—42no—
443C22×C3—42no—
444C22×C3—68no—
445C22×C3—62no—
446C22×C3—62no—
447C22×C3—82no—
448C22×C3—82no—
449C22×C3—88no—
450C22×C3—84no—
451C22×C3—84no—
452C22×C3—122no—
453C22×C3—122no—
454C22×C3—122no—
455C22×C3—244no—
456C22×C3D3×D812yes—
457C22×C3#91212yes—
458C22×C3C2×#21312yes—
459C22×C3#93812yes—
460C22×C3#93912yes—
461C22×C3#95012yes—
462C22×C3C2×D3×D411yescharacteristic
463C22×C3C22×#6711yescharacteristic
464C2×D3—22no—
465C2×D3—28no—
466C2×D3—22no—
467C2×D3—42no—
468C2×D3—42no—
469C2×D3—42no—
470C2×D3—84no—
471C2×D3C2×#21314yescomplemented
472C3×C4—21no—
473C3×C4—21no—
474C3×C4—22no—
475C3×C4—62no—
476C3×C4—122no—
477C3×C4#93812yes—
478C3×C4#93912yes—
479C3×C4C2×D3×D411yescharacteristic
480C3×C4C2×#23711yescharacteristic
481C3×C4C2×#23711yescharacteristic
482C3×C4C22×#6711yescharacteristic
483Dic3—22no—
484Dic3—42no—
485Dic3—122no—
486Dic3—122no—
487Dic3—242no—
488C32C2×#46611yescharacteristic, complemented, Sylow
489C23—22no—
490C23—32no—
491C23—34no—
492C23—42no—
493C23—42no—
494C23—42no—
495C23—62no—
496C23—62no—
497C23—62no—
498C23—122no—
499C23—122no—
500C23—122no—
501C23D3×#6711yescharacteristic
502D4—22no—
503D4—22no—
504D4—42no—
505D4—62no—
506D4—62no—
507D4—128no—
508D4—122no—
509D4—368no—
510C2×C4—32no—
511C2×C4—62no—
512C2×C4—62no—
513C2×C4—62no—
514C2×C4—64no—
515C2×C4—62no—
516C2×C4—122no—
517C2×C4—182no—
518C2×C4—362no—
519C2×C4#380512yes—
520C2×C4D3×#6712yes—
521C2×C4D3×#6711yescharacteristic
522C2×C4C22×D3211yescharacteristic
523C8—34no—
524C8—182no—
525C2×C3—24no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—64no—
530C2×C3—84no—
531C2×C3—82no—
532C2×C3—82no—
533C2×C3—242no—
534C2×C3#503814yescomplemented
535C2×C3#515714yescomplemented
536C2×C3C2×D3×D811yescharacteristic
537C2×C3C2×#91211yescharacteristic
538C2×C3C22×#21311yescharacteristic
539C2×C3C2×#93811yescharacteristic
540C2×C3C2×#93911yescharacteristic
541C2×C3C2×#95011yescharacteristic
542D3—24no—
543D3—82no—
544C22—34no—
545C22—42no—
546C22—42no—
547C22—42no—
548C22—68no—
549C22—62no—
550C22—62no—
551C22—84no—
552C22—122no—
553C22—122no—
554C22—122no—
555C22—244no—
556C22D3×#21312yes—
557C22#6393312yes—
558C22#6397012yes—
559C22C2×D3×#6711yescharacteristic
560C4—62no—
561C4—122no—
562C4—362no—
563C4#6397012yes—
564C4C2×#380511yescharacteristic
565C4C2×D3×#6711yescharacteristic
566C3—21no—
567C3C2×#503811yescharacteristic, complemented
568C3C2×#515711yescharacteristic, complemented
569C2—64no—
570C2—82no—
571C2—242no—
572C2#1059149814yesdirect product factor
573C2C2×D3×#21311yescharacteristic
574C2C2×#6393311yescharacteristic
575C2C2×#6397011yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
hypercenterC22×D4D32
hypocenterC32C2×#466
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. C2×C3×#938C2semidirect
2. C22×C3×#213C2semidirect
3. C2×#63908C2semidirect
4. C22×D3×C3⋊C8C2semidirect
5. C2×#63659C2semidirect
6. #10591498C2direct (N × H)
7. C2×#63575C2semidirect
8. C2×#63562C2semidirect
20. C3×#938C22semidirect
22. C2×C3×#213C22semidirect
27. #63908C22semidirect
29. C2×D3×C3⋊C8C22semidirect
30. #63659C22semidirect
31. #63575C22semidirect
32. #63562C22semidirect
36. C2×#938D3semidirect
37. C22×#213D3semidirect
81. C2×C3×C3⋊C8D4semidirect
109. #938C2×D3semidirect
111. C2×#213C2×D3semidirect
145. C22×C3×D3D8semidirect
169. C3×C3⋊C8C2×D4semidirect
256. C2×C3⋊C8#67semidirect
274. C2×C3×D3C2×D8semidirect
332. C22×D3#213semidirect
389. C3⋊C8C2×#67semidirect
391. C2×C32#466semidirect
471. C2×D3C2×#213semidirect
488. C32C2×#466semidirect
534. C2×C3#5038semidirect
535. C2×C3#5157semidirect
567. C3C2×#5038semidirect
568. C3C2×#5157semidirect
572. C2#10591498direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9382
C22×C3×#2132
C2×#639082
C22×D3×C3⋊C82
C2×#636592
#105914982
C2×#635752
C2×#635622
C2×#51573
C2×#50383