Finite Group Databasebeta

← C2×#10591429 #11865444

Subgroups — C2×#10591429 #11865444

Order 1152.

1465 conjugacy classes of subgroups.

The subgroup lattice has 598 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
3C2×#63894C211yesmaximal, characteristic, complemented
4C22×#3714C211yesmaximal, characteristic, complemented
5C2×C3×#832C211yesmaximal, characteristic, complemented
6#10591429C218yesmaximal, direct product factor
7C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8C2×#63562C211yesmaximal, characteristic, complemented
9C2×#5072—31nomaximal
10C2×#4786—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C3×#67—21no—
14C22×C3×#67—21no—
15C22×C3×D12C2211yescharacteristic
16C22×#624—21no—
17C2×#3753—24no—
18C2×#3753C2214yescomplemented
19C22×C3⋊(C3⋊C8)C2211yescharacteristic
20C3×#940—22no—
21C3×#940C2214yescomplemented
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4×Dic3C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C2×#3722—21no—
26#63894—22no—
27#63894C2214yescomplemented
28C2×#3714—24no—
29C2×#3714C2214yescomplemented
30C3×#832C2214yescomplemented
31Dic3⋊(C3⋊C8)C2214yescomplemented
32#63562C2214yescomplemented
33C2×C3×#127—31no—
34C2×#940D311yescharacteristic, complemented
35C22×#213—31no—
36C22×#213—31no—
37C22×#213—31no—
38C22×#213—61no—
39C22×D24—31no—
40C2×#893—31no—
41C2×C4×D12—31no—
42C2×C3×#102—31no—
43C2×#832—31no—
44C2×#832D311yescharacteristic, complemented
45C2×Dic3⋊C8—31no—
46#5072—38no—
47C2×#809—31no—
48C2×C4⋊(C3⋊C8)—31no—
49#4786—38no—
50C24×C32—21no—
51C23×C3⋊D3—21no—
52C23×C3×D3—21no—
53C2×C32×D4—22no—
54C2×C32×D4—21no—
55C2×C32×D4—22no—
56C2×C32×D4C2312yes—
57C22×C32×C4C2311yescharacteristic
58C2×C4⋊(C3⋊D3)—21no—
59C2×C4⋊(C3⋊D3)—22no—
60C2×C4⋊(C3⋊D3)D414yescomplemented
61C2×C4⋊(C3⋊D3)C2312yes—
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—
73C2×#624—24no—
74C2×#624—44no—
75#3753—28no—
76C2×C3⋊(C3⋊C8)—22no—
77C2×C3⋊(C3⋊C8)C2312yes—
78C3×C4⋊Dic3—21no—
79C3×C4⋊Dic3C2312yes—
80C3×C4×Dic3D412yes—
81C3×C4×Dic3C2312yes—
82C2×C3×C3⋊C8—22no—
83C2×C3×C3⋊C8C2312yes—
84#3722—24no—
85#3714—28no—
86C2×#459—91noSylow
87C22×C3×D4—21no—
88C22×C3×D4—31no—
89C22×C3×D4—61no—
90C22×C3×D4—61no—
91C22×C3×D4C2×D311yescharacteristic
92C22×C3×D4C2×D311yescharacteristic
93C22×#67—21no—
94C22×#67—21no—
95C22×D12—31no—
96C22×D12—31no—
97C22×D12—61no—
98C22×D12C2×D311yescharacteristic
99C22×C4×D3—61no—
100C22×C4×D3—61no—
101C22×C3×C8—31no—
102C3×#127—34no—
103C3×#127—62no—
104C2×C3×C4⋊C4—31no—
105C2×C3×C42—31no—
106#940—22no—
107#940C2×D314yescomplemented
108C2×#213—34no—
109C2×#213—34no—
110C2×#213—34no—
111C2×#213—64no—
112C2×#213—64no—
113C2×#213—64no—
114C2×#213—64no—
115C2×#213—68no—
116C2×(C2×D3)⋊C4—61no—
117C2×(C2×D3)⋊C4—61no—
118C2×C4⋊Dic3C2×D311yescharacteristic
119C2×C4×Dic3C2×D311yescharacteristic
120C22×C3⋊C8—31no—
121C22×C3⋊C8—31no—
122C22×C3⋊C8—61no—
123C22×C3⋊C8C2×D311yescharacteristic
124C2×D24—34no—
125C2×D24—64no—
126#893—34no—
127#893—62no—
128C4×D12—34no—
129C4×D12—62no—
130C3×#102—34no—
131#832—34no—
132#832C2×D314yescomplemented
133Dic3⋊C8—34no—
134#809—34no—
135C4⋊(C3⋊C8)—34no—
136C23×C32—22no—
137C23×C32—42no—
138C23×C32—42no—
139C23×C32—42no—
140C23×C32C2×D411yescharacteristic
141C22×C3⋊D3—24no—
142C22×C3⋊D3—22no—
143C22×C3⋊D3—42no—
144C22×C3⋊D3—42no—
145C22×C3×D3—22no—
146C22×C3×D3—42no—
147C22×C3×D3—42no—
148C22×C3×D3—42no—
149C32×D4—22no—
150C32×D4—22no—
151C32×D4—42no—
152C2×C32×C4C2×D412yes—
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4#4112yes—
155C2×C32×C4C2411yescharacteristic
156C4⋊(C3⋊D3)—24no—
157C4⋊(C3⋊D3)—22no—
158C4⋊(C3⋊D3)C2×D414yescomplemented
159C3×#67—48no—
160C3×#67—48no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3—42no—
164C2×C3×Dic3D814yescomplemented
165C2×C3×Dic3C2×D412yes—
166C2×C3×Dic3C2×D412yes—
167C3×D12—22no—
168C3×D12—22no—
169C3×D12—42no—
170#624—48no—
171C3⋊(C3⋊C8)—22no—
172C3×C3⋊C8—22no—
173C22×D8—91no—
174C22×D8—91no—
175C2×#127—31no—
176C2×C4×D4—91no—
177#459—98no—
178C2×C4⋊C8—91no—
179C2×#102—31no—
180C2×#102—91no—
181C24×C3—21no—
182C24×C3—21no—
183C24×C3—41no—
184C24×C3—61no—
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—42no—
199C2×C3×D4—41no—
200C2×C3×D4—64no—
201C2×C3×D4—64no—
202C2×C3×D4—62no—
203C2×C3×D4—62no—
204C2×C3×D4—61no—
205C2×C3×D4—124no—
206C2×C3×D4—124no—
207C2×C3×D4C22×D312yes—
208C2×C3×D4C22×D312yes—
209C22×C3×C4—21no—
210C22×C3×C4—31no—
211C22×C3×C4—31no—
212C22×C3×C4—61no—
213C22×C3×C4C22×D311yescharacteristic
214C22×C3×C4C22×D311yescharacteristic
215C2×#67—24no—
216C2×#67—24no—
217C2×#67—44no—
218C2×#67—44no—
219C22×Dic3—21no—
220C22×Dic3#6711yescharacteristic
221C22×Dic3#6711yescharacteristic
222C2×D12—22no—
223C2×D12—22no—
224C2×D12—21no—
225C2×D12—34no—
226C2×D12—34no—
227C2×D12—32no—
228C2×D12—32no—
229C2×D12—64no—
230C2×D12—62no—
231C2×D12—62no—
232C2×D12—61no—
233C2×D12—62no—
234C2×D12—61no—
235C2×D12—122no—
236C2×D12—121no—
237C2×D12C22×D312yes—
238C2×C4×D3—64no—
239C2×C4×D3—64no—
240C2×C4×D3—124no—
241C2×C4×D3—124no—
242C2×C3×C8—32no—
243C2×C3×C8—62no—
244C3×C4⋊C4—32no—
245C3×C4⋊C4—61no—
246C3×C42—32no—
247C3×C42—32no—
248#213—68no—
249#213—68no—
250#213—68no—
251#213—616no—
252(C2×D3)⋊C4—64no—
253(C2×D3)⋊C4—64no—
254C4⋊Dic3—21no—
255C4⋊Dic3C22×D312yes—
256C4×Dic3#6712yes—
257C4×Dic3C22×D312yes—
258C2×C3⋊C8—22no—
259C2×C3⋊C8—32no—
260C2×C3⋊C8—32no—
261C2×C3⋊C8—62no—
262C2×C3⋊C8—64no—
263C2×C3⋊C8—62no—
264C2×C3⋊C8—62no—
265C2×C3⋊C8C22×D312yes—
266D24—68no—
267C22×C32—42no—
268C22×C32—42no—
269C22×C32—42no—
270C22×C32—84no—
271C22×C32#12112yes—
272C22×C32C2×D812yes—
273C22×C32AGL(1,ℤ/8)12yes—
274C22×C32C22×D411yescharacteristic
275C2×C3⋊D3—24no—
276C2×C3⋊D3—42no—
277C2×C3⋊D3—42no—
278C2×C3⋊D3—48no—
279C2×C3×D3—42no—
280C2×C3×D3—42no—
281C2×C3×D3—42no—
282C2×C3×D3—84no—
283C32×C4#12112yes—
284C32×C4C22×D411yescharacteristic
285C32×C4C2×#4111yescharacteristic
286C3×Dic3—22no—
287C3×Dic3—42no—
288C3×Dic3C2×D814yescomplemented
289C22×D4—31no—
290C22×D4—61no—
291C22×D4—61no—
292C22×D4—91no—
293C22×D4D3211yescharacteristic
294C23×C4—181no—
295C2×D8—94no—
296C2×D8—94no—
297C2×D8—184no—
298C2×D8—184no—
299C22×C8—31no—
300C22×C8—91no—
301#127—34no—
302#127—62no—
303C4×D4—94no—
304C4×D4—182no—
305C2×C4⋊C4—31no—
306C2×C22⋊C4—181no—
307C2×C42—31no—
308C4⋊C8—94no—
309#102—34no—
310#102—94no—
311C23×C3—22no—
312C23×C3—22no—
313C23×C3—21no—
314C23×C3—42no—
315C23×C3—44no—
316C23×C3—42no—
317C23×C3—42no—
318C23×C3—42no—
319C23×C3—42no—
320C23×C3—42no—
321C23×C3—42no—
322C23×C3—62no—
323C23×C3—82no—
324C23×C3—82no—
325C23×C3—122no—
326C23×C3—122no—
327C23×C3—122no—
328C23×C3D3×D411yescharacteristic
329C23×C3C2×#6711yescharacteristic
330C22×D3—22no—
331C22×D3—42no—
332C22×D3—42no—
333C22×D3—42no—
334C22×D3—64no—
335C22×D3—64no—
336C22×D3—62no—
337C22×D3—62no—
338C22×D3—122no—
339C22×D3—124no—
340C22×D3—122no—
341C22×D3—122no—
342C22×D3—122no—
343C22×D3—122no—
344C22×D3—242no—
345C22×D3—242no—
346C3×D4—24no—
347C3×D4—22no—
348C3×D4—22no—
349C3×D4—22no—
350C3×D4—22no—
351C3×D4—42no—
352C3×D4—44no—
353C3×D4—42no—
354C3×D4—42no—
355C3×D4—62no—
356C3×D4—62no—
357C3×D4—128no—
358C3×D4—128no—
359C3×D4—122no—
360C2×C3×C4—21no—
361C2×C3×C4—22no—
362C2×C3×C4—21no—
363C2×C3×C4—22no—
364C2×C3×C4—34no—
365C2×C3×C4—32no—
366C2×C3×C4—32no—
367C2×C3×C4—62no—
368C2×C3×C4—62no—
369C2×C3×C4—122no—
370C2×C3×C4#23512yes—
371C2×C3×C4D3×D411yescharacteristic
372C2×C3×C4D3×D412yes—
373C2×C3×C4D3×D412yes—
374C2×C3×C4#23712yes—
375C2×C3×C4C2×#6711yescharacteristic
376C2×C3×C4C23×D311yescharacteristic
377C2×C3×C4C23×D311yescharacteristic
378#67—48no—
379#67—48no—
380C2×Dic3—22no—
381C2×Dic3—22no—
382C2×Dic3—42no—
383C2×Dic3#21314yescomplemented
384C2×Dic3C2×#6712yes—
385C2×Dic3C2×#6712yes—
386D12—22no—
387D12—22no—
388D12—34no—
389D12—34no—
390D12—42no—
391D12—64no—
392D12—64no—
393D12—64no—
394D12—62no—
395D12—62no—
396D12—122no—
397D12—124no—
398C4×D3—128no—
399C4×D3—128no—
400C3×C8—62no—
401C3⋊C8—22no—
402C3⋊C8—64no—
403C3⋊C8—62no—
404C3⋊C8—62no—
405C2×C32—82no—
406C2×C32#45914yescomplemented
407C2×C32C2×#12111yescharacteristic
408C2×C32C22×D811yescharacteristic
409C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
410C3⋊D3—44no—
411C3×D3—82no—
412C24—21no—
413C24—61no—
414C24—181no—
415C2×D4—22no—
416C2×D4—21no—
417C2×D4—22no—
418C2×D4—32no—
419C2×D4—64no—
420C2×D4—64no—
421C2×D4—62no—
422C2×D4—61no—
423C2×D4—62no—
424C2×D4—92no—
425C2×D4—94no—
426C2×D4—124no—
427C2×D4—124no—
428C2×D4—182no—
429C2×D4—181no—
430C2×D4C2×D3212yes—
431C22×C4—31no—
432C22×C4—31no—
433C22×C4—61no—
434C22×C4—184no—
435C22×C4—364no—
436C22×C4C2×D3211yescharacteristic
437D8—188no—
438D8—188no—
439C2×C8—32no—
440C2×C8—62no—
441C2×C8—92no—
442C2×C8—182no—
443C4⋊C4—32no—
444C4⋊C4—61no—
445C22⋊C4—184no—
446C42—32no—
447C42—32no—
448C22×C3—21no—
449C22×C3—22no—
450C22×C3—22no—
451C22×C3—22no—
452C22×C3—44no—
453C22×C3—42no—
454C22×C3—42no—
455C22×C3—42no—
456C22×C3—42no—
457C22×C3—42no—
458C22×C3—42no—
459C22×C3—82no—
460C22×C3—82no—
461C22×C3—88no—
462C22×C3—84no—
463C22×C3—84no—
464C22×C3—122no—
465C22×C3—122no—
466C22×C3—122no—
467C22×C3—244no—
468C22×C3#88412yes—
469C22×C3D3×D812yes—
470C22×C3#91412yes—
471C22×C3C2×#21312yes—
472C22×C3#93212yes—
473C22×C3#93812yes—
474C22×C3C2×D3×D411yescharacteristic
475C22×C3C22×#6711yescharacteristic
476C2×D3—42no—
477C2×D3—42no—
478C2×D3—42no—
479C2×D3—64no—
480C2×D3—64no—
481C2×D3—84no—
482C2×D3—124no—
483C2×D3—122no—
484C2×D3—122no—
485C2×D3—122no—
486C2×D3—122no—
487C2×D3—128no—
488C2×D3—128no—
489C2×D3—242no—
490C2×D3—242no—
491C2×D3—248no—
492C3×C4—21no—
493C3×C4—21no—
494C3×C4—22no—
495C3×C4—34no—
496C3×C4—62no—
497C3×C4—122no—
498C3×C4#88412yes—
499C3×C4#93812yes—
500C3×C4C2×#23511yescharacteristic
501C3×C4C2×D3×D411yescharacteristic
502C3×C4C2×D3×D411yescharacteristic
503C3×C4C2×#23711yescharacteristic
504Dic3—22no—
505Dic3—42no—
506Dic3C2×#21314yescomplemented
507C32C2×#45911yescharacteristic, complemented, Sylow
508C23—22no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—62no—
513C23—122no—
514C23—122no—
515C23—122no—
516C23—182no—
517C23—184no—
518C23—362no—
519C23—362no—
520C23D3×#6711yescharacteristic
521D4—22no—
522D4—22no—
523D4—42no—
524D4—62no—
525D4—62no—
526D4—94no—
527D4—128no—
528D4—128no—
529D4—122no—
530D4—182no—
531D4—184no—
532C2×C4—32no—
533C2×C4—34no—
534C2×C4—32no—
535C2×C4—62no—
536C2×C4—62no—
537C2×C4—122no—
538C2×C4—368no—
539C2×C4#380412yes—
540C2×C4D3×#6711yescharacteristic
541C2×C4#381112yes—
542C2×C4C22×D3211yescharacteristic
543C8—62no—
544C8—182no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—24no—
549C2×C3—84no—
550C2×C3—82no—
551C2×C3—82no—
552C2×C3—242no—
553C2×C3#478614yescomplemented
554C2×C3#507214yescomplemented
555C2×C3C2×#88411yescharacteristic
556C2×C3C2×D3×D811yescharacteristic
557C2×C3C2×#91411yescharacteristic
558C2×C3C22×#21311yescharacteristic
559C2×C3C2×#93211yescharacteristic
560C2×C3C2×#93811yescharacteristic
561D3—82no—
562D3—124no—
563D3—124no—
564D3—244no—
565C22—42no—
566C22—42no—
567C22—42no—
568C22—84no—
569C22—122no—
570C22—122no—
571C22—122no—
572C22—184no—
573C22—244no—
574C22—362no—
575C22—362no—
576C22—368no—
577C22D3×#21312yes—
578C22#6393412yes—
579C22#6395812yes—
580C22C2×D3×#6711yescharacteristic
581C4—34no—
582C4—62no—
583C4—122no—
584C4#6395812yes—
585C4C2×#380411yescharacteristic
586C4C2×#381111yescharacteristic
587C3—21no—
588C3C2×#478611yescharacteristic, complemented
589C3C2×#507211yescharacteristic, complemented
590C2—82no—
591C2—242no—
592C2—364no—
593C2#1059142914yesdirect product factor
594C2C2×D3×#21311yescharacteristic
595C2C2×#6393411yescharacteristic
596C2C2×#6395811yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
hypercenterC22×D4D32
hypocenterC32C2×#459
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. C2×#63894C2semidirect
4. C22×#3714C2semidirect
5. C2×C3×#832C2semidirect
6. #10591429C2direct (N × H)
7. C2×Dic3⋊(C3⋊C8)C2semidirect
8. C2×#63562C2semidirect
18. C2×#3753C22semidirect
21. C3×#940C22semidirect
27. #63894C22semidirect
29. C2×#3714C22semidirect
30. C3×#832C22semidirect
31. Dic3⋊(C3⋊C8)C22semidirect
32. #63562C22semidirect
34. C2×#940D3semidirect
44. C2×#832D3semidirect
60. C2×C4⋊(C3⋊D3)D4semidirect
107. #940C2×D3semidirect
132. #832C2×D3semidirect
158. C4⋊(C3⋊D3)C2×D4semidirect
164. C2×C3×Dic3D8semidirect
288. C3×Dic3C2×D8semidirect
383. C2×Dic3#213semidirect
406. C2×C32#459semidirect
506. Dic3C2×#213semidirect
507. C32C2×#459semidirect
553. C2×C3#4786semidirect
554. C2×C3#5072semidirect
588. C3C2×#4786semidirect
589. C3C2×#5072semidirect
593. C2#10591429direct (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
C2×#638942
C22×#37142
C2×C3×#8322
#105914292
C2×Dic3⋊(C3⋊C8)2
C2×#635622
C2×#50723
C2×#47863