Finite Group Databasebeta

← C2×#10595311 #11901341

Subgroups — C2×#10595311 #11901341

Order 1152.

2885 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64147C211yesmaximal, characteristic, complemented
2C2×C3×#939C212yesmaximal, complemented
3C2×#63983C212yesmaximal, complemented
4C2×#63961C212yesmaximal, complemented
5C2×#63959C212yesmaximal, complemented
6C2×#63952C212yesmaximal, complemented
7#10595311C2116yesmaximal, direct product factor
8C2×#63921C211yesmaximal, characteristic, complemented
9C2×#63865C211yesmaximal, characteristic, complemented
10C2×#63861C212yesmaximal, complemented
11C2×#5613—32nomaximal
12C23×D32C2211yescharacteristic
13C22×C32×D4C2211yescharacteristic, complemented
14C22×#638C2212yes—
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×C3×#67C2212yes—
17C22×C3×#67C2212yes—
18C23×C3×Dic3C2212yescomplemented
19C22×#627C2211yescharacteristic, complemented
20C22×#624C2211yescharacteristic
21C2×#3757C2212yescomplemented
22#64147C2218yescomplemented
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
24C2×C3×#217C2212yescomplemented
25C3×#939C22116yescomplemented
26C2×C3×(C2×D3)⋊C4C2212yes—
27C2×C3×Dic3⋊C4C2212yescomplemented
28#63983C22116yescomplemented
29C2×#3724C2212yescomplemented
30C2×#3724C2211yescharacteristic, complemented
31C2×#3722C2212yes—
32#63961C22116yescomplemented
33C2×(C2×D3)⋊Dic3C2212yes—
34C2×(C2×D3)⋊Dic3C2212yes—
35C2×(C2×D3)⋊Dic3C2212yes—
36#63959C22116yescomplemented
37C2×Dic32C2212yescomplemented
38#63952C22116yescomplemented
39#63921C2218yescomplemented
40#63865C2218yescomplemented
41#63861C22116yescomplemented
42C2×C3×#121—32no—
43C2×#939D312yescomplemented
44C2×#938—32no—
45C2×#938—61no—
46C2×#937—32no—
47C2×#937—32no—
48C2×#936—32no—
49C2×#935—32no—
50C2×#929—32no—
51C2×C4×#67—32no—
52#5613—332no—
53C2×#898—32no—
54C2×#896—32no—
55C2×#885—32no—
56C2×#67⋊C4—32no—
57C2×D3×C22⋊C4—32no—
58C2×#879—32no—
59C24×C32C2312yes—
60C23×C3⋊D3C2311yescharacteristic
61C23×C3×D3C2312yes—
62C22×D32—24no—
63C22×D32—42no—
64C22×D32—42no—
65C22×D32C2314yes—
66C2×C32×D4—42no—
67C2×C32×D4C2314yescomplemented
68C22×C32×C4C2311yescharacteristic
69C2×#638—28no—
70C2×#638C2318yes—
71C22×C3⋊Dic3C2311yescharacteristic
72C22×C3⋊Dic3C2312yes—
73C2×C4×C3⋊D3—42no—
74C2×C4×C3⋊D3C2314yes—
75C2×C3×#67—44no—
76C2×C3×#67—44no—
77C2×C3×#67C2318yes—
78C2×C3×#67C2318yes—
79C22×C3×Dic3—44no—
80C22×C3×Dic3C2312yes—
81C22×C3×Dic3C2312yes—
82C22×C3×Dic3C2312yes—
83C22×C3×Dic3C2318yescomplemented
84C2×#627—42no—
85C2×#627C2314yescomplemented
86C2×#624—42no—
87C2×#624C2314yes—
88#3757C2318yescomplemented
89C4⋊(C3⋊Dic3)C2314yescomplemented
90C3×#217C2318yescomplemented
91C3×(C2×D3)⋊C4C2318yes—
92C3×Dic3⋊C4C2318yescomplemented
93#3724C2318yescomplemented
94#3724C2314yescomplemented
95#3722C2318yes—
96(C2×D3)⋊Dic3C2318yes—
97(C2×D3)⋊Dic3C2318yes—
98(C2×D3)⋊Dic3C2318yes—
99Dic32C2318yescomplemented
100C2×#538—91noSylow
101C24×D3—32no—
102C22×C3×D4—21no—
103C22×C3×D4—32no—
104C22×C3×D4—32no—
105C22×C3×D4C2×D312yescomplemented
106C23×C3×C4—32no—
107C22×#67—32no—
108C22×#67—32no—
109C22×#67—62no—
110C22×#67C2×D312yes—
111C22×#67C2×D312yes—
112C23×Dic3C2×D312yescomplemented
113C22×C4×D3—32no—
114C22×C4×D3—32no—
115C22×C4×D3—61no—
116C22×Dic6—32no—
117C3×#121—316no—
118C2×C3×C4⋊C4—32no—
119C2×C3×C22⋊C4—32no—
120C2×C3×C22⋊C4—32no—
121C2×#217—32no—
122C2×#217—32no—
123C2×#217—32no—
124C2×#217—32no—
125C2×#217—32no—
126C2×#217—62no—
127C2×#217C2×D312yescomplemented
128#939C2×D3116yescomplemented
129#938—316no—
130#938—68no—
131#937—316no—
132#937—316no—
133#936—316no—
134#935—316no—
135#929—316no—
136C4×#67—316no—
137C2×(C2×D3)⋊C4—32no—
138C2×(C2×D3)⋊C4—32no—
139C2×(C2×D3)⋊C4—32no—
140C2×(C2×D3)⋊C4—32no—
141C2×(C2×D3)⋊C4—32no—
142C2×(C2×D3)⋊C4C2×D312yes—
143C2×C4⋊Dic3—32no—
144C2×C4⋊Dic3—61no—
145C2×Dic3⋊C4—32no—
146C2×Dic3⋊C4—32no—
147C2×Dic3⋊C4—32no—
148C2×Dic3⋊C4C2×D312yescomplemented
149C2×C4×Dic3—32no—
150C2×C4×Dic3—32no—
151#898—316no—
152#896—316no—
153#885—316no—
154#67⋊C4—316no—
155D3×C22⋊C4—316no—
156#879—316no—
157C23×C32—24no—
158C23×C32—24no—
159C23×C32—24no—
160C23×C32C2414yes—
161C23×C32C2411yescharacteristic
162C22×C3⋊D3—22no—
163C22×C3⋊D3—22no—
164C22×C3⋊D3#4114yes—
165C22×C3⋊D3C2412yes—
166C22×C3×D3—24no—
167C22×C3×D3—24no—
168C22×C3×D3—24no—
169C22×C3×D3C2414yes—
170C2×D32—28no—
171C2×D32—44no—
172C2×D32—44no—
173C2×D32—416no—
174C32×D4—44no—
175C2×C32×C4—22no—
176C2×C32×C4C2412yes—
177#638—216no—
178C2×C3⋊Dic3—24no—
179C2×C3⋊Dic3—22no—
180C2×C3⋊Dic3C2414yes—
181C2×C3⋊Dic3C2412yes—
182C4×C3⋊D3—44no—
183C3×#67—48no—
184C3×#67—48no—
185C2×C3×Dic3—24no—
186C2×C3×Dic3—24no—
187C2×C3×Dic3—24no—
188C2×C3×Dic3—48no—
189C2×C3×Dic3C2414yes—
190C2×C3×Dic3C2414yes—
191C2×C3×Dic3C2414yes—
192#627—44no—
193#624—44no—
194#538—916no—
195C2×#126—92no—
196C2×#124—92no—
197C2×#123—92no—
198C2×C22⋊Q8—91no—
199C2×#121—32no—
200C2×#121—91no—
201C2×#120—92no—
202C2×C4×D4—92no—
203C22×C22⋊C4—91no—
204C24×C3—22no—
205C24×C3—32no—
206C24×C3C22×D312yes—
207C24×C3C22×D312yes—
208C23×D3—32no—
209C23×D3—38no—
210C23×D3—61no—
211C23×D3—68no—
212C23×D3—124no—
213C23×D3—124no—
214C23×D3C22×D312yes—
215C2×C3×D4—24no—
216C2×C3×D4—38no—
217C2×C3×D4—38no—
218C2×C3×D4—44no—
219C2×C3×D4—44no—
220C2×C3×D4—124no—
221C2×C3×D4—124no—
222C2×C3×D4C22×D318yescomplemented
223C22×C3×C4—21no—
224C22×C3×C4—32no—
225C22×C3×C4—32no—
226C22×C3×C4—32no—
227C22×C3×C4—38no—
228C22×C3×C4—124no—
229C22×C3×C4C22×D312yes—
230C2×#67—38no—
231C2×#67—38no—
232C2×#67—44no—
233C2×#67—44no—
234C2×#67—68no—
235C2×#67—68no—
236C2×#67—68no—
237C2×#67—128no—
238C2×#67C22×D318yes—
239C2×#67C22×D318yes—
240C22×Dic3—32no—
241C22×Dic3—32no—
242C22×Dic3—32no—
243C22×Dic3—44no—
244C22×Dic3—62no—
245C22×Dic3—61no—
246C22×Dic3C22×D312yes—
247C22×Dic3C22×D312yes—
248C22×Dic3C22×D312yes—
249C22×Dic3C22×D318yescomplemented
250C2×C4×D3—38no—
251C2×C4×D3—38no—
252C2×C4×D3—64no—
253C2×C4×D3—124no—
254C2×C4×D3—124no—
255C2×C4×D3—124no—
256C2×Dic6—38no—
257C2×Dic6—124no—
258C3×C4⋊C4—38no—
259C3×C22⋊C4—38no—
260C3×C22⋊C4—38no—
261#217—38no—
262#217—38no—
263#217—38no—
264#217—38no—
265#217—38no—
266#217—68no—
267#217C22×D318yescomplemented
268(C2×D3)⋊C4—38no—
269(C2×D3)⋊C4—38no—
270(C2×D3)⋊C4—38no—
271(C2×D3)⋊C4—38no—
272(C2×D3)⋊C4—38no—
273(C2×D3)⋊C4C22×D318yes—
274C4⋊Dic3—38no—
275C4⋊Dic3—64no—
276Dic3⋊C4—38no—
277Dic3⋊C4—38no—
278Dic3⋊C4—38no—
279Dic3⋊C4C22×D318yescomplemented
280C4×Dic3—38no—
281C4×Dic3—38no—
282C22×C32—24no—
283C22×C32—24no—
284C22×C32—24no—
285C22×C32—48no—
286C22×C32C2×#4112yes—
287C22×C32H(5,𝔽2)12yes—
288C22×C32H(5,𝔽2)12yes—
289C22×C32C2511yescharacteristic
290C2×C3⋊D3—28no—
291C2×C3⋊D3—22no—
292C2×C3⋊D3—22no—
293C2×C3⋊D3C2×#4114yes—
294C2×C3×D3—24no—
295C2×C3×D3—24no—
296C2×C3×D3—24no—
297C2×C3×D3—48no—
298D32—416no—
299C32×C4—22no—
300C3⋊Dic3—24no—
301C3⋊Dic3—22no—
302C3×Dic3—24no—
303C3×Dic3—24no—
304C3×Dic3—24no—
305C25—91no—
306C22×Q8—91no—
307C22×D4—32no—
308C22×D4—32no—
309C22×D4—92no—
310C22×D4D3211yescharacteristic, complemented
311C23×C4—32no—
312C23×C4—91no—
313C23×C4—91no—
314#126—916no—
315#124—916no—
316#123—916no—
317C22⋊Q8—98no—
318#121—316no—
319#121—98no—
320#120—916no—
321C4×D4—916no—
322C2×C4⋊C4—32no—
323C2×C4⋊C4—92no—
324C2×C4⋊C4—91no—
325C2×C4⋊C4—91no—
326C2×C22⋊C4—32no—
327C2×C22⋊C4—32no—
328C2×C22⋊C4—98no—
329C2×C22⋊C4—92no—
330C2×C22⋊C4—92no—
331C2×C22⋊C4—92no—
332C2×C22⋊C4—92no—
333C2×C22⋊C4—92no—
334C2×C42—92no—
335C23×C3—24no—
336C23×C3—24no—
337C23×C3—24no—
338C23×C3—24no—
339C23×C3—24no—
340C23×C3—24no—
341C23×C3—24no—
342C23×C3—21no—
343C23×C3—34no—
344C23×C3—44no—
345C23×C3—44no—
346C23×C3—44no—
347C23×C3—64no—
348C23×C3—64no—
349C23×C3—64no—
350C23×C3C23×D314yes—
351C23×C3C23×D314yes—
352C23×C3C23×D312yes—
353C22×D3—24no—
354C22×D3—24no—
355C22×D3—24no—
356C22×D3—38no—
357C22×D3—34no—
358C22×D3—64no—
359C22×D3—62no—
360C22×D3—616no—
361C22×D3—64no—
362C22×D3—64no—
363C22×D3—122no—
364C22×D3—122no—
365C22×D3—128no—
366C22×D3—128no—
367C22×D3—1232no—
368C22×D3C23×D314yes—
369C3×D4—48no—
370C3×D4—48no—
371C3×D4—128no—
372C3×D4—128no—
373C2×C3×C4—24no—
374C2×C3×C4—24no—
375C2×C3×C4—22no—
376C2×C3×C4—34no—
377C2×C3×C4—34no—
378C2×C3×C4—34no—
379C2×C3×C4—64no—
380C2×C3×C4—64no—
381C2×C3×C4—64no—
382C2×C3×C4—128no—
383C2×C3×C4C23×D314yes—
384#67—48no—
385#67—48no—
386#67—616no—
387#67—616no—
388#67—1216no—
389C2×Dic3—24no—
390C2×Dic3—24no—
391C2×Dic3—24no—
392C2×Dic3—34no—
393C2×Dic3—34no—
394C2×Dic3—34no—
395C2×Dic3—48no—
396C2×Dic3—64no—
397C2×Dic3—62no—
398C2×Dic3—64no—
399C2×Dic3—64no—
400C2×Dic3—64no—
401C2×Dic3—122no—
402C2×Dic3—124no—
403C2×Dic3C23×D314yes—
404C2×Dic3C23×D314yes—
405C2×Dic3C23×D314yes—
406C4×D3—128no—
407C4×D3—128no—
408C4×D3—128no—
409Dic6—128no—
410C2×C32—44no—
411C2×C32#53814yescomplemented
412C2×C32C22×#4111yescharacteristic
413C2×C32C2×H(5,𝔽2)11yescharacteristic
414C2×C32C2×H(5,𝔽2)11yescharacteristic
415C3⋊D3—24no—
416C3×D3—44no—
417C24—32no—
418C24—94no—
419C24—91no—
420C24—184no—
421C24—362no—
422C24—362no—
423C24C2×D3212yes—
424C2×Q8—94no—
425C2×Q8—362no—
426C2×D4—38no—
427C2×D4—38no—
428C2×D4—42no—
429C2×D4—98no—
430C2×D4—124no—
431C2×D4—124no—
432C2×D4—188no—
433C2×D4C2×D3214yescomplemented
434C22×C4—32no—
435C22×C4—32no—
436C22×C4—32no—
437C22×C4—38no—
438C22×C4—94no—
439C22×C4—92no—
440C22×C4—91no—
441C22×C4—94no—
442C22×C4—124no—
443C22×C4—362no—
444C22×C4—362no—
445C22×C4C2×D3211yescharacteristic
446C4⋊C4—38no—
447C4⋊C4—98no—
448C4⋊C4—94no—
449C4⋊C4—94no—
450C22⋊C4—38no—
451C22⋊C4—38no—
452C22⋊C4—98no—
453C22⋊C4—98no—
454C22⋊C4—98no—
455C22⋊C4—98no—
456C22⋊C4—98no—
457C42—98no—
458C22×C3—24no—
459C22×C3—24no—
460C22×C3—24no—
461C22×C3—24no—
462C22×C3—24no—
463C22×C3—24no—
464C22×C3—22no—
465C22×C3—22no—
466C22×C3—22no—
467C22×C3—21no—
468C22×C3—44no—
469C22×C3—44no—
470C22×C3—44no—
471C22×C3—48no—
472C22×C3—48no—
473C22×C3—64no—
474C22×C3—64no—
475C22×C3—64no—
476C22×C3—88no—
477C22×C3—128no—
478C22×C3#100414yes—
479C22×C3#100414yes—
480C22×C3D3×#4114yes—
481C22×C3C24×D312yes—
482C2×D3—24no—
483C2×D3—24no—
484C2×D3—24no—
485C2×D3—38no—
486C2×D3—48no—
487C2×D3—64no—
488C2×D3—64no—
489C2×D3—64no—
490C2×D3—616no—
491C2×D3—122no—
492C2×D3—122no—
493C2×D3—128no—
494C2×D3—1232no—
495C3×C4—24no—
496C3×C4—24no—
497C3×C4—64no—
498C3×C4—64no—
499C3×C4—64no—
500Dic3—24no—
501Dic3—24no—
502Dic3—24no—
503Dic3—64no—
504Dic3—64no—
505Dic3—64no—
506Dic3—122no—
507Dic3—124no—
508C32C2×#53811yescharacteristic, complemented, Sylow
509C23—24no—
510C23—24no—
511C23—24no—
512C23—34no—
513C23—64no—
514C23—64no—
515C23—64no—
516C23—94no—
517C23—92no—
518C23—188no—
519C23—182no—
520C23—182no—
521C23—364no—
522C23—364no—
523C23—3616no—
524C23C22×D3214yes—
525C23C22×D3211yescharacteristic
526Q8—364no—
527D4—44no—
528D4—128no—
529D4—128no—
530D4—1816no—
531C2×C4—22no—
532C2×C4—34no—
533C2×C4—34no—
534C2×C4—34no—
535C2×C4—64no—
536C2×C4—64no—
537C2×C4—64no—
538C2×C4—94no—
539C2×C4—92no—
540C2×C4—128no—
541C2×C4—184no—
542C2×C4—182no—
543C2×C4—364no—
544C2×C4—364no—
545C2×C4C22×D3212yes—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—24no—
550C2×C3—44no—
551C2×C3—44no—
552C2×C3—84no—
553C2×C3—124no—
554C2×C3#561318yescomplemented
555C2×C3C2×#100412yes—
556C2×C3C2×#100412yes—
557C2×C3C2×D3×#4112yes—
558D3—44no—
559D3—68no—
560D3—124no—
561C22—24no—
562C22—24no—
563C22—24no—
564C22—48no—
565C22—64no—
566C22—64no—
567C22—64no—
568C22—94no—
569C22—128no—
570C22—182no—
571C22—182no—
572C22—188no—
573C22—3616no—
574C22#6431212yes—
575C22#6431312yes—
576C22#6433012yes—
577C22C23×D3211yescharacteristic
578C4—22no—
579C4—64no—
580C4—64no—
581C4—64no—
582C4—184no—
583C4—182no—
584C3—21no—
585C3C2×#561312yescomplemented
586C2—44no—
587C2—124no—
588C2—184no—
589C2#1059531114yesdirect product factor
590C2C2×#6431211yescharacteristic
591C2C2×#6431311yescharacteristic
592C2C2×#6433011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C2×#538
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#64147C2semidirect
2. C2×C3×#939C2semidirect
3. C2×#63983C2semidirect
4. C2×#63961C2semidirect
5. C2×#63959C2semidirect
6. C2×#63952C2semidirect
7. #10595311C2direct (N × H)
8. C2×#63921C2semidirect
9. C2×#63865C2semidirect
10. C2×#63861C2semidirect
13. C22×C32×D4C22semidirect
18. C23×C3×Dic3C22semidirect
19. C22×#627C22semidirect
21. C2×#3757C22semidirect
22. #64147C22semidirect
23. C2×C4⋊(C3⋊Dic3)C22semidirect
24. C2×C3×#217C22semidirect
25. C3×#939C22semidirect
27. C2×C3×Dic3⋊C4C22semidirect
28. #63983C22semidirect
29. C2×#3724C22semidirect
30. C2×#3724C22semidirect
32. #63961C22semidirect
36. #63959C22semidirect
37. C2×Dic32C22semidirect
38. #63952C22semidirect
39. #63921C22semidirect
40. #63865C22semidirect
41. #63861C22semidirect
43. C2×#939D3semidirect
67. C2×C32×D4C23semidirect
83. C22×C3×Dic3C23semidirect
85. C2×#627C23semidirect
88. #3757C23semidirect
89. C4⋊(C3⋊Dic3)C23semidirect
90. C3×#217C23semidirect
92. C3×Dic3⋊C4C23semidirect
93. #3724C23semidirect
94. #3724C23semidirect
99. Dic32C23semidirect
105. C22×C3×D4C2×D3semidirect
112. C23×Dic3C2×D3semidirect
127. C2×#217C2×D3semidirect
128. #939C2×D3semidirect
148. C2×Dic3⋊C4C2×D3semidirect
222. C2×C3×D4C22×D3semidirect
249. C22×Dic3C22×D3semidirect
267. #217C22×D3semidirect
279. Dic3⋊C4C22×D3semidirect
310. C22×D4D32semidirect
411. C2×C32#538semidirect
433. C2×D4C2×D32semidirect
508. C32C2×#538semidirect
554. C2×C3#5613semidirect
585. C3C2×#5613semidirect
589. C2#10595311direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641472
C2×C3×#9392
C2×#639832
C2×#639612
C2×#639592
C2×#639522
#105953112
C2×#639212
C2×#638652
C2×#638612
C2×#56133