Finite Group Databasebeta

← C2×#10595023 #11900455

Subgroups — C2×#10595023 #11900455

Order 1152.

4205 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3828C211yesmaximal, characteristic, complemented
2C23×C3×C4×D3C211yesmaximal, characteristic, complemented
3C2×C3×#926C211yesmaximal, characteristic, complemented
4C2×#63977C212yesmaximal, complemented
5C2×#63966C212yesmaximal, complemented
6#10595023C2116yesmaximal, direct product factor
7C2×#63909C212yesmaximal, complemented
8C2×C4×#626C214yesmaximal, complemented
9C2×#63857C212yesmaximal, complemented
10C2×#5791—31nomaximal
11C2×#5524—31nomaximal
12C24×C3×D3C2211yescharacteristic
13C23×C32×C4C2211yescharacteristic
14C22×#638C2212yes—
15C2×#3828—28no—
16C2×#3828C2218yescomplemented
17C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
18C22×C4×C3⋊D3C2212yescomplemented
19C22×#634C2211yescharacteristic, complemented
20C23×C3×Dic3C2211yescharacteristic
21C22×C3×C4×D3—28no—
22C22×C3×C4×D3C2212yes—
23C22×C3×C4×D3C2212yes—
24C22×C3×C4×D3C2218yescomplemented
25C22×#626C2214yes—
26C2×C3×#217C2212yes—
27C3×#926C2218yescomplemented
28C2×C3×C4⋊Dic3C2212yescomplemented
29C2×C3×C4×Dic3C2212yescomplemented
30#63977C22116yescomplemented
31#63966C22116yescomplemented
32C2×Dic3⋊Dic3C2214yescomplemented
33C2×#3722C2214yescomplemented
34C2×(C2×D3)⋊Dic3C2214yes—
35#63909C22116yescomplemented
36C4×#626C22132yescomplemented
37#63857C22116yescomplemented
38C24×C3×C4—31no—
39C22×#235—31no—
40C22×#235—31no—
41C22×#235—61no—
42C23×C4×D3D311yescharacteristic, complemented
43C2×C3×#117—31no—
44C2×#953—32no—
45#5791—316no—
46C2×#930—32no—
47C2×#929—32no—
48C2×C4×#67—34no—
49C2×#926D311yescharacteristic, complemented
50C2×#924—32no—
51#5524—316no—
52C2×#897—32no—
53C2×#895—32no—
54C2×#886—32no—
55C2×#882—32no—
56C2×C4×D12—34no—
57C24×C32C2311yescharacteristic
58C23×C3⋊D3C2312yes—
59C23×C3×D3—24no—
60C23×C3×D3—28no—
61C23×C3×D3C2314yes—
62C23×C3×D3C2312yes—
63C22×C32×C4D418yescomplemented
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C22×C32×C4C2314yes—
67C2×#638—28no—
68C2×#638C2318yes—
69C22×C3⋊Dic3C2312yes—
70#3828—232no—
71C2×C4⋊(C3⋊D3)—24no—
72C2×C4⋊(C3⋊D3)C2314yescomplemented
73C2×C4×C3⋊D3—28no—
74C2×C4×C3⋊D3C2318yescomplemented
75C2×#634—24no—
76C2×#634C2314yescomplemented
77C22×C3×Dic3—24no—
78C22×C3×Dic3C2314yes—
79C22×C3×Dic3C2312yes—
80C22×C3×Dic3C2314yes—
81C2×C3×C4×D3—28no—
82C2×C3×C4×D3—28no—
83C2×C3×C4×D3—232no—
84C2×C3×C4×D3C2318yes—
85C2×C3×C4×D3C2318yes—
86C2×#626—216no—
87C2×#626C23116yes—
88C3×#217C2318yes—
89C3×C4⋊Dic3C2318yescomplemented
90C3×C4×Dic3C2318yescomplemented
91Dic3⋊Dic3C23116yescomplemented
92#3722C23116yescomplemented
93(C2×D3)⋊Dic3C23116yes—
94C2×#525—91noSylow
95C25×C3—31no—
96C24×D3C2×D311yescharacteristic
97C23×C3×C4—21no—
98C23×C3×C4—31no—
99C23×C3×C4—32no—
100C23×C3×C4—32no—
101C23×C3×C4—38no—
102C23×C3×C4—68no—
103C23×C3×C4C2×D311yescharacteristic
104C23×C3×C4C2×D311yescharacteristic
105C22×#67—32no—
106C22×#67—32no—
107C22×#67—34no—
108C22×#67—62no—
109C23×Dic3C2×D311yescharacteristic
110C2×#235—38no—
111C2×#235—38no—
112C2×#235—68no—
113C2×#235—616no—
114C2×#235—68no—
115C2×#235—68no—
116C22×D12—34no—
117C22×D12—31no—
118C22×D12—31no—
119C22×D12—61no—
120C22×C4×D3—28no—
121C22×C4×D3—32no—
122C22×C4×D3—32no—
123C22×C4×D3—62no—
124C22×C4×D3C2×D312yes—
125C22×C4×D3C2×D312yes—
126C22×C4×D3C2×D318yescomplemented
127C22×Dic6—31no—
128C22×Dic6—31no—
129C22×Dic6—61no—
130C3×#117—38no—
131C2×C3×C4⋊C4—32no—
132C2×C3×C22⋊C4—32no—
133C2×C3×C42—32no—
134#953—316no—
135C2×#217—34no—
136C2×#217C2×D312yes—
137#930—316no—
138#929—316no—
139C4×#67—332no—
140C2×(C2×D3)⋊C4—34no—
141C2×(C2×D3)⋊C4—34no—
142C2×(C2×D3)⋊C4—34no—
143#926C2×D318yescomplemented
144C2×C4⋊Dic3—34no—
145C2×C4⋊Dic3C2×D312yescomplemented
146#924—316no—
147C2×Dic3⋊C4—34no—
148C2×C4×Dic3C2×D312yescomplemented
149#897—316no—
150#895—316no—
151#886—316no—
152#882—316no—
153C4×D12—332no—
154C23×C32—24no—
155C23×C32C2×D414yes—
156C23×C32C2412yes—
157C23×C32C2411yescharacteristic
158C22×C3⋊D3—24no—
159C22×C3⋊D3—28no—
160C22×C3⋊D3C2414yes—
161C22×C3×D3—232no—
162C22×C3×D3—28no—
163C22×C3×D3—24no—
164C22×C3×D3—24no—
165C22×C3×D3—216no—
166C22×C3×D3#4118yescomplemented
167C22×C3×D3C2414yes—
168C2×C32×C4C2×D414yes—
169C2×C32×C4C2×D414yes—
170C2×C32×C4C2×D4116yescomplemented
171C2×C32×C4C2412yes—
172C2×C32×C4C2412yes—
173#638—216no—
174C2×C3⋊Dic3—24no—
175C2×C3⋊Dic3C2414yes—
176C4⋊(C3⋊D3)—28no—
177C4×C3⋊D3—216no—
178#634—28no—
179C2×C3×Dic3—28no—
180C2×C3×Dic3—24no—
181C2×C3×Dic3—28no—
182C2×C3×Dic3C2418yes—
183C2×C3×Dic3C2414yes—
184C3×C4×D3—216no—
185C3×C4×D3—216no—
186#626—232no—
187C22×#41—91no—
188C24×C4—31no—
189#525—916no—
190C2×#123—92no—
191C2×C22⋊Q8—92no—
192C2×#121—92no—
193C2×#120—92no—
194C2×C4×D4—94no—
195C2×#117—31no—
196C24×C3—21no—
197C24×C3—32no—
198C24×C3—34no—
199C24×C3—68no—
200C24×C3—64no—
201C24×C3C22×D311yescharacteristic
202C24×C3C22×D311yescharacteristic
203C23×D3—24no—
204C23×D3—28no—
205C23×D3—32no—
206C23×D3—32no—
207C23×D3—62no—
208C23×D3C22×D314yes—
209C23×D3C22×D312yes—
210C22×C3×C4—28no—
211C22×C3×C4—21no—
212C22×C3×C4—24no—
213C22×C3×C4—21no—
214C22×C3×C4—32no—
215C22×C3×C4—34no—
216C22×C3×C4—34no—
217C22×C3×C4—38no—
218C22×C3×C4—38no—
219C22×C3×C4—64no—
220C22×C3×C4—68no—
221C22×C3×C4—68no—
222C22×C3×C4—632no—
223C22×C3×C4D1218yescomplemented
224C22×C3×C4#6718yescomplemented
225C22×C3×C4C22×D311yescharacteristic
226C22×C3×C4C22×D314yes—
227C22×C3×C4C22×D311yescharacteristic
228C22×C3×C4C22×D314yes—
229C22×C3×C4C22×D311yescharacteristic
230C22×C3×C4C22×D311yescharacteristic
231C2×#67—38no—
232C2×#67—38no—
233C2×#67—316no—
234C2×#67—68no—
235C2×#67—616no—
236C2×#67—616no—
237C2×#67—68no—
238C2×#67—68no—
239C22×Dic3—24no—
240C22×Dic3—32no—
241C22×Dic3—32no—
242C22×Dic3—62no—
243C22×Dic3C22×D314yes—
244C22×Dic3C22×D314yes—
245C22×Dic3C22×D312yes—
246#235—664no—
247#235—632no—
248#235—632no—
249C2×D12—316no—
250C2×D12—34no—
251C2×D12—34no—
252C2×D12—64no—
253C2×D12—68no—
254C2×D12—616no—
255C2×D12—64no—
256C2×D12—64no—
257C2×C4×D3—28no—
258C2×C4×D3—28no—
259C2×C4×D3—232no—
260C2×C4×D3—38no—
261C2×C4×D3—38no—
262C2×C4×D3—68no—
263C2×C4×D3—616no—
264C2×C4×D3—68no—
265C2×C4×D3—68no—
266C2×C4×D3C22×D318yes—
267C2×C4×D3C22×D318yes—
268C2×Dic6—34no—
269C2×Dic6—34no—
270C2×Dic6—64no—
271C2×Dic6—68no—
272C2×Dic6—64no—
273C2×Dic6—64no—
274C3×C4⋊C4—38no—
275C3×C22⋊C4—38no—
276C3×C42—38no—
277#217—316no—
278#217C22×D318yes—
279(C2×D3)⋊C4—316no—
280(C2×D3)⋊C4—316no—
281(C2×D3)⋊C4—316no—
282C4⋊Dic3—316no—
283C4⋊Dic3C22×D318yescomplemented
284Dic3⋊C4—316no—
285C4×Dic3C22×D318yescomplemented
286C22×C32—28no—
287C22×C32—24no—
288C22×C32C22×D414yes—
289C22×C32C22×D412yes—
290C22×C32C2×#4114yes—
291C22×C32C2511yescharacteristic
292C2×C3⋊D3—24no—
293C2×C3⋊D3—28no—
294C2×C3⋊D3—48no—
295C2×C3×D3—232no—
296C2×C3×D3—216no—
297C2×C3×D3—24no—
298C2×C3×D3—24no—
299C2×C3×D3C2×#4118yescomplemented
300C32×C4C22×D414yes—
301C32×C4C22×D414yes—
302C3⋊Dic3—24no—
303C3×Dic3—24no—
304C3×Dic3—28no—
305C25—31no—
306C2×#41—98no—
307C2×#41—188no—
308C22×Q8—91no—
309C22×D4—94no—
310C22×D4—92no—
311C22×D4—91no—
312C23×C4—31no—
313C23×C4—32no—
314C23×C4—38no—
315C23×C4—32no—
316C23×C4—68no—
317C23×C4—92no—
318C23×C4D3211yescharacteristic
319#123—916no—
320C22⋊Q8—916no—
321#121—916no—
322#120—916no—
323C4×D4—932no—
324#117—38no—
325C2×C4⋊C4—32no—
326C2×C4⋊C4—94no—
327C2×C22⋊C4—32no—
328C2×C22⋊C4—94no—
329C2×C22⋊C4—94no—
330C2×C42—32no—
331C23×C3—24no—
332C23×C3—24no—
333C23×C3—21no—
334C23×C3—22no—
335C23×C3—24no—
336C23×C3—38no—
337C23×C3—34no—
338C23×C3—44no—
339C23×C3—616no—
340C23×C3—632no—
341C23×C3—68no—
342C23×C3—64no—
343C23×C3—64no—
344C23×C3C2×D1214yes—
345C23×C3C2×#6714yes—
346C23×C3C23×D312yes—
347C23×C3C23×D312yes—
348C23×C3C23×D311yescharacteristic
349C23×C3C23×D311yescharacteristic
350C22×D3—232no—
351C22×D3—24no—
352C22×D3—28no—
353C22×D3—24no—
354C22×D3—216no—
355C22×D3—34no—
356C22×D3—34no—
357C22×D3—64no—
358C22×D3—68no—
359C22×D3—64no—
360C22×D3—68no—
361C22×D3—68no—
362C22×D3—64no—
363C22×D3—128no—
364C22×D3#23518yescomplemented
365C22×D3C23×D314yes—
366C2×C3×C4—22no—
367C2×C3×C4—22no—
368C2×C3×C4—24no—
369C2×C3×C4—24no—
370C2×C3×C4—216no—
371C2×C3×C4—34no—
372C2×C3×C4—38no—
373C2×C3×C4—68no—
374C2×C3×C4—64no—
375C2×C3×C4—68no—
376C2×C3×C4—616no—
377C2×C3×C4—616no—
378C2×C3×C4C2×D1214yes—
379C2×C3×C4C2×D1214yes—
380C2×C3×C4C2×D12116yescomplemented
381C2×C3×C4C2×#6714yes—
382C2×C3×C4C2×#6714yes—
383C2×C3×C4C2×#67116yescomplemented
384C2×C3×C4C23×D312yes—
385C2×C3×C4C23×D312yes—
386C2×C3×C4C23×D312yes—
387C2×C3×C4C23×D312yes—
388#67—632no—
389#67—632no—
390#67—616no—
391#67—616no—
392C2×Dic3—28no—
393C2×Dic3—28no—
394C2×Dic3—24no—
395C2×Dic3—34no—
396C2×Dic3—34no—
397C2×Dic3—64no—
398C2×Dic3—68no—
399C2×Dic3—64no—
400C2×Dic3—64no—
401C2×Dic3C23×D318yes—
402C2×Dic3C23×D314yes—
403D12—616no—
404D12—632no—
405D12—68no—
406D12—68no—
407C4×D3—216no—
408C4×D3—216no—
409C4×D3—632no—
410C4×D3—616no—
411C4×D3—616no—
412Dic6—616no—
413Dic6—68no—
414Dic6—68no—
415C2×C32—24no—
416C2×C32#52514yescomplemented
417C2×C32C23×D411yescharacteristic
418C2×C32C22×#4112yes—
419C3⋊D3—44no—
420C3×D3—28no—
421C24—32no—
422C24—34no—
423C24—68no—
424C24—64no—
425C24—92no—
426C24C2×D3211yescharacteristic
427#41—1832no—
428C2×Q8—94no—
429C2×Q8—184no—
430C2×D4—916no—
431C2×D4—98no—
432C2×D4—94no—
433C2×D4—1816no—
434C2×D4—188no—
435C2×D4—184no—
436C22×C4—34no—
437C22×C4—32no—
438C22×C4—34no—
439C22×C4—38no—
440C22×C4—38no—
441C22×C4—64no—
442C22×C4—68no—
443C22×C4—68no—
444C22×C4—632no—
445C22×C4—92no—
446C22×C4—98no—
447C22×C4—188no—
448C22×C4#62618yescomplemented
449C22×C4C2×D3211yescharacteristic
450C22×C4C2×D3214yes—
451C22×C4C2×D3211yescharacteristic
452C4⋊C4—38no—
453C4⋊C4—916no—
454C22⋊C4—38no—
455C22⋊C4—916no—
456C22⋊C4—916no—
457C42—38no—
458C22×C3—24no—
459C22×C3—24no—
460C22×C3—28no—
461C22×C3—28no—
462C22×C3—24no—
463C22×C3—22no—
464C22×C3—24no—
465C22×C3—21no—
466C22×C3—38no—
467C22×C3—44no—
468C22×C3—48no—
469C22×C3—632no—
470C22×C3—64no—
471C22×C3—64no—
472C22×C3—616no—
473C22×C3C22×D1214yes—
474C22×C3C22×D1212yes—
475C22×C3C2×#23514yes—
476C22×C3D3×#4114yes—
477C22×C3C22×#6714yes—
478C22×C3C22×#6712yes—
479C22×C3C24×D311yescharacteristic
480C22×C3C24×D311yescharacteristic
481C2×D3—232no—
482C2×D3—24no—
483C2×D3—24no—
484C2×D3—216no—
485C2×D3—68no—
486C2×D3—64no—
487C2×D3—68no—
488C2×D3—68no—
489C2×D3—64no—
490C2×D3—128no—
491C2×D3—1216no—
492C2×D3—128no—
493C2×D3—128no—
494C2×D3C2×#23518yescomplemented
495C3×C4—24no—
496C3×C4—24no—
497C3×C4—64no—
498C3×C4—68no—
499C3×C4C22×D1214yes—
500C3×C4C22×D1214yes—
501C3×C4C22×#6714yes—
502C3×C4C22×#6714yes—
503Dic3—28no—
504Dic3—24no—
505Dic3—68no—
506Dic3—64no—
507Dic3—64no—
508C32C2×#52511yescharacteristic, complemented, Sylow
509C23—24no—
510C23—38no—
511C23—34no—
512C23—616no—
513C23—632no—
514C23—64no—
515C23—68no—
516C23—64no—
517C23—94no—
518C23—188no—
519C23—184no—
520C23C2×#62614yes—
521C23C22×D3212yes—
522C23C22×D3211yescharacteristic
523Q8—188no—
524D4—1832no—
525D4—1816no—
526D4—188no—
527C2×C4—38no—
528C2×C4—34no—
529C2×C4—68no—
530C2×C4—68no—
531C2×C4—64no—
532C2×C4—616no—
533C2×C4—616no—
534C2×C4—94no—
535C2×C4—184no—
536C2×C4—1816no—
537C2×C4C2×#62614yes—
538C2×C4C2×#62614yes—
539C2×C4C2×#626116yescomplemented
540C2×C4C22×D3212yes—
541C2×C4C22×D3212yes—
542C2×C3—24no—
543C2×C3—24no—
544C2×C3—22no—
545C2×C3—21no—
546C2×C3—24no—
547C2×C3—44no—
548C2×C3—68no—
549C2×C3#552414yescomplemented
550C2×C3#579114yescomplemented
551C2×C3C23×D1211yescharacteristic
552C2×C3C22×#23512yes—
553C2×C3C2×D3×#4112yes—
554C2×C3C23×#6711yescharacteristic
555D3—28no—
556D3—128no—
557D3—124no—
558D3—124no—
559C22—24no—
560C22—28no—
561C22—38no—
562C22—632no—
563C22—64no—
564C22—64no—
565C22—616no—
566C22—188no—
567C22—184no—
568C22—368no—
569C22D3×#23514yes—
570C22C22×#62614yes—
571C22C22×#62612yes—
572C22C23×D3211yescharacteristic
573C4—68no—
574C4—64no—
575C4—184no—
576C4C22×#62614yes—
577C4C22×#62614yes—
578C3—21no—
579C3C2×#552411yescharacteristic, complemented
580C3C2×#579111yescharacteristic, complemented
581C2—24no—
582C2—68no—
583C2—364no—
584C2#1059502314yesdirect product factor
585C2C2×D3×#23512yes—
586C2C23×#62611yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×#525
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×#3828C2semidirect
2. C23×C3×C4×D3C2semidirect
3. C2×C3×#926C2semidirect
4. C2×#63977C2semidirect
5. C2×#63966C2semidirect
6. #10595023C2direct (N × H)
7. C2×#63909C2semidirect
8. C2×C4×#626C2semidirect
9. C2×#63857C2semidirect
16. C2×#3828C22semidirect
17. C22×C4⋊(C3⋊D3)C22semidirect
18. C22×C4×C3⋊D3C22semidirect
19. C22×#634C22semidirect
24. C22×C3×C4×D3C22semidirect
27. C3×#926C22semidirect
28. C2×C3×C4⋊Dic3C22semidirect
29. C2×C3×C4×Dic3C22semidirect
30. #63977C22semidirect
31. #63966C22semidirect
32. C2×Dic3⋊Dic3C22semidirect
33. C2×#3722C22semidirect
35. #63909C22semidirect
36. C4×#626C22semidirect
37. #63857C22semidirect
42. C23×C4×D3D3semidirect
49. C2×#926D3semidirect
63. C22×C32×C4D4semidirect
72. C2×C4⋊(C3⋊D3)C23semidirect
74. C2×C4×C3⋊D3C23semidirect
76. C2×#634C23semidirect
89. C3×C4⋊Dic3C23semidirect
90. C3×C4×Dic3C23semidirect
91. Dic3⋊Dic3C23semidirect
92. #3722C23semidirect
126. C22×C4×D3C2×D3semidirect
143. #926C2×D3semidirect
145. C2×C4⋊Dic3C2×D3semidirect
148. C2×C4×Dic3C2×D3semidirect
166. C22×C3×D3#41semidirect
170. C2×C32×C4C2×D4semidirect
223. C22×C3×C4D12semidirect
224. C22×C3×C4#67semidirect
283. C4⋊Dic3C22×D3semidirect
285. C4×Dic3C22×D3semidirect
299. C2×C3×D3C2×#41semidirect
364. C22×D3#235semidirect
380. C2×C3×C4C2×D12semidirect
383. C2×C3×C4C2×#67semidirect
416. C2×C32#525semidirect
448. C22×C4#626semidirect
494. C2×D3C2×#235semidirect
508. C32C2×#525semidirect
539. C2×C4C2×#626semidirect
549. C2×C3#5524semidirect
550. C2×C3#5791semidirect
579. C3C2×#5524semidirect
580. C3C2×#5791semidirect
584. C2#10595023direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38282
C23×C3×C4×D32
C2×C3×#9262
C2×#639772
C2×#639662
#105950232
C2×#639092
C2×C4×#6262
C2×#638572
C2×#57913
C2×#55243