Finite Group Databasebeta

← C2×#10595034 #11900456

Subgroups — C2×#10595034 #11900456

Order 1152.

4441 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
1C23×C4×C3⋊D3C211yesmaximal, characteristic, complemented
2C22×C3×#235C211yesmaximal, characteristic, complemented
3C2×C3×#926C211yesmaximal, characteristic, complemented
4C2×#63981C212yesmaximal, complemented
5C2×#63962C212yesmaximal, complemented
6#10595034C2116yesmaximal, direct product factor
7C2×#63916C212yesmaximal, complemented
8C2×C4×#626C214yesmaximal, complemented
9C2×#63871C212yesmaximal, complemented
10C2×#5828—31nomaximal
11C2×#5524—31nomaximal
12C24×C3⋊D3C2211yescharacteristic
13C23×C32×C4C2211yescharacteristic
14C23×C3⋊Dic3C2211yescharacteristic
15C22×C4×C3⋊D3—28no—
16C22×C4×C3⋊D3C2212yes—
17C22×C4×C3⋊D3C2212yes—
18C22×C4×C3⋊D3C2218yescomplemented
19C22×C3×#67C2212yes—
20C2×C3×#235—28no—
21C2×C3×#235C2218yescomplemented
22C22×C3×D12C2211yescharacteristic, complemented
23C22×C3×C4×D3C2212yescomplemented
24C22×C3×Dic6C2211yescharacteristic, complemented
25C22×#626C2214yes—
26C2×C3×#217C2212yes—
27C3×#926C2218yescomplemented
28C2×C3×C4⋊Dic3C2212yescomplemented
29C2×C3×C4×Dic3C2212yescomplemented
30#63981C22116yescomplemented
31C2×Dic3⋊Dic3C2214yescomplemented
32C2×#3722C2214yes—
33#63962C22116yescomplemented
34C2×(C2×D3)⋊Dic3C2214yescomplemented
35#63916C22116yescomplemented
36C4×#626C22132yescomplemented
37#63871C22116yescomplemented
38C22×C3×#41—31no—
39C22×#235D311yescharacteristic, complemented
40C23×C4×D3—31no—
41C23×C4×D3—31no—
42C23×C4×D3—61no—
43C2×C3×#117—31no—
44#5828—316no—
45C2×#946—32no—
46C2×#938—32no—
47C2×#937—32no—
48C2×#935—32no—
49C2×C4×#67—34no—
50C2×#926D311yescharacteristic, complemented
51#5524—316no—
52C2×#897—32no—
53C2×#895—32no—
54C2×#886—32no—
55C2×#882—32no—
56C2×C4×D12—34no—
57C24×C32C2311yescharacteristic
58C23×C3⋊D3—24no—
59C23×C3⋊D3—28no—
60C23×C3⋊D3C2314yes—
61C23×C3⋊D3C2312yes—
62C23×C3×D3C2312yes—
63C22×C32×C4D418yescomplemented
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C22×C32×C4C2314yes—
67C22×C3⋊Dic3—24no—
68C22×C3⋊Dic3C2312yes—
69C22×C3⋊Dic3C2314yes—
70C2×C4×C3⋊D3—28no—
71C2×C4×C3⋊D3—28no—
72C2×C4×C3⋊D3—232no—
73C2×C4×C3⋊D3C2318yes—
74C2×C4×C3⋊D3C2318yes—
75C2×C3×#67—28no—
76C2×C3×#67C2318yes—
77C22×C3×Dic3C2314yes—
78C22×C3×Dic3C2312yes—
79C3×#235—232no—
80C2×C3×D12—24no—
81C2×C3×D12C2314yescomplemented
82C2×C3×C4×D3—28no—
83C2×C3×C4×D3C2318yescomplemented
84C2×C3×Dic6—24no—
85C2×C3×Dic6C2314yescomplemented
86C2×#626—216no—
87C2×#626C23116yes—
88C3×#217C2318yes—
89C3×C4⋊Dic3C2318yescomplemented
90C3×C4×Dic3C2318yescomplemented
91Dic3⋊Dic3C23116yescomplemented
92#3722C23116yes—
93(C2×D3)⋊Dic3C23116yescomplemented
94C2×#525—91noSylow
95C24×D3—31no—
96C24×D3—31no—
97C24×D3—61no—
98C2×C3×#41—38no—
99C2×C3×#41—68no—
100C22×C3×Q8—31no—
101C22×C3×D4—32no—
102C22×C3×D4—31no—
103C23×C3×C4—21no—
104C23×C3×C4—32no—
105C23×C3×C4C2×D311yescharacteristic
106C23×C3×C4C2×D311yescharacteristic
107C22×#67—34no—
108C22×#67C2×D312yes—
109C23×Dic3—31no—
110C23×Dic3—31no—
111C23×Dic3—61no—
112C2×#235—28no—
113C2×#235C2×D318yescomplemented
114C22×D12—34no—
115C22×D12C2×D311yescharacteristic, complemented
116C22×C4×D3—32no—
117C22×C4×D3—32no—
118C22×C4×D3—32no—
119C22×C4×D3—32no—
120C22×C4×D3—38no—
121C22×C4×D3—38no—
122C22×C4×D3—62no—
123C22×C4×D3—62no—
124C22×C4×D3—68no—
125C22×C4×D3—616no—
126C22×C4×D3—68no—
127C22×C4×D3—68no—
128C22×C4×D3C2×D312yescomplemented
129C22×Dic6C2×D311yescharacteristic, complemented
130C3×#117—38no—
131C2×C3×C4⋊C4—32no—
132C2×C3×C22⋊C4—32no—
133C2×C3×C42—32no—
134C2×#217—34no—
135C2×#217C2×D312yes—
136#946—316no—
137#938—316no—
138#937—316no—
139#935—316no—
140C4×#67—332no—
141C2×(C2×D3)⋊C4—34no—
142C2×(C2×D3)⋊C4—34no—
143C2×(C2×D3)⋊C4—34no—
144#926C2×D318yescomplemented
145C2×C4⋊Dic3—34no—
146C2×C4⋊Dic3C2×D312yescomplemented
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—232no—
159C22×C3⋊D3—28no—
160C22×C3⋊D3—24no—
161C22×C3⋊D3—24no—
162C22×C3⋊D3—216no—
163C22×C3⋊D3#4118yescomplemented
164C22×C3⋊D3C2414yes—
165C22×C3×D3—24no—
166C22×C3×D3—28no—
167C22×C3×D3C2414yes—
168C2×C32×C4C2×D414yes—
169C2×C32×C4C2×D414yes—
170C2×C32×C4C2×D4116yescomplemented
171C2×C32×C4C2412yes—
172C2×C32×C4C2412yes—
173C2×C3⋊Dic3—28no—
174C2×C3⋊Dic3—24no—
175C2×C3⋊Dic3C2414yes—
176C4×C3⋊D3—216no—
177C4×C3⋊D3—216no—
178C3×#67—216no—
179C2×C3×Dic3—24no—
180C2×C3×Dic3—28no—
181C2×C3×Dic3C2418yes—
182C2×C3×Dic3C2414yes—
183C3×D12—28no—
184C3×C4×D3—216no—
185C3×Dic6—28no—
186#626—232no—
187C22×#41—31no—
188C24×C4—91no—
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×C3C22×D311yescharacteristic
199C24×C3C22×D311yescharacteristic
200C23×D3—32no—
201C23×D3—32no—
202C23×D3—34no—
203C23×D3—34no—
204C23×D3—62no—
205C23×D3—64no—
206C23×D3—68no—
207C23×D3—68no—
208C23×D3—68no—
209C23×D3—616no—
210C23×D3—64no—
211C23×D3—64no—
212C23×D3C22×D312yes—
213C3×#41—632no—
214C2×C3×Q8—34no—
215C2×C3×Q8—64no—
216C2×C3×D4—38no—
217C2×C3×D4—34no—
218C2×C3×D4—68no—
219C2×C3×D4—64no—
220C22×C3×C4—28no—
221C22×C3×C4—21no—
222C22×C3×C4—24no—
223C22×C3×C4—21no—
224C22×C3×C4—32no—
225C22×C3×C4—34no—
226C22×C3×C4—38no—
227C22×C3×C4—68no—
228C22×C3×C4D1218yescomplemented
229C22×C3×C4#6718yescomplemented
230C22×C3×C4C22×D311yescharacteristic
231C22×C3×C4C22×D314yes—
232C22×C3×C4C22×D311yescharacteristic
233C22×C3×C4C22×D314yes—
234C22×C3×C4C22×D311yescharacteristic
235C22×C3×C4C22×D311yescharacteristic
236C2×#67—28no—
237C2×#67—316no—
238C2×#67—616no—
239C2×#67C22×D318yes—
240C22×Dic3—34no—
241C22×Dic3—32no—
242C22×Dic3—32no—
243C22×Dic3—34no—
244C22×Dic3—62no—
245C22×Dic3—64no—
246C22×Dic3—68no—
247C22×Dic3—64no—
248C22×Dic3—64no—
249C22×Dic3C22×D314yes—
250C22×Dic3C22×D312yes—
251#235—232no—
252C2×D12—24no—
253C2×D12—316no—
254C2×D12—616no—
255C2×D12C22×D314yescomplemented
256C2×C4×D3—28no—
257C2×C4×D3—38no—
258C2×C4×D3—38no—
259C2×C4×D3—38no—
260C2×C4×D3—38no—
261C2×C4×D3—68no—
262C2×C4×D3—68no—
263C2×C4×D3—616no—
264C2×C4×D3—616no—
265C2×C4×D3—664no—
266C2×C4×D3—68no—
267C2×C4×D3—68no—
268C2×C4×D3—632no—
269C2×C4×D3—68no—
270C2×C4×D3—68no—
271C2×C4×D3—632no—
272C2×C4×D3C22×D318yescomplemented
273C2×Dic6—24no—
274C2×Dic6C22×D314yescomplemented
275C3×C4⋊C4—38no—
276C3×C22⋊C4—38no—
277C3×C42—38no—
278#217—316no—
279#217C22×D318yes—
280(C2×D3)⋊C4—316no—
281(C2×D3)⋊C4—316no—
282(C2×D3)⋊C4—316no—
283C4⋊Dic3—316no—
284C4⋊Dic3C22×D318yescomplemented
285Dic3⋊C4—316no—
286C4×Dic3C22×D318yescomplemented
287C22×C32—28no—
288C22×C32—24no—
289C22×C32C22×D414yes—
290C22×C32C22×D412yes—
291C22×C32C2×#4114yes—
292C22×C32C2511yescharacteristic
293C2×C3⋊D3—232no—
294C2×C3⋊D3—216no—
295C2×C3⋊D3—24no—
296C2×C3⋊D3—24no—
297C2×C3⋊D3C2×#4118yescomplemented
298C2×C3×D3—24no—
299C2×C3×D3—28no—
300C2×C3×D3—48no—
301C32×C4C22×D414yes—
302C32×C4C22×D414yes—
303C3⋊Dic3—24no—
304C3×Dic3—24no—
305C3×Dic3—28no—
306C25—91no—
307C2×#41—38no—
308C2×#41—68no—
309C22×Q8—31no—
310C22×D4—32no—
311C22×D4—31no—
312C22×D4—94no—
313C23×C4—32no—
314C23×C4—91no—
315C23×C4—92no—
316C23×C4—98no—
317C23×C4—92no—
318C23×C4—188no—
319C23×C4D3211yescharacteristic
320#123—916no—
321C22⋊Q8—916no—
322#121—916no—
323#120—916no—
324C4×D4—932no—
325#117—38no—
326C2×C4⋊C4—32no—
327C2×C4⋊C4—94no—
328C2×C22⋊C4—32no—
329C2×C22⋊C4—94no—
330C2×C22⋊C4—94no—
331C2×C42—32no—
332C23×C3—28no—
333C23×C3—24no—
334C23×C3—24no—
335C23×C3—22no—
336C23×C3—21no—
337C23×C3—24no—
338C23×C3—34no—
339C23×C3—64no—
340C23×C3—68no—
341C23×C3C2×D1214yes—
342C23×C3C2×#6714yes—
343C23×C3C23×D312yes—
344C23×C3C23×D312yes—
345C23×C3C23×D311yescharacteristic
346C23×C3C23×D311yescharacteristic
347C22×D3—28no—
348C22×D3—24no—
349C22×D3—38no—
350C22×D3—38no—
351C22×D3—34no—
352C22×D3—34no—
353C22×D3—68no—
354C22×D3—64no—
355C22×D3—616no—
356C22×D3—616no—
357C22×D3—616no—
358C22×D3—68no—
359C22×D3—632no—
360C22×D3—664no—
361C22×D3—632no—
362C22×D3—632no—
363C22×D3—68no—
364C22×D3—68no—
365C22×D3—64no—
366C22×D3—64no—
367C22×D3—64no—
368C22×D3—68no—
369C22×D3—64no—
370C22×D3C23×D314yes—
371C3×Q8—68no—
372C3×D4—616no—
373C3×D4—68no—
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—24no—
377C2×C3×C4—24no—
378C2×C3×C4—216no—
379C2×C3×C4—34no—
380C2×C3×C4—38no—
381C2×C3×C4—64no—
382C2×C3×C4—68no—
383C2×C3×C4—616no—
384C2×C3×C4C2×D1214yes—
385C2×C3×C4C2×D1214yes—
386C2×C3×C4C2×D12116yescomplemented
387C2×C3×C4C2×#6714yes—
388C2×C3×C4C2×#6714yes—
389C2×C3×C4C2×#67116yescomplemented
390C2×C3×C4C23×D312yes—
391C2×C3×C4C23×D312yes—
392C2×C3×C4C23×D312yes—
393C2×C3×C4C23×D312yes—
394#67—216no—
395#67—632no—
396C2×Dic3—28no—
397C2×Dic3—24no—
398C2×Dic3—34no—
399C2×Dic3—34no—
400C2×Dic3—64no—
401C2×Dic3—616no—
402C2×Dic3—68no—
403C2×Dic3—68no—
404C2×Dic3—64no—
405C2×Dic3—68no—
406C2×Dic3—64no—
407C2×Dic3C23×D318yes—
408C2×Dic3C23×D314yes—
409D12—28no—
410D12—632no—
411C4×D3—216no—
412C4×D3—632no—
413C4×D3—632no—
414C4×D3—616no—
415C4×D3—616no—
416C4×D3—616no—
417C4×D3—616no—
418Dic6—28no—
419C2×C32—24no—
420C2×C32#52514yescomplemented
421C2×C32C23×D411yescharacteristic
422C2×C32C22×#4112yes—
423C3⋊D3—28no—
424C3×D3—44no—
425C24—32no—
426C24—92no—
427C24—94no—
428C24—188no—
429C24—184no—
430C24C2×D3211yescharacteristic
431#41—632no—
432C2×Q8—34no—
433C2×Q8—64no—
434C2×D4—38no—
435C2×D4—34no—
436C2×D4—68no—
437C2×D4—64no—
438C2×D4—916no—
439C2×D4—1816no—
440C22×C4—34no—
441C22×C4—32no—
442C22×C4—38no—
443C22×C4—68no—
444C22×C4—92no—
445C22×C4—94no—
446C22×C4—98no—
447C22×C4—98no—
448C22×C4—184no—
449C22×C4—188no—
450C22×C4—188no—
451C22×C4—1832no—
452C22×C4#62618yescomplemented
453C22×C4C2×D3211yescharacteristic
454C22×C4C2×D3214yes—
455C22×C4C2×D3211yescharacteristic
456C4⋊C4—38no—
457C4⋊C4—916no—
458C22⋊C4—38no—
459C22⋊C4—916no—
460C22⋊C4—916no—
461C42—38no—
462C22×C3—28no—
463C22×C3—216no—
464C22×C3—24no—
465C22×C3—24no—
466C22×C3—28no—
467C22×C3—28no—
468C22×C3—24no—
469C22×C3—24no—
470C22×C3—22no—
471C22×C3—21no—
472C22×C3—64no—
473C22×C3—68no—
474C22×C3—128no—
475C22×C3C22×D1214yes—
476C22×C3C22×D1212yes—
477C22×C3D3×#4114yes—
478C22×C3D3×#4114yes—
479C22×C3C22×#6714yes—
480C22×C3C22×#6712yes—
481C22×C3C24×D311yescharacteristic
482C22×C3C24×D311yescharacteristic
483C2×D3—28no—
484C2×D3—24no—
485C2×D3—38no—
486C2×D3—38no—
487C2×D3—48no—
488C2×D3—68no—
489C2×D3—68no—
490C2×D3—664no—
491C2×D3—632no—
492C2×D3—632no—
493C2×D3—68no—
494C2×D3—632no—
495C2×D3—64no—
496C2×D3—64no—
497C2×D3—64no—
498C2×D3—64no—
499C2×D3—616no—
500C2×D3—616no—
501C3×C4—24no—
502C3×C4—24no—
503C3×C4—64no—
504C3×C4—68no—
505C3×C4C22×D1214yes—
506C3×C4C22×D1214yes—
507C3×C4C22×#6714yes—
508C3×C4C22×#6714yes—
509Dic3—28no—
510Dic3—24no—
511Dic3—68no—
512Dic3—64no—
513Dic3—64no—
514C32C2×#52511yescharacteristic, complemented, Sylow
515C23—24no—
516C23—34no—
517C23—68no—
518C23—64no—
519C23—98no—
520C23—94no—
521C23—1816no—
522C23—1832no—
523C23—184no—
524C23—188no—
525C23—184no—
526C23C2×#62614yes—
527C23C22×D3212yes—
528C23C22×D3211yescharacteristic
529Q8—68no—
530D4—616no—
531D4—68no—
532D4—1832no—
533C2×C4—38no—
534C2×C4—34no—
535C2×C4—68no—
536C2×C4—64no—
537C2×C4—616no—
538C2×C4—94no—
539C2×C4—188no—
540C2×C4—184no—
541C2×C4—1816no—
542C2×C4—1816no—
543C2×C4C2×#62614yes—
544C2×C4C2×#62614yes—
545C2×C4C2×#626116yescomplemented
546C2×C4C22×D3212yes—
547C2×C4C22×D3212yes—
548C2×C3—28no—
549C2×C3—24no—
550C2×C3—24no—
551C2×C3—22no—
552C2×C3—21no—
553C2×C3—24no—
554C2×C3—124no—
555C2×C3#552414yescomplemented
556C2×C3#582814yescomplemented
557C2×C3C23×D1211yescharacteristic
558C2×C3C2×D3×#4112yes—
559C2×C3C2×D3×#4112yes—
560C2×C3C23×#6711yescharacteristic
561D3—44no—
562D3—616no—
563D3—68no—
564D3—68no—
565C22—24no—
566C22—28no—
567C22—68no—
568C22—64no—
569C22—98no—
570C22—128no—
571C22—1832no—
572C22—184no—
573C22—184no—
574C22—1816no—
575C22#6430614yes—
576C22C22×#62614yes—
577C22C22×#62612yes—
578C22C23×D3211yescharacteristic
579C4—68no—
580C4—64no—
581C4—184no—
582C4C22×#62614yes—
583C4C22×#62614yes—
584C3—21no—
585C3C2×#552411yescharacteristic, complemented
586C3C2×#582811yescharacteristic, complemented
587C2—24no—
588C2—124no—
589C2—188no—
590C2#1059503414yesdirect product factor
591C2C2×#6430612yes—
592C2C23×#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. C23×C4×C3⋊D3C2semidirect
2. C22×C3×#235C2semidirect
3. C2×C3×#926C2semidirect
4. C2×#63981C2semidirect
5. C2×#63962C2semidirect
6. #10595034C2direct (N × H)
7. C2×#63916C2semidirect
8. C2×C4×#626C2semidirect
9. C2×#63871C2semidirect
18. C22×C4×C3⋊D3C22semidirect
21. C2×C3×#235C22semidirect
22. C22×C3×D12C22semidirect
23. C22×C3×C4×D3C22semidirect
24. C22×C3×Dic6C22semidirect
27. C3×#926C22semidirect
28. C2×C3×C4⋊Dic3C22semidirect
29. C2×C3×C4×Dic3C22semidirect
30. #63981C22semidirect
31. C2×Dic3⋊Dic3C22semidirect
33. #63962C22semidirect
34. C2×(C2×D3)⋊Dic3C22semidirect
35. #63916C22semidirect
36. C4×#626C22semidirect
37. #63871C22semidirect
39. C22×#235D3semidirect
50. C2×#926D3semidirect
63. C22×C32×C4D4semidirect
81. C2×C3×D12C23semidirect
83. C2×C3×C4×D3C23semidirect
85. C2×C3×Dic6C23semidirect
89. C3×C4⋊Dic3C23semidirect
90. C3×C4×Dic3C23semidirect
91. Dic3⋊Dic3C23semidirect
93. (C2×D3)⋊Dic3C23semidirect
113. C2×#235C2×D3semidirect
115. C22×D12C2×D3semidirect
128. C22×C4×D3C2×D3semidirect
129. C22×Dic6C2×D3semidirect
144. #926C2×D3semidirect
146. C2×C4⋊Dic3C2×D3semidirect
148. C2×C4×Dic3C2×D3semidirect
163. C22×C3⋊D3#41semidirect
170. C2×C32×C4C2×D4semidirect
228. C22×C3×C4D12semidirect
229. C22×C3×C4#67semidirect
255. C2×D12C22×D3semidirect
272. C2×C4×D3C22×D3semidirect
274. C2×Dic6C22×D3semidirect
284. C4⋊Dic3C22×D3semidirect
286. C4×Dic3C22×D3semidirect
297. C2×C3⋊D3C2×#41semidirect
386. C2×C3×C4C2×D12semidirect
389. C2×C3×C4C2×#67semidirect
420. C2×C32#525semidirect
452. C22×C4#626semidirect
514. C32C2×#525semidirect
545. C2×C4C2×#626semidirect
555. C2×C3#5524semidirect
556. C2×C3#5828semidirect
585. C3C2×#5524semidirect
586. C3C2×#5828semidirect
590. C2#10595034direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C4×C3⋊D32
C22×C3×#2352
C2×C3×#9262
C2×#639812
C2×#639622
#105950342
C2×#639162
C2×C4×#6262
C2×#638712
C2×#58283
C2×#55243