Finite Group Databasebeta

← C2×#10595165 #11900772

Subgroups — C2×#10595165 #11900772

Order 1152.

3901 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3830C211yesmaximal, characteristic, complemented
2C22×#3805C211yesmaximal, characteristic, complemented
3C2×C3×#939C212yesmaximal, complemented
4C2×#63979C211yesmaximal, characteristic, complemented
5C2×#63978C212yesmaximal, complemented
6C2×#67⋊Dic3C212yesmaximal, complemented
7C22×Dic32C211yesmaximal, characteristic, complemented
8C2×#63953C211yesmaximal, characteristic, complemented
9#10595165C2116yesmaximal, direct product factor
10C2×#63913C211yesmaximal, characteristic, complemented
11C2×#63881C212yesmaximal, complemented
12C2×#63840C211yesmaximal, characteristic, complemented
13C2×#5596—32nomaximal
14C22×C32×D4C2211yescharacteristic
15C22×#638C2211yescharacteristic
16C22×#638C2211yescharacteristic
17C23×C3⋊Dic3C2211yescharacteristic
18C23×C3⋊Dic3C2211yescharacteristic
19C2×#3830—28no—
20C2×#3830C2218yescomplemented
21C22×C4×C3⋊D3C2211yescharacteristic
22C22×#634C2211yescharacteristic
23C22×C3×#67C2212yes—
24C22×C3×#67C2212yes—
25C23×C3×Dic3C2212yes—
26C22×#627C2211yescharacteristic
27C22×#626C2212yes—
28C22×#625C2211yescharacteristic
29C2×#3805—28no—
30C2×#3805C2218yescomplemented
31C22×D3×Dic3C2212yes—
32C2×C3×#217C2212yes—
33C3×#939C22116yescomplemented
34C2×C3×(C2×D3)⋊C4C2212yes—
35C2×C3×Dic3⋊C4C2212yes—
36#63979C2218yescomplemented
37#63978C22116yescomplemented
38#67⋊Dic3C22116yescomplemented
39C2×Dic3⋊Dic3C2212yes—
40C2×#3722C2212yes—
41C2×(C2×D3)⋊Dic3C2212yes—
42C2×Dic32C2212yes—
43C2×Dic32C2211yescharacteristic
44C2×Dic32C2211yescharacteristic
45C2×Dic32C2218yescomplemented
46#63953C2218yescomplemented
47#63913C2218yescomplemented
48#63881C22116yescomplemented
49#63840C2218yescomplemented
50C22×#237—32no—
51C22×#237—32no—
52C22×#237—61no—
53C2×C3×#121—32no—
54C2×#940—32no—
55C2×#939—32no—
56C2×#939D312yescomplemented
57C2×D4×Dic3—32no—
58C2×#930—32no—
59C22×C4×Dic3—32no—
60#5596—332no—
61C2×#893—32no—
62C2×#888—32no—
63C2×#885—32no—
64C2×#885—32no—
65C2×#67⋊C4—32no—
66C2×#67⋊C4—32no—
67C24×C32C2311yescharacteristic
68C24×C32C2311yescharacteristic
69C23×C3⋊D3C2311yescharacteristic
70C23×C3×D3C2312yes—
71C2×C32×D4—24no—
72C2×C32×D4C2314yes—
73C22×C32×C4C2311yescharacteristic
74C2×#638—24no—
75C2×#638—24no—
76C2×#638C2314yes—
77C2×#638C2314yes—
78C22×C3⋊Dic3—24no—
79C22×C3⋊Dic3D418yescomplemented
80C22×C3⋊Dic3C2311yescharacteristic
81C22×C3⋊Dic3C2314yes—
82C22×C3⋊Dic3C2311yescharacteristic
83C22×C3⋊Dic3C2311yescharacteristic
84C22×C3⋊Dic3C2314yes—
85#3830—232no—
86C2×C4×C3⋊D3—24no—
87C2×C4×C3⋊D3C2314yes—
88C2×#634—24no—
89C2×#634C2314yes—
90C2×C3×#67—28no—
91C2×C3×#67—28no—
92C2×C3×#67C2318yes—
93C2×C3×#67C2318yes—
94C22×C3×Dic3—28no—
95C22×C3×Dic3C2312yes—
96C22×C3×Dic3C2312yes—
97C22×C3×Dic3C2318yes—
98C22×C3×Dic3C2312yes—
99C2×#627—24no—
100C2×#627C2314yes—
101C2×#626—28no—
102C2×#626C2318yes—
103C2×#625—24no—
104C2×#625C2314yes—
105#3805—232no—
106C2×D3×Dic3—28no—
107C2×D3×Dic3C2318yes—
108C3×#217C2318yes—
109C3×(C2×D3)⋊C4C2318yes—
110C3×Dic3⋊C4C2318yes—
111Dic3⋊Dic3C2318yes—
112#3722C2318yes—
113(C2×D3)⋊Dic3C2318yes—
114Dic32C2314yes—
115Dic32C2318yes—
116Dic32C2314yes—
117C2×#532—91noSylow
118C22×C3×D4—21no—
119C22×C3×D4—32no—
120C22×C3×D4—32no—
121C22×C3×D4C2×D312yes—
122C23×C3×C4—32no—
123C22×#67—32no—
124C22×#67—32no—
125C22×#67—32no—
126C22×#67—32no—
127C22×#67—61no—
128C22×#67—61no—
129C22×#67C2×D312yes—
130C22×#67C2×D312yes—
131C23×Dic3—32no—
132C23×Dic3—32no—
133C23×Dic3—32no—
134C23×Dic3—61no—
135C23×Dic3—61no—
136C23×Dic3C2×D312yes—
137C2×#237—316no—
138C2×#237—316no—
139C2×#237—68no—
140C2×#237—616no—
141C2×#237—616no—
142C2×#237—616no—
143C22×D12—32no—
144C22×C4×D3—32no—
145C22×C4×D3—32no—
146C22×C4×D3—61no—
147C22×Dic6—32no—
148C22×Dic6—32no—
149C22×Dic6—61no—
150C3×#121—316no—
151C2×C3×C4⋊C4—32no—
152C2×C3×C22⋊C4—32no—
153C2×C3×C22⋊C4—32no—
154C2×#217—32no—
155C2×#217C2×D312yes—
156#940—316no—
157#939—316no—
158#939C2×D3116yescomplemented
159D4×Dic3—316no—
160#930—316no—
161C2×(C2×D3)⋊C4—32no—
162C2×(C2×D3)⋊C4—32no—
163C2×(C2×D3)⋊C4—32no—
164C2×(C2×D3)⋊C4C2×D312yes—
165C2×C4⋊Dic3—32no—
166C2×Dic3⋊C4—32no—
167C2×Dic3⋊C4C2×D312yes—
168C2×C4×Dic3—32no—
169C2×C4×Dic3—32no—
170C2×C4×Dic3—32no—
171C2×C4×Dic3—32no—
172C2×C4×Dic3—316no—
173#893—316no—
174#888—316no—
175#885—316no—
176#885—316no—
177#67⋊C4—316no—
178#67⋊C4—316no—
179C23×C32—22no—
180C23×C32—24no—
181C23×C32—24no—
182C23×C32C2×D414yes—
183C23×C32C2412yes—
184C23×C32C2412yes—
185C23×C32C2411yescharacteristic
186C22×C3⋊D3—22no—
187C22×C3⋊D3—24no—
188C22×C3⋊D3C2412yes—
189C22×C3×D3—24no—
190C22×C3×D3—24no—
191C22×C3×D3—24no—
192C22×C3×D3C2414yes—
193C32×D4—28no—
194C2×C32×C4—22no—
195C2×C32×C4C2412yes—
196#638—28no—
197#638—28no—
198C2×C3⋊Dic3—22no—
199C2×C3⋊Dic3—28no—
200C2×C3⋊Dic3C2×D414yes—
201C2×C3⋊Dic3C2×D414yes—
202C2×C3⋊Dic3C2×D4116yescomplemented
203C2×C3⋊Dic3C2412yes—
204C2×C3⋊Dic3C2412yes—
205C2×C3⋊Dic3C2412yes—
206C4×C3⋊D3—28no—
207#634—28no—
208C3×#67—216no—
209C3×#67—216no—
210C2×C3×Dic3—24no—
211C2×C3×Dic3—24no—
212C2×C3×Dic3—216no—
213C2×C3×Dic3#4118yescomplemented
214C2×C3×Dic3C2414yes—
215C2×C3×Dic3C2414yes—
216C2×C3×Dic3C2414yes—
217#627—28no—
218#626—216no—
219#625—28no—
220D3×Dic3—216no—
221C22×#41—91no—
222C22×#41—91no—
223#532—916no—
224C2×C4⋊Q8—91no—
225C2×#127—91no—
226C2×#124—91no—
227C2×#124—91no—
228C2×#121—32no—
229C2×#121—92no—
230C2×C4×D4—92no—
231C2×C4×D4—92no—
232C22×C42—91no—
233C24×C3—21no—
234C24×C3—21no—
235C24×C3—32no—
236C24×C3C22×D312yes—
237C24×C3C22×D312yes—
238C23×D3—32no—
239C23×D3—61no—
240C23×D3C22×D312yes—
241C2×C3×D4—28no—
242C2×C3×D4—28no—
243C2×C3×D4—24no—
244C2×C3×D4—38no—
245C2×C3×D4—38no—
246C2×C3×D4—68no—
247C2×C3×D4—68no—
248C2×C3×D4C22×D318yes—
249C22×C3×C4—21no—
250C22×C3×C4—32no—
251C22×C3×C4—32no—
252C22×C3×C4—38no—
253C22×C3×C4—32no—
254C22×C3×C4—68no—
255C22×C3×C4C22×D312yes—
256C2×#67—28no—
257C2×#67—28no—
258C2×#67—38no—
259C2×#67—38no—
260C2×#67—38no—
261C2×#67—38no—
262C2×#67—64no—
263C2×#67—64no—
264C2×#67—68no—
265C2×#67—68no—
266C2×#67—68no—
267C2×#67—68no—
268C2×#67—68no—
269C2×#67—68no—
270C2×#67C22×D318yes—
271C2×#67C22×D318yes—
272C22×Dic3—28no—
273C22×Dic3—316no—
274C22×Dic3—32no—
275C22×Dic3—32no—
276C22×Dic3—38no—
277C22×Dic3—38no—
278C22×Dic3—32no—
279C22×Dic3—38no—
280C22×Dic3—61no—
281C22×Dic3—61no—
282C22×Dic3—61no—
283C22×Dic3—68no—
284C22×Dic3—64no—
285C22×Dic3—64no—
286C22×Dic3—68no—
287C22×Dic3—68no—
288C22×Dic3—68no—
289C22×Dic3C22×D312yes—
290C22×Dic3C22×D318yes—
291C22×Dic3C22×D312yes—
292C22×Dic3C22×D312yes—
293#237—664no—
294#237—664no—
295#237—664no—
296C2×D12—38no—
297C2×D12—68no—
298C2×C4×D3—38no—
299C2×C4×D3—38no—
300C2×C4×D3—64no—
301C2×C4×D3—68no—
302C2×C4×D3—68no—
303C2×C4×D3—68no—
304C2×Dic6—38no—
305C2×Dic6—38no—
306C2×Dic6—64no—
307C2×Dic6—68no—
308C2×Dic6—68no—
309C2×Dic6—68no—
310C3×C4⋊C4—38no—
311C3×C22⋊C4—38no—
312C3×C22⋊C4—38no—
313#217—38no—
314#217C22×D318yes—
315(C2×D3)⋊C4—38no—
316(C2×D3)⋊C4—38no—
317(C2×D3)⋊C4—38no—
318(C2×D3)⋊C4C22×D318yes—
319C4⋊Dic3—38no—
320Dic3⋊C4—38no—
321Dic3⋊C4C22×D318yes—
322C4×Dic3—38no—
323C4×Dic3—38no—
324C4×Dic3—38no—
325C4×Dic3—38no—
326C22×C32—22no—
327C22×C32—28no—
328C22×C32—24no—
329C22×C32—24no—
330C22×C32—44no—
331C22×C32C22×D414yes—
332C22×C32C22×D412yes—
333C22×C32C2×#4114yes—
334C22×C32C2511yescharacteristic
335C2×C3⋊D3—22no—
336C2×C3⋊D3—24no—
337C2×C3⋊D3—44no—
338C2×C3×D3—24no—
339C2×C3×D3—24no—
340C2×C3×D3—24no—
341C2×C3×D3—48no—
342C32×C4—22no—
343C3⋊Dic3—22no—
344C3⋊Dic3C22×D414yes—
345C3⋊Dic3C22×D414yes—
346C3×Dic3—24no—
347C3×Dic3—24no—
348C3×Dic3C2×#4118yescomplemented
349C2×#41—98no—
350C2×#41—98no—
351C2×#41—188no—
352C2×#41—188no—
353C22×Q8—91no—
354C22×Q8—91no—
355C22×D4—32no—
356C22×D4—32no—
357C22×D4—92no—
358C22×D4—91no—
359C22×D4—91no—
360C22×D4—91no—
361C22×D4D3211yescharacteristic
362C23×C4—32no—
363C23×C4—92no—
364C23×C4—91no—
365C23×C4—91no—
366C23×C4—91no—
367C4⋊Q8—98no—
368#127—98no—
369#124—98no—
370#124—98no—
371#121—316no—
372#121—916no—
373C4×D4—916no—
374C4×D4—916no—
375C2×C4⋊C4—32no—
376C2×C4⋊C4—92no—
377C2×C22⋊C4—32no—
378C2×C22⋊C4—32no—
379C2×C22⋊C4—92no—
380C2×C22⋊C4—92no—
381C2×C42—92no—
382C2×C42—91no—
383C2×C42—91no—
384C2×C42—98no—
385C23×C3—24no—
386C23×C3—24no—
387C23×C3—24no—
388C23×C3—24no—
389C23×C3—24no—
390C23×C3—24no—
391C23×C3—22no—
392C23×C3—22no—
393C23×C3—21no—
394C23×C3—24no—
395C23×C3—34no—
396C23×C3—44no—
397C23×C3—44no—
398C23×C3—64no—
399C23×C3—64no—
400C23×C3—64no—
401C23×C3D3×D418yes—
402C23×C3C23×D314yes—
403C23×C3C23×D314yes—
404C23×C3C23×D312yes—
405C22×D3—24no—
406C22×D3—24no—
407C22×D3—24no—
408C22×D3—34no—
409C22×D3—62no—
410C22×D3—64no—
411C22×D3—64no—
412C22×D3—64no—
413C22×D3—64no—
414C22×D3—124no—
415C22×D3C23×D314yes—
416C3×D4—216no—
417C3×D4—216no—
418C3×D4—616no—
419C3×D4—616no—
420C2×C3×C4—24no—
421C2×C3×C4—24no—
422C2×C3×C4—22no—
423C2×C3×C4—38no—
424C2×C3×C4—34no—
425C2×C3×C4—34no—
426C2×C3×C4—34no—
427C2×C3×C4—616no—
428C2×C3×C4—64no—
429C2×C3×C4—64no—
430C2×C3×C4C23×D314yes—
431#67—216no—
432#67—216no—
433#67—616no—
434#67—616no—
435#67—616no—
436#67—616no—
437#67—616no—
438#67—616no—
439C2×Dic3—24no—
440C2×Dic3—24no—
441C2×Dic3—216no—
442C2×Dic3—38no—
443C2×Dic3—38no—
444C2×Dic3—332no—
445C2×Dic3—34no—
446C2×Dic3—34no—
447C2×Dic3—34no—
448C2×Dic3—64no—
449C2×Dic3—64no—
450C2×Dic3—616no—
451C2×Dic3—62no—
452C2×Dic3—62no—
453C2×Dic3—62no—
454C2×Dic3—616no—
455C2×Dic3—616no—
456C2×Dic3—64no—
457C2×Dic3—616no—
458C2×Dic3—64no—
459C2×Dic3#23718yescomplemented
460C2×Dic3C23×D314yes—
461C2×Dic3C23×D314yes—
462C2×Dic3C23×D314yes—
463D12—616no—
464C4×D3—616no—
465C4×D3—616no—
466C4×D3—616no—
467Dic6—616no—
468Dic6—616no—
469Dic6—616no—
470C2×C32—24no—
471C2×C32—42no—
472C2×C32#53214yescomplemented
473C2×C32C23×D411yescharacteristic
474C2×C32C22×#4112yes—
475C3⋊D3—42no—
476C3×D3—44no—
477C24—32no—
478C24—91no—
479C24C2×D3211yescharacteristic
480C24C2×D3211yescharacteristic
481#41—1832no—
482#41—1832no—
483C2×Q8—94no—
484C2×Q8—94no—
485C2×Q8—184no—
486C2×Q8—184no—
487C2×D4—24no—
488C2×D4—38no—
489C2×D4—38no—
490C2×D4—68no—
491C2×D4—68no—
492C2×D4—98no—
493C2×D4—94no—
494C2×D4—94no—
495C2×D4—94no—
496C2×D4—188no—
497C2×D4—184no—
498C2×D4—184no—
499C2×D4—184no—
500C2×D4C2×D3214yes—
501C22×C4—32no—
502C22×C4—38no—
503C22×C4—32no—
504C22×C4—32no—
505C22×C4—68no—
506C22×C4—98no—
507C22×C4—94no—
508C22×C4—91no—
509C22×C4—91no—
510C22×C4—98no—
511C22×C4—94no—
512C22×C4—91no—
513C22×C4—94no—
514C22×C4—184no—
515C22×C4—188no—
516C22×C4—184no—
517C22×C4C2×D3211yescharacteristic
518C4⋊C4—38no—
519C4⋊C4—98no—
520C22⋊C4—38no—
521C22⋊C4—38no—
522C22⋊C4—98no—
523C22⋊C4—98no—
524C42—98no—
525C42—94no—
526C42—94no—
527C22×C3—24no—
528C22×C3—24no—
529C22×C3—216no—
530C22×C3—24no—
531C22×C3—24no—
532C22×C3—24no—
533C22×C3—24no—
534C22×C3—24no—
535C22×C3—22no—
536C22×C3—24no—
537C22×C3—21no—
538C22×C3—44no—
539C22×C3—48no—
540C22×C3—44no—
541C22×C3—48no—
542C22×C3—48no—
543C22×C3—64no—
544C22×C3—64no—
545C22×C3—64no—
546C22×C3—128no—
547C22×C3C2×D3×D418yes—
548C22×C3C2×D3×D414yes—
549C22×C3C2×#23714yes—
550C22×C3D3×#4114yes—
551C22×C3C24×D312yes—
552C2×D3—24no—
553C2×D3—24no—
554C2×D3—24no—
555C2×D3—48no—
556C2×D3—64no—
557C2×D3—64no—
558C2×D3—64no—
559C2×D3—64no—
560C2×D3—124no—
561C2×D3—128no—
562C2×D3—128no—
563C3×C4—24no—
564C3×C4—24no—
565C3×C4—38no—
566C3×C4—64no—
567C3×C4—64no—
568Dic3—24no—
569Dic3—24no—
570Dic3—38no—
571Dic3—38no—
572Dic3—64no—
573Dic3—64no—
574Dic3—64no—
575Dic3—64no—
576Dic3C2×#23718yescomplemented
577C32C2×#53211yescharacteristic, complemented, Sylow
578C23—24no—
579C23—24no—
580C23—22no—
581C23—34no—
582C23—64no—
583C23—64no—
584C23—64no—
585C23—92no—
586C23—184no—
587C23—182no—
588C23#381114yes—
589C23C22×D3212yes—
590C23C22×D3212yes—
591C23C22×D3211yescharacteristic
592Q8—188no—
593Q8—188no—
594D4—28no—
595D4—616no—
596D4—616no—
597D4—1816no—
598D4—188no—
599D4—188no—
600D4—188no—
601C2×C4—22no—
602C2×C4—38no—
603C2×C4—34no—
604C2×C4—34no—
605C2×C4—34no—
606C2×C4—616no—
607C2×C4—64no—
608C2×C4—64no—
609C2×C4—94no—
610C2×C4—94no—
611C2×C4—916no—
612C2×C4—92no—
613C2×C4—92no—
614C2×C4—92no—
615C2×C4—188no—
616C2×C4—1816no—
617C2×C4—188no—
618C2×C4—182no—
619C2×C4C22×D3212yes—
620C2×C3—28no—
621C2×C3—22no—
622C2×C3—24no—
623C2×C3—21no—
624C2×C3—44no—
625C2×C3—44no—
626C2×C3—44no—
627C2×C3—124no—
628C2×C3#559618yescomplemented
629C2×C3C22×D3×D412yes—
630C2×C3C22×#23712yes—
631C2×C3C2×D3×#4112yes—
632D3—44no—
633D3—124no—
634D3—124no—
635C22—24no—
636C22—28no—
637C22—24no—
638C22—22no—
639C22—44no—
640C22—64no—
641C22—64no—
642C22—64no—
643C22—128no—
644C22—184no—
645C22—182no—
646C22—364no—
647C22D3×#23714yes—
648C22C2×#381114yes—
649C22C2×#381112yes—
650C22C23×D3211yescharacteristic
651C4—22no—
652C4—38no—
653C4—64no—
654C4—64no—
655C4—94no—
656C4—94no—
657C4—182no—
658C3—21no—
659C3C2×#559612yescomplemented
660C2—24no—
661C2—42no—
662C2—124no—
663C2—362no—
664C2#1059516514yesdirect product factor
665C2C2×D3×#23712yes—
666C2C22×#381111yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C2×#532
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×#3830C2semidirect
2. C22×#3805C2semidirect
3. C2×C3×#939C2semidirect
4. C2×#63979C2semidirect
5. C2×#63978C2semidirect
6. C2×#67⋊Dic3C2semidirect
7. C22×Dic32C2semidirect
8. C2×#63953C2semidirect
9. #10595165C2direct (N × H)
10. C2×#63913C2semidirect
11. C2×#63881C2semidirect
12. C2×#63840C2semidirect
20. C2×#3830C22semidirect
30. C2×#3805C22semidirect
33. C3×#939C22semidirect
36. #63979C22semidirect
37. #63978C22semidirect
38. #67⋊Dic3C22semidirect
45. C2×Dic32C22semidirect
46. #63953C22semidirect
47. #63913C22semidirect
48. #63881C22semidirect
49. #63840C22semidirect
56. C2×#939D3semidirect
79. C22×C3⋊Dic3D4semidirect
158. #939C2×D3semidirect
202. C2×C3⋊Dic3C2×D4semidirect
213. C2×C3×Dic3#41semidirect
348. C3×Dic3C2×#41semidirect
459. C2×Dic3#237semidirect
472. C2×C32#532semidirect
576. Dic3C2×#237semidirect
577. C32C2×#532semidirect
628. C2×C3#5596semidirect
659. C3C2×#5596semidirect
664. C2#10595165direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38302
C22×#38052
C2×C3×#9392
C2×#639792
C2×#639782
C2×#67⋊Dic32
C22×Dic322
C2×#639532
#105951652
C2×#639132
C2×#638812
C2×#638402
C2×#55963