Finite Group Databasebeta

← C2×#10595166 #11901147

Subgroups — C2×#10595166 #11901147

Order 1152.

3725 conjugacy classes of subgroups.

The subgroup lattice has 692 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×#63982C211yesmaximal, characteristic, complemented
5C2×#63980C211yesmaximal, characteristic, complemented
6C2×#63978C212yesmaximal, complemented
7C2×#63971C212yesmaximal, complemented
8C22×#3724C211yesmaximal, characteristic, complemented
9#10595166C2116yesmaximal, direct product factor
10C2×#63912C211yesmaximal, characteristic, complemented
11C2×#63896C212yesmaximal, complemented
12C2×#63865C211yesmaximal, characteristic, complemented
13C2×#5597—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#63982C2218yescomplemented
37#63980C2218yescomplemented
38#63978C22116yescomplemented
39#63971C22116yescomplemented
40C2×#3724C2211yescharacteristic
41C2×#3724C2212yes—
42C2×#3724C2211yescharacteristic
43C2×#3724C2218yescomplemented
44C2×Dic3⋊Dic3C2212yes—
45C2×#3722C2212yes—
46C2×(C2×D3)⋊Dic3C2212yes—
47#63912C2218yescomplemented
48#63896C22116yescomplemented
49#63865C2218yescomplemented
50C22×#237—32no—
51C22×#237—32no—
52C22×#237—61no—
53C2×C3×#121—32no—
54C2×#939—32no—
55C2×#939—32no—
56C2×#939—32no—
57C2×#939D312yescomplemented
58C2×#930—32no—
59C22×Dic3⋊C4—32no—
60#5597—332no—
61C2×#896—32no—
62C2×#896—32no—
63C2×#884—32no—
64C2×#884—32no—
65C2×#878—32no—
66C2×#878—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—44no—
92C2×C3×#67C2318yes—
93C2×C3×#67C2318yes—
94C22×C3×Dic3—44no—
95C22×C3×Dic3C2312yes—
96C22×C3×Dic3C2312yes—
97C22×C3×Dic3C2312yes—
98C22×C3×Dic3C2318yes—
99C2×#627—24no—
100C2×#627C2314yes—
101C2×#626—44no—
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—
111#3724C2314yes—
112#3724C2318yes—
113#3724C2314yes—
114Dic3⋊Dic3C2318yes—
115#3722C2318yes—
116(C2×D3)⋊Dic3C2318yes—
117C2×#537—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#939—316no—
157#939—316no—
158#939—316no—
159#939C2×D3116yescomplemented
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⋊C4—32no—
168C2×Dic3⋊C4—32no—
169C2×Dic3⋊C4—32no—
170C2×Dic3⋊C4—32no—
171C2×Dic3⋊C4—316no—
172C2×Dic3⋊C4C2×D312yes—
173#896—316no—
174#896—316no—
175#884—316no—
176#884—316no—
177#878—316no—
178#878—316no—
179C23×C32—22no—
180C23×C32—22no—
181C23×C32—22no—
182C23×C32—22no—
183C23×C32—22no—
184C23×C32C2×D414yes—
185C23×C32C2412yes—
186C23×C32C2412yes—
187C23×C32C2411yescharacteristic
188C22×C3⋊D3—22no—
189C22×C3⋊D3—22no—
190C22×C3⋊D3—22no—
191C22×C3⋊D3C2412yes—
192C22×C3×D3—24no—
193C22×C3×D3—24no—
194C22×C3×D3—24no—
195C22×C3×D3C2414yes—
196C32×D4—28no—
197C2×C32×C4—22no—
198C2×C32×C4C2412yes—
199#638—28no—
200#638—28no—
201C2×C3⋊Dic3—22no—
202C2×C3⋊Dic3—28no—
203C2×C3⋊Dic3C2×D414yes—
204C2×C3⋊Dic3C2×D414yes—
205C2×C3⋊Dic3C2×D4116yescomplemented
206C2×C3⋊Dic3C2412yes—
207C2×C3⋊Dic3C2412yes—
208C2×C3⋊Dic3C2412yes—
209C4×C3⋊D3—28no—
210#634—28no—
211C3×#67—216no—
212C3×#67—48no—
213C2×C3×Dic3—24no—
214C2×C3×Dic3—24no—
215C2×C3×Dic3—24no—
216C2×C3×Dic3—48no—
217C2×C3×Dic3C2414yes—
218C2×C3×Dic3C2414yes—
219C2×C3×Dic3C2414yes—
220#627—28no—
221#626—48no—
222#625—28no—
223D3×Dic3—216no—
224C22×#41—91no—
225C22×#41—91no—
226#537—916no—
227C2×C22⋊Q8—91no—
228C2×C22⋊Q8—92no—
229C2×C22⋊Q8—91no—
230C2×#121—32no—
231C2×#121—91no—
232C2×#121—92no—
233C2×#121—92no—
234C2×#121—91no—
235C22×C4⋊C4—91no—
236C24×C3—21no—
237C24×C3—21no—
238C24×C3—32no—
239C24×C3C22×D312yes—
240C24×C3C22×D312yes—
241C23×D3—32no—
242C23×D3—61no—
243C23×D3C22×D312yes—
244C2×C3×D4—28no—
245C2×C3×D4—28no—
246C2×C3×D4—24no—
247C2×C3×D4—38no—
248C2×C3×D4—38no—
249C2×C3×D4—68no—
250C2×C3×D4—124no—
251C2×C3×D4C22×D318yes—
252C22×C3×C4—21no—
253C22×C3×C4—32no—
254C22×C3×C4—32no—
255C22×C3×C4—32no—
256C22×C3×C4—38no—
257C22×C3×C4—124no—
258C22×C3×C4C22×D312yes—
259C2×#67—28no—
260C2×#67—38no—
261C2×#67—38no—
262C2×#67—38no—
263C2×#67—38no—
264C2×#67—44no—
265C2×#67—64no—
266C2×#67—64no—
267C2×#67—68no—
268C2×#67—68no—
269C2×#67—68no—
270C2×#67—68no—
271C2×#67—68no—
272C2×#67—124no—
273C2×#67C22×D318yes—
274C2×#67C22×D318yes—
275C22×Dic3—316no—
276C22×Dic3—32no—
277C22×Dic3—32no—
278C22×Dic3—38no—
279C22×Dic3—38no—
280C22×Dic3—32no—
281C22×Dic3—38no—
282C22×Dic3—44no—
283C22×Dic3—61no—
284C22×Dic3—61no—
285C22×Dic3—61no—
286C22×Dic3—68no—
287C22×Dic3—64no—
288C22×Dic3—64no—
289C22×Dic3—68no—
290C22×Dic3—68no—
291C22×Dic3—68no—
292C22×Dic3C22×D312yes—
293C22×Dic3C22×D312yes—
294C22×Dic3C22×D312yes—
295C22×Dic3C22×D318yes—
296#237—664no—
297#237—664no—
298#237—664no—
299C2×D12—38no—
300C2×D12—124no—
301C2×C4×D3—38no—
302C2×C4×D3—38no—
303C2×C4×D3—64no—
304C2×C4×D3—68no—
305C2×C4×D3—68no—
306C2×C4×D3—68no—
307C2×Dic6—38no—
308C2×Dic6—38no—
309C2×Dic6—64no—
310C2×Dic6—68no—
311C2×Dic6—68no—
312C2×Dic6—68no—
313C3×C4⋊C4—38no—
314C3×C22⋊C4—38no—
315C3×C22⋊C4—38no—
316#217—38no—
317#217C22×D318yes—
318(C2×D3)⋊C4—38no—
319(C2×D3)⋊C4—38no—
320(C2×D3)⋊C4—38no—
321(C2×D3)⋊C4C22×D318yes—
322C4⋊Dic3—38no—
323Dic3⋊C4—38no—
324Dic3⋊C4—38no—
325Dic3⋊C4—38no—
326Dic3⋊C4—38no—
327Dic3⋊C4—38no—
328Dic3⋊C4C22×D318yes—
329C22×C32—22no—
330C22×C32—28no—
331C22×C32—22no—
332C22×C32—22no—
333C22×C32—22no—
334C22×C32—22no—
335C22×C32—44no—
336C22×C32C22×D414yes—
337C22×C32C22×D412yes—
338C22×C32H(5,𝔽2)12yes—
339C22×C322−1+412yes—
340C22×C32C2511yescharacteristic
341C2×C3⋊D3—22no—
342C2×C3⋊D3—22no—
343C2×C3⋊D3—22no—
344C2×C3⋊D3—44no—
345C2×C3×D3—24no—
346C2×C3×D3—24no—
347C2×C3×D3—24no—
348C2×C3×D3—48no—
349C32×C4—22no—
350C3⋊Dic3—22no—
351C3⋊Dic3C22×D414yes—
352C3⋊Dic3C22×D414yes—
353C3×Dic3—24no—
354C3×Dic3—24no—
355C3×Dic3—24no—
356C2×#41—98no—
357C2×#41—98no—
358C2×#41—188no—
359C2×#41—188no—
360C22×Q8—91no—
361C22×Q8—91no—
362C22×D4—32no—
363C22×D4—32no—
364C22×D4—92no—
365C22×D4—91no—
366C22×D4—91no—
367C22×D4—91no—
368C22×D4D3211yescharacteristic
369C23×C4—32no—
370C23×C4—92no—
371C23×C4—91no—
372C23×C4—91no—
373C23×C4—91no—
374C22⋊Q8—98no—
375C22⋊Q8—916no—
376C22⋊Q8—98no—
377#121—316no—
378#121—98no—
379#121—916no—
380#121—916no—
381#121—98no—
382C2×C4⋊C4—32no—
383C2×C4⋊C4—91no—
384C2×C4⋊C4—92no—
385C2×C4⋊C4—91no—
386C2×C4⋊C4—98no—
387C2×C4⋊C4—92no—
388C2×C22⋊C4—32no—
389C2×C22⋊C4—32no—
390C2×C22⋊C4—92no—
391C2×C22⋊C4—92no—
392C23×C3—24no—
393C23×C3—24no—
394C23×C3—24no—
395C23×C3—24no—
396C23×C3—24no—
397C23×C3—24no—
398C23×C3—22no—
399C23×C3—22no—
400C23×C3—21no—
401C23×C3—24no—
402C23×C3—34no—
403C23×C3—42no—
404C23×C3—42no—
405C23×C3—42no—
406C23×C3—42no—
407C23×C3—64no—
408C23×C3—64no—
409C23×C3—64no—
410C23×C3D3×D418yes—
411C23×C3C23×D314yes—
412C23×C3C23×D314yes—
413C23×C3C23×D312yes—
414C22×D3—24no—
415C22×D3—24no—
416C22×D3—24no—
417C22×D3—34no—
418C22×D3—62no—
419C22×D3—64no—
420C22×D3—64no—
421C22×D3—64no—
422C22×D3—64no—
423C22×D3—122no—
424C22×D3—122no—
425C22×D3C23×D314yes—
426C3×D4—216no—
427C3×D4—216no—
428C3×D4—616no—
429C3×D4—128no—
430C2×C3×C4—24no—
431C2×C3×C4—24no—
432C2×C3×C4—22no—
433C2×C3×C4—34no—
434C2×C3×C4—34no—
435C2×C3×C4—34no—
436C2×C3×C4—64no—
437C2×C3×C4—64no—
438C2×C3×C4—64no—
439C2×C3×C4—128no—
440C2×C3×C4C23×D314yes—
441#67—216no—
442#67—48no—
443#67—616no—
444#67—616no—
445#67—616no—
446#67—616no—
447#67—616no—
448#67—128no—
449C2×Dic3—24no—
450C2×Dic3—24no—
451C2×Dic3—24no—
452C2×Dic3—38no—
453C2×Dic3—38no—
454C2×Dic3—332no—
455C2×Dic3—34no—
456C2×Dic3—34no—
457C2×Dic3—34no—
458C2×Dic3—48no—
459C2×Dic3—64no—
460C2×Dic3—64no—
461C2×Dic3—616no—
462C2×Dic3—62no—
463C2×Dic3—62no—
464C2×Dic3—62no—
465C2×Dic3—616no—
466C2×Dic3—616no—
467C2×Dic3—64no—
468C2×Dic3—616no—
469C2×Dic3—64no—
470C2×Dic3C23×D314yes—
471C2×Dic3C23×D314yes—
472C2×Dic3C23×D314yes—
473D12—128no—
474C4×D3—616no—
475C4×D3—616no—
476C4×D3—616no—
477Dic6—616no—
478Dic6—616no—
479Dic6—616no—
480C2×C32—24no—
481C2×C32—42no—
482C2×C32#53714yescomplemented
483C2×C32C23×D411yescharacteristic
484C2×C32C2×H(5,𝔽2)11yescharacteristic
485C2×C32C2×2−1+411yescharacteristic
486C3⋊D3—42no—
487C3×D3—44no—
488C24—32no—
489C24—91no—
490C24C2×D3211yescharacteristic
491C24C2×D3211yescharacteristic
492#41—1832no—
493#41—1832no—
494C2×Q8—94no—
495C2×Q8—94no—
496C2×Q8—184no—
497C2×Q8—184no—
498C2×D4—24no—
499C2×D4—38no—
500C2×D4—38no—
501C2×D4—68no—
502C2×D4—98no—
503C2×D4—94no—
504C2×D4—94no—
505C2×D4—94no—
506C2×D4—124no—
507C2×D4—184no—
508C2×D4—184no—
509C2×D4—184no—
510C2×D4—364no—
511C2×D4C2×D3214yes—
512C22×C4—32no—
513C22×C4—32no—
514C22×C4—32no—
515C22×C4—38no—
516C22×C4—98no—
517C22×C4—94no—
518C22×C4—91no—
519C22×C4—91no—
520C22×C4—98no—
521C22×C4—94no—
522C22×C4—91no—
523C22×C4—94no—
524C22×C4—124no—
525C22×C4—184no—
526C22×C4—188no—
527C22×C4—184no—
528C22×C4C2×D3211yescharacteristic
529C4⋊C4—38no—
530C4⋊C4—94no—
531C4⋊C4—98no—
532C4⋊C4—94no—
533C4⋊C4—98no—
534C22⋊C4—38no—
535C22⋊C4—38no—
536C22⋊C4—98no—
537C22⋊C4—98no—
538C22×C3—24no—
539C22×C3—24no—
540C22×C3—216no—
541C22×C3—24no—
542C22×C3—24no—
543C22×C3—24no—
544C22×C3—24no—
545C22×C3—22no—
546C22×C3—22no—
547C22×C3—22no—
548C22×C3—24no—
549C22×C3—21no—
550C22×C3—42no—
551C22×C3—42no—
552C22×C3—48no—
553C22×C3—42no—
554C22×C3—42no—
555C22×C3—48no—
556C22×C3—48no—
557C22×C3—64no—
558C22×C3—64no—
559C22×C3—64no—
560C22×C3—128no—
561C22×C3C2×D3×D418yes—
562C22×C3C2×D3×D414yes—
563C22×C3#100414yes—
564C22×C3#101014yes—
565C22×C3C24×D312yes—
566C2×D3—24no—
567C2×D3—24no—
568C2×D3—24no—
569C2×D3—48no—
570C2×D3—64no—
571C2×D3—64no—
572C2×D3—64no—
573C2×D3—64no—
574C2×D3—122no—
575C2×D3—122no—
576C2×D3—128no—
577C2×D3—128no—
578C3×C4—24no—
579C3×C4—24no—
580C3×C4—64no—
581C3×C4—64no—
582C3×C4—64no—
583Dic3—24no—
584Dic3—24no—
585Dic3—24no—
586Dic3—38no—
587Dic3—38no—
588Dic3—64no—
589Dic3—64no—
590Dic3—64no—
591Dic3—64no—
592C32C2×#53711yescharacteristic, complemented, Sylow
593C23—22no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—34no—
599C23—64no—
600C23—64no—
601C23—64no—
602C23—92no—
603C23—182no—
604C23—182no—
605C23—182no—
606C23#381114yes—
607C23C22×D3212yes—
608C23C22×D3212yes—
609C23C22×D3211yescharacteristic
610Q8—188no—
611Q8—188no—
612D4—28no—
613D4—616no—
614D4—128no—
615D4—188no—
616D4—188no—
617D4—188no—
618D4—368no—
619C2×C4—22no—
620C2×C4—34no—
621C2×C4—34no—
622C2×C4—34no—
623C2×C4—64no—
624C2×C4—64no—
625C2×C4—64no—
626C2×C4—94no—
627C2×C4—94no—
628C2×C4—916no—
629C2×C4—92no—
630C2×C4—92no—
631C2×C4—92no—
632C2×C4—128no—
633C2×C4—188no—
634C2×C4—1816no—
635C2×C4—188no—
636C2×C4—182no—
637C2×C4C22×D3212yes—
638C2×C3—28no—
639C2×C3—21no—
640C2×C3—21no—
641C2×C3—24no—
642C2×C3—21no—
643C2×C3—44no—
644C2×C3—44no—
645C2×C3—44no—
646C2×C3—124no—
647C2×C3#559718yescomplemented
648C2×C3C22×D3×D412yes—
649C2×C3C2×#100412yes—
650C2×C3C2×#101012yes—
651D3—44no—
652D3—124no—
653D3—124no—
654C22—22no—
655C22—22no—
656C22—28no—
657C22—22no—
658C22—22no—
659C22—22no—
660C22—44no—
661C22—64no—
662C22—64no—
663C22—64no—
664C22—128no—
665C22—182no—
666C22—182no—
667C22—182no—
668C22—364no—
669C22#6430912yes—
670C22#6431312yes—
671C22C2×#381114yes—
672C22C2×#381112yes—
673C22C23×D3211yescharacteristic
674C4—22no—
675C4—64no—
676C4—64no—
677C4—64no—
678C4—94no—
679C4—94no—
680C4—182no—
681C3—21no—
682C3C2×#559712yescomplemented
683C2—24no—
684C2—42no—
685C2—124no—
686C2—362no—
687C2#1059516614yesdirect product factor
688C2C2×#6430911yescharacteristic
689C2C2×#6431311yescharacteristic
690C2C22×#381111yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C2×#537
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×#63982C2semidirect
5. C2×#63980C2semidirect
6. C2×#63978C2semidirect
7. C2×#63971C2semidirect
8. C22×#3724C2semidirect
9. #10595166C2direct (N × H)
10. C2×#63912C2semidirect
11. C2×#63896C2semidirect
12. C2×#63865C2semidirect
20. C2×#3830C22semidirect
30. C2×#3805C22semidirect
33. C3×#939C22semidirect
36. #63982C22semidirect
37. #63980C22semidirect
38. #63978C22semidirect
39. #63971C22semidirect
43. C2×#3724C22semidirect
47. #63912C22semidirect
48. #63896C22semidirect
49. #63865C22semidirect
57. C2×#939D3semidirect
79. C22×C3⋊Dic3D4semidirect
159. #939C2×D3semidirect
205. C2×C3⋊Dic3C2×D4semidirect
482. C2×C32#537semidirect
592. C32C2×#537semidirect
647. C2×C3#5597semidirect
682. C3C2×#5597semidirect
687. C2#10595166direct (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×#639822
C2×#639802
C2×#639782
C2×#639712
C22×#37242
#105951662
C2×#639122
C2×#638962
C2×#638652
C2×#55973