Finite Group Databasebeta

← #11824418

Subgroups — #11824418

Order 1152.

2844 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#121C211yesmaximal, characteristic, complemented
2C2×#64149C211yesmaximal, characteristic, complemented
3C2×#64149C212yesmaximal, complemented
4C2×#64147C211yesmaximal, characteristic, complemented
5C2×#64139C211yesmaximal, characteristic, complemented
6C2×C4×#638C211yesmaximal, characteristic, complemented
7C2×#64104C211yesmaximal, characteristic, complemented
8#10592922C212yesmaximal, complemented
9C4⋊C4×C3⋊Dic3C211yesmaximal, characteristic, complemented
10#10592659C212yesmaximal, complemented
11#10592656C212yesmaximal, complemented
12#82669—34nomaximal
13C22×C32×D4C2211yescharacteristic
14C22×C32×D4C2212yes—
15C23×C32×C4C2211yescharacteristic
16C22×#638C2212yes—
17C22×#638C2212yes—
18C22×#638C2212yes—
19C22×#638C2211yescharacteristic
20C22×#638C2212yes—
21C22×C4⋊(C3⋊D3)C2211yescharacteristic
22C22×C4⋊(C3⋊D3)C2212yes—
23C22×C4×C3⋊D3C2211yescharacteristic
24C32×#121—24no—
25C2×C32×C4⋊C4C2211yescharacteristic
26C2×C32×C22⋊C4C2212yes—
27C2×#3757C2212yes—
28C2×#3757C2211yescharacteristic
29#64149—28no—
30#64149—24no—
31#64147—24no—
32#64139—24no—
33C4×#638—24no—
34C2×#3752C2212yes—
35C2×#3752C2212yes—
36C2×#3752C2211yescharacteristic
37C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
38C2×#3750C2211yescharacteristic
39C2×C4×C3⋊Dic3C2212yes—
40C2×C4×C3⋊Dic3C2211yescharacteristic
41#64104—24no—
42#63658C2212yes—
43C2×C3×#121D314yescomplemented
44C2×#940—34no—
45C2×#940—38no—
46C2×#938—34no—
47C2×#930—34no—
48C2×C4×#67—34no—
49C2×#895—34no—
50#5223—38no—
51Dic3×C4⋊C4—34no—
52#4960—38no—
53#4957—38no—
54C24×C32C2312yes—
55C24×C32C2311yescharacteristic
56C23×C3⋊D3C2312yes—
57C23×C3⋊D3C2311yescharacteristic
58C2×C32×D4—24no—
59C2×C32×D4—22no—
60C2×C32×D4—22no—
61C2×C32×D4—24no—
62C2×C32×D4—22no—
63C2×C32×D4—42no—
64C22×C32×C4—22no—
65C22×C32×C4—22no—
66C22×C32×C4—22no—
67C22×C32×C4C2311yescharacteristic
68C22×C32×C4C2312yes—
69C22×C32×C4C2311yescharacteristic
70C2×#638—24no—
71C2×#638—24no—
72C2×#638—22no—
73C2×#638—24no—
74C2×#638—24no—
75C2×#638—24no—
76C2×#638—24no—
77C2×#638—24no—
78C2×#638—22no—
79C2×#638—24no—
80C2×#638—42no—
81C2×#638—42no—
82C2×#638—42no—
83C2×#638—42no—
84C2×#638D414yescomplemented
85C22×C3⋊Dic3C2311yescharacteristic
86C22×C3⋊Dic3C2312yes—
87C22×C3⋊Dic3C2311yescharacteristic
88C22×C3⋊Dic3C2311yescharacteristic
89C2×C4⋊(C3⋊D3)—24no—
90C2×C4⋊(C3⋊D3)—24no—
91C2×C4⋊(C3⋊D3)—22no—
92C2×C4⋊(C3⋊D3)—22no—
93C2×C4⋊(C3⋊D3)—22no—
94C2×C4⋊(C3⋊D3)—42no—
95C2×C4×C3⋊D3—22no—
96C2×C4×C3⋊D3—22no—
97C2×C4×C3⋊D3—22no—
98C32×C4⋊C4D414yescomplemented
99C32×C22⋊C4—24no—
100#3757—22no—
101#3757—24no—
102#3752—24no—
103#3752—22no—
104#3752—24no—
105C4⋊(C3⋊Dic3)D414yescomplemented
106#3750—22no—
107C4×C3⋊Dic3—24no—
108C4×C3⋊Dic3D414yescomplemented
109#2541—91noSylow
110C22×C3×D4C2×D314yes—
111C22×C3×D4C2×D318yes—
112C23×C3×C4C2×D314yes—
113C22×#67—34no—
114C22×#67—38no—
115C22×#67—38no—
116C22×#67—38no—
117C22×#67—38no—
118C22×D12—34no—
119C22×D12—38no—
120C22×C4×D3—34no—
121C3×#121—216no—
122C2×C3×C4⋊C4C2×D314yes—
123C2×C3×C22⋊C4C2×D318yes—
124C2×#217—38no—
125C2×#217—34no—
126#940—616no—
127#940—632no—
128#938—616no—
129#930—616no—
130C4×#67—616no—
131C2×(C2×D3)⋊C4—38no—
132C2×(C2×D3)⋊C4—38no—
133C2×(C2×D3)⋊C4—34no—
134C2×C4⋊Dic3—34no—
135C2×Dic3⋊C4—34no—
136C2×C4×Dic3—34no—
137C2×C4×Dic3—38no—
138#895—616no—
139C3⋊#95—38no—
140C23×C32—21no—
141C23×C32—21no—
142C23×C32—21no—
143C23×C32—21no—
144C23×C32—21no—
145C23×C32—21no—
146C23×C32—22no—
147C23×C32—22no—
148C23×C32—22no—
149C23×C32—22no—
150C23×C32—22no—
151C23×C32—22no—
152C23×C32—22no—
153C23×C32C2×D412yes—
154C23×C32C2411yescharacteristic
155C22×C3⋊D3—21no—
156C22×C3⋊D3—21no—
157C22×C3⋊D3—21no—
158C22×C3⋊D3—21no—
159C22×C3⋊D3—21no—
160C22×C3⋊D3—21no—
161C22×C3⋊D3—22no—
162C22×C3⋊D3—22no—
163C22×C3⋊D3—22no—
164C22×C3⋊D3—22no—
165C22×C3⋊D3—22no—
166C22×C3⋊D3—22no—
167C22×C3⋊D3—22no—
168C22×C3⋊D3C2×D412yes—
169C32×D4—48no—
170C32×D4—44no—
171C2×C32×C4—22no—
172C2×C32×C4—22no—
173C2×C32×C4—21no—
174C2×C32×C4—21no—
175C2×C32×C4—21no—
176C2×C32×C4—44no—
177C2×C32×C4C2×D412yes—
178C2×C32×C4C2×D412yes—
179C2×C32×C4C2×D414yes—
180C2×C32×C4C2×D412yes—
181#638—28no—
182#638—48no—
183#638—48no—
184#638—48no—
185#638—48no—
186C2×C3⋊Dic3—22no—
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3—22no—
190C2×C3⋊Dic3—21no—
191C2×C3⋊Dic3—21no—
192C2×C3⋊Dic3—21no—
193C2×C3⋊Dic3C2×D412yes—
194C2×C3⋊Dic3C2×D414yes—
195C2×C3⋊Dic3C2×D412yes—
196C2×C3⋊Dic3C2×D412yes—
197C2×C3⋊Dic3#4112yes—
198C4⋊(C3⋊D3)—48no—
199C4⋊(C3⋊D3)—44no—
200C4×C3⋊D3—44no—
201C2×#127—91no—
202C2×#127—92no—
203C2×#121—91no—
204C2×#121—91no—
205C2×#121—91no—
206C2×#121C3⋊D311yescharacteristic, complemented
207C2×C4×D4—91no—
208#392—92no—
209#392—92no—
210#390—92no—
211C4×C4⋊C4—91no—
212C24×C3C22×D318yes—
213C24×C3C22×D314yes—
214C23×D3—34no—
215C23×D3—38no—
216C2×C3×D4—216no—
217C2×C3×D4—28no—
218C2×C3×D4—28no—
219C2×C3×D4—216no—
220C2×C3×D4—28no—
221C2×C3×D4—48no—
222C22×C3×C4—28no—
223C22×C3×C4—28no—
224C22×C3×C4—28no—
225C22×C3×C4C22×D314yes—
226C22×C3×C4C22×D318yes—
227C22×C3×C4C22×D314yes—
228C2×#67—316no—
229C2×#67—68no—
230C2×#67—68no—
231C2×#67—616no—
232C2×#67—616no—
233C2×#67—616no—
234C2×#67—616no—
235C2×#67—616no—
236C2×#67—616no—
237C2×#67—616no—
238C2×#67—616no—
239C2×#67—128no—
240C2×#67—128no—
241C2×#67—128no—
242C2×#67—128no—
243C22×Dic3—34no—
244C22×Dic3—34no—
245C22×Dic3—38no—
246C22×Dic3—34no—
247C2×D12—616no—
248C2×D12—68no—
249C2×D12—68no—
250C2×D12—616no—
251C2×D12—68no—
252C2×D12—128no—
253C2×C4×D3—68no—
254C2×C4×D3—68no—
255C2×C4×D3—68no—
256C3×C4⋊C4#67116yescomplemented
257C3×C22⋊C4—216no—
258#217—68no—
259#217—616no—
260(C2×D3)⋊C4—68no—
261(C2×D3)⋊C4—616no—
262(C2×D3)⋊C4—616no—
263C4⋊Dic3—316no—
264Dic3⋊C4—68no—
265C4×Dic3—316no—
266C4×Dic3—616no—
267C22×C32—22no—
268C22×C32—22no—
269C22×C32—22no—
270C22×C32—41no—
271C22×C32—41no—
272C22×C32—41no—
273C22×C32—41no—
274C22×C32—42no—
275C22×C32—42no—
276C22×C32—42no—
277C22×C32—42no—
278C22×C32—42no—
279C22×C32—42no—
280C22×C32—42no—
281C22×C32C22×D411yescharacteristic
282C22×C32C22×D411yescharacteristic
283C22×C32C22×D411yescharacteristic
284C22×C32C22×D411yescharacteristic
285C22×C32C2×#4111yescharacteristic
286C22×C32H(5,𝔽2)11yescharacteristic
287C22×C32H(5,𝔽2)11yescharacteristic
288C2×C3⋊D3—22no—
289C2×C3⋊D3—22no—
290C2×C3⋊D3—22no—
291C2×C3⋊D3—41no—
292C2×C3⋊D3—41no—
293C2×C3⋊D3—41no—
294C2×C3⋊D3—41no—
295C2×C3⋊D3—42no—
296C2×C3⋊D3—42no—
297C2×C3⋊D3—42no—
298C2×C3⋊D3—42no—
299C2×C3⋊D3—42no—
300C2×C3⋊D3—42no—
301C2×C3⋊D3—42no—
302C32×C4—24no—
303C32×C4—41no—
304C32×C4#12714yescomplemented
305C3⋊Dic3—22no—
306C3⋊Dic3—24no—
307C3⋊Dic3—41no—
308C3⋊Dic3#12114yescomplemented
309C22×D4—91no—
310C22×D4—92no—
311C22×D4—92no—
312C22×D4—92no—
313C22×D4—92no—
314C22×D4—91no—
315C22×D4—92no—
316C22×D4C2×C3⋊D311yescharacteristic
317C22×D4C2×C3⋊D312yes—
318C23×C4—91no—
319C23×C4C2×C3⋊D311yescharacteristic
320#127—184no—
321#127—188no—
322#121—24no—
323#121—184no—
324#121—184no—
325#121—184no—
326C4×D4—184no—
327C2×C4⋊C4—91no—
328C2×C4⋊C4—91no—
329C2×C4⋊C4C2×C3⋊D311yescharacteristic
330C2×C22⋊C4—91no—
331C2×C22⋊C4—92no—
332C2×C22⋊C4—91no—
333C2×C22⋊C4—92no—
334C2×C22⋊C4—92no—
335C2×C22⋊C4C2×C3⋊D312yes—
336C2×C42—91no—
337C2×C42—92no—
338#95—92no—
339C23×C3—24no—
340C23×C3—24no—
341C23×C3—24no—
342C23×C3—24no—
343C23×C3—24no—
344C23×C3—24no—
345C23×C3—28no—
346C23×C3—28no—
347C23×C3—28no—
348C23×C3—28no—
349C23×C3—28no—
350C23×C3—28no—
351C23×C3—28no—
352C23×C3D3×D418yes—
353C23×C3C23×D314yes—
354C22×D3—38no—
355C22×D3—64no—
356C22×D3—64no—
357C22×D3—64no—
358C22×D3—64no—
359C22×D3—64no—
360C22×D3—64no—
361C22×D3—68no—
362C22×D3—68no—
363C22×D3—68no—
364C22×D3—68no—
365C22×D3—68no—
366C22×D3—68no—
367C22×D3—68no—
368C3×D4—432no—
369C3×D4—416no—
370C2×C3×C4—28no—
371C2×C3×C4—28no—
372C2×C3×C4—24no—
373C2×C3×C4—24no—
374C2×C3×C4—24no—
375C2×C3×C4—416no—
376C2×C3×C4D3×D418yes—
377C2×C3×C4D3×D418yes—
378C2×C3×C4C2×#67116yes—
379C2×C3×C4C2×#6718yes—
380#67—632no—
381#67—1232no—
382#67—1232no—
383#67—1232no—
384#67—1232no—
385C2×Dic3—38no—
386C2×Dic3—38no—
387C2×Dic3—38no—
388C2×Dic3—38no—
389C2×Dic3—316no—
390C2×Dic3—68no—
391C2×Dic3—64no—
392C2×Dic3—64no—
393C2×Dic3—68no—
394C2×Dic3—64no—
395C2×Dic3—64no—
396C2×Dic3—64no—
397D12—1232no—
398D12—1216no—
399C4×D3—1216no—
400C2×C32—42no—
401C2×C32—82no—
402C2×C32C2×#12111yescharacteristic
403C2×C32C2×#12711yescharacteristic
404C2×C32#53511yescharacteristic
405C2×C32D4211yescharacteristic
406C2×C32D4211yescharacteristic
407C2×C32#55011yescharacteristic
408C2×C32#55011yescharacteristic
409C3⋊D3—42no—
410C3⋊D3—82no—
411C24—91no—
412C24—92no—
413C24C22×C3⋊D312yes—
414C24C22×C3⋊D311yescharacteristic
415C2×D4—24no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—24no—
419C2×D4—22no—
420C2×D4—42no—
421C2×D4—94no—
422C2×D4—184no—
423C2×D4—182no—
424C2×D4—182no—
425C2×D4—184no—
426C2×D4—184no—
427C2×D4—184no—
428C2×D4—184no—
429C2×D4—184no—
430C2×D4—184no—
431C2×D4—184no—
432C2×D4—184no—
433C2×D4—182no—
434C2×D4—182no—
435C2×D4—184no—
436C2×D4—182no—
437C2×D4—362no—
438C2×D4—362no—
439C2×D4—362no—
440C2×D4—362no—
441C2×D4—362no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—91no—
446C22×C4—91no—
447C22×C4—92no—
448C22×C4—91no—
449C22×C4—182no—
450C22×C4—182no—
451C22×C4—182no—
452C22×C4C22×C3⋊D311yescharacteristic
453C22×C4C22×C3⋊D312yes—
454C22×C4C22×C3⋊D311yescharacteristic
455C4⋊C4—94no—
456C4⋊C4—182no—
457C4⋊C4#63814yescomplemented
458C22⋊C4—24no—
459C22⋊C4—182no—
460C22⋊C4—184no—
461C22⋊C4—182no—
462C22⋊C4—184no—
463C22⋊C4—184no—
464C42—94no—
465C42—184no—
466C22×C3—28no—
467C22×C3—28no—
468C22×C3—28no—
469C22×C3—44no—
470C22×C3—44no—
471C22×C3—44no—
472C22×C3—44no—
473C22×C3—48no—
474C22×C3—48no—
475C22×C3—48no—
476C22×C3—48no—
477C22×C3—48no—
478C22×C3—48no—
479C22×C3—48no—
480C22×C3C2×D3×D414yes—
481C22×C3C2×D3×D414yes—
482C22×C3C2×D3×D414yes—
483C22×C3#100414yes—
484C22×C3D3×#4114yes—
485C22×C3#100914yes—
486C22×C3C22×#6714yes—
487C2×D3—68no—
488C2×D3—68no—
489C2×D3—68no—
490C2×D3—124no—
491C2×D3—124no—
492C2×D3—124no—
493C2×D3—124no—
494C2×D3—128no—
495C2×D3—128no—
496C2×D3—128no—
497C2×D3—128no—
498C2×D3—128no—
499C2×D3—128no—
500C2×D3—128no—
501C3×C4—216no—
502C3×C4—44no—
503C3×C4#940116yescomplemented
504Dic3—316no—
505Dic3—68no—
506Dic3—616no—
507Dic3—124no—
508C32#254111yescharacteristic, complemented, Sylow
509C23—21no—
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—22no—
516C23—22no—
517C23—22no—
518C23—22no—
519C23—22no—
520C23—22no—
521C23—22no—
522C23—92no—
523C23—181no—
524C23—181no—
525C23—181no—
526C23—181no—
527C23—181no—
528C23—181no—
529C23—182no—
530C23—182no—
531C23—182no—
532C23—182no—
533C23—182no—
534C23—182no—
535C23—182no—
536C23D4×C3⋊D312yes—
537C23C23×C3⋊D311yescharacteristic
538D4—48no—
539D4—44no—
540D4—188no—
541D4—368no—
542D4—368no—
543D4—368no—
544D4—368no—
545D4—368no—
546D4—364no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—44no—
553C2×C4—92no—
554C2×C4—92no—
555C2×C4—92no—
556C2×C4—92no—
557C2×C4—94no—
558C2×C4—182no—
559C2×C4—181no—
560C2×C4—181no—
561C2×C4—182no—
562C2×C4—181no—
563C2×C4—181no—
564C2×C4—181no—
565C2×C4—364no—
566C2×C4D4×C3⋊D312yes—
567C2×C4D4×C3⋊D312yes—
568C2×C4C2×#63814yes—
569C2×C4C2×#63812yes—
570C2×C3—48no—
571C2×C3—88no—
572C2×C3#559914yes—
573C2×C3D3×#12114yes—
574C2×C3#560714yes—
575C2×C3#560914yes—
576C2×C3D4×#6714yes—
577C2×C3C2×#94014yes—
578C2×C3#583414yes—
579D3—128no—
580D3—248no—
581C22—22no—
582C22—22no—
583C22—22no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—42no—
589C22—42no—
590C22—42no—
591C22—42no—
592C22—42no—
593C22—42no—
594C22—42no—
595C22—182no—
596C22—182no—
597C22—182no—
598C22—361no—
599C22—361no—
600C22—361no—
601C22—361no—
602C22—362no—
603C22—362no—
604C22—362no—
605C22—362no—
606C22—362no—
607C22—362no—
608C22—362no—
609C22C2×D4×C3⋊D311yescharacteristic
610C22C2×D4×C3⋊D311yescharacteristic
611C22C2×D4×C3⋊D311yescharacteristic
612C22#6436111yescharacteristic
613C22#41×C3⋊D311yescharacteristic
614C22#6436611yescharacteristic
615C22C22×#63811yescharacteristic
616C4—24no—
617C4—41no—
618C4—94no—
619C4—182no—
620C4—184no—
621C4—361no—
622C4#6414914yescomplemented
623C3#8266914yescomplemented
624C2—42no—
625C2—82no—
626C2—362no—
627C2—722no—
628C2#1059607011yescharacteristic
629C2C3⋊D3×#12111yescharacteristic
630C2#1059607811yescharacteristic
631C2#1059608011yescharacteristic
632C2D4×#63811yescharacteristic
633C2C2×#6414911yescharacteristic
634C2#1059630511yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutator, socle, cosocleC23×C32C24
FittingC2×C32×#121C2
hypercenterC2×#121C3⋊D3
hypocenterC32#2541
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×C32×#121C2semidirect
2. C2×#64149C2semidirect
3. C2×#64149C2semidirect
4. C2×#64147C2semidirect
5. C2×#64139C2semidirect
6. C2×C4×#638C2semidirect
7. C2×#64104C2semidirect
8. #10592922C2semidirect
9. C4⋊C4×C3⋊Dic3C2semidirect
10. #10592659C2semidirect
11. #10592656C2semidirect
43. C2×C3×#121D3semidirect
84. C2×#638D4semidirect
98. C32×C4⋊C4D4semidirect
105. C4⋊(C3⋊Dic3)D4semidirect
108. C4×C3⋊Dic3D4semidirect
206. C2×#121C3⋊D3semidirect
256. C3×C4⋊C4#67semidirect
304. C32×C4#127semidirect
308. C3⋊Dic3#121semidirect
457. C4⋊C4#638semidirect
503. C3×C4#940semidirect
508. C32#2541semidirect
622. C4#64149semidirect
623. C3#82669semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1212
C2×#641492
C2×#641472
C2×#641392
C2×C4×#6382
C2×#641042
#105929222
C4⋊C4×C3⋊Dic32
#105926592
#105926562
#826693