Finite Group Databasebeta

← #11856272

Subgroups — #11856272

Order 1152.

2375 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D32C211yesmaximal, characteristic, complemented
2C2×#64092C211yesmaximal, characteristic, complemented
3C2×#63983C211yesmaximal, characteristic
4C2×#63975C211yesmaximal, characteristic, complemented
5C3×#4956C212yesmaximal, complemented
6#10591721C212yesmaximal, complemented
7#10591399C211yesmaximal, characteristic, complemented
8#10591379C212yesmaximal, complemented
9#10591371C211yesmaximal, characteristic, complemented
10#10591278C212yesmaximal, complemented
11#10591219C211yesmaximal, characteristic, complemented
12#74936—32nomaximal
13C23×D32C2211yescharacteristic
14C22×#638C2211yescharacteristic
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×C3×#67C2212yes—
17C22×C3×C4×D3C2212yes—
18C22×#624C2211yescharacteristic
19C22×D3×Dic3C2212yes—
20C2×C4×D32—24no—
21C2×C4×D32—24no—
22C2×C4×D32—24no—
23C2×C32×C22⋊C4C2211yescharacteristic, complemented
24C2×#3757C2211yescharacteristic, complemented
25C2×#3752C2211yescharacteristic
26C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
27C2×#3750C2211yescharacteristic, complemented
28#64092—24no—
29C2×C3×#217C2212yescomplemented
30C2×C3×(C2×D3)⋊C4C2212yes—
31#63983—24no—
32#63975—24no—
33C2×Dic3⋊Dic3C2212yescomplemented
34C2×#3722C2211yescharacteristic
35C2×#3722C2211yescharacteristic
36C2×(C2×D3)⋊Dic3C2212yes—
37C2×(C2×D3)⋊Dic3C2212yes—
38C3×C3⋊#95C2212yescomplemented
39C3×C3⋊#95C2212yescomplemented
40#63579C2212yescomplemented
41#63579C2212yescomplemented
42C23×C4×D3—32no—
43C2×#937—32no—
44C2×#883—32no—
45C2×#883—32no—
46C2×#883—61no—
47C3×#386—32no—
48#5220—32no—
49#5210—32no—
50#4956—32no—
51#4956D312yescomplemented
52#4955—32no—
53#4950—32no—
54#4668—32no—
55#4668—32no—
56#4664—32no—
57#4664—32no—
58C24×C32C2311yescharacteristic
59C23×C3⋊D3C2311yescharacteristic
60C23×C3×D3C2312yes—
61C22×D32—22no—
62C22×D32—22no—
63C22×D32—24no—
64C22×D32—24no—
65C22×D32D414yes—
66C22×C32×C4C2311yescharacteristic
67C22×C32×C4C2311yescharacteristic
68C2×#638—22no—
69C2×#638—22no—
70C2×#638—22no—
71C22×C3⋊Dic3C2311yescharacteristic
72C22×C3⋊Dic3C2311yescharacteristic
73C22×C3⋊Dic3C2311yescharacteristic
74C2×C4×C3⋊D3—22no—
75C2×C4×C3⋊D3—22no—
76C2×C4×C3⋊D3D414yescomplemented
77C2×C3×#67—24no—
78C2×C3×#67—24no—
79C2×C3×#67—24no—
80C22×C3×Dic3C2312yes—
81C22×C3×Dic3C2312yes—
82C22×C3×Dic3C2312yes—
83C2×C3×C4×D3—24no—
84C2×C3×C4×D3—24no—
85C2×C3×C4×D3—24no—
86C2×#624—22no—
87C2×#624—22no—
88C2×#624D414yescomplemented
89C2×D3×Dic3—24no—
90C2×D3×Dic3—24no—
91C2×D3×Dic3—24no—
92C4×D32—232no—
93C32×C22⋊C4—22no—
94#3757—22no—
95#3752—22no—
96C4⋊(C3⋊Dic3)—22no—
97#3750—22no—
98C3×#217—24no—
99C3×(C2×D3)⋊C4—24no—
100Dic3⋊Dic3—24no—
101#3722—22no—
102#3722—22no—
103(C2×D3)⋊Dic3—24no—
104(C2×D3)⋊Dic3—24no—
105#2849—91noSylow
106C24×D3—32no—
107C22×C3×D4—32no—
108C23×C3×C4—32no—
109C22×#67—32no—
110C22×#67—61no—
111C22×#67C2×D312yes—
112C23×Dic3—32no—
113C22×C4×D3—32no—
114C22×C4×D3—32no—
115C22×C4×D3—32no—
116C22×C4×D3—61no—
117C22×C4×D3—68no—
118C22×C4×D3—68no—
119C22×C4×D3—68no—
120C22×C4×D3C2×D312yes—
121C2×C3×C22⋊C4—21no—
122C2×C3×C22⋊C4—32no—
123C2×C3×C22⋊C4—32no—
124C2×C3×C22⋊C4C2×D312yescomplemented
125C2×#217—32no—
126C2×#217—32no—
127C2×#217—32no—
128C2×#217—61no—
129C2×#217C2×D312yescomplemented
130#937—68no—
131C2×(C2×D3)⋊C4—32no—
132C2×(C2×D3)⋊C4—32no—
133C2×(C2×D3)⋊C4—32no—
134C2×(C2×D3)⋊C4—32no—
135C2×(C2×D3)⋊C4—32no—
136C2×(C2×D3)⋊C4—61no—
137C2×(C2×D3)⋊C4C2×D312yes—
138C2×C4⋊Dic3—32no—
139C2×C4⋊Dic3—32no—
140C2×C4⋊Dic3—61no—
141C2×Dic3⋊C4—32no—
142C2×Dic3⋊C4—32no—
143C2×Dic3⋊C4—61no—
144#883—68no—
145#883—68no—
146#883—68no—
147C3×#95—32no—
148C3×#95—32no—
149C3⋊#95—32no—
150C3⋊#95—32no—
151C3⋊#95—32no—
152C3⋊#95—32no—
153C3⋊#95C2×D312yescomplemented
154C3⋊#95C2×D312yescomplemented
155C23×C32—21no—
156C23×C32—21no—
157C23×C32—21no—
158C23×C32—22no—
159C23×C32—22no—
160C23×C32C2411yescharacteristic
161C22×C3⋊D3—22no—
162C22×C3⋊D3—22no—
163C22×C3⋊D3C2×D412yes—
164C22×C3⋊D3C2×D412yes—
165C22×C3⋊D3C2×D412yes—
166C22×C3×D3—22no—
167C22×C3×D3—22no—
168C22×C3×D3—22no—
169C22×C3×D3—22no—
170C22×C3×D3C2×D414yes—
171C22×C3×D3#4114yes—
172C22×C3×D3#4114yes—
173C2×D32—28no—
174C2×D32—216no—
175C2×D32—28no—
176C2×D32—28no—
177C2×D32—216no—
178C2×C32×C4—21no—
179C2×C32×C4—21no—
180C2×C32×C4—21no—
181C2×C32×C4—22no—
182C2×C32×C4C2×D412yes—
183#638—44no—
184C2×C3⋊Dic3—21no—
185C2×C3⋊Dic3—21no—
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3—22no—
191C2×C3⋊Dic3C2×D412yes—
192C4×C3⋊D3—28no—
193C3×#67—48no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—22no—
200C2×C3×Dic3—22no—
201C2×C3×Dic3—22no—
202C2×C3×Dic3C2×D414yes—
203C3×C4×D3—216no—
204#624—28no—
205D3×Dic3—216no—
206C24×C4—91no—
207C2×#123—91no—
208C2×#123—91no—
209C2×#120—91no—
210#386—32no—
211#386—92no—
212#385—92no—
213#385—92no—
214#381—91no—
215#381—91no—
216#379—91no—
217C24×C3—21no—
218C24×C3—32no—
219C24×C3C22×D312yes—
220C23×D3—32no—
221C23×D3—38no—
222C23×D3—61no—
223C23×D3—64no—
224C23×D3—64no—
225C23×D3—64no—
226C23×D3—64no—
227C23×D3—64no—
228C23×D3—64no—
229C23×D3C22×D312yes—
230C2×C3×D4—64no—
231C2×C3×D4—64no—
232C2×C3×D4—64no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—32no—
236C22×C3×C4—32no—
237C22×C3×C4—32no—
238C22×C3×C4—64no—
239C22×C3×C4—64no—
240C22×C3×C4—64no—
241C22×C3×C4C22×D312yes—
242C22×C3×C4C22×D312yes—
243C2×#67—24no—
244C2×#67—24no—
245C2×#67—24no—
246C2×#67—64no—
247C2×#67—64no—
248C2×#67—64no—
249C2×#67—64no—
250C2×#67—122no—
251C2×#67—122no—
252C22×Dic3—32no—
253C22×Dic3—32no—
254C22×Dic3—32no—
255C22×Dic3—61no—
256C22×Dic3—61no—
257C22×Dic3—61no—
258C22×Dic3—64no—
259C22×Dic3—64no—
260C22×Dic3—64no—
261C22×Dic3C22×D312yes—
262C22×Dic3C22×D312yes—
263C22×Dic3C22×D312yes—
264C2×C4×D3—24no—
265C2×C4×D3—24no—
266C2×C4×D3—24no—
267C2×C4×D3—38no—
268C2×C4×D3—38no—
269C2×C4×D3—64no—
270C2×C4×D3—664no—
271C2×C4×D3—64no—
272C2×C4×D3—64no—
273C2×C4×D3—64no—
274C2×C4×D3—64no—
275C2×C4×D3—64no—
276C2×C4×D3—64no—
277C2×C4×D3—64no—
278C2×C4×D3—122no—
279C2×C4×D3—122no—
280C3×C22⋊C4—24no—
281C3×C22⋊C4—24no—
282C3×C22⋊C4—64no—
283C3×C22⋊C4—64no—
284#217—24no—
285#217—64no—
286#217—64no—
287#217—64no—
288#217—64no—
289(C2×D3)⋊C4—24no—
290(C2×D3)⋊C4—64no—
291(C2×D3)⋊C4—64no—
292(C2×D3)⋊C4—64no—
293(C2×D3)⋊C4—64no—
294(C2×D3)⋊C4—64no—
295(C2×D3)⋊C4—64no—
296C4⋊Dic3—64no—
297C4⋊Dic3—64no—
298C4⋊Dic3—64no—
299Dic3⋊C4—64no—
300Dic3⋊C4—64no—
301Dic3⋊C4—64no—
302C22×C32—41no—
303C22×C32—41no—
304C22×C32—41no—
305C22×C32—42no—
306C22×C32—42no—
307C22×C32C22×D411yescharacteristic
308C22×C32C22×D411yescharacteristic
309C22×C32C22×D411yescharacteristic
310C22×C32C2×#4112yes—
311C22×C32C2×#4112yes—
312C2×C3⋊D3—24no—
313C2×C3⋊D3—22no—
314C2×C3⋊D3—24no—
315C2×C3⋊D3—22no—
316C2×C3⋊D3#12014yes—
317C2×C3×D3—24no—
318C2×C3×D3—24no—
319C2×C3×D3—24no—
320C2×C3×D3—24no—
321C2×C3×D3—24no—
322C2×C3×D3—24no—
323C2×C3×D3#12318yescomplemented
324D32—232no—
325C32×C4—22no—
326C32×C4—41no—
327C3⋊Dic3—22no—
328C3⋊Dic3—41no—
329C3⋊Dic3—41no—
330C3×Dic3—24no—
331C3×Dic3—42no—
332C3×Dic3—42no—
333C25—91no—
334C22×D4—32no—
335C22×D4—91no—
336C23×C4—32no—
337C23×C4—91no—
338C23×C4—92no—
339C23×C4—91no—
340C23×C4—184no—
341C23×C4—184no—
342C23×C4—184no—
343#123—184no—
344#123—184no—
345#120—184no—
346C2×C4⋊C4—92no—
347C2×C4⋊C4—91no—
348C2×C4⋊C4—91no—
349C2×C22⋊C4—32no—
350C2×C22⋊C4—32no—
351C2×C22⋊C4—91no—
352C2×C22⋊C4—91no—
353C2×C22⋊C4—92no—
354C2×C22⋊C4—92no—
355C2×C22⋊C4—91no—
356C2×C22⋊C4—91no—
357C2×C22⋊C4D3211yescharacteristic, complemented
358#95—32no—
359#95—32no—
360#95—92no—
361#95—92no—
362C23×C3—22no—
363C23×C3—22no—
364C23×C3—22no—
365C23×C3—22no—
366C23×C3—22no—
367C23×C3—22no—
368C23×C3—22no—
369C23×C3—22no—
370C23×C3—21no—
371C23×C3—34no—
372C23×C3—34no—
373C23×C3—34no—
374C23×C3—41no—
375C23×C3—41no—
376C23×C3—42no—
377C23×C3—42no—
378C23×C3—62no—
379C23×C3—62no—
380C23×C3—62no—
381C23×C3—62no—
382C23×C3C23×D312yes—
383C22×D3—22no—
384C22×D3—22no—
385C22×D3—22no—
386C22×D3—22no—
387C22×D3—34no—
388C22×D3—34no—
389C22×D3—34no—
390C22×D3—62no—
391C22×D3—62no—
392C22×D3—62no—
393C22×D3—616no—
394C22×D3—616no—
395C22×D3—616no—
396C22×D3—616no—
397C22×D3—616no—
398C22×D3—616no—
399C22×D3—62no—
400C22×D3—62no—
401C22×D3—62no—
402C22×D3—62no—
403C22×D3—616no—
404C22×D3—122no—
405C22×D3—122no—
406C22×D3#23514yes—
407C22×D3D3×D414yes—
408C22×D3#23714yes—
409C3×D4—128no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—34no—
418C2×C3×C4—41no—
419C2×C3×C4—41no—
420C2×C3×C4—42no—
421C2×C3×C4—616no—
422C2×C3×C4—62no—
423C2×C3×C4—62no—
424C2×C3×C4—62no—
425C2×C3×C4—62no—
426C2×C3×C4—62no—
427C2×C3×C4—62no—
428C2×C3×C4—62no—
429C2×C3×C4—62no—
430C2×C3×C4D3×D414yes—
431#67—48no—
432#67—128no—
433#67—128no—
434C2×Dic3—22no—
435C2×Dic3—22no—
436C2×Dic3—22no—
437C2×Dic3—22no—
438C2×Dic3—22no—
439C2×Dic3—22no—
440C2×Dic3—22no—
441C2×Dic3—22no—
442C2×Dic3—34no—
443C2×Dic3—62no—
444C2×Dic3—616no—
445C2×Dic3—62no—
446C2×Dic3—62no—
447C2×Dic3—62no—
448C2×Dic3—62no—
449C2×Dic3—62no—
450C2×Dic3—62no—
451C2×Dic3—62no—
452C2×Dic3—62no—
453C2×Dic3—62no—
454C2×Dic3—62no—
455C2×Dic3—121no—
456C2×Dic3—121no—
457C2×Dic3—122no—
458C2×Dic3—121no—
459C2×Dic3—121no—
460C2×Dic3D3×D414yes—
461C4×D3—216no—
462C4×D3—616no—
463C4×D3—616no—
464C4×D3—616no—
465C4×D3—128no—
466C2×C32—81no—
467C2×C32C2×#12011yescharacteristic
468C2×C32C2×#12312yes—
469C2×C32#52511yescharacteristic
470C2×C32#52512yes—
471C2×C32#52511yescharacteristic
472C3⋊D3—24no—
473C3×D3—28no—
474C24—32no—
475C24—94no—
476C24—91no—
477C24—184no—
478C24—184no—
479C24—182no—
480C24—182no—
481C24C2×D3211yescharacteristic
482C2×D4—64no—
483C2×D4—64no—
484C2×D4—64no—
485C2×D4—182no—
486C2×D4—182no—
487C2×D4—182no—
488C22×C4—32no—
489C22×C4—32no—
490C22×C4—32no—
491C22×C4—64no—
492C22×C4—64no—
493C22×C4—64no—
494C22×C4—94no—
495C22×C4—91no—
496C22×C4—94no—
497C22×C4—91no—
498C22×C4—91no—
499C22×C4—182no—
500C22×C4—182no—
501C22×C4—184no—
502C22×C4—182no—
503C22×C4—182no—
504C22×C4—1832no—
505C22×C4—184no—
506C22×C4—184no—
507C22×C4C2×D3211yescharacteristic
508C22×C4C2×D3211yescharacteristic
509C4⋊C4—182no—
510C4⋊C4—184no—
511C4⋊C4—182no—
512C22⋊C4—22no—
513C22⋊C4—64no—
514C22⋊C4—64no—
515C22⋊C4—182no—
516C22⋊C4—182no—
517C22⋊C4—182no—
518C22⋊C4—184no—
519C22⋊C4—184no—
520C22⋊C4—182no—
521C22×C3—22no—
522C22×C3—21no—
523C22×C3—21no—
524C22×C3—22no—
525C22×C3—21no—
526C22×C3—38no—
527C22×C3—42no—
528C22×C3—42no—
529C22×C3—42no—
530C22×C3—42no—
531C22×C3—42no—
532C22×C3—42no—
533C22×C3—42no—
534C22×C3—42no—
535C22×C3—42no—
536C22×C3—42no—
537C22×C3—64no—
538C22×C3—64no—
539C22×C3—64no—
540C22×C3—64no—
541C22×C3—64no—
542C22×C3—64no—
543C22×C3—82no—
544C22×C3—82no—
545C22×C3C2×#23512yes—
546C22×C3C2×D3×D412yes—
547C22×C3C2×D3×D412yes—
548C22×C3C2×D3×D412yes—
549C22×C3C2×#23712yes—
550C22×C3D3×#4112yes—
551C22×C3D3×#4112yes—
552C2×D3—24no—
553C2×D3—24no—
554C2×D3—24no—
555C2×D3—24no—
556C2×D3—24no—
557C2×D3—24no—
558C2×D3—38no—
559C2×D3—64no—
560C2×D3—664no—
561C2×D3—64no—
562C2×D3—64no—
563C2×D3—64no—
564C2×D3—64no—
565C2×D3—64no—
566C2×D3—64no—
567C2×D3—122no—
568C2×D3—124no—
569C2×D3—122no—
570C2×D3—124no—
571C2×D3#88318yescomplemented
572C3×C4—24no—
573C3×C4—42no—
574C3×C4—42no—
575C3×C4—42no—
576C3×C4—64no—
577C3×C4—122no—
578C3×C4—122no—
579Dic3—24no—
580Dic3—42no—
581Dic3—42no—
582Dic3—64no—
583Dic3—122no—
584Dic3—122no—
585Dic3—122no—
586Dic3—122no—
587Dic3—122no—
588C32#284911yescharacteristic, complemented, Sylow
589C23—22no—
590C23—21no—
591C23—21no—
592C23—22no—
593C23—21no—
594C23—34no—
595C23—34no—
596C23—34no—
597C23—62no—
598C23—62no—
599C23—62no—
600C23—62no—
601C23—92no—
602C23—92no—
603C23—92no—
604C23—1816no—
605C23—188no—
606C23—188no—
607C23—188no—
608C23—1816no—
609C23—182no—
610C23—182no—
611C23C22×D3211yescharacteristic
612D4—128no—
613D4—364no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—22no—
617C2×C4—21no—
618C2×C4—34no—
619C2×C4—616no—
620C2×C4—62no—
621C2×C4—62no—
622C2×C4—62no—
623C2×C4—62no—
624C2×C4—62no—
625C2×C4—62no—
626C2×C4—62no—
627C2×C4—62no—
628C2×C4—92no—
629C2×C4—188no—
630C2×C4—188no—
631C2×C4—1816no—
632C2×C4—181no—
633C2×C4—181no—
634C2×C4—182no—
635C2×C4—181no—
636C2×C4—181no—
637C2×C4—181no—
638C2×C4—181no—
639C2×C4#381112yes—
640C2×C3—21no—
641C2×C3—21no—
642C2×C3—22no—
643C2×C3—21no—
644C2×C3—22no—
645C2×C3—68no—
646C2×C3—82no—
647C2×C3—82no—
648C2×C3C2×#88312yes—
649C2×C3#554712yes—
650C2×C3#554712yes—
651C2×C3D3×#12012yes—
652C2×C3#560612yes—
653C2×C3#560612yes—
654C2×C3D3×#12312yes—
655D3—28no—
656D3—68no—
657D3—124no—
658C22—38no—
659C22—41no—
660C22—41no—
661C22—42no—
662C22—41no—
663C22—42no—
664C22—64no—
665C22—64no—
666C22—64no—
667C22—64no—
668C22—64no—
669C22—64no—
670C22—94no—
671C22—1832no—
672C22—182no—
673C22—184no—
674C22—182no—
675C22—184no—
676C22D3×#23512yes—
677C22D32×D411yescharacteristic
678C22D32×D411yescharacteristic
679C22D3×#23712yes—
680C22C2×#381111yescharacteristic
681C4—22no—
682C4—41no—
683C4—64no—
684C4—122no—
685C4—122no—
686C4—182no—
687C4—361no—
688C4—361no—
689C3—21no—
690C3#7493612yescomplemented
691C2—68no—
692C2—81no—
693C2—184no—
694C2D3×#88312yes—
695C2#1059428612yes—
696C2#1059507611yescharacteristic
697C2#1059527811yescharacteristic
698C2#1059530611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC2×#63983C2
hypercenterC2×C22⋊C4D32
hypocenterC32#2849
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C4×D32C2semidirect
2. C2×#64092C2semidirect
4. C2×#63975C2semidirect
5. C3×#4956C2semidirect
6. #10591721C2semidirect
7. #10591399C2semidirect
8. #10591379C2semidirect
9. #10591371C2semidirect
10. #10591278C2semidirect
11. #10591219C2semidirect
23. C2×C32×C22⋊C4C22semidirect
24. C2×#3757C22semidirect
26. C2×C4⋊(C3⋊Dic3)C22semidirect
27. C2×#3750C22semidirect
29. C2×C3×#217C22semidirect
33. C2×Dic3⋊Dic3C22semidirect
38. C3×C3⋊#95C22semidirect
39. C3×C3⋊#95C22semidirect
40. #63579C22semidirect
41. #63579C22semidirect
51. #4956D3semidirect
76. C2×C4×C3⋊D3D4semidirect
88. C2×#624D4semidirect
124. C2×C3×C22⋊C4C2×D3semidirect
129. C2×#217C2×D3semidirect
153. C3⋊#95C2×D3semidirect
154. C3⋊#95C2×D3semidirect
323. C2×C3×D3#123semidirect
357. C2×C22⋊C4D32semidirect
571. C2×D3#883semidirect
588. C32#2849semidirect
690. C3#74936semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D322
C2×#640922
C2×#639832
C2×#639752
C3×#49562
#105917212
#105913992
#105913792
#105913712
#105912782
#105912192
#749363