Finite Group Databasebeta

← #11856277

Subgroups — #11856277

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×#64103C211yesmaximal, characteristic, complemented
3C2×#63923C211yesmaximal, characteristic
4C2×#63897C211yesmaximal, characteristic, complemented
5C3×#4989C212yesmaximal, complemented
6#10591399C211yesmaximal, characteristic, complemented
7#10591382C212yesmaximal, complemented
8#10591372C212yesmaximal, complemented
9#10591371C211yesmaximal, characteristic, complemented
10#10591364C212yesmaximal, complemented
11#10591219C211yesmaximal, characteristic, complemented
12#74656—32nomaximal
13C23×D32C2211yescharacteristic
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×C3×C4×D3C2212yes—
17C22×#626C2212yes—
18C22×#624C2211yescharacteristic
19C22×D3×Dic3C2212yes—
20C2×C4×D32—24no—
21C2×C4×D32—24no—
22C2×C4×D32—24no—
23C2×C32×C4⋊C4C2211yescharacteristic, complemented
24C2×#3752C2211yescharacteristic
25C2×#3752C2211yescharacteristic, complemented
26C2×#3752C2211yescharacteristic, complemented
27C2×#3750C2211yescharacteristic, complemented
28#64103—24no—
29C2×C3×(C2×D3)⋊C4C2212yes—
30C2×C3×(C2×D3)⋊C4C2212yes—
31C2×C3×Dic3⋊C4C2212yescomplemented
32C2×#3722C2211yescharacteristic
33C2×#3722C2211yescharacteristic
34C2×#3722C2212yescomplemented
35C2×(C2×D3)⋊Dic3C2212yes—
36#63923—24no—
37#63897—24no—
38C3×C3⋊#95C2212yescomplemented
39C3×C3⋊#95C2212yescomplemented
40#63579C2212yescomplemented
41#63579C2212yescomplemented
42C23×C4×D3—32no—
43C2×#894—32no—
44C2×#894—32no—
45C2×#894—61no—
46C2×#882—32no—
47C3×#385—32no—
48#5213—32no—
49#4989—32no—
50#4989D312yescomplemented
51#4958—32no—
52#4955—32no—
53#4946—32no—
54#4665—32no—
55#4665—32no—
56#4664—32no—
57#4664—32no—
58C23×C3⋊D3C2311yescharacteristic
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
68C22×C32×C4C2311yescharacteristic
69C22×C3⋊Dic3C2311yescharacteristic
70C22×C3⋊Dic3C2311yescharacteristic
71C2×C4⋊(C3⋊D3)—22no—
72C2×C4⋊(C3⋊D3)—22no—
73C2×C4⋊(C3⋊D3)—22no—
74C2×C4×C3⋊D3—22no—
75C2×C4×C3⋊D3—22no—
76C2×C4×C3⋊D3D414yescomplemented
77C22×C3×Dic3C2312yes—
78C22×C3×Dic3C2312yes—
79C22×C3×Dic3C2312yes—
80C2×C3×C4×D3—24no—
81C2×C3×C4×D3—24no—
82C2×C3×C4×D3—24no—
83C2×#626—24no—
84C2×#626—24no—
85C2×#626—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×C4⋊C4—22no—
94#3752—22no—
95#3752—22no—
96#3752—22no—
97#3750—22no—
98C3×(C2×D3)⋊C4—24no—
99C3×(C2×D3)⋊C4—24no—
100C3×Dic3⋊C4—24no—
101#3722—22no—
102#3722—22no—
103#3722—24no—
104(C2×D3)⋊Dic3—24no—
105#2849—91noSylow
106C24×D3—32no—
107C23×C3×C4—32no—
108C22×#67—32no—
109C23×Dic3—32no—
110C22×D12—32no—
111C22×D12—32no—
112C22×D12—61no—
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×C4⋊C4—21no—
122C2×C3×C4⋊C4—32no—
123C2×C3×C4⋊C4C2×D312yescomplemented
124C2×C3×C22⋊C4—32no—
125C2×C3×C22⋊C4—32no—
126C2×#217—32no—
127C2×(C2×D3)⋊C4—32no—
128C2×(C2×D3)⋊C4—32no—
129C2×(C2×D3)⋊C4—32no—
130C2×(C2×D3)⋊C4—32no—
131C2×(C2×D3)⋊C4—32no—
132C2×(C2×D3)⋊C4—32no—
133C2×(C2×D3)⋊C4—32no—
134C2×(C2×D3)⋊C4—32no—
135C2×(C2×D3)⋊C4—61no—
136C2×(C2×D3)⋊C4—61no—
137C2×(C2×D3)⋊C4—61no—
138C2×(C2×D3)⋊C4C2×D312yes—
139C2×(C2×D3)⋊C4C2×D312yes—
140C2×Dic3⋊C4—32no—
141C2×Dic3⋊C4—61no—
142C2×Dic3⋊C4C2×D312yescomplemented
143#894—68no—
144#894—68no—
145#894—68no—
146#882—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×C32C2411yescharacteristic
156C22×C3⋊D3—21no—
157C22×C3⋊D3—22no—
158C22×C3⋊D3—22no—
159C22×C3⋊D3—21no—
160C22×C3⋊D3—21no—
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—21no—
182C2×C32×C4—21no—
183C2×C32×C4—21no—
184C2×C32×C4—22no—
185C2×C32×C4C2×D412yes—
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3—22no—
190C2×C3⋊Dic3C2×D412yes—
191C4⋊(C3⋊D3)—44no—
192C4×C3⋊D3—28no—
193C2×C3×Dic3—22no—
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×Dic3C2×D414yes—
202C3×C4×D3—216no—
203#626—48no—
204#624—28no—
205D3×Dic3—216no—
206C24×C4—91no—
207C2×#123—91no—
208C2×#123—91no—
209C2×#120—91no—
210#386—92no—
211#386—92no—
212#385—32no—
213#385—92no—
214#381—91no—
215#381—91no—
216#379—91no—
217C24×C3—32no—
218C23×D3—32no—
219C23×D3—38no—
220C23×D3—32no—
221C23×D3—61no—
222C23×D3—61no—
223C23×D3—64no—
224C23×D3—64no—
225C23×D3—64no—
226C23×D3—64no—
227C23×D3—64no—
228C23×D3—64no—
229C23×D3C22×D312yes—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—32no—
234C22×C3×C4—32no—
235C22×C3×C4—32no—
236C22×C3×C4—64no—
237C22×C3×C4—64no—
238C22×C3×C4—64no—
239C22×C3×C4C22×D312yes—
240C22×C3×C4C22×D312yes—
241C22×C3×C4C22×D312yes—
242C2×#67—64no—
243C2×#67—64no—
244C2×#67—64no—
245C22×Dic3—32no—
246C22×Dic3—32no—
247C22×Dic3—61no—
248C22×Dic3—61no—
249C22×Dic3—64no—
250C22×Dic3—64no—
251C22×Dic3—64no—
252C22×Dic3C22×D312yes—
253C22×Dic3C22×D312yes—
254C22×Dic3C22×D312yes—
255C2×D12—64no—
256C2×D12—64no—
257C2×D12—64no—
258C2×D12—64no—
259C2×D12—64no—
260C2×D12—64no—
261C2×D12—64no—
262C2×D12—122no—
263C2×D12—122no—
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×C4⋊C4—24no—
281C3×C4⋊C4—24no—
282C3×C4⋊C4—64no—
283C3×C22⋊C4—64no—
284C3×C22⋊C4—64no—
285#217—64no—
286(C2×D3)⋊C4—24no—
287(C2×D3)⋊C4—24no—
288(C2×D3)⋊C4—64no—
289(C2×D3)⋊C4—64no—
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—
296(C2×D3)⋊C4—64no—
297(C2×D3)⋊C4—64no—
298(C2×D3)⋊C4—64no—
299Dic3⋊C4—24no—
300Dic3⋊C4—64no—
301Dic3⋊C4—64no—
302C22×C32C22×D411yescharacteristic
303C22×C32C22×D411yescharacteristic
304C22×C32C22×D411yescharacteristic
305C22×C32C2×#4112yes—
306C22×C32C2×#4112yes—
307C2×C3⋊D3—24no—
308C2×C3⋊D3—22no—
309C2×C3⋊D3—24no—
310C2×C3⋊D3—22no—
311C2×C3⋊D3—41no—
312C2×C3⋊D3—41no—
313C2×C3⋊D3—41no—
314C2×C3⋊D3—42no—
315C2×C3⋊D3—42no—
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—
327C32×C4—41no—
328C3⋊Dic3—22no—
329C3⋊Dic3—41no—
330C3×Dic3—24no—
331C3×Dic3—42no—
332C3×Dic3—42no—
333C25—91no—
334C22×D4—92no—
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—32no—
347C2×C4⋊C4—91no—
348C2×C4⋊C4D3211yescharacteristic, complemented
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⋊C4—91no—
358#95—32no—
359#95—32no—
360#95—92no—
361#95—92no—
362C23×C3—21no—
363C23×C3—34no—
364C23×C3—34no—
365C23×C3—34no—
366C23×C3—62no—
367C23×C3—62no—
368C23×C3—62no—
369C23×C3—62no—
370C23×C3C23×D312yes—
371C22×D3—22no—
372C22×D3—22no—
373C22×D3—22no—
374C22×D3—22no—
375C22×D3—34no—
376C22×D3—34no—
377C22×D3—34no—
378C22×D3—62no—
379C22×D3—62no—
380C22×D3—62no—
381C22×D3—616no—
382C22×D3—616no—
383C22×D3—616no—
384C22×D3—616no—
385C22×D3—616no—
386C22×D3—616no—
387C22×D3—62no—
388C22×D3—62no—
389C22×D3—62no—
390C22×D3—62no—
391C22×D3—616no—
392C22×D3—62no—
393C22×D3—62no—
394C22×D3—62no—
395C22×D3—62no—
396C22×D3—62no—
397C22×D3—62no—
398C22×D3—62no—
399C22×D3—62no—
400C22×D3—122no—
401C22×D3—122no—
402C22×D3—121no—
403C22×D3—121no—
404C22×D3—122no—
405C22×D3—122no—
406C22×D3#23514yes—
407C22×D3D3×D414yes—
408C22×D3#23914yes—
409C2×C3×C4—22no—
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—22no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—34no—
421C2×C3×C4—41no—
422C2×C3×C4—41no—
423C2×C3×C4—41no—
424C2×C3×C4—41no—
425C2×C3×C4—42no—
426C2×C3×C4—616no—
427C2×C3×C4—62no—
428C2×C3×C4—62no—
429C2×C3×C4—62no—
430C2×C3×C4—62no—
431C2×C3×C4—62no—
432C2×C3×C4—62no—
433C2×C3×C4—62no—
434C2×C3×C4—62no—
435C2×C3×C4D3×D414yes—
436#67—128no—
437C2×Dic3—22no—
438C2×Dic3—22no—
439C2×Dic3—22no—
440C2×Dic3—22no—
441C2×Dic3—22no—
442C2×Dic3—22no—
443C2×Dic3—22no—
444C2×Dic3—22no—
445C2×Dic3—34no—
446C2×Dic3—62no—
447C2×Dic3—616no—
448C2×Dic3—62no—
449C2×Dic3—62no—
450C2×Dic3—62no—
451C2×Dic3—62no—
452C2×Dic3—62no—
453C2×Dic3—62no—
454C2×Dic3—121no—
455C2×Dic3—121no—
456C2×Dic3—122no—
457C2×Dic3D3×D414yes—
458D12—128no—
459D12—128no—
460D12—128no—
461C4×D3—216no—
462C4×D3—616no—
463C4×D3—616no—
464C4×D3—616no—
465C4×D3—128no—
466C2×C32C2×#12011yescharacteristic
467C2×C32C2×#12312yes—
468C2×C32#52511yescharacteristic
469C2×C32#52512yes—
470C2×C32#52511yescharacteristic
471C3⋊D3—24no—
472C3⋊D3—81no—
473C3×D3—28no—
474C24—32no—
475C24—94no—
476C24—91no—
477C24—91no—
478C24—184no—
479C24—184no—
480C24—182no—
481C24—182no—
482C2×D4—182no—
483C2×D4—182no—
484C2×D4—182no—
485C2×D4—184no—
486C2×D4—184no—
487C2×D4—184no—
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—182no—
499C22×C4—182no—
500C22×C4—184no—
501C22×C4—182no—
502C22×C4—182no—
503C22×C4—1832no—
504C22×C4—184no—
505C22×C4—184no—
506C22×C4C2×D3211yescharacteristic
507C22×C4C2×D3211yescharacteristic
508C22×C4C2×D3211yescharacteristic
509C4⋊C4—22no—
510C4⋊C4—64no—
511C4⋊C4—182no—
512C22⋊C4—64no—
513C22⋊C4—64no—
514C22⋊C4—182no—
515C22⋊C4—182no—
516C22⋊C4—184no—
517C22⋊C4—182no—
518C22⋊C4—182no—
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—64no—
528C22×C3—64no—
529C22×C3—64no—
530C22×C3—64no—
531C22×C3—64no—
532C22×C3—64no—
533C22×C3C2×#23512yes—
534C22×C3C2×D3×D412yes—
535C22×C3C2×D3×D412yes—
536C22×C3C2×D3×D412yes—
537C22×C3C2×#23912yes—
538C22×C3D3×#4112yes—
539C22×C3D3×#4112yes—
540C2×D3—24no—
541C2×D3—24no—
542C2×D3—24no—
543C2×D3—24no—
544C2×D3—24no—
545C2×D3—24no—
546C2×D3—38no—
547C2×D3—64no—
548C2×D3—664no—
549C2×D3—64no—
550C2×D3—64no—
551C2×D3—64no—
552C2×D3—64no—
553C2×D3—64no—
554C2×D3—64no—
555C2×D3—122no—
556C2×D3—124no—
557C2×D3—124no—
558C2×D3—122no—
559C2×D3—122no—
560C2×D3—122no—
561C2×D3—122no—
562C2×D3—122no—
563C2×D3—122no—
564C2×D3—122no—
565C2×D3—122no—
566C2×D3—122no—
567C2×D3—122no—
568C2×D3—122no—
569C2×D3—242no—
570C2×D3—242no—
571C2×D3#89418yescomplemented
572C3×C4—24no—
573C3×C4—42no—
574C3×C4—42no—
575C3×C4—42no—
576C3×C4—42no—
577C3×C4—42no—
578C3×C4—64no—
579C3×C4—122no—
580C3×C4—122no—
581Dic3—24no—
582Dic3—42no—
583Dic3—42no—
584Dic3—64no—
585Dic3—122no—
586Dic3—122no—
587Dic3—122no—
588C32#284911yescharacteristic, complemented, Sylow
589C23—34no—
590C23—34no—
591C23—34no—
592C23—62no—
593C23—62no—
594C23—62no—
595C23—62no—
596C23—92no—
597C23—92no—
598C23—92no—
599C23—1816no—
600C23—188no—
601C23—188no—
602C23—1816no—
603C23—188no—
604C23—182no—
605C23—182no—
606C23—182no—
607C23—181no—
608C23—181no—
609C23—182no—
610C23—181no—
611C23C22×D3211yescharacteristic
612D4—364no—
613D4—368no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—22no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—34no—
622C2×C4—616no—
623C2×C4—62no—
624C2×C4—62no—
625C2×C4—62no—
626C2×C4—62no—
627C2×C4—62no—
628C2×C4—62no—
629C2×C4—62no—
630C2×C4—62no—
631C2×C4—92no—
632C2×C4—188no—
633C2×C4—188no—
634C2×C4—1816no—
635C2×C4—181no—
636C2×C4—181no—
637C2×C4—182no—
638C2×C4—181no—
639C2×C4#381112yes—
640C2×C3—21no—
641C2×C3—22no—
642C2×C3—22no—
643C2×C3—21no—
644C2×C3—21no—
645C2×C3—68no—
646C2×C3C2×#89412yes—
647C2×C3#554712yes—
648C2×C3#554712yes—
649C2×C3D3×#12012yes—
650C2×C3#562712yes—
651C2×C3#562712yes—
652C2×C3D3×#12312yes—
653D3—28no—
654D3—68no—
655D3—124no—
656D3—242no—
657D3—242no—
658C22—38no—
659C22—64no—
660C22—64no—
661C22—64no—
662C22—64no—
663C22—64no—
664C22—64no—
665C22—94no—
666C22—1832no—
667C22—182no—
668C22—184no—
669C22—184no—
670C22—182no—
671C22—361no—
672C22—362no—
673C22—362no—
674C22—361no—
675C22—361no—
676C22D3×#23512yes—
677C22D32×D411yescharacteristic
678C22D32×D411yescharacteristic
679C22D3×#23912yes—
680C22C2×#381111yescharacteristic
681C4—22no—
682C4—41no—
683C4—41no—
684C4—64no—
685C4—122no—
686C4—122no—
687C4—182no—
688C4—361no—
689C3—21no—
690C3#7465612yescomplemented
691C2—68no—
692C2—184no—
693C2—721no—
694C2D3×#89412yes—
695C2#1059462312yes—
696C2#1059507611yescharacteristic
697C2#1059527811yescharacteristic
698C2#1059543011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC2×#63923C2
hypercenterC2×C4⋊C4D32
hypocenterC32#2849
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C4×D32C2semidirect
2. C2×#64103C2semidirect
4. C2×#63897C2semidirect
5. C3×#4989C2semidirect
6. #10591399C2semidirect
7. #10591382C2semidirect
8. #10591372C2semidirect
9. #10591371C2semidirect
10. #10591364C2semidirect
11. #10591219C2semidirect
23. C2×C32×C4⋊C4C22semidirect
25. C2×#3752C22semidirect
26. C2×#3752C22semidirect
27. C2×#3750C22semidirect
31. C2×C3×Dic3⋊C4C22semidirect
34. C2×#3722C22semidirect
38. C3×C3⋊#95C22semidirect
39. C3×C3⋊#95C22semidirect
40. #63579C22semidirect
41. #63579C22semidirect
50. #4989D3semidirect
76. C2×C4×C3⋊D3D4semidirect
88. C2×#624D4semidirect
123. C2×C3×C4⋊C4C2×D3semidirect
142. C2×Dic3⋊C4C2×D3semidirect
153. C3⋊#95C2×D3semidirect
154. C3⋊#95C2×D3semidirect
323. C2×C3×D3#123semidirect
348. C2×C4⋊C4D32semidirect
571. C2×D3#894semidirect
588. C32#2849semidirect
690. C3#74656semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D322
C2×#641032
C2×#639232
C2×#638972
C3×#49892
#105913992
#105913822
#105913722
#105913712
#105913642
#105912192
#746563