Finite Group Databasebeta

← #11805763

Subgroups — #11805763

Order 1152.

1389 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic
2C3×#4937C211yesmaximal, characteristic, complemented
3C3×#4932C211yesmaximal, characteristic, complemented
4#10591380C212yesmaximal
5#10591370C211yesmaximal, characteristic, complemented
6#10591355C211yesmaximal, characteristic, complemented
7#10591271C212yesmaximal, complemented
8#10591260C211yesmaximal, characteristic, complemented
9#10591233C212yesmaximal, complemented
10#10591219C211yesmaximal, characteristic, complemented
11#10591202C212yesmaximal, complemented
12#74297—31nomaximal
13#73417—31nomaximal
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C22×#624C2212yes—
18C2×C32×C42C2211yescharacteristic
19C2×#3752C2211yescharacteristic
20C2×#3752C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C4×C4⋊(C3⋊D3)C418yescomplemented
23C2×C3×C4×Dic3C2212yes—
24C2×#3724C2212yes—
25C2×#3722C2212yes—
26C2×#3722C2212yes—
27C2×#3722C2212yes—
28C2×Dic32C2212yes—
29C3×C3⋊#95C2212yes—
30C3×C3⋊#95C2211yescharacteristic
31C3×C3⋊#95C2211yescharacteristic
32C3×C3⋊#95C2212yes—
33C3×C3⋊#95C2211yescharacteristic
34C3×C3⋊#95C2212yes—
35C3×C3⋊#95C2211yescharacteristic
36#63579C2212yes—
37#63579C2212yes—
38C2×C4×D12—31no—
39C2×C4×D12—31no—
40C2×C4×D12—61no—
41C3×#383—31no—
42C3×#376—31no—
43#4940—32no—
44C4×(C2×D3)⋊C4—32no—
45#4937D311yescharacteristic, complemented
46#4932D311yescharacteristic, complemented
47#4669—32no—
48#4667—31no—
49#4667—31no—
50#4666—32no—
51#4666—31no—
52#4666—31no—
53#4665—32no—
54#4665—32no—
55#4664—31no—
56#4664—31no—
57D3×#95—31no—
58D3×#95—31no—
59#4654—32no—
60#4653—32no—
61C23×C3⋊D3C2311yescharacteristic
62C23×C3⋊D3C2311yescharacteristic
63C22×C32×C4C2311yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3⋊Dic3C2311yescharacteristic
68C2×C4⋊(C3⋊D3)—22no—
69C2×C4⋊(C3⋊D3)—22no—
70C2×C4⋊(C3⋊D3)C2×C414yes—
71C2×C4×C3⋊D3—42no—
72C2×C4×C3⋊D3—42no—
73C2×C4×C3⋊D3C2×C414yes—
74C2×C4×C3⋊D3C2×C414yescomplemented
75C22×C3×Dic3C2312yes—
76C22×C3×Dic3C2312yes—
77C22×C3×Dic3C2312yes—
78C22×C3×Dic3C2312yes—
79C2×#624—24no—
80C2×#624—24no—
81C2×#624—42no—
82C32×C42C2×C414yescomplemented
83#3752C2×C414yes—
84#3752C2×C414yescomplemented
85C4⋊(C3⋊Dic3)C2×C414yescomplemented
86C3×C4×Dic3—24no—
87#3724—42no—
88#3722—24no—
89#3722—24no—
90#3722—42no—
91Dic32—42no—
92#2353—91noSylow
93C22×D12—31no—
94C22×D12—31no—
95C22×D12—61no—
96C22×C4×D3—31no—
97C22×C4×D3—31no—
98C22×C4×D3—31no—
99C22×C4×D3—31no—
100C22×C4×D3—32no—
101C22×C4×D3—32no—
102C22×C4×D3—61no—
103C22×C4×D3—61no—
104C2×C3×C42—21no—
105C2×C3×C42—32no—
106C2×C3×C42C2×D311yescharacteristic
107C2×C3×C42C2×D311yescharacteristic
108C2×(C2×D3)⋊C4—31no—
109C2×(C2×D3)⋊C4—31no—
110C2×(C2×D3)⋊C4—31no—
111C2×(C2×D3)⋊C4—31no—
112C2×(C2×D3)⋊C4—32no—
113C2×(C2×D3)⋊C4—32no—
114C2×(C2×D3)⋊C4—32no—
115C2×(C2×D3)⋊C4—32no—
116C2×(C2×D3)⋊C4—32no—
117C2×(C2×D3)⋊C4—32no—
118C2×(C2×D3)⋊C4—61no—
119C2×(C2×D3)⋊C4—61no—
120C2×C4⋊Dic3—31no—
121C2×C4⋊Dic3—31no—
122C2×C4⋊Dic3—61no—
123C2×Dic3⋊C4—32no—
124C2×Dic3⋊C4—32no—
125C2×C4×Dic3—32no—
126C2×C4×Dic3—32no—
127C2×C4×Dic3C2×D312yes—
128C4×D12—38no—
129C4×D12—38no—
130C4×D12—68no—
131C3×#95—32no—
132C3×#95—32no—
133C3×#95—31no—
134C3×#95—31no—
135C3×#95—31no—
136C3×#95—31no—
137C3×#95—32no—
138C3⋊#95—32no—
139C3⋊#95—32no—
140C3⋊#95—32no—
141C3⋊#95—32no—
142C3⋊#95C2×D312yes—
143C3⋊#95C2×D312yes—
144C3⋊#95C2×D311yescharacteristic
145C3⋊#95C2×D311yescharacteristic
146C3⋊#95C2×D311yescharacteristic
147C3⋊#95C2×D311yescharacteristic
148C3⋊#95C2×D312yes—
149C23×C32C2411yescharacteristic
150C22×C3⋊D3—21no—
151C22×C3⋊D3—21no—
152C22×C3⋊D3—22no—
153C22×C3⋊D3—22no—
154C22×C3⋊D3—22no—
155C22×C3⋊D3—22no—
156C22×C3⋊D3C22×C412yes—
157C22×C3⋊D3C22×C412yes—
158C22×C3⋊D3#4112yes—
159C22×C3⋊D3#4112yes—
160C2×C32×C4—21no—
161C2×C32×C4—21no—
162C2×C32×C4—22no—
163C2×C32×C4—22no—
164C2×C32×C4C22×C412yes—
165C2×C32×C4C22×C412yes—
166C2×C32×C4C22×C412yes—
167C2×C3⋊Dic3—22no—
168C2×C3⋊Dic3—22no—
169C2×C3⋊Dic3C22×C412yes—
170C2×C3⋊Dic3C22×C412yes—
171C4⋊(C3⋊D3)—28no—
172C4×C3⋊D3—44no—
173C4×C3⋊D3—44no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3#4114yes—
186#624—48no—
187C2×C4×D4—91no—
188#388—92no—
189#387—92no—
190#386—92no—
191#383—31no—
192#381—91no—
193#380—91no—
194C4×C22⋊C4—91no—
195C4×C22⋊C4—92no—
196#376—31no—
197C2×#95—91no—
198C23×D3—31no—
199C23×D3—31no—
200C23×D3—31no—
201C23×D3—31no—
202C23×D3—61no—
203C23×D3—61no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—32no—
208C22×C3×C4—32no—
209C22×C3×C4—32no—
210C22×C3×C4—32no—
211C22×C3×C4C22×D311yescharacteristic
212C22×C3×C4C22×D311yescharacteristic
213C22×C3×C4C22×D311yescharacteristic
214C22×C3×C4C22×D311yescharacteristic
215C22×C3×C4C22×D311yescharacteristic
216C22×C3×C4C22×D311yescharacteristic
217C22×Dic3—31no—
218C22×Dic3—31no—
219C22×Dic3—31no—
220C22×Dic3—31no—
221C22×Dic3—61no—
222C22×Dic3—61no—
223C22×Dic3C22×D312yes—
224C22×Dic3C22×D312yes—
225C22×Dic3C22×D312yes—
226C22×Dic3C22×D312yes—
227C2×D12—34no—
228C2×D12—34no—
229C2×D12—64no—
230C2×D12—62no—
231C2×D12—62no—
232C2×D12—62no—
233C2×D12—62no—
234C2×D12—64no—
235C2×D12—64no—
236C2×C4×D3—34no—
237C2×C4×D3—34no—
238C2×C4×D3—34no—
239C2×C4×D3—34no—
240C2×C4×D3—64no—
241C2×C4×D3—64no—
242C2×C4×D3—64no—
243C2×C4×D3—64no—
244C2×C4×D3—64no—
245C2×C4×D3—64no—
246C2×C4×D3—122no—
247C2×C4×D3—122no—
248C2×C4×D3—122no—
249C2×C4×D3—122no—
250C2×C4×D3—122no—
251C2×C4×D3—122no—
252C2×C4×D3—124no—
253C2×C4×D3—124no—
254C3×C42—24no—
255C3×C42—64no—
256C3×C42C4×D314yescomplemented
257C3×C42C4×D314yescomplemented
258(C2×D3)⋊C4—34no—
259(C2×D3)⋊C4—34no—
260(C2×D3)⋊C4—34no—
261(C2×D3)⋊C4—34no—
262(C2×D3)⋊C4—64no—
263(C2×D3)⋊C4—64no—
264(C2×D3)⋊C4—64no—
265(C2×D3)⋊C4—64no—
266(C2×D3)⋊C4—64no—
267(C2×D3)⋊C4—64no—
268(C2×D3)⋊C4—122no—
269(C2×D3)⋊C4—122no—
270C4⋊Dic3—34no—
271C4⋊Dic3—34no—
272C4⋊Dic3—64no—
273Dic3⋊C4—122no—
274Dic3⋊C4—122no—
275C4×Dic3—24no—
276C4×Dic3—122no—
277C4×Dic3—122no—
278C22×C32C23×C411yescharacteristic
279C22×C32C2×#4112yes—
280C22×C32C2×#4111yescharacteristic
281C22×C32C2×#4111yescharacteristic
282C22×C32H(5,𝔽2)12yes—
283C2×C3⋊D3—22no—
284C2×C3⋊D3—22no—
285C2×C3⋊D3—22no—
286C2×C3⋊D3—24no—
287C2×C3⋊D3—24no—
288C2×C3⋊D3—22no—
289C2×C3⋊D3—22no—
290C2×C3⋊D3—42no—
291C2×C3⋊D3—42no—
292C2×C3⋊D3#11714yes—
293C32×C4—22no—
294C32×C4—22no—
295C32×C4—22no—
296C3⋊Dic3—22no—
297C3⋊Dic3—22no—
298C3×Dic3—24no—
299C3×Dic3—42no—
300C3×Dic3—42no—
301C3×Dic3—42no—
302C22×D4—91no—
303C23×C4—92no—
304C23×C4—91no—
305C23×C4—91no—
306C4×D4—98no—
307C2×C4⋊C4—91no—
308C2×C4⋊C4—92no—
309C2×C22⋊C4—91no—
310C2×C22⋊C4—91no—
311C2×C22⋊C4—92no—
312C2×C22⋊C4—92no—
313C2×C22⋊C4—92no—
314C2×C42—32no—
315C2×C42—92no—
316C2×C42D3211yescharacteristic
317#95—31no—
318#95—31no—
319#95—31no—
320#95—32no—
321#95—31no—
322#95—32no—
323#95—32no—
324#95—92no—
325#95—92no—
326C23×C3—21no—
327C23×C3C23×D311yescharacteristic
328C23×C3C23×D311yescharacteristic
329C22×D3—32no—
330C22×D3—32no—
331C22×D3—32no—
332C22×D3—32no—
333C22×D3—32no—
334C22×D3—32no—
335C22×D3—32no—
336C22×D3—32no—
337C22×D3—62no—
338C22×D3—62no—
339C22×D3—62no—
340C22×D3—62no—
341C22×D3—62no—
342C22×D3—62no—
343C22×D3—62no—
344C22×D3—62no—
345C22×D3—62no—
346C22×D3—62no—
347C22×D3—62no—
348C22×D3—62no—
349C22×D3—61no—
350C22×D3—61no—
351C22×D3—61no—
352C22×D3—61no—
353C22×D3—62no—
354C22×D3—62no—
355C22×D3—122no—
356C22×D3—122no—
357C22×D3—122no—
358C22×D3—122no—
359C2×C3×C4—24no—
360C2×C3×C4—22no—
361C2×C3×C4—22no—
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—22no—
369C2×C3×C4—22no—
370C2×C3×C4—22no—
371C2×C3×C4—22no—
372C2×C3×C4—22no—
373C2×C3×C4—34no—
374C2×C3×C4—42no—
375C2×C3×C4—62no—
376C2×C3×C4—62no—
377C2×C3×C4—62no—
378C2×C3×C4—62no—
379C2×C3×C4—62no—
380C2×C3×C4—62no—
381C2×C3×C4—62no—
382C2×C3×C4—62no—
383C2×C3×C4—62no—
384C2×C3×C4—62no—
385C2×C3×C4—62no—
386C2×C3×C4C2×C4×D312yes—
387C2×C3×C4C2×C4×D312yes—
388C2×C3×C4C2×C4×D312yes—
389C2×C3×C4C2×C4×D312yes—
390C2×C3×C4C2×C4×D312yes—
391C2×C3×C4C2×C4×D312yes—
392C2×Dic3—22no—
393C2×Dic3—22no—
394C2×Dic3—22no—
395C2×Dic3—22no—
396C2×Dic3—22no—
397C2×Dic3—22no—
398C2×Dic3—22no—
399C2×Dic3—22no—
400C2×Dic3—22no—
401C2×Dic3—22no—
402C2×Dic3—22no—
403C2×Dic3—32no—
404C2×Dic3—32no—
405C2×Dic3—32no—
406C2×Dic3—32no—
407C2×Dic3—62no—
408C2×Dic3—62no—
409C2×Dic3—62no—
410C2×Dic3—62no—
411C2×Dic3—62no—
412C2×Dic3—62no—
413C2×Dic3—122no—
414C2×Dic3—122no—
415C2×Dic3#23514yes—
416D12—68no—
417D12—68no—
418D12—616no—
419C4×D3—128no—
420C4×D3—128no—
421C4×D3—124no—
422C4×D3—124no—
423C4×D3—124no—
424C4×D3—124no—
425C4×D3—128no—
426C4×D3—128no—
427C2×C32C2×#11711yescharacteristic
428C2×C32C4×#4111yescharacteristic
429C2×C32#51811yescharacteristic
430C2×C32#55112yes—
431C2×C32#55312yes—
432C3⋊D3—24no—
433C3⋊D3—42no—
434C24—91no—
435C24—91no—
436C2×D4—94no—
437C2×D4—182no—
438C2×D4—182no—
439C22×C4—32no—
440C22×C4—32no—
441C22×C4—32no—
442C22×C4—32no—
443C22×C4—91no—
444C22×C4—91no—
445C22×C4—94no—
446C22×C4—94no—
447C22×C4—184no—
448C22×C4—184no—
449C22×C4—362no—
450C22×C4—362no—
451C22×C4—362no—
452C22×C4C2×D3211yescharacteristic
453C22×C4C2×D3211yescharacteristic
454C22×C4C2×D3211yescharacteristic
455C4⋊C4—94no—
456C4⋊C4—362no—
457C22⋊C4—94no—
458C22⋊C4—94no—
459C22⋊C4—184no—
460C22⋊C4—184no—
461C22⋊C4—362no—
462C42—64no—
463C42—362no—
464C42#62414yescomplemented
465C22×C3—22no—
466C22×C3—21no—
467C22×C3—21no—
468C22×C3—22no—
469C22×C3—21no—
470C22×C3C22×C4×D311yescharacteristic
471C22×C3C22×C4×D311yescharacteristic
472C22×C3C2×#23512yes—
473C22×C3D3×#4112yes—
474C22×C3D3×#4111yescharacteristic
475C22×C3D3×#4111yescharacteristic
476C22×C3D3×#4111yescharacteristic
477C22×C3D3×#4111yescharacteristic
478C22×C3#100912yes—
479C22×C3#100912yes—
480C2×D3—34no—
481C2×D3—34no—
482C2×D3—64no—
483C2×D3—64no—
484C2×D3—64no—
485C2×D3—62no—
486C2×D3—62no—
487C2×D3—62no—
488C2×D3—62no—
489C2×D3—64no—
490C2×D3—64no—
491C2×D3—64no—
492C2×D3—62no—
493C2×D3—62no—
494C2×D3—62no—
495C2×D3—62no—
496C2×D3—62no—
497C2×D3—62no—
498C2×D3—122no—
499C2×D3—122no—
500C2×D3—122no—
501C2×D3—124no—
502C2×D3—124no—
503C2×D3—122no—
504C2×D3—124no—
505C2×D3—124no—
506C2×D3—122no—
507C2×D3—122no—
508C2×D3—122no—
509C2×D3—122no—
510C3×C4—24no—
511C3×C4—24no—
512C3×C4—22no—
513C3×C4—22no—
514C3×C4—22no—
515C3×C4—22no—
516C3×C4—22no—
517C3×C4—22no—
518C3×C4—42no—
519C3×C4—64no—
520C3×C4—122no—
521C3×C4—122no—
522C3×C4—122no—
523Dic3—24no—
524Dic3—42no—
525Dic3—42no—
526Dic3—42no—
527Dic3—62no—
528Dic3—62no—
529Dic3—62no—
530Dic3—62no—
531Dic3—122no—
532Dic3—122no—
533C32#235311yescharacteristic, complemented, Sylow
534C23—92no—
535C23—92no—
536C23—92no—
537C23—92no—
538C23—182no—
539C23—182no—
540C23—182no—
541C23—181no—
542C23—181no—
543C23—182no—
544C23C22×D3211yescharacteristic
545D4—188no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—22no—
550C2×C4—34no—
551C2×C4—62no—
552C2×C4—62no—
553C2×C4—62no—
554C2×C4—62no—
555C2×C4—62no—
556C2×C4—62no—
557C2×C4—62no—
558C2×C4—62no—
559C2×C4—62no—
560C2×C4—62no—
561C2×C4—62no—
562C2×C4—92no—
563C2×C4—92no—
564C2×C4—182no—
565C2×C4—182no—
566C2×C4—364no—
567C2×C4—364no—
568C2×C4—368no—
569C2×C4C2×#62412yes—
570C2×C4C2×#62412yes—
571C2×C4C2×#62412yes—
572C2×C3—21no—
573C2×C3—22no—
574C2×C3—21no—
575C2×C3—21no—
576C2×C3—22no—
577C2×C3C4×#23511yescharacteristic
578C2×C3D3×#11711yescharacteristic
579C2×C3D3×#11711yescharacteristic
580C2×C3#552111yescharacteristic
581C2×C3#552111yescharacteristic
582C2×C3#552211yescharacteristic
583C2×C3#552712yes—
584C2×C3#553012yes—
585C2×C3#570512yes—
586C2×C3#570912yes—
587D3—64no—
588D3—64no—
589D3—124no—
590D3—124no—
591D3—122no—
592D3—122no—
593C22—94no—
594C22—182no—
595C22—184no—
596C22—182no—
597C22—184no—
598C22—182no—
599C22—182no—
600C22—182no—
601C22—362no—
602C22—362no—
603C22D3×#23512yes—
604C22#6430611yescharacteristic
605C22#6430611yescharacteristic
606C22#6430812yes—
607C22C22×#62411yescharacteristic
608C4—22no—
609C4—22no—
610C4—22no—
611C4—64no—
612C4—122no—
613C4—122no—
614C4—122no—
615C4—182no—
616C4—182no—
617C3—21no—
618C3#7341711yescharacteristic, complemented
619C3#7429711yescharacteristic, complemented
620C2—184no—
621C2—362no—
622C2#1059393712yes—
623C2#1059401712yes—
624C2#1059495411yescharacteristic
625C2#1059496911yescharacteristic
626C2#1059499611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC2×C42D32
hypocenterC32#2353
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C3×#4937C2semidirect
3. C3×#4932C2semidirect
5. #10591370C2semidirect
6. #10591355C2semidirect
7. #10591271C2semidirect
8. #10591260C2semidirect
9. #10591233C2semidirect
10. #10591219C2semidirect
11. #10591202C2semidirect
22. C4×C4⋊(C3⋊D3)C4semidirect
45. #4937D3semidirect
46. #4932D3semidirect
74. C2×C4×C3⋊D3C2×C4semidirect
82. C32×C42C2×C4semidirect
84. #3752C2×C4semidirect
85. C4⋊(C3⋊Dic3)C2×C4semidirect
256. C3×C42C4×D3semidirect
257. C3×C42C4×D3semidirect
464. C42#624semidirect
533. C32#2353semidirect
618. C3#73417semidirect
619. C3#74297semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C4⋊(C3⋊D3)2
C3×#49372
C3×#49322
#105913802
#105913702
#105913552
#105912712
#105912602
#105912332
#105912192
#105912022
#742973
#734173