Finite Group Databasebeta

← #11808344

Subgroups — #11808344

Order 1152.

1593 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic
2C2×#63900C211yesmaximal, characteristic
3C2×#63883C211yesmaximal, characteristic
4C2×#63883C211yesmaximal, characteristic
5C3×#4982C212yesmaximal, complemented
6#10591370C211yesmaximal, characteristic
7#10591370C211yesmaximal, characteristic
8#10591370C211yesmaximal, characteristic
9#10591351C212yesmaximal, complemented
10#10591342C212yesmaximal, complemented
11#10591198C212yesmaximal, complemented
12D3×#398—32nomaximal
13C22×C4×C3⋊D3C2211yescharacteristic
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×#624C2211yescharacteristic
17C22×#624C2211yescharacteristic
18C22×#624C2211yescharacteristic
19C22×#624C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C2×#3750C2211yescharacteristic
23C2×#3750C2211yescharacteristic
24C4⋊C4×C3⋊D3—24no—
25C2×C3×C4⋊Dic3C2212yes—
26C2×C3×Dic3⋊C4C2212yes—
27C2×C3×Dic3⋊C4C2212yes—
28C2×#3724C2212yes—
29C2×Dic3⋊Dic3C2212yes—
30C2×Dic3⋊Dic3C2212yes—
31#63900—24no—
32#63883—24no—
33#63883—24no—
34C3×C3⋊#95C2212yes—
35C3×C3⋊#95C2212yes—
36C3×C3⋊#95C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C2×D3×C4⋊C4—32no—
41C2×D3×C4⋊C4—32no—
42C2×D3×C4⋊C4—32no—
43C2×D3×C4⋊C4—32no—
44C2×D3×C4⋊C4—61no—
45C3×#398—32no—
46#4983—32no—
47#4982—32no—
48#4982D312yescomplemented
49#4981—32no—
50D3×#95—32no—
51D3×#95—32no—
52D3×#95—32no—
53#4661—32no—
54#4657—32no—
55#4657—32no—
56C23×C3⋊D3C2311yescharacteristic
57C22×C32×C4C2311yescharacteristic
58C22×C32×C4C2311yescharacteristic
59C22×C32×C4C2311yescharacteristic
60C22×C3⋊Dic3C2311yescharacteristic
61C22×C3⋊Dic3C2311yescharacteristic
62C22×C3⋊Dic3C2311yescharacteristic
63C2×C4×C3⋊D3—22no—
64C2×C4×C3⋊D3—22no—
65C2×C4×C3⋊D3—22no—
66C2×C4×C3⋊D3—22no—
67C2×C4×C3⋊D3—22no—
68C2×C4×C3⋊D3—22no—
69C2×C4×C3⋊D3—22no—
70C2×C4×C3⋊D3D414yes—
71C2×C4×C3⋊D3Q814yes—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2312yes—
76C2×#624—22no—
77C2×#624—22no—
78C2×#624—22no—
79C2×#624—22no—
80C2×#624—22no—
81C2×#624—22no—
82C2×#624—22no—
83C2×#624—22no—
84C2×#624—22no—
85C2×#624—22no—
86C2×#624D414yes—
87C2×#624Q814yes—
88C32×C4⋊C4—22no—
89C4⋊(C3⋊Dic3)—22no—
90#3750—22no—
91#3750—22no—
92C3×C4⋊Dic3—24no—
93C3×Dic3⋊C4—24no—
94C3×Dic3⋊C4—24no—
95#3724—24no—
96Dic3⋊Dic3—24no—
97Dic3⋊Dic3—24no—
98C2×#398—91noSylow
99C22×C4×D3—32no—
100C22×C4×D3—32no—
101C22×C4×D3—32no—
102C22×C4×D3—32no—
103C22×C4×D3—32no—
104C22×C4×D3—32no—
105C22×C4×D3—32no—
106C22×C4×D3—61no—
107C22×C4×D3—61no—
108C22×C4×D3—61no—
109C2×C3×C4⋊C4—21no—
110C2×C3×C4⋊C4—32no—
111C2×C3×C4⋊C4—32no—
112C2×C3×C4⋊C4—32no—
113C2×C3×C4⋊C4C2×D312yes—
114C2×C4⋊Dic3—32no—
115C2×C4⋊Dic3—32no—
116C2×C4⋊Dic3—32no—
117C2×C4⋊Dic3—61no—
118C2×C4⋊Dic3C2×D312yes—
119C2×Dic3⋊C4—32no—
120C2×Dic3⋊C4—32no—
121C2×Dic3⋊C4—32no—
122C2×Dic3⋊C4—32no—
123C2×Dic3⋊C4—32no—
124C2×Dic3⋊C4—32no—
125C2×Dic3⋊C4—61no—
126C2×Dic3⋊C4—61no—
127C2×Dic3⋊C4C2×D312yes—
128C2×Dic3⋊C4C2×D312yes—
129D3×C4⋊C4—68no—
130D3×C4⋊C4—68no—
131D3×C4⋊C4—68no—
132D3×C4⋊C4—68no—
133D3×C4⋊C4—68no—
134C3×#95—32no—
135C3×#95—32no—
136C3×#95—32no—
137C3⋊#95—32no—
138C3⋊#95—32no—
139C3⋊#95—32no—
140C3⋊#95—32no—
141C3⋊#95—32no—
142C3⋊#95—32no—
143C3⋊#95C2×D312yes—
144C3⋊#95C2×D312yes—
145C3⋊#95C2×D312yes—
146C23×C32C2411yescharacteristic
147C22×C3⋊D3C2×D412yes—
148C22×C3⋊D3C2×D412yes—
149C22×C3⋊D3C2×Q812yes—
150C22×C3⋊D3C2×Q812yes—
151C22×C3⋊D3#4112yes—
152C22×C3⋊D3#4112yes—
153C22×C3⋊D3#4112yes—
154C2×C32×C4—21no—
155C2×C32×C4—21no—
156C2×C32×C4—21no—
157C2×C32×C4—21no—
158C2×C32×C4—21no—
159C2×C32×C4—21no—
160C2×C32×C4—21no—
161C2×C32×C4C2×D412yes—
162C2×C32×C4C2×Q812yes—
163C2×C3⋊Dic3—21no—
164C2×C3⋊Dic3—21no—
165C2×C3⋊Dic3—21no—
166C2×C3⋊Dic3—21no—
167C2×C3⋊Dic3—21no—
168C2×C3⋊Dic3—21no—
169C2×C3⋊Dic3—21no—
170C2×C3⋊Dic3C2×D412yes—
171C2×C3⋊Dic3C2×Q812yes—
172C4×C3⋊D3—28no—
173C4×C3⋊D3—28no—
174C4×C3⋊D3—44no—
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×Dic3C2×D414yes—
186C2×C3×Dic3C2×Q814yes—
187#624—28no—
188#624—28no—
189#624—44no—
190#624—44no—
191C22×C4⋊C4—91no—
192C22×C4⋊C4—91no—
193C22×C4⋊C4—91no—
194C22×C4⋊C4—91no—
195#398—32no—
196#398—92no—
197#398—92no—
198#398—92no—
199C2×#95—91no—
200C2×#95—91no—
201C2×#95—91no—
202C23×D3—32no—
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×D312yes—
212C22×C3×C4C22×D312yes—
213C22×C3×C4C22×D312yes—
214C22×Dic3—32no—
215C22×Dic3—32no—
216C22×Dic3—32no—
217C22×Dic3—61no—
218C22×Dic3—61no—
219C22×Dic3—61no—
220C22×Dic3C22×D312yes—
221C22×Dic3C22×D312yes—
222C22×Dic3C22×D312yes—
223C22×Dic3C22×D312yes—
224C2×C4×D3—38no—
225C2×C4×D3—38no—
226C2×C4×D3—38no—
227C2×C4×D3—38no—
228C2×C4×D3—64no—
229C2×C4×D3—64no—
230C2×C4×D3—64no—
231C2×C4×D3—64no—
232C2×C4×D3—64no—
233C2×C4×D3—64no—
234C2×C4×D3—64no—
235C2×C4×D3—64no—
236C2×C4×D3—64no—
237C2×C4×D3—64no—
238C2×C4×D3—64no—
239C2×C4×D3—64no—
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—64no—
247C2×C4×D3—64no—
248C2×C4×D3—64no—
249C2×C4×D3—64no—
250C2×C4×D3—122no—
251C2×C4×D3—122no—
252C2×C4×D3—122no—
253C2×C4×D3—122no—
254C3×C4⋊C4—24no—
255C3×C4⋊C4—24no—
256C3×C4⋊C4—64no—
257C3×C4⋊C4—64no—
258C3×C4⋊C4—64no—
259C4⋊Dic3—24no—
260C4⋊Dic3—64no—
261C4⋊Dic3—64no—
262C4⋊Dic3—64no—
263C4⋊Dic3—64no—
264Dic3⋊C4—24no—
265Dic3⋊C4—24no—
266Dic3⋊C4—64no—
267Dic3⋊C4—64no—
268Dic3⋊C4—64no—
269Dic3⋊C4—64no—
270Dic3⋊C4—64no—
271Dic3⋊C4—64no—
272Dic3⋊C4—64no—
273Dic3⋊C4—64no—
274C22×C32C22×D411yescharacteristic
275C22×C32C22×D411yescharacteristic
276C22×C32C22×Q811yescharacteristic
277C22×C32C22×Q811yescharacteristic
278C22×C32C2×#4111yescharacteristic
279C22×C32C2×#4111yescharacteristic
280C22×C32C2×#4111yescharacteristic
281C2×C3⋊D3#12114yes—
282C2×C3⋊D3C22⋊Q814yes—
283C2×C3⋊D3C22⋊Q814yes—
284C2×C3⋊D3#12314yes—
285C2×C3⋊D3#12514yes—
286C2×C3⋊D3#12514yes—
287C2×C3⋊D3C4⋊Q814yes—
288C32×C4—22no—
289C32×C4—22no—
290C32×C4—41no—
291C3⋊Dic3—22no—
292C3⋊Dic3—22no—
293C3⋊Dic3—41no—
294C3×Dic3—24no—
295C3×Dic3—24no—
296C3×Dic3—42no—
297C3×Dic3—42no—
298C23×C4—91no—
299C23×C4—91no—
300C23×C4—91no—
301C23×C4—91no—
302C23×C4—91no—
303C23×C4—91no—
304C23×C4—91no—
305C2×C4⋊C4—32no—
306C2×C4⋊C4—32no—
307C2×C4⋊C4—32no—
308C2×C4⋊C4—92no—
309C2×C4⋊C4—92no—
310C2×C4⋊C4—92no—
311C2×C4⋊C4—91no—
312C2×C4⋊C4—91no—
313C2×C4⋊C4—91no—
314C2×C4⋊C4—184no—
315C2×C4⋊C4—184no—
316C2×C4⋊C4—184no—
317C2×C4⋊C4—184no—
318C2×C4⋊C4D3211yescharacteristic
319#95—32no—
320#95—32no—
321#95—32no—
322#95—92no—
323#95—92no—
324#95—92no—
325C23×C3—21no—
326C23×C3C23×D312yes—
327C22×D3—34no—
328C22×D3—34no—
329C22×D3—34no—
330C22×D3—34no—
331C22×D3—34no—
332C22×D3—34no—
333C22×D3—34no—
334C22×D3—62no—
335C22×D3—62no—
336C22×D3—62no—
337C22×D3—62no—
338C22×D3—62no—
339C22×D3—62no—
340C22×D3—62no—
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—22no—
349C2×C3×C4—22no—
350C2×C3×C4—22no—
351C2×C3×C4—22no—
352C2×C3×C4—22no—
353C2×C3×C4—34no—
354C2×C3×C4—34no—
355C2×C3×C4—41no—
356C2×C3×C4—41no—
357C2×C3×C4—41no—
358C2×C3×C4—41no—
359C2×C3×C4—62no—
360C2×C3×C4—62no—
361C2×C3×C4—62no—
362C2×C3×C4—62no—
363C2×C3×C4—62no—
364C2×C3×C4—62no—
365C2×C3×C4—62no—
366C2×C3×C4—62no—
367C2×C3×C4—62no—
368C2×C3×C4—62no—
369C2×C3×C4D3×D414yes—
370C2×C3×C4D3×Q814yes—
371C2×Dic3—22no—
372C2×Dic3—22no—
373C2×Dic3—22no—
374C2×Dic3—22no—
375C2×Dic3—22no—
376C2×Dic3—22no—
377C2×Dic3—22no—
378C2×Dic3—22no—
379C2×Dic3—22no—
380C2×Dic3—22no—
381C2×Dic3—34no—
382C2×Dic3—34no—
383C2×Dic3—62no—
384C2×Dic3—62no—
385C2×Dic3—62no—
386C2×Dic3—62no—
387C2×Dic3—62no—
388C2×Dic3—62no—
389C2×Dic3—62no—
390C2×Dic3—62no—
391C2×Dic3—62no—
392C2×Dic3—62no—
393C2×Dic3—62no—
394C2×Dic3—62no—
395C2×Dic3—121no—
396C2×Dic3—121no—
397C2×Dic3—121no—
398C2×Dic3—121no—
399C2×Dic3D3×D414yes—
400C2×Dic3D3×Q814yes—
401C4×D3—616no—
402C4×D3—616no—
403C4×D3—616no—
404C4×D3—616no—
405C4×D3—616no—
406C4×D3—128no—
407C4×D3—128no—
408C4×D3—128no—
409C4×D3—128no—
410C4×D3—128no—
411C2×C32C2×#12111yescharacteristic
412C2×C32C2×C22⋊Q811yescharacteristic
413C2×C32C2×C22⋊Q811yescharacteristic
414C2×C32C2×#12311yescharacteristic
415C2×C32C2×#12511yescharacteristic
416C2×C32C2×#12511yescharacteristic
417C2×C32C2×C4⋊Q811yescharacteristic
418C3⋊D3#39818yescomplemented
419C24—91no—
420C22×C4—32no—
421C22×C4—32no—
422C22×C4—32no—
423C22×C4—32no—
424C22×C4—94no—
425C22×C4—94no—
426C22×C4—91no—
427C22×C4—91no—
428C22×C4—94no—
429C22×C4—94no—
430C22×C4—91no—
431C22×C4—182no—
432C22×C4—182no—
433C22×C4—182no—
434C22×C4—182no—
435C22×C4—182no—
436C22×C4—182no—
437C22×C4—182no—
438C22×C4—182no—
439C22×C4—182no—
440C22×C4—182no—
441C22×C4—182no—
442C22×C4—182no—
443C22×C4—182no—
444C22×C4—182no—
445C22×C4—182no—
446C22×C4—182no—
447C22×C4—182no—
448C22×C4C2×D3211yescharacteristic
449C22×C4C2×D3211yescharacteristic
450C22×C4C2×D3211yescharacteristic
451C4⋊C4—22no—
452C4⋊C4—64no—
453C4⋊C4—64no—
454C4⋊C4—64no—
455C4⋊C4—182no—
456C4⋊C4—182no—
457C4⋊C4—184no—
458C4⋊C4—184no—
459C4⋊C4—184no—
460C4⋊C4—182no—
461C22×C3—21no—
462C22×C3—21no—
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—21no—
466C22×C3—21no—
467C22×C3—21no—
468C22×C3C2×D3×D412yes—
469C22×C3C2×D3×D412yes—
470C22×C3C2×D3×Q812yes—
471C22×C3C2×D3×Q812yes—
472C22×C3D3×#4112yes—
473C22×C3D3×#4112yes—
474C22×C3D3×#4112yes—
475C2×D3—38no—
476C2×D3—38no—
477C2×D3—38no—
478C2×D3—38no—
479C2×D3—38no—
480C2×D3—38no—
481C2×D3—38no—
482C2×D3—64no—
483C2×D3—64no—
484C2×D3—64no—
485C2×D3—64no—
486C2×D3—64no—
487C2×D3—64no—
488C2×D3—64no—
489C3×C4—24no—
490C3×C4—24no—
491C3×C4—24no—
492C3×C4—42no—
493C3×C4—42no—
494C3×C4—42no—
495C3×C4—64no—
496C3×C4—64no—
497C3×C4—122no—
498C3×C4—122no—
499Dic3—24no—
500Dic3—24no—
501Dic3—42no—
502Dic3—42no—
503Dic3—64no—
504Dic3—64no—
505Dic3—64no—
506Dic3—122no—
507Dic3—122no—
508Dic3—122no—
509C32C2×#39811yescharacteristic, complemented, Sylow
510C23—92no—
511C23—92no—
512C23—92no—
513C23—92no—
514C23—92no—
515C23—92no—
516C23—92no—
517C23C22×D3211yescharacteristic
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—34no—
526C2×C4—34no—
527C2×C4—62no—
528C2×C4—62no—
529C2×C4—62no—
530C2×C4—62no—
531C2×C4—62no—
532C2×C4—62no—
533C2×C4—62no—
534C2×C4—62no—
535C2×C4—62no—
536C2×C4—62no—
537C2×C4—92no—
538C2×C4—92no—
539C2×C4—188no—
540C2×C4—188no—
541C2×C4—188no—
542C2×C4—188no—
543C2×C4—181no—
544C2×C4—181no—
545C2×C4—181no—
546C2×C4—181no—
547C2×C4—181no—
548C2×C4—181no—
549C2×C4—181no—
550C2×C4—364no—
551C2×C4—364no—
552C2×C4—364no—
553C2×C4#379712yes—
554C2×C4#381112yes—
555C2×C3—21no—
556C2×C3—21no—
557C2×C3—21no—
558C2×C3—21no—
559C2×C3—21no—
560C2×C3—21no—
561C2×C3—21no—
562C2×C3D3×#12112yes—
563C2×C3D3×C22⋊Q812yes—
564C2×C3D3×C22⋊Q812yes—
565C2×C3D3×#12312yes—
566C2×C3D3×#12512yes—
567C2×C3D3×#12512yes—
568C2×C3D3×C4⋊Q812yes—
569D3—316no—
570D3—68no—
571C22—94no—
572C22—94no—
573C22—94no—
574C22—94no—
575C22—94no—
576C22—94no—
577C22—94no—
578C22C2×#379711yescharacteristic
579C22#6430611yescharacteristic
580C22D32×D411yescharacteristic
581C22#6431211yescharacteristic
582C22D32×Q811yescharacteristic
583C22#6431911yescharacteristic
584C22C2×#381111yescharacteristic
585C4—22no—
586C4—22no—
587C4—41no—
588C4—64no—
589C4—64no—
590C4—122no—
591C4—122no—
592C4—182no—
593C4—182no—
594C4—361no—
595C3—21no—
596C3D3×#39812yescomplemented
597C2—98no—
598C2#1059437411yescharacteristic
599C2#1059439911yescharacteristic
600C2#1059448211yescharacteristic
601C2#1059460811yescharacteristic
602C2#1059492511yescharacteristic
603C2#1059529811yescharacteristic
604C2#1059542911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC23×C3⋊D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#398
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
5. C3×#4982C2semidirect
9. #10591351C2semidirect
10. #10591342C2semidirect
11. #10591198C2semidirect
48. #4982D3semidirect
418. C3⋊D3#398semidirect
509. C32C2×#398semidirect
596. C3D3×#398semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×C3⋊D32
C2×#639002
C2×#638832
C3×#49822
#105913702
#105913512
#105913422
#105911982
D3×#3983