Finite Group Databasebeta

← #11801366

Subgroups — #11801366

Order 1152.

1633 conjugacy classes of subgroups.

The subgroup lattice has 595 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×C4×#624C211yesmaximal, characteristic
4C3×#4980C212yesmaximal, complemented
5#10591370C211yesmaximal, characteristic
6#10591370C211yesmaximal, characteristic
7#10591370C211yesmaximal, characteristic
8#10591370C211yesmaximal, characteristic
9#10591271C212yesmaximal, complemented
10#10591263C212yesmaximal, complemented
11#10591197C212yesmaximal, complemented
12D3×#387—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⋊D3C418yescomplemented
25C2×C3×C4⋊Dic3C2212yes—
26C2×C3×C4×Dic3C2212yes—
27C2×#3724C2212yes—
28C2×Dic32C2212yes—
29#63900—24no—
30C4×#624—24no—
31C3×C3⋊#95C2212yes—
32C3×C3⋊#95C2212yes—
33C3×C3⋊#95C2212yes—
34C3×C3⋊#95C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39C2×D3×C4⋊C4—32no—
40C2×D3×C4⋊C4—32no—
41C2×D3×C4⋊C4—61no—
42C2×C42×D3—32no—
43C3×#387—32no—
44#4980D312yescomplemented
45#4978—32no—
46#4933—32no—
47D3×#95—32no—
48D3×#95—32no—
49D3×#95—32no—
50D3×#95—32no—
51#4655—32no—
52#4654—32no—
53#4653—32no—
54#4652—32no—
55C23×C3⋊D3C2311yescharacteristic
56C22×C32×C4C2311yescharacteristic
57C22×C32×C4C2311yescharacteristic
58C22×C32×C4C2311yescharacteristic
59C22×C3⋊Dic3C2311yescharacteristic
60C22×C3⋊Dic3C2311yescharacteristic
61C22×C3⋊Dic3C2311yescharacteristic
62C2×C4×C3⋊D3—22no—
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⋊D3C2×C414yes—
69C2×C4×C3⋊D3C2×C414yes—
70C2×C4×C3⋊D3C2×C414yes—
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2312yes—
75C2×#624—22no—
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×#624D414yes—
86C2×#624Q814yes—
87C32×C4⋊C4C2×C414yescomplemented
88C4⋊(C3⋊Dic3)C2×C414yescomplemented
89#3750C2×C414yescomplemented
90#3750C2×C414yescomplemented
91C3×C4⋊Dic3—24no—
92C3×C4×Dic3—24no—
93#3724—24no—
94Dic32—24no—
95C2×#387—91noSylow
96C22×C4×D3—32no—
97C22×C4×D3—32no—
98C22×C4×D3—32no—
99C22×C4×D3—32no—
100C22×C4×D3—32no—
101C22×C4×D3—32no—
102C22×C4×D3—32no—
103C22×C4×D3—61no—
104C22×C4×D3—61no—
105C22×C4×D3—61no—
106C2×C3×C4⋊C4—21no—
107C2×C3×C4⋊C4—32no—
108C2×C3×C4⋊C4C2×D312yes—
109C2×C3×C42—32no—
110C2×C4⋊Dic3—32no—
111C2×C4⋊Dic3—61no—
112C2×C4⋊Dic3C2×D312yes—
113C2×Dic3⋊C4—32no—
114C2×Dic3⋊C4—32no—
115C2×Dic3⋊C4—32no—
116C2×Dic3⋊C4—32no—
117C2×Dic3⋊C4—61no—
118C2×Dic3⋊C4—61no—
119C2×C4×Dic3—32no—
120C2×C4×Dic3—32no—
121C2×C4×Dic3C2×D312yes—
122D3×C4⋊C4—316no—
123D3×C4⋊C4—68no—
124D3×C4⋊C4—68no—
125C42×D3—68no—
126C3×#95—32no—
127C3×#95—32no—
128C3×#95—32no—
129C3×#95—32no—
130C3⋊#95—32no—
131C3⋊#95—32no—
132C3⋊#95—32no—
133C3⋊#95—32no—
134C3⋊#95—32no—
135C3⋊#95—32no—
136C3⋊#95—32no—
137C3⋊#95—32no—
138C3⋊#95C2×D312yes—
139C3⋊#95C2×D312yes—
140C3⋊#95C2×D312yes—
141C3⋊#95C2×D312yes—
142C23×C32C2411yescharacteristic
143C22×C3⋊D3C22×C412yes—
144C22×C3⋊D3C2×D412yes—
145C22×C3⋊D3C2×Q812yes—
146C22×C3⋊D3#4112yes—
147C22×C3⋊D3#4112yes—
148C22×C3⋊D3#4112yes—
149C22×C3⋊D3#4112yes—
150C2×C32×C4—21no—
151C2×C32×C4—21no—
152C2×C32×C4—21no—
153C2×C32×C4—21no—
154C2×C32×C4—21no—
155C2×C32×C4—21no—
156C2×C32×C4C22×C412yes—
157C2×C32×C4C22×C412yes—
158C2×C32×C4C22×C412yes—
159C2×C3⋊Dic3—21no—
160C2×C3⋊Dic3—21no—
161C2×C3⋊Dic3—21no—
162C2×C3⋊Dic3—21no—
163C2×C3⋊Dic3—21no—
164C2×C3⋊Dic3—21no—
165C2×C3⋊Dic3C22×C412yes—
166C2×C3⋊Dic3C22×C412yes—
167C2×C3⋊Dic3C22×C412yes—
168C4×C3⋊D3—28no—
169C4×C3⋊D3—28no—
170C4×C3⋊D3—28no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—22no—
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×Dic3C2×D414yes—
182C2×C3×Dic3C2×Q814yes—
183#624—28no—
184#624—28no—
185#624—44no—
186#624—44no—
187C22×C4⋊C4—91no—
188C22×C4⋊C4—91no—
189C22×C42—91no—
190#387—32no—
191#387—92no—
192#387—92no—
193#387—92no—
194C2×#95—91no—
195C2×#95—91no—
196C2×#95—91no—
197C2×#95—91no—
198C23×D3—32no—
199C23×D3—61no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—32no—
204C22×C3×C4—32no—
205C22×C3×C4—32no—
206C22×C3×C4—32no—
207C22×C3×C4C22×D312yes—
208C22×C3×C4C22×D312yes—
209C22×C3×C4C22×D312yes—
210C22×Dic3—32no—
211C22×Dic3—32no—
212C22×Dic3—32no—
213C22×Dic3—61no—
214C22×Dic3—61no—
215C22×Dic3—61no—
216C22×Dic3C22×D312yes—
217C22×Dic3C22×D312yes—
218C22×Dic3C22×D312yes—
219C22×Dic3C22×D312yes—
220C2×C4×D3—38no—
221C2×C4×D3—38no—
222C2×C4×D3—38no—
223C2×C4×D3—38no—
224C2×C4×D3—38no—
225C2×C4×D3—64no—
226C2×C4×D3—64no—
227C2×C4×D3—64no—
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—122no—
247C2×C4×D3—122no—
248C2×C4×D3—122no—
249C2×C4×D3—122no—
250C3×C4⋊C4—24no—
251C3×C4⋊C4—64no—
252C3×C4⋊C4C4×D318yescomplemented
253C3×C42—64no—
254C4⋊Dic3—24no—
255C4⋊Dic3—38no—
256C4⋊Dic3—64no—
257Dic3⋊C4—38no—
258Dic3⋊C4—38no—
259Dic3⋊C4—64no—
260Dic3⋊C4—64no—
261Dic3⋊C4—64no—
262Dic3⋊C4—64no—
263C4×Dic3—24no—
264C4×Dic3—64no—
265C4×Dic3—64no—
266C22×C32C23×C411yescharacteristic
267C22×C32C22×D411yescharacteristic
268C22×C32C22×Q811yescharacteristic
269C22×C32C2×#4111yescharacteristic
270C22×C32C2×#4111yescharacteristic
271C22×C32C2×#4111yescharacteristic
272C22×C32C2×#4111yescharacteristic
273C2×C3⋊D3#11714yes—
274C2×C3⋊D3C4×D414yes—
275C2×C3⋊D3C4×Q814yes—
276C2×C3⋊D3C22⋊Q814yes—
277C2×C3⋊D3#12314yes—
278C2×C3⋊D3#12514yes—
279C2×C3⋊D3#12614yes—
280C32×C4—22no—
281C32×C4—22no—
282C32×C4—22no—
283C3⋊Dic3—22no—
284C3⋊Dic3—22no—
285C3⋊Dic3—22no—
286C3×Dic3—24no—
287C3×Dic3—24no—
288C3×Dic3—42no—
289C3×Dic3—42no—
290C23×C4—91no—
291C23×C4—91no—
292C23×C4—91no—
293C23×C4—91no—
294C23×C4—91no—
295C23×C4—91no—
296C23×C4—91no—
297C2×C4⋊C4—32no—
298C2×C4⋊C4—91no—
299C2×C4⋊C4—91no—
300C2×C4⋊C4—91no—
301C2×C4⋊C4—98no—
302C2×C4⋊C4—92no—
303C2×C4⋊C4—184no—
304C2×C4⋊C4D3211yescharacteristic
305C2×C42—32no—
306C2×C42—92no—
307C2×C42—184no—
308#95—32no—
309#95—32no—
310#95—32no—
311#95—32no—
312#95—92no—
313#95—92no—
314#95—92no—
315#95—92no—
316C23×C3—21no—
317C23×C3C23×D312yes—
318C22×D3—34no—
319C22×D3—34no—
320C22×D3—34no—
321C22×D3—34no—
322C22×D3—34no—
323C22×D3—34no—
324C22×D3—34no—
325C22×D3—62no—
326C22×D3—62no—
327C22×D3—62no—
328C22×D3—62no—
329C22×D3—62no—
330C22×D3—62no—
331C22×D3—62no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—34no—
344C2×C3×C4—34no—
345C2×C3×C4—41no—
346C2×C3×C4—41no—
347C2×C3×C4—41no—
348C2×C3×C4—41no—
349C2×C3×C4—62no—
350C2×C3×C4—62no—
351C2×C3×C4—62no—
352C2×C3×C4—62no—
353C2×C3×C4—62no—
354C2×C3×C4—62no—
355C2×C3×C4—62no—
356C2×C3×C4—62no—
357C2×C3×C4—62no—
358C2×C3×C4—62no—
359C2×C3×C4C2×C4×D314yes—
360C2×C3×C4C2×C4×D314yes—
361C2×C3×C4C2×C4×D314yes—
362C2×Dic3—22no—
363C2×Dic3—22no—
364C2×Dic3—22no—
365C2×Dic3—22no—
366C2×Dic3—22no—
367C2×Dic3—22no—
368C2×Dic3—22no—
369C2×Dic3—22no—
370C2×Dic3—22no—
371C2×Dic3—22no—
372C2×Dic3—34no—
373C2×Dic3—34no—
374C2×Dic3—34no—
375C2×Dic3—62no—
376C2×Dic3—62no—
377C2×Dic3—62no—
378C2×Dic3—62no—
379C2×Dic3—62no—
380C2×Dic3—62no—
381C2×Dic3—62no—
382C2×Dic3—62no—
383C2×Dic3—62no—
384C2×Dic3—62no—
385C2×Dic3—62no—
386C2×Dic3—121no—
387C2×Dic3—121no—
388C2×Dic3—121no—
389C2×Dic3—121no—
390C2×Dic3D3×D414yes—
391C2×Dic3D3×Q814yes—
392C4×D3—616no—
393C4×D3—616no—
394C4×D3—616no—
395C4×D3—616no—
396C4×D3—616no—
397C4×D3—616no—
398C4×D3—128no—
399C4×D3—128no—
400C4×D3—128no—
401C4×D3—128no—
402C2×C32C2×#11711yescharacteristic
403C2×C32C2×C4×D411yescharacteristic
404C2×C32C2×C4×Q811yescharacteristic
405C2×C32C2×C22⋊Q811yescharacteristic
406C2×C32C2×#12311yescharacteristic
407C2×C32C2×#12511yescharacteristic
408C2×C32C2×#12611yescharacteristic
409C3⋊D3#38718yescomplemented
410C24—91no—
411C22×C4—32no—
412C22×C4—32no—
413C22×C4—32no—
414C22×C4—32no—
415C22×C4—94no—
416C22×C4—94no—
417C22×C4—91no—
418C22×C4—91no—
419C22×C4—91no—
420C22×C4—94no—
421C22×C4—94no—
422C22×C4—94no—
423C22×C4—182no—
424C22×C4—182no—
425C22×C4—182no—
426C22×C4—182no—
427C22×C4—182no—
428C22×C4—182no—
429C22×C4—182no—
430C22×C4—182no—
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×C4C2×D3211yescharacteristic
440C22×C4C2×D3211yescharacteristic
441C22×C4C2×D3211yescharacteristic
442C4⋊C4—64no—
443C4⋊C4—94no—
444C4⋊C4—94no—
445C4⋊C4—94no—
446C4⋊C4—184no—
447C4⋊C4#62414yescomplemented
448C42—64no—
449C42—184no—
450C22×C3—21no—
451C22×C3—21no—
452C22×C3—21no—
453C22×C3—21no—
454C22×C3—21no—
455C22×C3—21no—
456C22×C3—21no—
457C22×C3C22×C4×D312yes—
458C22×C3C2×D3×D412yes—
459C22×C3C2×D3×Q812yes—
460C22×C3D3×#4112yes—
461C22×C3D3×#4112yes—
462C22×C3D3×#4112yes—
463C22×C3D3×#4112yes—
464C2×D3—38no—
465C2×D3—38no—
466C2×D3—38no—
467C2×D3—38no—
468C2×D3—38no—
469C2×D3—38no—
470C2×D3—38no—
471C2×D3—64no—
472C2×D3—64no—
473C2×D3—64no—
474C2×D3—64no—
475C2×D3—64no—
476C2×D3—64no—
477C2×D3—64no—
478C3×C4—24no—
479C3×C4—24no—
480C3×C4—24no—
481C3×C4—24no—
482C3×C4—42no—
483C3×C4—42no—
484C3×C4—64no—
485C3×C4—64no—
486C3×C4—122no—
487C3×C4—122no—
488Dic3—24no—
489Dic3—24no—
490Dic3—42no—
491Dic3—42no—
492Dic3—64no—
493Dic3—64no—
494Dic3—64no—
495Dic3—64no—
496Dic3—122no—
497Dic3—122no—
498C32C2×#38711yescharacteristic, complemented, Sylow
499C23—92no—
500C23—92no—
501C23—92no—
502C23—92no—
503C23—92no—
504C23—92no—
505C23—92no—
506C23C22×D3211yescharacteristic
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—34no—
514C2×C4—34no—
515C2×C4—62no—
516C2×C4—62no—
517C2×C4—62no—
518C2×C4—62no—
519C2×C4—62no—
520C2×C4—62no—
521C2×C4—62no—
522C2×C4—62no—
523C2×C4—62no—
524C2×C4—62no—
525C2×C4—92no—
526C2×C4—92no—
527C2×C4—92no—
528C2×C4—188no—
529C2×C4—188no—
530C2×C4—188no—
531C2×C4—188no—
532C2×C4—188no—
533C2×C4—181no—
534C2×C4—181no—
535C2×C4—181no—
536C2×C4—181no—
537C2×C4—181no—
538C2×C4—181no—
539C2×C4—364no—
540C2×C4—364no—
541C2×C4C2×#62412yes—
542C2×C4C2×#62412yes—
543C2×C4C2×#62412yes—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—21no—
551C2×C3D3×#11712yes—
552C2×C3C4×D3×D412yes—
553C2×C3C4×D3×Q812yes—
554C2×C3D3×C22⋊Q812yes—
555C2×C3D3×#12312yes—
556C2×C3D3×#12512yes—
557C2×C3D3×#12612yes—
558D3—316no—
559D3—68no—
560C22—94no—
561C22—94no—
562C22—94no—
563C22—94no—
564C22—94no—
565C22—94no—
566C22—94no—
567C22#6430611yescharacteristic
568C22#6430611yescharacteristic
569C22D32×D411yescharacteristic
570C22#6431211yescharacteristic
571C22D32×Q811yescharacteristic
572C22#6431911yescharacteristic
573C22C22×#62411yescharacteristic
574C4—22no—
575C4—22no—
576C4—22no—
577C4—64no—
578C4—64no—
579C4—122no—
580C4—122no—
581C4—182no—
582C4—182no—
583C4—182no—
584C3—21no—
585C3D3×#38712yescomplemented
586C2—98no—
587C2#1059439911yescharacteristic
588C2#1059460811yescharacteristic
589C2#1059462411yescharacteristic
590C2#1059465611yescharacteristic
591C2#1059496911yescharacteristic
592C2D4×#62411yescharacteristic
593C2Q8×#62411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#387
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C3×#4980C2semidirect
9. #10591271C2semidirect
10. #10591263C2semidirect
11. #10591197C2semidirect
24. C4⋊C4×C3⋊D3C4semidirect
44. #4980D3semidirect
87. C32×C4⋊C4C2×C4semidirect
88. C4⋊(C3⋊Dic3)C2×C4semidirect
89. #3750C2×C4semidirect
90. #3750C2×C4semidirect
252. C3×C4⋊C4C4×D3semidirect
409. C3⋊D3#387semidirect
447. C4⋊C4#624semidirect
498. C32C2×#387semidirect
585. C3D3×#387semidirect

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×C4×#6242
C3×#49802
#105913702
#105912712
#105912632
#105911972
D3×#3873