Finite Group Databasebeta

← #11805600

Subgroups — #11805600

Order 1152.

1201 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×Dic6C211yesmaximal, characteristic
2C2×#63843C211yesmaximal, characteristic
3C2×#63843C211yesmaximal, characteristic
4C4×#3750C211yesmaximal, characteristic
5C3×#4928C211yesmaximal, characteristic
6#10591357C211yesmaximal, characteristic
7#10591330C212yesmaximal
8#10591245C212yesmaximal
9Dic3×Dic3⋊C4C212yesmaximal
10#10591234C212yesmaximal
11#10591230C211yesmaximal, characteristic
12#82461—31nomaximal
13#75982—31nomaximal
14C22×C3×Dic6C2211yescharacteristic
15C2×C32×C42C2211yescharacteristic
16C2×#3750C2211yescharacteristic
17C2×#3750C2211yescharacteristic
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×Dic3⋊C4C2212yes—
24C2×C3×Dic3⋊C4C2212yes—
25C2×C3×C4×Dic3C2212yes—
26C3×C4×Dic6—24no—
27C2×Dic3⋊Dic3C2212yes—
28C2×Dic3⋊Dic3C2212yes—
29C2×Dic3⋊Dic3C2212yes—
30C2×Dic32C2212yes—
31C2×Dic32C2212yes—
32#63843—24no—
33#63843C418yescomplemented
34#63658C2211yescharacteristic
35#63658C2211yescharacteristic
36C3×C3⋊#95C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C2×C3×C4×Q8—31no—
41C2×Q8×Dic3—31no—
42C2×Q8×Dic3—31no—
43C2×#887—31no—
44C2×#887—31no—
45C2×C4×Dic6D311yescharacteristic
46C3×#389—31no—
47#4984—31no—
48#4977—31no—
49#4977—31no—
50#4977—32no—
51#4976—32no—
52Dic3×C4⋊C4—32no—
53#4972—31no—
54#4972—32no—
55C4×Dic3⋊C4—31no—
56C4×Dic3⋊C4—31no—
57C4×Dic3⋊C4—32no—
58C4×Dic3⋊C4—61no—
59#4928—32no—
60#4928D311yescharacteristic
61#4650—32no—
62#4647—32no—
63C22×C32×C4C2311yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3⋊Dic3C2311yescharacteristic
68C22×C3⋊Dic3C2311yescharacteristic
69C22×C3⋊Dic3C2311yescharacteristic
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2312yes—
74C2×C3×Dic6C2×C414yes—
75C2×C3×Dic6D414yes—
76C2×C3×Dic6Q814yes—
77C32×C42—22no—
78#3750—22no—
79#3750—22no—
80C4×C3⋊Dic3—22no—
81C4×C3⋊Dic3C2×C414yes—
82C3×C4⋊Dic3—22no—
83C3×C4⋊Dic3—22no—
84C3×C4⋊Dic3C2×C414yes—
85C3×Dic3⋊C4—24no—
86C3×Dic3⋊C4—24no—
87C3×C4×Dic3—24no—
88Dic3⋊Dic3—24no—
89Dic3⋊Dic3—24no—
90Dic3⋊Dic3C2×C418yes—
91Dic32—24no—
92Dic32C2×C418yes—
93#2351—91noSylow
94C22×C3×Q8—31no—
95C22×Dic6C2×D311yescharacteristic
96C3×C4×Q8—64no—
97C2×C3×C4⋊C4—31no—
98C2×C3×C4⋊C4—32no—
99C2×C3×C4⋊C4—32no—
100C2×C3×C4⋊C4—31no—
101C2×C3×C4⋊C4—31no—
102C2×C3×C42—21no—
103C2×C3×C42—32no—
104C2×C3×C42C2×D311yescharacteristic
105C2×C3×C42C2×D311yescharacteristic
106Q8×Dic3—38no—
107Q8×Dic3—64no—
108C2×C4⋊Dic3—32no—
109C2×C4⋊Dic3—32no—
110C2×C4⋊Dic3—32no—
111C2×C4⋊Dic3C2×D311yescharacteristic
112C2×C4⋊Dic3C2×D311yescharacteristic
113C2×C4⋊Dic3C2×D311yescharacteristic
114C2×Dic3⋊C4—32no—
115C2×Dic3⋊C4—31no—
116C2×Dic3⋊C4—31no—
117C2×Dic3⋊C4—31no—
118C2×Dic3⋊C4—31no—
119C2×Dic3⋊C4—32no—
120C2×Dic3⋊C4—32no—
121C2×Dic3⋊C4—61no—
122C2×Dic3⋊C4—61no—
123C2×Dic3⋊C4C2×D312yes—
124C2×Dic3⋊C4C2×D312yes—
125C2×C4×Dic3—31no—
126C2×C4×Dic3—31no—
127C2×C4×Dic3—32no—
128C2×C4×Dic3—32no—
129C2×C4×Dic3—31no—
130C2×C4×Dic3—31no—
131C2×C4×Dic3—32no—
132C2×C4×Dic3—32no—
133C2×C4×Dic3—61no—
134C2×C4×Dic3—61no—
135C2×C4×Dic3C2×D312yes—
136#887—38no—
137#887—64no—
138C4×Dic6—24no—
139C3×#95—32no—
140C3⋊#95—31no—
141C3⋊#95—31no—
142C3⋊#95—31no—
143C3⋊#95—31no—
144C3⋊#95—32no—
145C3⋊#95—32no—
146C3⋊#95—32no—
147C3⋊#95—32no—
148C3⋊#95—32no—
149C3⋊#95—32no—
150C3⋊#95—61no—
151C3⋊#95—61no—
152C3⋊#95C2×D312yes—
153C23×C32C2411yescharacteristic
154C2×C32×C4—21no—
155C2×C32×C4—21no—
156C2×C32×C4—21no—
157C2×C32×C4—21no—
158C2×C32×C4—21no—
159C2×C32×C4C22×C412yes—
160C2×C32×C4C2×D412yes—
161C2×C32×C4C2×Q812yes—
162C2×C32×C4#4112yes—
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⋊Dic3—21no—
171C2×C3⋊Dic3—21no—
172C2×C3⋊Dic3C22×C412yes—
173C2×C3⋊Dic3C22×C412yes—
174C2×C3⋊Dic3#4112yes—
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×Dic3C22×C414yes—
184C2×C3×Dic3C22×C414yes—
185C2×C3×Dic3C2×D414yes—
186C2×C3×Dic3C2×Q814yes—
187C3×Dic6C4⋊C4116yescomplemented
188C2×C4×Q8—31no—
189C2×C4×Q8—91no—
190C2×C4×Q8—91no—
191#389—31no—
192#389—92no—
193#389—92no—
194#389—91no—
195#382—92no—
196#382—91no—
197C4×C4⋊C4—92no—
198C4×C4⋊C4—91no—
199C2×C3×Q8—34no—
200C2×C3×Q8—34no—
201C2×C3×Q8—34no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—32no—
206C22×C3×C4—32no—
207C22×C3×C4—32no—
208C22×C3×C4—32no—
209C22×C3×C4C22×D311yescharacteristic
210C22×C3×C4C22×D311yescharacteristic
211C22×C3×C4C22×D311yescharacteristic
212C22×C3×C4C22×D311yescharacteristic
213C22×C3×C4C22×D311yescharacteristic
214C22×C3×C4C22×D311yescharacteristic
215C22×Dic3—31no—
216C22×Dic3—31no—
217C22×Dic3—31no—
218C22×Dic3—31no—
219C22×Dic3—31no—
220C22×Dic3—31no—
221C22×Dic3—31no—
222C22×Dic3—31no—
223C22×Dic3—61no—
224C22×Dic3—61no—
225C22×Dic3—61no—
226C22×Dic3—61no—
227C22×Dic3C22×D312yes—
228C22×Dic3C22×D312yes—
229C22×Dic3C22×D312yes—
230C22×Dic3C22×D312yes—
231C2×Dic6Dic614yes—
232C2×Dic6C4×D314yes—
233C2×Dic6#6714yes—
234C3×C4⋊C4—34no—
235C3×C4⋊C4—64no—
236C3×C4⋊C4—62no—
237C3×C4⋊C4—64no—
238C3×C4⋊C4—62no—
239C3×C42—22no—
240C3×C42—22no—
241C3×C42—42no—
242C3×C42—64no—
243C4⋊Dic3—22no—
244C4⋊Dic3—22no—
245C4⋊Dic3—38no—
246C4⋊Dic3—64no—
247C4⋊Dic3—64no—
248C4⋊Dic3C4×D314yes—
249Dic3⋊C4—24no—
250Dic3⋊C4—24no—
251Dic3⋊C4—38no—
252Dic3⋊C4—64no—
253Dic3⋊C4—62no—
254Dic3⋊C4—62no—
255Dic3⋊C4—64no—
256Dic3⋊C4—64no—
257Dic3⋊C4—62no—
258Dic3⋊C4—62no—
259Dic3⋊C4—64no—
260C4×Dic3—24no—
261C4×Dic3—34no—
262C4×Dic3—34no—
263C4×Dic3—38no—
264C4×Dic3—38no—
265C4×Dic3—64no—
266C4×Dic3—64no—
267C4×Dic3—62no—
268C4×Dic3—62no—
269C4×Dic3—64no—
270C4×Dic3—122no—
271C22×C32C23×C411yescharacteristic
272C22×C32C22×D411yescharacteristic
273C22×C32C22×Q811yescharacteristic
274C22×C32C2×#4111yescharacteristic
275C22×C32C2×#4111yescharacteristic
276C22×C322−1+411yescharacteristic
277C22×C322−1+411yescharacteristic
278C32×C4—22no—
279C32×C4—41no—
280C32×C4C2×C4⋊C414yes—
281C3⋊Dic3—22no—
282C3⋊Dic3—22no—
283C3⋊Dic3—22no—
284C3⋊Dic3—41no—
285C3×Dic3—24no—
286C3×Dic3—42no—
287C3×Dic3—42no—
288C3×Dic3C2×C4⋊C418yes—
289C22×Q8—31no—
290C4×Q8—64no—
291C4×Q8—98no—
292C4×Q8—184no—
293C2×C4⋊C4—31no—
294C2×C4⋊C4—32no—
295C2×C4⋊C4—31no—
296C2×C4⋊C4—31no—
297C2×C4⋊C4—32no—
298C2×C4⋊C4—92no—
299C2×C4⋊C4—92no—
300C2×C4⋊C4—92no—
301C2×C4⋊C4—91no—
302C2×C4⋊C4—91no—
303C2×C42—32no—
304C2×C42—92no—
305C2×C42—91no—
306C2×C42—92no—
307C2×C42—91no—
308C2×C42D3211yescharacteristic
309#95—32no—
310#95—92no—
311#95—92no—
312#95—92no—
313#95—91no—
314#95—91no—
315C23×C3—21no—
316C23×C3C23×D311yescharacteristic
317C23×C3C23×D311yescharacteristic
318C3×Q8—316no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—22no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4—34no—
335C2×C3×C4—34no—
336C2×C3×C4—34no—
337C2×C3×C4—34no—
338C2×C3×C4—41no—
339C2×C3×C4—41no—
340C2×C3×C4—41no—
341C2×C3×C4—41no—
342C2×C3×C4—62no—
343C2×C3×C4—62no—
344C2×C3×C4—62no—
345C2×C3×C4—62no—
346C2×C3×C4—62no—
347C2×C3×C4—62no—
348C2×C3×C4—62no—
349C2×C3×C4—62no—
350C2×C3×C4C2×Dic612yes—
351C2×C3×C4C2×C4×D312yes—
352C2×C3×C4C2×C4×D312yes—
353C2×C3×C4D3×D412yes—
354C2×C3×C4#23712yes—
355C2×C3×C4D3×Q812yes—
356C2×C3×C4#23912yes—
357C2×C3×C4C2×#6712yes—
358C2×Dic3—22no—
359C2×Dic3—22no—
360C2×Dic3—22no—
361C2×Dic3—22no—
362C2×Dic3—22no—
363C2×Dic3—22no—
364C2×Dic3—22no—
365C2×Dic3—22no—
366C2×Dic3—32no—
367C2×Dic3—32no—
368C2×Dic3—32no—
369C2×Dic3—32no—
370C2×Dic3—32no—
371C2×Dic3—32no—
372C2×Dic3—62no—
373C2×Dic3—62no—
374C2×Dic3—62no—
375C2×Dic3—62no—
376C2×Dic3—62no—
377C2×Dic3—61no—
378C2×Dic3—61no—
379C2×Dic3—61no—
380C2×Dic3—61no—
381C2×Dic3—61no—
382C2×Dic3—61no—
383C2×Dic3—61no—
384C2×Dic3—61no—
385C2×Dic3—61no—
386C2×Dic3—61no—
387C2×Dic3—61no—
388C2×Dic3—61no—
389C2×Dic3—62no—
390C2×Dic3—61no—
391C2×Dic3—61no—
392C2×Dic3—61no—
393C2×Dic3—61no—
394C2×Dic3—61no—
395C2×Dic3—61no—
396C2×Dic3—121no—
397C2×Dic3—121no—
398C2×Dic3—121no—
399C2×Dic3—121no—
400C2×Dic3—121no—
401C2×Dic3—121no—
402C2×Dic3C2×Dic614yes—
403C2×Dic3C2×C4×D314yes—
404C2×Dic3C2×C4×D314yes—
405C2×Dic3C2×#6714yes—
406Dic6Dic3⋊C4116yescomplemented
407C2×C32C22×C4⋊C411yescharacteristic
408C2×C32C4×#4111yescharacteristic
409C2×C32#51911yescharacteristic
410C2×C32#54811yescharacteristic
411C2×C32#54811yescharacteristic
412C2×C32#55711yescharacteristic
413C2×C32#55711yescharacteristic
414C2×Q8—34no—
415C2×Q8—34no—
416C2×Q8—34no—
417C22×C4—32no—
418C22×C4—32no—
419C22×C4—32no—
420C22×C4—32no—
421C22×C4—91no—
422C22×C4—91no—
423C22×C4—91no—
424C22×C4—91no—
425C22×C4C2×D3211yescharacteristic
426C22×C4C2×D3211yescharacteristic
427C22×C4C2×D3211yescharacteristic
428C4⋊C4—34no—
429C4⋊C4—64no—
430C4⋊C4—64no—
431C4⋊C4—62no—
432C4⋊C4—62no—
433C4⋊C4—98no—
434C4⋊C4—182no—
435C4⋊C4—184no—
436C4⋊C4—184no—
437C4⋊C4—182no—
438C42—22no—
439C42—64no—
440C42—98no—
441C42—94no—
442C42—184no—
443C42—182no—
444C22×C3—21no—
445C22×C3—21no—
446C22×C3—21no—
447C22×C3—21no—
448C22×C3—21no—
449C22×C3—21no—
450C22×C3—21no—
451C22×C3C22×Dic611yescharacteristic
452C22×C3C22×C4×D311yescharacteristic
453C22×C3C22×C4×D311yescharacteristic
454C22×C3C2×D3×D411yescharacteristic
455C22×C3C2×#23711yescharacteristic
456C22×C3C2×D3×Q811yescharacteristic
457C22×C3C2×#23911yescharacteristic
458C22×C3#100711yescharacteristic
459C22×C3#100711yescharacteristic
460C22×C3D3×#4111yescharacteristic
461C22×C3D3×#4111yescharacteristic
462C22×C3#101011yescharacteristic
463C22×C3#101011yescharacteristic
464C22×C3C22×#6711yescharacteristic
465C3×C4—22no—
466C3×C4—22no—
467C3×C4—24no—
468C3×C4—38no—
469C3×C4—42no—
470C3×C4—42no—
471C3×C4—41no—
472C3×C4—41no—
473C3×C4—64no—
474C3×C4—122no—
475C3×C4—122no—
476C3×C4D3×C4⋊C414yes—
477C3×C4C2×Dic3⋊C414yes—
478Dic3—24no—
479Dic3—42no—
480Dic3—42no—
481Dic3—64no—
482Dic3—62no—
483Dic3—62no—
484Dic3—62no—
485Dic3—62no—
486Dic3—62no—
487Dic3—62no—
488Dic3—122no—
489Dic3—122no—
490Dic3—122no—
491Dic3—121no—
492Dic3—121no—
493Dic3C2×Dic3⋊C418yes—
494C32#235111yescharacteristic, complemented, Sylow
495C23C22×D3211yescharacteristic
496Q8—316no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—34no—
503C2×C4—34no—
504C2×C4—34no—
505C2×C4—34no—
506C2×C4—62no—
507C2×C4—62no—
508C2×C4—62no—
509C2×C4—62no—
510C2×C4—62no—
511C2×C4—62no—
512C2×C4—62no—
513C2×C4—62no—
514C2×C4—92no—
515C2×C4—92no—
516C2×C4—92no—
517C2×C4—181no—
518C2×C4—181no—
519C2×C4—181no—
520C2×C4—181no—
521C2×C4—181no—
522C2×C4—181no—
523C2×C4—181no—
524C2×C4—181no—
525C2×C4—181no—
526C2×C4D3×Dic612yes—
527C2×C4#379612yes—
528C2×C4C4×D3212yes—
529C2×C4D3×#6712yes—
530C2×C3—21no—
531C2×C3—21no—
532C2×C3—21no—
533C2×C3—21no—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—21no—
537C2×C3C2×D3×C4⋊C411yescharacteristic
538C2×C3C4×#23711yescharacteristic
539C2×C3#556911yescharacteristic
540C2×C3#557011yescharacteristic
541C2×C3#557211yescharacteristic
542C2×C3#557211yescharacteristic
543C2×C3C4×#23911yescharacteristic
544C2×C3#559811yescharacteristic
545C2×C3#563311yescharacteristic
546C2×C3#568511yescharacteristic
547C2×C3#572111yescharacteristic
548C2×C3C22×Dic3⋊C411yescharacteristic
549C2×C3#581711yescharacteristic
550C2×C3#583111yescharacteristic
551C22C2×D3×Dic611yescharacteristic
552C22C2×#379611yescharacteristic
553C22#6429711yescharacteristic
554C22#6429711yescharacteristic
555C22C2×C4×D3211yescharacteristic
556C22#6430611yescharacteristic
557C22C2×D3×#6711yescharacteristic
558C4—22no—
559C4—38no—
560C4—41no—
561C4—64no—
562C4—122no—
563C4—122no—
564C4—182no—
565C4—182no—
566C4—182no—
567C4—361no—
568C4D3×Dic3⋊C414yes—
569C3—21no—
570C3#7598211yescharacteristic, complemented
571C3#8246111yescharacteristic, complemented
572C2#1059384811yescharacteristic
573C2#1059385311yescharacteristic
574C2#1059386111yescharacteristic
575C2C4×#379611yescharacteristic
576C2#1059483011yescharacteristic
577C2C2×D3×Dic3⋊C411yescharacteristic
578C2#1059490011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C42D32
hypocenterC32#2351
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
33. #63843C4semidirect
187. C3×Dic6C4⋊C4semidirect
406. Dic6Dic3⋊C4semidirect
494. C32#2351semidirect
570. C3#75982semidirect
571. C3#82461semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×Dic62
C2×#638432
C4×#37502
C3×#49282
#105913572
#105913302
#105912452
Dic3×Dic3⋊C42
#105912342
#105912302
#824613
#759823