Finite Group Databasebeta

← #11805561

Subgroups — #11805561

Order 1152.

1233 conjugacy classes of subgroups.

The subgroup lattice has 588 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#10591359C211yesmaximal, characteristic
7#10591357C211yesmaximal, characteristic
8#10591327C212yesmaximal
9#10591246C212yesmaximal
10#10591244C212yesmaximal
11#10591243C212yesmaximal
12Q8×Dic3⋊C4—31nomaximal
13#75981—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×#3724C2212yes—
28C2×#3724C2212yes—
29C2×Dic3⋊Dic3C2212yes—
30C2×Dic3⋊Dic3C2212yes—
31C2×Dic3⋊Dic3C2212yes—
32C2×Dic32C2212yes—
33C2×Dic32C2212yes—
34#63843—24no—
35#63843C418yescomplemented
36#63658C2211yescharacteristic
37#63658C2211yescharacteristic
38C3×C3⋊#95C2212yes—
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#4976—32no—
49#4975—31no—
50#4975—31no—
51#4975—32no—
52#4975—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#4649—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#3750Q814yescomplemented
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—42no—
87C3×C4×Dic3—24no—
88#3724—24no—
89#3724—42no—
90Dic3⋊Dic3—24no—
91Dic3⋊Dic3—42no—
92Dic3⋊Dic3C2×C418yes—
93Dic32—24no—
94Dic32C2×C418yes—
95Q8×C4⋊C4—91noSylow
96C22×C3×Q8—31no—
97C22×Dic6C2×D311yescharacteristic
98C3×C4×Q8—64no—
99C2×C3×C4⋊C4—31no—
100C2×C3×C4⋊C4—32no—
101C2×C3×C4⋊C4—31no—
102C2×C3×C4⋊C4—31no—
103C2×C3×C4⋊C4—32no—
104C2×C3×C42—21no—
105C2×C3×C42—32no—
106C2×C3×C42C2×D311yescharacteristic
107C2×C3×C42C2×D311yescharacteristic
108Q8×Dic3—38no—
109Q8×Dic3—64no—
110C2×C4⋊Dic3—32no—
111C2×C4⋊Dic3—32no—
112C2×C4⋊Dic3—32no—
113C2×C4⋊Dic3C2×D311yescharacteristic
114C2×C4⋊Dic3C2×D311yescharacteristic
115C2×C4⋊Dic3C2×D311yescharacteristic
116C2×Dic3⋊C4—31no—
117C2×Dic3⋊C4—31no—
118C2×Dic3⋊C4—32no—
119C2×Dic3⋊C4—31no—
120C2×Dic3⋊C4—31no—
121C2×Dic3⋊C4—32no—
122C2×Dic3⋊C4—32no—
123C2×Dic3⋊C4—32no—
124C2×Dic3⋊C4—32no—
125C2×Dic3⋊C4—32no—
126C2×Dic3⋊C4—32no—
127C2×Dic3⋊C4—61no—
128C2×Dic3⋊C4—61no—
129C2×Dic3⋊C4C2×D312yes—
130C2×Dic3⋊C4C2×D312yes—
131C2×C4×Dic3—31no—
132C2×C4×Dic3—31no—
133C2×C4×Dic3—32no—
134C2×C4×Dic3—32no—
135C2×C4×Dic3—31no—
136C2×C4×Dic3—31no—
137C2×C4×Dic3—32no—
138C2×C4×Dic3—32no—
139C2×C4×Dic3—61no—
140C2×C4×Dic3—61no—
141C2×C4×Dic3C2×D312yes—
142#887—38no—
143#887—64no—
144C4×Dic6—24no—
145C3×#95—32no—
146C3⋊#95—31no—
147C3⋊#95—31no—
148C3⋊#95—31no—
149C3⋊#95—31no—
150C3⋊#95—32no—
151C3⋊#95—32no—
152C3⋊#95—61no—
153C3⋊#95—61no—
154C3⋊#95C2×D312yes—
155C23×C32C2411yescharacteristic
156C2×C32×C4—21no—
157C2×C32×C4—21no—
158C2×C32×C4—21no—
159C2×C32×C4—21no—
160C2×C32×C4—21no—
161C2×C32×C4C22×C412yes—
162C2×C32×C4C2×D412yes—
163C2×C32×C4C2×Q812yes—
164C2×C32×C4C2×Q812yes—
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⋊Dic3C2×Q812yes—
175C2×C3⋊Dic3C2×Q812yes—
176C2×C3⋊Dic3#4112yes—
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×Dic3C22×C414yes—
186C2×C3×Dic3C22×C414yes—
187C2×C3×Dic3C2×D414yes—
188C2×C3×Dic3C2×Q814yes—
189C3×Dic6C4⋊C4116yescomplemented
190C2×C4×Q8—31no—
191C2×C4×Q8—91no—
192C2×C4×Q8—91no—
193#389—31no—
194#389—92no—
195#389—92no—
196#389—91no—
197#384—92no—
198#384—91no—
199C4×C4⋊C4—92no—
200C4×C4⋊C4—91no—
201C2×C3×Q8—34no—
202C2×C3×Q8—34no—
203C2×C3×Q8—34no—
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—31no—
222C22×Dic3—31no—
223C22×Dic3—31no—
224C22×Dic3—31no—
225C22×Dic3—61no—
226C22×Dic3—61no—
227C22×Dic3—61no—
228C22×Dic3—61no—
229C22×Dic3C22×D312yes—
230C22×Dic3C22×D312yes—
231C22×Dic3C22×D312yes—
232C22×Dic3C22×D312yes—
233C2×Dic6Dic614yes—
234C2×Dic6C4×D314yes—
235C2×Dic6#6714yes—
236C3×C4⋊C4—34no—
237C3×C4⋊C4—64no—
238C3×C4⋊C4—62no—
239C3×C4⋊C4—62no—
240C3×C4⋊C4—122no—
241C3×C42—22no—
242C3×C42—22no—
243C3×C42—42no—
244C3×C42—64no—
245C4⋊Dic3—22no—
246C4⋊Dic3—22no—
247C4⋊Dic3—38no—
248C4⋊Dic3—64no—
249C4⋊Dic3—122no—
250C4⋊Dic3C4×D314yes—
251Dic3⋊C4—24no—
252Dic3⋊C4—34no—
253Dic3⋊C4—34no—
254Dic3⋊C4—38no—
255Dic3⋊C4—42no—
256Dic3⋊C4—64no—
257Dic3⋊C4—64no—
258Dic3⋊C4—64no—
259Dic3⋊C4—62no—
260Dic3⋊C4—62no—
261Dic3⋊C4—64no—
262Dic3⋊C4—64no—
263Dic3⋊C4—122no—
264Dic3⋊C4—122no—
265Dic3⋊C4—122no—
266C4×Dic3—24no—
267C4×Dic3—34no—
268C4×Dic3—34no—
269C4×Dic3—38no—
270C4×Dic3—38no—
271C4×Dic3—64no—
272C4×Dic3—64no—
273C4×Dic3—62no—
274C4×Dic3—62no—
275C4×Dic3—64no—
276C4×Dic3—122no—
277C22×C32C23×C411yescharacteristic
278C22×C32C22×D411yescharacteristic
279C22×C32C22×Q811yescharacteristic
280C22×C32C22×Q811yescharacteristic
281C22×C32C2×#4111yescharacteristic
282C22×C32H(5,𝔽2)11yescharacteristic
283C22×C322−1+411yescharacteristic
284C32×C4—22no—
285C32×C4—41no—
286C32×C4C2×C4⋊C414yes—
287C3⋊Dic3—22no—
288C3⋊Dic3—22no—
289C3⋊Dic3—41no—
290C3⋊Dic3C4×Q814yescomplemented
291C3×Dic3—24no—
292C3×Dic3—42no—
293C3×Dic3—42no—
294C3×Dic3C2×C4⋊C418yes—
295C22×Q8—31no—
296C4×Q8—64no—
297C4×Q8—98no—
298C4×Q8—184no—
299C2×C4⋊C4—31no—
300C2×C4⋊C4—32no—
301C2×C4⋊C4—31no—
302C2×C4⋊C4—31no—
303C2×C4⋊C4—32no—
304C2×C4⋊C4—92no—
305C2×C4⋊C4—91no—
306C2×C4⋊C4—92no—
307C2×C4⋊C4—92no—
308C2×C4⋊C4—91no—
309C2×C4⋊C4—92no—
310C2×C4⋊C4—92no—
311C2×C42—32no—
312C2×C42—92no—
313C2×C42—91no—
314C2×C42—92no—
315C2×C42—91no—
316C2×C42D3211yescharacteristic
317#95—32no—
318#95—92no—
319#95—91no—
320#95—91no—
321C23×C3—21no—
322C23×C3C23×D311yescharacteristic
323C23×C3C23×D311yescharacteristic
324C3×Q8—316no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—22no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—34no—
341C2×C3×C4—34no—
342C2×C3×C4—34no—
343C2×C3×C4—34no—
344C2×C3×C4—41no—
345C2×C3×C4—41no—
346C2×C3×C4—41no—
347C2×C3×C4—41no—
348C2×C3×C4—62no—
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×C4C2×Dic612yes—
357C2×C3×C4C2×C4×D312yes—
358C2×C3×C4C2×C4×D312yes—
359C2×C3×C4D3×D412yes—
360C2×C3×C4D3×Q812yes—
361C2×C3×C4D3×Q812yes—
362C2×C3×C4D3×Q812yes—
363C2×C3×C4C2×#6712yes—
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—32no—
373C2×Dic3—32no—
374C2×Dic3—32no—
375C2×Dic3—32no—
376C2×Dic3—32no—
377C2×Dic3—32no—
378C2×Dic3—32no—
379C2×Dic3—32no—
380C2×Dic3—32no—
381C2×Dic3—32no—
382C2×Dic3—62no—
383C2×Dic3—62no—
384C2×Dic3—62no—
385C2×Dic3—62no—
386C2×Dic3—62no—
387C2×Dic3—61no—
388C2×Dic3—61no—
389C2×Dic3—61no—
390C2×Dic3—61no—
391C2×Dic3—61no—
392C2×Dic3—61no—
393C2×Dic3—61no—
394C2×Dic3—61no—
395C2×Dic3—62no—
396C2×Dic3—61no—
397C2×Dic3—61no—
398C2×Dic3—61no—
399C2×Dic3—61no—
400C2×Dic3—61no—
401C2×Dic3—61no—
402C2×Dic3—121no—
403C2×Dic3—121no—
404C2×Dic3—121no—
405C2×Dic3—121no—
406C2×Dic3—121no—
407C2×Dic3—121no—
408C2×Dic3C2×Dic614yes—
409C2×Dic3C2×C4×D314yes—
410C2×Dic3C2×C4×D314yes—
411C2×Dic3C2×#6714yes—
412Dic6Dic3⋊C4116yescomplemented
413C2×C32C22×C4⋊C411yescharacteristic
414C2×C32C2×C4×Q811yescharacteristic
415C2×C32#52011yescharacteristic
416C2×C32D4×Q811yescharacteristic
417C2×C32#55011yescharacteristic
418C2×C32#55711yescharacteristic
419C2×C32Q8211yescharacteristic
420C2×Q8—34no—
421C2×Q8—34no—
422C2×Q8—34no—
423C22×C4—32no—
424C22×C4—32no—
425C22×C4—32no—
426C22×C4—32no—
427C22×C4—91no—
428C22×C4—91no—
429C22×C4—91no—
430C22×C4—91no—
431C22×C4C2×D3211yescharacteristic
432C22×C4C2×D3211yescharacteristic
433C22×C4C2×D3211yescharacteristic
434C4⋊C4—34no—
435C4⋊C4—64no—
436C4⋊C4—62no—
437C4⋊C4—62no—
438C4⋊C4—98no—
439C4⋊C4—94no—
440C4⋊C4—122no—
441C4⋊C4—182no—
442C4⋊C4—184no—
443C4⋊C4—184no—
444C4⋊C4—362no—
445C4⋊C4—362no—
446C42—22no—
447C42—64no—
448C42—98no—
449C42—94no—
450C42—184no—
451C42—182no—
452C22×C3—21no—
453C22×C3—21no—
454C22×C3—21no—
455C22×C3—21no—
456C22×C3—21no—
457C22×C3—21no—
458C22×C3—21no—
459C22×C3C22×Dic611yescharacteristic
460C22×C3C22×C4×D311yescharacteristic
461C22×C3C22×C4×D311yescharacteristic
462C22×C3C2×D3×D411yescharacteristic
463C22×C3#100411yescharacteristic
464C22×C3C2×D3×Q811yescharacteristic
465C22×C3C2×D3×Q811yescharacteristic
466C22×C3C2×D3×Q811yescharacteristic
467C22×C3#100711yescharacteristic
468C22×C3D3×#4111yescharacteristic
469C22×C3D3×#4111yescharacteristic
470C22×C3#100911yescharacteristic
471C22×C3#101011yescharacteristic
472C22×C3C22×#6711yescharacteristic
473C3×C4—22no—
474C3×C4—22no—
475C3×C4—24no—
476C3×C4—38no—
477C3×C4—42no—
478C3×C4—42no—
479C3×C4—41no—
480C3×C4—41no—
481C3×C4—64no—
482C3×C4—122no—
483C3×C4—122no—
484C3×C4D3×C4⋊C414yes—
485C3×C4C2×Dic3⋊C414yes—
486Dic3—24no—
487Dic3—34no—
488Dic3—34no—
489Dic3—42no—
490Dic3—42no—
491Dic3—64no—
492Dic3—62no—
493Dic3—62no—
494Dic3—62no—
495Dic3—62no—
496Dic3—122no—
497Dic3—122no—
498Dic3—122no—
499Dic3—121no—
500Dic3—121no—
501Dic3C2×Dic3⋊C418yes—
502C32Q8×C4⋊C411yescharacteristic, complemented, Sylow
503C23C22×D3211yescharacteristic
504Q8—316no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—34no—
511C2×C4—34no—
512C2×C4—34no—
513C2×C4—34no—
514C2×C4—62no—
515C2×C4—62no—
516C2×C4—62no—
517C2×C4—62no—
518C2×C4—62no—
519C2×C4—62no—
520C2×C4—62no—
521C2×C4—62no—
522C2×C4—92no—
523C2×C4—92no—
524C2×C4—92no—
525C2×C4—92no—
526C2×C4—92no—
527C2×C4—181no—
528C2×C4—181no—
529C2×C4—181no—
530C2×C4—181no—
531C2×C4—181no—
532C2×C4—181no—
533C2×C4—181no—
534C2×C4D3×Dic612yes—
535C2×C4#379712yes—
536C2×C4C4×D3212yes—
537C2×C4D3×#6712yes—
538C2×C3—21no—
539C2×C3—21no—
540C2×C3—21no—
541C2×C3—21no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3C2×D3×C4⋊C411yescharacteristic
546C2×C3#554611yescharacteristic
547C2×C3Q8×Dic611yescharacteristic
548C2×C3#556911yescharacteristic
549C2×C3C4×D3×Q811yescharacteristic
550C2×C3C4×D3×Q811yescharacteristic
551C2×C3#557411yescharacteristic
552C2×C3#559911yescharacteristic
553C2×C3#563211yescharacteristic
554C2×C3#568511yescharacteristic
555C2×C3#572211yescharacteristic
556C2×C3C22×Dic3⋊C411yescharacteristic
557C2×C3Q8×#6711yescharacteristic
558C2×C3#583411yescharacteristic
559C22C2×D3×Dic611yescharacteristic
560C22#6429711yescharacteristic
561C22C2×#379711yescharacteristic
562C22C2×C4×D3211yescharacteristic
563C22#6430611yescharacteristic
564C22#6430711yescharacteristic
565C22C2×D3×#6711yescharacteristic
566C4—22no—
567C4—38no—
568C4—41no—
569C4—64no—
570C4—94no—
571C4—122no—
572C4—122no—
573C4—182no—
574C4—182no—
575C4—361no—
576C4D3×Dic3⋊C414yes—
577C3—21no—
578C3#7598111yescharacteristic, complemented
579C3Q8×Dic3⋊C411yescharacteristic, complemented
580C2#1059385311yescharacteristic
581C2#1059385611yescharacteristic
582C2#1059388911yescharacteristic
583C2C4×#379711yescharacteristic
584C2#1059480311yescharacteristic
585C2C2×D3×Dic3⋊C411yescharacteristic
586C2#1059500611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C42D32
hypocenterC32Q8×C4⋊C4
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
35. #63843C4semidirect
79. #3750Q8semidirect
189. C3×Dic6C4⋊C4semidirect
290. C3⋊Dic3C4×Q8semidirect
412. Dic6Dic3⋊C4semidirect
502. C32Q8×C4⋊C4semidirect
578. C3#75981semidirect
579. C3Q8×Dic3⋊C4semidirect

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
#105913592
#105913572
#105913272
#105912462
#105912442
#105912432
Q8×Dic3⋊C43
#759813