Finite Group Databasebeta

← #11819074

Subgroups — #11819074

Order 1152.

1177 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64133C211yesmaximal, characteristic
2C2×#63918C211yesmaximal, characteristic, complemented
3C3×#5212C211yesmaximal, characteristic
4C3×C4×#217C211yesmaximal, characteristic
5#10591701C212yesmaximal
6#10591692C212yesmaximal
7Dic3×C4⋊Dic3C211yesmaximal, characteristic, complemented
8#10591236C212yesmaximal, complemented
9#10591213C211yesmaximal, characteristic, complemented
10#10591213C211yesmaximal, characteristic, complemented
11#10591210C212yesmaximal, complemented
12#73916—31nomaximal
13#73508—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C22×#634C2211yescharacteristic
16C22×#627C2212yes—
17C2×#3757C2212yes—
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19#64133—24no—
20C2×#3750C2212yes—
21C2×C3×#217C2211yescharacteristic
22C2×C3×#217C2212yes—
23C2×C3×#217C2211yescharacteristic
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×C4×Dic3C2211yescharacteristic
27C2×C3×C4×Dic3C2211yescharacteristic
28C2×Dic3⋊Dic3C2212yes—
29C2×Dic32C2212yes—
30#63918—24no—
31C3×C3⋊#95C2211yescharacteristic
32C3×C3⋊#95C2212yes—
33C3×C3⋊#95C2211yescharacteristic
34#63579C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39C2×#924—31no—
40C2×#924—31no—
41C2×#924—61no—
42C2×#888—31no—
43C2×#869—31no—
44C3×#380—31no—
45C3×C4×C22⋊C4—31no—
46#5212D311yescharacteristic
47C4×#217D311yescharacteristic
48Dic3×C4⋊C4—31no—
49#4973—31no—
50#4973—31no—
51#4951—32no—
52#4947—32no—
53#4947—32no—
54#4944—32no—
55C4×C4⋊Dic3—31no—
56#4929—31no—
57#4929—31no—
58#4660—32no—
59#4658—32no—
60#4646—32no—
61#4646—32no—
62C24×C32C2311yescharacteristic
63C22×C32×C4—22no—
64C22×C32×C4—22no—
65C22×C32×C4—22no—
66C22×C32×C4C2311yescharacteristic
67C22×C32×C4C2311yescharacteristic
68C22×C3⋊Dic3C2312yes—
69C22×C3⋊Dic3C2312yes—
70C2×#634—22no—
71C2×#634—22no—
72C2×#634—22no—
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2312yes—
76C22×C3×Dic3C2311yescharacteristic
77C22×C3×Dic3C2311yescharacteristic
78C22×C3×Dic3C2311yescharacteristic
79C2×#627—24no—
80C2×#627—24no—
81C2×#627—42no—
82#3757—24no—
83C4⋊(C3⋊Dic3)D414yes—
84#3750—24no—
85C3×#217—22no—
86C3×#217—42no—
87C3×#217Q814yescomplemented
88C3×C4⋊Dic3—22no—
89C3×C4⋊Dic3—22no—
90C3×C4×Dic3—22no—
91C3×C4×Dic3—22no—
92Dic3⋊Dic3—24no—
93Dic32—42no—
94#2492—91noSylow
95C23×C3×C4—21no—
96C23×C3×C4C2×D311yescharacteristic
97C23×C3×C4C2×D311yescharacteristic
98C22×Dic6—31no—
99C22×Dic6—31no—
100C22×Dic6—32no—
101C22×Dic6—32no—
102C22×Dic6—61no—
103C2×C3×C4⋊C4—31no—
104C2×C3×C4⋊C4—31no—
105C2×C3×C22⋊C4—31no—
106C2×C3×C22⋊C4—31no—
107C2×C3×C22⋊C4—32no—
108C2×C3×C42—31no—
109C2×C3×C42—31no—
110C2×#217—32no—
111C2×#217—32no—
112C2×#217—62no—
113C2×#217C2×D311yescharacteristic
114C2×#217C2×D312yes—
115C2×#217C2×D311yescharacteristic
116C2×C4⋊Dic3—31no—
117C2×C4⋊Dic3—31no—
118C2×C4⋊Dic3—32no—
119C2×C4⋊Dic3—61no—
120C2×C4⋊Dic3C2×D311yescharacteristic
121C2×C4⋊Dic3C2×D311yescharacteristic
122#924—64no—
123#924—64no—
124#924—68no—
125C2×Dic3⋊C4—32no—
126C2×Dic3⋊C4—32no—
127C2×Dic3⋊C4—32no—
128C2×Dic3⋊C4—62no—
129C2×C4×Dic3—32no—
130C2×C4×Dic3—32no—
131C2×C4×Dic3C2×D311yescharacteristic
132C2×C4×Dic3C2×D311yescharacteristic
133#888—64no—
134#869—64no—
135C3×#95—31no—
136C3×#95—32no—
137C3×#95—31no—
138C3⋊#95—32no—
139C3⋊#95—32no—
140C3⋊#95—32no—
141C3⋊#95—32no—
142C3⋊#95—32no—
143C3⋊#95—32no—
144C3⋊#95—32no—
145C3⋊#95—32no—
146C3⋊#95—32no—
147C3⋊#95—32no—
148C3⋊#95C2×D311yescharacteristic
149C3⋊#95C2×D312yes—
150C3⋊#95C2×D311yescharacteristic
151C23×C32—21no—
152C23×C32—21no—
153C23×C32—21no—
154C23×C32—21no—
155C23×C32—21no—
156C23×C32—21no—
157C23×C32C2×Q812yes—
158C23×C32C2411yescharacteristic
159C2×C32×C4—21no—
160C2×C32×C4—21no—
161C2×C32×C4—21no—
162C2×C32×C4—44no—
163C2×C32×C4C2×D412yes—
164C2×C32×C4#4112yes—
165C2×C32×C4#4112yes—
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3—22no—
168C2×C3⋊Dic3—22no—
169C2×C3⋊Dic3—22no—
170C2×C3⋊Dic3—22no—
171C2×C3⋊Dic3C2×D414yes—
172#634—44no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—21no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—21no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3C2×Q812yes—
189C2×C3×Dic3C2×Q812yes—
190C2×C3×Dic3#4112yes—
191#627—48no—
192C2×C4⋊Q8—91no—
193C2×C22⋊Q8—91no—
194#400—92no—
195#393—92no—
196#391—92no—
197#391—91no—
198#391—91no—
199#388—92no—
200#380—31no—
201C4×C4⋊C4—91no—
202C4×C22⋊C4—31no—
203C24×C3—21no—
204C24×C3C22×D311yescharacteristic
205C24×C3C22×D311yescharacteristic
206C22×C3×C4—24no—
207C22×C3×C4—22no—
208C22×C3×C4—22no—
209C22×C3×C4—22no—
210C22×C3×C4—22no—
211C22×C3×C4—22no—
212C22×C3×C4—22no—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—31no—
216C22×C3×C4—31no—
217C22×C3×C4—31no—
218C22×C3×C4—31no—
219C22×C3×C4—32no—
220C22×C3×C4—32no—
221C22×C3×C4—42no—
222C22×C3×C4—42no—
223C22×C3×C4C22×D311yescharacteristic
224C22×C3×C4C22×D311yescharacteristic
225C22×C3×C4C22×D311yescharacteristic
226C22×C3×C4C22×D311yescharacteristic
227C22×Dic3—32no—
228C22×Dic3—32no—
229C22×Dic3—32no—
230C22×Dic3—32no—
231C22×Dic3—62no—
232C22×Dic3—62no—
233C22×Dic3C22×D311yescharacteristic
234C22×Dic3C22×D312yes—
235C22×Dic3C22×D312yes—
236C22×Dic3C22×D311yescharacteristic
237C22×Dic3C22×D311yescharacteristic
238C22×Dic3C22×D311yescharacteristic
239C2×Dic6—64no—
240C2×Dic6—64no—
241C2×Dic6—64no—
242C2×Dic6—64no—
243C2×Dic6—62no—
244C2×Dic6—62no—
245C2×Dic6—62no—
246C2×Dic6—62no—
247C2×Dic6—62no—
248C2×Dic6—62no—
249C2×Dic6—64no—
250C2×Dic6—122no—
251C2×Dic6—122no—
252C2×Dic6—122no—
253C2×Dic6—122no—
254C3×C4⋊C4—62no—
255C3×C4⋊C4—62no—
256C3×C22⋊C4—34no—
257C3×C22⋊C4—62no—
258C3×C22⋊C4—122no—
259C3×C42—62no—
260C3×C42—62no—
261#217—22no—
262#217—42no—
263#217—64no—
264#217—64no—
265#217—68no—
266#217Dic614yescomplemented
267C4⋊Dic3—22no—
268C4⋊Dic3—22no—
269C4⋊Dic3—34no—
270C4⋊Dic3—34no—
271C4⋊Dic3—64no—
272C4⋊Dic3—64no—
273Dic3⋊C4—64no—
274Dic3⋊C4—64no—
275Dic3⋊C4—64no—
276Dic3⋊C4—68no—
277C4×Dic3—22no—
278C4×Dic3—22no—
279C4×Dic3—122no—
280C4×Dic3—122no—
281C22×C32—22no—
282C22×C32—22no—
283C22×C32—22no—
284C22×C32—41no—
285C22×C32—41no—
286C22×C32—41no—
287C22×C32—41no—
288C22×C32C22×D411yescharacteristic
289C22×C32C22×Q811yescharacteristic
290C22×C32C2×#4111yescharacteristic
291C22×C32C2×#4111yescharacteristic
292C22×C32C2×#4111yescharacteristic
293C22×C32H(5,𝔽2)11yescharacteristic
294C22×C322−1+411yescharacteristic
295C32×C4—41no—
296C32×C4#12414yes—
297C3⋊Dic3—24no—
298C3⋊Dic3—42no—
299C3×Dic3—22no—
300C3×Dic3—22no—
301C3×Dic3—22no—
302C3×Dic3—42no—
303C3×Dic3—42no—
304C3×Dic3—41no—
305C22×Q8—92no—
306C22×Q8—91no—
307C23×C4D3211yescharacteristic
308C4⋊Q8—184no—
309C22⋊Q8—184no—
310C2×C4⋊C4—31no—
311C2×C4⋊C4—31no—
312C2×C4⋊C4—91no—
313C2×C4⋊C4—92no—
314C2×C4⋊C4—92no—
315C2×C22⋊C4—31no—
316C2×C22⋊C4—31no—
317C2×C22⋊C4—32no—
318C2×C22⋊C4—92no—
319C2×C42—31no—
320C2×C42—31no—
321C2×C42—92no—
322#95—31no—
323#95—31no—
324#95—32no—
325#95—92no—
326#95—92no—
327#95—92no—
328#95—92no—
329#95—92no—
330C23×C3—22no—
331C23×C3—22no—
332C23×C3—21no—
333C23×C3—21no—
334C23×C3—21no—
335C23×C3—21no—
336C23×C3—21no—
337C23×C3—21no—
338C23×C3—21no—
339C23×C3—21no—
340C23×C3—21no—
341C23×C3—21no—
342C23×C3—21no—
343C23×C3—21no—
344C23×C3—21no—
345C23×C3—22no—
346C23×C3—41no—
347C23×C3—41no—
348C23×C3—41no—
349C23×C3—41no—
350C23×C3C2×Dic612yes—
351C23×C3D3×Q812yes—
352C23×C3C23×D311yescharacteristic
353C23×C3C23×D311yescharacteristic
354C2×C3×C4—22no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—22no—
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—32no—
365C2×C3×C4—32no—
366C2×C3×C4—32no—
367C2×C3×C4—41no—
368C2×C3×C4—41no—
369C2×C3×C4—48no—
370C2×C3×C4—44no—
371C2×C3×C4—44no—
372C2×C3×C4—61no—
373C2×C3×C4—61no—
374C2×C3×C4—61no—
375C2×C3×C4—61no—
376C2×C3×C4—61no—
377C2×C3×C4—61no—
378C2×C3×C4—61no—
379C2×C3×C4—62no—
380C2×C3×C4—62no—
381C2×C3×C4—62no—
382C2×C3×C4—61no—
383C2×C3×C4—62no—
384C2×C3×C4—62no—
385C2×C3×C4—61no—
386C2×C3×C4—62no—
387C2×C3×C4#23512yes—
388C2×C3×C4#23512yes—
389C2×C3×C4D3×D412yes—
390C2×C3×C4D3×D412yes—
391C2×C3×C4#23712yes—
392C2×C3×C4#23712yes—
393C2×Dic3—21no—
394C2×Dic3—21no—
395C2×Dic3—21no—
396C2×Dic3—21no—
397C2×Dic3—21no—
398C2×Dic3—21no—
399C2×Dic3—21no—
400C2×Dic3—22no—
401C2×Dic3—21no—
402C2×Dic3—22no—
403C2×Dic3—22no—
404C2×Dic3—22no—
405C2×Dic3—22no—
406C2×Dic3—21no—
407C2×Dic3—22no—
408C2×Dic3—34no—
409C2×Dic3—34no—
410C2×Dic3—64no—
411C2×Dic3—62no—
412C2×Dic3—62no—
413C2×Dic3—62no—
414C2×Dic3—62no—
415C2×Dic3—64no—
416C2×Dic3—62no—
417C2×Dic3—62no—
418C2×Dic3—62no—
419C2×Dic3—62no—
420C2×Dic3—62no—
421C2×Dic3—62no—
422C2×Dic3—122no—
423C2×Dic3—122no—
424C2×Dic3—122no—
425C2×Dic3—122no—
426C2×Dic3C2×Dic612yes—
427C2×Dic3C2×Dic612yes—
428C2×Dic3#23512yes—
429Dic6—128no—
430Dic6—128no—
431Dic6—128no—
432Dic6—124no—
433Dic6—124no—
434C2×C32—42no—
435C2×C32C2×#12411yescharacteristic
436C2×C32#53311yescharacteristic
437C2×C32#54211yescharacteristic
438C2×C32#54611yescharacteristic
439C2×C32D4×Q811yescharacteristic
440C2×C32#55411yescharacteristic
441C2×C32#55611yescharacteristic
442C24C2×D3211yescharacteristic
443C2×Q8—184no—
444C2×Q8—184no—
445C2×Q8—182no—
446C2×Q8—182no—
447C2×Q8—182no—
448C2×Q8—362no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—31no—
453C22×C4—31no—
454C22×C4—31no—
455C22×C4—31no—
456C22×C4—32no—
457C22×C4—32no—
458C22×C4—92no—
459C22×C4—92no—
460C22×C4C2×D3211yescharacteristic
461C22×C4C2×D3211yescharacteristic
462C4⋊C4—62no—
463C4⋊C4—62no—
464C4⋊C4—94no—
465C4⋊C4—184no—
466C4⋊C4—184no—
467C22⋊C4—34no—
468C22⋊C4—62no—
469C22⋊C4—122no—
470C22⋊C4—184no—
471C42—62no—
472C42—62no—
473C42—362no—
474C22×C3—24no—
475C22×C3—22no—
476C22×C3—22no—
477C22×C3—22no—
478C22×C3—22no—
479C22×C3—22no—
480C22×C3—22no—
481C22×C3—21no—
482C22×C3—21no—
483C22×C3—21no—
484C22×C3—21no—
485C22×C3—21no—
486C22×C3—21no—
487C22×C3—21no—
488C22×C3—42no—
489C22×C3—42no—
490C22×C3—42no—
491C22×C3—42no—
492C22×C3—42no—
493C22×C3—42no—
494C22×C3—41no—
495C22×C3—41no—
496C22×C3—41no—
497C22×C3—41no—
498C22×C3—41no—
499C22×C3—41no—
500C22×C3—41no—
501C22×C3—41no—
502C22×C3C22×Dic611yescharacteristic
503C22×C3C2×#23511yescharacteristic
504C22×C3C2×#23511yescharacteristic
505C22×C3C2×#23511yescharacteristic
506C22×C3C2×D3×D411yescharacteristic
507C22×C3C2×D3×D411yescharacteristic
508C22×C3C2×#23711yescharacteristic
509C22×C3C2×#23711yescharacteristic
510C22×C3#100411yescharacteristic
511C22×C3C2×D3×Q811yescharacteristic
512C22×C3D3×#4111yescharacteristic
513C22×C3#100911yescharacteristic
514C22×C3#101011yescharacteristic
515C22×C3#101011yescharacteristic
516C3×C4—24no—
517C3×C4—42no—
518C3×C4—41no—
519C3×C4—41no—
520C3×C4—62no—
521C3×C4—62no—
522C3×C4—62no—
523C3×C4—121no—
524C3×C4—122no—
525C3×C4—122no—
526C3×C4#88514yes—
527C3×C4#88514yes—
528Dic3—22no—
529Dic3—22no—
530Dic3—22no—
531Dic3—41no—
532Dic3—42no—
533Dic3—42no—
534Dic3—64no—
535Dic3—64no—
536Dic3—124no—
537Dic3—124no—
538Dic3—122no—
539Dic3—122no—
540C32#249211yescharacteristic, complemented, Sylow
541C23—21no—
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23D3×Dic612yes—
548C23C22×D3211yescharacteristic
549Q8—368no—
550Q8—364no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—32no—
555C2×C4—32no—
556C2×C4—32no—
557C2×C4—44no—
558C2×C4—61no—
559C2×C4—61no—
560C2×C4—61no—
561C2×C4—61no—
562C2×C4—61no—
563C2×C4—61no—
564C2×C4—61no—
565C2×C4—62no—
566C2×C4—61no—
567C2×C4—62no—
568C2×C4—62no—
569C2×C4—62no—
570C2×C4—61no—
571C2×C4—62no—
572C2×C4—62no—
573C2×C4—94no—
574C2×C4—182no—
575C2×C4—182no—
576C2×C4—182no—
577C2×C4—182no—
578C2×C4—182no—
579C2×C4#380412yes—
580C2×C4#380412yes—
581C2×C4#381112yes—
582C2×C3—21no—
583C2×C3—21no—
584C2×C3—21no—
585C2×C3—21no—
586C2×C3—21no—
587C2×C3—21no—
588C2×C3—21no—
589C2×C3—44no—
590C2×C3—42no—
591C2×C3—42no—
592C2×C3#547011yescharacteristic
593C2×C3C2×#88511yescharacteristic
594C2×C3C2×#88511yescharacteristic
595C2×C3#551111yescharacteristic
596C2×C3#553311yescharacteristic
597C2×C3#553411yescharacteristic
598C2×C3D4×Dic611yescharacteristic
599C2×C3#554211yescharacteristic
600C2×C3#554311yescharacteristic
601C2×C3#555011yescharacteristic
602C2×C3#560311yescharacteristic
603C2×C3#561211yescharacteristic
604C2×C3#562211yescharacteristic
605C2×C3#563211yescharacteristic
606C22—22no—
607C22—22no—
608C22—22no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22C2×D3×Dic611yescharacteristic
614C22#6429811yescharacteristic
615C22D3×#23511yescharacteristic
616C22#6430711yescharacteristic
617C22C2×#380411yescharacteristic
618C22C2×#380411yescharacteristic
619C22C2×#381111yescharacteristic
620C4—41no—
621C4—62no—
622C4—62no—
623C4—62no—
624C4—122no—
625C4—121no—
626C4—122no—
627C4—184no—
628C4—362no—
629C4#6395314yes—
630C3—21no—
631C3#7350811yescharacteristic, complemented
632C3#7391611yescharacteristic, complemented
633C2—42no—
634C2#1059480811yescharacteristic
635C2#1059484011yescharacteristic
636C2#1059491511yescharacteristic
637C2#1059498311yescharacteristic
638C2#1059498811yescharacteristic
639C2#1059507811yescharacteristic
640C2C2×#6395311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC23×C32×C4C22
prime radicalC24×C32C23
hypercenterC23×C4D32
hypocenterC32#2492
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×#63918C2semidirect
7. Dic3×C4⋊Dic3C2semidirect
8. #10591236C2semidirect
9. #10591213C2semidirect
10. #10591213C2semidirect
11. #10591210C2semidirect
87. C3×#217Q8semidirect
266. #217Dic6semidirect
540. C32#2492semidirect
631. C3#73508semidirect
632. C3#73916semidirect

Maximal subgroups

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

subgroupindex
C2×#641332
C2×#639182
C3×#52122
C3×C4×#2172
#105917012
#105916922
Dic3×C4⋊Dic32
#105912362
#105912132
#105912102
#739163
#735083