Finite Group Databasebeta

← #11803129

Subgroups — #11803129

Order 1152.

1169 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63898C211yesmaximal, characteristic
2#10592631C211yesmaximal, characteristic, complemented
3C3×#4939C211yesmaximal, characteristic
4C3×#4928C211yesmaximal, characteristic, complemented
5#10591366C212yesmaximal, complemented
6#10591362C212yesmaximal, complemented
7#10591357C211yesmaximal, characteristic, complemented
8#10591323C211yesmaximal, characteristic
9#10591285C212yesmaximal, complemented
10#10591284C212yesmaximal, complemented
11#10591274C211yesmaximal, characteristic, complemented
12#76295—31nomaximal
13#75969—31nomaximal
14C22×C3×D12C2211yescharacteristic
15C22×D3×Dic3C2212yes—
16C2×C32×C42C2211yescharacteristic
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C2×C3×(C2×D3)⋊C4C2212yes—
20C2×C3×(C2×D3)⋊C4C2212yes—
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×Dic3⋊C4C2212yes—
25C2×Dic3⋊Dic3C2212yes—
26C2×(C2×D3)⋊Dic3C2212yes—
27C2×(C2×D3)⋊Dic3C2212yes—
28C2×(C2×D3)⋊Dic3C2212yes—
29C2×Dic32C2212yes—
30#63898C418yescomplemented
31#63658C2211yescharacteristic
32#63658C2211yescharacteristic
33#63658C2211yescharacteristic
34#63658C2211yescharacteristic
35C3×C3⋊#95C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38C2×D4×Dic3—31no—
39C2×#893—31no—
40C3×#390—31no—
41C3×#389—31no—
42#5221—31no—
43#4990—32no—
44#4988—31no—
45#4987—32no—
46#4984—31no—
47Dic3×C4⋊C4—31no—
48Dic3×C4⋊C4—31no—
49#4972—31no—
50#4945—32no—
51#4944—32no—
52#4943—32no—
53#4942—32no—
54#4939D311yescharacteristic
55#4932—31no—
56#4932—31no—
57#4932—61no—
58#4928D311yescharacteristic, complemented
59#4670—32no—
60#4664—32no—
61C23×C3×D3C2312yes—
62C22×C32×C4C2311yescharacteristic
63C22×C32×C4C2311yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C22×C3⋊Dic3C2311yescharacteristic
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3⋊Dic3C2311yescharacteristic
68C22×C3⋊Dic3C2311yescharacteristic
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2312yes—
72C2×C3×D12—22no—
73C2×C3×D12—22no—
74C2×C3×D12C2×C414yes—
75C2×D3×Dic3—42no—
76C2×D3×Dic3—42no—
77C2×D3×Dic3C2×C418yes—
78C32×C42—22no—
79C4×C3⋊Dic3—22no—
80C4×C3⋊Dic3C2×C414yes—
81C3×(C2×D3)⋊C4—42no—
82C3×(C2×D3)⋊C4—42no—
83C3×C4⋊Dic3—22no—
84C3×C4⋊Dic3—22no—
85C3×C4⋊Dic3C2×C414yes—
86C3×Dic3⋊C4—42no—
87Dic3⋊Dic3—42no—
88(C2×D3)⋊Dic3—42no—
89(C2×D3)⋊Dic3—42no—
90(C2×D3)⋊Dic3C2×C418yes—
91Dic32—42no—
92#2319—91noSylow
93C22×C3×D4—31no—
94C23×Dic3—32no—
95C22×D12C2×D311yescharacteristic
96C22×C4×D3—32no—
97C2×C3×C4⋊C4—31no—
98C2×C3×C4⋊C4—31no—
99C2×C3×C4⋊C4—31no—
100C2×C3×C4⋊C4—32no—
101C2×C3×C22⋊C4—32no—
102C2×C3×C22⋊C4—32no—
103C2×C3×C42—21no—
104C2×C3×C42C2×D311yescharacteristic
105C2×C3×C42C2×D311yescharacteristic
106C2×#217—32no—
107C2×#217—32no—
108C2×#217—32no—
109D4×Dic3—38no—
110C2×(C2×D3)⋊C4—32no—
111C2×(C2×D3)⋊C4—32no—
112C2×(C2×D3)⋊C4—32no—
113C2×(C2×D3)⋊C4C2×D312yes—
114C2×(C2×D3)⋊C4C2×D312yes—
115C2×C4⋊Dic3—32no—
116C2×C4⋊Dic3C2×D311yescharacteristic
117C2×C4⋊Dic3C2×D311yescharacteristic
118C2×C4⋊Dic3C2×D311yescharacteristic
119C2×Dic3⋊C4—32no—
120C2×Dic3⋊C4C2×D312yes—
121C2×C4×Dic3—31no—
122C2×C4×Dic3—31no—
123C2×C4×Dic3—31no—
124C2×C4×Dic3—31no—
125C2×C4×Dic3—32no—
126C2×C4×Dic3—32no—
127C2×C4×Dic3—61no—
128C2×C4×Dic3—61no—
129#893—38no—
130C3×#95—32no—
131C3⋊#95—31no—
132C3⋊#95—31no—
133C3⋊#95—31no—
134C3⋊#95—31no—
135C3⋊#95—31no—
136C3⋊#95—31no—
137C3⋊#95—31no—
138C3⋊#95—31no—
139C3⋊#95—32no—
140C3⋊#95—32no—
141C3⋊#95—32no—
142C3⋊#95—32no—
143C3⋊#95—61no—
144C3⋊#95—61no—
145C3⋊#95—61no—
146C3⋊#95—61no—
147C3⋊#95C2×D312yes—
148C23×C32C2411yescharacteristic
149C22×C3×D3—22no—
150C22×C3×D3—22no—
151C22×C3×D3—22no—
152C22×C3×D3—22no—
153C22×C3×D3—22no—
154C22×C3×D3—22no—
155C22×C3×D3C22×C414yes—
156C2×C32×C4—21no—
157C2×C32×C4—21no—
158C2×C32×C4—21no—
159C2×C32×C4—21no—
160C2×C32×C4—21no—
161C2×C32×C4—21no—
162C2×C32×C4C22×C412yes—
163C2×C32×C4#4112yes—
164C2×C32×C4#4112yes—
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⋊Dic3—21no—
173C2×C3⋊Dic3—21no—
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3C22×C412yes—
176C2×C3⋊Dic3C22×C412yes—
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—
186C3×D12—28no—
187D3×Dic3—48no—
188C2×C4×D4—91no—
189#390—31no—
190#390—91no—
191#389—31no—
192#389—91no—
193#388—92no—
194#388—92no—
195#381—92no—
196#380—92no—
197C4×C4⋊C4—91no—
198#376—91no—
199C24×C3—32no—
200C23×D3C22×D312yes—
201C2×C3×D4—34no—
202C2×C3×D4—62no—
203C2×C3×D4—62no—
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×C4C22×D311yescharacteristic
211C22×C3×C4C22×D311yescharacteristic
212C22×C3×C4C22×D311yescharacteristic
213C22×C3×C4C22×D311yescharacteristic
214C22×C3×C4C22×D311yescharacteristic
215C22×C3×C4C22×D311yescharacteristic
216C22×Dic3—31no—
217C22×Dic3—31no—
218C22×Dic3—31no—
219C22×Dic3—31no—
220C22×Dic3—38no—
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×Dic3—122no—
230C22×Dic3—122no—
231C22×Dic3C22×D312yes—
232C22×Dic3C22×D312yes—
233C22×Dic3C22×D312yes—
234C2×D12—22no—
235C2×D12—22no—
236C2×D12C4×D314yes—
237C2×C4×D3—38no—
238C2×C4×D3—122no—
239C2×C4×D3—122no—
240C3×C4⋊C4—34no—
241C3×C4⋊C4—62no—
242C3×C4⋊C4—62no—
243C3×C4⋊C4—122no—
244C3×C22⋊C4—122no—
245C3×C22⋊C4—122no—
246C3×C42—24no—
247C3×C42—22no—
248C3×C42—22no—
249#217—38no—
250#217—122no—
251#217—122no—
252(C2×D3)⋊C4—38no—
253(C2×D3)⋊C4—42no—
254(C2×D3)⋊C4—42no—
255(C2×D3)⋊C4—122no—
256(C2×D3)⋊C4—122no—
257C4⋊Dic3—22no—
258C4⋊Dic3—22no—
259C4⋊Dic3—122no—
260C4⋊Dic3C4×D314yes—
261Dic3⋊C4—42no—
262Dic3⋊C4—122no—
263C4×Dic3—34no—
264C4×Dic3—34no—
265C4×Dic3—64no—
266C4×Dic3—64no—
267C4×Dic3—62no—
268C4×Dic3—62no—
269C4×Dic3—122no—
270C4×Dic3—122no—
271C22×C32C23×C411yescharacteristic
272C22×C32C2×#4111yescharacteristic
273C22×C32C2×#4111yescharacteristic
274C22×C32H(5,𝔽2)11yescharacteristic
275C22×C32H(5,𝔽2)11yescharacteristic
276C22×C32H(5,𝔽2)11yescharacteristic
277C22×C322−1+411yescharacteristic
278C2×C3×D3—24no—
279C2×C3×D3—24no—
280C2×C3×D3—24no—
281C2×C3×D3—42no—
282C2×C3×D3—42no—
283C2×C3×D3—42no—
284C2×C3×D3—42no—
285C32×C4—41no—
286C32×C4—41no—
287C32×C4#11714yes—
288C3⋊Dic3—22no—
289C3⋊Dic3—22no—
290C3⋊Dic3—41no—
291C3⋊Dic3—41no—
292C3×Dic3—24no—
293C3×Dic3—42no—
294C3×Dic3—42no—
295C22×D4—31no—
296C23×C4—92no—
297C4×D4—98no—
298C2×C4⋊C4—31no—
299C2×C4⋊C4—31no—
300C2×C4⋊C4—31no—
301C2×C4⋊C4—32no—
302C2×C4⋊C4—92no—
303C2×C22⋊C4—32no—
304C2×C22⋊C4—32no—
305C2×C22⋊C4—92no—
306C2×C22⋊C4—92no—
307C2×C22⋊C4—92no—
308C2×C42—91no—
309C2×C42—91no—
310C2×C42—92no—
311C2×C42D3211yescharacteristic
312#95—32no—
313#95—92no—
314#95—92no—
315#95—91no—
316#95—91no—
317#95—91no—
318#95—91no—
319C23×C3—21no—
320C23×C3—34no—
321C23×C3—62no—
322C23×C3—62no—
323C23×C3—62no—
324C23×C3—62no—
325C23×C3—62no—
326C23×C3—62no—
327C23×C3C23×D311yescharacteristic
328C23×C3C23×D311yescharacteristic
329C22×D3—22no—
330C22×D3—22no—
331C22×D3—22no—
332C22×D3—22no—
333C22×D3—22no—
334C22×D3—22no—
335C22×D3C2×C4×D314yes—
336C3×D4—68no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—22no—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
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×C4C2×C4×D312yes—
368C2×C3×C4C2×C4×D312yes—
369C2×C3×C4#23712yes—
370C2×C3×C4#23712yes—
371C2×C3×C4#23712yes—
372C2×C3×C4#23912yes—
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—32no—
382C2×Dic3—32no—
383C2×Dic3—32no—
384C2×Dic3—32no—
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—62no—
397C2×Dic3—61no—
398C2×Dic3—61no—
399C2×Dic3—61no—
400C2×Dic3—61no—
401C2×Dic3—61no—
402C2×Dic3—61no—
403C2×Dic3—61no—
404C2×Dic3—61no—
405C2×Dic3—61no—
406C2×Dic3—61no—
407C2×Dic3—61no—
408C2×Dic3—61no—
409C2×Dic3—121no—
410C2×Dic3—121no—
411C2×Dic3—121no—
412C2×Dic3—121no—
413C2×Dic3—121no—
414C2×Dic3—121no—
415C2×Dic3—121no—
416C2×Dic3—121no—
417C2×Dic3—128no—
418C2×Dic3C2×C4×D314yes—
419D12—28no—
420C4×D3—128no—
421C2×C32C2×#11711yescharacteristic
422C2×C32#51811yescharacteristic
423C2×C32#52011yescharacteristic
424C2×C32#54011yescharacteristic
425C2×C32#54011yescharacteristic
426C2×C32#54211yescharacteristic
427C2×C32#54211yescharacteristic
428C3×D3—44no—
429C24—32no—
430C2×D4—34no—
431C2×D4—62no—
432C2×D4—62no—
433C22×C4—32no—
434C22×C4—32no—
435C22×C4—32no—
436C22×C4—98no—
437C22×C4—91no—
438C22×C4—91no—
439C22×C4—91no—
440C22×C4—91no—
441C22×C4—362no—
442C22×C4—362no—
443C22×C4C2×D3211yescharacteristic
444C22×C4C2×D3211yescharacteristic
445C22×C4C2×D3211yescharacteristic
446C4⋊C4—34no—
447C4⋊C4—62no—
448C4⋊C4—62no—
449C4⋊C4—122no—
450C4⋊C4—362no—
451C22⋊C4—98no—
452C22⋊C4—122no—
453C22⋊C4—122no—
454C22⋊C4—362no—
455C22⋊C4—362no—
456C42—22no—
457C42—94no—
458C42—182no—
459C42—362no—
460C22×C3—21no—
461C22×C3—21no—
462C22×C3—21no—
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—21no—
466C22×C3—21no—
467C22×C3—64no—
468C22×C3—64no—
469C22×C3—64no—
470C22×C3—122no—
471C22×C3—122no—
472C22×C3—122no—
473C22×C3—122no—
474C22×C3C22×C4×D311yescharacteristic
475C22×C3C22×C4×D311yescharacteristic
476C22×C3C2×#23711yescharacteristic
477C22×C3C2×#23711yescharacteristic
478C22×C3C2×#23711yescharacteristic
479C22×C3#100411yescharacteristic
480C22×C3#100411yescharacteristic
481C22×C3#100411yescharacteristic
482C22×C3C2×#23911yescharacteristic
483C22×C3#100711yescharacteristic
484C22×C3#100911yescharacteristic
485C22×C3#100911yescharacteristic
486C22×C3#100911yescharacteristic
487C22×C3#101011yescharacteristic
488C2×D3—24no—
489C2×D3—24no—
490C2×D3—24no—
491C2×D3—42no—
492C2×D3—42no—
493C2×D3—42no—
494C2×D3—42no—
495C3×C4—24no—
496C3×C4—42no—
497C3×C4—42no—
498C3×C4—41no—
499C3×C4—41no—
500C3×C4—41no—
501C3×C4—41no—
502C3×C4—64no—
503C3×C4—122no—
504C3×C4—122no—
505C3×C4#87714yes—
506C3×C4#89214yes—
507Dic3—24no—
508Dic3—42no—
509Dic3—42no—
510Dic3—62no—
511Dic3—62no—
512Dic3—62no—
513Dic3—62no—
514Dic3—122no—
515Dic3—122no—
516Dic3—122no—
517Dic3—122no—
518Dic3—121no—
519Dic3—121no—
520Dic3—121no—
521Dic3—121no—
522C32#231911yescharacteristic, complemented, Sylow
523C23—34no—
524C23—62no—
525C23—62no—
526C23—62no—
527C23—62no—
528C23—62no—
529C23—62no—
530C23C22×D3211yescharacteristic
531D4—68no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—34no—
539C2×C4—62no—
540C2×C4—62no—
541C2×C4—62no—
542C2×C4—62no—
543C2×C4—62no—
544C2×C4—62no—
545C2×C4—62no—
546C2×C4—62no—
547C2×C4—92no—
548C2×C4—92no—
549C2×C4—181no—
550C2×C4—181no—
551C2×C4—181no—
552C2×C4—181no—
553C2×C4—181no—
554C2×C4—181no—
555C2×C4—181no—
556C2×C4—181no—
557C2×C4—181no—
558C2×C4—181no—
559C2×C4—368no—
560C2×C4#379612yes—
561C2×C4C4×D3212yes—
562C2×C4#380512yes—
563C2×C3—21no—
564C2×C3—21no—
565C2×C3—21no—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—124no—
571C2×C3C2×#87711yescharacteristic
572C2×C3C2×#89211yescharacteristic
573C2×C3#554511yescharacteristic
574C2×C3#554511yescharacteristic
575C2×C3#554611yescharacteristic
576C2×C3#557411yescharacteristic
577C2×C3#560311yescharacteristic
578C2×C3#561911yescharacteristic
579C2×C3#561911yescharacteristic
580C2×C3#564311yescharacteristic
581C2×C3#568211yescharacteristic
582C2×C3#569711yescharacteristic
583C2×C3#571911yescharacteristic
584C2×C3#573311yescharacteristic
585D3—44no—
586C22—64no—
587C22—64no—
588C22—64no—
589C22—122no—
590C22—122no—
591C22—122no—
592C22—122no—
593C22C2×#379611yescharacteristic
594C22#6429711yescharacteristic
595C22C2×C4×D3211yescharacteristic
596C22#6430711yescharacteristic
597C22#6430711yescharacteristic
598C22#6430711yescharacteristic
599C22C2×#380511yescharacteristic
600C4—41no—
601C4—41no—
602C4—64no—
603C4—122no—
604C4—122no—
605C4—182no—
606C4—182no—
607C4—361no—
608C4—361no—
609C4#6387814yes—
610C3—21no—
611C3#7596911yescharacteristic, complemented
612C3#7629511yescharacteristic, complemented
613C2—124no—
614C2#1059388911yescharacteristic
615C2#1059395011yescharacteristic
616C2#1059395511yescharacteristic
617C2#1059399611yescharacteristic
618C2C2×#6387811yescharacteristic
619C2#1059498411yescharacteristic
620C2#1059504111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC22×C3×D12C22
hypercenterC2×C42D32
hypocenterC32#2319
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #10592631C2semidirect
4. C3×#4928C2semidirect
5. #10591366C2semidirect
6. #10591362C2semidirect
7. #10591357C2semidirect
9. #10591285C2semidirect
10. #10591284C2semidirect
11. #10591274C2semidirect
30. #63898C4semidirect
58. #4928D3semidirect
522. C32#2319semidirect
611. C3#75969semidirect
612. C3#76295semidirect

Maximal subgroups

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

subgroupindex
C2×#638982
#105926312
C3×#49392
C3×#49282
#105913662
#105913622
#105913572
#105913232
#105912852
#105912842
#105912742
#762953
#759693