Finite Group Databasebeta

← #11805315

Subgroups — #11805315

Order 1152.

1137 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63849C211yesmaximal, characteristic
2C4×#3752C211yesmaximal, characteristic
3C3×C4×C4⋊Dic3C211yesmaximal, characteristic, complemented
4C3×#4928C211yesmaximal, characteristic, complemented
5#10591357C211yesmaximal, characteristic, complemented
6#10591325C211yesmaximal, characteristic
7#10591274C211yesmaximal, characteristic, complemented
8#10591258C212yesmaximal
9#10591245C212yesmaximal, complemented
10#10591239C212yesmaximal, complemented
11#10591194C212yesmaximal
12#75979—31nomaximal
13#73633—31nomaximal
14C22×C4×C3⋊D3C2211yescharacteristic
15C2×C32×C42C2211yescharacteristic
16C2×#3752C2211yescharacteristic
17C2×#3752C2211yescharacteristic
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×Dic3⋊C4C2212yes—
24C2×C3×C4×Dic3C2212yes—
25C2×Dic3⋊Dic3C2212yes—
26C2×#3722C2212yes—
27C2×#3722C2212yes—
28C2×Dic32C2212yes—
29C2×Dic32C2212yes—
30#63849C418yescomplemented
31#63658C2211yescharacteristic
32#63658C2211yescharacteristic
33C3×C3⋊#95C2212yes—
34C3×C3⋊#95C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38C2×#892—31no—
39C2×#892—31no—
40C3×#389—31no—
41C3×C4×C4⋊C4—31no—
42#4990—32no—
43#4987—31no—
44#4987—31no—
45#4984—31no—
46#4977—32no—
47Dic3×C4⋊C4—31no—
48Dic3×C4⋊C4—31no—
49#4972—31no—
50#4940—32no—
51C4×(C2×D3)⋊C4—31no—
52C4×(C2×D3)⋊C4—31no—
53C4×(C2×D3)⋊C4—61no—
54C4×C4⋊Dic3D311yescharacteristic, complemented
55#4932—32no—
56#4928D311yescharacteristic, complemented
57#4670—32no—
58#4669—32no—
59#4650—32no—
60#4648—32no—
61C23×C3⋊D3C2311yescharacteristic
62C22×C32×C4C2311yescharacteristic
63C22×C32×C4C2311yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C22×C3⋊Dic3C2311yescharacteristic
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3⋊Dic3C2311yescharacteristic
68C2×C4×C3⋊D3—22no—
69C2×C4×C3⋊D3—22no—
70C2×C4×C3⋊D3C2×C414yes—
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2312yes—
75C32×C42—22no—
76#3752—22no—
77#3752—22no—
78C4×C3⋊Dic3—22no—
79C3×C4⋊Dic3—22no—
80C3×C4⋊Dic3—22no—
81C3×C4⋊Dic3C2×C414yes—
82C3×C4⋊Dic3C2×C414yes—
83C3×Dic3⋊C4—42no—
84C3×C4×Dic3—24no—
85Dic3⋊Dic3—42no—
86#3722—42no—
87#3722C2×C418yes—
88Dic32—24no—
89Dic32C2×C418yes—
90#2346—91noSylow
91C22×C4×D3—31no—
92C22×C4×D3—31no—
93C22×C4×D3—61no—
94C2×C3×C4⋊C4—31no—
95C2×C3×C4⋊C4—31no—
96C2×C3×C4⋊C4—31no—
97C2×C3×C4⋊C4—31no—
98C2×C3×C4⋊C4—32no—
99C2×C3×C42—21no—
100C2×C3×C42—32no—
101C2×C3×C42C2×D311yescharacteristic
102C2×C3×C42C2×D311yescharacteristic
103C2×(C2×D3)⋊C4—32no—
104C2×(C2×D3)⋊C4—32no—
105C2×(C2×D3)⋊C4—31no—
106C2×(C2×D3)⋊C4—31no—
107C2×(C2×D3)⋊C4—31no—
108C2×(C2×D3)⋊C4—31no—
109C2×(C2×D3)⋊C4—32no—
110C2×(C2×D3)⋊C4—32no—
111C2×(C2×D3)⋊C4—61no—
112C2×(C2×D3)⋊C4—61no—
113C2×C4⋊Dic3—32no—
114C2×C4⋊Dic3C2×D311yescharacteristic
115C2×C4⋊Dic3C2×D311yescharacteristic
116C2×C4⋊Dic3C2×D311yescharacteristic
117C2×C4⋊Dic3C2×D311yescharacteristic
118C2×Dic3⋊C4—32no—
119C2×Dic3⋊C4C2×D312yes—
120C2×C4×Dic3—32no—
121C2×C4×Dic3—32no—
122C2×C4×Dic3—31no—
123C2×C4×Dic3—31no—
124C2×C4×Dic3—32no—
125C2×C4×Dic3—32no—
126C2×C4×Dic3—61no—
127C2×C4×Dic3C2×D312yes—
128#892—38no—
129#892—38no—
130C3×#95—32no—
131C3×#95—32no—
132C3⋊#95—31no—
133C3⋊#95—31no—
134C3⋊#95—31no—
135C3⋊#95—31no—
136C3⋊#95—32no—
137C3⋊#95—32no—
138C3⋊#95—32no—
139C3⋊#95—32no—
140C3⋊#95—32no—
141C3⋊#95—32no—
142C3⋊#95—61no—
143C3⋊#95—61no—
144C3⋊#95C2×D312yes—
145C3⋊#95C2×D312yes—
146C23×C32C2411yescharacteristic
147C22×C3⋊D3—21no—
148C22×C3⋊D3—21no—
149C22×C3⋊D3—21no—
150C22×C3⋊D3—21no—
151C22×C3⋊D3—21no—
152C22×C3⋊D3—21no—
153C22×C3⋊D3C22×C412yes—
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×C4#4112yes—
161C2×C32×C4#4112yes—
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⋊Dic3C22×C412yes—
171C2×C3⋊Dic3#4112yes—
172C4×C3⋊D3—28no—
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×Dic3—22no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3C22×C414yes—
184C2×C3×Dic3C22×C414yes—
185C2×#117—91no—
186#389—31no—
187#389—91no—
188#388—92no—
189#388—92no—
190#382—92no—
191#380—91no—
192C4×C4⋊C4—31no—
193C4×C4⋊C4—91no—
194C4×C22⋊C4—91no—
195#376—92no—
196C23×D3—31no—
197C23×D3—31no—
198C23×D3—61no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—32no—
203C22×C3×C4—32no—
204C22×C3×C4—32no—
205C22×C3×C4—32no—
206C22×C3×C4C22×D311yescharacteristic
207C22×C3×C4C22×D311yescharacteristic
208C22×C3×C4C22×D311yescharacteristic
209C22×C3×C4C22×D311yescharacteristic
210C22×C3×C4C22×D311yescharacteristic
211C22×C3×C4C22×D311yescharacteristic
212C22×Dic3—31no—
213C22×Dic3—31no—
214C22×Dic3—31no—
215C22×Dic3—31no—
216C22×Dic3—31no—
217C22×Dic3—31no—
218C22×Dic3—61no—
219C22×Dic3—61no—
220C22×Dic3—61no—
221C22×Dic3C22×D312yes—
222C22×Dic3C22×D312yes—
223C22×Dic3C22×D312yes—
224C22×Dic3C22×D312yes—
225C2×C4×D3—34no—
226C2×C4×D3—34no—
227C2×C4×D3—64no—
228C2×C4×D3—62no—
229C2×C4×D3—62no—
230C2×C4×D3—62no—
231C2×C4×D3—62no—
232C2×C4×D3—122no—
233C2×C4×D3—122no—
234C3×C4⋊C4—34no—
235C3×C4⋊C4—34no—
236C3×C4⋊C4—62no—
237C3×C4⋊C4—62no—
238C3×C4⋊C4—122no—
239C3×C42—22no—
240C3×C42—22no—
241C3×C42—42no—
242C3×C42—64no—
243(C2×D3)⋊C4—38no—
244(C2×D3)⋊C4—38no—
245(C2×D3)⋊C4—62no—
246(C2×D3)⋊C4—62no—
247(C2×D3)⋊C4—64no—
248(C2×D3)⋊C4—64no—
249(C2×D3)⋊C4—62no—
250(C2×D3)⋊C4—62no—
251(C2×D3)⋊C4—122no—
252(C2×D3)⋊C4—122no—
253C4⋊Dic3—22no—
254C4⋊Dic3—22no—
255C4⋊Dic3—122no—
256C4⋊Dic3C4×D314yes—
257C4⋊Dic3C4×D314yes—
258Dic3⋊C4—42no—
259Dic3⋊C4—122no—
260C4×Dic3—24no—
261C4×Dic3—38no—
262C4×Dic3—38no—
263C4×Dic3—64no—
264C4×Dic3—64no—
265C4×Dic3—62no—
266C4×Dic3—62no—
267C4×Dic3—122no—
268C22×C32C23×C411yescharacteristic
269C22×C32C2×#4111yescharacteristic
270C22×C32C2×#4111yescharacteristic
271C22×C32C2×#4111yescharacteristic
272C22×C32C2×#4111yescharacteristic
273C22×C32H(5,𝔽2)11yescharacteristic
274C22×C322−1+411yescharacteristic
275C2×C3⋊D3—22no—
276C2×C3⋊D3—22no—
277C2×C3⋊D3—22no—
278C2×C3⋊D3—41no—
279C2×C3⋊D3—41no—
280C2×C3⋊D3—41no—
281C2×C3⋊D3—41no—
282C32×C4—22no—
283C32×C4—41no—
284C32×C4#11714yes—
285C3⋊Dic3—22no—
286C3⋊Dic3—22no—
287C3⋊Dic3—41no—
288C3×Dic3—24no—
289C3×Dic3—24no—
290C3×Dic3—42no—
291C3×Dic3—42no—
292C23×C4—91no—
293#117—98no—
294C2×C4⋊C4—31no—
295C2×C4⋊C4—31no—
296C2×C4⋊C4—31no—
297C2×C4⋊C4—31no—
298C2×C4⋊C4—32no—
299C2×C4⋊C4—92no—
300C2×C22⋊C4—92no—
301C2×C22⋊C4—91no—
302C2×C22⋊C4—91no—
303C2×C22⋊C4—92no—
304C2×C42—32no—
305C2×C42—92no—
306C2×C42—92no—
307C2×C42—91no—
308C2×C42D3211yescharacteristic
309#95—32no—
310#95—32no—
311#95—92no—
312#95—92no—
313#95—92no—
314#95—91no—
315#95—91no—
316C23×C3—21no—
317C23×C3C23×D311yescharacteristic
318C23×C3C23×D311yescharacteristic
319C22×D3—32no—
320C22×D3—32no—
321C22×D3—62no—
322C22×D3—62no—
323C22×D3—62no—
324C22×D3—61no—
325C22×D3—61no—
326C22×D3—61no—
327C22×D3—61no—
328C22×D3—61no—
329C22×D3—61no—
330C22×D3—61no—
331C22×D3—61no—
332C22×D3—61no—
333C22×D3—61no—
334C22×D3—61no—
335C22×D3—61no—
336C22×D3—121no—
337C22×D3—121no—
338C22×D3—121no—
339C22×D3—121no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—22no—
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—22no—
355C2×C3×C4—34no—
356C2×C3×C4—34no—
357C2×C3×C4—41no—
358C2×C3×C4—41no—
359C2×C3×C4—41no—
360C2×C3×C4—41no—
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×C4—62no—
368C2×C3×C4—62no—
369C2×C3×C4—62no—
370C2×C3×C4—62no—
371C2×C3×C4C2×C4×D312yes—
372C2×C3×C4C2×C4×D312yes—
373C2×C3×C4#23512yes—
374C2×C3×C4#23512yes—
375C2×C3×C4#23712yes—
376C2×C3×C4#23712yes—
377C2×C3×C4#23912yes—
378C2×C3×C4#23912yes—
379C2×Dic3—22no—
380C2×Dic3—22no—
381C2×Dic3—22no—
382C2×Dic3—22no—
383C2×Dic3—22no—
384C2×Dic3—22no—
385C2×Dic3—22no—
386C2×Dic3—22no—
387C2×Dic3—22no—
388C2×Dic3—22no—
389C2×Dic3—32no—
390C2×Dic3—32no—
391C2×Dic3—32no—
392C2×Dic3—32no—
393C2×Dic3—62no—
394C2×Dic3—62no—
395C2×Dic3—61no—
396C2×Dic3—61no—
397C2×Dic3—61no—
398C2×Dic3—61no—
399C2×Dic3—61no—
400C2×Dic3—61no—
401C2×Dic3—61no—
402C2×Dic3—61no—
403C2×Dic3—62no—
404C2×Dic3—61no—
405C2×Dic3—61no—
406C2×Dic3—61no—
407C2×Dic3—61no—
408C2×Dic3—61no—
409C2×Dic3—61no—
410C2×Dic3—121no—
411C2×Dic3—121no—
412C2×Dic3—121no—
413C2×Dic3—121no—
414C2×Dic3—121no—
415C2×Dic3—121no—
416C2×Dic3C2×C4×D314yes—
417C2×Dic3C2×C4×D314yes—
418C4×D3—68no—
419C4×D3—68no—
420C4×D3—128no—
421C2×C32C2×#11711yescharacteristic
422C2×C32C4×#4111yescharacteristic
423C2×C32#52011yescharacteristic
424C2×C32#55211yescharacteristic
425C2×C32#55211yescharacteristic
426C2×C32#55511yescharacteristic
427C2×C32#55511yescharacteristic
428C3⋊D3—42no—
429C24—91no—
430C22×C4—32no—
431C22×C4—32no—
432C22×C4—32no—
433C22×C4—32no—
434C22×C4—91no—
435C22×C4—91no—
436C22×C4—94no—
437C22×C4—91no—
438C22×C4—182no—
439C22×C4—182no—
440C22×C4C2×D3211yescharacteristic
441C22×C4C2×D3211yescharacteristic
442C22×C4C2×D3211yescharacteristic
443C4⋊C4—34no—
444C4⋊C4—34no—
445C4⋊C4—62no—
446C4⋊C4—62no—
447C4⋊C4—122no—
448C4⋊C4—362no—
449C22⋊C4—98no—
450C22⋊C4—182no—
451C22⋊C4—182no—
452C22⋊C4—362no—
453C42—22no—
454C42—64no—
455C42—98no—
456C42—184no—
457C42—182no—
458C22×C3—21no—
459C22×C3—21no—
460C22×C3—21no—
461C22×C3—21no—
462C22×C3—21no—
463C22×C3—21no—
464C22×C3—21no—
465C22×C3C22×C4×D311yescharacteristic
466C22×C3C22×C4×D311yescharacteristic
467C22×C3C2×#23511yescharacteristic
468C22×C3C2×#23511yescharacteristic
469C22×C3C2×#23711yescharacteristic
470C22×C3C2×#23711yescharacteristic
471C22×C3#100411yescharacteristic
472C22×C3C2×#23911yescharacteristic
473C22×C3C2×#23911yescharacteristic
474C22×C3#100711yescharacteristic
475C22×C3D3×#4111yescharacteristic
476C22×C3D3×#4111yescharacteristic
477C22×C3#100911yescharacteristic
478C22×C3#101011yescharacteristic
479C2×D3—64no—
480C2×D3—62no—
481C2×D3—62no—
482C2×D3—62no—
483C2×D3—62no—
484C2×D3—62no—
485C2×D3—62no—
486C2×D3—122no—
487C2×D3—122no—
488C2×D3—122no—
489C2×D3—122no—
490C2×D3—122no—
491C2×D3—122no—
492C2×D3—121no—
493C2×D3—121no—
494C2×D3—121no—
495C2×D3—121no—
496C2×D3—121no—
497C2×D3—121no—
498C2×D3—121no—
499C2×D3—121no—
500C3×C4—22no—
501C3×C4—22no—
502C3×C4—24no—
503C3×C4—42no—
504C3×C4—42no—
505C3×C4—41no—
506C3×C4—41no—
507C3×C4—64no—
508C3×C4—64no—
509C3×C4—122no—
510C3×C4—122no—
511C3×C4#87214yes—
512C3×C4#89214yes—
513Dic3—24no—
514Dic3—24no—
515Dic3—42no—
516Dic3—42no—
517Dic3—62no—
518Dic3—62no—
519Dic3—62no—
520Dic3—62no—
521Dic3—122no—
522Dic3—122no—
523Dic3—122no—
524Dic3—121no—
525Dic3—121no—
526C32#234611yescharacteristic, complemented, Sylow
527C23—92no—
528C23—181no—
529C23—181no—
530C23—181no—
531C23—181no—
532C23—181no—
533C23—181no—
534C23C22×D3211yescharacteristic
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—34no—
541C2×C4—34no—
542C2×C4—62no—
543C2×C4—62no—
544C2×C4—62no—
545C2×C4—62no—
546C2×C4—62no—
547C2×C4—62no—
548C2×C4—62no—
549C2×C4—62no—
550C2×C4—62no—
551C2×C4—62no—
552C2×C4—92no—
553C2×C4—92no—
554C2×C4—181no—
555C2×C4—181no—
556C2×C4—181no—
557C2×C4—181no—
558C2×C4—188no—
559C2×C4—181no—
560C2×C4—181no—
561C2×C4—181no—
562C2×C4#379612yes—
563C2×C4#379912yes—
564C2×C4C4×D3212yes—
565C2×C4#380412yes—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—21no—
572C2×C3—21no—
573C2×C3C2×#87211yescharacteristic
574C2×C3C2×#89211yescharacteristic
575C2×C3#551311yescharacteristic
576C2×C3#553211yescharacteristic
577C2×C3C4×#23711yescharacteristic
578C2×C3#554611yescharacteristic
579C2×C3#556311yescharacteristic
580C2×C3C4×#23911yescharacteristic
581C2×C3#557411yescharacteristic
582C2×C3#558111yescharacteristic
583C2×C3#561611yescharacteristic
584C2×C3#564211yescharacteristic
585C2×C3#569411yescharacteristic
586C2×C3#573411yescharacteristic
587D3—124no—
588D3—122no—
589D3—122no—
590C22—182no—
591C22—182no—
592C22—182no—
593C22—361no—
594C22—361no—
595C22—361no—
596C22—361no—
597C22C2×#379611yescharacteristic
598C22#6429711yescharacteristic
599C22C2×#379911yescharacteristic
600C22C2×C4×D3211yescharacteristic
601C22#6430611yescharacteristic
602C22#6430711yescharacteristic
603C22C2×#380411yescharacteristic
604C4—22no—
605C4—41no—
606C4—64no—
607C4—64no—
608C4—122no—
609C4—122no—
610C4—182no—
611C4—182no—
612C4—361no—
613C4#6383614yes—
614C3—21no—
615C3#7363311yescharacteristic, complemented
616C3#7597911yescharacteristic, complemented
617C2—362no—
618C2C4×#379611yescharacteristic
619C2#1059388911yescharacteristic
620C2#1059394711yescharacteristic
621C2#1059398711yescharacteristic
622C2C2×#6383611yescharacteristic
623C2#1059482511yescharacteristic
624C2#1059496111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC2×C42D32
hypocenterC32#2346
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. C3×C4×C4⋊Dic3C2semidirect
4. C3×#4928C2semidirect
5. #10591357C2semidirect
7. #10591274C2semidirect
9. #10591245C2semidirect
10. #10591239C2semidirect
30. #63849C4semidirect
54. C4×C4⋊Dic3D3semidirect
56. #4928D3semidirect
526. C32#2346semidirect
615. C3#73633semidirect
616. C3#75979semidirect

Maximal subgroups

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

subgroupindex
C2×#638492
C4×#37522
C3×C4×C4⋊Dic32
C3×#49282
#105913572
#105913252
#105912742
#105912582
#105912452
#105912392
#105911942
#759793
#736333