Finite Group Databasebeta

← #11803496

Subgroups — #11803496

Order 1152.

1205 conjugacy classes of subgroups.

The subgroup lattice has 629 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63857C211yesmaximal, characteristic
2C2×#63855C211yesmaximal, characteristic
3C2×#63844C211yesmaximal, characteristic, complemented
4#10592672C211yesmaximal, characteristic, complemented
5C3×#4987C211yesmaximal, characteristic
6C3×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
7#10591357C211yesmaximal, characteristic, complemented
8#10591327C212yesmaximal, complemented
9#10591284C212yesmaximal
10#10591279C212yesmaximal
11#10591253C212yesmaximal, complemented
12#73871—31nomaximal
13#73762—31nomaximal
14C22×#634C2211yescharacteristic
15C22×C3×C4×D3C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C2×C3×(C2×D3)⋊C4C2212yes—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4×Dic3C2212yes—
22C2×C3×C4×Dic3C2211yescharacteristic
23C2×#3724C2212yes—
24C2×Dic3⋊Dic3C2211yescharacteristic
25C2×Dic3⋊Dic3C2211yescharacteristic
26C2×Dic3⋊Dic3C2212yes—
27C2×Dic3⋊Dic3C2212yes—
28C2×(C2×D3)⋊Dic3C2211yescharacteristic
29C2×(C2×D3)⋊Dic3C2211yescharacteristic
30C2×(C2×D3)⋊Dic3C2212yes—
31C2×Dic32C2212yes—
32#63857C418yescomplemented
33#63855—24no—
34#63844—24no—
35#63658C2212yes—
36#63658C2212yes—
37C3×C3⋊#95C2212yes—
38C3×C3⋊#95C2212yes—
39#63579C2212yes—
40C2×#926—31no—
41C2×#924—31no—
42C2×#897—31no—
43C2×#887—31no—
44C2×#872—31no—
45C2×C4×Dic6—31no—
46C3×#380—31no—
47C3×C4×C4⋊C4—31no—
48#4987D311yescharacteristic
49#4984—31no—
50Dic3×C4⋊C4D311yescharacteristic, complemented
51#4973—31no—
52#4973—31no—
53#4973—61no—
54#4972—31no—
55#4945—32no—
56#4944—32no—
57#4940—32no—
58#4928—32no—
59#4670—32no—
60#4655—32no—
61#4653—32no—
62#4647—32no—
63C23×C3×D3C2311yescharacteristic
64C22×C32×C4C2312yes—
65C22×C32×C4C2311yescharacteristic
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3⋊Dic3C2311yescharacteristic
68C22×C3⋊Dic3C2312yes—
69C2×#634—22no—
70C2×#634—22no—
71C2×#634C2×C414yes—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2311yescharacteristic
75C22×C3×Dic3C2311yescharacteristic
76C22×C3×Dic3C2311yescharacteristic
77C2×C3×C4×D3—22no—
78C2×C3×C4×D3—22no—
79C2×C3×C4×D3C2×C414yes—
80C32×C4⋊C4—22no—
81C4×C3⋊Dic3—22no—
82C3×(C2×D3)⋊C4—42no—
83C3×C4⋊Dic3—22no—
84C3×C4⋊Dic3C2×C414yes—
85C3×C4×Dic3—42no—
86C3×C4×Dic3D414yes—
87#3724—24no—
88Dic3⋊Dic3—22no—
89Dic3⋊Dic3—22no—
90Dic3⋊Dic3—42no—
91Dic3⋊Dic3C2×C418yes—
92(C2×D3)⋊Dic3—22no—
93(C2×D3)⋊Dic3—22no—
94(C2×D3)⋊Dic3C2×C418yes—
95Dic32—24no—
96#2323—91noSylow
97C23×C3×C4—31no—
98C22×C4×D3C2×D311yescharacteristic
99C22×Dic6—31no—
100C22×Dic6—31no—
101C22×Dic6—61no—
102C2×C3×C4⋊C4—21no—
103C2×C3×C4⋊C4—31no—
104C2×C3×C4⋊C4—31no—
105C2×C3×C4⋊C4C2×D311yescharacteristic
106C2×C3×C4⋊C4C2×D311yescharacteristic
107C2×C3×C22⋊C4—32no—
108C2×C3×C42—31no—
109C2×C3×C42—32no—
110C2×#217—32no—
111C2×#217—31no—
112C2×#217—31no—
113C2×(C2×D3)⋊C4—32no—
114C2×(C2×D3)⋊C4—31no—
115C2×(C2×D3)⋊C4—31no—
116C2×(C2×D3)⋊C4C2×D312yes—
117#926—64no—
118C2×C4⋊Dic3—32no—
119C2×C4⋊Dic3—31no—
120C2×C4⋊Dic3—31no—
121C2×C4⋊Dic3—32no—
122C2×C4⋊Dic3C2×D311yescharacteristic
123C2×C4⋊Dic3C2×D311yescharacteristic
124#924—38no—
125C2×Dic3⋊C4—32no—
126C2×Dic3⋊C4—32no—
127C2×Dic3⋊C4—31no—
128C2×Dic3⋊C4—31no—
129C2×Dic3⋊C4—32no—
130C2×Dic3⋊C4—32no—
131C2×C4×Dic3—31no—
132C2×C4×Dic3—31no—
133C2×C4×Dic3—32no—
134C2×C4×Dic3—32no—
135C2×C4×Dic3—61no—
136C2×C4×Dic3C2×D312yes—
137C2×C4×Dic3C2×D311yescharacteristic
138#897—38no—
139#887—64no—
140#872—64no—
141C4×Dic6—64no—
142C3×#95—32no—
143C3×#95—32no—
144C3⋊#95—32no—
145C3⋊#95—32no—
146C3⋊#95—32no—
147C3⋊#95—32no—
148C3⋊#95—32no—
149C3⋊#95—32no—
150C3⋊#95—62no—
151C3⋊#95—62no—
152C3⋊#95C2×D312yes—
153C3⋊#95C2×D312yes—
154C23×C32C2411yescharacteristic
155C22×C3×D3—21no—
156C22×C3×D3—21no—
157C22×C3×D3—21no—
158C22×C3×D3—21no—
159C22×C3×D3—21no—
160C22×C3×D3—21no—
161C22×C3×D3C22×C412yes—
162C2×C32×C4—22no—
163C2×C32×C4—22no—
164C2×C32×C4—22no—
165C2×C32×C4C22×C412yes—
166C2×C32×C4C2×D412yes—
167C2×C32×C4#4112yes—
168C2×C3⋊Dic3—21no—
169C2×C3⋊Dic3—21no—
170C2×C3⋊Dic3—22no—
171C2×C3⋊Dic3—22no—
172C2×C3⋊Dic3—21no—
173C2×C3⋊Dic3—21no—
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3—21no—
176C2×C3⋊Dic3C22×C414yes—
177#634—28no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—21no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—21no—
182C2×C3×Dic3—21no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3—21no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3C22×C414yes—
190C2×C3×Dic3C22×C412yes—
191C2×C3×Dic3C2×D412yes—
192C2×C3×Dic3C2×D412yes—
193C3×C4×D3—28no—
194C2×C22⋊Q8—91no—
195C2×C4×Q8—91no—
196C2×#117—91no—
197#391—91no—
198#389—92no—
199#389—91no—
200#388—92no—
201#388—92no—
202#387—92no—
203#380—31no—
204C4×C4⋊C4—31no—
205C24×C3—31no—
206C23×D3C22×D311yescharacteristic
207C22×C3×C4—21no—
208C22×C3×C4—22no—
209C22×C3×C4—32no—
210C22×C3×C4—31no—
211C22×C3×C4—31no—
212C22×C3×C4—31no—
213C22×C3×C4—34no—
214C22×C3×C4—32no—
215C22×C3×C4—62no—
216C22×C3×C4—62no—
217C22×C3×C4C22×D312yes—
218C22×C3×C4C22×D312yes—
219C22×C3×C4C22×D311yescharacteristic
220C22×C3×C4C22×D311yescharacteristic
221C22×Dic3—32no—
222C22×Dic3—32no—
223C22×Dic3—31no—
224C22×Dic3—31no—
225C22×Dic3—31no—
226C22×Dic3—31no—
227C22×Dic3—61no—
228C22×Dic3—61no—
229C22×Dic3—62no—
230C22×Dic3C22×D312yes—
231C22×Dic3C22×D312yes—
232C22×Dic3C22×D311yescharacteristic
233C22×Dic3C22×D311yescharacteristic
234C22×Dic3C22×D311yescharacteristic
235C2×C4×D3—22no—
236C2×C4×D3—22no—
237C2×C4×D3C4×D314yes—
238C2×Dic6—34no—
239C2×Dic6—34no—
240C2×Dic6—64no—
241C2×Dic6—62no—
242C2×Dic6—62no—
243C2×Dic6—62no—
244C2×Dic6—62no—
245C2×Dic6—122no—
246C2×Dic6—122no—
247C3×C4⋊C4—22no—
248C3×C4⋊C4—22no—
249C3×C4⋊C4—34no—
250C3×C4⋊C4—42no—
251C3×C4⋊C4—62no—
252C3×C22⋊C4—122no—
253C3×C42—34no—
254C3×C42—122no—
255#217—38no—
256#217—62no—
257#217—62no—
258(C2×D3)⋊C4—38no—
259(C2×D3)⋊C4—42no—
260(C2×D3)⋊C4—62no—
261(C2×D3)⋊C4—62no—
262C4⋊Dic3—22no—
263C4⋊Dic3—38no—
264C4⋊Dic3—62no—
265C4⋊Dic3—62no—
266C4⋊Dic3—122no—
267C4⋊Dic3C4×D314yes—
268Dic3⋊C4—38no—
269Dic3⋊C4—64no—
270Dic3⋊C4—62no—
271Dic3⋊C4—62no—
272Dic3⋊C4—64no—
273Dic3⋊C4—122no—
274C4×Dic3—42no—
275C4×Dic3—64no—
276C4×Dic3—62no—
277C4×Dic3—62no—
278C4×Dic3—64no—
279C4×Dic3—122no—
280C4×Dic3D1214yes—
281C22×C32C23×C411yescharacteristic
282C22×C32C22×D411yescharacteristic
283C22×C32C2×#4111yescharacteristic
284C22×C32H(5,𝔽2)11yescharacteristic
285C22×C322−1+411yescharacteristic
286C22×C322−1+411yescharacteristic
287C22×C322−1+411yescharacteristic
288C2×C3×D3—22no—
289C2×C3×D3—22no—
290C2×C3×D3—22no—
291C2×C3×D3—41no—
292C2×C3×D3—41no—
293C2×C3×D3—41no—
294C2×C3×D3—41no—
295C32×C4—42no—
296C32×C4C4×D414yes—
297C3⋊Dic3—24no—
298C3⋊Dic3—41no—
299C3⋊Dic3—41no—
300C3×Dic3—22no—
301C3×Dic3—24no—
302C3×Dic3—22no—
303C3×Dic3—22no—
304C3×Dic3—42no—
305C22×Q8—91no—
306C23×C4—31no—
307C22⋊Q8—98no—
308C4×Q8—184no—
309#117—184no—
310C2×C4⋊C4—31no—
311C2×C4⋊C4—31no—
312C2×C4⋊C4—92no—
313C2×C4⋊C4—91no—
314C2×C4⋊C4—91no—
315C2×C4⋊C4—92no—
316C2×C4⋊C4—92no—
317C2×C4⋊C4D3211yescharacteristic
318C2×C22⋊C4—32no—
319C2×C22⋊C4—92no—
320C2×C22⋊C4—91no—
321C2×C22⋊C4—91no—
322C2×C42—31no—
323C2×C42—32no—
324C2×C42—92no—
325C2×C42—91no—
326#95—32no—
327#95—32no—
328#95—92no—
329#95—92no—
330#95—92no—
331C23×C3—21no—
332C23×C3—32no—
333C23×C3—61no—
334C23×C3—61no—
335C23×C3—61no—
336C23×C3—61no—
337C23×C3—61no—
338C23×C3—61no—
339C23×C3C23×D311yescharacteristic
340C23×C3C23×D311yescharacteristic
341C22×D3—21no—
342C22×D3—21no—
343C22×D3—21no—
344C22×D3—21no—
345C22×D3—21no—
346C22×D3—21no—
347C22×D3C2×C4×D312yes—
348C2×C3×C4—22no—
349C2×C3×C4—22no—
350C2×C3×C4—22no—
351C2×C3×C4—22no—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—32no—
358C2×C3×C4—34no—
359C2×C3×C4—32no—
360C2×C3×C4—32no—
361C2×C3×C4—42no—
362C2×C3×C4—42no—
363C2×C3×C4—42no—
364C2×C3×C4—61no—
365C2×C3×C4—61no—
366C2×C3×C4—62no—
367C2×C3×C4—61no—
368C2×C3×C4—62no—
369C2×C3×C4—61no—
370C2×C3×C4—61no—
371C2×C3×C4—61no—
372C2×C3×C4—68no—
373C2×C3×C4—62no—
374C2×C3×C4—62no—
375C2×C3×C4—62no—
376C2×C3×C4C2×C4×D312yes—
377C2×C3×C4C2×C4×D312yes—
378C2×C3×C4C2×D1212yes—
379C2×C3×C4#23512yes—
380C2×C3×C4D3×D412yes—
381C2×C3×C4#23712yes—
382C2×Dic3—21no—
383C2×Dic3—21no—
384C2×Dic3—21no—
385C2×Dic3—22no—
386C2×Dic3—21no—
387C2×Dic3—21no—
388C2×Dic3—21no—
389C2×Dic3—22no—
390C2×Dic3—22no—
391C2×Dic3—22no—
392C2×Dic3—22no—
393C2×Dic3—34no—
394C2×Dic3—34no—
395C2×Dic3—64no—
396C2×Dic3—62no—
397C2×Dic3—62no—
398C2×Dic3—62no—
399C2×Dic3—62no—
400C2×Dic3—62no—
401C2×Dic3—62no—
402C2×Dic3—61no—
403C2×Dic3—61no—
404C2×Dic3—61no—
405C2×Dic3—61no—
406C2×Dic3—61no—
407C2×Dic3—61no—
408C2×Dic3—61no—
409C2×Dic3—61no—
410C2×Dic3—61no—
411C2×Dic3—61no—
412C2×Dic3—61no—
413C2×Dic3—61no—
414C2×Dic3—121no—
415C2×Dic3—121no—
416C2×Dic3—122no—
417C2×Dic3—122no—
418C2×Dic3—121no—
419C2×Dic3—121no—
420C2×Dic3C2×C4×D314yes—
421C2×Dic3C2×C4×D312yes—
422C2×Dic3C2×D1212yes—
423C2×Dic3C2×D1212yes—
424C4×D3—28no—
425Dic6—68no—
426Dic6—68no—
427Dic6—128no—
428C2×C32C2×C4×D411yescharacteristic
429C2×C32#51911yescharacteristic
430C2×C32#52011yescharacteristic
431C2×C32#53611yescharacteristic
432C2×C32#53711yescharacteristic
433C2×C32#54111yescharacteristic
434C2×C32#54211yescharacteristic
435C3×D3—42no—
436C24—31no—
437C2×Q8—94no—
438C2×Q8—182no—
439C2×Q8—182no—
440C22×C4—31no—
441C22×C4—31no—
442C22×C4—32no—
443C22×C4—31no—
444C22×C4—34no—
445C22×C4—32no—
446C22×C4—62no—
447C22×C4—62no—
448C22×C4—92no—
449C22×C4—91no—
450C22×C4—91no—
451C22×C4C2×D3212yes—
452C22×C4C2×D3211yescharacteristic
453C4⋊C4—22no—
454C4⋊C4—34no—
455C4⋊C4—62no—
456C4⋊C4—98no—
457C4⋊C4—182no—
458C4⋊C4—182no—
459C4⋊C4—184no—
460C4⋊C4—362no—
461C22⋊C4—98no—
462C22⋊C4—122no—
463C22⋊C4—182no—
464C22⋊C4—182no—
465C42—34no—
466C42—122no—
467C42—184no—
468C42—182no—
469C22×C3—21no—
470C22×C3—21no—
471C22×C3—21no—
472C22×C3—21no—
473C22×C3—21no—
474C22×C3—21no—
475C22×C3—21no—
476C22×C3—62no—
477C22×C3—62no—
478C22×C3—62no—
479C22×C3—121no—
480C22×C3—121no—
481C22×C3—121no—
482C22×C3—121no—
483C22×C3C22×C4×D311yescharacteristic
484C22×C3C22×C4×D311yescharacteristic
485C22×C3C22×D1211yescharacteristic
486C22×C3C2×#23511yescharacteristic
487C22×C3C2×D3×D411yescharacteristic
488C22×C3C2×#23711yescharacteristic
489C22×C3#100411yescharacteristic
490C22×C3#100411yescharacteristic
491C22×C3#100711yescharacteristic
492C22×C3#100711yescharacteristic
493C22×C3#101011yescharacteristic
494C22×C3#101011yescharacteristic
495C22×C3#101011yescharacteristic
496C22×C3#101011yescharacteristic
497C2×D3—22no—
498C2×D3—22no—
499C2×D3—22no—
500C2×D3—41no—
501C2×D3—41no—
502C2×D3—41no—
503C2×D3—41no—
504C3×C4—24no—
505C3×C4—42no—
506C3×C4—42no—
507C3×C4—62no—
508C3×C4—64no—
509C3×C4—62no—
510C3×C4—62no—
511C3×C4—82no—
512C3×C4—122no—
513C3×C4C4×D1214yes—
514C3×C4#67⋊C414yes—
515Dic3—22no—
516Dic3—22no—
517Dic3—22no—
518Dic3—24no—
519Dic3—42no—
520Dic3—64no—
521Dic3—64no—
522Dic3—124no—
523Dic3—122no—
524Dic3—122no—
525Dic3—121no—
526Dic3—121no—
527Dic3—121no—
528Dic3—121no—
529C32#232311yescharacteristic, complemented, Sylow
530C23—32no—
531C23—61no—
532C23—61no—
533C23—61no—
534C23—61no—
535C23—61no—
536C23—61no—
537C23C22×D3211yescharacteristic
538Q8—188no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—34no—
543C2×C4—32no—
544C2×C4—32no—
545C2×C4—32no—
546C2×C4—61no—
547C2×C4—61no—
548C2×C4—61no—
549C2×C4—62no—
550C2×C4—62no—
551C2×C4—61no—
552C2×C4—61no—
553C2×C4—61no—
554C2×C4—68no—
555C2×C4—62no—
556C2×C4—62no—
557C2×C4—62no—
558C2×C4—94no—
559C2×C4—182no—
560C2×C4—182no—
561C2×C4—181no—
562C2×C4—181no—
563C2×C4—181no—
564C2×C4—181no—
565C2×C4—181no—
566C2×C4—181no—
567C2×C4C4×D3212yes—
568C2×C4D3×D1212yes—
569C2×C4#380412yes—
570C2×C3—21no—
571C2×C3—21no—
572C2×C3—21no—
573C2×C3—21no—
574C2×C3—21no—
575C2×C3—21no—
576C2×C3—21no—
577C2×C3—122no—
578C2×C3C2×C4×D1211yescharacteristic
579C2×C3C2×#67⋊C411yescharacteristic
580C2×C3#550411yescharacteristic
581C2×C3#551011yescharacteristic
582C2×C3#551611yescharacteristic
583C2×C3#552611yescharacteristic
584C2×C3#554611yescharacteristic
585C2×C3#556111yescharacteristic
586C2×C3#557211yescharacteristic
587C2×C3#558311yescharacteristic
588C2×C3#560311yescharacteristic
589C2×C3#560811yescharacteristic
590C2×C3#562511yescharacteristic
591C2×C3#562811yescharacteristic
592D3—42no—
593C22—62no—
594C22—62no—
595C22—62no—
596C22—121no—
597C22—121no—
598C22—121no—
599C22—121no—
600C22C2×C4×D3211yescharacteristic
601C22C2×D3×D1211yescharacteristic
602C22#6430911yescharacteristic
603C22#6431311yescharacteristic
604C22#6431511yescharacteristic
605C22#6431511yescharacteristic
606C22C2×#380411yescharacteristic
607C4—42no—
608C4—64no—
609C4—62no—
610C4—62no—
611C4—62no—
612C4—122no—
613C4—184no—
614C4—361no—
615C4—361no—
616C4#6388014yes—
617C3—21no—
618C3#7376211yescharacteristic, complemented
619C3#7387111yescharacteristic, complemented
620C2—122no—
621C2#1059435711yescharacteristic
622C2#1059435911yescharacteristic
623C2#1059438011yescharacteristic
624C2#1059452211yescharacteristic
625C2C2×#6388011yescharacteristic
626C2#1059512411yescharacteristic
627C2#1059534811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32#2323
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#63844C2semidirect
4. #10592672C2semidirect
6. C3×Dic3×C4⋊C4C2semidirect
7. #10591357C2semidirect
8. #10591327C2semidirect
11. #10591253C2semidirect
32. #63857C4semidirect
50. Dic3×C4⋊C4D3semidirect
529. C32#2323semidirect
618. C3#73762semidirect
619. C3#73871semidirect

Maximal subgroups

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

subgroupindex
C2×#638572
C2×#638552
C2×#638442
#105926722
C3×#49872
C3×Dic3×C4⋊C42
#105913572
#105913272
#105912842
#105912792
#105912532
#738713
#737623