Finite Group Databasebeta

← #11805452

Subgroups — #11805452

Order 1152.

1765 conjugacy classes of subgroups.

The subgroup lattice has 651 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64090C211yesmaximal, characteristic
2C22×#3724C211yesmaximal, characteristic, complemented
3C2×#63952C212yesmaximal
4C2×#63900C211yesmaximal, characteristic, complemented
5C3×#4950C212yesmaximal, complemented
6#10591720C211yesmaximal, characteristic, complemented
7#10591378C212yesmaximal, complemented
8#10591359C211yesmaximal, characteristic, complemented
9#10591355C211yesmaximal, characteristic, complemented
10#10591264C212yesmaximal, complemented
11#10591257C211yesmaximal, characteristic, complemented
12#74393—32nomaximal
13C22×#638C2211yescharacteristic
14C23×C3⋊Dic3C2211yescharacteristic
15C22×C4×C3⋊D3C2211yescharacteristic
16C23×C3×Dic3C2212yes—
17C22×#624C2212yes—
18C2×C32×C22⋊C4C2211yescharacteristic
19C2×#3752C2211yescharacteristic
20C2×#3750C2211yescharacteristic
21C2×C4×C3⋊Dic3C2211yescharacteristic
22#64090C418yescomplemented
23C2×C3×#217C2212yes—
24C2×C3×C4⋊Dic3C2212yes—
25C2×C3×C4⋊Dic3C2212yes—
26C2×#3724—24no—
27C2×#3724C2211yescharacteristic
28C2×#3724C2212yes—
29C2×#3724C2212yes—
30C2×#3724C2211yescharacteristic
31C2×#3724C2211yescharacteristic
32C2×#3724C2211yescharacteristic
33C2×#3722C2212yes—
34C2×Dic32C2212yes—
35#63952—28no—
36#63900—24no—
37C3×C3⋊#95C2212yes—
38C3×C3⋊#95C2212yes—
39#63579C2212yes—
40C2×C4×#67—32no—
41C22×Dic3⋊C4—32no—
42C2×D3×C4⋊C4—32no—
43C2×#67⋊C4—32no—
44C2×#67⋊C4—32no—
45C2×#67⋊C4—61no—
46C3×#385—32no—
47#4989—32no—
48#4976—32no—
49#4975—32no—
50#4950D312yescomplemented
51#4942—32no—
52#4668—32no—
53#4667—32no—
54#4649—32no—
55#4647—32no—
56C24×C32C2311yescharacteristic
57C23×C3⋊D3C2311yescharacteristic
58C22×C32×C4C2311yescharacteristic
59C22×C32×C4C2311yescharacteristic
60C2×#638C2×C414yes—
61C2×#638D414yes—
62C2×#638Q814yes—
63C22×C3⋊Dic3—22no—
64C22×C3⋊Dic3—22no—
65C22×C3⋊Dic3C2×C414yescomplemented
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3⋊Dic3C2311yescharacteristic
68C22×C3⋊Dic3C2311yescharacteristic
69C2×C4×C3⋊D3—22no—
70C2×C4×C3⋊D3—22no—
71C2×C4×C3⋊D3C2×C414yescomplemented
72C22×C3×Dic3—24no—
73C22×C3×Dic3—24no—
74C22×C3×Dic3—42no—
75C22×C3×Dic3C2312yes—
76C22×C3×Dic3C2312yes—
77C22×C3×Dic3C2312yes—
78C22×C3×Dic3C2312yes—
79C2×#624—24no—
80C2×#624—24no—
81C2×#624—42no—
82C32×C22⋊C4C2×C414yescomplemented
83#3752C2×C414yescomplemented
84#3750C2×C414yescomplemented
85C4×C3⋊Dic3C2×C414yescomplemented
86C3×#217—24no—
87C3×C4⋊Dic3—24no—
88C3×C4⋊Dic3—42no—
89#3724—22no—
90#3724—24no—
91#3724—22no—
92#3724—22no—
93#3724—24no—
94#3724D414yescomplemented
95#3722—24no—
96Dic32—24no—
97D4×C4⋊C4—91noSylow
98C23×C3×C4—32no—
99C22×#67—32no—
100C22×#67—61no—
101C23×Dic3—32no—
102C23×Dic3—61no—
103C23×Dic3C2×D312yes—
104C22×C4×D3—32no—
105C22×C4×D3—32no—
106C22×C4×D3—32no—
107C22×C4×D3—61no—
108C2×C3×C4⋊C4—32no—
109C2×C3×C4⋊C4—32no—
110C2×C3×C22⋊C4—21no—
111C2×C3×C22⋊C4—32no—
112C2×C3×C22⋊C4C2×D312yes—
113C2×#217C2×D312yes—
114C4×#67—68no—
115C2×(C2×D3)⋊C4—32no—
116C2×(C2×D3)⋊C4—32no—
117C2×(C2×D3)⋊C4—32no—
118C2×(C2×D3)⋊C4—61no—
119C2×C4⋊Dic3C2×D312yes—
120C2×C4⋊Dic3C2×D312yes—
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—32no—
128C2×Dic3⋊C4—32no—
129C2×Dic3⋊C4—32no—
130C2×Dic3⋊C4—61no—
131C2×Dic3⋊C4—68no—
132C2×C4×Dic3—32no—
133C2×C4×Dic3—32no—
134C2×C4×Dic3—32no—
135C2×C4×Dic3—61no—
136D3×C4⋊C4—68no—
137#67⋊C4—316no—
138#67⋊C4—68no—
139#67⋊C4—68no—
140C3×#95—32no—
141C3×#95—32no—
142C3⋊#95—32no—
143C3⋊#95—32no—
144C3⋊#95C2×D312yes—
145C3⋊#95C2×D312yes—
146C23×C32—21no—
147C23×C32—21no—
148C23×C32—21no—
149C23×C32—21no—
150C23×C32C22×C412yes—
151C23×C32C2×D412yes—
152C23×C32C2×Q812yes—
153C23×C32C2411yescharacteristic
154C22×C3⋊D3—21no—
155C22×C3⋊D3—21no—
156C22×C3⋊D3—21no—
157C22×C3⋊D3—21no—
158C22×C3⋊D3C22×C412yes—
159C22×C3⋊D3C2×D412yes—
160C22×C3⋊D3C2×Q812yes—
161C2×C32×C4—21no—
162C2×C32×C4—21no—
163C2×C32×C4—21no—
164C2×C32×C4—21no—
165C2×C32×C4C22×C412yes—
166C2×C32×C4C22×C412yes—
167#638C4⋊C4116yescomplemented
168C2×C3⋊Dic3—21no—
169C2×C3⋊Dic3—21no—
170C2×C3⋊Dic3—28no—
171C2×C3⋊Dic3C22×C412yes—
172C2×C3⋊Dic3C22×C412yes—
173C2×C3⋊Dic3C22×C412yes—
174C2×C3⋊Dic3C2×D412yes—
175C2×C3⋊Dic3C2×D412yes—
176C2×C3⋊Dic3C2×Q812yes—
177C2×C3⋊Dic3#4112yes—
178C4×C3⋊D3—28no—
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×Dic3—22no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—48no—
191C2×C3×Dic3C2×D414yes—
192#624—48no—
193C2×C4×D4—92no—
194C2×C4×D4—91no—
195C22×C4⋊C4—91no—
196C22×C4⋊C4—91no—
197#389—92no—
198#385—32no—
199#385—92no—
200#384—91no—
201#380—91no—
202#380—91no—
203C4×C4⋊C4—91no—
204C24×C3—21no—
205C24×C3C22×D312yes—
206C23×D3—32no—
207C23×D3—61no—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—32no—
211C22×C3×C4—32no—
212C22×C3×C4—32no—
213C22×C3×C4—32no—
214C22×C3×C4—64no—
215C22×C3×C4—64no—
216C22×C3×C4—122no—
217C22×C3×C4C22×D312yes—
218C22×C3×C4C22×D312yes—
219C2×#67—38no—
220C2×#67—38no—
221C2×#67—38no—
222C2×#67—64no—
223C2×#67—64no—
224C2×#67—64no—
225C22×Dic3—24no—
226C22×Dic3—24no—
227C22×Dic3—32no—
228C22×Dic3—32no—
229C22×Dic3—38no—
230C22×Dic3—32no—
231C22×Dic3—42no—
232C22×Dic3—61no—
233C22×Dic3—61no—
234C22×Dic3—64no—
235C22×Dic3—61no—
236C22×Dic3—64no—
237C22×Dic3—64no—
238C22×Dic3—122no—
239C22×Dic3—122no—
240C22×Dic3C22×D312yes—
241C22×Dic3C22×D312yes—
242C22×Dic3C22×D312yes—
243C22×Dic3C22×D312yes—
244C2×C4×D3—38no—
245C2×C4×D3—64no—
246C2×C4×D3—64no—
247C2×C4×D3—64no—
248C2×C4×D3—64no—
249C2×C4×D3—64no—
250C2×C4×D3—64no—
251C2×C4×D3—64no—
252C2×C4×D3—122no—
253C2×C4×D3—122no—
254C2×C4×D3—122no—
255C2×C4×D3—122no—
256C3×C4⋊C4—64no—
257C3×C4⋊C4—122no—
258C3×C22⋊C4—24no—
259C3×C22⋊C4—64no—
260C3×C22⋊C4C4×D318yescomplemented
261#217—24no—
262(C2×D3)⋊C4—38no—
263(C2×D3)⋊C4—64no—
264(C2×D3)⋊C4—64no—
265(C2×D3)⋊C4—64no—
266C4⋊Dic3—24no—
267C4⋊Dic3—42no—
268Dic3⋊C4—38no—
269Dic3⋊C4—38no—
270Dic3⋊C4—64no—
271Dic3⋊C4—64no—
272Dic3⋊C4—64no—
273Dic3⋊C4—64no—
274Dic3⋊C4—64no—
275Dic3⋊C4—64no—
276Dic3⋊C4—64no—
277Dic3⋊C4—64no—
278C4×Dic3—38no—
279C4×Dic3—64no—
280C4×Dic3—64no—
281C4×Dic3—64no—
282C22×C32—22no—
283C22×C32—22no—
284C22×C32—22no—
285C22×C32—22no—
286C22×C32—22no—
287C22×C32—22no—
288C22×C32C2×C4⋊C414yescomplemented
289C22×C32C23×C411yescharacteristic
290C22×C32C22×D411yescharacteristic
291C22×C32C22×D411yescharacteristic
292C22×C32C22×Q811yescharacteristic
293C22×C32C2×#4111yescharacteristic
294C22×C32H(5,𝔽2)11yescharacteristic
295C22×C322−1+411yescharacteristic
296C2×C3⋊D3—22no—
297C2×C3⋊D3—22no—
298C2×C3⋊D3—22no—
299C2×C3⋊D3—22no—
300C2×C3⋊D3—22no—
301C2×C3⋊D3—22no—
302C2×C3⋊D3C2×C4⋊C414yescomplemented
303C32×C4—22no—
304C32×C4—22no—
305C3⋊Dic3—22no—
306C3⋊Dic3C2×C4⋊C414yescomplemented
307C3⋊Dic3C4×D414yescomplemented
308C3×Dic3—24no—
309C3×Dic3—42no—
310C3×Dic3—42no—
311C3×Dic3—42no—
312C22×D4—91no—
313C23×C4—32no—
314C23×C4—92no—
315C23×C4—91no—
316C23×C4—91no—
317C4×D4—98no—
318C4×D4—188no—
319C2×C4⋊C4—32no—
320C2×C4⋊C4—32no—
321C2×C4⋊C4—91no—
322C2×C4⋊C4—91no—
323C2×C4⋊C4—91no—
324C2×C4⋊C4—91no—
325C2×C4⋊C4—92no—
326C2×C4⋊C4—92no—
327C2×C4⋊C4—91no—
328C2×C4⋊C4—184no—
329C2×C4⋊C4—184no—
330C2×C22⋊C4—32no—
331C2×C22⋊C4—91no—
332C2×C22⋊C4—92no—
333C2×C22⋊C4D3211yescharacteristic
334C2×C42—91no—
335C2×C42—92no—
336#95—32no—
337#95—32no—
338#95—92no—
339C23×C3—22no—
340C23×C3—22no—
341C23×C3—22no—
342C23×C3—22no—
343C23×C3—21no—
344C23×C3—22no—
345C23×C3—22no—
346C23×C3—22no—
347C23×C3—41no—
348C23×C3—41no—
349C23×C3—41no—
350C23×C3—41no—
351C23×C3C2×C4×D314yes—
352C23×C3D3×D414yes—
353C23×C3D3×Q814yes—
354C23×C3C23×D312yes—
355C22×D3—34no—
356C22×D3—34no—
357C22×D3—34no—
358C22×D3—62no—
359C22×D3—62no—
360C22×D3—62no—
361C22×D3—62no—
362C22×D3—62no—
363C22×D3—62no—
364C22×D3—62no—
365C22×D3—121no—
366C22×D3—121no—
367C22×D3—121no—
368C22×D3—121no—
369C2×C3×C4—22no—
370C2×C3×C4—22no—
371C2×C3×C4—22no—
372C2×C3×C4—22no—
373C2×C3×C4—22no—
374C2×C3×C4—22no—
375C2×C3×C4—34no—
376C2×C3×C4—41no—
377C2×C3×C4—41no—
378C2×C3×C4—41no—
379C2×C3×C4—41no—
380C2×C3×C4—62no—
381C2×C3×C4—62no—
382C2×C3×C4—62no—
383C2×C3×C4—62no—
384C2×C3×C4—62no—
385C2×C3×C4—62no—
386C2×C3×C4—62no—
387C2×C3×C4—62no—
388C2×C3×C4—62no—
389C2×C3×C4—62no—
390C2×C3×C4—62no—
391C2×C3×C4—128no—
392C2×C3×C4C2×C4×D314yes—
393C2×C3×C4C2×C4×D314yes—
394#67—332no—
395#67—616no—
396C2×Dic3—22no—
397C2×Dic3—22no—
398C2×Dic3—22no—
399C2×Dic3—22no—
400C2×Dic3—22no—
401C2×Dic3—22no—
402C2×Dic3—22no—
403C2×Dic3—22no—
404C2×Dic3—22no—
405C2×Dic3—22no—
406C2×Dic3—22no—
407C2×Dic3—34no—
408C2×Dic3—34no—
409C2×Dic3—34no—
410C2×Dic3—34no—
411C2×Dic3—34no—
412C2×Dic3—34no—
413C2×Dic3—34no—
414C2×Dic3—48no—
415C2×Dic3—62no—
416C2×Dic3—62no—
417C2×Dic3—62no—
418C2×Dic3—62no—
419C2×Dic3—62no—
420C2×Dic3—62no—
421C2×Dic3—62no—
422C2×Dic3—616no—
423C2×Dic3—62no—
424C2×Dic3—62no—
425C2×Dic3—128no—
426C2×Dic3—121no—
427C2×Dic3—121no—
428C2×Dic3D3×D414yes—
429C4×D3—616no—
430C4×D3—128no—
431C4×D3—128no—
432C4×D3—128no—
433C2×C32—24no—
434C2×C32C22×C4⋊C411yescharacteristic
435C2×C32C2×C4×D411yescharacteristic
436C2×C32#52011yescharacteristic
437C2×C32D4211yescharacteristic
438C2×C32#54711yescharacteristic
439C2×C32D4×Q811yescharacteristic
440C2×C32#55411yescharacteristic
441C3⋊D3—24no—
442C24—91no—
443C24C2×D3211yescharacteristic
444C2×D4—94no—
445C2×D4—94no—
446C2×D4—94no—
447C22×C4—32no—
448C22×C4—32no—
449C22×C4—32no—
450C22×C4—32no—
451C22×C4—64no—
452C22×C4—64no—
453C22×C4—91no—
454C22×C4—91no—
455C22×C4—91no—
456C22×C4—94no—
457C22×C4—94no—
458C22×C4—122no—
459C22×C4—182no—
460C22×C4—182no—
461C22×C4—184no—
462C22×C4—184no—
463C22×C4—182no—
464C22×C4—182no—
465C22×C4—362no—
466C22×C4C2×D3211yescharacteristic
467C22×C4C2×D3211yescharacteristic
468C4⋊C4—64no—
469C4⋊C4—94no—
470C4⋊C4—94no—
471C4⋊C4—122no—
472C4⋊C4—184no—
473C4⋊C4—182no—
474C4⋊C4—182no—
475C4⋊C4—184no—
476C4⋊C4—182no—
477C22⋊C4—64no—
478C22⋊C4—94no—
479C22⋊C4—184no—
480C22⋊C4#62414yescomplemented
481C42—94no—
482C42—184no—
483C22×C3—24no—
484C22×C3—24no—
485C22×C3—24no—
486C22×C3—24no—
487C22×C3—24no—
488C22×C3—24no—
489C22×C3—21no—
490C22×C3—21no—
491C22×C3—21no—
492C22×C3—21no—
493C22×C3—21no—
494C22×C3—21no—
495C22×C3—21no—
496C22×C3—24no—
497C22×C3—42no—
498C22×C3—42no—
499C22×C3—42no—
500C22×C3—42no—
501C22×C3—42no—
502C22×C3—42no—
503C22×C3D3×C4⋊C418yescomplemented
504C22×C3C22×C4×D312yes—
505C22×C3C2×D3×D412yes—
506C22×C3C2×D3×D412yes—
507C22×C3#100412yes—
508C22×C3C2×D3×Q812yes—
509C22×C3D3×#4112yes—
510C22×C3#101012yes—
511C2×D3—38no—
512C2×D3—64no—
513C2×D3—64no—
514C2×D3—64no—
515C2×D3—64no—
516C2×D3—64no—
517C2×D3—64no—
518C2×D3—64no—
519C2×D3—122no—
520C2×D3—122no—
521C2×D3—122no—
522C2×D3—122no—
523C2×D3—122no—
524C2×D3—122no—
525C3×C4—24no—
526C3×C4—24no—
527C3×C4—42no—
528C3×C4—42no—
529C3×C4—64no—
530C3×C4—122no—
531C3×C4—122no—
532C3×C4—122no—
533Dic3—24no—
534Dic3—38no—
535Dic3—38no—
536Dic3—42no—
537Dic3—42no—
538Dic3—42no—
539Dic3—64no—
540Dic3—64no—
541Dic3—64no—
542Dic3—122no—
543C32D4×C4⋊C411yescharacteristic, complemented, Sylow
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—92no—
549C23—92no—
550C23—92no—
551C23—181no—
552C23—181no—
553C23—181no—
554C23—181no—
555C23#379712yes—
556C23#380212yes—
557C23C2×#62412yes—
558C23C22×D3211yescharacteristic
559D4—916no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—34no—
565C2×C4—62no—
566C2×C4—62no—
567C2×C4—62no—
568C2×C4—62no—
569C2×C4—62no—
570C2×C4—62no—
571C2×C4—62no—
572C2×C4—62no—
573C2×C4—62no—
574C2×C4—62no—
575C2×C4—62no—
576C2×C4—92no—
577C2×C4—92no—
578C2×C4—92no—
579C2×C4—92no—
580C2×C4—92no—
581C2×C4—92no—
582C2×C4—92no—
583C2×C4—128no—
584C2×C4—188no—
585C2×C4—188no—
586C2×C4—181no—
587C2×C4—181no—
588C2×C4—368no—
589C2×C4C2×#62412yes—
590C2×C4C2×#62412yes—
591C2×C3—28no—
592C2×C3—21no—
593C2×C3—21no—
594C2×C3—21no—
595C2×C3—21no—
596C2×C3—21no—
597C2×C3—21no—
598C2×C3—21no—
599C2×C3—44no—
600C2×C3C2×D3×C4⋊C412yes—
601C2×C3C4×D3×D412yes—
602C2×C3#554612yes—
603C2×C3#559012yes—
604C2×C3#563212yes—
605C2×C3#563612yes—
606C2×C3#565512yes—
607D3—68no—
608D3—124no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—22no—
615C22—94no—
616C22—182no—
617C22—182no—
618C22—182no—
619C22—182no—
620C22—182no—
621C22—182no—
622C22#6390014yescomplemented
623C22C2×#379711yescharacteristic
624C22C2×#380211yescharacteristic
625C22#6430911yescharacteristic
626C22D32×D411yescharacteristic
627C22#6431211yescharacteristic
628C22#6431311yescharacteristic
629C22C22×#62411yescharacteristic
630C4—22no—
631C4—22no—
632C4—64no—
633C4—94no—
634C4—94no—
635C4—122no—
636C4—122no—
637C4—122no—
638C4—182no—
639C3—21no—
640C3#7439312yescomplemented
641C2—24no—
642C2—184no—
643C2#1059407211yescharacteristic
644C2#1059408311yescharacteristic
645C2#1059416811yescharacteristic
646C2#1059427111yescharacteristic
647C2C2×#6390011yescharacteristic
648C2D4×#62411yescharacteristic
649C2#1059521911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC22×#638C22
hypercenterC2×C22⋊C4D32
hypocenterC32D4×C4⋊C4
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×#3724C2semidirect
4. C2×#63900C2semidirect
5. C3×#4950C2semidirect
6. #10591720C2semidirect
7. #10591378C2semidirect
8. #10591359C2semidirect
9. #10591355C2semidirect
10. #10591264C2semidirect
11. #10591257C2semidirect
22. #64090C4semidirect
50. #4950D3semidirect
65. C22×C3⋊Dic3C2×C4semidirect
71. C2×C4×C3⋊D3C2×C4semidirect
82. C32×C22⋊C4C2×C4semidirect
83. #3752C2×C4semidirect
84. #3750C2×C4semidirect
85. C4×C3⋊Dic3C2×C4semidirect
94. #3724D4semidirect
167. #638C4⋊C4semidirect
260. C3×C22⋊C4C4×D3semidirect
288. C22×C32C2×C4⋊C4semidirect
302. C2×C3⋊D3C2×C4⋊C4semidirect
306. C3⋊Dic3C2×C4⋊C4semidirect
307. C3⋊Dic3C4×D4semidirect
480. C22⋊C4#624semidirect
503. C22×C3D3×C4⋊C4semidirect
543. C32D4×C4⋊C4semidirect
622. C22#63900semidirect
640. C3#74393semidirect

Maximal subgroups

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

subgroupindex
C2×#640902
C22×#37242
C2×#639522
C2×#639002
C3×#49502
#105917202
#105913782
#105913592
#105913552
#105912642
#105912572
#743933