Finite Group Databasebeta

← #11800914

Subgroups — #11800914

Order 1152.

1657 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#625C211yesmaximal, characteristic
2C2×#63879C212yesmaximal
3#10592348C211yesmaximal, characteristic, complemented
4C3×#4666C211yesmaximal, characteristic, complemented
5C3×D3×#95C211yesmaximal, characteristic, complemented
6#10591368C212yesmaximal, complemented
7D3×C3⋊#95C211yesmaximal, characteristic, complemented
8C4×(C2×D3)⋊Dic3C212yesmaximal, complemented
9#10591252C211yesmaximal, characteristic, complemented
10#10591243C212yesmaximal, complemented
11#10591237C211yesmaximal, characteristic, complemented
12#73436—31nomaximal
13#73322—31nomaximal
14C22×C3×C4×D3C2211yescharacteristic
15C22×C3×C4×D3C2212yes—
16C22×C3×C4×D3C2211yescharacteristic
17C22×#625C2211yescharacteristic
18C22×D3×Dic3C2212yes—
19C2×#3750C2212yes—
20C2×C4×C3⋊Dic3C2212yes—
21C2×C4×C3⋊Dic3C2211yescharacteristic
22C2×C3×(C2×D3)⋊C4C2212yes—
23C2×C3×C4×Dic3C2212yes—
24C2×#3724C2211yescharacteristic
25C2×(C2×D3)⋊Dic3C2212yes—
26C2×(C2×D3)⋊Dic3C2211yescharacteristic
27C2×(C2×D3)⋊Dic3C2211yescharacteristic
28C2×Dic32C2212yes—
29C2×Dic32C2212yes—
30C4×#625C418yescomplemented
31#63879C4116yescomplemented
32C32×#95C2211yescharacteristic
33#63658C2211yescharacteristic
34C3×C3⋊#95C2211yescharacteristic
35C3×C3⋊#95C2212yes—
36C3×C3⋊#95C2211yescharacteristic
37#63579C2212yes—
38#63579C2212yes—
39C2×C4×#67—31no—
40C2×C4×#67—31no—
41C2×C4×#67—32no—
42C2×#67⋊C4—32no—
43C3×C4×C22⋊C4—31no—
44C2×C3×#95—31no—
45C4×#217—32no—
46C4×#217—31no—
47C2×C3⋊#95—31no—
48Dic3×C22⋊C4—32no—
49C4×(C2×D3)⋊C4—32no—
50C4×Dic3⋊C4—32no—
51#4666—31no—
52#4666—32no—
53#4666D311yescharacteristic, complemented
54D3×#95—31no—
55D3×#95D311yescharacteristic, complemented
56#4649—32no—
57#4649—31no—
58#4649—31no—
59#4649—61no—
60#4648—31no—
61#4648—31no—
62C23×C3×D3C2311yescharacteristic
63C23×C3×D3C2311yescharacteristic
64C22×C32×C4C2312yes—
65C22×C32×C4C2311yescharacteristic
66C22×C3⋊Dic3C2312yes—
67C22×C3⋊Dic3C2311yescharacteristic
68C22×C3⋊Dic3C2311yescharacteristic
69C22×C3×Dic3C2311yescharacteristic
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2311yescharacteristic
73C2×C3×C4×D3—42no—
74C2×C3×C4×D3—42no—
75C2×C3×C4×D3—42no—
76C2×C3×C4×D3—42no—
77C2×C3×C4×D3C2×C418yescomplemented
78C2×C3×C4×D3C2×C414yescomplemented
79C2×C3×C4×D3C2×C414yescomplemented
80C2×#625C2×C418yes—
81C2×#625C2×C414yes—
82C2×D3×Dic3—42no—
83C2×D3×Dic3—42no—
84C2×D3×Dic3C2×C418yescomplemented
85#3750C2×C418yescomplemented
86C4×C3⋊Dic3—42no—
87C4×C3⋊Dic3C2×C414yescomplemented
88C3×(C2×D3)⋊C4C2×C418yescomplemented
89C3×C4×Dic3—42no—
90#3724C2×C414yescomplemented
91(C2×D3)⋊Dic3C2×C418yescomplemented
92(C2×D3)⋊Dic3C2×C414yescomplemented
93(C2×D3)⋊Dic3C2×C414yescomplemented
94Dic32—42no—
95Dic32C2×C418yescomplemented
96#2275—91noSylow
97C23×C3×C4—31no—
98C23×C3×C4—32no—
99C23×C3×C4—31no—
100C22×#67—31no—
101C22×#67—31no—
102C23×Dic3—32no—
103C22×C4×D3—32no—
104C22×C4×D3C2×D311yescharacteristic
105C22×C4×D3C2×D311yescharacteristic
106C22×C4×D3C2×D312yes—
107C2×C3×C22⋊C4—32no—
108C2×C3×C42—32no—
109C2×#217—31no—
110C2×#217—31no—
111C2×#217—32no—
112C4×#67—38no—
113C4×#67—38no—
114C4×#67—316no—
115C2×(C2×D3)⋊C4—31no—
116C2×(C2×D3)⋊C4—32no—
117C2×(C2×D3)⋊C4—31no—
118C2×(C2×D3)⋊C4C2×D312yes—
119C2×Dic3⋊C4—32no—
120C2×Dic3⋊C4—32no—
121C2×Dic3⋊C4—31no—
122C2×Dic3⋊C4—31no—
123C2×Dic3⋊C4—62no—
124C2×C4×Dic3—31no—
125C2×C4×Dic3—31no—
126C2×C4×Dic3—32no—
127C2×C4×Dic3—32no—
128C2×C4×Dic3—32no—
129C2×C4×Dic3—32no—
130C2×C4×Dic3—32no—
131C2×C4×Dic3—32no—
132C2×C4×Dic3—61no—
133C2×C4×Dic3—62no—
134C2×C4×Dic3C2×D312yes—
135#67⋊C4—316no—
136C3×#95—21no—
137C3×#95—31no—
138C3×#95—31no—
139C3×#95—32no—
140C3×#95C2×D311yescharacteristic
141C3×#95C2×D311yescharacteristic
142C3⋊#95—31no—
143C3⋊#95—31no—
144C3⋊#95—32no—
145C3⋊#95—32no—
146C3⋊#95—32no—
147C3⋊#95—32no—
148C3⋊#95—61no—
149C3⋊#95C2×D311yescharacteristic
150C3⋊#95C2×D311yescharacteristic
151C3⋊#95C2×D312yes—
152C23×C32C2411yescharacteristic
153C22×C3×D3—21no—
154C22×C3×D3—22no—
155C22×C3×D3—22no—
156C22×C3×D3—21no—
157C22×C3×D3—21no—
158C22×C3×D3—21no—
159C22×C3×D3C22×C412yes—
160C22×C3×D3C22×C414yes—
161C22×C3×D3C22×C412yes—
162C22×C3×D3C22×C414yes—
163C2×C32×C4—22no—
164C2×C32×C4—22no—
165C2×C32×C4—22no—
166C2×C32×C4C22×C414yes—
167C2×C32×C4C22×C412yes—
168C2×C3⋊Dic3—21no—
169C2×C3⋊Dic3—21no—
170C2×C3⋊Dic3—22no—
171C2×C3⋊Dic3—22no—
172C2×C3⋊Dic3C22×C412yes—
173C2×C3⋊Dic3C22×C414yes—
174C2×C3⋊Dic3C22×C414yes—
175C2×C3⋊Dic3C22×C412yes—
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×Dic3C22×C414yes—
183C2×C3×Dic3C22×C414yes—
184C2×C3×Dic3C22×C412yes—
185C2×C3×Dic3C22×C412yes—
186C3×C4×D3—48no—
187C3×C4×D3—44no—
188C3×C4×D3—44no—
189#625C42116yescomplemented
190D3×Dic3—48no—
191C2×C4×D4—92no—
192C2×C4×D4—91no—
193C4×C4⋊C4—92no—
194C4×C4⋊C4—91no—
195C4×C22⋊C4—31no—
196C4×C22⋊C4—92no—
197C4×C22⋊C4—91no—
198C4×C22⋊C4—92no—
199#376—91no—
200C2×#95—31no—
201C2×#95—91no—
202C24×C3—31no—
203C24×C3—31no—
204C23×D3C22×D311yescharacteristic
205C23×D3C22×D311yescharacteristic
206C22×C3×C4—21no—
207C22×C3×C4—22no—
208C22×C3×C4—32no—
209C22×C3×C4—31no—
210C22×C3×C4—32no—
211C22×C3×C4—31no—
212C22×C3×C4—38no—
213C22×C3×C4—34no—
214C22×C3×C4—34no—
215C22×C3×C4—122no—
216C22×C3×C4—122no—
217C22×C3×C4—122no—
218C22×C3×C4—122no—
219C22×C3×C4C22×D311yescharacteristic
220C22×C3×C4C22×D311yescharacteristic
221C22×C3×C4C22×D312yes—
222C22×C3×C4C22×D312yes—
223C2×#67—38no—
224C2×#67—34no—
225C2×#67—34no—
226C2×#67—38no—
227C22×Dic3—31no—
228C22×Dic3—31no—
229C22×Dic3—31no—
230C22×Dic3—31no—
231C22×Dic3—32no—
232C22×Dic3—32no—
233C22×Dic3—38no—
234C22×Dic3—61no—
235C22×Dic3—61no—
236C22×Dic3—62no—
237C22×Dic3—122no—
238C22×Dic3—122no—
239C22×Dic3C22×D312yes—
240C22×Dic3C22×D311yescharacteristic
241C22×Dic3C22×D312yes—
242C22×Dic3C22×D311yescharacteristic
243C2×C4×D3—38no—
244C2×C4×D3—42no—
245C2×C4×D3—42no—
246C2×C4×D3—42no—
247C2×C4×D3—42no—
248C2×C4×D3—122no—
249C2×C4×D3—122no—
250C2×C4×D3C4×D318yescomplemented
251C2×C4×D3C4×D314yescomplemented
252C2×C4×D3C4×D314yescomplemented
253C3×C22⋊C4—38no—
254C3×C42—122no—
255#217—34no—
256#217—34no—
257#217—38no—
258(C2×D3)⋊C4—38no—
259(C2×D3)⋊C4—34no—
260(C2×D3)⋊C4—34no—
261(C2×D3)⋊C4C4×D318yescomplemented
262Dic3⋊C4—38no—
263Dic3⋊C4—38no—
264Dic3⋊C4—34no—
265Dic3⋊C4—34no—
266Dic3⋊C4—68no—
267C4×Dic3—34no—
268C4×Dic3—34no—
269C4×Dic3—38no—
270C4×Dic3—38no—
271C4×Dic3—42no—
272C4×Dic3—64no—
273C4×Dic3—122no—
274C4×Dic3—122no—
275C4×Dic3—122no—
276C4×Dic3—122no—
277C4×Dic3—124no—
278C22×C32C23×C411yescharacteristic
279C22×C32C23×C412yes—
280C22×C32H(5,𝔽2)12yes—
281C22×C32H(5,𝔽2)11yescharacteristic
282C22×C322−1+411yescharacteristic
283C2×C3×D3—24no—
284C2×C3×D3—22no—
285C2×C3×D3—22no—
286C2×C3×D3—24no—
287C2×C3×D3—22no—
288C2×C3×D3—24no—
289C2×C3×D3—22no—
290C2×C3×D3—24no—
291C2×C3×D3C2×C4214yes—
292C2×C3×D3C2×C4214yes—
293C32×C4—22no—
294C32×C4—24no—
295C3⋊Dic3—22no—
296C3⋊Dic3—24no—
297C3⋊Dic3C2×C4214yes—
298C3×Dic3—24no—
299C3×Dic3—22no—
300C3×Dic3—22no—
301C3×Dic3—24no—
302C22×D4—91no—
303C23×C4—32no—
304C23×C4—31no—
305C23×C4—31no—
306C23×C4—92no—
307C4×D4—916no—
308C4×D4—98no—
309C2×C4⋊C4—91no—
310C2×C4⋊C4—92no—
311C2×C22⋊C4—32no—
312C2×C22⋊C4—91no—
313C2×C22⋊C4—92no—
314C2×C22⋊C4—91no—
315C2×C42—32no—
316C2×C42—92no—
317C2×C42—91no—
318C2×C42—92no—
319C2×C42—92no—
320#95—31no—
321#95—32no—
322#95—31no—
323#95—92no—
324#95—92no—
325#95—91no—
326#95D3211yescharacteristic
327C23×C3—21no—
328C23×C3—32no—
329C23×C3—32no—
330C23×C3—34no—
331C23×C3—34no—
332C23×C3—61no—
333C23×C3—62no—
334C23×C3—62no—
335C23×C3—61no—
336C23×C3—61no—
337C23×C3—61no—
338C23×C3C23×D311yescharacteristic
339C23×C3C23×D311yescharacteristic
340C22×D3—22no—
341C22×D3—21no—
342C22×D3—22no—
343C22×D3—21no—
344C22×D3—21no—
345C22×D3—21no—
346C22×D3C2×C4×D314yes—
347C22×D3C2×C4×D312yes—
348C22×D3C2×C4×D312yes—
349C22×D3C2×C4×D314yes—
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—24no—
358C2×C3×C4—34no—
359C2×C3×C4—34no—
360C2×C3×C4—32no—
361C2×C3×C4—32no—
362C2×C3×C4—42no—
363C2×C3×C4—42no—
364C2×C3×C4—42no—
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×C4—124no—
372C2×C3×C4—124no—
373C2×C3×C4—128no—
374C2×C3×C4C2×C4×D312yes—
375C2×C3×C4C2×C4×D312yes—
376C2×C3×C4C2×C4×D314yes—
377C2×C3×C4C2×C4×D314yes—
378#67—316no—
379#67—316no—
380C2×Dic3—22no—
381C2×Dic3—22no—
382C2×Dic3—22no—
383C2×Dic3—22no—
384C2×Dic3—22no—
385C2×Dic3—22no—
386C2×Dic3—34no—
387C2×Dic3—32no—
388C2×Dic3—32no—
389C2×Dic3—34no—
390C2×Dic3—32no—
391C2×Dic3—32no—
392C2×Dic3—34no—
393C2×Dic3—34no—
394C2×Dic3—62no—
395C2×Dic3—62no—
396C2×Dic3—64no—
397C2×Dic3—64no—
398C2×Dic3—62no—
399C2×Dic3—62no—
400C2×Dic3—61no—
401C2×Dic3—62no—
402C2×Dic3—62no—
403C2×Dic3—62no—
404C2×Dic3—61no—
405C2×Dic3—61no—
406C2×Dic3—62no—
407C2×Dic3—61no—
408C2×Dic3—122no—
409C2×Dic3—122no—
410C2×Dic3—128no—
411C2×Dic3C2×C4×D314yes—
412C2×Dic3C2×C4×D314yes—
413C2×Dic3C2×C4×D312yes—
414C2×Dic3C2×C4×D312yes—
415C4×D3—48no—
416C4×D3—44no—
417C4×D3—44no—
418C4×D3—128no—
419C2×C32C22×C4211yescharacteristic
420C2×C32#51811yescharacteristic
421C2×C32#51812yes—
422C2×C32#52011yescharacteristic
423C2×C32#52012yes—
424C3×D3—24no—
425C3×D3—24no—
426C24—31no—
427C24—31no—
428C2×D4—98no—
429C2×D4—94no—
430C22×C4—32no—
431C22×C4—31no—
432C22×C4—32no—
433C22×C4—31no—
434C22×C4—38no—
435C22×C4—34no—
436C22×C4—34no—
437C22×C4—98no—
438C22×C4—91no—
439C22×C4—91no—
440C22×C4—92no—
441C22×C4—122no—
442C22×C4—122no—
443C22×C4—122no—
444C22×C4—122no—
445C22×C4—362no—
446C22×C4—362no—
447C22×C4C2×D3211yescharacteristic
448C22×C4C2×D3212yes—
449C4⋊C4—94no—
450C4⋊C4—98no—
451C22⋊C4—38no—
452C22⋊C4—98no—
453C22⋊C4—94no—
454C22⋊C4—94no—
455C42—98no—
456C42—94no—
457C42—122no—
458C42—362no—
459C42—362no—
460C22×C3—22no—
461C22×C3—21no—
462C22×C3—22no—
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—34no—
466C22×C3—34no—
467C22×C3—64no—
468C22×C3—62no—
469C22×C3—62no—
470C22×C3—64no—
471C22×C3—62no—
472C22×C3—62no—
473C22×C3—64no—
474C22×C3—64no—
475C22×C3C22×C4×D312yes—
476C22×C3C22×C4×D311yescharacteristic
477C22×C3C22×C4×D311yescharacteristic
478C22×C3C22×C4×D312yes—
479C22×C3#100412yes—
480C22×C3#100412yes—
481C22×C3#100411yescharacteristic
482C22×C3#100711yescharacteristic
483C22×C3#100911yescharacteristic
484C22×C3#101011yescharacteristic
485C2×D3—22no—
486C2×D3—22no—
487C2×D3—24no—
488C2×D3—24no—
489C2×D3—22no—
490C2×D3—22no—
491C2×D3—24no—
492C2×D3—24no—
493C2×D3C42×D314yes—
494C2×D3C42×D314yes—
495C3×C4—22no—
496C3×C4—22no—
497C3×C4—24no—
498C3×C4—24no—
499C3×C4—42no—
500C3×C4—44no—
501C3×C4—62no—
502C3×C4—62no—
503C3×C4—64no—
504C3×C4—64no—
505Dic3—24no—
506Dic3—22no—
507Dic3—22no—
508Dic3—24no—
509Dic3—34no—
510Dic3—34no—
511Dic3—64no—
512Dic3—64no—
513Dic3—64no—
514Dic3—62no—
515Dic3—62no—
516Dic3—64no—
517Dic3—124no—
518C32#227511yescharacteristic, complemented, Sylow
519C23—34no—
520C23—34no—
521C23—32no—
522C23—32no—
523C23—62no—
524C23—62no—
525C23—61no—
526C23—61no—
527C23—61no—
528C23—61no—
529C23C22×D3211yescharacteristic
530D4—916no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—34no—
535C2×C4—34no—
536C2×C4—32no—
537C2×C4—32no—
538C2×C4—62no—
539C2×C4—62no—
540C2×C4—62no—
541C2×C4—62no—
542C2×C4—62no—
543C2×C4—62no—
544C2×C4—94no—
545C2×C4—92no—
546C2×C4—92no—
547C2×C4—94no—
548C2×C4—124no—
549C2×C4—124no—
550C2×C4—128no—
551C2×C4—182no—
552C2×C4—181no—
553C2×C4—182no—
554C2×C4—181no—
555C2×C4—368no—
556C2×C4C4×D3212yes—
557C2×C4C4×D3214yes—
558C2×C3—22no—
559C2×C3—21no—
560C2×C3—21no—
561C2×C3—22no—
562C2×C3—21no—
563C2×C3—64no—
564C2×C3—64no—
565C2×C3C2×C42×D311yescharacteristic
566C2×C3C2×C42×D311yescharacteristic
567C2×C3#548611yescharacteristic
568C2×C3#548611yescharacteristic
569C2×C3#548612yes—
570C2×C3#550412yes—
571C2×C3#550411yescharacteristic
572C2×C3#552311yescharacteristic
573C2×C3#554512yes—
574C2×C3#554612yes—
575D3—24no—
576D3—24no—
577C22—34no—
578C22—34no—
579C22—64no—
580C22—64no—
581C22—62no—
582C22—62no—
583C22—64no—
584C22—64no—
585C22—62no—
586C22—62no—
587C22C2×C4×D3212yes—
588C22C2×C4×D3211yescharacteristic
589C22#6431312yes—
590C22#6431411yescharacteristic
591C22#6431511yescharacteristic
592C4—22no—
593C4—24no—
594C4—64no—
595C4—62no—
596C4—62no—
597C4—64no—
598C4—94no—
599C4—184no—
600C4—182no—
601C3—21no—
602C3#7332211yescharacteristic, complemented
603C3#7343611yescharacteristic, complemented
604C2—64no—
605C2—64no—
606C2C42×D3211yescharacteristic
607C2#1059418111yescharacteristic
608C2#1059425412yes—
609C2#1059435912yes—
610C2#1059451011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC2×C32C22×C42
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC22×#625C22
hypercenter#95D32
hypocenterC32#2275
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
3. #10592348C2semidirect
4. C3×#4666C2semidirect
5. C3×D3×#95C2semidirect
6. #10591368C2semidirect
7. D3×C3⋊#95C2semidirect
8. C4×(C2×D3)⋊Dic3C2semidirect
9. #10591252C2semidirect
10. #10591243C2semidirect
11. #10591237C2semidirect
30. C4×#625C4semidirect
31. #63879C4semidirect
53. #4666D3semidirect
55. D3×#95D3semidirect
77. C2×C3×C4×D3C2×C4semidirect
78. C2×C3×C4×D3C2×C4semidirect
79. C2×C3×C4×D3C2×C4semidirect
84. C2×D3×Dic3C2×C4semidirect
85. #3750C2×C4semidirect
87. C4×C3⋊Dic3C2×C4semidirect
88. C3×(C2×D3)⋊C4C2×C4semidirect
90. #3724C2×C4semidirect
91. (C2×D3)⋊Dic3C2×C4semidirect
92. (C2×D3)⋊Dic3C2×C4semidirect
93. (C2×D3)⋊Dic3C2×C4semidirect
95. Dic32C2×C4semidirect
189. #625C42semidirect
250. C2×C4×D3C4×D3semidirect
251. C2×C4×D3C4×D3semidirect
252. C2×C4×D3C4×D3semidirect
261. (C2×D3)⋊C4C4×D3semidirect
518. C32#2275semidirect
602. C3#73322semidirect
603. C3#73436semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6252
C2×#638792
#105923482
C3×#46662
C3×D3×#952
#105913682
D3×C3⋊#952
C4×(C2×D3)⋊Dic32
#105912522
#105912432
#105912372
#734363
#733223