Finite Group Databasebeta

← #11805507

Subgroups — #11805507

Order 1152.

1485 conjugacy classes of subgroups.

The subgroup lattice has 615 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#625C211yesmaximal, characteristic
2C2×#63879C212yesmaximal
3#10592349C211yesmaximal, characteristic, complemented
4C3×#4667C211yesmaximal, characteristic, complemented
5C3×D3×#95C211yesmaximal, characteristic, complemented
6#10591373C212yesmaximal, complemented
7D3×C3⋊#95C211yesmaximal, characteristic, complemented
8#10591295C211yesmaximal, characteristic, complemented
9#10591277C212yesmaximal, complemented
10#10591257C211yesmaximal, characteristic, complemented
11#10591256C212yesmaximal, complemented
12#74011—31nomaximal
13#73369—31nomaximal
14C22×C3×C4×D3C2212yes—
15C22×C3×C4×D3C2211yescharacteristic
16C22×C3×C4×D3C2211yescharacteristic
17C22×#625C2211yescharacteristic
18C22×D3×Dic3C2212yes—
19C2×#3750C2212yes—
20C2×C4×C3⋊Dic3C2211yescharacteristic
21C2×C3×(C2×D3)⋊C4C2212yes—
22C2×C3×Dic3⋊C4C2212yes—
23C2×#3724C2212yes—
24C2×#3724C2211yescharacteristic
25C2×Dic3⋊Dic3C2212yes—
26C2×(C2×D3)⋊Dic3C2212yes—
27C2×(C2×D3)⋊Dic3C2211yescharacteristic
28C2×(C2×D3)⋊Dic3C2211yescharacteristic
29C2×Dic32C2212yes—
30C4×#625C418yescomplemented
31#63879—28no—
32C32×#95C2211yescharacteristic
33#63658C2212yes—
34#63658C2211yescharacteristic
35C3×C3⋊#95C2212yes—
36C3×C3⋊#95C2211yescharacteristic
37C3×C3⋊#95C2211yescharacteristic
38#63579C2212yes—
39C2×C4×#67—31no—
40C2×C4×#67—31no—
41C2×C4×#67—32no—
42C2×#67⋊C4—32no—
43C3×#380—31no—
44C2×C3×#95—31no—
45#5212—31no—
46#5210—32no—
47C2×C3⋊#95—31no—
48#4989—32no—
49#4976—32no—
50#4946—32no—
51#4668—32no—
52#4667—31no—
53#4667D311yescharacteristic, complemented
54D3×#95—31no—
55D3×#95D311yescharacteristic, complemented
56#4650—31no—
57#4650—31no—
58#4650—61no—
59#4649—31no—
60#4649—31no—
61#4647—32no—
62C23×C3×D3C2311yescharacteristic
63C23×C3×D3C2311yescharacteristic
64C22×C32×C4C2312yes—
65C22×C32×C4C2311yescharacteristic
66C22×C3⋊Dic3C2312yes—
67C22×C3⋊Dic3C2311yescharacteristic
68C22×C3⋊Dic3C2311yescharacteristic
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2311yescharacteristic
72C22×C3×Dic3C2312yes—
73C2×C3×C4×D3—24no—
74C2×C3×C4×D3—24no—
75C2×C3×C4×D3—42no—
76C2×C3×C4×D3—42no—
77C2×C3×C4×D3—42no—
78C2×C3×C4×D3C2×C414yescomplemented
79C2×C3×C4×D3C2×C414yescomplemented
80C2×#625C2×C414yes—
81C2×#625D414yes—
82C2×#625Q814yes—
83C2×D3×Dic3—24no—
84C2×D3×Dic3—24no—
85C2×D3×Dic3—42no—
86#3750—24no—
87C4×C3⋊Dic3C2×C414yescomplemented
88C3×(C2×D3)⋊C4—24no—
89C3×Dic3⋊C4—42no—
90#3724—24no—
91#3724C2×C414yescomplemented
92Dic3⋊Dic3—42no—
93(C2×D3)⋊Dic3—24no—
94(C2×D3)⋊Dic3C2×C414yescomplemented
95(C2×D3)⋊Dic3C2×C414yescomplemented
96Dic32—24no—
97#2349—91noSylow
98C23×C3×C4—31no—
99C23×C3×C4—31no—
100C23×C3×C4—32no—
101C22×#67—31no—
102C22×#67—31no—
103C23×Dic3—32no—
104C22×C4×D3—32no—
105C22×C4×D3C2×D312yes—
106C22×C4×D3C2×D311yescharacteristic
107C22×C4×D3C2×D311yescharacteristic
108C2×C3×C4⋊C4—32no—
109C2×C3×C22⋊C4—32no—
110C2×#217—31no—
111C2×#217—31no—
112C2×#217—32no—
113C4×#67—38no—
114C4×#67—38no—
115C4×#67—68no—
116C2×(C2×D3)⋊C4—31no—
117C2×(C2×D3)⋊C4—31no—
118C2×(C2×D3)⋊C4—32no—
119C2×(C2×D3)⋊C4C2×D312yes—
120C2×C4⋊Dic3—32no—
121C2×Dic3⋊C4—31no—
122C2×Dic3⋊C4—31no—
123C2×Dic3⋊C4—32no—
124C2×Dic3⋊C4—32no—
125C2×Dic3⋊C4—32no—
126C2×Dic3⋊C4—32no—
127C2×Dic3⋊C4—32no—
128C2×Dic3⋊C4—62no—
129C2×Dic3⋊C4C2×D312yes—
130C2×C4×Dic3—31no—
131C2×C4×Dic3—31no—
132C2×C4×Dic3—32no—
133C2×C4×Dic3—32no—
134C2×C4×Dic3—61no—
135#67⋊C4—68no—
136C3×#95—21no—
137C3×#95—32no—
138C3×#95—31no—
139C3×#95—31no—
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⋊#95—62no—
150C3⋊#95C2×D311yescharacteristic
151C3⋊#95C2×D311yescharacteristic
152C3⋊#95C2×D312yes—
153C23×C32C2411yescharacteristic
154C22×C3×D3—22no—
155C22×C3×D3—22no—
156C22×C3×D3—22no—
157C22×C3×D3—22no—
158C22×C3×D3C22×C412yes—
159C22×C3×D3C22×C412yes—
160C22×C3×D3C2×D412yes—
161C22×C3×D3C2×D412yes—
162C22×C3×D3C2×Q812yes—
163C22×C3×D3C2×Q812yes—
164C2×C32×C4—22no—
165C2×C32×C4—22no—
166C2×C32×C4—22no—
167C2×C32×C4—22no—
168C2×C32×C4C22×C412yes—
169C2×C3⋊Dic3—22no—
170C2×C3⋊Dic3—22no—
171C2×C3⋊Dic3—22no—
172C2×C3⋊Dic3—22no—
173C2×C3⋊Dic3C22×C412yes—
174C2×C3⋊Dic3C22×C412yes—
175C2×C3⋊Dic3C2×D412yes—
176C2×C3⋊Dic3C2×Q812yes—
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×Dic3C22×C412yes—
185C2×C3×Dic3C22×C412yes—
186C2×C3×Dic3#4114yes—
187C3×C4×D3—44no—
188C3×C4×D3—44no—
189C3×C4×D3—48no—
190#625C4⋊C4116yescomplemented
191D3×Dic3—48no—
192C2×C4×D4—92no—
193C2×C4×D4—91no—
194#389—92no—
195#385—92no—
196#385—92no—
197#382—91no—
198#380—31no—
199#380—91no—
200C4×C4⋊C4—91no—
201C2×#95—31no—
202C2×#95—91no—
203C24×C3—31no—
204C24×C3—31no—
205C23×D3C22×D311yescharacteristic
206C23×D3C22×D311yescharacteristic
207C22×C3×C4—21no—
208C22×C3×C4—22no—
209C22×C3×C4—31no—
210C22×C3×C4—32no—
211C22×C3×C4—31no—
212C22×C3×C4—34no—
213C22×C3×C4—34no—
214C22×C3×C4—32no—
215C22×C3×C4—64no—
216C22×C3×C4—64no—
217C22×C3×C4—122no—
218C22×C3×C4—122no—
219C22×C3×C4—122no—
220C22×C3×C4C22×D312yes—
221C22×C3×C4C22×D312yes—
222C22×C3×C4C22×D311yescharacteristic
223C22×C3×C4C22×D311yescharacteristic
224C2×#67—34no—
225C2×#67—34no—
226C2×#67—34no—
227C2×#67—34no—
228C2×#67—34no—
229C2×#67—34no—
230C22×Dic3—31no—
231C22×Dic3—31no—
232C22×Dic3—31no—
233C22×Dic3—31no—
234C22×Dic3—32no—
235C22×Dic3—32no—
236C22×Dic3—61no—
237C22×Dic3—61no—
238C22×Dic3—62no—
239C22×Dic3—64no—
240C22×Dic3—64no—
241C22×Dic3—122no—
242C22×Dic3C22×D312yes—
243C22×Dic3C22×D311yescharacteristic
244C22×Dic3C22×D311yescharacteristic
245C22×Dic3C22×D312yes—
246C2×C4×D3—24no—
247C2×C4×D3—24no—
248C2×C4×D3—42no—
249C2×C4×D3—42no—
250C2×C4×D3—42no—
251C2×C4×D3—64no—
252C2×C4×D3—64no—
253C2×C4×D3—122no—
254C2×C4×D3C4×D314yescomplemented
255C2×C4×D3C4×D314yescomplemented
256C3×C4⋊C4—122no—
257C3×C22⋊C4—64no—
258#217—34no—
259#217—34no—
260#217—64no—
261(C2×D3)⋊C4—24no—
262(C2×D3)⋊C4—34no—
263(C2×D3)⋊C4—34no—
264(C2×D3)⋊C4—64no—
265C4⋊Dic3—122no—
266Dic3⋊C4—34no—
267Dic3⋊C4—34no—
268Dic3⋊C4—42no—
269Dic3⋊C4—64no—
270Dic3⋊C4—64no—
271Dic3⋊C4—64no—
272Dic3⋊C4—64no—
273Dic3⋊C4—124no—
274Dic3⋊C4—122no—
275C4×Dic3—34no—
276C4×Dic3—34no—
277C4×Dic3—64no—
278C4×Dic3—64no—
279C4×Dic3—64no—
280C22×C32C23×C411yescharacteristic
281C22×C32C22×D411yescharacteristic
282C22×C32C22×Q811yescharacteristic
283C22×C32C2×#4112yes—
284C22×C32H(5,𝔽2)12yes—
285C2×C3×D3—22no—
286C2×C3×D3—22no—
287C2×C3×D3—22no—
288C2×C3×D3—22no—
289C2×C3×D3—24no—
290C2×C3×D3—24no—
291C2×C3×D3—24no—
292C2×C3×D3—24no—
293C2×C3×D3C2×C4⋊C414yes—
294C2×C3×D3C2×C4⋊C414yes—
295C32×C4—22no—
296C32×C4—42no—
297C3⋊Dic3—22no—
298C3⋊Dic3—42no—
299C3⋊Dic3C2×C4⋊C414yes—
300C3×Dic3—22no—
301C3×Dic3—22no—
302C3×Dic3—24no—
303C3×Dic3—42no—
304C22×D4—91no—
305C23×C4—31no—
306C23×C4—31no—
307C23×C4—32no—
308C23×C4—92no—
309C4×D4—98no—
310C4×D4—188no—
311C2×C4⋊C4—32no—
312C2×C4⋊C4—91no—
313C2×C4⋊C4—92no—
314C2×C4⋊C4—92no—
315C2×C4⋊C4—92no—
316C2×C22⋊C4—32no—
317C2×C22⋊C4—91no—
318C2×C22⋊C4—91no—
319C2×C22⋊C4—92no—
320C2×C42—91no—
321C2×C42—92no—
322#95—31no—
323#95—32no—
324#95—31no—
325#95—92no—
326#95—91no—
327#95—92no—
328#95D3211yescharacteristic
329C23×C3—21no—
330C23×C3—32no—
331C23×C3—32no—
332C23×C3—32no—
333C23×C3—32no—
334C23×C3—32no—
335C23×C3—32no—
336C23×C3—62no—
337C23×C3—62no—
338C23×C3—62no—
339C23×C3—62no—
340C23×C3C23×D311yescharacteristic
341C23×C3C23×D311yescharacteristic
342C22×D3—22no—
343C22×D3—22no—
344C22×D3—22no—
345C22×D3—22no—
346C22×D3C2×C4×D312yes—
347C22×D3C2×C4×D312yes—
348C22×D3D3×D412yes—
349C22×D3D3×D412yes—
350C22×D3D3×Q812yes—
351C22×D3D3×Q812yes—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—32no—
362C2×C3×C4—32no—
363C2×C3×C4—34no—
364C2×C3×C4—42no—
365C2×C3×C4—42no—
366C2×C3×C4—42no—
367C2×C3×C4—42no—
368C2×C3×C4—62no—
369C2×C3×C4—62no—
370C2×C3×C4—62no—
371C2×C3×C4—62no—
372C2×C3×C4—62no—
373C2×C3×C4—62no—
374C2×C3×C4—62no—
375C2×C3×C4—124no—
376C2×C3×C4—124no—
377C2×C3×C4—128no—
378C2×C3×C4C2×C4×D312yes—
379C2×C3×C4C2×C4×D312yes—
380#67—316no—
381#67—316no—
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—32no—
394C2×Dic3—32no—
395C2×Dic3—32no—
396C2×Dic3—32no—
397C2×Dic3—62no—
398C2×Dic3—62no—
399C2×Dic3—62no—
400C2×Dic3—62no—
401C2×Dic3—62no—
402C2×Dic3—62no—
403C2×Dic3—62no—
404C2×Dic3—62no—
405C2×Dic3—62no—
406C2×Dic3—62no—
407C2×Dic3—62no—
408C2×Dic3—62no—
409C2×Dic3—122no—
410C2×Dic3—122no—
411C2×Dic3—122no—
412C2×Dic3—122no—
413C2×Dic3—128no—
414C2×Dic3C2×C4×D312yes—
415C2×Dic3C2×C4×D312yes—
416C2×Dic3#23514yes—
417C4×D3—44no—
418C4×D3—44no—
419C4×D3—48no—
420C4×D3—128no—
421C2×C32C22×C4⋊C411yescharacteristic
422C2×C32C4×#4111yescharacteristic
423C2×C32#51811yescharacteristic
424C2×C32#54612yes—
425C2×C32#55412yes—
426C3×D3—24no—
427C3×D3—24no—
428C24—31no—
429C24—31no—
430C2×D4—94no—
431C2×D4—94no—
432C2×D4—94no—
433C22×C4—32no—
434C22×C4—31no—
435C22×C4—31no—
436C22×C4—34no—
437C22×C4—34no—
438C22×C4—32no—
439C22×C4—64no—
440C22×C4—64no—
441C22×C4—91no—
442C22×C4—91no—
443C22×C4—92no—
444C22×C4—122no—
445C22×C4—122no—
446C22×C4—122no—
447C22×C4—184no—
448C22×C4—184no—
449C22×C4—362no—
450C22×C4C2×D3212yes—
451C22×C4C2×D3211yescharacteristic
452C4⋊C4—94no—
453C4⋊C4—122no—
454C4⋊C4—184no—
455C4⋊C4—184no—
456C4⋊C4—362no—
457C22⋊C4—64no—
458C22⋊C4—94no—
459C22⋊C4—94no—
460C22⋊C4—184no—
461C42—94no—
462C42—184no—
463C22×C3—21no—
464C22×C3—22no—
465C22×C3—21no—
466C22×C3—22no—
467C22×C3—21no—
468C22×C3—34no—
469C22×C3—34no—
470C22×C3—64no—
471C22×C3—62no—
472C22×C3—62no—
473C22×C3—62no—
474C22×C3—64no—
475C22×C3—64no—
476C22×C3—62no—
477C22×C3—64no—
478C22×C3C22×C4×D311yescharacteristic
479C22×C3C22×C4×D311yescharacteristic
480C22×C3C2×#23512yes—
481C22×C3C2×D3×D411yescharacteristic
482C22×C3C2×D3×D411yescharacteristic
483C22×C3#100412yes—
484C22×C3#100412yes—
485C22×C3C2×D3×Q811yescharacteristic
486C22×C3C2×D3×Q811yescharacteristic
487C22×C3D3×#4112yes—
488C2×D3—24no—
489C2×D3—22no—
490C2×D3—22no—
491C2×D3—22no—
492C2×D3—24no—
493C2×D3—24no—
494C2×D3—22no—
495C2×D3—24no—
496C2×D3D3×C4⋊C414yes—
497C2×D3D3×C4⋊C414yes—
498C3×C4—22no—
499C3×C4—22no—
500C3×C4—42no—
501C3×C4—42no—
502C3×C4—42no—
503C3×C4—62no—
504C3×C4—62no—
505C3×C4—64no—
506C3×C4—82no—
507C3×C4—122no—
508Dic3—22no—
509Dic3—22no—
510Dic3—24no—
511Dic3—34no—
512Dic3—34no—
513Dic3—42no—
514Dic3—64no—
515Dic3—62no—
516Dic3—62no—
517Dic3—122no—
518Dic3—122no—
519Dic3—122no—
520Dic3—242no—
521C32#234911yescharacteristic, complemented, Sylow
522C23—32no—
523C23—32no—
524C23—32no—
525C23—32no—
526C23—32no—
527C23—32no—
528C23—62no—
529C23—62no—
530C23—62no—
531C23—62no—
532C23C22×D3211yescharacteristic
533D4—916no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—32no—
539C2×C4—32no—
540C2×C4—34no—
541C2×C4—62no—
542C2×C4—62no—
543C2×C4—62no—
544C2×C4—62no—
545C2×C4—62no—
546C2×C4—62no—
547C2×C4—62no—
548C2×C4—92no—
549C2×C4—92no—
550C2×C4—92no—
551C2×C4—92no—
552C2×C4—124no—
553C2×C4—124no—
554C2×C4—128no—
555C2×C4—182no—
556C2×C4—182no—
557C2×C4—182no—
558C2×C4—182no—
559C2×C4—368no—
560C2×C4C4×D3212yes—
561C2×C3—21no—
562C2×C3—21no—
563C2×C3—21no—
564C2×C3—22no—
565C2×C3—22no—
566C2×C3—64no—
567C2×C3—64no—
568C2×C3C4×#23511yescharacteristic
569C2×C3#548611yescharacteristic
570C2×C3#548611yescharacteristic
571C2×C3#549012yes—
572C2×C3C2×D3×C4⋊C411yescharacteristic
573C2×C3C2×D3×C4⋊C411yescharacteristic
574C2×C3#551112yes—
575C2×C3#552211yescharacteristic
576C2×C3#561012yes—
577C2×C3#563612yes—
578D3—24no—
579D3—24no—
580C22—34no—
581C22—34no—
582C22—62no—
583C22—62no—
584C22—62no—
585C22—62no—
586C22—64no—
587C22—64no—
588C22—64no—
589C22—64no—
590C22C2×C4×D3211yescharacteristic
591C22D3×#23512yes—
592C22D32×D411yescharacteristic
593C22#6431312yes—
594C22D32×Q811yescharacteristic
595C4—22no—
596C4—42no—
597C4—62no—
598C4—62no—
599C4—64no—
600C4—94no—
601C4—122no—
602C4—182no—
603C4—362no—
604C3—21no—
605C3#7336911yescharacteristic, complemented
606C3#7401111yescharacteristic, complemented
607C2—64no—
608C2—64no—
609C2#1059396511yescharacteristic
610C2#1059418111yescharacteristic
611C2#1059427312yes—
612C2#1059453312yes—
613C2D32×C4⋊C411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC22×#625C22
hypercenter#95D32
hypocenterC32#2349
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
3. #10592349C2semidirect
4. C3×#4667C2semidirect
5. C3×D3×#95C2semidirect
6. #10591373C2semidirect
7. D3×C3⋊#95C2semidirect
8. #10591295C2semidirect
9. #10591277C2semidirect
10. #10591257C2semidirect
11. #10591256C2semidirect
30. C4×#625C4semidirect
53. #4667D3semidirect
55. D3×#95D3semidirect
78. C2×C3×C4×D3C2×C4semidirect
79. C2×C3×C4×D3C2×C4semidirect
87. C4×C3⋊Dic3C2×C4semidirect
91. #3724C2×C4semidirect
94. (C2×D3)⋊Dic3C2×C4semidirect
95. (C2×D3)⋊Dic3C2×C4semidirect
190. #625C4⋊C4semidirect
254. C2×C4×D3C4×D3semidirect
255. C2×C4×D3C4×D3semidirect
521. C32#2349semidirect
605. C3#73369semidirect
606. C3#74011semidirect

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
#105923492
C3×#46672
C3×D3×#952
#105913732
D3×C3⋊#952
#105912952
#105912772
#105912572
#105912562
#740113
#733693