Finite Group Databasebeta

← #11805511

Subgroups — #11805511

Order 1152.

1525 conjugacy classes of subgroups.

The subgroup lattice has 625 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#626C211yesmaximal, characteristic
2C2×#63880C212yesmaximal
3#10592366C211yesmaximal, characteristic, complemented
4C3×#4667C211yesmaximal, characteristic, complemented
5C3×#4649C211yesmaximal, characteristic, complemented
6#10591374C212yesmaximal, complemented
7#10591372C212yesmaximal, complemented
8#10591370C211yesmaximal, characteristic, complemented
9D3×C3⋊#95C211yesmaximal, characteristic, complemented
10#10591330C212yesmaximal, complemented
11#10591206C211yesmaximal, characteristic, complemented
12#74011—31nomaximal
13#73770—31nomaximal
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×C3×C4×D3C2211yescharacteristic
16C22×#626C2211yescharacteristic
17C22×#624C2212yes—
18C22×D3×Dic3C2212yes—
19C2×#3752C2212yes—
20C2×#3750C2212yes—
21C2×C3×(C2×D3)⋊C4C2212yes—
22C2×C3×Dic3⋊C4C2212yes—
23C2×C3×Dic3⋊C4C2212yes—
24C2×C3×C4×Dic3C2212yes—
25C2×C3×C4×Dic3C2211yescharacteristic
26C2×Dic3⋊Dic3C2212yes—
27C2×Dic3⋊Dic3C2211yescharacteristic
28C2×#3722C2211yescharacteristic
29C2×(C2×D3)⋊Dic3C2211yescharacteristic
30C4×#626C418yescomplemented
31#63880—28no—
32C32×#95C2211yescharacteristic
33#63658C2211yescharacteristic
34C3×C3⋊#95C2211yescharacteristic
35C3×C3⋊#95C2211yescharacteristic
36#63579C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39C2×C4×#67—31no—
40C2×#67⋊C4—32no—
41C2×C4×D12—31no—
42C2×C4×D12—32no—
43C3×#380—31no—
44C3×C4×C4⋊C4—31no—
45C2×C3⋊#95—31no—
46#4989—32no—
47#4989—32no—
48#4989—32no—
49#4976—32no—
50#4946—32no—
51#4936—31no—
52#4928—32no—
53#4667—31no—
54#4667—31no—
55#4667—61no—
56#4667D311yescharacteristic, complemented
57D3×#95—31no—
58D3×#95—31no—
59D3×#95—31no—
60#4650—31no—
61#4649D311yescharacteristic, complemented
62C23×C3⋊D3C2311yescharacteristic
63C23×C3×D3C2311yescharacteristic
64C22×C32×C4C2312yes—
65C22×C32×C4C2311yescharacteristic
66C22×C3⋊Dic3C2312yes—
67C22×C3⋊Dic3C2311yescharacteristic
68C2×C4×C3⋊D3—42no—
69C2×C4×C3⋊D3C2×C414yescomplemented
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2311yescharacteristic
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2311yescharacteristic
75C2×C3×C4×D3—42no—
76C2×C3×C4×D3C2×C414yescomplemented
77C2×#626C2×C414yes—
78C2×#626D414yes—
79C2×#626Q814yes—
80C2×#624—24no—
81C2×#624—24no—
82C2×#624—42no—
83C2×D3×Dic3—24no—
84C2×D3×Dic3—24no—
85C2×D3×Dic3—42no—
86#3752—24no—
87#3750—42no—
88C3×(C2×D3)⋊C4—24no—
89C3×Dic3⋊C4—24no—
90C3×Dic3⋊C4—42no—
91C3×C4×Dic3—24no—
92C3×C4×Dic3C2×C414yescomplemented
93Dic3⋊Dic3—24no—
94Dic3⋊Dic3C2×C414yescomplemented
95#3722C2×C414yescomplemented
96(C2×D3)⋊Dic3C2×C414yescomplemented
97#2349—91noSylow
98C23×C3×C4—31no—
99C22×#67—31no—
100C23×Dic3—32no—
101C22×D12—31no—
102C22×C4×D3—31no—
103C22×C4×D3—31no—
104C22×C4×D3—32no—
105C22×C4×D3—32no—
106C22×C4×D3—32no—
107C22×C4×D3—61no—
108C22×C4×D3C2×D311yescharacteristic
109C2×C3×C4⋊C4—32no—
110C2×C3×C4⋊C4—32no—
111C2×C3×C22⋊C4—32no—
112C2×C3×C42—31no—
113C2×C3×C42—32no—
114C2×#217—31no—
115C4×#67—38no—
116C2×(C2×D3)⋊C4—31no—
117C2×(C2×D3)⋊C4—31no—
118C2×(C2×D3)⋊C4—31no—
119C2×(C2×D3)⋊C4—32no—
120C2×(C2×D3)⋊C4—32no—
121C2×(C2×D3)⋊C4—62no—
122C2×(C2×D3)⋊C4C2×D312yes—
123C2×C4⋊Dic3—31no—
124C2×C4⋊Dic3—32no—
125C2×Dic3⋊C4—31no—
126C2×Dic3⋊C4—32no—
127C2×Dic3⋊C4—32no—
128C2×Dic3⋊C4—32no—
129C2×Dic3⋊C4—62no—
130C2×Dic3⋊C4C2×D312yes—
131C2×Dic3⋊C4C2×D312yes—
132C2×C4×Dic3C2×D312yes—
133C2×C4×Dic3C2×D311yescharacteristic
134#67⋊C4—68no—
135C4×D12—38no—
136C4×D12—68no—
137C3×#95—21no—
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—32no—
149C3⋊#95—32no—
150C3⋊#95—61no—
151C3⋊#95C2×D311yescharacteristic
152C3⋊#95C2×D311yescharacteristic
153C23×C32C2411yescharacteristic
154C22×C3⋊D3—22no—
155C22×C3⋊D3—22no—
156C22×C3⋊D3C22×C412yes—
157C22×C3⋊D3C2×D412yes—
158C22×C3⋊D3C2×Q812yes—
159C22×C3×D3—22no—
160C22×C3×D3—22no—
161C22×C3×D3C22×C412yes—
162C22×C3×D3C2×D412yes—
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—
174C4×C3⋊D3—44no—
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×Dic3C22×C412yes—
183C2×C3×Dic3C22×C412yes—
184C2×C3×Dic3C22×C412yes—
185C2×C3×Dic3C2×D412yes—
186C2×C3×Dic3C2×Q812yes—
187C2×C3×Dic3#4114yes—
188C3×C4×D3—44no—
189#626C4⋊C4116yescomplemented
190#624—48no—
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—31no—
201C2×#95—91no—
202C2×#95—91no—
203C24×C3—31no—
204C23×D3—31no—
205C23×D3—31no—
206C23×D3—61no—
207C23×D3C22×D311yescharacteristic
208C22×C3×C4—21no—
209C22×C3×C4—22no—
210C22×C3×C4—31no—
211C22×C3×C4—32no—
212C22×C3×C4—31no—
213C22×C3×C4—31no—
214C22×C3×C4—34no—
215C22×C3×C4—32no—
216C22×C3×C4—122no—
217C22×C3×C4C22×D312yes—
218C22×C3×C4C22×D312yes—
219C22×C3×C4C22×D311yescharacteristic
220C22×C3×C4C22×D311yescharacteristic
221C2×#67—34no—
222C2×#67—34no—
223C2×#67—34no—
224C22×Dic3—31no—
225C22×Dic3—31no—
226C22×Dic3—32no—
227C22×Dic3—32no—
228C22×Dic3—61no—
229C22×Dic3—62no—
230C22×Dic3—64no—
231C22×Dic3—64no—
232C22×Dic3—122no—
233C22×Dic3C22×D312yes—
234C22×Dic3C22×D311yescharacteristic
235C22×Dic3C22×D311yescharacteristic
236C22×Dic3C22×D312yes—
237C22×Dic3C22×D311yescharacteristic
238C2×D12—34no—
239C2×D12—34no—
240C2×D12—34no—
241C2×C4×D3—34no—
242C2×C4×D3—34no—
243C2×C4×D3—42no—
244C2×C4×D3—64no—
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—122no—
252C2×C4×D3—122no—
253C2×C4×D3—122no—
254C2×C4×D3—122no—
255C2×C4×D3—124no—
256C2×C4×D3—122no—
257C2×C4×D3C4×D314yescomplemented
258C3×C4⋊C4—64no—
259C3×C4⋊C4—122no—
260C3×C22⋊C4—64no—
261C3×C42—34no—
262C3×C42—64no—
263#217—34no—
264(C2×D3)⋊C4—24no—
265(C2×D3)⋊C4—34no—
266(C2×D3)⋊C4—34no—
267(C2×D3)⋊C4—34no—
268(C2×D3)⋊C4—64no—
269(C2×D3)⋊C4—64no—
270(C2×D3)⋊C4—124no—
271C4⋊Dic3—34no—
272C4⋊Dic3—64no—
273Dic3⋊C4—24no—
274Dic3⋊C4—34no—
275Dic3⋊C4—42no—
276Dic3⋊C4—64no—
277Dic3⋊C4—122no—
278Dic3⋊C4—122no—
279Dic3⋊C4—124no—
280C4×Dic3—24no—
281C4×Dic3C4×D314yescomplemented
282C22×C32C23×C411yescharacteristic
283C22×C32C22×D411yescharacteristic
284C22×C32C22×Q811yescharacteristic
285C22×C32C2×#4112yes—
286C22×C32H(5,𝔽2)12yes—
287C2×C3⋊D3—22no—
288C2×C3⋊D3—22no—
289C2×C3⋊D3—24no—
290C2×C3⋊D3—24no—
291C2×C3⋊D3C2×C4⋊C414yes—
292C2×C3×D3—22no—
293C2×C3×D3—22no—
294C2×C3×D3—24no—
295C2×C3×D3—24no—
296C2×C3×D3C2×C4⋊C414yes—
297C32×C4—22no—
298C32×C4—42no—
299C3⋊Dic3—22no—
300C3⋊Dic3—42no—
301C3×Dic3—22no—
302C3×Dic3—22no—
303C3×Dic3—24no—
304C3×Dic3—42no—
305C3×Dic3C2×C4⋊C414yes—
306C22×D4—91no—
307C23×C4—31no—
308C23×C4—92no—
309C23×C4—92no—
310C23×C4—91no—
311C4×D4—98no—
312C4×D4—188no—
313C2×C4⋊C4—32no—
314C2×C4⋊C4—32no—
315C2×C4⋊C4—91no—
316C2×C4⋊C4—92no—
317C2×C4⋊C4—92no—
318C2×C22⋊C4—32no—
319C2×C22⋊C4—91no—
320C2×C22⋊C4—91no—
321C2×C22⋊C4—92no—
322C2×C42—31no—
323C2×C42—32no—
324#95—31no—
325#95—31no—
326#95—92no—
327#95—92no—
328#95—92no—
329#95—91no—
330#95D3211yescharacteristic
331C23×C3—21no—
332C23×C3—32no—
333C23×C3—32no—
334C23×C3—32no—
335C23×C3—62no—
336C23×C3—62no—
337C23×C3C23×D311yescharacteristic
338C23×C3C23×D311yescharacteristic
339C22×D3—22no—
340C22×D3—22no—
341C22×D3—32no—
342C22×D3—32no—
343C22×D3—32no—
344C22×D3—32no—
345C22×D3—32no—
346C22×D3—32no—
347C22×D3—62no—
348C22×D3—62no—
349C22×D3—62no—
350C22×D3—62no—
351C22×D3—62no—
352C22×D3—62no—
353C22×D3—62no—
354C22×D3—122no—
355C22×D3—122no—
356C22×D3C2×C4×D312yes—
357C22×D3D3×D412yes—
358C22×D3D3×Q812yes—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—22no—
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—22no—
365C2×C3×C4—22no—
366C2×C3×C4—22no—
367C2×C3×C4—22no—
368C2×C3×C4—32no—
369C2×C3×C4—32no—
370C2×C3×C4—32no—
371C2×C3×C4—32no—
372C2×C3×C4—32no—
373C2×C3×C4—34no—
374C2×C3×C4—42no—
375C2×C3×C4—42no—
376C2×C3×C4—42no—
377C2×C3×C4—42no—
378C2×C3×C4—62no—
379C2×C3×C4—62no—
380C2×C3×C4—62no—
381C2×C3×C4—62no—
382C2×C3×C4—62no—
383C2×C3×C4—62no—
384C2×C3×C4—62no—
385C2×C3×C4—124no—
386C2×C3×C4C2×C4×D312yes—
387C2×C3×C4C2×C4×D312yes—
388#67—316no—
389C2×Dic3—22no—
390C2×Dic3—22no—
391C2×Dic3—22no—
392C2×Dic3—22no—
393C2×Dic3—22no—
394C2×Dic3—22no—
395C2×Dic3—22no—
396C2×Dic3—32no—
397C2×Dic3—32no—
398C2×Dic3—62no—
399C2×Dic3—64no—
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—122no—
409C2×Dic3—122no—
410C2×Dic3—122no—
411C2×Dic3—128no—
412C2×Dic3C2×C4×D312yes—
413C2×Dic3C2×C4×D312yes—
414C2×Dic3C2×C4×D312yes—
415C2×Dic3#23514yes—
416C2×Dic3D3×D412yes—
417C2×Dic3D3×Q812yes—
418D12—316no—
419C4×D3—44no—
420C4×D3—128no—
421C4×D3—128no—
422C4×D3—124no—
423C4×D3—124no—
424C4×D3—128no—
425C4×D3—128no—
426C2×C32C22×C4⋊C411yescharacteristic
427C2×C32C4×#4111yescharacteristic
428C2×C32#51811yescharacteristic
429C2×C32#54612yes—
430C2×C32#55412yes—
431C3⋊D3—24no—
432C3×D3—24no—
433C24—31no—
434C24—91no—
435C2×D4—94no—
436C2×D4—94no—
437C2×D4—94no—
438C22×C4—31no—
439C22×C4—32no—
440C22×C4—31no—
441C22×C4—31no—
442C22×C4—34no—
443C22×C4—32no—
444C22×C4—91no—
445C22×C4—94no—
446C22×C4—92no—
447C22×C4—122no—
448C22×C4—184no—
449C22×C4—184no—
450C22×C4—184no—
451C22×C4—184no—
452C22×C4—362no—
453C22×C4—362no—
454C22×C4—362no—
455C22×C4C2×D3212yes—
456C22×C4C2×D3211yescharacteristic
457C4⋊C4—64no—
458C4⋊C4—94no—
459C4⋊C4—122no—
460C4⋊C4—184no—
461C4⋊C4—362no—
462C22⋊C4—64no—
463C22⋊C4—94no—
464C22⋊C4—94no—
465C22⋊C4—184no—
466C42—34no—
467C42—64no—
468C22×C3—21no—
469C22×C3—22no—
470C22×C3—21no—
471C22×C3—22no—
472C22×C3—21no—
473C22×C3—34no—
474C22×C3—62no—
475C22×C3—62no—
476C22×C3—64no—
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×C3C2×D3×Q811yescharacteristic
485C22×C3C2×D3×Q811yescharacteristic
486C22×C3D3×#4112yes—
487C22×C3#100912yes—
488C2×D3—24no—
489C2×D3—22no—
490C2×D3—22no—
491C2×D3—24no—
492C2×D3—34no—
493C2×D3—34no—
494C2×D3—64no—
495C2×D3—64no—
496C2×D3—62no—
497C2×D3—62no—
498C2×D3—62no—
499C2×D3—62no—
500C2×D3—64no—
501C2×D3—64no—
502C2×D3—64no—
503C2×D3—122no—
504C2×D3—124no—
505C2×D3—122no—
506C2×D3—124no—
507C2×D3D3×C4⋊C414yes—
508C3×C4—22no—
509C3×C4—22no—
510C3×C4—34no—
511C3×C4—42no—
512C3×C4—42no—
513C3×C4—42no—
514C3×C4—62no—
515C3×C4—62no—
516C3×C4—64no—
517C3×C4—82no—
518C3×C4—122no—
519Dic3—22no—
520Dic3—22no—
521Dic3—24no—
522Dic3—42no—
523Dic3—64no—
524Dic3—62no—
525Dic3—62no—
526Dic3—122no—
527Dic3—122no—
528Dic3—242no—
529Dic3D3×C4⋊C414yes—
530C32#234911yescharacteristic, complemented, Sylow
531C23—32no—
532C23—32no—
533C23—32no—
534C23—62no—
535C23—62no—
536C23—92no—
537C23—92no—
538C23—92no—
539C23—182no—
540C23—182no—
541C23C22×D3211yescharacteristic
542D4—916no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—32no—
548C2×C4—32no—
549C2×C4—32no—
550C2×C4—32no—
551C2×C4—32no—
552C2×C4—34no—
553C2×C4—62no—
554C2×C4—62no—
555C2×C4—62no—
556C2×C4—62no—
557C2×C4—62no—
558C2×C4—62no—
559C2×C4—62no—
560C2×C4—92no—
561C2×C4—124no—
562C2×C4—182no—
563C2×C4—182no—
564C2×C4—182no—
565C2×C4—182no—
566C2×C4—364no—
567C2×C4—368no—
568C2×C4—368no—
569C2×C4C4×D3212yes—
570C2×C3—21no—
571C2×C3—22no—
572C2×C3—21no—
573C2×C3—21no—
574C2×C3—22no—
575C2×C3—64no—
576C2×C3C4×#23511yescharacteristic
577C2×C3#548611yescharacteristic
578C2×C3C2×D3×C4⋊C411yescharacteristic
579C2×C3C2×D3×C4⋊C411yescharacteristic
580C2×C3#552111yescharacteristic
581C2×C3#552211yescharacteristic
582C2×C3#555012yes—
583C2×C3#557912yes—
584C2×C3#561012yes—
585C2×C3#563612yes—
586D3—24no—
587D3—64no—
588D3—64no—
589D3—124no—
590C22—34no—
591C22—64no—
592C22—62no—
593C22—62no—
594C22—64no—
595C22—94no—
596C22—184no—
597C22—182no—
598C22—182no—
599C22—184no—
600C22C2×C4×D3211yescharacteristic
601C22D3×#23512yes—
602C22D32×D411yescharacteristic
603C22#6431412yes—
604C22D32×Q811yescharacteristic
605C4—22no—
606C4—34no—
607C4—42no—
608C4—62no—
609C4—62no—
610C4—64no—
611C4—122no—
612C4—182no—
613C4—362no—
614C3—21no—
615C3#7377011yescharacteristic, complemented
616C3#7401111yescharacteristic, complemented
617C2—64no—
618C2—184no—
619C2#1059396511yescharacteristic
620C2#1059418211yescharacteristic
621C2#1059428312yes—
622C2#1059439212yes—
623C2D32×C4⋊C411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC22×#626C22
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. #10592366C2semidirect
4. C3×#4667C2semidirect
5. C3×#4649C2semidirect
6. #10591374C2semidirect
7. #10591372C2semidirect
8. #10591370C2semidirect
9. D3×C3⋊#95C2semidirect
10. #10591330C2semidirect
11. #10591206C2semidirect
30. C4×#626C4semidirect
56. #4667D3semidirect
61. #4649D3semidirect
69. C2×C4×C3⋊D3C2×C4semidirect
76. C2×C3×C4×D3C2×C4semidirect
92. C3×C4×Dic3C2×C4semidirect
94. Dic3⋊Dic3C2×C4semidirect
95. #3722C2×C4semidirect
96. (C2×D3)⋊Dic3C2×C4semidirect
189. #626C4⋊C4semidirect
257. C2×C4×D3C4×D3semidirect
281. C4×Dic3C4×D3semidirect
530. C32#2349semidirect
615. C3#73770semidirect
616. C3#74011semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6262
C2×#638802
#105923662
C3×#46672
C3×#46492
#105913742
#105913722
#105913702
D3×C3⋊#952
#105913302
#105912062
#740113
#737703