Finite Group Databasebeta

← #11806914

Subgroups — #11806914

Order 1152.

1761 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63914C211yesmaximal, characteristic
2C2×#63902C211yesmaximal, characteristic, complemented
3C2×C4×#625C211yesmaximal, characteristic, complemented
4C2×#63879C212yesmaximal, complemented
5#10592348C211yesmaximal, characteristic, complemented
6C3×#4665C212yesmaximal, complemented
7#10591386C212yesmaximal, complemented
8#10591385C211yesmaximal, characteristic, complemented
9#10591385C211yesmaximal, characteristic, complemented
10#10591376C212yesmaximal, complemented
11#10591257C211yesmaximal, characteristic, complemented
12#74679—32nomaximal
13C22×C3×D12C2212yes—
14C22×C3×C4×D3C2212yes—
15C22×#625C2212yes—
16C22×#625C2211yescharacteristic
17C22×#625C2211yescharacteristic
18C22×D3×Dic3C2212yes—
19C2×#3750C2211yescharacteristic
20C2×#3750C2211yescharacteristic
21C2×C4×C3⋊Dic3C2211yescharacteristic
22C2×C4×C3⋊Dic3C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×C3×(C2×D3)⋊C4C2212yes—
25C2×C3×(C2×D3)⋊C4C2212yes—
26C2×C3×(C2×D3)⋊C4C2212yes—
27C2×#3724C2211yescharacteristic
28C2×#3724C2211yescharacteristic
29C2×(C2×D3)⋊Dic3C2212yes—
30C2×(C2×D3)⋊Dic3C2212yes—
31C2×(C2×D3)⋊Dic3C2212yes—
32C2×Dic32C2212yes—
33#63914C418yescomplemented
34#63902—24no—
35C4×#625—24no—
36#63879—28no—
37C32×#95C2211yescharacteristic
38#63658C2211yescharacteristic
39C3×C3⋊#95C2212yes—
40C2×#940—32no—
41C2×C4×#67—32no—
42C2×C4×#67—32no—
43C2×#67⋊C4—32no—
44C2×#67⋊C4—32no—
45C3×#386—32no—
46#5220—32no—
47#4957—32no—
48#4957—32no—
49#4957—32no—
50#4957—32no—
51#4665—32no—
52#4665D312yescomplemented
53#4649—32no—
54#4649—32no—
55#4649—61no—
56C23×C3×D3C2312yes—
57C23×C3×D3C2312yes—
58C22×C32×C4C2311yescharacteristic
59C22×C32×C4C2311yescharacteristic
60C22×C32×C4C2311yescharacteristic
61C22×C3⋊Dic3C2311yescharacteristic
62C22×C3⋊Dic3C2311yescharacteristic
63C22×C3⋊Dic3C2311yescharacteristic
64C22×C3⋊Dic3C2311yescharacteristic
65C22×C3×Dic3C2312yes—
66C22×C3×Dic3C2312yes—
67C2×C3×D12—42no—
68C2×C3×D12—42no—
69C2×C3×D12C2×C418yescomplemented
70C2×C3×C4×D3—24no—
71C2×C3×C4×D3—24no—
72C2×C3×C4×D3—42no—
73C2×#625—24no—
74C2×#625—22no—
75C2×#625—22no—
76C2×#625—22no—
77C2×#625—22no—
78C2×#625—24no—
79C2×#625C2×C418yescomplemented
80C2×#625C2×C414yescomplemented
81C2×#625C2×C414yescomplemented
82C2×D3×Dic3—24no—
83C2×D3×Dic3—24no—
84C2×D3×Dic3—42no—
85#3750—22no—
86#3750D414yescomplemented
87C4×C3⋊Dic3—22no—
88C4×C3⋊Dic3—22no—
89C4×C3⋊Dic3C2×C414yescomplemented
90C3×(C2×D3)⋊C4—24no—
91C3×(C2×D3)⋊C4—24no—
92C3×(C2×D3)⋊C4—42no—
93#3724—22no—
94#3724D414yescomplemented
95(C2×D3)⋊Dic3—24no—
96(C2×D3)⋊Dic3—24no—
97(C2×D3)⋊Dic3—42no—
98Dic32—24no—
99#2366—91noSylow
100C22×C3×D4—32no—
101C23×C3×C4—32no—
102C22×#67—32no—
103C22×#67—32no—
104C22×#67—32no—
105C22×#67—32no—
106C23×Dic3—32no—
107C22×D12C2×D312yes—
108C22×C4×D3—32no—
109C22×C4×D3C2×D312yes—
110C2×C3×C22⋊C4—32no—
111C2×C3×C22⋊C4—32no—
112C2×C3×C22⋊C4—32no—
113C2×#217—32no—
114C2×#217—32no—
115C2×#217—32no—
116#940—316no—
117C4×#67—68no—
118C4×#67—68no—
119C2×(C2×D3)⋊C4—32no—
120C2×(C2×D3)⋊C4—32no—
121C2×(C2×D3)⋊C4—32no—
122C2×(C2×D3)⋊C4C2×D312yes—
123C2×(C2×D3)⋊C4C2×D312yes—
124C2×(C2×D3)⋊C4C2×D312yes—
125C2×Dic3⋊C4—32no—
126C2×Dic3⋊C4—32no—
127C2×Dic3⋊C4—32no—
128C2×Dic3⋊C4—32no—
129C2×Dic3⋊C4—61no—
130C2×Dic3⋊C4—61no—
131C2×C4×Dic3—32no—
132C2×C4×Dic3—32no—
133C2×C4×Dic3—32no—
134C2×C4×Dic3—32no—
135C2×C4×Dic3—32no—
136C2×C4×Dic3—61no—
137C2×C4×Dic3—61no—
138C2×C4×Dic3—61no—
139#67⋊C4—68no—
140#67⋊C4—68no—
141C3×#95—21no—
142C3×#95—32no—
143C3×#95C2×D312yes—
144C3⋊#95—32no—
145C3⋊#95—61no—
146C3⋊#95C2×D312yes—
147C23×C32C2411yescharacteristic
148C22×C3×D3—22no—
149C22×C3×D3—22no—
150C22×C3×D3—22no—
151C22×C3×D3—22no—
152C22×C3×D3—22no—
153C22×C3×D3—22no—
154C22×C3×D3—22no—
155C22×C3×D3—22no—
156C22×C3×D3—22no—
157C22×C3×D3—22no—
158C22×C3×D3—22no—
159C22×C3×D3—22no—
160C22×C3×D3C22×C414yes—
161C22×C3×D3C22×C414yes—
162C2×C32×C4—21no—
163C2×C32×C4—21no—
164C2×C32×C4—21no—
165C2×C32×C4—21no—
166C2×C32×C4—21no—
167C2×C32×C4—21no—
168C2×C32×C4—21no—
169C2×C32×C4C22×C412yes—
170C2×C32×C4C2×D412yes—
171C2×C3⋊Dic3—21no—
172C2×C3⋊Dic3—21no—
173C2×C3⋊Dic3—21no—
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3—21no—
176C2×C3⋊Dic3C22×C412yes—
177C2×C3⋊Dic3C22×C412yes—
178C2×C3⋊Dic3C2×D412yes—
179C2×C3⋊Dic3C2×D412yes—
180C2×C3⋊Dic3C2×D412yes—
181C2×C3⋊Dic3#4112yes—
182C2×C3⋊Dic3#4112yes—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3C2×D414yes—
189C3×D12—48no—
190C3×C4×D3—48no—
191#625—216no—
192#625—28no—
193#625—28no—
194D3×Dic3—48no—
195C2×#127—91no—
196C2×C4×D4—91no—
197C2×C4×D4—92no—
198C2×C4×D4—91no—
199#390—92no—
200#390—91no—
201#390—91no—
202#386—32no—
203#386—92no—
204C4×C4⋊C4—91no—
205C4×C4⋊C4—91no—
206C24×C3—32no—
207C24×C3—32no—
208C23×D3C22×D312yes—
209C23×D3C22×D312yes—
210C2×C3×D4—38no—
211C2×C3×D4—122no—
212C2×C3×D4—122no—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—32no—
217C22×C3×C4—32no—
218C22×C3×C4—64no—
219C22×C3×C4—64no—
220C22×C3×C4—122no—
221C22×C3×C4C22×D312yes—
222C22×C3×C4C22×D312yes—
223C22×C3×C4C22×D312yes—
224C2×#67—38no—
225C2×#67—38no—
226C2×#67—38no—
227C2×#67—38no—
228C2×#67—64no—
229C2×#67—64no—
230C2×#67—64no—
231C2×#67—64no—
232C2×#67—64no—
233C2×#67—64no—
234C2×#67—64no—
235C2×#67—64no—
236C22×Dic3—32no—
237C22×Dic3—32no—
238C22×Dic3—32no—
239C22×Dic3—32no—
240C22×Dic3—61no—
241C22×Dic3—61no—
242C22×Dic3—61no—
243C22×Dic3—61no—
244C22×Dic3—64no—
245C22×Dic3—64no—
246C22×Dic3—122no—
247C22×Dic3C22×D312yes—
248C22×Dic3C22×D312yes—
249C2×D12—42no—
250C2×D12—42no—
251C2×D12C4×D318yescomplemented
252C2×C4×D3—24no—
253C2×C4×D3—24no—
254C2×C4×D3—42no—
255C2×C4×D3—64no—
256C2×C4×D3—64no—
257C2×C4×D3—122no—
258C3×C22⋊C4—64no—
259C3×C22⋊C4—64no—
260C3×C22⋊C4—122no—
261#217—64no—
262#217—64no—
263#217—122no—
264(C2×D3)⋊C4—24no—
265(C2×D3)⋊C4—24no—
266(C2×D3)⋊C4—42no—
267(C2×D3)⋊C4—64no—
268(C2×D3)⋊C4—64no—
269(C2×D3)⋊C4—122no—
270Dic3⋊C4—38no—
271Dic3⋊C4—38no—
272Dic3⋊C4—64no—
273Dic3⋊C4—64no—
274Dic3⋊C4—64no—
275Dic3⋊C4—64no—
276C4×Dic3—38no—
277C4×Dic3—64no—
278C4×Dic3—64no—
279C4×Dic3—64no—
280C4×Dic3—64no—
281C4×Dic3—64no—
282C4×Dic3—122no—
283C4×Dic3—122no—
284C22×C32C23×C411yescharacteristic
285C22×C32C22×D411yescharacteristic
286C22×C32C22×D411yescharacteristic
287C22×C32C2×#4111yescharacteristic
288C22×C32C2×#4111yescharacteristic
289C22×C32H(5,𝔽2)11yescharacteristic
290C22×C32H(5,𝔽2)11yescharacteristic
291C2×C3×D3—24no—
292C2×C3×D3—24no—
293C2×C3×D3—24no—
294C2×C3×D3—24no—
295C2×C3×D3—24no—
296C2×C3×D3—24no—
297C2×C3×D3—42no—
298C2×C3×D3—42no—
299C2×C3×D3—42no—
300C2×C3×D3—42no—
301C2×C3×D3—42no—
302C2×C3×D3—42no—
303C2×C3×D3—42no—
304C2×C3×D3—42no—
305C32×C4—22no—
306C32×C4—22no—
307C32×C4—41no—
308C3⋊Dic3—22no—
309C3⋊Dic3—41no—
310C3⋊Dic3C4×D414yescomplemented
311C3⋊Dic3C4×D414yescomplemented
312C3×Dic3—24no—
313C3×Dic3—42no—
314C22×D4—32no—
315C22×D4—91no—
316C22×D4—92no—
317C22×D4—91no—
318C23×C4—32no—
319C23×C4—92no—
320#127—98no—
321C4×D4—184no—
322C4×D4—188no—
323C4×D4—184no—
324C2×C4⋊C4—91no—
325C2×C4⋊C4—91no—
326C2×C4⋊C4—91no—
327C2×C4⋊C4—91no—
328C2×C22⋊C4—32no—
329C2×C22⋊C4—32no—
330C2×C22⋊C4—32no—
331C2×C22⋊C4—92no—
332C2×C22⋊C4—92no—
333C2×C22⋊C4—92no—
334C2×C42—91no—
335C2×C42—92no—
336C2×C42—91no—
337C2×C42—91no—
338#95—32no—
339#95—91no—
340#95D3211yescharacteristic
341C23×C3—21no—
342C23×C3—34no—
343C23×C3—34no—
344C23×C3—62no—
345C23×C3—62no—
346C23×C3—62no—
347C23×C3—62no—
348C23×C3—62no—
349C23×C3—62no—
350C23×C3—62no—
351C23×C3—62no—
352C23×C3—62no—
353C23×C3—62no—
354C23×C3—62no—
355C23×C3—62no—
356C23×C3C23×D312yes—
357C22×D3—22no—
358C22×D3—22no—
359C22×D3—22no—
360C22×D3—22no—
361C22×D3—22no—
362C22×D3—22no—
363C22×D3—22no—
364C22×D3—22no—
365C22×D3—22no—
366C22×D3—22no—
367C22×D3—22no—
368C22×D3—22no—
369C22×D3C2×C4×D314yes—
370C22×D3C2×C4×D314yes—
371C3×D4—128no—
372C2×C3×C4—22no—
373C2×C3×C4—22no—
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—34no—
383C2×C3×C4—41no—
384C2×C3×C4—41no—
385C2×C3×C4—41no—
386C2×C3×C4—41no—
387C2×C3×C4—41no—
388C2×C3×C4—41no—
389C2×C3×C4—62no—
390C2×C3×C4—62no—
391C2×C3×C4—62no—
392C2×C3×C4—62no—
393C2×C3×C4—62no—
394C2×C3×C4—128no—
395C2×C3×C4C2×C4×D314yes—
396C2×C3×C4D3×D414yes—
397#67—616no—
398#67—616no—
399#67—616no—
400#67—616no—
401C2×Dic3—22no—
402C2×Dic3—22no—
403C2×Dic3—22no—
404C2×Dic3—22no—
405C2×Dic3—22no—
406C2×Dic3—34no—
407C2×Dic3—34no—
408C2×Dic3—34no—
409C2×Dic3—34no—
410C2×Dic3—34no—
411C2×Dic3—34no—
412C2×Dic3—34no—
413C2×Dic3—62no—
414C2×Dic3—62no—
415C2×Dic3—62no—
416C2×Dic3—62no—
417C2×Dic3—62no—
418C2×Dic3—62no—
419C2×Dic3—62no—
420C2×Dic3—62no—
421C2×Dic3—62no—
422C2×Dic3—62no—
423C2×Dic3—62no—
424C2×Dic3—62no—
425C2×Dic3—62no—
426C2×Dic3—121no—
427C2×Dic3—121no—
428C2×Dic3—121no—
429C2×Dic3—121no—
430C2×Dic3—128no—
431C2×Dic3D3×D414yes—
432D12—48no—
433C4×D3—48no—
434C4×D3—128no—
435C2×C32C2×C4×D411yescharacteristic
436C2×C32C2×C4×D411yescharacteristic
437C2×C32#51811yescharacteristic
438C2×C32D4211yescharacteristic
439C2×C32#55011yescharacteristic
440C2×C32#55011yescharacteristic
441C2×C32#55911yescharacteristic
442C3×D3—44no—
443C3×D3—44no—
444C24—32no—
445C24—32no—
446C2×D4—38no—
447C2×D4—94no—
448C2×D4—94no—
449C2×D4—98no—
450C2×D4—122no—
451C2×D4—122no—
452C2×D4—184no—
453C2×D4—182no—
454C2×D4—182no—
455C2×D4—184no—
456C2×D4—182no—
457C2×D4—182no—
458C22×C4—32no—
459C22×C4—32no—
460C22×C4—64no—
461C22×C4—64no—
462C22×C4—91no—
463C22×C4—91no—
464C22×C4—91no—
465C22×C4—91no—
466C22×C4—122no—
467C22×C4—184no—
468C22×C4—184no—
469C22×C4—362no—
470C22×C4C2×D3211yescharacteristic
471C22×C4C2×D3211yescharacteristic
472C22×C4C2×D3211yescharacteristic
473C4⋊C4—94no—
474C4⋊C4—94no—
475C4⋊C4—182no—
476C4⋊C4—182no—
477C22⋊C4—64no—
478C22⋊C4—64no—
479C22⋊C4—122no—
480C22⋊C4—184no—
481C22⋊C4—184no—
482C22⋊C4—362no—
483C42—94no—
484C42—182no—
485C42—182no—
486C42—184no—
487C22×C3—21no—
488C22×C3—21no—
489C22×C3—21no—
490C22×C3—21no—
491C22×C3—21no—
492C22×C3—21no—
493C22×C3—21no—
494C22×C3—64no—
495C22×C3—64no—
496C22×C3—64no—
497C22×C3—64no—
498C22×C3—64no—
499C22×C3—64no—
500C22×C3—122no—
501C22×C3—122no—
502C22×C3—122no—
503C22×C3—122no—
504C22×C3—122no—
505C22×C3—122no—
506C22×C3—122no—
507C22×C3—122no—
508C22×C3C22×C4×D312yes—
509C22×C3C2×D3×D412yes—
510C22×C3C2×D3×D412yes—
511C22×C3#100412yes—
512C22×C3#100412yes—
513C22×C3D3×#4112yes—
514C22×C3D3×#4112yes—
515C2×D3—24no—
516C2×D3—24no—
517C2×D3—24no—
518C2×D3—24no—
519C2×D3—24no—
520C2×D3—24no—
521C2×D3—42no—
522C2×D3—42no—
523C2×D3—42no—
524C2×D3—42no—
525C2×D3—42no—
526C2×D3—42no—
527C2×D3—42no—
528C2×D3—42no—
529C3×C4—24no—
530C3×C4—24no—
531C3×C4—42no—
532C3×C4—42no—
533C3×C4—42no—
534C3×C4—42no—
535C3×C4—64no—
536C3×C4—122no—
537Dic3—24no—
538Dic3—38no—
539Dic3—38no—
540Dic3—42no—
541Dic3—64no—
542Dic3—64no—
543Dic3—64no—
544Dic3—122no—
545Dic3—122no—
546Dic3—122no—
547C32#236611yescharacteristic, complemented, Sylow
548C23—34no—
549C23—34no—
550C23—62no—
551C23—62no—
552C23—62no—
553C23—62no—
554C23—62no—
555C23—62no—
556C23—62no—
557C23—62no—
558C23—62no—
559C23—62no—
560C23—62no—
561C23—62no—
562C23C22×D3211yescharacteristic
563D4—128no—
564D4—188no—
565D4—188no—
566D4—1816no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—34no—
575C2×C4—62no—
576C2×C4—62no—
577C2×C4—62no—
578C2×C4—62no—
579C2×C4—62no—
580C2×C4—92no—
581C2×C4—92no—
582C2×C4—92no—
583C2×C4—92no—
584C2×C4—92no—
585C2×C4—92no—
586C2×C4—92no—
587C2×C4—128no—
588C2×C4—181no—
589C2×C4—181no—
590C2×C4—181no—
591C2×C4—181no—
592C2×C4—181no—
593C2×C4—368no—
594C2×C4C4×D3212yes—
595C2×C4#380212yes—
596C2×C3—21no—
597C2×C3—21no—
598C2×C3—21no—
599C2×C3—21no—
600C2×C3—21no—
601C2×C3—21no—
602C2×C3—21no—
603C2×C3—124no—
604C2×C3—124no—
605C2×C3#548612yes—
606C2×C3C4×D3×D412yes—
607C2×C3C4×D3×D412yes—
608C2×C3#559012yes—
609C2×C3#559912yes—
610C2×C3#559912yes—
611C2×C3#566412yes—
612D3—44no—
613D3—44no—
614C22—64no—
615C22—64no—
616C22—64no—
617C22—64no—
618C22—64no—
619C22—64no—
620C22—122no—
621C22—122no—
622C22—122no—
623C22—122no—
624C22—122no—
625C22—122no—
626C22—122no—
627C22—122no—
628C22C2×C4×D3211yescharacteristic
629C22C2×#380211yescharacteristic
630C22#6430611yescharacteristic
631C22D32×D411yescharacteristic
632C22#6431311yescharacteristic
633C22#6431311yescharacteristic
634C22#6431911yescharacteristic
635C4—22no—
636C4—22no—
637C4—41no—
638C4—64no—
639C4—94no—
640C4—94no—
641C4—122no—
642C4—182no—
643C4—361no—
644C3—21no—
645C3#7467912yescomplemented
646C2—124no—
647C2—124no—
648C2C4×#380211yescharacteristic
649C2#1059418111yescharacteristic
650C2#1059419011yescharacteristic
651C2#1059427111yescharacteristic
652C2#1059452711yescharacteristic
653C2#1059457011yescharacteristic
654C2#1059460511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC2×#63914C2
hypercenter#95D32
hypocenterC32#2366
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C2×#63902C2semidirect
3. C2×C4×#625C2semidirect
4. C2×#63879C2semidirect
5. #10592348C2semidirect
6. C3×#4665C2semidirect
7. #10591386C2semidirect
8. #10591385C2semidirect
9. #10591385C2semidirect
10. #10591376C2semidirect
11. #10591257C2semidirect
33. #63914C4semidirect
52. #4665D3semidirect
69. C2×C3×D12C2×C4semidirect
79. C2×#625C2×C4semidirect
80. C2×#625C2×C4semidirect
81. C2×#625C2×C4semidirect
86. #3750D4semidirect
89. C4×C3⋊Dic3C2×C4semidirect
94. #3724D4semidirect
251. C2×D12C4×D3semidirect
310. C3⋊Dic3C4×D4semidirect
311. C3⋊Dic3C4×D4semidirect
547. C32#2366semidirect
645. C3#74679semidirect

Maximal subgroups

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

subgroupindex
C2×#639142
C2×#639022
C2×C4×#6252
C2×#638792
#105923482
C3×#46652
#105913862
#105913852
#105913762
#105912572
#746793