Finite Group Databasebeta

← #11803858

Subgroups — #11803858

Order 1152.

1693 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64090C211yesmaximal, characteristic, complemented
2C2×#63979C211yesmaximal, characteristic
3C2×C4×#625C211yesmaximal, characteristic, complemented
4C3×#4956C212yesmaximal, complemented
5#10591713C212yesmaximal, complemented
6#10591704C211yesmaximal, characteristic, complemented
7#10591387C212yesmaximal, complemented
8#10591386C211yesmaximal, characteristic, complemented
9#10591382C212yesmaximal, complemented
10#10591252C211yesmaximal, characteristic, complemented
11#10591247C211yesmaximal, characteristic, complemented
12#74667—32nomaximal
13C22×#638C2211yescharacteristic
14C23×C3⋊Dic3C2211yescharacteristic
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×C3×#67C2212yes—
17C22×C3×C4×D3C2212yes—
18C22×#626C2212yes—
19C22×#625C2211yescharacteristic
20C2×C32×C22⋊C4C2211yescharacteristic
21C2×#3752C2211yescharacteristic
22C2×#3750C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24#64090—24no—
25C2×C3×#217C2212yes—
26C2×C3×(C2×D3)⋊C4C2212yes—
27#63979C418yescomplemented
28C2×#3724C2211yescharacteristic
29C2×#3722C2212yes—
30C2×(C2×D3)⋊Dic3C2212yes—
31C2×(C2×D3)⋊Dic3C2212yes—
32C2×Dic32C2211yescharacteristic
33C2×Dic32C2211yescharacteristic
34C4×#625—24no—
35C3×C3⋊#95C2212yes—
36C3×C3⋊#95C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39C2×#940—32no—
40C2×C4×#67—32no—
41C2×#67⋊C4—32no—
42C2×#67⋊C4—61no—
43C3×#386—32no—
44#5220—32no—
45#5213—32no—
46#4958—32no—
47#4957—32no—
48#4957—32no—
49#4956—32no—
50#4956D312yescomplemented
51#4665—32no—
52#4665—32no—
53#4650—32no—
54#4648—32no—
55C24×C32C2311yescharacteristic
56C23×C3⋊D3C2311yescharacteristic
57C23×C3×D3C2312yes—
58C22×C32×C4C2311yescharacteristic
59C22×C32×C4C2311yescharacteristic
60C2×#638—22no—
61C2×#638—22no—
62C2×#638C2×C414yescomplemented
63C22×C3⋊Dic3—22no—
64C22×C3⋊Dic3—42no—
65C22×C3⋊Dic3C2311yescharacteristic
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3⋊Dic3C2311yescharacteristic
68C2×C4×C3⋊D3—22no—
69C2×C4×C3⋊D3—42no—
70C2×C3×#67—42no—
71C2×C3×#67—42no—
72C2×C3×#67C2×C418yescomplemented
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2312yes—
76C2×C3×C4×D3—24no—
77C2×C3×C4×D3—42no—
78C2×C3×C4×D3—42no—
79C2×#626—42no—
80C2×#626—42no—
81C2×#626C2×C418yescomplemented
82C2×#625—22no—
83C2×#625—22no—
84C2×#625C2×C414yescomplemented
85C32×C22⋊C4—22no—
86#3752—22no—
87#3750—22no—
88C4×C3⋊Dic3D414yescomplemented
89C3×#217—42no—
90C3×(C2×D3)⋊C4—42no—
91#3724—22no—
92#3722—42no—
93(C2×D3)⋊Dic3—24no—
94(C2×D3)⋊Dic3—42no—
95Dic32—22no—
96Dic32C2×C414yescomplemented
97#2328—91noSylow
98C22×C3×D4—32no—
99C23×C3×C4—32no—
100C22×#67—32no—
101C22×#67—32no—
102C22×#67—32no—
103C22×#67—61no—
104C22×#67C2×D312yes—
105C23×Dic3—32no—
106C23×Dic3—61no—
107C22×D12—32no—
108C22×C4×D3—32no—
109C22×C4×D3—61no—
110C22×C4×D3C2×D312yes—
111C2×C3×C22⋊C4—21no—
112C2×C3×C22⋊C4—32no—
113C2×C3×C22⋊C4—32no—
114C2×C3×C22⋊C4C2×D312yes—
115C2×#217—32no—
116C2×#217—32no—
117C2×#217C2×D312yes—
118#940—316no—
119C4×#67—68no—
120C2×(C2×D3)⋊C4—32no—
121C2×(C2×D3)⋊C4—32no—
122C2×(C2×D3)⋊C4—32no—
123C2×(C2×D3)⋊C4—32no—
124C2×(C2×D3)⋊C4—32no—
125C2×(C2×D3)⋊C4—61no—
126C2×(C2×D3)⋊C4C2×D312yes—
127C2×Dic3⋊C4—32no—
128C2×Dic3⋊C4—32no—
129C2×Dic3⋊C4—61no—
130C2×C4×Dic3—32no—
131C2×C4×Dic3—32no—
132C2×C4×Dic3—32no—
133C2×C4×Dic3—61no—
134#67⋊C4—68no—
135#67⋊C4—68no—
136C3×#95—32no—
137C3×#95—32no—
138C3⋊#95—32no—
139C3⋊#95—32no—
140C3⋊#95—32no—
141C3⋊#95—32no—
142C3⋊#95C2×D312yes—
143C3⋊#95C2×D312yes—
144C23×C32—21no—
145C23×C32—21no—
146C23×C32—22no—
147C23×C32—22no—
148C23×C32C22×C412yes—
149C23×C32C2411yescharacteristic
150C22×C3⋊D3—21no—
151C22×C3⋊D3—21no—
152C22×C3⋊D3—22no—
153C22×C3⋊D3—22no—
154C22×C3⋊D3C22×C412yes—
155C22×C3×D3—22no—
156C22×C3×D3—22no—
157C22×C3×D3—22no—
158C22×C3×D3—22no—
159C22×C3×D3—22no—
160C22×C3×D3—22no—
161C22×C3×D3C22×C414yes—
162C2×C32×C4—21no—
163C2×C32×C4—22no—
164C2×C32×C4—22no—
165C2×C32×C4C2×D412yes—
166#638—28no—
167C2×C3⋊Dic3—22no—
168C2×C3⋊Dic3—21no—
169C2×C3⋊Dic3—22no—
170C2×C3⋊Dic3—44no—
171C2×C3⋊Dic3C22×C412yes—
172C2×C3⋊Dic3C2×D412yes—
173C2×C3⋊Dic3C2×D412yes—
174C2×C3⋊Dic3#4112yes—
175C4×C3⋊D3—44no—
176C3×#67—48no—
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×Dic3—22no—
185C2×C3×Dic3C22×C414yes—
186C3×C4×D3—48no—
187#626—48no—
188#625—28no—
189C2×#127—91no—
190C2×C4×D4—91no—
191C2×C4×D4—91no—
192#390—91no—
193#390—91no—
194#386—32no—
195#386—92no—
196#386—92no—
197#386—92no—
198#382—91no—
199#376—91no—
200C24×C3—21no—
201C24×C3—32no—
202C24×C3C22×D312yes—
203C23×D3—32no—
204C23×D3—61no—
205C23×D3C22×D312yes—
206C2×C3×D4—38no—
207C2×C3×D4—122no—
208C2×C3×D4—122no—
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—32no—
212C22×C3×C4—32no—
213C22×C3×C4—32no—
214C22×C3×C4—64no—
215C22×C3×C4—122no—
216C22×C3×C4—122no—
217C22×C3×C4C22×D312yes—
218C22×C3×C4C22×D312yes—
219C2×#67—38no—
220C2×#67—38no—
221C2×#67—38no—
222C2×#67—42no—
223C2×#67—42no—
224C2×#67—64no—
225C2×#67—64no—
226C2×#67—64no—
227C2×#67—64no—
228C2×#67—64no—
229C2×#67—64no—
230C2×#67—64no—
231C2×#67—122no—
232C2×#67—122no—
233C2×#67C4×D318yescomplemented
234C22×Dic3—32no—
235C22×Dic3—32no—
236C22×Dic3—32no—
237C22×Dic3—61no—
238C22×Dic3—61no—
239C22×Dic3—61no—
240C22×Dic3—64no—
241C22×Dic3—64no—
242C22×Dic3—122no—
243C22×Dic3—122no—
244C22×Dic3—124no—
245C22×Dic3C22×D312yes—
246C22×Dic3C22×D312yes—
247C22×Dic3C22×D312yes—
248C2×D12—38no—
249C2×D12—122no—
250C2×D12—122no—
251C2×C4×D3—24no—
252C2×C4×D3—42no—
253C2×C4×D3—42no—
254C2×C4×D3—64no—
255C2×C4×D3—64no—
256C2×C4×D3—122no—
257C2×C4×D3—122no—
258C2×C4×D3—124no—
259C3×C22⋊C4—24no—
260C3×C22⋊C4—24no—
261C3×C22⋊C4—122no—
262C3×C22⋊C4—122no—
263#217—42no—
264#217—64no—
265#217—122no—
266(C2×D3)⋊C4—42no—
267(C2×D3)⋊C4—64no—
268(C2×D3)⋊C4—64no—
269(C2×D3)⋊C4—64no—
270(C2×D3)⋊C4—122no—
271(C2×D3)⋊C4—122no—
272(C2×D3)⋊C4—122no—
273Dic3⋊C4—64no—
274Dic3⋊C4—64no—
275Dic3⋊C4—64no—
276C4×Dic3—38no—
277C4×Dic3—38no—
278C4×Dic3—64no—
279C4×Dic3—64no—
280C22×C32—22no—
281C22×C32—24no—
282C22×C32—41no—
283C22×C32—41no—
284C22×C32—42no—
285C22×C32C23×C411yescharacteristic
286C22×C32C22×D411yescharacteristic
287C22×C32C2×#4111yescharacteristic
288C22×C32H(5,𝔽2)12yes—
289C22×C32H(5,𝔽2)12yes—
290C2×C3⋊D3—22no—
291C2×C3⋊D3—24no—
292C2×C3⋊D3—41no—
293C2×C3⋊D3—41no—
294C2×C3⋊D3—42no—
295C2×C3×D3—24no—
296C2×C3×D3—24no—
297C2×C3×D3—24no—
298C2×C3×D3—42no—
299C2×C3×D3—42no—
300C2×C3×D3—42no—
301C2×C3×D3—42no—
302C32×C4—22no—
303C32×C4—41no—
304C3⋊Dic3—22no—
305C3⋊Dic3—41no—
306C3⋊Dic3C4×D414yes—
307C3×Dic3—24no—
308C3×Dic3—42no—
309C3×Dic3—42no—
310C22×D4—32no—
311C22×D4—92no—
312C22×D4—91no—
313C22×D4—91no—
314C23×C4—32no—
315C23×C4—91no—
316C23×C4—91no—
317#127—98no—
318C4×D4—184no—
319C4×D4—184no—
320C2×C4⋊C4—91no—
321C2×C4⋊C4—91no—
322C2×C22⋊C4—32no—
323C2×C22⋊C4—32no—
324C2×C22⋊C4—92no—
325C2×C22⋊C4—91no—
326C2×C22⋊C4—92no—
327C2×C22⋊C4—92no—
328C2×C22⋊C4D3211yescharacteristic
329C2×C42—91no—
330C2×C42—91no—
331C2×C42—91no—
332#95—32no—
333#95—32no—
334#95—92no—
335#95—92no—
336C23×C3—22no—
337C23×C3—22no—
338C23×C3—22no—
339C23×C3—22no—
340C23×C3—22no—
341C23×C3—22no—
342C23×C3—22no—
343C23×C3—22no—
344C23×C3—21no—
345C23×C3—22no—
346C23×C3—34no—
347C23×C3—42no—
348C23×C3—42no—
349C23×C3—62no—
350C23×C3—62no—
351C23×C3—62no—
352C23×C3—62no—
353C23×C3—62no—
354C23×C3—62no—
355C23×C3C2×C4×D314yes—
356C23×C3C23×D312yes—
357C22×D3—22no—
358C22×D3—22no—
359C22×D3—22no—
360C22×D3—22no—
361C22×D3—22no—
362C22×D3—22no—
363C22×D3—34no—
364C22×D3—62no—
365C22×D3—62no—
366C22×D3—62no—
367C22×D3—62no—
368C22×D3—62no—
369C22×D3—62no—
370C22×D3—62no—
371C22×D3—62no—
372C22×D3—62no—
373C22×D3—122no—
374C22×D3—122no—
375C22×D3C2×C4×D314yes—
376C3×D4—128no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—22no—
384C2×C3×C4—34no—
385C2×C3×C4—42no—
386C2×C3×C4—42no—
387C2×C3×C4—62no—
388C2×C3×C4—62no—
389C2×C3×C4—62no—
390C2×C3×C4—62no—
391C2×C3×C4—62no—
392C2×C3×C4—62no—
393C2×C3×C4—62no—
394C2×C3×C4—62no—
395C2×C3×C4—128no—
396C2×C3×C4D3×D414yes—
397#67—48no—
398#67—616no—
399#67—616no—
400#67—616no—
401#67—128no—
402C2×Dic3—22no—
403C2×Dic3—22no—
404C2×Dic3—22no—
405C2×Dic3—22no—
406C2×Dic3—22no—
407C2×Dic3—22no—
408C2×Dic3—22no—
409C2×Dic3—22no—
410C2×Dic3—34no—
411C2×Dic3—34no—
412C2×Dic3—34no—
413C2×Dic3—34no—
414C2×Dic3—62no—
415C2×Dic3—62no—
416C2×Dic3—62no—
417C2×Dic3—62no—
418C2×Dic3—64no—
419C2×Dic3—62no—
420C2×Dic3—62no—
421C2×Dic3—62no—
422C2×Dic3—62no—
423C2×Dic3—62no—
424C2×Dic3—62no—
425C2×Dic3—122no—
426C2×Dic3—128no—
427C2×Dic3—128no—
428C2×Dic3C2×C4×D314yes—
429D12—128no—
430C4×D3—48no—
431C4×D3—128no—
432C4×D3—128no—
433C2×C32—42no—
434C2×C32C2×C4×D411yescharacteristic
435C2×C32#51812yes—
436C2×C32#53511yescharacteristic
437C2×C32#53511yescharacteristic
438C2×C32#54012yes—
439C3⋊D3—42no—
440C3×D3—44no—
441C24—32no—
442C24—91no—
443C24C2×D3211yescharacteristic
444C2×D4—38no—
445C2×D4—98no—
446C2×D4—94no—
447C2×D4—94no—
448C2×D4—122no—
449C2×D4—122no—
450C2×D4—182no—
451C2×D4—182no—
452C2×D4—182no—
453C2×D4—182no—
454C2×D4—362no—
455C2×D4—362no—
456C22×C4—32no—
457C22×C4—32no—
458C22×C4—32no—
459C22×C4—64no—
460C22×C4—91no—
461C22×C4—91no—
462C22×C4—91no—
463C22×C4—122no—
464C22×C4—122no—
465C22×C4—182no—
466C22×C4—182no—
467C22×C4—362no—
468C22×C4—362no—
469C22×C4C2×D3211yescharacteristic
470C22×C4C2×D3211yescharacteristic
471C4⋊C4—182no—
472C4⋊C4—182no—
473C22⋊C4—22no—
474C22⋊C4—122no—
475C22⋊C4—122no—
476C22⋊C4—184no—
477C22⋊C4—182no—
478C22⋊C4—362no—
479C22⋊C4—362no—
480C42—94no—
481C42—94no—
482C42—182no—
483C22×C3—24no—
484C22×C3—24no—
485C22×C3—24no—
486C22×C3—24no—
487C22×C3—21no—
488C22×C3—21no—
489C22×C3—22no—
490C22×C3—22no—
491C22×C3—21no—
492C22×C3—44no—
493C22×C3—42no—
494C22×C3—44no—
495C22×C3—42no—
496C22×C3—42no—
497C22×C3—42no—
498C22×C3—42no—
499C22×C3—42no—
500C22×C3—64no—
501C22×C3—64no—
502C22×C3—64no—
503C22×C3—122no—
504C22×C3—122no—
505C22×C3—122no—
506C22×C3—122no—
507C22×C3C22×C4×D312yes—
508C22×C3C2×D3×D412yes—
509C22×C3#100412yes—
510C22×C3#100412yes—
511C22×C3#100412yes—
512C22×C3D3×#4112yes—
513C22×C3#100912yes—
514C2×D3—24no—
515C2×D3—24no—
516C2×D3—24no—
517C2×D3—42no—
518C2×D3—42no—
519C2×D3—42no—
520C2×D3—42no—
521C2×D3—64no—
522C2×D3—64no—
523C2×D3—64no—
524C2×D3—64no—
525C2×D3—124no—
526C2×D3—122no—
527C2×D3—124no—
528C2×D3—122no—
529C2×D3—122no—
530C2×D3—122no—
531C2×D3—122no—
532C2×D3—122no—
533C3×C4—24no—
534C3×C4—42no—
535C3×C4—42no—
536C3×C4—42no—
537C3×C4—64no—
538C3×C4—122no—
539C3×C4—122no—
540Dic3—24no—
541Dic3—38no—
542Dic3—42no—
543Dic3—42no—
544Dic3—64no—
545Dic3—64no—
546Dic3—64no—
547Dic3—122no—
548Dic3—122no—
549C32#232811yescharacteristic, complemented, Sylow
550C23—21no—
551C23—22no—
552C23—22no—
553C23—21no—
554C23—34no—
555C23—62no—
556C23—62no—
557C23—62no—
558C23—62no—
559C23—62no—
560C23—62no—
561C23—92no—
562C23—181no—
563C23—182no—
564C23—182no—
565C23—181no—
566C23C4×D3212yes—
567C23C22×D3211yescharacteristic
568D4—128no—
569D4—188no—
570D4—188no—
571D4—368no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—21no—
575C2×C4—34no—
576C2×C4—62no—
577C2×C4—62no—
578C2×C4—62no—
579C2×C4—62no—
580C2×C4—62no—
581C2×C4—62no—
582C2×C4—62no—
583C2×C4—62no—
584C2×C4—92no—
585C2×C4—92no—
586C2×C4—92no—
587C2×C4—92no—
588C2×C4—128no—
589C2×C4—182no—
590C2×C4—182no—
591C2×C4—181no—
592C2×C4—364no—
593C2×C4—364no—
594C2×C4#381112yes—
595C2×C3—22no—
596C2×C3—21no—
597C2×C3—21no—
598C2×C3—22no—
599C2×C3—21no—
600C2×C3—44no—
601C2×C3—44no—
602C2×C3—124no—
603C2×C3#548612yes—
604C2×C3C4×D3×D412yes—
605C2×C3#554512yes—
606C2×C3#559212yes—
607C2×C3#560712yes—
608C2×C3#561512yes—
609C2×C3#566312yes—
610D3—44no—
611D3—124no—
612D3—124no—
613C22—24no—
614C22—22no—
615C22—42no—
616C22—41no—
617C22—41no—
618C22—64no—
619C22—64no—
620C22—64no—
621C22—122no—
622C22—122no—
623C22—122no—
624C22—122no—
625C22—184no—
626C22—182no—
627C22—362no—
628C22—361no—
629C22—361no—
630C22C2×C4×D3211yescharacteristic
631C22#6430611yescharacteristic
632C22#6431312yes—
633C22#6431412yes—
634C22C2×#381111yescharacteristic
635C4—22no—
636C4—41no—
637C4—64no—
638C4—94no—
639C4—122no—
640C4—122no—
641C4—182no—
642C4—361no—
643C3—21no—
644C3#7466712yescomplemented
645C2—42no—
646C2—124no—
647C2—362no—
648C2#1059415112yes—
649C2#1059425412yes—
650C2C4×#381111yescharacteristic
651C2#1059523911yescharacteristic
652C2#1059524111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63979C2
hypercenterC2×C22⋊C4D32
hypocenterC32#2328
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64090C2semidirect
3. C2×C4×#625C2semidirect
4. C3×#4956C2semidirect
5. #10591713C2semidirect
6. #10591704C2semidirect
7. #10591387C2semidirect
8. #10591386C2semidirect
9. #10591382C2semidirect
10. #10591252C2semidirect
11. #10591247C2semidirect
27. #63979C4semidirect
50. #4956D3semidirect
62. C2×#638C2×C4semidirect
72. C2×C3×#67C2×C4semidirect
81. C2×#626C2×C4semidirect
84. C2×#625C2×C4semidirect
88. C4×C3⋊Dic3D4semidirect
96. Dic32C2×C4semidirect
233. C2×#67C4×D3semidirect
549. C32#2328semidirect
644. C3#74667semidirect

Maximal subgroups

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

subgroupindex
C2×#640902
C2×#639792
C2×C4×#6252
C3×#49562
#105917132
#105917042
#105913872
#105913862
#105913822
#105912522
#105912472
#746673