Finite Group Databasebeta

← #11808228

Subgroups — #11808228

Order 1152.

2101 conjugacy classes of subgroups.

The subgroup lattice has 669 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3805C211yesmaximal, characteristic, complemented
2C2×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C2×#67⋊Dic3C212yesmaximal, complemented
4C3×#5223C212yesmaximal, complemented
5#10591723C211yesmaximal, characteristic, complemented
6#10591709C212yesmaximal, complemented
7#10591705C211yesmaximal, characteristic, complemented
8#10591692C211yesmaximal, characteristic, complemented
9#10591397C211yesmaximal, characteristic, complemented
10#10591394C211yesmaximal, characteristic, complemented
11#10591368C212yesmaximal, complemented
12#76665—32nomaximal
13C22×C32×D4C2211yescharacteristic
14C23×C3⋊Dic3C2211yescharacteristic
15C23×C3⋊Dic3C2211yescharacteristic
16C22×C3×#67C2212yes—
17C22×C3×#67C2212yes—
18C22×#627C2211yescharacteristic
19C22×#625C2211yescharacteristic
20C2×#3805—24no—
21C2×#3805—28no—
22C22×D3×Dic3C2212yes—
23C2×#3757C2211yescharacteristic
24C2×#3757C2211yescharacteristic
25D4×C3⋊Dic3—24no—
26C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
27C2×C4×C3⋊Dic3C2211yescharacteristic
28C2×C3×#217C2212yes—
29C2×C3×#217C2212yes—
30C2×C3×(C2×D3)⋊C4C2212yes—
31#67⋊Dic3—28no—
32C2×Dic3⋊Dic3C2212yes—
33C2×(C2×D3)⋊Dic3C2212yes—
34C2×(C2×D3)⋊Dic3C2212yes—
35C2×Dic32C2212yes—
36C3×C3⋊#95C2212yes—
37#63579C2212yes—
38#63579C2211yescharacteristic
39#63579C2211yescharacteristic
40C22×#237—32no—
41C2×D4×Dic3—32no—
42C2×D4×Dic3—32no—
43C2×D4×Dic3—61no—
44C2×#67⋊C4—32no—
45C3×#392—32no—
46#5223—32no—
47#5223D312yescomplemented
48#5222—32no—
49#4961—32no—
50#4961—32no—
51#4947—32no—
52Dic3×C22⋊C4—32no—
53Dic3×C22⋊C4—32no—
54#4666—32no—
55#4656—32no—
56C24×C32C2311yescharacteristic
57C24×C32C2311yescharacteristic
58C23×C3×D3C2312yes—
59C2×C32×D4—22no—
60C2×C32×D4—22no—
61C2×C32×D4—22no—
62C22×C32×C4C2311yescharacteristic
63C22×C3⋊Dic3—24no—
64C22×C3⋊Dic3—22no—
65C22×C3⋊Dic3—24no—
66C22×C3⋊Dic3D414yescomplemented
67C22×C3⋊Dic3C2311yescharacteristic
68C22×C3⋊Dic3C2311yescharacteristic
69C22×C3⋊Dic3C2311yescharacteristic
70C22×C3⋊Dic3C2311yescharacteristic
71C2×C3×#67—24no—
72C2×C3×#67—24no—
73C2×C3×#67—24no—
74C2×C3×#67—24no—
75C2×C3×#67—24no—
76C2×C3×#67—24no—
77C22×C3×Dic3C2312yes—
78C22×C3×Dic3C2312yes—
79C22×C3×Dic3C2312yes—
80C2×#627—22no—
81C2×#627—24no—
82C2×#625—24no—
83C2×#625—22no—
84#3805—232no—
85C2×D3×Dic3—24no—
86C2×D3×Dic3—24no—
87C2×D3×Dic3D418yescomplemented
88#3757—22no—
89#3757—22no—
90C4⋊(C3⋊Dic3)—22no—
91C4×C3⋊Dic3—22no—
92C3×#217—24no—
93C3×#217—24no—
94C3×(C2×D3)⋊C4—24no—
95Dic3⋊Dic3—24no—
96(C2×D3)⋊Dic3—24no—
97(C2×D3)⋊Dic3—24no—
98Dic32—24no—
99#2388—91noSylow
100C22×C3×D4—21no—
101C22×C3×D4—32no—
102C22×C3×D4—32no—
103C22×C3×D4C2×D312yes—
104C22×#67—32no—
105C22×#67C2×D312yes—
106C22×#67C2×D312yes—
107C23×Dic3—32no—
108C23×Dic3—32no—
109C23×Dic3—32no—
110C23×Dic3—61no—
111C23×Dic3—61no—
112C2×#237—68no—
113C2×#237—68no—
114C2×#237—68no—
115C22×C4×D3—32no—
116C22×Dic6—32no—
117C2×C3×C22⋊C4—32no—
118C2×C3×C22⋊C4—32no—
119C2×C3×C22⋊C4—32no—
120C2×#217—32no—
121C2×#217—32no—
122C2×#217—32no—
123C2×#217—32no—
124C2×#217—61no—
125C2×#217—61no—
126C2×#217C2×D312yes—
127C2×#217C2×D312yes—
128D4×Dic3—68no—
129D4×Dic3—68no—
130D4×Dic3—68no—
131C2×(C2×D3)⋊C4—32no—
132C2×(C2×D3)⋊C4—32no—
133C2×(C2×D3)⋊C4C2×D312yes—
134C2×C4⋊Dic3—32no—
135C2×C4⋊Dic3—32no—
136C2×C4⋊Dic3—61no—
137C2×Dic3⋊C4—32no—
138C2×C4×Dic3—32no—
139C2×C4×Dic3—32no—
140C2×C4×Dic3—32no—
141C2×C4×Dic3—61no—
142#67⋊C4—68no—
143C3×#95—32no—
144C3⋊#95—32no—
145C3⋊#95—32no—
146C3⋊#95—32no—
147C3⋊#95—32no—
148C3⋊#95C2×D312yes—
149C23×C32—21no—
150C23×C32—21no—
151C23×C32—21no—
152C23×C32—21no—
153C23×C32—22no—
154C23×C32—22no—
155C23×C32—22no—
156C23×C32—22no—
157C23×C32C2×D412yes—
158C23×C32#4112yescomplemented
159C23×C32C2411yescharacteristic
160C22×C3×D3—22no—
161C22×C3×D3—22no—
162C22×C3×D3—22no—
163C22×C3×D3—22no—
164C22×C3×D3—22no—
165C22×C3×D3—22no—
166C22×C3×D3C2×D414yes—
167C32×D4—28no—
168C2×C32×C4—21no—
169C2×C32×C4—21no—
170C2×C32×C4#4112yescomplemented
171C2×C3⋊Dic3—21no—
172C2×C3⋊Dic3—21no—
173C2×C3⋊Dic3—22no—
174C2×C3⋊Dic3—28no—
175C2×C3⋊Dic3—22no—
176C2×C3⋊Dic3—22no—
177C2×C3⋊Dic3—44no—
178C2×C3⋊Dic3C2×D412yes—
179C2×C3⋊Dic3C2×D414yes—
180C2×C3⋊Dic3C2×D412yes—
181C3×#67—216no—
182C3×#67—216no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3C2×D414yes—
191C2×C3×Dic3#4114yescomplemented
192#627—28no—
193#625—28no—
194D3×Dic3—216no—
195C22×#41—91no—
196C2×C4×D4—92no—
197C2×C4×D4—91no—
198#395—91no—
199#394—91no—
200#394—92no—
201#393—91no—
202#392—32no—
203#392—91no—
204C4×C22⋊C4—92no—
205C4×C22⋊C4—91no—
206C24×C3—21no—
207C24×C3—21no—
208C24×C3—32no—
209C24×C3C22×D312yes—
210C24×C3C22×D312yes—
211C23×D3C22×D312yes—
212C2×C3×D4—24no—
213C2×C3×D4—24no—
214C2×C3×D4—24no—
215C2×C3×D4—24no—
216C2×C3×D4—24no—
217C2×C3×D4—24no—
218C2×C3×D4—64no—
219C2×C3×D4—64no—
220C2×C3×D4—64no—
221C2×C3×D4—64no—
222C2×C3×D4—64no—
223C2×C3×D4—64no—
224C22×C3×C4—21no—
225C22×C3×C4—32no—
226C22×C3×C4—32no—
227C22×C3×C4—32no—
228C22×C3×C4C22×D312yes—
229C2×#67—24no—
230C2×#67—24no—
231C2×#67—24no—
232C2×#67—24no—
233C2×#67—24no—
234C2×#67—24no—
235C2×#67—64no—
236C2×#67—64no—
237C2×#67—64no—
238C22×Dic3—32no—
239C22×Dic3—38no—
240C22×Dic3—32no—
241C22×Dic3—38no—
242C22×Dic3—32no—
243C22×Dic3—32no—
244C22×Dic3—61no—
245C22×Dic3—61no—
246C22×Dic3—61no—
247C22×Dic3—61no—
248C22×Dic3—64no—
249C22×Dic3—64no—
250C22×Dic3—64no—
251C22×Dic3—64no—
252C22×Dic3—64no—
253C22×Dic3—64no—
254C22×Dic3—64no—
255C22×Dic3—64no—
256C22×Dic3—64no—
257C22×Dic3—124no—
258C22×Dic3—124no—
259C22×Dic3C22×D312yes—
260C22×Dic3C22×D312yes—
261C22×Dic3C22×D312yes—
262#237—664no—
263C2×C4×D3—38no—
264C2×C4×D3—64no—
265C2×C4×D3—64no—
266C2×Dic6—64no—
267C2×Dic6—64no—
268C2×Dic6—64no—
269C3×C22⋊C4—64no—
270C3×C22⋊C4—64no—
271C3×C22⋊C4—64no—
272#217—24no—
273#217—24no—
274#217—64no—
275#217—64no—
276#217—64no—
277#217—64no—
278#217—64no—
279#217—64no—
280(C2×D3)⋊C4—24no—
281(C2×D3)⋊C4—64no—
282(C2×D3)⋊C4—64no—
283C4⋊Dic3—64no—
284C4⋊Dic3—64no—
285C4⋊Dic3—64no—
286Dic3⋊C4—64no—
287C4×Dic3—64no—
288C4×Dic3—64no—
289C4×Dic3—64no—
290C4×Dic3—64no—
291C22×C32—22no—
292C22×C32—22no—
293C22×C32—22no—
294C22×C32—24no—
295C22×C32—22no—
296C22×C32—41no—
297C22×C32—42no—
298C22×C32—42no—
299C22×C32—42no—
300C22×C32—41no—
301C22×C32C22×D412yes—
302C22×C32C22×D411yescharacteristic
303C22×C32C2×#4111yescharacteristic
304C22×C32C2×#4111yescharacteristic
305C22×C32C2×#4112yes—
306C2×C3×D3—24no—
307C2×C3×D3—24no—
308C2×C3×D3—24no—
309C2×C3×D3—42no—
310C2×C3×D3—42no—
311C2×C3×D3—42no—
312C2×C3×D3—42no—
313C32×C4—22no—
314C3⋊Dic3—22no—
315C3⋊Dic3—41no—
316C3⋊Dic3—41no—
317C3⋊Dic3#12014yes—
318C3×Dic3—24no—
319C3×Dic3—24no—
320C3×Dic3—42no—
321C2×#41—188no—
322C2×#41—184no—
323C22×Q8—91no—
324C22×D4—32no—
325C22×D4—32no—
326C22×D4—91no—
327C22×D4D3211yescharacteristic
328C23×C4—92no—
329C23×C4—91no—
330C23×C4—91no—
331C4×D4—188no—
332C4×D4—184no—
333C2×C4⋊C4—92no—
334C2×C4⋊C4—91no—
335C2×C22⋊C4—32no—
336C2×C22⋊C4—32no—
337C2×C22⋊C4—32no—
338C2×C22⋊C4—92no—
339C2×C22⋊C4—92no—
340C2×C22⋊C4—91no—
341C2×C22⋊C4—91no—
342C2×C42—92no—
343C2×C42—91no—
344#95—32no—
345#95—91no—
346#95—92no—
347#95—91no—
348C23×C3—22no—
349C23×C3—22no—
350C23×C3—22no—
351C23×C3—22no—
352C23×C3—22no—
353C23×C3—22no—
354C23×C3—22no—
355C23×C3—22no—
356C23×C3—22no—
357C23×C3—22no—
358C23×C3—22no—
359C23×C3—22no—
360C23×C3—22no—
361C23×C3—22no—
362C23×C3—22no—
363C23×C3—22no—
364C23×C3—21no—
365C23×C3—22no—
366C23×C3—22no—
367C23×C3—34no—
368C23×C3—42no—
369C23×C3—42no—
370C23×C3—42no—
371C23×C3—42no—
372C23×C3—62no—
373C23×C3—62no—
374C23×C3—62no—
375C23×C3—62no—
376C23×C3—62no—
377C23×C3—62no—
378C23×C3D3×D414yes—
379C23×C3#23714yescomplemented
380C23×C3C23×D312yes—
381C22×D3—22no—
382C22×D3—22no—
383C22×D3—22no—
384C22×D3—22no—
385C22×D3—22no—
386C22×D3—22no—
387C22×D3D3×D414yes—
388C3×D4—216no—
389C3×D4—216no—
390C3×D4—616no—
391C3×D4—616no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—34no—
398C2×C3×C4—34no—
399C2×C3×C4—62no—
400C2×C3×C4—62no—
401C2×C3×C4—62no—
402C2×C3×C4—62no—
403C2×C3×C4—62no—
404C2×C3×C4—62no—
405C2×C3×C4—62no—
406C2×C3×C4#23714yescomplemented
407#67—216no—
408#67—216no—
409#67—616no—
410C2×Dic3—22no—
411C2×Dic3—22no—
412C2×Dic3—22no—
413C2×Dic3—22no—
414C2×Dic3—22no—
415C2×Dic3—22no—
416C2×Dic3—22no—
417C2×Dic3—34no—
418C2×Dic3—34no—
419C2×Dic3—34no—
420C2×Dic3—34no—
421C2×Dic3—62no—
422C2×Dic3—64no—
423C2×Dic3—62no—
424C2×Dic3—616no—
425C2×Dic3—616no—
426C2×Dic3—62no—
427C2×Dic3—62no—
428C2×Dic3—62no—
429C2×Dic3—62no—
430C2×Dic3—62no—
431C2×Dic3—62no—
432C2×Dic3—62no—
433C2×Dic3—62no—
434C2×Dic3—62no—
435C2×Dic3—62no—
436C2×Dic3—128no—
437C2×Dic3—122no—
438C2×Dic3—122no—
439C2×Dic3—122no—
440C2×Dic3—128no—
441C2×Dic3—128no—
442C2×Dic3D3×D414yes—
443C2×Dic3#23714yescomplemented
444C4×D3—616no—
445Dic6—616no—
446C2×C32—42no—
447C2×C32—42no—
448C2×C32C2×#12011yescharacteristic
449C2×C32#52511yescharacteristic
450C2×C32#52512yes—
451C2×C32#53212yes—
452C2×C32#53211yescharacteristic
453C3×D3—44no—
454C24—32no—
455C24C2×D3211yescharacteristic
456C24C2×D3211yescharacteristic
457#41—1832no—
458C2×Q8—184no—
459C2×Q8—182no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—64no—
464C2×D4—64no—
465C2×D4—64no—
466C2×D4—64no—
467C2×D4—64no—
468C2×D4—64no—
469C2×D4—182no—
470C2×D4—184no—
471C22×C4—32no—
472C22×C4—32no—
473C22×C4—32no—
474C22×C4—98no—
475C22×C4—91no—
476C22×C4—91no—
477C22×C4—94no—
478C22×C4—91no—
479C22×C4—91no—
480C22×C4—184no—
481C22×C4—184no—
482C22×C4—184no—
483C22×C4—182no—
484C22×C4—184no—
485C22×C4C2×D3211yescharacteristic
486C4⋊C4—182no—
487C4⋊C4—184no—
488C22⋊C4—64no—
489C22⋊C4—64no—
490C22⋊C4—64no—
491C22⋊C4—184no—
492C22⋊C4—184no—
493C22⋊C4—182no—
494C22⋊C4—182no—
495C42—182no—
496C42—184no—
497C22×C3—24no—
498C22×C3—24no—
499C22×C3—24no—
500C22×C3—24no—
501C22×C3—24no—
502C22×C3—24no—
503C22×C3—24no—
504C22×C3—24no—
505C22×C3—22no—
506C22×C3—22no—
507C22×C3—21no—
508C22×C3—21no—
509C22×C3—21no—
510C22×C3—42no—
511C22×C3—44no—
512C22×C3—42no—
513C22×C3—42no—
514C22×C3—44no—
515C22×C3—44no—
516C22×C3—44no—
517C22×C3—42no—
518C22×C3—42no—
519C22×C3—42no—
520C22×C3—42no—
521C22×C3—42no—
522C22×C3—42no—
523C22×C3—42no—
524C22×C3—42no—
525C22×C3—42no—
526C22×C3—64no—
527C22×C3—64no—
528C22×C3—64no—
529C22×C3—122no—
530C22×C3—122no—
531C22×C3—122no—
532C22×C3—122no—
533C22×C3C2×D3×D412yes—
534C22×C3C2×D3×D412yes—
535C22×C3C2×D3×D412yes—
536C22×C3C2×#23712yes—
537C22×C3C2×#23712yes—
538C22×C3C2×#23712yes—
539C22×C3D3×#4112yes—
540C2×D3—24no—
541C2×D3—24no—
542C2×D3—24no—
543C2×D3—42no—
544C2×D3—42no—
545C2×D3—42no—
546C2×D3—42no—
547C3×C4—24no—
548C3×C4—24no—
549C3×C4—64no—
550C3×C4—64no—
551C3×C4—122no—
552Dic3—24no—
553Dic3—24no—
554Dic3—38no—
555Dic3—42no—
556Dic3—64no—
557Dic3—64no—
558Dic3—122no—
559Dic3—122no—
560Dic3—122no—
561Dic3—122no—
562Dic3—122no—
563C32#238811yescharacteristic, complemented, Sylow
564C23—22no—
565C23—22no—
566C23—22no—
567C23—22no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—34no—
573C23—62no—
574C23—62no—
575C23—62no—
576C23—62no—
577C23—62no—
578C23—62no—
579C23#380512yescomplemented
580C23#381112yes—
581C23C22×D3211yescharacteristic
582Q8—188no—
583D4—28no—
584D4—616no—
585D4—616no—
586D4—188no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—34no—
590C2×C4—34no—
591C2×C4—62no—
592C2×C4—62no—
593C2×C4—62no—
594C2×C4—62no—
595C2×C4—62no—
596C2×C4—62no—
597C2×C4—62no—
598C2×C4—94no—
599C2×C4—92no—
600C2×C4—92no—
601C2×C4—1816no—
602C2×C4—188no—
603C2×C4—182no—
604C2×C4—182no—
605C2×C4—182no—
606C2×C4—181no—
607C2×C4—181no—
608C2×C4—364no—
609C2×C4#380512yescomplemented
610C2×C3—22no—
611C2×C3—22no—
612C2×C3—21no—
613C2×C3—21no—
614C2×C3—21no—
615C2×C3—44no—
616C2×C3—44no—
617C2×C3—44no—
618C2×C3—44no—
619C2×C3—124no—
620C2×C3#558612yes—
621C2×C3#558612yes—
622C2×C3D3×#12012yes—
623C2×C3#559612yes—
624C2×C3#559612yes—
625C2×C3#560612yes—
626C2×C3#571612yes—
627D3—44no—
628C22—24no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—22no—
633C22—42no—
634C22—42no—
635C22—42no—
636C22—41no—
637C22—41no—
638C22—64no—
639C22—64no—
640C22—64no—
641C22—122no—
642C22—122no—
643C22—122no—
644C22—122no—
645C22D32×D412yes—
646C22D3×#23712yes—
647C22C2×#380511yescharacteristic
648C22C2×#380511yescharacteristic
649C22C2×#381111yescharacteristic
650C4—22no—
651C4—64no—
652C4—64no—
653C4—94no—
654C4—122no—
655C4—182no—
656C4—361no—
657C4—361no—
658C3—21no—
659C3#7666512yescomplemented
660C2—42no—
661C2—42no—
662C2—124no—
663C2#1059513012yes—
664C2#1059513312yes—
665C2#1059516511yescharacteristic
666C2#1059527811yescharacteristic
667C2#1059550111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC22×C32×D4C22
hypercenterC22×D4D32
hypocenterC32#2388
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×#3805C2semidirect
2. C2×D4×C3⋊Dic3C2semidirect
3. C2×#67⋊Dic3C2semidirect
4. C3×#5223C2semidirect
5. #10591723C2semidirect
6. #10591709C2semidirect
7. #10591705C2semidirect
8. #10591692C2semidirect
9. #10591397C2semidirect
10. #10591394C2semidirect
11. #10591368C2semidirect
47. #5223D3semidirect
66. C22×C3⋊Dic3D4semidirect
87. C2×D3×Dic3D4semidirect
158. C23×C32#41semidirect
170. C2×C32×C4#41semidirect
191. C2×C3×Dic3#41semidirect
379. C23×C3#237semidirect
406. C2×C3×C4#237semidirect
443. C2×Dic3#237semidirect
563. C32#2388semidirect
579. C23#3805semidirect
609. C2×C4#3805semidirect
659. C3#76665semidirect

Maximal subgroups

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

subgroupindex
C22×#38052
C2×D4×C3⋊Dic32
C2×#67⋊Dic32
C3×#52232
#105917232
#105917092
#105917052
#105916922
#105913972
#105913942
#105913682
#766653