Finite Group Databasebeta

← #11808235

Subgroups — #11808235

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×#3798C211yesmaximal, characteristic, complemented
2C2×C4×#638C211yesmaximal, characteristic, complemented
3C2×C3×C4×#67C212yesmaximal, complemented
4#10591724C212yesmaximal, complemented
5#10591723C211yesmaximal, characteristic, complemented
6#10591692C211yesmaximal, characteristic, complemented
7#10591388C211yesmaximal, characteristic, complemented
8#10591291C212yesmaximal, complemented
9C4×#3722C211yesmaximal, characteristic, complemented
10C4×(C2×D3)⋊Dic3C212yesmaximal, complemented
11#10591195C211yesmaximal, characteristic, complemented
12#82400—32nomaximal
13C23×C32×C4C2211yescharacteristic
14C22×#638C2211yescharacteristic
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×C3×#67C2212yes—
17C22×C3×C4×D3C2212yes—
18C22×#627C2211yescharacteristic
19C22×#626C2212yes—
20C22×#625C2211yescharacteristic
21C2×#3798—24no—
22C2×#3798—28no—
23C2×#3757C2211yescharacteristic
24C4×#638—24no—
25C2×#3752C2211yescharacteristic
26C2×#3750C2211yescharacteristic
27C2×C4×C3⋊Dic3C2211yescharacteristic
28C2×C3×#217C2212yes—
29C3×C4×#67—28no—
30C2×C3×(C2×D3)⋊C4C2212yes—
31C2×C3×Dic3⋊C4C2212yes—
32C2×C3×C4×Dic3C2212yes—
33C2×#3722C2212yes—
34C2×(C2×D3)⋊Dic3C2212yes—
35C2×(C2×D3)⋊Dic3C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38#63579C2211yescharacteristic
39#63579C2211yescharacteristic
40C22×#235—32no—
41C2×C3×C4×D4—32no—
42C2×C4×#67—32no—
43C2×C4×#67—61no—
44C2×C4×#67D312yescomplemented
45#5223—32no—
46#5223—32no—
47C4×#217—32no—
48#4991—32no—
49#4979—32no—
50#4960—32no—
51#4959—32no—
52#4959—32no—
53#4947—32no—
54C4×(C2×D3)⋊C4—32no—
55C4×(C2×D3)⋊C4—32no—
56C24×C32C2311yescharacteristic
57C23×C3⋊D3C2311yescharacteristic
58C23×C3×D3C2312yes—
59C22×C32×C4—22no—
60C22×C32×C4—24no—
61C22×C32×C4C2311yescharacteristic
62C22×C32×C4C2311yescharacteristic
63C2×#638—22no—
64C2×#638—22no—
65C2×#638—22no—
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3⋊Dic3C2311yescharacteristic
68C22×C3⋊Dic3C2311yescharacteristic
69C2×C4×C3⋊D3—24no—
70C2×C4×C3⋊D3D414yescomplemented
71C2×C3×#67—24no—
72C2×C3×#67—24no—
73C2×C3×#67—24no—
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2312yes—
76C22×C3×Dic3C2312yes—
77C2×C3×C4×D3—24no—
78C2×C3×C4×D3—24no—
79C2×C3×C4×D3D418yescomplemented
80C2×#627—22no—
81C2×#627—24no—
82C2×#626—24no—
83C2×#626—24no—
84C2×#626—24no—
85C2×#625—24no—
86C2×#625—22no—
87#3798—232no—
88#3757—22no—
89#3752—22no—
90#3750—22no—
91C4×C3⋊Dic3—22no—
92C3×#217—24no—
93C3×(C2×D3)⋊C4—24no—
94C3×Dic3⋊C4—24no—
95C3×C4×Dic3—24no—
96#3722—24no—
97(C2×D3)⋊Dic3—24no—
98(C2×D3)⋊Dic3—24no—
99#2388—91noSylow
100C22×C3×D4—32no—
101C23×C3×C4—21no—
102C23×C3×C4—32no—
103C23×C3×C4C2×D312yes—
104C22×#67—32no—
105C22×#67—32no—
106C22×#67—32no—
107C22×#67—61no—
108C22×#67C2×D312yes—
109C2×#235—68no—
110C2×#235—68no—
111C2×#235—68no—
112C22×D12—32no—
113C22×C4×D3—32no—
114C22×C4×D3—61no—
115C22×C4×D3C2×D312yes—
116C22×Dic6—32no—
117C3×C4×D4—68no—
118C2×C3×C4⋊C4—32no—
119C2×C3×C22⋊C4—32no—
120C2×C3×C22⋊C4—32no—
121C2×C3×C42—32no—
122C2×#217—32no—
123C2×#217—32no—
124C2×#217—32no—
125C2×#217—61no—
126C2×#217C2×D312yes—
127C4×#67—28no—
128C4×#67—68no—
129C4×#67—68no—
130C2×(C2×D3)⋊C4—32no—
131C2×(C2×D3)⋊C4—32no—
132C2×(C2×D3)⋊C4—32no—
133C2×(C2×D3)⋊C4—32no—
134C2×(C2×D3)⋊C4—32no—
135C2×(C2×D3)⋊C4—61no—
136C2×(C2×D3)⋊C4C2×D312yes—
137C2×Dic3⋊C4—32no—
138C2×Dic3⋊C4—61no—
139C2×Dic3⋊C4C2×D312yes—
140C2×C4×Dic3—32no—
141C2×C4×Dic3—61no—
142C2×C4×Dic3C2×D312yes—
143C3⋊#95—32no—
144C3⋊#95—32no—
145C3⋊#95—32no—
146C3⋊#95—32no—
147C3⋊#95—32no—
148C3⋊#95—32no—
149C23×C32—21no—
150C23×C32—21no—
151C23×C32—22no—
152C23×C32—22no—
153C23×C32#4112yescomplemented
154C23×C32C2411yescharacteristic
155C22×C3⋊D3—21no—
156C22×C3⋊D3—21no—
157C22×C3⋊D3—22no—
158C22×C3⋊D3—22no—
159C22×C3⋊D3C2×D412yes—
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—
167C2×C32×C4—21no—
168C2×C32×C4—22no—
169C2×C32×C4—44no—
170C2×C32×C4C2×D412yes—
171C2×C32×C4C2×D414yes—
172#638—28no—
173C2×C3⋊Dic3—21no—
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3—21no—
176C2×C3⋊Dic3—22no—
177C2×C3⋊Dic3—22no—
178C2×C3⋊Dic3C2×D412yes—
179C2×C3⋊Dic3#4112yescomplemented
180C4×C3⋊D3—28no—
181C3×#67—216no—
182C2×C3×Dic3—22no—
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×Dic3C2×D414yes—
190C2×C3×Dic3#4114yescomplemented
191C3×C4×D3—216no—
192#627—28no—
193#626—216no—
194#625—28no—
195C22×#41—91no—
196C2×C4×D4—32no—
197C2×C4×D4—91no—
198#395—91no—
199#394—91no—
200#394—92no—
201#393—91no—
202#392—92no—
203#392—91no—
204C4×C22⋊C4—91no—
205C4×C22⋊C4—92no—
206C24×C3—21no—
207C24×C3—32no—
208C24×C3C22×D312yes—
209C23×D3—32no—
210C23×D3—61no—
211C23×D3C22×D312yes—
212C2×C3×D4—64no—
213C2×C3×D4—64no—
214C2×C3×D4—64no—
215C22×C3×C4—24no—
216C22×C3×C4—24no—
217C22×C3×C4—24no—
218C22×C3×C4—24no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—32no—
222C22×C3×C4—32no—
223C22×C3×C4—38no—
224C22×C3×C4—32no—
225C22×C3×C4—44no—
226C22×C3×C4—64no—
227C22×C3×C4—64no—
228C22×C3×C4C22×D312yes—
229C22×C3×C4C22×D312yes—
230C2×#67—24no—
231C2×#67—24no—
232C2×#67—24no—
233C2×#67—64no—
234C2×#67—64no—
235C2×#67—64no—
236C2×#67—64no—
237C2×#67—64no—
238C2×#67—64no—
239C2×#67—64no—
240C2×#67—64no—
241C2×#67—64no—
242C2×#67—64no—
243C2×#67—64no—
244C2×#67—64no—
245C22×Dic3—32no—
246C22×Dic3—32no—
247C22×Dic3—32no—
248C22×Dic3—61no—
249C22×Dic3—61no—
250C22×Dic3—61no—
251C22×Dic3C22×D312yes—
252C22×Dic3C22×D312yes—
253C22×Dic3C22×D312yes—
254#235—664no—
255C2×D12—64no—
256C2×D12—64no—
257C2×D12—64no—
258C2×C4×D3—24no—
259C2×C4×D3—24no—
260C2×C4×D3—38no—
261C2×C4×D3—64no—
262C2×C4×D3—64no—
263C2×C4×D3—64no—
264C2×C4×D3—124no—
265C2×C4×D3#6718yescomplemented
266C2×Dic6—64no—
267C2×Dic6—64no—
268C2×Dic6—64no—
269C3×C4⋊C4—64no—
270C3×C22⋊C4—64no—
271C3×C22⋊C4—64no—
272C3×C42—64no—
273#217—24no—
274#217—64no—
275#217—64no—
276#217—64no—
277#217—64no—
278(C2×D3)⋊C4—24no—
279(C2×D3)⋊C4—64no—
280(C2×D3)⋊C4—64no—
281(C2×D3)⋊C4—64no—
282(C2×D3)⋊C4—64no—
283(C2×D3)⋊C4—64no—
284(C2×D3)⋊C4—64no—
285Dic3⋊C4—24no—
286Dic3⋊C4—64no—
287Dic3⋊C4—64no—
288C4×Dic3—24no—
289C4×Dic3—64no—
290C4×Dic3—64no—
291C22×C32—22no—
292C22×C32—24no—
293C22×C32—41no—
294C22×C32—41no—
295C22×C32—42no—
296C22×C32C22×D411yescharacteristic
297C22×C32C22×D412yes—
298C22×C32C2×#4111yescharacteristic
299C22×C32C2×#4112yes—
300C22×C32C2×#4111yescharacteristic
301C2×C3⋊D3—22no—
302C2×C3⋊D3—22no—
303C2×C3⋊D3—22no—
304C2×C3⋊D3—42no—
305C2×C3⋊D3—42no—
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—41no—
314C32×C4#12014yes—
315C3⋊Dic3—22no—
316C3⋊Dic3—22no—
317C3⋊Dic3—41no—
318C3×Dic3—24no—
319C3×Dic3—24no—
320C3×Dic3—42no—
321C2×#41—188no—
322C2×#41—184no—
323C22×Q8—91no—
324C22×D4—32no—
325C22×D4—92no—
326C22×D4—91no—
327C22×D4—91no—
328C23×C4—32no—
329C23×C4—91no—
330C23×C4D3211yescharacteristic
331C4×D4—68no—
332C4×D4—184no—
333C2×C4⋊C4—32no—
334C2×C4⋊C4—91no—
335C2×C22⋊C4—32no—
336C2×C22⋊C4—32no—
337C2×C22⋊C4—92no—
338C2×C22⋊C4—92no—
339C2×C22⋊C4—92no—
340C2×C22⋊C4—91no—
341C2×C22⋊C4—91no—
342C2×C42—32no—
343C2×C42—91no—
344#95—91no—
345#95—92no—
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—21no—
357C23×C3—22no—
358C23×C3—34no—
359C23×C3—42no—
360C23×C3—42no—
361C23×C3—62no—
362C23×C3—62no—
363C23×C3—62no—
364C23×C3—62no—
365C23×C3—62no—
366C23×C3—62no—
367C23×C3#23514yescomplemented
368C23×C3C23×D312yes—
369C22×D3—22no—
370C22×D3—22no—
371C22×D3—22no—
372C22×D3—22no—
373C22×D3—22no—
374C22×D3—22no—
375C22×D3—34no—
376C22×D3—62no—
377C22×D3—62no—
378C22×D3—62no—
379C22×D3—62no—
380C22×D3—62no—
381C22×D3—62no—
382C22×D3—62no—
383C22×D3—62no—
384C22×D3—62no—
385C22×D3—122no—
386C22×D3—122no—
387C22×D3C2×#6714yes—
388C3×D4—616no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—24no—
394C2×C3×C4—22no—
395C2×C3×C4—34no—
396C2×C3×C4—34no—
397C2×C3×C4—42no—
398C2×C3×C4—48no—
399C2×C3×C4—48no—
400C2×C3×C4—62no—
401C2×C3×C4—62no—
402C2×C3×C4—62no—
403C2×C3×C4—62no—
404C2×C3×C4—616no—
405C2×C3×C4—62no—
406C2×C3×C4—62no—
407C2×C3×C4—62no—
408C2×C3×C4D3×D414yes—
409C2×C3×C4D3×D414yes—
410C2×C3×C4C2×#6714yes—
411#67—216no—
412#67—616no—
413#67—616no—
414#67—616no—
415#67—616no—
416C2×Dic3—22no—
417C2×Dic3—22no—
418C2×Dic3—22no—
419C2×Dic3—22no—
420C2×Dic3—22no—
421C2×Dic3—22no—
422C2×Dic3—22no—
423C2×Dic3—34no—
424C2×Dic3—34no—
425C2×Dic3—62no—
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—62no—
437C2×Dic3—122no—
438C2×Dic3—122no—
439C2×Dic3#23514yescomplemented
440C2×Dic3C2×#6714yes—
441D12—616no—
442C4×D3—216no—
443C4×D3—616no—
444C4×D3—128no—
445Dic6—616no—
446C2×C32—42no—
447C2×C32C2×#12011yescharacteristic
448C2×C32#52512yes—
449C2×C32#52511yescharacteristic
450C2×C32#53211yescharacteristic
451C2×C32#53212yes—
452C3⋊D3—42no—
453C3×D3—44no—
454C24—32no—
455C24—91no—
456C24C2×D3211yescharacteristic
457#41—1832no—
458C2×Q8—184no—
459C2×Q8—182no—
460C2×D4—64no—
461C2×D4—64no—
462C2×D4—64no—
463C2×D4—184no—
464C2×D4—184no—
465C2×D4—184no—
466C2×D4—182no—
467C2×D4—182no—
468C2×D4—182no—
469C2×D4—184no—
470C2×D4—182no—
471C22×C4—24no—
472C22×C4—22no—
473C22×C4—32no—
474C22×C4—32no—
475C22×C4—38no—
476C22×C4—32no—
477C22×C4—64no—
478C22×C4—64no—
479C22×C4—91no—
480C22×C4—91no—
481C22×C4—94no—
482C22×C4—91no—
483C22×C4—184no—
484C22×C4C2×D3211yescharacteristic
485C22×C4C2×D3211yescharacteristic
486C4⋊C4—64no—
487C4⋊C4—182no—
488C22⋊C4—64no—
489C22⋊C4—64no—
490C22⋊C4—182no—
491C22⋊C4—184no—
492C22⋊C4—184no—
493C22⋊C4—184no—
494C22⋊C4—182no—
495C42—64no—
496C42—182no—
497C22×C3—24no—
498C22×C3—24no—
499C22×C3—24no—
500C22×C3—24no—
501C22×C3—21no—
502C22×C3—22no—
503C22×C3—21no—
504C22×C3—22no—
505C22×C3—21no—
506C22×C3—44no—
507C22×C3—42no—
508C22×C3—44no—
509C22×C3—42no—
510C22×C3—42no—
511C22×C3—42no—
512C22×C3—42no—
513C22×C3—42no—
514C22×C3—64no—
515C22×C3—64no—
516C22×C3—64no—
517C22×C3—122no—
518C22×C3—122no—
519C22×C3—122no—
520C22×C3—122no—
521C22×C3C2×#23512yes—
522C22×C3C2×#23512yes—
523C22×C3C2×D3×D412yes—
524C22×C3C2×D3×D412yes—
525C22×C3D3×#4112yes—
526C22×C3D3×#4112yes—
527C22×C3C22×#6712yes—
528C2×D3—24no—
529C2×D3—24no—
530C2×D3—24no—
531C2×D3—42no—
532C2×D3—42no—
533C2×D3—42no—
534C2×D3—42no—
535C2×D3—64no—
536C2×D3—64no—
537C2×D3—64no—
538C2×D3—64no—
539C2×D3—122no—
540C2×D3—122no—
541C2×D3—124no—
542C2×D3—124no—
543C2×D3—122no—
544C2×D3—122no—
545C2×D3—122no—
546C2×D3—122no—
547C3×C4—24no—
548C3×C4—42no—
549C3×C4—42no—
550C3×C4—64no—
551C3×C4—64no—
552C3×C4—122no—
553C3×C4#93718yes—
554Dic3—24no—
555Dic3—24no—
556Dic3—42no—
557Dic3—64no—
558Dic3—64no—
559Dic3—64no—
560Dic3—122no—
561Dic3—122no—
562Dic3—122no—
563C32#238811yescharacteristic, complemented, Sylow
564C23—22no—
565C23—21no—
566C23—22no—
567C23—21no—
568C23—34no—
569C23—62no—
570C23—62no—
571C23—62no—
572C23—62no—
573C23—62no—
574C23—62no—
575C23—92no—
576C23—181no—
577C23—182no—
578C23—181no—
579C23—182no—
580C23#379812yescomplemented
581C23C22×D3211yescharacteristic
582Q8—188no—
583D4—616no—
584D4—1816no—
585D4—188no—
586D4—188no—
587C2×C4—22no—
588C2×C4—21no—
589C2×C4—34no—
590C2×C4—34no—
591C2×C4—44no—
592C2×C4—62no—
593C2×C4—62no—
594C2×C4—62no—
595C2×C4—62no—
596C2×C4—616no—
597C2×C4—62no—
598C2×C4—62no—
599C2×C4—62no—
600C2×C4—92no—
601C2×C4—92no—
602C2×C4—181no—
603C2×C4—182no—
604C2×C4—181no—
605C2×C4—188no—
606C2×C4—182no—
607C2×C4—181no—
608C2×C4D3×#6714yes—
609C2×C4#381112yes—
610C2×C3—22no—
611C2×C3—22no—
612C2×C3—21no—
613C2×C3—21no—
614C2×C3—21no—
615C2×C3—44no—
616C2×C3—44no—
617C2×C3—124no—
618C2×C3#554712yes—
619C2×C3#554712yes—
620C2×C3#554812yes—
621C2×C3#554812yes—
622C2×C3#579112yes—
623C2×C3C2×#93712yes—
624C2×C3#583212yes—
625D3—44no—
626D3—124no—
627D3—124no—
628C22—24no—
629C22—22no—
630C22—42no—
631C22—41no—
632C22—41no—
633C22—64no—
634C22—64no—
635C22—64no—
636C22—122no—
637C22—122no—
638C22—122no—
639C22—122no—
640C22—182no—
641C22—182no—
642C22—182no—
643C22—362no—
644C22—362no—
645C22C2×#379811yescharacteristic
646C22D3×#23512yes—
647C22#6430611yescharacteristic
648C22C2×D3×#6712yes—
649C22C2×#381111yescharacteristic
650C4—41no—
651C4—64no—
652C4—64no—
653C4—122no—
654C4—182no—
655C4—182no—
656C4—361no—
657C4#6398314yes—
658C3—21no—
659C3#8240012yescomplemented
660C2—42no—
661C2—124no—
662C2—362no—
663C2#1059500212yes—
664C2#1059500312yes—
665C2#1059501611yescharacteristic
666C2#1059501711yescharacteristic
667C2C2×#6398311yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutator, socle, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC23×C32×C4C22
hypercenterC23×C4D32
hypocenterC32#2388
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×#3798C2semidirect
2. C2×C4×#638C2semidirect
3. C2×C3×C4×#67C2semidirect
4. #10591724C2semidirect
5. #10591723C2semidirect
6. #10591692C2semidirect
7. #10591388C2semidirect
8. #10591291C2semidirect
9. C4×#3722C2semidirect
10. C4×(C2×D3)⋊Dic3C2semidirect
11. #10591195C2semidirect
44. C2×C4×#67D3semidirect
70. C2×C4×C3⋊D3D4semidirect
79. C2×C3×C4×D3D4semidirect
153. C23×C32#41semidirect
179. C2×C3⋊Dic3#41semidirect
190. C2×C3×Dic3#41semidirect
265. C2×C4×D3#67semidirect
367. C23×C3#235semidirect
439. C2×Dic3#235semidirect
563. C32#2388semidirect
580. C23#3798semidirect
659. C3#82400semidirect

Maximal subgroups

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

subgroupindex
C22×#37982
C2×C4×#6382
C2×C3×C4×#672
#105917242
#105917232
#105916922
#105913882
#105912912
C4×#37222
C4×(C2×D3)⋊Dic32
#105911952
#824003