Finite Group Databasebeta

← #11773363

Subgroups — #11773363

Order 1152.

1337 conjugacy classes of subgroups.

The subgroup lattice has 619 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic
2C22×C3×Dic3⋊C4C211yesmaximal, characteristic
3C2×C3×C3⋊#95C211yesmaximal, characteristic
4C2×#63579C212yesmaximal
5C2×#63579C212yesmaximal
6#71565—31nomaximal
7#69410—31nomaximal
8C23×C32×C4C2211yescharacteristic
9C23×C3⋊Dic3C2212yes—
10C23×C3×Dic3C2211yescharacteristic
11C23×C3×Dic3C2212yes—
12C23×C3×Dic3C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)—22no—
14C2×C4⋊(C3⋊Dic3)—24no—
15C2×C3×Dic3⋊C4—22no—
16C2×C3×Dic3⋊C4—22no—
17C2×C3×Dic3⋊C4C414yescomplemented
18C3×C3⋊#95—22no—
19#63579—24no—
20#63579—24no—
21C22×C3×C4⋊C4—31no—
22C22×C4⋊Dic3—31no—
23C22×C4⋊Dic3—31no—
24C22×C4⋊Dic3—61no—
25C22×Dic3⋊C4D311yescharacteristic
26C2×C3×#95—31no—
27C2×C3⋊#95—32no—
28C2×C3⋊#95—32no—
29C2×C3⋊#95—32no—
30C2×C3⋊#95—32no—
31C2×C3⋊#95D311yescharacteristic
32C24×C32C2311yescharacteristic
33C22×C32×C4—22no—
34C22×C32×C4—22no—
35C22×C32×C4C2×C412yes—
36C22×C32×C4D412yes—
37C22×C32×C4D412yes—
38C22×C3⋊Dic3—22no—
39C22×C3⋊Dic3—22no—
40C22×C3⋊Dic3—22no—
41C22×C3⋊Dic3—22no—
42C22×C3⋊Dic3—22no—
43C22×C3⋊Dic3—22no—
44C22×C3⋊Dic3D414yes—
45C22×C3×Dic3—21no—
46C22×C3×Dic3—21no—
47C22×C3×Dic3—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3—21no—
50C22×C3×Dic3—21no—
51C22×C3×Dic3—22no—
52C22×C3×Dic3—22no—
53C22×C3×Dic3—22no—
54C22×C3×Dic3—22no—
55C22×C3×Dic3—22no—
56C22×C3×Dic3—22no—
57C22×C3×Dic3—22no—
58C22×C3×Dic3—22no—
59C22×C3×Dic3C2×C412yes—
60C22×C3×Dic3C2×C412yes—
61C22×C3×Dic3D412yes—
62C22×C3×Dic3Q814yes—
63C22×C3×Dic3Q812yes—
64C4⋊(C3⋊Dic3)—28no—
65C3×Dic3⋊C4—28no—
66#1441—91noSylow
67C23×C3×C4—21no—
68C23×C3×C4—31no—
69C23×C3×C4—32no—
70C23×C3×C4—31no—
71C23×C3×C4C2×D311yescharacteristic
72C23×C3×C4C2×D311yescharacteristic
73C23×Dic3—32no—
74C23×Dic3—32no—
75C23×Dic3—62no—
76C23×Dic3C2×D312yes—
77C23×Dic3C2×D311yescharacteristic
78C23×Dic3C2×D311yescharacteristic
79C2×C3×C4⋊C4—34no—
80C2×C3×C4⋊C4—62no—
81C2×C3×C4⋊C4—62no—
82C2×C4⋊Dic3—64no—
83C2×C4⋊Dic3—64no—
84C2×C4⋊Dic3—68no—
85C2×C4⋊Dic3—64no—
86C2×C4⋊Dic3—62no—
87C2×C4⋊Dic3—62no—
88C2×Dic3⋊C4—22no—
89C2×Dic3⋊C4—22no—
90C2×Dic3⋊C4Dic314yescomplemented
91C3×#95—62no—
92C3⋊#95—22no—
93C3⋊#95—64no—
94C3⋊#95—64no—
95C3⋊#95—64no—
96C3⋊#95—64no—
97C23×C32C22×C411yescharacteristic
98C23×C32C2×D411yescharacteristic
99C23×C32C2×D411yescharacteristic
100C23×C32C2×D412yes—
101C23×C32C2×D411yescharacteristic
102C23×C32C2×Q811yescharacteristic
103C23×C32C2×Q812yes—
104C23×C32#4111yescharacteristic
105C23×C32#4111yescharacteristic
106C23×C32#4112yes—
107C23×C32#4112yes—
108C2×C32×C4—24no—
109C2×C32×C4—22no—
110C2×C32×C4—24no—
111C2×C32×C4—22no—
112C2×C32×C4C22⋊C414yes—
113C2×C3⋊Dic3—24no—
114C2×C3⋊Dic3—24no—
115C2×C3⋊Dic3—24no—
116C2×C3⋊Dic3—42no—
117C2×C3⋊Dic3—42no—
118C2×C3⋊Dic3—42no—
119C2×C3⋊Dic3—42no—
120C2×C3×Dic3—22no—
121C2×C3×Dic3—22no—
122C2×C3×Dic3—22no—
123C2×C3×Dic3—22no—
124C2×C3×Dic3—22no—
125C2×C3×Dic3—22no—
126C2×C3×Dic3—22no—
127C2×C3×Dic3—24no—
128C2×C3×Dic3—24no—
129C2×C3×Dic3—24no—
130C2×C3×Dic3—24no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3—42no—
133C2×C3×Dic3—42no—
134C2×C3×Dic3—42no—
135C2×C3×Dic3—42no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3—42no—
138C2×C3×Dic3C4⋊C414yescomplemented
139C22×C4⋊C4—31no—
140C22×C4⋊C4—91no—
141C2×#95—31no—
142C2×#95—92no—
143C2×#95—92no—
144C24×C3—21no—
145C24×C3C22×D311yescharacteristic
146C24×C3C22×D311yescharacteristic
147C22×C3×C4—24no—
148C22×C3×C4—24no—
149C22×C3×C4—22no—
150C22×C3×C4—22no—
151C22×C3×C4—22no—
152C22×C3×C4—22no—
153C22×C3×C4—22no—
154C22×C3×C4—22no—
155C22×C3×C4—22no—
156C22×C3×C4—32no—
157C22×C3×C4—32no—
158C22×C3×C4—32no—
159C22×C3×C4—32no—
160C22×C3×C4—34no—
161C22×C3×C4—61no—
162C22×C3×C4—61no—
163C22×C3×C4—61no—
164C22×C3×C4—61no—
165C22×C3×C4—62no—
166C22×C3×C4—61no—
167C22×C3×C4—62no—
168C22×C3×C4—62no—
169C22×C3×C4—62no—
170C22×C3×C4—62no—
171C22×C3×C4—62no—
172C22×C3×C4—62no—
173C22×C3×C4—62no—
174C22×C3×C4—61no—
175C22×C3×C4C4×D312yes—
176C22×C3×C4D1212yes—
177C22×C3×C4C2×Dic312yes—
178C22×C3×C4#6712yes—
179C22×C3×C4#6712yes—
180C22×C3×C4#6712yes—
181C22×Dic3—21no—
182C22×Dic3—21no—
183C22×Dic3—21no—
184C22×Dic3—21no—
185C22×Dic3—22no—
186C22×Dic3—22no—
187C22×Dic3—22no—
188C22×Dic3—22no—
189C22×Dic3—22no—
190C22×Dic3—22no—
191C22×Dic3—22no—
192C22×Dic3—22no—
193C22×Dic3—21no—
194C22×Dic3—21no—
195C22×Dic3—34no—
196C22×Dic3—34no—
197C22×Dic3—64no—
198C22×Dic3—64no—
199C22×Dic3—64no—
200C22×Dic3—62no—
201C22×Dic3—62no—
202C22×Dic3—62no—
203C22×Dic3—62no—
204C22×Dic3—62no—
205C22×Dic3—62no—
206C22×Dic3—62no—
207C22×Dic3—62no—
208C22×Dic3—62no—
209C22×Dic3—62no—
210C22×Dic3—62no—
211C22×Dic3—62no—
212C22×Dic3—122no—
213C22×Dic3—122no—
214C22×Dic3—122no—
215C22×Dic3—122no—
216C22×Dic3Dic614yes—
217C22×Dic3Dic612yes—
218C22×Dic3D1212yes—
219C22×Dic3C2×Dic312yes—
220C22×Dic3C2×Dic312yes—
221C3×C4⋊C4—68no—
222C4⋊Dic3—616no—
223C4⋊Dic3—68no—
224C4⋊Dic3—68no—
225Dic3⋊C4—28no—
226C22×C32C2×C22⋊C411yescharacteristic
227C22×C32C2×C4⋊C411yescharacteristic
228C22×C32#11711yescharacteristic
229C22×C32C4×D412yes—
230C22×C32C4×Q812yes—
231C22×C32#12011yescharacteristic
232C22×C32#12112yes—
233C22×C32#12111yescharacteristic
234C22×C32#12111yescharacteristic
235C22×C32#12112yes—
236C22×C32C22⋊Q812yes—
237C22×C32C22⋊Q812yes—
238C22×C32C22⋊Q811yescharacteristic
239C22×C32C22⋊Q811yescharacteristic
240C22×C32C22⋊Q812yes—
241C22×C32#12311yescharacteristic
242C22×C32#12312yes—
243C22×C32#12411yescharacteristic
244C22×C32#12512yes—
245C22×C32#12512yes—
246C22×C32#12612yes—
247C22×C32C4⋊Q811yescharacteristic
248C22×C32C4⋊Q812yes—
249C32×C4—24no—
250C3⋊Dic3—44no—
251C3×Dic3—24no—
252C3×Dic3—42no—
253C3×Dic3—44no—
254C23×C4—31no—
255C23×C4—31no—
256C23×C4—32no—
257C23×C4—92no—
258C23×C4D3211yescharacteristic
259C2×C4⋊C4—34no—
260C2×C4⋊C4—62no—
261C2×C4⋊C4—62no—
262C2×C4⋊C4—184no—
263C2×C4⋊C4—182no—
264#95—62no—
265#95—184no—
266#95—184no—
267C23×C3—21no—
268C23×C3—22no—
269C23×C3—21no—
270C23×C3—21no—
271C23×C3—22no—
272C23×C3—21no—
273C23×C3—21no—
274C23×C3—22no—
275C23×C3—21no—
276C23×C3—21no—
277C23×C3—22no—
278C23×C3C2×Dic612yes—
279C23×C3C2×Dic611yescharacteristic
280C23×C3C2×C4×D311yescharacteristic
281C23×C3C2×D1211yescharacteristic
282C23×C3C2×D1211yescharacteristic
283C23×C3#23511yescharacteristic
284C23×C3#23512yes—
285C23×C3#23511yescharacteristic
286C23×C3D3×D411yescharacteristic
287C23×C3D3×D412yes—
288C23×C3D3×D412yes—
289C23×C3#23711yescharacteristic
290C23×C3#23712yes—
291C23×C3#23712yes—
292C23×C3D3×Q811yescharacteristic
293C23×C3D3×Q812yes—
294C23×C3#23911yescharacteristic
295C23×C3#23912yes—
296C23×C3C22×Dic311yescharacteristic
297C23×C3C2×#6711yescharacteristic
298C23×C3C2×#6711yescharacteristic
299C23×C3C2×#6711yescharacteristic
300C2×C3×C4—24no—
301C2×C3×C4—24no—
302C2×C3×C4—28no—
303C2×C3×C4—28no—
304C2×C3×C4—24no—
305C2×C3×C4—22no—
306C2×C3×C4—22no—
307C2×C3×C4—24no—
308C2×C3×C4—22no—
309C2×C3×C4—22no—
310C2×C3×C4—24no—
311C2×C3×C4—24no—
312C2×C3×C4—24no—
313C2×C3×C4—34no—
314C2×C3×C4—62no—
315C2×C3×C4—62no—
316C2×C3×C4—62no—
317C2×C3×C4—62no—
318C2×C3×C4—62no—
319C2×C3×C4—62no—
320C2×C3×C4—64no—
321C2×C3×C4—64no—
322C2×C3×C4—64no—
323C2×C3×C4—62no—
324C2×C3×C4—64no—
325C2×C3×C4—121no—
326C2×C3×C4—121no—
327C2×C3×C4—122no—
328C2×C3×C4—122no—
329C2×C3×C4—122no—
330C2×C3×C4—122no—
331C2×C3×C4—122no—
332C2×C3×C4(C2×D3)⋊C414yes—
333C2×C3×C4#21714yes—
334C2×Dic3—22no—
335C2×Dic3—22no—
336C2×Dic3—22no—
337C2×Dic3—22no—
338C2×Dic3—22no—
339C2×Dic3—22no—
340C2×Dic3—24no—
341C2×Dic3—24no—
342C2×Dic3—24no—
343C2×Dic3—24no—
344C2×Dic3—22no—
345C2×Dic3—42no—
346C2×Dic3—42no—
347C2×Dic3—41no—
348C2×Dic3—41no—
349C2×Dic3—42no—
350C2×Dic3—42no—
351C2×Dic3—42no—
352C2×Dic3—68no—
353C2×Dic3—64no—
354C2×Dic3—64no—
355C2×Dic3—64no—
356C2×Dic3—64no—
357C2×Dic3—64no—
358C2×Dic3—64no—
359C2×Dic3—124no—
360C2×Dic3—124no—
361C2×Dic3—124no—
362C2×Dic3—124no—
363C2×Dic3—124no—
364C2×Dic3—124no—
365C2×Dic3—122no—
366C2×Dic3—122no—
367C2×Dic3—122no—
368C2×Dic3—122no—
369C2×Dic3—122no—
370C2×Dic3—122no—
371C2×Dic3—122no—
372C2×Dic3—122no—
373C2×Dic3C4⋊Dic314yescomplemented
374C2×C32#38011yescharacteristic
375C2×C32#38611yescharacteristic
376C2×C32#38712yes—
377C2×C32#38912yes—
378C2×C32#39111yescharacteristic
379C2×C32#39411yescharacteristic
380C2×C32#39511yescharacteristic
381C2×C32#39612yes—
382C2×C32#39811yescharacteristic
383C2×C32#39812yes—
384C2×C32#40011yescharacteristic
385C24C2×D3211yescharacteristic
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—32no—
389C22×C4—32no—
390C22×C4—32no—
391C22×C4—34no—
392C22×C4—32no—
393C22×C4—61no—
394C22×C4—61no—
395C22×C4—61no—
396C22×C4—61no—
397C22×C4—62no—
398C22×C4—62no—
399C22×C4—62no—
400C22×C4—62no—
401C22×C4—62no—
402C22×C4—62no—
403C22×C4—61no—
404C22×C4—61no—
405C22×C4—62no—
406C22×C4—62no—
407C22×C4—94no—
408C22×C4—182no—
409C22×C4—182no—
410C22×C4—182no—
411C22×C4—182no—
412C22×C4—182no—
413C22×C4—182no—
414C22×C4D3×Dic312yes—
415C22×C4#62512yes—
416C22×C4#62612yes—
417C4⋊C4—68no—
418C4⋊C4—188no—
419C22×C3—22no—
420C22×C3—21no—
421C22×C3—22no—
422C22×C3—22no—
423C22×C3—22no—
424C22×C3—21no—
425C22×C3—22no—
426C22×C3—21no—
427C22×C3—22no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—22no—
432C22×C3—22no—
433C22×C3—22no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—22no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—22no—
440C22×C3—22no—
441C22×C3—21no—
442C22×C3C4×Dic612yes—
443C22×C3#86911yescharacteristic
444C22×C3#87511yescharacteristic
445C22×C3#87812yes—
446C22×C3#87812yes—
447C22×C3#87912yes—
448C22×C3#67⋊C412yes—
449C22×C3#88211yescharacteristic
450C22×C3#88412yes—
451C22×C3#88611yescharacteristic
452C22×C3#88812yes—
453C22×C3#88812yes—
454C22×C3#88912yes—
455C22×C3#88912yes—
456C22×C3#89012yes—
457C22×C3#89012yes—
458C22×C3D3×C4⋊C411yescharacteristic
459C22×C3#89211yescharacteristic
460C22×C3#89412yes—
461C22×C3#89412yes—
462C22×C3#89511yescharacteristic
463C22×C3#89512yes—
464C22×C3#89612yes—
465C22×C3#89711yescharacteristic
466C22×C3#89712yes—
467C22×C3#89812yes—
468C22×C3#92412yes—
469C22×C3#92411yescharacteristic
470C22×C3#92411yescharacteristic
471C22×C3C2×C4⋊Dic311yescharacteristic
472C22×C3#92611yescharacteristic
473C22×C3C2×(C2×D3)⋊C411yescharacteristic
474C22×C3#93011yescharacteristic
475C22×C3#93011yescharacteristic
476C22×C3D4×Dic312yes—
477C22×C3#93511yescharacteristic
478C22×C3#93711yescharacteristic
479C22×C3#93811yescharacteristic
480C22×C3#93912yes—
481C22×C3#93912yes—
482C22×C3#94411yescharacteristic
483C22×C3Q8×Dic312yes—
484C22×C3#94612yes—
485C22×C3#94611yescharacteristic
486C22×C3#94711yescharacteristic
487C22×C3C2×#21711yescharacteristic
488C3×C4—28no—
489C3×C4—24no—
490C3×C4—24no—
491C3×C4—64no—
492C3×C4—122no—
493C3×C4—124no—
494Dic3—24no—
495Dic3—44no—
496Dic3—42no—
497Dic3—128no—
498Dic3—124no—
499Dic3—124no—
500C32#144111yescharacteristic, complemented, Sylow
501C23D3×Dic611yescharacteristic
502C23D3×Dic612yes—
503C23#379511yescharacteristic
504C23#379911yescharacteristic
505C23#379912yes—
506C23D3×D1211yescharacteristic
507C23C2×D3×Dic311yescharacteristic
508C23#380512yes—
509C23C2×#62511yescharacteristic
510C23C2×#62611yescharacteristic
511C23#381112yes—
512C2×C4—22no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—22no—
516C2×C4—34no—
517C2×C4—62no—
518C2×C4—62no—
519C2×C4—62no—
520C2×C4—62no—
521C2×C4—62no—
522C2×C4—62no—
523C2×C4—64no—
524C2×C4—64no—
525C2×C4—64no—
526C2×C4—62no—
527C2×C4—64no—
528C2×C4—122no—
529C2×C4—122no—
530C2×C4—122no—
531C2×C4—121no—
532C2×C4—122no—
533C2×C4—122no—
534C2×C4—121no—
535C2×C4—184no—
536C2×C4—184no—
537C2×C4—184no—
538C2×C4—362no—
539C2×C4—362no—
540C2×C4—362no—
541C2×C4—362no—
542C2×C4(C2×D3)⋊Dic314yes—
543C2×C3—22no—
544C2×C3—22no—
545C2×C3—21no—
546C2×C3—22no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—21no—
551C2×C3—22no—
552C2×C3—21no—
553C2×C3—21no—
554C2×C3#464712yes—
555C2×C3#465512yes—
556C2×C3#465611yescharacteristic
557C2×C3#465911yescharacteristic
558C2×C3#466111yescharacteristic
559C2×C3#467211yescharacteristic
560C2×C3#492911yescharacteristic
561C2×C3#494812yes—
562C2×C3#495811yescharacteristic
563C2×C3#497911yescharacteristic
564C2×C3#498012yes—
565C2×C3#498111yescharacteristic
566C2×C3#498212yes—
567C2×C3#498212yes—
568C2×C3#498412yes—
569C2×C3#498611yescharacteristic
570C2×C3#498711yescharacteristic
571C2×C3#499111yescharacteristic
572C2×C3#499412yes—
573C2×C3#521211yescharacteristic
574C2×C3#522011yescharacteristic
575C2×C3#522911yescharacteristic
576C22#6384012yes—
577C22#6384111yescharacteristic
578C22Dic3×Dic612yes—
579C22#6384512yes—
580C22#6384512yes—
581C22#6385611yescharacteristic
582C22#6385612yes—
583C22#6385711yescharacteristic
584C22#6386112yes—
585C22#6386411yescharacteristic
586C22#6386611yescharacteristic
587C22D3×C4⋊Dic311yescharacteristic
588C22#6389312yes—
589C22#6389612yes—
590C22#6389712yes—
591C22#6390811yescharacteristic
592C22#6390911yescharacteristic
593C22#6391012yes—
594C22C2×(C2×D3)⋊Dic311yescharacteristic
595C22#6396211yescharacteristic
596C22#67⋊Dic312yes—
597C22#6398012yes—
598C22#6398111yescharacteristic
599C4—24no—
600C4—64no—
601C4—124no—
602C4—122no—
603C4—364no—
604C3—21no—
605C3#6941011yescharacteristic, complemented
606C3#7156511yescharacteristic, complemented
607C2#1059121512yes—
608C2#1059122011yescharacteristic
609C2#1059122611yescharacteristic
610C2#1059126812yes—
611C2#1059127212yes—
612C2#1059131311yescharacteristic
613C2#1059131912yes—
614C2#1059132111yescharacteristic
615C2#1059135311yescharacteristic
616C2#1059135411yescharacteristic
617C2#1059171311yescharacteristic
subgroupG/H
center, FrattiniC24C2×D32
commutatorC23×C32C22×C4
FittingC23×C32×C4C22
socle, prime radical, cosocleC24×C32C23
hypercenterC23×C4D32
hypocenterC32#1441
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
17. C2×C3×Dic3⋊C4C4semidirect
90. C2×Dic3⋊C4Dic3semidirect
138. C2×C3×Dic3C4⋊C4semidirect
373. C2×Dic3C4⋊Dic3semidirect
500. C32#1441semidirect
605. C3#69410semidirect
606. C3#71565semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊(C3⋊Dic3)2
C22×C3×Dic3⋊C42
C2×C3×C3⋊#952
C2×#635792
#715653
#694103