Finite Group Databasebeta

← #11773365

Subgroups — #11773365

Order 1152.

1293 conjugacy classes of subgroups.

The subgroup lattice has 617 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4⋊Dic3C211yesmaximal, characteristic
2C22×C3×Dic3⋊C4C211yesmaximal, characteristic
3C2×#63658C211yesmaximal, characteristic
4C2×#63579C212yesmaximal
5C2×#63579C212yesmaximal
6#71566—31nomaximal
7#71565—31nomaximal
8C23×C32×C4C2211yescharacteristic
9C23×C3⋊Dic3C2212yes—
10C23×C3×Dic3C2211yescharacteristic
11C23×C3×Dic3C2212yes—
12C23×C3×Dic3C2211yescharacteristic
13C2×C3×C4⋊Dic3—22no—
14C2×C3×C4⋊Dic3—24no—
15C2×C3×Dic3⋊C4—22no—
16C2×C3×Dic3⋊C4—22no—
17C2×C3×Dic3⋊C4C414yescomplemented
18#63658—22no—
19#63579—24no—
20#63579—24no—
21C22×C3×C4⋊C4—31no—
22C22×C3×C4⋊C4—31no—
23C22×C4⋊Dic3D311yescharacteristic
24C22×Dic3⋊C4D311yescharacteristic
25C2×C3⋊#95—31no—
26C2×C3⋊#95—31no—
27C2×C3⋊#95—32no—
28C2×C3⋊#95—32no—
29C2×C3⋊#95—32no—
30C2×C3⋊#95—32no—
31C2×C3⋊#95—61no—
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⋊Dic3Q814yes—
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×Dic3D414yes—
62C22×C3×Dic3D412yes—
63C22×C3×Dic3Q812yes—
64C3×C4⋊Dic3—28no—
65C3×Dic3⋊C4—28no—
66#1441—91noSylow
67C23×C3×C4—21no—
68C23×C3×C4—31no—
69C23×C3×C4—31no—
70C23×C3×C4—32no—
71C23×C3×C4C2×D311yescharacteristic
72C23×C3×C4C2×D311yescharacteristic
73C23×Dic3—32no—
74C23×Dic3—32no—
75C23×Dic3—62no—
76C23×Dic3C2×D311yescharacteristic
77C23×Dic3C2×D312yes—
78C23×Dic3C2×D311yescharacteristic
79C2×C3×C4⋊C4—34no—
80C2×C3×C4⋊C4—64no—
81C2×C3×C4⋊C4—62no—
82C2×C3×C4⋊C4—62no—
83C2×C3×C4⋊C4—62no—
84C2×C4⋊Dic3—22no—
85C2×C4⋊Dic3—24no—
86C2×Dic3⋊C4—22no—
87C2×Dic3⋊C4—22no—
88C2×Dic3⋊C4Dic314yescomplemented
89C3⋊#95—64no—
90C3⋊#95—64no—
91C3⋊#95—64no—
92C3⋊#95—62no—
93C3⋊#95—62no—
94C3⋊#95—64no—
95C3⋊#95—64no—
96C23×C32C22×C411yescharacteristic
97C23×C32C2×D411yescharacteristic
98C23×C32C2×D411yescharacteristic
99C23×C32C2×D412yes—
100C23×C32C2×D411yescharacteristic
101C23×C32C2×Q811yescharacteristic
102C23×C32C2×Q812yes—
103C23×C32#4111yescharacteristic
104C23×C32#4112yes—
105C23×C32#4111yescharacteristic
106C23×C32#4112yes—
107C2×C32×C4—24no—
108C2×C32×C4—22no—
109C2×C32×C4—24no—
110C2×C32×C4—22no—
111C2×C32×C4C22⋊C414yes—
112C2×C3⋊Dic3—24no—
113C2×C3⋊Dic3—24no—
114C2×C3⋊Dic3—24no—
115C2×C3⋊Dic3—42no—
116C2×C3⋊Dic3—42no—
117C2×C3⋊Dic3—42no—
118C2×C3⋊Dic3—42no—
119C2×C3×Dic3—22no—
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—24no—
127C2×C3×Dic3—24no—
128C2×C3×Dic3—24no—
129C2×C3×Dic3—24no—
130C2×C3×Dic3—41no—
131C2×C3×Dic3—42no—
132C2×C3×Dic3—42no—
133C2×C3×Dic3—42no—
134C2×C3×Dic3—42no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—42no—
137C2×C3×Dic3C4⋊C414yescomplemented
138C22×C4⋊C4—31no—
139C22×C4⋊C4—31no—
140C2×#95—92no—
141C2×#95—92no—
142C2×#95—91no—
143C24×C3—21no—
144C24×C3C22×D311yescharacteristic
145C24×C3C22×D311yescharacteristic
146C22×C3×C4—22no—
147C22×C3×C4—22no—
148C22×C3×C4—22no—
149C22×C3×C4—22no—
150C22×C3×C4—22no—
151C22×C3×C4—22no—
152C22×C3×C4—22no—
153C22×C3×C4—32no—
154C22×C3×C4—32no—
155C22×C3×C4—32no—
156C22×C3×C4—32no—
157C22×C3×C4—34no—
158C22×C3×C4—42no—
159C22×C3×C4—42no—
160C22×C3×C4—61no—
161C22×C3×C4—61no—
162C22×C3×C4—61no—
163C22×C3×C4—61no—
164C22×C3×C4—62no—
165C22×C3×C4—61no—
166C22×C3×C4—62no—
167C22×C3×C4—62no—
168C22×C3×C4—62no—
169C22×C3×C4—62no—
170C22×C3×C4—62no—
171C22×C3×C4—62no—
172C22×C3×C4—61no—
173C22×C3×C4—62no—
174C22×C3×C4C4×D312yes—
175C22×C3×C4D1212yes—
176C22×C3×C4C2×Dic312yes—
177C22×C3×C4#6712yes—
178C22×C3×C4#6712yes—
179C22×C3×C4#6712yes—
180C22×Dic3—21no—
181C22×Dic3—21no—
182C22×Dic3—21no—
183C22×Dic3—21no—
184C22×Dic3—22no—
185C22×Dic3—22no—
186C22×Dic3—22no—
187C22×Dic3—22no—
188C22×Dic3—22no—
189C22×Dic3—22no—
190C22×Dic3—21no—
191C22×Dic3—21no—
192C22×Dic3—22no—
193C22×Dic3—22no—
194C22×Dic3—34no—
195C22×Dic3—34no—
196C22×Dic3—64no—
197C22×Dic3—64no—
198C22×Dic3—64no—
199C22×Dic3—62no—
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—122no—
212C22×Dic3—122no—
213C22×Dic3—122no—
214C22×Dic3—122no—
215C22×Dic3Dic612yes—
216C22×Dic3D1212yes—
217C22×Dic3C2×Dic312yes—
218C22×Dic3C2×Dic312yes—
219C22×Dic3#6714yes—
220C3×C4⋊C4—68no—
221C3×C4⋊C4—68no—
222C4⋊Dic3—28no—
223Dic3⋊C4—28no—
224C22×C32C2×C22⋊C411yescharacteristic
225C22×C32C2×C4⋊C411yescharacteristic
226C22×C32#11711yescharacteristic
227C22×C32C4×D412yes—
228C22×C32C4×Q812yes—
229C22×C32#12011yescharacteristic
230C22×C32#12111yescharacteristic
231C22×C32#12112yes—
232C22×C32#12111yescharacteristic
233C22×C32#12112yes—
234C22×C32C22⋊Q812yes—
235C22×C32C22⋊Q812yes—
236C22×C32C22⋊Q811yescharacteristic
237C22×C32C22⋊Q812yes—
238C22×C32C22⋊Q811yescharacteristic
239C22×C32#12312yes—
240C22×C32#12311yescharacteristic
241C22×C32#12411yescharacteristic
242C22×C32#12512yes—
243C22×C32#12512yes—
244C22×C32#12612yes—
245C22×C32C4⋊Q812yes—
246C22×C32C4⋊Q811yescharacteristic
247C32×C4—24no—
248C3⋊Dic3—44no—
249C3×Dic3—24no—
250C3×Dic3—42no—
251C3×Dic3—44no—
252C23×C4—31no—
253C23×C4—31no—
254C23×C4—32no—
255C23×C4—92no—
256C23×C4D3211yescharacteristic
257C2×C4⋊C4—34no—
258C2×C4⋊C4—64no—
259C2×C4⋊C4—62no—
260C2×C4⋊C4—62no—
261C2×C4⋊C4—62no—
262#95—184no—
263#95—184no—
264#95—182no—
265C23×C3—21no—
266C23×C3—21no—
267C23×C3—22no—
268C23×C3—22no—
269C23×C3—21no—
270C23×C3—21no—
271C23×C3—21no—
272C23×C3—22no—
273C23×C3—21no—
274C23×C3—21no—
275C23×C3—22no—
276C23×C3C2×Dic611yescharacteristic
277C23×C3C2×C4×D311yescharacteristic
278C23×C3C2×D1211yescharacteristic
279C23×C3C2×D1211yescharacteristic
280C23×C3#23511yescharacteristic
281C23×C3#23511yescharacteristic
282C23×C3#23512yes—
283C23×C3D3×D411yescharacteristic
284C23×C3D3×D412yes—
285C23×C3#23711yescharacteristic
286C23×C3#23712yes—
287C23×C3#23712yes—
288C23×C3D3×Q811yescharacteristic
289C23×C3D3×Q812yes—
290C23×C3D3×Q812yes—
291C23×C3#23912yes—
292C23×C3#23911yescharacteristic
293C23×C3C22×Dic311yescharacteristic
294C23×C3C2×#6711yescharacteristic
295C23×C3C2×#6711yescharacteristic
296C23×C3C2×#6711yescharacteristic
297C23×C3C2×#6712yes—
298C2×C3×C4—24no—
299C2×C3×C4—22no—
300C2×C3×C4—24no—
301C2×C3×C4—24no—
302C2×C3×C4—22no—
303C2×C3×C4—22no—
304C2×C3×C4—24no—
305C2×C3×C4—22no—
306C2×C3×C4—24no—
307C2×C3×C4—34no—
308C2×C3×C4—42no—
309C2×C3×C4—44no—
310C2×C3×C4—42no—
311C2×C3×C4—44no—
312C2×C3×C4—62no—
313C2×C3×C4—62no—
314C2×C3×C4—62no—
315C2×C3×C4—62no—
316C2×C3×C4—62no—
317C2×C3×C4—62no—
318C2×C3×C4—64no—
319C2×C3×C4—64no—
320C2×C3×C4—62no—
321C2×C3×C4—64no—
322C2×C3×C4—64no—
323C2×C3×C4—122no—
324C2×C3×C4—122no—
325C2×C3×C4—121no—
326C2×C3×C4—122no—
327C2×C3×C4—122no—
328C2×C3×C4—122no—
329C2×C3×C4—121no—
330C2×C3×C4(C2×D3)⋊C414yes—
331C2×C3×C4#21714yes—
332C2×Dic3—22no—
333C2×Dic3—22no—
334C2×Dic3—22no—
335C2×Dic3—22no—
336C2×Dic3—22no—
337C2×Dic3—22no—
338C2×Dic3—24no—
339C2×Dic3—24no—
340C2×Dic3—24no—
341C2×Dic3—22no—
342C2×Dic3—24no—
343C2×Dic3—42no—
344C2×Dic3—41no—
345C2×Dic3—42no—
346C2×Dic3—41no—
347C2×Dic3—42no—
348C2×Dic3—42no—
349C2×Dic3—42no—
350C2×Dic3—68no—
351C2×Dic3—64no—
352C2×Dic3—64no—
353C2×Dic3—64no—
354C2×Dic3—64no—
355C2×Dic3—64no—
356C2×Dic3—64no—
357C2×Dic3—124no—
358C2×Dic3—124no—
359C2×Dic3—124no—
360C2×Dic3—124no—
361C2×Dic3—124no—
362C2×Dic3—124no—
363C2×Dic3—122no—
364C2×Dic3—122no—
365C2×Dic3—122no—
366C2×Dic3—122no—
367C2×Dic3—122no—
368C2×Dic3—122no—
369C2×Dic3—122no—
370C2×Dic3—122no—
371C2×Dic3C4⋊Dic314yescomplemented
372C2×C32#38011yescharacteristic
373C2×C32#38611yescharacteristic
374C2×C32#38712yes—
375C2×C32#38912yes—
376C2×C32#39111yescharacteristic
377C2×C32#39411yescharacteristic
378C2×C32#39511yescharacteristic
379C2×C32#39612yes—
380C2×C32#39812yes—
381C2×C32#39811yescharacteristic
382C2×C32#40011yescharacteristic
383C24C2×D3211yescharacteristic
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—32no—
387C22×C4—32no—
388C22×C4—32no—
389C22×C4—32no—
390C22×C4—34no—
391C22×C4—61no—
392C22×C4—61no—
393C22×C4—61no—
394C22×C4—61no—
395C22×C4—62no—
396C22×C4—62no—
397C22×C4—62no—
398C22×C4—62no—
399C22×C4—62no—
400C22×C4—61no—
401C22×C4—62no—
402C22×C4—61no—
403C22×C4—62no—
404C22×C4—62no—
405C22×C4—94no—
406C22×C4—182no—
407C22×C4—182no—
408C22×C4—182no—
409C22×C4—182no—
410C22×C4—182no—
411C22×C4—182no—
412C22×C4D3×Dic312yes—
413C22×C4#62512yes—
414C22×C4#62612yes—
415C4⋊C4—68no—
416C4⋊C4—68no—
417C22×C3—22no—
418C22×C3—21no—
419C22×C3—22no—
420C22×C3—22no—
421C22×C3—22no—
422C22×C3—22no—
423C22×C3—21no—
424C22×C3—21no—
425C22×C3—21no—
426C22×C3—22no—
427C22×C3—21no—
428C22×C3—22no—
429C22×C3—22no—
430C22×C3—22no—
431C22×C3—21no—
432C22×C3—22no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—21no—
437C22×C3—22no—
438C22×C3—21no—
439C22×C3—22no—
440C22×C3#88712yes—
441C22×C3#88812yes—
442C22×C3#88912yes—
443C22×C3#88912yes—
444C22×C3#88912yes—
445C22×C3#89012yes—
446C22×C3D3×C4⋊C411yescharacteristic
447C22×C3#89211yescharacteristic
448C22×C3#89412yes—
449C22×C3#89512yes—
450C22×C3#89511yescharacteristic
451C22×C3#89612yes—
452C22×C3#89612yes—
453C22×C3#89711yescharacteristic
454C22×C3#89712yes—
455C22×C3#89712yes—
456C22×C3#89812yes—
457C22×C3#89812yes—
458C22×C3#92411yescharacteristic
459C22×C3#92411yescharacteristic
460C22×C3C2×C4⋊Dic311yescharacteristic
461C22×C3#92611yescharacteristic
462C22×C3C2×(C2×D3)⋊C411yescharacteristic
463C22×C3C4×#6712yes—
464C22×C3#92911yescharacteristic
465C22×C3#93011yescharacteristic
466C22×C3#93011yescharacteristic
467C22×C3#93012yes—
468C22×C3D4×Dic312yes—
469C22×C3#93512yes—
470C22×C3#93511yescharacteristic
471C22×C3#93611yescharacteristic
472C22×C3#93711yescharacteristic
473C22×C3#93811yescharacteristic
474C22×C3#93912yes—
475C22×C3#93912yes—
476C22×C3#94412yes—
477C22×C3#94411yescharacteristic
478C22×C3#94411yescharacteristic
479C22×C3Q8×Dic312yes—
480C22×C3#94611yescharacteristic
481C22×C3#94612yes—
482C22×C3#94612yes—
483C22×C3#94711yescharacteristic
484C22×C3C2×#21711yescharacteristic
485C22×C3#95311yescharacteristic
486C3×C4—24no—
487C3×C4—24no—
488C3×C4—44no—
489C3×C4—64no—
490C3×C4—122no—
491C3×C4—124no—
492Dic3—24no—
493Dic3—42no—
494Dic3—44no—
495Dic3—128no—
496Dic3—124no—
497Dic3—124no—
498C32#144111yescharacteristic, complemented, Sylow
499C23D3×Dic611yescharacteristic
500C23#379511yescharacteristic
501C23#379612yes—
502C23#379712yes—
503C23#379911yescharacteristic
504C23D3×D1211yescharacteristic
505C23C2×D3×Dic311yescharacteristic
506C23#380412yes—
507C23C2×#62511yescharacteristic
508C23C2×#62611yescharacteristic
509C23D3×#6712yes—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—24no—
514C2×C4—34no—
515C2×C4—62no—
516C2×C4—62no—
517C2×C4—62no—
518C2×C4—62no—
519C2×C4—62no—
520C2×C4—62no—
521C2×C4—64no—
522C2×C4—64no—
523C2×C4—62no—
524C2×C4—64no—
525C2×C4—64no—
526C2×C4—122no—
527C2×C4—122no—
528C2×C4—122no—
529C2×C4—122no—
530C2×C4—121no—
531C2×C4—121no—
532C2×C4—122no—
533C2×C4—184no—
534C2×C4—184no—
535C2×C4—184no—
536C2×C4—362no—
537C2×C4—362no—
538C2×C4—362no—
539C2×C4—362no—
540C2×C4(C2×D3)⋊Dic314yes—
541C2×C3—22no—
542C2×C3—22no—
543C2×C3—21no—
544C2×C3—22no—
545C2×C3—21no—
546C2×C3—22no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—21no—
551C2×C3—21no—
552C2×C3#497311yescharacteristic
553C2×C3#497612yes—
554C2×C3#497812yes—
555C2×C3#497911yescharacteristic
556C2×C3#498012yes—
557C2×C3#498112yes—
558C2×C3#498111yescharacteristic
559C2×C3#498212yes—
560C2×C3#498311yescharacteristic
561C2×C3#498412yes—
562C2×C3#498511yescharacteristic
563C2×C3#498611yescharacteristic
564C2×C3#498711yescharacteristic
565C2×C3#499111yescharacteristic
566C2×C3#499412yes—
567C2×C3#499412yes—
568C2×C3#521211yescharacteristic
569C2×C3#521311yescharacteristic
570C2×C3#522011yescharacteristic
571C2×C3#522211yescharacteristic
572C2×C3#522911yescharacteristic
573C2×C3#523011yescharacteristic
574C22#6383912yes—
575C22#6384111yescharacteristic
576C22#6384312yes—
577C22#6384612yes—
578C22#6384712yes—
579C22#6384812yes—
580C22#6385611yescharacteristic
581C22#6385711yescharacteristic
582C22#6386311yescharacteristic
583C22#6387112yes—
584C22#6387311yescharacteristic
585C22#6388412yes—
586C22#6388612yes—
587C22#6388812yes—
588C22D3×C4⋊Dic311yescharacteristic
589C22#6389512yes—
590C22#6390811yescharacteristic
591C22#6390911yescharacteristic
592C22C2×(C2×D3)⋊Dic311yescharacteristic
593C22#6396111yescharacteristic
594C22Dic3×#6712yes—
595C22#6397611yescharacteristic
596C22#6397812yes—
597C4—24no—
598C4—64no—
599C4—124no—
600C4—122no—
601C4—364no—
602C3—21no—
603C3#7156511yescharacteristic, complemented
604C3#7156611yescharacteristic, complemented
605C2#1059121411yescharacteristic
606C2#1059122111yescharacteristic
607C2#1059122511yescharacteristic
608C2#1059126212yes—
609C2#1059126512yes—
610C2#1059130011yescharacteristic
611C2#1059131112yes—
612C2#1059131311yescharacteristic
613C2#1059134212yes—
614C2#1059134411yescharacteristic
615C2#1059171011yescharacteristic
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
88. C2×Dic3⋊C4Dic3semidirect
137. C2×C3×Dic3C4⋊C4semidirect
371. C2×Dic3C4⋊Dic3semidirect
498. C32#1441semidirect
603. C3#71565semidirect
604. C3#71566semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C4⋊Dic32
C22×C3×Dic3⋊C42
C2×#636582
C2×#635792
#715663
#715653