Finite Group Databasebeta

← #11773444

Subgroups — #11773444

Order 1152.

1425 conjugacy classes of subgroups.

The subgroup lattice has 603 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic
2C22×Dic3⋊Dic3C212yesmaximal
3C2×C3×C3⋊#95C211yesmaximal, characteristic
4C2×C3×C3⋊#95C211yesmaximal, characteristic
5C2×#63579C212yesmaximal
6#69420—31nomaximal
7#69419—31nomaximal
8C23×C32×C4C2211yescharacteristic
9C23×C3⋊Dic3C2212yes—
10C23×C3×Dic3C2211yescharacteristic
11C23×C3×Dic3C2211yescharacteristic
12C23×C3×Dic3C2212yes—
13C2×C4⋊(C3⋊Dic3)—22no—
14C2×C4⋊(C3⋊Dic3)—24no—
15C2×Dic3⋊Dic3—24no—
16C2×Dic3⋊Dic3—24no—
17C2×Dic3⋊Dic3—24no—
18C3×C3⋊#95—22no—
19C3×C3⋊#95C414yescomplemented
20#63579—24no—
21C22×C4⋊Dic3—31no—
22C22×C4⋊Dic3—31no—
23C22×C4⋊Dic3—32no—
24C22×C4⋊Dic3—61no—
25C22×Dic3⋊C4—32no—
26C2×C3×#95—31no—
27C2×C3×#95—31no—
28C2×C3⋊#95—32no—
29C2×C3⋊#95—32no—
30C2×C3⋊#95D311yescharacteristic
31C2×C3⋊#95D311yescharacteristic
32C24×C32C2311yescharacteristic
33C22×C32×C4—22no—
34C22×C32×C4—22no—
35C22×C32×C4C2×C412yes—
36C22×C32×C4D412yes—
37C22×C32×C4Q812yes—
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—22no—
46C22×C3×Dic3—22no—
47C22×C3×Dic3—22no—
48C22×C3×Dic3—22no—
49C22×C3×Dic3—22no—
50C22×C3×Dic3—21no—
51C22×C3×Dic3—21no—
52C22×C3×Dic3—22no—
53C22×C3×Dic3—22no—
54C22×C3×Dic3—21no—
55C22×C3×Dic3—21no—
56C22×C3×Dic3—22no—
57C22×C3×Dic3C2×C414yes—
58C22×C3×Dic3D412yes—
59C22×C3×Dic3D414yes—
60C22×C3×Dic3Q812yes—
61C22×C3×Dic3Q814yes—
62C4⋊(C3⋊Dic3)—28no—
63Dic3⋊Dic3—216no—
64#1444—91noSylow
65C23×C3×C4—21no—
66C23×C3×C4—32no—
67C23×C3×C4—31no—
68C23×C3×C4—31no—
69C23×C3×C4C2×D311yescharacteristic
70C23×C3×C4C2×D311yescharacteristic
71C23×Dic3—32no—
72C23×Dic3—32no—
73C23×Dic3—62no—
74C23×Dic3C2×D311yescharacteristic
75C23×Dic3C2×D311yescharacteristic
76C23×Dic3C2×D312yes—
77C2×C4⋊Dic3—64no—
78C2×C4⋊Dic3—64no—
79C2×C4⋊Dic3—64no—
80C2×C4⋊Dic3—64no—
81C2×C4⋊Dic3—68no—
82C2×C4⋊Dic3—64no—
83C2×C4⋊Dic3—62no—
84C2×C4⋊Dic3—62no—
85C2×C4⋊Dic3—64no—
86C2×Dic3⋊C4—64no—
87C2×Dic3⋊C4—64no—
88C2×Dic3⋊C4—64no—
89C3×#95—34no—
90C3×#95—62no—
91C3⋊#95—22no—
92C3⋊#95—64no—
93C3⋊#95—64no—
94C3⋊#95Dic314yescomplemented
95C23×C32C22×C411yescharacteristic
96C23×C32C2×D412yes—
97C23×C32C2×D411yescharacteristic
98C23×C32C2×D411yescharacteristic
99C23×C32C2×D412yes—
100C23×C32C2×Q811yescharacteristic
101C23×C32C2×Q812yes—
102C23×C32C2×Q811yescharacteristic
103C23×C32#4111yescharacteristic
104C23×C32#4111yescharacteristic
105C23×C32#4112yes—
106C2×C32×C4—24no—
107C2×C32×C4—22no—
108C2×C32×C4—24no—
109C2×C32×C4—22no—
110C2×C32×C4C4⋊C414yescomplemented
111C2×C3⋊Dic3—24no—
112C2×C3⋊Dic3—24no—
113C2×C3⋊Dic3—24no—
114C2×C3⋊Dic3—42no—
115C2×C3⋊Dic3—42no—
116C2×C3⋊Dic3—42no—
117C2×C3⋊Dic3—42no—
118C2×C3×Dic3—24no—
119C2×C3×Dic3—24no—
120C2×C3×Dic3—24no—
121C2×C3×Dic3—24no—
122C2×C3×Dic3—24no—
123C2×C3×Dic3—24no—
124C2×C3×Dic3—24no—
125C2×C3×Dic3—22no—
126C2×C3×Dic3—24no—
127C2×C3×Dic3—22no—
128C2×C3×Dic3—41no—
129C2×C3×Dic3—42no—
130C2×C3×Dic3—42no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3C4⋊C418yescomplemented
135C22×C4⋊C4—92no—
136C22×C4⋊C4—91no—
137C2×#95—31no—
138C2×#95—31no—
139C2×#95—92no—
140C24×C3—21no—
141C24×C3C22×D311yescharacteristic
142C24×C3C22×D311yescharacteristic
143C22×C3×C4—24no—
144C22×C3×C4—24no—
145C22×C3×C4—22no—
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—34no—
153C22×C3×C4—34no—
154C22×C3×C4—34no—
155C22×C3×C4—32no—
156C22×C3×C4—32no—
157C22×C3×C4—62no—
158C22×C3×C4—62no—
159C22×C3×C4—62no—
160C22×C3×C4—62no—
161C22×C3×C4—62no—
162C22×C3×C4—61no—
163C22×C3×C4—61no—
164C22×C3×C4—62no—
165C22×C3×C4—62no—
166C22×C3×C4—61no—
167C22×C3×C4—62no—
168C22×C3×C4—61no—
169C22×C3×C4Dic612yes—
170C22×C3×C4Dic612yes—
171C22×C3×C4C4×D312yes—
172C22×C3×C4D1212yes—
173C22×C3×C4C2×Dic312yes—
174C22×C3×C4#6712yes—
175C22×Dic3—22no—
176C22×Dic3—22no—
177C22×Dic3—22no—
178C22×Dic3—22no—
179C22×Dic3—21no—
180C22×Dic3—21no—
181C22×Dic3—22no—
182C22×Dic3—22no—
183C22×Dic3—22no—
184C22×Dic3—22no—
185C22×Dic3—21no—
186C22×Dic3—21no—
187C22×Dic3—34no—
188C22×Dic3—34no—
189C22×Dic3—64no—
190C22×Dic3—64no—
191C22×Dic3—64no—
192C22×Dic3—62no—
193C22×Dic3—62no—
194C22×Dic3—62no—
195C22×Dic3—62no—
196C22×Dic3—62no—
197C22×Dic3—62no—
198C22×Dic3—62no—
199C22×Dic3—62no—
200C22×Dic3—62no—
201C22×Dic3—62no—
202C22×Dic3—62no—
203C22×Dic3—62no—
204C22×Dic3—122no—
205C22×Dic3—122no—
206C22×Dic3—122no—
207C22×Dic3—122no—
208C22×Dic3Dic612yes—
209C22×Dic3Dic614yes—
210C22×Dic3D1212yes—
211C22×Dic3D1214yes—
212C22×Dic3C2×Dic314yes—
213C4⋊Dic3—616no—
214C4⋊Dic3—616no—
215C4⋊Dic3—68no—
216C4⋊Dic3—68no—
217Dic3⋊C4—616no—
218C22×C32C2×C4⋊C412yes—
219C22×C32C2×C4⋊C411yescharacteristic
220C22×C32C4×D411yescharacteristic
221C22×C32C4×D412yes—
222C22×C32C4×Q811yescharacteristic
223C22×C32#12012yes—
224C22×C32#12011yescharacteristic
225C22×C32#12112yes—
226C22×C32#12111yescharacteristic
227C22×C32C22⋊Q812yes—
228C22×C32C22⋊Q812yes—
229C22×C32C22⋊Q812yes—
230C22×C32C22⋊Q812yes—
231C22×C32C22⋊Q811yescharacteristic
232C22×C32#12312yes—
233C22×C32#12311yescharacteristic
234C22×C32#12511yescharacteristic
235C22×C32#12512yes—
236C22×C32#12711yescharacteristic
237C22×C32C4⋊Q812yes—
238C22×C32C4⋊Q811yescharacteristic
239C22×C32C4⋊Q811yescharacteristic
240C22×C32C4⋊Q812yes—
241C32×C4—24no—
242C3⋊Dic3—44no—
243C3×Dic3—28no—
244C3×Dic3—42no—
245C3×Dic3—42no—
246C23×C4—32no—
247C23×C4—31no—
248C23×C4—31no—
249C23×C4—92no—
250C23×C4D3211yescharacteristic
251C2×C4⋊C4—184no—
252C2×C4⋊C4—184no—
253C2×C4⋊C4—184no—
254C2×C4⋊C4—184no—
255C2×C4⋊C4—182no—
256#95—34no—
257#95—62no—
258#95—184no—
259C23×C3—21no—
260C23×C3—22no—
261C23×C3—21no—
262C23×C3—21no—
263C23×C3—22no—
264C23×C3—21no—
265C23×C3—21no—
266C23×C3—22no—
267C23×C3—21no—
268C23×C3—21no—
269C23×C3—22no—
270C23×C3C2×Dic611yescharacteristic
271C23×C3C2×Dic612yes—
272C23×C3C2×Dic611yescharacteristic
273C23×C3C2×Dic611yescharacteristic
274C23×C3C2×C4×D311yescharacteristic
275C23×C3C2×D1211yescharacteristic
276C23×C3C2×D1212yes—
277C23×C3C2×D1211yescharacteristic
278C23×C3#23511yescharacteristic
279C23×C3#23511yescharacteristic
280C23×C3D3×D411yescharacteristic
281C23×C3D3×D412yes—
282C23×C3D3×D412yes—
283C23×C3D3×D412yes—
284C23×C3#23711yescharacteristic
285C23×C3#23712yes—
286C23×C3#23712yes—
287C23×C3D3×Q811yescharacteristic
288C23×C3D3×Q812yes—
289C23×C3#23911yescharacteristic
290C23×C3C22×Dic311yescharacteristic
291C23×C3C2×#6711yescharacteristic
292C2×C3×C4—24no—
293C2×C3×C4—24no—
294C2×C3×C4—28no—
295C2×C3×C4—28no—
296C2×C3×C4—24no—
297C2×C3×C4—24no—
298C2×C3×C4—24no—
299C2×C3×C4—22no—
300C2×C3×C4—22no—
301C2×C3×C4—24no—
302C2×C3×C4—22no—
303C2×C3×C4—22no—
304C2×C3×C4—24no—
305C2×C3×C4—38no—
306C2×C3×C4—64no—
307C2×C3×C4—64no—
308C2×C3×C4—64no—
309C2×C3×C4—64no—
310C2×C3×C4—64no—
311C2×C3×C4—64no—
312C2×C3×C4—64no—
313C2×C3×C4—62no—
314C2×C3×C4—62no—
315C2×C3×C4—64no—
316C2×C3×C4—121no—
317C2×C3×C4—121no—
318C2×C3×C4—121no—
319C2×C3×C4—122no—
320C2×C3×C4—121no—
321C2×C3×C4—122no—
322C2×C3×C4Dic3⋊C414yescomplemented
323C2×C3×C4C4⋊Dic314yescomplemented
324C2×Dic3—24no—
325C2×Dic3—24no—
326C2×Dic3—24no—
327C2×Dic3—24no—
328C2×Dic3—24no—
329C2×Dic3—24no—
330C2×Dic3—24no—
331C2×Dic3—24no—
332C2×Dic3—22no—
333C2×Dic3—22no—
334C2×Dic3—42no—
335C2×Dic3—42no—
336C2×Dic3—41no—
337C2×Dic3—41no—
338C2×Dic3—41no—
339C2×Dic3—41no—
340C2×Dic3—68no—
341C2×Dic3—64no—
342C2×Dic3—64no—
343C2×Dic3—64no—
344C2×Dic3—64no—
345C2×Dic3—64no—
346C2×Dic3—64no—
347C2×Dic3—124no—
348C2×Dic3—124no—
349C2×Dic3—124no—
350C2×Dic3—124no—
351C2×Dic3—124no—
352C2×Dic3—124no—
353C2×Dic3—122no—
354C2×Dic3—122no—
355C2×Dic3—122no—
356C2×Dic3—122no—
357C2×Dic3—122no—
358C2×Dic3—122no—
359C2×Dic3—122no—
360C2×Dic3—122no—
361C2×Dic3C4⋊Dic318yescomplemented
362C2×C32#38411yescharacteristic
363C2×C32#38512yes—
364C2×C32#38511yescharacteristic
365C2×C32#38912yes—
366C2×C32#38911yescharacteristic
367C2×C32#39211yescharacteristic
368C2×C32#39512yes—
369C2×C32#39511yescharacteristic
370C2×C32#39812yes—
371C2×C32#39811yescharacteristic
372C2×C32#39911yescharacteristic
373C24C2×D3211yescharacteristic
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—34no—
377C22×C4—34no—
378C22×C4—34no—
379C22×C4—32no—
380C22×C4—32no—
381C22×C4—62no—
382C22×C4—62no—
383C22×C4—62no—
384C22×C4—62no—
385C22×C4—61no—
386C22×C4—61no—
387C22×C4—62no—
388C22×C4—62no—
389C22×C4—62no—
390C22×C4—61no—
391C22×C4—61no—
392C22×C4—62no—
393C22×C4—94no—
394C22×C4—182no—
395C22×C4—182no—
396C22×C4—182no—
397C22×C4—182no—
398C22×C4—182no—
399C22×C4—182no—
400C22×C4D3×Dic312yes—
401C22×C4#62612yes—
402C22×C4#62712yes—
403C4⋊C4—188no—
404C4⋊C4—1816no—
405C22×C3—22no—
406C22×C3—21no—
407C22×C3—22no—
408C22×C3—21no—
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—22no—
412C22×C3—22no—
413C22×C3—21no—
414C22×C3—22no—
415C22×C3—22no—
416C22×C3—22no—
417C22×C3—21no—
418C22×C3—22no—
419C22×C3—21no—
420C22×C3—22no—
421C22×C3—21no—
422C22×C3—22no—
423C22×C3—21no—
424C22×C3—21no—
425C22×C3—22no—
426C22×C3—21no—
427C22×C3—22no—
428C22×C3C4×Dic611yescharacteristic
429C22×C3#86911yescharacteristic
430C22×C3#86911yescharacteristic
431C22×C3#86912yes—
432C22×C3#87011yescharacteristic
433C22×C3C4×D1211yescharacteristic
434C22×C3#87411yescharacteristic
435C22×C3#87812yes—
436C22×C3#87812yes—
437C22×C3#87812yes—
438C22×C3#87812yes—
439C22×C3#87812yes—
440C22×C3#67⋊C412yes—
441C22×C3#88212yes—
442C22×C3#88212yes—
443C22×C3#88211yescharacteristic
444C22×C3#88312yes—
445C22×C3#88412yes—
446C22×C3#88612yes—
447C22×C3#88611yescharacteristic
448C22×C3#88812yes—
449C22×C3#88812yes—
450C22×C3#88811yescharacteristic
451C22×C3#88812yes—
452C22×C3#88912yes—
453C22×C3#89012yes—
454C22×C3#89011yescharacteristic
455C22×C3D3×C4⋊C412yes—
456C22×C3#89511yescharacteristic
457C22×C3#89512yes—
458C22×C3#89612yes—
459C22×C3#89711yescharacteristic
460C22×C3#89712yes—
461C22×C3#89712yes—
462C22×C3C2×Dic3⋊C411yescharacteristic
463C22×C3#92411yescharacteristic
464C22×C3C2×C4⋊Dic312yes—
465C22×C3C2×C4⋊Dic311yescharacteristic
466C22×C3#93011yescharacteristic
467C22×C3D4×Dic311yescharacteristic
468C22×C3D4×Dic312yes—
469C22×C3#93511yescharacteristic
470C22×C3#93711yescharacteristic
471C22×C3#94011yescharacteristic
472C22×C3#94411yescharacteristic
473C22×C3Q8×Dic311yescharacteristic
474C3×C4—28no—
475C3×C4—24no—
476C3×C4—24no—
477C3×C4—68no—
478C3×C4—122no—
479C3×C4—122no—
480Dic3—28no—
481Dic3—42no—
482Dic3—42no—
483Dic3—128no—
484Dic3—124no—
485Dic3—124no—
486C32#144411yescharacteristic, complemented, Sylow
487C23D3×Dic611yescharacteristic
488C23D3×Dic612yes—
489C23#379511yescharacteristic
490C23#379911yescharacteristic
491C23D3×D1212yes—
492C23D3×D1211yescharacteristic
493C23C2×D3×Dic311yescharacteristic
494C23#380512yes—
495C23C2×#62611yescharacteristic
496C23C2×#62711yescharacteristic
497C23#381112yes—
498C2×C4—22no—
499C2×C4—24no—
500C2×C4—22no—
501C2×C4—24no—
502C2×C4—38no—
503C2×C4—64no—
504C2×C4—64no—
505C2×C4—64no—
506C2×C4—64no—
507C2×C4—64no—
508C2×C4—64no—
509C2×C4—62no—
510C2×C4—64no—
511C2×C4—62no—
512C2×C4—64no—
513C2×C4—122no—
514C2×C4—122no—
515C2×C4—121no—
516C2×C4—121no—
517C2×C4—121no—
518C2×C4—121no—
519C2×C4—184no—
520C2×C4—184no—
521C2×C4—184no—
522C2×C4—362no—
523C2×C4—362no—
524C2×C4—362no—
525C2×C4—362no—
526C2×C4Dic3⋊Dic314yescomplemented
527C2×C3—22no—
528C2×C3—21no—
529C2×C3—21no—
530C2×C3—22no—
531C2×C3—21no—
532C2×C3—21no—
533C2×C3—21no—
534C2×C3—22no—
535C2×C3—21no—
536C2×C3—22no—
537C2×C3—21no—
538C2×C3#464712yes—
539C2×C3#465611yescharacteristic
540C2×C3#465612yes—
541C2×C3#465612yes—
542C2×C3#465712yes—
543C2×C3#466112yes—
544C2×C3#466111yescharacteristic
545C2×C3#466812yes—
546C2×C3#467111yescharacteristic
547C2×C3#467711yescharacteristic
548C2×C3#492811yescharacteristic
549C2×C3#493511yescharacteristic
550C2×C3#494611yescharacteristic
551C2×C3#494911yescharacteristic
552C2×C3#495012yes—
553C2×C3#495011yescharacteristic
554C2×C3#496011yescharacteristic
555C2×C3#497511yescharacteristic
556C2×C3#497911yescharacteristic
557C2×C3#498111yescharacteristic
558C2×C3#498412yes—
559C2×C3#498411yescharacteristic
560C22#6384012yes—
561C22Dic3×Dic611yescharacteristic
562C22#6384512yes—
563C22#6385711yescharacteristic
564C22#6386611yescharacteristic
565C22#6386911yescharacteristic
566C22D3×C4⋊Dic312yes—
567C22#6389112yes—
568C22Dic3×D1211yescharacteristic
569C22#6389312yes—
570C22#6389312yes—
571C22#6389612yes—
572C22#6390911yescharacteristic
573C22#6391012yes—
574C22#6391111yescharacteristic
575C22#6391812yes—
576C22#6391811yescharacteristic
577C22#6392312yes—
578C22#6396211yescharacteristic
579C22C2×Dic3⋊Dic311yescharacteristic
580C22#67⋊Dic312yes—
581C22#6398111yescharacteristic
582C22#6398212yes—
583C4—24no—
584C4—68no—
585C4—122no—
586C4—122no—
587C4—364no—
588C3—21no—
589C3#6941911yescharacteristic, complemented
590C3#6942011yescharacteristic, complemented
591C2#1059126812yes—
592C2#1059131711yescharacteristic
593C2#1059134911yescharacteristic
594C2#1059135112yes—
595C2#1059135211yescharacteristic
596C2#1059135311yescharacteristic
597C2#1059135411yescharacteristic
598C2#1059137912yes—
599C2#1059139511yescharacteristic
600C2#1059139712yes—
601C2#1059171911yescharacteristic
subgroupG/H
center, FrattiniC24C2×D32
commutatorC23×C32C22×C4
FittingC23×C32×C4C22
socle, prime radical, cosocleC24×C32C23
hypercenterC23×C4D32
hypocenterC32#1444
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
19. C3×C3⋊#95C4semidirect
94. C3⋊#95Dic3semidirect
110. C2×C32×C4C4⋊C4semidirect
134. C2×C3×Dic3C4⋊C4semidirect
322. C2×C3×C4Dic3⋊C4semidirect
323. C2×C3×C4C4⋊Dic3semidirect
361. C2×Dic3C4⋊Dic3semidirect
486. C32#1444semidirect
526. C2×C4Dic3⋊Dic3semidirect
589. C3#69419semidirect
590. C3#69420semidirect

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×Dic3⋊Dic32
C2×C3×C3⋊#952
C2×#635792
#694203
#694193