Finite Group Databasebeta

← #11773404

Subgroups — #11773404

Order 1152.

1205 conjugacy classes of subgroups.

The subgroup lattice has 589 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4⋊Dic3C211yesmaximal, characteristic
2C2×#63658C211yesmaximal, characteristic
3C2×C3×C3⋊#95C211yesmaximal, characteristic
4C2×#63579C212yesmaximal
5C2×#63579C212yesmaximal
6#71567—31nomaximal
7#69415—31nomaximal
8C23×C32×C4C2211yescharacteristic
9C23×C3⋊Dic3C2212yes—
10C23×C3×Dic3C2212yes—
11C23×C3×Dic3C2211yescharacteristic
12C23×C3×Dic3C2211yescharacteristic
13C2×C3×C4⋊Dic3—22no—
14C2×C3×C4⋊Dic3—24no—
15#63658C414yescomplemented
16C3×C3⋊#95—22no—
17#63579—24no—
18#63579—24no—
19C22×C3×C4⋊C4—31no—
20C22×C4⋊Dic3D311yescharacteristic
21C2×C3×#95—31no—
22C2×C3⋊#95—31no—
23C2×C3⋊#95—31no—
24C2×C3⋊#95—32no—
25C2×C3⋊#95—32no—
26C2×C3⋊#95—32no—
27C2×C3⋊#95—32no—
28C2×C3⋊#95—61no—
29C2×C3⋊#95D311yescharacteristic
30C24×C32C2311yescharacteristic
31C22×C32×C4—22no—
32C22×C32×C4—22no—
33C22×C32×C4C2×C412yes—
34C22×C32×C4D412yes—
35C22×C32×C4Q812yes—
36C22×C3⋊Dic3—22no—
37C22×C3⋊Dic3—22no—
38C22×C3⋊Dic3—22no—
39C22×C3⋊Dic3—22no—
40C22×C3⋊Dic3—22no—
41C22×C3⋊Dic3—22no—
42C22×C3⋊Dic3C2×C414yes—
43C22×C3×Dic3—22no—
44C22×C3×Dic3—22no—
45C22×C3×Dic3—22no—
46C22×C3×Dic3—22no—
47C22×C3×Dic3—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3—22no—
50C22×C3×Dic3—21no—
51C22×C3×Dic3—21no—
52C22×C3×Dic3—22no—
53C22×C3×Dic3—22no—
54C22×C3×Dic3—22no—
55C22×C3×Dic3—22no—
56C22×C3×Dic3—22no—
57C22×C3×Dic3D412yes—
58C22×C3×Dic3D414yes—
59C22×C3×Dic3Q812yes—
60C3×C4⋊Dic3—28no—
61#1442—91noSylow
62C23×C3×C4—21no—
63C23×C3×C4—31no—
64C23×C3×C4—31no—
65C23×C3×C4—32no—
66C23×C3×C4C2×D311yescharacteristic
67C23×C3×C4C2×D311yescharacteristic
68C23×Dic3—32no—
69C23×Dic3—32no—
70C23×Dic3—62no—
71C23×Dic3C2×D311yescharacteristic
72C23×Dic3C2×D311yescharacteristic
73C23×Dic3C2×D312yes—
74C2×C3×C4⋊C4—64no—
75C2×C3×C4⋊C4—62no—
76C2×C4⋊Dic3—22no—
77C2×C4⋊Dic3—24no—
78C3×#95—62no—
79C3⋊#95—22no—
80C3⋊#95—34no—
81C3⋊#95—34no—
82C3⋊#95—64no—
83C3⋊#95—64no—
84C3⋊#95—64no—
85C3⋊#95—64no—
86C3⋊#95—64no—
87C23×C32C22×C411yescharacteristic
88C23×C32C2×D411yescharacteristic
89C23×C32C2×D412yes—
90C23×C32C2×D411yescharacteristic
91C23×C32C2×Q811yescharacteristic
92C23×C32C2×Q811yescharacteristic
93C23×C32#4112yes—
94C23×C32#4111yescharacteristic
95C23×C32#4111yescharacteristic
96C23×C32#4112yes—
97C23×C32#4112yes—
98C2×C32×C4—24no—
99C2×C32×C4—22no—
100C2×C32×C4—24no—
101C2×C32×C4—22no—
102C2×C32×C4C4⋊C414yes—
103C2×C3⋊Dic3—24no—
104C2×C3⋊Dic3—24no—
105C2×C3⋊Dic3—24no—
106C2×C3⋊Dic3—42no—
107C2×C3⋊Dic3—42no—
108C2×C3⋊Dic3—42no—
109C2×C3⋊Dic3—42no—
110C2×C3×Dic3—24no—
111C2×C3×Dic3—22no—
112C2×C3×Dic3—24no—
113C2×C3×Dic3—24no—
114C2×C3×Dic3—22no—
115C2×C3×Dic3—24no—
116C2×C3×Dic3—24no—
117C2×C3×Dic3—41no—
118C2×C3×Dic3—42no—
119C2×C3×Dic3—42no—
120C2×C3×Dic3—42no—
121C2×C3×Dic3—41no—
122C2×C3×Dic3—42no—
123C2×C3×Dic3—41no—
124C2×C3×Dic3—42no—
125C2×C3×Dic3—41no—
126C2×C3×Dic3—42no—
127C22×C4⋊C4—31no—
128C2×#95—31no—
129C2×#95—91no—
130C2×#95—92no—
131C2×#95—92no—
132C24×C3—21no—
133C24×C3C22×D311yescharacteristic
134C24×C3C22×D311yescharacteristic
135C22×C3×C4—22no—
136C22×C3×C4—22no—
137C22×C3×C4—22no—
138C22×C3×C4—22no—
139C22×C3×C4—22no—
140C22×C3×C4—22no—
141C22×C3×C4—22no—
142C22×C3×C4—32no—
143C22×C3×C4—34no—
144C22×C3×C4—32no—
145C22×C3×C4—42no—
146C22×C3×C4—42no—
147C22×C3×C4—62no—
148C22×C3×C4—62no—
149C22×C3×C4—62no—
150C22×C3×C4—62no—
151C22×C3×C4—61no—
152C22×C3×C4—62no—
153C22×C3×C4—62no—
154C22×C3×C4—62no—
155C22×C3×C4—62no—
156C22×C3×C4—61no—
157C22×C3×C4—62no—
158C22×C3×C4—61no—
159C22×C3×C4—61no—
160C22×C3×C4—62no—
161C22×C3×C4Dic612yes—
162C22×C3×C4Dic612yes—
163C22×C3×C4C4×D312yes—
164C22×C3×C4C4×D312yes—
165C22×C3×C4#6712yes—
166C22×C3×C4#6712yes—
167C22×Dic3—21no—
168C22×Dic3—21no—
169C22×Dic3—22no—
170C22×Dic3—22no—
171C22×Dic3—22no—
172C22×Dic3—22no—
173C22×Dic3—22no—
174C22×Dic3—22no—
175C22×Dic3—22no—
176C22×Dic3—22no—
177C22×Dic3—21no—
178C22×Dic3—21no—
179C22×Dic3—22no—
180C22×Dic3—22no—
181C22×Dic3—34no—
182C22×Dic3—34no—
183C22×Dic3—64no—
184C22×Dic3—64no—
185C22×Dic3—64no—
186C22×Dic3—62no—
187C22×Dic3—62no—
188C22×Dic3—62no—
189C22×Dic3—62no—
190C22×Dic3—62no—
191C22×Dic3—62no—
192C22×Dic3—62no—
193C22×Dic3—62no—
194C22×Dic3—62no—
195C22×Dic3—62no—
196C22×Dic3—62no—
197C22×Dic3—62no—
198C22×Dic3—122no—
199C22×Dic3—122no—
200C22×Dic3—122no—
201C22×Dic3—122no—
202C22×Dic3Dic612yes—
203C22×Dic3D1212yes—
204C22×Dic3#6714yes—
205C3×C4⋊C4—68no—
206C4⋊Dic3—28no—
207C22×C32C2×C4⋊C411yescharacteristic
208C22×C32#11712yes—
209C22×C32C4×D411yescharacteristic
210C22×C32C4×D412yes—
211C22×C32C4×Q811yescharacteristic
212C22×C32#12011yescharacteristic
213C22×C32#12112yes—
214C22×C32#12111yescharacteristic
215C22×C32C22⋊Q812yes—
216C22×C32C22⋊Q812yes—
217C22×C32C22⋊Q811yescharacteristic
218C22×C32#12312yes—
219C22×C32#12312yes—
220C22×C32#12311yescharacteristic
221C22×C32#12412yes—
222C22×C32#12411yescharacteristic
223C22×C32#12411yescharacteristic
224C22×C32#12511yescharacteristic
225C22×C32#12512yes—
226C22×C32#12512yes—
227C22×C32#12612yes—
228C22×C32#12612yes—
229C22×C32C4⋊Q811yescharacteristic
230C32×C4—24no—
231C3⋊Dic3—44no—
232C3×Dic3—42no—
233C3×Dic3—44no—
234C3×Dic3—42no—
235C23×C4—32no—
236C23×C4—31no—
237C23×C4—31no—
238C23×C4—92no—
239C23×C4D3211yescharacteristic
240C2×C4⋊C4—64no—
241C2×C4⋊C4—62no—
242#95—62no—
243#95—94no—
244#95—184no—
245#95—184no—
246C23×C3—21no—
247C23×C3—21no—
248C23×C3—22no—
249C23×C3—22no—
250C23×C3—21no—
251C23×C3—21no—
252C23×C3—22no—
253C23×C3—21no—
254C23×C3—21no—
255C23×C3—21no—
256C23×C3—22no—
257C23×C3C2×Dic611yescharacteristic
258C23×C3C2×Dic611yescharacteristic
259C23×C3C2×Dic611yescharacteristic
260C23×C3C2×C4×D311yescharacteristic
261C23×C3C2×C4×D311yescharacteristic
262C23×C3C2×D1211yescharacteristic
263C23×C3#23511yescharacteristic
264C23×C3#23511yescharacteristic
265C23×C3#23512yes—
266C23×C3D3×D411yescharacteristic
267C23×C3D3×D412yes—
268C23×C3#23711yescharacteristic
269C23×C3#23712yes—
270C23×C3#23712yes—
271C23×C3#23712yes—
272C23×C3D3×Q811yescharacteristic
273C23×C3#23912yes—
274C23×C3#23912yes—
275C23×C3#23911yescharacteristic
276C23×C3C2×#6711yescharacteristic
277C23×C3C2×#6711yescharacteristic
278C23×C3C2×#6712yes—
279C2×C3×C4—24no—
280C2×C3×C4—24no—
281C2×C3×C4—24no—
282C2×C3×C4—24no—
283C2×C3×C4—22no—
284C2×C3×C4—22no—
285C2×C3×C4—22no—
286C2×C3×C4—22no—
287C2×C3×C4—24no—
288C2×C3×C4—44no—
289C2×C3×C4—42no—
290C2×C3×C4—44no—
291C2×C3×C4—42no—
292C2×C3×C4—64no—
293C2×C3×C4—64no—
294C2×C3×C4—64no—
295C2×C3×C4—64no—
296C2×C3×C4—62no—
297C2×C3×C4—62no—
298C2×C3×C4—64no—
299C2×C3×C4—122no—
300C2×C3×C4—122no—
301C2×C3×C4—122no—
302C2×C3×C4—121no—
303C2×C3×C4—122no—
304C2×C3×C4—121no—
305C2×C3×C4—122no—
306C2×C3×C4—121no—
307C2×C3×C4—122no—
308C2×C3×C4—121no—
309C2×C3×C4Dic3⋊C414yes—
310C2×C3×C4Dic3⋊C414yes—
311C2×Dic3—24no—
312C2×Dic3—24no—
313C2×Dic3—22no—
314C2×Dic3—22no—
315C2×Dic3—24no—
316C2×Dic3—24no—
317C2×Dic3—24no—
318C2×Dic3—42no—
319C2×Dic3—42no—
320C2×Dic3—42no—
321C2×Dic3—41no—
322C2×Dic3—41no—
323C2×Dic3—41no—
324C2×Dic3—42no—
325C2×Dic3—41no—
326C2×Dic3—42no—
327C2×Dic3—42no—
328C2×Dic3—68no—
329C2×Dic3—64no—
330C2×Dic3—64no—
331C2×Dic3—64no—
332C2×Dic3—64no—
333C2×Dic3—64no—
334C2×Dic3—64no—
335C2×Dic3—124no—
336C2×Dic3—124no—
337C2×Dic3—124no—
338C2×Dic3—124no—
339C2×Dic3—124no—
340C2×Dic3—124no—
341C2×Dic3—122no—
342C2×Dic3—122no—
343C2×Dic3—122no—
344C2×Dic3—122no—
345C2×Dic3—122no—
346C2×Dic3—122no—
347C2×Dic3—122no—
348C2×Dic3—122no—
349C2×C32#38211yescharacteristic
350C2×C32#38511yescharacteristic
351C2×C32#38712yes—
352C2×C32#38812yes—
353C2×C32#38911yescharacteristic
354C2×C32#39311yescharacteristic
355C2×C32#39411yescharacteristic
356C2×C32#39711yescharacteristic
357C2×C32#39812yes—
358C2×C32#40012yes—
359C2×C32#40011yescharacteristic
360C24C2×D3211yescharacteristic
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—32no—
364C22×C4—32no—
365C22×C4—34no—
366C22×C4—62no—
367C22×C4—61no—
368C22×C4—62no—
369C22×C4—62no—
370C22×C4—62no—
371C22×C4—62no—
372C22×C4—61no—
373C22×C4—62no—
374C22×C4—62no—
375C22×C4—61no—
376C22×C4—61no—
377C22×C4—62no—
378C22×C4—62no—
379C22×C4—62no—
380C22×C4—94no—
381C22×C4—182no—
382C22×C4—182no—
383C22×C4—182no—
384C22×C4—182no—
385C22×C4—182no—
386C22×C4—182no—
387C22×C4#62412yes—
388C22×C4#62512yes—
389C22×C4#62712yes—
390C4⋊C4—68no—
391C22×C3—21no—
392C22×C3—22no—
393C22×C3—22no—
394C22×C3—22no—
395C22×C3—21no—
396C22×C3—22no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—22no—
401C22×C3—22no—
402C22×C3—22no—
403C22×C3—22no—
404C22×C3—22no—
405C22×C3—21no—
406C22×C3—22no—
407C22×C3—21no—
408C22×C3—21no—
409C22×C3—22no—
410C22×C3—21no—
411C22×C3—22no—
412C22×C3—21no—
413C22×C3—21no—
414C22×C3C4×Dic611yescharacteristic
415C22×C3#86911yescharacteristic
416C22×C3#87011yescharacteristic
417C22×C3C4×D1211yescharacteristic
418C22×C3#87812yes—
419C22×C3#87812yes—
420C22×C3#87912yes—
421C22×C3#67⋊C412yes—
422C22×C3#88512yes—
423C22×C3#88612yes—
424C22×C3#88711yescharacteristic
425C22×C3#88811yescharacteristic
426C22×C3#88912yes—
427C22×C3#89012yes—
428C22×C3#89011yescharacteristic
429C22×C3#89012yes—
430C22×C3#89012yes—
431C22×C3#89212yes—
432C22×C3#89212yes—
433C22×C3#89311yescharacteristic
434C22×C3#89412yes—
435C22×C3#89412yes—
436C22×C3#89512yes—
437C22×C3#89812yes—
438C22×C3#89812yes—
439C22×C3#89812yes—
440C22×C3C2×Dic3⋊C411yescharacteristic
441C22×C3C2×Dic3⋊C411yescharacteristic
442C22×C3#92411yescharacteristic
443C22×C3#92412yes—
444C22×C3C4×#6712yes—
445C22×C3#92911yescharacteristic
446C22×C3#93011yescharacteristic
447C22×C3#93512yes—
448C22×C3#93511yescharacteristic
449C22×C3#93611yescharacteristic
450C22×C3#93611yescharacteristic
451C22×C3#93711yescharacteristic
452C22×C3#93811yescharacteristic
453C22×C3#93912yes—
454C22×C3#94611yescharacteristic
455C22×C3#94612yes—
456C22×C3#94711yescharacteristic
457C22×C3#94711yescharacteristic
458C22×C3#94712yes—
459C22×C3#95311yescharacteristic
460C3×C4—24no—
461C3×C4—24no—
462C3×C4—44no—
463C3×C4—122no—
464C3×C4—124no—
465C3×C4—122no—
466Dic3—42no—
467Dic3—42no—
468Dic3—44no—
469Dic3—128no—
470Dic3—124no—
471Dic3—124no—
472C32#144211yescharacteristic, complemented, Sylow
473C23D3×Dic611yescharacteristic
474C23#379511yescharacteristic
475C23#379612yes—
476C23#379612yes—
477C23#379911yescharacteristic
478C23D3×D1211yescharacteristic
479C23#380412yes—
480C23C2×#62411yescharacteristic
481C23C2×#62511yescharacteristic
482C23C2×#62711yescharacteristic
483C23D3×#6712yes—
484C2×C4—24no—
485C2×C4—22no—
486C2×C4—24no—
487C2×C4—22no—
488C2×C4—62no—
489C2×C4—64no—
490C2×C4—64no—
491C2×C4—64no—
492C2×C4—64no—
493C2×C4—62no—
494C2×C4—64no—
495C2×C4—122no—
496C2×C4—122no—
497C2×C4—121no—
498C2×C4—121no—
499C2×C4—122no—
500C2×C4—122no—
501C2×C4—122no—
502C2×C4—122no—
503C2×C4—121no—
504C2×C4—121no—
505C2×C4—184no—
506C2×C4—184no—
507C2×C4—184no—
508C2×C4—362no—
509C2×C4—362no—
510C2×C4—362no—
511C2×C4—362no—
512C2×C4#372414yes—
513C2×C3—22no—
514C2×C3—22no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—22no—
519C2×C3—22no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—21no—
524C2×C3#465512yes—
525C2×C3#466012yes—
526C2×C3#466112yes—
527C2×C3#467012yes—
528C2×C3#492811yescharacteristic
529C2×C3#494611yescharacteristic
530C2×C3#494711yescharacteristic
531C2×C3#495311yescharacteristic
532C2×C3#497211yescharacteristic
533C2×C3#497711yescharacteristic
534C2×C3#497711yescharacteristic
535C2×C3#497812yes—
536C2×C3#498212yes—
537C2×C3#498511yescharacteristic
538C2×C3#498612yes—
539C2×C3#498611yescharacteristic
540C2×C3#499012yes—
541C2×C3#499111yescharacteristic
542C2×C3#499211yescharacteristic
543C2×C3#521011yescharacteristic
544C2×C3#522211yescharacteristic
545C2×C3#523111yescharacteristic
546C22#6384411yescharacteristic
547C22#6384612yes—
548C22#6384812yes—
549C22#6384912yes—
550C22#6385611yescharacteristic
551C22#6385812yes—
552C22#6386311yescharacteristic
553C22#6386311yescharacteristic
554C22#6386911yescharacteristic
555C22#6387212yes—
556C22#6388412yes—
557C22#6388612yes—
558C22#6388712yes—
559C22#6389012yes—
560C22#6389411yescharacteristic
561C22#6390712yes—
562C22#6390811yescharacteristic
563C22#6391811yescharacteristic
564C22#6395212yes—
565C22#6396111yescharacteristic
566C22#6396412yes—
567C22C2×#372411yescharacteristic
568C22#6397611yescharacteristic
569C4—24no—
570C4—124no—
571C4—122no—
572C4—122no—
573C4—364no—
574C3—21no—
575C3#6941511yescharacteristic, complemented
576C3#7156711yescharacteristic, complemented
577C2#1059121211yescharacteristic
578C2#1059122511yescharacteristic
579C2#1059123011yescharacteristic
580C2#1059126312yes—
581C2#1059126612yes—
582C2#1059130011yescharacteristic
583C2#1059130411yescharacteristic
584C2#1059131411yescharacteristic
585C2#1059134312yes—
586C2#1059134812yes—
587C2#1059169311yescharacteristic
subgroupG/H
center, FrattiniC24C2×D32
commutatorC23×C32C22×C4
FittingC23×C32×C4C22
socle, prime radical, cosocleC24×C32C23
hypercenterC23×C4D32
hypocenterC32#1442
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
15. #63658C4semidirect
472. C32#1442semidirect
575. C3#69415semidirect
576. C3#71567semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C4⋊Dic32
C2×#636582
C2×C3×C3⋊#952
C2×#635792
#715673
#694153