Finite Group Databasebeta

← #11773405

Subgroups — #11773405

Order 1152.

1249 conjugacy classes of subgroups.

The subgroup lattice has 591 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic
2C2×C3×C3⋊#95C211yesmaximal, characteristic
3C2×C3×C3⋊#95C211yesmaximal, characteristic
4C2×#63579C212yesmaximal
5C2×#63579C212yesmaximal
6#69415—31nomaximal
7#69412—31nomaximal
8C23×C32×C4C2211yescharacteristic
9C23×C3⋊Dic3C2212yes—
10C23×C3×Dic3C2212yes—
11C23×C3×Dic3C2211yescharacteristic
12C23×C3×Dic3C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)—22no—
14C2×C4⋊(C3⋊Dic3)—24no—
15C3×C3⋊#95—22no—
16C3×C3⋊#95C414yescomplemented
17#63579—24no—
18#63579—24no—
19C22×C4⋊Dic3—31no—
20C22×C4⋊Dic3—31no—
21C22×C4⋊Dic3—61no—
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⋊#95D311yescharacteristic
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⋊Dic3D414yes—
43C22×C3×Dic3—22no—
44C22×C3×Dic3—22no—
45C22×C3×Dic3—22no—
46C22×C3×Dic3—21no—
47C22×C3×Dic3—21no—
48C22×C3×Dic3—22no—
49C22×C3×Dic3—22no—
50C22×C3×Dic3—22no—
51C22×C3×Dic3—22no—
52C22×C3×Dic3—21no—
53C22×C3×Dic3—22no—
54C22×C3×Dic3—21no—
55C22×C3×Dic3—22no—
56C22×C3×Dic3—22no—
57C22×C3×Dic3C2×C414yes—
58C22×C3×Dic3D412yes—
59C22×C3×Dic3Q812yes—
60C4⋊(C3⋊Dic3)—28no—
61#1442—91noSylow
62C23×C3×C4—21no—
63C23×C3×C4—32no—
64C23×C3×C4—31no—
65C23×C3×C4—31no—
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×C4⋊Dic3—64no—
75C2×C4⋊Dic3—64no—
76C2×C4⋊Dic3—68no—
77C2×C4⋊Dic3—64no—
78C2×C4⋊Dic3—62no—
79C2×C4⋊Dic3—62no—
80C3×#95—34no—
81C3×#95—62no—
82C3⋊#95—22no—
83C3⋊#95—64no—
84C3⋊#95—64no—
85C3⋊#95—64no—
86C3⋊#95—64no—
87C3⋊#95Dic314yescomplemented
88C23×C32C22×C411yescharacteristic
89C23×C32C2×D411yescharacteristic
90C23×C32C2×D411yescharacteristic
91C23×C32C2×D412yes—
92C23×C32C2×Q811yescharacteristic
93C23×C32C2×Q811yescharacteristic
94C23×C32#4112yes—
95C23×C32#4111yescharacteristic
96C23×C32#4112yes—
97C23×C32#4111yescharacteristic
98C23×C32#4112yes—
99C2×C32×C4—24no—
100C2×C32×C4—22no—
101C2×C32×C4—24no—
102C2×C32×C4—22no—
103C2×C32×C4C4⋊C414yes—
104C2×C3⋊Dic3—24no—
105C2×C3⋊Dic3—24no—
106C2×C3⋊Dic3—24no—
107C2×C3⋊Dic3—42no—
108C2×C3⋊Dic3—42no—
109C2×C3⋊Dic3—42no—
110C2×C3⋊Dic3—42no—
111C2×C3×Dic3—24no—
112C2×C3×Dic3—24no—
113C2×C3×Dic3—24no—
114C2×C3×Dic3—22no—
115C2×C3×Dic3—24no—
116C2×C3×Dic3—22no—
117C2×C3×Dic3—24no—
118C2×C3×Dic3—41no—
119C2×C3×Dic3—42no—
120C2×C3×Dic3—42no—
121C2×C3×Dic3—41no—
122C2×C3×Dic3—42no—
123C2×C3×Dic3—42no—
124C2×C3×Dic3—41no—
125C2×C3×Dic3—41no—
126C2×C3×Dic3—42no—
127C2×C3×Dic3—42no—
128C22×C4⋊C4—91no—
129C2×#95—31no—
130C2×#95—31no—
131C2×#95—92no—
132C2×#95—92no—
133C24×C3—21no—
134C24×C3C22×D311yescharacteristic
135C24×C3C22×D311yescharacteristic
136C22×C3×C4—24no—
137C22×C3×C4—24no—
138C22×C3×C4—22no—
139C22×C3×C4—22no—
140C22×C3×C4—22no—
141C22×C3×C4—22no—
142C22×C3×C4—22no—
143C22×C3×C4—22no—
144C22×C3×C4—22no—
145C22×C3×C4—34no—
146C22×C3×C4—32no—
147C22×C3×C4—32no—
148C22×C3×C4—62no—
149C22×C3×C4—61no—
150C22×C3×C4—61no—
151C22×C3×C4—62no—
152C22×C3×C4—62no—
153C22×C3×C4—62no—
154C22×C3×C4—62no—
155C22×C3×C4—62no—
156C22×C3×C4—62no—
157C22×C3×C4—61no—
158C22×C3×C4—62no—
159C22×C3×C4—62no—
160C22×C3×C4—62no—
161C22×C3×C4—61no—
162C22×C3×C4Dic612yes—
163C22×C3×C4Dic612yes—
164C22×C3×C4C4×D312yes—
165C22×C3×C4D1212yes—
166C22×C3×C4C2×Dic312yes—
167C22×C3×C4#6712yes—
168C22×Dic3—21no—
169C22×Dic3—22no—
170C22×Dic3—22no—
171C22×Dic3—21no—
172C22×Dic3—22no—
173C22×Dic3—22no—
174C22×Dic3—22no—
175C22×Dic3—22no—
176C22×Dic3—22no—
177C22×Dic3—22no—
178C22×Dic3—22no—
179C22×Dic3—22no—
180C22×Dic3—21no—
181C22×Dic3—21no—
182C22×Dic3—34no—
183C22×Dic3—34no—
184C22×Dic3—64no—
185C22×Dic3—64no—
186C22×Dic3—64no—
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—62no—
199C22×Dic3—122no—
200C22×Dic3—122no—
201C22×Dic3—122no—
202C22×Dic3—122no—
203C22×Dic3Dic612yes—
204C22×Dic3D1212yes—
205C22×Dic3C2×Dic314yes—
206C4⋊Dic3—616no—
207C4⋊Dic3—68no—
208C4⋊Dic3—68no—
209C22×C32C2×C4⋊C411yescharacteristic
210C22×C32#11712yes—
211C22×C32C4×D411yescharacteristic
212C22×C32C4×D412yes—
213C22×C32C4×Q811yescharacteristic
214C22×C32#12011yescharacteristic
215C22×C32#12112yes—
216C22×C32#12111yescharacteristic
217C22×C32C22⋊Q812yes—
218C22×C32C22⋊Q812yes—
219C22×C32C22⋊Q811yescharacteristic
220C22×C32#12312yes—
221C22×C32#12311yescharacteristic
222C22×C32#12312yes—
223C22×C32#12411yescharacteristic
224C22×C32#12411yescharacteristic
225C22×C32#12412yes—
226C22×C32#12512yes—
227C22×C32#12511yescharacteristic
228C22×C32#12512yes—
229C22×C32#12612yes—
230C22×C32#12612yes—
231C22×C32C4⋊Q811yescharacteristic
232C32×C4—24no—
233C3⋊Dic3—44no—
234C3×Dic3—44no—
235C3×Dic3—42no—
236C3×Dic3—42no—
237C23×C4—31no—
238C23×C4—31no—
239C23×C4—32no—
240C23×C4—92no—
241C23×C4D3211yescharacteristic
242C2×C4⋊C4—184no—
243C2×C4⋊C4—182no—
244#95—34no—
245#95—62no—
246#95—184no—
247#95—184no—
248C23×C3—21no—
249C23×C3—22no—
250C23×C3—21no—
251C23×C3—22no—
252C23×C3—21no—
253C23×C3—21no—
254C23×C3—21no—
255C23×C3—22no—
256C23×C3—21no—
257C23×C3—21no—
258C23×C3—22no—
259C23×C3C2×Dic611yescharacteristic
260C23×C3C2×Dic611yescharacteristic
261C23×C3C2×Dic611yescharacteristic
262C23×C3C2×C4×D311yescharacteristic
263C23×C3C2×D1211yescharacteristic
264C23×C3C2×D1211yescharacteristic
265C23×C3#23511yescharacteristic
266C23×C3#23512yes—
267C23×C3#23511yescharacteristic
268C23×C3#23512yes—
269C23×C3D3×D411yescharacteristic
270C23×C3D3×D412yes—
271C23×C3D3×D412yes—
272C23×C3#23712yes—
273C23×C3#23711yescharacteristic
274C23×C3#23712yes—
275C23×C3#23712yes—
276C23×C3D3×Q811yescharacteristic
277C23×C3#23912yes—
278C23×C3#23911yescharacteristic
279C23×C3C22×Dic311yescharacteristic
280C23×C3C2×#6711yescharacteristic
281C2×C3×C4—24no—
282C2×C3×C4—24no—
283C2×C3×C4—28no—
284C2×C3×C4—28no—
285C2×C3×C4—24no—
286C2×C3×C4—24no—
287C2×C3×C4—24no—
288C2×C3×C4—22no—
289C2×C3×C4—22no—
290C2×C3×C4—24no—
291C2×C3×C4—22no—
292C2×C3×C4—22no—
293C2×C3×C4—24no—
294C2×C3×C4—64no—
295C2×C3×C4—64no—
296C2×C3×C4—64no—
297C2×C3×C4—64no—
298C2×C3×C4—62no—
299C2×C3×C4—64no—
300C2×C3×C4—62no—
301C2×C3×C4—121no—
302C2×C3×C4—121no—
303C2×C3×C4—121no—
304C2×C3×C4—122no—
305C2×C3×C4—122no—
306C2×C3×C4—122no—
307C2×C3×C4—121no—
308C2×C3×C4—122no—
309C2×C3×C4—122no—
310C2×C3×C4—122no—
311C2×C3×C4Dic3⋊C414yes—
312C2×C3×C4C4⋊Dic314yes—
313C2×Dic3—24no—
314C2×Dic3—24no—
315C2×Dic3—22no—
316C2×Dic3—24no—
317C2×Dic3—22no—
318C2×Dic3—24no—
319C2×Dic3—24no—
320C2×Dic3—42no—
321C2×Dic3—42no—
322C2×Dic3—42no—
323C2×Dic3—42no—
324C2×Dic3—42no—
325C2×Dic3—42no—
326C2×Dic3—41no—
327C2×Dic3—41no—
328C2×Dic3—41no—
329C2×Dic3—41no—
330C2×Dic3—68no—
331C2×Dic3—64no—
332C2×Dic3—64no—
333C2×Dic3—64no—
334C2×Dic3—64no—
335C2×Dic3—64no—
336C2×Dic3—64no—
337C2×Dic3—124no—
338C2×Dic3—124no—
339C2×Dic3—124no—
340C2×Dic3—124no—
341C2×Dic3—124no—
342C2×Dic3—124no—
343C2×Dic3—122no—
344C2×Dic3—122no—
345C2×Dic3—122no—
346C2×Dic3—122no—
347C2×Dic3—122no—
348C2×Dic3—122no—
349C2×Dic3—122no—
350C2×Dic3—122no—
351C2×C32#38211yescharacteristic
352C2×C32#38511yescharacteristic
353C2×C32#38712yes—
354C2×C32#38812yes—
355C2×C32#38911yescharacteristic
356C2×C32#39311yescharacteristic
357C2×C32#39411yescharacteristic
358C2×C32#39711yescharacteristic
359C2×C32#39812yes—
360C2×C32#40011yescharacteristic
361C2×C32#40012yes—
362C24C2×D3211yescharacteristic
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—32no—
366C22×C4—32no—
367C22×C4—34no—
368C22×C4—62no—
369C22×C4—61no—
370C22×C4—62no—
371C22×C4—62no—
372C22×C4—62no—
373C22×C4—62no—
374C22×C4—61no—
375C22×C4—62no—
376C22×C4—62no—
377C22×C4—62no—
378C22×C4—61no—
379C22×C4—61no—
380C22×C4—62no—
381C22×C4—62no—
382C22×C4—94no—
383C22×C4—182no—
384C22×C4—182no—
385C22×C4—182no—
386C22×C4—182no—
387C22×C4—182no—
388C22×C4—182no—
389C22×C4D3×Dic312yes—
390C22×C4#62612yes—
391C22×C4#62712yes—
392C4⋊C4—188no—
393C22×C3—22no—
394C22×C3—21no—
395C22×C3—22no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—22no—
399C22×C3—22no—
400C22×C3—21no—
401C22×C3—22no—
402C22×C3—21no—
403C22×C3—22no—
404C22×C3—21no—
405C22×C3—22no—
406C22×C3—22no—
407C22×C3—21no—
408C22×C3—22no—
409C22×C3—22no—
410C22×C3—21no—
411C22×C3—21no—
412C22×C3—21no—
413C22×C3—22no—
414C22×C3—21no—
415C22×C3—22no—
416C22×C3C4×Dic611yescharacteristic
417C22×C3#86911yescharacteristic
418C22×C3#87012yes—
419C22×C3#87011yescharacteristic
420C22×C3C4×D1211yescharacteristic
421C22×C3#87511yescharacteristic
422C22×C3#87511yescharacteristic
423C22×C3#87812yes—
424C22×C3#87812yes—
425C22×C3#87812yes—
426C22×C3#87912yes—
427C22×C3#87912yes—
428C22×C3#67⋊C412yes—
429C22×C3#88211yescharacteristic
430C22×C3#88312yes—
431C22×C3#88412yes—
432C22×C3#88512yes—
433C22×C3#88512yes—
434C22×C3#88612yes—
435C22×C3#88611yescharacteristic
436C22×C3#88811yescharacteristic
437C22×C3#88912yes—
438C22×C3#89012yes—
439C22×C3#89011yescharacteristic
440C22×C3#89012yes—
441C22×C3#89212yes—
442C22×C3#89412yes—
443C22×C3#89412yes—
444C22×C3#89511yescharacteristic
445C22×C3#89512yes—
446C22×C3#89612yes—
447C22×C3#89711yescharacteristic
448C22×C3#89812yes—
449C22×C3#89812yes—
450C22×C3C2×Dic3⋊C411yescharacteristic
451C22×C3#92411yescharacteristic
452C22×C3C2×C4⋊Dic311yescharacteristic
453C22×C3#92612yes—
454C22×C3#93011yescharacteristic
455C22×C3D4×Dic311yescharacteristic
456C22×C3D4×Dic312yes—
457C22×C3#93511yescharacteristic
458C22×C3#93611yescharacteristic
459C22×C3#93711yescharacteristic
460C22×C3Q8×Dic311yescharacteristic
461C22×C3#94711yescharacteristic
462C3×C4—28no—
463C3×C4—24no—
464C3×C4—24no—
465C3×C4—124no—
466C3×C4—122no—
467C3×C4—122no—
468Dic3—42no—
469Dic3—44no—
470Dic3—42no—
471Dic3—128no—
472Dic3—124no—
473Dic3—124no—
474C32#144211yescharacteristic, complemented, Sylow
475C23D3×Dic611yescharacteristic
476C23#379512yes—
477C23#379511yescharacteristic
478C23#379912yes—
479C23#379911yescharacteristic
480C23D3×D1211yescharacteristic
481C23C2×D3×Dic311yescharacteristic
482C23#380512yes—
483C23C2×#62611yescharacteristic
484C23C2×#62711yescharacteristic
485C23#381112yes—
486C2×C4—22no—
487C2×C4—24no—
488C2×C4—22no—
489C2×C4—24no—
490C2×C4—64no—
491C2×C4—62no—
492C2×C4—64no—
493C2×C4—64no—
494C2×C4—64no—
495C2×C4—62no—
496C2×C4—64no—
497C2×C4—121no—
498C2×C4—121no—
499C2×C4—122no—
500C2×C4—122no—
501C2×C4—122no—
502C2×C4—122no—
503C2×C4—122no—
504C2×C4—122no—
505C2×C4—121no—
506C2×C4—121no—
507C2×C4—184no—
508C2×C4—184no—
509C2×C4—184no—
510C2×C4—362no—
511C2×C4—362no—
512C2×C4—362no—
513C2×C4—362no—
514C2×C4Dic3⋊Dic314yes—
515C2×C3—22no—
516C2×C3—21no—
517C2×C3—22no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—22no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—22no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3#465512yes—
527C2×C3#465712yes—
528C2×C3#465911yescharacteristic
529C2×C3#466012yes—
530C2×C3#466012yes—
531C2×C3#466112yes—
532C2×C3#467012yes—
533C2×C3#467211yescharacteristic
534C2×C3#467311yescharacteristic
535C2×C3#467411yescharacteristic
536C2×C3#492811yescharacteristic
537C2×C3#493611yescharacteristic
538C2×C3#494611yescharacteristic
539C2×C3#494711yescharacteristic
540C2×C3#495011yescharacteristic
541C2×C3#495112yes—
542C2×C3#495311yescharacteristic
543C2×C3#497711yescharacteristic
544C2×C3#498012yes—
545C2×C3#498411yescharacteristic
546C2×C3#498611yescharacteristic
547C2×C3#499111yescharacteristic
548C22#6384112yes—
549C22Dic3×Dic611yescharacteristic
550C22#6384512yes—
551C22#6385711yescharacteristic
552C22#6386011yescharacteristic
553C22#6386112yes—
554C22#6386112yes—
555C22#6386411yescharacteristic
556C22#6386912yes—
557C22#6386911yescharacteristic
558C22#6389112yes—
559C22Dic3×D1211yescharacteristic
560C22#6389612yes—
561C22#6389712yes—
562C22#6390911yescharacteristic
563C22#6391012yes—
564C22#6391312yes—
565C22#6391811yescharacteristic
566C22#6396211yescharacteristic
567C22C2×Dic3⋊Dic311yescharacteristic
568C22#67⋊Dic312yes—
569C22#6398111yescharacteristic
570C22#6398212yes—
571C4—24no—
572C4—122no—
573C4—124no—
574C4—122no—
575C4—364no—
576C3—21no—
577C3#6941211yescharacteristic, complemented
578C3#6941511yescharacteristic, complemented
579C2#1059121812yes—
580C2#1059122411yescharacteristic
581C2#1059122611yescharacteristic
582C2#1059127212yes—
583C2#1059131511yescharacteristic
584C2#1059131612yes—
585C2#1059132111yescharacteristic
586C2#1059132211yescharacteristic
587C2#1059135112yes—
588C2#1059135211yescharacteristic
589C2#1059171911yescharacteristic
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
16. C3×C3⋊#95C4semidirect
87. C3⋊#95Dic3semidirect
474. C32#1442semidirect
577. C3#69412semidirect
578. C3#69415semidirect

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
C2×C3×C3⋊#952
C2×#635792
#694153
#694123