Finite Group Databasebeta

← #11773447

Subgroups — #11773447

Order 1152.

1381 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3724C211yesmaximal, characteristic
2C22×Dic3⋊Dic3C212yesmaximal
3C2×#63658C211yesmaximal, characteristic
4C2×C3×C3⋊#95C212yesmaximal
5C2×#63579C211yesmaximal, characteristic
6#69420—32nomaximal
7C23×C32×C4C2211yescharacteristic
8C23×C3⋊Dic3C2211yescharacteristic
9C23×C3⋊Dic3C2211yescharacteristic
10C23×C3×Dic3C2212yes—
11C23×C3×Dic3C2212yes—
12C2×#3724—22no—
13C2×#3724—24no—
14C2×Dic3⋊Dic3—24no—
15C2×Dic3⋊Dic3—24no—
16C2×Dic3⋊Dic3—24no—
17#63658—22no—
18C3×C3⋊#95—24no—
19#63579C414yescomplemented
20C22×C4⋊Dic3—32no—
21C22×Dic3⋊C4—32no—
22C22×Dic3⋊C4—32no—
23C2×C3×#95—32no—
24C2×C3⋊#95—32no—
25C2×C3⋊#95—32no—
26C2×C3⋊#95—61no—
27C2×C3⋊#95D312yes—
28C24×C32C2311yescharacteristic
29C22×C32×C4—21no—
30C22×C32×C4—22no—
31C22×C32×C4—21no—
32C22×C32×C4—22no—
33C22×C32×C4Q812yes—
34C22×C3⋊Dic3—22no—
35C22×C3⋊Dic3—22no—
36C22×C3⋊Dic3—21no—
37C22×C3⋊Dic3—22no—
38C22×C3⋊Dic3—22no—
39C22×C3⋊Dic3—21no—
40C22×C3⋊Dic3C2×C412yes—
41C22×C3⋊Dic3D412yes—
42C22×C3⋊Dic3D412yes—
43C22×C3⋊Dic3Q812yes—
44C22×C3×Dic3—22no—
45C22×C3×Dic3—22no—
46C22×C3×Dic3—22no—
47C22×C3×Dic3—22no—
48C22×C3×Dic3—22no—
49C22×C3×Dic3—22no—
50C22×C3×Dic3—22no—
51C22×C3×Dic3—22no—
52C22×C3×Dic3—22no—
53C22×C3×Dic3—22no—
54C22×C3×Dic3C2×C414yes—
55C22×C3×Dic3D414yes—
56C22×C3×Dic3D414yes—
57C22×C3×Dic3Q814yes—
58#3724—28no—
59Dic3⋊Dic3—216no—
60#1444—91noSylow
61C23×C3×C4—21no—
62C23×C3×C4—32no—
63C23×C3×C4—32no—
64C23×C3×C4C2×D312yes—
65C23×Dic3—32no—
66C23×Dic3—32no—
67C23×Dic3—61no—
68C23×Dic3—61no—
69C23×Dic3C2×D312yes—
70C23×Dic3C2×D312yes—
71C2×C4⋊Dic3—64no—
72C2×C4⋊Dic3—64no—
73C2×C4⋊Dic3—64no—
74C2×Dic3⋊C4—64no—
75C2×Dic3⋊C4—64no—
76C2×Dic3⋊C4—64no—
77C2×Dic3⋊C4—64no—
78C2×Dic3⋊C4—64no—
79C2×Dic3⋊C4—64no—
80C3×#95—64no—
81C3⋊#95—24no—
82C3⋊#95—38no—
83C3⋊#95—64no—
84C3⋊#95—64no—
85C23×C32C22×C411yescharacteristic
86C23×C32C2×D412yes—
87C23×C32C2×D411yescharacteristic
88C23×C32C2×D411yescharacteristic
89C23×C32C2×D412yes—
90C23×C32C2×Q811yescharacteristic
91C23×C32C2×Q812yes—
92C23×C32C2×Q811yescharacteristic
93C23×C32#4111yescharacteristic
94C23×C32#4112yes—
95C23×C32#4111yescharacteristic
96C2×C32×C4—22no—
97C2×C32×C4—24no—
98C2×C32×C4—41no—
99C2×C32×C4—42no—
100C2×C32×C4—41no—
101C2×C3⋊Dic3—22no—
102C2×C3⋊Dic3—24no—
103C2×C3⋊Dic3—22no—
104C2×C3⋊Dic3—24no—
105C2×C3⋊Dic3—22no—
106C2×C3⋊Dic3—24no—
107C2×C3⋊Dic3—41no—
108C2×C3⋊Dic3—42no—
109C2×C3⋊Dic3—41no—
110C2×C3⋊Dic3C4⋊C414yescomplemented
111C2×C3×Dic3—24no—
112C2×C3×Dic3—24no—
113C2×C3×Dic3—24no—
114C2×C3×Dic3—24no—
115C2×C3×Dic3—24no—
116C2×C3×Dic3—24no—
117C2×C3×Dic3—24no—
118C2×C3×Dic3—24no—
119C2×C3×Dic3—24no—
120C2×C3×Dic3—42no—
121C2×C3×Dic3—42no—
122C2×C3×Dic3—42no—
123C2×C3×Dic3—42no—
124C2×C3×Dic3C4⋊C418yescomplemented
125C22×C4⋊C4—91no—
126C22×C4⋊C4—92no—
127C2×#95—32no—
128C2×#95—91no—
129C2×#95—91no—
130C24×C3—21no—
131C24×C3C22×D312yes—
132C22×C3×C4—22no—
133C22×C3×C4—22no—
134C22×C3×C4—22no—
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—34no—
142C22×C3×C4—34no—
143C22×C3×C4—34no—
144C22×C3×C4—34no—
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—62no—
152C22×C3×C4—62no—
153C22×C3×C4—62no—
154C22×C3×C4—62no—
155C22×C3×C4—62no—
156C22×C3×C4—62no—
157C22×C3×C4Dic614yes—
158C22×Dic3—22no—
159C22×Dic3—22no—
160C22×Dic3—22no—
161C22×Dic3—22no—
162C22×Dic3—22no—
163C22×Dic3—22no—
164C22×Dic3—22no—
165C22×Dic3—22no—
166C22×Dic3—22no—
167C22×Dic3—22no—
168C22×Dic3—34no—
169C22×Dic3—34no—
170C22×Dic3—34no—
171C22×Dic3—34no—
172C22×Dic3—62no—
173C22×Dic3—62no—
174C22×Dic3—62no—
175C22×Dic3—62no—
176C22×Dic3—62no—
177C22×Dic3—62no—
178C22×Dic3—62no—
179C22×Dic3—62no—
180C22×Dic3—62no—
181C22×Dic3—62no—
182C22×Dic3—62no—
183C22×Dic3—62no—
184C22×Dic3—62no—
185C22×Dic3—62no—
186C22×Dic3—62no—
187C22×Dic3—62no—
188C22×Dic3—122no—
189C22×Dic3—122no—
190C22×Dic3—122no—
191C22×Dic3—122no—
192C22×Dic3Dic614yes—
193C22×Dic3C4×D314yes—
194C22×Dic3D1214yes—
195C22×Dic3#6714yes—
196C4⋊Dic3—616no—
197Dic3⋊C4—616no—
198Dic3⋊C4—616no—
199C22×C32C2×C4⋊C411yescharacteristic
200C22×C32C2×C4⋊C412yes—
201C22×C32C4×D412yes—
202C22×C32C4×D411yescharacteristic
203C22×C32C4×Q811yescharacteristic
204C22×C32#12011yescharacteristic
205C22×C32#12012yes—
206C22×C32#12111yescharacteristic
207C22×C32#12112yes—
208C22×C32C22⋊Q811yescharacteristic
209C22×C32C22⋊Q812yes—
210C22×C32C22⋊Q812yes—
211C22×C32C22⋊Q812yes—
212C22×C32C22⋊Q812yes—
213C22×C32#12311yescharacteristic
214C22×C32#12312yes—
215C22×C32#12512yes—
216C22×C32#12511yescharacteristic
217C22×C32#12711yescharacteristic
218C22×C32C4⋊Q812yes—
219C22×C32C4⋊Q811yescharacteristic
220C22×C32C4⋊Q811yescharacteristic
221C22×C32C4⋊Q812yes—
222C32×C4—42no—
223C3⋊Dic3—24no—
224C3⋊Dic3—42no—
225C3×Dic3—28no—
226C3×Dic3—44no—
227C23×C4—32no—
228C23×C4—32no—
229C23×C4—91no—
230C23×C4—91no—
231C23×C4D3211yescharacteristic
232C2×C4⋊C4—184no—
233C2×C4⋊C4—184no—
234C2×C4⋊C4—184no—
235C2×C4⋊C4—182no—
236C2×C4⋊C4—184no—
237#95—64no—
238#95—94no—
239#95—182no—
240C23×C3—22no—
241C23×C3—21no—
242C23×C3—21no—
243C23×C3—21no—
244C23×C3—22no—
245C23×C3—21no—
246C23×C3—22no—
247C23×C3—21no—
248C23×C3—21no—
249C23×C3—22no—
250C23×C3—21no—
251C23×C3C2×Dic612yes—
252C23×C3C2×Dic612yes—
253C23×C3C2×C4×D312yes—
254C23×C3C2×D1212yes—
255C23×C3#23512yes—
256C23×C3#23512yes—
257C23×C3D3×D412yes—
258C23×C3D3×D412yes—
259C23×C3D3×D412yes—
260C23×C3D3×D412yes—
261C23×C3#23712yes—
262C23×C3#23712yes—
263C23×C3D3×Q812yes—
264C23×C3D3×Q812yes—
265C23×C3C2×#6712yes—
266C2×C3×C4—24no—
267C2×C3×C4—24no—
268C2×C3×C4—24no—
269C2×C3×C4—24no—
270C2×C3×C4—38no—
271C2×C3×C4—44no—
272C2×C3×C4—44no—
273C2×C3×C4—42no—
274C2×C3×C4—42no—
275C2×C3×C4—42no—
276C2×C3×C4—42no—
277C2×C3×C4—42no—
278C2×C3×C4—42no—
279C2×C3×C4—64no—
280C2×C3×C4—64no—
281C2×C3×C4—64no—
282C2×C3×C4—64no—
283C2×C3×C4—64no—
284C2×C3×C4—64no—
285C2×C3×C4—64no—
286C2×C3×C4—64no—
287C2×C3×C4—64no—
288C2×C3×C4—122no—
289C2×C3×C4—122no—
290C2×C3×C4—122no—
291C2×C3×C4—122no—
292C2×Dic3—24no—
293C2×Dic3—24no—
294C2×Dic3—24no—
295C2×Dic3—24no—
296C2×Dic3—24no—
297C2×Dic3—24no—
298C2×Dic3—24no—
299C2×Dic3—24no—
300C2×Dic3—24no—
301C2×Dic3—38no—
302C2×Dic3—42no—
303C2×Dic3—42no—
304C2×Dic3—42no—
305C2×Dic3—42no—
306C2×Dic3—64no—
307C2×Dic3—64no—
308C2×Dic3—64no—
309C2×Dic3—64no—
310C2×Dic3—64no—
311C2×Dic3—64no—
312C2×Dic3—64no—
313C2×Dic3—64no—
314C2×Dic3—64no—
315C2×Dic3—64no—
316C2×Dic3—64no—
317C2×Dic3—124no—
318C2×Dic3—124no—
319C2×Dic3—122no—
320C2×Dic3—122no—
321C2×Dic3—124no—
322C2×Dic3—124no—
323C2×Dic3—122no—
324C2×Dic3—122no—
325C2×Dic3—122no—
326C2×Dic3—122no—
327C2×Dic3—122no—
328C2×Dic3—122no—
329C2×Dic3Dic3⋊C418yescomplemented
330C2×C32#38411yescharacteristic
331C2×C32#38511yescharacteristic
332C2×C32#38512yes—
333C2×C32#38911yescharacteristic
334C2×C32#38912yes—
335C2×C32#39211yescharacteristic
336C2×C32#39511yescharacteristic
337C2×C32#39512yes—
338C2×C32#39811yescharacteristic
339C2×C32#39812yes—
340C2×C32#39911yescharacteristic
341C24C2×D3211yescharacteristic
342C22×C4—22no—
343C22×C4—21no—
344C22×C4—22no—
345C22×C4—21no—
346C22×C4—34no—
347C22×C4—34no—
348C22×C4—34no—
349C22×C4—34no—
350C22×C4—62no—
351C22×C4—62no—
352C22×C4—62no—
353C22×C4—62no—
354C22×C4—62no—
355C22×C4—62no—
356C22×C4—62no—
357C22×C4—62no—
358C22×C4—62no—
359C22×C4—62no—
360C22×C4—92no—
361C22×C4—92no—
362C22×C4—92no—
363C22×C4—92no—
364C22×C4—182no—
365C22×C4—182no—
366C22×C4—181no—
367C22×C4—182no—
368C22×C4—182no—
369C22×C4—181no—
370C22×C4#62712yes—
371C4⋊C4—188no—
372C4⋊C4—1816no—
373C22×C3—22no—
374C22×C3—21no—
375C22×C3—22no—
376C22×C3—21no—
377C22×C3—22no—
378C22×C3—22no—
379C22×C3—21no—
380C22×C3—22no—
381C22×C3—22no—
382C22×C3—22no—
383C22×C3—21no—
384C22×C3—22no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—22no—
388C22×C3—21no—
389C22×C3—22no—
390C22×C3—21no—
391C22×C3—22no—
392C22×C3—22no—
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3C4×Dic612yes—
397C22×C3#86912yes—
398C22×C3#87012yes—
399C22×C3C4×D1212yes—
400C22×C3#87812yes—
401C22×C3#87812yes—
402C22×C3#87812yes—
403C22×C3#87812yes—
404C22×C3#67⋊C412yes—
405C22×C3#67⋊C412yes—
406C22×C3#88212yes—
407C22×C3#88212yes—
408C22×C3#88312yes—
409C22×C3#88312yes—
410C22×C3#88412yes—
411C22×C3#88412yes—
412C22×C3#88812yes—
413C22×C3#88812yes—
414C22×C3#88812yes—
415C22×C3#88812yes—
416C22×C3#88912yes—
417C22×C3#88912yes—
418C22×C3D3×C4⋊C412yes—
419C22×C3D3×C4⋊C412yes—
420C22×C3#89612yes—
421C22×C3#89612yes—
422C22×C3#89712yes—
423C22×C3#89712yes—
424C22×C3C2×Dic3⋊C412yes—
425C22×C3#92412yes—
426C22×C3#93012yes—
427C22×C3#93512yes—
428C22×C3#93712yes—
429C22×C3#94012yes—
430C22×C3#94412yes—
431C3×C4—44no—
432C3×C4—44no—
433C3×C4—68no—
434C3×C4—124no—
435Dic3—28no—
436Dic3—44no—
437Dic3—68no—
438Dic3—124no—
439Dic3—124no—
440Dic3—124no—
441C32#144411yescharacteristic, complemented, Sylow
442C23D3×Dic612yes—
443C23#379711yescharacteristic
444C23#379811yescharacteristic
445C23C4×D3211yescharacteristic
446C23D3×D1212yes—
447C23#380211yescharacteristic
448C23#380412yes—
449C23#380511yescharacteristic
450C23C2×#62711yescharacteristic
451C23D3×#6712yes—
452C23#381111yescharacteristic
453C2×C4—24no—
454C2×C4—22no—
455C2×C4—38no—
456C2×C4—42no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—64no—
460C2×C4—64no—
461C2×C4—64no—
462C2×C4—64no—
463C2×C4—64no—
464C2×C4—64no—
465C2×C4—64no—
466C2×C4—64no—
467C2×C4—64no—
468C2×C4—94no—
469C2×C4—122no—
470C2×C4—122no—
471C2×C4—122no—
472C2×C4—122no—
473C2×C4—184no—
474C2×C4—184no—
475C2×C4—182no—
476C2×C4—182no—
477C2×C4—182no—
478C2×C4—184no—
479C2×C4—362no—
480C2×C4—361no—
481C2×C4—361no—
482C2×C3—21no—
483C2×C3—22no—
484C2×C3—21no—
485C2×C3—22no—
486C2×C3—22no—
487C2×C3—21no—
488C2×C3—22no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3#464712yes—
494C2×C3#464712yes—
495C2×C3#465612yes—
496C2×C3#465612yes—
497C2×C3#465712yes—
498C2×C3#465712yes—
499C2×C3#466812yes—
500C2×C3#466812yes—
501C2×C3#492812yes—
502C2×C3#494612yes—
503C2×C3#494912yes—
504C2×C3#496012yes—
505C2×C3#497512yes—
506C2×C3#497912yes—
507C2×C3#498112yes—
508C22#6383912yes—
509C22#6384011yescharacteristic
510C22#6386712yes—
511C22#6387011yescharacteristic
512C22D3×Dic3⋊C412yes—
513C22#6388012yes—
514C22#6388311yescharacteristic
515C22#6389312yes—
516C22#6389512yes—
517C22#6389912yes—
518C22#6390211yescharacteristic
519C22#6390612yes—
520C22#6391211yescharacteristic
521C22C4×#62711yescharacteristic
522C22#6391812yes—
523C22#6391911yescharacteristic
524C22#6392212yes—
525C22#6392311yescharacteristic
526C22#6396412yes—
527C22#6396912yes—
528C22#6397511yescharacteristic
529C22#6397911yescharacteristic
530C22#6398211yescharacteristic
531C4—42no—
532C4—68no—
533C4—124no—
534C4—184no—
535C4—362no—
536C3—21no—
537C3#6942012yescomplemented
538C2#1059124411yescharacteristic
539C2#1059132712yes—
540C2#1059132811yescharacteristic
541C2#1059133812yes—
542C2#1059133912yes—
543C2#1059135611yescharacteristic
544C2#1059137312yes—
545C2#1059137511yescharacteristic
546C2#1059139311yescharacteristic
547C2#1059139711yescharacteristic
548C2#1059171511yescharacteristic
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. #63579C4semidirect
110. C2×C3⋊Dic3C4⋊C4semidirect
124. C2×C3×Dic3C4⋊C4semidirect
329. C2×Dic3Dic3⋊C4semidirect
441. C32#1444semidirect
537. C3#69420semidirect

Maximal subgroups

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

subgroupindex
C22×#37242
C22×Dic3⋊Dic32
C2×#636582
C2×C3×C3⋊#952
C2×#635792
#694203