Finite Group Databasebeta

← #11808696

Subgroups — #11808696

Order 1152.

1153 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#872C211yesmaximal, characteristic
2C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
3C4×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
4#10591344C211yesmaximal, characteristic, complemented
5C4×#3724C212yesmaximal, complemented
6#10591324C211yesmaximal, characteristic
7#10591319C212yesmaximal
8#10591304C211yesmaximal, characteristic
9C4×(C2×D3)⋊Dic3C212yesmaximal
10#10591225C211yesmaximal, characteristic, complemented
11#10591215C212yesmaximal, complemented
12#82491—31nomaximal
13#82245—31nomaximal
14C22×C3×C4×D3C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C2×C32×C42C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2212yes—
18C2×C4×C3⋊Dic3C2212yes—
19C2×C3×(C2×D3)⋊C4C2211yescharacteristic
20C2×C3×(C2×D3)⋊C4C2211yescharacteristic
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×Dic3⋊C4C2212yes—
23C2×C3×Dic3⋊C4C2211yescharacteristic
24C2×C3×Dic3⋊C4C2211yescharacteristic
25C2×C3×C4×Dic3C2212yes—
26C2×C3×C4×Dic3C2211yescharacteristic
27C3×#872—24no—
28C3×C4×Dic6—24no—
29C2×#3724C2212yes—
30C2×#3724C2212yes—
31C2×(C2×D3)⋊Dic3C2212yes—
32C2×(C2×D3)⋊Dic3C2212yes—
33#63658C2211yescharacteristic
34#63658C2211yescharacteristic
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39C2×C3×C4×Q8—31no—
40C2×C3×#117—31no—
41C2×#872D311yescharacteristic
42C2×C4×Dic6D311yescharacteristic, complemented
43#5231—31no—
44#5230—31no—
45C4×#217—32no—
46#4994—32no—
47#4993—31no—
48#4986—31no—
49#4985—31no—
50#4982—32no—
51#4982—32no—
52#4979—31no—
53#4949—31no—
54#4948—32no—
55#4947—31no—
56C4×(C2×D3)⋊C4—32no—
57C4×C4⋊Dic3—31no—
58C4×C4⋊Dic3—31no—
59C4×C4⋊Dic3—61no—
60C4×Dic3⋊C4—32no—
61C4×Dic3⋊C4—32no—
62C23×C3×D3C2311yescharacteristic
63C22×C32×C4C2311yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C22×C3⋊Dic3C2312yes—
67C22×C3⋊Dic3C2312yes—
68C22×C3×Dic3C2312yes—
69C22×C3×Dic3C2311yescharacteristic
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2311yescharacteristic
72C22×C3×Dic3C2312yes—
73C2×C3×C4×D3—22no—
74C2×C3×C4×D3—22no—
75C2×C3×C4×D3Q814yescomplemented
76C2×C3×Dic6—22no—
77C2×C3×Dic6—24no—
78C32×C42D414yes—
79C4⋊(C3⋊Dic3)—24no—
80C4×C3⋊Dic3—24no—
81C3×(C2×D3)⋊C4—22no—
82C3×(C2×D3)⋊C4—22no—
83C3×C4⋊Dic3—22no—
84C3×Dic3⋊C4—24no—
85C3×Dic3⋊C4—22no—
86C3×Dic3⋊C4—22no—
87C3×C4×Dic3—24no—
88C3×C4×Dic3—22no—
89#3724—24no—
90#3724—24no—
91(C2×D3)⋊Dic3—24no—
92(C2×D3)⋊Dic3—24no—
93#2396—91noSylow
94C22×C3×Q8—31no—
95C23×C3×C4—31no—
96C22×C4×D3C2×D311yescharacteristic
97C22×Dic6C2×D311yescharacteristic
98C3×C4×Q8—64no—
99C3×#117—64no—
100C2×C3×C4⋊C4—31no—
101C2×C3×C4⋊C4—31no—
102C2×C3×C4⋊C4—32no—
103C2×C3×C4⋊C4—31no—
104C2×C3×C22⋊C4—31no—
105C2×C3×C22⋊C4—31no—
106C2×C3×C42—21no—
107C2×C3×C42—31no—
108C2×C3×C42—32no—
109C2×C3×C42C2×D311yescharacteristic
110C2×C3×C42C2×D311yescharacteristic
111C2×#217—32no—
112C2×#217—32no—
113C2×(C2×D3)⋊C4—32no—
114C2×(C2×D3)⋊C4—32no—
115C2×(C2×D3)⋊C4C2×D311yescharacteristic
116C2×(C2×D3)⋊C4C2×D311yescharacteristic
117C2×C4⋊Dic3—32no—
118C2×C4⋊Dic3—32no—
119C2×C4⋊Dic3—62no—
120C2×C4⋊Dic3C2×D311yescharacteristic
121C2×Dic3⋊C4—32no—
122C2×Dic3⋊C4—32no—
123C2×Dic3⋊C4—32no—
124C2×Dic3⋊C4—32no—
125C2×Dic3⋊C4C2×D312yes—
126C2×Dic3⋊C4C2×D311yescharacteristic
127C2×Dic3⋊C4C2×D311yescharacteristic
128C2×C4×Dic3—32no—
129C2×C4×Dic3—32no—
130C2×C4×Dic3—62no—
131C2×C4×Dic3C2×D311yescharacteristic
132C2×C4×Dic3C2×D312yes—
133#872—24no—
134C4×Dic6—24no—
135C3⋊#95—31no—
136C3⋊#95—31no—
137C3⋊#95—31no—
138C3⋊#95—31no—
139C3⋊#95—32no—
140C3⋊#95—32no—
141C3⋊#95—32no—
142C3⋊#95—32no—
143C3⋊#95—32no—
144C3⋊#95—32no—
145C3⋊#95—32no—
146C3⋊#95—32no—
147C3⋊#95—61no—
148C3⋊#95—61no—
149C23×C32C2411yescharacteristic
150C22×C3×D3—21no—
151C22×C3×D3—22no—
152C22×C3×D3—22no—
153C22×C3×D3—21no—
154C22×C3×D3C2×Q812yes—
155C2×C32×C4—22no—
156C2×C32×C4—22no—
157C2×C32×C4C2×D412yes—
158C2×C32×C4C2×D412yes—
159C2×C32×C4C2×D412yes—
160C2×C32×C4C2×Q812yes—
161C2×C32×C4#4112yes—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3#4114yes—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—21no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—21no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3C2×Q812yes—
180C2×C3×Dic3#4114yes—
181C3×C4×D3—28no—
182C3×Dic6—28no—
183C2×C4×Q8—31no—
184C2×#117—31no—
185#400—91no—
186#399—91no—
187#398—92no—
188#396—92no—
189#395—91no—
190#393—91no—
191C4×C4⋊C4—92no—
192C4×C4⋊C4—91no—
193C4×C22⋊C4—92no—
194C24×C3—31no—
195C23×D3C22×D311yescharacteristic
196C2×C3×Q8—64no—
197C2×C3×Q8—62no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—31no—
202C22×C3×C4—32no—
203C22×C3×C4—34no—
204C22×C3×C4—31no—
205C22×C3×C4—31no—
206C22×C3×C4—32no—
207C22×C3×C4—62no—
208C22×C3×C4—62no—
209C22×C3×C4C22×D311yescharacteristic
210C22×C3×C4C22×D311yescharacteristic
211C22×C3×C4C22×D311yescharacteristic
212C22×C3×C4C22×D311yescharacteristic
213C22×C3×C4C22×D311yescharacteristic
214C22×C3×C4C22×D311yescharacteristic
215C22×Dic3—32no—
216C22×Dic3—32no—
217C22×Dic3—32no—
218C22×Dic3—32no—
219C22×Dic3—62no—
220C22×Dic3—62no—
221C22×Dic3C22×D311yescharacteristic
222C22×Dic3C22×D311yescharacteristic
223C22×Dic3C22×D312yes—
224C22×Dic3C22×D311yescharacteristic
225C22×Dic3C22×D312yes—
226C2×C4×D3—22no—
227C2×C4×D3—22no—
228C2×C4×D3Dic614yescomplemented
229C2×Dic6—22no—
230C2×Dic6—24no—
231C3×C4⋊C4—62no—
232C3×C4⋊C4—62no—
233C3×C4⋊C4—64no—
234C3×C4⋊C4—62no—
235C3×C22⋊C4—62no—
236C3×C22⋊C4—62no—
237C3×C42—24no—
238C3×C42—62no—
239C3×C42—64no—
240C3×C42#6714yes—
241C3×C42#6714yes—
242#217—64no—
243#217—64no—
244(C2×D3)⋊C4—22no—
245(C2×D3)⋊C4—22no—
246(C2×D3)⋊C4—64no—
247(C2×D3)⋊C4—64no—
248C4⋊Dic3—22no—
249C4⋊Dic3—64no—
250C4⋊Dic3—64no—
251C4⋊Dic3—68no—
252Dic3⋊C4—24no—
253Dic3⋊C4—22no—
254Dic3⋊C4—22no—
255Dic3⋊C4—64no—
256Dic3⋊C4—64no—
257Dic3⋊C4—64no—
258Dic3⋊C4—64no—
259C4×Dic3—24no—
260C4×Dic3—22no—
261C4×Dic3—64no—
262C4×Dic3—64no—
263C4×Dic3—124no—
264C22×C32C22×D411yescharacteristic
265C22×C32C22×Q811yescharacteristic
266C22×C32C2×#4111yescharacteristic
267C22×C32C2×#4112yes—
268C22×C32C2×#4112yes—
269C2×C3×D3—22no—
270C2×C3×D3—24no—
271C2×C3×D3—41no—
272C2×C3×D3—42no—
273C2×C3×D3—41no—
274C32×C4—22no—
275C32×C4—22no—
276C32×C4C22⋊Q814yes—
277C3⋊Dic3—24no—
278C3⋊Dic3—42no—
279C3×Dic3—22no—
280C3×Dic3—24no—
281C3×Dic3—41no—
282C3×Dic3—42no—
283C3×Dic3—41no—
284C22×Q8—31no—
285C23×C4—31no—
286C4×Q8—64no—
287#117—64no—
288C2×C4⋊C4—31no—
289C2×C4⋊C4—31no—
290C2×C4⋊C4—32no—
291C2×C4⋊C4—31no—
292C2×C4⋊C4—92no—
293C2×C4⋊C4—92no—
294C2×C4⋊C4—92no—
295C2×C22⋊C4—31no—
296C2×C22⋊C4—31no—
297C2×C22⋊C4—92no—
298C2×C22⋊C4—92no—
299C2×C42—31no—
300C2×C42—32no—
301C2×C42—92no—
302C2×C42D3211yescharacteristic
303#95—92no—
304#95—92no—
305#95—92no—
306#95—92no—
307#95—91no—
308#95—91no—
309C23×C3—21no—
310C23×C3—32no—
311C23×C3—62no—
312C23×C3—61no—
313C23×C3—62no—
314C23×C3—61no—
315C23×C3C23×D311yescharacteristic
316C23×C3C23×D311yescharacteristic
317C22×D3—21no—
318C22×D3—22no—
319C22×D3—22no—
320C22×D3—21no—
321C22×D3C2×Dic612yes—
322C3×Q8—68no—
323C2×C3×C4—24no—
324C2×C3×C4—22no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—32no—
334C2×C3×C4—34no—
335C2×C3×C4—42no—
336C2×C3×C4—61no—
337C2×C3×C4—62no—
338C2×C3×C4—62no—
339C2×C3×C4—61no—
340C2×C3×C4—68no—
341C2×C3×C4—62no—
342C2×C3×C4—62no—
343C2×C3×C4—62no—
344C2×C3×C4—62no—
345C2×C3×C4—61no—
346C2×C3×C4—61no—
347C2×C3×C4—62no—
348C2×C3×C4C2×Dic612yes—
349C2×C3×C4#23512yes—
350C2×C3×C4D3×Q812yes—
351C2×C3×C4#23912yes—
352C2×C3×C4C2×#6712yes—
353C2×C3×C4C2×#6712yes—
354C2×C3×C4C2×#6712yes—
355C2×C3×C4C2×#6712yes—
356C2×C3×C4C2×#6712yes—
357C2×C3×C4C2×#6712yes—
358C2×Dic3—22no—
359C2×Dic3—21no—
360C2×Dic3—22no—
361C2×Dic3—21no—
362C2×Dic3—22no—
363C2×Dic3—22no—
364C2×Dic3—22no—
365C2×Dic3—22no—
366C2×Dic3—22no—
367C2×Dic3—21no—
368C2×Dic3—21no—
369C2×Dic3—34no—
370C2×Dic3—34no—
371C2×Dic3—64no—
372C2×Dic3—62no—
373C2×Dic3—62no—
374C2×Dic3—62no—
375C2×Dic3—62no—
376C2×Dic3—64no—
377C2×Dic3—62no—
378C2×Dic3—62no—
379C2×Dic3—62no—
380C2×Dic3—62no—
381C2×Dic3—62no—
382C2×Dic3—62no—
383C2×Dic3—122no—
384C2×Dic3—122no—
385C2×Dic3—122no—
386C2×Dic3—122no—
387C2×Dic3C2×Dic612yes—
388C2×Dic3#23514yes—
389C4×D3—28no—
390Dic6—28no—
391C2×C32C2×C22⋊Q811yescharacteristic
392C2×C32#52511yescharacteristic
393C2×C32#52912yes—
394C2×C32#53211yescharacteristic
395C2×C32#53312yes—
396C3×D3—42no—
397C24—31no—
398C2×Q8—64no—
399C2×Q8—62no—
400C22×C4—31no—
401C22×C4—32no—
402C22×C4—34no—
403C22×C4—31no—
404C22×C4—31no—
405C22×C4—32no—
406C22×C4—62no—
407C22×C4—62no—
408C22×C4—92no—
409C22×C4—92no—
410C22×C4C2×D3211yescharacteristic
411C22×C4C2×D3211yescharacteristic
412C22×C4C2×D3211yescharacteristic
413C4⋊C4—62no—
414C4⋊C4—62no—
415C4⋊C4—64no—
416C4⋊C4—62no—
417C4⋊C4—184no—
418C4⋊C4—184no—
419C4⋊C4—184no—
420C22⋊C4—62no—
421C22⋊C4—62no—
422C22⋊C4—184no—
423C22⋊C4—184no—
424C42—62no—
425C42—64no—
426C42—184no—
427C42#62514yes—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—22no—
431C22×C3—22no—
432C22×C3—21no—
433C22×C3—62no—
434C22×C3—64no—
435C22×C3—121no—
436C22×C3—121no—
437C22×C3—122no—
438C22×C3C22×Dic611yescharacteristic
439C22×C3C2×#23511yescharacteristic
440C22×C3C2×#23512yes—
441C22×C3C2×D3×Q811yescharacteristic
442C22×C3C2×#23911yescharacteristic
443C22×C3D3×#4112yes—
444C22×C3D3×#4112yes—
445C22×C3D3×#4112yes—
446C22×C3C22×#6711yescharacteristic
447C22×C3C22×#6711yescharacteristic
448C2×D3—24no—
449C2×D3—22no—
450C2×D3—42no—
451C2×D3—41no—
452C2×D3—41no—
453C3×C4—24no—
454C3×C4—22no—
455C3×C4—22no—
456C3×C4—22no—
457C3×C4—22no—
458C3×C4—24no—
459C3×C4—42no—
460C3×C4—62no—
461C3×C4—64no—
462C3×C4—121no—
463C3×C4—121no—
464C3×C4—122no—
465C3×C4#92414yes—
466C3×C4#94614yes—
467Dic3—22no—
468Dic3—24no—
469Dic3—41no—
470Dic3—42no—
471Dic3—41no—
472Dic3—64no—
473Dic3—64no—
474Dic3—124no—
475Dic3—124no—
476Dic3—122no—
477Dic3—122no—
478C32#239611yescharacteristic, complemented, Sylow
479C23—32no—
480C23—61no—
481C23—62no—
482C23—62no—
483C23—61no—
484C23C22×D3211yescharacteristic
485Q8—68no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—32no—
489C2×C4—34no—
490C2×C4—61no—
491C2×C4—62no—
492C2×C4—62no—
493C2×C4—61no—
494C2×C4—68no—
495C2×C4—62no—
496C2×C4—62no—
497C2×C4—62no—
498C2×C4—62no—
499C2×C4—61no—
500C2×C4—61no—
501C2×C4—62no—
502C2×C4—94no—
503C2×C4—182no—
504C2×C4—182no—
505C2×C4—182no—
506C2×C4—182no—
507C2×C4—182no—
508C2×C4D3×Dic612yes—
509C2×C4#379912yes—
510C2×C4C2×#62512yes—
511C2×C4C2×#62512yes—
512C2×C4C2×#62512yes—
513C2×C3—21no—
514C2×C3—22no—
515C2×C3—22no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—122no—
519C2×C3#551712yes—
520C2×C3#552812yes—
521C2×C3#557812yes—
522C2×C3#558012yes—
523C2×C3C2×#92411yescharacteristic
524C2×C3#579111yescharacteristic
525C2×C3C2×#94611yescharacteristic
526C2×C3#582811yescharacteristic
527C2×C3#583211yescharacteristic
528C2×C3#583211yescharacteristic
529D3—42no—
530C22—62no—
531C22—64no—
532C22—122no—
533C22—121no—
534C22—121no—
535C22C2×D3×Dic611yescharacteristic
536C22C2×#379911yescharacteristic
537C22D3×#23512yes—
538C22#6430612yes—
539C22C22×#62511yescharacteristic
540C4—22no—
541C4—22no—
542C4—62no—
543C4—64no—
544C4—121no—
545C4—122no—
546C4—121no—
547C4—184no—
548C4—362no—
549C4#6385614yes—
550C3—21no—
551C3#8224511yescharacteristic, complemented
552C3#8249111yescharacteristic, complemented
553C2—122no—
554C2#1059392612yes—
555C2#1059393412yes—
556C2C2×#6385611yescharacteristic
557C2#1059502211yescharacteristic
558C2#1059503211yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutator, socle, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC2×C32×C42C22
prime radicalC23×C3×D3C23
hypercenterC2×C42D32
hypocenterC32#2396
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×Dic6C2semidirect
3. C4×C4⋊(C3⋊Dic3)C2semidirect
4. #10591344C2semidirect
5. C4×#3724C2semidirect
10. #10591225C2semidirect
11. #10591215C2semidirect
42. C2×C4×Dic6D3semidirect
75. C2×C3×C4×D3Q8semidirect
228. C2×C4×D3Dic6semidirect
478. C32#2396semidirect
551. C3#82245semidirect
552. C3#82491semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8722
C2×C3×C4×Dic62
C4×C4⋊(C3⋊Dic3)2
#105913442
C4×#37242
#105913242
#105913192
#105913042
C4×(C2×D3)⋊Dic32
#105912252
#105912152
#824913
#822453