Finite Group Databasebeta

← #11857361

Subgroups — #11857361

Order 1152.

2117 conjugacy classes of subgroups.

The subgroup lattice has 601 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D32C211yesmaximal, characteristic
2C2×#63791C212yesmaximal, complemented
3C3⋊D3×C22⋊C8C211yesmaximal, characteristic, complemented
4C3×#4726C212yesmaximal, complemented
5#10591154C212yesmaximal, complemented
6#10591152C211yesmaximal, characteristic, complemented
7#10590936C214yesmaximal, complemented
8#10590935C212yesmaximal, complemented
9D3×#407—32nomaximal
10C23×D32C411yescharacteristic
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×C3×C4×D3C2212yes—
13C22×#624C411yescharacteristic
14C22×D3×Dic3C412yes—
15C2×C4×D32—28no—
16C2×C4×D32C412yes—
17C2×C4×D32C411yescharacteristic
18C2×C4×D32C411yescharacteristic
19C2×C4×D32C2211yescharacteristic
20C2×C4×D32C2212yes—
21C2×C4×D32C2211yescharacteristic
22C2×C8×C3⋊D3C2212yescomplemented
23C2×C3×ΓL(1,𝔽25)C2214yescomplemented
24C2×#3711C2214yescomplemented
25C2×#3710C2212yescomplemented
26#63791—28no—
27C32×C22⋊C8C2211yescharacteristic, complemented
28#63657C2211yescharacteristic, complemented
29#63647C2212yescomplemented
30C3×#830C2212yescomplemented
31C3×(C2×D3)⋊C8C2214yescomplemented
32#63557C2212yescomplemented
33(C2×D3)⋊(C3⋊C8)C2214yescomplemented
34C23×C4×D3—32no—
35C2×D3×M16—34no—
36C3×#407—32no—
37#5207—32no—
38#5126—34no—
39#4726—32no—
40#4726—34no—
41#4726D312yescomplemented
42D3×C22⋊C8—32no—
43D3×C22⋊C8—32no—
44D3×C22⋊C8—34no—
45D3×C22⋊C8—61no—
46C23×C3⋊D3C2×C411yescharacteristic
47C23×C3×D3C2×C412yes—
48C22×D32—24no—
49C22×D32—24no—
50C22×D32—24no—
51C22×D32C2×C412yes—
52C22×D32C2×C411yescharacteristic
53C22×D32C2×C411yescharacteristic
54C22×C32×C4C2311yescharacteristic
55C22×C3⋊Dic3C2×C411yescharacteristic
56C2×C4×C3⋊D3—24no—
57C2×C4×C3⋊D3C2×C411yescharacteristic
58C2×C4×C3⋊D3C2×C411yescharacteristic
59C2×C4×C3⋊D3C2311yescharacteristic
60C2×C4×C3⋊D3C2311yescharacteristic
61C22×C3×Dic3C2×C412yes—
62C2×C3×C4×D3—28no—
63C2×C3×C4×D3C2×C412yes—
64C2×C3×C4×D3C2×C412yes—
65C2×C3×C4×D3C2312yes—
66C2×C3×C4×D3C2312yes—
67C2×#624—24no—
68C2×#624C2×C411yescharacteristic
69C2×#624C2×C412yes—
70C2×#624C2×C411yescharacteristic
71C2×D3×Dic3—28no—
72C2×D3×Dic3C2×C412yes—
73C2×D3×Dic3C2×C412yes—
74C2×D3×Dic3C2×C412yes—
75C2×D3×Dic3C2×C412yes—
76C4×D32—24no—
77C4×D32—24no—
78C4×D32—28no—
79C4×D32—24no—
80C4×D32—28no—
81C4×D32D418yes—
82C2×C32×C8C2312yescomplemented
83C2×C3⋊(C3⋊C8)C2312yescomplemented
84C8×C3⋊D3—24no—
85C2×C3×C3⋊C8C2314yescomplemented
86C3×ΓL(1,𝔽25)—28no—
87#3711—28no—
88#3710—24no—
89C2×#407—91noSylow
90C24×D3—32no—
91C23×C3×C4—32no—
92C23×Dic3—32no—
93C22×C4×D3—32no—
94C22×C4×D3—32no—
95C22×C4×D3—32no—
96C22×C4×D3—32no—
97C22×C4×D3—32no—
98C22×C4×D3—32no—
99C22×C4×D3—32no—
100C22×C4×D3—32no—
101C22×C4×D3—32no—
102C22×C4×D3—32no—
103C22×C4×D3—32no—
104C22×C4×D3—61no—
105C22×C4×D3—616no—
106C22×C4×D3C2×D312yes—
107C2×C3×M16—34no—
108C2×#208—34no—
109D3×M16—616no—
110C2×ΓL(1,𝔽25)—34no—
111C2×ΓL(1,𝔽25)C2×D314yescomplemented
112C2×D3×C8—34no—
113C2×D3×C8—34no—
114C2×D3×C8—62no—
115C3×C22⋊C8—21no—
116C3×C22⋊C8—32no—
117C3×C22⋊C8—34no—
118C3×C22⋊C8C2×D312yescomplemented
119#830—32no—
120#830—34no—
121#830—61no—
122#830C2×D312yescomplemented
123(C2×D3)⋊C8—34no—
124(C2×D3)⋊C8—34no—
125(C2×D3)⋊C8—34no—
126(C2×D3)⋊C8—62no—
127(C2×D3)⋊C8C2×D314yescomplemented
128C23×C32C22×C411yescharacteristic
129C22×C3⋊D3—22no—
130C22×C3⋊D3—22no—
131C22×C3⋊D3M1614yescomplemented
132C22×C3⋊D3C22×C411yescharacteristic
133C22×C3⋊D3C22×C411yescharacteristic
134C22×C3×D3—24no—
135C22×C3×D3—24no—
136C22×C3×D3—24no—
137C22×C3×D3C22×C412yes—
138C22×C3×D3C22×C412yes—
139C2×D32—232no—
140C2×D32—22no—
141C2×D32—22no—
142C2×D32—22no—
143C2×D32—22no—
144C2×D32—24no—
145C2×D32—24no—
146C2×D32—24no—
147C2×D32C22⋊C414yes—
148C2×D32M1614yescomplemented
149C2×C32×C4—22no—
150C2×C32×C4C22×C411yescharacteristic
151C2×C32×C4C2411yescharacteristic
152C2×C3⋊Dic3—22no—
153C2×C3⋊Dic3C22×C411yescharacteristic
154C2×C3⋊Dic3C22×C411yescharacteristic
155C4×C3⋊D3—22no—
156C4×C3⋊D3—22no—
157C4×C3⋊D3—22no—
158C4×C3⋊D3C2×D414yes—
159C2×C3×Dic3—24no—
160C2×C3×Dic3C22×C412yes—
161C2×C3×Dic3C22×C412yes—
162C3×C4×D3—24no—
163C3×C4×D3—24no—
164C3×C4×D3—24no—
165C3×C4×D3C2×D418yes—
166#624—22no—
167#624—24no—
168#624C22⋊C414yes—
169D3×Dic3—24no—
170D3×Dic3—24no—
171D3×Dic3—24no—
172D3×Dic3C22⋊C418yes—
173C32×C8—22no—
174C3⋊(C3⋊C8)—22no—
175C3×C3⋊C8—24no—
176C24×C4—91no—
177C22×M16—92no—
178#407—32no—
179#407—94no—
180#407—92no—
181C2×C22⋊C8—91no—
182C2×C22⋊C8—92no—
183C2×C22⋊C8—91no—
184C24×C3—32no—
185C23×D3—32no—
186C23×D3—32no—
187C23×D3—32no—
188C23×D3—32no—
189C23×D3—32no—
190C23×D3—61no—
191C23×D3—68no—
192C23×D3—68no—
193C23×D3—68no—
194C23×D3C4×D312yes—
195C22×C3×C4—21no—
196C22×C3×C4—32no—
197C22×C3×C4—32no—
198C22×C3×C4—32no—
199C22×C3×C4—32no—
200C22×C3×C4—32no—
201C22×C3×C4—68no—
202C22×C3×C4C22×D312yes—
203C22×Dic3—32no—
204C22×Dic3—32no—
205C22×Dic3—32no—
206C22×Dic3—32no—
207C22×Dic3—32no—
208C22×Dic3—61no—
209C22×Dic3—68no—
210C22×Dic3C4×D312yes—
211C2×C4×D3—28no—
212C2×C4×D3—32no—
213C2×C4×D3—32no—
214C2×C4×D3—32no—
215C2×C4×D3—316no—
216C2×C4×D3—32no—
217C2×C4×D3—32no—
218C2×C4×D3—32no—
219C2×C4×D3—32no—
220C2×C4×D3—32no—
221C2×C4×D3—32no—
222C2×C4×D3—32no—
223C2×C4×D3—32no—
224C2×C4×D3—32no—
225C2×C4×D3—61no—
226C2×C4×D3—61no—
227C2×C4×D3—61no—
228C2×C4×D3—61no—
229C2×C4×D3—68no—
230C2×C4×D3—68no—
231C2×C4×D3—68no—
232C2×C4×D3—68no—
233C2×C4×D3—68no—
234C2×C4×D3—68no—
235C2×C4×D3—68no—
236C2×C4×D3—68no—
237C2×C4×D3—68no—
238C2×C4×D3—68no—
239C2×C4×D3—124no—
240C2×C4×D3C4×D312yes—
241C2×C4×D3C4×D312yes—
242C2×C4×D3C22×D312yes—
243C2×C4×D3C22×D312yes—
244C3×M16—68no—
245C2×C3×C8—22no—
246C2×C3×C8—34no—
247C2×C3×C8C22×D314yescomplemented
248#208—68no—
249C2×C3⋊C8—34no—
250C2×C3⋊C8—62no—
251C2×C3⋊C8C22×D314yescomplemented
252ΓL(1,𝔽25)—28no—
253ΓL(1,𝔽25)—68no—
254D3×C8—68no—
255D3×C8—68no—
256D3×C8—124no—
257C22×C32—21no—
258C22×C32—21no—
259C22×C32C2×M1612yescomplemented
260C22×C32C23×C411yescharacteristic
261C2×C3⋊D3—21no—
262C2×C3⋊D3—21no—
263C2×C3⋊D3—28no—
264C2×C3⋊D3C2×C22⋊C412yes—
265C2×C3⋊D3C2×M1612yes—
266C2×C3⋊D3C2×M1612yes—
267C2×C3⋊D3C2×M1612yescomplemented
268C2×C3×D3—216no—
269C2×C3×D3—22no—
270C2×C3×D3—22no—
271C2×C3×D3—22no—
272C2×C3×D3—22no—
273C2×C3×D3C2×C22⋊C414yes—
274C2×C3×D3C2×M1614yescomplemented
275D32—216no—
276D32—28no—
277D32—28no—
278C32×C4—21no—
279C32×C4C22×D412yes—
280C3⋊Dic3—21no—
281C3⋊Dic3C2×C22⋊C412yes—
282C3×Dic3—22no—
283C3×Dic3C2×C22⋊C414yes—
284C25—91no—
285C23×C4—32no—
286C23×C4—91no—
287C23×C4—91no—
288C23×C4—92no—
289C23×C4—91no—
290C23×C4—91no—
291C23×C4—92no—
292C23×C4—91no—
293C23×C4—92no—
294C23×C4—91no—
295C23×C4—188no—
296C2×M16—34no—
297C2×M16—94no—
298C2×M16—188no—
299C22×C8—92no—
300C22×C8—92no—
301C22⋊C8—32no—
302C22⋊C8—34no—
303C22⋊C8—92no—
304C22⋊C8—94no—
305C22⋊C8—91no—
306C22⋊C8—92no—
307C22⋊C8D3211yescharacteristic, complemented
308C23×C3—21no—
309C23×C3—32no—
310C23×C3—32no—
311C23×C3—64no—
312C23×C3—64no—
313C23×C3—64no—
314C23×C3C2×C4×D312yes—
315C22×D3—24no—
316C22×D3—24no—
317C22×D3—24no—
318C22×D3—32no—
319C22×D3—38no—
320C22×D3—32no—
321C22×D3—38no—
322C22×D3—38no—
323C22×D3—61no—
324C22×D3—64no—
325C22×D3—61no—
326C22×D3—64no—
327C22×D3—64no—
328C22×D3—64no—
329C22×D3—64no—
330C22×D3—64no—
331C22×D3—64no—
332C22×D3—64no—
333C22×D3—64no—
334C22×D3—664no—
335C22×D3—64no—
336C22×D3—64no—
337C22×D3—64no—
338C22×D3—64no—
339C22×D3—122no—
340C22×D3—122no—
341C22×D3C2×C4×D312yes—
342C22×D3C2×C4×D312yes—
343C2×C3×C4—24no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—32no—
347C2×C3×C4—38no—
348C2×C3×C4—32no—
349C2×C3×C4—42no—
350C2×C3×C4—64no—
351C2×C3×C4—64no—
352C2×C3×C4—64no—
353C2×C3×C4—64no—
354C2×C3×C4C2×C4×D312yes—
355C2×C3×C4C23×D312yes—
356C2×Dic3—24no—
357C2×Dic3—32no—
358C2×Dic3—38no—
359C2×Dic3—32no—
360C2×Dic3—61no—
361C2×Dic3—61no—
362C2×Dic3—64no—
363C2×Dic3—64no—
364C2×Dic3—64no—
365C2×Dic3—64no—
366C2×Dic3—122no—
367C2×Dic3C2×C4×D312yes—
368C2×Dic3C2×C4×D312yes—
369C4×D3—24no—
370C4×D3—24no—
371C4×D3—24no—
372C4×D3—38no—
373C4×D3—38no—
374C4×D3—38no—
375C4×D3—64no—
376C4×D3—64no—
377C4×D3—64no—
378C4×D3—64no—
379C4×D3—64no—
380C4×D3—64no—
381C4×D3—64no—
382C4×D3—64no—
383C4×D3—64no—
384C4×D3—64no—
385C4×D3—122no—
386C4×D3—122no—
387C4×D3—122no—
388C4×D3D3×D418yes—
389C3×C8—24no—
390C3×C8—42no—
391C3×C8—64no—
392C3⋊C8—24no—
393C3⋊C8—64no—
394C3⋊C8—122no—
395C2×C32—22no—
396C2×C32C22×C22⋊C411yescharacteristic
397C2×C32C22×M1611yescharacteristic
398C2×C32C22×M1611yescharacteristic
399C3⋊D3—22no—
400C3⋊D3#40714yescomplemented
401C3×D3—24no—
402C3×D3—24no—
403C24—32no—
404C24—91no—
405C24—91no—
406C24—92no—
407C24—91no—
408C24—184no—
409C24—184no—
410C24—184no—
411C22×C4—32no—
412C22×C4—32no—
413C22×C4—32no—
414C22×C4—32no—
415C22×C4—32no—
416C22×C4—68no—
417C22×C4—98no—
418C22×C4—91no—
419C22×C4—92no—
420C22×C4—91no—
421C22×C4—92no—
422C22×C4—92no—
423C22×C4—92no—
424C22×C4—92no—
425C22×C4—91no—
426C22×C4—91no—
427C22×C4—91no—
428C22×C4—91no—
429C22×C4—91no—
430C22×C4—184no—
431C22×C4—188no—
432C22×C4—184no—
433C22×C4—188no—
434C22×C4—184no—
435C22×C4—184no—
436C22×C4—184no—
437C22×C4—188no—
438C22×C4C2×D3211yescharacteristic
439M16—68no—
440M16—188no—
441C2×C8—34no—
442C2×C8—92no—
443C2×C8—184no—
444C2×C8—184no—
445C2×C8C2×D3212yescomplemented
446C22×C3—22no—
447C22×C3—22no—
448C22×C3—21no—
449C22×C3—22no—
450C22×C3—34no—
451C22×C3—34no—
452C22×C3—41no—
453C22×C3—41no—
454C22×C3—616no—
455C22×C3—62no—
456C22×C3—62no—
457C22×C3—62no—
458C22×C3—62no—
459C22×C3D3×M1614yescomplemented
460C22×C3C22×C4×D312yes—
461C2×D3—216no—
462C2×D3—22no—
463C2×D3—22no—
464C2×D3—22no—
465C2×D3—22no—
466C2×D3—34no—
467C2×D3—34no—
468C2×D3—34no—
469C2×D3—34no—
470C2×D3—62no—
471C2×D3—62no—
472C2×D3—62no—
473C2×D3—62no—
474C2×D3—616no—
475C2×D3—616no—
476C2×D3—616no—
477C2×D3—616no—
478C2×D3—616no—
479C2×D3—62no—
480C2×D3—62no—
481C2×D3—128no—
482C2×D3—121no—
483C2×D3—121no—
484C2×D3D3×C22⋊C414yes—
485C2×D3D3×M1614yescomplemented
486C3×C4—22no—
487C3×C4—22no—
488C3×C4—34no—
489C3×C4—41no—
490C3×C4—62no—
491C3×C4C2×D3×D414yes—
492Dic3—22no—
493Dic3—34no—
494Dic3—62no—
495Dic3—62no—
496Dic3—121no—
497Dic3D3×C22⋊C414yes—
498C32C2×#40711yescharacteristic, complemented, Sylow
499C23—32no—
500C23—32no—
501C23—64no—
502C23—64no—
503C23—64no—
504C23—94no—
505C23—94no—
506C23—91no—
507C23—91no—
508C23—94no—
509C23—182no—
510C23—182no—
511C23—184no—
512C23—184no—
513C23—182no—
514C23—182no—
515C23—182no—
516C23—184no—
517C23—182no—
518C23—1832no—
519C23C4×D3211yescharacteristic
520C2×C4—22no—
521C2×C4—32no—
522C2×C4—38no—
523C2×C4—32no—
524C2×C4—64no—
525C2×C4—64no—
526C2×C4—64no—
527C2×C4—64no—
528C2×C4—94no—
529C2×C4—98no—
530C2×C4—91no—
531C2×C4—94no—
532C2×C4—91no—
533C2×C4—182no—
534C2×C4—182no—
535C2×C4—184no—
536C2×C4—184no—
537C2×C4—182no—
538C2×C4—184no—
539C2×C4—184no—
540C2×C4—182no—
541C2×C4—182no—
542C2×C4C4×D3211yescharacteristic
543C2×C4C22×D3211yescharacteristic
544C8—22no—
545C8—64no—
546C8—182no—
547C2×C3—24no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—21no—
551C2×C3—42no—
552C2×C3—64no—
553C2×C3—64no—
554C2×C3C2×D3×C22⋊C412yes—
555C2×C3C2×D3×M1612yes—
556C2×C3C2×D3×M1612yes—
557D3—24no—
558D3—24no—
559D3—38no—
560D3—64no—
561D3—64no—
562D3—122no—
563C22—21no—
564C22—21no—
565C22—34no—
566C22—34no—
567C22—616no—
568C22—62no—
569C22—62no—
570C22—62no—
571C22—62no—
572C22—92no—
573C22—92no—
574C22—92no—
575C22—92no—
576C22—188no—
577C22—188no—
578C22—188no—
579C22—1816no—
580C22—181no—
581C22—181no—
582C22#6379112yescomplemented
583C22C2×C4×D3211yescharacteristic
584C4—21no—
585C4—34no—
586C4—62no—
587C4—92no—
588C4—181no—
589C4D32×D412yes—
590C3—21no—
591C3D3×#40712yescomplemented
592C2—22no—
593C2—64no—
594C2—64no—
595C2—94no—
596C2—182no—
597C2D32×C22⋊C411yescharacteristic
598C2C2×#6379111yescharacteristic
599C2D32×M1611yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×C22⋊C8C22
prime radicalC23×D32C4
cosocleC2×C32×C4C24
hypercenterC22⋊C8D32
hypocenterC32C2×#407
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#63791C2semidirect
3. C3⋊D3×C22⋊C8C2semidirect
4. C3×#4726C2semidirect
5. #10591154C2semidirect
6. #10591152C2semidirect
7. #10590936C2semidirect
8. #10590935C2semidirect
22. C2×C8×C3⋊D3C22semidirect
23. C2×C3×ΓL(1,𝔽25)C22semidirect
24. C2×#3711C22semidirect
25. C2×#3710C22semidirect
27. C32×C22⋊C8C22semidirect
28. #63657C22semidirect
29. #63647C22semidirect
30. C3×#830C22semidirect
31. C3×(C2×D3)⋊C8C22semidirect
32. #63557C22semidirect
33. (C2×D3)⋊(C3⋊C8)C22semidirect
41. #4726D3semidirect
82. C2×C32×C8C23semidirect
83. C2×C3⋊(C3⋊C8)C23semidirect
85. C2×C3×C3⋊C8C23semidirect
111. C2×ΓL(1,𝔽25)C2×D3semidirect
118. C3×C22⋊C8C2×D3semidirect
122. #830C2×D3semidirect
127. (C2×D3)⋊C8C2×D3semidirect
131. C22×C3⋊D3M16semidirect
148. C2×D32M16semidirect
247. C2×C3×C8C22×D3semidirect
251. C2×C3⋊C8C22×D3semidirect
259. C22×C32C2×M16semidirect
267. C2×C3⋊D3C2×M16semidirect
274. C2×C3×D3C2×M16semidirect
307. C22⋊C8D32semidirect
400. C3⋊D3#407semidirect
445. C2×C8C2×D32semidirect
459. C22×C3D3×M16semidirect
485. C2×D3D3×M16semidirect
498. C32C2×#407semidirect
582. C22#63791semidirect
591. C3D3×#407semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D322
C2×#637912
C3⋊D3×C22⋊C82
C3×#47262
#105911542
#105911522
#105909362
#105909352
D3×#4073