Finite Group Databasebeta

← #11824450

Subgroups — #11824450

Order 1152.

2145 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64149C211yesmaximal, characteristic, complemented
2C2×C3×#938C212yesmaximal, complemented
3C2×#63979C212yesmaximal, complemented
4C2×#63909C212yesmaximal, complemented
5C2×C4×#625C211yesmaximal, characteristic, complemented
6#10591724C214yesmaximal, complemented
7#10591704C212yesmaximal, complemented
8#10591274C211yesmaximal, characteristic, complemented
9#82669—32nomaximal
10C22×C32×D4C2211yescharacteristic
11C22×#638C2212yes—
12C22×#638C2212yes—
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C22×C3×#67C2214yes—
15C22×C3×C4×D3C2212yes—
16C22×#626C2214yes—
17C22×#625C2211yescharacteristic
18#64149—24no—
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C3×#217C2214yes—
21C3×#938—28no—
22C2×C3×C4⋊Dic3C2212yes—
23#63979—28no—
24C2×#3724C2211yescharacteristic
25C2×#3722C2214yes—
26C2×(C2×D3)⋊Dic3C2212yes—
27C2×Dic32C2212yes—
28#63909—28no—
29C4×#625—24no—
30#63579C2212yes—
31C2×C3×#121—32no—
32C2×#940—32no—
33C2×#940—34no—
34C2×#940—61no—
35C2×#938D312yescomplemented
36C2×#930—32no—
37C2×C4×#67—32no—
38C2×#895—32no—
39#5223—34no—
40Dic3×C4⋊C4—32no—
41#4960—34no—
42#4957—34no—
43C24×C32C2312yes—
44C23×C3⋊D3C2312yes—
45C23×C3×D3C2312yes—
46C2×C32×D4—22no—
47C2×C32×D4—24no—
48C22×C32×C4C2311yescharacteristic
49C2×#638—24no—
50C2×#638—24no—
51C2×#638—24no—
52C2×#638—24no—
53C2×#638—44no—
54C22×C3⋊Dic3C2311yescharacteristic
55C22×C3⋊Dic3C2311yescharacteristic
56C2×C4⋊(C3⋊D3)—22no—
57C2×C4⋊(C3⋊D3)—24no—
58C2×C3×#67—28no—
59C2×C3×#67—28no—
60C2×C3×#67—44no—
61C22×C3×Dic3C2312yes—
62C22×C3×Dic3C2314yes—
63C2×C3×C4×D3—24no—
64C2×C3×C4×D3—24no—
65C2×C3×C4×D3—24no—
66C2×#626—28no—
67C2×#626—28no—
68C2×#626—44no—
69C2×#625—22no—
70C2×#625—22no—
71C2×#625D414yescomplemented
72C4×C3⋊Dic3D414yescomplemented
73C3×#217—28no—
74C3×C4⋊Dic3D418yescomplemented
75#3724—22no—
76#3722—28no—
77(C2×D3)⋊Dic3—24no—
78Dic32—24no—
79#2541—91noSylow
80C22×C3×D4—21no—
81C22×C3×D4—34no—
82C22×C3×D4C2×D312yes—
83C23×C3×C4—32no—
84C22×#67—32no—
85C22×#67—34no—
86C22×#67—34no—
87C22×#67—34no—
88C22×#67—62no—
89C22×#67—62no—
90C22×#67C2×D314yes—
91C22×D12—32no—
92C22×D12—34no—
93C22×D12—61no—
94C22×C4×D3C2×D312yes—
95C3×#121—68no—
96C2×C3×C4⋊C4—32no—
97C2×C3×C22⋊C4—34no—
98C2×#217—32no—
99C2×#217C2×D314yes—
100#940—68no—
101#940—616no—
102#940—68no—
103#938—28no—
104#930—68no—
105C4×#67—68no—
106C2×(C2×D3)⋊C4—32no—
107C2×(C2×D3)⋊C4—34no—
108C2×(C2×D3)⋊C4—34no—
109C2×C4⋊Dic3C2×D312yes—
110C2×Dic3⋊C4—32no—
111C2×C4×Dic3—32no—
112C2×C4×Dic3—34no—
113C2×C4×Dic3—61no—
114#895—68no—
115C3⋊#95—34no—
116C23×C32—22no—
117C23×C32—24no—
118C23×C32—22no—
119C23×C32—22no—
120C23×C32—24no—
121C23×C32C2411yescharacteristic
122C22×C3⋊D3—22no—
123C22×C3⋊D3—24no—
124C22×C3⋊D3—22no—
125C22×C3⋊D3—22no—
126C22×C3⋊D3—24no—
127C22×C3×D3—22no—
128C22×C3×D3—22no—
129C22×C3×D3—22no—
130C22×C3×D3—22no—
131C22×C3×D3—22no—
132C22×C3×D3—22no—
133C22×C3×D3C2×D414yes—
134C32×D4—44no—
135C2×C32×C4C2×D412yes—
136C2×C32×C4C2×D414yes—
137#638—48no—
138#638—48no—
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3C2×D412yes—
141C2×C3⋊Dic3C2×D412yes—
142C2×C3⋊Dic3C2×D412yes—
143C2×C3⋊Dic3#4112yes—
144C4⋊(C3⋊D3)—44no—
145C3×#67—416no—
146C2×C3×Dic3—24no—
147C2×C3×Dic3—24no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3C2×D418yes—
152C3×C4×D3—48no—
153#626—416no—
154#625—28no—
155C2×#127—92no—
156C2×#127—91no—
157C2×#121—32no—
158C2×#121—92no—
159C2×C4×D4—91no—
160#392—94no—
161#390—92no—
162C4×C4⋊C4—91no—
163C24×C3—22no—
164C24×C3—32no—
165C24×C3C22×D314yes—
166C23×D3—34no—
167C23×D3—62no—
168C23×D3C22×D312yes—
169C2×C3×D4—24no—
170C2×C3×D4—24no—
171C2×C3×D4—24no—
172C2×C3×D4—24no—
173C2×C3×D4—44no—
174C2×C3×D4—68no—
175C2×C3×D4—68no—
176C2×C3×D4—124no—
177C22×C3×C4—21no—
178C22×C3×C4—34no—
179C22×C3×C4—32no—
180C22×C3×C4—64no—
181C22×C3×C4—64no—
182C22×C3×C4—64no—
183C22×C3×C4C22×D312yes—
184C2×#67—28no—
185C2×#67—28no—
186C2×#67—38no—
187C2×#67—44no—
188C2×#67—68no—
189C2×#67—64no—
190C2×#67—64no—
191C2×#67—68no—
192C2×#67—68no—
193C2×#67—68no—
194C2×#67—68no—
195C2×#67—68no—
196C2×#67—68no—
197C2×#67—68no—
198C2×#67—124no—
199C2×#67—124no—
200C2×#67—124no—
201C2×#67—124no—
202C2×#67—124no—
203C2×#67—128no—
204C22×Dic3—32no—
205C22×Dic3—32no—
206C22×Dic3—61no—
207C22×Dic3—61no—
208C22×Dic3C22×D312yes—
209C22×Dic3C22×D314yes—
210C2×D12—64no—
211C2×D12—68no—
212C2×D12—68no—
213C2×D12—64no—
214C2×D12—64no—
215C2×D12—64no—
216C2×D12—124no—
217C2×D12—124no—
218C2×C4×D3—24no—
219C2×C4×D3—24no—
220C2×C4×D3—24no—
221C3×C4⋊C4—38no—
222C3×C22⋊C4—68no—
223#217—28no—
224#217—64no—
225(C2×D3)⋊C4—68no—
226(C2×D3)⋊C4—64no—
227(C2×D3)⋊C4—68no—
228C4⋊Dic3#6718yescomplemented
229Dic3⋊C4—64no—
230C4×Dic3—38no—
231C4×Dic3—64no—
232C4×Dic3—68no—
233C22×C32—42no—
234C22×C32—42no—
235C22×C32—42no—
236C22×C32—44no—
237C22×C32—44no—
238C22×C32C22×D411yescharacteristic
239C22×C32C22×D411yescharacteristic
240C22×C32C22×D412yes—
241C22×C32C2×#4111yescharacteristic
242C22×C32H(5,𝔽2)12yes—
243C2×C3⋊D3—42no—
244C2×C3⋊D3—42no—
245C2×C3⋊D3—42no—
246C2×C3⋊D3—44no—
247C2×C3⋊D3—44no—
248C2×C3×D3—24no—
249C2×C3×D3—24no—
250C2×C3×D3—24no—
251C2×C3×D3—42no—
252C2×C3×D3—42no—
253C2×C3×D3—42no—
254C2×C3×D3—42no—
255C32×C4#12714yescomplemented
256C3⋊Dic3—22no—
257C3⋊Dic3#12114yescomplemented
258C3×Dic3—28no—
259C3×Dic3—42no—
260C22×D4—34no—
261C22×D4—94no—
262C22×D4—91no—
263C22×D4—92no—
264C22×D4—92no—
265C22×D4—91no—
266C22×D4D3211yescharacteristic
267C23×C4—32no—
268#127—184no—
269#127—188no—
270#121—68no—
271#121—188no—
272C4×D4—184no—
273C2×C4⋊C4—32no—
274C2×C4⋊C4—91no—
275C2×C22⋊C4—34no—
276C2×C22⋊C4—94no—
277C2×C22⋊C4—92no—
278C2×C42—91no—
279C2×C42—92no—
280#95—92no—
281C23×C3—24no—
282C23×C3—24no—
283C23×C3—24no—
284C23×C3—24no—
285C23×C3—24no—
286C23×C3—24no—
287C23×C3—24no—
288C23×C3—24no—
289C23×C3—21no—
290C23×C3—34no—
291C23×C3—42no—
292C23×C3—42no—
293C23×C3—44no—
294C23×C3—44no—
295C23×C3—62no—
296C23×C3—62no—
297C23×C3—62no—
298C23×C3—62no—
299C23×C3—62no—
300C23×C3—62no—
301C23×C3C23×D312yes—
302C22×D3—22no—
303C22×D3—22no—
304C22×D3—22no—
305C22×D3—22no—
306C22×D3—22no—
307C22×D3—22no—
308C22×D3—64no—
309C22×D3—64no—
310C22×D3—64no—
311C22×D3—64no—
312C22×D3—64no—
313C22×D3—64no—
314C22×D3—64no—
315C22×D3—64no—
316C22×D3—124no—
317C22×D3—122no—
318C22×D3—122no—
319C22×D3—124no—
320C22×D3D3×D414yes—
321C3×D4—48no—
322C3×D4—48no—
323C3×D4—1216no—
324C2×C3×C4—24no—
325C2×C3×C4—22no—
326C2×C3×C4—38no—
327C2×C3×C4—64no—
328C2×C3×C4—64no—
329C2×C3×C4—62no—
330C2×C3×C4—62no—
331C2×C3×C4—62no—
332C2×C3×C4—128no—
333C2×C3×C4D3×D414yes—
334C2×C3×C4D3×D414yes—
335C2×C3×C4C2×#6714yes—
336#67—416no—
337#67—616no—
338#67—1216no—
339#67—1216no—
340#67—1216no—
341#67—1216no—
342#67—1216no—
343C2×Dic3—24no—
344C2×Dic3—24no—
345C2×Dic3—22no—
346C2×Dic3—22no—
347C2×Dic3—22no—
348C2×Dic3—34no—
349C2×Dic3—34no—
350C2×Dic3—34no—
351C2×Dic3—34no—
352C2×Dic3—62no—
353C2×Dic3—62no—
354C2×Dic3—62no—
355C2×Dic3—62no—
356C2×Dic3—64no—
357C2×Dic3—62no—
358C2×Dic3—62no—
359C2×Dic3C2×#6718yes—
360D12—128no—
361D12—1216no—
362D12—128no—
363C4×D3—48no—
364C2×C32—82no—
365C2×C32C2×#12111yescharacteristic
366C2×C32C2×#12711yescharacteristic
367C2×C32#53511yescharacteristic
368C2×C32D4212yes—
369C2×C32#55012yes—
370C3⋊D3—82no—
371C3×D3—44no—
372C24—32no—
373C24—92no—
374C24C2×D3212yes—
375C2×D4—24no—
376C2×D4—22no—
377C2×D4—68no—
378C2×D4—68no—
379C2×D4—94no—
380C2×D4—124no—
381C2×D4—188no—
382C2×D4—188no—
383C2×D4—182no—
384C2×D4—182no—
385C2×D4—184no—
386C2×D4—184no—
387C2×D4—184no—
388C2×D4—184no—
389C2×D4—184no—
390C2×D4—182no—
391C2×D4—364no—
392C2×D4—364no—
393C22×C4—34no—
394C22×C4—32no—
395C22×C4—64no—
396C22×C4—64no—
397C22×C4—64no—
398C22×C4—91no—
399C22×C4—91no—
400C22×C4C2×D3211yescharacteristic
401C4⋊C4—38no—
402C4⋊C4—182no—
403C22⋊C4—68no—
404C22⋊C4—188no—
405C22⋊C4—184no—
406C42—94no—
407C42—184no—
408C22×C3—21no—
409C22×C3—21no—
410C22×C3—22no—
411C22×C3—22no—
412C22×C3—21no—
413C22×C3—44no—
414C22×C3—44no—
415C22×C3—44no—
416C22×C3—44no—
417C22×C3—44no—
418C22×C3—44no—
419C22×C3—44no—
420C22×C3—44no—
421C22×C3—44no—
422C22×C3—44no—
423C22×C3—64no—
424C22×C3—64no—
425C22×C3—64no—
426C22×C3—84no—
427C22×C3—84no—
428C22×C3—122no—
429C22×C3—122no—
430C22×C3—122no—
431C22×C3—122no—
432C22×C3C2×D3×D412yes—
433C22×C3C2×D3×D412yes—
434C22×C3C2×D3×D412yes—
435C22×C3#100412yes—
436C22×C3D3×#4112yes—
437C22×C3#100912yes—
438C22×C3C22×#6712yes—
439C2×D3—24no—
440C2×D3—24no—
441C2×D3—24no—
442C2×D3—42no—
443C2×D3—42no—
444C2×D3—42no—
445C2×D3—42no—
446C2×D3—124no—
447C2×D3—124no—
448C2×D3—124no—
449C2×D3—124no—
450C2×D3—124no—
451C2×D3—124no—
452C2×D3—124no—
453C2×D3—124no—
454C2×D3—124no—
455C2×D3—124no—
456C2×D3—244no—
457C2×D3—244no—
458C3×C4—24no—
459C3×C4—68no—
460C3×C4—122no—
461C3×C4#94018yescomplemented
462Dic3—28no—
463Dic3—38no—
464Dic3—42no—
465Dic3—64no—
466Dic3—64no—
467Dic3—64no—
468C32#254111yescharacteristic, complemented, Sylow
469C23—22no—
470C23—22no—
471C23—24no—
472C23—24no—
473C23—22no—
474C23—34no—
475C23—62no—
476C23—62no—
477C23—62no—
478C23—62no—
479C23—62no—
480C23—62no—
481C23—182no—
482C23—182no—
483C23—184no—
484C23—184no—
485C23—182no—
486C23C22×D3211yescharacteristic
487D4—44no—
488D4—1216no—
489D4—188no—
490D4—3616no—
491D4—368no—
492D4—368no—
493D4—364no—
494C2×C4—38no—
495C2×C4—64no—
496C2×C4—64no—
497C2×C4—62no—
498C2×C4—62no—
499C2×C4—62no—
500C2×C4—92no—
501C2×C4—92no—
502C2×C4—92no—
503C2×C4—92no—
504C2×C4—128no—
505C2×C4—182no—
506C2×C4D3×#6714yes—
507C2×C4#381112yes—
508C2×C3—22no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—22no—
513C2×C3—84no—
514C2×C3—84no—
515C2×C3—124no—
516C2×C3#559912yes—
517C2×C3D3×#12112yes—
518C2×C3#560712yes—
519C2×C3#560912yes—
520C2×C3D4×#6712yes—
521C2×C3C2×#94012yes—
522C2×C3#583412yes—
523D3—44no—
524D3—244no—
525D3—244no—
526C22—44no—
527C22—42no—
528C22—42no—
529C22—42no—
530C22—44no—
531C22—64no—
532C22—64no—
533C22—64no—
534C22—122no—
535C22—122no—
536C22—122no—
537C22—122no—
538C22—364no—
539C22—362no—
540C22—362no—
541C22—362no—
542C22—364no—
543C22D32×D411yescharacteristic
544C22#6431211yescharacteristic
545C22#6431412yes—
546C22C2×D3×#6712yes—
547C22C2×#381111yescharacteristic
548C4—68no—
549C4—94no—
550C4—122no—
551C4—182no—
552C4#6397914yescomplemented
553C3—21no—
554C3#8266912yescomplemented
555C2—82no—
556C2—124no—
557C2—722no—
558C2#1059523612yes—
559C2#1059524111yescharacteristic
560C2#1059528211yescharacteristic
561C2#1059528812yes—
562C2C2×#6397911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC22×C32×D4C22
hypercenterC22×D4D32
hypocenterC32#2541
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#64149C2semidirect
2. C2×C3×#938C2semidirect
3. C2×#63979C2semidirect
4. C2×#63909C2semidirect
5. C2×C4×#625C2semidirect
6. #10591724C2semidirect
7. #10591704C2semidirect
8. #10591274C2semidirect
35. C2×#938D3semidirect
71. C2×#625D4semidirect
72. C4×C3⋊Dic3D4semidirect
74. C3×C4⋊Dic3D4semidirect
228. C4⋊Dic3#67semidirect
255. C32×C4#127semidirect
257. C3⋊Dic3#121semidirect
461. C3×C4#940semidirect
468. C32#2541semidirect
552. C4#63979semidirect
554. C3#82669semidirect

Maximal subgroups

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

subgroupindex
C2×#641492
C2×C3×#9382
C2×#639792
C2×#639092
C2×C4×#6252
#105917242
#105917042
#105912742
#826693