Finite Group Databasebeta

← #11808429

Subgroups — #11808429

Order 1152.

1557 conjugacy classes of subgroups.

The subgroup lattice has 593 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64135C211yesmaximal, characteristic, complemented
2C2×C3×C4×#67C212yesmaximal, complemented
3C2×C4×#625C211yesmaximal, characteristic, complemented
4#10591723C211yesmaximal, characteristic
5#10591708C212yesmaximal, complemented
6#10591694C211yesmaximal, characteristic, complemented
7#10591394C211yesmaximal, characteristic, complemented
8C4×#3724C211yesmaximal, characteristic, complemented
9#10591319C212yesmaximal, complemented
10C4×(C2×D3)⋊Dic3C212yesmaximal, complemented
11#10591215C211yesmaximal, characteristic, complemented
12#82345—32nomaximal
13C23×C32×C4C2211yescharacteristic
14C22×C3×#67C2212yes—
15C22×C3×C4×D3C2212yes—
16C22×#625C2211yescharacteristic
17C2×#3757C2211yescharacteristic
18C2×#3757C2211yescharacteristic
19#64135—24no—
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C2×C4×C3⋊Dic3C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×C3×#217C2212yes—
25C3×C4×#67—28no—
26C2×C3×(C2×D3)⋊C4C2212yes—
27C2×C3×Dic3⋊C4C2212yes—
28C2×C3×C4×Dic3C2212yes—
29C2×#3724C2212yes—
30C2×#3724C2211yescharacteristic
31C2×(C2×D3)⋊Dic3C2212yes—
32C2×(C2×D3)⋊Dic3C2212yes—
33C2×(C2×D3)⋊Dic3C2212yes—
34C4×#625—24no—
35#63579C2212yes—
36#63579C2212yes—
37#63579C2211yescharacteristic
38#63579C2211yescharacteristic
39C2×C3×C4×D4—32no—
40C2×C4×#67—32no—
41C2×C4×#67D312yescomplemented
42C2×#926—32no—
43C2×#926—61no—
44#5223—32no—
45#5222—32no—
46C4×#217—32no—
47#4994—32no—
48#4982—32no—
49#4961—32no—
50#4959—32no—
51#4952—32no—
52#4948—32no—
53C4×(C2×D3)⋊C4—32no—
54C4×Dic3⋊C4—32no—
55C24×C32C2311yescharacteristic
56C23×C3×D3C2312yes—
57C22×C32×C4—22no—
58C22×C32×C4—22no—
59C22×C32×C4D414yescomplemented
60C22×C32×C4C2311yescharacteristic
61C22×C32×C4C2311yescharacteristic
62C22×C3⋊Dic3C2311yescharacteristic
63C22×C3⋊Dic3C2311yescharacteristic
64C22×C3⋊Dic3C2311yescharacteristic
65C22×C3⋊Dic3C2311yescharacteristic
66C2×C3×#67—24no—
67C2×C3×#67—24no—
68C2×C3×#67—24no—
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2312yes—
72C2×C3×C4×D3—24no—
73C2×C3×C4×D3—24no—
74C2×C3×C4×D3—24no—
75C2×#625—24no—
76C2×#625—22no—
77#3757—22no—
78#3757—22no—
79C4⋊(C3⋊Dic3)—22no—
80C4⋊(C3⋊Dic3)—22no—
81C4×C3⋊Dic3—22no—
82C4×C3⋊Dic3D414yescomplemented
83C3×#217—24no—
84C3×(C2×D3)⋊C4—24no—
85C3×Dic3⋊C4—24no—
86C3×C4×Dic3—24no—
87#3724—22no—
88#3724—24no—
89(C2×D3)⋊Dic3—24no—
90(C2×D3)⋊Dic3—24no—
91(C2×D3)⋊Dic3—24no—
92#2392—91noSylow
93C22×C3×D4—32no—
94C23×C3×C4—21no—
95C23×C3×C4—32no—
96C23×C3×C4C2×D312yes—
97C22×#67—32no—
98C22×#67C2×D312yes—
99C22×C4×D3C2×D312yes—
100C3×C4×D4—68no—
101C2×C3×C4⋊C4—32no—
102C2×C3×C22⋊C4—32no—
103C2×C3×C22⋊C4—32no—
104C2×C3×C42—32no—
105C2×#217—32no—
106C2×#217—32no—
107C2×#217—32no—
108C2×#217—32no—
109C2×#217—32no—
110C2×#217—61no—
111C2×#217—61no—
112C2×#217C2×D312yes—
113C4×#67—28no—
114C4×#67—68no—
115C2×(C2×D3)⋊C4—32no—
116C2×(C2×D3)⋊C4—32no—
117C2×(C2×D3)⋊C4—32no—
118C2×(C2×D3)⋊C4C2×D312yes—
119#926—68no—
120#926—68no—
121C2×C4⋊Dic3—32no—
122C2×C4⋊Dic3—32no—
123C2×C4⋊Dic3—61no—
124C2×C4⋊Dic3—61no—
125C2×Dic3⋊C4—32no—
126C2×Dic3⋊C4—32no—
127C2×Dic3⋊C4—32no—
128C2×Dic3⋊C4C2×D312yes—
129C2×C4×Dic3—32no—
130C2×C4×Dic3—32no—
131C2×C4×Dic3—61no—
132C2×C4×Dic3—61no—
133C2×C4×Dic3C2×D312yes—
134C3⋊#95—32no—
135C3⋊#95—32no—
136C3⋊#95—32no—
137C3⋊#95—32no—
138C3⋊#95—32no—
139C3⋊#95—32no—
140C23×C32—21no—
141C23×C32—21no—
142C23×C32—22no—
143C23×C32—22no—
144C23×C32C2×D412yes—
145C23×C32C2411yescharacteristic
146C22×C3×D3—22no—
147C22×C3×D3—22no—
148C22×C3×D3—22no—
149C22×C3×D3—22no—
150C22×C3×D3—22no—
151C22×C3×D3—22no—
152C22×C3×D3#4114yes—
153C2×C32×C4—21no—
154C2×C32×C4—21no—
155C2×C32×C4—28no—
156C2×C32×C4C2×D412yes—
157C2×C32×C4C2×D412yes—
158C2×C32×C4C2×D412yes—
159C2×C32×C4#4112yes—
160C2×C3⋊Dic3—21no—
161C2×C3⋊Dic3—21no—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3C2×D412yes—
167C2×C3⋊Dic3C2×D412yes—
168C3×#67—216no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3#4114yes—
178C3×C4×D3—48no—
179#625—28no—
180C2×C4×D4—32no—
181C2×C4×D4—91no—
182C2×#117—91no—
183#398—91no—
184#397—91no—
185#396—92no—
186#394—91no—
187#394—92no—
188#392—91no—
189C4×C4⋊C4—91no—
190C4×C22⋊C4—92no—
191C24×C3—21no—
192C24×C3—32no—
193C24×C3C22×D312yes—
194C23×D3C22×D312yes—
195C2×C3×D4—64no—
196C2×C3×D4—64no—
197C2×C3×D4—64no—
198C22×C3×C4—24no—
199C22×C3×C4—24no—
200C22×C3×C4—24no—
201C22×C3×C4—24no—
202C22×C3×C4—24no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—32no—
206C22×C3×C4—32no—
207C22×C3×C4—32no—
208C22×C3×C4—64no—
209C22×C3×C4—64no—
210C22×C3×C4—64no—
211C22×C3×C4#6718yescomplemented
212C22×C3×C4C22×D312yes—
213C22×C3×C4C22×D312yes—
214C2×#67—24no—
215C2×#67—24no—
216C2×#67—24no—
217C2×#67—64no—
218C2×#67—64no—
219C2×#67—64no—
220C22×Dic3—32no—
221C22×Dic3—32no—
222C22×Dic3—32no—
223C22×Dic3—32no—
224C22×Dic3—61no—
225C22×Dic3—61no—
226C22×Dic3—61no—
227C22×Dic3—61no—
228C22×Dic3C22×D312yes—
229C22×Dic3C22×D312yes—
230C22×Dic3C22×D312yes—
231C2×C4×D3—24no—
232C2×C4×D3—24no—
233C2×C4×D3—24no—
234C3×C4⋊C4—64no—
235C3×C22⋊C4—64no—
236C3×C22⋊C4—64no—
237C3×C42—64no—
238#217—24no—
239#217—64no—
240#217—64no—
241#217—64no—
242#217—64no—
243#217—64no—
244#217—64no—
245#217—64no—
246(C2×D3)⋊C4—24no—
247(C2×D3)⋊C4—64no—
248(C2×D3)⋊C4—64no—
249(C2×D3)⋊C4—64no—
250C4⋊Dic3—64no—
251C4⋊Dic3—64no—
252C4⋊Dic3—64no—
253C4⋊Dic3—64no—
254Dic3⋊C4—24no—
255Dic3⋊C4—64no—
256Dic3⋊C4—64no—
257Dic3⋊C4—64no—
258C4×Dic3—24no—
259C4×Dic3—38no—
260C4×Dic3—64no—
261C4×Dic3—64no—
262C4×Dic3—64no—
263C22×C32—22no—
264C22×C32—24no—
265C22×C32—41no—
266C22×C32—42no—
267C22×C32—41no—
268C22×C32C22×D411yescharacteristic
269C22×C32C22×D411yescharacteristic
270C22×C32C2×#4112yes—
271C22×C32C2×#4112yes—
272C22×C32C2×#4111yescharacteristic
273C2×C3×D3—24no—
274C2×C3×D3—24no—
275C2×C3×D3—24no—
276C2×C3×D3—42no—
277C2×C3×D3—42no—
278C2×C3×D3—42no—
279C2×C3×D3—42no—
280C32×C4—22no—
281C32×C4#12114yes—
282C3⋊Dic3—22no—
283C3⋊Dic3—22no—
284C3⋊Dic3—41no—
285C3⋊Dic3—41no—
286C3×Dic3—24no—
287C3×Dic3—42no—
288C3×Dic3—42no—
289C22×D4—32no—
290C22×D4—91no—
291C23×C4—32no—
292C23×C4D3211yescharacteristic
293C4×D4—68no—
294C4×D4—184no—
295#117—184no—
296C2×C4⋊C4—32no—
297C2×C4⋊C4—91no—
298C2×C4⋊C4—92no—
299C2×C4⋊C4—91no—
300C2×C4⋊C4—91no—
301C2×C22⋊C4—32no—
302C2×C22⋊C4—32no—
303C2×C22⋊C4—92no—
304C2×C22⋊C4—92no—
305C2×C22⋊C4—92no—
306C2×C22⋊C4—91no—
307C2×C22⋊C4—91no—
308C2×C42—32no—
309C2×C42—91no—
310C2×C42—91no—
311#95—92no—
312#95—92no—
313#95—91no—
314#95—91no—
315C23×C3—22no—
316C23×C3—22no—
317C23×C3—22no—
318C23×C3—22no—
319C23×C3—22no—
320C23×C3—22no—
321C23×C3—22no—
322C23×C3—22no—
323C23×C3—21no—
324C23×C3—22no—
325C23×C3—34no—
326C23×C3—42no—
327C23×C3—42no—
328C23×C3—62no—
329C23×C3—62no—
330C23×C3—62no—
331C23×C3—62no—
332C23×C3—62no—
333C23×C3—62no—
334C23×C3C2×#6714yes—
335C23×C3C23×D312yes—
336C22×D3—22no—
337C22×D3—22no—
338C22×D3—22no—
339C22×D3—22no—
340C22×D3—22no—
341C22×D3—22no—
342C22×D3#23514yes—
343C3×D4—616no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—216no—
347C2×C3×C4—22no—
348C2×C3×C4—22no—
349C2×C3×C4—216no—
350C2×C3×C4—22no—
351C2×C3×C4—22no—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
354C2×C3×C4—34no—
355C2×C3×C4—62no—
356C2×C3×C4—62no—
357C2×C3×C4—62no—
358C2×C3×C4—62no—
359C2×C3×C4—62no—
360C2×C3×C4—62no—
361C2×C3×C4—62no—
362C2×C3×C4—62no—
363C2×C3×C4—128no—
364C2×C3×C4D3×D414yes—
365C2×C3×C4#23714yes—
366C2×C3×C4C2×#6714yes—
367C2×C3×C4C2×#6714yes—
368#67—216no—
369#67—616no—
370C2×Dic3—22no—
371C2×Dic3—22no—
372C2×Dic3—22no—
373C2×Dic3—22no—
374C2×Dic3—22no—
375C2×Dic3—22no—
376C2×Dic3—22no—
377C2×Dic3—22no—
378C2×Dic3—34no—
379C2×Dic3—34no—
380C2×Dic3—62no—
381C2×Dic3—62no—
382C2×Dic3—62no—
383C2×Dic3—62no—
384C2×Dic3—62no—
385C2×Dic3—62no—
386C2×Dic3—62no—
387C2×Dic3—62no—
388C2×Dic3—62no—
389C2×Dic3—62no—
390C2×Dic3—62no—
391C2×Dic3—62no—
392C2×Dic3—62no—
393C2×Dic3—62no—
394C2×Dic3—122no—
395C2×Dic3—122no—
396C2×Dic3—122no—
397C2×Dic3—122no—
398C2×Dic3#23514yes—
399C4×D3—48no—
400C2×C32—42no—
401C2×C32C2×#12111yescharacteristic
402C2×C32#52512yes—
403C2×C32#52511yescharacteristic
404C2×C32#52912yes—
405C2×C32#53211yescharacteristic
406C3×D3—44no—
407C24—32no—
408C24C2×D3211yescharacteristic
409C2×D4—64no—
410C2×D4—64no—
411C2×D4—64no—
412C2×D4—182no—
413C2×D4—184no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—32no—
417C22×C4—32no—
418C22×C4—32no—
419C22×C4—64no—
420C22×C4—64no—
421C22×C4—64no—
422C22×C4—91no—
423C22×C4—91no—
424C22×C4—91no—
425C22×C4—91no—
426C22×C4#62514yescomplemented
427C22×C4C2×D3211yescharacteristic
428C22×C4C2×D3211yescharacteristic
429C4⋊C4—64no—
430C4⋊C4—182no—
431C4⋊C4—182no—
432C4⋊C4—184no—
433C4⋊C4—182no—
434C22⋊C4—64no—
435C22⋊C4—64no—
436C22⋊C4—184no—
437C22⋊C4—184no—
438C22⋊C4—184no—
439C22⋊C4—182no—
440C22⋊C4—182no—
441C42—64no—
442C42—94no—
443C42—182no—
444C22×C3—24no—
445C22×C3—24no—
446C22×C3—24no—
447C22×C3—24no—
448C22×C3—22no—
449C22×C3—22no—
450C22×C3—21no—
451C22×C3—21no—
452C22×C3—21no—
453C22×C3—44no—
454C22×C3—42no—
455C22×C3—44no—
456C22×C3—42no—
457C22×C3—42no—
458C22×C3—42no—
459C22×C3—42no—
460C22×C3—42no—
461C22×C3—64no—
462C22×C3—64no—
463C22×C3—64no—
464C22×C3—122no—
465C22×C3—122no—
466C22×C3—122no—
467C22×C3—122no—
468C22×C3C2×#23512yes—
469C22×C3C2×#23512yes—
470C22×C3C2×D3×D412yes—
471C22×C3C2×#23712yes—
472C22×C3D3×#4112yes—
473C22×C3D3×#4112yes—
474C22×C3C22×#6712yes—
475C2×D3—24no—
476C2×D3—24no—
477C2×D3—24no—
478C2×D3—42no—
479C2×D3—42no—
480C2×D3—42no—
481C2×D3—42no—
482C3×C4—24no—
483C3×C4—24no—
484C3×C4—24no—
485C3×C4—64no—
486C3×C4—122no—
487C3×C4—122no—
488C3×C4#93918yes—
489Dic3—24no—
490Dic3—42no—
491Dic3—42no—
492Dic3—64no—
493Dic3—64no—
494Dic3—122no—
495Dic3—122no—
496Dic3—122no—
497Dic3—122no—
498Dic3—122no—
499Dic3—122no—
500C32#239211yescharacteristic, complemented, Sylow
501C23—22no—
502C23—22no—
503C23—21no—
504C23—21no—
505C23—34no—
506C23—62no—
507C23—62no—
508C23—62no—
509C23—62no—
510C23—62no—
511C23—62no—
512C23C2×#62512yes—
513C23C22×D3211yescharacteristic
514D4—616no—
515D4—188no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—28no—
519C2×C4—34no—
520C2×C4—62no—
521C2×C4—62no—
522C2×C4—62no—
523C2×C4—62no—
524C2×C4—62no—
525C2×C4—62no—
526C2×C4—62no—
527C2×C4—62no—
528C2×C4—92no—
529C2×C4—92no—
530C2×C4—128no—
531C2×C4—182no—
532C2×C4—182no—
533C2×C4—182no—
534C2×C4—182no—
535C2×C4—181no—
536C2×C4—181no—
537C2×C4#380512yes—
538C2×C4C2×#62512yes—
539C2×C4C2×#62512yes—
540C2×C4#381112yes—
541C2×C3—21no—
542C2×C3—22no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—22no—
546C2×C3—44no—
547C2×C3—44no—
548C2×C3—124no—
549C2×C3#553812yes—
550C2×C3#554712yes—
551C2×C3#554812yes—
552C2×C3#555712yes—
553C2×C3#579112yes—
554C2×C3C2×#93912yes—
555C2×C3#582812yes—
556D3—44no—
557C22—22no—
558C22—24no—
559C22—41no—
560C22—42no—
561C22—41no—
562C22—64no—
563C22—64no—
564C22—64no—
565C22—122no—
566C22—122no—
567C22—122no—
568C22—122no—
569C22D3×#23512yes—
570C22D3×#23512yes—
571C22C2×#380511yescharacteristic
572C22C22×#62511yescharacteristic
573C22C2×#381111yescharacteristic
574C4—22no—
575C4—64no—
576C4—122no—
577C4—122no—
578C4—182no—
579C4—182no—
580C4—361no—
581C4—361no—
582C4#6398014yes—
583C3—21no—
584C3#8234512yescomplemented
585C2—42no—
586C2—124no—
587C2#1059493412yes—
588C2#1059501711yescharacteristic
589C2#1059502212yes—
590C2#1059507611yescharacteristic
591C2C2×#6398011yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutator, socle, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC23×C32×C4C22
prime radical#10591723C2
hypercenterC23×C4D32
hypocenterC32#2392
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×#64135C2semidirect
2. C2×C3×C4×#67C2semidirect
3. C2×C4×#625C2semidirect
5. #10591708C2semidirect
6. #10591694C2semidirect
7. #10591394C2semidirect
8. C4×#3724C2semidirect
9. #10591319C2semidirect
10. C4×(C2×D3)⋊Dic3C2semidirect
11. #10591215C2semidirect
41. C2×C4×#67D3semidirect
59. C22×C32×C4D4semidirect
82. C4×C3⋊Dic3D4semidirect
211. C22×C3×C4#67semidirect
426. C22×C4#625semidirect
500. C32#2392semidirect
584. C3#82345semidirect

Maximal subgroups

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

subgroupindex
C2×#641352
C2×C3×C4×#672
C2×C4×#6252
#105917232
#105917082
#105916942
#105913942
C4×#37242
#105913192
C4×(C2×D3)⋊Dic32
#105912152
#823453