Finite Group Databasebeta

← #11788345

Subgroups — #11788345

Order 1152.

749 conjugacy classes of subgroups.

The subgroup lattice has 591 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×M16C211yesmaximal, characteristic
2C2×#63857C211yesmaximal, characteristic
3C2×#63651C211yesmaximal, characteristic, complemented
4C2×#63561C211yesmaximal, characteristic, complemented
5#10591069C211yesmaximal, characteristic
6C3×#4554C211yesmaximal, characteristic, complemented
7#10589167C211yesmaximal, characteristic, complemented
8#72003—31nomaximal
9#68993—31nomaximal
10C22×#634C2211yescharacteristic
11C22×C3×C4×D3C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×D3×M16—22no—
18C3×D3×M16—22no—
19C2×C3×ΓL(1,𝔽25)—21no—
20C2×C3×D3×C8—21no—
21C2×Dic3⋊Dic3C412yes—
22C2×(C2×D3)⋊Dic3C412yes—
23#63857—21no—
24#63857—21no—
25#63857—21no—
26#63857—21no—
27#63651—22no—
28#63561—22no—
29(C2×D3)⋊(C3⋊C8)—21no—
30(C2×D3)⋊(C3⋊C8)—21no—
31C22×C3×M16—31no—
32C2×#924—31no—
33C2×D3×M16D311yescharacteristic
34C2×#897—31no—
35#5207—31no—
36C2×#824—31no—
37C2×#824—31no—
38C2×#824—31no—
39C2×#824—31no—
40C2×#824—61no—
41#5126—31no—
42C3×#343—31no—
43#4554—31no—
44#4554D311yescharacteristic, complemented
45#4530—31no—
46C23×C3×D3C2×C411yescharacteristic
47C22×C32×C4C2311yescharacteristic
48C22×C3⋊Dic3C2×C412yes—
49C2×#634—21no—
50C2×#634—21no—
51C2×#634—21no—
52C2×#634—21no—
53C2×#634—21no—
54C2×#634—21no—
55C22×C3×Dic3C2×C411yescharacteristic
56C22×C3×Dic3C2×C412yes—
57C2×C3×C4×D3—21no—
58C2×C3×C4×D3—21no—
59C2×C3×C4×D3—21no—
60C2×C3×C4×D3—21no—
61C2×C3×C4×D3D411yescharacteristic
62C2×C3×C4×D3D411yescharacteristic
63C2×C3×C4×D3D411yescharacteristic
64C2×C3×C4×D3D411yescharacteristic
65C32×M16—21no—
66C32×M16D412yes—
67C2×C32×C8—21no—
68#3748—21no—
69#3748—21no—
70C2×C3⋊(C3⋊C8)—21no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3—21no—
73C3×#208—21no—
74C3×#208—21no—
75C3×#208—21no—
76C3×#208D412yes—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8—21no—
79C3×ΓL(1,𝔽25)—24no—
80C3×D3×C8—24no—
81Dic3⋊Dic3—22no—
82Dic3⋊Dic3—22no—
83(C2×D3)⋊Dic3—22no—
84(C2×D3)⋊Dic3—22no—
85#1901—91noSylow
86C23×C3×C4—31no—
87C22×C4×D3C2×D311yescharacteristic
88C22×Dic6—31no—
89C22×Dic6—31no—
90C22×Dic6—61no—
91C2×C3×M16—21no—
92C2×C3×M16—31no—
93C2×C3×M16—31no—
94C2×C3×M16—61no—
95C2×C3×M16—62no—
96C2×C3×M16—62no—
97C2×C3×M16C2×D311yescharacteristic
98C2×C3×M16C2×D311yescharacteristic
99C22×C3×C8—61no—
100C2×C3×C4⋊C4—31no—
101C2×#217—32no—
102C2×(C2×D3)⋊C4—32no—
103C2×C4⋊Dic3—32no—
104C2×C4⋊Dic3C2×D311yescharacteristic
105#924—61no—
106#924—61no—
107#924—61no—
108#924—61no—
109C2×Dic3⋊C4—32no—
110C2×#208—31no—
111C2×#208—31no—
112C2×#208—61no—
113C2×#208C2×D311yescharacteristic
114C2×#208C2×D311yescharacteristic
115D3×M16—22no—
116D3×M16—22no—
117C2×ΓL(1,𝔽25)—21no—
118C2×D3×C8—21no—
119#897—61no—
120#897—61no—
121#897—61no—
122#897—61no—
123#830—61no—
124#830—61no—
125#824—62no—
126#824—64no—
127#824—62no—
128#824—62no—
129#824—62no—
130(C2×D3)⋊C8—61no—
131(C2×D3)⋊C8—61no—
132C23×C32C22×C411yescharacteristic
133C22×C3×D3—21no—
134C22×C3×D3—21no—
135C22×C3×D3—22no—
136C22×C3×D3—41no—
137C22×C3×D3C22⋊C411yescharacteristic
138C22×C3×D3C22⋊C411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4#4111yescharacteristic
144C2×C32×C4#4111yescharacteristic
145C2×C3⋊Dic3—22no—
146C2×C3⋊Dic3—22no—
147C2×C3⋊Dic3—22no—
148#634—41no—
149#634—41no—
150#634—41no—
151#634—41no—
152C2×C3×Dic3—21no—
153C2×C3×Dic3—21no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—42no—
156C2×C3×Dic3C22⋊C411yescharacteristic
157C2×C3×Dic3C22⋊C411yescharacteristic
158C3×C4×D3—21no—
159C3×C4×D3—21no—
160C3×C4×D3—21no—
161C3×C4×D3—21no—
162C3×C4×D3—21no—
163C3×C4×D3—21no—
164C3×C4×D3—21no—
165C3×C4×D3—21no—
166C32×C8—22no—
167C3⋊(C3⋊C8)—41no—
168C3×C3⋊C8—22no—
169C3×C3⋊C8—41no—
170C22×M16—31no—
171C2×C22⋊Q8—91no—
172C2×#101—91no—
173C2×#101—91no—
174#407—91no—
175#343—31no—
176#343—91no—
177C24×C3—31no—
178C23×D3C4×D311yescharacteristic
179C22×C3×C4—21no—
180C22×C3×C4—31no—
181C22×C3×C4—31no—
182C22×C3×C4—31no—
183C22×C3×C4—31no—
184C22×C3×C4—31no—
185C22×C3×C4—32no—
186C22×C3×C4—61no—
187C22×C3×C4—61no—
188C22×C3×C4—61no—
189C22×C3×C4—61no—
190C22×C3×C4C22×D311yescharacteristic
191C22×C3×C4C22×D311yescharacteristic
192C22×Dic3—32no—
193C22×Dic3—32no—
194C22×Dic3—62no—
195C22×Dic3C4×D311yescharacteristic
196C22×Dic3C4×D312yes—
197C2×C4×D3—21no—
198C2×C4×D3—21no—
199C2×C4×D3—21no—
200C2×C4×D3—21no—
201C2×C4×D3D1211yescharacteristic
202C2×C4×D3D1211yescharacteristic
203C2×C4×D3#6711yescharacteristic
204C2×C4×D3#6711yescharacteristic
205C2×Dic6—62no—
206C2×Dic6—62no—
207C2×Dic6—61no—
208C2×Dic6—61no—
209C2×Dic6—61no—
210C2×Dic6—61no—
211C2×Dic6—61no—
212C2×Dic6—61no—
213C2×Dic6—61no—
214C2×Dic6—61no—
215C2×Dic6—61no—
216C2×Dic6—61no—
217C2×Dic6—61no—
218C2×Dic6—61no—
219C2×Dic6—121no—
220C2×Dic6—121no—
221C2×Dic6—121no—
222C2×Dic6—121no—
223C3×M16—21no—
224C3×M16—21no—
225C3×M16—22no—
226C3×M16—32no—
227C3×M16—41no—
228C3×M16—64no—
229C3×M16—61no—
230C3×M16—61no—
231C3×M16—61no—
232C3×M16D1212yes—
233C3×M16#6712yes—
234C2×C3×C8—21no—
235C2×C3×C8—21no—
236C2×C3×C8—41no—
237C2×C3×C8—64no—
238C2×C3×C8—61no—
239C2×C3×C8—61no—
240C3×C4⋊C4—61no—
241C3×C4⋊C4—61no—
242#217—62no—
243#217—62no—
244(C2×D3)⋊C4—62no—
245(C2×D3)⋊C4—62no—
246C4⋊Dic3—21no—
247C4⋊Dic3—21no—
248C4⋊Dic3—62no—
249C4⋊Dic3—62no—
250Dic3⋊C4—62no—
251Dic3⋊C4—62no—
252#208—21no—
253#208—21no—
254#208—21no—
255#208—62no—
256#208—61no—
257#208—61no—
258#208—61no—
259#208—61no—
260#208—121no—
261#208#6712yes—
262C2×C3⋊C8—21no—
263C2×C3⋊C8—21no—
264C2×C3⋊C8—61no—
265C2×C3⋊C8—61no—
266C2×C3⋊C8—121no—
267ΓL(1,𝔽25)—24no—
268D3×C8—24no—
269C22×C32—21no—
270C22×C32—21no—
271C22×C32C2×C22⋊C411yescharacteristic
272C22×C32C4×D411yescharacteristic
273C22×C32C4×D411yescharacteristic
274C2×C3×D3—21no—
275C2×C3×D3—21no—
276C2×C3×D3—21no—
277C2×C3×D3—21no—
278C2×C3×D3—21no—
279C2×C3×D3—42no—
280C2×C3×D3—42no—
281C2×C3×D3#10112yescomplemented
282C32×C4#12011yescharacteristic
283C32×C4#12111yescharacteristic
284C32×C4#12111yescharacteristic
285C32×C4#12311yescharacteristic
286C3⋊Dic3—42no—
287C3×Dic3—21no—
288C3×Dic3—21no—
289C3×Dic3—42no—
290C22×Q8—91no—
291C23×C4—31no—
292C2×M16—31no—
293C2×M16—31no—
294C2×M16—61no—
295C2×M16—62no—
296C2×M16—62no—
297C2×M16—91no—
298C2×M16D3211yescharacteristic
299C22×C8—61no—
300C22⋊Q8—181no—
301C22⋊Q8—181no—
302C22⋊Q8—181no—
303C22⋊Q8—181no—
304C2×C4⋊C4—31no—
305C2×C4⋊C4—92no—
306C2×C22⋊C4—92no—
307#101—182no—
308#101—182no—
309C22⋊C8—181no—
310C22⋊C8—181no—
311C23×C3—21no—
312C23×C3—31no—
313C23×C3—31no—
314C23×C3—62no—
315C23×C3—61no—
316C23×C3—61no—
317C23×C3—121no—
318C23×C3C2×C4×D311yescharacteristic
319C23×C3C2×C4×D311yescharacteristic
320C22×D3—21no—
321C22×D3—21no—
322C22×D3—22no—
323C22×D3—41no—
324C22×D3(C2×D3)⋊C411yescharacteristic
325C22×D3(C2×D3)⋊C411yescharacteristic
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—31no—
333C2×C3×C4—31no—
334C2×C3×C4—61no—
335C2×C3×C4—61no—
336C2×C3×C4—61no—
337C2×C3×C4—61no—
338C2×C3×C4—61no—
339C2×C3×C4—61no—
340C2×C3×C4—61no—
341C2×C3×C4—61no—
342C2×C3×C4—61no—
343C2×C3×C4—61no—
344C2×C3×C4—62no—
345C2×C3×C4—122no—
346C2×C3×C4C2×D1211yescharacteristic
347C2×C3×C4C2×D1211yescharacteristic
348C2×C3×C4#23511yescharacteristic
349C2×C3×C4#23511yescharacteristic
350C2×C3×C4#23511yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4D3×D411yescharacteristic
354C2×C3×C4#23911yescharacteristic
355C2×C3×C4C2×#6711yescharacteristic
356C2×C3×C4C2×#6711yescharacteristic
357C2×C3×C4C2×#6711yescharacteristic
358C2×Dic3—21no—
359C2×Dic3—21no—
360C2×Dic3—22no—
361C2×Dic3—42no—
362C2×Dic3—64no—
363C2×Dic3—62no—
364C2×Dic3—62no—
365C2×Dic3—62no—
366C2×Dic3—62no—
367C2×Dic3—62no—
368C2×Dic3—62no—
369C2×Dic3—122no—
370C2×Dic3—122no—
371C2×Dic3(C2×D3)⋊C411yescharacteristic
372C2×Dic3(C2×D3)⋊C411yescharacteristic
373C4×D3—21no—
374C4×D3—21no—
375C4×D3—21no—
376C4×D3—21no—
377C4×D3—21no—
378C4×D3—21no—
379C4×D3—21no—
380C4×D3—21no—
381Dic6—122no—
382Dic6—122no—
383Dic6—122no—
384Dic6—122no—
385Dic6—121no—
386Dic6—121no—
387Dic6—121no—
388Dic6—121no—
389Dic6—121no—
390Dic6—121no—
391Dic6—121no—
392Dic6—121no—
393C3×C8—22no—
394C3×C8—22no—
395C3×C8—42no—
396C3×C8—62no—
397C3×C8—121no—
398C3⋊C8—22no—
399C3⋊C8—41no—
400C3⋊C8—122no—
401C3⋊C8—121no—
402C3⋊C8—121no—
403C2×C32—21no—
404C2×C32—21no—
405C2×C32#38611yescharacteristic
406C2×C32C2×#10111yescharacteristic
407C2×C32#41311yescharacteristic
408C3×D3—22no—
409C3×D3—41no—
410C24—31no—
411C2×Q8—181no—
412C2×Q8—181no—
413C2×Q8—181no—
414C2×Q8—181no—
415C2×Q8—181no—
416C2×Q8—181no—
417C22×C4—31no—
418C22×C4—31no—
419C22×C4—31no—
420C22×C4—31no—
421C22×C4—31no—
422C22×C4—32no—
423C22×C4—61no—
424C22×C4—61no—
425C22×C4—61no—
426C22×C4—61no—
427C22×C4—92no—
428C22×C4C2×D3211yescharacteristic
429M16—21no—
430M16—32no—
431M16—64no—
432M16—61no—
433M16—61no—
434M16—61no—
435M16—181no—
436M16—181no—
437M16#62612yes—
438C2×C8—21no—
439C2×C8—64no—
440C2×C8—61no—
441C2×C8—61no—
442C2×C8—181no—
443C4⋊C4—61no—
444C4⋊C4—61no—
445C4⋊C4—182no—
446C4⋊C4—182no—
447C22⋊C4—182no—
448C22⋊C4—182no—
449C22×C3—21no—
450C22×C3—21no—
451C22×C3—21no—
452C22×C3—21no—
453C22×C3—21no—
454C22×C3—21no—
455C22×C3—21no—
456C22×C3—32no—
457C22×C3—41no—
458C22×C3—41no—
459C22×C3—61no—
460C22×C3—61no—
461C22×C3—61no—
462C22×C3—61no—
463C22×C3—61no—
464C22×C3—122no—
465C22×C3—122no—
466C22×C3C4×D1211yescharacteristic
467C22×C3D3×C22⋊C411yescharacteristic
468C22×C3#89311yescharacteristic
469C22×C3C2×(C2×D3)⋊C411yescharacteristic
470C22×C3C4×#6711yescharacteristic
471C22×C3C4×#6711yescharacteristic
472C2×D3—21no—
473C2×D3—21no—
474C2×D3—21no—
475C2×D3—21no—
476C2×D3—21no—
477C2×D3—42no—
478C2×D3—42no—
479C2×D3#82412yescomplemented
480C3×C4—21no—
481C3×C4—21no—
482C3×C4—21no—
483C3×C4—21no—
484C3×C4—61no—
485C3×C4—61no—
486C3×C4—122no—
487C3×C4#88211yescharacteristic
488C3×C4#88411yescharacteristic
489C3×C4#89411yescharacteristic
490C3×C4#89511yescharacteristic
491C3×C4#92911yescharacteristic
492C3×C4#93011yescharacteristic
493C3×C4#93011yescharacteristic
494C3×C4#95311yescharacteristic
495Dic3—21no—
496Dic3—21no—
497Dic3—42no—
498Dic3—124no—
499Dic3—122no—
500Dic3—122no—
501C32#190111yescharacteristic, complemented, Sylow
502C23—31no—
503C23—31no—
504C23—62no—
505C23—61no—
506C23—61no—
507C23—121no—
508C23C4×D3211yescharacteristic
509Q8—361no—
510Q8—361no—
511Q8—361no—
512Q8—361no—
513C2×C4—31no—
514C2×C4—31no—
515C2×C4—61no—
516C2×C4—61no—
517C2×C4—61no—
518C2×C4—61no—
519C2×C4—61no—
520C2×C4—61no—
521C2×C4—61no—
522C2×C4—61no—
523C2×C4—61no—
524C2×C4—61no—
525C2×C4—62no—
526C2×C4—122no—
527C2×C4—182no—
528C2×C4—182no—
529C2×C4—182no—
530C2×C4#379811yescharacteristic
531C2×C4#379911yescharacteristic
532C2×C4D3×D1211yescharacteristic
533C2×C4C2×#62611yescharacteristic
534C2×C4D3×#6711yescharacteristic
535C2×C4D3×#6711yescharacteristic
536C8—22no—
537C8—62no—
538C8—121no—
539C8—361no—
540C2×C3—21no—
541C2×C3—21no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—41no—
548C2×C3—41no—
549C2×C3—62no—
550C2×C3—121no—
551C2×C3#466511yescharacteristic
552C2×C3#474511yescharacteristic
553C2×C3D3×#10111yescharacteristic
554C2×C3#513211yescharacteristic
555C2×C3C2×#82411yescharacteristic
556C2×C3#521311yescharacteristic
557D3—22no—
558D3—41no—
559C22—21no—
560C22—21no—
561C22—32no—
562C22—61no—
563C22—61no—
564C22—61no—
565C22—61no—
566C22—61no—
567C22—122no—
568C22—122no—
569C22C4×#62611yescharacteristic
570C22#6390411yescharacteristic
571C22D3×(C2×D3)⋊C411yescharacteristic
572C4—61no—
573C4—61no—
574C4—122no—
575C4—362no—
576C4#6385011yescharacteristic
577C4#6390611yescharacteristic
578C4#6390911yescharacteristic
579C4#6397711yescharacteristic
580C3—21no—
581C3#6899311yescharacteristic, complemented
582C3#7200311yescharacteristic, complemented
583C2—21no—
584C2—21no—
585C2—62no—
586C2—121no—
587C2D3×#82411yescharacteristic
588C2#1059100611yescharacteristic
589C2#1059138211yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C3×D3C2×C4
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1901
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. C2×#63651C2semidirect
4. C2×#63561C2semidirect
6. C3×#4554C2semidirect
7. #10589167C2semidirect
44. #4554D3semidirect
281. C2×C3×D3#101semidirect
479. C2×D3#824semidirect
501. C32#1901semidirect
581. C3#68993semidirect
582. C3#72003semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×M162
C2×#638572
C2×#636512
C2×#635612
#105910692
C3×#45542
#105891672
#720033
#689933