Finite Group Databasebeta

← #11788307

Subgroups — #11788307

Order 1152.

873 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63909C211yesmaximal, characteristic
2C2×D3×#208C211yesmaximal, characteristic, complemented
3C2×#63650C211yesmaximal, characteristic, complemented
4C3×#5126C211yesmaximal, characteristic, complemented
5C2×#63559C211yesmaximal, characteristic, complemented
6C3×#4554C211yesmaximal, characteristic, complemented
7#10589167C211yesmaximal, characteristic, complemented
8#69985—31nomaximal
9#68992—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C3×C4×D3C2211yescharacteristic
12C22×#626C412yes—
13C2×C32×M16C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18C2×#3722C412yes—
19#63909—21no—
20#63909—21no—
21#63909—21no—
22#63909—21no—
23C2×#3711—21no—
24D3×#208—22no—
25D3×#208—22no—
26C2×D3×C3⋊C8—21no—
27#63650—22no—
28C3×(C2×D3)⋊C8—21no—
29C3×(C2×D3)⋊C8—21no—
30#63559—22no—
31C2×#930—31no—
32C22×#208—31no—
33C2×D3×M16—31no—
34C2×#895—31no—
35C3×#407—31no—
36C2×#823—31no—
37C2×#823—31no—
38C2×#823—31no—
39C2×#823—31no—
40C2×#823—61no—
41#5126D311yescharacteristic, complemented
42C3×#343—31no—
43#4554—31no—
44#4554D311yescharacteristic, complemented
45#4530—31no—
46C23×C3⋊D3C2×C412yes—
47C23×C3×D3C2×C411yescharacteristic
48C22×C32×C4C2311yescharacteristic
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)—21no—
51C2×C4⋊(C3⋊D3)—21no—
52C2×C4⋊(C3⋊D3)—21no—
53C2×C4⋊(C3⋊D3)—21no—
54C2×C4⋊(C3⋊D3)—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
65C2×#626—22no—
66C2×#626—22no—
67C2×#626—44no—
68C32×M16—21no—
69C32×M16—21no—
70C2×C32×C8—21no—
71#3748—21no—
72#3748D412yescomplemented
73C2×C3⋊(C3⋊C8)—21no—
74C3×C4⋊Dic3—21no—
75C3×C4⋊Dic3—21no—
76C3×#208—21no—
77C3×#208—21no—
78C3×#208—21no—
79C3×#208D412yescomplemented
80C2×C3×C3⋊C8—21no—
81C2×C3×C3⋊C8—21no—
82#3722—22no—
83#3722—22no—
84#3711—24no—
85D3×C3⋊C8—24no—
86#1900—91noSylow
87C23×C3×C4—31no—
88C22×#67—32no—
89C22×D12—31no—
90C22×D12—31no—
91C22×D12—32no—
92C22×D12—61no—
93C22×C4×D3C2×D311yescharacteristic
94C2×C3×M16—21no—
95C2×C3×M16—31no—
96C2×C3×M16—31no—
97C2×C3×M16C2×D311yescharacteristic
98C2×C3×M16C2×D311yescharacteristic
99C2×C3×C4⋊C4—31no—
100#930—61no—
101#930—61no—
102#930—61no—
103#930—61no—
104C2×(C2×D3)⋊C4—32no—
105C2×(C2×D3)⋊C4—32no—
106C2×C4⋊Dic3C2×D311yescharacteristic
107C2×#208—31no—
108C2×#208—31no—
109C2×#208—61no—
110C2×#208—61no—
111C2×#208—62no—
112C2×#208—62no—
113C2×#208C2×D311yescharacteristic
114C2×#208C2×D311yescharacteristic
115C22×C3⋊C8—61no—
116D3×M16—62no—
117D3×M16—62no—
118C2×ΓL(1,𝔽25)—61no—
119C2×D3×C8—61no—
120#895—61no—
121#895—61no—
122#895—61no—
123#895—61no—
124C3×C22⋊C8—61no—
125C3×C22⋊C8—61no—
126#823—62no—
127#823—62no—
128#823—62no—
129#823—64no—
130#823—62no—
131(C2×D3)⋊C8—21no—
132(C2×D3)⋊C8—21no—
133C23×C32C22×C411yescharacteristic
134C22×C3⋊D3—22no—
135C22×C3⋊D3—22no—
136C22×C3⋊D3—22no—
137C22×C3⋊D3—42no—
138C22×C3⋊D3—42no—
139C22×C3×D3—21no—
140C22×C3×D3—21no—
141C22×C3×D3—22no—
142C22×C3×D3—41no—
143C22×C3×D3C22⋊C411yescharacteristic
144C22×C3×D3C22⋊C411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4#4111yescharacteristic
150C2×C32×C4#4111yescharacteristic
151C4⋊(C3⋊D3)—41no—
152C4⋊(C3⋊D3)—41no—
153C4⋊(C3⋊D3)—41no—
154C4⋊(C3⋊D3)—41no—
155C2×C3×Dic3—21no—
156C2×C3×Dic3—21no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—42no—
159C2×C3×Dic3C22⋊C411yescharacteristic
160C2×C3×Dic3C22⋊C411yescharacteristic
161C3×C4×D3—21no—
162C3×C4×D3—21no—
163C3×C4×D3—21no—
164C3×C4×D3—21no—
165C3×C4×D3—21no—
166C3×C4×D3—21no—
167C3×C4×D3—21no—
168C3×C4×D3—21no—
169#626—44no—
170#626—44no—
171C32×C8—41no—
172C3⋊(C3⋊C8)—22no—
173C3×C3⋊C8—22no—
174C3×C3⋊C8—41no—
175C22×M16—91no—
176C2×#121—91no—
177C2×#100—91no—
178C2×#100—91no—
179#407—31no—
180#343—31no—
181#343—91no—
182C24×C3—31no—
183C23×D3—32no—
184C23×D3—32no—
185C23×D3—62no—
186C23×D3C4×D311yescharacteristic
187C22×C3×C4—21no—
188C22×C3×C4—31no—
189C22×C3×C4—31no—
190C22×C3×C4—31no—
191C22×C3×C4—31no—
192C22×C3×C4—31no—
193C22×C3×C4—32no—
194C22×C3×C4—61no—
195C22×C3×C4—61no—
196C22×C3×C4—61no—
197C22×C3×C4—61no—
198C22×C3×C4C22×D311yescharacteristic
199C22×C3×C4C22×D311yescharacteristic
200C2×#67—62no—
201C2×#67—62no—
202C2×#67—124no—
203C22×Dic3C4×D311yescharacteristic
204C22×Dic3C4×D312yes—
205C2×D12—62no—
206C2×D12—62no—
207C2×D12—62no—
208C2×D12—62no—
209C2×D12—61no—
210C2×D12—61no—
211C2×D12—61no—
212C2×D12—61no—
213C2×D12—61no—
214C2×D12—61no—
215C2×D12—61no—
216C2×D12—61no—
217C2×D12—61no—
218C2×D12—61no—
219C2×D12—61no—
220C2×D12—61no—
221C2×D12—121no—
222C2×D12—121no—
223C2×D12—121no—
224C2×D12—121no—
225C2×D12—124no—
226C2×C4×D3—21no—
227C2×C4×D3—21no—
228C2×C4×D3—21no—
229C2×C4×D3—21no—
230C2×C4×D3D1211yescharacteristic
231C2×C4×D3D1211yescharacteristic
232C2×C4×D3#6711yescharacteristic
233C2×C4×D3#6711yescharacteristic
234C3×M16—22no—
235C3×M16—21no—
236C3×M16—21no—
237C3×M16—21no—
238C3×M16—21no—
239C3×M16—32no—
240C3×M16—41no—
241C3×M16—61no—
242C3×M16—61no—
243C3×M16—61no—
244C2×C3×C8—21no—
245C2×C3×C8—21no—
246C2×C3×C8—41no—
247C2×C3×C8—61no—
248C2×C3×C8—61no—
249C3×C4⋊C4—61no—
250C3×C4⋊C4—61no—
251(C2×D3)⋊C4—62no—
252(C2×D3)⋊C4—62no—
253(C2×D3)⋊C4—62no—
254(C2×D3)⋊C4—62no—
255C4⋊Dic3—21no—
256C4⋊Dic3—21no—
257#208—21no—
258#208—21no—
259#208—21no—
260#208—32no—
261#208—32no—
262#208—62no—
263#208—64no—
264#208—61no—
265#208—61no—
266#208—121no—
267#208D1212yescomplemented
268C2×C3⋊C8—21no—
269C2×C3⋊C8—21no—
270C2×C3⋊C8—64no—
271C2×C3⋊C8—61no—
272C2×C3⋊C8—61no—
273C2×C3⋊C8—121no—
274ΓL(1,𝔽25)—64no—
275D3×C8—64no—
276C22×C32—21no—
277C22×C32—21no—
278C22×C32C2×C22⋊C411yescharacteristic
279C22×C32C4×D411yescharacteristic
280C22×C32C4×D411yescharacteristic
281C2×C3⋊D3—42no—
282C2×C3⋊D3—42no—
283C2×C3⋊D3—42no—
284C2×C3⋊D3—82no—
285C2×C3⋊D3—82no—
286C2×C3×D3—21no—
287C2×C3×D3—21no—
288C2×C3×D3—21no—
289C2×C3×D3—21no—
290C2×C3×D3—21no—
291C2×C3×D3—42no—
292C2×C3×D3—42no—
293C2×C3×D3#10012yescomplemented
294C32×C4#12011yescharacteristic
295C32×C4#12111yescharacteristic
296C32×C4#12111yescharacteristic
297C32×C4#12311yescharacteristic
298C3×Dic3—21no—
299C3×Dic3—21no—
300C3×Dic3—42no—
301C22×D4—92no—
302C22×D4—91no—
303C23×C4—31no—
304C2×M16—31no—
305C2×M16—31no—
306C2×M16—91no—
307C2×M16—181no—
308C2×M16—182no—
309C2×M16—182no—
310C2×M16D3211yescharacteristic
311C22×C8—181no—
312#121—181no—
313#121—181no—
314#121—181no—
315#121—181no—
316C2×C4⋊C4—31no—
317C2×C22⋊C4—92no—
318#100—182no—
319#100—182no—
320C22⋊C8—61no—
321C22⋊C8—61no—
322C23×C3—21no—
323C23×C3—31no—
324C23×C3—31no—
325C23×C3—62no—
326C23×C3—61no—
327C23×C3—61no—
328C23×C3—121no—
329C23×C3C2×C4×D311yescharacteristic
330C23×C3C2×C4×D311yescharacteristic
331C22×D3—21no—
332C22×D3—21no—
333C22×D3—22no—
334C22×D3—41no—
335C22×D3—62no—
336C22×D3—62no—
337C22×D3—64no—
338C22×D3—62no—
339C22×D3—62no—
340C22×D3—62no—
341C22×D3—62no—
342C22×D3—122no—
343C22×D3—122no—
344C22×D3—122no—
345C22×D3—122no—
346C22×D3—122no—
347C22×D3—122no—
348C22×D3—242no—
349C22×D3—242no—
350C22×D3(C2×D3)⋊C411yescharacteristic
351C22×D3(C2×D3)⋊C411yescharacteristic
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—31no—
359C2×C3×C4—31no—
360C2×C3×C4—61no—
361C2×C3×C4—61no—
362C2×C3×C4—61no—
363C2×C3×C4—61no—
364C2×C3×C4—61no—
365C2×C3×C4—61no—
366C2×C3×C4—61no—
367C2×C3×C4—61no—
368C2×C3×C4—61no—
369C2×C3×C4—61no—
370C2×C3×C4—62no—
371C2×C3×C4—122no—
372C2×C3×C4C2×D1211yescharacteristic
373C2×C3×C4C2×D1211yescharacteristic
374C2×C3×C4#23511yescharacteristic
375C2×C3×C4D3×D411yescharacteristic
376C2×C3×C4D3×D411yescharacteristic
377C2×C3×C4D3×D411yescharacteristic
378C2×C3×C4D3×D411yescharacteristic
379C2×C3×C4D3×D411yescharacteristic
380C2×C3×C4#23711yescharacteristic
381C2×C3×C4#23711yescharacteristic
382C2×C3×C4#23911yescharacteristic
383C2×C3×C4C2×#6711yescharacteristic
384#67—124no—
385#67—124no—
386C2×Dic3—21no—
387C2×Dic3—21no—
388C2×Dic3—22no—
389C2×Dic3—42no—
390C2×Dic3(C2×D3)⋊C411yescharacteristic
391C2×Dic3(C2×D3)⋊C411yescharacteristic
392D12—122no—
393D12—122no—
394D12—122no—
395D12—122no—
396D12—124no—
397D12—124no—
398D12—121no—
399D12—121no—
400D12—121no—
401D12—121no—
402D12—121no—
403D12—121no—
404D12—121no—
405D12—121no—
406C4×D3—21no—
407C4×D3—21no—
408C4×D3—21no—
409C4×D3—21no—
410C4×D3—21no—
411C4×D3—21no—
412C4×D3—21no—
413C4×D3—21no—
414C3×C8—42no—
415C3×C8—41no—
416C3×C8—41no—
417C3×C8—62no—
418C3×C8—121no—
419C3⋊C8—22no—
420C3⋊C8—41no—
421C3⋊C8—62no—
422C3⋊C8—62no—
423C3⋊C8—122no—
424C2×C32—21no—
425C2×C32—21no—
426C2×C32#38611yescharacteristic
427C2×C32C2×#10011yescharacteristic
428C2×C32#41311yescharacteristic
429C3⋊D3—82no—
430C3×D3—22no—
431C3×D3—41no—
432C24—31no—
433C24—92no—
434C2×D4—182no—
435C2×D4—182no—
436C2×D4—181no—
437C2×D4—181no—
438C2×D4—181no—
439C2×D4—181no—
440C2×D4—181no—
441C2×D4—181no—
442C2×D4—364no—
443C22×C4—31no—
444C22×C4—31no—
445C22×C4—31no—
446C22×C4—31no—
447C22×C4—31no—
448C22×C4—32no—
449C22×C4—61no—
450C22×C4—61no—
451C22×C4—61no—
452C22×C4—61no—
453C22×C4C2×D3211yescharacteristic
454M16—21no—
455M16—21no—
456M16—32no—
457M16—61no—
458M16—61no—
459M16—61no—
460M16—92no—
461M16—184no—
462M16—181no—
463C2×C8—21no—
464C2×C8—61no—
465C2×C8—61no—
466C2×C8—184no—
467C2×C8—181no—
468C4⋊C4—61no—
469C4⋊C4—61no—
470C22⋊C4—182no—
471C22⋊C4—182no—
472C22×C3—21no—
473C22×C3—21no—
474C22×C3—21no—
475C22×C3—21no—
476C22×C3—21no—
477C22×C3—21no—
478C22×C3—21no—
479C22×C3—32no—
480C22×C3—41no—
481C22×C3—41no—
482C22×C3—61no—
483C22×C3—61no—
484C22×C3—61no—
485C22×C3—61no—
486C22×C3—61no—
487C22×C3—122no—
488C22×C3—122no—
489C22×C3C4×D1211yescharacteristic
490C22×C3D3×C22⋊C411yescharacteristic
491C22×C3#67⋊C411yescharacteristic
492C22×C3#67⋊C411yescharacteristic
493C22×C3#89311yescharacteristic
494C22×C3C2×(C2×D3)⋊C411yescharacteristic
495C2×D3—21no—
496C2×D3—21no—
497C2×D3—21no—
498C2×D3—21no—
499C2×D3—21no—
500C2×D3—42no—
501C2×D3—42no—
502C2×D3—124no—
503C2×D3—122no—
504C2×D3—122no—
505C2×D3—122no—
506C2×D3—122no—
507C2×D3—122no—
508C2×D3—122no—
509C2×D3—242no—
510C2×D3—242no—
511C2×D3—244no—
512C2×D3—242no—
513C2×D3—242no—
514C2×D3—242no—
515C2×D3—242no—
516C2×D3—244no—
517C2×D3#82312yescomplemented
518C3×C4—21no—
519C3×C4—21no—
520C3×C4—21no—
521C3×C4—21no—
522C3×C4—61no—
523C3×C4—61no—
524C3×C4—122no—
525C3×C4#88211yescharacteristic
526C3×C4#88211yescharacteristic
527C3×C4#88411yescharacteristic
528C3×C4#88611yescharacteristic
529C3×C4#89411yescharacteristic
530C3×C4#89511yescharacteristic
531C3×C4#93911yescharacteristic
532C3×C4#93911yescharacteristic
533Dic3—21no—
534Dic3—21no—
535Dic3—42no—
536C32#190011yescharacteristic, complemented, Sylow
537C23—31no—
538C23—31no—
539C23—62no—
540C23—61no—
541C23—61no—
542C23—121no—
543C23—182no—
544C23—182no—
545C23—182no—
546C23—362no—
547C23—362no—
548C23C4×D3211yescharacteristic
549D4—364no—
550D4—364no—
551D4—361no—
552D4—361no—
553D4—361no—
554D4—361no—
555C2×C4—31no—
556C2×C4—31no—
557C2×C4—61no—
558C2×C4—61no—
559C2×C4—61no—
560C2×C4—61no—
561C2×C4—61no—
562C2×C4—61no—
563C2×C4—61no—
564C2×C4—61no—
565C2×C4—61no—
566C2×C4—61no—
567C2×C4—62no—
568C2×C4—122no—
569C2×C4#379611yescharacteristic
570C2×C4D3×D1211yescharacteristic
571C2×C4D3×D1211yescharacteristic
572C2×C4#380411yescharacteristic
573C2×C4D3×#6711yescharacteristic
574C2×C4#381111yescharacteristic
575C8—41no—
576C8—62no—
577C8—121no—
578C8—182no—
579C2×C3—21no—
580C2×C3—21no—
581C2×C3—21no—
582C2×C3—21no—
583C2×C3—21no—
584C2×C3—21no—
585C2×C3—21no—
586C2×C3—41no—
587C2×C3—41no—
588C2×C3—62no—
589C2×C3—121no—
590C2×C3#466511yescharacteristic
591C2×C3D3×#10011yescharacteristic
592C2×C3#475111yescharacteristic
593C2×C3#495811yescharacteristic
594C2×C3C2×#82311yescharacteristic
595C2×C3#513211yescharacteristic
596D3—22no—
597D3—41no—
598D3—244no—
599D3—242no—
600D3—242no—
601C22—21no—
602C22—21no—
603C22—32no—
604C22—61no—
605C22—61no—
606C22—61no—
607C22—61no—
608C22—61no—
609C22—122no—
610C22—122no—
611C22—362no—
612C22—362no—
613C22—362no—
614C22—722no—
615C22—722no—
616C22#6388011yescharacteristic
617C22#6388111yescharacteristic
618C22D3×(C2×D3)⋊C411yescharacteristic
619C4—61no—
620C4—61no—
621C4—122no—
622C4#6388611yescharacteristic
623C4#6389011yescharacteristic
624C4#6392311yescharacteristic
625C4#6397111yescharacteristic
626C3—21no—
627C3#6899211yescharacteristic, complemented
628C3#6998511yescharacteristic, complemented
629C2—21no—
630C2—21no—
631C2—62no—
632C2—121no—
633C2—722no—
634C2D3×#82311yescharacteristic
635C2#1059100711yescharacteristic
636C2#1059136411yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C2×C22⋊C4
prime radicalC2×#63909C2
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1900
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
2. C2×D3×#208C2semidirect
3. C2×#63650C2semidirect
4. C3×#5126C2semidirect
5. C2×#63559C2semidirect
6. C3×#4554C2semidirect
7. #10589167C2semidirect
41. #5126D3semidirect
44. #4554D3semidirect
72. #3748D4semidirect
79. C3×#208D4semidirect
267. #208D12semidirect
293. C2×C3×D3#100semidirect
517. C2×D3#823semidirect
536. C32#1900semidirect
627. C3#68992semidirect
628. C3#69985semidirect

Maximal subgroups

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

subgroupindex
C2×#639092
C2×D3×#2082
C2×#636502
C3×#51262
C2×#635592
C3×#45542
#105891672
#699853
#689923