Finite Group Databasebeta

← #11885790

Subgroups — #11885790

Order 1152.

1578 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64125C211yesmaximal, characteristic, complemented
2C2×D8×C3⋊D3C211yesmaximal, characteristic, complemented
3#10596147C211yesmaximal, characteristic, complemented
4#10596025C211yesmaximal, characteristic, complemented
5C32×#463C211yesmaximal, characteristic, complemented
6#10592868C211yesmaximal, characteristic, complemented
7#10592857C211yesmaximal, characteristic, complemented
8#10592758C211yesmaximal, characteristic, complemented
9C4×#3753C211yesmaximal, characteristic, complemented
10#10592543C211yesmaximal, characteristic, complemented
11#10592533C211yesmaximal, characteristic, complemented
12#10592512C211yesmaximal, characteristic, complemented
13#10592509C211yesmaximal, characteristic, complemented
14#10592475C211yesmaximal, characteristic, complemented
15#10592474C211yesmaximal, characteristic, complemented
16#80557—34nomaximal
17C2×#3832C2211yescharacteristic, complemented
18C2×#3830C2211yescharacteristic, complemented
19C2×D4×C3⋊D3C2211yescharacteristic
20C2×D4×C3⋊D3C2211yescharacteristic
21C2×C32×SD16C2211yescharacteristic, complemented
22C2×C32×D8C2211yescharacteristic
23C32×#124C2211yescharacteristic, complemented
24C32×C4×D4C2211yescharacteristic, complemented
25#64155C2211yescharacteristic
26C2×#3756C2211yescharacteristic, complemented
27C2×#3755C2211yescharacteristic, complemented
28#64147C2211yescharacteristic, complemented
29C2×#3754C2211yescharacteristic, complemented
30C2×#3753C2211yescharacteristic
31C2×#3753C2211yescharacteristic
32#64139—21no—
33C2×#3752—21no—
34#64125—24no—
35D8×C3⋊D3—24no—
36C2×#3745C2211yescharacteristic
37C2×#3744C2211yescharacteristic, complemented
38C2×C8×C3⋊D3C2211yescharacteristic
39C2×C8×C3⋊D3C2211yescharacteristic, complemented
40#64106C2211yescharacteristic
41#64104C2211yescharacteristic, complemented
42#64095—21no—
43#64093—21no—
44#64092—21no—
45#64091—21no—
46#64091—21no—
47C22⋊C4×C3⋊D3—21no—
48#64084C2211yescharacteristic, complemented
49C4×C4⋊(C3⋊D3)C2211yescharacteristic
50C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
51C32×C4⋊C8C2211yescharacteristic, complemented
52C32×#103C2211yescharacteristic, complemented
53C32×#102C2211yescharacteristic, complemented
54#63659C2211yescharacteristic, complemented
55#63648C2211yescharacteristic, complemented
56#63647C2211yescharacteristic
57#63647C2211yescharacteristic, complemented
58#63643C2211yescharacteristic, complemented
59#63636C2211yescharacteristic, complemented
60#63634C2211yescharacteristic, complemented
61C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
62C2×#916—34no—
63C2×D3×D8—34no—
64#5676—34no—
65#5554—34no—
66C3×#463D314yescomplemented
67#5169—34no—
68#5158—34no—
69#5059—34no—
70C4×#213—34no—
71#4844—34no—
72#4834—34no—
73#4813—34no—
74#4810—34no—
75#4776—34no—
76#4775—34no—
77C23×C3⋊D3—21no—
78C23×C3⋊D3—21no—
79C2×C32×Q8C2311yescharacteristic
80C2×C32×D4C2311yescharacteristic
81C2×C32×D4C2311yescharacteristic
82C22×C32×C4—21no—
83C2×#638—21no—
84C2×#638—21no—
85C2×#638—21no—
86C2×#638—21no—
87C22×C3⋊Dic3—21no—
88#3832—22no—
89#3832—41no—
90#3830—22no—
91#3830—41no—
92D4×C3⋊D3—22no—
93D4×C3⋊D3—22no—
94D4×C3⋊D3—41no—
95D4×C3⋊D3—41no—
96C2×C4⋊(C3⋊D3)—21no—
97C2×C4⋊(C3⋊D3)—21no—
98C2×C4⋊(C3⋊D3)D411yescharacteristic
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C4×C3⋊D3—21no—
102C2×C4×C3⋊D3—21no—
103C2×C4×C3⋊D3C2311yescharacteristic
104C2×C4×C3⋊D3C2311yescharacteristic
105C2×#634C2311yescharacteristic
106C32×SD16—22no—
107C32×D8—22no—
108C2×C32×C8C2311yescharacteristic
109C2×C32×C8C2311yescharacteristic
110C32×C4⋊C4C2311yescharacteristic
111C32×C22⋊C4—21no—
112C32×C22⋊C4—21no—
113C32×C22⋊C4—21no—
114C32×C42C2311yescharacteristic
115#3757—21no—
116#3756—22no—
117#3755—41no—
118#3754—41no—
119#3753—22no—
120#3753D414yescomplemented
121#3752—21no—
122#3752—21no—
123#3752—21no—
124#3752—21no—
125#3752—21no—
126#3752—21no—
127#3752D411yescharacteristic
128#3752D411yescharacteristic
129C4⋊(C3⋊Dic3)—21no—
130C4⋊(C3⋊Dic3)D411yescharacteristic
131C4⋊(C3⋊Dic3)C2311yescharacteristic
132#3750—21no—
133C2×C3⋊(C3⋊C8)C2311yescharacteristic
134C2×C3⋊(C3⋊C8)C2311yescharacteristic
135#3745—22no—
136#3744—22no—
137C8×C3⋊D3—22no—
138C8×C3⋊D3—22no—
139#3280—91noSylow
140C2×#239—34no—
141C2×#237—34no—
142C2×D3×D4—34no—
143C2×D3×D4—34no—
144C2×C3×SD16C2×D314yescomplemented
145C2×C3×D8C2×D314yes—
146C3×#124C2×D314yescomplemented
147C3×C4×D4C2×D314yescomplemented
148#946—34no—
149C2×#216—34no—
150C2×#215—34no—
151#938—34no—
152C2×#214—34no—
153C2×#213—34no—
154C2×#213—34no—
155#930—64no—
156C2×(C2×D3)⋊C4—64no—
157#916—616no—
158D3×D8—616no—
159C2×D24—34no—
160C2×#204—34no—
161C2×D3×C8—34no—
162C2×D3×C8—34no—
163#897—34no—
164#895—34no—
165#886—64no—
166#884—64no—
167#883—64no—
168#882—64no—
169#882—64no—
170D3×C22⋊C4—64no—
171#875—34no—
172C4×D12—34no—
173C4×D12—34no—
174C3×C4⋊C8C2×D314yescomplemented
175C3×#103C2×D314yescomplemented
176C3×#102C2×D314yescomplemented
177#832—34no—
178#821—34no—
179(C2×D3)⋊C8—34no—
180(C2×D3)⋊C8—34no—
181#816—34no—
182#809—34no—
183#807—34no—
184C4×C3⋊C8—34no—
185C23×C32—21no—
186C23×C32—21no—
187C22×C3⋊D3—21no—
188C22×C3⋊D3—21no—
189C22×C3⋊D3—42no—
190C22×C3⋊D3—42no—
191C22×C3⋊D3—42no—
192C22×C3⋊D3—42no—
193C22×C3⋊D3—81no—
194C22×C3⋊D3—81no—
195C22×C3⋊D3C2×D411yescharacteristic
196C22×C3⋊D3C2×D411yescharacteristic
197C32×Q8—21no—
198C32×Q8—21no—
199C32×D4—21no—
200C32×D4—21no—
201C32×D4—21no—
202C32×D4C2×D412yes—
203C2×C32×C4—21no—
204C2×C32×C4—21no—
205C2×C32×C4—81no—
206C2×C32×C4C2×D411yescharacteristic
207C2×C32×C4C2×D411yescharacteristic
208C2×C32×C4C2411yescharacteristic
209#638—42no—
210#638—42no—
211#638—42no—
212#638—81no—
213C2×C3⋊Dic3—21no—
214C2×C3⋊Dic3—21no—
215C2×C3⋊Dic3—42no—
216C2×C3⋊Dic3C2×D411yescharacteristic
217C2×C3⋊Dic3C2×D411yescharacteristic
218C4⋊(C3⋊D3)—22no—
219C4⋊(C3⋊D3)—21no—
220C4⋊(C3⋊D3)—21no—
221C4⋊(C3⋊D3)—21no—
222C4⋊(C3⋊D3)—42no—
223C4⋊(C3⋊D3)—81no—
224C4⋊(C3⋊D3)C2×D412yes—
225C4×C3⋊D3—21no—
226C4×C3⋊D3—21no—
227C4×C3⋊D3—21no—
228C4×C3⋊D3—21no—
229C4×C3⋊D3—42no—
230C4×C3⋊D3—81no—
231#634—21no—
232#634—21no—
233C32×C8—21no—
234C32×C8—21no—
235C3⋊(C3⋊C8)—21no—
236C3⋊(C3⋊C8)C2×D412yes—
237C2×#135—91no—
238C22×D8—91no—
239#546—91no—
240#546—91no—
241#495—91no—
242#467—91no—
243#466—91no—
244#463—91no—
245#463C3⋊D311yescharacteristic, complemented
246#450—91no—
247#450—91no—
248#449—91no—
249#449—91no—
250C4×D8—91no—
251C8×D4—91no—
252C23×D3—64no—
253C23×D3—64no—
254C2×C3×Q8C22×D314yes—
255C2×C3×D4C22×D314yes—
256C2×C3×D4C22×D314yes—
257C22×C3×C4—24no—
258C2×#67—64no—
259C2×#67—64no—
260C2×#67—64no—
261C2×#67—64no—
262C22×Dic3—64no—
263#239—68no—
264#239—124no—
265#237—68no—
266#237—124no—
267D3×D4—68no—
268D3×D4—68no—
269D3×D4—124no—
270D3×D4—124no—
271C2×D12—34no—
272C2×D12—34no—
273C2×D12—34no—
274C2×D12—64no—
275C2×D12—64no—
276C2×C4×D3—34no—
277C2×C4×D3—34no—
278C2×C4×D3—64no—
279C2×C4×D3—64no—
280C2×Dic6—34no—
281C3×SD16—28no—
282C3×D8—28no—
283C2×C3×C8C22×D314yes—
284C2×C3×C8C22×D314yes—
285C3×C4⋊C4C22×D314yes—
286C3×C22⋊C4—24no—
287C3×C22⋊C4—24no—
288C3×C22⋊C4—24no—
289C3×C42C22×D314yes—
290#217—64no—
291#216—68no—
292#215—124no—
293#214—124no—
294#213—316no—
295#213—68no—
296(C2×D3)⋊C4—34no—
297(C2×D3)⋊C4—34no—
298(C2×D3)⋊C4—64no—
299(C2×D3)⋊C4—64no—
300(C2×D3)⋊C4—64no—
301(C2×D3)⋊C4—64no—
302(C2×D3)⋊C4—64no—
303(C2×D3)⋊C4—64no—
304C4⋊Dic3—34no—
305C4⋊Dic3—34no—
306C4⋊Dic3—64no—
307Dic3⋊C4—64no—
308C2×C3⋊C8—34no—
309C2×C3⋊C8—34no—
310D24—68no—
311#204—68no—
312D3×C8—68no—
313D3×C8—68no—
314C22×C32—22no—
315C22×C32—41no—
316C22×C32—41no—
317C22×C32—41no—
318C22×C32—41no—
319C22×C32—41no—
320C22×C32C22×D411yescharacteristic
321C2×C3⋊D3—21no—
322C2×C3⋊D3—21no—
323C2×C3⋊D3—21no—
324C2×C3⋊D3—22no—
325C2×C3⋊D3—21no—
326C2×C3⋊D3—21no—
327C2×C3⋊D3—41no—
328C2×C3⋊D3—41no—
329C2×C3⋊D3—41no—
330C2×C3⋊D3—41no—
331C2×C3⋊D3—41no—
332C2×C3⋊D3—84no—
333C2×C3⋊D3—84no—
334C2×C3⋊D3#13512yescomplemented
335C32×C4—21no—
336C32×C4—21no—
337C32×C4—41no—
338C32×C4—41no—
339C32×C4C22×D411yescharacteristic
340C32×C4H(5,𝔽2)11yescharacteristic
341C3⋊Dic3—21no—
342C3⋊Dic3—21no—
343C3⋊Dic3—41no—
344C3⋊Dic3—41no—
345C2×#41—91no—
346C2×#41—91no—
347C22×D4—91no—
348C22×D4—91no—
349#135—184no—
350C2×Q16—91no—
351C2×SD16—91no—
352C2×SD16—91no—
353C2×SD16—91no—
354C2×SD16C2×C3⋊D311yescharacteristic, complemented
355C2×D8—91no—
356C2×D8—91no—
357C2×D8—91no—
358C2×D8—184no—
359C2×D8C2×C3⋊D311yescharacteristic
360C22×C8—91no—
361C22×C8—91no—
362#124—91no—
363#124C2×C3⋊D311yescharacteristic, complemented
364#123—181no—
365#123—181no—
366C22⋊Q8—91no—
367C22⋊Q8—91no—
368#121—91no—
369#121—91no—
370#121—181no—
371#121—181no—
372#120—181no—
373#120—181no—
374C4×D4—91no—
375C4×D4—91no—
376C4×D4C2×C3⋊D311yescharacteristic, complemented
377C2×C22⋊C4—181no—
378C2×C22⋊C4—181no—
379#107—91no—
380C4⋊C8C2×C3⋊D311yescharacteristic, complemented
381#103—91no—
382#103C2×C3⋊D311yescharacteristic, complemented
383#102—91no—
384#102—91no—
385#102—91no—
386#102C2×C3⋊D311yescharacteristic, complemented
387C22⋊C8—91no—
388C22⋊C8—91no—
389C4×C8—91no—
390C23×C3—24no—
391C23×C3—24no—
392C22×D3—34no—
393C22×D3—34no—
394C22×D3—64no—
395C22×D3—64no—
396C22×D3—128no—
397C22×D3—128no—
398C22×D3—128no—
399C22×D3—128no—
400C22×D3—244no—
401C22×D3—244no—
402C3×Q8—24no—
403C3×Q8—24no—
404C3×D4—24no—
405C3×D4—24no—
406C3×D4—24no—
407C3×D4D3×D418yes—
408C2×C3×C4—24no—
409C2×C3×C4—24no—
410C2×C3×C4—84no—
411C2×C3×C4D3×D414yes—
412C2×C3×C4D3×D414yes—
413C2×C3×C4C23×D314yes—
414#67—128no—
415#67—128no—
416#67—128no—
417#67—244no—
418C2×Dic3—34no—
419C2×Dic3—34no—
420C2×Dic3—64no—
421C2×Dic3—64no—
422C2×Dic3—128no—
423D12—38no—
424D12—68no—
425D12—64no—
426D12—64no—
427D12—64no—
428D12—128no—
429D12—244no—
430C4×D3—64no—
431C4×D3—64no—
432C4×D3—64no—
433C4×D3—64no—
434C4×D3—128no—
435C4×D3—244no—
436Dic6—64no—
437Dic6—64no—
438C3×C8—24no—
439C3×C8—24no—
440C3⋊C8—38no—
441C3⋊C8—64no—
442C2×C32—42no—
443C2×C32—81no—
444C2×C32D4211yescharacteristic
445C2×C32C2×#13511yescharacteristic
446C2×C32#57611yescharacteristic
447C3⋊D3—22no—
448C3⋊D3—41no—
449C3⋊D3—42no—
450C3⋊D3—81no—
451C24—181no—
452C24—181no—
453#41—182no—
454#41—182no—
455#41—361no—
456#41—361no—
457C2×Q8—91no—
458C2×Q8C22×C3⋊D311yescharacteristic
459C2×D4—91no—
460C2×D4—91no—
461C2×D4—91no—
462C2×D4—181no—
463C2×D4—181no—
464C2×D4—181no—
465C2×D4—181no—
466C2×D4—182no—
467C2×D4—182no—
468C2×D4—181no—
469C2×D4—181no—
470C2×D4—361no—
471C2×D4—361no—
472C2×D4C22×C3⋊D311yescharacteristic
473C2×D4C22×C3⋊D311yescharacteristic
474C22×C4—21no—
475C22×C4—91no—
476C22×C4—91no—
477C22×C4—181no—
478C22×C4—181no—
479C22×C4—181no—
480Q16—182no—
481SD16—22no—
482SD16—182no—
483SD16—361no—
484SD16—361no—
485D8—22no—
486D8—94no—
487D8—182no—
488D8—182no—
489C2×C8—91no—
490C2×C8—91no—
491C2×C8—182no—
492C2×C8—182no—
493C2×C8C22×C3⋊D311yescharacteristic
494C2×C8C22×C3⋊D311yescharacteristic
495C4⋊C4—91no—
496C4⋊C4—91no—
497C4⋊C4—181no—
498C4⋊C4—181no—
499C4⋊C4C22×C3⋊D311yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—91no—
504C22⋊C4—91no—
505C22⋊C4—181no—
506C22⋊C4—181no—
507C22⋊C4—181no—
508C22⋊C4—181no—
509C22⋊C4—181no—
510C22⋊C4—181no—
511C22⋊C4—181no—
512C42C22×C3⋊D311yescharacteristic
513C22×C3—28no—
514C22×C3—44no—
515C22×C3—44no—
516C22×C3—44no—
517C22×C3—44no—
518C22×C3—44no—
519C22×C3C2×D3×D414yes—
520C2×D3—38no—
521C2×D3—64no—
522C2×D3—64no—
523C2×D3—64no—
524C2×D3—64no—
525C2×D3—64no—
526C2×D3—68no—
527C2×D3—124no—
528C2×D3—124no—
529C2×D3—124no—
530C2×D3—124no—
531C2×D3—124no—
532C2×D3—2416no—
533C2×D3—2416no—
534C3×C4—24no—
535C3×C4—24no—
536C3×C4—44no—
537C3×C4—44no—
538C3×C4C2×D3×D414yes—
539C3×C4#100914yes—
540Dic3—64no—
541Dic3—64no—
542Dic3—124no—
543Dic3—124no—
544C32#328011yescharacteristic, complemented, Sylow
545C23—21no—
546C23—21no—
547C23—91no—
548C23—91no—
549C23—181no—
550C23—181no—
551C23—362no—
552C23—362no—
553C23—362no—
554C23—362no—
555C23—721no—
556C23—721no—
557Q8—21no—
558Q8—21no—
559Q8—181no—
560Q8—181no—
561D4—21no—
562D4—21no—
563D4—21no—
564D4—92no—
565D4—182no—
566D4—181no—
567D4—181no—
568D4—181no—
569D4—362no—
570D4—362no—
571D4—362no—
572D4—362no—
573D4—721no—
574D4—721no—
575D4D4×C3⋊D312yes—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—81no—
579C2×C4—91no—
580C2×C4—91no—
581C2×C4—181no—
582C2×C4—181no—
583C2×C4—181no—
584C2×C4—181no—
585C2×C4—181no—
586C2×C4—181no—
587C2×C4—362no—
588C2×C4—362no—
589C2×C4—721no—
590C2×C4D4×C3⋊D311yescharacteristic
591C2×C4D4×C3⋊D311yescharacteristic
592C2×C4C23×C3⋊D311yescharacteristic
593C8—21no—
594C8—21no—
595C8—92no—
596C8—181no—
597C2×C3—48no—
598C2×C3—84no—
599C2×C3#560914yes—
600C2×C3D3×#13514yes—
601C2×C3#577414yes—
602D3—68no—
603D3—124no—
604D3—128no—
605D3—244no—
606C22—22no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—92no—
613C22—181no—
614C22—181no—
615C22—181no—
616C22—181no—
617C22—181no—
618C22—182no—
619C22—361no—
620C22—361no—
621C22—361no—
622C22—361no—
623C22—361no—
624C22—724no—
625C22—724no—
626C22C2×D4×C3⋊D311yescharacteristic
627C4—21no—
628C4—21no—
629C4—41no—
630C4—41no—
631C4—181no—
632C4—181no—
633C4—361no—
634C4—361no—
635C4C2×D4×C3⋊D311yescharacteristic
636C4#6436611yescharacteristic
637C3#8055714yescomplemented
638C2—42no—
639C2—81no—
640C2—182no—
641C2—361no—
642C2—362no—
643C2—721no—
644C2#1059608011yescharacteristic
645C2C3⋊D3×#13511yescharacteristic
646C2#1059624511yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#463C2
socleC22×C32C22×D4
hypercenter#463C3⋊D3
hypocenterC32#3280
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#64125C2semidirect
2. C2×D8×C3⋊D3C2semidirect
3. #10596147C2semidirect
4. #10596025C2semidirect
5. C32×#463C2semidirect
6. #10592868C2semidirect
7. #10592857C2semidirect
8. #10592758C2semidirect
9. C4×#3753C2semidirect
10. #10592543C2semidirect
11. #10592533C2semidirect
12. #10592512C2semidirect
13. #10592509C2semidirect
14. #10592475C2semidirect
15. #10592474C2semidirect
17. C2×#3832C22semidirect
18. C2×#3830C22semidirect
21. C2×C32×SD16C22semidirect
23. C32×#124C22semidirect
24. C32×C4×D4C22semidirect
26. C2×#3756C22semidirect
27. C2×#3755C22semidirect
28. #64147C22semidirect
29. C2×#3754C22semidirect
37. C2×#3744C22semidirect
39. C2×C8×C3⋊D3C22semidirect
41. #64104C22semidirect
48. #64084C22semidirect
50. C4×C4⋊(C3⋊D3)C22semidirect
51. C32×C4⋊C8C22semidirect
52. C32×#103C22semidirect
53. C32×#102C22semidirect
54. #63659C22semidirect
55. #63648C22semidirect
57. #63647C22semidirect
58. #63643C22semidirect
59. #63636C22semidirect
60. #63634C22semidirect
61. C4×C3⋊(C3⋊C8)C22semidirect
66. C3×#463D3semidirect
120. #3753D4semidirect
144. C2×C3×SD16C2×D3semidirect
146. C3×#124C2×D3semidirect
147. C3×C4×D4C2×D3semidirect
174. C3×C4⋊C8C2×D3semidirect
175. C3×#103C2×D3semidirect
176. C3×#102C2×D3semidirect
245. #463C3⋊D3semidirect
334. C2×C3⋊D3#135semidirect
354. C2×SD16C2×C3⋊D3semidirect
363. #124C2×C3⋊D3semidirect
376. C4×D4C2×C3⋊D3semidirect
380. C4⋊C8C2×C3⋊D3semidirect
382. #103C2×C3⋊D3semidirect
386. #102C2×C3⋊D3semidirect
544. C32#3280semidirect
637. C3#80557semidirect

Maximal subgroups

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

subgroupindex
C2×#641252
C2×D8×C3⋊D32
#105961472
#105960252
C32×#4632
#105928682
#105928572
#105927582
C4×#37532
#105925432
#105925332
#105925122
#105925092
#105924752
#105924742
#805573