Finite Group Databasebeta

← #11885799

Subgroups — #11885799

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
1#10596300C211yesmaximal, characteristic, complemented
2C2×#64159C211yesmaximal, characteristic, complemented
3C2×D8×C3⋊D3C211yesmaximal, characteristic, complemented
4#10596083C211yesmaximal, characteristic, complemented
5C32×#449C211yesmaximal, characteristic, complemented
6#10592868C211yesmaximal, characteristic, complemented
7#10592867C211yesmaximal, characteristic, complemented
8#10592852C211yesmaximal, characteristic, complemented
9#10592737C211yesmaximal, characteristic, complemented
10#10592518C211yesmaximal, characteristic, complemented
11#10592512C211yesmaximal, characteristic, complemented
12#10592475C211yesmaximal, characteristic, complemented
13#10592455C211yesmaximal, characteristic, complemented
14#10592433C211yesmaximal, characteristic, complemented
15#10592424C211yesmaximal, characteristic, complemented
16#80101—34nomaximal
17C2×C32×#41C2211yescharacteristic, complemented
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×D4×C3⋊D3C2211yescharacteristic
20C2×#3828C2211yescharacteristic, complemented
21C2×C32×SD16C2211yescharacteristic, complemented
22C2×C32×D8C2211yescharacteristic
23C32×#121C2211yescharacteristic, complemented
24#64159—24no—
25#64156C2211yescharacteristic, complemented
26#64155C2211yescharacteristic
27C2×#3756C2211yescharacteristic, complemented
28C2×#3755C2211yescharacteristic, complemented
29#64148—21no—
30#64147—21no—
31#64146—21no—
32#64146—21no—
33#64145C2211yescharacteristic, complemented
34D4×C3⋊Dic3C2211yescharacteristic, complemented
35C2×#3754C2211yescharacteristic, complemented
36C2×#3753C2211yescharacteristic
37C2×#3753C2211yescharacteristic
38#64139C2211yescharacteristic, complemented
39#64138—21no—
40C4×#638C2211yescharacteristic
41C2×#3752—21no—
42C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
43D8×C3⋊D3—24no—
44C2×#3745C2211yescharacteristic
45C2×#3744C2211yescharacteristic, complemented
46C2×C8×C3⋊D3C2211yescharacteristic
47#64106C2211yescharacteristic
48#64102C2211yescharacteristic, complemented
49#64092—21no—
50C22⋊C4×C3⋊D3—21no—
51C32×#103C2211yescharacteristic, complemented
52C32×#102C2211yescharacteristic, complemented
53C32×C22⋊C8C2211yescharacteristic, complemented
54#63659C2211yescharacteristic, complemented
55#63648C2211yescharacteristic, complemented
56#63647C2211yescharacteristic
57#63643C2211yescharacteristic, complemented
58#63641C2211yescharacteristic, complemented
59C8×C3⋊Dic3C2211yescharacteristic, complemented
60#63636C2211yescharacteristic, complemented
61#63634C2211yescharacteristic, complemented
62#5829—34no—
63C2×#950—34no—
64C2×D3×D8—34no—
65#5612—34no—
66C3×#449D314yescomplemented
67#5169—34no—
68#5168—34no—
69#5153—34no—
70#5038—34no—
71#4819—34no—
72#4813—34no—
73#4776—34no—
74#4756—34no—
75#4734—34no—
76#67⋊C8—34no—
77C23×C3⋊D3—21no—
78C23×C3⋊D3—21no—
79C32×#41—22no—
80C32×#41—41no—
81C2×C32×Q8C2311yescharacteristic
82C2×C32×D4—21no—
83C2×C32×D4—21no—
84C2×C32×D4C2311yescharacteristic
85C2×C32×D4C2311yescharacteristic
86C22×C32×C4—21no—
87C22×C32×C4C2311yescharacteristic
88C2×#638—21no—
89C2×#638—21no—
90C2×#638—21no—
91C2×#638—21no—
92C2×#638D411yescharacteristic
93C22×C3⋊Dic3—21no—
94D4×C3⋊D3—22no—
95D4×C3⋊D3—22no—
96D4×C3⋊D3—41no—
97D4×C3⋊D3—41no—
98#3828—22no—
99#3828—41no—
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C4⋊(C3⋊D3)C2311yescharacteristic
102C2×C4×C3⋊D3—21no—
103C2×C4×C3⋊D3—21no—
104C2×C4×C3⋊D3C2311yescharacteristic
105C2×#634C2311yescharacteristic
106C32×SD16—41no—
107C32×D8—22no—
108C2×C32×C8C2311yescharacteristic
109C2×C32×C8C2311yescharacteristic
110C32×C4⋊C4C2311yescharacteristic
111C32×C22⋊C4—21no—
112#3757—21no—
113#3757—21no—
114#3757—21no—
115#3757D411yescharacteristic
116#3756—22no—
117#3755—22no—
118#3754—22no—
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
128C4⋊(C3⋊Dic3)—21no—
129C4⋊(C3⋊Dic3)C2311yescharacteristic
130#3750—21no—
131#3750D411yescharacteristic
132C4×C3⋊Dic3C2311yescharacteristic
133C2×C3⋊(C3⋊C8)—22no—
134C2×C3⋊(C3⋊C8)C2311yescharacteristic
135C2×C3⋊(C3⋊C8)C2311yescharacteristic
136#3745—22no—
137#3744—41no—
138C8×C3⋊D3—22no—
139#3280—91noSylow
140C2×C3×#41C2×D314yescomplemented
141C2×D3×D4—34no—
142C2×D3×D4—34no—
143C2×#235—34no—
144C2×C3×SD16C2×D314yescomplemented
145C2×C3×D8C2×D314yes—
146C3×#121C2×D314yescomplemented
147#950—616no—
148#947—34no—
149#946—34no—
150C2×#216—34no—
151C2×#215—34no—
152#939—64no—
153#938—64no—
154#937—64no—
155#937—64no—
156#936—34no—
157D4×Dic3—34no—
158C2×#214—34no—
159C2×#213—34no—
160C2×#213—34no—
161#930—34no—
162#929—64no—
163C4×#67—34no—
164C2×(C2×D3)⋊C4—64no—
165C22×C3⋊C8—34no—
166D3×D8—616no—
167C2×D24—34no—
168C2×#204—34no—
169C2×D3×C8—34no—
170#897—34no—
171#893—34no—
172#883—64no—
173D3×C22⋊C4—64no—
174C3×#103C2×D314yescomplemented
175C3×#102C2×D314yescomplemented
176C3×C22⋊C8C2×D314yescomplemented
177#832—34no—
178#821—34no—
179(C2×D3)⋊C8—34no—
180#816—34no—
181Dic3⋊C8—34no—
182C8×Dic3—34no—
183#809—34no—
184#807—34no—
185C23×C32—21no—
186C23×C32—21no—
187C23×C32C2×D411yescharacteristic
188C22×C3⋊D3—21no—
189C22×C3⋊D3—21no—
190C22×C3⋊D3—42no—
191C22×C3⋊D3—42no—
192C22×C3⋊D3—42no—
193C22×C3⋊D3—42no—
194C22×C3⋊D3—81no—
195C22×C3⋊D3—81no—
196C22×C3⋊D3C2×D411yescharacteristic
197C32×Q8—21no—
198C32×Q8—21no—
199C32×D4—21no—
200C32×D4—21no—
201C32×D4—21no—
202C32×D4—42no—
203C32×D4—81no—
204C32×D4C2×D412yes—
205C2×C32×C4—21no—
206C2×C32×C4—21no—
207C2×C32×C4—21no—
208C2×C32×C4—21no—
209C2×C32×C4—42no—
210C2×C32×C4C2×D411yescharacteristic
211C2×C32×C4C2411yescharacteristic
212#638—22no—
213#638—42no—
214#638—42no—
215#638—42no—
216#638—81no—
217C2×C3⋊Dic3—21no—
218C2×C3⋊Dic3—21no—
219C2×C3⋊Dic3—81no—
220C2×C3⋊Dic3C2×D411yescharacteristic
221C2×C3⋊Dic3C2×D411yescharacteristic
222C2×C3⋊Dic3C2×D411yescharacteristic
223C4⋊(C3⋊D3)—21no—
224C4⋊(C3⋊D3)—21no—
225C4⋊(C3⋊D3)—21no—
226C4⋊(C3⋊D3)C2×D412yes—
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#463—91no—
246#450—91no—
247#450—91no—
248#449—91no—
249#449C3⋊D311yescharacteristic, complemented
250C4×D8—91no—
251C8×D4—91no—
252C23×D3—64no—
253C23×D3—64no—
254C3×#41—28no—
255C3×#41—44no—
256C2×C3×Q8C22×D314yes—
257C2×C3×D4—24no—
258C2×C3×D4—24no—
259C2×C3×D4C22×D314yes—
260C2×C3×D4C22×D314yes—
261C22×C3×C4—24no—
262C22×C3×C4C22×D314yes—
263C2×#67—34no—
264C2×#67—64no—
265C2×#67—64no—
266C2×#67—64no—
267C2×#67—64no—
268C22×Dic3—64no—
269D3×D4—68no—
270D3×D4—68no—
271D3×D4—124no—
272D3×D4—124no—
273#235—68no—
274#235—124no—
275C2×D12—34no—
276C2×D12—34no—
277C2×C4×D3—34no—
278C2×C4×D3—64no—
279C2×C4×D3—64no—
280C2×Dic6—34no—
281C3×SD16—44no—
282C3×D8—28no—
283C2×C3×C8C22×D314yes—
284C2×C3×C8C22×D314yes—
285C3×C4⋊C4C22×D314yes—
286C3×C22⋊C4—24no—
287#217—34no—
288#217—64no—
289#217—64no—
290#217—64no—
291#216—68no—
292#215—68no—
293#214—68no—
294#213—316no—
295#213—68no—
296(C2×D3)⋊C4—34no—
297(C2×D3)⋊C4—64no—
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—
303C4⋊Dic3—34no—
304C4⋊Dic3—64no—
305Dic3⋊C4—34no—
306Dic3⋊C4—64no—
307C4×Dic3—34no—
308C2×C3⋊C8—34no—
309C2×C3⋊C8—34no—
310C2×C3⋊C8—68no—
311D24—68no—
312#204—124no—
313D3×C8—68no—
314C22×C32—21no—
315C22×C32—22no—
316C22×C32—21no—
317C22×C32—21no—
318C22×C32—41no—
319C22×C32—41no—
320C22×C32—41no—
321C22×C32—41no—
322C22×C32—41no—
323C22×C32C22×D411yescharacteristic
324C2×C3⋊D3—21no—
325C2×C3⋊D3—21no—
326C2×C3⋊D3—22no—
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—41no—
337C32×C4—41no—
338C32×C4C22×D411yescharacteristic
339C32×C4H(5,𝔽2)11yescharacteristic
340C3⋊Dic3—21no—
341C3⋊Dic3—21no—
342C3⋊Dic3—21no—
343C3⋊Dic3—41no—
344C3⋊Dic3—41no—
345C2×#41—91no—
346C2×#41C2×C3⋊D311yescharacteristic, complemented
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#124—91no—
364#123—181no—
365#123—181no—
366C22⋊Q8—91no—
367C22⋊Q8—91no—
368#121—91no—
369#121—181no—
370#121—181no—
371#121C2×C3⋊D311yescharacteristic, complemented
372#120—181no—
373#120—181no—
374C4×D4—91no—
375C4×D4—91no—
376C4×D4—91no—
377C2×C22⋊C4—181no—
378C2×C22⋊C4—181no—
379#107—91no—
380C4⋊C8—91no—
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⋊C8C2×C3⋊D311yescharacteristic, complemented
389C4×C8—91no—
390C23×C3—24no—
391C23×C3—24no—
392C23×C3D3×D414yes—
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×D4—48no—
408C3×D4—84no—
409C3×D4D3×D418yes—
410C2×C3×C4—24no—
411C2×C3×C4—24no—
412C2×C3×C4—24no—
413C2×C3×C4—24no—
414C2×C3×C4—48no—
415C2×C3×C4D3×D414yes—
416C2×C3×C4C23×D314yes—
417#67—68no—
418#67—128no—
419#67—128no—
420#67—128no—
421#67—244no—
422C2×Dic3—34no—
423C2×Dic3—34no—
424C2×Dic3—34no—
425C2×Dic3—64no—
426C2×Dic3—64no—
427C2×Dic3—244no—
428D12—38no—
429D12—64no—
430D12—64no—
431D12—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—41no—
444C2×C32—81no—
445C2×C32D4211yescharacteristic
446C2×C32C2×#13511yescharacteristic
447C2×C32#57611yescharacteristic
448C3⋊D3—22no—
449C3⋊D3—42no—
450C3⋊D3—81no—
451C24—181no—
452C24—181no—
453#41—22no—
454#41—41no—
455#41—182no—
456#41—361no—
457C2×Q8—91no—
458C2×Q8C22×C3⋊D311yescharacteristic
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—91no—
462C2×D4—91no—
463C2×D4—91no—
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—181no—
477C22×C4—181no—
478C22×C4—181no—
479C22×C4C22×C3⋊D311yescharacteristic
480Q16—182no—
481SD16—41no—
482SD16—182no—
483SD16—182no—
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—91no—
502C22⋊C4—91no—
503C22⋊C4—181no—
504C22⋊C4—181no—
505C22⋊C4—181no—
506C22⋊C4—181no—
507C22⋊C4—181no—
508C22⋊C4—181no—
509C22⋊C4—181no—
510C22⋊C4—181no—
511C22⋊C4—181no—
512C42—91no—
513C22×C3—24no—
514C22×C3—24no—
515C22×C3—24no—
516C22×C3—28no—
517C22×C3—44no—
518C22×C3—44no—
519C22×C3—44no—
520C22×C3—44no—
521C22×C3—44no—
522C22×C3C2×D3×D414yes—
523C2×D3—38no—
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—44no—
536C3×C4—44no—
537C3×C4C2×D3×D414yes—
538C3×C4#100414yes—
539Dic3—64no—
540Dic3—64no—
541Dic3—64no—
542Dic3—124no—
543Dic3—124no—
544C32#328011yescharacteristic, complemented, Sylow
545C23—21no—
546C23—21no—
547C23—91no—
548C23—181no—
549C23—181no—
550C23—362no—
551C23—362no—
552C23—362no—
553C23—362no—
554C23—721no—
555C23—721no—
556C23D4×C3⋊D311yescharacteristic
557Q8—21no—
558Q8—21no—
559Q8—181no—
560Q8—181no—
561D4—21no—
562D4—21no—
563D4—21no—
564D4—42no—
565D4—81no—
566D4—92no—
567D4—182no—
568D4—181no—
569D4—181no—
570D4—181no—
571D4—362no—
572D4—362no—
573D4—362no—
574D4—721no—
575D4D4×C3⋊D312yes—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—42no—
581C2×C4—91no—
582C2×C4—91no—
583C2×C4—91no—
584C2×C4—181no—
585C2×C4—181no—
586C2×C4—181no—
587C2×C4—181no—
588C2×C4—362no—
589C2×C4—721no—
590C2×C4—721no—
591C2×C4D4×C3⋊D311yescharacteristic
592C2×C4C23×C3⋊D311yescharacteristic
593C8—21no—
594C8—21no—
595C8—92no—
596C8—181no—
597C2×C3—48no—
598C2×C3—44no—
599C2×C3—84no—
600C2×C3#559014yes—
601C2×C3D3×#13514yes—
602C2×C3#577414yes—
603D3—68no—
604D3—128no—
605D3—244no—
606C22—21no—
607C22—21no—
608C22—21no—
609C22—22no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—41no—
614C22—41no—
615C22—92no—
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—41no—
629C4—41no—
630C4—181no—
631C4—181no—
632C4—181no—
633C4—361no—
634C4—361no—
635C4C2×D4×C3⋊D311yescharacteristic
636C4#6436111yescharacteristic
637C3#8010114yescomplemented
638C2—41no—
639C2—42no—
640C2—81no—
641C2—182no—
642C2—362no—
643C2—721no—
644C2#1059606111yescharacteristic
645C2C3⋊D3×#13511yescharacteristic
646C2#1059624511yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#449C2
socleC22×C32C22×D4
hypercenter#449C3⋊D3
hypocenterC32#3280
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #10596300C2semidirect
2. C2×#64159C2semidirect
3. C2×D8×C3⋊D3C2semidirect
4. #10596083C2semidirect
5. C32×#449C2semidirect
6. #10592868C2semidirect
7. #10592867C2semidirect
8. #10592852C2semidirect
9. #10592737C2semidirect
10. #10592518C2semidirect
11. #10592512C2semidirect
12. #10592475C2semidirect
13. #10592455C2semidirect
14. #10592433C2semidirect
15. #10592424C2semidirect
17. C2×C32×#41C22semidirect
20. C2×#3828C22semidirect
21. C2×C32×SD16C22semidirect
23. C32×#121C22semidirect
25. #64156C22semidirect
27. C2×#3756C22semidirect
28. C2×#3755C22semidirect
33. #64145C22semidirect
34. D4×C3⋊Dic3C22semidirect
35. C2×#3754C22semidirect
38. #64139C22semidirect
42. C22×C3⋊(C3⋊C8)C22semidirect
45. C2×#3744C22semidirect
48. #64102C22semidirect
51. C32×#103C22semidirect
52. C32×#102C22semidirect
53. C32×C22⋊C8C22semidirect
54. #63659C22semidirect
55. #63648C22semidirect
57. #63643C22semidirect
58. #63641C22semidirect
59. C8×C3⋊Dic3C22semidirect
60. #63636C22semidirect
61. #63634C22semidirect
66. C3×#449D3semidirect
120. #3753D4semidirect
140. C2×C3×#41C2×D3semidirect
144. C2×C3×SD16C2×D3semidirect
146. C3×#121C2×D3semidirect
174. C3×#103C2×D3semidirect
175. C3×#102C2×D3semidirect
176. C3×C22⋊C8C2×D3semidirect
249. #449C3⋊D3semidirect
334. C2×C3⋊D3#135semidirect
346. C2×#41C2×C3⋊D3semidirect
354. C2×SD16C2×C3⋊D3semidirect
371. #121C2×C3⋊D3semidirect
382. #103C2×C3⋊D3semidirect
386. #102C2×C3⋊D3semidirect
388. C22⋊C8C2×C3⋊D3semidirect
544. C32#3280semidirect
637. C3#80101semidirect

Maximal subgroups

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

subgroupindex
#105963002
C2×#641592
C2×D8×C3⋊D32
#105960832
C32×#4492
#105928682
#105928672
#105928522
#105927372
#105925182
#105925122
#105924752
#105924552
#105924332
#105924242
#801013