Finite Group Databasebeta

← #11885784

Subgroups — #11885784

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#10596277C211yesmaximal, characteristic, complemented
2C22×#3753C211yesmaximal, characteristic, complemented
3C2×#64125C211yesmaximal, characteristic, complemented
4#10596101C211yesmaximal, characteristic, complemented
5C32×#450C211yesmaximal, characteristic, complemented
6#10592871C211yesmaximal, characteristic, complemented
7#10592867C211yesmaximal, characteristic, complemented
8#10592864C211yesmaximal, characteristic, complemented
9#10592750C211yesmaximal, characteristic, complemented
10#10592486C211yesmaximal, characteristic, complemented
11#10592480C211yesmaximal, characteristic, complemented
12#10592474C211yesmaximal, characteristic, complemented
13#10592455C211yesmaximal, characteristic, complemented
14#10592430C211yesmaximal, characteristic, complemented
15#10592424C211yesmaximal, characteristic, complemented
16#80168—34nomaximal
17C22×C32×D4C2211yescharacteristic
18C2×#3832C2211yescharacteristic, complemented
19C2×#3830C2211yescharacteristic, complemented
20C22×C4⋊(C3⋊D3)C2211yescharacteristic
21C2×C32×SD16C2211yescharacteristic, complemented
22C2×C32×SD16C2211yescharacteristic, complemented
23C32×C22⋊Q8C2211yescharacteristic
24#64162—21no—
25C2×#3757—21no—
26#64156C2211yescharacteristic, complemented
27C2×#3756C2211yescharacteristic, complemented
28#64148—21no—
29#64147C2211yescharacteristic, complemented
30#64145C2211yescharacteristic, complemented
31#64144—21no—
32D4×C3⋊Dic3C2211yescharacteristic, complemented
33C2×#3753—24no—
34C2×#3753C2211yescharacteristic
35C2×#3753C2211yescharacteristic
36C2×#3753C2211yescharacteristic
37C2×#3753C2211yescharacteristic
38C4×#638C2211yescharacteristic
39#64133C2211yescharacteristic
40C22×C3⋊(C3⋊C8)C2211yescharacteristic
41#64125—24no—
42C2×#3744C2211yescharacteristic, complemented
43C2×#3744C2211yescharacteristic, complemented
44C2×C8×C3⋊D3C2211yescharacteristic, complemented
45#64104—21no—
46#64104C2211yescharacteristic, complemented
47#64103—21no—
48#64102C2211yescharacteristic, complemented
49#64091—21no—
50C22⋊C4×C3⋊D3—21no—
51C32×#102C2211yescharacteristic, complemented
52C32×#102C2211yescharacteristic, complemented
53C32×C22⋊C8C2211yescharacteristic
54#63662C2211yescharacteristic, complemented
55#63648C2211yescharacteristic, complemented
56#63648C2211yescharacteristic, complemented
57#63647C2211yescharacteristic, complemented
58#63641C2211yescharacteristic, complemented
59C8×C3⋊Dic3C2211yescharacteristic, complemented
60#63637C2211yescharacteristic, complemented
61#63634C2211yescharacteristic, complemented
62#5806—34no—
63C22×#213—34no—
64C2×#916—34no—
65#5630—34no—
66C3×#450D314yescomplemented
67#5172—34no—
68#5168—34no—
69#5165—34no—
70#5051—34no—
71#4787—34no—
72#4781—34no—
73#4775—34no—
74#4756—34no—
75#4731—34no—
76#67⋊C8—34no—
77C24×C32—21no—
78C23×C3⋊D3—21no—
79C2×C32×Q8C2311yescharacteristic
80C2×C32×D4—22no—
81C2×C32×D4—21no—
82C2×C32×D4—41no—
83C2×C32×D4C2311yescharacteristic
84C2×C32×D4C2311yescharacteristic
85C22×C32×C4C2311yescharacteristic
86C2×#638—21no—
87C2×#638—21no—
88C2×#638D411yescharacteristic
89C22×C3⋊Dic3—21no—
90C22×C3⋊Dic3—21no—
91#3832—22no—
92#3832—41no—
93#3830—22no—
94#3830—41no—
95C2×C4⋊(C3⋊D3)—22no—
96C2×C4⋊(C3⋊D3)—21no—
97C2×C4⋊(C3⋊D3)—21no—
98C2×C4⋊(C3⋊D3)—21no—
99C2×C4⋊(C3⋊D3)—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—22no—
107C32×SD16—41no—
108C2×C32×C8C2311yescharacteristic
109C2×C32×C8C2311yescharacteristic
110C32×C4⋊C4—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C22⋊C4—21no—
113#3757—21no—
114#3757—21no—
115#3757—21no—
116#3757—21no—
117#3757—21no—
118#3757D411yescharacteristic
119#3756—22no—
120#3753—22no—
121#3753—22no—
122#3753—22no—
123#3753D414yescomplemented
124#3752—21no—
125#3752—21no—
126#3752—21no—
127#3752—21no—
128#3752D411yescharacteristic
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#3744—22no—
137#3744—41no—
138C8×C3⋊D3—22no—
139#3280—91noSylow
140C22×C3×D4C2×D314yes—
141C2×#239—34no—
142C2×#237—34no—
143C22×D12—34no—
144C2×C3×SD16C2×D314yescomplemented
145C2×C3×SD16C2×D314yescomplemented
146C3×C22⋊Q8C2×D314yes—
147#953—64no—
148C2×#217—64no—
149#947—34no—
150C2×#216—34no—
151#939—64no—
152#938—34no—
153#936—34no—
154#935—64no—
155D4×Dic3—34no—
156C2×#213—34no—
157C2×#213—34no—
158C2×#213—34no—
159C2×#213—34no—
160C2×#213—616no—
161C4×#67—34no—
162#924—34no—
163C22×C3⋊C8—34no—
164#916—616no—
165C2×#204—34no—
166C2×#204—34no—
167C2×D3×C8—34no—
168#895—34no—
169#895—64no—
170#894—64no—
171#893—34no—
172#882—64no—
173D3×C22⋊C4—64no—
174C3×#102C2×D314yescomplemented
175C3×#102C2×D314yescomplemented
176C3×C22⋊C8C2×D314yes—
177#835—34no—
178#821—34no—
179#821—34no—
180(C2×D3)⋊C8—34no—
181Dic3⋊C8—34no—
182C8×Dic3—34no—
183#810—34no—
184#807—34no—
185C23×C32—21no—
186C23×C32—21no—
187C23×C32—42no—
188C23×C32—42no—
189C23×C32—81no—
190C23×C32C2×D411yescharacteristic
191C22×C3⋊D3—21no—
192C22×C3⋊D3—21no—
193C22×C3⋊D3—42no—
194C22×C3⋊D3—42no—
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×D4C2×D412yes—
204C2×C32×C4—21no—
205C2×C32×C4—21no—
206C2×C32×C4—21no—
207C2×C32×C4—21no—
208C2×C32×C4C2×D411yescharacteristic
209C2×C32×C4C2411yescharacteristic
210#638—22no—
211#638—42no—
212#638—81no—
213C2×C3⋊Dic3—21no—
214C2×C3⋊Dic3—21no—
215C2×C3⋊Dic3—42no—
216C2×C3⋊Dic3—81no—
217C2×C3⋊Dic3C2×D411yescharacteristic
218C2×C3⋊Dic3C2×D411yescharacteristic
219C2×C3⋊Dic3C2×D411yescharacteristic
220C4⋊(C3⋊D3)—21no—
221C4⋊(C3⋊D3)—21no—
222C4⋊(C3⋊D3)—21no—
223C4⋊(C3⋊D3)—42no—
224C4⋊(C3⋊D3)—42no—
225C4⋊(C3⋊D3)—81no—
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#450C3⋊D311yescharacteristic, complemented
248#449—91no—
249#449—91no—
250C4×D8—91no—
251C8×D4—91no—
252C24×C3—24no—
253C23×D3—64no—
254C2×C3×Q8C22×D314yes—
255C2×C3×D4—28no—
256C2×C3×D4—24no—
257C2×C3×D4—44no—
258C2×C3×D4C22×D314yes—
259C2×C3×D4C22×D314yes—
260C22×C3×C4C22×D314yes—
261C2×#67—34no—
262C2×#67—64no—
263C2×#67—64no—
264C22×Dic3—64no—
265C22×Dic3—64no—
266#239—68no—
267#239—124no—
268#237—68no—
269#237—124no—
270C2×D12—34no—
271C2×D12—34no—
272C2×D12—68no—
273C2×D12—64no—
274C2×D12—64no—
275C2×D12—64no—
276C2×D12—124no—
277C2×C4×D3—34no—
278C2×C4×D3—64no—
279C2×C4×D3—64no—
280C2×Dic6—34no—
281C3×SD16—28no—
282C3×SD16—44no—
283C2×C3×C8C22×D314yes—
284C2×C3×C8C22×D314yes—
285C3×C4⋊C4—24no—
286C3×C4⋊C4C22×D314yes—
287C3×C22⋊C4—24no—
288#217—34no—
289#217—64no—
290#217—64no—
291#217—64no—
292#217—64no—
293#217—64no—
294#216—68no—
295#213—316no—
296#213—68no—
297#213—68no—
298#213—68no—
299(C2×D3)⋊C4—34no—
300(C2×D3)⋊C4—64no—
301(C2×D3)⋊C4—64no—
302(C2×D3)⋊C4—64no—
303(C2×D3)⋊C4—64no—
304C4⋊Dic3—34no—
305Dic3⋊C4—34no—
306Dic3⋊C4—64no—
307C4×Dic3—34no—
308C2×C3⋊C8—34no—
309C2×C3⋊C8—34no—
310C2×C3⋊C8—68no—
311#204—68no—
312#204—124no—
313D3×C8—68no—
314C22×C32—21no—
315C22×C32—21no—
316C22×C32—22no—
317C22×C32—41no—
318C22×C32—41no—
319C22×C32—41no—
320C22×C32—41no—
321C22×C32—41no—
322C22×C32—84no—
323C22×C32#13512yescomplemented
324C22×C32C22×D411yescharacteristic
325C2×C3⋊D3—21no—
326C2×C3⋊D3—22no—
327C2×C3⋊D3—21no—
328C2×C3⋊D3—21no—
329C2×C3⋊D3—41no—
330C2×C3⋊D3—41no—
331C2×C3⋊D3—41no—
332C2×C3⋊D3—41no—
333C2×C3⋊D3—41no—
334C2×C3⋊D3—84no—
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×#41—91no—
347C22×D4—91no—
348C22×D4C2×C3⋊D311yescharacteristic
349#135—184no—
350C2×Q16—91no—
351C2×SD16—91no—
352C2×SD16—91no—
353C2×SD16C2×C3⋊D311yescharacteristic, complemented
354C2×SD16C2×C3⋊D311yescharacteristic, complemented
355C2×D8—91no—
356C2×D8—91no—
357C2×D8—91no—
358C2×D8—91no—
359C2×D8—184no—
360C22×C8—91no—
361C22×C8—91no—
362#124—91no—
363#124—91no—
364#123—181no—
365#123—181no—
366C22⋊Q8—91no—
367C22⋊Q8C2×C3⋊D311yescharacteristic
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×D4—91no—
377C2×C22⋊C4—181no—
378C2×C22⋊C4—181no—
379#107—91no—
380C4⋊C8—91no—
381#103—91no—
382#103—91no—
383#102—91no—
384#102—91no—
385#102C2×C3⋊D311yescharacteristic, complemented
386#102C2×C3⋊D311yescharacteristic, complemented
387C22⋊C8—91no—
388C22⋊C8C2×C3⋊D311yescharacteristic
389C4×C8—91no—
390C23×C3—24no—
391C23×C3—24no—
392C23×C3—48no—
393C23×C3—48no—
394C23×C3—84no—
395C23×C3D3×D414yes—
396C22×D3—34no—
397C22×D3—64no—
398C22×D3—64no—
399C22×D3—128no—
400C22×D3—128no—
401C22×D3—244no—
402C3×Q8—24no—
403C3×Q8—24no—
404C3×D4—24no—
405C3×D4—24no—
406C3×D4—24no—
407C3×D4—48no—
408C3×D4D3×D418yes—
409C2×C3×C4—24no—
410C2×C3×C4—24no—
411C2×C3×C4—24no—
412C2×C3×C4—24no—
413C2×C3×C4D3×D414yes—
414C2×C3×C4C23×D314yes—
415#67—68no—
416#67—128no—
417#67—244no—
418C2×Dic3—34no—
419C2×Dic3—34no—
420C2×Dic3—34no—
421C2×Dic3—64no—
422C2×Dic3—64no—
423C2×Dic3—128no—
424C2×Dic3—244no—
425D12—38no—
426D12—64no—
427D12—64no—
428D12—64no—
429D12—128no—
430D12—128no—
431D12—244no—
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—22no—
443C2×C32—42no—
444C2×C32—81no—
445C2×C32D4211yescharacteristic
446C2×C32C2×#13511yescharacteristic
447C2×C32#57611yescharacteristic
448C3⋊D3—41no—
449C3⋊D3—42no—
450C3⋊D3—81no—
451C24—21no—
452C24—181no—
453#41—182no—
454#41—182no—
455#41—361no—
456#41—361no—
457C2×Q8—91no—
458C2×Q8C22×C3⋊D311yescharacteristic
459C2×D4—22no—
460C2×D4—21no—
461C2×D4—41no—
462C2×D4—91no—
463C2×D4—91no—
464C2×D4—91no—
465C2×D4—182no—
466C2×D4—181no—
467C2×D4—181no—
468C2×D4—181no—
469C2×D4—181no—
470C2×D4—181no—
471C2×D4—361no—
472C2×D4C22×C3⋊D311yescharacteristic
473C2×D4C22×C3⋊D311yescharacteristic
474C22×C4—91no—
475C22×C4—181no—
476C22×C4—181no—
477C22×C4—181no—
478C22×C4—181no—
479C22×C4C22×C3⋊D311yescharacteristic
480Q16—182no—
481SD16—22no—
482SD16—41no—
483SD16—182no—
484SD16—361no—
485D8—94no—
486D8—182no—
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—21no—
496C4⋊C4—91no—
497C4⋊C4—91no—
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—28no—
516C22×C3—44no—
517C22×C3—44no—
518C22×C3—44no—
519C22×C3—44no—
520C22×C3—44no—
521C22×C3—816no—
522C22×C3#91618yescomplemented
523C22×C3C2×D3×D414yes—
524C2×D3—64no—
525C2×D3—64no—
526C2×D3—64no—
527C2×D3—68no—
528C2×D3—124no—
529C2×D3—124no—
530C2×D3—124no—
531C2×D3—124no—
532C2×D3—124no—
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—42no—
548C23—42no—
549C23—81no—
550C23—91no—
551C23—181no—
552C23—181no—
553C23—362no—
554C23—362no—
555C23—721no—
556C23D4×C3⋊D311yescharacteristic
557Q8—21no—
558Q8—21no—
559Q8—181no—
560Q8—181no—
561D4—21no—
562D4—21no—
563D4—21no—
564D4—42no—
565D4—92no—
566D4—182no—
567D4—181no—
568D4—181no—
569D4—181no—
570D4—362no—
571D4—362no—
572D4—362no—
573D4—721no—
574D4—721no—
575D4D4×C3⋊D312yes—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—91no—
581C2×C4—91no—
582C2×C4—91no—
583C2×C4—181no—
584C2×C4—181no—
585C2×C4—181no—
586C2×C4—181no—
587C2×C4—362no—
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—28no—
598C2×C3—48no—
599C2×C3—84no—
600C2×C3#559014yes—
601C2×C3C2×#91614yes—
602C2×C3#577414yes—
603D3—124no—
604D3—128no—
605D3—244no—
606C22—21no—
607C22—21no—
608C22—22no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—41no—
614C22—84no—
615C22—181no—
616C22—181no—
617C22—181no—
618C22—182no—
619C22—361no—
620C22—361no—
621C22—361no—
622C22—361no—
623C22—361no—
624C22—724no—
625C22#6412512yescomplemented
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#8016814yescomplemented
638C2—22no—
639C2—42no—
640C2—81no—
641C2—361no—
642C2—362no—
643C2—721no—
644C2#1059606111yescharacteristic
645C2C2×#6412511yescharacteristic
646C2#1059624511yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#450C2
socleC22×C32C22×D4
hypercenter#450C3⋊D3
hypocenterC32#3280
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #10596277C2semidirect
2. C22×#3753C2semidirect
3. C2×#64125C2semidirect
4. #10596101C2semidirect
5. C32×#450C2semidirect
6. #10592871C2semidirect
7. #10592867C2semidirect
8. #10592864C2semidirect
9. #10592750C2semidirect
10. #10592486C2semidirect
11. #10592480C2semidirect
12. #10592474C2semidirect
13. #10592455C2semidirect
14. #10592430C2semidirect
15. #10592424C2semidirect
18. C2×#3832C22semidirect
19. C2×#3830C22semidirect
21. C2×C32×SD16C22semidirect
22. C2×C32×SD16C22semidirect
26. #64156C22semidirect
27. C2×#3756C22semidirect
29. #64147C22semidirect
30. #64145C22semidirect
32. D4×C3⋊Dic3C22semidirect
42. C2×#3744C22semidirect
43. C2×#3744C22semidirect
44. C2×C8×C3⋊D3C22semidirect
46. #64104C22semidirect
48. #64102C22semidirect
51. C32×#102C22semidirect
52. C32×#102C22semidirect
54. #63662C22semidirect
55. #63648C22semidirect
56. #63648C22semidirect
57. #63647C22semidirect
58. #63641C22semidirect
59. C8×C3⋊Dic3C22semidirect
60. #63637C22semidirect
61. #63634C22semidirect
66. C3×#450D3semidirect
123. #3753D4semidirect
144. C2×C3×SD16C2×D3semidirect
145. C2×C3×SD16C2×D3semidirect
174. C3×#102C2×D3semidirect
175. C3×#102C2×D3semidirect
247. #450C3⋊D3semidirect
323. C22×C32#135semidirect
353. C2×SD16C2×C3⋊D3semidirect
354. C2×SD16C2×C3⋊D3semidirect
385. #102C2×C3⋊D3semidirect
386. #102C2×C3⋊D3semidirect
522. C22×C3#916semidirect
544. C32#3280semidirect
625. C22#64125semidirect
637. C3#80168semidirect

Maximal subgroups

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

subgroupindex
#105962772
C22×#37532
C2×#641252
#105961012
C32×#4502
#105928712
#105928672
#105928642
#105927502
#105924862
#105924802
#105924742
#105924552
#105924302
#105924242
#801683