Finite Group Databasebeta

← #25146108

Subgroups — #25146108

Order 11008.

850 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583103C211yesmaximal, characteristic
2C2×C8×Dic86C211yesmaximal, characteristic, complemented
3#19139809C211yesmaximal, characteristic, complemented
4#19139516C211yesmaximal, characteristic
5#19135974C211yesmaximal, characteristic, complemented
6#19135973C211yesmaximal, characteristic, complemented
7#19135914C211yesmaximal, characteristic
8#19135910C211yesmaximal, characteristic
9#19135449C211yesmaximal, characteristic
10#19135446C211yesmaximal, characteristic
11#19135395C211yesmaximal, characteristic, complemented
12#19135357C211yesmaximal, characteristic, complemented
13#19135269C211yesmaximal, characteristic, complemented
14#19134409C211yesmaximal, characteristic
15C43×#1933C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C22×#10621884C2211yescharacteristic
18C2×#13063323C2211yescharacteristic
19C2×#13063303—21no—
20C2×C4×Dic86C2211yescharacteristic
21C2×#13063287C2211yescharacteristic
22#14583103—24no—
23C8×Dic86—24no—
24C2×#13063257C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×C4⋊(C43⋊C8)C2211yescharacteristic
27C2×Dic43⋊C8C2211yescharacteristic
28C2×Dic43⋊C8C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063249C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×#13063248C2211yescharacteristic
33C2×#13063247C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×C8×Dic43C2211yescharacteristic
36C2×C8×Dic43C2211yescharacteristic
37#14582841—21no—
38#14582840—21no—
39#14582823—21no—
40#14582821—21no—
41#14582806C2211yescharacteristic
42#14582805C2211yescharacteristic
43#14582804C2211yescharacteristic
44#14582803—21no—
45#14582801C2211yescharacteristic
46#14582800C2211yescharacteristic
47#14582795C2211yescharacteristic
48#14582768C2211yescharacteristic
49#14582763—21no—
50#14582758—21no—
51C4⋊C4×Dic43C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C2×C4×C8×C43C2211yescharacteristic
57C43×#391C2211yescharacteristic
58C43×#389C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×Dic86D411yescharacteristic
62C22×Dic86C2311yescharacteristic
63C22×D172C2311yescharacteristic
64C22×C4×D43—21no—
65C2×#10621873—22no—
66C2×#10621873—22no—
67C2×#10621873—41no—
68C2×#10621884—22no—
69C2×#10621884—22no—
70C2×#10621884—41no—
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73#13063323—22no—
74#13063323—22no—
75#13063303—44no—
76C4×Dic86—22no—
77C4×Dic86—22no—
78#13063287—22no—
79#13063287—22no—
80C2×C4⋊Dic43D411yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4D411yescharacteristic
89C2×Dic43⋊C4D411yescharacteristic
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×C4×Dic43—21no—
96C2×C4×Dic43C2311yescharacteristic
97C2×C4×Dic43C2311yescharacteristic
98#13063257—41no—
99#13063256—41no—
100C4⋊(C43⋊C8)—22no—
101Dic43⋊C8—22no—
102Dic43⋊C8D414yes—
103#13063250—22no—
104#13063249—41no—
105#13063248—22no—
106#13063248—41no—
107#13063247—22no—
108#13063245—22no—
109C8×Dic43—22no—
110C8×Dic43—22no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C22×Q8×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C2×C4⋊C4×C43—21no—
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C42×C43C2311yescharacteristic
127#103×C43—22no—
128#103×C43—22no—
129C4×C8×C43—22no—
130#95×C43—21no—
131#95×C43—21no—
132#95×C43—21no—
133C23×D43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43—21no—
139C2×Q8×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2411yescharacteristic
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C22×Dic43C2×D411yescharacteristic
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—21no—
159C2×D172#4112yes—
160C2×C4×D43—42no—
161C2×C4×D43—42no—
162C2×C4×D43—42no—
163C2×Dic86—22no—
164C2×Dic86—22no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86SD1614yescomplemented
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43C2×D412yes—
177C2×C8×C43#4112yes—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—42no—
185C42×C43—21no—
186C42×C43—21no—
187#10621884—44no—
188(C2×D43)⋊C4—42no—
189(C2×D43)⋊C4—42no—
190(C2×D43)⋊C4—42no—
191(C2×D43)⋊C4—81no—
192(C2×D43)⋊C4—81no—
193C4⋊Dic43—22no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198Dic43⋊C4—22no—
199Dic43⋊C4—22no—
200Dic43⋊C4—42no—
201Dic43⋊C4—42no—
202Dic43⋊C4—42no—
203Dic43⋊C4—42no—
204Dic43⋊C4—81no—
205C4×Dic43—21no—
206C4×Dic43—21no—
207C4×Dic43—42no—
208C4×Dic43C2×D412yes—
209C4×Dic43#4112yes—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8C2×D412yes—
216#10621873—44no—
217C23×C43C22×D411yescharacteristic
218C22×D43—22no—
219C22×D43—41no—
220C22×D43—41no—
221C22×D43—41no—
222C22×D43—41no—
223C22×D43—41no—
224C22×D43—41no—
225Q8×C43—41no—
226Q8×C43—41no—
227Q8×C43—41no—
228Q8×C43—41no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43C2×SD1612yes—
247C2×C4×C43C22×D411yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C43H(5,𝔽2)11yescharacteristic
252C2×C4×C432−1+411yescharacteristic
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43#12112yes—
270C2×Dic43#12112yes—
271C2×Dic43C2×SD1612yes—
272C2×Dic43C2×SD1612yes—
273C2×Dic43#13512yes—
274D172—22no—
275D172—22no—
276D172—41no—
277D172—41no—
278C4×D43—84no—
279Dic86—28no—
280Dic86—41no—
281Dic86—41no—
282Dic86—41no—
283Dic86—41no—
284C8×C43—22no—
285C8×C43—22no—
286C43⋊C8—22no—
287C43⋊C8—41no—
288#25293—431nomaximal, Sylow
289C22×C43C2×#12111yescharacteristic
290C22×C43#54811yescharacteristic
291C22×C43#55011yescharacteristic
292C22×C43C22×SD1611yescharacteristic
293C22×C43C2×#13511yescharacteristic
294C22×C43#57711yescharacteristic
295C22×C43#57811yescharacteristic
296C2×D43—42no—
297C2×D43—42no—
298C2×D43—42no—
299C2×D43—81no—
300C2×D43—81no—
301C2×D43—81no—
302C2×D43—81no—
303C4×C43—22no—
304C4×C43—41no—
305C4×C43—81no—
306C4×C43—81no—
307C4×C43—81no—
308C4×C43—81no—
309C4×C43#52911yescharacteristic
310C4×C43#54211yescharacteristic
311C4×C43#54611yescharacteristic
312C4×C43#54811yescharacteristic
313Dic43—22no—
314Dic43—22no—
315Dic43—41no—
316Dic43—81no—
317Dic43—81no—
318Dic43—81no—
319Dic43#46514yes—
320C2×#461—431no—
321C2×C8×Q8—431no—
322#2568—431no—
323#2538—431no—
324#2066—431no—
325#2066—431no—
326#2055—431no—
327#2055—431no—
328#1968—431no—
329#1968—431no—
330#1956—431no—
331#1948—431no—
332#1933—431no—
333#1933D4311yescharacteristic, complemented
334C4×#102—431no—
335C2×C43#242611yescharacteristic
336C2×C43C2×#46511yescharacteristic
337C2×C43#306311yescharacteristic
338C2×C43#335911yescharacteristic
339C2×C43#336011yescharacteristic
340C2×C43#339211yescharacteristic
341C2×C43#339311yescharacteristic
342D43—82no—
343C22×SD16—431no—
344C22×SD16—431no—
345C2×C4⋊Q8—431no—
346C2×C22⋊Q8—861no—
347C2×C4×Q8—431no—
348C2×C4×D4—431no—
349#461—864no—
350C8×Q8—864no—
351C2×#106—431no—
352C2×#106—431no—
353C2×C4⋊C8—431no—
354C2×C4⋊C8—431no—
355C2×C4⋊C8—431no—
356C2×#103—431no—
357C2×#103—431no—
358C2×#103—431no—
359C2×#103—431no—
360C2×#103C2×D4311yescharacteristic
361C2×#103C2×D4311yescharacteristic
362C2×#102—431no—
363C2×#102—431no—
364C2×C4×C8—431no—
365C2×C4×C8—431no—
366C2×C4×C8C2×D4311yescharacteristic
367#400—861no—
368#400—861no—
369#396—861no—
370#396—861no—
371#391—431no—
372#391—431no—
373#391—431no—
374#391—861no—
375#391C2×D4311yescharacteristic
376#390—431no—
377#390—431no—
378#389—431no—
379#389C2×D4311yescharacteristic
380#384—431no—
381#382—861no—
382#380—861no—
383C4×C4⋊C4—431no—
384#340—431no—
385#340—431no—
386#340C2×D4311yescharacteristic
387#340C2×D4311yescharacteristic
388C43#2529311yescharacteristic, complemented, Sylow
389C22×Q8—431no—
390C22×Q8—431no—
391C22×Q8C22×D4311yescharacteristic
392C22×D4—431no—
393C23×C4—861no—
394C2×SD16—862no—
395C2×SD16—862no—
396C2×SD16—862no—
397C2×SD16—862no—
398C2×SD16—1721no—
399C2×SD16—1721no—
400C22×C8—431no—
401C22×C8—431no—
402C22×C8C22×D4311yescharacteristic
403C22×C8C22×D4311yescharacteristic
404C4⋊Q8—862no—
405C4⋊Q8—862no—
406C22⋊Q8—1724no—
407C4×Q8—862no—
408C4×Q8—862no—
409C4×D4—862no—
410C4×D4—862no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—431no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—431no—
415C2×C4⋊C4—431no—
416C2×C4⋊C4—431no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4—861no—
419C2×C4⋊C4—861no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4—861no—
422C2×C4⋊C4C22×D4311yescharacteristic
423C2×C4⋊C4C22×D4311yescharacteristic
424C2×C4⋊C4C22×D4311yescharacteristic
425C2×C22⋊C4—861no—
426C2×C22⋊C4—861no—
427C2×C22⋊C4—861no—
428C2×C22⋊C4—861no—
429C2×C22⋊C4—861no—
430C2×C42—431no—
431C2×C42—431no—
432C2×C42—861no—
433C2×C42C22×D4311yescharacteristic
434#106—1721no—
435#106—1721no—
436C4⋊C8—434no—
437C4⋊C8—862no—
438C4⋊C8—862no—
439#103—22no—
440#103—22no—
441#103—862no—
442#103—862no—
443#103—1721no—
444#103—1721no—
445#102—862no—
446#102—862no—
447C4×C8—22no—
448C4×C8—862no—
449C4×C8—862no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95—861no—
454#95—861no—
455#95—861no—
456#95—861no—
457#95—861no—
458#95—861no—
459#95—861no—
460#95—861no—
461C24—861no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—434no—
469C2×Q8—862no—
470C2×Q8—862no—
471C2×Q8—861no—
472C2×Q8—861no—
473C2×Q8—861no—
474C2×Q8—861no—
475C2×Q8—861no—
476C2×Q8—861no—
477C2×D4—432no—
478C2×D4—861no—
479C2×D4—861no—
480C2×D4—861no—
481C2×D4—861no—
482C2×D4—861no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—431no—
488C22×C4—431no—
489C22×C4—431no—
490C22×C4—431no—
491C22×C4—861no—
492C22×C4—861no—
493C22×C4—861no—
494C22×C4—1722no—
495C22×C4—1722no—
496C22×C4—1722no—
497C22×C4D4×D4311yescharacteristic
498C22×C4D4×D4311yescharacteristic
499C22×C4C23×D4311yescharacteristic
500SD16—1724no—
501SD16—1724no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—432no—
507C2×C8—861no—
508C2×C8—861no—
509C2×C8—861no—
510C2×C8—861no—
511C2×C8—861no—
512C2×C8#1062189812yes—
513C2×C8D4×D4312yes—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—42no—
521C4⋊C4—862no—
522C4⋊C4—862no—
523C4⋊C4—862no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—3441no—
529C4⋊C4—1722no—
530C4⋊C4—1722no—
531C4⋊C4—1722no—
532C4⋊C4—1722no—
533C22⋊C4—3441no—
534C22⋊C4—3441no—
535C22⋊C4—1722no—
536C22⋊C4—1722no—
537C22⋊C4—1722no—
538C42—21no—
539C42—21no—
540C42—432no—
541C42—432no—
542C42—861no—
543C42—861no—
544C42—1722no—
545C23—862no—
546C23—1721no—
547C23—1721no—
548C23—1721no—
549C23—1721no—
550C23—1721no—
551C23—1721no—
552C23C2×D4×D4311yescharacteristic
553Q8—41no—
554Q8—41no—
555Q8—41no—
556Q8—41no—
557Q8—868no—
558Q8—1721no—
559Q8—1721no—
560Q8—1721no—
561Q8—1721no—
562D4—862no—
563D4—862no—
564D4—1721no—
565D4—1721no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—432no—
584C2×C4—432no—
585C2×C4—432no—
586C2×C4—432no—
587C2×C4—432no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—861no—
591C2×C4—861no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—861no—
595C2×C4—3444no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4SD16×D4312yes—
606C2×C4C2×D4×D4311yescharacteristic
607C2×C4#41×D4311yescharacteristic
608C2×C4#41×D4311yescharacteristic
609C2×C4C2×#1062189811yescharacteristic
610C2×C4#1306337111yescharacteristic
611C2×C4#1306337211yescharacteristic
612C8—22no—
613C8—22no—
614C8—862no—
615C8—1721no—
616C22—3441no—
617C22—3441no—
618C22—3441no—
619C22—3441no—
620C22—1722no—
621C22—1722no—
622C22—1722no—
623C22#121×D4311yescharacteristic
624C22#1458355711yescharacteristic
625C22#1458357011yescharacteristic
626C22C2×SD16×D4311yescharacteristic
627C22#135×D4311yescharacteristic
628C22#1458370611yescharacteristic
629C22#1458371211yescharacteristic
630C4—22no—
631C4—41no—
632C4—81no—
633C4—81no—
634C4—81no—
635C4—81no—
636C4—434no—
637C4—862no—
638C4—862no—
639C4—3441no—
640C4—3441no—
641C4—3441no—
642C4—1721no—
643C4#1458342711yescharacteristic
644C4#1458351511yescharacteristic
645C4#1458354111yescharacteristic
646C4#1458355811yescharacteristic
647C2—3442no—
648C2#1913816011yescharacteristic
649C2#465×D4311yescharacteristic
650C2#1914428511yescharacteristic
651C2#1914723411yescharacteristic
652C2#1914724111yescharacteristic
653C2#1914757411yescharacteristic
654C2#1914758311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1933C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#1933D43
hypocenterC43#25293
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1933

Complements

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

NH ≅ G/Ntype
2. C2×C8×Dic86C2semidirect
3. #19139809C2semidirect
5. #19135974C2semidirect
6. #19135973C2semidirect
11. #19135395C2semidirect
12. #19135357C2semidirect
13. #19135269C2semidirect
15. C43×#1933C2semidirect
171. C2×Dic86SD16semidirect
333. #1933D43semidirect
388. C43#25293semidirect

Maximal subgroups

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

subgroupindex
C2×#145831032
C2×C8×Dic862
#191398092
#191395162
#191359742
#191359732
#191359142
#191359102
#191354492
#191354462
#191353952
#191353572
#191352692
#191344092
C43×#19332
#2529343