Finite Group Databasebeta

← #25156759

Subgroups — #25156759

Order 11008.

868 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×#14583105C211yesmaximal, characteristic
2C2×C4×#10621873C211yesmaximal, characteristic
3#19138371C211yesmaximal, characteristic, complemented
4#19137506C211yesmaximal, characteristic
5#19136142C211yesmaximal, characteristic, complemented
6#19136093C211yesmaximal, characteristic, complemented
7#19136015C211yesmaximal, characteristic, complemented
8#19135842C211yesmaximal, characteristic, complemented
9#19135271C211yesmaximal, characteristic, complemented
10#19134928C211yesmaximal, characteristic
11#19134928C211yesmaximal, characteristic
12#19134928C211yesmaximal, characteristic
13#19134852C211yesmaximal, characteristic, complemented
14#19134845C211yesmaximal, characteristic
15C43×#1916C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C22×#10621873C2211yescharacteristic
18C2×#13063325C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C2×C4×D172C2211yescharacteristic
22C2×C4×D172C2211yescharacteristic
23#14583105—24no—
24C4×#10621873—24no—
25C2×#13063259C2211yescharacteristic
26C2×#13063257C2211yescharacteristic
27C2×#13063250C2211yescharacteristic
28C2×#13063250C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063250C2211yescharacteristic
32C2×#13063250C2211yescharacteristic
33C2×#13063247C2211yescharacteristic
34C2×#13063247C2211yescharacteristic
35#14582841—21no—
36#14582832—21no—
37#14582805C2211yescharacteristic
38#14582805C2211yescharacteristic
39#14582805C2211yescharacteristic
40#14582797C2211yescharacteristic
41#14582797C2211yescharacteristic
42#14582797C2211yescharacteristic
43#14582786—21no—
44#14582785—21no—
45#14582770—21no—
46#14582770—21no—
47#14582765C2211yescharacteristic
48#14582758—21no—
49#95×D43—21no—
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582662C2211yescharacteristic
54C2×C4⋊C8×C43C2211yescharacteristic
55C2×C4×C8×C43C2211yescharacteristic
56C4×C4⋊C4×C43C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C22×Dic86C2311yescharacteristic
62C22×Dic86C2311yescharacteristic
63C22×D172C2311yescharacteristic
64C22×C4×D43—21no—
65C22×C4×D43—21no—
66C22×C4×D43—21no—
67C2×#10621873—22no—
68C2×#10621873—22no—
69C2×#10621873—22no—
70C2×#10621873—22no—
71C2×#10621873—22no—
72C2×#10621873D414yes—
73#13063325—22no—
74#13063325—41no—
75C4×Dic86—22no—
76C4×Dic86—41no—
77C4×D172—22no—
78C4×D172—22no—
79C4×D172—22no—
80C4×D172—22no—
81C4×D172—41no—
82C4×D172—41no—
83C2×C4⋊Dic43—21no—
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×C4×Dic43—21no—
98#13063259—41no—
99#13063257—22no—
100#13063250—22no—
101#13063250—22no—
102#13063250—22no—
103#13063250—22no—
104#13063250—22no—
105#13063250—41no—
106#13063247—22no—
107#13063247—22no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
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×C8×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C22×C8×C43C2311yescharacteristic
123C2×C4⋊C4×C43D411yescharacteristic
124C2×C4⋊C4×C43D411yescharacteristic
125C2×C42×C43C2311yescharacteristic
126C2×C42×C43C2311yescharacteristic
127C2×C42×C43C2311yescharacteristic
128C4⋊C8×C43—22no—
129C4×C8×C43—22no—
130#95×C43D411yescharacteristic
131#95×C43D411yescharacteristic
132C23×D43—21no—
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2411yescharacteristic
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C2×D172—21no—
148C2×D172—21no—
149C2×D172—21no—
150C2×D172C2×D412yes—
151C2×D172#4112yes—
152C2×D172#4112yes—
153C2×C4×D43—24no—
154C2×C4×D43—42no—
155C2×C4×D43—42no—
156C2×C4×D43—42no—
157C2×C4×D43—42no—
158C2×C4×D43—81no—
159C2×C4×D43—81no—
160C2×C4×D43—81no—
161C2×C4×D43—81no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—21no—
172C2×Dic86—21no—
173C2×Dic86C2×D412yes—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43C2×D412yes—
186C4⋊C4×C43—22no—
187C4⋊C4×C43—22no—
188C42×C43—21no—
189C42×C43—21no—
190C42×C43—21no—
191C42×C43—21no—
192C42×C43—21no—
193C42×C43—21no—
194(C2×D43)⋊C4—24no—
195(C2×D43)⋊C4—42no—
196(C2×D43)⋊C4—42no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43—42no—
207C4⋊Dic43—42no—
208C4⋊Dic43#4112yes—
209Dic43⋊C4—42no—
210Dic43⋊C4—42no—
211Dic43⋊C4—81no—
212Dic43⋊C4—81no—
213C4×Dic43—42no—
214#10621873—28no—
215#10621873—44no—
216C23×C43C22×D411yescharacteristic
217C22×D43—22no—
218C22×D43—22no—
219C22×D43—22no—
220C22×D43—41no—
221C22×D43—41no—
222C22×D43—41no—
223C22×D43—41no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43#13512yes—
241C2×C4×C43#13712yes—
242C2×C4×C43C22×D411yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C43H(5,𝔽2)11yescharacteristic
247C2×C4×C432−1+411yescharacteristic
248C2×Dic43—22no—
249C2×Dic43—22no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
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—
269D172—22no—
270D172—22no—
271D172—22no—
272D172#12314yes—
273C4×D43—84no—
274C4×D43—84no—
275C4×D43—84no—
276Dic86—22no—
277Dic86—22no—
278Dic86—41no—
279Dic86—41no—
280Dic86—41no—
281Dic86—41no—
282Dic86—41no—
283Dic86—41no—
284C8×C43—22no—
285C8×C43—41no—
286C8×C43—41no—
287C8×C43—41no—
288#26170—431nomaximal, Sylow
289C22×C43#52511yescharacteristic
290C22×C43D4211yescharacteristic
291C22×C43#54811yescharacteristic
292C22×C43C2×#13511yescharacteristic
293C22×C43C2×#13711yescharacteristic
294C22×C43#57711yescharacteristic
295C22×C43#57711yescharacteristic
296C2×D43—24no—
297C2×D43—42no—
298C2×D43—42no—
299C2×D43—42no—
300C2×D43—42no—
301C2×D43—42no—
302C2×D43—42no—
303C4×C43—22no—
304C4×C43—22no—
305C4×C43—41no—
306C4×C43—41no—
307C4×C43—41no—
308C4×C43—41no—
309C4×C43C2×#12311yescharacteristic
310C4×C43#53911yescharacteristic
311C4×C43#54711yescharacteristic
312C4×C43#55311yescharacteristic
313Dic43—42no—
314Dic43—42no—
315Dic43—81no—
316Dic43—81no—
317Dic43—81no—
318Dic43—81no—
319Dic43—81no—
320C2×#461—431no—
321C2×C4×SD16—431no—
322#2446—431no—
323#2349—431no—
324#2097—431no—
325#2088—431no—
326#2074—431no—
327#2043—431no—
328#1933—431no—
329#1916D4311yescharacteristic, complemented
330#1877—431no—
331#1877—431no—
332#1877—431no—
333#1863—431no—
334#1862—431no—
335C2×C43#244311yescharacteristic
336C2×C43#310711yescharacteristic
337C2×C43#312311yescharacteristic
338C2×C43#326611yescharacteristic
339C2×C43#328211yescharacteristic
340C2×C43#336011yescharacteristic
341C2×C43#337211yescharacteristic
342D43—44no—
343C22×SD16—431no—
344C22×SD16—431no—
345C2×C4⋊Q8—431no—
346C2×C4×Q8—431no—
347C2×C4×D4—431no—
348C2×C4×D4—431no—
349C2×C4×D4—431no—
350#461—864no—
351C4×SD16—864no—
352C2×#107—431no—
353C2×#106—431no—
354C2×C4⋊C8C2×D4311yescharacteristic
355C2×#103—431no—
356C2×#103—431no—
357C2×#103—431no—
358C2×#103—431no—
359C2×#103—431no—
360C2×#103—431no—
361C2×#102—431no—
362C2×#102—431no—
363C2×C4×C8C2×D4311yescharacteristic
364#400—861no—
365#398—861no—
366#391—431no—
367#391—431no—
368#391—431no—
369#389—431no—
370#389—431no—
371#389—431no—
372#387—861no—
373#387—861no—
374#385—861no—
375#385—861no—
376#382—431no—
377#380—861no—
378C4×C4⋊C4C2×D4311yescharacteristic
379C2×#95—861no—
380#340—431no—
381#340—431no—
382#340—431no—
383#340—431no—
384#336C2×D4311yescharacteristic
385#336C2×D4311yescharacteristic
386#336C2×D4311yescharacteristic
387#336C2×D4311yescharacteristic
388C43#2617011yescharacteristic, complemented, Sylow
389C22×Q8—431no—
390C22×Q8—431no—
391C22×D4—431no—
392C23×C4—861no—
393C23×C4—861no—
394C23×C4—861no—
395C2×SD16—434no—
396C2×SD16—862no—
397C2×SD16—862no—
398C2×SD16—862no—
399C2×SD16—862no—
400C2×SD16—862no—
401C22×C8C22×D4311yescharacteristic
402C22×C8C22×D4311yescharacteristic
403C22×C8C22×D4311yescharacteristic
404C22×C8C22×D4311yescharacteristic
405C4⋊Q8—862no—
406C4⋊Q8—1721no—
407C4×Q8—862no—
408C4×Q8—1721no—
409C4×D4—862no—
410C4×D4—862no—
411C4×D4—862no—
412C4×D4—862no—
413C4×D4—1721no—
414C4×D4—1721no—
415C2×C4⋊C4—431no—
416C2×C4⋊C4—431no—
417C2×C4⋊C4—431no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4—861no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4D17211yescharacteristic
427C2×C4⋊C4D17211yescharacteristic
428C2×C22⋊C4—861no—
429C2×C22⋊C4—861no—
430C2×C22⋊C4—861no—
431C2×C42—861no—
432C2×C42C22×D4311yescharacteristic
433C2×C42C22×D4311yescharacteristic
434C2×C42C22×D4311yescharacteristic
435#107—1721no—
436#106—862no—
437C4⋊C8—22no—
438#103—862no—
439#103—862no—
440#103—862no—
441#103—862no—
442#103—862no—
443#103—1721no—
444#102—862no—
445#102—862no—
446C4×C8—22no—
447#95—861no—
448#95—861no—
449#95—861no—
450#95—861no—
451#95—861no—
452#95—861no—
453#95—861no—
454#95—861no—
455#95—861no—
456#95—861no—
457#95—861no—
458#95D17211yescharacteristic
459#95D17211yescharacteristic
460C24—861no—
461C2×Q8—432no—
462C2×Q8—861no—
463C2×Q8—861no—
464C2×Q8—861no—
465C2×Q8—861no—
466C2×Q8—861no—
467C2×Q8—861no—
468C2×Q8—861no—
469C2×Q8—861no—
470C2×Q8—861no—
471C2×Q8—861no—
472C2×Q8—861no—
473C2×D4—432no—
474C2×D4—432no—
475C2×D4—432no—
476C2×D4—861no—
477C2×D4—861no—
478C2×D4—861no—
479C22×C4—864no—
480C22×C4—861no—
481C22×C4—861no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4—3441no—
488C22×C4—3441no—
489C22×C4—3441no—
490C22×C4—3441no—
491C22×C4—1722no—
492C22×C4—1722no—
493C22×C4—1722no—
494C22×C4—1722no—
495C22×C4C2×D17211yescharacteristic
496C22×C4C2×D17211yescharacteristic
497C22×C4C2×D17211yescharacteristic
498C22×C4C2×D17211yescharacteristic
499C22×C4C2×D17211yescharacteristic
500C22×C4C2×D17211yescharacteristic
501C22×C4C23×D4311yescharacteristic
502SD16—868no—
503SD16—1724no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8D4×D4312yes—
516C4⋊C4—22no—
517C4⋊C4—22no—
518C4⋊C4—432no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—3441no—
529C4⋊C4—3441no—
530C4⋊C4—1722no—
531C4⋊C4—1722no—
532C4⋊C4—1722no—
533C4⋊C4—1722no—
534C22⋊C4—864no—
535C22⋊C4—1722no—
536C22⋊C4—1722no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—1722no—
544C23—862no—
545C23—862no—
546C23—862no—
547C23—1721no—
548C23—1721no—
549C23—1721no—
550C23—1721no—
551C23C22×D17211yescharacteristic
552Q8—862no—
553Q8—862no—
554Q8—1721no—
555Q8—1721no—
556Q8—1721no—
557Q8—1721no—
558Q8—1721no—
559Q8—1721no—
560D4—434no—
561D4—862no—
562D4—862no—
563D4—862no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—862no—
581C2×C4—862no—
582C2×C4—3444no—
583C2×C4—3444no—
584C2×C4—3444no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
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#1306334712yes—
605C2×C4#1306335812yes—
606C2×C4C2×D4×D4311yescharacteristic
607C2×C4#41×D4311yescharacteristic
608C2×C4#41×D4311yescharacteristic
609C2×C4#41×D4311yescharacteristic
610C2×C4#1306337111yescharacteristic
611C2×C4#1306337311yescharacteristic
612C8—22no—
613C8—41no—
614C8—41no—
615C8—41no—
616C22—864no—
617C22—1722no—
618C22—1722no—
619C22—1722no—
620C22—1722no—
621C22—1722no—
622C22—1722no—
623C22#1458341111yescharacteristic
624C22D4×D17211yescharacteristic
625C22#1458356111yescharacteristic
626C22C2×#1306334711yescharacteristic
627C22C2×#1306335811yescharacteristic
628C22#1458371111yescharacteristic
629C22#1458371111yescharacteristic
630C4—22no—
631C4—22no—
632C4—41no—
633C4—41no—
634C4—41no—
635C4—41no—
636C4—3441no—
637C4—3441no—
638C4—3441no—
639C4—3441no—
640C4—3441no—
641C4—1722no—
642C4—1722no—
643C4#123×D4311yescharacteristic
644C4#1458349711yescharacteristic
645C4#1458355111yescharacteristic
646C4#1458360011yescharacteristic
647C2—1724no—
648C2#1913833511yescharacteristic
649C2#1914466711yescharacteristic
650C2#1914484811yescharacteristic
651C2#1914611011yescharacteristic
652C2#1914630711yescharacteristic
653C2#1914724611yescharacteristic
654C2#1914737811yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1916C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#1916D43
hypocenterC43#26170
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1916

Complements

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

NH ≅ G/Ntype
3. #19138371C2semidirect
5. #19136142C2semidirect
6. #19136093C2semidirect
7. #19136015C2semidirect
8. #19135842C2semidirect
9. #19135271C2semidirect
13. #19134852C2semidirect
15. C43×#1916C2semidirect
329. #1916D43semidirect
388. C43#26170semidirect

Maximal subgroups

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

subgroupindex
C2×#145831052
C2×C4×#106218732
#191383712
#191375062
#191361422
#191360932
#191360152
#191358422
#191352712
#191349282
#191348522
#191348452
C43×#19162
#2617043