Finite Group Databasebeta

← #25159703

Subgroups — #25159703

Order 11008.

848 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583200C211yesmaximal, characteristic
2C2×C4×#10621873C211yesmaximal, characteristic
3#19138456C211yesmaximal, characteristic, complemented
4#19137506C211yesmaximal, characteristic
5#19136142C211yesmaximal, characteristic, complemented
6#19136078C211yesmaximal, characteristic, complemented
7#19135975C211yesmaximal, characteristic, complemented
8#19135934C211yesmaximal, characteristic, complemented
9#19135323C211yesmaximal, characteristic, complemented
10#19134928C211yesmaximal, characteristic
11#19134928C211yesmaximal, characteristic
12#19134859C211yesmaximal, characteristic
13#19134852C211yesmaximal, characteristic, complemented
14#19134845C211yesmaximal, characteristic
15C43×#1916C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C2×#13063317C2211yescharacteristic
18C2×C4×Dic86C2211yescharacteristic
19C2×C4×D172C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C2×C4×D172C2211yescharacteristic
22#14583200—24no—
23C4×#10621873—24no—
24C2×#13063259C2211yescharacteristic
25C2×#13063259C2211yescharacteristic
26C2×#13063257C2211yescharacteristic
27C2×#13063257C2211yescharacteristic
28C2×#13063257C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063250C2211yescharacteristic
32C2×#13063247C2211yescharacteristic
33C2×#13063247C2211yescharacteristic
34C2×#13063247C2211yescharacteristic
35#14582840—21no—
36#14582830—21no—
37#14582805C2211yescharacteristic
38#14582805C2211yescharacteristic
39#14582797C2211yescharacteristic
40#14582797C2211yescharacteristic
41#14582797C2211yescharacteristic
42#14582797C2211yescharacteristic
43#14582794—21no—
44#14582781—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×D172C2311yescharacteristic
63C22×C4×D43—21no—
64C22×C4×D43—21no—
65C22×C4×D43—21no—
66C2×#10621873—22no—
67C2×#10621873—22no—
68C2×#10621873Q814yes—
69#13063317—22no—
70#13063317—41no—
71C4×Dic86—22no—
72C4×Dic86—41no—
73C4×D172—22no—
74C4×D172—22no—
75C4×D172—22no—
76C4×D172—22no—
77C4×D172—41no—
78C4×D172—41no—
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×C4×Dic43—21no—
96#13063259—22no—
97#13063259—41no—
98#13063257—22no—
99#13063257—22no—
100#13063257—22no—
101#13063250—22no—
102#13063250—22no—
103#13063250—41no—
104#13063247—22no—
105#13063247—22no—
106#13063247D414yes—
107C43⋊#95—21no—
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—
117C22×C8×C43C2311yescharacteristic
118C22×C8×C43C2311yescharacteristic
119C22×C8×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121C2×C4⋊C4×C43D411yescharacteristic
122C2×C4⋊C4×C43D411yescharacteristic
123C2×C42×C43C2311yescharacteristic
124C2×C42×C43C2311yescharacteristic
125C2×C42×C43C2311yescharacteristic
126C4⋊C8×C43—22no—
127C4×C8×C43—22no—
128#95×C43D411yescharacteristic
129#95×C43D411yescharacteristic
130C23×D43—21no—
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2411yescharacteristic
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C2×D172—21no—
146C2×D172—21no—
147C2×D172—21no—
148C2×D172C2×D412yes—
149C2×D172C2×Q812yes—
150C2×D172#4112yes—
151C2×C4×D43—24no—
152C2×C4×D43—42no—
153C2×C4×D43—42no—
154C2×C4×D43—42no—
155C2×C4×D43—42no—
156C2×C4×D43—81no—
157C2×C4×D43—81no—
158C2×C4×D43—81no—
159C2×C4×D43—81no—
160C2×Dic86—21no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86C2×Q812yes—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43C2×D412yes—
177C2×C8×C43C2×Q812yes—
178C4⋊C4×C43—22no—
179C4⋊C4×C43—41no—
180C42×C43—21no—
181C42×C43—21no—
182C42×C43—21no—
183C42×C43—21no—
184C42×C43—21no—
185C42×C43—21no—
186(C2×D43)⋊C4—24no—
187(C2×D43)⋊C4—42no—
188(C2×D43)⋊C4—42no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43C2×D412yes—
200C4⋊Dic43#4112yes—
201Dic43⋊C4—42no—
202Dic43⋊C4—42no—
203Dic43⋊C4—42no—
204Dic43⋊C4—42no—
205Dic43⋊C4—42no—
206Dic43⋊C4—81no—
207Dic43⋊C4—81no—
208C4×Dic43—42no—
209#10621873—28no—
210C23×C43C22×D411yescharacteristic
211C22×D43—22no—
212C22×D43—22no—
213C22×D43—22no—
214C22×D43—41no—
215C22×D43—41no—
216C22×D43—41no—
217C22×D43—41no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
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#13512yes—
236C2×C4×C43C22×D411yescharacteristic
237C2×C4×C43C22×Q811yescharacteristic
238C2×C4×C43C2×#4111yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C2×C4×C43H(5,𝔽2)11yescharacteristic
241C2×C4×C432−1+411yescharacteristic
242C2×Dic43—22no—
243C2×Dic43—22no—
244C2×Dic43—22no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
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—
263D172—22no—
264D172—22no—
265D172—22no—
266D172C22⋊Q814yes—
267C4×D43—84no—
268C4×D43—84no—
269C4×D43—84no—
270Dic86—22no—
271Dic86—22no—
272Dic86—41no—
273Dic86—41no—
274C8×C43—22no—
275C8×C43—22no—
276C8×C43—41no—
277C8×C43—41no—
278#26378—431nomaximal, Sylow
279C22×C43#52511yescharacteristic
280C22×C43D4211yescharacteristic
281C22×C43D4×Q811yescharacteristic
282C22×C43C2×#13511yescharacteristic
283C22×C43#57511yescharacteristic
284C22×C43#57711yescharacteristic
285C22×C43#57711yescharacteristic
286C2×D43—24no—
287C2×D43—42no—
288C2×D43—42no—
289C2×D43—42no—
290C2×D43—42no—
291C2×D43—42no—
292C2×D43—42no—
293C4×C43—22no—
294C4×C43—41no—
295C4×C43—41no—
296C4×C43—41no—
297C4×C43—41no—
298C4×C43—41no—
299C4×C43C2×C22⋊Q811yescharacteristic
300C4×C43#53911yescharacteristic
301C4×C43#54711yescharacteristic
302C4×C43#55411yescharacteristic
303Dic43—42no—
304Dic43—42no—
305Dic43—42no—
306Dic43—81no—
307Dic43—81no—
308Dic43—81no—
309Dic43—81no—
310C2×#478—431no—
311C2×C4×SD16—431no—
312#2453—431no—
313#2349—431no—
314#2097—431no—
315#2085—431no—
316#2066—431no—
317#2059—431no—
318#1941—431no—
319#1916D4311yescharacteristic, complemented
320#1877—431no—
321#1877—431no—
322#1864—431no—
323#1863—431no—
324#1862—431no—
325C2×C43#244911yescharacteristic
326C2×C43#310211yescharacteristic
327C2×C43#312311yescharacteristic
328C2×C43#326711yescharacteristic
329C2×C43#328211yescharacteristic
330C2×C43#338111yescharacteristic
331C2×C43#338811yescharacteristic
332D43—44no—
333C22×SD16—431no—
334C2×#125—431no—
335C2×C4×Q8—431no—
336C2×C4×D4—431no—
337C2×C4×D4—431no—
338C2×C4×D4—431no—
339#478—864no—
340C4×SD16—864no—
341C2×#107—431no—
342C2×#107—431no—
343C2×#106—431no—
344C2×#106—431no—
345C2×#106—431no—
346C2×C4⋊C8C2×D4311yescharacteristic
347C2×#103—431no—
348C2×#103—431no—
349C2×#103—431no—
350C2×#102—431no—
351C2×#102—431no—
352C2×#102—431no—
353C2×C4×C8C2×D4311yescharacteristic
354#400—861no—
355#398—861no—
356#391—431no—
357#391—431no—
358#389—431no—
359#389—431no—
360#389—431no—
361#389—431no—
362#389—861no—
363#387—861no—
364#385—861no—
365#385—861no—
366#382—431no—
367#380—861no—
368C4×C4⋊C4C2×D4311yescharacteristic
369C2×#95—861no—
370#340—431no—
371#340—431no—
372#340—431no—
373#340—431no—
374#336C2×D4311yescharacteristic
375#336C2×D4311yescharacteristic
376#336C2×D4311yescharacteristic
377#336C2×D4311yescharacteristic
378C43#2637811yescharacteristic, complemented, Sylow
379C22×Q8—431no—
380C22×D4—431no—
381C23×C4—861no—
382C23×C4—861no—
383C23×C4—861no—
384C2×SD16—434no—
385C2×SD16—862no—
386C2×SD16—862no—
387C22×C8C22×D4311yescharacteristic
388C22×C8C22×D4311yescharacteristic
389C22×C8C22×D4311yescharacteristic
390C22×C8C22×D4311yescharacteristic
391#125—862no—
392#125—1721no—
393C4×Q8—862no—
394C4×Q8—1721no—
395C4×D4—862no—
396C4×D4—862no—
397C4×D4—862no—
398C4×D4—862no—
399C4×D4—1721no—
400C4×D4—1721no—
401C2×C4⋊C4—431no—
402C2×C4⋊C4—431no—
403C2×C4⋊C4—431no—
404C2×C4⋊C4—431no—
405C2×C4⋊C4—431no—
406C2×C4⋊C4—431no—
407C2×C4⋊C4—861no—
408C2×C4⋊C4—861no—
409C2×C4⋊C4—861no—
410C2×C4⋊C4—861no—
411C2×C4⋊C4—861no—
412C2×C4⋊C4—861no—
413C2×C4⋊C4—861no—
414C2×C4⋊C4D17211yescharacteristic
415C2×C4⋊C4D17211yescharacteristic
416C2×C22⋊C4—861no—
417C2×C22⋊C4—861no—
418C2×C22⋊C4—861no—
419C2×C42—861no—
420C2×C42C22×D4311yescharacteristic
421C2×C42C22×D4311yescharacteristic
422C2×C42C22×D4311yescharacteristic
423#107—862no—
424#107—1721no—
425#106—862no—
426#106—862no—
427#106—862no—
428C4⋊C8—22no—
429#103—862no—
430#103—862no—
431#103—1721no—
432#102—434no—
433#102—862no—
434#102—862no—
435C4×C8—22no—
436#95—861no—
437#95—861no—
438#95—861no—
439#95—861no—
440#95—861no—
441#95—861no—
442#95—861no—
443#95—861no—
444#95—861no—
445#95—861no—
446#95D17211yescharacteristic
447#95D17211yescharacteristic
448C24—861no—
449C2×Q8—432no—
450C2×Q8—861no—
451C2×Q8—861no—
452C2×Q8—861no—
453C2×Q8—861no—
454C2×Q8—861no—
455C2×D4—432no—
456C2×D4—432no—
457C2×D4—432no—
458C2×D4—861no—
459C2×D4—861no—
460C2×D4—861no—
461C22×C4—864no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—861no—
466C22×C4—861no—
467C22×C4—861no—
468C22×C4—861no—
469C22×C4—3441no—
470C22×C4—3441no—
471C22×C4—3441no—
472C22×C4—3441no—
473C22×C4—1722no—
474C22×C4—1722no—
475C22×C4—1722no—
476C22×C4—1722no—
477C22×C4C2×D17211yescharacteristic
478C22×C4C2×D17211yescharacteristic
479C22×C4C2×D17211yescharacteristic
480C22×C4C2×D17211yescharacteristic
481C22×C4C2×D17211yescharacteristic
482C22×C4C2×D17211yescharacteristic
483C22×C4C23×D4311yescharacteristic
484SD16—868no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8D4×D4312yes—
496C2×C8Q8×D4312yes—
497C4⋊C4—22no—
498C4⋊C4—41no—
499C4⋊C4—432no—
500C4⋊C4—432no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4—861no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C4⋊C4—861no—
509C4⋊C4—861no—
510C4⋊C4—861no—
511C4⋊C4—3441no—
512C4⋊C4—3441no—
513C4⋊C4—1722no—
514C4⋊C4—1722no—
515C4⋊C4—1722no—
516C4⋊C4—1722no—
517C4⋊C4—1722no—
518C22⋊C4—864no—
519C22⋊C4—1722no—
520C22⋊C4—1722no—
521C42—21no—
522C42—21no—
523C42—21no—
524C42—21no—
525C42—21no—
526C42—21no—
527C42—1722no—
528C23—862no—
529C23—862no—
530C23—862no—
531C23—1721no—
532C23—1721no—
533C23—1721no—
534C23—1721no—
535C23C22×D17211yescharacteristic
536Q8—862no—
537Q8—862no—
538Q8—1721no—
539Q8—1721no—
540D4—434no—
541D4—862no—
542D4—862no—
543D4—862no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—862no—
562C2×C4—862no—
563C2×C4—862no—
564C2×C4—3444no—
565C2×C4—3444no—
566C2×C4—3444no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4—1721no—
578C2×C4—1721no—
579C2×C4—1721no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4#1306334712yes—
586C2×C4C2×D4×D4311yescharacteristic
587C2×C4C2×Q8×D4311yescharacteristic
588C2×C4#41×D4311yescharacteristic
589C2×C4#41×D4311yescharacteristic
590C2×C4#1306337111yescharacteristic
591C2×C4#1306337211yescharacteristic
592C8—22no—
593C8—22no—
594C8—41no—
595C8—41no—
596C22—864no—
597C22—1722no—
598C22—1722no—
599C22—1722no—
600C22—1722no—
601C22—1722no—
602C22—1722no—
603C22#1458341111yescharacteristic
604C22D4×D17211yescharacteristic
605C22Q8×D17211yescharacteristic
606C22C2×#1306334711yescharacteristic
607C22#1458369911yescharacteristic
608C22#1458371111yescharacteristic
609C22#1458371111yescharacteristic
610C4—22no—
611C4—41no—
612C4—41no—
613C4—41no—
614C4—41no—
615C4—41no—
616C4—3441no—
617C4—3441no—
618C4—3441no—
619C4—3441no—
620C4—1722no—
621C4—1722no—
622C4—1722no—
623C4C22⋊Q8×D4311yescharacteristic
624C4#1458349011yescharacteristic
625C4#1458354711yescharacteristic
626C4#1458360511yescharacteristic
627C2—1724no—
628C2#1913840911yescharacteristic
629C2#1914461511yescharacteristic
630C2#1914484811yescharacteristic
631C2#1914612511yescharacteristic
632C2#1914630711yescharacteristic
633C2#1914747211yescharacteristic
634C2#1914754211yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1916C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#1916D43
hypocenterC43#26378
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. #19138456C2semidirect
5. #19136142C2semidirect
6. #19136078C2semidirect
7. #19135975C2semidirect
8. #19135934C2semidirect
9. #19135323C2semidirect
13. #19134852C2semidirect
15. C43×#1916C2semidirect
319. #1916D43semidirect
378. C43#26378semidirect

Maximal subgroups

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

subgroupindex
C2×#145832002
C2×C4×#106218732
#191384562
#191375062
#191361422
#191360782
#191359752
#191359342
#191353232
#191349282
#191348592
#191348522
#191348452
C43×#19162
#2637843