Finite Group Databasebeta

← #25159718

Subgroups — #25159718

Order 11008.

828 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×#14583207C211yesmaximal, characteristic, complemented
2C2×C4×#10621873C211yesmaximal, characteristic
3#19138467C211yesmaximal, characteristic
4C4⋊C4×Dic86C211yesmaximal, characteristic, complemented
5#19136122C211yesmaximal, characteristic
6#19136073C211yesmaximal, characteristic, complemented
7#19135982C211yesmaximal, characteristic
8#19135934C211yesmaximal, characteristic, complemented
9#19135328C211yesmaximal, characteristic, complemented
10#19134949C211yesmaximal, characteristic
11#19134949C211yesmaximal, characteristic
12#19134859C211yesmaximal, characteristic
13#19134852C211yesmaximal, characteristic, complemented
14#19134852C211yesmaximal, characteristic, complemented
15C43×#1916C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C2×#13063317C2211yescharacteristic
18C2×C4×Dic86C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20C2×C4×Dic86C2211yescharacteristic
21C2×C4×D172C2211yescharacteristic
22#14583207—24no—
23C4×#10621873—24no—
24C2×#13063259C2211yescharacteristic
25C2×#13063259C2211yescharacteristic
26C2×#13063259C2211yescharacteristic
27C2×#13063257C2211yescharacteristic
28C2×#13063257C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063250C2211yescharacteristic
32C2×#13063247C2211yescharacteristic
33C2×#13063247C2211yescharacteristic
34C2×#13063247C2211yescharacteristic
35#14582834—21no—
36#14582823—21no—
37#14582801C2211yescharacteristic
38#14582801C2211yescharacteristic
39#14582797C2211yescharacteristic
40#14582797C2211yescharacteristic
41#14582797C2211yescharacteristic
42#14582797C2211yescharacteristic
43#14582796—21no—
44#14582796—21no—
45#14582770—21no—
46#14582769C2211yescharacteristic
47#14582768—21no—
48#14582758—21no—
49C4⋊C4×Dic43—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—
64C2×#10621873—22no—
65C2×#10621873—22no—
66C2×#10621873Q814yes—
67#13063317—22no—
68#13063317—41no—
69C4×Dic86—22no—
70C4×Dic86—22no—
71C4×Dic86—22no—
72C4×Dic86—22no—
73C4×Dic86—41no—
74C4×Dic86—41no—
75C4×D172—22no—
76C4×D172—41no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43—21no—
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×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×C4×Dic43—21no—
100C2×C4×Dic43—21no—
101C2×C4×Dic43—21no—
102#13063259—22no—
103#13063259—22no—
104#13063259—41no—
105#13063257—22no—
106#13063257—22no—
107#13063250—22no—
108#13063250—22no—
109#13063250D414yes—
110#13063247—22no—
111#13063247—22no—
112#13063247—41no—
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×D172—21no—
149C2×D172—21no—
150C2×D172C2×Q812yes—
151C2×C4×D43—42no—
152C2×C4×D43—42no—
153C2×C4×D43—81no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86C2×D412yes—
158C2×Dic86C2×Q812yes—
159C2×Dic86#4112yes—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43C2×D412yes—
171C2×C8×C43C2×Q812yes—
172C4⋊C4×C43—22no—
173C4⋊C4×C43—22no—
174C42×C43—21no—
175C42×C43—21no—
176C42×C43—21no—
177C42×C43—21no—
178C42×C43—21no—
179C42×C43—21no—
180(C2×D43)⋊C4—42no—
181(C2×D43)⋊C4—42no—
182(C2×D43)⋊C4—81no—
183(C2×D43)⋊C4—81no—
184(C2×D43)⋊C4—81no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—42no—
196C4⋊Dic43—81no—
197C4⋊Dic43C2×D412yes—
198C4⋊Dic43#4112yes—
199Dic43⋊C4—24no—
200Dic43⋊C4—42no—
201Dic43⋊C4—42no—
202Dic43⋊C4—42no—
203Dic43⋊C4—42no—
204Dic43⋊C4—81no—
205Dic43⋊C4—81no—
206Dic43⋊C4—81no—
207Dic43⋊C4—81no—
208C4×Dic43—24no—
209C4×Dic43—42no—
210C4×Dic43—42no—
211#10621873—28no—
212C23×C43C22×D411yescharacteristic
213C22×D43—22no—
214C22×D43—41no—
215C22×D43—41no—
216C22×D43—41no—
217C22×D43—41no—
218C22×D43—41no—
219C22×D43—41no—
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—21no—
236C2×C4×C43#13512yes—
237C2×C4×C43#13712yes—
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C43C22×Q811yescharacteristic
240C2×C4×C43C2×#4111yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C2×C4×C43H(5,𝔽2)11yescharacteristic
243C2×C4×C432−1+411yescharacteristic
244C2×Dic43—22no—
245C2×Dic43—22no—
246C2×Dic43—22no—
247C2×Dic43—22no—
248C2×Dic43—22no—
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—
263C2×Dic43—41no—
264C2×Dic43—41no—
265D172—22no—
266D172—22no—
267D172—41no—
268D172—41no—
269C4×D43—84no—
270Dic86—22no—
271Dic86—22no—
272Dic86—22no—
273Dic86C22⋊Q814yes—
274C8×C43—22no—
275C8×C43—22no—
276C8×C43—41no—
277C8×C43—41no—
278#26379—431nomaximal, Sylow
279C22×C43#52511yescharacteristic
280C22×C43D4211yescharacteristic
281C22×C43D4×Q811yescharacteristic
282C22×C43C2×#13511yescharacteristic
283C22×C43C2×#13711yescharacteristic
284C22×C43#57611yescharacteristic
285C22×C43#57711yescharacteristic
286C2×D43—42no—
287C2×D43—42no—
288C2×D43—42no—
289C2×D43—81no—
290C2×D43—81no—
291C2×D43—81no—
292C2×D43—81no—
293C4×C43—22no—
294C4×C43—22no—
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—24no—
304Dic43—42no—
305Dic43—42no—
306Dic43—81no—
307Dic43—81no—
308Dic43—81no—
309Dic43—81no—
310C2×#479—431no—
311C2×C4×SD16—431no—
312#2454—431no—
313Q8×C4⋊C4—431no—
314#2093—431no—
315#2084—431no—
316#2067—431no—
317#2059—431no—
318#1942—431no—
319#1916D4311yescharacteristic, complemented
320#1880—431no—
321#1880—431no—
322#1864—431no—
323#1863—431no—
324#1863—431no—
325C2×C43#244911yescharacteristic
326C2×C43#310811yescharacteristic
327C2×C43#311911yescharacteristic
328C2×C43#326611yescharacteristic
329C2×C43#328711yescharacteristic
330C2×C43#338111yescharacteristic
331C2×C43#338511yescharacteristic
332D43—82no—
333C22×SD16—431no—
334C2×#125—431no—
335C2×C4×Q8—431no—
336C2×C4×Q8—431no—
337C2×C4×Q8—431no—
338C2×C4×D4—431no—
339#479—864no—
340C4×SD16—864no—
341C2×#107—431no—
342C2×#107—431no—
343C2×#107—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#399—861no—
355#396—861no—
356#390—431no—
357#390—431no—
358#389—431no—
359#389—431no—
360#389—431no—
361#389—431no—
362#389—861no—
363#389—861no—
364#385—861no—
365#384—431no—
366#384—861no—
367#380—861no—
368C4×C4⋊C4—861no—
369C4×C4⋊C4C2×D4311yescharacteristic
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#2637911yescharacteristic, complemented, Sylow
379C22×Q8—431no—
380C22×D4—431no—
381C23×C4—861no—
382C2×SD16—434no—
383C2×SD16—862no—
384C2×SD16—862no—
385C22×C8C22×D4311yescharacteristic
386C22×C8C22×D4311yescharacteristic
387C22×C8C22×D4311yescharacteristic
388C22×C8C22×D4311yescharacteristic
389#125—862no—
390#125—1721no—
391C4×Q8—862no—
392C4×Q8—862no—
393C4×Q8—862no—
394C4×Q8—862no—
395C4×Q8—1721no—
396C4×Q8—1721no—
397C4×D4—862no—
398C4×D4—1721no—
399C2×C4⋊C4—431no—
400C2×C4⋊C4—431no—
401C2×C4⋊C4—431no—
402C2×C4⋊C4—431no—
403C2×C4⋊C4—431no—
404C2×C4⋊C4—431no—
405C2×C4⋊C4—861no—
406C2×C4⋊C4—861no—
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⋊C4—861no—
415C2×C4⋊C4—861no—
416C2×C4⋊C4D17211yescharacteristic
417C2×C4⋊C4D17211yescharacteristic
418C2×C22⋊C4—861no—
419C2×C22⋊C4—861no—
420C2×C22⋊C4—861no—
421C2×C22⋊C4—861no—
422C2×C22⋊C4—861no—
423C2×C42—861no—
424C2×C42—861no—
425C2×C42—861no—
426C2×C42C22×D4311yescharacteristic
427C2×C42C22×D4311yescharacteristic
428C2×C42C22×D4311yescharacteristic
429#107—862no—
430#107—862no—
431#107—1721no—
432#106—862no—
433#106—862no—
434C4⋊C8—22no—
435#103—434no—
436#103—862no—
437#103—862no—
438#102—862no—
439#102—862no—
440#102—1721no—
441C4×C8—22no—
442#95—861no—
443#95—861no—
444#95—861no—
445#95—861no—
446#95D17211yescharacteristic
447#95D17211yescharacteristic
448C24—861no—
449C2×Q8—432no—
450C2×Q8—432no—
451C2×Q8—432no—
452C2×Q8—861no—
453C2×Q8—861no—
454C2×Q8—861no—
455C2×D4—432no—
456C2×D4—861no—
457C2×D4—861no—
458C2×D4—861no—
459C2×D4—861no—
460C2×D4—861no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—861no—
466C22×C4—861no—
467C22×C4—861no—
468C22×C4—3441no—
469C22×C4—1722no—
470C22×C4—1722no—
471C22×C4C2×D17211yescharacteristic
472C22×C4C2×D17211yescharacteristic
473C22×C4C2×D17211yescharacteristic
474C22×C4C2×D17211yescharacteristic
475C22×C4C2×D17211yescharacteristic
476C22×C4C2×D17211yescharacteristic
477C22×C4C23×D4311yescharacteristic
478SD16—868no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8D4×D4312yes—
490C2×C8Q8×D4312yes—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—432no—
494C4⋊C4—432no—
495C4⋊C4—864no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4—861no—
506C4⋊C4—3441no—
507C4⋊C4—3441no—
508C4⋊C4—3441no—
509C4⋊C4—3441no—
510C4⋊C4—3441no—
511C4⋊C4—1722no—
512C4⋊C4—1722no—
513C4⋊C4—1722no—
514C4⋊C4—1722no—
515C4⋊C4—1722no—
516C22⋊C4—3441no—
517C22⋊C4—3441no—
518C22⋊C4—3441no—
519C22⋊C4—1722no—
520C22⋊C4—1722no—
521C42—21no—
522C42—21no—
523C42—21no—
524C42—21no—
525C42—21no—
526C42—21no—
527C42—864no—
528C42—1722no—
529C42—1722no—
530C23—862no—
531C23—1721no—
532C23—1721no—
533C23—1721no—
534C23—1721no—
535C23—1721no—
536C23—1721no—
537C23C22×D17211yescharacteristic
538Q8—434no—
539Q8—862no—
540Q8—862no—
541Q8—862no—
542D4—862no—
543D4—862no—
544D4—1721no—
545D4—1721no—
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—21no—
562C2×C4—862no—
563C2×C4—862no—
564C2×C4—862no—
565C2×C4—862no—
566C2×C4—862no—
567C2×C4—3444no—
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#1306334712yes—
585C2×C4#1306335812yes—
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—3441no—
597C22—3441no—
598C22—3441no—
599C22—3441no—
600C22—1722no—
601C22—1722no—
602C22—1722no—
603C22#1458341111yescharacteristic
604C22D4×D17211yescharacteristic
605C22Q8×D17211yescharacteristic
606C22C2×#1306334711yescharacteristic
607C22C2×#1306335811yescharacteristic
608C22#1458370411yescharacteristic
609C22#1458371111yescharacteristic
610C4—22no—
611C4—22no—
612C4—41no—
613C4—41no—
614C4—41no—
615C4—41no—
616C4—864no—
617C4—3441no—
618C4—3441no—
619C4—3441no—
620C4—3441no—
621C4—1722no—
622C4—1722no—
623C4C22⋊Q8×D4311yescharacteristic
624C4#1458349011yescharacteristic
625C4#1458354711yescharacteristic
626C4#1458360511yescharacteristic
627C2—3442no—
628C2#1913840911yescharacteristic
629C2#1914467711yescharacteristic
630C2#1914479611yescharacteristic
631C2#1914611011yescharacteristic
632C2#1914635511yescharacteristic
633C2#1914747211yescharacteristic
634C2#1914750711yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1916C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#1916D43
hypocenterC43#26379
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
1. C2×#14583207C2semidirect
4. C4⋊C4×Dic86C2semidirect
6. #19136073C2semidirect
8. #19135934C2semidirect
9. #19135328C2semidirect
13. #19134852C2semidirect
14. #19134852C2semidirect
15. C43×#1916C2semidirect
319. #1916D43semidirect
378. C43#26379semidirect

Maximal subgroups

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

subgroupindex
C2×#145832072
C2×C4×#106218732
#191384672
C4⋊C4×Dic862
#191361222
#191360732
#191359822
#191359342
#191353282
#191349492
#191348592
#191348522
C43×#19162
#2637943