Finite Group Databasebeta

← #25159649

Subgroups — #25159649

Order 11008.

820 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582984C211yesmaximal, characteristic
2#19138463C211yesmaximal, characteristic
3#19137513C211yesmaximal, characteristic, complemented
4#19136117C211yesmaximal, characteristic
5#19136079C211yesmaximal, characteristic, complemented
6#19135968C211yesmaximal, characteristic
7#19135930C211yesmaximal, characteristic, complemented
8#19135321C211yesmaximal, characteristic, complemented
9#19135149C211yesmaximal, characteristic, complemented
10#19134950C211yesmaximal, characteristic
11#19134948C211yesmaximal, characteristic
12#19134865C211yesmaximal, characteristic, complemented
13#19134847C211yesmaximal, characteristic, complemented
14#19134839C211yesmaximal, characteristic
15C2×C43×#479C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C2×Q8×Dic43C2211yescharacteristic
18C2×Q8×Dic43C2211yescharacteristic
19C2×#13063287C2211yescharacteristic
20#14582984—24no—
21C2×#13063258C2211yescharacteristic
22C2×#13063257C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×C8×Dic43C2211yescharacteristic
29#14582834—21no—
30#14582821—21no—
31#14582801C2211yescharacteristic
32#14582800C2211yescharacteristic
33#14582798C2211yescharacteristic
34#14582797—21no—
35#14582797C2211yescharacteristic
36#14582795—21no—
37#14582795C2211yescharacteristic
38#14582795C2211yescharacteristic
39#14582770—21no—
40#14582764—21no—
41#14582764C2211yescharacteristic
42#14582756—21no—
43C4×Dic43⋊C4—21no—
44C4×Dic43⋊C4C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53C2×#125×C43C2211yescharacteristic
54C2×C4×Q8×C43C2211yescharacteristic
55C43×#479—24no—
56C2×#107×C43C2211yescharacteristic
57C2×#106×C43C2211yescharacteristic
58C2×C4⋊C8×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#103×C43C2211yescharacteristic
61C22×D172C2311yescharacteristic
62C22×C4×D43—21no—
63C2×#10621884—22no—
64C2×#10621884—22no—
65C2×#10621884Q814yes—
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68Q8×Dic43—22no—
69Q8×Dic43—22no—
70Q8×Dic43—22no—
71Q8×Dic43—41no—
72#13063287—22no—
73#13063287—41no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4D411yescharacteristic
84C2×Dic43⋊C4D411yescharacteristic
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43C2311yescharacteristic
93C2×C4×Dic43C2311yescharacteristic
94#13063258—41no—
95#13063257—22no—
96#13063256—22no—
97#13063249—22no—
98#13063247—22no—
99#13063247—22no—
100#13063245—41no—
101C8×Dic43—22no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95D411yescharacteristic
109C43⋊#95D411yescharacteristic
110C22×Q8×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113#125×C43—22no—
114#125×C43—41no—
115C4×Q8×C43—22no—
116C4×Q8×C43—41no—
117C2×C4⋊C4×C43—21no—
118C2×C4⋊C4×C43—21no—
119C2×C4⋊C4×C43—21no—
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C42×C43—21no—
124C2×C42×C43C2311yescharacteristic
125#107×C43—22no—
126#106×C43—22no—
127C4⋊C8×C43—22no—
128#103×C43—22no—
129#103×C43D414yes—
130C23×D43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43C2×D412yes—
135C2×Q8×C43C2×Q812yes—
136C2×Q8×C43#4112yes—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2411yescharacteristic
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43C2×D411yescharacteristic
148C22×Dic43C2×D411yescharacteristic
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151C2×D172—21no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172C2×Q812yes—
157C2×C4×D43—42no—
158C2×C4×D43—42no—
159C2×C4×D43—81no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43C2×D412yes—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—42no—
172C4⋊C4×C43—42no—
173C4⋊C4×C43—42no—
174C4⋊C4×C43C2×D412yes—
175C42×C43—21no—
176C42×C43—21no—
177C42×C43—42no—
178#10621884—28no—
179(C2×D43)⋊C4—42no—
180(C2×D43)⋊C4—42no—
181(C2×D43)⋊C4—81no—
182(C2×D43)⋊C4—81no—
183(C2×D43)⋊C4—81no—
184C4⋊Dic43—24no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—42no—
191C4⋊Dic43—81no—
192C4⋊Dic43#4112yes—
193Dic43⋊C4—22no—
194Dic43⋊C4—41no—
195Dic43⋊C4—42no—
196Dic43⋊C4—42no—
197Dic43⋊C4—81no—
198C4×Dic43—24no—
199C4×Dic43—21no—
200C4×Dic43—21no—
201C4×Dic43—21no—
202C4×Dic43—21no—
203C4×Dic43—42no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8C2×Q812yes—
210C23×C43C22×D411yescharacteristic
211C22×D43—22no—
212C22×D43—41no—
213C22×D43—41no—
214C22×D43—41no—
215C22×D43—41no—
216C22×D43—41no—
217C22×D43—41no—
218Q8×C43—22no—
219Q8×C43—22no—
220Q8×C43—22no—
221Q8×C43C22⋊Q814yes—
222C2×C4×C43—22no—
223C2×C4×C43—22no—
224C2×C4×C43—22no—
225C2×C4×C43—22no—
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—41no—
233C2×C4×C43—41no—
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×C43C22×D411yescharacteristic
241C2×C4×C43C22×Q811yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43H(5,𝔽2)11yescharacteristic
245C2×C4×C432−1+411yescharacteristic
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—22no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
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#13512yes—
267D172—22no—
268D172—22no—
269D172—41no—
270D172—41no—
271C4×D43—84no—
272C8×C43—22no—
273C8×C43—41no—
274C43⋊C8—22no—
275C43⋊C8—41no—
276#26375—431nomaximal, Sylow
277C22×C43#52511yescharacteristic
278C22×C43D4211yescharacteristic
279C22×C43D4×Q811yescharacteristic
280C22×C43C2×#13511yescharacteristic
281C22×C43#57511yescharacteristic
282C22×C43#57711yescharacteristic
283C22×C43#57711yescharacteristic
284C2×D43—42no—
285C2×D43—42no—
286C2×D43—42no—
287C2×D43—81no—
288C2×D43—81no—
289C2×D43—81no—
290C2×D43—81no—
291C4×C43—24no—
292C4×C43—41no—
293C4×C43—42no—
294C4×C43—41no—
295C4×C43—81no—
296C4×C43—81no—
297C4×C43C2×C22⋊Q811yescharacteristic
298C4×C43#53911yescharacteristic
299C4×C43#54711yescharacteristic
300C4×C43#55411yescharacteristic
301Dic43—22no—
302Dic43—41no—
303Dic43—42no—
304Dic43—41no—
305Dic43—41no—
306Dic43—81no—
307Dic43—81no—
308C2×#479D4311yescharacteristic, complemented
309C2×C4×SD16—431no—
310#2454—431no—
311#2351—431no—
312#2092—431no—
313#2085—431no—
314#2065—431no—
315#2059—431no—
316#1941—431no—
317#1916—431no—
318#1880—431no—
319#1880—431no—
320#1865—431no—
321#1863—431no—
322#1862—431no—
323C2×C43#244911yescharacteristic
324C2×C43#310211yescharacteristic
325C2×C43#312611yescharacteristic
326C2×C43#327111yescharacteristic
327C2×C43#328211yescharacteristic
328C2×C43#338111yescharacteristic
329C2×C43#338811yescharacteristic
330D43—82no—
331C22×SD16—431no—
332C2×#125C2×D4311yescharacteristic
333C2×C4×Q8—431no—
334C2×C4×Q8—431no—
335C2×C4×Q8C2×D4311yescharacteristic
336C2×C4×D4—431no—
337#479—24no—
338C4×SD16—864no—
339C2×#107—431no—
340C2×#107C2×D4311yescharacteristic
341C2×#106—431no—
342C2×#106—431no—
343C2×#106C2×D4311yescharacteristic
344C2×C4⋊C8C2×D4311yescharacteristic
345C2×#103—431no—
346C2×#103C2×D4311yescharacteristic
347C2×#103C2×D4311yescharacteristic
348C2×#102—431no—
349C2×#102—431no—
350C2×#102—431no—
351C2×C4×C8—431no—
352#399—861no—
353#396—861no—
354#390—431no—
355#390—431no—
356#389—431no—
357#389—431no—
358#389—431no—
359#389—431no—
360#389—861no—
361#389—861no—
362#385—861no—
363#382—431no—
364#382—861no—
365#380—861no—
366C4×C4⋊C4—431no—
367C4×C4⋊C4—861no—
368#340—431no—
369#340—431no—
370#340—431no—
371#340—431no—
372#336—431no—
373#336—431no—
374#336—431no—
375#336—431no—
376C43#2637511yescharacteristic, complemented, Sylow
377C22×Q8C22×D4311yescharacteristic
378C22×D4—431no—
379C23×C4—861no—
380C2×SD16—434no—
381C2×SD16—862no—
382C2×SD16—862no—
383C22×C8—431no—
384C22×C8—431no—
385C22×C8C22×D4311yescharacteristic
386C22×C8C22×D4311yescharacteristic
387#125—22no—
388#125—41no—
389C4×Q8—22no—
390C4×Q8—41no—
391C4×Q8—862no—
392C4×Q8—862no—
393C4×Q8—862no—
394C4×Q8—1721no—
395C4×D4—862no—
396C4×D4—1721no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
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⋊C4C22×D4311yescharacteristic
412C2×C4⋊C4C22×D4311yescharacteristic
413C2×C4⋊C4C22×D4311yescharacteristic
414C2×C22⋊C4—861no—
415C2×C22⋊C4—861no—
416C2×C22⋊C4—861no—
417C2×C22⋊C4—861no—
418C2×C22⋊C4—861no—
419C2×C42—21no—
420C2×C42—431no—
421C2×C42—431no—
422C2×C42—861no—
423C2×C42—861no—
424C2×C42C22×D4311yescharacteristic
425#107—22no—
426#107—1721no—
427#106—22no—
428#106—862no—
429#106—862no—
430C4⋊C8—22no—
431#103—22no—
432#103—862no—
433#103C22⋊D4314yes—
434#102—862no—
435#102—862no—
436#102—1721no—
437C4×C8—862no—
438#95—431no—
439#95—431no—
440#95—861no—
441#95—861no—
442#95—861no—
443#95—861no—
444#95—861no—
445#95—861no—
446C24—861no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8Q8×D4312yes—
451C2×Q8#1062190212yes—
452C2×Q8C2×C22⋊D4312yes—
453C2×D4—432no—
454C2×D4—861no—
455C2×D4—861no—
456C2×D4—861no—
457C2×D4—861no—
458C2×D4—861no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—431no—
464C22×C4—431no—
465C22×C4—431no—
466C22×C4—431no—
467C22×C4—861no—
468C22×C4—861no—
469C22×C4—861no—
470C22×C4—3441no—
471C22×C4—1722no—
472C22×C4—1722no—
473C22×C4D4×D4311yescharacteristic
474C22×C4D4×D4311yescharacteristic
475C22×C4C23×D4311yescharacteristic
476SD16—868no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—432no—
483C2×C8—861no—
484C2×C8—861no—
485C2×C8—861no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8C2×C22⋊D4312yes—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—42no—
495C4⋊C4—42no—
496C4⋊C4—42no—
497C4⋊C4—432no—
498C4⋊C4—862no—
499C4⋊C4—864no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4—3441no—
506C4⋊C4—3441no—
507C4⋊C4—1721no—
508C4⋊C4—1722no—
509C4⋊C4—1722no—
510C4⋊C4—1722no—
511C4⋊C4C2×C22⋊D4312yes—
512C22⋊C4—3441no—
513C22⋊C4—3441no—
514C22⋊C4—3441no—
515C22⋊C4—1722no—
516C22⋊C4—1722no—
517C42—21no—
518C42—21no—
519C42—42no—
520C42—864no—
521C42—861no—
522C42—861no—
523C42—861no—
524C42—861no—
525C42—1722no—
526C23—862no—
527C23—1721no—
528C23—1721no—
529C23—1721no—
530C23—1721no—
531C23—1721no—
532C23—1721no—
533C23C2×D4×D4311yescharacteristic
534Q8—22no—
535Q8—22no—
536Q8—22no—
537Q8#1306330114yes—
538D4—862no—
539D4—862no—
540D4—1721no—
541D4—1721no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—432no—
561C2×C4—861no—
562C2×C4—861no—
563C2×C4—861no—
564C2×C4—862no—
565C2×C4—861no—
566C2×C4—861no—
567C2×C4—861no—
568C2×C4—861no—
569C2×C4—861no—
570C2×C4—861no—
571C2×C4—861no—
572C2×C4—861no—
573C2×C4—3444no—
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×C4C22×C22⋊D4311yescharacteristic
583C2×C4C2×Q8×D4311yescharacteristic
584C2×C4#41×D4311yescharacteristic
585C2×C4C2×#1062190211yescharacteristic
586C2×C4#1306337011yescharacteristic
587C2×C4#1306337211yescharacteristic
588C8—22no—
589C8—41no—
590C8—862no—
591C8—1721no—
592C22—3441no—
593C22—3441no—
594C22—3441no—
595C22—3441no—
596C22—1722no—
597C22—1722no—
598C22—1722no—
599C22#1458341211yescharacteristic
600C22D4×C22⋊D4311yescharacteristic
601C22#1458356211yescharacteristic
602C22#135×D4311yescharacteristic
603C22#1458369811yescharacteristic
604C22#1458370611yescharacteristic
605C22#1458370811yescharacteristic
606C4—24no—
607C4—41no—
608C4—42no—
609C4—41no—
610C4—81no—
611C4—81no—
612C4—862no—
613C4—3441no—
614C4—3441no—
615C4—1721no—
616C4—1722no—
617C4—1721no—
618C4—1721no—
619C4C2×#1306330111yescharacteristic
620C4#1458349811yescharacteristic
621C4#1458354811yescharacteristic
622C4#1458360311yescharacteristic
623C2—3442no—
624C2#1913840011yescharacteristic
625C2#1914462011yescharacteristic
626C2#1914488811yescharacteristic
627C2#1914617411yescharacteristic
628C2#1914629611yescharacteristic
629C2#1914747311yescharacteristic
630C2#1914754311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#479C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenterC2×#479D43
hypocenterC43#26375
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
3. #19137513C2semidirect
5. #19136079C2semidirect
7. #19135930C2semidirect
8. #19135321C2semidirect
9. #19135149C2semidirect
12. #19134865C2semidirect
13. #19134847C2semidirect
15. C2×C43×#479C2semidirect
308. C2×#479D43semidirect
376. C43#26375semidirect

Maximal subgroups

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

subgroupindex
C2×#145829842
#191384632
#191375132
#191361172
#191360792
#191359682
#191359302
#191353212
#191351492
#191349502
#191349482
#191348652
#191348472
#191348392
C2×C43×#4792
#2637543