Finite Group Databasebeta

← #25118628

Subgroups — #25118628

Order 11008.

850 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583178C211yesmaximal, characteristic
2#19137682C211yesmaximal, characteristic, complemented
3#19137504C211yesmaximal, characteristic
4#19135566C211yesmaximal, characteristic, complemented
5#19135366C211yesmaximal, characteristic, complemented
6#19135330C211yesmaximal, characteristic, complemented
7#19135329C211yesmaximal, characteristic, complemented
8#19135190C211yesmaximal, characteristic, complemented
9#19134857C211yesmaximal, characteristic
10#19134845C211yesmaximal, characteristic
11#19134468C211yesmaximal, characteristic, complemented
12#19134423C211yesmaximal, characteristic
13#19134419C211yesmaximal, characteristic
14#19134409C211yesmaximal, characteristic
15C43×#1918C211yesmaximal, characteristic, complemented
16C2×#13063324C2211yescharacteristic
17C2×C4×D172C2211yescharacteristic
18C2×#13063287C2211yescharacteristic
19C2×#13063287C2211yescharacteristic
20#14583178C418yescomplemented
21C2×#13063259C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×Dic43⋊C8C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063236C2211yescharacteristic
30C2×#13063235C2211yescharacteristic
31C2×C8×Dic43C2211yescharacteristic
32#14582805—21no—
33#14582803—21no—
34#14582798C2211yescharacteristic
35#14582798C2211yescharacteristic
36#14582797C2211yescharacteristic
37#14582796—21no—
38#14582773—21no—
39#14582770—21no—
40#14582764C2211yescharacteristic
41#14582756—21no—
42C4⋊C4×Dic43C2211yescharacteristic
43C4⋊C4×Dic43C2211yescharacteristic
44C4×Dic43⋊C4—21no—
45C4×Dic43⋊C4C2211yescharacteristic
46#95×D43—21no—
47#14582662C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582653C2211yescharacteristic
53C2×#107×C43C2211yescharacteristic
54C43×#389C2211yescharacteristic
55C4×C4⋊C4×C43C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C22×Dic86—21no—
61C22×D172C2311yescharacteristic
62C22×C4×D43—21no—
63C22×C4×D43—21no—
64C22×C4×D43—21no—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67#13063324—22no—
68#13063324C2×C414yescomplemented
69C4×D172—22no—
70C4×D172—41no—
71#13063287—22no—
72#13063287—22no—
73#13063287—41no—
74#13063287C2×C414yes—
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⋊C4D411yescharacteristic
83C2×Dic43⋊C4D411yescharacteristic
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43C2311yescharacteristic
90C2×C4×Dic43C2311yescharacteristic
91#13063259—41no—
92#13063258C2×C414yescomplemented
93#13063256—41no—
94Dic43⋊C8C2×C414yescomplemented
95#13063247—22no—
96#13063247C2×C414yes—
97#13063245C2×C414yes—
98#13063245Q814yescomplemented
99#13063236—41no—
100#13063235—22no—
101C8×Dic43—41no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95D411yescharacteristic
110C43⋊#95D411yescharacteristic
111C22×C8×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C2×C4⋊C4×C43—21no—
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C42×C43—21no—
119C2×C42×C43C2311yescharacteristic
120#107×C43C2×C414yescomplemented
121#95×C43—21no—
122#95×C43—21no—
123C23×D43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2411yescharacteristic
131C22×Dic43—21no—
132C22×Dic43—21no—
133C22×Dic43—21no—
134C22×Dic43C2×D411yescharacteristic
135C22×Dic43C2×D411yescharacteristic
136C22×Dic43C2×D411yescharacteristic
137C22×Dic43C2×D411yescharacteristic
138C2×D172—21no—
139C2×D172—21no—
140C2×D172—21no—
141C2×D172C22×C412yes—
142C2×D172C2×Q812yes—
143C2×D172#4112yes—
144C2×C4×D43—24no—
145C2×C4×D43—42no—
146C2×C4×D43—42no—
147C2×C4×D43—42no—
148C2×C4×D43—42no—
149C2×C4×D43—81no—
150C2×C4×D43—81no—
151C2×C4×D43—81no—
152C2×C4×D43—81no—
153C2×Dic86—24no—
154C2×Dic86—81no—
155C2×Dic86—81no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43C22×C412yes—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—81no—
168C4⋊C4×C43C22×C412yes—
169C4⋊C4×C43C22×C412yes—
170C4⋊C4×C43C2×Q812yes—
171C42×C43—21no—
172C42×C43—21no—
173C42×C43—81no—
174(C2×D43)⋊C4—24no—
175(C2×D43)⋊C4—42no—
176(C2×D43)⋊C4—42no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—81no—
183C4⋊Dic43—81no—
184C4⋊Dic43C22×C412yes—
185Dic43⋊C4—24no—
186Dic43⋊C4—22no—
187Dic43⋊C4—41no—
188Dic43⋊C4—81no—
189C4×Dic43—21no—
190C4×Dic43—21no—
191C4×Dic43—42no—
192C4×Dic43—81no—
193C4×Dic43C22×C412yes—
194C4×Dic43#4112yes—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8C22×C412yes—
200C2×C43⋊C8C2×Q812yes—
201C23×C43C22×D411yescharacteristic
202C22×D43—22no—
203C22×D43—22no—
204C22×D43—22no—
205C22×D43—41no—
206C22×D43—41no—
207C22×D43—41no—
208C22×D43—41no—
209C2×C4×C43—22no—
210C2×C4×C43—22no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—22no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43C23×C411yescharacteristic
228C2×C4×C43C22×Q811yescharacteristic
229C2×C4×C43C2×#4111yescharacteristic
230C2×C4×C43C2×#4111yescharacteristic
231C2×C4×C43H(5,𝔽2)11yescharacteristic
232C2×C4×C432−1+411yescharacteristic
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—22no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43C4×D412yes—
252C2×Dic43C4×D412yes—
253C2×Dic43#13712yes—
254D172—22no—
255D172—22no—
256D172—22no—
257D172C4×Q814yes—
258C4×D43—84no—
259C4×D43—84no—
260C4×D43—84no—
261Dic86—84no—
262C8×C43—22no—
263C8×C43—41no—
264C43⋊C8—22no—
265C43⋊C8—22no—
266#22979—431nomaximal, Sylow
267C22×C43C2×C4×D411yescharacteristic
268C22×C43#54611yescharacteristic
269C22×C43D4×Q811yescharacteristic
270C22×C43C2×#13711yescharacteristic
271C22×C43#57511yescharacteristic
272C22×C43#57611yescharacteristic
273C22×C43#57611yescharacteristic
274C2×D43—24no—
275C2×D43—42no—
276C2×D43—42no—
277C2×D43—42no—
278C2×D43—42no—
279C2×D43—42no—
280C2×D43—42no—
281C4×C43—42no—
282C4×C43—42no—
283C4×C43—42no—
284C4×C43—41no—
285C4×C43—41no—
286C4×C43—81no—
287C4×C43C2×C4×Q811yescharacteristic
288C4×C43#52011yescharacteristic
289C4×C43#55211yescharacteristic
290C4×C43#55411yescharacteristic
291Dic43—22no—
292Dic43—22no—
293Dic43—22no—
294Dic43—42no—
295Dic43—41no—
296Dic43—81no—
297Dic43—81no—
298C2×#474—431no—
299#2369—431no—
300#2349—431no—
301#1993—431no—
302#1949—431no—
303#1943—431no—
304#1942—431no—
305#1921—431no—
306#1918D4311yescharacteristic, complemented
307#1864—431no—
308#1862—431no—
309#1771—431no—
310#1762—431no—
311#1762—431no—
312C4×#102—431no—
313C2×C43#236011yescharacteristic
314C2×C43C4×#13711yescharacteristic
315C2×C43#294811yescharacteristic
316C2×C43#331411yescharacteristic
317C2×C43#331911yescharacteristic
318C2×C43#338511yescharacteristic
319C2×C43#338911yescharacteristic
320D43—44no—
321C2×C4⋊Q8—431no—
322C2×C4×D4—431no—
323C2×C4×D4—431no—
324C2×C4×D4—431no—
325#474—438no—
326C2×#107—431no—
327C2×#107—431no—
328C2×#107C2×D4311yescharacteristic
329C2×#106—431no—
330C2×C4⋊C8—431no—
331C2×#102—431no—
332C2×#102—431no—
333C2×#102—431no—
334C2×#102—431no—
335C2×#97—431no—
336C2×#97—431no—
337C2×C4×C8—431no—
338#391—861no—
339#391—861no—
340#389—431no—
341#389—431no—
342#389—431no—
343#389—861no—
344#389C2×D4311yescharacteristic
345#385—861no—
346#385—861no—
347#382—431no—
348#380—861no—
349C4×C4⋊C4—431no—
350C4×C4⋊C4—431no—
351C4×C4⋊C4—431no—
352C4×C4⋊C4—861no—
353C4×C4⋊C4C2×D4311yescharacteristic
354C2×#95—861no—
355#340—431no—
356#340—431no—
357#340—431no—
358#340—431no—
359#340—431no—
360#340C2×D4311yescharacteristic
361#340C2×D4311yescharacteristic
362#340C2×D4311yescharacteristic
363#336—431no—
364#336C2×D4311yescharacteristic
365C43#2297911yescharacteristic, complemented, Sylow
366C22×Q8—861no—
367C22×D4—431no—
368C23×C4—861no—
369C23×C4—861no—
370C23×C4—861no—
371C22×C8—431no—
372C22×C8—431no—
373C22×C8C22×D4311yescharacteristic
374C22×C8C22×D4311yescharacteristic
375C4⋊Q8—434no—
376C4⋊Q8—862no—
377C4×D4—434no—
378C4×D4—862no—
379C4×D4—862no—
380C4×D4—862no—
381C4×D4—1721no—
382C4×D4—1721no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—431no—
385C2×C4⋊C4—431no—
386C2×C4⋊C4—431no—
387C2×C4⋊C4—431no—
388C2×C4⋊C4—431no—
389C2×C4⋊C4—861no—
390C2×C4⋊C4—861no—
391C2×C4⋊C4—861no—
392C2×C4⋊C4—861no—
393C2×C4⋊C4C22×D4311yescharacteristic
394C2×C4⋊C4C22×D4311yescharacteristic
395C2×C4⋊C4C22×D4311yescharacteristic
396C2×C4⋊C4C22×D4311yescharacteristic
397C2×C22⋊C4—861no—
398C2×C22⋊C4—861no—
399C2×C22⋊C4—861no—
400C2×C42—21no—
401C2×C42—431no—
402C2×C42—431no—
403C2×C42—861no—
404C2×C42—861no—
405C2×C42C22×D4311yescharacteristic
406#107—434no—
407#107—1721no—
408#107C4×D4314yescomplemented
409#106—1721no—
410C4⋊C8—434no—
411#102—434no—
412#102—434no—
413#102—434no—
414#102—862no—
415#97—862no—
416#97—1721no—
417C4×C8—1721no—
418#95—21no—
419#95—21no—
420#95—431no—
421#95—431no—
422#95—861no—
423#95—861no—
424#95—861no—
425#95—861no—
426#95—861no—
427#95—861no—
428#95—861no—
429C24—861no—
430C2×Q8—864no—
431C2×Q8—3441no—
432C2×Q8—3441no—
433C2×D4—432no—
434C2×D4—432no—
435C2×D4—432no—
436C2×D4—861no—
437C2×D4—861no—
438C2×D4—861no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—431no—
444C22×C4—431no—
445C22×C4—431no—
446C22×C4—431no—
447C22×C4—864no—
448C22×C4—861no—
449C22×C4—861no—
450C22×C4—861no—
451C22×C4—3441no—
452C22×C4—3441no—
453C22×C4—3441no—
454C22×C4—3441no—
455C22×C4—1722no—
456C22×C4—1722no—
457C22×C4—1722no—
458C22×C4—1722no—
459C22×C4D4×D4311yescharacteristic
460C22×C4D4×D4311yescharacteristic
461C22×C4C23×D4311yescharacteristic
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—432no—
468C2×C8—432no—
469C2×C8—861no—
470C2×C8—861no—
471C2×C8—861no—
472C2×C8—861no—
473C2×C8C2×C4×D4312yes—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—81no—
480C4⋊C4—432no—
481C4⋊C4—862no—
482C4⋊C4—864no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—3441no—
489C4⋊C4—3441no—
490C4⋊C4—3441no—
491C4⋊C4—1721no—
492C4⋊C4C2×C4×D4312yes—
493C4⋊C4C2×C4×D4312yes—
494C4⋊C4Q8×D4312yes—
495C22⋊C4—864no—
496C22⋊C4—1722no—
497C22⋊C4—1722no—
498C42—21no—
499C42—21no—
500C42—81no—
501C42—432no—
502C42—432no—
503C42—861no—
504C42—861no—
505C42—3441no—
506C42—1722no—
507C23—862no—
508C23—862no—
509C23—862no—
510C23—1721no—
511C23—1721no—
512C23—1721no—
513C23—1721no—
514C23C2×D4×D4311yescharacteristic
515Q8—3444no—
516D4—434no—
517D4—862no—
518D4—862no—
519D4—862no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—432no—
539C2×C4—432no—
540C2×C4—432no—
541C2×C4—861no—
542C2×C4—861no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—861no—
547C2×C4—862no—
548C2×C4—861no—
549C2×C4—861no—
550C2×C4—861no—
551C2×C4—3444no—
552C2×C4—3444no—
553C2×C4—3444no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4C22×C4×D4311yescharacteristic
563C2×C4C2×Q8×D4311yescharacteristic
564C2×C4#41×D4311yescharacteristic
565C2×C4#41×D4311yescharacteristic
566C2×C4#1306337111yescharacteristic
567C2×C4#1306337211yescharacteristic
568C8—22no—
569C8—41no—
570C8—862no—
571C8—862no—
572C22—864no—
573C22—1722no—
574C22—1722no—
575C22—1722no—
576C22—1722no—
577C22—1722no—
578C22—1722no—
579C22C4×D4×D4311yescharacteristic
580C22#1458354111yescharacteristic
581C22#1458356211yescharacteristic
582C22#137×D4311yescharacteristic
583C22#1458369811yescharacteristic
584C22#1458370011yescharacteristic
585C22#1458370111yescharacteristic
586C4—41no—
587C4—42no—
588C4—42no—
589C4—42no—
590C4—41no—
591C4—81no—
592C4—862no—
593C4—862no—
594C4—862no—
595C4—3441no—
596C4—3441no—
597C4—1721no—
598C4—1722no—
599C4C4×Q8×D4311yescharacteristic
600C4#1458337911yescharacteristic
601C4#1458358511yescharacteristic
602C4#1458360511yescharacteristic
603C2—1724no—
604C2#1913760311yescharacteristic
605C2#1914341111yescharacteristic
606C2#1914344211yescharacteristic
607C2#1914667911yescharacteristic
608C2#1914675411yescharacteristic
609C2#1914750811yescharacteristic
610C2#1914754811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1918C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenter#1918D43
hypocenterC43#22979
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1918

Complements

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

NH ≅ G/Ntype
2. #19137682C2semidirect
4. #19135566C2semidirect
5. #19135366C2semidirect
6. #19135330C2semidirect
7. #19135329C2semidirect
8. #19135190C2semidirect
11. #19134468C2semidirect
15. C43×#1918C2semidirect
20. #14583178C4semidirect
68. #13063324C2×C4semidirect
92. #13063258C2×C4semidirect
94. Dic43⋊C8C2×C4semidirect
98. #13063245Q8semidirect
120. #107×C43C2×C4semidirect
306. #1918D43semidirect
365. C43#22979semidirect
408. #107C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145831782
#191376822
#191375042
#191355662
#191353662
#191353302
#191353292
#191351902
#191348572
#191348452
#191344682
#191344232
#191344192
#191344092
C43×#19182
#2297943