Finite Group Databasebeta

← #25148485

Subgroups — #25148485

Order 11008.

774 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583199C211yesmaximal, characteristic
2C2×C8×Dic86C211yesmaximal, characteristic, complemented
3#19139978C211yesmaximal, characteristic, complemented
4#19139949C211yesmaximal, characteristic
5#19136099C211yesmaximal, characteristic, complemented
6#19136092C211yesmaximal, characteristic, complemented
7#19135979C211yesmaximal, characteristic
8#19135965C211yesmaximal, characteristic
9#19135560C211yesmaximal, characteristic, complemented
10#19135363C211yesmaximal, characteristic, complemented
11#19135327C211yesmaximal, characteristic, complemented
12#19135322C211yesmaximal, characteristic, complemented
13#19135280C211yesmaximal, characteristic
14#19135280C211yesmaximal, characteristic
15C4×#102×C43C211yesmaximal, characteristic
16C2×#13063317C2211yescharacteristic
17C2×C4×Dic86C2211yescharacteristic
18#14583199—24no—
19C8×Dic86—24no—
20C2×#13063258C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×C4⋊(C43⋊C8)C2211yescharacteristic
25C2×Dic43⋊C8C2211yescharacteristic
26C2×Dic43⋊C8C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×C8×Dic43C2211yescharacteristic
30C2×C8×Dic43C2211yescharacteristic
31#14582835—21no—
32#14582831—21no—
33#14582820—21no—
34#14582811—21no—
35#14582802C2211yescharacteristic
36#14582802C2211yescharacteristic
37#14582798C2211yescharacteristic
38#14582798C2211yescharacteristic
39#14582798C2211yescharacteristic
40#14582798C2211yescharacteristic
41#14582797—21no—
42#14582797—21no—
43#14582795C2211yescharacteristic
44#14582795C2211yescharacteristic
45#14582772—21no—
46#14582772—21no—
47#14582765C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54C2×C4×D4×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×C4×C8×C43C2211yescharacteristic
58C4×C4⋊C4×C43C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×Dic86D411yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64#13063317—22no—
65#13063317—22no—
66C4×Dic86—22no—
67C4×Dic86—22no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43D411yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4D411yescharacteristic
82C2×Dic43⋊C4D411yescharacteristic
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—21no—
87C2×C4×Dic43C2311yescharacteristic
88C2×C4×Dic43C2311yescharacteristic
89#13063258—22no—
90#13063258—22no—
91#13063256—22no—
92#13063256—22no—
93C4⋊(C43⋊C8)D414yes—
94Dic43⋊C8—22no—
95Dic43⋊C8—22no—
96#13063246—22no—
97#13063246—22no—
98C8×Dic43—22no—
99C8×Dic43—22no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C22×D4×C43C2311yescharacteristic
109C23×C4×C43—21no—
110C22×C8×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112C4×D4×C43—22no—
113C4×D4×C43—22no—
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C22⋊C4×C43—21no—
118C2×C42×C43—21no—
119C2×C42×C43C2311yescharacteristic
120#102×C43—22no—
121#102×C43Q814yescomplemented
122C4×C8×C43—22no—
123#95×C43—21no—
124C24×C43—21no—
125C2×D4×C43—21no—
126C2×D4×C43—21no—
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43C2×Q812yes—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—42no—
135C22×C4×C43—81no—
136C22×C4×C43—81no—
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2411yescharacteristic
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43C2×D411yescharacteristic
145C22×Dic43C2×D411yescharacteristic
146C22×Dic43C2×D411yescharacteristic
147C22×Dic43C2×D411yescharacteristic
148C2×Dic86—22no—
149C2×Dic86—22no—
150C2×Dic86—22no—
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43C2×Q812yes—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43C2×Q812yes—
162C4⋊C4×C43#4112yes—
163C22⋊C4×C43—42no—
164C42×C43—81no—
165C42×C43C2×D412yes—
166C42×C43#4112yes—
167C22⋊Dic43—42no—
168C22⋊Dic43—42no—
169C22⋊Dic43—81no—
170C22⋊Dic43—81no—
171C4⋊Dic43—22no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—42no—
181C4⋊Dic43—42no—
182C4⋊Dic43—81no—
183C4⋊Dic43—81no—
184Dic43⋊C4—22no—
185Dic43⋊C4—22no—
186Dic43⋊C4—42no—
187Dic43⋊C4—42no—
188Dic43⋊C4—81no—
189Dic43⋊C4—81no—
190C4×Dic43—21no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8C2×D412yes—
199C2×C43⋊C8C2×D412yes—
200C23×C43—22no—
201C23×C43—41no—
202C23×C43—41no—
203C23×C43—41no—
204C23×C43—41no—
205C23×C43—41no—
206C23×C43—41no—
207C23×C43C22×D411yescharacteristic
208D4×C43—22no—
209D4×C43—22no—
210D4×C43—41no—
211D4×C43—41no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—22no—
217C2×C4×C43—22no—
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—84no—
226C2×C4×C43#12112yes—
227C2×C4×C43#12112yes—
228C2×C4×C43C22×D411yescharacteristic
229C2×C4×C43C22×Q811yescharacteristic
230C2×C4×C43C2×#4111yescharacteristic
231C2×C4×C43C2×#4111yescharacteristic
232C2×C4×C432−1+411yescharacteristic
233C2×C4×C432−1+411yescharacteristic
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—41no—
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#13512yes—
257C2×Dic43#13512yes—
258Dic86—28no—
259C8×C43—22no—
260C8×C43—41no—
261C43⋊C8—22no—
262C43⋊C8—22no—
263#25473—431nomaximal, Sylow
264C22×C43—42no—
265C22×C43—42no—
266C22×C43—42no—
267C22×C43—81no—
268C22×C43—81no—
269C22×C43—81no—
270C22×C43—81no—
271C22×C43C2×#12111yescharacteristic
272C22×C43#54811yescharacteristic
273C22×C43D4×Q811yescharacteristic
274C22×C43C2×#13511yescharacteristic
275C22×C43C2×#13511yescharacteristic
276C22×C43#57611yescharacteristic
277C22×C43#57711yescharacteristic
278C4×C43—22no—
279C4×C43—22no—
280C4×C43—42no—
281C4×C43—42no—
282C4×C43—81no—
283C4×C43#53311yescharacteristic
284C4×C43#54111yescharacteristic
285C4×C43#54711yescharacteristic
286C4×C43D4×Q811yescharacteristic
287Dic43—22no—
288Dic43—22no—
289Dic43—41no—
290Dic43—41no—
291Dic43—81no—
292Dic43—81no—
293Dic43—81no—
294Dic43—81no—
295C2×#478—431no—
296C2×C8×Q8—431no—
297#2584—431no—
298#2580—431no—
299#2088—431no—
300#2087—431no—
301#2067—431no—
302#2065—431no—
303#1991—431no—
304#1949—431no—
305#1942—431no—
306#1941—431no—
307#1934—431no—
308#1934—431no—
309C4×#102D4311yescharacteristic
310C2×C43—82no—
311C2×C43#242911yescharacteristic
312C2×C43#305011yescharacteristic
313C2×C43#306211yescharacteristic
314C2×C43#336111yescharacteristic
315C2×C43#336511yescharacteristic
316C2×C43#338011yescharacteristic
317C2×C43#338111yescharacteristic
318C2×#125—431no—
319C2×C4×Q8—431no—
320C2×C4×D4C2×D4311yescharacteristic
321#478—864no—
322C8×Q8—864no—
323C2×#107—431no—
324C2×#107—431no—
325C2×#106—431no—
326C2×#106—431no—
327C2×C4⋊C8—431no—
328C2×C4⋊C8—431no—
329C2×C4⋊C8—431no—
330C2×#102—431no—
331C2×#102—431no—
332C2×#102C2×D4311yescharacteristic
333C2×#102C2×D4311yescharacteristic
334C2×C4×C8—431no—
335C2×C4×C8—431no—
336C2×C4×C8C2×D4311yescharacteristic
337#399—861no—
338#398—861no—
339#395—861no—
340#393—861no—
341#390—431no—
342#390—431no—
343#389—431no—
344#389—431no—
345#389—431no—
346#389—431no—
347#389—431no—
348#389—431no—
349#389—861no—
350#389—861no—
351#385—861no—
352#385—861no—
353#382—431no—
354C4×C4⋊C4C2×D4311yescharacteristic
355#340—431no—
356#340—431no—
357#340—431no—
358#340—431no—
359#340—431no—
360#340—431no—
361#340C2×D4311yescharacteristic
362#340C2×D4311yescharacteristic
363C43#2547311yescharacteristic, complemented, Sylow
364C22×Q8—431no—
365C22×D4C22×D4311yescharacteristic
366C23×C4—21no—
367C22×C8—431no—
368C22×C8—431no—
369C22×C8C22×D4311yescharacteristic
370C22×C8C22×D4311yescharacteristic
371#125—862no—
372#125—862no—
373C4×Q8—862no—
374C4×Q8—862no—
375C4×D4—22no—
376C4×D4—22no—
377C2×C4⋊C4—431no—
378C2×C4⋊C4—431no—
379C2×C4⋊C4—431no—
380C2×C4⋊C4—431no—
381C2×C4⋊C4—431no—
382C2×C4⋊C4—431no—
383C2×C4⋊C4—431no—
384C2×C4⋊C4—861no—
385C2×C4⋊C4—861no—
386C2×C4⋊C4—861no—
387C2×C4⋊C4—861no—
388C2×C4⋊C4—861no—
389C2×C4⋊C4—861no—
390C2×C4⋊C4—861no—
391C2×C4⋊C4—861no—
392C2×C4⋊C4C22×D4311yescharacteristic
393C2×C4⋊C4C22×D4311yescharacteristic
394C2×C4⋊C4C22×D4311yescharacteristic
395C2×C22⋊C4—21no—
396C2×C22⋊C4—861no—
397C2×C22⋊C4—861no—
398C2×C22⋊C4—861no—
399C2×C22⋊C4—861no—
400C2×C42—21no—
401C2×C42—431no—
402C2×C42—431no—
403C2×C42C22×D4311yescharacteristic
404#107—862no—
405#107—862no—
406#106—862no—
407#106—862no—
408C4⋊C8—434no—
409C4⋊C8—862no—
410C4⋊C8—862no—
411#102—22no—
412#102—862no—
413#102—862no—
414#102Dic8614yescomplemented
415C4×C8—22no—
416C4×C8—862no—
417C4×C8—862no—
418#95—21no—
419#95—861no—
420#95—861no—
421#95—861no—
422#95—861no—
423#95—861no—
424#95—861no—
425#95—861no—
426#95—861no—
427C24—21no—
428C2×Q8—862no—
429C2×Q8—862no—
430C2×Q8—862no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4C2×Dic8612yes—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—42no—
441C22×C4—81no—
442C22×C4—81no—
443C22×C4—431no—
444C22×C4—431no—
445C22×C4—431no—
446C22×C4—431no—
447C22×C4—861no—
448C22×C4—861no—
449C22×C4—861no—
450C22×C4—861no—
451C22×C4D4×D4311yescharacteristic
452C22×C4D4×D4311yescharacteristic
453C22×C4C23×D4311yescharacteristic
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—432no—
460C2×C8—432no—
461C2×C8—861no—
462C2×C8—861no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8C2×Dic8612yes—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—862no—
471C4⋊C4—862no—
472C4⋊C4—862no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—3441no—
482C4⋊C4—3441no—
483C4⋊C4—3441no—
484C4⋊C4—3441no—
485C4⋊C4—1722no—
486C4⋊C4—1722no—
487C4⋊C4—1722no—
488C4⋊C4—1722no—
489C4⋊C4C2×Dic8612yes—
490C4⋊C4#1062189812yes—
491C22⋊C4—42no—
492C22⋊C4—3441no—
493C22⋊C4—3441no—
494C22⋊C4—1722no—
495C22⋊C4—1722no—
496C42—81no—
497C42—861no—
498C42—861no—
499C42—861no—
500C42—861no—
501C42#1062189812yes—
502C42D4×D4312yes—
503C23—22no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23C2×D4×D4311yescharacteristic
511Q8—868no—
512D4—22no—
513D4—22no—
514D4—41no—
515D4—41no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—84no—
530C2×C4—432no—
531C2×C4—432no—
532C2×C4—861no—
533C2×C4—861no—
534C2×C4—861no—
535C2×C4—861no—
536C2×C4—861no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—861no—
541C2×C4—861no—
542C2×C4—1721no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4—1721no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4#1306329812yes—
555C2×C4#1306329812yes—
556C2×C4C2×D4×D4311yescharacteristic
557C2×C4C22×Dic8611yescharacteristic
558C2×C4C2×#1062189811yescharacteristic
559C2×C4C2×#1062189811yescharacteristic
560C2×C4#1306337211yescharacteristic
561C2×C4#1306337211yescharacteristic
562C8—22no—
563C8—41no—
564C8—862no—
565C8—862no—
566C22—42no—
567C22—42no—
568C22—42no—
569C22—81no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22C2×#1306329811yescharacteristic
574C22#1458355811yescharacteristic
575C22D4×Dic8611yescharacteristic
576C22#135×D4311yescharacteristic
577C22#135×D4311yescharacteristic
578C22#1458370011yescharacteristic
579C22#1458370511yescharacteristic
580C4—22no—
581C4—22no—
582C4—42no—
583C4—42no—
584C4—81no—
585C4—862no—
586C4—862no—
587C4—3441no—
588C4—3441no—
589C4—3441no—
590C4—3441no—
591C4—1721no—
592C4—1721no—
593C4#1458345611yescharacteristic
594C4#1458351111yescharacteristic
595C4#1458355411yescharacteristic
596C4D4×Dic8611yescharacteristic
597C2—82no—
598C2#1913819411yescharacteristic
599C2#1914417511yescharacteristic
600C2#1914427311yescharacteristic
601C2#1914725611yescharacteristic
602C2#1914729211yescharacteristic
603C2#1914746211yescharacteristic
604C2#1914747111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC4×#102×C43C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenterC4×#102D43
hypocenterC43#25473
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
2. C2×C8×Dic86C2semidirect
3. #19139978C2semidirect
5. #19136099C2semidirect
6. #19136092C2semidirect
9. #19135560C2semidirect
10. #19135363C2semidirect
11. #19135327C2semidirect
12. #19135322C2semidirect
121. #102×C43Q8semidirect
363. C43#25473semidirect
414. #102Dic86semidirect

Maximal subgroups

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

subgroupindex
C2×#145831992
C2×C8×Dic862
#191399782
#191399492
#191360992
#191360922
#191359792
#191359652
#191355602
#191353632
#191353272
#191353222
#191352802
C4×#102×C432
#2547343