Finite Group Databasebeta

← #25100844

Subgroups — #25100844

Order 11008.

874 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582984C211yesmaximal, characteristic
2#19137070C211yesmaximal, characteristic, complemented
3#19137053C211yesmaximal, characteristic
4#19135479C211yesmaximal, characteristic
5#19135473C211yesmaximal, characteristic
6#19135337C211yesmaximal, characteristic, complemented
7#19135335C211yesmaximal, characteristic, complemented
8#19135292C211yesmaximal, characteristic
9#19135290C211yesmaximal, characteristic
10#19135287C211yesmaximal, characteristic, complemented
11#19134487C211yesmaximal, characteristic, complemented
12#103×Dic43C211yesmaximal, characteristic, complemented
13#19134409C211yesmaximal, characteristic
14#97×Dic43C211yesmaximal, characteristic, complemented
15C43×#1935C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C2×Q8×Dic43C2211yescharacteristic
18C2×#13063287C2211yescharacteristic
19C2×#13063283—21no—
20#14582984C418yescomplemented
21C2×#13063258C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063236C2211yescharacteristic
29C2×#13063235C2211yescharacteristic
30C2×#13063235C2211yescharacteristic
31C2×C8×Dic43C2211yescharacteristic
32C2×C8×Dic43C2211yescharacteristic
33#14582806C2211yescharacteristic
34#14582801C2211yescharacteristic
35#14582800C2211yescharacteristic
36#14582798C2211yescharacteristic
37#14582797C2211yescharacteristic
38#14582795C2211yescharacteristic
39#14582791—21no—
40#14582789—21no—
41#14582784—21no—
42#14582782—21no—
43C4⋊C4×Dic43C2211yescharacteristic
44C4⋊C4×Dic43C2211yescharacteristic
45#14582750—21no—
46#14582746—21no—
47#14582744—21no—
48C42×Dic43C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53C2×#103×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#97×C43C2211yescharacteristic
56C43×#391C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C22×D172C2311yescharacteristic
61C22×C4×D43—21no—
62C2×#10621884—22no—
63C2×#10621884—22no—
64C2×#10621884C2×C414yes—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67Q8×Dic43—22no—
68Q8×Dic43C2×C414yes—
69#13063287—22no—
70#13063287C2×C414yes—
71#13063283—44no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43D411yescharacteristic
88C2×C4×Dic43D411yescharacteristic
89C2×C4×Dic43D411yescharacteristic
90C2×C4×Dic43D411yescharacteristic
91C2×C4×Dic43C2311yescharacteristic
92C2×C4×Dic43C2311yescharacteristic
93#13063258—22no—
94#13063258—22no—
95#13063256C2×C414yes—
96#13063249—22no—
97#13063247—22no—
98#13063247C2×C414yes—
99#13063245—22no—
100#13063236—22no—
101#13063235—22no—
102#13063235—22no—
103C8×Dic43—22no—
104C8×Dic43C2×C414yes—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C22×Q8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C2×C4⋊C4×C43—21no—
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C42×C43C2311yescharacteristic
120#103×C43—22no—
121#103×C43C2×C414yes—
122#97×C43—22no—
123#95×C43—21no—
124#95×C43—21no—
125#95×C43—21no—
126C23×D43—21no—
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43C22×C412yes—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2411yescharacteristic
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43C2×D411yescharacteristic
144C22×Dic43C2×D411yescharacteristic
145C22×Dic43C2×D411yescharacteristic
146C22×Dic43C2×D411yescharacteristic
147C2×D172—21no—
148C2×D172—21no—
149C2×D172—21no—
150C2×D172—21no—
151C2×D172—21no—
152C2×D172C22×C412yes—
153C2×C4×D43—24no—
154C2×C4×D43—42no—
155C2×C4×D43—42no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43C22×C412yes—
161C2×C8×C43#4112yes—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—42no—
168C4⋊C4×C43C22×C412yes—
169C42×C43—21no—
170C42×C43—21no—
171#10621884—28no—
172(C2×D43)⋊C4—24no—
173(C2×D43)⋊C4—42no—
174(C2×D43)⋊C4—42no—
175(C2×D43)⋊C4—42no—
176(C2×D43)⋊C4—42no—
177C4⋊Dic43—21no—
178C4⋊Dic43—24no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—42no—
184C4⋊Dic43C22×C412yes—
185Dic43⋊C4—42no—
186Dic43⋊C4—42no—
187C4×Dic43—21no—
188C4×Dic43—21no—
189C4×Dic43—24no—
190C4×Dic43—22no—
191C4×Dic43—22no—
192C4×Dic43—41no—
193C4×Dic43—41no—
194C4×Dic43—42no—
195C4×Dic43—42no—
196C4×Dic43C22×C412yes—
197C4×Dic43#4112yes—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8C22×C412yes—
201C2×C43⋊C8#4112yes—
202C2×C43⋊C8#4112yes—
203C2×C43⋊C8#4112yes—
204C23×C43C22×D411yescharacteristic
205C22×D43—22no—
206C22×D43—41no—
207C22×D43—41no—
208C22×D43—41no—
209C22×D43—41no—
210C22×D43—41no—
211C22×D43—41no—
212Q8×C43—22no—
213Q8×C43—22no—
214Q8×C43—41no—
215Q8×C43—41no—
216C2×C4×C43—22no—
217C2×C4×C43—22no—
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—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43C23×C411yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C2×C4×C43C2×#4111yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—22no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
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×Dic43C4×D412yes—
258C2×Dic43C4×D412yes—
259C2×Dic43AGL(1,ℤ/8)12yes—
260C2×Dic43#13712yes—
261D172—22no—
262D172—22no—
263D172—41no—
264D172—41no—
265C4×D43—48no—
266C8×C43—22no—
267C8×C43—22no—
268C43⋊C8—22no—
269C43⋊C8#11714yescomplemented
270#21279—431nomaximal, Sylow
271C22×C43C2×C4×D411yescharacteristic
272C22×C43#53211yescharacteristic
273C22×C43#53211yescharacteristic
274C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
275C22×C43C2×#13711yescharacteristic
276C22×C43#57511yescharacteristic
277C22×C43#57511yescharacteristic
278C2×D43—42no—
279C2×D43—42no—
280C2×D43—42no—
281C2×D43—81no—
282C2×D43—81no—
283C2×D43—81no—
284C2×D43—81no—
285C4×C43—41no—
286C4×C43—41no—
287C4×C43—42no—
288C4×C43—42no—
289C4×C43—81no—
290C4×C43—81no—
291C4×C43C2×#11711yescharacteristic
292C4×C43C4×#4111yescharacteristic
293C4×C43#52911yescharacteristic
294C4×C43#52911yescharacteristic
295Dic43—22no—
296Dic43—41no—
297Dic43—41no—
298Dic43—42no—
299Dic43—81no—
300Dic43—81no—
301Dic43#44014yes—
302C2×C4×SD16—431no—
303#2295—431no—
304#2293—431no—
305#1973—431no—
306#1973—431no—
307#1944—431no—
308#1944—431no—
309#1936—431no—
310#1936—431no—
311#1935—431no—
312#1935D4311yescharacteristic, complemented
313C4×#107—431no—
314C4×#103—431no—
315C4×#102—431no—
316C4×#97—431no—
317C2×C43#229311yescharacteristic
318C2×C43C2×#44011yescharacteristic
319C2×C43#294311yescharacteristic
320C2×C43#317111yescharacteristic
321C2×C43#317111yescharacteristic
322C2×C43#317211yescharacteristic
323C2×C43#317211yescharacteristic
324D43—82no—
325C22×SD16—431no—
326C2×C4×Q8—431no—
327C2×C4×D4—431no—
328C2×#117—861no—
329C4×SD16—438no—
330C2×#107—431no—
331C2×#107—431no—
332C2×#106—431no—
333C2×#103—431no—
334C2×#103C2×D4311yescharacteristic
335C2×#103C2×D4311yescharacteristic
336C2×#102—431no—
337C2×#102—431no—
338C2×#102—431no—
339C2×#97—431no—
340C2×#97—431no—
341C2×#97—431no—
342C2×#97C2×D4311yescharacteristic
343C2×C4×C8—431no—
344C2×C4×C8—431no—
345#391—431no—
346#391C2×D4311yescharacteristic
347#390—431no—
348#390—431no—
349#389—431no—
350#389—431no—
351#389—431no—
352#389C2×D4311yescharacteristic
353#388—861no—
354#388—861no—
355#387—861no—
356#387—861no—
357C4×C4⋊C4—431no—
358C4×C4⋊C4—431no—
359C4×C4⋊C4—861no—
360C4×C22⋊C4—861no—
361#376—861no—
362C43—431no—
363#340—431no—
364#340—431no—
365#340—431no—
366#340—431no—
367#340C2×D4311yescharacteristic
368#340C2×D4311yescharacteristic
369C43#2127911yescharacteristic, complemented, Sylow
370C22×Q8C22×D4311yescharacteristic
371C22×D4—431no—
372C23×C4—861no—
373C2×SD16—434no—
374C2×SD16—862no—
375C2×SD16—862no—
376C22×C8—431no—
377C22×C8—431no—
378C22×C8C22×D4311yescharacteristic
379C22×C8C22×D4311yescharacteristic
380C4×Q8—434no—
381C4×Q8—862no—
382C4×D4—434no—
383C4×D4—862no—
384#117—1724no—
385C2×C4⋊C4—21no—
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×C22⋊C4—861no—
397C2×C22⋊C4—861no—
398C2×C22⋊C4—861no—
399C2×C22⋊C4—861no—
400C2×C22⋊C4—861no—
401C2×C42—431no—
402C2×C42—431no—
403C2×C42—431no—
404C2×C42—431no—
405C2×C42—431no—
406C2×C42—431no—
407C2×C42—861no—
408C2×C42—861no—
409C2×C42—861no—
410C2×C42C22×D4311yescharacteristic
411#107—862no—
412#107—862no—
413#106—434no—
414#103—22no—
415#103—862no—
416#103C4×D4314yes—
417#102—434no—
418#102—862no—
419#102—862no—
420#97—22no—
421#97—862no—
422#97—862no—
423#97—862no—
424C4×C8—434no—
425C4×C8—862no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—861no—
430#95—861no—
431#95—861no—
432#95—861no—
433#95—861no—
434#95—861no—
435#95—861no—
436C24—861no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8C2×C4×D4312yes—
443C2×D4—432no—
444C2×D4—861no—
445C2×D4—861no—
446C2×D4—861no—
447C2×D4—861no—
448C2×D4—861no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—431no—
454C22×C4—431no—
455C22×C4—431no—
456C22×C4—431no—
457C22×C4—864no—
458C22×C4—861no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4—1722no—
462C22×C4—1722no—
463C22×C4D4×D4311yescharacteristic
464C22×C4D4×D4311yescharacteristic
465C22×C4C23×D4311yescharacteristic
466SD16—868no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—432no—
472C2×C8—432no—
473C2×C8—432no—
474C2×C8—432no—
475C2×C8—861no—
476C2×C8—861no—
477C2×C8C2×C4×D4312yes—
478C2×C8#1062190012yes—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—42no—
485C4⋊C4—432no—
486C4⋊C4—864no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—1722no—
493C4⋊C4—1722no—
494C4⋊C4—1722no—
495C4⋊C4C2×C4×D4312yes—
496C22⋊C4—864no—
497C22⋊C4—1722no—
498C22⋊C4—1722no—
499C22⋊C4—1722no—
500C22⋊C4—1722no—
501C42—21no—
502C42—21no—
503C42—432no—
504C42—432no—
505C42—862no—
506C42—862no—
507C42—864no—
508C42—861no—
509C42—861no—
510C42—1721no—
511C42—1721no—
512C42—1722no—
513C42—1722no—
514C23—862no—
515C23—1721no—
516C23—1721no—
517C23—1721no—
518C23—1721no—
519C23—1721no—
520C23—1721no—
521C23C2×D4×D4311yescharacteristic
522Q8—22no—
523Q8—22no—
524Q8—41no—
525Q8—41no—
526D4—862no—
527D4—862no—
528D4—1721no—
529D4—1721no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—432no—
549C2×C4—432no—
550C2×C4—432no—
551C2×C4—432no—
552C2×C4—861no—
553C2×C4—861no—
554C2×C4—862no—
555C2×C4—861no—
556C2×C4—861no—
557C2×C4—861no—
558C2×C4—861no—
559C2×C4—861no—
560C2×C4—861no—
561C2×C4—1728no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4C22×C4×D4311yescharacteristic
571C2×C4#41×D4311yescharacteristic
572C2×C4#41×D4311yescharacteristic
573C2×C4#41×D4311yescharacteristic
574C2×C4#41×D4311yescharacteristic
575C2×C4C2×#1062190011yescharacteristic
576C8—22no—
577C8—22no—
578C8—434no—
579C8—862no—
580C22—3441no—
581C22—3441no—
582C22—3441no—
583C22—3441no—
584C22—1722no—
585C22—1722no—
586C22—1722no—
587C22C4×D4×D4311yescharacteristic
588C22#1458344411yescharacteristic
589C22#1458344811yescharacteristic
590C22AGL(1,ℤ/8)×D4311yescharacteristic
591C22#137×D4311yescharacteristic
592C22#1458369811yescharacteristic
593C22#1458369811yescharacteristic
594C4—42no—
595C4—42no—
596C4—41no—
597C4—41no—
598C4—81no—
599C4—81no—
600C4—434no—
601C4—862no—
602C4—3441no—
603C4—3441no—
604C4—1722no—
605C4—1721no—
606C4—1721no—
607C4#117×D4311yescharacteristic
608C4C4×#1062190011yescharacteristic
609C4#1458342611yescharacteristic
610C4#1458343211yescharacteristic
611C2—3442no—
612C2#1913705511yescharacteristic
613C2#440×D4311yescharacteristic
614C2#1914339411yescharacteristic
615C2#1914518311yescharacteristic
616C2#1914519311yescharacteristic
617C2#1914519611yescharacteristic
618C2#1914520011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1935C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenter#1935D43
hypocenterC43#21279
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1935

Complements

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

NH ≅ G/Ntype
2. #19137070C2semidirect
6. #19135337C2semidirect
7. #19135335C2semidirect
10. #19135287C2semidirect
11. #19134487C2semidirect
12. #103×Dic43C2semidirect
14. #97×Dic43C2semidirect
15. C43×#1935C2semidirect
20. #14582984C4semidirect
269. C43⋊C8#117semidirect
312. #1935D43semidirect
369. C43#21279semidirect

Maximal subgroups

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

subgroupindex
C2×#145829842
#191370702
#191370532
#191354792
#191354732
#191353372
#191353352
#191352922
#191352902
#191352872
#191344872
#103×Dic432
#191344092
#97×Dic432
C43×#19352
#2127943