Finite Group Databasebeta

← #25099692

Subgroups — #25099692

Order 11008.

938 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137238C211yesmaximal, characteristic, complemented
2#19136956C211yesmaximal, characteristic, complemented
3#19135224C211yesmaximal, characteristic, complemented
4#19135217C211yesmaximal, characteristic, complemented
5#19135182C211yesmaximal, characteristic, complemented
6#19135175C211yesmaximal, characteristic, complemented
7#19134945C211yesmaximal, characteristic
8#19134945C211yesmaximal, characteristic
9#19134858C211yesmaximal, characteristic, complemented
10#19134844C211yesmaximal, characteristic, complemented
11#19134492C211yesmaximal, characteristic, complemented
12C4×#13063246C211yesmaximal, characteristic, complemented
13C4×#13063246C211yesmaximal, characteristic, complemented
14#19134348C211yesmaximal, characteristic, complemented
15C2×C43×#442C211yesmaximal, characteristic
16C2×D4×Dic43C2211yescharacteristic
17C2×D4×Dic43C2211yescharacteristic
18C2×#13063259C2211yescharacteristic
19C2×#13063257C2211yescharacteristic
20C2×#13063246C2211yescharacteristic
21C2×#13063246C2211yescharacteristic
22C2×#13063246C2211yescharacteristic
23C2×#13063246C2211yescharacteristic
24C2×C4×C43⋊C8C2211yescharacteristic
25#14582802C2211yescharacteristic
26#14582802C2211yescharacteristic
27#14582798C2211yescharacteristic
28#14582798C2211yescharacteristic
29#14582792—21no—
30#14582792—21no—
31#14582762—21no—
32#14582759—21no—
33C4⋊C4×Dic43C2211yescharacteristic
34C4⋊C4×Dic43C2211yescharacteristic
35C4×C4⋊Dic43C2211yescharacteristic
36C4×C4⋊Dic43C2211yescharacteristic
37C22⋊C4×Dic43—21no—
38C22⋊C4×Dic43—21no—
39C4×C22⋊Dic43—21no—
40#14582745C2211yescharacteristic
41C2×C43⋊#95—21no—
42#14582662C2211yescharacteristic
43#14582662C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582653C2211yescharacteristic
49#14582653C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C22×D8×C43C2211yescharacteristic
53C2×C4×D4×C43C2211yescharacteristic
54C2×C4×D4×C43C2211yescharacteristic
55C43×#442C418yescomplemented
56C2×#106×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×#97×C43C2211yescharacteristic
60C23×Dic43—21no—
61C23×Dic43—21no—
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64D4×Dic43—22no—
65D4×Dic43—22no—
66D4×Dic43—22no—
67D4×Dic43—22no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C22⋊Dic43—21no—
75C2×C22⋊Dic43—21no—
76C2×C22⋊Dic43—21no—
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C4×Dic43—21no—
81C2×C4×Dic43—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43C2311yescharacteristic
85C2×C4×Dic43C2311yescharacteristic
86#13063259—22no—
87#13063257—22no—
88#13063246—22no—
89#13063246—22no—
90#13063246—22no—
91#13063246—22no—
92C4×C43⋊C8—22no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95D411yescharacteristic
100C43⋊#95D411yescharacteristic
101C43⋊#95D411yescharacteristic
102C43⋊#95D411yescharacteristic
103C22×D4×C43C2311yescharacteristic
104C22×D4×C43C2311yescharacteristic
105C23×C4×C43—21no—
106C23×C4×C43—21no—
107C2×D8×C43—22no—
108C2×D8×C43—22no—
109C2×D8×C43C2×C414yes—
110C22×C8×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112C4×D4×C43—22no—
113C4×D4×C43—22no—
114C4×D4×C43C2×C414yes—
115C4×D4×C43C2×C414yescomplemented
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C22⋊C4×C43—21no—
119C2×C22⋊C4×C43—21no—
120C2×C42×C43C2311yescharacteristic
121#106×C43C2×C414yescomplemented
122#102×C43C2×C414yes—
123#102×C43C2×C414yescomplemented
124#97×C43C2×C414yescomplemented
125C24×C43—21no—
126C24×C43—21no—
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43C22×C412yes—
136C2×D4×C43C22×C412yes—
137C2×D4×C43#4112yes—
138C2×D4×C43#4112yes—
139C22×C4×C43—24no—
140C22×C4×C43—24no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—81no—
144C22×C4×C43—81no—
145C22×C4×C43—81no—
146C22×C4×C43—81no—
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2411yescharacteristic
150C22×Dic43—24no—
151C22×Dic43—24no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—81no—
157C22×Dic43—81no—
158C22×Dic43—81no—
159C22×Dic43—81no—
160C22×Dic43C2×D411yescharacteristic
161C22×Dic43C2×D411yescharacteristic
162C22×Dic43C2×D411yescharacteristic
163C22×Dic43C2×D411yescharacteristic
164D8×C43—28no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43C22×C412yes—
170C2×C8×C43C22×C412yes—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43C22×C412yes—
174C4⋊C4×C43C22×C412yes—
175C22⋊C4×C43—24no—
176C22⋊C4×C43—24no—
177C42×C43C22×C412yes—
178C42×C43#4112yes—
179C22⋊Dic43—24no—
180C22⋊Dic43—24no—
181C22⋊Dic43—81no—
182C22⋊Dic43—81no—
183C22⋊Dic43—81no—
184C22⋊Dic43—81no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—81no—
192C4⋊Dic43—81no—
193C4⋊Dic43#4112yes—
194C4⋊Dic43#4112yes—
195C4×Dic43—21no—
196C4×Dic43—21no—
197C4×Dic43—21no—
198C4×Dic43—21no—
199C4×Dic43—81no—
200C4×Dic43—81no—
201C4×Dic43—81no—
202C4×Dic43—81no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C23×C43—22no—
210C23×C43—22no—
211C23×C43—22no—
212C23×C43—22no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43—41no—
223C23×C43C22×D411yescharacteristic
224D4×C43—22no—
225D4×C43—22no—
226D4×C43—22no—
227D4×C43—22no—
228D4×C43—22no—
229D4×C43—41no—
230D4×C43—41no—
231D4×C43#11714yes—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—22no—
237C2×C4×C43—22no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—84no—
243C2×C4×C43—84no—
244C2×C4×C43C4×D412yes—
245C2×C4×C43C4×D412yes—
246C2×C4×C43C23×C411yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—22no—
257C2×Dic43—22no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—84no—
277C2×Dic43—84no—
278C8×C43—22no—
279C8×C43—22no—
280C43⋊C8—41no—
281C43⋊C8—41no—
282#21126—431nomaximal, Sylow
283C22×C43—24no—
284C22×C43—42no—
285C22×C43—42no—
286C22×C43—42no—
287C22×C43—42no—
288C22×C43—42no—
289C22×C43—42no—
290C22×C43—42no—
291C22×C43—42no—
292C22×C43—42no—
293C22×C43—81no—
294C22×C43—81no—
295C22×C43—81no—
296C22×C43—81no—
297C22×C43C2×C4×D411yescharacteristic
298C22×C43#52511yescharacteristic
299C22×C43#52511yescharacteristic
300C22×C43#57611yescharacteristic
301C22×C43#57611yescharacteristic
302C22×C43#57711yescharacteristic
303C22×C43#57711yescharacteristic
304C4×C43—22no—
305C4×C43—22no—
306C4×C43—42no—
307C4×C43—42no—
308C4×C43C2×#11711yescharacteristic
309C4×C43C4×#4111yescharacteristic
310C4×C43#52911yescharacteristic
311C4×C43#52911yescharacteristic
312Dic43—41no—
313Dic43—42no—
314Dic43—41no—
315Dic43—41no—
316Dic43—42no—
317Dic43—41no—
318Dic43—81no—
319Dic43—81no—
320C2×#442D4311yescharacteristic
321#2319—431no—
322#2275—431no—
323#1926—431no—
324#1925—431no—
325#1920—431no—
326#1919—431no—
327#1879—431no—
328#1879—431no—
329#1864—431no—
330#1862—431no—
331#1776—431no—
332C4×#102—431no—
333C4×#102—431no—
334#1746—431no—
335C2×C43—44no—
336C2×C43—82no—
337C2×C43#229011yescharacteristic
338C2×C43#294611yescharacteristic
339C2×C43#294611yescharacteristic
340C2×C43#311811yescharacteristic
341C2×C43#311911yescharacteristic
342C2×C43#312211yescharacteristic
343C2×C43#312511yescharacteristic
344C22×D8C2×D4311yescharacteristic
345C2×C4×D4—431no—
346C2×C4×D4—431no—
347C2×C4×D4C2×D4311yescharacteristic
348C2×C4×D4C2×D4311yescharacteristic
349#442Dic4318yescomplemented
350C2×#107—431no—
351C2×#106—431no—
352C2×#106C2×D4311yescharacteristic
353C2×#102—431no—
354C2×#102—431no—
355C2×#102—431no—
356C2×#102—431no—
357C2×#102C2×D4311yescharacteristic
358C2×#102C2×D4311yescharacteristic
359C2×#97C2×D4311yescharacteristic
360C2×C4×C8—431no—
361#390—431no—
362#390—431no—
363#389—431no—
364#389—431no—
365#388—861no—
366#388—861no—
367#381—861no—
368#380—861no—
369C4×C4⋊C4—431no—
370C4×C4⋊C4—431no—
371C4×C4⋊C4—431no—
372C4×C4⋊C4—431no—
373C4×C22⋊C4—861no—
374C4×C22⋊C4—861no—
375C4×C22⋊C4—861no—
376#376—431no—
377C2×#95—861no—
378#340—431no—
379#340—431no—
380#340—431no—
381#340—431no—
382#340—431no—
383#340—431no—
384#336—431no—
385#336—431no—
386#336—431no—
387#336—431no—
388C43#2112611yescharacteristic, complemented, Sylow
389C22×D4C22×D4311yescharacteristic
390C22×D4C22×D4311yescharacteristic
391C23×C4—21no—
392C23×C4—21no—
393C23×C4—861no—
394C23×C4—861no—
395C2×D8—22no—
396C2×D8—22no—
397C2×D8C2×Dic4314yes—
398C22×C8—431no—
399C22×C8—431no—
400C22×C8C22×D4311yescharacteristic
401C22×C8C22×D4311yescharacteristic
402C4×D4—22no—
403C4×D4—22no—
404C4×D4—862no—
405C4×D4—862no—
406C4×D4—862no—
407C4×D4—862no—
408C4×D4C2×Dic4314yes—
409C4×D4C2×Dic4314yescomplemented
410C2×C4⋊C4—431no—
411C2×C4⋊C4—431no—
412C2×C4⋊C4—431no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4—861no—
416C2×C4⋊C4C22×D4311yescharacteristic
417C2×C4⋊C4C22×D4311yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—861no—
421C2×C22⋊C4—861no—
422C2×C22⋊C4—861no—
423C2×C22⋊C4—861no—
424C2×C22⋊C4—861no—
425C2×C22⋊C4—861no—
426C2×C42—431no—
427C2×C42—431no—
428C2×C42—861no—
429C2×C42—861no—
430C2×C42—861no—
431C2×C42—861no—
432C2×C42C22×D4311yescharacteristic
433#107—862no—
434#106—862no—
435#106C2×Dic4314yescomplemented
436#102—862no—
437#102—862no—
438#102—862no—
439#102—862no—
440#102C2×Dic4314yes—
441#102C2×Dic4314yescomplemented
442#97C2×Dic4314yescomplemented
443C4×C8—862no—
444#95—431no—
445#95—431no—
446#95—431no—
447#95—431no—
448#95—861no—
449#95—861no—
450#95—861no—
451#95—861no—
452#95—861no—
453#95—861no—
454C24—21no—
455C24—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4#1062189812yes—
465C2×D4#1062189812yes—
466C2×D4C22×Dic4312yes—
467C2×D4C22×Dic4312yes—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—81no—
473C22×C4—81no—
474C22×C4—81no—
475C22×C4—81no—
476C22×C4—431no—
477C22×C4—431no—
478C22×C4—431no—
479C22×C4—431no—
480C22×C4—864no—
481C22×C4—864no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4—3441no—
487C22×C4—3441no—
488C22×C4—3441no—
489C22×C4—3441no—
490C22×C4D4×D4311yescharacteristic
491C22×C4D4×D4311yescharacteristic
492C22×C4C23×D4311yescharacteristic
493D8—28no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—861no—
499C2×C8—861no—
500C2×C8—861no—
501C2×C8—861no—
502C2×C8—861no—
503C2×C8—861no—
504C2×C8C22×Dic4312yes—
505C2×C8C22×Dic4312yes—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—432no—
509C4⋊C4—432no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—3441no—
517C4⋊C4—3441no—
518C4⋊C4C22×Dic4312yes—
519C4⋊C4C22×Dic4312yes—
520C22⋊C4—24no—
521C22⋊C4—24no—
522C22⋊C4—864no—
523C22⋊C4—864no—
524C22⋊C4—3441no—
525C22⋊C4—3441no—
526C22⋊C4—3441no—
527C22⋊C4—3441no—
528C42—861no—
529C42—861no—
530C42—861no—
531C42—861no—
532C42—3441no—
533C42—3441no—
534C42—3441no—
535C42—3441no—
536C42#1062190012yes—
537C42C22×Dic4312yes—
538C23—22no—
539C23—22no—
540C23—22no—
541C23—22no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23C2×D4×D4311yescharacteristic
553D4—22no—
554D4—22no—
555D4—22no—
556D4—22no—
557D4—22no—
558D4—41no—
559D4—41no—
560D4#1306328414yes—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—84no—
572C2×C4—84no—
573C2×C4—861no—
574C2×C4—861no—
575C2×C4—861no—
576C2×C4—861no—
577C2×C4—862no—
578C2×C4—862no—
579C2×C4—861no—
580C2×C4—861no—
581C2×C4—861no—
582C2×C4—861no—
583C2×C4—861no—
584C2×C4—861no—
585C2×C4—861no—
586C2×C4—861no—
587C2×C4—3444no—
588C2×C4—3444no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4D4×Dic4312yes—
600C2×C4D4×Dic4312yes—
601C2×C4C23×Dic4311yescharacteristic
602C2×C4#41×D4311yescharacteristic
603C2×C4#41×D4311yescharacteristic
604C2×C4C2×#1062190011yescharacteristic
605C2×C4C2×#1062189811yescharacteristic
606C2×C4C2×#1062189811yescharacteristic
607C8—22no—
608C8—22no—
609C8—1721no—
610C8—1721no—
611C22—24no—
612C22—42no—
613C22—42no—
614C22—42no—
615C22—42no—
616C22—42no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22—81no—
622C22—81no—
623C22—81no—
624C22—81no—
625C22C2×D4×Dic4311yescharacteristic
626C22#1458340811yescharacteristic
627C22#1458340811yescharacteristic
628C22#1458370311yescharacteristic
629C22#1458370311yescharacteristic
630C22#1458370911yescharacteristic
631C22#1458370911yescharacteristic
632C4—22no—
633C4—22no—
634C4—42no—
635C4—42no—
636C4—3441no—
637C4—3441no—
638C4—1721no—
639C4—1722no—
640C4—1721no—
641C4—1721no—
642C4—1722no—
643C4—1721no—
644C4C2×#1306328411yescharacteristic
645C4#41×Dic4311yescharacteristic
646C4#1458342911yescharacteristic
647C4#1458342911yescharacteristic
648C2—44no—
649C2—82no—
650C2#1913704011yescharacteristic
651C2#1914342811yescharacteristic
652C2#1914342811yescharacteristic
653C2#1914477711yescharacteristic
654C2#1914479811yescharacteristic
655C2#1914483711yescharacteristic
656C2#1914487611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#442C2
socleC23×C43C22×D4
prime radicalC22×D8×C43C22
cosocleC22×C4×C43C24
hypercenterC2×#442D43
hypocenterC43#21126
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. #19137238C2semidirect
2. #19136956C2semidirect
3. #19135224C2semidirect
4. #19135217C2semidirect
5. #19135182C2semidirect
6. #19135175C2semidirect
9. #19134858C2semidirect
10. #19134844C2semidirect
11. #19134492C2semidirect
12. C4×#13063246C2semidirect
13. C4×#13063246C2semidirect
14. #19134348C2semidirect
55. C43×#442C4semidirect
115. C4×D4×C43C2×C4semidirect
121. #106×C43C2×C4semidirect
123. #102×C43C2×C4semidirect
124. #97×C43C2×C4semidirect
349. #442Dic43semidirect
388. C43#21126semidirect
409. C4×D4C2×Dic43semidirect
435. #106C2×Dic43semidirect
441. #102C2×Dic43semidirect
442. #97C2×Dic43semidirect

Maximal subgroups

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

subgroupindex
#191372382
#191369562
#191352242
#191352172
#191351822
#191351752
#191349452
#191348582
#191348442
#191344922
C4×#130632462
#191343482
C2×C43×#4422
#2112643