Finite Group Databasebeta

← #25106983

Subgroups — #25106983

Order 11008.

862 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C8×D43C211yesmaximal, characteristic
2#19136999C211yesmaximal, characteristic
3#19136988C211yesmaximal, characteristic
4#19135365C211yesmaximal, characteristic, complemented
5#19135363C211yesmaximal, characteristic, complemented
6#19135361C211yesmaximal, characteristic, complemented
7#19135357C211yesmaximal, characteristic, complemented
8#19135355C211yesmaximal, characteristic, complemented
9#19135352C211yesmaximal, characteristic, complemented
10#19135350C211yesmaximal, characteristic, complemented
11#19134623C211yesmaximal, characteristic
12#19134621C211yesmaximal, characteristic
13#19134619C211yesmaximal, characteristic
14#19134617C211yesmaximal, characteristic
15C43×#1949C211yesmaximal, characteristic, complemented
16C22×C8×D43C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18C2×#13063282—21no—
19C2×C42×D43C2211yescharacteristic
20C2×#13063259C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063257C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×C4⋊(C43⋊C8)C2211yescharacteristic
27C2×Dic43⋊C8C2211yescharacteristic
28C2×Dic43⋊C8C2211yescharacteristic
29C4⋊C8×D43C418yescomplemented
30#14582768C2211yescharacteristic
31#14582768C2211yescharacteristic
32#14582766—21no—
33#14582765C2211yescharacteristic
34#14582763—21no—
35#14582761—21no—
36#14582758—21no—
37#14582756C2211yescharacteristic
38#14582756C2211yescharacteristic
39#14582756C2211yescharacteristic
40#14582756C2211yescharacteristic
41C4⋊C4×Dic43C2211yescharacteristic
42C4⋊C4×Dic43C2211yescharacteristic
43C4×Dic43⋊C4—21no—
44C4×C4⋊Dic43C2211yescharacteristic
45#14582746—21no—
46#14582744—21no—
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53C2×#107×C43C2211yescharacteristic
54C2×#106×C43C2211yescharacteristic
55C2×C4⋊C8×C43C2211yescharacteristic
56C43×#382C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C22×C4×D43D411yescharacteristic
61C22×C4×D43D411yescharacteristic
62C22×C4×D43C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65C2×C8×D43—41no—
66C2×C8×D43—41no—
67C2×C8×D43—41no—
68C2×C8×D43—41no—
69C2×C8×D43C2×C414yes—
70C2×C8×D43C2×C414yes—
71#13063282—44no—
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊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×Dic43C2311yescharacteristic
90C42×D43C2×C414yes—
91C42×D43Q814yes—
92#13063259—41no—
93#13063258—41no—
94#13063258—41no—
95#13063257—41no—
96#13063256—41no—
97#13063256—41no—
98C4⋊(C43⋊C8)C2×C414yes—
99Dic43⋊C8C2×C414yes—
100Dic43⋊C8C2×C414yes—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C22×C8×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C42×C43—21no—
117C2×C42×C43C2311yescharacteristic
118#107×C43—41no—
119#106×C43—41no—
120C4⋊C8×C43C2×C414yes—
121#95×C43—21no—
122#95×C43—21no—
123#95×C43—21no—
124C23×D43C2×D411yescharacteristic
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2411yescharacteristic
132C22×Dic43—21no—
133C22×Dic43—21no—
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43C2×D411yescharacteristic
137C22×Dic43C2×D411yescharacteristic
138C22×Dic43C2×D411yescharacteristic
139C2×C4×D43—21no—
140C2×C4×D43—21no—
141C2×C4×D43—21no—
142C2×C4×D43—21no—
143C2×C4×D43—22no—
144C2×C4×D43—22no—
145C2×C4×D43—22no—
146C2×C4×D43—22no—
147C2×C4×D43C4⋊C414yes—
148C2×C4×D43C4⋊C414yes—
149C2×C4×D43C22×C412yes—
150C2×C4×D43C2×Q812yes—
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43C22×C412yes—
156C2×C8×C43C22×C412yes—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C42×C43—42no—
166C42×C43C22×C412yes—
167C42×C43C2×Q812yes—
168(C2×D43)⋊C4—42no—
169(C2×D43)⋊C4—42no—
170(C2×D43)⋊C4—42no—
171(C2×D43)⋊C4—42no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180Dic43⋊C4—42no—
181Dic43⋊C4—42no—
182Dic43⋊C4—42no—
183Dic43⋊C4—42no—
184C4×Dic43—42no—
185C4×Dic43—42no—
186C4×Dic43—42no—
187C4×Dic43C4⋊C414yes—
188C4×Dic43C4⋊C414yes—
189C4×Dic43C22×C412yes—
190C4×Dic43C2×Q812yes—
191C2×C43⋊C8—21no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8C22×C412yes—
196C2×C43⋊C8C22×C412yes—
197C8×D43—44no—
198C8×D43—44no—
199C23×C43C22×D411yescharacteristic
200C22×D43—21no—
201C22×D43—21no—
202C22×D43—21no—
203C22×D43—21no—
204C22×D43C2×C4⋊C412yes—
205C22×D43AGL(1,ℤ/8)12yes—
206C22×D43#13712yes—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—41no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43C2×C4⋊C412yes—
224C2×C4×C43C2×C4⋊C412yes—
225C2×C4×C43C23×C411yescharacteristic
226C2×C4×C43C22×Q811yescharacteristic
227C2×C4×C43H(5,𝔽2)11yescharacteristic
228C2×C4×C43H(5,𝔽2)11yescharacteristic
229C2×C4×C432−1+411yescharacteristic
230C2×C4×C432−1+411yescharacteristic
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43C2×C4⋊C412yes—
248C2×Dic43C2×C4⋊C412yes—
249C2×Dic43C2×C4⋊C412yes—
250C2×Dic43#13512yes—
251C2×Dic43#13512yes—
252C4×D43—28no—
253C4×D43—22no—
254C4×D43—22no—
255C4×D43—22no—
256C4×D43—22no—
257C4×D43—28no—
258C8×C43—22no—
259C8×C43—22no—
260C43⋊C8—22no—
261C43⋊C8—22no—
262#21962—431nomaximal, Sylow
263C22×C43C22×C4⋊C411yescharacteristic
264C22×C43#53711yescharacteristic
265C22×C43#53711yescharacteristic
266C22×C43C2×#13511yescharacteristic
267C22×C43C2×#13511yescharacteristic
268C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
269C22×C43C2×#13711yescharacteristic
270C2×D43—22no—
271C2×D43—22no—
272C2×D43—22no—
273C2×D43—22no—
274C2×D43—22no—
275C2×D43—22no—
276C2×D43#42814yes—
277C4×C43—22no—
278C4×C43—22no—
279C4×C43—81no—
280C4×C43—81no—
281C4×C43—81no—
282C4×C43—81no—
283C4×C43#51811yescharacteristic
284C4×C43#51911yescharacteristic
285C4×C43#54411yescharacteristic
286C4×C43#54411yescharacteristic
287Dic43—22no—
288Dic43—22no—
289Dic43—81no—
290Dic43—81no—
291Dic43—81no—
292Dic43—81no—
293Dic43#42714yes—
294C22×C4⋊C8—431no—
295#2285—431no—
296#2283—431no—
297#1949—431no—
298#1949—431no—
299#1949—431no—
300#1949D4311yescharacteristic, complemented
301#1948—431no—
302#1948—431no—
303#1947—431no—
304#1947—431no—
305#1808—431no—
306#1808—431no—
307#1807—431no—
308#1807—431no—
309C2×C43#231611yescharacteristic
310C2×C43C2×#42711yescharacteristic
311C2×C43C2×#42811yescharacteristic
312C2×C43#324711yescharacteristic
313C2×C43#324711yescharacteristic
314C2×C43#324811yescharacteristic
315C2×C43#324811yescharacteristic
316D43—24no—
317C23×C8—431no—
318C23×C8—431no—
319C2×#117—861no—
320C22×C42—431no—
321C2×#107—431no—
322C2×#107—431no—
323C2×#107—431no—
324C2×#107C2×D4311yescharacteristic
325C2×#106—431no—
326C2×#106—431no—
327C2×#106—431no—
328C2×#106C2×D4311yescharacteristic
329C2×C4⋊C8—431no—
330C2×C4⋊C8—431no—
331C2×C4⋊C8—431no—
332C2×C4⋊C8—438no—
333C2×C4⋊C8C2×D4311yescharacteristic
334#384—431no—
335#384—431no—
336#383—861no—
337#382—431no—
338#382—861no—
339#382C2×D4311yescharacteristic
340#381—861no—
341#380—431no—
342#380—431no—
343#380—431no—
344#380—431no—
345#380—861no—
346C4×C4⋊C4—431no—
347C4×C4⋊C4—431no—
348C4×C4⋊C4—431no—
349C4×C4⋊C4—861no—
350C4×C4⋊C4C2×D4311yescharacteristic
351C4×C22⋊C4—861no—
352#376—861no—
353#340—431no—
354#340—431no—
355#340—431no—
356#340—431no—
357#340—431no—
358#340—431no—
359#340C2×D4311yescharacteristic
360#340C2×D4311yescharacteristic
361C43#2196211yescharacteristic, complemented, Sylow
362C23×C4—431no—
363C23×C4—431no—
364C23×C4—431no—
365C22×C8—431no—
366C22×C8—431no—
367C22×C8—434no—
368C22×C8—434no—
369C22×C8—1721no—
370C22×C8—1721no—
371C22×C8—1721no—
372C22×C8—1721no—
373C22×C8C22×D4311yescharacteristic
374C22×C8C22×D4311yescharacteristic
375#117—1724no—
376C2×C4⋊C4—431no—
377C2×C4⋊C4—431no—
378C2×C4⋊C4—431no—
379C2×C4⋊C4—431no—
380C2×C4⋊C4—861no—
381C2×C4⋊C4—861no—
382C2×C4⋊C4—861no—
383C2×C4⋊C4—861no—
384C2×C4⋊C4C22×D4311yescharacteristic
385C2×C4⋊C4C22×D4311yescharacteristic
386C2×C4⋊C4C22×D4311yescharacteristic
387C2×C4⋊C4C22×D4311yescharacteristic
388C2×C22⋊C4—861no—
389C2×C22⋊C4—861no—
390C2×C22⋊C4—861no—
391C2×C22⋊C4—861no—
392C2×C42—21no—
393C2×C42—431no—
394C2×C42—431no—
395C2×C42—431no—
396C2×C42—434no—
397C2×C42—434no—
398C2×C42—861no—
399C2×C42—861no—
400C2×C42—861no—
401C2×C42C22×D4311yescharacteristic
402#107—41no—
403#107—1721no—
404#107—1721no—
405#107—1721no—
406#106—41no—
407#106—1721no—
408#106—1721no—
409#106—1721no—
410C4⋊C8—434no—
411C4⋊C8—434no—
412C4⋊C8—434no—
413C4⋊C8C4×D4314yes—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—861no—
418#95—861no—
419#95—861no—
420#95—861no—
421#95—861no—
422#95—861no—
423#95—861no—
424#95—861no—
425#95—861no—
426C24—431no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—431no—
432C22×C4—431no—
433C22×C4—431no—
434C22×C4—434no—
435C22×C4—434no—
436C22×C4—432no—
437C22×C4—432no—
438C22×C4—862no—
439C22×C4—862no—
440C22×C4—862no—
441C22×C4—862no—
442C22×C4—861no—
443C22×C4—861no—
444C22×C4—861no—
445C22×C4—861no—
446C22×C4—861no—
447C22×C4—861no—
448C22×C4—861no—
449C22×C4—861no—
450C22×C4D4×D4311yescharacteristic
451C22×C4D4×D4311yescharacteristic
452C22×C4C23×D4311yescharacteristic
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—432no—
458C2×C8—432no—
459C2×C8—861no—
460C2×C8—861no—
461C2×C8—861no—
462C2×C8—861no—
463C2×C8—1724no—
464C2×C8—1724no—
465C2×C8C2×C4×D4312yes—
466C2×C8C2×C4×D4312yes—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—1722no—
484C4⋊C4—1722no—
485C4⋊C4—1722no—
486C4⋊C4—1722no—
487C22⋊C4—1722no—
488C22⋊C4—1722no—
489C22⋊C4—1722no—
490C22⋊C4—1722no—
491C42—42no—
492C42—434no—
493C42—434no—
494C42—432no—
495C42—432no—
496C42—1722no—
497C42—1722no—
498C42—1722no—
499C42C2×C4×D4312yes—
500C42Q8×D4312yes—
501C23—432no—
502C23—432no—
503C23—432no—
504C23—861no—
505C23—861no—
506C23—861no—
507C23—861no—
508C23C2×D4×D4311yescharacteristic
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—432no—
526C2×C4—432no—
527C2×C4—432no—
528C2×C4—432no—
529C2×C4—432no—
530C2×C4—868no—
531C2×C4—868no—
532C2×C4—861no—
533C2×C4—861no—
534C2×C4—861no—
535C2×C4—861no—
536C2×C4—862no—
537C2×C4—862no—
538C2×C4—862no—
539C2×C4—862no—
540C2×C4—1721no—
541C2×C4—1721no—
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×C4C4⋊C4×D4312yes—
553C2×C4C4⋊C4×D4312yes—
554C2×C4C22×C4×D4311yescharacteristic
555C2×C4C2×Q8×D4311yescharacteristic
556C2×C4#1306337011yescharacteristic
557C2×C4#1306337111yescharacteristic
558C2×C4#1306337211yescharacteristic
559C2×C4#1306337311yescharacteristic
560C8—22no—
561C8—22no—
562C8—862no—
563C8—862no—
564C22—434no—
565C22—862no—
566C22—862no—
567C22—862no—
568C22—862no—
569C22—862no—
570C22—862no—
571C22C2×C4⋊C4×D4311yescharacteristic
572C22#1458347811yescharacteristic
573C22#1458347911yescharacteristic
574C22#135×D4311yescharacteristic
575C22#135×D4311yescharacteristic
576C22AGL(1,ℤ/8)×D4311yescharacteristic
577C22#137×D4311yescharacteristic
578C4—22no—
579C4—22no—
580C4—81no—
581C4—81no—
582C4—81no—
583C4—81no—
584C4—434no—
585C4—862no—
586C4—862no—
587C4—3441no—
588C4—3441no—
589C4—3441no—
590C4—3441no—
591C4#1458337111yescharacteristic
592C4#1458337511yescharacteristic
593C4#1458352611yescharacteristic
594C4#1458352911yescharacteristic
595C2—864no—
596C2#1913721011yescharacteristic
597C2#427×D4311yescharacteristic
598C2#428×D4311yescharacteristic
599C2#1914591811yescharacteristic
600C2#1914592011yescharacteristic
601C2#1914592911yescharacteristic
602C2#1914593111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1949C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
cosocleC22×C4×C43C24
hypercenter#1949D43
hypocenterC43#21962
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1949

Complements

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

NH ≅ G/Ntype
4. #19135365C2semidirect
5. #19135363C2semidirect
6. #19135361C2semidirect
7. #19135357C2semidirect
8. #19135355C2semidirect
9. #19135352C2semidirect
10. #19135350C2semidirect
15. C43×#1949C2semidirect
29. C4⋊C8×D43C4semidirect
300. #1949D43semidirect
361. C43#21962semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C8×D432
#191369992
#191369882
#191353652
#191353632
#191353612
#191353572
#191353552
#191353522
#191353502
#191346232
#191346212
#191346192
#191346172
C43×#19492
#2196243