Finite Group Databasebeta

← #25106970

Subgroups — #25106970

Order 11008.

818 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C8×D43C211yesmaximal, characteristic
2#19136991C211yesmaximal, characteristic
3#19136988C211yesmaximal, characteristic
4#19135366C211yesmaximal, characteristic, complemented
5#19135365C211yesmaximal, characteristic, complemented
6#19135364C211yesmaximal, characteristic, complemented
7#19135363C211yesmaximal, characteristic, complemented
8#19135362C211yesmaximal, characteristic, complemented
9#19135361C211yesmaximal, characteristic, complemented
10#19135360C211yesmaximal, 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×C42×D43C2211yescharacteristic
19C2×#13063259C2211yescharacteristic
20C2×#13063258C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×#13063257C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×C4⋊(C43⋊C8)C2211yescharacteristic
26C2×Dic43⋊C8C2211yescharacteristic
27C2×Dic43⋊C8C2211yescharacteristic
28C4⋊C8×D43C418yescomplemented
29#14582766—21no—
30#14582766—21no—
31#14582765C2211yescharacteristic
32#14582764C2211yescharacteristic
33#14582764C2211yescharacteristic
34#14582761—21no—
35#14582761—21no—
36#14582756C2211yescharacteristic
37#14582756C2211yescharacteristic
38#14582756C2211yescharacteristic
39#14582756C2211yescharacteristic
40C4⋊C4×Dic43C2211yescharacteristic
41C4⋊C4×Dic43C2211yescharacteristic
42C4×C4⋊Dic43C2211yescharacteristic
43C4×(C2×D43)⋊C4—21no—
44#14582746—21no—
45#14582745—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—
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×(C2×D43)⋊C4—21no—
76C2×(C2×D43)⋊C4—21no—
77C2×(C2×D43)⋊C4—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×C4×Dic43—21no—
80C2×C4×Dic43—21no—
81C2×C4×Dic43—21no—
82C2×C4×Dic43D411yescharacteristic
83C2×C4×Dic43D411yescharacteristic
84C2×C4×Dic43C2311yescharacteristic
85C42×D43C2×C414yes—
86C42×D43Q814yes—
87#13063259—41no—
88#13063258—41no—
89#13063258—41no—
90#13063257—41no—
91#13063256—41no—
92#13063256—41no—
93C4⋊(C43⋊C8)C2×C414yes—
94Dic43⋊C8C2×C414yes—
95Dic43⋊C8C2×C414yes—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C22×C8×C43C2311yescharacteristic
110C22×C8×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C42×C43—21no—
116C2×C42×C43C2311yescharacteristic
117#107×C43—41no—
118#106×C43—41no—
119C4⋊C8×C43C2×C414yes—
120#95×C43—21no—
121#95×C43—21no—
122#95×C43—21no—
123C23×D43C2×D411yescharacteristic
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×Dic43—21no—
135C22×Dic43C2×D411yescharacteristic
136C22×Dic43C2×D411yescharacteristic
137C22×Dic43C2×D411yescharacteristic
138C2×C4×D43—21no—
139C2×C4×D43—21no—
140C2×C4×D43—21no—
141C2×C4×D43—21no—
142C2×C4×D43—22no—
143C2×C4×D43—22no—
144C2×C4×D43—41no—
145C2×C4×D43—41no—
146C2×C4×D43C4⋊C414yes—
147C2×C4×D43C4⋊C414yes—
148C2×C4×D43C22×C412yes—
149C2×C4×D43C2×Q812yes—
150C2×C8×C43—21no—
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43C22×C412yes—
155C2×C8×C43C22×C412yes—
156C4⋊C4×C43—21no—
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—
164C42×C43—42no—
165C42×C43C22×C412yes—
166C42×C43C2×Q812yes—
167(C2×D43)⋊C4—42no—
168(C2×D43)⋊C4—42no—
169(C2×D43)⋊C4—42no—
170(C2×D43)⋊C4—42no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4×Dic43—42no—
180C4×Dic43—42no—
181C4×Dic43—42no—
182C4×Dic43C4⋊C414yes—
183C4×Dic43C4⋊C414yes—
184C4×Dic43C22×C412yes—
185C4×Dic43C2×Q812yes—
186C2×C43⋊C8—21no—
187C2×C43⋊C8—21no—
188C2×C43⋊C8—21no—
189C2×C43⋊C8—21no—
190C2×C43⋊C8C22×C412yes—
191C2×C43⋊C8C22×C412yes—
192C8×D43—44no—
193C8×D43—44no—
194C23×C43C22×D411yescharacteristic
195C22×D43—21no—
196C22×D43—21no—
197C22×D43—21no—
198C22×D43—21no—
199C22×D43C2×C4⋊C412yes—
200C22×D43#13512yes—
201C22×D43#13512yes—
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—41no—
207C2×C4×C43—41no—
208C2×C4×C43—41no—
209C2×C4×C43—41no—
210C2×C4×C43—41no—
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×C43C2×C4⋊C412yes—
219C2×C4×C43C2×C4⋊C412yes—
220C2×C4×C43C23×C411yescharacteristic
221C2×C4×C43C22×Q811yescharacteristic
222C2×C4×C43H(5,𝔽2)11yescharacteristic
223C2×C4×C43H(5,𝔽2)11yescharacteristic
224C2×C4×C432−1+411yescharacteristic
225C2×C4×C432−1+411yescharacteristic
226C2×Dic43—21no—
227C2×Dic43—21no—
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—41no—
233C2×Dic43—41no—
234C2×Dic43—41no—
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×Dic43C2×C4⋊C412yes—
245C2×Dic43C2×C4⋊C412yes—
246C2×Dic43C2×C4⋊C412yes—
247C4×D43—28no—
248C4×D43—22no—
249C4×D43—22no—
250C4×D43—22no—
251C4×D43—22no—
252C4×D43—44no—
253C8×C43—22no—
254C8×C43—22no—
255C43⋊C8—22no—
256C43⋊C8—22no—
257#21960—431nomaximal, Sylow
258C22×C43C22×C4⋊C411yescharacteristic
259C22×C43#53711yescharacteristic
260C22×C43#53711yescharacteristic
261C22×C43C2×#13511yescharacteristic
262C22×C43C2×#13511yescharacteristic
263C22×C43#57511yescharacteristic
264C22×C43#57511yescharacteristic
265C2×D43—22no—
266C2×D43—22no—
267C2×D43—22no—
268C2×D43—22no—
269C2×D43—22no—
270C2×D43—22no—
271C2×D43#42714yes—
272C4×C43—22no—
273C4×C43—22no—
274C4×C43—81no—
275C4×C43—81no—
276C4×C43—81no—
277C4×C43—81no—
278C4×C43#51811yescharacteristic
279C4×C43#51911yescharacteristic
280C4×C43#54411yescharacteristic
281C4×C43#54411yescharacteristic
282Dic43—22no—
283Dic43—22no—
284Dic43—22no—
285Dic43—81no—
286Dic43—81no—
287Dic43—81no—
288Dic43—81no—
289C22×C4⋊C8—431no—
290#2283—431no—
291#2283—431no—
292#1949—431no—
293#1949—431no—
294#1949—431no—
295#1949—431no—
296#1949—431no—
297#1949—431no—
298#1949—431no—
299#1949D4311yescharacteristic, complemented
300#1808—431no—
301#1808—431no—
302#1807—431no—
303#1807—431no—
304C2×C43#231611yescharacteristic
305C2×C43C2×#42711yescharacteristic
306C2×C43#291111yescharacteristic
307C2×C43#325011yescharacteristic
308C2×C43#325011yescharacteristic
309C2×C43#325011yescharacteristic
310C2×C43#325011yescharacteristic
311D43—24no—
312C23×C8—431no—
313C23×C8—431no—
314C22×C42—431no—
315C2×#107—431no—
316C2×#107—431no—
317C2×#107—431no—
318C2×#107C2×D4311yescharacteristic
319C2×#106—431no—
320C2×#106—431no—
321C2×#106—431no—
322C2×#106C2×D4311yescharacteristic
323C2×C4⋊C8—431no—
324C2×C4⋊C8—431no—
325C2×C4⋊C8—431no—
326C2×C4⋊C8—438no—
327C2×C4⋊C8C2×D4311yescharacteristic
328#383—861no—
329#383—861no—
330#382—431no—
331#382—431no—
332#382—431no—
333#382C2×D4311yescharacteristic
334#381—861no—
335#381—861no—
336#380—431no—
337#380—431no—
338#380—431no—
339#380—431no—
340C4×C4⋊C4—431no—
341C4×C4⋊C4—431no—
342C4×C4⋊C4—431no—
343C4×C4⋊C4C2×D4311yescharacteristic
344C4×C22⋊C4—861no—
345C4×C22⋊C4—861no—
346#376—861no—
347#376—861no—
348#340—431no—
349#340—431no—
350#340—431no—
351#340—431no—
352#340—431no—
353#340—431no—
354#340C2×D4311yescharacteristic
355#340C2×D4311yescharacteristic
356C43#2196011yescharacteristic, complemented, Sylow
357C23×C4—431no—
358C23×C4—431no—
359C23×C4—431no—
360C22×C8—431no—
361C22×C8—431no—
362C22×C8—434no—
363C22×C8—434no—
364C22×C8—1721no—
365C22×C8—1721no—
366C22×C8—1721no—
367C22×C8—1721no—
368C22×C8C22×D4311yescharacteristic
369C22×C8C22×D4311yescharacteristic
370C2×C4⋊C4—431no—
371C2×C4⋊C4—431no—
372C2×C4⋊C4—431no—
373C2×C4⋊C4—431no—
374C2×C4⋊C4C22×D4311yescharacteristic
375C2×C4⋊C4C22×D4311yescharacteristic
376C2×C4⋊C4C22×D4311yescharacteristic
377C2×C4⋊C4C22×D4311yescharacteristic
378C2×C22⋊C4—861no—
379C2×C22⋊C4—861no—
380C2×C22⋊C4—861no—
381C2×C22⋊C4—861no—
382C2×C42—21no—
383C2×C42—431no—
384C2×C42—431no—
385C2×C42—431no—
386C2×C42—434no—
387C2×C42—434no—
388C2×C42—861no—
389C2×C42—861no—
390C2×C42—861no—
391C2×C42C22×D4311yescharacteristic
392#107—41no—
393#107—1721no—
394#107—1721no—
395#107—1721no—
396#106—41no—
397#106—1721no—
398#106—1721no—
399#106—1721no—
400C4⋊C8—434no—
401C4⋊C8—434no—
402C4⋊C8—434no—
403C4⋊C8C4×D4314yes—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—861no—
408#95—861no—
409#95—861no—
410#95—861no—
411#95—861no—
412#95—861no—
413#95—861no—
414#95—861no—
415#95—861no—
416#95—861no—
417#95—861no—
418#95—861no—
419#95—861no—
420C24—431no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—431no—
426C22×C4—431no—
427C22×C4—431no—
428C22×C4—434no—
429C22×C4—432no—
430C22×C4—432no—
431C22×C4—434no—
432C22×C4—862no—
433C22×C4—862no—
434C22×C4—861no—
435C22×C4—861no—
436C22×C4—861no—
437C22×C4—861no—
438C22×C4—861no—
439C22×C4—861no—
440C22×C4—861no—
441C22×C4—861no—
442C22×C4—1721no—
443C22×C4—1721no—
444C22×C4D4×D4311yescharacteristic
445C22×C4D4×D4311yescharacteristic
446C22×C4C23×D4311yescharacteristic
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—432no—
452C2×C8—432no—
453C2×C8—861no—
454C2×C8—861no—
455C2×C8—861no—
456C2×C8—861no—
457C2×C8—1724no—
458C2×C8—1724no—
459C2×C8C2×C4×D4312yes—
460C2×C8C2×C4×D4312yes—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C22⋊C4—1722no—
478C22⋊C4—1722no—
479C22⋊C4—1722no—
480C22⋊C4—1722no—
481C42—42no—
482C42—434no—
483C42—434no—
484C42—432no—
485C42—432no—
486C42—1722no—
487C42—1722no—
488C42—1722no—
489C42C2×C4×D4312yes—
490C42Q8×D4312yes—
491C23—432no—
492C23—432no—
493C23—432no—
494C23—861no—
495C23—861no—
496C23—861no—
497C23—861no—
498C23C2×D4×D4311yescharacteristic
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—432no—
516C2×C4—432no—
517C2×C4—432no—
518C2×C4—868no—
519C2×C4—861no—
520C2×C4—861no—
521C2×C4—861no—
522C2×C4—861no—
523C2×C4—861no—
524C2×C4—861no—
525C2×C4—862no—
526C2×C4—862no—
527C2×C4—862no—
528C2×C4—862no—
529C2×C4—1724no—
530C2×C4—1721no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4—1721no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4—1721no—
537C2×C4—1721no—
538C2×C4—1721no—
539C2×C4—1721no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4C4⋊C4×D4312yes—
543C2×C4C4⋊C4×D4312yes—
544C2×C4C22×C4×D4311yescharacteristic
545C2×C4C2×Q8×D4311yescharacteristic
546C2×C4#1306337011yescharacteristic
547C2×C4#1306337111yescharacteristic
548C2×C4#1306337211yescharacteristic
549C2×C4#1306337311yescharacteristic
550C8—22no—
551C8—22no—
552C8—862no—
553C8—862no—
554C22—434no—
555C22—862no—
556C22—862no—
557C22—862no—
558C22—862no—
559C22—862no—
560C22—862no—
561C22C2×C4⋊C4×D4311yescharacteristic
562C22#1458347811yescharacteristic
563C22#1458347911yescharacteristic
564C22#135×D4311yescharacteristic
565C22#135×D4311yescharacteristic
566C22#1458369511yescharacteristic
567C22#1458369811yescharacteristic
568C4—22no—
569C4—22no—
570C4—81no—
571C4—81no—
572C4—81no—
573C4—81no—
574C4—862no—
575C4—862no—
576C4—862no—
577C4—3441no—
578C4—3441no—
579C4—3441no—
580C4—3441no—
581C4#1458337111yescharacteristic
582C4#1458337511yescharacteristic
583C4#1458352611yescharacteristic
584C4#1458352911yescharacteristic
585C2—864no—
586C2#1913721011yescharacteristic
587C2#427×D4311yescharacteristic
588C2#1914318211yescharacteristic
589C2#1914594411yescharacteristic
590C2#1914594511yescharacteristic
591C2#1914594611yescharacteristic
592C2#1914594911yescharacteristic
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#21960
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. #19135366C2semidirect
5. #19135365C2semidirect
6. #19135364C2semidirect
7. #19135363C2semidirect
8. #19135362C2semidirect
9. #19135361C2semidirect
10. #19135360C2semidirect
15. C43×#1949C2semidirect
28. C4⋊C8×D43C4semidirect
299. #1949D43semidirect
356. C43#21960semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C8×D432
#191369912
#191369882
#191353662
#191353652
#191353642
#191353632
#191353622
#191353612
#191353602
#191346232
#191346212
#191346192
#191346172
C43×#19492
#2196043