Finite Group Databasebeta

← #25021850

Subgroups — #25021850

Order 11008.

1646 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582760C211yesmaximal, characteristic
2C2×C22⋊C4×Dic43C212yesmaximal
3#19132840C211yesmaximal, characteristic
4#19132838C212yesmaximal
5#19132830C212yesmaximal, complemented
6#19132829C212yesmaximal, complemented
7#19132827C212yesmaximal, complemented
8#19132826C212yesmaximal, complemented
9C43×#1439C211yesmaximal, characteristic
10C24×Dic43C2211yescharacteristic
11C22×C4⋊Dic43C2211yescharacteristic
12C22×Dic43⋊C4C2212yes—
13C22×C22⋊Dic43C2212yes—
14C22×C22⋊Dic43C2211yescharacteristic
15C22×C4×Dic43C2212yes—
16C22×C4×Dic43C2212yes—
17#14582760C418yescomplemented
18C22⋊C4×Dic43—28no—
19C2×C43⋊#95C2212yes—
20C2×C43⋊#95C2212yes—
21C2×C43⋊#95C2212yes—
22C2×C43⋊#95C2212yes—
23C2×C43⋊#95C2212yes—
24C2×C43⋊#95C2212yes—
25C2×C43⋊#95C2211yescharacteristic
26C2×C43⋊#95C2212yes—
27C2×C43⋊#95C2212yes—
28C22×C4⋊C4×C43C2211yescharacteristic
29C22×C22⋊C4×C43C2212yes—
30C22×C22⋊C4×C43C2211yescharacteristic
31C2×#95×C43C2212yes—
32C2×#95×C43C2211yescharacteristic
33C23×Dic43—41no—
34C23×Dic43—41no—
35C23×Dic43—41no—
36C23×Dic43—41no—
37C23×Dic43C2×C414yes—
38C23×Dic43D414yes—
39C23×Dic43Q814yes—
40C23×Dic43C2312yes—
41C23×Dic43C2312yes—
42C23×Dic43C2312yes—
43C23×Dic43C2312yes—
44C2×C4⋊Dic43—24no—
45C2×C4⋊Dic43—41no—
46C2×Dic43⋊C4—24no—
47C2×Dic43⋊C4—24no—
48C2×Dic43⋊C4—42no—
49C2×C22⋊Dic43—24no—
50C2×C22⋊Dic43—24no—
51C2×C22⋊Dic43—24no—
52C2×C22⋊Dic43—41no—
53C2×C22⋊Dic43—41no—
54C2×C22⋊Dic43C2×C414yes—
55C2×C4×Dic43—24no—
56C2×C4×Dic43—24no—
57C2×C4×Dic43—42no—
58C2×C4×Dic43—42no—
59C2×C4×Dic43—42no—
60C2×C4×Dic43—42no—
61C43⋊#95—24no—
62C43⋊#95—24no—
63C43⋊#95—24no—
64C43⋊#95—24no—
65C43⋊#95—24no—
66C43⋊#95—41no—
67C43⋊#95—42no—
68C43⋊#95C2×C418yes—
69C43⋊#95C2×C418yes—
70C25×C43C2311yescharacteristic
71C23×C4×C43C2311yescharacteristic
72C23×C4×C43C2311yescharacteristic
73C23×C4×C43C2312yes—
74C23×C4×C43C2312yes—
75C2×C4⋊C4×C43—24no—
76C2×C4⋊C4×C43—41no—
77C2×C22⋊C4×C43—24no—
78C2×C22⋊C4×C43—24no—
79C2×C22⋊C4×C43—24no—
80C2×C22⋊C4×C43—41no—
81C2×C22⋊C4×C43—41no—
82C2×C22⋊C4×C43C2×C414yes—
83#95×C43—24no—
84#95×C43—41no—
85C24×C43—22no—
86C24×C43—22no—
87C24×C43—22no—
88C24×C43—22no—
89C24×C43—21no—
90C24×C43—21no—
91C24×C43—21no—
92C24×C43—21no—
93C24×C43C22×C412yes—
94C24×C43C2×D412yes—
95C24×C43C2×Q812yes—
96C24×C43C2411yescharacteristic
97C22×C4×C43—22no—
98C22×C4×C43—22no—
99C22×C4×C43—22no—
100C22×C4×C43—22no—
101C22×C4×C43—22no—
102C22×C4×C43—22no—
103C22×C4×C43—22no—
104C22×C4×C43—22no—
105C22×C4×C43—22no—
106C22×C4×C43—22no—
107C22×C4×C43—22no—
108C22×C4×C43—22no—
109C22×C4×C43—21no—
110C22×C4×C43—22no—
111C22×C4×C43—21no—
112C22×C4×C43—21no—
113C22×C4×C43—21no—
114C22×C4×C43—22no—
115C22×C4×C43—22no—
116C22×C4×C43—22no—
117C22×C4×C43C22×C412yes—
118C22×C4×C43C22×C412yes—
119C22×C4×C43#4114yes—
120C22×C4×C43#4114yes—
121C22×Dic43—22no—
122C22×Dic43—22no—
123C22×Dic43—22no—
124C22×Dic43—22no—
125C22×Dic43—22no—
126C22×Dic43—22no—
127C22×Dic43—22no—
128C22×Dic43—22no—
129C22×Dic43—22no—
130C22×Dic43—22no—
131C22×Dic43—22no—
132C22×Dic43—22no—
133C22×Dic43—22no—
134C22×Dic43—22no—
135C22×Dic43—22no—
136C22×Dic43—22no—
137C22×Dic43—22no—
138C22×Dic43—22no—
139C22×Dic43—22no—
140C22×Dic43—22no—
141C22×Dic43—22no—
142C22×Dic43—22no—
143C22×Dic43—44no—
144C22×Dic43—44no—
145C22×Dic43—44no—
146C22×Dic43—44no—
147C22×Dic43—44no—
148C22×Dic43—44no—
149C22×Dic43C4⋊C4116yescomplemented
150C22×Dic43C22×C414yes—
151C22×Dic43C22×C414yes—
152C22×Dic43C2×D414yes—
153C22×Dic43C2×Q814yes—
154C22×Dic43#4114yes—
155C22×Dic43#4114yes—
156C4⋊C4×C43—44no—
157C22⋊C4×C43—216no—
158C22⋊C4×C43—44no—
159C22⋊Dic43—216no—
160C22⋊Dic43—44no—
161C4⋊Dic43—44no—
162Dic43⋊C4—48no—
163C4×Dic43—48no—
164C4×Dic43—48no—
165C23×C43—24no—
166C23×C43—24no—
167C23×C43—22no—
168C23×C43—22no—
169C23×C43—24no—
170C23×C43—24no—
171C23×C43—24no—
172C23×C43—24no—
173C23×C43—22no—
174C23×C43—22no—
175C23×C43—22no—
176C23×C43—22no—
177C23×C43—42no—
178C23×C43—41no—
179C23×C43—41no—
180C23×C43—42no—
181C23×C43—42no—
182C23×C43—42no—
183C23×C43—42no—
184C23×C43—42no—
185C23×C43—41no—
186C23×C43—41no—
187C23×C43C2×C4⋊C414yes—
188C23×C43C23×C411yescharacteristic
189C23×C43C22×D411yescharacteristic
190C23×C43C22×Q811yescharacteristic
191C23×C43C2×#4112yes—
192C23×C43C2×#4112yes—
193C23×C43C2×#4112yes—
194C23×C43C2×#4112yes—
195C23×C43H(5,𝔽2)11yescharacteristic
196C23×C43H(5,𝔽2)11yescharacteristic
197C23×C43H(5,𝔽2)11yescharacteristic
198C23×C43H(5,𝔽2)11yescharacteristic
199C2×C4×C43—24no—
200C2×C4×C43—24no—
201C2×C4×C43—22no—
202C2×C4×C43—22no—
203C2×C4×C43—24no—
204C2×C4×C43—24no—
205C2×C4×C43—24no—
206C2×C4×C43—24no—
207C2×C4×C43—24no—
208C2×C4×C43—24no—
209C2×C4×C43—42no—
210C2×C4×C43—42no—
211C2×C4×C43—42no—
212C2×C4×C43—42no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43—42no—
216C2×C4×C43—42no—
217C2×C4×C43—42no—
218C2×C4×C43—42no—
219C2×C4×C43—42no—
220C2×C4×C43—41no—
221C2×C4×C43—42no—
222C2×C4×C43—41no—
223C2×Dic43—24no—
224C2×Dic43—24no—
225C2×Dic43—24no—
226C2×Dic43—24no—
227C2×Dic43—24no—
228C2×Dic43—24no—
229C2×Dic43—24no—
230C2×Dic43—24no—
231C2×Dic43—24no—
232C2×Dic43—24no—
233C2×Dic43—24no—
234C2×Dic43—24no—
235C2×Dic43—24no—
236C2×Dic43—24no—
237C2×Dic43—24no—
238C2×Dic43—416no—
239C2×Dic43—42no—
240C2×Dic43—42no—
241C2×Dic43—42no—
242C2×Dic43—42no—
243C2×Dic43—42no—
244C2×Dic43—42no—
245C2×Dic43—42no—
246C2×Dic43—42no—
247C2×Dic43—42no—
248C2×Dic43—42no—
249C2×Dic43—42no—
250C2×Dic43—42no—
251C2×Dic43C2×C4⋊C418yes—
252#14165—431nomaximal, Sylow
253C22×C43—24no—
254C22×C43—28no—
255C22×C43—42no—
256C22×C43—44no—
257C22×C43—42no—
258C22×C43—42no—
259C22×C43—42no—
260C22×C43—44no—
261C22×C43—44no—
262C22×C43—42no—
263C22×C43—42no—
264C22×C43C22×C4⋊C411yescharacteristic
265C22×C43C4×#4112yes—
266C22×C43C4×#4112yes—
267C22×C43#51811yescharacteristic
268C22×C43#51811yescharacteristic
269C22×C43#52512yes—
270C22×C43#52512yes—
271C22×C43#53312yes—
272C22×C43#53312yes—
273C22×C43#53411yescharacteristic
274C22×C43#53411yescharacteristic
275C22×C43#54311yescharacteristic
276C22×C43#54311yescharacteristic
277C22×C43#55112yes—
278C22×C43#55111yescharacteristic
279C22×C43#55111yescharacteristic
280C22×C43#55312yes—
281C22×C43#55312yes—
282C22×C43#55312yes—
283C22×C43#55312yes—
284C22×C43#55912yes—
285C22×C43#55911yescharacteristic
286C22×C43#55911yescharacteristic
287C4×C43—44no—
288C4×C43—44no—
289C4×C43—42no—
290C4×C43—42no—
291Dic43—28no—
292Dic43—44no—
293Dic43—44no—
294Dic43—44no—
295C2×#381—431no—
296C2×C4×C22⋊C4—432no—
297#1439—432no—
298#1439—431no—
299#1439D4311yescharacteristic
300#1436—432no—
301#1436—432no—
302#1436—432no—
303#1436—432no—
304C2×C43—44no—
305C2×C43#229612yes—
306C2×C43#231511yescharacteristic
307C2×C43#237412yes—
308C2×C43#237411yescharacteristic
309C2×C43#237411yescharacteristic
310C2×C43#260011yescharacteristic
311C2×C43#260012yes—
312C2×C43#260011yescharacteristic
313C2×C43#260711yescharacteristic
314C2×C43#260711yescharacteristic
315C2×C43#260812yes—
316C24×C4—431no—
317C22×C4⋊C4—432no—
318C22×C4⋊C4—431no—
319C22×C4⋊C4C2×D4311yescharacteristic
320C22×C22⋊C4—431no—
321C22×C22⋊C4—432no—
322C22×C22⋊C4C2×D4312yes—
323C22×C22⋊C4C2×D4311yescharacteristic
324C22×C42—432no—
325C22×C42—432no—
326#381—438no—
327C4×C22⋊C4—868no—
328C2×#95—432no—
329C2×#95—432no—
330C2×#95—432no—
331C2×#95—432no—
332C2×#95—432no—
333C2×#95—432no—
334C2×#95—432no—
335C2×#95—432no—
336C2×#95—431no—
337C2×#95C2×D4312yes—
338C2×#95C2×D4311yescharacteristic
339C43#1416511yescharacteristic, complemented, Sylow
340C25C22×D4311yescharacteristic
341C23×C4—432no—
342C23×C4—434no—
343C23×C4—434no—
344C23×C4—434no—
345C23×C4—432no—
346C23×C4—432no—
347C23×C4—432no—
348C23×C4—1721no—
349C23×C4—1721no—
350C23×C4—1721no—
351C23×C4—1721no—
352C23×C4C22×D4311yescharacteristic
353C23×C4C22×D4311yescharacteristic
354C23×C4C22×D4312yes—
355C23×C4C22×D4312yes—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—41no—
358C2×C4⋊C4—864no—
359C2×C4⋊C4—864no—
360C2×C4⋊C4—864no—
361C2×C4⋊C4—1722no—
362C2×C4⋊C4—1721no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—41no—
367C2×C22⋊C4—41no—
368C2×C22⋊C4—434no—
369C2×C22⋊C4—864no—
370C2×C22⋊C4—864no—
371C2×C22⋊C4—864no—
372C2×C22⋊C4—1721no—
373C2×C22⋊C4—1721no—
374C2×C22⋊C4C4×D4314yes—
375C2×C42—864no—
376C2×C42—864no—
377C2×C42—1722no—
378C2×C42—1722no—
379C2×C42—1722no—
380C2×C42—1722no—
381#95—24no—
382#95—41no—
383#95—438no—
384#95—438no—
385#95—864no—
386#95—864no—
387#95—864no—
388#95—864no—
389#95—864no—
390#95—1721no—
391#95—1722no—
392C24—22no—
393C24—22no—
394C24—22no—
395C24—22no—
396C24—21no—
397C24—21no—
398C24—21no—
399C24—21no—
400C24C2×C4×D4312yes—
401C24D4×D4312yes—
402C24Q8×D4312yes—
403C24C23×D4311yescharacteristic
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—434no—
425C22×C4—434no—
426C22×C4—434no—
427C22×C4—4316no—
428C22×C4—434no—
429C22×C4—434no—
430C22×C4—434no—
431C22×C4—862no—
432C22×C4—862no—
433C22×C4—862no—
434C22×C4—862no—
435C22×C4—862no—
436C22×C4—862no—
437C22×C4—862no—
438C22×C4—862no—
439C22×C4—862no—
440C22×C4—862no—
441C22×C4—862no—
442C22×C4—862no—
443C22×C4—862no—
444C22×C4—862no—
445C22×C4—862no—
446C22×C4—862no—
447C22×C4—862no—
448C22×C4—862no—
449C22×C4—862no—
450C22×C4—862no—
451C22×C4—862no—
452C22×C4—862no—
453C22×C4—1724no—
454C22×C4—1724no—
455C22×C4—1724no—
456C22×C4—1724no—
457C22×C4—1724no—
458C22×C4—1724no—
459C22×C4C2×C4×D4312yes—
460C22×C4C2×C4×D4312yes—
461C22×C4#1062190014yes—
462C22×C4#1062190014yes—
463C4⋊C4—44no—
464C4⋊C4—1728no—
465C4⋊C4—1724no—
466C22⋊C4—216no—
467C22⋊C4—44no—
468C22⋊C4—8616no—
469C22⋊C4—1724no—
470C42—1728no—
471C42—1728no—
472C23—24no—
473C23—24no—
474C23—22no—
475C23—22no—
476C23—24no—
477C23—24no—
478C23—24no—
479C23—24no—
480C23—22no—
481C23—22no—
482C23—22no—
483C23—22no—
484C23—42no—
485C23—41no—
486C23—41no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23—41no—
493C23—41no—
494C23C4⋊C4×D4314yes—
495C23C22×C4×D4311yescharacteristic
496C23C2×D4×D4311yescharacteristic
497C23C2×Q8×D4311yescharacteristic
498C23#41×D4312yes—
499C23#41×D4312yes—
500C23C2×#1062190012yes—
501C23C2×#1062190012yes—
502C23#1306337011yescharacteristic
503C23#1306337011yescharacteristic
504C23#1306337111yescharacteristic
505C23#1306337111yescharacteristic
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—41no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—438no—
531C2×C4—864no—
532C2×C4—864no—
533C2×C4—864no—
534C2×C4—864no—
535C2×C4—864no—
536C2×C4—864no—
537C2×C4—864no—
538C2×C4—864no—
539C2×C4—864no—
540C2×C4—864no—
541C2×C4—864no—
542C2×C4—864no—
543C2×C4—864no—
544C2×C4—864no—
545C2×C4—864no—
546C2×C4—17216no—
547C2×C4—1722no—
548C2×C4—1722no—
549C2×C4—1722no—
550C2×C4—1722no—
551C2×C4—1722no—
552C2×C4—1722no—
553C2×C4—1722no—
554C2×C4—1722no—
555C2×C4—1722no—
556C2×C4—1722no—
557C2×C4—1722no—
558C2×C4—1722no—
559C22—28no—
560C22—24no—
561C22—42no—
562C22—44no—
563C22—42no—
564C22—42no—
565C22—42no—
566C22—44no—
567C22—44no—
568C22—42no—
569C22—42no—
570C22C2×C4⋊C4×D4311yescharacteristic
571C22C4×#1062190012yes—
572C22C4×#1062190012yes—
573C22#1458337211yescharacteristic
574C22#1458337311yescharacteristic
575C22#1458340512yes—
576C22#1458340712yes—
577C22#1458345112yes—
578C22#1458345112yes—
579C22#1458345711yescharacteristic
580C22#1458345711yescharacteristic
581C22#1458352411yescharacteristic
582C22#1458352411yescharacteristic
583C22#1458357212yes—
584C22#1458357911yescharacteristic
585C22#1458358011yescharacteristic
586C22#1458359212yes—
587C22#1458359612yes—
588C22#1458360012yes—
589C22#1458360112yes—
590C22#1458363112yes—
591C22#1458363311yescharacteristic
592C22#1458363511yescharacteristic
593C4—44no—
594C4—44no—
595C4—42no—
596C4—42no—
597C4—868no—
598C4—1724no—
599C4—1724no—
600C4—1724no—
601C2—44no—
602C2#1913707412yes—
603C2#1913720811yescharacteristic
604C2#1913772512yes—
605C2#1913772811yescharacteristic
606C2#1913773011yescharacteristic
607C2#1914017611yescharacteristic
608C2#1914017812yes—
609C2#1914018311yescharacteristic
610C2#1914025511yescharacteristic
611C2#1914025711yescharacteristic
612C2#1914026112yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1439C2
socle, cosocleC24×C43C24
prime radicalC25×C43C23
hypercenter#1439D43
hypocenterC43#14165
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
5. #19132830C2semidirect
6. #19132829C2semidirect
7. #19132827C2semidirect
8. #19132826C2semidirect
17. #14582760C4semidirect
149. C22×Dic43C4⋊C4semidirect
339. C43#14165semidirect

Maximal subgroups

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

subgroupindex
C2×#145827602
C2×C22⋊C4×Dic432
#191328402
#191328382
#191328302
#191328292
#191328272
#191328262
C43×#14392
#1416543