Finite Group Databasebeta

← #24995419

Subgroups — #24995419

Order 11008.

936 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582799C211yesmaximal, characteristic
2#19134573C211yesmaximal, characteristic, complemented
3C22⋊C8×Dic43C211yesmaximal, characteristic, complemented
4C2×#14582623C211yesmaximal, characteristic, complemented
5C2×#14582622C211yesmaximal, characteristic, complemented
6C2×#14582622C211yesmaximal, characteristic, complemented
7C2×C43×#323C211yesmaximal, characteristic, complemented
8C23×C22⋊D43C411yescharacteristic
9C22×Dic43⋊C4C411yescharacteristic
10C22×C22⋊Dic43C411yescharacteristic
11C22×(C2×D43)⋊C4C411yescharacteristic
12C22×(C2×D43)⋊C4C2211yescharacteristic
13C22×C4×Dic43C2211yescharacteristic
14C2×Dic43⋊C8—21no—
15C2×C22⋊(C43⋊C8)C2211yescharacteristic
16C2×C22⋊(C43⋊C8)C2211yescharacteristic
17C2×C8×Dic43—21no—
18#14582799—21no—
19#14582799—21no—
20#14582799—21no—
21#14582799—21no—
22#14582653—21no—
23#14582653—21no—
24#14582623—22no—
25#14582622—22no—
26#14582622—22no—
27C22×C22⋊C4×C43C2211yescharacteristic
28C2×C22⋊C8×C43C2211yescharacteristic
29C2×C22⋊C8×C43C2211yescharacteristic
30C43×#323—22no—
31C24×D43C2×C411yescharacteristic
32C22×C22⋊D43—21no—
33C22×C22⋊D43—21no—
34C22×C22⋊D43—22no—
35C22×C22⋊D43—42no—
36C22×C22⋊D43—42no—
37C22×C22⋊D43C814yescomplemented
38C23×Dic43C2×C411yescharacteristic
39C23×Dic43C2×C411yescharacteristic
40C23×Dic43C2×C411yescharacteristic
41C22×C43⋊C8—21no—
42C22×C43⋊C8—21no—
43C2×Dic43⋊C4—21no—
44C2×Dic43⋊C4—21no—
45C2×Dic43⋊C4—42no—
46C2×C22⋊Dic43—21no—
47C2×C22⋊Dic43—21no—
48C2×C22⋊Dic43—42no—
49C2×(C2×D43)⋊C4—21no—
50C2×(C2×D43)⋊C4—21no—
51C2×(C2×D43)⋊C4—21no—
52C2×(C2×D43)⋊C4—21no—
53C2×(C2×D43)⋊C4—21no—
54C2×(C2×D43)⋊C4—21no—
55C2×(C2×D43)⋊C4—21no—
56C2×(C2×D43)⋊C4—21no—
57C2×(C2×D43)⋊C4—42no—
58C2×C4×Dic43—42no—
59C2×C4×Dic43D411yescharacteristic
60C2×C4×Dic43D411yescharacteristic
61C2×C4×Dic43D411yescharacteristic
62C2×C4×Dic43D411yescharacteristic
63Dic43⋊C8—42no—
64C22⋊(C43⋊C8)—21no—
65C22⋊(C43⋊C8)—21no—
66C22⋊(C43⋊C8)—21no—
67C22⋊(C43⋊C8)D412yescomplemented
68C8×Dic43—42no—
69C25×C43C2×C411yescharacteristic
70C23×C4×C43C2×C411yescharacteristic
71C23×C4×C43C2311yescharacteristic
72C22×C8×C43—21no—
73C22×C8×C43—21no—
74C2×C22⋊C4×C43—21no—
75C2×C22⋊C4×C43—21no—
76C2×C22⋊C4×C43—21no—
77C2×C22⋊C4×C43—21no—
78C2×C22⋊C4×C43—21no—
79C2×C22⋊C4×C43—21no—
80C22⋊C8×C43—21no—
81C22⋊C8×C43—21no—
82C22⋊C8×C43—21no—
83C22⋊C8×C43D412yescomplemented
84C24×C43—21no—
85C24×C43—21no—
86C24×C43—21no—
87C24×C43—21no—
88C24×C43—21no—
89C24×C43—21no—
90C24×C43—41no—
91C24×C43—41no—
92C24×C43—41no—
93C24×C43—41no—
94C24×C43C2×C812yes—
95C24×C43C22×C411yescharacteristic
96C23×D43—21no—
97C23×D43—21no—
98C23×D43—21no—
99C23×D43—21no—
100C23×D43—21no—
101C23×D43—21no—
102C23×D43—41no—
103C23×D43—41no—
104C23×D43—41no—
105C23×D43—41no—
106C23×D43C2×C812yes—
107C22×C4×C43—21no—
108C22×C4×C43—21no—
109C22×C4×C43—21no—
110C22×C4×C43—41no—
111C22×C4×C43—41no—
112C22×C4×C43—41no—
113C22×C4×C43—41no—
114C22×C4×C43C2×D411yescharacteristic
115C22×C4×C43C2×D411yescharacteristic
116C22×C4×C43C2×D411yescharacteristic
117C22×C4×C43C2×D411yescharacteristic
118C22×C4×C43#4111yescharacteristic
119C22×C4×C43#4111yescharacteristic
120C2×C22⋊D43—24no—
121C2×C22⋊D43—24no—
122C2×C22⋊D43—48no—
123C2×C22⋊D43—48no—
124C2×C22⋊D43—42no—
125C2×C22⋊D43—42no—
126C2×C22⋊D43—42no—
127C2×C22⋊D43—42no—
128C22×Dic43—22no—
129C22×Dic43—22no—
130C22×Dic43—22no—
131C22×Dic43—21no—
132C22×Dic43—21no—
133C22×Dic43—21no—
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43—41no—
137C22×Dic43—41no—
138C22×Dic43—41no—
139C22×Dic43C22⋊C411yescharacteristic
140C22×Dic43C22⋊C411yescharacteristic
141C22×Dic43C22⋊C411yescharacteristic
142C22×Dic43C22⋊C411yescharacteristic
143C22×Dic43C2×C812yes—
144C22×Dic43M1612yes—
145C2×C8×C43—22no—
146C2×C8×C43—41no—
147C2×C8×C43—41no—
148C2×C8×C43—41no—
149C2×C8×C43—41no—
150C2×C8×C43—41no—
151C22⋊C4×C43—41no—
152C22⋊C4×C43—41no—
153C22⋊C4×C43—41no—
154C22⋊C4×C43—41no—
155C22⋊Dic43—42no—
156C22⋊Dic43—42no—
157(C2×D43)⋊C4—42no—
158(C2×D43)⋊C4—41no—
159(C2×D43)⋊C4—41no—
160(C2×D43)⋊C4—41no—
161(C2×D43)⋊C4—41no—
162(C2×D43)⋊C4—42no—
163Dic43⋊C4—42no—
164Dic43⋊C4—42no—
165C4×Dic43—22no—
166C4×Dic43—22no—
167C4×Dic43—41no—
168C4×Dic43—41no—
169C2×C43⋊C8—22no—
170C2×C43⋊C8—41no—
171C2×C43⋊C8—41no—
172C2×C43⋊C8—41no—
173C2×C43⋊C8—41no—
174C2×C43⋊C8—41no—
175C23×C43—21no—
176C23×C43—21no—
177C23×C43—21no—
178C23×C43—21no—
179C23×C43—22no—
180C23×C43—22no—
181C23×C43—22no—
182C23×C43—42no—
183C23×C43—42no—
184C23×C43—42no—
185C23×C43—42no—
186C23×C43—41no—
187C23×C43—41no—
188C23×C43—41no—
189C23×C43—41no—
190C23×C43—41no—
191C23×C43—41no—
192C23×C43—41no—
193C23×C43—41no—
194C23×C43—81no—
195C23×C43—81no—
196C23×C43—81no—
197C23×C43—81no—
198C23×C43—81no—
199C23×C43—81no—
200C23×C43—81no—
201C23×C43—81no—
202C23×C43C2×C22⋊C411yescharacteristic
203C23×C43C4×D411yescharacteristic
204C23×C43C4×D411yescharacteristic
205C23×C43C22×C811yescharacteristic
206C23×C43C2×M1611yescharacteristic
207C23×C43#13111yescharacteristic
208C23×C43#13111yescharacteristic
209C22×D43—22no—
210C22×D43—22no—
211C22×D43—22no—
212C22×D43—42no—
213C22×D43—42no—
214C22×D43—41no—
215C22×D43—41no—
216C22×D43—41no—
217C22×D43—41no—
218C22×D43—41no—
219C22×D43—41no—
220C22×D43—41no—
221C22×D43—41no—
222C22×D43—42no—
223C22×D43—42no—
224C22×D43—81no—
225C22×D43—81no—
226C22×D43—81no—
227C22×D43—81no—
228C22×D43—81no—
229C22×D43—81no—
230C22×D43—81no—
231C22×D43—81no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—81no—
244C2×C4×C43—81no—
245C2×C4×C43#12111yescharacteristic
246C2×C4×C43#12111yescharacteristic
247C2×C4×C43#12411yescharacteristic
248C2×C4×C43#12711yescharacteristic
249C22⋊D43—48no—
250C22⋊D43—48no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—24no—
256C2×Dic43—24no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—42no—
261C2×Dic43—42no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—81no—
266C2×Dic43—81no—
267C2×Dic43C22⋊C812yes—
268C2×Dic43C22⋊C812yes—
269C2×Dic43#9912yes—
270C2×Dic43#10012yes—
271C2×Dic43#10012yes—
272C8×C43—42no—
273C8×C43—81no—
274C43⋊C8—42no—
275C43⋊C8—81no—
276#9649—431nomaximal, Sylow
277C22×C43—21no—
278C22×C43—21no—
279C22×C43—21no—
280C22×C43—21no—
281C22×C43—21no—
282C22×C43—21no—
283C22×C43—21no—
284C22×C43—21no—
285C22×C43—21no—
286C22×C43—21no—
287C22×C43—21no—
288C22×C43—21no—
289C22×C43—42no—
290C22×C43—42no—
291C22×C43—42no—
292C22×C43—82no—
293C22×C43—82no—
294C22×C43—82no—
295C22×C43—82no—
296C22×C43—81no—
297C22×C43—81no—
298C22×C43—81no—
299C22×C43—81no—
300C22×C43#39011yescharacteristic
301C22×C43C2×C22⋊C811yescharacteristic
302C22×C43#40811yescharacteristic
303C22×C43C2×#9911yescharacteristic
304C22×C43#41011yescharacteristic
305C22×C43C2×#10011yescharacteristic
306C22×C43C2×#10011yescharacteristic
307C22×C43C8×D411yescharacteristic
308C22×C43C8×D411yescharacteristic
309C22×C43#43611yescharacteristic
310C22×C43#43611yescharacteristic
311C2×D43—42no—
312C2×D43—42no—
313C2×D43—42no—
314C2×D43—82no—
315C2×D43—82no—
316C2×D43—81no—
317C2×D43—81no—
318C2×D43—81no—
319C2×D43—81no—
320C2×D43—82no—
321C2×D43—82no—
322C4×C43—21no—
323C4×C43—21no—
324C4×C43—21no—
325C4×C43—21no—
326C4×C43—81no—
327Dic43—22no—
328Dic43—22no—
329Dic43—41no—
330Dic43—81no—
331Dic43#32314yescomplemented
332C2×#390—431no—
333#1797—431no—
334C4×C22⋊C8—431no—
335C2×#323—431no—
336C2×#323—431no—
337C2×#323—431no—
338C2×#323D4311yescharacteristic, complemented
339C2×C43—21no—
340C2×C43—21no—
341C2×C43—21no—
342C2×C43—21no—
343C2×C43—82no—
344C2×C43C2×#32311yescharacteristic
345C2×C43#146011yescharacteristic
346C2×C43#146911yescharacteristic
347C2×C43#147111yescharacteristic
348C2×C43#195411yescharacteristic
349C2×C43#196411yescharacteristic
350C2×C43#196511yescharacteristic
351D43—82no—
352C23×D4—431no—
353C22×C4⋊C4—431no—
354C22×C22⋊C4—431no—
355C22×C22⋊C4—431no—
356C22×C22⋊C4—431no—
357C22×C22⋊C4C2×D4311yescharacteristic
358C22×C42—431no—
359C2×C4⋊C8—861no—
360C2×C22⋊C8—431no—
361C2×C22⋊C8—431no—
362C2×C22⋊C8C2×D4311yescharacteristic
363C2×C22⋊C8C2×D4311yescharacteristic
364C2×C4×C8—861no—
365#390—861no—
366#390—861no—
367#390—861no—
368#390—861no—
369#336—861no—
370#336—861no—
371#323—22no—
372#323—862no—
373#323—862no—
374#323—862no—
375C43#964911yescharacteristic, complemented, Sylow
376C25—431no—
377C25C4×D4311yescharacteristic
378C22×D4—434no—
379C22×D4—861no—
380C22×D4—861no—
381C22×D4—862no—
382C22×D4—1722no—
383C22×D4—1722no—
384C23×C4—431no—
385C23×C4—431no—
386C23×C4—431no—
387C23×C4C4×D4311yescharacteristic
388C23×C4C22×D4311yescharacteristic
389C22×C8—21no—
390C22×C8—21no—
391C22×C8—861no—
392C22×C8—861no—
393C2×C4⋊C4—861no—
394C2×C4⋊C4—861no—
395C2×C4⋊C4—1722no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—861no—
403C2×C22⋊C4—861no—
404C2×C22⋊C4—861no—
405C2×C22⋊C4—861no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C22⋊C4—861no—
409C2×C22⋊C4—861no—
410C2×C22⋊C4—861no—
411C2×C22⋊C4—861no—
412C2×C22⋊C4—1722no—
413C2×C22⋊C4—1722no—
414C2×C42—431no—
415C2×C42—431no—
416C2×C42—431no—
417C2×C42—431no—
418C2×C42—1722no—
419C4⋊C8—1722no—
420C22⋊C8—21no—
421C22⋊C8—21no—
422C22⋊C8—21no—
423C22⋊C8—432no—
424C22⋊C8—861no—
425C22⋊C8—861no—
426C22⋊C8—861no—
427C22⋊C8C22⋊D4312yescomplemented
428C4×C8—1722no—
429C24—21no—
430C24—21no—
431C24—21no—
432C24—21no—
433C24—21no—
434C24—21no—
435C24—41no—
436C24—41no—
437C24—41no—
438C24—41no—
439C24—432no—
440C24—861no—
441C24—861no—
442C24—861no—
443C24—861no—
444C24—861no—
445C24—861no—
446C24—1721no—
447C24—1721no—
448C24—1721no—
449C24—1721no—
450C24C8×D4312yes—
451C24C2×C4×D4311yescharacteristic
452C2×D4—864no—
453C2×D4—864no—
454C2×D4—1722no—
455C2×D4—1722no—
456C2×D4—1728no—
457C2×D4—1722no—
458C2×D4—1722no—
459C2×D4—1728no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—431no—
468C22×C4—431no—
469C22×C4—431no—
470C22×C4—432no—
471C22×C4—432no—
472C22×C4—431no—
473C22×C4—862no—
474C22×C4—862no—
475C22×C4—862no—
476C22×C4—861no—
477C22×C4—861no—
478C22×C4—861no—
479C22×C4—861no—
480C22×C4—861no—
481C22×C4—1721no—
482C22×C4—1721no—
483C22×C4—1721no—
484C22×C4#1062189811yescharacteristic
485C22×C4D4×D4311yescharacteristic
486C22×C4D4×D4311yescharacteristic
487C22×C4D4×D4311yescharacteristic
488C22×C4#1062190011yescharacteristic
489C22×C4C2×C22⋊D4311yescharacteristic
490C2×C8—22no—
491C2×C8—41no—
492C2×C8—41no—
493C2×C8—41no—
494C2×C8—41no—
495C2×C8—41no—
496C2×C8—862no—
497C2×C8—1721no—
498C2×C8—1721no—
499C2×C8—1721no—
500C2×C8—1721no—
501C2×C8—1721no—
502C4⋊C4—1722no—
503C4⋊C4—1722no—
504C22⋊C4—41no—
505C22⋊C4—41no—
506C22⋊C4—41no—
507C22⋊C4—41no—
508C22⋊C4—1722no—
509C22⋊C4—1722no—
510C22⋊C4—1722no—
511C22⋊C4—1722no—
512C22⋊C4—1721no—
513C22⋊C4—1721no—
514C22⋊C4—1721no—
515C22⋊C4—1721no—
516C42—862no—
517C42—862no—
518C42—1721no—
519C42—1721no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—22no—
525C23—22no—
526C23—22no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—42no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—81no—
540C23—81no—
541C23—81no—
542C23—81no—
543C23—81no—
544C23—81no—
545C23—81no—
546C23—81no—
547C23—862no—
548C23—862no—
549C23—862no—
550C23—3441no—
551C23—3441no—
552C23—3441no—
553C23—3441no—
554C23—3441no—
555C23—3441no—
556C23—3441no—
557C23—3441no—
558C23—1722no—
559C23—1722no—
560C23—1722no—
561C23—1722no—
562C23—1721no—
563C23—1721no—
564C23—1721no—
565C23—1721no—
566C23—1721no—
567C23—1721no—
568C23—1721no—
569C23—1721no—
570C23C22⋊C4×D4311yescharacteristic
571C23(C22⋊D43)⋊C411yescharacteristic
572C23C4×C22⋊D4311yescharacteristic
573C23C2×C8×D4311yescharacteristic
574C23M16×D4311yescharacteristic
575C23#1306333111yescharacteristic
576C23#1306333311yescharacteristic
577D4—1728no—
578D4—1728no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—81no—
591C2×C4—81no—
592C2×C4—432no—
593C2×C4—432no—
594C2×C4—432no—
595C2×C4—432no—
596C2×C4—432no—
597C2×C4—864no—
598C2×C4—864no—
599C2×C4—861no—
600C2×C4—861no—
601C2×C4—861no—
602C2×C4—861no—
603C2×C4—861no—
604C2×C4—861no—
605C2×C4—861no—
606C2×C4—3441no—
607C2×C4—3441no—
608C2×C4—1722no—
609C2×C4—1722no—
610C2×C4—1721no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4#1306329711yescharacteristic
614C2×C4#1306329811yescharacteristic
615C2×C4#1306331111yescharacteristic
616C2×C4#1306332111yescharacteristic
617C8—42no—
618C8—81no—
619C8—3441no—
620C8—1722no—
621C22—21no—
622C22—21no—
623C22—21no—
624C22—21no—
625C22—21no—
626C22—21no—
627C22—21no—
628C22—21no—
629C22—21no—
630C22—21no—
631C22—21no—
632C22—21no—
633C22—42no—
634C22—42no—
635C22—42no—
636C22—82no—
637C22—82no—
638C22—82no—
639C22—82no—
640C22—81no—
641C22—81no—
642C22—81no—
643C22—81no—
644C22—3442no—
645C22—3442no—
646C22—3442no—
647C22—3442no—
648C22—3441no—
649C22—3441no—
650C22—3441no—
651C22—3441no—
652C22—1722no—
653C22—1722no—
654C22—1722no—
655C22#1458279911yescharacteristic
656C22C22⋊C8×D4311yescharacteristic
657C22#1458286411yescharacteristic
658C22#99×D4311yescharacteristic
659C22#1458287111yescharacteristic
660C22#100×D4311yescharacteristic
661C22#100×D4311yescharacteristic
662C22(C22⋊D43)⋊C811yescharacteristic
663C22C8×C22⋊D4311yescharacteristic
664C22#1458297411yescharacteristic
665C22#1458297511yescharacteristic
666C4—21no—
667C4—21no—
668C4—21no—
669C4—21no—
670C4—81no—
671C4—434no—
672C4—862no—
673C4—862no—
674C4—3441no—
675C4—1721no—
676C2—21no—
677C2—21no—
678C2—21no—
679C2—21no—
680C2—82no—
681C2—3442no—
682C2#323×D4311yescharacteristic
683C2#1913291411yescharacteristic
684C2#1913294511yescharacteristic
685C2#1913295311yescharacteristic
686C2#1913538711yescharacteristic
687C2#1913542911yescharacteristic
688C2#1913543311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC23×C43C22×C8
FrattiniC23×C4C22×D43
FittingC2×C43×#323C2
socleC23×C43C2×C22⋊C4
prime radicalC23×C22⋊D43C4
cosocleC23×C4×C43C23
hypercenterC2×#323D43
hypocenterC43#9649
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#323

Complements

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

NH ≅ G/Ntype
2. #19134573C2semidirect
3. C22⋊C8×Dic43C2semidirect
4. C2×#14582623C2semidirect
5. C2×#14582622C2semidirect
6. C2×#14582622C2semidirect
7. C2×C43×#323C2semidirect
37. C22×C22⋊D43C8semidirect
67. C22⋊(C43⋊C8)D4semidirect
83. C22⋊C8×C43D4semidirect
331. Dic43#323semidirect
338. C2×#323D43semidirect
375. C43#9649semidirect
427. C22⋊C8C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145827992
#191345732
C22⋊C8×Dic432
C2×#145826232
C2×#145826222
C2×C43×#3232
#964943