Finite Group Databasebeta

← #25004476

Subgroups — #25004476

Order 11008.

1146 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582862C211yesmaximal, characteristic
2#19136974C211yesmaximal, characteristic
3C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic
4C2×#14582660C211yesmaximal, characteristic, complemented
5C2×#14582659C211yesmaximal, characteristic, complemented
6C2×#14582658C211yesmaximal, characteristic, complemented
7C2×C43×#339C211yesmaximal, characteristic, complemented
8C23×C4×D43C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10C2×#13063284C2211yescharacteristic
11C22×(C2×D43)⋊C4—21no—
12C22×C4×Dic43C2211yescharacteristic
13#14582862—22no—
14#14582862—22no—
15C2×(C2×D43)⋊C8—22no—
16#14582760—21no—
17#14582756C412yescomplemented
18#14582756C412yescomplemented
19#14582754—21no—
20C4×(C2×D43)⋊C4—22no—
21C4×(C2×D43)⋊C4—22no—
22C4×(C2×D43)⋊C4—22no—
23C2×C43⋊#95—21no—
24#14582660—22no—
25#14582659—22no—
26#14582658—22no—
27C22×M16×C43C2211yescharacteristic
28C2×#117×C43C2211yescharacteristic
29C22×C42×C43C2211yescharacteristic
30C43×#339—22no—
31C24×D43D411yescharacteristic
32C23×Dic43—21no—
33C23×Dic43D411yescharacteristic
34C22×C4×D43—21no—
35C22×C4×D43—21no—
36C22×C4×D43—21no—
37C22×C4×D43—21no—
38C22×C4×D43—21no—
39C22×C4×D43—21no—
40C22×C4×D43—21no—
41C22×C4×D43—21no—
42C22×C4×D43—21no—
43C22×C4×D43—21no—
44C22×C4×D43—21no—
45C22×C4×D43—21no—
46C22×C4×D43C2×C412yes—
47C22×C4×D43D412yes—
48C2×#10621877—21no—
49C2×#10621877—21no—
50C2×#10621877—21no—
51C2×#10621877—21no—
52C2×#10621877—21no—
53C2×#10621877D412yes—
54C22×C43⋊C8—21no—
55#13063284—21no—
56#13063284—21no—
57#13063284—21no—
58#13063284—21no—
59C2×C4⋊Dic43C2×C412yes—
60C2×C22⋊Dic43—21no—
61C2×(C2×D43)⋊C4—28no—
62C2×(C2×D43)⋊C4—24no—
63C2×(C2×D43)⋊C4—22no—
64C2×(C2×D43)⋊C4—22no—
65C2×C4×Dic43—21no—
66C2×C4×Dic43—21no—
67C2×C4×Dic43—21no—
68C2×C4×Dic43—21no—
69C2×C4×Dic43—21no—
70C2×C4×Dic43—21no—
71C2×C4×Dic43D412yes—
72(C2×D43)⋊C8—28no—
73C43⋊#95—24no—
74C43⋊#95—22no—
75C43⋊#95—22no—
76C23×C4×C43—21no—
77C23×C4×C43C2311yescharacteristic
78C2×M16×C43—21no—
79C2×M16×C43—21no—
80C2×M16×C43—21no—
81C2×M16×C43—21no—
82C2×M16×C43—21no—
83C2×M16×C43D412yes—
84C22×C8×C43—21no—
85#117×C43—21no—
86#117×C43—21no—
87#117×C43—21no—
88#117×C43—21no—
89C2×C4⋊C4×C43C2×C411yescharacteristic
90C2×C4⋊C4×C43C2×C411yescharacteristic
91C2×C22⋊C4×C43—21no—
92C2×C42×C43—21no—
93C2×C42×C43—21no—
94C2×C42×C43—21no—
95C2×C42×C43—21no—
96C2×C42×C43—21no—
97C2×C42×C43—21no—
98C2×C42×C43D412yes—
99C24×C43C2×D411yescharacteristic
100C23×D43—21no—
101C23×D43—21no—
102C23×D43—24no—
103C23×D43—21no—
104C23×D43—21no—
105C23×D43—21no—
106C23×D43—21no—
107C23×D43—42no—
108C23×D43C22⋊C412yes—
109C22×C4×C43—24no—
110C22×C4×C43—21no—
111C22×C4×C43—21no—
112C22×C4×C43—22no—
113C22×C4×C43—42no—
114C22×C4×C43—41no—
115C22×C4×C43—41no—
116C22×C4×C43C22×C411yescharacteristic
117C22×C4×C43C2×D411yescharacteristic
118C22×C4×C43C2×D411yescharacteristic
119C22×C4×C43C2×D411yescharacteristic
120C22×C4×C43C2×D411yescharacteristic
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43#4111yescharacteristic
123C22×C4×C43#4111yescharacteristic
124C22×C4×C43#4111yescharacteristic
125C22×C4×C43#4111yescharacteristic
126C22×C4×C43#4111yescharacteristic
127C22×C4×C43#4111yescharacteristic
128C22×C4×C43#4111yescharacteristic
129C22×C4×C43#4111yescharacteristic
130C22×Dic43—24no—
131C22×Dic43—22no—
132C22×Dic43—21no—
133C22×Dic43—22no—
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—42no—
140C22×Dic43—41no—
141C22×Dic43—41no—
142C22×Dic43C22⋊C412yes—
143C2×C4×D43—22no—
144C2×C4×D43—22no—
145C2×C4×D43—22no—
146C2×C4×D43—22no—
147C2×C4×D43—22no—
148C2×C4×D43—22no—
149C2×C4×D43—22no—
150C2×C4×D43—22no—
151C2×C4×D43—22no—
152C2×C4×D43—22no—
153C2×C4×D43—22no—
154C2×C4×D43—22no—
155C2×C4×D43—41no—
156C2×C4×D43—41no—
157C2×C4×D43—41no—
158C2×C4×D43—41no—
159C2×C4×D43—41no—
160C2×C4×D43—41no—
161C2×C4×D43—41no—
162C2×C4×D43—41no—
163C2×C4×D43—41no—
164C2×C4×D43—41no—
165C2×C4×D43—41no—
166C2×C4×D43—41no—
167C2×C4×D43—41no—
168C2×C4×D43—41no—
169C2×C4×D43—41no—
170C2×C4×D43—41no—
171M16×C43—22no—
172M16×C43—22no—
173M16×C43—41no—
174M16×C43—41no—
175C2×C8×C43—22no—
176C2×C8×C43—41no—
177C2×C8×C43—41no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C22⋊C4×C43—41no—
183C22⋊C4×C43—41no—
184C42×C43—22no—
185C42×C43—22no—
186C42×C43—41no—
187C42×C43—41no—
188C42×C43—41no—
189C42×C43—41no—
190C22⋊Dic43—41no—
191C22⋊Dic43—41no—
192(C2×D43)⋊C4—216no—
193(C2×D43)⋊C4—44no—
194(C2×D43)⋊C4—44no—
195C4⋊Dic43—22no—
196C4⋊Dic43—22no—
197C4×Dic43—22no—
198C4×Dic43—22no—
199C4×Dic43—41no—
200C4×Dic43—41no—
201C4×Dic43—41no—
202C4×Dic43—41no—
203#10621877—22no—
204#10621877—22no—
205#10621877—41no—
206#10621877—41no—
207C2×C43⋊C8—22no—
208C2×C43⋊C8—41no—
209C2×C43⋊C8—41no—
210C23×C43—22no—
211C23×C43—22no—
212C23×C43C2×C22⋊C411yescharacteristic
213C23×C43#12011yescharacteristic
214C23×C43#12111yescharacteristic
215C23×C43#12111yescharacteristic
216C23×C43#12311yescharacteristic
217C23×C43#12311yescharacteristic
218C23×C43#12311yescharacteristic
219C22×D43—24no—
220C22×D43—24no—
221C22×D43—22no—
222C22×D43—22no—
223C22×D43—22no—
224C22×D43—22no—
225C22×D43—22no—
226C22×D43—22no—
227C22×D43—44no—
228C22×D43—44no—
229C22×D43—44no—
230C22×D43—44no—
231C22×D43—42no—
232C22×D43—42no—
233C22×D43—41no—
234C22×D43—41no—
235C22×D43—41no—
236C22×D43—41no—
237C22×D43#10414yes—
238C2×C4×C43—24no—
239C2×C4×C43—44no—
240C2×C4×C43—44no—
241C2×C4×C43—42no—
242C2×C4×C43—42no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—42no—
246C2×C4×C43—42no—
247C2×C4×C43#11711yescharacteristic
248C2×C4×C43#11711yescharacteristic
249C2×C4×C43C4×D411yescharacteristic
250C2×C4×C43C4×D411yescharacteristic
251C2×C4×C43C4×D411yescharacteristic
252C2×C4×C43C4×D411yescharacteristic
253C2×C4×C43#12011yescharacteristic
254C2×C4×C43#12111yescharacteristic
255C2×C4×C43#12111yescharacteristic
256C2×C4×C43#12111yescharacteristic
257C2×C4×C43#12111yescharacteristic
258C2×C4×C43#12111yescharacteristic
259C2×C4×C43#12111yescharacteristic
260C2×C4×C43#12311yescharacteristic
261C2×C4×C43#12311yescharacteristic
262C2×C4×C43#12311yescharacteristic
263C2×C4×C43#12311yescharacteristic
264C2×C4×C43#12311yescharacteristic
265C2×C4×C43#12311yescharacteristic
266C2×C4×C43#12311yescharacteristic
267C2×C4×C43#12411yescharacteristic
268C2×C4×C43#12411yescharacteristic
269C2×C4×C43#12411yescharacteristic
270C2×C4×C43#12411yescharacteristic
271C2×C4×C43#12611yescharacteristic
272C2×C4×C43#12611yescharacteristic
273C2×C4×C43#12611yescharacteristic
274C2×C4×C43#12611yescharacteristic
275C2×Dic43—24no—
276C2×Dic43—22no—
277C2×Dic43—22no—
278C2×Dic43—22no—
279C2×Dic43—44no—
280C2×Dic43—44no—
281C2×Dic43—42no—
282C2×Dic43—42no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287C2×Dic43—42no—
288C2×Dic43—42no—
289C2×Dic43—42no—
290C4×D43—42no—
291C4×D43—42no—
292C4×D43—42no—
293C4×D43—42no—
294C4×D43—42no—
295C4×D43—42no—
296C4×D43—42no—
297C4×D43—42no—
298C8×C43—42no—
299C43⋊C8—42no—
300#11201—431nomaximal, Sylow
301C22×C43—22no—
302C22×C43—22no—
303C22×C43—22no—
304C22×C43—22no—
305C22×C43—21no—
306C22×C43—21no—
307C22×C43—21no—
308C22×C43—21no—
309C22×C43#38111yescharacteristic
310C22×C43#38611yescharacteristic
311C22×C43#38611yescharacteristic
312C22×C43#39411yescharacteristic
313C22×C43#39411yescharacteristic
314C22×C43#39711yescharacteristic
315C22×C43#39711yescharacteristic
316C22×C43C2×#10412yes—
317C22×C43#42112yes—
318C2×D43—24no—
319C2×D43—24no—
320C2×D43—24no—
321C2×D43—44no—
322C2×D43—44no—
323C2×D43—44no—
324C2×D43—44no—
325C2×D43—42no—
326C2×D43—42no—
327C2×D43—42no—
328C2×D43—42no—
329C4×C43—44no—
330C4×C43—81no—
331C4×C43—81no—
332C4×C43#38811yescharacteristic
333C4×C43#38811yescharacteristic
334C4×C43#38811yescharacteristic
335C4×C43#38811yescharacteristic
336C4×C43#39411yescharacteristic
337C4×C43#39411yescharacteristic
338C4×C43#39711yescharacteristic
339C4×C43#39711yescharacteristic
340Dic43—44no—
341Dic43—42no—
342Dic43—82no—
343C2×#407—431no—
344#2280—431no—
345C2×C4×C22⋊C4—431no—
346C2×#339—431no—
347C2×#339—431no—
348C2×#339—431no—
349C2×#339D4311yescharacteristic, complemented
350C2×C43—21no—
351C2×C43—21no—
352C2×C43—21no—
353C2×C43—21no—
354C2×C43#144011yescharacteristic
355C2×C43#182612yes—
356C2×C43#187112yes—
357C2×C43#189611yescharacteristic
358C2×C43#189711yescharacteristic
359D43—44no—
360C24×C4—431no—
361C22×M16—431no—
362C22×M16C2×D4311yescharacteristic
363C2×#117—431no—
364C2×#117C2×D4311yescharacteristic
365C22×C22⋊C4—861no—
366C22×C42—431no—
367C22×C42C2×D4311yescharacteristic
368#407—862no—
369#407—862no—
370C2×C22⋊C8—862no—
371#381—861no—
372#380—432no—
373#380—432no—
374#379—861no—
375C4×C22⋊C4—862no—
376C4×C22⋊C4—862no—
377C4×C22⋊C4—862no—
378C2×#95—861no—
379#339—22no—
380#339—862no—
381#339—862no—
382#339—862no—
383C43#1120111yescharacteristic, complemented, Sylow
384C25—431no—
385C23×C4—21no—
386C23×C4—431no—
387C23×C4—432no—
388C23×C4—432no—
389C23×C4—861no—
390C23×C4—861no—
391C23×C4—861no—
392C23×C4—861no—
393C23×C4—861no—
394C23×C4—861no—
395C23×C4—861no—
396C23×C4—861no—
397C23×C4—861no—
398C23×C4—861no—
399C23×C4—861no—
400C23×C4—861no—
401C23×C4—861no—
402C23×C4C22×D4311yescharacteristic
403C2×M16—21no—
404C2×M16—21no—
405C2×M16—21no—
406C2×M16—21no—
407C2×M16—21no—
408C2×M16—432no—
409C2×M16—861no—
410C2×M16—861no—
411C2×M16—861no—
412C2×M16—861no—
413C2×M16—861no—
414C2×M16D17212yes—
415C22×C8—21no—
416C22×C8—861no—
417#117—21no—
418#117—21no—
419#117—21no—
420#117—21no—
421#117—861no—
422#117—861no—
423#117—861no—
424#117—861no—
425C2×C4⋊C4—432no—
426C2×C4⋊C4C4×D4311yescharacteristic
427C2×C4⋊C4C4×D4311yescharacteristic
428C2×C22⋊C4—21no—
429C2×C22⋊C4—868no—
430C2×C22⋊C4—864no—
431C2×C22⋊C4—862no—
432C2×C22⋊C4—862no—
433C2×C22⋊C4—861no—
434C2×C42—21no—
435C2×C42—21no—
436C2×C42—21no—
437C2×C42—21no—
438C2×C42—21no—
439C2×C42—21no—
440C2×C42—432no—
441C2×C42—861no—
442C2×C42—861no—
443C2×C42—861no—
444C2×C42—861no—
445C2×C42—861no—
446C2×C42—861no—
447C2×C42C22⋊D4312yes—
448C22⋊C8—868no—
449#95—862no—
450#95—862no—
451#95—864no—
452C24—432no—
453C24—864no—
454C24—861no—
455C24—861no—
456C24—861no—
457C24—861no—
458C24—861no—
459C24—861no—
460C24—1722no—
461C24D4×D4311yescharacteristic
462C22×C4—24no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—42no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—432no—
470C22×C4—864no—
471C22×C4—861no—
472C22×C4—862no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4—861no—
476C22×C4—861no—
477C22×C4—861no—
478C22×C4—862no—
479C22×C4—862no—
480C22×C4—862no—
481C22×C4—862no—
482C22×C4—862no—
483C22×C4—862no—
484C22×C4—862no—
485C22×C4—862no—
486C22×C4—862no—
487C22×C4—862no—
488C22×C4—862no—
489C22×C4—862no—
490C22×C4—862no—
491C22×C4—1722no—
492C22×C4—1721no—
493C22×C4—1721no—
494C22×C4—1721no—
495C22×C4—1721no—
496C22×C4—1721no—
497C22×C4—1721no—
498C22×C4—1721no—
499C22×C4—1721no—
500C22×C4—1721no—
501C22×C4—1721no—
502C22×C4—1721no—
503C22×C4—1721no—
504C22×C4—1721no—
505C22×C4—1721no—
506C22×C4—1721no—
507C22×C4—1721no—
508C22×C4—1721no—
509C22×C4—1721no—
510C22×C4C2×C4×D4311yescharacteristic
511C22×C4C2×D17211yescharacteristic
512C22×C4#1062189811yescharacteristic
513C22×C4#1062189811yescharacteristic
514C22×C4#1062189811yescharacteristic
515C22×C4#1062189811yescharacteristic
516C22×C4D4×D4311yescharacteristic
517C22×C4D4×D4311yescharacteristic
518C22×C4D4×D4311yescharacteristic
519C22×C4#1062190011yescharacteristic
520C22×C4#1062190011yescharacteristic
521C22×C4#1062190211yescharacteristic
522C22×C4#1062190211yescharacteristic
523C22×C4C2×C22⋊D4311yescharacteristic
524M16—22no—
525M16—22no—
526M16—41no—
527M16—41no—
528M16—862no—
529M16—862no—
530M16—1721no—
531M16—1721no—
532C2×C8—22no—
533C2×C8—41no—
534C2×C8—41no—
535C2×C8—862no—
536C2×C8—1721no—
537C2×C8—1721no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—862no—
543C4⋊C4—862no—
544C22⋊C4—41no—
545C22⋊C4—41no—
546C22⋊C4—8616no—
547C22⋊C4—1724no—
548C22⋊C4—1724no—
549C22⋊C4—1721no—
550C22⋊C4—1721no—
551C42—22no—
552C42—22no—
553C42—41no—
554C42—41no—
555C42—41no—
556C42—41no—
557C42—862no—
558C42—862no—
559C42—1721no—
560C42—1721no—
561C42—1721no—
562C42—1721no—
563C23—22no—
564C23—22no—
565C23—434no—
566C23—864no—
567C23—864no—
568C23—862no—
569C23—862no—
570C23—862no—
571C23—862no—
572C23—862no—
573C23—862no—
574C23—1724no—
575C23—1724no—
576C23—1724no—
577C23—1724no—
578C23—1722no—
579C23—1722no—
580C23—1721no—
581C23—1721no—
582C23—1721no—
583C23—1721no—
584C23C22⋊C4×D4311yescharacteristic
585C23#1306329311yescharacteristic
586C23#1306329811yescharacteristic
587C23#1306330011yescharacteristic
588C23#1306330711yescharacteristic
589C23#1306330711yescharacteristic
590C23#1306331011yescharacteristic
591C2×C4—24no—
592C2×C4—42no—
593C2×C4—44no—
594C2×C4—44no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—864no—
601C2×C4—862no—
602C2×C4—862no—
603C2×C4—862no—
604C2×C4—1722no—
605C2×C4—1722no—
606C2×C4—1722no—
607C2×C4—1722no—
608C2×C4—1724no—
609C2×C4—1724no—
610C2×C4—1721no—
611C2×C4—1722no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4—1722no—
616C2×C4—1722no—
617C2×C4—1722no—
618C2×C4—1722no—
619C2×C4—1722no—
620C2×C4—1722no—
621C2×C4—1722no—
622C2×C4—1722no—
623C2×C4#1306328211yescharacteristic
624C2×C4#1306328311yescharacteristic
625C2×C4(C22⋊D43)⋊C411yescharacteristic
626C2×C4C4×C22⋊D4311yescharacteristic
627C2×C4#1306328711yescharacteristic
628C2×C4C4×D17211yescharacteristic
629C2×C4#1306329511yescharacteristic
630C2×C4#1306329611yescharacteristic
631C2×C4#1306329711yescharacteristic
632C2×C4#1306329811yescharacteristic
633C2×C4#1306329811yescharacteristic
634C2×C4#1306329911yescharacteristic
635C2×C4#1306330011yescharacteristic
636C2×C4#1306330711yescharacteristic
637C2×C4#1306330811yescharacteristic
638C2×C4#1306330911yescharacteristic
639C2×C4#1306331011yescharacteristic
640C2×C4#1306331011yescharacteristic
641C2×C4#1306331011yescharacteristic
642C2×C4#1306331011yescharacteristic
643C2×C4#1306331111yescharacteristic
644C2×C4#1306331111yescharacteristic
645C2×C4#1306331311yescharacteristic
646C2×C4#1306331411yescharacteristic
647C2×C4#1306331911yescharacteristic
648C2×C4#1306332011yescharacteristic
649C2×C4#1306332011yescharacteristic
650C2×C4#1306332011yescharacteristic
651C8—42no—
652C8—1722no—
653C22—21no—
654C22—21no—
655C22—21no—
656C22—21no—
657C22—22no—
658C22—22no—
659C22—22no—
660C22—22no—
661C22—864no—
662C22—864no—
663C22—864no—
664C22—1724no—
665C22—1724no—
666C22—1724no—
667C22—1724no—
668C22—1722no—
669C22—1722no—
670C22—1722no—
671C22—1722no—
672C22#1458276111yescharacteristic
673C22#1458277511yescharacteristic
674C22#1458277711yescharacteristic
675C22#1458281411yescharacteristic
676C22#1458281611yescharacteristic
677C22#1458282611yescharacteristic
678C22#1458282811yescharacteristic
679C22#104×D4312yes—
680C22#1458291412yes—
681C4—44no—
682C4—81no—
683C4—81no—
684C4—3442no—
685C4—1724no—
686C4—1722no—
687C4#1458278811yescharacteristic
688C4#1458278911yescharacteristic
689C4#1458279011yescharacteristic
690C4#1458279111yescharacteristic
691C4#1458281511yescharacteristic
692C4#1458281711yescharacteristic
693C4#1458282511yescharacteristic
694C4#1458282811yescharacteristic
695C2—21no—
696C2—21no—
697C2—21no—
698C2—21no—
699C2—1724no—
700C2#1913284311yescharacteristic
701C2#1913469312yes—
702C2#1913489612yes—
703C2#1913503511yescharacteristic
704C2#1913504011yescharacteristic
subgroupG/H
centerC22×C4D4×D43
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#339C2
socleC23×C43C2×C22⋊C4
prime radicalC24×D43D4
cosocleC23×C4×C43C23
hypercenterC2×#339D43
hypocenterC43#11201
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
4. C2×#14582660C2semidirect
5. C2×#14582659C2semidirect
6. C2×#14582658C2semidirect
7. C2×C43×#339C2semidirect
17. #14582756C4semidirect
18. #14582756C4semidirect
349. C2×#339D43semidirect
383. C43#11201semidirect

Maximal subgroups

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

subgroupindex
C2×#145828622
#191369742
C2×C4×(C2×D43)⋊C42
C2×#145826602
C2×#145826592
C2×#145826582
C2×C43×#3392
#1120143