Finite Group Databasebeta

← #25003704

Subgroups — #25003704

Order 11008.

1110 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063253C211yesmaximal, characteristic
2C22×#13063251C211yesmaximal, characteristic
3#19137083C211yesmaximal, characteristic
4C2×C4×Dic43⋊C4C211yesmaximal, characteristic, complemented
5C2×#14582658C211yesmaximal, characteristic, complemented
6#19134288C211yesmaximal, characteristic, complemented
7C2×C43×#339C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10C22×Dic43⋊C4—21no—
11C22×C4×Dic43C2211yescharacteristic
12C22×C4×Dic43C2211yescharacteristic
13C2×#13063253—22no—
14C2×#13063253—22no—
15C2×#13063253—22no—
16C2×#13063251—22no—
17C2×#13063251—22no—
18C2×#13063251—22no—
19#14582804C412yescomplemented
20#14582800C412yescomplemented
21#14582776—21no—
22#14582776—21no—
23C4×Dic43⋊C4—22no—
24C4×Dic43⋊C4—22no—
25C4×(C2×D43)⋊C4—22no—
26C2×C43⋊#95—21no—
27#14582658—22no—
28#14582653—22no—
29C22×M16×C43C2211yescharacteristic
30C2×#117×C43C2211yescharacteristic
31C22×C42×C43C2211yescharacteristic
32C43×#339—22no—
33C2×#10621898—21no—
34C2×#10621898—21no—
35C2×#10621898—21no—
36C2×#10621898—21no—
37C2×#10621898—21no—
38C2×#10621898—21no—
39C2×#10621898—21no—
40C2×#10621898—21no—
41C2×#10621898—21no—
42C2×#10621898—21no—
43C2×#10621898D412yes—
44C2×#10621898Q812yes—
45C22×Dic86C2×C411yescharacteristic
46C22×D172C2×C411yescharacteristic
47C22×C22⋊D43—21no—
48C23×Dic43—21no—
49C23×Dic43D411yescharacteristic
50C23×Dic43D411yescharacteristic
51C22×C4×D43—21no—
52C2×#10621877—21no—
53C2×#10621877—21no—
54C2×#10621877—21no—
55C2×#10621877—21no—
56C2×#10621877—21no—
57C2×#10621877D412yes—
58C22×C43⋊C8—21no—
59C2×Dic43⋊C4—28no—
60C2×Dic43⋊C4—24no—
61C2×(C2×D43)⋊C4—22no—
62C2×(C2×D43)⋊C4—22no—
63C2×C4×Dic43—21no—
64C2×C4×Dic43—21no—
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×Dic43—21no—
72C2×C4×Dic43C2×C412yes—
73C2×C4×Dic43D412yes—
74C2×C4×Dic43D412yes—
75#13063253—28no—
76#13063251—28no—
77C43⋊#95—24no—
78C43⋊#95—22no—
79C43⋊#95—22no—
80C23×C4×C43—21no—
81C23×C4×C43C2311yescharacteristic
82C2×M16×C43—21no—
83C2×M16×C43—21no—
84C2×M16×C43—21no—
85C2×M16×C43—21no—
86C2×M16×C43—21no—
87C2×M16×C43D412yes—
88C22×C8×C43—21no—
89#117×C43—21no—
90#117×C43—21no—
91#117×C43—21no—
92#117×C43—21no—
93C2×C4⋊C4×C43C2×C412yes—
94C2×C22⋊C4×C43—21no—
95C2×C42×C43—21no—
96C2×C42×C43—21no—
97C2×C42×C43—21no—
98C2×C42×C43—21no—
99C2×C42×C43—21no—
100C2×C42×C43—21no—
101C2×C42×C43D412yes—
102C24×C43C2×D411yescharacteristic
103C23×D43—21no—
104C22×C4×C43—24no—
105C22×C4×C43—22no—
106C22×C4×C43—22no—
107C22×C4×C43—42no—
108C22×C4×C43—41no—
109C22×C4×C43—41no—
110C22×C4×C43C22×C411yescharacteristic
111C22×C4×C43C2×D411yescharacteristic
112C22×C4×C43C2×D411yescharacteristic
113C22×C4×C43C2×D411yescharacteristic
114C22×C4×C43C2×D411yescharacteristic
115C22×C4×C43C2×D411yescharacteristic
116C22×C4×C43C2×D411yescharacteristic
117C22×C4×C43C2×Q811yescharacteristic
118C22×C4×C43#4111yescharacteristic
119C22×C4×C43#4111yescharacteristic
120C22×C4×C43#4111yescharacteristic
121C22×C4×C43#4111yescharacteristic
122C22×C4×C43#4111yescharacteristic
123C22×C4×C43#4111yescharacteristic
124C2×C22⋊D43—22no—
125C2×C22⋊D43—22no—
126C2×C22⋊D43—41no—
127C2×C22⋊D43—41no—
128C2×C22⋊D43—41no—
129C2×C22⋊D43—41no—
130C22×Dic43—24no—
131C22×Dic43—24no—
132C22×Dic43—21no—
133C22×Dic43—21no—
134C22×Dic43—21no—
135C22×Dic43—22no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—42no—
139C22×Dic43—42no—
140C22×Dic43—41no—
141C22×Dic43—41no—
142C22×Dic43C22⋊C412yes—
143C22×Dic43C22⋊C412yes—
144#10621898—22no—
145#10621898—22no—
146#10621898—22no—
147#10621898—22no—
148#10621898—22no—
149#10621898—22no—
150#10621898—22no—
151#10621898—22no—
152#10621898—41no—
153#10621898—41no—
154#10621898—41no—
155#10621898—41no—
156#10621898—41no—
157#10621898—41no—
158#10621898—41no—
159#10621898—41no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172—21no—
164C2×D172—21no—
165C2×D172C4⋊C412yescomplemented
166C2×C4×D43—22no—
167C2×C4×D43—22no—
168C2×C4×D43—41no—
169C2×C4×D43—41no—
170C2×C4×D43—41no—
171C2×C4×D43—41no—
172C2×Dic86—21no—
173C2×Dic86—21no—
174C2×Dic86—21no—
175C2×Dic86—21no—
176C2×Dic86—21no—
177C2×Dic86C4⋊C412yescomplemented
178M16×C43—22no—
179M16×C43—22no—
180M16×C43—41no—
181M16×C43—41no—
182C2×C8×C43—22no—
183C2×C8×C43—41no—
184C2×C8×C43—41no—
185C4⋊C4×C43—22no—
186C4⋊C4×C43—22no—
187C22⋊C4×C43—41no—
188C22⋊C4×C43—41no—
189C42×C43—22no—
190C42×C43—22no—
191C42×C43—41no—
192C42×C43—41no—
193C42×C43—41no—
194C42×C43—41no—
195(C2×D43)⋊C4—44no—
196(C2×D43)⋊C4—44no—
197Dic43⋊C4—216no—
198C4×Dic43—22no—
199C4×Dic43—22no—
200C4×Dic43—22no—
201C4×Dic43—22no—
202C4×Dic43—22no—
203C4×Dic43—22no—
204C4×Dic43—41no—
205C4×Dic43—41no—
206#10621877—22no—
207#10621877—22no—
208#10621877—41no—
209#10621877—41no—
210C2×C43⋊C8—22no—
211C2×C43⋊C8—41no—
212C2×C43⋊C8—41no—
213C23×C43—22no—
214C23×C43—22no—
215C23×C43C2×C22⋊C411yescharacteristic
216C23×C43#12011yescharacteristic
217C23×C43#12111yescharacteristic
218C23×C43C22⋊Q811yescharacteristic
219C23×C43#12311yescharacteristic
220C23×C43#12411yescharacteristic
221C23×C43#12711yescharacteristic
222C22×D43—22no—
223C22×D43—41no—
224C22×D43—41no—
225C22×D43—42no—
226C22×D43—42no—
227C2×C4×C43—24no—
228C2×C4×C43—44no—
229C2×C4×C43—42no—
230C2×C4×C43—44no—
231C2×C4×C43—42no—
232C2×C4×C43—42no—
233C2×C4×C43—42no—
234C2×C4×C43—42no—
235C2×C4×C43C2×C4⋊C411yescharacteristic
236C2×C4×C43#11711yescharacteristic
237C2×C4×C43C4×D411yescharacteristic
238C2×C4×C43C4×D411yescharacteristic
239C2×C4×C43C4×D411yescharacteristic
240C2×C4×C43C4×D411yescharacteristic
241C2×C4×C43#12011yescharacteristic
242C2×C4×C43#12011yescharacteristic
243C2×C4×C43#12111yescharacteristic
244C2×C4×C43#12111yescharacteristic
245C2×C4×C43#12111yescharacteristic
246C2×C4×C43#12111yescharacteristic
247C2×C4×C43#12111yescharacteristic
248C2×C4×C43#12111yescharacteristic
249C2×C4×C43#12111yescharacteristic
250C2×C4×C43C22⋊Q811yescharacteristic
251C2×C4×C43C22⋊Q811yescharacteristic
252C2×C4×C43C22⋊Q811yescharacteristic
253C2×C4×C43C22⋊Q811yescharacteristic
254C2×C4×C43C22⋊Q811yescharacteristic
255C2×C4×C43#12311yescharacteristic
256C2×C4×C43#12311yescharacteristic
257C2×C4×C43#12311yescharacteristic
258C2×C4×C43#12311yescharacteristic
259C2×C4×C43#12411yescharacteristic
260C2×C4×C43#12411yescharacteristic
261C2×C4×C43#12611yescharacteristic
262C2×C4×C43#12611yescharacteristic
263C22⋊D43—42no—
264C22⋊D43—42no—
265C22⋊D43—42no—
266C22⋊D43—42no—
267C2×Dic43—24no—
268C2×Dic43—24no—
269C2×Dic43—22no—
270C2×Dic43—22no—
271C2×Dic43—24no—
272C2×Dic43—22no—
273C2×Dic43—22no—
274C2×Dic43—22no—
275C2×Dic43—22no—
276C2×Dic43—44no—
277C2×Dic43—42no—
278C2×Dic43—44no—
279C2×Dic43—42no—
280C2×Dic43—42no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—42no—
284C2×Dic43#10414yescomplemented
285D172—22no—
286D172—22no—
287D172—41no—
288D172—41no—
289C4×D43—42no—
290C4×D43—42no—
291C4×D43—42no—
292C4×D43—42no—
293Dic86—22no—
294Dic86—22no—
295Dic86—41no—
296Dic86—41no—
297C8×C43—42no—
298C43⋊C8—42no—
299#11075—431nomaximal, Sylow
300C22×C43—22no—
301C22×C43—22no—
302C22×C43—21no—
303C22×C43—21no—
304C22×C43—21no—
305C22×C43—21no—
306C22×C43—22no—
307C22×C43—22no—
308C22×C43#38011yescharacteristic
309C22×C43#38611yescharacteristic
310C22×C43#39011yescharacteristic
311C22×C43#39211yescharacteristic
312C22×C43#39311yescharacteristic
313C22×C43#39711yescharacteristic
314C22×C43#39911yescharacteristic
315C22×C43C2×#10412yes—
316C22×C43#42112yes—
317C2×D43—44no—
318C2×D43—42no—
319C2×D43—81no—
320C2×D43—81no—
321C2×D43—82no—
322C4×C43—44no—
323C4×C43—82no—
324C4×C43#38511yescharacteristic
325C4×C43#38511yescharacteristic
326C4×C43#38811yescharacteristic
327C4×C43#38811yescharacteristic
328C4×C43#39411yescharacteristic
329C4×C43#39411yescharacteristic
330C4×C43#39611yescharacteristic
331C4×C43#39611yescharacteristic
332Dic43—24no—
333Dic43—44no—
334Dic43—42no—
335Dic43—42no—
336C22×#104—431no—
337C22×#104—431no—
338#2297—431no—
339C2×C4×C4⋊C4—431no—
340C2×#339—431no—
341C2×#339D4311yescharacteristic, complemented
342#1728—431no—
343C2×C43—21no—
344C2×C43—21no—
345C2×C43—21no—
346C2×C43—21no—
347C2×C43#143911yescharacteristic
348C2×C43#180612yes—
349C2×C43#189611yescharacteristic
350C2×C43#189711yescharacteristic
351C2×C43#198012yes—
352D43—82no—
353C22×#41—431no—
354C22×M16—431no—
355C22×M16C2×D4311yescharacteristic
356C2×#117C2×D4311yescharacteristic
357C22×C4⋊C4—861no—
358C22×C42—431no—
359C22×C42—431no—
360C22×C42C2×D4311yescharacteristic
361C2×#104—862no—
362C2×#104—862no—
363C2×#104—862no—
364C2×#104—862no—
365C2×#104—862no—
366C2×#104—862no—
367#391—432no—
368#390—432no—
369#386—861no—
370#386—861no—
371C4×C4⋊C4—862no—
372C4×C4⋊C4—862no—
373C4×C22⋊C4—862no—
374C2×#95—861no—
375#339—22no—
376#339—862no—
377#336—862no—
378C43#1107511yescharacteristic, complemented, Sylow
379C2×#41—432no—
380C2×#41—432no—
381C2×#41—861no—
382C2×#41—861no—
383C2×#41—861no—
384C2×#41—861no—
385C2×#41—861no—
386C2×#41—861no—
387C2×#41—861no—
388C2×#41—861no—
389C2×#41—861no—
390C2×#41—861no—
391C22×Q8—431no—
392C22×D4—431no—
393C22×D4—861no—
394C23×C4—21no—
395C23×C4—431no—
396C23×C4—431no—
397C23×C4—861no—
398C23×C4—861no—
399C23×C4C22×D4311yescharacteristic
400C2×M16—21no—
401C2×M16—21no—
402C2×M16—21no—
403C2×M16—21no—
404C2×M16—21no—
405C2×M16—432no—
406C2×M16—861no—
407C2×M16—861no—
408C2×M16—861no—
409C2×M16—861no—
410C2×M16—861no—
411C2×M16C22⋊D4312yes—
412C22×C8—21no—
413C22×C8—861no—
414#117—21no—
415#117—21no—
416#117—21no—
417#117—21no—
418C2×C4⋊C4—868no—
419C2×C4⋊C4—864no—
420C2×C4⋊C4C4×D4312yes—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—862no—
423C2×C22⋊C4—862no—
424C2×C42—21no—
425C2×C42—21no—
426C2×C42—21no—
427C2×C42—21no—
428C2×C42—21no—
429C2×C42—21no—
430C2×C42—432no—
431C2×C42—432no—
432C2×C42—432no—
433C2×C42—861no—
434C2×C42—861no—
435C2×C42—861no—
436C2×C42—861no—
437C2×C42—861no—
438C2×C42—861no—
439C2×C42—861no—
440C2×C42—861no—
441C2×C42—861no—
442C2×C42D17212yes—
443#104—868no—
444#104—868no—
445#95—862no—
446#95—862no—
447#95—864no—
448C24—861no—
449C24D4×D4311yescharacteristic
450#41—862no—
451#41—862no—
452#41—862no—
453#41—862no—
454#41—862no—
455#41—862no—
456#41—862no—
457#41—862no—
458#41—1721no—
459#41—1721no—
460#41—1721no—
461#41—1721no—
462#41—1721no—
463#41—1721no—
464#41—1721no—
465#41—1721no—
466C2×Q8—432no—
467C2×Q8—861no—
468C2×Q8—861no—
469C2×Q8—861no—
470C2×Q8—861no—
471C2×Q8—861no—
472C2×D4—432no—
473C2×D4—862no—
474C2×D4—862no—
475C2×D4—861no—
476C2×D4—861no—
477C2×D4—861no—
478C2×D4—861no—
479C2×D4—861no—
480C2×D4—1721no—
481C2×D4—1721no—
482C2×D4—1721no—
483C2×D4—1721no—
484C22×C4—24no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—42no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—432no—
491C22×C4—432no—
492C22×C4—864no—
493C22×C4—861no—
494C22×C4—861no—
495C22×C4—864no—
496C22×C4—861no—
497C22×C4—861no—
498C22×C4—862no—
499C22×C4—861no—
500C22×C4—862no—
501C22×C4—862no—
502C22×C4—1722no—
503C22×C4—1722no—
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×C4D4×D4311yescharacteristic
520C22×C4#1062190011yescharacteristic
521C22×C4Q8×D4311yescharacteristic
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—22no—
539C4⋊C4—22no—
540C4⋊C4—8616no—
541C22⋊C4—41no—
542C22⋊C4—41no—
543C22⋊C4—1724no—
544C22⋊C4—1724no—
545C42—22no—
546C42—22no—
547C42—41no—
548C42—41no—
549C42—41no—
550C42—41no—
551C42—862no—
552C42—862no—
553C42—862no—
554C42—862no—
555C42—862no—
556C42—862no—
557C42—1721no—
558C42—1721no—
559C23—22no—
560C23—22no—
561C23—862no—
562C23—1721no—
563C23—1722no—
564C23—1722no—
565C23—1721no—
566C23C22⋊C4×D4311yescharacteristic
567C23#1306329511yescharacteristic
568C23#1306329811yescharacteristic
569C23#1306330311yescharacteristic
570C23#1306331011yescharacteristic
571C23#1306331111yescharacteristic
572C23#1306332111yescharacteristic
573Q8—862no—
574Q8—862no—
575Q8—1721no—
576Q8—1721no—
577D4—862no—
578D4—862no—
579D4—1722no—
580D4—1722no—
581D4—1722no—
582D4—1722no—
583D4—1721no—
584D4—1721no—
585C2×C4—24no—
586C2×C4—44no—
587C2×C4—42no—
588C2×C4—44no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—434no—
594C2×C4—864no—
595C2×C4—864no—
596C2×C4—862no—
597C2×C4—862no—
598C2×C4—864no—
599C2×C4—862no—
600C2×C4—862no—
601C2×C4—862no—
602C2×C4—862no—
603C2×C4—1724no—
604C2×C4—1722no—
605C2×C4—1724no—
606C2×C4—1722no—
607C2×C4—1722no—
608C2×C4—1721no—
609C2×C4—1722no—
610C2×C4—1721no—
611C2×C4—1722no—
612C2×C4—1722no—
613C2×C4—1722no—
614C2×C4—1722no—
615C2×C4C4⋊C4×D4311yescharacteristic
616C2×C4#1306328211yescharacteristic
617C2×C4(C22⋊D43)⋊C411yescharacteristic
618C2×C4C4×C22⋊D4311yescharacteristic
619C2×C4#1306328711yescharacteristic
620C2×C4C4×D17211yescharacteristic
621C2×C4#1306329311yescharacteristic
622C2×C4#1306329511yescharacteristic
623C2×C4#1306329711yescharacteristic
624C2×C4#1306329811yescharacteristic
625C2×C4#1306329811yescharacteristic
626C2×C4#1306329811yescharacteristic
627C2×C4#1306329811yescharacteristic
628C2×C4#1306329911yescharacteristic
629C2×C4#1306330011yescharacteristic
630C2×C4#1306330111yescharacteristic
631C2×C4#1306330311yescharacteristic
632C2×C4#1306330311yescharacteristic
633C2×C4#1306330311yescharacteristic
634C2×C4#1306330511yescharacteristic
635C2×C4#1306330711yescharacteristic
636C2×C4#1306330811yescharacteristic
637C2×C4#1306331011yescharacteristic
638C2×C4#1306331011yescharacteristic
639C2×C4#1306331111yescharacteristic
640C2×C4#1306331311yescharacteristic
641C2×C4#1306331911yescharacteristic
642C2×C4#1306332011yescharacteristic
643C8—42no—
644C8—1722no—
645C22—22no—
646C22—22no—
647C22—21no—
648C22—21no—
649C22—21no—
650C22—21no—
651C22—22no—
652C22—22no—
653C22—3442no—
654C22—3441no—
655C22—3441no—
656C22—1724no—
657C22—1722no—
658C22#1458275811yescharacteristic
659C22#1458277711yescharacteristic
660C22#1458279911yescharacteristic
661C22#1458280811yescharacteristic
662C22#1458281211yescharacteristic
663C22#1458282811yescharacteristic
664C22#1458283411yescharacteristic
665C22#104×D4312yes—
666C22#1458291412yes—
667C4—44no—
668C4—82no—
669C4—864no—
670C4—1724no—
671C4—1722no—
672C4—1722no—
673C4#1458277011yescharacteristic
674C4#1458277311yescharacteristic
675C4#1458278811yescharacteristic
676C4#1458279011yescharacteristic
677C4#1458281411yescharacteristic
678C4#1458281711yescharacteristic
679C4#1458282111yescharacteristic
680C4#1458282311yescharacteristic
681C2—21no—
682C2—21no—
683C2—21no—
684C2—21no—
685C2—3442no—
686C2#1913283911yescharacteristic
687C2#1913461412yes—
688C2#1913503711yescharacteristic
689C2#1913504211yescharacteristic
690C2#1913551212yes—
subgroupG/H
centerC22×C4D4×D43
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#339C2
socleC23×C43C2×C22⋊C4
prime radicalC22×#10621898C22
cosocleC23×C4×C43C23
hypercenterC2×#339D43
hypocenterC43#11075
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×C4×Dic43⋊C4C2semidirect
5. C2×#14582658C2semidirect
6. #19134288C2semidirect
7. C2×C43×#339C2semidirect
19. #14582804C4semidirect
20. #14582800C4semidirect
165. C2×D172C4⋊C4semidirect
177. C2×Dic86C4⋊C4semidirect
284. C2×Dic43#104semidirect
341. C2×#339D43semidirect
378. C43#11075semidirect

Maximal subgroups

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

subgroupindex
C22×#130632532
C22×#130632512
#191370832
C2×C4×Dic43⋊C42
C2×#145826582
#191342882
C2×C43×#3392
#1107543