Finite Group Databasebeta

← #25003594

Subgroups — #25003594

Order 11008.

910 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582917C211yesmaximal, characteristic
2C2×#14582901C211yesmaximal, characteristic
3C2×#14582872C211yesmaximal, characteristic
4#19137211C211yesmaximal, characteristic, complemented
5C2×#14582670C211yesmaximal, characteristic, complemented
6#19134316C211yesmaximal, characteristic, complemented
7C2×C43×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10C2×#13063284C2211yescharacteristic
11C22×C4⋊Dic43C2211yescharacteristic
12#14582917—22no—
13#14582917—22no—
14C2×#13063253—22no—
15#14582901—22no—
16#14582901—22no—
17C2×#13063250C412yescomplemented
18C2×#13063247C412yescomplemented
19#14582872—22no—
20#14582872—22no—
21C2×#13063239—22no—
22#14582797—22no—
23#14582795—22no—
24#14582757—22no—
25#14582670—22no—
26#14582661—22no—
27C22×M16×C43C2211yescharacteristic
28C2×#117×C43C2211yescharacteristic
29C2×#117×C43C2211yescharacteristic
30C43×H(3,ℤ/4)—22no—
31C2×#10621898—21no—
32C2×#10621898—21no—
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×#10621898D412yes—
42C2×#10621898Q812yes—
43C22×Dic86C2×C411yescharacteristic
44C22×D172C2×C411yescharacteristic
45C22×C22⋊D43—21no—
46C23×Dic43—21no—
47C22×C4×D43—21no—
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⋊Dic43—21no—
60C2×C4⋊Dic43—21no—
61C2×C4⋊Dic43—21no—
62C2×C4⋊Dic43—21no—
63C2×C4⋊Dic43C2×C412yes—
64C2×C4⋊Dic43D412yes—
65C2×C4⋊Dic43D412yes—
66C2×Dic43⋊C4—24no—
67C2×C22⋊Dic43D412yes—
68C2×C4×Dic43—21no—
69#13063253—28no—
70#13063250—24no—
71#13063247—24no—
72#13063239—28no—
73C43⋊#95—24no—
74C23×C4×C43C2311yescharacteristic
75C2×M16×C43—21no—
76C2×M16×C43—21no—
77C2×M16×C43—21no—
78C2×M16×C43—21no—
79C2×M16×C43—21no—
80C2×M16×C43—21no—
81C22×C8×C43C2×C412yes—
82#117×C43—21no—
83#117×C43—21no—
84#117×C43—21no—
85#117×C43—21no—
86#117×C43—21no—
87#117×C43—21no—
88#117×C43—21no—
89#117×C43D412yes—
90C2×C4⋊C4×C43—21no—
91C2×C4⋊C4×C43—21no—
92C2×C22⋊C4×C43—21no—
93C2×C22⋊C4×C43—21no—
94C2×C42×C43—21no—
95C2×C42×C43D412yes—
96C24×C43C2×D411yescharacteristic
97C23×D43—21no—
98C22×C4×C43—22no—
99C22×C4×C43—41no—
100C22×C4×C43C22×C411yescharacteristic
101C22×C4×C43C2×D411yescharacteristic
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43C2×D411yescharacteristic
104C22×C4×C43C2×D411yescharacteristic
105C22×C4×C43C2×D411yescharacteristic
106C22×C4×C43C2×D411yescharacteristic
107C22×C4×C43C2×Q811yescharacteristic
108C22×C4×C43#4111yescharacteristic
109C22×C4×C43#4111yescharacteristic
110C22×C4×C43#4111yescharacteristic
111C22×C4×C43#4111yescharacteristic
112C22×C4×C43#4111yescharacteristic
113C22×C4×C43#4111yescharacteristic
114C2×C22⋊D43—22no—
115C2×C22⋊D43—22no—
116C2×C22⋊D43—41no—
117C2×C22⋊D43—41no—
118C2×C22⋊D43—41no—
119C2×C22⋊D43—41no—
120C22×Dic43—21no—
121C22×Dic43—22no—
122C22×Dic43—22no—
123C22×Dic43—22no—
124C22×Dic43—22no—
125C22×Dic43—82no—
126#10621898—22no—
127#10621898—22no—
128#10621898—22no—
129#10621898—22no—
130#10621898—22no—
131#10621898—22no—
132#10621898—22no—
133#10621898—22no—
134#10621898—41no—
135#10621898—41no—
136#10621898—41no—
137#10621898—41no—
138#10621898—41no—
139#10621898—41no—
140#10621898—41no—
141#10621898—41no—
142C2×D172—21no—
143C2×D172—21no—
144C2×D172—21no—
145C2×D172—21no—
146C2×D172—21no—
147C2×D172C4⋊C412yescomplemented
148C2×C4×D43—22no—
149C2×C4×D43—22no—
150C2×C4×D43—41no—
151C2×C4×D43—41no—
152C2×C4×D43—41no—
153C2×C4×D43—41no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86C4⋊C412yescomplemented
160M16×C43—41no—
161M16×C43—41no—
162M16×C43—41no—
163M16×C43—41no—
164C2×C8×C43—22no—
165C2×C8×C43—22no—
166C2×C8×C43—22no—
167C4⋊C4×C43—22no—
168C4⋊C4×C43—41no—
169C4⋊C4×C43—41no—
170C4⋊C4×C43—41no—
171C22⋊C4×C43—22no—
172C22⋊C4×C43—41no—
173C22⋊C4×C43—41no—
174C22⋊C4×C43—41no—
175C42×C43—22no—
176C42×C43—22no—
177C42×C43—22no—
178C42×C43—41no—
179C22⋊Dic43—22no—
180C22⋊Dic43—22no—
181C4⋊Dic43—22no—
182C4⋊Dic43—22no—
183C4⋊Dic43—22no—
184C4⋊Dic43—41no—
185C4⋊Dic43—41no—
186C4⋊Dic43C22⋊C414yes—
187Dic43⋊C4—84no—
188C4×Dic43—41no—
189C4×Dic43—41no—
190#10621877—22no—
191#10621877—22no—
192#10621877—41no—
193#10621877—41no—
194C2×C43⋊C8—22no—
195C2×C43⋊C8—41no—
196C2×C43⋊C8—41no—
197C23×C43—41no—
198C23×C43—41no—
199C23×C43C4×D411yescharacteristic
200C23×C43#12011yescharacteristic
201C23×C43#12011yescharacteristic
202C23×C43#12111yescharacteristic
203C23×C43#12111yescharacteristic
204C23×C43C22⋊Q811yescharacteristic
205C23×C43#12411yescharacteristic
206C22×D43—22no—
207C22×D43—41no—
208C22×D43—41no—
209C22×D43—81no—
210C22×D43—81no—
211C2×C4×C43—42no—
212C2×C4×C43—42no—
213C2×C4×C43—42no—
214C2×C4×C43—42no—
215C2×C4×C43—81no—
216C2×C4×C43—81no—
217C2×C4×C43C2×C22⋊C411yescharacteristic
218C2×C4×C43C2×C4⋊C411yescharacteristic
219C2×C4×C43#11711yescharacteristic
220C2×C4×C43C4×D411yescharacteristic
221C2×C4×C43C4×D411yescharacteristic
222C2×C4×C43C4×D411yescharacteristic
223C2×C4×C43#12011yescharacteristic
224C2×C4×C43#12111yescharacteristic
225C2×C4×C43#12111yescharacteristic
226C2×C4×C43#12111yescharacteristic
227C2×C4×C43#12111yescharacteristic
228C2×C4×C43#12111yescharacteristic
229C2×C4×C43#12111yescharacteristic
230C2×C4×C43C22⋊Q811yescharacteristic
231C2×C4×C43C22⋊Q811yescharacteristic
232C2×C4×C43C22⋊Q811yescharacteristic
233C2×C4×C43C22⋊Q811yescharacteristic
234C2×C4×C43C22⋊Q811yescharacteristic
235C2×C4×C43#12311yescharacteristic
236C2×C4×C43#12311yescharacteristic
237C2×C4×C43#12311yescharacteristic
238C2×C4×C43#12311yescharacteristic
239C2×C4×C43#12311yescharacteristic
240C2×C4×C43#12411yescharacteristic
241C2×C4×C43#12411yescharacteristic
242C2×C4×C43#12611yescharacteristic
243C2×C4×C43#12611yescharacteristic
244C2×C4×C43#12711yescharacteristic
245C22⋊D43—42no—
246C22⋊D43—42no—
247C22⋊D43—42no—
248C22⋊D43—42no—
249C2×Dic43—22no—
250C2×Dic43—24no—
251C2×Dic43—44no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—42no—
255C2×Dic43—42no—
256C2×Dic43—42no—
257C2×Dic43—82no—
258C2×Dic43—82no—
259D172—22no—
260D172—22no—
261D172—41no—
262D172—41no—
263C4×D43—42no—
264C4×D43—42no—
265C4×D43—42no—
266C4×D43—42no—
267Dic86—22no—
268Dic86—22no—
269Dic86—41no—
270Dic86—41no—
271C8×C43—42no—
272C43⋊C8—42no—
273#11057—431nomaximal, Sylow
274C22×C43—21no—
275C22×C43—21no—
276C22×C43—21no—
277C22×C43—21no—
278C22×C43—21no—
279C22×C43—21no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43—41no—
284C22×C43#38511yescharacteristic
285C22×C43#38611yescharacteristic
286C22×C43#38811yescharacteristic
287C22×C43#39211yescharacteristic
288C22×C43#39311yescharacteristic
289C22×C43#39411yescharacteristic
290C22×C43#39611yescharacteristic
291C2×D43—42no—
292C2×D43—82no—
293C2×D43—81no—
294C2×D43—81no—
295C2×D43—82no—
296C4×C43—82no—
297C4×C43—82no—
298C4×C43#38011yescharacteristic
299C4×C43#38511yescharacteristic
300C4×C43#38811yescharacteristic
301C4×C43#39011yescharacteristic
302C4×C43#39411yescharacteristic
303C4×C43#39611yescharacteristic
304C4×C43#39711yescharacteristic
305C4×C43#39911yescharacteristic
306Dic43—44no—
307Dic43—42no—
308Dic43—82no—
309C2×#421—431no—
310C2×#417—431no—
311C2×#410—431no—
312#2316—431no—
313C2×#344—431no—
314#1736—431no—
315C2×H(3,ℤ/4)D4311yescharacteristic, complemented
316C2×C43—21no—
317C2×C43—21no—
318C2×C43—21no—
319C2×C43—21no—
320C2×C43—21no—
321C2×C43—21no—
322C2×C43#143911yescharacteristic
323C2×C43#190411yescharacteristic
324C2×C43#190511yescharacteristic
325D43—82no—
326C22×#41—431no—
327C22×M16—431no—
328C22×M16C2×D4311yescharacteristic
329C2×#117—431no—
330C2×#117C2×D4311yescharacteristic
331C2×#117C2×D4311yescharacteristic
332C22×C4⋊C4—431no—
333#421—862no—
334#421—862no—
335C2×#104—862no—
336#417—862no—
337#417—862no—
338C2×#103—432no—
339C2×#102—432no—
340#410—862no—
341#410—862no—
342C2×#99—862no—
343#389—862no—
344#389—862no—
345#380—862no—
346#344—862no—
347#340—862no—
348H(3,ℤ/4)—22no—
349C43#1105711yescharacteristic, complemented, Sylow
350C2×#41—432no—
351C2×#41—432no—
352C2×#41—861no—
353C2×#41—861no—
354C2×#41—861no—
355C2×#41—861no—
356C2×#41—861no—
357C2×#41—861no—
358C2×#41—861no—
359C2×#41—861no—
360C2×#41—861no—
361C2×#41—861no—
362C22×Q8—431no—
363C22×D4—431no—
364C22×D4—861no—
365C23×C4—861no—
366C23×C4—861no—
367C23×C4C22×D4311yescharacteristic
368C2×M16—21no—
369C2×M16—21no—
370C2×M16—21no—
371C2×M16—21no—
372C2×M16—21no—
373C2×M16—21no—
374C2×M16—432no—
375C2×M16—861no—
376C2×M16—861no—
377C2×M16—861no—
378C2×M16—861no—
379C2×M16—861no—
380C22×C8—861no—
381C22×C8C4×D4312yes—
382#117—21no—
383#117—21no—
384#117—21no—
385#117—21no—
386#117—21no—
387#117—21no—
388#117—21no—
389#117—861no—
390#117—861no—
391#117—861no—
392#117—861no—
393#117C22⋊D4312yes—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—432no—
397C2×C4⋊C4—432no—
398C2×C4⋊C4—432no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—864no—
403C2×C4⋊C4—861no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—432no—
407C2×C42—21no—
408C2×C42—861no—
409C2×C42D17212yes—
410#104—868no—
411#103—864no—
412#102—864no—
413#99—868no—
414#95—864no—
415C24—861no—
416C24D4×D4311yescharacteristic
417#41—862no—
418#41—862no—
419#41—862no—
420#41—862no—
421#41—862no—
422#41—862no—
423#41—862no—
424#41—862no—
425#41—1721no—
426#41—1721no—
427#41—1721no—
428#41—1721no—
429#41—1721no—
430#41—1721no—
431#41—1721no—
432#41—1721no—
433C2×Q8—432no—
434C2×Q8—861no—
435C2×Q8—861no—
436C2×Q8—861no—
437C2×Q8—861no—
438C2×Q8—861no—
439C2×D4—432no—
440C2×D4—862no—
441C2×D4—862no—
442C2×D4—861no—
443C2×D4—861no—
444C2×D4—861no—
445C2×D4—861no—
446C2×D4—861no—
447C2×D4—1721no—
448C2×D4—1721no—
449C2×D4—1721no—
450C2×D4—1721no—
451C22×C4—22no—
452C22×C4—41no—
453C22×C4—862no—
454C22×C4—862no—
455C22×C4—861no—
456C22×C4—862no—
457C22×C4—862no—
458C22×C4—862no—
459C22×C4—862no—
460C22×C4—3442no—
461C22×C4—1721no—
462C22×C4—1721no—
463C22×C4—1721no—
464C22×C4—1721no—
465C22×C4C2×C4×D4311yescharacteristic
466C22×C4C2×D17211yescharacteristic
467C22×C4#1062189811yescharacteristic
468C22×C4#1062189811yescharacteristic
469C22×C4#1062189811yescharacteristic
470C22×C4#1062189811yescharacteristic
471C22×C4D4×D4311yescharacteristic
472C22×C4D4×D4311yescharacteristic
473C22×C4D4×D4311yescharacteristic
474C22×C4D4×D4311yescharacteristic
475C22×C4#1062190011yescharacteristic
476C22×C4Q8×D4311yescharacteristic
477C22×C4#1062190211yescharacteristic
478C22×C4C2×C22⋊D4311yescharacteristic
479M16—41no—
480M16—41no—
481M16—41no—
482M16—41no—
483M16—862no—
484M16—862no—
485M16—1721no—
486M16—1721no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—22no—
490C2×C8—862no—
491C2×C8—1721no—
492C2×C8—1721no—
493C4⋊C4—22no—
494C4⋊C4—41no—
495C4⋊C4—41no—
496C4⋊C4—41no—
497C4⋊C4—434no—
498C4⋊C4—862no—
499C4⋊C4—862no—
500C4⋊C4—862no—
501C4⋊C4—3444no—
502C4⋊C4—1721no—
503C4⋊C4—1721no—
504C22⋊C4—22no—
505C22⋊C4—41no—
506C22⋊C4—41no—
507C22⋊C4—41no—
508C22⋊C4—862no—
509C22⋊C4—862no—
510C42—22no—
511C42—22no—
512C42—22no—
513C42—41no—
514C42—1721no—
515C42—1721no—
516C23—41no—
517C23—41no—
518C23—862no—
519C23—3441no—
520C23—3441no—
521C23—1721no—
522C23—1721no—
523C23#1306328711yescharacteristic
524C23#1306329311yescharacteristic
525C23#1306329511yescharacteristic
526C23#1306329811yescharacteristic
527C23#1306329811yescharacteristic
528C23#1306330311yescharacteristic
529C23#1306331111yescharacteristic
530Q8—862no—
531Q8—862no—
532Q8—1721no—
533Q8—1721no—
534D4—862no—
535D4—862no—
536D4—1722no—
537D4—1722no—
538D4—1722no—
539D4—1722no—
540D4—1721no—
541D4—1721no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—81no—
547C2×C4—81no—
548C2×C4—862no—
549C2×C4—864no—
550C2×C4—3442no—
551C2×C4—3442no—
552C2×C4—1722no—
553C2×C4—1722no—
554C2×C4—1722no—
555C2×C4—1724no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4—1722no—
559C2×C4—1722no—
560C2×C4—1722no—
561C2×C4—1722no—
562C2×C4C22⋊C4×D4311yescharacteristic
563C2×C4C4⋊C4×D4311yescharacteristic
564C2×C4#1306328211yescharacteristic
565C2×C4(C22⋊D43)⋊C411yescharacteristic
566C2×C4C4×C22⋊D4311yescharacteristic
567C2×C4C4×D17211yescharacteristic
568C2×C4#1306329511yescharacteristic
569C2×C4#1306329711yescharacteristic
570C2×C4#1306329811yescharacteristic
571C2×C4#1306329811yescharacteristic
572C2×C4#1306329811yescharacteristic
573C2×C4#1306329911yescharacteristic
574C2×C4#1306330011yescharacteristic
575C2×C4#1306330111yescharacteristic
576C2×C4#1306330311yescharacteristic
577C2×C4#1306330311yescharacteristic
578C2×C4#1306330311yescharacteristic
579C2×C4#1306330511yescharacteristic
580C2×C4#1306330711yescharacteristic
581C2×C4#1306330811yescharacteristic
582C2×C4#1306331011yescharacteristic
583C2×C4#1306331011yescharacteristic
584C2×C4#1306331011yescharacteristic
585C2×C4#1306331111yescharacteristic
586C2×C4#1306331311yescharacteristic
587C2×C4#1306331911yescharacteristic
588C2×C4#1306332011yescharacteristic
589C2×C4#1306332111yescharacteristic
590C8—42no—
591C8—1722no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—21no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—3442no—
603C22—3442no—
604C22—3441no—
605C22—3441no—
606C22—1722no—
607C22#1458277011yescharacteristic
608C22#1458277711yescharacteristic
609C22#1458278811yescharacteristic
610C22#1458280811yescharacteristic
611C22#1458281211yescharacteristic
612C22#1458281411yescharacteristic
613C22#1458282311yescharacteristic
614C4—82no—
615C4—82no—
616C4—3442no—
617C4—1724no—
618C4—1722no—
619C4#1458275811yescharacteristic
620C4#1458277311yescharacteristic
621C4#1458279011yescharacteristic
622C4#1458279911yescharacteristic
623C4#1458281711yescharacteristic
624C4#1458282111yescharacteristic
625C4#1458282811yescharacteristic
626C4#1458283411yescharacteristic
627C2—21no—
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—21no—
633C2—3442no—
634C2#1913283911yescharacteristic
635C2#1913508311yescharacteristic
636C2#1913509011yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×H(3,ℤ/4)C2
socleC22×C43#386
prime radicalC22×#10621898C22
cosocleC23×C4×C43C23
hypercenterC2×H(3,ℤ/4)D43
hypocenterC43#11057
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
4. #19137211C2semidirect
5. C2×#14582670C2semidirect
6. #19134316C2semidirect
7. C2×C43×H(3,ℤ/4)C2semidirect
17. C2×#13063250C4semidirect
18. C2×#13063247C4semidirect
147. C2×D172C4⋊C4semidirect
159. C2×Dic86C4⋊C4semidirect
315. C2×H(3,ℤ/4)D43semidirect
349. C43#11057semidirect

Maximal subgroups

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

subgroupindex
C2×#145829172
C2×#145829012
C2×#145828722
#191372112
C2×#145826702
#191343162
C2×C43×H(3,ℤ/4)2
#1105743