Finite Group Databasebeta

← #25113295

Subgroups — #25113295

Order 11008.

1096 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148173C211yesmaximal, characteristic
2M16×Dic86C211yesmaximal, characteristic, complemented
3C4×#13063290C211yesmaximal, characteristic, complemented
4#19135573C211yesmaximal, characteristic, complemented
5#19135570C212yesmaximal, complemented
6#19135537C212yesmaximal, complemented
7#19134616C211yesmaximal, characteristic
8#19134614C212yesmaximal
9C4×#13063251C211yesmaximal, characteristic
10#19134399C212yesmaximal
11C43×#1986C211yesmaximal, characteristic, complemented
12#14583629C411yescharacteristic, complemented
13#14583626C412yescomplemented
14#14583624C411yescharacteristic, complemented
15#14583610C411yescharacteristic, complemented
16#14583607—21no—
17#14583605C412yescomplemented
18#14583603—22no—
19#14583564C411yescharacteristic, complemented
20#14583562—21no—
21#14583453—21no—
22#14583453—22no—
23#14583452C2212yes—
24C4×#10621898C2211yescharacteristic
25#14583367C2212yes—
26C2×C4×Dic86C2211yescharacteristic
27C2×#13063290—21no—
28C4×Q8×D43—21no—
29#14583029—21no—
30#14583027—22no—
31C8×Dic86—21no—
32#14582923C2211yescharacteristic
33#14582922C2212yes—
34C2×#13063253C2212yes—
35C2×#13063251C2211yescharacteristic
36C2×#13063251C2211yescharacteristic
37M16×Dic43C2212yes—
38C4⋊C4×Dic43—21no—
39C4×Dic43⋊C4C2212yes—
40#14582750—22no—
41C42×Dic43C2212yes—
42C42×Dic43C2211yescharacteristic
43#14582660C2211yescharacteristic
44#14582660C2211yescharacteristic
45#14582659C2212yes—
46#14582658C2212yes—
47#14582658C2212yes—
48C43×#533C2211yescharacteristic
49C4×M16×C43C2211yescharacteristic
50C4×C4⋊C4×C43C2211yescharacteristic
51C43×#339C2212yes—
52C43×#339C2212yes—
53C2×#10621898C2311yescharacteristic
54C22×Dic86D411yescharacteristic
55C2×Q8×D43—21no—
56C2×#10621877C2312yes—
57#13063324—22no—
58#13063324—21no—
59#13063324C2×C412yes—
60#13063324C2×C412yes—
61#13063323—21no—
62#13063323—22no—
63#13063316C2×C412yes—
64#13063316C2×C412yes—
65#13063315—22no—
66#13063315—22no—
67#13063315—22no—
68#13063305—21no—
69#13063305—22no—
70#13063303—22no—
71#13063303—22no—
72#13063303—22no—
73#13063302—22no—
74#13063302—22no—
75#13063301—21no—
76#13063301—22no—
77Q8×Dic43—21no—
78C4×Dic86—22no—
79C4×Dic86—22no—
80C4×Dic86C2×C411yescharacteristic
81C4×Dic86C2×C411yescharacteristic
82C4×Dic86C2×C411yescharacteristic
83C4×Dic86C2×C412yes—
84C4×Dic86C2×C411yescharacteristic
85C4×Dic86D411yescharacteristic
86C4×Dic86D412yes—
87C4×Dic86D411yescharacteristic
88#13063290—28no—
89#13063290—21no—
90#13063290—22no—
91#13063290C2×C412yes—
92#13063290C2×C412yes—
93C4×D172C2×C411yescharacteristic
94C4×D172C2×C411yescharacteristic
95#13063287C2×C412yes—
96#13063287C2×C412yes—
97C4×C22⋊D43—21no—
98C4×C22⋊D43—21no—
99(C22⋊D43)⋊C4—22no—
100(C22⋊D43)⋊C4—22no—
101#13063284C2311yescharacteristic
102#13063282—21no—
103#13063282—22no—
104C2×C4⋊Dic43D411yescharacteristic
105C2×Dic43⋊C4—22no—
106C2×Dic43⋊C4D412yes—
107C4⋊C4×D43—21no—
108C4⋊C4×D43—22no—
109C2×C4×Dic43—21no—
110C2×C4×Dic43—22no—
111C2×C4×Dic43—21no—
112C2×C4×Dic43—22no—
113C2×C4×Dic43C2311yescharacteristic
114C2×C4×Dic43C2311yescharacteristic
115C2×C4×Dic43C2312yes—
116C42×D43—21no—
117C42×D43—22no—
118C4⋊(C43⋊C8)—21no—
119C4⋊(C43⋊C8)—21no—
120Dic43⋊C8—22no—
121Dic43⋊C8—22no—
122#13063253—24no—
123#13063251—22no—
124#13063251Q814yescomplemented
125#13063235—22no—
126C8×Dic43—22no—
127C43⋊#95—22no—
128C2×M16×C43C2311yescharacteristic
129C2×M16×C43C2311yescharacteristic
130C4⋊Q8×C43C2×C411yescharacteristic
131C4⋊Q8×C43C2×C411yescharacteristic
132#125×C43C2×C412yes—
133C22⋊Q8×C43—21no—
134C22⋊Q8×C43—21no—
135C4×Q8×C43—21no—
136C4×Q8×C43—21no—
137#117×C43C2312yes—
138C2×C4⋊C4×C43—21no—
139C2×C42×C43C2312yes—
140C2×C42×C43C2311yescharacteristic
141#97×C43—21no—
142C4×C8×C43—21no—
143#95×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C22×C4×C43—22no—
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2411yescharacteristic
150C2×C22⋊D43—21no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43C2×D412yes—
154C22×Dic43C2×D412yes—
155Q8×D43—44no—
156#10621898—21no—
157#10621898—21no—
158#10621898C2×Q812yes—
159#10621898#4112yes—
160C2×D172C22×C411yescharacteristic
161C2×C4×D43—21no—
162C2×C4×D43—21no—
163C2×C4×D43—22no—
164C2×C4×D43—21no—
165C2×C4×D43—22no—
166C2×Dic86—24no—
167C2×Dic86—22no—
168C2×Dic86—22no—
169C2×Dic86C22⋊C412yes—
170C2×Dic86C22⋊C411yescharacteristic
171C2×Dic86C22⋊C411yescharacteristic
172C2×Dic86C22×C411yescharacteristic
173M16×C43—21no—
174M16×C43—21no—
175M16×C43—21no—
176M16×C43C2×Q812yescomplemented
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C4⋊C4×C43—24no—
180C4⋊C4×C43—22no—
181C4⋊C4×C43—22no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43C22×C412yes—
185C4⋊C4×C43C22×C412yes—
186C22⋊C4×C43—22no—
187C42×C43—22no—
188C42×C43—22no—
189C42×C43—22no—
190C42×C43C22×C411yescharacteristic
191C42×C43C22×C411yescharacteristic
192C42×C43C2×D411yescharacteristic
193C42×C43C2×D411yescharacteristic
194C22⋊Dic43—21no—
195(C2×D43)⋊C4—21no—
196(C2×D43)⋊C4—21no—
197(C2×D43)⋊C4—22no—
198(C2×D43)⋊C4—22no—
199C4⋊Dic43—22no—
200C4⋊Dic43—22no—
201C4⋊Dic43C22⋊C411yescharacteristic
202C4⋊Dic43C22⋊C411yescharacteristic
203C4⋊Dic43C22⋊C412yes—
204C4⋊Dic43C22×C411yescharacteristic
205C4⋊Dic43C22×C411yescharacteristic
206Dic43⋊C4—28no—
207Dic43⋊C4—21no—
208Dic43⋊C4—21no—
209Dic43⋊C4—22no—
210Dic43⋊C4—22no—
211Dic43⋊C4—22no—
212Dic43⋊C4—22no—
213Dic43⋊C4—22no—
214Dic43⋊C4—22no—
215Dic43⋊C4C22⋊C412yes—
216Dic43⋊C4C22⋊C412yes—
217Dic43⋊C4C22⋊C412yes—
218Dic43⋊C4C22⋊C412yes—
219C4×Dic43—28no—
220C4×Dic43—24no—
221C4×Dic43—21no—
222C4×Dic43—21no—
223C4×Dic43—21no—
224C4×Dic43—21no—
225C4×Dic43—22no—
226C4×Dic43—22no—
227C4×Dic43—21no—
228C4×Dic43—21no—
229C4×Dic43—44no—
230C4×Dic43—42no—
231C4×Dic43C22×C412yes—
232C4×Dic43C22×C412yes—
233C4×Dic43C2×D412yes—
234C4×Dic43C2×D412yes—
235C4×Dic43C2×Q812yescomplemented
236#10621877—22no—
237#10621877—22no—
238C2×C43⋊C8—22no—
239C23×C43C22×D411yescharacteristic
240C22×D43—21no—
241Q8×C43—42no—
242Q8×C43—81no—
243C2×C4×C43—22no—
244C2×C4×C43—24no—
245C2×C4×C43—22no—
246C2×C4×C43—22no—
247C2×C4×C43—41no—
248C2×C4×C43—42no—
249C2×C4×C43—42no—
250C2×C4×C43C2×C22⋊C411yescharacteristic
251C2×C4×C43C2×C22⋊C411yescharacteristic
252C2×C4×C43C2×C22⋊C411yescharacteristic
253C2×C4×C43C2×C22⋊C411yescharacteristic
254C2×C4×C43C23×C411yescharacteristic
255C2×C4×C43C22×D411yescharacteristic
256C2×C4×C43C22×Q811yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C432−1+411yescharacteristic
259C2×C4×C432−1+411yescharacteristic
260C22⋊D43—22no—
261C22⋊D43—22no—
262C2×Dic43—22no—
263C2×Dic43—22no—
264C2×Dic43—21no—
265C2×Dic43—22no—
266C2×Dic43—24no—
267C2×Dic43—22no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—42no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43C2×C22⋊C412yes—
274C2×Dic43C2×C22⋊C412yes—
275C2×Dic43C2×C22⋊C412yes—
276C2×Dic43C2×C22⋊C412yes—
277D172—21no—
278D172C4×Q812yescomplemented
279C4×D43—22no—
280C4×D43—22no—
281C4×D43—42no—
282C4×D43—44no—
283C4×D43—82no—
284C4×D43—81no—
285Dic86—21no—
286Dic86—22no—
287Dic86—24no—
288Dic86—44no—
289Dic86—82no—
290Dic86#10414yescomplemented
291Dic86C4×Q812yescomplemented
292C8×C43—22no—
293C8×C43—41no—
294C43⋊C8—42no—
295Q8×#104—431nomaximal, Sylow
296C22×C43—21no—
297C22×C43—21no—
298C22×C43C22×C22⋊C411yescharacteristic
299C22×C43#54811yescharacteristic
300C22×C43D4×Q811yescharacteristic
301C2×D43—22no—
302C2×D43—41no—
303C2×D43—41no—
304C4×C43—21no—
305C4×C43—21no—
306C4×C43—21no—
307C4×C43—44no—
308C4×C43—42no—
309C4×C43—42no—
310C4×C43C2×#10412yes—
311C4×C43C2×C4×Q811yescharacteristic
312C4×C43#51911yescharacteristic
313C4×C43#54811yescharacteristic
314C4×C43D4×Q811yescharacteristic
315Dic43—24no—
316Dic43—22no—
317Dic43—22no—
318Dic43—22no—
319Dic43—22no—
320Dic43—42no—
321Dic43—41no—
322Dic43—41no—
323Dic43C2×#10414yes—
324Q8×#41—431no—
325Q8×M16—431no—
326C42×Q8—431no—
327#1994—432no—
328#1994—431no—
329#1986—432no—
330#1986D4311yescharacteristic, complemented
331#1806—431no—
332#1806—432no—
333C4×#104—431no—
334C4×#104—432no—
335C2×C43—21no—
336C2×C43—21no—
337C2×C43Q8×C22⋊C411yescharacteristic
338C2×C43C22×#10411yescharacteristic
339C2×C43#290111yescharacteristic
340D43—42no—
341Q82—431no—
342#557—431no—
343#557—432no—
344#554—431no—
345#554—432no—
346#554—862no—
347#554—861no—
348D4×Q8—431no—
349D4×Q8—861no—
350#533—432no—
351#533—862no—
352#533—861no—
353#533C2×D4311yescharacteristic
354C4×#41—432no—
355C4×#41—431no—
356C2×C4×Q8—431no—
357C2×C4×Q8—861no—
358C2×C4×Q8—861no—
359#446—861no—
360#446—862no—
361C8×Q8—861no—
362#423—432no—
363#423—431no—
364C2×#104—431no—
365C2×#104—431no—
366C2×#104—432no—
367C4×M16—432no—
368C4×M16C2×D4311yescharacteristic
369C4×C4⋊C4—432no—
370C4×C4⋊C4—862no—
371C4×C4⋊C4—861no—
372C4×C4⋊C4C2×D4311yescharacteristic
373C43—432no—
374C43—431no—
375#339—431no—
376#339—431no—
377#339—432no—
378#339—432no—
379#339—432no—
380#339C2×D4312yes—
381#339C2×D4312yes—
382C43Q8×#10411yescharacteristic, complemented, Sylow
383C2×#41—431no—
384C22×Q8—431no—
385C22×Q8—861no—
386C2×M16—432no—
387C2×M16C22×D4311yescharacteristic
388C2×M16C22×D4311yescharacteristic
389C4⋊Q8—432no—
390C4⋊Q8—432no—
391C4⋊Q8—861no—
392C4⋊Q8—862no—
393C4⋊Q8—862no—
394C4⋊Q8—861no—
395C4⋊Q8C4×D4311yescharacteristic
396C4⋊Q8C4×D4311yescharacteristic
397#125—432no—
398#125—432no—
399#125—862no—
400#125—862no—
401#125—862no—
402#125C4×D4312yes—
403C22⋊Q8—21no—
404C22⋊Q8—21no—
405C22⋊Q8—862no—
406C22⋊Q8—862no—
407C22⋊Q8—862no—
408C22⋊Q8—862no—
409C22⋊Q8—862no—
410C22⋊Q8—862no—
411C22⋊Q8—861no—
412C22⋊Q8—861no—
413C22⋊Q8—862no—
414C4×Q8—21no—
415C4×Q8—21no—
416C4×Q8—431no—
417C4×Q8—431no—
418C4×Q8—432no—
419C4×Q8—431no—
420C4×Q8—432no—
421C4×Q8—431no—
422C4×Q8—432no—
423C4×Q8—432no—
424C4×Q8—431no—
425C4×Q8—431no—
426C4×Q8—862no—
427C4×Q8—862no—
428C4×Q8—862no—
429C4×Q8—861no—
430C4×Q8—868no—
431C4×Q8—861no—
432C4×D4—432no—
433C4×D4—432no—
434C4×D4—431no—
435C4×D4—431no—
436C4×D4—862no—
437C4×D4—862no—
438C4×D4—861no—
439C4×D4—861no—
440#117—431no—
441#117—862no—
442#117—861no—
443#117C22×D4312yes—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—432no—
446C2×C4⋊C4—431no—
447C2×C4⋊C4—862no—
448C2×C4⋊C4—861no—
449C2×C4⋊C4—862no—
450C2×C42—432no—
451C2×C42—431no—
452C2×C42—431no—
453C2×C42—862no—
454C2×C42—862no—
455C2×C42—861no—
456C2×C42—861no—
457C2×C42—862no—
458C2×C42—861no—
459C2×C42C22×D4312yes—
460C2×C42C22×D4311yescharacteristic
461C4⋊C8—862no—
462C4⋊C8—862no—
463C4⋊C8—861no—
464C4⋊C8—861no—
465#104—434no—
466#104—864no—
467#104—862no—
468#97—21no—
469#97—862no—
470C4×C8—21no—
471C4×C8—862no—
472#95—21no—
473#95—862no—
474#41—432no—
475#41—432no—
476#41—861no—
477#41—861no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—431no—
481C2×Q8—432no—
482C2×Q8—431no—
483C2×Q8—431no—
484C2×Q8—862no—
485C2×Q8—862no—
486C2×Q8—864no—
487C2×Q8—1724no—
488C2×D4—431no—
489C2×D4—861no—
490C22×C4—22no—
491C22×C4—432no—
492C22×C4—432no—
493C22×C4—862no—
494C22×C4—862no—
495C22×C4—861no—
496C22×C4—861no—
497C22×C4—861no—
498C22×C4—861no—
499C22×C4—861no—
500C22×C4D4×D4311yescharacteristic
501C22×C4D4×D4311yescharacteristic
502C22×C4C23×D4311yescharacteristic
503M16—21no—
504M16—21no—
505M16—21no—
506M16—862no—
507M16—862no—
508M16Q8×D4312yescomplemented
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—862no—
512C4⋊C4—24no—
513C4⋊C4—22no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—22no—
517C4⋊C4—432no—
518C4⋊C4—431no—
519C4⋊C4—432no—
520C4⋊C4—432no—
521C4⋊C4—432no—
522C4⋊C4—432no—
523C4⋊C4—431no—
524C4⋊C4—431no—
525C4⋊C4—431no—
526C4⋊C4—862no—
527C4⋊C4—862no—
528C4⋊C4—862no—
529C4⋊C4—862no—
530C4⋊C4—862no—
531C4⋊C4—862no—
532C4⋊C4—862no—
533C4⋊C4—862no—
534C4⋊C4—868no—
535C4⋊C4—861no—
536C4⋊C4—861no—
537C4⋊C4C2×C4×D4312yes—
538C4⋊C4C2×C4×D4312yes—
539C22⋊C4—22no—
540C22⋊C4—862no—
541C22⋊C4—862no—
542C22⋊C4—861no—
543C22⋊C4—861no—
544C22⋊C4—861no—
545C42—22no—
546C42—22no—
547C42—22no—
548C42—432no—
549C42—432no—
550C42—432no—
551C42—432no—
552C42—432no—
553C42—862no—
554C42—862no—
555C42—864no—
556C42—868no—
557C42—861no—
558C42—861no—
559C42—861no—
560C42—861no—
561C42—861no—
562C42—861no—
563C42—1722no—
564C42—1724no—
565C42C2×C4×D4311yescharacteristic
566C42C2×C4×D4311yescharacteristic
567C42D4×D4311yescharacteristic
568C42D4×D4311yescharacteristic
569C23—861no—
570C23C2×D4×D4311yescharacteristic
571Q8—42no—
572Q8—81no—
573Q8—434no—
574Q8—432no—
575Q8—864no—
576Q8—861no—
577Q8—862no—
578Q8—3442no—
579Q8—1724no—
580D4—432no—
581D4—862no—
582D4—862no—
583D4—861no—
584C2×C4—22no—
585C2×C4—24no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—41no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—432no—
592C2×C4—432no—
593C2×C4—432no—
594C2×C4—432no—
595C2×C4—864no—
596C2×C4—862no—
597C2×C4—862no—
598C2×C4—862no—
599C2×C4—861no—
600C2×C4—862no—
601C2×C4—862no—
602C2×C4—862no—
603C2×C4—861no—
604C2×C4—861no—
605C2×C4—3441no—
606C2×C4—3442no—
607C2×C4—1724no—
608C2×C4—1722no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4—1722no—
612C2×C4C22⋊C4×D4311yescharacteristic
613C2×C4C22⋊C4×D4311yescharacteristic
614C2×C4C22⋊C4×D4311yescharacteristic
615C2×C4C22⋊C4×D4311yescharacteristic
616C2×C4C22×C4×D4311yescharacteristic
617C2×C4C2×D4×D4311yescharacteristic
618C2×C4C2×Q8×D4311yescharacteristic
619C2×C4#41×D4311yescharacteristic
620C2×C4#1306337211yescharacteristic
621C2×C4#1306337311yescharacteristic
622C8—22no—
623C8—41no—
624C8—1722no—
625C22—21no—
626C22—21no—
627C22—862no—
628C22—1721no—
629C22—1721no—
630C22C2×C22⋊C4×D4311yescharacteristic
631C22#1458355711yescharacteristic
632C22#1458356411yescharacteristic
633C4—21no—
634C4—21no—
635C4—21no—
636C4—44no—
637C4—42no—
638C4—42no—
639C4—434no—
640C4—864no—
641C4—862no—
642C4—862no—
643C4—862no—
644C4—862no—
645C4—1722no—
646C4—1721no—
647C4—1721no—
648C4#104×D4312yes—
649C4C4×Q8×D4311yescharacteristic
650C4#1458337511yescharacteristic
651C4#1458355911yescharacteristic
652C4#1458356211yescharacteristic
653C2—21no—
654C2—21no—
655C2—1722no—
656C2#1913742911yescharacteristic
657C2C2×#104×D4311yescharacteristic
658C2#1914314111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1986C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#10621898C23
cosocleC22×C4×C43C24
hypercenter#1986D43
hypocenterC43Q8×#104
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1986

Complements

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

NH ≅ G/Ntype
2. M16×Dic86C2semidirect
3. C4×#13063290C2semidirect
4. #19135573C2semidirect
5. #19135570C2semidirect
6. #19135537C2semidirect
11. C43×#1986C2semidirect
12. #14583629C4semidirect
13. #14583626C4semidirect
14. #14583624C4semidirect
15. #14583610C4semidirect
17. #14583605C4semidirect
19. #14583564C4semidirect
124. #13063251Q8semidirect
176. M16×C43C2×Q8semidirect
235. C4×Dic43C2×Q8semidirect
278. D172C4×Q8semidirect
290. Dic86#104semidirect
291. Dic86C4×Q8semidirect
330. #1986D43semidirect
382. C43Q8×#104semidirect
508. M16Q8×D43semidirect

Maximal subgroups

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

subgroupindex
#191481732
M16×Dic862
C4×#130632902
#191355732
#191355702
#191355372
#191346162
#191346142
C4×#130632512
#191343992
C43×#19862
Q8×#10443