Finite Group Databasebeta

← #25152723

Subgroups — #25152723

Order 11008.

1056 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583610C211yesmaximal, characteristic
2C2×#14583307C211yesmaximal, characteristic, complemented
3C2×#14583178C211yesmaximal, characteristic
4#19139802C211yesmaximal, characteristic, complemented
5#19135932C211yesmaximal, characteristic, complemented
6#19135931C211yesmaximal, characteristic, complemented
7#19135920C211yesmaximal, characteristic, complemented
8#19135551C211yesmaximal, characteristic, complemented
9#19135533C211yesmaximal, characteristic, complemented
10#19134859C211yesmaximal, characteristic
11#19134855C211yesmaximal, characteristic
12#19134843C211yesmaximal, characteristic
13#19134839C211yesmaximal, characteristic
14#19134419C211yesmaximal, characteristic
15C43×#2057C211yesmaximal, characteristic, complemented
16#14583610—24no—
17#14583610—24no—
18C2×#13063324C2211yescharacteristic
19C2×#13063316C2211yescharacteristic
20C2×#13063316C2211yescharacteristic
21C2×#13063305—21no—
22C2×#13063301—21no—
23C2×#13063301—21no—
24C2×C4×Dic86C2211yescharacteristic
25C2×C4×D172C2211yescharacteristic
26C2×#13063287C2211yescharacteristic
27C2×#13063287C2211yescharacteristic
28C2×C4⋊C4×D43—21no—
29#14583307—24no—
30#14583178—24no—
31C2×#13063258C2211yescharacteristic
32C2×#13063258C2211yescharacteristic
33C2×#13063257C2211yescharacteristic
34C2×#13063256C2211yescharacteristic
35C2×Dic43⋊C8C2211yescharacteristic
36C2×#13063247C2211yescharacteristic
37C2×#13063247C2211yescharacteristic
38C2×#13063245C2211yescharacteristic
39C2×#13063245C2211yescharacteristic
40C2×#13063235C2211yescharacteristic
41#14582820—21no—
42#14582819—21no—
43#14582803—21no—
44#14582798C2211yescharacteristic
45#14582797C2211yescharacteristic
46#14582795C2211yescharacteristic
47#14582768—21no—
48C4⋊C4×Dic43C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582654C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C2×C4⋊Q8×C43C2211yescharacteristic
57C2×#107×C43C2211yescharacteristic
58C2×#107×C43C2211yescharacteristic
59C43×#389C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C22×Dic86—21no—
64C22×Dic86D411yescharacteristic
65C22×D172C2311yescharacteristic
66C22×C4×D43—21no—
67C22×C4×D43—21no—
68C22×C4×D43—21no—
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71#13063324—22no—
72#13063324—22no—
73#13063316—22no—
74#13063316—22no—
75#13063316—22no—
76#13063316D414yes—
77#13063305—28no—
78#13063301—28no—
79#13063301—28no—
80C4×Dic86—22no—
81C4×Dic86—22no—
82C4×D172—22no—
83C4×D172—22no—
84#13063287—22no—
85#13063287—22no—
86#13063287—22no—
87#13063287D414yes—
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43—21no—
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43D411yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4D411yescharacteristic
101C2×Dic43⋊C4D411yescharacteristic
102C4⋊C4×D43—28no—
103C2×(C2×D43)⋊C4—21no—
104C2×(C2×D43)⋊C4—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×C4×Dic43—21no—
107C2×C4×Dic43C2311yescharacteristic
108C2×C4×Dic43C2311yescharacteristic
109#13063258—22no—
110#13063258—22no—
111#13063257—22no—
112#13063256—22no—
113Dic43⋊C8—22no—
114#13063247—22no—
115#13063247Q814yescomplemented
116#13063245—22no—
117#13063245Q814yescomplemented
118#13063235—22no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C22×Q8×C43—21no—
124C22×C8×C43C2311yescharacteristic
125C22×C8×C43C2311yescharacteristic
126C4⋊Q8×C43—22no—
127C4⋊Q8×C43—22no—
128C2×C4⋊C4×C43—21no—
129C2×C4⋊C4×C43—21no—
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C4⋊C4×C43C2311yescharacteristic
132C2×C4⋊C4×C43C2311yescharacteristic
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C42×C43C2311yescharacteristic
135#107×C43—22no—
136#107×C43—22no—
137#95×C43—21no—
138C23×D43—21no—
139C2×Q8×C43—24no—
140C2×Q8×C43—81no—
141C2×Q8×C43—81no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2411yescharacteristic
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43C2×D411yescharacteristic
153C22×Dic43C2×D411yescharacteristic
154C22×Dic43C2×D411yescharacteristic
155C22×Dic43C2×D411yescharacteristic
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—21no—
159C2×D172C2×D412yes—
160C2×D172C2×Q812yes—
161C2×D172C2×Q812yes—
162C2×C4×D43—24no—
163C2×C4×D43—24no—
164C2×C4×D43—24no—
165C2×C4×D43—42no—
166C2×C4×D43—42no—
167C2×C4×D43—81no—
168C2×C4×D43—81no—
169C2×C4×D43—81no—
170C2×C4×D43—81no—
171C2×Dic86—22no—
172C2×Dic86—22no—
173C2×Dic86—41no—
174C2×Dic86—42no—
175C2×Dic86—81no—
176C2×Dic86—81no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43C2×Q812yes—
183C4⋊C4×C43—24no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—81no—
190C4⋊C4×C43C2×D412yes—
191C4⋊C4×C43C2×D412yes—
192C4⋊C4×C43C2×Q812yes—
193C42×C43—21no—
194C42×C43—21no—
195(C2×D43)⋊C4—24no—
196(C2×D43)⋊C4—24no—
197(C2×D43)⋊C4—24no—
198C4⋊Dic43—24no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—22no—
202C4⋊Dic43—24no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—81no—
206C4⋊Dic43C2×D412yes—
207C4⋊Dic43C2×Q812yes—
208Dic43⋊C4—24no—
209Dic43⋊C4—24no—
210Dic43⋊C4—22no—
211Dic43⋊C4—22no—
212Dic43⋊C4—42no—
213Dic43⋊C4—81no—
214Dic43⋊C4—81no—
215C4×Dic43—21no—
216C4×Dic43—21no—
217C4×Dic43—42no—
218C4×Dic43C2×D412yes—
219C4×Dic43C2×D412yes—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8C2×Q812yes—
226C23×C43C22×D411yescharacteristic
227C22×D43—22no—
228C22×D43—22no—
229C22×D43—22no—
230C22×D43—41no—
231C22×D43—41no—
232C22×D43—41no—
233C22×D43—41no—
234Q8×C43—84no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—22no—
239C2×C4×C43—22no—
240C2×C4×C43—22no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43#13712yes—
253C2×C4×C43C22×D411yescharacteristic
254C2×C4×C43C22×D411yescharacteristic
255C2×C4×C43C22×Q811yescharacteristic
256C2×C4×C43C22×Q811yescharacteristic
257C2×C4×C432−1+411yescharacteristic
258C2×C4×C432−1+411yescharacteristic
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—22no—
266C2×Dic43—22no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43#12012yes—
279C2×Dic43#12012yes—
280D172—22no—
281D172—22no—
282D172—22no—
283D172C4⋊Q814yes—
284C4×D43—48no—
285C4×D43—84no—
286C4×D43—84no—
287Dic86—44no—
288Dic86—84no—
289C8×C43—22no—
290C8×C43—41no—
291C43⋊C8—22no—
292C43⋊C8—41no—
293#25850—431nomaximal, Sylow
294C22×C43C2×#12011yescharacteristic
295C22×C43D4×Q811yescharacteristic
296C22×C43D4×Q811yescharacteristic
297C22×C43C2×#13711yescharacteristic
298C22×C43#57511yescharacteristic
299C22×C43#57611yescharacteristic
300C22×C43#57611yescharacteristic
301C2×D43—24no—
302C2×D43—42no—
303C2×D43—42no—
304C2×D43—42no—
305C2×D43—42no—
306C2×D43—42no—
307C2×D43—42no—
308C4×C43—22no—
309C4×C43—42no—
310C4×C43—42no—
311C4×C43—42no—
312C4×C43—41no—
313C4×C43—81no—
314C4×C43C2×C4⋊Q811yescharacteristic
315C4×C43#53611yescharacteristic
316C4×C43D4×Q811yescharacteristic
317C4×C43D4×Q811yescharacteristic
318Dic43—22no—
319Dic43—22no—
320Dic43—42no—
321Dic43—41no—
322Dic43—42no—
323Dic43—41no—
324Dic43—81no—
325C2×#554—431no—
326C2×#501—431no—
327C2×#474—431no—
328#2567—431no—
329#2059—431no—
330#2059—431no—
331#2057—431no—
332#2057D4311yescharacteristic, complemented
333#1989—431no—
334#1985—431no—
335#1864—431no—
336#1864—431no—
337#1862—431no—
338#1862—431no—
339#1762—431no—
340C2×C43#243411yescharacteristic
341C2×C43#300711yescharacteristic
342C2×C43#300811yescharacteristic
343C2×C43#338511yescharacteristic
344C2×C43#338511yescharacteristic
345C2×C43#338911yescharacteristic
346C2×C43#338911yescharacteristic
347D43—44no—
348#554—864no—
349#554—864no—
350C2×C4⋊Q8—431no—
351C2×C4⋊Q8C2×D4311yescharacteristic
352C2×#125—431no—
353C2×#125—431no—
354C2×C22⋊Q8—861no—
355C2×C22⋊Q8—861no—
356C2×C22⋊Q8—861no—
357C2×C4×Q8—431no—
358C2×C4×D4—431no—
359C2×C4×D4—431no—
360C2×C4×D4—431no—
361C22×C4⋊C4—861no—
362#501—864no—
363#474—864no—
364C2×#107—431no—
365C2×#107—431no—
366C2×#107C2×D4311yescharacteristic
367C2×#107C2×D4311yescharacteristic
368C2×#106—431no—
369C2×#106—431no—
370C2×C4⋊C8—431no—
371C2×#102—431no—
372C2×#102—431no—
373C2×#102—431no—
374C2×#102—431no—
375C2×#97—431no—
376#395—861no—
377#395—861no—
378#391—861no—
379#389—431no—
380#389—431no—
381#389—431no—
382#389C2×D4311yescharacteristic
383#384—861no—
384C4×C4⋊C4—431no—
385#340—431no—
386#340—431no—
387#340—431no—
388#340—431no—
389#340C2×D4311yescharacteristic
390#340C2×D4311yescharacteristic
391#336—431no—
392#336—431no—
393#336—431no—
394#336C2×D4311yescharacteristic
395C43#2585011yescharacteristic, complemented, Sylow
396C22×Q8—21no—
397C22×Q8—431no—
398C22×Q8—861no—
399C22×D4—431no—
400C23×C4—861no—
401C23×C4—861no—
402C23×C4—861no—
403C22×C8—431no—
404C22×C8—431no—
405C22×C8C22×D4311yescharacteristic
406C22×C8C22×D4311yescharacteristic
407C4⋊Q8—22no—
408C4⋊Q8—22no—
409C4⋊Q8—862no—
410C4⋊Q8—862no—
411#125—434no—
412#125—862no—
413#125—862no—
414#125—862no—
415C22⋊Q8—868no—
416C22⋊Q8—868no—
417C22⋊Q8—868no—
418C4×Q8—862no—
419C4×Q8—862no—
420C4×D4—434no—
421C4×D4—862no—
422C4×D4—862no—
423C4×D4—862no—
424C4×D4—862no—
425C4×D4—862no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—431no—
429C2×C4⋊C4—431no—
430C2×C4⋊C4—431no—
431C2×C4⋊C4—431no—
432C2×C4⋊C4—431no—
433C2×C4⋊C4—431no—
434C2×C4⋊C4—868no—
435C2×C4⋊C4—861no—
436C2×C4⋊C4—861no—
437C2×C4⋊C4—861no—
438C2×C4⋊C4—861no—
439C2×C4⋊C4—861no—
440C2×C4⋊C4—861no—
441C2×C4⋊C4—861no—
442C2×C4⋊C4—861no—
443C2×C4⋊C4C22×D4311yescharacteristic
444C2×C4⋊C4C22×D4311yescharacteristic
445C2×C4⋊C4C22×D4311yescharacteristic
446C2×C4⋊C4C22×D4311yescharacteristic
447C2×C22⋊C4—861no—
448C2×C22⋊C4—861no—
449C2×C22⋊C4—861no—
450C2×C42—431no—
451C2×C42—431no—
452C2×C42—861no—
453C2×C42C22×D4311yescharacteristic
454#107—22no—
455#107—22no—
456#107—862no—
457#107—862no—
458#106—862no—
459#106—862no—
460C4⋊C8—862no—
461#102—434no—
462#102—434no—
463#102—862no—
464#102—862no—
465#97—862no—
466#95—21no—
467#95—861no—
468#95—861no—
469#95—861no—
470#95—861no—
471C24—861no—
472C2×Q8—24no—
473C2×Q8—81no—
474C2×Q8—81no—
475C2×Q8—862no—
476C2×Q8—862no—
477C2×Q8—3441no—
478C2×Q8—3441no—
479C2×Q8—1721no—
480C2×Q8—1722no—
481C2×D4—432no—
482C2×D4—432no—
483C2×D4—432no—
484C2×D4—861no—
485C2×D4—861no—
486C2×D4—861no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—431no—
492C22×C4—431no—
493C22×C4—431no—
494C22×C4—431no—
495C22×C4—864no—
496C22×C4—864no—
497C22×C4—864no—
498C22×C4—861no—
499C22×C4—861no—
500C22×C4—861no—
501C22×C4—3441no—
502C22×C4—3441no—
503C22×C4—3441no—
504C22×C4—3441no—
505C22×C4—1722no—
506C22×C4—1722no—
507C22×C4D4×D4311yescharacteristic
508C22×C4D4×D4311yescharacteristic
509C22×C4C23×D4311yescharacteristic
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—432no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—861no—
519C2×C8—861no—
520C2×C8—861no—
521C2×C8Q8×D4312yes—
522C4⋊C4—24no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—81no—
529C4⋊C4—432no—
530C4⋊C4—432no—
531C4⋊C4—862no—
532C4⋊C4—862no—
533C4⋊C4—862no—
534C4⋊C4—864no—
535C4⋊C4—864no—
536C4⋊C4—864no—
537C4⋊C4—864no—
538C4⋊C4—861no—
539C4⋊C4—861no—
540C4⋊C4—861no—
541C4⋊C4—861no—
542C4⋊C4—3441no—
543C4⋊C4—3441no—
544C4⋊C4—3441no—
545C4⋊C4—1722no—
546C4⋊C4D4×D4312yes—
547C4⋊C4D4×D4312yes—
548C4⋊C4Q8×D4312yes—
549C22⋊C4—864no—
550C22⋊C4—864no—
551C22⋊C4—864no—
552C42—21no—
553C42—21no—
554C42—432no—
555C42—432no—
556C42—861no—
557C42—861no—
558C42—1722no—
559C23—862no—
560C23—862no—
561C23—862no—
562C23—1721no—
563C23—1721no—
564C23—1721no—
565C23—1721no—
566C23C2×D4×D4311yescharacteristic
567Q8—84no—
568Q8—3444no—
569Q8—1724no—
570D4—434no—
571D4—862no—
572D4—862no—
573D4—862no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—432no—
592C2×C4—432no—
593C2×C4—861no—
594C2×C4—861no—
595C2×C4—861no—
596C2×C4—861no—
597C2×C4—862no—
598C2×C4—861no—
599C2×C4—861no—
600C2×C4—862no—
601C2×C4—861no—
602C2×C4—861no—
603C2×C4—861no—
604C2×C4—861no—
605C2×C4—3444no—
606C2×C4—3444no—
607C2×C4—1728no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4#1306335712yes—
616C2×C4C2×D4×D4311yescharacteristic
617C2×C4C2×D4×D4311yescharacteristic
618C2×C4C2×Q8×D4311yescharacteristic
619C2×C4C2×Q8×D4311yescharacteristic
620C2×C4#1306337211yescharacteristic
621C2×C4#1306337311yescharacteristic
622C8—22no—
623C8—41no—
624C8—862no—
625C8—1721no—
626C22—864no—
627C22—1722no—
628C22—1722no—
629C22—1722no—
630C22—1722no—
631C22—1722no—
632C22—1722no—
633C22#120×D4311yescharacteristic
634C22#1458356211yescharacteristic
635C22#1458356411yescharacteristic
636C22C2×#1306335711yescharacteristic
637C22#1458369811yescharacteristic
638C22#1458370011yescharacteristic
639C22#1458370311yescharacteristic
640C4—22no—
641C4—42no—
642C4—41no—
643C4—42no—
644C4—42no—
645C4—81no—
646C4—862no—
647C4—862no—
648C4—3441no—
649C4—1722no—
650C4—1721no—
651C4—1722no—
652C4—1721no—
653C4C4⋊Q8×D4311yescharacteristic
654C4#1458347211yescharacteristic
655C4#1458356211yescharacteristic
656C4#1458356411yescharacteristic
657C2—1724no—
658C2#1913823411yescharacteristic
659C2#1914385411yescharacteristic
660C2#1914385811yescharacteristic
661C2#1914750411yescharacteristic
662C2#1914751011yescharacteristic
663C2#1914754811yescharacteristic
664C2#1914755011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2057C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#2057D43
hypocenterC43#25850
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2057

Complements

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

NH ≅ G/Ntype
2. C2×#14583307C2semidirect
4. #19139802C2semidirect
5. #19135932C2semidirect
6. #19135931C2semidirect
7. #19135920C2semidirect
8. #19135551C2semidirect
9. #19135533C2semidirect
15. C43×#2057C2semidirect
115. #13063247Q8semidirect
117. #13063245Q8semidirect
332. #2057D43semidirect
395. C43#25850semidirect

Maximal subgroups

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

subgroupindex
C2×#145836102
C2×#145833072
C2×#145831782
#191398022
#191359322
#191359312
#191359202
#191355512
#191355332
#191348592
#191348552
#191348432
#191348392
#191344192
C43×#20572
#2585043