Finite Group Databasebeta

← #25133208

Subgroups — #25133208

Order 11008.

1064 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583627C211yesmaximal, characteristic, complemented
2C2×#14583199C211yesmaximal, characteristic
3C2×#14582999C211yesmaximal, characteristic
4#19135933C211yesmaximal, characteristic, complemented
5#19135923C211yesmaximal, characteristic, complemented
6#19135741C211yesmaximal, characteristic
7#19135731C211yesmaximal, characteristic
8#19135563C211yesmaximal, characteristic, complemented
9#19135536C211yesmaximal, characteristic, complemented
10#19134953C211yesmaximal, characteristic
11#19134953C211yesmaximal, characteristic
12#19134862C211yesmaximal, characteristic, complemented
13#19134848C211yesmaximal, characteristic, complemented
14#19134597C211yesmaximal, characteristic, complemented
15C43×#2538C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17#14583627—24no—
18#14583627—24no—
19C2×#13063325C2211yescharacteristic
20C2×#13063323—21no—
21C2×#13063317C2211yescharacteristic
22C2×#13063317C2211yescharacteristic
23C2×#13063315—21no—
24C2×#13063315—21no—
25C2×C4×Dic86C2211yescharacteristic
26C2×C4×Dic86C2211yescharacteristic
27C2×C4×Dic86C2211yescharacteristic
28C2×#13063290—21no—
29#14583199—24no—
30#14582999—24no—
31C2×#13063258C2211yescharacteristic
32C2×#13063258C2211yescharacteristic
33C2×#13063256C2211yescharacteristic
34C2×C4⋊(C43⋊C8)C2211yescharacteristic
35C2×#13063248C2211yescharacteristic
36C2×#13063248C2211yescharacteristic
37C2×#13063248C2211yescharacteristic
38C2×#13063246C2211yescharacteristic
39C2×#13063246C2211yescharacteristic
40C2×#13063246C2211yescharacteristic
41C2×#13063236C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582654C2211yescharacteristic
52C2×C22⋊Q8×C43—21no—
53C2×C4×Q8×C43C2211yescharacteristic
54C2×C4×D4×C43C2211yescharacteristic
55C43×#396—21no—
56C43×#396—21no—
57C43×#390C2211yescharacteristic
58C43×#390C2211yescharacteristic
59C43×#389C2211yescharacteristic
60C43×#389C2211yescharacteristic
61C43×#384C2211yescharacteristic
62C43×#380—21no—
63C22×Dic86—21no—
64C22×Dic86C2311yescharacteristic
65C2×#10621883—22no—
66C2×#10621883—22no—
67C2×#10621883Q814yescomplemented
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72#13063325—22no—
73#13063325—22no—
74#13063323—28no—
75#13063317—22no—
76#13063317—22no—
77#13063317—22no—
78#13063317D414yes—
79#13063315—28no—
80#13063315—28no—
81C4×Dic86—22no—
82C4×Dic86—22no—
83C4×Dic86—22no—
84C4×Dic86—22no—
85C4×Dic86—22no—
86C4×Dic86D414yes—
87#13063290—28no—
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×C4⋊Dic43C2311yescharacteristic
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×C4×Dic43—21no—
100C2×C4×Dic43—21no—
101C2×C4×Dic43—21no—
102#13063258—22no—
103#13063258—22no—
104#13063256—22no—
105C4⋊(C43⋊C8)—22no—
106#13063248—22no—
107#13063248—22no—
108#13063248—22no—
109#13063246—22no—
110#13063246—22no—
111#13063246—22no—
112#13063236—22no—
113C22×Q8×C43D411yescharacteristic
114C22×D4×C43C2311yescharacteristic
115C23×C4×C43—21no—
116C22⋊Q8×C43—44no—
117C4×Q8×C43—22no—
118C4×Q8×C43—22no—
119C4×D4×C43—22no—
120C4×D4×C43—22no—
121C2×C4⋊C4×C43—21no—
122C2×C4⋊C4×C43—21no—
123C2×C4⋊C4×C43—21no—
124C2×C4⋊C4×C43—21no—
125C2×C4⋊C4×C43D411yescharacteristic
126C2×C4⋊C4×C43D411yescharacteristic
127C2×C4⋊C4×C43D411yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C22⋊C4×C43—21no—
132C2×C22⋊C4×C43—21no—
133C2×C22⋊C4×C43—21no—
134C2×C22⋊C4×C43—21no—
135C2×C22⋊C4×C43—21no—
136C2×C42×C43C2311yescharacteristic
137C2×C42×C43C2311yescharacteristic
138C2×C42×C43C2311yescharacteristic
139#95×C43—21no—
140#95×C43—21no—
141C24×C43—21no—
142C2×Q8×C43—22no—
143C2×Q8×C43—22no—
144C2×Q8×C43—41no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43C2×Q812yes—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—42no—
155C22×C4×C43—42no—
156C22×C4×C43—42no—
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2411yescharacteristic
164C22×Dic43—21no—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—24no—
172C2×Dic86—42no—
173C2×Dic86—42no—
174C2×Dic86C2×D412yes—
175C2×Dic86C2×Q812yes—
176C2×Dic86#4112yes—
177C4⋊C4×C43—22no—
178C4⋊C4×C43—22no—
179C4⋊C4×C43—22no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—42no—
187C4⋊C4×C43—42no—
188C4⋊C4×C43—42no—
189C4⋊C4×C43—81no—
190C22⋊C4×C43—42no—
191C22⋊C4×C43—42no—
192C22⋊C4×C43—42no—
193C22⋊C4×C43—81no—
194C22⋊C4×C43—81no—
195C42×C43—21no—
196C42×C43—21no—
197C42×C43—21no—
198C42×C43—21no—
199C42×C43C2×D412yes—
200C42×C43C2×D412yes—
201#10621883—28no—
202C4⋊Dic43—24no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43C2×D412yes—
207C4⋊Dic43C2×D412yes—
208C4⋊Dic43C2×D412yes—
209Dic43⋊C4—24no—
210Dic43⋊C4—24no—
211Dic43⋊C4—24no—
212Dic43⋊C4—24no—
213Dic43⋊C4—24no—
214Dic43⋊C4—24no—
215Dic43⋊C4—24no—
216C4×Dic43—24no—
217C4×Dic43—24no—
218C4×Dic43—24no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8C2×Q812yes—
231C23×C43—22no—
232C23×C43—41no—
233C23×C43—41no—
234C23×C43—41no—
235C23×C43—41no—
236C23×C43—41no—
237C23×C43—41no—
238C23×C43C22×D411yescharacteristic
239Q8×C43—44no—
240D4×C43—22no—
241D4×C43—22no—
242D4×C43—41no—
243D4×C43—41no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—21no—
256C2×C4×C43—21no—
257C2×C4×C43—21no—
258C2×C4×C43—21no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43—41no—
267C2×C4×C43—41no—
268C2×C4×C43—84no—
269C2×C4×C43#12012yes—
270C2×C4×C43#12012yes—
271C2×C4×C43AGL(1,ℤ/8)12yes—
272C2×C4×C43C22×D411yescharacteristic
273C2×C4×C43C22×D411yescharacteristic
274C2×C4×C43C22×Q811yescharacteristic
275C2×C4×C43C2×#4111yescharacteristic
276C2×C4×C432−1+411yescharacteristic
277C2×C4×C432−1+411yescharacteristic
278C2×Dic43—22no—
279C2×Dic43—22no—
280C2×Dic43—22no—
281C2×Dic43—22no—
282C2×Dic43—22no—
283C2×Dic43—22no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287C2×Dic43—41no—
288C2×Dic43—41no—
289C2×Dic43—41no—
290Dic86—22no—
291Dic86—22no—
292Dic86—22no—
293Dic86—48no—
294Dic86C22⋊Q814yescomplemented
295C43⋊C8—22no—
296C43⋊C8—41no—
297C43⋊C8—41no—
298C43⋊C8—41no—
299#24346—431nomaximal, Sylow
300C22×C43—42no—
301C22×C43—42no—
302C22×C43—42no—
303C22×C43—81no—
304C22×C43—81no—
305C22×C43—81no—
306C22×C43—81no—
307C22×C43C2×#12011yescharacteristic
308C22×C43#54811yescharacteristic
309C22×C43D4×Q811yescharacteristic
310C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
311C22×C43#57511yescharacteristic
312C22×C43#57711yescharacteristic
313C22×C43#57811yescharacteristic
314C4×C43—22no—
315C4×C43—22no—
316C4×C43—22no—
317C4×C43—41no—
318C4×C43—41no—
319C4×C43—41no—
320C4×C43—81no—
321C4×C43—81no—
322C4×C43—81no—
323C4×C43C2×C22⋊Q811yescharacteristic
324C4×C43#53611yescharacteristic
325C4×C43#54811yescharacteristic
326C4×C43D4×Q811yescharacteristic
327Dic43—24no—
328Dic43—42no—
329Dic43—42no—
330Dic43—42no—
331C2×#557—431no—
332C2×#478—431no—
333C2×#440—431no—
334#2538D4311yescharacteristic
335#2059—431no—
336#2057—431no—
337#2025—431no—
338#2023—431no—
339#1992—431no—
340#1985—431no—
341#1880—431no—
342#1880—431no—
343#1865—431no—
344#1863—431no—
345#1803—431no—
346C2×C43—82no—
347C2×C43#240911yescharacteristic
348C2×C43#300611yescharacteristic
349C2×C43#301311yescharacteristic
350C2×C43#336811yescharacteristic
351C2×C43#337711yescharacteristic
352C2×C43#338611yescharacteristic
353C2×C43#338811yescharacteristic
354C22×SD16—431no—
355#557—864no—
356#557—864no—
357C2×C4⋊Q8—431no—
358C2×C4⋊Q8—861no—
359C2×#125—431no—
360C2×#125—431no—
361C2×#125—861no—
362C2×#125—861no—
363C2×C22⋊Q8—21no—
364C2×C4×Q8—431no—
365C2×C4×Q8—431no—
366C2×C4×Q8—431no—
367C2×C4×Q8—861no—
368C2×C4×Q8C2×D4311yescharacteristic
369C2×C4×D4C2×D4311yescharacteristic
370#478—864no—
371#440—864no—
372C2×#107—431no—
373C2×#107—431no—
374C2×#106—431no—
375C2×C4⋊C8—431no—
376C2×#103—431no—
377C2×#103—431no—
378C2×#103—431no—
379C2×#102—431no—
380C2×#102—431no—
381C2×#102—431no—
382C2×#97—431no—
383#396—21no—
384#396—21no—
385#390C2×D4311yescharacteristic
386#390C2×D4311yescharacteristic
387#389C2×D4311yescharacteristic
388#389C2×D4311yescharacteristic
389#384C2×D4311yescharacteristic
390#380—21no—
391#340—431no—
392#340—431no—
393#340—431no—
394#340—431no—
395#340—431no—
396#340—431no—
397#336—431no—
398#336—431no—
399#336—431no—
400#336—431no—
401C43#2434611yescharacteristic, complemented, Sylow
402C22×Q8—431no—
403C22×Q8—861no—
404C22×Q8C22⋊D4311yescharacteristic
405C22×D4C22×D4311yescharacteristic
406C23×C4—21no—
407C2×SD16—434no—
408C2×SD16—862no—
409C2×SD16—862no—
410C22×C8—431no—
411C22×C8—431no—
412C22×C8—431no—
413C22×C8—431no—
414C4⋊Q8—862no—
415C4⋊Q8—862no—
416C4⋊Q8—868no—
417#125—434no—
418#125—862no—
419#125—862no—
420#125—868no—
421#125—868no—
422#125—862no—
423C22⋊Q8—44no—
424C4×Q8—22no—
425C4×Q8—22no—
426C4×Q8—434no—
427C4×Q8—862no—
428C4×Q8—862no—
429C4×Q8—862no—
430C4×Q8—862no—
431C4×Q8—868no—
432C4×Q8—862no—
433C4×D4—22no—
434C4×D4—22no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—431no—
440C2×C4⋊C4—431no—
441C2×C4⋊C4—431no—
442C2×C4⋊C4—861no—
443C2×C4⋊C4—861no—
444C2×C4⋊C4—861no—
445C2×C4⋊C4—861no—
446C2×C4⋊C4—861no—
447C2×C4⋊C4—861no—
448C2×C4⋊C4—861no—
449C2×C4⋊C4—861no—
450C2×C4⋊C4C22⋊D4311yescharacteristic
451C2×C4⋊C4C22⋊D4311yescharacteristic
452C2×C4⋊C4C22⋊D4311yescharacteristic
453C2×C4⋊C4C22×D4311yescharacteristic
454C2×C4⋊C4C22×D4311yescharacteristic
455C2×C4⋊C4C22×D4311yescharacteristic
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C42—861no—
462C2×C42—861no—
463C2×C42—861no—
464C2×C42C22×D4311yescharacteristic
465C2×C42C22×D4311yescharacteristic
466C2×C42C22×D4311yescharacteristic
467#107—862no—
468#107—862no—
469#106—862no—
470C4⋊C8—862no—
471#103—862no—
472#103—862no—
473#103—862no—
474#102—862no—
475#102—862no—
476#102—862no—
477#97—862no—
478#95—21no—
479#95—21no—
480C24—21no—
481C2×Q8—22no—
482C2×Q8—22no—
483C2×Q8—41no—
484C2×Q8—432no—
485C2×Q8—432no—
486C2×Q8—432no—
487C2×Q8—864no—
488C2×Q8—861no—
489C2×Q8—861no—
490C2×Q8—861no—
491C2×Q8—1722no—
492C2×Q8—1722no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4Q8×D4312yes—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—861no—
506C22×C4—861no—
507C22×C4—861no—
508C22×C4—861no—
509C22×C4C2×C22⋊D4311yescharacteristic
510C22×C4C2×C22⋊D4311yescharacteristic
511C22×C4C2×C22⋊D4311yescharacteristic
512C22×C4C2×C22⋊D4311yescharacteristic
513C22×C4C2×C22⋊D4311yescharacteristic
514C22×C4C2×C22⋊D4311yescharacteristic
515C22×C4C23×D4311yescharacteristic
516SD16—868no—
517C2×C8—432no—
518C2×C8—861no—
519C2×C8—861no—
520C2×C8—861no—
521C2×C8—861no—
522C2×C8—861no—
523C2×C8—861no—
524C2×C8—861no—
525C2×C8—861no—
526C2×C8—861no—
527C2×C8—861no—
528C2×C8—861no—
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—42no—
539C4⋊C4—42no—
540C4⋊C4—42no—
541C4⋊C4—81no—
542C4⋊C4—432no—
543C4⋊C4—432no—
544C4⋊C4—432no—
545C4⋊C4—864no—
546C4⋊C4—864no—
547C4⋊C4—864no—
548C4⋊C4—864no—
549C4⋊C4—864no—
550C4⋊C4—864no—
551C4⋊C4—864no—
552C4⋊C4—864no—
553C4⋊C4—861no—
554C4⋊C4—861no—
555C4⋊C4—861no—
556C22⋊C4—42no—
557C22⋊C4—42no—
558C22⋊C4—42no—
559C22⋊C4—81no—
560C22⋊C4—81no—
561C42—21no—
562C42—21no—
563C42—21no—
564C42—21no—
565C42—864no—
566C42—864no—
567C42—864no—
568C42D4×D4312yes—
569C42D4×D4312yes—
570C23—22no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23C22×C22⋊D4311yescharacteristic
578Q8—44no—
579Q8—434no—
580Q8—862no—
581Q8—862no—
582Q8—862no—
583Q8—1728no—
584D4—22no—
585D4—22no—
586D4—41no—
587D4—41no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—84no—
613C2×C4—862no—
614C2×C4—862no—
615C2×C4—862no—
616C2×C4—862no—
617C2×C4—862no—
618C2×C4—862no—
619C2×C4—1721no—
620C2×C4—1721no—
621C2×C4—1721no—
622C2×C4—1721no—
623C2×C4—1721no—
624C2×C4—1721no—
625C2×C4#1306329312yes—
626C2×C4#1306329312yes—
627C2×C4#1306335112yes—
628C2×C4C2×D4×D4311yescharacteristic
629C2×C4C2×D4×D4311yescharacteristic
630C2×C4C2×Q8×D4311yescharacteristic
631C2×C4#41×D4311yescharacteristic
632C2×C4#1306337211yescharacteristic
633C2×C4#1306337311yescharacteristic
634C8—862no—
635C8—1721no—
636C8—1721no—
637C8—1721no—
638C22—42no—
639C22—42no—
640C22—42no—
641C22—81no—
642C22—81no—
643C22—81no—
644C22—81no—
645C22C2×#1306329311yescharacteristic
646C22#1458355611yescharacteristic
647C22Q8×C22⋊D4311yescharacteristic
648C22C2×#1306335111yescharacteristic
649C22#1458369711yescharacteristic
650C22#1458371011yescharacteristic
651C22#1458371411yescharacteristic
652C4—22no—
653C4—22no—
654C4—22no—
655C4—41no—
656C4—41no—
657C4—41no—
658C4—81no—
659C4—81no—
660C4—81no—
661C4—864no—
662C4—1722no—
663C4—1722no—
664C4—1722no—
665C4C22⋊Q8×D4311yescharacteristic
666C4#1458347211yescharacteristic
667C4#1458355911yescharacteristic
668C4#1458356211yescharacteristic
669C2—82no—
670C2#1913795611yescharacteristic
671C2#1914384511yescharacteristic
672C2#1914390711yescharacteristic
673C2#1914732011yescharacteristic
674C2#1914743111yescharacteristic
675C2#1914751611yescharacteristic
676C2#1914754011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2538C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#2538D43
hypocenterC43#24346
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2538

Complements

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

NH ≅ G/Ntype
1. C2×#14583627C2semidirect
4. #19135933C2semidirect
5. #19135923C2semidirect
8. #19135563C2semidirect
9. #19135536C2semidirect
12. #19134862C2semidirect
13. #19134848C2semidirect
14. #19134597C2semidirect
67. C2×#10621883Q8semidirect
294. Dic86C22⋊Q8semidirect
401. C43#24346semidirect

Maximal subgroups

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

subgroupindex
C2×#145836272
C2×#145831992
C2×#145829992
#191359332
#191359232
#191357412
#191357312
#191355632
#191355362
#191349532
#191348622
#191348482
#191345972
C43×#25382
#2434643