Finite Group Databasebeta

← #25166487

Subgroups — #25166487

Order 11008.

868 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583258C211yesmaximal, characteristic, complemented
2C2×#14582997C211yesmaximal, characteristic, complemented
3#19138445C211yesmaximal, characteristic, complemented
4#19135983C211yesmaximal, characteristic, complemented
5#19135923C211yesmaximal, characteristic, complemented
6#19135910C211yesmaximal, characteristic, complemented
7#19135672C211yesmaximal, characteristic
8#19135460C211yesmaximal, characteristic
9#19135295C211yesmaximal, characteristic, complemented
10#19135291C211yesmaximal, characteristic, complemented
11#19135274C211yesmaximal, characteristic, complemented
12#19134946C211yesmaximal, characteristic
13#19134849C211yesmaximal, characteristic, complemented
14#19134464C211yesmaximal, characteristic, complemented
15C43×#2448C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C2×#13063325C2211yescharacteristic
19C2×#13063303—21no—
20C2×C4×D172C2211yescharacteristic
21#14583258—24no—
22#14582997—24no—
23C2×#13063258C2211yescharacteristic
24C2×#13063258C2211yescharacteristic
25C2×C4⋊(C43⋊C8)C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C2×#13063236C2211yescharacteristic
35C2×#13063236C2211yescharacteristic
36C2×C4×C43⋊C8C2211yescharacteristic
37#14582821—21no—
38#14582812—21no—
39#14582801C2211yescharacteristic
40#14582801C2211yescharacteristic
41#14582797C2211yescharacteristic
42#14582797C2211yescharacteristic
43#14582773—21no—
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582654C2211yescharacteristic
50C2×#124×C43C2211yescharacteristic
51C2×C4×Q8×C43C2211yescharacteristic
52C43×#399—21no—
53C43×#397—21no—
54C43×#391C2211yescharacteristic
55C43×#390C2211yescharacteristic
56C43×#390C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#388—21no—
59C43×#388—21no—
60C4×C4⋊C4×C43C2211yescharacteristic
61C22×Dic86—21no—
62C22×D172C2311yescharacteristic
63C22×C4×D43—21no—
64C2×#10621884—22no—
65C2×#10621884—22no—
66C2×#10621884—22no—
67C2×#10621882—22no—
68C2×#10621882—22no—
69C2×#10621882—41no—
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74#13063325—22no—
75#13063325—41no—
76#13063303—44no—
77C4×D172—22no—
78C4×D172—41no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90#13063258—22no—
91#13063258—41no—
92C4⋊(C43⋊C8)—22no—
93#13063249—22no—
94#13063249—22no—
95#13063249D414yes—
96#13063246—22no—
97#13063246—22no—
98#13063246—22no—
99#13063245—22no—
100#13063245—22no—
101#13063236—22no—
102#13063236—22no—
103C4×C43⋊C8—22no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C22×Q8×C43C2311yescharacteristic
107C22×D4×C43C2311yescharacteristic
108#124×C43—22no—
109#124×C43—41no—
110C4×Q8×C43—22no—
111C4×Q8×C43—41no—
112C2×C4⋊C4×C43—21no—
113C2×C4⋊C4×C43—21no—
114C2×C4⋊C4×C43D411yescharacteristic
115C2×C4⋊C4×C43D411yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C22⋊C4×C43—21no—
119C2×C22⋊C4×C43—21no—
120C2×C22⋊C4×C43—21no—
121C2×C22⋊C4×C43—21no—
122C2×C22⋊C4×C43—21no—
123C2×C22⋊C4×C43—21no—
124C2×C42×C43—21no—
125C2×C42×C43C2311yescharacteristic
126C2×C42×C43C2311yescharacteristic
127C2×C42×C43C2311yescharacteristic
128#95×C43—21no—
129#95×C43—21no—
130#95×C43—21no—
131#95×C43D411yescharacteristic
132#95×C43D411yescharacteristic
133C24×C43—21no—
134C23×D43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43—21no—
139C2×Q8×C43—21no—
140C2×Q8×C43C2×D412yes—
141C2×D4×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2411yescharacteristic
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172—21no—
164C2×D172—21no—
165C2×D172#4112yes—
166C2×C4×D43—42no—
167C2×C4×D43—42no—
168C2×C4×D43—81no—
169C2×Dic86—42no—
170C2×Dic86—42no—
171C2×Dic86—81no—
172C4⋊C4×C43—22no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—41no—
178C4⋊C4×C43—42no—
179C4⋊C4×C43—81no—
180C22⋊C4×C43—42no—
181C22⋊C4×C43—42no—
182C22⋊C4×C43—42no—
183C22⋊C4×C43—42no—
184C22⋊C4×C43—81no—
185C22⋊C4×C43—81no—
186C42×C43—21no—
187C42×C43—21no—
188C42×C43—21no—
189C42×C43—21no—
190C42×C43—21no—
191C42×C43—21no—
192C42×C43—42no—
193#10621884—28no—
194#10621882—44no—
195(C2×D43)⋊C4—42no—
196(C2×D43)⋊C4—42no—
197(C2×D43)⋊C4—42no—
198(C2×D43)⋊C4—42no—
199(C2×D43)⋊C4—81no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—42no—
206C4⋊Dic43C2×D412yes—
207Dic43⋊C4—42no—
208Dic43⋊C4—42no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8C2×D412yes—
219C2×C43⋊C8#4112yes—
220C2×C43⋊C8#4112yes—
221C23×C43—41no—
222C23×C43—41no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43C22×D411yescharacteristic
229C22×D43—22no—
230C22×D43—41no—
231C22×D43—41no—
232C22×D43—41no—
233C22×D43—41no—
234C22×D43—41no—
235C22×D43—41no—
236Q8×C43—22no—
237Q8×C43—22no—
238Q8×C43—41no—
239Q8×C43—41no—
240D4×C43—41no—
241D4×C43—41no—
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—22no—
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—21no—
260C2×C4×C43—21no—
261C2×C4×C43—21no—
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—41no—
269C2×C4×C43—41no—
270C2×C4×C43AGL(1,ℤ/8)12yes—
271C2×C4×C43C22×D411yescharacteristic
272C2×C4×C43C2×#4111yescharacteristic
273C2×C4×C43C2×#4111yescharacteristic
274C2×C4×C43C2×#4111yescharacteristic
275C2×C4×C43H(5,𝔽2)11yescharacteristic
276C2×C4×C432−1+411yescharacteristic
277C2×Dic43—22no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286D172—22no—
287D172—22no—
288D172—41no—
289D172—41no—
290C4×D43—84no—
291Dic86—84no—
292C43⋊C8—22no—
293C43⋊C8—22no—
294C43⋊C8—22no—
295C43⋊C8—41no—
296#26844—431nomaximal, Sylow
297C22×C43—81no—
298C22×C43—81no—
299C22×C43—81no—
300C22×C43—81no—
301C22×C43—81no—
302C22×C43—81no—
303C22×C43—81no—
304C22×C43#53211yescharacteristic
305C22×C43D4211yescharacteristic
306C22×C43#54811yescharacteristic
307C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
308C22×C43#57511yescharacteristic
309C22×C43#57611yescharacteristic
310C22×C43#57811yescharacteristic
311C2×D43—42no—
312C2×D43—42no—
313C2×D43—42no—
314C2×D43—81no—
315C2×D43—81no—
316C2×D43—81no—
317C2×D43—81no—
318C4×C43—22no—
319C4×C43—41no—
320C4×C43—42no—
321C4×C43—41no—
322C4×C43—41no—
323C4×C43—41no—
324C4×C43—41no—
325C4×C43—81no—
326C4×C43—81no—
327C4×C43#52511yescharacteristic
328C4×C43#54211yescharacteristic
329C4×C43#54711yescharacteristic
330C4×C43#55111yescharacteristic
331Dic43—42no—
332Dic43—81no—
333Dic43—81no—
334C2×#489—431no—
335C2×#440—431no—
336#2452—431no—
337#2448D4311yescharacteristic, complemented
338#2067—431no—
339#2057—431no—
340#2055—431no—
341#2012—431no—
342#1970—431no—
343#1936—431no—
344#1936—431no—
345#1933—431no—
346#1879—431no—
347#1863—431no—
348#1770—431no—
349C2×C43—161no—
350C2×C43#246111yescharacteristic
351C2×C43#317511yescharacteristic
352C2×C43#318011yescharacteristic
353C2×C43#327411yescharacteristic
354C2×C43#327711yescharacteristic
355C2×C43#336711yescharacteristic
356C2×C43#337011yescharacteristic
357D43—82no—
358C22×SD16—431no—
359C22×D8—431no—
360C2×C4⋊Q8—431no—
361C2×#124C2×D4311yescharacteristic
362C2×C22⋊Q8—861no—
363C2×C4×Q8C2×D4311yescharacteristic
364C2×C4×D4—431no—
365#489—864no—
366#440—864no—
367C2×#107—431no—
368C2×#107—431no—
369C2×C4⋊C8—431no—
370C2×#103—431no—
371C2×#103—431no—
372C2×#103—431no—
373C2×#102—431no—
374C2×#102—431no—
375C2×#102—431no—
376C2×#102—431no—
377C2×#102—431no—
378C2×#97—431no—
379C2×#97—431no—
380C2×C4×C8—431no—
381#399—21no—
382#397—21no—
383#396—861no—
384#393—861no—
385#391C2×D4311yescharacteristic
386#390—431no—
387#390—431no—
388#390C2×D4311yescharacteristic
389#390C2×D4311yescharacteristic
390#389—431no—
391#389—431no—
392#389C2×D4311yescharacteristic
393#388—21no—
394#388—21no—
395#385—861no—
396C4×C4⋊C4C2×D4311yescharacteristic
397#340—431no—
398#340—431no—
399#340—431no—
400#340—431no—
401#336—431no—
402#336—431no—
403C43#2684411yescharacteristic, complemented, Sylow
404C22×Q8—861no—
405C22×Q8C22×D4311yescharacteristic
406C22×D4—431no—
407C22×D4C22×D4311yescharacteristic
408C23×C4—861no—
409C2×SD16—862no—
410C2×SD16—862no—
411C2×SD16—862no—
412C2×D8—862no—
413C2×D8—862no—
414C2×D8—1721no—
415C22×C8—431no—
416C22×C8—431no—
417C22×C8—431no—
418C22×C8—431no—
419C4⋊Q8—862no—
420C4⋊Q8—1721no—
421#124—22no—
422#124—41no—
423C22⋊Q8—1724no—
424C4×Q8—22no—
425C4×Q8—41no—
426C4×D4—862no—
427C4×D4—1721no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—431no—
431C2×C4⋊C4—431no—
432C2×C4⋊C4—431no—
433C2×C4⋊C4—861no—
434C2×C4⋊C4—861no—
435C2×C4⋊C4—861no—
436C2×C4⋊C4C22⋊D4311yescharacteristic
437C2×C4⋊C4C22⋊D4311yescharacteristic
438C2×C4⋊C4C22×D4311yescharacteristic
439C2×C4⋊C4C22×D4311yescharacteristic
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—861no—
447C2×C22⋊C4—861no—
448C2×C22⋊C4—861no—
449C2×C22⋊C4—861no—
450C2×C22⋊C4—861no—
451C2×C42—21no—
452C2×C42C22×D4311yescharacteristic
453C2×C42C22×D4311yescharacteristic
454C2×C42C22×D4311yescharacteristic
455#107—862no—
456#107—1721no—
457C4⋊C8—862no—
458#103—434no—
459#103—862no—
460#103—862no—
461#102—862no—
462#102—862no—
463#102—862no—
464#102—862no—
465#102—862no—
466#97—862no—
467#97—862no—
468C4×C8—862no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—861no—
473#95—861no—
474#95C22⋊D4311yescharacteristic
475#95C22⋊D4311yescharacteristic
476C24—21no—
477C24—861no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—3441no—
484C2×Q8—1722no—
485C2×Q8—1722no—
486C2×Q8D4×D4312yes—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—432no—
494C2×D4—861no—
495C2×D4—861no—
496C2×D4—861no—
497C2×D4—861no—
498C2×D4—861no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—861no—
503C22×C4—861no—
504C22×C4—861no—
505C22×C4—3441no—
506C22×C4—1722no—
507C22×C4—1722no—
508C22×C4C2×C22⋊D4311yescharacteristic
509C22×C4C2×C22⋊D4311yescharacteristic
510C22×C4C2×C22⋊D4311yescharacteristic
511C22×C4C2×C22⋊D4311yescharacteristic
512C22×C4C2×C22⋊D4311yescharacteristic
513C22×C4C2×C22⋊D4311yescharacteristic
514C22×C4C23×D4311yescharacteristic
515SD16—868no—
516D8—1724no—
517C2×C8—432no—
518C2×C8—432no—
519C2×C8—432no—
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—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—41no—
535C4⋊C4—42no—
536C4⋊C4—81no—
537C4⋊C4—432no—
538C4⋊C4—861no—
539C4⋊C4—861no—
540C4⋊C4—861no—
541C4⋊C4—861no—
542C4⋊C4—861no—
543C4⋊C4—1722no—
544C4⋊C4—1722no—
545C4⋊C4—1722no—
546C22⋊C4—42no—
547C22⋊C4—42no—
548C22⋊C4—42no—
549C22⋊C4—42no—
550C22⋊C4—81no—
551C22⋊C4—81no—
552C22⋊C4—3441no—
553C22⋊C4—1722no—
554C22⋊C4—1722no—
555C22⋊C4—1722no—
556C22⋊C4—1722no—
557C42—21no—
558C42—21no—
559C42—21no—
560C42—21no—
561C42—21no—
562C42—21no—
563C42—42no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—862no—
572C23—1721no—
573C23—1721no—
574C23—1721no—
575C23—1721no—
576C23—1721no—
577C23—1721no—
578C23C22×C22⋊D4311yescharacteristic
579Q8—22no—
580Q8—22no—
581Q8—41no—
582Q8—41no—
583Q8—3444no—
584D4—41no—
585D4—41no—
586D4—41no—
587D4—41no—
588D4—862no—
589D4—862no—
590D4—1721no—
591D4—1721no—
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—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—22no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—862no—
619C2×C4—3444no—
620C2×C4—1721no—
621C2×C4—1721no—
622C2×C4—1721no—
623C2×C4—1721no—
624C2×C4—1721no—
625C2×C4—1721no—
626C2×C4—1721no—
627C2×C4—1721no—
628C2×C4#1306335012yes—
629C2×C4C2×D4×D4311yescharacteristic
630C2×C4#41×D4311yescharacteristic
631C2×C4#41×D4311yescharacteristic
632C2×C4#41×D4311yescharacteristic
633C2×C4#1306337011yescharacteristic
634C2×C4#1306337211yescharacteristic
635C8—862no—
636C8—862no—
637C8—862no—
638C8—1721no—
639C22—81no—
640C22—81no—
641C22—81no—
642C22—81no—
643C22—81no—
644C22—81no—
645C22—81no—
646C22—3441no—
647C22—3441no—
648C22—3441no—
649C22—3441no—
650C22—1722no—
651C22—1722no—
652C22—1722no—
653C22#1458344511yescharacteristic
654C22D4×C22⋊D4311yescharacteristic
655C22#1458355611yescharacteristic
656C22C2×#1306335011yescharacteristic
657C22#1458369711yescharacteristic
658C22#1458370211yescharacteristic
659C22#1458371411yescharacteristic
660C4—22no—
661C4—42no—
662C4—41no—
663C4—41no—
664C4—41no—
665C4—41no—
666C4—41no—
667C4—81no—
668C4—81no—
669C4—3441no—
670C4—3441no—
671C4—1722no—
672C4#1458340711yescharacteristic
673C4#1458351711yescharacteristic
674C4#1458354711yescharacteristic
675C4#1458357711yescharacteristic
676C2—161no—
677C2—3442no—
678C2#1913856111yescharacteristic
679C2#1914522811yescharacteristic
680C2#1914529411yescharacteristic
681C2#1914621511yescharacteristic
682C2#1914624811yescharacteristic
683C2#1914730911yescharacteristic
684C2#1914734211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2448C2
socleC23×C43C22×D4
prime radicalC22×#10621882C22
hypercenter#2448D43
hypocenterC43#26844
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2448

Complements

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

NH ≅ G/Ntype
1. C2×#14583258C2semidirect
2. C2×#14582997C2semidirect
3. #19138445C2semidirect
4. #19135983C2semidirect
5. #19135923C2semidirect
6. #19135910C2semidirect
9. #19135295C2semidirect
10. #19135291C2semidirect
11. #19135274C2semidirect
13. #19134849C2semidirect
14. #19134464C2semidirect
15. C43×#2448C2semidirect
337. #2448D43semidirect
403. C43#26844semidirect

Maximal subgroups

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

subgroupindex
C2×#145832582
C2×#145829972
#191384452
#191359832
#191359232
#191359102
#191356722
#191354602
#191352952
#191352912
#191352742
#191349462
#191348492
#191344642
C43×#24482
#2684443