Finite Group Databasebeta

← #25113765

Subgroups — #25113765

Order 11008.

978 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×#14582894C211yesmaximal, characteristic
2#19137476C211yesmaximal, characteristic, complemented
3#19137433C211yesmaximal, characteristic
4#19135278C211yesmaximal, characteristic, complemented
5#19135276C211yesmaximal, characteristic, complemented
6#19135215C211yesmaximal, characteristic, complemented
7#19135213C211yesmaximal, characteristic, complemented
8#19134849C211yesmaximal, characteristic, complemented
9#19134847C211yesmaximal, characteristic, complemented
10#19134688C211yesmaximal, characteristic, complemented
11#19134623C211yesmaximal, characteristic, complemented
12#19134534C211yesmaximal, characteristic
13#103×Dic43C211yesmaximal, characteristic, complemented
14C8×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
15C4×#103×C43C211yesmaximal, characteristic, complemented
16C22×#10621902C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18C2×Q8×Dic43C2211yescharacteristic
19C2×#13063283C2211yescharacteristic
20C2×#13063258C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22#14582894C418yescomplemented
23C2×#13063249C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×(C2×D43)⋊C8C2211yescharacteristic
30C2×C8×Dic43C2211yescharacteristic
31#14582801—21no—
32#14582801C2211yescharacteristic
33#14582800—21no—
34#14582800C2211yescharacteristic
35#14582797C2211yescharacteristic
36#14582795C2211yescharacteristic
37#14582790—21no—
38#14582788—21no—
39#14582763—21no—
40#14582756—21no—
41#14582756C2211yescharacteristic
42#14582756C2211yescharacteristic
43C4⋊C4×Dic43C2211yescharacteristic
44C4×(C2×D43)⋊C4—21no—
45C4×(C2×D43)⋊C4C2211yescharacteristic
46#14582745—21no—
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582654C2211yescharacteristic
52#14582653C2211yescharacteristic
53C2×C4×Q8×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C2×C4×C8×C43C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C2×#10621902—22no—
61C2×#10621902—22no—
62C2×#10621902—22no—
63C2×#10621902—41no—
64C2×#10621902—41no—
65C2×#10621902C2×C414yes—
66C22×D172—21no—
67C22×D172C2311yescharacteristic
68C22×C4×D43—21no—
69C22×C4×D43C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72C2×C8×D43—41no—
73C2×C8×D43—41no—
74C2×C8×D43C2×C414yes—
75Q8×Dic43—22no—
76Q8×Dic43—41no—
77#13063283—22no—
78#13063283C2×C414yes—
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—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4D411yescharacteristic
93C2×(C2×D43)⋊C4D411yescharacteristic
94C2×C4×Dic43—21no—
95C2×C4×Dic43—21no—
96C2×C4×Dic43—21no—
97C2×C4×Dic43C2311yescharacteristic
98#13063258—41no—
99#13063258—41no—
100#13063249—22no—
101#13063249C2×C414yes—
102#13063247—41no—
103#13063247C2×C414yes—
104#13063245—41no—
105#13063245C2×C414yes—
106(C2×D43)⋊C8—22no—
107C8×Dic43—41no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95D411yescharacteristic
114C43⋊#95D411yescharacteristic
115C22×Q8×C43C2311yescharacteristic
116C22×C8×C43C2311yescharacteristic
117C22×C8×C43C2311yescharacteristic
118C4×Q8×C43—22no—
119C4×Q8×C43—41no—
120C2×C4⋊C4×C43—21no—
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C42×C43—21no—
125C2×C42×C43—21no—
126C2×C42×C43C2311yescharacteristic
127#103×C43—22no—
128#103×C43C2×C414yes—
129C4×C8×C43—41no—
130#95×C43—21no—
131C23×D43—21no—
132C23×D43C2×D411yescharacteristic
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43C22×C412yes—
137C2×Q8×C43#4112yes—
138C2×Q8×C43#4112yes—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2411yescharacteristic
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152#10621902—28no—
153#10621902—44no—
154#10621902—44no—
155#10621902—44no—
156C2×D172—21no—
157C2×D172—24no—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—42no—
163C2×D172—42no—
164C2×D172C22×C412yes—
165C2×C4×D43—21no—
166C2×C4×D43—21no—
167C2×C4×D43—21no—
168C2×C4×D43—21no—
169C2×C4×D43—24no—
170C2×C4×D43—42no—
171C2×C4×D43—42no—
172C2×C4×D43C22×C412yes—
173C2×C4×D43#4112yes—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43C22×C412yes—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—42no—
186C4⋊C4×C43C22×C412yes—
187C42×C43—21no—
188C42×C43—21no—
189C42×C43—42no—
190C42×C43—42no—
191(C2×D43)⋊C4—22no—
192(C2×D43)⋊C4—22no—
193(C2×D43)⋊C4—24no—
194(C2×D43)⋊C4—42no—
195(C2×D43)⋊C4—42no—
196(C2×D43)⋊C4—81no—
197(C2×D43)⋊C4—81no—
198(C2×D43)⋊C4—81no—
199(C2×D43)⋊C4—81no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—42no—
206C4⋊Dic43C22×C412yes—
207Dic43⋊C4—81no—
208Dic43⋊C4—81no—
209C4×Dic43—21no—
210C4×Dic43—21no—
211C4×Dic43—24no—
212C4×Dic43—42no—
213C4×Dic43—42no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8C22×C412yes—
220C8×D43—44no—
221C23×C43C22×D411yescharacteristic
222C22×D43—21no—
223C22×D43—21no—
224C22×D43—21no—
225C22×D43—21no—
226C22×D43—21no—
227C22×D43—21no—
228C22×D43—22no—
229C22×D43—41no—
230C22×D43—41no—
231C22×D43—41no—
232C22×D43—41no—
233C22×D43—41no—
234C22×D43—41no—
235C22×D43C4×D412yes—
236Q8×C43—22no—
237Q8×C43—22no—
238Q8×C43—22no—
239Q8×C43#11714yes—
240C2×C4×C43—22no—
241C2×C4×C43—22no—
242C2×C4×C43—21no—
243C2×C4×C43—22no—
244C2×C4×C43—21no—
245C2×C4×C43—22no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43#13512yes—
258C2×C4×C43C23×C411yescharacteristic
259C2×C4×C43C2×#4111yescharacteristic
260C2×C4×C43C2×#4111yescharacteristic
261C2×C4×C43C2×#4111yescharacteristic
262C2×C4×C43H(5,𝔽2)11yescharacteristic
263C2×C4×C43H(5,𝔽2)11yescharacteristic
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—22no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43C4×D412yes—
281C2×Dic43#13512yes—
282D172—22no—
283D172—22no—
284D172—48no—
285D172—41no—
286D172—41no—
287C4×D43—22no—
288C4×D43—22no—
289C4×D43—22no—
290C4×D43—22no—
291C4×D43—48no—
292C8×C43—22no—
293C8×C43—41no—
294C43⋊C8—22no—
295C43⋊C8—41no—
296#22573—431nomaximal, Sylow
297C22×C43C2×C4×D411yescharacteristic
298C22×C43#54611yescharacteristic
299C22×C43#54611yescharacteristic
300C22×C43C2×#13511yescharacteristic
301C22×C43C2×#13511yescharacteristic
302C22×C43#57611yescharacteristic
303C22×C43#57811yescharacteristic
304C2×D43—22no—
305C2×D43—22no—
306C2×D43—22no—
307C2×D43—41no—
308C2×D43—41no—
309C2×D43—41no—
310C2×D43—41no—
311C2×D43—42no—
312C2×D43—42no—
313C2×D43—42no—
314C2×D43—81no—
315C2×D43—81no—
316C2×D43—81no—
317C2×D43—81no—
318C4×C43—24no—
319C4×C43—22no—
320C4×C43—42no—
321C4×C43—41no—
322C4×C43—81no—
323C4×C43—81no—
324C4×C43C2×#11711yescharacteristic
325C4×C43#51811yescharacteristic
326C4×C43#55111yescharacteristic
327C4×C43#55111yescharacteristic
328Dic43—22no—
329Dic43—22no—
330Dic43—42no—
331Dic43—41no—
332Dic43—81no—
333Dic43—81no—
334C2×#416—431no—
335#2346—431no—
336#2341—431no—
337#1934—431no—
338#1934—431no—
339#1925—431no—
340#1925—431no—
341#1863—431no—
342#1863—431no—
343#1825—431no—
344#1808—431no—
345#1788—431no—
346C4×#103—431no—
347C4×#103D4311yescharacteristic, complemented
348C8×C22⋊C4—431no—
349C2×C43#234211yescharacteristic
350C2×C43C4×#13511yescharacteristic
351C2×C43#295111yescharacteristic
352C2×C43#330011yescharacteristic
353C2×C43#330011yescharacteristic
354C2×C43#330511yescharacteristic
355C2×C43#330511yescharacteristic
356D43—42no—
357D43—82no—
358C22×#41—431no—
359C23×C8—431no—
360C2×C4×Q8—431no—
361C2×C4×Q8C2×D4311yescharacteristic
362C2×#117—431no—
363C2×#107—431no—
364C2×#107—431no—
365#416—438no—
366C2×#103—431no—
367C2×#103—431no—
368C2×#103C2×D4311yescharacteristic
369C2×#103C2×D4311yescharacteristic
370C2×#102—431no—
371C2×#102—431no—
372C2×#102—431no—
373C2×#102—431no—
374C2×C22⋊C8—431no—
375C2×C4×C8—431no—
376C2×C4×C8C2×D4311yescharacteristic
377#390—431no—
378#390—431no—
379#390—861no—
380#390—861no—
381#389—431no—
382#389—431no—
383#388—861no—
384#388—861no—
385#382—861no—
386#380—431no—
387#380—431no—
388#380—861no—
389C4×C4⋊C4—431no—
390C4×C4⋊C4C2×D4311yescharacteristic
391C4×C22⋊C4—431no—
392C4×C22⋊C4—861no—
393#376—861no—
394#340—431no—
395#340—431no—
396#340—431no—
397#340—431no—
398#340C2×D4311yescharacteristic
399#340C2×D4311yescharacteristic
400#336—431no—
401#336—431no—
402C43#2257311yescharacteristic, complemented, Sylow
403C2×#41—434no—
404C2×#41—862no—
405C2×#41—862no—
406C2×#41—862no—
407C2×#41—1721no—
408C2×#41—1721no—
409C22×Q8C22×D4311yescharacteristic
410C22×D4—431no—
411C22×D4—861no—
412C23×C4—431no—
413C23×C4—861no—
414C22×C8—431no—
415C22×C8—434no—
416C22×C8—431no—
417C22×C8—1721no—
418C22×C8—1721no—
419C22×C8C22×D4311yescharacteristic
420C22×C8C22×D4311yescharacteristic
421C4×Q8—22no—
422C4×Q8—41no—
423C4×Q8—862no—
424C4×Q8—1721no—
425#117—434no—
426#117—862no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—431no—
429C2×C4⋊C4—431no—
430C2×C4⋊C4—431no—
431C2×C4⋊C4—861no—
432C2×C4⋊C4—861no—
433C2×C4⋊C4—861no—
434C2×C4⋊C4C22×D4311yescharacteristic
435C2×C4⋊C4C22×D4311yescharacteristic
436C2×C4⋊C4C22×D4311yescharacteristic
437C2×C22⋊C4—431no—
438C2×C22⋊C4—431no—
439C2×C22⋊C4—861no—
440C2×C22⋊C4—861no—
441C2×C22⋊C4—861no—
442C2×C22⋊C4—861no—
443C2×C22⋊C4—861no—
444C2×C22⋊C4—861no—
445C2×C22⋊C4—861no—
446C2×C42—21no—
447C2×C42—21no—
448C2×C42—431no—
449C2×C42—861no—
450C2×C42—861no—
451C2×C42—861no—
452C2×C42C22×D4311yescharacteristic
453#107—1721no—
454#107—1721no—
455#103—22no—
456#103—434no—
457#103—862no—
458#103C4×D4314yes—
459#102—434no—
460#102—434no—
461#102—1721no—
462#102—1721no—
463C22⋊C8—862no—
464C4×C8—41no—
465C4×C8—1721no—
466#95—21no—
467#95—431no—
468#95—431no—
469#95—861no—
470#95—861no—
471#95—861no—
472#95—861no—
473#95—861no—
474C24—431no—
475C24—861no—
476#41—868no—
477#41—1724no—
478#41—1724no—
479#41—1724no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8C2×C4×D4312yes—
484C2×Q8#1062189812yes—
485C2×Q8#1062189812yes—
486C2×D4—432no—
487C2×D4—864no—
488C2×D4—861no—
489C2×D4—861no—
490C2×D4—861no—
491C2×D4—861no—
492C2×D4—861no—
493C2×D4—1722no—
494C2×D4—1722no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—431no—
500C22×C4—431no—
501C22×C4—432no—
502C22×C4—432no—
503C22×C4—431no—
504C22×C4—864no—
505C22×C4—861no—
506C22×C4—861no—
507C22×C4—861no—
508C22×C4—861no—
509C22×C4—861no—
510C22×C4—861no—
511C22×C4—861no—
512C22×C4—1722no—
513C22×C4—1722no—
514C22×C4D4×D4311yescharacteristic
515C22×C4D4×D4311yescharacteristic
516C22×C4C23×D4311yescharacteristic
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—432no—
523C2×C8—861no—
524C2×C8—861no—
525C2×C8—861no—
526C2×C8—861no—
527C2×C8—861no—
528C2×C8—1724no—
529C2×C8C2×C4×D4312yes—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—42no—
536C4⋊C4—432no—
537C4⋊C4—861no—
538C4⋊C4—861no—
539C4⋊C4—861no—
540C4⋊C4—861no—
541C4⋊C4—861no—
542C4⋊C4—3441no—
543C4⋊C4—3441no—
544C4⋊C4—1722no—
545C4⋊C4C2×C4×D4312yes—
546C22⋊C4—862no—
547C22⋊C4—864no—
548C22⋊C4—862no—
549C22⋊C4—3441no—
550C22⋊C4—3441no—
551C22⋊C4—3441no—
552C22⋊C4—3441no—
553C22⋊C4—1722no—
554C22⋊C4—1722no—
555C42—21no—
556C42—21no—
557C42—42no—
558C42—42no—
559C42—864no—
560C42—861no—
561C42—861no—
562C42—1722no—
563C42—1722no—
564C23—432no—
565C23—861no—
566C23—861no—
567C23—861no—
568C23—861no—
569C23—861no—
570C23—861no—
571C23—862no—
572C23—1721no—
573C23—1721no—
574C23—1721no—
575C23—1721no—
576C23—1721no—
577C23—1721no—
578C23C2×D4×D4311yescharacteristic
579Q8—22no—
580Q8—22no—
581Q8—22no—
582Q8#1306328214yes—
583D4—862no—
584D4—862no—
585D4—1728no—
586D4—1721no—
587D4—1721no—
588C2×C4—22no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—432no—
606C2×C4—432no—
607C2×C4—861no—
608C2×C4—861no—
609C2×C4—861no—
610C2×C4—861no—
611C2×C4—862no—
612C2×C4—862no—
613C2×C4—862no—
614C2×C4—862no—
615C2×C4—862no—
616C2×C4—861no—
617C2×C4—861no—
618C2×C4—861no—
619C2×C4—1728no—
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#1306334612yes—
629C2×C4C22×C4×D4311yescharacteristic
630C2×C4#41×D4311yescharacteristic
631C2×C4C2×#1062189811yescharacteristic
632C2×C4C2×#1062189811yescharacteristic
633C2×C4#1306337011yescharacteristic
634C2×C4#1306337111yescharacteristic
635C8—22no—
636C8—41no—
637C8—862no—
638C8—1721no—
639C22—862no—
640C22—862no—
641C22—862no—
642C22—3441no—
643C22—3441no—
644C22—3441no—
645C22—3441no—
646C22—1722no—
647C22—1722no—
648C22—1722no—
649C22—1721no—
650C22—1721no—
651C22—1721no—
652C22—1721no—
653C22C4×D4×D4311yescharacteristic
654C22#1458353911yescharacteristic
655C22#1458354511yescharacteristic
656C22#135×D4311yescharacteristic
657C22C2×#1306334611yescharacteristic
658C22#1458370111yescharacteristic
659C22#1458371211yescharacteristic
660C4—24no—
661C4—22no—
662C4—41no—
663C4—42no—
664C4—81no—
665C4—81no—
666C4—862no—
667C4—862no—
668C4—3441no—
669C4—3441no—
670C4—1722no—
671C4—1721no—
672C4C2×#1306328211yescharacteristic
673C4#1458337111yescharacteristic
674C4#1458357311yescharacteristic
675C4#1458357811yescharacteristic
676C2—3442no—
677C2—1722no—
678C2#1913743811yescharacteristic
679C2C4×#1306334611yescharacteristic
680C2#1914347011yescharacteristic
681C2#1914647811yescharacteristic
682C2#1914648711yescharacteristic
683C2#1914654111yescharacteristic
684C2#1914654711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×#103×C43C2
socleC23×C43C22×D4
prime radicalC22×#10621902C22
cosocleC22×C4×C43C24
hypercenterC4×#103D43
hypocenterC43#22573
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#103

Complements

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

NH ≅ G/Ntype
2. #19137476C2semidirect
4. #19135278C2semidirect
5. #19135276C2semidirect
6. #19135215C2semidirect
7. #19135213C2semidirect
8. #19134849C2semidirect
9. #19134847C2semidirect
10. #19134688C2semidirect
11. #19134623C2semidirect
13. #103×Dic43C2semidirect
14. C8×(C2×D43)⋊C4C2semidirect
15. C4×#103×C43C2semidirect
22. #14582894C4semidirect
347. C4×#103D43semidirect
402. C43#22573semidirect

Maximal subgroups

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

subgroupindex
C2×#145828942
#191374762
#191374332
#191352782
#191352762
#191352152
#191352132
#191348492
#191348472
#191346882
#191346232
#191345342
#103×Dic432
C8×(C2×D43)⋊C42
C4×#103×C432
#2257343