Finite Group Databasebeta

← #25113831

Subgroups — #25113831

Order 11008.

1010 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582901C211yesmaximal, characteristic
2#19137470C211yesmaximal, characteristic, complemented
3#19137426C211yesmaximal, characteristic
4#19135285C211yesmaximal, characteristic, complemented
5#19135271C211yesmaximal, characteristic, complemented
6#19135237C211yesmaximal, characteristic, complemented
7#19135230C211yesmaximal, characteristic, complemented
8#19134859C211yesmaximal, characteristic, complemented
9#19134845C211yesmaximal, characteristic, complemented
10#19134682C211yesmaximal, characteristic, complemented
11#19134628C211yesmaximal, characteristic, complemented
12#19134536C211yesmaximal, characteristic
13#19134421C211yesmaximal, characteristic, complemented
14C4×#13063247C211yesmaximal, characteristic, complemented
15C43×#1753C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C2×C4×D172C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19C22×C4⋊Dic43C2211yescharacteristic
20C2×#13063259C2211yescharacteristic
21C2×#13063257C2211yescharacteristic
22#14582901C418yescomplemented
23C2×#13063250C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063250C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063247C2211yescharacteristic
29C2×#13063247C2211yescharacteristic
30C2×#13063247C2211yescharacteristic
31#14582805C2211yescharacteristic
32#14582805C2211yescharacteristic
33#14582797C2211yescharacteristic
34#14582797C2211yescharacteristic
35#14582782—21no—
36#14582782—21no—
37#14582775—21no—
38#14582775—21no—
39#14582761—21no—
40#14582759C2211yescharacteristic
41#14582759C2211yescharacteristic
42#14582757—21no—
43C4×C4⋊Dic43C2211yescharacteristic
44C4×C4⋊Dic43C2211yescharacteristic
45C22⋊C4×Dic43—21no—
46#95×D43—21no—
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53C22×M16×C43C2211yescharacteristic
54C2×C22⋊C8×C43C2211yescharacteristic
55C2×#97×C43C2211yescharacteristic
56C2×C4×C8×C43C2211yescharacteristic
57C4×C22⋊C4×C43C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C2×#10621898—22no—
61C2×#10621898—22no—
62C2×#10621898—22no—
63C2×#10621898—41no—
64C2×#10621898—41no—
65C2×#10621898C2×C414yes—
66C22×Dic86C2311yescharacteristic
67C22×D172C2311yescharacteristic
68C22×C22⋊D43—21no—
69C23×Dic43—21no—
70C22×C4×D43—21no—
71C22×C4×D43—21no—
72C22×C4×D43—21no—
73C4×D172—22no—
74C4×D172—22no—
75C4×D172—41no—
76C4×D172—41no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43—22no—
79C2×C4⋊Dic43C2×C414yescomplemented
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43—21no—
94#13063259—41no—
95#13063257—41no—
96#13063250—41no—
97#13063250—41no—
98#13063250C2×C414yescomplemented
99#13063250C2×C414yescomplemented
100#13063247—22no—
101#13063247—22no—
102#13063247C2×C414yes—
103#13063247C2×C414yes—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C23×C4×C43C2311yescharacteristic
115C2×M16×C43—41no—
116C2×M16×C43—41no—
117C2×M16×C43C2×C414yescomplemented
118C22×C8×C43C2311yescharacteristic
119C22×C8×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C2×C22⋊C4×C43D411yescharacteristic
123C2×C22⋊C4×C43D411yescharacteristic
124C2×C42×C43C2311yescharacteristic
125C2×C42×C43C2311yescharacteristic
126C22⋊C8×C43—22no—
127#97×C43—41no—
128C4×C8×C43—41no—
129#95×C43D411yescharacteristic
130#95×C43D411yescharacteristic
131C24×C43C2×D411yescharacteristic
132C23×D43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43C22×C412yes—
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43#4112yes—
144C22×C4×C43C2411yescharacteristic
145C2×C22⋊D43—24no—
146C2×C22⋊D43—42no—
147C2×C22⋊D43—42no—
148C22×Dic43—24no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—81no—
157C22×Dic43—81no—
158#10621898—28no—
159#10621898—44no—
160#10621898—44no—
161#10621898—44no—
162C2×D172—21no—
163C2×D172—21no—
164C2×D172—21no—
165C2×D172C22×C412yes—
166C2×D172#4112yes—
167C2×D172#4112yes—
168C2×C4×D43—24no—
169C2×C4×D43—42no—
170C2×C4×D43—42no—
171C2×C4×D43—42no—
172C2×C4×D43—42no—
173C2×C4×D43—42no—
174C2×C4×D43—42no—
175C2×C4×D43—81no—
176C2×C4×D43—81no—
177C2×Dic86—21no—
178C2×Dic86—21no—
179C2×Dic86—21no—
180C2×Dic86—21no—
181C2×Dic86—21no—
182C2×Dic86C22×C412yes—
183M16×C43—44no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43C22×C412yes—
195C2×C8×C43C22×C412yes—
196C22⋊C4×C43—22no—
197C22⋊C4×C43—41no—
198C42×C43—21no—
199C42×C43—21no—
200C42×C43—21no—
201C42×C43—21no—
202C22⋊Dic43—42no—
203C22⋊Dic43—81no—
204(C2×D43)⋊C4—42no—
205(C2×D43)⋊C4—42no—
206C4⋊Dic43—24no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43—21no—
212C4⋊Dic43—21no—
213C4⋊Dic43—21no—
214C4⋊Dic43—21no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43C22×C412yes—
218C4⋊Dic43C22×C412yes—
219Dic43⋊C4—81no—
220Dic43⋊C4—81no—
221C4×Dic43—81no—
222C4×Dic43—81no—
223C23×C43—21no—
224C23×C43—21no—
225C23×C43—21no—
226C23×C43—21no—
227C23×C43—21no—
228C23×C43—21no—
229C23×C43C4×D412yes—
230C23×C43C22×D411yescharacteristic
231C22×D43—22no—
232C22×D43—22no—
233C22×D43—22no—
234C22×D43—41no—
235C22×D43—41no—
236C22×D43—41no—
237C22×D43—41no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—22no—
243C2×C4×C43—22no—
244C2×C4×C43—22no—
245C2×C4×C43—22no—
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×C43C4×D412yes—
256C2×C4×C43#13712yes—
257C2×C4×C43C23×C411yescharacteristic
258C2×C4×C43C2×#4111yescharacteristic
259C2×C4×C43C2×#4111yescharacteristic
260C2×C4×C43C2×#4111yescharacteristic
261C2×C4×C43H(5,𝔽2)11yescharacteristic
262C2×C4×C43H(5,𝔽2)11yescharacteristic
263C22⋊D43—48no—
264C2×Dic43—22no—
265C2×Dic43—22no—
266C2×Dic43—22no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
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×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43—84no—
286D172—22no—
287D172—22no—
288D172—22no—
289D172#11714yes—
290C4×D43—48no—
291C4×D43—84no—
292C4×D43—84no—
293Dic86—22no—
294Dic86—22no—
295Dic86—41no—
296Dic86—41no—
297C8×C43—22no—
298C8×C43—22no—
299C8×C43—41no—
300C8×C43—41no—
301#22578—431nomaximal, Sylow
302C22×C43—22no—
303C22×C43—22no—
304C22×C43—22no—
305C22×C43—41no—
306C22×C43—41no—
307C22×C43—41no—
308C22×C43—41no—
309C22×C43C2×C4×D411yescharacteristic
310C22×C43#54611yescharacteristic
311C22×C43#54611yescharacteristic
312C22×C43C2×#13711yescharacteristic
313C22×C43#57511yescharacteristic
314C22×C43#57611yescharacteristic
315C22×C43#57711yescharacteristic
316C2×D43—24no—
317C2×D43—42no—
318C2×D43—42no—
319C2×D43—42no—
320C2×D43—42no—
321C2×D43—42no—
322C2×D43—42no—
323C4×C43—22no—
324C4×C43—22no—
325C4×C43—41no—
326C4×C43—41no—
327C4×C43—41no—
328C4×C43C2×#11711yescharacteristic
329C4×C43#51811yescharacteristic
330C4×C43#55111yescharacteristic
331C4×C43#55111yescharacteristic
332Dic43—42no—
333Dic43—42no—
334Dic43—42no—
335Dic43—81no—
336Dic43—81no—
337Dic43—81no—
338Dic43—81no—
339C2×#417—431no—
340#2345—431no—
341#2339—431no—
342#1935—431no—
343#1933—431no—
344#1928—431no—
345#1927—431no—
346#1864—431no—
347#1862—431no—
348#1823—431no—
349#1809—431no—
350#1788—431no—
351#1762—431no—
352C4×#102—431no—
353#1753D4311yescharacteristic, complemented
354C2×C43—42no—
355C2×C43#234211yescharacteristic
356C2×C43C4×#13711yescharacteristic
357C2×C43#294611yescharacteristic
358C2×C43#330711yescharacteristic
359C2×C43#331411yescharacteristic
360C2×C43#332211yescharacteristic
361C2×C43#333111yescharacteristic
362D43—44no—
363C22×#41—431no—
364C22×M16C2×D4311yescharacteristic
365C2×C4×D4—431no—
366C2×C4×D4—431no—
367C22×C4⋊C4—431no—
368C2×#107—431no—
369C2×#106—431no—
370#417—438no—
371C2×#103—431no—
372C2×#103—431no—
373C2×#103—431no—
374C2×#103—431no—
375C2×#102—431no—
376C2×#102—431no—
377C2×#102—431no—
378C2×#102—431no—
379C2×C22⋊C8C2×D4311yescharacteristic
380C2×#97C2×D4311yescharacteristic
381C2×C4×C8C2×D4311yescharacteristic
382#391—431no—
383#391—431no—
384#389—431no—
385#389—431no—
386#387—861no—
387#387—861no—
388#386—861no—
389#386—861no—
390#381—861no—
391#380—431no—
392#380—431no—
393#380—861no—
394C4×C4⋊C4—431no—
395C4×C4⋊C4—431no—
396C4×C22⋊C4—861no—
397C4×C22⋊C4C2×D4311yescharacteristic
398C2×#95—861no—
399#340—431no—
400#340—431no—
401#340—431no—
402#340—431no—
403#340—431no—
404#340—431no—
405#336C2×D4311yescharacteristic
406#336C2×D4311yescharacteristic
407C43#2257811yescharacteristic, complemented, Sylow
408C2×#41—434no—
409C2×#41—862no—
410C2×#41—862no—
411C2×#41—862no—
412C2×#41—1721no—
413C2×#41—1721no—
414C22×Q8—431no—
415C22×D4—431no—
416C22×D4—861no—
417C23×C4—861no—
418C23×C4—861no—
419C23×C4—861no—
420C23×C4—861no—
421C23×C4C22×D4311yescharacteristic
422C2×M16—41no—
423C2×M16—41no—
424C2×M16C4×D4314yescomplemented
425C22×C8C22×D4311yescharacteristic
426C22×C8C22×D4311yescharacteristic
427C22×C8C22×D4311yescharacteristic
428C22×C8C22×D4311yescharacteristic
429C4×D4—862no—
430C4×D4—862no—
431C4×D4—1721no—
432C4×D4—1721no—
433C2×C4⋊C4—434no—
434C2×C4⋊C4—431no—
435C2×C4⋊C4—431no—
436C2×C4⋊C4—431no—
437C2×C4⋊C4—431no—
438C2×C4⋊C4—431no—
439C2×C4⋊C4—431no—
440C2×C4⋊C4—861no—
441C2×C4⋊C4—862no—
442C2×C4⋊C4—861no—
443C2×C4⋊C4—861no—
444C2×C22⋊C4—861no—
445C2×C22⋊C4—861no—
446C2×C22⋊C4—861no—
447C2×C22⋊C4—861no—
448C2×C22⋊C4D17211yescharacteristic
449C2×C22⋊C4D17211yescharacteristic
450C2×C42—861no—
451C2×C42—861no—
452C2×C42C22×D4311yescharacteristic
453C2×C42C22×D4311yescharacteristic
454#107—1721no—
455#106—1721no—
456#103—434no—
457#103—434no—
458#103—1721no—
459#103—1721no—
460#102—434no—
461#102—434no—
462#102—862no—
463#102—862no—
464C22⋊C8—22no—
465#97—41no—
466C4×C8—41no—
467#95—861no—
468#95—861no—
469#95—861no—
470#95—861no—
471#95—861no—
472#95—861no—
473#95—861no—
474#95—861no—
475#95—861no—
476#95—861no—
477#95D17211yescharacteristic
478#95D17211yescharacteristic
479C24—861no—
480C24C2×D17211yescharacteristic
481#41—868no—
482#41—1724no—
483#41—1724no—
484#41—1724no—
485C2×Q8—432no—
486C2×Q8—861no—
487C2×Q8—861no—
488C2×Q8—861no—
489C2×Q8—861no—
490C2×Q8—861no—
491C2×D4—432no—
492C2×D4—432no—
493C2×D4—432no—
494C2×D4—864no—
495C2×D4—861no—
496C2×D4—861no—
497C2×D4—861no—
498C2×D4—1722no—
499C2×D4—1722no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—864no—
505C22×C4—861no—
506C22×C4—861no—
507C22×C4—861no—
508C22×C4—864no—
509C22×C4—861no—
510C22×C4—861no—
511C22×C4—861no—
512C22×C4—861no—
513C22×C4—3441no—
514C22×C4—3441no—
515C22×C4—3441no—
516C22×C4—3441no—
517C22×C4—1722no—
518C22×C4—1722no—
519C22×C4—1722no—
520C22×C4—1722no—
521C22×C4—1722no—
522C22×C4—1722no—
523C22×C4C2×C4×D4312yes—
524C22×C4C2×D17211yescharacteristic
525C22×C4C2×D17211yescharacteristic
526C22×C4C2×D17211yescharacteristic
527C22×C4C2×D17211yescharacteristic
528C22×C4C2×D17211yescharacteristic
529C22×C4#1062189812yes—
530C22×C4C23×D4311yescharacteristic
531M16—44no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8C2×C4×D4312yes—
543C2×C8C2×C4×D4312yes—
544C4⋊C4—432no—
545C4⋊C4—432no—
546C4⋊C4—864no—
547C4⋊C4—861no—
548C4⋊C4—861no—
549C4⋊C4—861no—
550C4⋊C4—861no—
551C4⋊C4—861no—
552C4⋊C4—861no—
553C4⋊C4—861no—
554C4⋊C4—861no—
555C4⋊C4—861no—
556C4⋊C4—861no—
557C4⋊C4—3441no—
558C4⋊C4—3441no—
559C22⋊C4—22no—
560C22⋊C4—41no—
561C22⋊C4—3441no—
562C22⋊C4—1722no—
563C22⋊C4—1722no—
564C22⋊C4—1722no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—3441no—
570C42—3441no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—862no—
578C23—862no—
579C23—862no—
580C23—1721no—
581C23—1721no—
582C23—1721no—
583C23—1721no—
584C23C4×D17212yes—
585C23C22×D17211yescharacteristic
586Q8—862no—
587Q8—862no—
588Q8—1721no—
589Q8—1721no—
590D4—434no—
591D4—862no—
592D4—862no—
593D4—862no—
594D4—1728no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—862no—
613C2×C4—862no—
614C2×C4—862no—
615C2×C4—3444no—
616C2×C4—3444no—
617C2×C4—3444no—
618C2×C4—1728no—
619C2×C4—1721no—
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—1721no—
629C2×C4—1721no—
630C2×C4—1721no—
631C2×C4—1721no—
632C2×C4—1721no—
633C2×C4—1721no—
634C2×C4—1721no—
635C2×C4—1721no—
636C2×C4—1721no—
637C2×C4C4×D17212yes—
638C2×C4#1306335812yes—
639C2×C4C22×C4×D4311yescharacteristic
640C2×C4#41×D4311yescharacteristic
641C2×C4#41×D4311yescharacteristic
642C2×C4C2×#1062189811yescharacteristic
643C2×C4#1306337011yescharacteristic
644C2×C4#1306337011yescharacteristic
645C8—22no—
646C8—22no—
647C8—41no—
648C8—41no—
649C22—22no—
650C22—22no—
651C22—22no—
652C22—41no—
653C22—41no—
654C22—41no—
655C22—41no—
656C22—864no—
657C22—1722no—
658C22—1722no—
659C22—1722no—
660C22—1722no—
661C22—1722no—
662C22—1722no—
663C22C2×C4×D17211yescharacteristic
664C22#1458354411yescharacteristic
665C22#1458354411yescharacteristic
666C22C2×#1306335811yescharacteristic
667C22#1458369911yescharacteristic
668C22#1458370411yescharacteristic
669C22#1458371111yescharacteristic
670C4—22no—
671C4—22no—
672C4—41no—
673C4—41no—
674C4—41no—
675C4—3441no—
676C4—3441no—
677C4—3441no—
678C4—3441no—
679C4—1722no—
680C4—1722no—
681C4—1722no—
682C4#117×D4311yescharacteristic
683C4#1458337211yescharacteristic
684C4#1458357811yescharacteristic
685C4#1458357811yescharacteristic
686C2—42no—
687C2—1724no—
688C2#1913744711yescharacteristic
689C2C4×#1306335811yescharacteristic
690C2#1914342911yescharacteristic
691C2#1914657311yescharacteristic
692C2#1914667811yescharacteristic
693C2#1914679811yescharacteristic
694C2#1914691211yescharacteristic
subgroupG/H
centerC23C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1753C2
socleC23×C43C22×D4
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenter#1753D43
hypocenterC43#22578
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1753

Complements

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

NH ≅ G/Ntype
2. #19137470C2semidirect
4. #19135285C2semidirect
5. #19135271C2semidirect
6. #19135237C2semidirect
7. #19135230C2semidirect
8. #19134859C2semidirect
9. #19134845C2semidirect
10. #19134682C2semidirect
11. #19134628C2semidirect
13. #19134421C2semidirect
14. C4×#13063247C2semidirect
15. C43×#1753C2semidirect
22. #14582901C4semidirect
79. C2×C4⋊Dic43C2×C4semidirect
98. #13063250C2×C4semidirect
99. #13063250C2×C4semidirect
117. C2×M16×C43C2×C4semidirect
353. #1753D43semidirect
407. C43#22578semidirect
424. C2×M16C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145829012
#191374702
#191374262
#191352852
#191352712
#191352372
#191352302
#191348592
#191348452
#191346822
#191346282
#191345362
#191344212
C4×#130632472
C43×#17532
#2257843