Finite Group Databasebeta

← #25140932

Subgroups — #25140932

Order 11008.

854 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19138899C211yesmaximal, characteristic
2#19137491C211yesmaximal, characteristic
3#19136155C211yesmaximal, characteristic, complemented
4#19136069C211yesmaximal, characteristic, complemented
5#19136021C211yesmaximal, characteristic, complemented
6#19135169C211yesmaximal, characteristic, complemented
7#19135164C211yesmaximal, characteristic, complemented
8#19134884C211yesmaximal, characteristic
9#19134782C211yesmaximal, characteristic, complemented
10#19134781C211yesmaximal, characteristic, complemented
11#19134682C211yesmaximal, characteristic, complemented
12#19134680C211yesmaximal, characteristic, complemented
13#19134623C211yesmaximal, characteristic, complemented
14#340×D43C211yesmaximal, characteristic, complemented
15C43×#2075C211yesmaximal, characteristic, complemented
16C22×C8×D43C2211yescharacteristic
17C2×#13063307—21no—
18C2×C4×C22⋊D43C2211yescharacteristic
19C2×(C22⋊D43)⋊C4—21no—
20C22×C4⋊Dic43C2211yescharacteristic
21C2×C4⋊C4×D43C2211yescharacteristic
22C2×C4⋊C4×D43C2211yescharacteristic
23C2×#13063258C2211yescharacteristic
24C2×#13063258C2211yescharacteristic
25C2×#13063258C2211yescharacteristic
26C2×C22⋊(C43⋊C8)C2211yescharacteristic
27C2×(C2×D43)⋊C8C2211yescharacteristic
28#14582833—21no—
29#14582827—21no—
30#14582798C2211yescharacteristic
31#14582796—21no—
32#14582795C2211yescharacteristic
33#14582773—21no—
34#14582771—21no—
35#14582768C2211yescharacteristic
36#14582761—21no—
37#14582759C2211yescharacteristic
38#14582756C2211yescharacteristic
39#14582756C2211yescharacteristic
40C4⋊C4×Dic43C2211yescharacteristic
41#14582662C2211yescharacteristic
42#14582662C2211yescharacteristic
43#14582662C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#107×C43C2211yescharacteristic
53C2×C22⋊C8×C43C2211yescharacteristic
54C43×#380C2211yescharacteristic
55C43×#380C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×C22⋊D43D411yescharacteristic
60C23×Dic43—21no—
61C22×C4×D43—21no—
62C22×C4×D43—21no—
63C22×C4×D43C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66C2×C8×D43—22no—
67C2×C8×D43—22no—
68C2×C8×D43—41no—
69#13063307—44no—
70C4×C22⋊D43—22no—
71C4×C22⋊D43—22no—
72(C22⋊D43)⋊C4—44no—
73C2×C4⋊Dic43—22no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43—41no—
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4D411yescharacteristic
87C4⋊C4×D43—22no—
88C4⋊C4×D43—22no—
89C4⋊C4×D43—22no—
90C4⋊C4×D43—41no—
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43D411yescharacteristic
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4D411yescharacteristic
96C2×C4×Dic43—21no—
97C2×C4×Dic43C2311yescharacteristic
98#13063258—22no—
99#13063258—22no—
100#13063258—41no—
101C22⋊(C43⋊C8)—22no—
102(C2×D43)⋊C8—22no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C23×C4×C43C2311yescharacteristic
110C22×C8×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C22⋊C4×C43—21no—
117C2×C22⋊C4×C43—21no—
118#107×C43—41no—
119C22⋊C8×C43—41no—
120#95×C43—21no—
121#95×C43—21no—
122C24×C43C2×D411yescharacteristic
123C23×D43C2×D411yescharacteristic
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2411yescharacteristic
136C2×C22⋊D43—22no—
137C2×C22⋊D43—22no—
138C2×C22⋊D43D814yes—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—42no—
144C22×Dic43—42no—
145C22×Dic43—81no—
146C22×Dic43C2×D411yescharacteristic
147C22×Dic43C2×D411yescharacteristic
148C22×Dic43C2×D411yescharacteristic
149C2×C4×D43—21no—
150C2×C4×D43—21no—
151C2×C4×D43—21no—
152C2×C4×D43—21no—
153C2×C4×D43—42no—
154C2×C4×D43—42no—
155C2×C4×D43—42no—
156C2×C4×D43—42no—
157C2×C4×D43—42no—
158C2×C4×D43—81no—
159C2×C4×D43#4112yes—
160C2×C4×D43#4112yes—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C22⋊C4×C43—42no—
176C22⋊C4×C43—42no—
177C22⋊Dic43—22no—
178C22⋊Dic43—42no—
179(C2×D43)⋊C4—22no—
180(C2×D43)⋊C4—42no—
181(C2×D43)⋊C4—42no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—42no—
190C4⋊Dic43—42no—
191C4⋊Dic43#4112yes—
192Dic43⋊C4—22no—
193Dic43⋊C4—42no—
194Dic43⋊C4—42no—
195Dic43⋊C4—42no—
196Dic43⋊C4—42no—
197Dic43⋊C4—81no—
198C4×Dic43—21no—
199C4×Dic43—21no—
200C4×Dic43—42no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8#4112yes—
207C8×D43—44no—
208C23×C43—21no—
209C23×C43—21no—
210C23×C43—21no—
211C23×C43—21no—
212C23×C43—21no—
213C23×C43—21no—
214C23×C43C2×D812yes—
215C23×C43C22×D411yescharacteristic
216C22×D43—21no—
217C22×D43—21no—
218C22×D43—21no—
219C22×D43—21no—
220C22×D43#12312yes—
221C22×D43C2×D812yes—
222C22×D43#13712yes—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43C2×#4111yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C43H(5,𝔽2)11yescharacteristic
247C2×C4×C432−1+411yescharacteristic
248C22⋊D43—28no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—22no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—84no—
269C2×Dic43#12312yes—
270C2×Dic43C2×D812yes—
271C4×D43—22no—
272C4×D43—22no—
273C4×D43—22no—
274C4×D43—22no—
275C4×D43—84no—
276C4×D43—84no—
277C8×C43—41no—
278C8×C43—41no—
279C43⋊C8—22no—
280C43⋊C8—41no—
281#24933—431nomaximal, Sylow
282C22×C43—22no—
283C22×C43—22no—
284C22×C43—22no—
285C22×C43—41no—
286C22×C43—41no—
287C22×C43—41no—
288C22×C43—41no—
289C22×C43C2×#12311yescharacteristic
290C22×C43#54611yescharacteristic
291C22×C43#54711yescharacteristic
292C22×C43C22×D811yescharacteristic
293C22×C43C2×#13711yescharacteristic
294C22×C43#57711yescharacteristic
295C22×C43#57811yescharacteristic
296C2×D43—22no—
297C2×D43—22no—
298C2×D43—22no—
299C2×D43—22no—
300C2×D43—22no—
301C2×D43—22no—
302C2×D43#48014yes—
303C4×C43—41no—
304C4×C43—81no—
305C4×C43—81no—
306C4×C43—81no—
307C4×C43—81no—
308C4×C43#52911yescharacteristic
309C4×C43#53911yescharacteristic
310C4×C43#55111yescharacteristic
311C4×C43#55211yescharacteristic
312Dic43—22no—
313Dic43—22no—
314Dic43—41no—
315Dic43—42no—
316Dic43—81no—
317Dic43—81no—
318Dic43—81no—
319#2486—431no—
320D4×C4⋊C4—431no—
321#2099—431no—
322#2083—431no—
323#2075—431no—
324#2075D4311yescharacteristic, complemented
325#1918—431no—
326#1918—431no—
327#1869—431no—
328#1852—431no—
329#1852—431no—
330#1823—431no—
331#1823—431no—
332#1808—431no—
333C2×#340—431no—
334C2×C43—42no—
335C2×C43#241911yescharacteristic
336C2×C43C2×#48011yescharacteristic
337C2×C43#309711yescharacteristic
338C2×C43#329411yescharacteristic
339C2×C43#331211yescharacteristic
340C2×C43#333411yescharacteristic
341C2×C43#334411yescharacteristic
342D43—24no—
343C23×C8—431no—
344C2×#123—861no—
345C2×C4×D4—431no—
346C2×C4×D4—861no—
347C22×C4⋊C4—431no—
348C22×C4⋊C4—431no—
349C22×C4⋊C4—431no—
350C2×#107—431no—
351C2×#107—431no—
352C2×#107—431no—
353C2×#107C2×D4311yescharacteristic
354C2×C22⋊C8—431no—
355C2×C22⋊C8—431no—
356C2×C22⋊C8C2×D4311yescharacteristic
357#398—861no—
358#397—861no—
359#389—431no—
360#389—431no—
361#389—861no—
362#385—861no—
363#385—861no—
364#384—431no—
365#381—861no—
366#380—431no—
367#380—431no—
368#380—431no—
369#380C2×D4311yescharacteristic
370#380C2×D4311yescharacteristic
371C4×C4⋊C4—431no—
372#340—431no—
373#340—431no—
374#340—431no—
375#340—431no—
376#340—431no—
377#340—431no—
378#340—431no—
379#340—431no—
380#340—431no—
381#340C2×D4311yescharacteristic
382#340C2×D4311yescharacteristic
383#340C2×D4311yescharacteristic
384#336—431no—
385#336—431no—
386C43#2493311yescharacteristic, complemented, Sylow
387C22×D4—431no—
388C23×C4—431no—
389C23×C4—861no—
390C23×C4—861no—
391C23×C4—861no—
392C23×C4C22×D4311yescharacteristic
393C22×C8—431no—
394C22×C8—431no—
395C22×C8—862no—
396C22×C8—862no—
397C22×C8—1721no—
398C22×C8C22×D4311yescharacteristic
399C22×C8C22×D4311yescharacteristic
400#123—1724no—
401C4×D4—862no—
402C4×D4—862no—
403C4×D4—1724no—
404C2×C4⋊C4—431no—
405C2×C4⋊C4—431no—
406C2×C4⋊C4—431no—
407C2×C4⋊C4—431no—
408C2×C4⋊C4—431no—
409C2×C4⋊C4—862no—
410C2×C4⋊C4—862no—
411C2×C4⋊C4—862no—
412C2×C4⋊C4—862no—
413C2×C4⋊C4—861no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4—861no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4—861no—
419C2×C4⋊C4—861no—
420C2×C4⋊C4—1721no—
421C2×C4⋊C4—1721no—
422C2×C4⋊C4C22×D4311yescharacteristic
423C2×C4⋊C4C22×D4311yescharacteristic
424C2×C4⋊C4C22×D4311yescharacteristic
425C2×C4⋊C4C22×D4311yescharacteristic
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—431no—
429C2×C22⋊C4—431no—
430C2×C22⋊C4—861no—
431C2×C22⋊C4—861no—
432C2×C22⋊C4—861no—
433C2×C42—431no—
434C2×C42—861no—
435#107—41no—
436#107—862no—
437#107—862no—
438#107—1721no—
439C22⋊C8—41no—
440C22⋊C8—862no—
441C22⋊C8—862no—
442#95—21no—
443#95—21no—
444#95—861no—
445#95—861no—
446#95—861no—
447#95—861no—
448#95—861no—
449#95—861no—
450C24—431no—
451C24D4×D4311yescharacteristic
452C2×D4—434no—
453C2×D4—862no—
454C2×D4—862no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—431no—
466C22×C4—431no—
467C22×C4—432no—
468C22×C4—432no—
469C22×C4—431no—
470C22×C4—861no—
471C22×C4—861no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4—861no—
476C22×C4—861no—
477C22×C4—861no—
478C22×C4—3441no—
479C22×C4—3441no—
480C22×C4—1722no—
481C22×C4—1722no—
482C22×C4—1722no—
483C22×C4—1722no—
484C22×C4—1722no—
485C22×C4—1722no—
486C22×C4—1722no—
487C22×C4D4×D4311yescharacteristic
488C22×C4C23×D4311yescharacteristic
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—432no—
496C2×C8—861no—
497C2×C8—861no—
498C2×C8—861no—
499C2×C8—861no—
500C2×C8—861no—
501C2×C8—1724no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—432no—
511C4⋊C4—862no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4—3441no—
520C4⋊C4—1722no—
521C4⋊C4—1722no—
522C4⋊C4—1722no—
523C4⋊C4—1722no—
524C4⋊C4—1722no—
525C4⋊C4—1722no—
526C22⋊C4—42no—
527C22⋊C4—42no—
528C22⋊C4—862no—
529C22⋊C4—862no—
530C22⋊C4—1722no—
531C22⋊C4—1722no—
532C22⋊C4—1722no—
533C42—861no—
534C42—861no—
535C42—1722no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23—432no—
543C23—432no—
544C23—432no—
545C23—861no—
546C23—861no—
547C23—861no—
548C23—861no—
549C23D8×D4312yes—
550C23C2×D4×D4311yescharacteristic
551D4—868no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—432no—
572C2×C4—432no—
573C2×C4—861no—
574C2×C4—861no—
575C2×C4—861no—
576C2×C4—861no—
577C2×C4—862no—
578C2×C4—862no—
579C2×C4—862no—
580C2×C4—862no—
581C2×C4—861no—
582C2×C4—861no—
583C2×C4—861no—
584C2×C4—862no—
585C2×C4—3444no—
586C2×C4—3444no—
587C2×C4—3444no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4#41×D4311yescharacteristic
600C2×C4#41×D4311yescharacteristic
601C2×C4#41×D4311yescharacteristic
602C2×C4#41×D4311yescharacteristic
603C2×C4#1306337011yescharacteristic
604C2×C4#1306337211yescharacteristic
605C8—41no—
606C8—41no—
607C8—862no—
608C8—1721no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—41no—
613C22—41no—
614C22—41no—
615C22—41no—
616C22—434no—
617C22—862no—
618C22—862no—
619C22—862no—
620C22—862no—
621C22—862no—
622C22—862no—
623C22#123×D4311yescharacteristic
624C22#1458353811yescharacteristic
625C22#1458354711yescharacteristic
626C22C2×D8×D4311yescharacteristic
627C22#137×D4311yescharacteristic
628C22#1458370611yescharacteristic
629C22#1458371511yescharacteristic
630C4—41no—
631C4—81no—
632C4—81no—
633C4—81no—
634C4—81no—
635C4—862no—
636C4—862no—
637C4—3441no—
638C4—3441no—
639C4—3441no—
640C4—1721no—
641C4—1722no—
642C4#1458343211yescharacteristic
643C4#1458349211yescharacteristic
644C4#1458357911yescharacteristic
645C4#1458358511yescharacteristic
646C2—42no—
647C2—864no—
648C2#1913806711yescharacteristic
649C2#480×D4311yescharacteristic
650C2#1914456111yescharacteristic
651C2#1914640311yescharacteristic
652C2#1914664111yescharacteristic
653C2#1914693711yescharacteristic
654C2#1914704311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2075C2
socleC23×C43C22×D4
prime radicalC22×C22⋊D43D4
hypercenter#2075D43
hypocenterC43#24933
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2075

Complements

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

NH ≅ G/Ntype
3. #19136155C2semidirect
4. #19136069C2semidirect
5. #19136021C2semidirect
6. #19135169C2semidirect
7. #19135164C2semidirect
9. #19134782C2semidirect
10. #19134781C2semidirect
11. #19134682C2semidirect
12. #19134680C2semidirect
13. #19134623C2semidirect
14. #340×D43C2semidirect
15. C43×#2075C2semidirect
324. #2075D43semidirect
386. C43#24933semidirect

Maximal subgroups

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

subgroupindex
#191388992
#191374912
#191361552
#191360692
#191360212
#191351692
#191351642
#191348842
#191347822
#191347812
#191346822
#191346802
#191346232
#340×D432
C43×#20752
#2493343