Finite Group Databasebeta

← #25116305

Subgroups — #25116305

Order 11008.

710 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143393C211yesmaximal, characteristic
2#19143263C211yesmaximal, characteristic, complemented
3#19143261C211yesmaximal, characteristic, complemented
4#19135485C211yesmaximal, characteristic
5#19135480C211yesmaximal, characteristic
6#19135246C211yesmaximal, characteristic, complemented
7#19135246C211yesmaximal, characteristic, complemented
8#19135241C211yesmaximal, characteristic, complemented
9#19135241C211yesmaximal, characteristic, complemented
10#19134769C211yesmaximal, characteristic, complemented
11#19134616C211yesmaximal, characteristic, complemented
12#19134478C211yesmaximal, characteristic, complemented
13#19134473C211yesmaximal, characteristic, complemented
14#19134470C211yesmaximal, characteristic, complemented
15C43×#1806C211yesmaximal, characteristic, complemented
16C2×#13063345C2211yescharacteristic
17C4×#10621898C2211yescharacteristic
18#14583009C411yescharacteristic, complemented
19#14583009C411yescharacteristic, complemented
20#14583004C411yescharacteristic, complemented
21#14583004C411yescharacteristic, complemented
22#14582999C411yescharacteristic, complemented
23#14582999C411yescharacteristic, complemented
24#14582997C411yescharacteristic, complemented
25#14582997C411yescharacteristic, complemented
26#14582960—21no—
27#14582960—21no—
28#14582959—21no—
29#14582959—21no—
30#14582956—21no—
31#14582955—21no—
32#14582952—21no—
33#14582951—21no—
34C2×#13063260C2211yescharacteristic
35C2×#13063260C2211yescharacteristic
36C2×#13063260C2211yescharacteristic
37C2×#13063260C2211yescharacteristic
38#14582935C2211yescharacteristic
39#14582923C2211yescharacteristic
40C2×C4⋊(C43⋊C8)C2211yescharacteristic
41C2×#13063253C2211yescharacteristic
42C2×#13063253C2211yescharacteristic
43#14582895C2211yescharacteristic
44#14582893C2211yescharacteristic
45#14582867C2211yescharacteristic
46#14582867C2211yescharacteristic
47#14582866C2211yescharacteristic
48#14582866C2211yescharacteristic
49#14582857C2211yescharacteristic
50#14582857C2211yescharacteristic
51#14582855C2211yescharacteristic
52#14582855C2211yescharacteristic
53C2×#13063236C2211yescharacteristic
54C2×#13063236C2211yescharacteristic
55C2×C4×C43⋊C8C2211yescharacteristic
56#14582659C2211yescharacteristic
57#14582659C2211yescharacteristic
58#14582654C2211yescharacteristic
59#14582654C2211yescharacteristic
60C4×#41×C43C2211yescharacteristic
61C43×#423C2211yescharacteristic
62C2×#104×C43C2211yescharacteristic
63C2×#104×C43C2211yescharacteristic
64C4×C4⋊C4×C43C2211yescharacteristic
65C43×#339C2211yescharacteristic
66C43×#339C2211yescharacteristic
67C2×#10621898C2311yescharacteristic
68#13063345—22no—
69#13063345—22no—
70C2×#10621885C2×C411yescharacteristic
71C2×#10621883C2×C411yescharacteristic
72C2×#10621884C2×C411yescharacteristic
73C2×#10621882C2×C411yescharacteristic
74C2×#10621877C2311yescharacteristic
75C2×#10621877C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79C22×C43⋊C8C2311yescharacteristic
80C4×Dic86C2×C411yescharacteristic
81C4×Dic86C2×C411yescharacteristic
82C4×D172C2×C411yescharacteristic
83C4×D172C2×C411yescharacteristic
84C4×C22⋊D43—21no—
85C4×C22⋊D43—21no—
86#13063284C2311yescharacteristic
87#13063282—21no—
88C42×D43—21no—
89#13063260—22no—
90#13063260—22no—
91#13063260—41no—
92#13063260—41no—
93#13063258C2×C411yescharacteristic
94#13063258C2×C411yescharacteristic
95#13063256C2×C411yescharacteristic
96#13063256C2×C411yescharacteristic
97C4⋊(C43⋊C8)—21no—
98C4⋊(C43⋊C8)—21no—
99C4⋊(C43⋊C8)D411yescharacteristic
100C4⋊(C43⋊C8)D411yescharacteristic
101C4⋊(C43⋊C8)D411yescharacteristic
102C4⋊(C43⋊C8)D411yescharacteristic
103#13063253—41no—
104#13063253—41no—
105#13063249C2×C411yescharacteristic
106#13063249C2×C411yescharacteristic
107#13063248C2×C411yescharacteristic
108#13063248C2×C411yescharacteristic
109#13063246C2×C411yescharacteristic
110#13063246C2×C411yescharacteristic
111#13063245C2×C411yescharacteristic
112#13063245C2×C411yescharacteristic
113C22⋊(C43⋊C8)—21no—
114C22⋊(C43⋊C8)—21no—
115C22⋊(C43⋊C8)—21no—
116C22⋊(C43⋊C8)—21no—
117(C2×D43)⋊C8—21no—
118(C2×D43)⋊C8—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8—21no—
121#13063236—21no—
122#13063236—21no—
123#13063236—22no—
124#13063236C2×C411yescharacteristic
125#13063236C2×C411yescharacteristic
126#13063236C2×C411yescharacteristic
127#13063236C2×C411yescharacteristic
128#13063235—21no—
129#13063235—21no—
130C4×C43⋊C8—21no—
131C4×C43⋊C8—21no—
132C4×C43⋊C8—22no—
133C8×Dic43—21no—
134C8×Dic43—21no—
135C2×#41×C43C2311yescharacteristic
136C2×M16×C43C2311yescharacteristic
137C2×M16×C43C2311yescharacteristic
138C4×Q8×C43C2×C411yescharacteristic
139C4×Q8×C43C2×C411yescharacteristic
140C4×D4×C43—21no—
141C4×D4×C43—21no—
142C4×D4×C43C2×C411yescharacteristic
143C4×D4×C43C2×C411yescharacteristic
144#117×C43—21no—
145#117×C43C2311yescharacteristic
146C2×C4⋊C4×C43—21no—
147C2×C42×C43—21no—
148C2×C42×C43C2311yescharacteristic
149C2×C42×C43C2311yescharacteristic
150C2×C42×C43C2311yescharacteristic
151C4⋊C8×C43—21no—
152C4⋊C8×C43—21no—
153#104×C43—41no—
154#104×C43—41no—
155#95×C43—21no—
156#41×C43—21no—
157#41×C43—21no—
158#41×C43—21no—
159#41×C43—21no—
160C2×Q8×C43C22×C411yescharacteristic
161C2×D4×C43—21no—
162C2×D4×C43C22×C411yescharacteristic
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43#4111yescharacteristic
169C22×C4×C43#4111yescharacteristic
170C22×C4×C43C2411yescharacteristic
171C2×C22⋊D43—21no—
172#10621898—21no—
173#10621898—21no—
174#10621898—21no—
175#10621898—21no—
176C2×D172C22×C411yescharacteristic
177C2×C4×D43—21no—
178C2×C4×D43—21no—
179C2×C4×D43—21no—
180C2×Dic86C22×C411yescharacteristic
181M16×C43—21no—
182M16×C43—21no—
183M16×C43—21no—
184M16×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—42no—
190C4⋊C4×C43C22×C411yescharacteristic
191C4⋊C4×C43C22×C411yescharacteristic
192C22⋊C4×C43—21no—
193C22⋊C4×C43—21no—
194C22⋊C4×C43—21no—
195C42×C43—21no—
196C42×C43—21no—
197C42×C43—21no—
198C42×C43—21no—
199C42×C43—21no—
200C42×C43—21no—
201C42×C43—21no—
202C42×C43C22×C411yescharacteristic
203C42×C43C22×C411yescharacteristic
204C42×C43C2×D411yescharacteristic
205C42×C43C2×D411yescharacteristic
206C22⋊Dic43—21no—
207#10621885—22no—
208#10621884—22no—
209#10621883—22no—
210#10621882—22no—
211(C2×D43)⋊C4—21no—
212(C2×D43)⋊C4—21no—
213C4⋊Dic43C22×C411yescharacteristic
214C4⋊Dic43C22×C411yescharacteristic
215Dic43⋊C4—21no—
216Dic43⋊C4—21no—
217C4×Dic43—21no—
218C4×Dic43—21no—
219C4×Dic43—21no—
220#10621877—21no—
221#10621877—21no—
222#10621877—21no—
223#10621877—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⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8C22×C411yescharacteristic
233C2×C43⋊C8C22×C411yescharacteristic
234C2×C43⋊C8C22×C411yescharacteristic
235C2×C43⋊C8C22×C411yescharacteristic
236C2×C43⋊C8C2×D411yescharacteristic
237C2×C43⋊C8C2×D411yescharacteristic
238C2×C43⋊C8C2×D411yescharacteristic
239C2×C43⋊C8C2×D411yescharacteristic
240C2×C43⋊C8#4112yes—
241C2×C43⋊C8#4112yes—
242C23×C43—21no—
243C23×C43C2×#4111yescharacteristic
244C22×D43—21no—
245Q8×C43—21no—
246Q8×C43—21no—
247D4×C43—21no—
248D4×C43—21no—
249D4×C43—41no—
250D4×C43—41no—
251C2×C4×C43—22no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—42no—
258C2×C4×C43—41no—
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—81no—
266C2×C4×C43C4×D411yescharacteristic
267C2×C4×C43C4×D411yescharacteristic
268C2×C4×C43C4×D411yescharacteristic
269C2×C4×C43C4×D411yescharacteristic
270C2×C4×C43C23×C411yescharacteristic
271C2×C4×C43C22×D411yescharacteristic
272C2×C4×C43C2×#4111yescharacteristic
273C2×C4×C43C2×#4111yescharacteristic
274C2×C4×C43H(5,𝔽2)11yescharacteristic
275C2×C4×C432−1+411yescharacteristic
276C22⋊D43—41no—
277C22⋊D43—41no—
278C2×Dic43—21no—
279C2×Dic43—21no—
280C2×Dic43—21no—
281D172—21no—
282D172—21no—
283C4×D43—42no—
284C4×D43—41no—
285C4×D43—41no—
286C4×D43—81no—
287Dic86—21no—
288Dic86—21no—
289C8×C43—41no—
290C8×C43—41no—
291C43⋊C8—21no—
292C43⋊C8—21no—
293C43⋊C8—21no—
294C43⋊C8—21no—
295C43⋊C8—21no—
296C43⋊C8—21no—
297C43⋊C8—41no—
298C43⋊C8—41no—
299C43⋊C8#11712yes—
300C43⋊C8#11712yes—
301#22804—431nomaximal, Sylow
302C22×C43—21no—
303C22×C43—21no—
304C22×C43—41no—
305C22×C43—41no—
306C22×C43—41no—
307C22×C43C2×C4×D411yescharacteristic
308C22×C43#55511yescharacteristic
309C22×C43#55611yescharacteristic
310C2×D43—41no—
311C2×D43—41no—
312C2×D43—41no—
313C4×C43—21no—
314C4×C43—21no—
315C4×C43—21no—
316C4×C43—21no—
317C4×C43—42no—
318C4×C43—41no—
319C4×C43—41no—
320C4×C43—41no—
321C4×C43—81no—
322C4×C43C2×#11711yescharacteristic
323C4×C43#52011yescharacteristic
324C4×C43#54711yescharacteristic
325C4×C43#55011yescharacteristic
326Dic43—41no—
327Dic43—41no—
328Dic43—41no—
329#2943—431no—
330#2925—431no—
331#2925—431no—
332#1975—431no—
333#1974—431no—
334#1929—431no—
335#1929—431no—
336#1929—431no—
337#1929—431no—
338#1849—431no—
339#1806—431no—
340#1806D4311yescharacteristic, complemented
341#1773—431no—
342#1772—431no—
343#1771—431no—
344C2×C43—21no—
345C2×C43—21no—
346C2×C43—81no—
347C2×C43#235411yescharacteristic
348C2×C43#295511yescharacteristic
349C2×C43#295611yescharacteristic
350D43—81no—
351C2×#135—431no—
352C4×#41—431no—
353C4×#41C2×D4311yescharacteristic
354#442—431no—
355#442—431no—
356#441—431no—
357#441—431no—
358#440—431no—
359#440—431no—
360#440—431no—
361#440—431no—
362#433—861no—
363#433—861no—
364#433—861no—
365#433—861no—
366#432—861no—
367#432—861no—
368#431—861no—
369#431—861no—
370C2×#108—431no—
371C2×#108—431no—
372C2×#108—431no—
373C2×#108—431no—
374#427—431no—
375#423—431no—
376#423C2×D4311yescharacteristic
377C2×C4⋊C8—431no—
378C2×#104—431no—
379C2×#104—431no—
380C2×#104C2×D4311yescharacteristic
381C2×#104C2×D4311yescharacteristic
382#416—431no—
383#416—431no—
384#408—431no—
385#408—431no—
386#408—431no—
387#408—431no—
388#405—431no—
389#405—431no—
390#405—431no—
391#405—431no—
392C2×#97—431no—
393C2×#97—431no—
394C2×C4×C8—431no—
395C4×C4⋊C4C2×D4311yescharacteristic
396#339—431no—
397#339—431no—
398#339C2×D4311yescharacteristic
399#339C2×D4311yescharacteristic
400#336—431no—
401#336—431no—
402C43#2280411yescharacteristic, complemented, Sylow
403C2×#41—431no—
404C2×#41C22×D4311yescharacteristic
405#135—862no—
406#135—862no—
407C2×Q16—431no—
408C2×SD16—431no—
409C2×SD16—431no—
410C2×D8—431no—
411C2×M16—431no—
412C2×M16—431no—
413C2×M16C22×D4311yescharacteristic
414C2×M16C22×D4311yescharacteristic
415C22×C8—431no—
416C22×C8—431no—
417C22×C8—431no—
418C22×C8—431no—
419C4×Q8—431no—
420C4×Q8—431no—
421C4×Q8C4×D4311yescharacteristic
422C4×Q8C4×D4311yescharacteristic
423C4×D4—21no—
424C4×D4—21no—
425C4×D4—431no—
426C4×D4—431no—
427C4×D4—861no—
428C4×D4—861no—
429C4×D4C4×D4311yescharacteristic
430C4×D4C4×D4311yescharacteristic
431#117—21no—
432#117—431no—
433#117—861no—
434#117C22×D4311yescharacteristic
435C2×C4⋊C4—21no—
436C2×C42—21no—
437C2×C42—861no—
438C2×C42C22×D4311yescharacteristic
439C2×C42C22×D4311yescharacteristic
440C2×C42C22×D4311yescharacteristic
441#108—862no—
442#108—862no—
443#108—1721no—
444#108—1721no—
445#107—431no—
446#107—431no—
447#106—431no—
448#106—431no—
449C4⋊C8—21no—
450C4⋊C8—21no—
451C4⋊C8—431no—
452C4⋊C8—431no—
453C4⋊C8—431no—
454C4⋊C8—431no—
455C4⋊C8—861no—
456C4⋊C8—861no—
457#104—41no—
458#104—41no—
459#104—1721no—
460#104—1721no—
461#103—431no—
462#103—431no—
463#103—431no—
464#103—431no—
465#102—431no—
466#102—431no—
467#102—431no—
468#102—431no—
469C22⋊C8—861no—
470C22⋊C8—861no—
471C22⋊C8—861no—
472C22⋊C8—861no—
473C22⋊C8—861no—
474C22⋊C8—861no—
475C22⋊C8—861no—
476C22⋊C8—861no—
477#97—431no—
478#97—431no—
479#97—431no—
480#97—431no—
481#97—862no—
482#97—861no—
483#97—861no—
484#97—861no—
485#97—861no—
486C4×C8—862no—
487C4×C8—861no—
488C4×C8—861no—
489C4×C8—861no—
490C4×C8—861no—
491#95—21no—
492#41—21no—
493#41—21no—
494#41—21no—
495#41—21no—
496#41—861no—
497#41—861no—
498#41—861no—
499#41—861no—
500C2×Q8—431no—
501C2×Q8C2×C4×D4311yescharacteristic
502C2×D4—21no—
503C2×D4—431no—
504C2×D4—861no—
505C2×D4C2×C4×D4311yescharacteristic
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—861no—
512C22×C4—861no—
513C22×C4—861no—
514C22×C4#1062190011yescharacteristic
515C22×C4#1062190011yescharacteristic
516C22×C4C23×D4311yescharacteristic
517Q16—862no—
518SD16—862no—
519SD16—862no—
520D8—862no—
521M16—21no—
522M16—21no—
523M16—21no—
524M16—21no—
525M16—861no—
526M16—861no—
527M16—861no—
528M16—861no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—431no—
532C2×C8—431no—
533C2×C8—432no—
534C2×C8—432no—
535C2×C8—431no—
536C2×C8—431no—
537C2×C8—431no—
538C2×C8—431no—
539C2×C8—431no—
540C2×C8—431no—
541C2×C8—861no—
542C2×C8—861no—
543C2×C8—861no—
544C2×C8—861no—
545C2×C8—861no—
546C2×C8—861no—
547C2×C8—861no—
548C2×C8—861no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—42no—
552C4⋊C4—431no—
553C4⋊C4—431no—
554C4⋊C4—861no—
555C4⋊C4—861no—
556C4⋊C4C2×C4×D4311yescharacteristic
557C4⋊C4C2×C4×D4311yescharacteristic
558C22⋊C4—21no—
559C22⋊C4—21no—
560C22⋊C4—21no—
561C22⋊C4—861no—
562C22⋊C4—861no—
563C22⋊C4—861no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—861no—
572C42—861no—
573C42—861no—
574C42C2×C4×D4311yescharacteristic
575C42C2×C4×D4311yescharacteristic
576C42D4×D4311yescharacteristic
577C42D4×D4311yescharacteristic
578C23—21no—
579C23—861no—
580C23C2×#1062190011yescharacteristic
581Q8—21no—
582Q8—21no—
583Q8—861no—
584Q8—861no—
585D4—21no—
586D4—21no—
587D4—41no—
588D4—41no—
589D4—861no—
590D4—861no—
591D4—1721no—
592D4—1721no—
593C2×C4—22no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—42no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—81no—
608C2×C4—861no—
609C2×C4—861no—
610C2×C4—861no—
611C2×C4—3441no—
612C2×C4—1722no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4(C22⋊D43)⋊C411yescharacteristic
616C2×C4(C22⋊D43)⋊C411yescharacteristic
617C2×C4(C22⋊D43)⋊C411yescharacteristic
618C2×C4(C22⋊D43)⋊C411yescharacteristic
619C2×C4C22×C4×D4311yescharacteristic
620C2×C4C2×D4×D4311yescharacteristic
621C2×C4#41×D4311yescharacteristic
622C2×C4#41×D4311yescharacteristic
623C2×C4#1306337011yescharacteristic
624C2×C4#1306337311yescharacteristic
625C8—41no—
626C8—41no—
627C8—432no—
628C8—432no—
629C8—861no—
630C8—861no—
631C8—861no—
632C8—861no—
633C8—861no—
634C8—861no—
635C8—1721no—
636C8—1721no—
637C22—21no—
638C22—21no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—1721no—
643C22—1721no—
644C22—1721no—
645C22C2×(C22⋊D43)⋊C411yescharacteristic
646C22#1458361311yescharacteristic
647C22#1458362011yescharacteristic
648C4—21no—
649C4—21no—
650C4—21no—
651C4—21no—
652C4—42no—
653C4—41no—
654C4—41no—
655C4—41no—
656C4—81no—
657C4—1721no—
658C4—1721no—
659C4—1721no—
660C4#117×D4311yescharacteristic
661C4#1458338011yescharacteristic
662C4#1458355111yescharacteristic
663C4#1458356711yescharacteristic
664C2—21no—
665C2—21no—
666C2—81no—
667C2—3441no—
668C2#1913753911yescharacteristic
669C2#1914349411yescharacteristic
670C2#1914350111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1806C2
socleC22×C43C2×C4×D4
prime radicalC2×#13063345C22
cosocleC22×C4×C43C24
hypercenter#1806D43
hypocenterC43#22804
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1806

Complements

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

NH ≅ G/Ntype
2. #19143263C2semidirect
3. #19143261C2semidirect
6. #19135246C2semidirect
7. #19135246C2semidirect
8. #19135241C2semidirect
9. #19135241C2semidirect
10. #19134769C2semidirect
11. #19134616C2semidirect
12. #19134478C2semidirect
13. #19134473C2semidirect
14. #19134470C2semidirect
15. C43×#1806C2semidirect
18. #14583009C4semidirect
19. #14583009C4semidirect
20. #14583004C4semidirect
21. #14583004C4semidirect
22. #14582999C4semidirect
23. #14582999C4semidirect
24. #14582997C4semidirect
25. #14582997C4semidirect
340. #1806D43semidirect
402. C43#22804semidirect

Maximal subgroups

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

subgroupindex
#191433932
#191432632
#191432612
#191354852
#191354802
#191352462
#191352412
#191347692
#191346162
#191344782
#191344732
#191344702
C43×#18062
#2280443