Finite Group Databasebeta

← #25099690

Subgroups — #25099690

Order 11008.

938 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583012C211yesmaximal, characteristic
2#19137239C211yesmaximal, characteristic, complemented
3#19136957C211yesmaximal, characteristic, complemented
4#19135223C211yesmaximal, characteristic, complemented
5#19135216C211yesmaximal, characteristic, complemented
6#19135181C211yesmaximal, characteristic, complemented
7#19135174C211yesmaximal, characteristic, complemented
8#19134942C211yesmaximal, characteristic
9#19134942C211yesmaximal, characteristic
10#19134859C211yesmaximal, characteristic, complemented
11#19134845C211yesmaximal, characteristic, complemented
12#19134492C211yesmaximal, characteristic, complemented
13C4×#13063247C211yesmaximal, characteristic, complemented
14C4×#13063247C211yesmaximal, characteristic, complemented
15C43×#1746C211yesmaximal, characteristic, complemented
16C22×D344C2211yescharacteristic
17C2×C4×D172C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19C2×C4×D172C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21#14583012C418yescomplemented
22C2×#13063259C2211yescharacteristic
23C2×#13063257C2211yescharacteristic
24C2×#13063257C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063247C2211yescharacteristic
29C2×#13063247C2211yescharacteristic
30C2×#13063247C2211yescharacteristic
31#14582801C2211yescharacteristic
32#14582801C2211yescharacteristic
33#14582797C2211yescharacteristic
34#14582797C2211yescharacteristic
35#14582788—21no—
36#14582788—21no—
37#14582761—21no—
38#14582758—21no—
39C4×C4⋊Dic43C2211yescharacteristic
40C4×C4⋊Dic43C2211yescharacteristic
41C4×C4⋊Dic43C2211yescharacteristic
42C4×C4⋊Dic43C2211yescharacteristic
43#14582746—21no—
44#14582746—21no—
45#14582746—21no—
46#95×D43—21no—
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53C2×#97×C43C2211yescharacteristic
54C2×C4×C8×C43C2211yescharacteristic
55C43×#376C2211yescharacteristic
56C43×#336C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C22×D172C2311yescharacteristic
61C22×D172C2311yescharacteristic
62C22×C4×D43—21no—
63C22×C4×D43—21no—
64C22×C4×D43—21no—
65C22×C4×D43—21no—
66C2×D344—22no—
67C2×D344—22no—
68C2×D344C2×C414yes—
69C4×D172—22no—
70C4×D172—22no—
71C4×D172—22no—
72C4×D172—22no—
73C4×D172—22no—
74C4×D172—22no—
75C4×D172C2×C414yes—
76C4×D172C2×C414yescomplemented
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
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)⋊C4—21no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43—21no—
96C2×C4×Dic43—21no—
97#13063259—22no—
98#13063257—22no—
99#13063257C2×C414yescomplemented
100#13063247—22no—
101#13063247—22no—
102#13063247—22no—
103#13063247—22no—
104#13063247C2×C414yes—
105#13063247C2×C414yescomplemented
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C22×C8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116C2×C42×C43C2311yescharacteristic
117C2×C42×C43C2311yescharacteristic
118C2×C42×C43C2311yescharacteristic
119#97×C43C2×C414yescomplemented
120C4×C8×C43—22no—
121#95×C43D411yescharacteristic
122#95×C43D411yescharacteristic
123#95×C43D411yescharacteristic
124#95×C43D411yescharacteristic
125C23×D43—21no—
126C23×D43—21no—
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2411yescharacteristic
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C2×D172—21no—
141C2×D172—21no—
142C2×D172—21no—
143C2×D172—21no—
144C2×D172—21no—
145C2×D172—21no—
146C2×D172—21no—
147C2×D172—21no—
148C2×D172C22×C412yes—
149C2×D172C22×C412yes—
150C2×D172#4112yes—
151C2×D172#4112yes—
152C2×C4×D43—24no—
153C2×C4×D43—24no—
154C2×C4×D43—24no—
155C2×C4×D43—24no—
156C2×C4×D43—81no—
157C2×C4×D43—81no—
158C2×C4×D43—81no—
159C2×C4×D43—81no—
160C2×C4×D43—81no—
161C2×C4×D43—81no—
162C2×C4×D43—81no—
163C2×C4×D43—81no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43C22×C412yes—
175C2×C8×C43C22×C412yes—
176C42×C43—21no—
177C42×C43—21no—
178C42×C43—21no—
179C42×C43—21no—
180C42×C43C22×C412yes—
181C42×C43#4112yes—
182(C2×D43)⋊C4—24no—
183(C2×D43)⋊C4—24no—
184(C2×D43)⋊C4—24no—
185(C2×D43)⋊C4—24no—
186(C2×D43)⋊C4—81no—
187(C2×D43)⋊C4—81no—
188(C2×D43)⋊C4—81no—
189(C2×D43)⋊C4—81no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43C22×C412yes—
199C4⋊Dic43C22×C412yes—
200C4⋊Dic43#4112yes—
201C4⋊Dic43#4112yes—
202Dic43⋊C4—81no—
203Dic43⋊C4—81no—
204C4×Dic43—81no—
205C4×Dic43—81no—
206C4×Dic43—81no—
207C4×Dic43—81no—
208D344—28no—
209C23×C43C22×D411yescharacteristic
210C22×D43—22no—
211C22×D43—22no—
212C22×D43—22no—
213C22×D43—22no—
214C22×D43—41no—
215C22×D43—41no—
216C22×D43—41no—
217C22×D43—41no—
218C22×D43—41no—
219C22×D43—41no—
220C22×D43—41no—
221C22×D43—41no—
222C22×D43—41no—
223C22×D43—41no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43C4×D412yes—
241C2×C4×C43C4×D412yes—
242C2×C4×C43C23×C411yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×Dic43—22no—
249C2×Dic43—22no—
250C2×Dic43—22no—
251C2×Dic43—22no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
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—
266D172—22no—
267D172—22no—
268D172—22no—
269D172—22no—
270D172—22no—
271D172—41no—
272D172—41no—
273D172#11714yes—
274C4×D43—84no—
275C4×D43—84no—
276C4×D43—84no—
277C4×D43—84no—
278C8×C43—22no—
279C8×C43—22no—
280C8×C43—41no—
281C8×C43—41no—
282#21126—431nomaximal, Sylow
283C22×C43C2×C4×D411yescharacteristic
284C22×C43#52511yescharacteristic
285C22×C43#52511yescharacteristic
286C22×C43#57611yescharacteristic
287C22×C43#57611yescharacteristic
288C22×C43#57711yescharacteristic
289C22×C43#57711yescharacteristic
290C2×D43—24no—
291C2×D43—42no—
292C2×D43—42no—
293C2×D43—42no—
294C2×D43—42no—
295C2×D43—42no—
296C2×D43—42no—
297C2×D43—42no—
298C2×D43—42no—
299C2×D43—42no—
300C2×D43—81no—
301C2×D43—81no—
302C2×D43—81no—
303C2×D43—81no—
304C4×C43—22no—
305C4×C43—22no—
306C4×C43—41no—
307C4×C43—41no—
308C4×C43—41no—
309C4×C43—41no—
310C4×C43C2×#11711yescharacteristic
311C4×C43C4×#4111yescharacteristic
312C4×C43#52911yescharacteristic
313C4×C43#52911yescharacteristic
314Dic43—42no—
315Dic43—42no—
316Dic43—42no—
317Dic43—42no—
318Dic43—81no—
319Dic43—81no—
320C2×#442—431no—
321#2319—431no—
322#2275—431no—
323#1926—431no—
324#1925—431no—
325#1920—431no—
326#1919—431no—
327#1879—431no—
328#1879—431no—
329#1864—431no—
330#1862—431no—
331#1776—431no—
332C4×#102—431no—
333C4×#102—431no—
334#1746D4311yescharacteristic, complemented
335C2×C43#229011yescharacteristic
336C2×C43#294611yescharacteristic
337C2×C43#294611yescharacteristic
338C2×C43#311811yescharacteristic
339C2×C43#311911yescharacteristic
340C2×C43#312211yescharacteristic
341C2×C43#312511yescharacteristic
342D43—44no—
343D43—82no—
344C22×D8—431no—
345C2×C4×D4—431no—
346C2×C4×D4—431no—
347C2×C4×D4—431no—
348C2×C4×D4—431no—
349#442—438no—
350C2×#107—431no—
351C2×#106—431no—
352C2×#106—431no—
353C2×#102—431no—
354C2×#102—431no—
355C2×#102—431no—
356C2×#102—431no—
357C2×#102—431no—
358C2×#102—431no—
359C2×#97C2×D4311yescharacteristic
360C2×C4×C8C2×D4311yescharacteristic
361#390—431no—
362#390—431no—
363#389—431no—
364#389—431no—
365#388—861no—
366#388—861no—
367#381—861no—
368#380—861no—
369C4×C4⋊C4—431no—
370C4×C4⋊C4—431no—
371C4×C4⋊C4—431no—
372C4×C4⋊C4—431no—
373C4×C22⋊C4—861no—
374C4×C22⋊C4—861no—
375C4×C22⋊C4—861no—
376#376C2×D4311yescharacteristic
377C2×#95—861no—
378#340—431no—
379#340—431no—
380#340—431no—
381#340—431no—
382#340—431no—
383#340—431no—
384#336C2×D4311yescharacteristic
385#336C2×D4311yescharacteristic
386#336C2×D4311yescharacteristic
387#336C2×D4311yescharacteristic
388C43#2112611yescharacteristic, complemented, Sylow
389C22×D4—431no—
390C22×D4—431no—
391C23×C4—861no—
392C23×C4—861no—
393C23×C4—861no—
394C23×C4—861no—
395C2×D8—434no—
396C2×D8—862no—
397C2×D8—862no—
398C22×C8C22×D4311yescharacteristic
399C22×C8C22×D4311yescharacteristic
400C22×C8C22×D4311yescharacteristic
401C22×C8C22×D4311yescharacteristic
402C4×D4—434no—
403C4×D4—434no—
404C4×D4—862no—
405C4×D4—862no—
406C4×D4—862no—
407C4×D4—862no—
408C4×D4—862no—
409C4×D4—862no—
410C2×C4⋊C4—431no—
411C2×C4⋊C4—431no—
412C2×C4⋊C4—431no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—431no—
415C2×C4⋊C4—431no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4—861no—
418C2×C22⋊C4—861no—
419C2×C22⋊C4—861no—
420C2×C22⋊C4—861no—
421C2×C22⋊C4—861no—
422C2×C22⋊C4—861no—
423C2×C22⋊C4—861no—
424C2×C22⋊C4—861no—
425C2×C22⋊C4—861no—
426C2×C42—861no—
427C2×C42—861no—
428C2×C42—861no—
429C2×C42—861no—
430C2×C42C22×D4311yescharacteristic
431C2×C42C22×D4311yescharacteristic
432C2×C42C22×D4311yescharacteristic
433#107—862no—
434#106—434no—
435#106—862no—
436#102—434no—
437#102—434no—
438#102—862no—
439#102—862no—
440#102—862no—
441#102—862no—
442#97C4×D4314yescomplemented
443C4×C8—22no—
444#95—861no—
445#95—861no—
446#95—861no—
447#95—861no—
448#95—861no—
449#95—861no—
450#95D17211yescharacteristic
451#95D17211yescharacteristic
452#95D17211yescharacteristic
453#95D17211yescharacteristic
454C24—861no—
455C24—861no—
456C2×D4—432no—
457C2×D4—432no—
458C2×D4—432no—
459C2×D4—432no—
460C2×D4—861no—
461C2×D4—861no—
462C2×D4—861no—
463C2×D4—861no—
464C2×D4—861no—
465C2×D4—861no—
466C2×D4—861no—
467C2×D4—861no—
468C22×C4—864no—
469C22×C4—864no—
470C22×C4—861no—
471C22×C4—861no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4—864no—
475C22×C4—864no—
476C22×C4—861no—
477C22×C4—861no—
478C22×C4—3441no—
479C22×C4—3441no—
480C22×C4—3441no—
481C22×C4—3441no—
482C22×C4—3441no—
483C22×C4—3441no—
484C22×C4—3441no—
485C22×C4—3441no—
486C22×C4C2×D17211yescharacteristic
487C22×C4C2×D17211yescharacteristic
488C22×C4C2×D17211yescharacteristic
489C22×C4C2×D17211yescharacteristic
490C22×C4C2×D17211yescharacteristic
491C22×C4C2×D17211yescharacteristic
492C22×C4C23×D4311yescharacteristic
493D8—868no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8C2×C4×D4312yes—
505C2×C8C2×C4×D4312yes—
506C4⋊C4—432no—
507C4⋊C4—432no—
508C4⋊C4—432no—
509C4⋊C4—432no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C4⋊C4—3441no—
519C4⋊C4—3441no—
520C22⋊C4—864no—
521C22⋊C4—864no—
522C22⋊C4—864no—
523C22⋊C4—864no—
524C22⋊C4—3441no—
525C22⋊C4—3441no—
526C22⋊C4—3441no—
527C22⋊C4—3441no—
528C42—21no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—3441no—
533C42—3441no—
534C42—3441no—
535C42—3441no—
536C42C2×C4×D4312yes—
537C42#1062189812yes—
538C23—862no—
539C23—862no—
540C23—862no—
541C23—862no—
542C23—1721no—
543C23—1721no—
544C23—1721no—
545C23—1721no—
546C23—1721no—
547C23—1721no—
548C23—1721no—
549C23—1721no—
550C23—1721no—
551C23—1721no—
552C23C22×D17211yescharacteristic
553D4—434no—
554D4—862no—
555D4—862no—
556D4—862no—
557D4—862no—
558D4—862no—
559D4—1721no—
560D4—1721no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—862no—
578C2×C4—862no—
579C2×C4—862no—
580C2×C4—862no—
581C2×C4—3444no—
582C2×C4—3444no—
583C2×C4—3444no—
584C2×C4—3444no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1721no—
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×C4C4×D17212yes—
600C2×C4C4×D17212yes—
601C2×C4C22×C4×D4311yescharacteristic
602C2×C4#41×D4311yescharacteristic
603C2×C4#41×D4311yescharacteristic
604C2×C4#41×D4311yescharacteristic
605C2×C4#41×D4311yescharacteristic
606C2×C4C2×#1062189811yescharacteristic
607C8—22no—
608C8—22no—
609C8—41no—
610C8—41no—
611C22—864no—
612C22—3441no—
613C22—3441no—
614C22—3441no—
615C22—3441no—
616C22—1722no—
617C22—1722no—
618C22—1722no—
619C22—1722no—
620C22—1722no—
621C22—1722no—
622C22—1722no—
623C22—1722no—
624C22—1722no—
625C22C2×C4×D17211yescharacteristic
626C22#1458341111yescharacteristic
627C22#1458341111yescharacteristic
628C22#1458370411yescharacteristic
629C22#1458370411yescharacteristic
630C22#1458371111yescharacteristic
631C22#1458371111yescharacteristic
632C4—22no—
633C4—22no—
634C4—41no—
635C4—41no—
636C4—41no—
637C4—41no—
638C4—3441no—
639C4—3441no—
640C4—1722no—
641C4—1722no—
642C4—1722no—
643C4—1722no—
644C4#117×D4311yescharacteristic
645C4#1458336711yescharacteristic
646C4#1458342711yescharacteristic
647C4#1458342711yescharacteristic
648C2—3442no—
649C2—1724no—
650C2#1913703911yescharacteristic
651C2#1914342911yescharacteristic
652C2#1914342911yescharacteristic
653C2#1914478111yescharacteristic
654C2#1914479611yescharacteristic
655C2#1914483911yescharacteristic
656C2#1914487411yescharacteristic
subgroupG/H
centerC23C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1746C2
socleC23×C43C22×D4
prime radicalC22×D344C22
cosocleC22×C4×C43C24
hypercenter#1746D43
hypocenterC43#21126
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ #376 ◁ #1746

Complements

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

NH ≅ G/Ntype
2. #19137239C2semidirect
3. #19136957C2semidirect
4. #19135223C2semidirect
5. #19135216C2semidirect
6. #19135181C2semidirect
7. #19135174C2semidirect
10. #19134859C2semidirect
11. #19134845C2semidirect
12. #19134492C2semidirect
13. C4×#13063247C2semidirect
14. C4×#13063247C2semidirect
15. C43×#1746C2semidirect
21. #14583012C4semidirect
76. C4×D172C2×C4semidirect
99. #13063257C2×C4semidirect
105. #13063247C2×C4semidirect
119. #97×C43C2×C4semidirect
334. #1746D43semidirect
388. C43#21126semidirect
442. #97C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830122
#191372392
#191369572
#191352232
#191352162
#191351812
#191351742
#191349422
#191348592
#191348452
#191344922
C4×#130632472
C43×#17462
#2112643