Finite Group Databasebeta

← #25164716

Subgroups — #25164716

Order 11008.

764 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19138969C211yesmaximal, characteristic
2#19137598C211yesmaximal, characteristic
3#19135918C211yesmaximal, characteristic, complemented
4#19135799C211yesmaximal, characteristic
5#19135737C211yesmaximal, characteristic, complemented
6#19135605C211yesmaximal, characteristic
7#19135542C211yesmaximal, characteristic, complemented
8#19135271C211yesmaximal, characteristic, complemented
9#19135237C211yesmaximal, characteristic, complemented
10#19135188C211yesmaximal, characteristic, complemented
11#19134935C211yesmaximal, characteristic, complemented
12#19134900C211yesmaximal, characteristic
13#19134686C211yesmaximal, characteristic
14C4×#13063250C211yesmaximal, characteristic, complemented
15C43×#1923C211yesmaximal, characteristic
16C22×Dic172C2211yescharacteristic
17C2×#13063325C2211yescharacteristic
18C2×#13063304C2211yescharacteristic
19C2×#13063304C2211yescharacteristic
20C2×C4×Dic86C2211yescharacteristic
21C22×C4⋊Dic43C2211yescharacteristic
22C2×#13063259C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063250C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063250C2211yescharacteristic
28C2×#13063250C2211yescharacteristic
29#14582841—21no—
30#14582811—21no—
31#14582805C2211yescharacteristic
32#14582805C2211yescharacteristic
33#14582805C2211yescharacteristic
34#14582803—21no—
35#14582797C2211yescharacteristic
36#14582796—21no—
37#14582792—21no—
38#14582786—21no—
39#14582771—21no—
40#14582759C2211yescharacteristic
41C4×C4⋊Dic43C2211yescharacteristic
42C4×C4⋊Dic43C2211yescharacteristic
43C22⋊C4×Dic43—21no—
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52C2×C4⋊C8×C43C2211yescharacteristic
53C2×C22⋊C8×C43C2211yescharacteristic
54C2×C22⋊C8×C43C2211yescharacteristic
55C2×C4×C8×C43C2211yescharacteristic
56C4×C22⋊C4×C43C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86—21no—
60C22×Dic86C2311yescharacteristic
61C22×Dic86C2311yescharacteristic
62C23×Dic43—21no—
63C2×Dic172—22no—
64C2×Dic172—41no—
65C2×Dic172—41no—
66#13063325—22no—
67#13063325—41no—
68#13063304—22no—
69#13063304—22no—
70#13063304—22no—
71#13063304—41no—
72C4×Dic86—22no—
73C4×Dic86—41no—
74C2×C4⋊Dic43—22no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43—41no—
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43—21no—
94#13063259—22no—
95#13063250—22no—
96#13063250—22no—
97#13063250—22no—
98#13063250—22no—
99#13063250—41no—
100#13063250—41no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C23×C4×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116C2×C22⋊C4×C43D411yescharacteristic
117C2×C22⋊C4×C43D411yescharacteristic
118C2×C42×C43C2311yescharacteristic
119C2×C42×C43C2311yescharacteristic
120C4⋊C8×C43—41no—
121C22⋊C8×C43—41no—
122C22⋊C8×C43—41no—
123C4×C8×C43—41no—
124#95×C43D411yescharacteristic
125#95×C43D411yescharacteristic
126C24×C43C2×D411yescharacteristic
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×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2411yescharacteristic
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—42no—
148C22×Dic43—42no—
149C22×Dic43—81no—
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86—42no—
162C2×Dic86—42no—
163C2×Dic86—81no—
164C2×Dic86#4112yes—
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×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C22⋊C4×C43—41no—
178C22⋊C4×C43Q1614yescomplemented
179C42×C43—21no—
180C42×C43—21no—
181C42×C43—21no—
182C42×C43—21no—
183C22⋊Dic43—24no—
184C22⋊Dic43—42no—
185C22⋊Dic43—81no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—42no—
196C4⋊Dic43—42no—
197C4⋊Dic43#4112yes—
198C4⋊Dic43#4112yes—
199C4⋊Dic43#4112yes—
200Dic43⋊C4—24no—
201Dic43⋊C4—42no—
202Dic43⋊C4—42no—
203Dic43⋊C4—81no—
204C4×Dic43—42no—
205C4×Dic43—81no—
206C4×Dic43—81no—
207Dic172—44no—
208C23×C43—21no—
209C23×C43—21no—
210C23×C43—21no—
211C23×C43—21no—
212C23×C43—21no—
213C23×C43—21no—
214C23×C43C2×Q1612yes—
215C23×C43C22×D411yescharacteristic
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43C2×Q1612yes—
234C2×C4×C43C2×Q1612yes—
235C2×C4×C43C2×#4111yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C2×C4×C43C2×#4111yescharacteristic
239C2×C4×C43H(5,𝔽2)11yescharacteristic
240C2×C4×C43H(5,𝔽2)11yescharacteristic
241C2×Dic43—22no—
242C2×Dic43—22no—
243C2×Dic43—22no—
244C2×Dic43—22no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
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—84no—
266Dic86—22no—
267Dic86—22no—
268Dic86—41no—
269Dic86—41no—
270Dic86—41no—
271Dic86—41no—
272Dic86—41no—
273Dic86—41no—
274Dic86—84no—
275C8×C43—41no—
276C8×C43—41no—
277C8×C43—41no—
278C8×C43—41no—
279#26726—431nomaximal, Sylow
280C22×C43—22no—
281C22×C43—22no—
282C22×C43—22no—
283C22×C43—41no—
284C22×C43—41no—
285C22×C43—41no—
286C22×C43—41no—
287C22×C43#52511yescharacteristic
288C22×C43#54611yescharacteristic
289C22×C43#54611yescharacteristic
290C22×C43C22×Q1611yescharacteristic
291C22×C43#57511yescharacteristic
292C22×C43#57711yescharacteristic
293C22×C43#57711yescharacteristic
294C4×C43—22no—
295C4×C43—22no—
296C4×C43—41no—
297C4×C43—41no—
298C4×C43—41no—
299C4×C43#52911yescharacteristic
300C4×C43#53811yescharacteristic
301C4×C43#55511yescharacteristic
302C4×C43#55911yescharacteristic
303Dic43—42no—
304Dic43—42no—
305Dic43—42no—
306Dic43—42no—
307Dic43—81no—
308Dic43—81no—
309Dic43—81no—
310Dic43—81no—
311#2492—431no—
312#2360—431no—
313#2056—431no—
314#2036—431no—
315#2024—431no—
316#2001—431no—
317#1987—431no—
318#1933—431no—
319#1928—431no—
320#1923D4311yescharacteristic
321#1921—431no—
322#1878—431no—
323#1872—431no—
324#1824—431no—
325C4×#103—431no—
326C2×C43—42no—
327C2×C43#245911yescharacteristic
328C2×C43#310411yescharacteristic
329C2×C43#312511yescharacteristic
330C2×C43#329911yescharacteristic
331C2×C43#329911yescharacteristic
332C2×C43#331111yescharacteristic
333C2×C43#332311yescharacteristic
334C22×Q16—431no—
335C2×C4⋊Q8—431no—
336C2×C22⋊Q8—431no—
337C2×C22⋊Q8—431no—
338C2×C4×Q8—431no—
339C22×C4⋊C4—431no—
340C2×#107—431no—
341C2×C4⋊C8C2×D4311yescharacteristic
342C2×#103—431no—
343C2×#103—431no—
344C2×#103—431no—
345C2×#103—431no—
346C2×#103—431no—
347C2×#103—431no—
348C2×C22⋊C8C2×D4311yescharacteristic
349C2×C22⋊C8C2×D4311yescharacteristic
350C2×C4×C8C2×D4311yescharacteristic
351#400—861no—
352#393—861no—
353#391—431no—
354#391—431no—
355#391—431no—
356#391—861no—
357#389—431no—
358#389—861no—
359#388—861no—
360#387—861no—
361#385—861no—
362#380—431no—
363C4×C4⋊C4—431no—
364C4×C4⋊C4—431no—
365C4×C22⋊C4—861no—
366C4×C22⋊C4C2×D4311yescharacteristic
367#340—431no—
368#340—431no—
369#340—431no—
370#340—431no—
371#340—431no—
372#340—431no—
373#340—431no—
374#340—431no—
375#336C2×D4311yescharacteristic
376#336C2×D4311yescharacteristic
377C43#2672611yescharacteristic, complemented, Sylow
378C22×Q8—431no—
379C22×Q8—431no—
380C22×Q8—861no—
381C23×C4—861no—
382C23×C4C22×D4311yescharacteristic
383C2×Q16—862no—
384C2×Q16—1721no—
385C2×Q16—1721no—
386C22×C8C22×D4311yescharacteristic
387C22×C8C22×D4311yescharacteristic
388C22×C8C22×D4311yescharacteristic
389C22×C8C22×D4311yescharacteristic
390C4⋊Q8—862no—
391C4⋊Q8—1721no—
392C22⋊Q8—862no—
393C22⋊Q8—862no—
394C22⋊Q8—862no—
395C22⋊Q8—1721no—
396C4×Q8—862no—
397C4×Q8—1721no—
398C2×C4⋊C4—431no—
399C2×C4⋊C4—431no—
400C2×C4⋊C4—431no—
401C2×C4⋊C4—431no—
402C2×C4⋊C4—431no—
403C2×C4⋊C4—431no—
404C2×C4⋊C4—862no—
405C2×C4⋊C4—861no—
406C2×C4⋊C4—861no—
407C2×C4⋊C4—861no—
408C2×C4⋊C4—861no—
409C2×C4⋊C4—861no—
410C2×C4⋊C4—861no—
411C2×C4⋊C4—1721no—
412C2×C22⋊C4—861no—
413C2×C22⋊C4—861no—
414C2×C22⋊C4—861no—
415C2×C22⋊C4D17211yescharacteristic
416C2×C22⋊C4D17211yescharacteristic
417C2×C42—861no—
418C2×C42—861no—
419C2×C42—861no—
420C2×C42C22×D4311yescharacteristic
421C2×C42C22×D4311yescharacteristic
422#107—862no—
423C4⋊C8—41no—
424#103—862no—
425#103—862no—
426#103—862no—
427#103—862no—
428#103—1721no—
429#103—1721no—
430C22⋊C8—41no—
431C22⋊C8—41no—
432C4×C8—41no—
433#95—861no—
434#95—861no—
435#95—861no—
436#95—861no—
437#95—861no—
438#95—861no—
439#95—861no—
440#95—861no—
441#95—861no—
442#95—861no—
443#95D17211yescharacteristic
444#95D17211yescharacteristic
445C24C2×D17211yescharacteristic
446C2×Q8—432no—
447C2×Q8—861no—
448C2×Q8—861no—
449C2×Q8—861no—
450C2×Q8—861no—
451C2×Q8—861no—
452C2×Q8—861no—
453C2×Q8—861no—
454C2×Q8—861no—
455C2×Q8—861no—
456C2×Q8—861no—
457C2×Q8—861no—
458C2×Q8—3441no—
459C2×Q8—1722no—
460C2×Q8—1722no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—861no—
468C22×C4—861no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4—861no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4—3441no—
476C22×C4—1722no—
477C22×C4—1722no—
478C22×C4C2×D17211yescharacteristic
479C22×C4C2×D17211yescharacteristic
480C22×C4C2×D17211yescharacteristic
481C22×C4C2×D17211yescharacteristic
482C22×C4C2×D17211yescharacteristic
483C22×C4C23×D4311yescharacteristic
484Q16—1724no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C4⋊C4—432no—
498C4⋊C4—432no—
499C4⋊C4—432no—
500C4⋊C4—864no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4—861no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C4⋊C4—861no—
509C4⋊C4—861no—
510C4⋊C4—3441no—
511C4⋊C4—1722no—
512C4⋊C4—1722no—
513C4⋊C4—1722no—
514C4⋊C4—1722no—
515C22⋊C4—41no—
516C22⋊C4—864no—
517C22⋊C4—3441no—
518C22⋊C4—1722no—
519C22⋊C4Dic17214yescomplemented
520C42—21no—
521C42—21no—
522C42—21no—
523C42—21no—
524C42—3441no—
525C42—3441no—
526C42—1722no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23C2×Dic17212yes—
534C23C22×D17211yescharacteristic
535Q8—862no—
536Q8—862no—
537Q8—3444no—
538Q8—1721no—
539Q8—1721no—
540Q8—1721no—
541Q8—1721no—
542Q8—1721no—
543Q8—1721no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—862no—
562C2×C4—862no—
563C2×C4—862no—
564C2×C4—862no—
565C2×C4—3444no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4—1721no—
578C2×C4—1721no—
579C2×C4—1721no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4C2×Dic17212yes—
587C2×C4C2×Dic17212yes—
588C2×C4#41×D4311yescharacteristic
589C2×C4#41×D4311yescharacteristic
590C2×C4#41×D4311yescharacteristic
591C2×C4#41×D4311yescharacteristic
592C2×C4#1306337011yescharacteristic
593C2×C4#1306337011yescharacteristic
594C8—41no—
595C8—41no—
596C8—41no—
597C8—41no—
598C22—22no—
599C22—22no—
600C22—22no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22#1458341111yescharacteristic
606C22#1458354411yescharacteristic
607C22#1458354411yescharacteristic
608C22C22×Dic17211yescharacteristic
609C22#1458369911yescharacteristic
610C22#1458371111yescharacteristic
611C22#1458371111yescharacteristic
612C4—22no—
613C4—22no—
614C4—41no—
615C4—41no—
616C4—41no—
617C4—3441no—
618C4—3441no—
619C4—3441no—
620C4—3441no—
621C4—1722no—
622C4—1722no—
623C4—1722no—
624C4—1722no—
625C4#1458343211yescharacteristic
626C4#1458348111yescharacteristic
627C4#1458361111yescharacteristic
628C4#1458363311yescharacteristic
629C2—42no—
630C2#1913853011yescharacteristic
631C2#1914463511yescharacteristic
632C2#1914487411yescharacteristic
633C2#1914647211yescharacteristic
634C2#1914647211yescharacteristic
635C2#1914663311yescharacteristic
636C2#1914681311yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1923C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenter#1923D43
hypocenterC43#26726
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
3. #19135918C2semidirect
5. #19135737C2semidirect
7. #19135542C2semidirect
8. #19135271C2semidirect
9. #19135237C2semidirect
10. #19135188C2semidirect
11. #19134935C2semidirect
14. C4×#13063250C2semidirect
178. C22⋊C4×C43Q16semidirect
377. C43#26726semidirect
519. C22⋊C4Dic172semidirect

Maximal subgroups

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

subgroupindex
#191389692
#191375982
#191359182
#191357992
#191357372
#191356052
#191355422
#191352712
#191352372
#191351882
#191349352
#191349002
#191346862
C4×#130632502
C43×#19232
#2672643