Finite Group Databasebeta

← #25116457

Subgroups — #25116457

Order 11008.

810 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583001C211yesmaximal, characteristic
2#19137566C211yesmaximal, characteristic
3#19137550C211yesmaximal, characteristic, complemented
4#19135476C211yesmaximal, characteristic
5#19135449C211yesmaximal, characteristic
6#19135237C211yesmaximal, characteristic, complemented
7#19135230C211yesmaximal, characteristic, complemented
8#19135223C211yesmaximal, characteristic
9#19135216C211yesmaximal, characteristic
10#19134763C211yesmaximal, characteristic, complemented
11#19134611C211yesmaximal, characteristic, complemented
12#19134596C211yesmaximal, characteristic
13#19134492C211yesmaximal, characteristic, complemented
14C4×#13063259C211yesmaximal, characteristic, complemented
15C43×#1771C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C2×C4×Dic86C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19#14583001C418yescomplemented
20C2×#13063259C2211yescharacteristic
21C2×#13063259C2211yescharacteristic
22C2×#13063259C2211yescharacteristic
23C2×#13063257C2211yescharacteristic
24C2×#13063257C2211yescharacteristic
25C2×#13063250C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063250C2211yescharacteristic
28C2×#13063247C2211yescharacteristic
29C2×#13063247C2211yescharacteristic
30C2×#13063247C2211yescharacteristic
31#14582805C2211yescharacteristic
32#14582805C2211yescharacteristic
33#14582801C2211yescharacteristic
34#14582801C2211yescharacteristic
35#14582789—21no—
36#14582789—21no—
37#14582786—21no—
38#14582786—21no—
39#14582769C2211yescharacteristic
40#14582765C2211yescharacteristic
41#14582764—21no—
42#14582761—21no—
43C4⋊C4×Dic43—21no—
44C4×C4⋊Dic43C2211yescharacteristic
45C4×C4⋊Dic43C2211yescharacteristic
46C4×C4⋊Dic43C2211yescharacteristic
47C4×C4⋊Dic43C2211yescharacteristic
48#14582746—21no—
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53C2×C4⋊C8×C43C2211yescharacteristic
54C2×#97×C43C2211yescharacteristic
55C2×#97×C43C2211yescharacteristic
56C2×C4×C8×C43C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C22×Dic86C2311yescharacteristic
61C22×D172C2311yescharacteristic
62C22×C4×D43—21no—
63C2×#10621873—22no—
64C2×#10621873—22no—
65C2×#10621873C2×C414yes—
66C4×Dic86—22no—
67C4×Dic86C2×C414yes—
68C4×D172—22no—
69C4×D172C2×C414yes—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×Dic43⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43—21no—
89#13063259—22no—
90#13063259—41no—
91#13063259C2×C414yes—
92#13063257—22no—
93#13063257—41no—
94#13063250—41no—
95#13063250—41no—
96#13063250C2×C414yes—
97#13063247—41no—
98#13063247—41no—
99#13063247C2×C414yes—
100C43⋊#95—21no—
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—
110C22×C8×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C2×C4⋊C4×C43D411yescharacteristic
115C2×C4⋊C4×C43D411yescharacteristic
116C2×C42×C43C2311yescharacteristic
117C2×C42×C43C2311yescharacteristic
118C2×C42×C43C2311yescharacteristic
119C4⋊C8×C43—22no—
120#97×C43—22no—
121#97×C43C2×C414yes—
122C4×C8×C43—22no—
123#95×C43D411yescharacteristic
124#95×C43D411yescharacteristic
125C23×D43—21no—
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2411yescharacteristic
133C22×Dic43—21no—
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×D172C22×C412yes—
146C2×C4×D43—24no—
147C2×C4×D43—81no—
148C2×C4×D43—81no—
149C2×Dic86—21no—
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86C22×C412yes—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43C22×C412yes—
164C2×C8×C43C22×C412yes—
165C2×C8×C43#4112yes—
166C2×C8×C43#4112yes—
167C4⋊C4×C43—22no—
168C4⋊C4×C43—41no—
169C42×C43—21no—
170C42×C43—21no—
171C42×C43—21no—
172C42×C43—21no—
173C42×C43C22×C412yes—
174C42×C43#4112yes—
175(C2×D43)⋊C4—24no—
176(C2×D43)⋊C4—42no—
177(C2×D43)⋊C4—42no—
178(C2×D43)⋊C4—81no—
179(C2×D43)⋊C4—81no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—42no—
191C4⋊Dic43—81no—
192C4⋊Dic43C22×C412yes—
193C4⋊Dic43C22×C412yes—
194Dic43⋊C4—24no—
195C4×Dic43—24no—
196C4×Dic43—81no—
197C4×Dic43—81no—
198C4×Dic43—81no—
199C4×Dic43—81no—
200#10621873—28no—
201C23×C43C22×D411yescharacteristic
202C22×D43—22no—
203C22×D43—41no—
204C22×D43—41no—
205C22×D43—41no—
206C22×D43—41no—
207C22×D43—41no—
208C22×D43—41no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
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×C43C4×D412yes—
225C2×C4×C43C4×D412yes—
226C2×C4×C43#13712yes—
227C2×C4×C43C23×C411yescharacteristic
228C2×C4×C43C2×#4111yescharacteristic
229C2×C4×C43C2×#4111yescharacteristic
230C2×C4×C43C2×#4111yescharacteristic
231C2×C4×C43H(5,𝔽2)11yescharacteristic
232C2×C4×C432−1+411yescharacteristic
233C2×Dic43—22no—
234C2×Dic43—22no—
235C2×Dic43—22no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
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—
254D172—22no—
255D172—22no—
256D172—41no—
257D172—41no—
258C4×D43—84no—
259Dic86—22no—
260Dic86—22no—
261Dic86—41no—
262Dic86—41no—
263C8×C43—22no—
264C8×C43—41no—
265C8×C43—41no—
266C8×C43#11714yes—
267#22819—431nomaximal, Sylow
268C22×C43C2×C4×D411yescharacteristic
269C22×C43#54711yescharacteristic
270C22×C43#55011yescharacteristic
271C22×C43C2×#13711yescharacteristic
272C22×C43#57511yescharacteristic
273C22×C43#57611yescharacteristic
274C22×C43#57711yescharacteristic
275C2×D43—42no—
276C2×D43—42no—
277C2×D43—42no—
278C2×D43—81no—
279C2×D43—81no—
280C2×D43—81no—
281C2×D43—81no—
282C4×C43—22no—
283C4×C43—22no—
284C4×C43—22no—
285C4×C43—41no—
286C4×C43—41no—
287C4×C43—41no—
288C4×C43C2×#11711yescharacteristic
289C4×C43#52011yescharacteristic
290C4×C43#55511yescharacteristic
291C4×C43#55611yescharacteristic
292Dic43—42no—
293Dic43—42no—
294Dic43—42no—
295Dic43—81no—
296Dic43—81no—
297Dic43—81no—
298Dic43—81no—
299C2×#440—431no—
300#2357—431no—
301#2355—431no—
302#1973—431no—
303#1968—431no—
304#1928—431no—
305#1927—431no—
306#1926—431no—
307#1925—431no—
308#1847—431no—
309#1805—431no—
310#1802—431no—
311#1776—431no—
312C4×#107—431no—
313#1771D4311yescharacteristic, complemented
314C2×C43#235411yescharacteristic
315C2×C43C4×#13711yescharacteristic
316C2×C43#294611yescharacteristic
317C2×C43#334611yescharacteristic
318C2×C43#335011yescharacteristic
319C2×C43#340011yescharacteristic
320C2×C43#340311yescharacteristic
321D43—82no—
322C22×SD16—431no—
323C2×C4×Q8—431no—
324C2×C4×D4—431no—
325#440—438no—
326C2×#107—431no—
327C2×#107—431no—
328C2×#107—431no—
329C2×#106—431no—
330C2×#106—431no—
331C2×C4⋊C8C2×D4311yescharacteristic
332C2×#103—431no—
333C2×#103—431no—
334C2×#103—431no—
335C2×#102—431no—
336C2×#102—431no—
337C2×#102—431no—
338C2×#97C2×D4311yescharacteristic
339C2×#97C2×D4311yescharacteristic
340C2×C4×C8C2×D4311yescharacteristic
341#391—431no—
342#391—431no—
343#390—431no—
344#390—431no—
345#388—861no—
346#388—861no—
347#387—861no—
348#387—861no—
349#384—431no—
350#382—431no—
351#382—861no—
352#381—861no—
353C4×C4⋊C4—431no—
354C4×C4⋊C4—431no—
355C4×C4⋊C4—431no—
356C4×C4⋊C4—431no—
357C4×C4⋊C4—861no—
358C4×C4⋊C4C2×D4311yescharacteristic
359C4×C22⋊C4—861no—
360#340—431no—
361#340—431no—
362#340—431no—
363#340—431no—
364#336C2×D4311yescharacteristic
365#336C2×D4311yescharacteristic
366C43#2281911yescharacteristic, complemented, Sylow
367C22×Q8—431no—
368C22×D4—431no—
369C23×C4—861no—
370C2×SD16—434no—
371C2×SD16—862no—
372C2×SD16—862no—
373C22×C8C22×D4311yescharacteristic
374C22×C8C22×D4311yescharacteristic
375C22×C8C22×D4311yescharacteristic
376C22×C8C22×D4311yescharacteristic
377C4×Q8—434no—
378C4×Q8—862no—
379C4×D4—434no—
380C4×D4—862no—
381C2×C4⋊C4—431no—
382C2×C4⋊C4—431no—
383C2×C4⋊C4—431no—
384C2×C4⋊C4—431no—
385C2×C4⋊C4—431no—
386C2×C4⋊C4—431no—
387C2×C4⋊C4—861no—
388C2×C4⋊C4—861no—
389C2×C4⋊C4—861no—
390C2×C4⋊C4D17211yescharacteristic
391C2×C4⋊C4D17211yescharacteristic
392C2×C22⋊C4—861no—
393C2×C22⋊C4—861no—
394C2×C22⋊C4—861no—
395C2×C22⋊C4—861no—
396C2×C22⋊C4—861no—
397C2×C42—861no—
398C2×C42—861no—
399C2×C42—861no—
400C2×C42—861no—
401C2×C42—861no—
402C2×C42C22×D4311yescharacteristic
403C2×C42C22×D4311yescharacteristic
404C2×C42C22×D4311yescharacteristic
405#107—434no—
406#107—862no—
407#107—1721no—
408#106—862no—
409#106—1721no—
410C4⋊C8—22no—
411#103—434no—
412#103—1721no—
413#103—1721no—
414#102—434no—
415#102—1721no—
416#102—1721no—
417#97—22no—
418#97C4×D4314yes—
419C4×C8—22no—
420#95—861no—
421#95—861no—
422#95—861no—
423#95—861no—
424#95—861no—
425#95—861no—
426#95—861no—
427#95—861no—
428#95—861no—
429#95—861no—
430#95D17211yescharacteristic
431#95D17211yescharacteristic
432C24—861no—
433C2×Q8—432no—
434C2×Q8—861no—
435C2×Q8—861no—
436C2×Q8—861no—
437C2×Q8—861no—
438C2×Q8—861no—
439C2×D4—432no—
440C2×D4—861no—
441C2×D4—861no—
442C2×D4—861no—
443C2×D4—861no—
444C2×D4—861no—
445C22×C4—861no—
446C22×C4—861no—
447C22×C4—861no—
448C22×C4—864no—
449C22×C4—861no—
450C22×C4—861no—
451C22×C4—861no—
452C22×C4—861no—
453C22×C4—3441no—
454C22×C4—3441no—
455C22×C4C2×D17211yescharacteristic
456C22×C4C2×D17211yescharacteristic
457C22×C4C2×D17211yescharacteristic
458C22×C4C2×D17211yescharacteristic
459C22×C4C2×D17211yescharacteristic
460C22×C4C2×D17211yescharacteristic
461C22×C4C23×D4311yescharacteristic
462SD16—868no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8C2×C4×D4312yes—
472C2×C8C2×C4×D4312yes—
473C2×C8#1062190012yes—
474C2×C8#1062190212yes—
475C4⋊C4—22no—
476C4⋊C4—41no—
477C4⋊C4—432no—
478C4⋊C4—432no—
479C4⋊C4—864no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—3441no—
491C4⋊C4—1722no—
492C22⋊C4—864no—
493C22⋊C4—3441no—
494C22⋊C4—3441no—
495C22⋊C4—1722no—
496C22⋊C4—1722no—
497C42—21no—
498C42—21no—
499C42—21no—
500C42—21no—
501C42—864no—
502C42—3441no—
503C42—3441no—
504C42—3441no—
505C42—3441no—
506C42C2×C4×D4312yes—
507C42#1062189812yes—
508C23—862no—
509C23—1721no—
510C23—1721no—
511C23—1721no—
512C23—1721no—
513C23—1721no—
514C23—1721no—
515C23C22×D17211yescharacteristic
516Q8—862no—
517Q8—862no—
518Q8—1721no—
519Q8—1721no—
520D4—862no—
521D4—862no—
522D4—1721no—
523D4—1721no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—862no—
540C2×C4—862no—
541C2×C4—862no—
542C2×C4—3444no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4—1721no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4C4×D17212yes—
562C2×C4C4×D17212yes—
563C2×C4#1306335812yes—
564C2×C4C22×C4×D4311yescharacteristic
565C2×C4C2×#1062190011yescharacteristic
566C2×C4C2×#1062189811yescharacteristic
567C2×C4C2×#1062190211yescharacteristic
568C2×C4#1306337111yescharacteristic
569C2×C4#1306337211yescharacteristic
570C8—22no—
571C8—41no—
572C8—41no—
573C8#1306328314yes—
574C22—3441no—
575C22—3441no—
576C22—3441no—
577C22—3441no—
578C22—1722no—
579C22—1722no—
580C22—1722no—
581C22C2×C4×D17211yescharacteristic
582C22#1458355311yescharacteristic
583C22#1458357111yescharacteristic
584C22C2×#1306335811yescharacteristic
585C22#1458369911yescharacteristic
586C22#1458370411yescharacteristic
587C22#1458371111yescharacteristic
588C4—22no—
589C4—22no—
590C4—22no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—3441no—
595C4—3441no—
596C4—3441no—
597C4—3441no—
598C4—1722no—
599C4—1722no—
600C4—1722no—
601C4C2×#1306328311yescharacteristic
602C4#1458337911yescharacteristic
603C4#1458361411yescharacteristic
604C4#1458362211yescharacteristic
605C2—3442no—
606C2#1913754211yescharacteristic
607C2C4×#1306335811yescharacteristic
608C2#1914342911yescharacteristic
609C2#1914708211yescharacteristic
610C2#1914714211yescharacteristic
611C2#1914765011yescharacteristic
612C2#1914768511yescharacteristic
subgroupG/H
centerC23C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1771C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenter#1771D43
hypocenterC43#22819
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1771

Complements

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

NH ≅ G/Ntype
3. #19137550C2semidirect
6. #19135237C2semidirect
7. #19135230C2semidirect
10. #19134763C2semidirect
11. #19134611C2semidirect
13. #19134492C2semidirect
14. C4×#13063259C2semidirect
15. C43×#1771C2semidirect
19. #14583001C4semidirect
313. #1771D43semidirect
366. C43#22819semidirect

Maximal subgroups

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

subgroupindex
C2×#145830012
#191375662
#191375502
#191354762
#191354492
#191352372
#191352302
#191352232
#191352162
#191347632
#191346112
#191345962
#191344922
C4×#130632592
C43×#17712
#2281943