Finite Group Databasebeta

← #25104595

Subgroups — #25104595

Order 11008.

818 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583254C211yesmaximal, characteristic
2#19137336C211yesmaximal, characteristic, complemented
3#19137306C211yesmaximal, characteristic
4#19135564C211yesmaximal, characteristic, complemented
5#19135411C211yesmaximal, characteristic
6#19135292C211yesmaximal, characteristic
7#19135285C211yesmaximal, characteristic, complemented
8#19135278C211yesmaximal, characteristic
9#19135271C211yesmaximal, characteristic, complemented
10#19134723C211yesmaximal, characteristic, complemented
11#19134426C211yesmaximal, characteristic, complemented
12#19134421C211yesmaximal, characteristic
13C4×#13063250C211yesmaximal, characteristic, complemented
14C4×#13063247C211yesmaximal, characteristic
15C43×#1726C211yesmaximal, characteristic, complemented
16C2×#13063317C2211yescharacteristic
17C2×#13063313C2211yescharacteristic
18C2×C4×Dic86C2211yescharacteristic
19C2×C4×D172C2211yescharacteristic
20#14583254C418yescomplemented
21C2×#13063250C2211yescharacteristic
22C2×#13063250C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063247C2211yescharacteristic
29#14582805C2211yescharacteristic
30#14582801C2211yescharacteristic
31#14582797C2211yescharacteristic
32#14582797C2211yescharacteristic
33#14582796—21no—
34#14582796—21no—
35#14582791—21no—
36#14582791—21no—
37#14582786—21no—
38#14582786—21no—
39#14582773—21no—
40#14582773—21no—
41#14582769C2211yescharacteristic
42#14582769C2211yescharacteristic
43C4×C4⋊Dic43C2211yescharacteristic
44C4×C4⋊Dic43C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53C2×#97×C43C2211yescharacteristic
54C2×#97×C43C2211yescharacteristic
55C2×#97×C43C2211yescharacteristic
56C2×C4×C8×C43C2211yescharacteristic
57C2×C4×C8×C43C2211yescharacteristic
58C2×C4×C8×C43C2211yescharacteristic
59C43×#376C2211yescharacteristic
60C22×Dic86C2311yescharacteristic
61C22×D172C2311yescharacteristic
62C22×C4×D43—21no—
63#13063317—22no—
64#13063317C2×C414yescomplemented
65#13063313—22no—
66#13063313C2×C414yes—
67C4×Dic86—22no—
68C4×Dic86—22no—
69C4×D172—22no—
70C4×D172—22no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
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×(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×C4×Dic43—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43—21no—
94#13063250—22no—
95#13063250—22no—
96#13063250C2×C414yescomplemented
97#13063250C2×C414yescomplemented
98#13063247—22no—
99#13063247—22no—
100#13063247C2×C414yes—
101#13063247C2×C414yes—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C22×C8×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110C22×C8×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112C2×C42×C43C2311yescharacteristic
113C2×C42×C43C2311yescharacteristic
114C2×C42×C43C2311yescharacteristic
115#97×C43—22no—
116#97×C43—22no—
117#97×C43—22no—
118C4×C8×C43—22no—
119C4×C8×C43—22no—
120C4×C8×C43C2×C414yescomplemented
121#95×C43D411yescharacteristic
122#95×C43D411yescharacteristic
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—42no—
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—
167C42×C43—21no—
168C42×C43—21no—
169C42×C43C22×C412yes—
170C42×C43#4112yes—
171C42×C43#4112yes—
172C42×C43#4112yes—
173(C2×D43)⋊C4—24no—
174(C2×D43)⋊C4—24no—
175(C2×D43)⋊C4—42no—
176(C2×D43)⋊C4—81no—
177(C2×D43)⋊C4—81no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
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—81no—
189C4⋊Dic43—81no—
190C4⋊Dic43—81no—
191C4⋊Dic43—81no—
192C4⋊Dic43C22×C412yes—
193C4⋊Dic43C22×C412yes—
194Dic43⋊C4—24no—
195Dic43⋊C4—24no—
196Dic43⋊C4—42no—
197Dic43⋊C4—81no—
198Dic43⋊C4—81no—
199C4×Dic43—42no—
200C4×Dic43—81no—
201C4×Dic43—81no—
202C23×C43C22×D411yescharacteristic
203C22×D43—22no—
204C22×D43—41no—
205C22×D43—41no—
206C22×D43—41no—
207C22×D43—41no—
208C22×D43—41no—
209C22×D43—41no—
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#12412yes—
227C2×C4×C43#12412yes—
228C2×C4×C43C23×C411yescharacteristic
229C2×C4×C43C2×#4111yescharacteristic
230C2×C4×C43C2×#4111yescharacteristic
231C2×C4×C43C2×#4111yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C2×Dic43—22no—
235C2×Dic43—22no—
236C2×Dic43—22no—
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—
254C2×Dic43—41no—
255D172—22no—
256D172—22no—
257D172—41no—
258D172—41no—
259C4×D43—84no—
260Dic86—22no—
261Dic86—22no—
262Dic86—41no—
263Dic86—41no—
264C8×C43—22no—
265C8×C43—22no—
266C8×C43—22no—
267C8×C43—22no—
268#21643—431nomaximal, Sylow
269C22×C43C2×C4×D411yescharacteristic
270C22×C43C2×#12411yescharacteristic
271C22×C43#53211yescharacteristic
272C22×C43#57611yescharacteristic
273C22×C43#57711yescharacteristic
274C22×C43#57711yescharacteristic
275C22×C43#57811yescharacteristic
276C2×D43—42no—
277C2×D43—42no—
278C2×D43—42no—
279C2×D43—81no—
280C2×D43—81no—
281C2×D43—81no—
282C2×D43—81no—
283C4×C43—22no—
284C4×C43—22no—
285C4×C43—22no—
286C4×C43—22no—
287C4×C43—41no—
288C4×C43—41no—
289C4×C43C4×#4111yescharacteristic
290C4×C43C4×#4111yescharacteristic
291C4×C43#52911yescharacteristic
292C4×C43#52911yescharacteristic
293Dic43—42no—
294Dic43—42no—
295Dic43—42no—
296Dic43—81no—
297Dic43—81no—
298Dic43—81no—
299Dic43—81no—
300C2×#488—431no—
301#2330—431no—
302#2326—431no—
303#1992—431no—
304#1959—431no—
305#1936—431no—
306#1935—431no—
307#1934—431no—
308#1933—431no—
309#1834—431no—
310#1763—431no—
311#1762—431no—
312C4×#103—431no—
313C4×#102—431no—
314#1726D4311yescharacteristic, complemented
315C2×C43C4×#12411yescharacteristic
316C2×C43#295111yescharacteristic
317C2×C43#295211yescharacteristic
318C2×C43#313611yescharacteristic
319C2×C43#313711yescharacteristic
320C2×C43#317811yescharacteristic
321C2×C43#317911yescharacteristic
322D43—82no—
323C2×#125—431no—
324C2×#124—431no—
325C2×C4×Q8—431no—
326C2×C4×D4—431no—
327#488—438no—
328C2×#103—431no—
329C2×#103—431no—
330C2×#103—431no—
331C2×#103—431no—
332C2×#102—431no—
333C2×#102—431no—
334C2×#102—431no—
335C2×#102—431no—
336C2×#97C2×D4311yescharacteristic
337C2×#97C2×D4311yescharacteristic
338C2×#97C2×D4311yescharacteristic
339C2×C4×C8C2×D4311yescharacteristic
340C2×C4×C8C2×D4311yescharacteristic
341C2×C4×C8C2×D4311yescharacteristic
342#391—431no—
343#390—431no—
344#389—431no—
345#389—431no—
346#389—861no—
347#389—861no—
348#388—861no—
349#388—861no—
350#387—861no—
351#387—861no—
352#385—861no—
353#385—861no—
354#384—431no—
355#384—431no—
356C4×C4⋊C4—431no—
357C4×C4⋊C4—431no—
358#376C2×D4311yescharacteristic
359#340—431no—
360#340—431no—
361#340—431no—
362#340—431no—
363#340—431no—
364#340—431no—
365#340—431no—
366#340—431no—
367C43#2164311yescharacteristic, complemented, Sylow
368C22×Q8—431no—
369C22×D4—431no—
370C23×C4—861no—
371C22×C8C22×D4311yescharacteristic
372C22×C8C22×D4311yescharacteristic
373C22×C8C22×D4311yescharacteristic
374C22×C8C22×D4311yescharacteristic
375#125—434no—
376#125—862no—
377#124—434no—
378#124—862no—
379C4×Q8—862no—
380C4×Q8—862no—
381C4×D4—862no—
382C4×D4—862no—
383C2×C4⋊C4—431no—
384C2×C4⋊C4—431no—
385C2×C4⋊C4—431no—
386C2×C4⋊C4—431no—
387C2×C4⋊C4—431no—
388C2×C4⋊C4—431no—
389C2×C4⋊C4—861no—
390C2×C4⋊C4—861no—
391C2×C4⋊C4—861no—
392C2×C4⋊C4—861no—
393C2×C4⋊C4—861no—
394C2×C4⋊C4—861no—
395C2×C4⋊C4—861no—
396C2×C4⋊C4—861no—
397C2×C4⋊C4—861no—
398C2×C22⋊C4—861no—
399C2×C22⋊C4—861no—
400C2×C22⋊C4—861no—
401C2×C22⋊C4—861no—
402C2×C22⋊C4—861no—
403C2×C42—861no—
404C2×C42—861no—
405C2×C42—861no—
406C2×C42C22×D4311yescharacteristic
407C2×C42C22×D4311yescharacteristic
408C2×C42C22×D4311yescharacteristic
409#103—434no—
410#103—434no—
411#103—862no—
412#103—862no—
413#102—434no—
414#102—434no—
415#102—862no—
416#102—862no—
417#97—22no—
418#97—22no—
419#97—22no—
420C4×C8—22no—
421C4×C8—22no—
422C4×C8C4×D4314yescomplemented
423#95—861no—
424#95—861no—
425#95—861no—
426#95—861no—
427#95—861no—
428#95—861no—
429#95D17211yescharacteristic
430#95D17211yescharacteristic
431#95D17211yescharacteristic
432#95D17211yescharacteristic
433C24—861no—
434C2×Q8—432no—
435C2×Q8—861no—
436C2×Q8—861no—
437C2×Q8—861no—
438C2×Q8—861no—
439C2×Q8—861no—
440C2×D4—432no—
441C2×D4—861no—
442C2×D4—861no—
443C2×D4—861no—
444C2×D4—861no—
445C2×D4—861no—
446C22×C4—861no—
447C22×C4—861no—
448C22×C4—861no—
449C22×C4—861no—
450C22×C4—861no—
451C22×C4—861no—
452C22×C4—861no—
453C22×C4—3441no—
454C22×C4—3441no—
455C22×C4—1722no—
456C22×C4C2×D17211yescharacteristic
457C22×C4C2×D17211yescharacteristic
458C22×C4C2×D17211yescharacteristic
459C22×C4C2×D17211yescharacteristic
460C22×C4C2×D17211yescharacteristic
461C22×C4C2×D17211yescharacteristic
462C22×C4C23×D4311yescharacteristic
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#1062189812yes—
474C2×C8#1062189812yes—
475C4⋊C4—432no—
476C4⋊C4—432no—
477C4⋊C4—864no—
478C4⋊C4—864no—
479C4⋊C4—861no—
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—3441no—
490C4⋊C4—3441no—
491C4⋊C4—3441no—
492C4⋊C4—3441no—
493C4⋊C4—3441no—
494C4⋊C4—3441no—
495C4⋊C4—1722no—
496C22⋊C4—864no—
497C22⋊C4—864no—
498C22⋊C4—3441no—
499C22⋊C4—3441no—
500C22⋊C4—1722no—
501C42—21no—
502C42—21no—
503C42—3441no—
504C42—3441no—
505C42—1722no—
506C42C2×C4×D4312yes—
507C42#1062189812yes—
508C42#1062189812yes—
509C42#1062189812yes—
510C23—862no—
511C23—1721no—
512C23—1721no—
513C23—1721no—
514C23—1721no—
515C23—1721no—
516C23—1721no—
517C23C22×D17211yescharacteristic
518Q8—862no—
519Q8—862no—
520Q8—1721no—
521Q8—1721no—
522D4—862no—
523D4—862no—
524D4—1721no—
525D4—1721no—
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—21no—
540C2×C4—862no—
541C2×C4—862no—
542C2×C4—862no—
543C2×C4—3444no—
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×C4—1721no—
562C2×C4C4×D17212yes—
563C2×C4C4×D17212yes—
564C2×C4#1306331312yes—
565C2×C4#1306331312yes—
566C2×C4C22×C4×D4311yescharacteristic
567C2×C4C2×#1062189811yescharacteristic
568C2×C4C2×#1062189811yescharacteristic
569C2×C4C2×#1062189811yescharacteristic
570C2×C4C2×#1062189811yescharacteristic
571C2×C4C2×#1062189811yescharacteristic
572C8—22no—
573C8—22no—
574C8—22no—
575C8—22no—
576C22—3441no—
577C22—3441no—
578C22—3441no—
579C22—3441no—
580C22—1722no—
581C22—1722no—
582C22—1722no—
583C22C2×C4×D17211yescharacteristic
584C22C2×#1306331311yescharacteristic
585C22#1458344911yescharacteristic
586C22#1458370411yescharacteristic
587C22#1458371111yescharacteristic
588C22#1458371111yescharacteristic
589C22#1458371611yescharacteristic
590C4—22no—
591C4—22no—
592C4—22no—
593C4—22no—
594C4—41no—
595C4—41no—
596C4—3441no—
597C4—3441no—
598C4—3441no—
599C4—3441no—
600C4—1722no—
601C4—1722no—
602C4—1722no—
603C4C4×#1062189811yescharacteristic
604C4C4×#1062189811yescharacteristic
605C4#1458343311yescharacteristic
606C4#1458343311yescharacteristic
607C2—3442no—
608C2C4×#1306331311yescharacteristic
609C2#1914347211yescharacteristic
610C2#1914348011yescharacteristic
611C2#1914495111yescharacteristic
612C2#1914496211yescharacteristic
613C2#1914526311yescharacteristic
614C2#1914527811yescharacteristic
subgroupG/H
centerC23C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1726C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenter#1726D43
hypocenterC43#21643
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ #376 ◁ #1726

Complements

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

NH ≅ G/Ntype
2. #19137336C2semidirect
4. #19135564C2semidirect
7. #19135285C2semidirect
9. #19135271C2semidirect
10. #19134723C2semidirect
11. #19134426C2semidirect
13. C4×#13063250C2semidirect
15. C43×#1726C2semidirect
20. #14583254C4semidirect
64. #13063317C2×C4semidirect
96. #13063250C2×C4semidirect
97. #13063250C2×C4semidirect
120. C4×C8×C43C2×C4semidirect
314. #1726D43semidirect
367. C43#21643semidirect
422. C4×C8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145832542
#191373362
#191373062
#191355642
#191354112
#191352922
#191352852
#191352782
#191352712
#191347232
#191344262
#191344212
C4×#130632502
C4×#130632472
C43×#17262
#2164343