Finite Group Databasebeta

← #25138044

Subgroups — #25138044

Order 11008.

738 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×#14583208C211yesmaximal, characteristic, complemented
2C2×#14582961C211yesmaximal, characteristic
3#19140430C211yesmaximal, characteristic
4#19137280C211yesmaximal, characteristic
5#19136034C211yesmaximal, characteristic
6#19136025C211yesmaximal, characteristic
7#19135790C211yesmaximal, characteristic
8#19135789C211yesmaximal, characteristic
9#19135551C211yesmaximal, characteristic, complemented
10#19135357C211yesmaximal, characteristic, complemented
11#19135338C211yesmaximal, characteristic, complemented
12#19135320C211yesmaximal, characteristic, complemented
13#19135274C211yesmaximal, characteristic, complemented
14#19134598C211yesmaximal, characteristic, complemented
15C43×#1935C211yesmaximal, characteristic, complemented
16C2×#13063316C2211yescharacteristic
17C2×#13063301C2211yescharacteristic
18C2×Q8×Dic43C2211yescharacteristic
19C2×#13063282C2211yescharacteristic
20#14583208—24no—
21#14582961—24no—
22C2×#13063259C2211yescharacteristic
23C2×#13063257C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×Dic43⋊C8C2211yescharacteristic
27C2×Dic43⋊C8C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×#13063249C2211yescharacteristic
30C2×(C2×D43)⋊C8C2211yescharacteristic
31C2×(C2×D43)⋊C8C2211yescharacteristic
32C2×C4×C43⋊C8C2211yescharacteristic
33#14582833—21no—
34#14582830—21no—
35#14582823—21no—
36#14582821—21no—
37#14582797C2211yescharacteristic
38#14582797C2211yescharacteristic
39#14582796—21no—
40#14582791—21no—
41#14582788—21no—
42#14582781—21no—
43#14582768C2211yescharacteristic
44#14582756C2211yescharacteristic
45#14582756C2211yescharacteristic
46#14582756C2211yescharacteristic
47C4⋊C4×Dic43C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C2×#97×C43C2211yescharacteristic
57C43×#391C2211yescharacteristic
58C43×#389C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×C4×D43C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64#13063316—22no—
65#13063316—22no—
66#13063301—22no—
67#13063301—22no—
68Q8×Dic43—22no—
69Q8×Dic43—22no—
70#13063282—22no—
71#13063282—22no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4D411yescharacteristic
85C2×Dic43⋊C4D411yescharacteristic
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4D411yescharacteristic
91C2×(C2×D43)⋊C4D411yescharacteristic
92C2×C4×Dic43—21no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43C2311yescharacteristic
95#13063259—22no—
96#13063257—22no—
97#13063256—22no—
98#13063256—22no—
99Dic43⋊C8—22no—
100Dic43⋊C8D414yes—
101#13063249—22no—
102#13063249—22no—
103(C2×D43)⋊C8—22no—
104(C2×D43)⋊C8—22no—
105C4×C43⋊C8—22no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C22×Q8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C2×C4⋊C4×C43—21no—
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C42×C43C2311yescharacteristic
120#103×C43—22no—
121#103×C43—22no—
122#97×C43—22no—
123#95×C43—21no—
124#95×C43—21no—
125#95×C43—21no—
126C23×D43C2×D411yescharacteristic
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43#4112yes—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2411yescharacteristic
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43C2×D411yescharacteristic
145C22×Dic43C2×D411yescharacteristic
146C22×Dic43C2×D411yescharacteristic
147C2×C4×D43—21no—
148C2×C4×D43—21no—
149C2×C4×D43—21no—
150C2×C4×D43—21no—
151C2×C4×D43—21no—
152C2×C4×D43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43C2×D412yes—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—81no—
166C42×C43—21no—
167C42×C43—21no—
168(C2×D43)⋊C4—24no—
169(C2×D43)⋊C4—22no—
170(C2×D43)⋊C4—22no—
171(C2×D43)⋊C4—81no—
172(C2×D43)⋊C4—81no—
173(C2×D43)⋊C4—81no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—42no—
182C4⋊Dic43—42no—
183C4⋊Dic43#4112yes—
184Dic43⋊C4—24no—
185Dic43⋊C4—22no—
186Dic43⋊C4—22no—
187Dic43⋊C4—42no—
188Dic43⋊C4—81no—
189Dic43⋊C4—81no—
190Dic43⋊C4—81no—
191Dic43⋊C4—81no—
192C4×Dic43—42no—
193C4×Dic43—81no—
194C4×Dic43C2×D412yes—
195C4×Dic43#4112yes—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8C2×D412yes—
202C23×C43C22×D411yescharacteristic
203C22×D43—21no—
204C22×D43—21no—
205C22×D43—21no—
206C22×D43—21no—
207C22×D43—21no—
208C22×D43—21no—
209C22×D43—21no—
210Q8×C43—22no—
211Q8×C43—22no—
212Q8×C43—41no—
213Q8×C43—41no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—22no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43C22×D411yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×C4×C432−1+411yescharacteristic
237C2×C4×C432−1+411yescharacteristic
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—22no—
245C2×Dic43—21no—
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#12112yes—
258C2×Dic43#12112yes—
259C4×D43—41no—
260C4×D43—41no—
261C4×D43—41no—
262C4×D43—41no—
263C8×C43—22no—
264C8×C43—41no—
265C43⋊C8—22no—
266C43⋊C8—41no—
267#24719—431nomaximal, Sylow
268C22×C43C2×#12111yescharacteristic
269C22×C43#52511yescharacteristic
270C22×C43#53611yescharacteristic
271C22×C43#57711yescharacteristic
272C22×C43#57711yescharacteristic
273C22×C43#57711yescharacteristic
274C22×C43#57811yescharacteristic
275C2×D43—41no—
276C2×D43—41no—
277C2×D43—41no—
278C2×D43—41no—
279C2×D43—41no—
280C2×D43—41no—
281C2×D43—41no—
282C4×C43—42no—
283C4×C43—41no—
284C4×C43—41no—
285C4×C43—81no—
286C4×C43—81no—
287C4×C43—81no—
288C4×C43#54711yescharacteristic
289C4×C43#54811yescharacteristic
290C4×C43#55211yescharacteristic
291C4×C43#55611yescharacteristic
292Dic43—22no—
293Dic43—22no—
294Dic43—42no—
295Dic43—41no—
296Dic43—81no—
297Dic43—81no—
298Dic43—81no—
299C2×#479—431no—
300C2×#433—431no—
301#2629—431no—
302#2323—431no—
303#2077—431no—
304#2076—431no—
305#2035—431no—
306#2035—431no—
307#1989—431no—
308#1948—431no—
309#1944—431no—
310#1941—431no—
311#1935D4311yescharacteristic, complemented
312#1933—431no—
313#1803—431no—
314C2×C43#241511yescharacteristic
315C2×C43#306011yescharacteristic
316C2×C43#306311yescharacteristic
317C2×C43#312011yescharacteristic
318C2×C43#312611yescharacteristic
319C2×C43#324211yescharacteristic
320C2×C43#324411yescharacteristic
321D43—81no—
322C2×#125—431no—
323C2×C22⋊Q8—431no—
324C2×C4×Q8—431no—
325C2×#117—431no—
326#479—864no—
327#433—864no—
328C2×#107—431no—
329C2×#106—431no—
330C2×#106—431no—
331C2×#106—431no—
332C2×C4⋊C8—431no—
333C2×C4⋊C8—431no—
334C2×#103—431no—
335C2×#103—431no—
336C2×#103C2×D4311yescharacteristic
337C2×#103C2×D4311yescharacteristic
338C2×C22⋊C8—431no—
339C2×C22⋊C8—431no—
340C2×#97C2×D4311yescharacteristic
341C2×C4×C8—431no—
342#398—861no—
343#398—861no—
344#396—861no—
345#396—861no—
346#391C2×D4311yescharacteristic
347#389—431no—
348#389—431no—
349#389—861no—
350#389C2×D4311yescharacteristic
351#388—861no—
352#388—861no—
353#387—861no—
354#384—431no—
355#380—431no—
356#380—431no—
357#380—431no—
358C4×C4⋊C4—431no—
359#340—431no—
360#340—431no—
361#340—431no—
362#340—431no—
363#340—431no—
364#340—431no—
365#340C2×D4311yescharacteristic
366#340C2×D4311yescharacteristic
367C43#2471911yescharacteristic, complemented, Sylow
368C22×Q8C22×D4311yescharacteristic
369C23×C4—431no—
370C22×C8—431no—
371C22×C8—431no—
372C22×C8C22×D4311yescharacteristic
373C22×C8C22×D4311yescharacteristic
374#125—862no—
375#125—862no—
376C22⋊Q8—862no—
377C22⋊Q8—862no—
378C4×Q8—862no—
379C4×Q8—862no—
380#117—862no—
381#117—862no—
382C2×C4⋊C4—21no—
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⋊C4C22×D4311yescharacteristic
398C2×C4⋊C4C22×D4311yescharacteristic
399C2×C4⋊C4C22×D4311yescharacteristic
400C2×C22⋊C4—431no—
401C2×C22⋊C4—431no—
402C2×C22⋊C4—861no—
403C2×C22⋊C4—861no—
404C2×C22⋊C4—861no—
405C2×C22⋊C4—861no—
406C2×C42—431no—
407C2×C42—861no—
408C2×C42—861no—
409C2×C42C22×D4311yescharacteristic
410#107—862no—
411#106—862no—
412#106—862no—
413#106—862no—
414C4⋊C8—434no—
415C4⋊C8—862no—
416#103—22no—
417#103—22no—
418#103—862no—
419#103—862no—
420C22⋊C8—862no—
421C22⋊C8—862no—
422#97—22no—
423C4×C8—862no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—861no—
428#95—861no—
429#95—861no—
430#95—861no—
431#95—861no—
432#95—861no—
433C24—431no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8#1062189812yes—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—431no—
445C22×C4—431no—
446C22×C4—431no—
447C22×C4—861no—
448C22×C4—861no—
449C22×C4—861no—
450C22×C4—861no—
451C22×C4—861no—
452C22×C4—861no—
453C22×C4—861no—
454C22×C4—861no—
455C22×C4—861no—
456C22×C4—861no—
457C22×C4D4×D4311yescharacteristic
458C22×C4D4×D4311yescharacteristic
459C22×C4C23×D4311yescharacteristic
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—432no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8—861no—
469C2×C8—861no—
470C2×C8—861no—
471C2×C8D4×D4312yes—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—81no—
479C4⋊C4—432no—
480C4⋊C4—862no—
481C4⋊C4—862no—
482C4⋊C4—864no—
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—3441no—
492C4⋊C4—3441no—
493C4⋊C4—3441no—
494C4⋊C4—1722no—
495C4⋊C4—1722no—
496C4⋊C4—1722no—
497C22⋊C4—862no—
498C22⋊C4—862no—
499C22⋊C4—864no—
500C22⋊C4—3441no—
501C22⋊C4—3441no—
502C22⋊C4—3441no—
503C42—21no—
504C42—21no—
505C42—432no—
506C42—432no—
507C42—3441no—
508C42—1722no—
509C23—861no—
510C23—861no—
511C23—861no—
512C23—861no—
513C23—861no—
514C23—861no—
515C23—861no—
516C23C2×D4×D4311yescharacteristic
517Q8—22no—
518Q8—22no—
519Q8—41no—
520Q8—41no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—22no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—432no—
540C2×C4—432no—
541C2×C4—861no—
542C2×C4—861no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—862no—
547C2×C4—861no—
548C2×C4—861no—
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×C4—1721no—
563C2×C4—1721no—
564C2×C4C2×D4×D4311yescharacteristic
565C2×C4#41×D4311yescharacteristic
566C2×C4#41×D4311yescharacteristic
567C2×C4C2×#1062189811yescharacteristic
568C2×C4#1306337211yescharacteristic
569C2×C4#1306337211yescharacteristic
570C8—22no—
571C8—41no—
572C8—862no—
573C8—1721no—
574C22—1721no—
575C22—1721no—
576C22—1721no—
577C22—1721no—
578C22—1721no—
579C22—1721no—
580C22—1721no—
581C22#121×D4311yescharacteristic
582C22#1458340811yescharacteristic
583C22#1458346911yescharacteristic
584C22#1458370811yescharacteristic
585C22#1458370811yescharacteristic
586C22#1458370911yescharacteristic
587C22#1458371511yescharacteristic
588C4—41no—
589C4—41no—
590C4—42no—
591C4—81no—
592C4—81no—
593C4—81no—
594C4—862no—
595C4—862no—
596C4—3441no—
597C4—3441no—
598C4—3441no—
599C4—1722no—
600C4—1721no—
601C4#1458354711yescharacteristic
602C4#1458355811yescharacteristic
603C4#1458358211yescharacteristic
604C4#1458361611yescharacteristic
605C2—3441no—
606C2#1913802111yescharacteristic
607C2#1914425911yescharacteristic
608C2#1914428111yescharacteristic
609C2#1914480711yescharacteristic
610C2#1914488511yescharacteristic
611C2#1914585811yescharacteristic
612C2#1914588811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1935C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#1935D43
hypocenterC43#24719
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1935

Complements

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

NH ≅ G/Ntype
1. C2×#14583208C2semidirect
9. #19135551C2semidirect
10. #19135357C2semidirect
11. #19135338C2semidirect
12. #19135320C2semidirect
13. #19135274C2semidirect
14. #19134598C2semidirect
15. C43×#1935C2semidirect
311. #1935D43semidirect
367. C43#24719semidirect

Maximal subgroups

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

subgroupindex
C2×#145832082
C2×#145829612
#191404302
#191372802
#191360342
#191360252
#191357902
#191357892
#191355512
#191353572
#191353382
#191353202
#191352742
#191345982
C43×#19352
#2471943