Finite Group Databasebeta

← #25113491

Subgroups — #25113491

Order 11008.

1150 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148188C211yesmaximal, characteristic
2#19143546C211yesmaximal, characteristic, complemented
3C4×#13063290C211yesmaximal, characteristic, complemented
4#19135513C211yesmaximal, characteristic, complemented
5#19135512C212yesmaximal, complemented
6#19135422C211yesmaximal, characteristic, complemented
7#19135421C212yesmaximal, complemented
8#19134614C212yesmaximal, complemented
9C4×#13063252C211yesmaximal, characteristic, complemented
10#19134399C212yesmaximal, complemented
11C43×#1806C211yesmaximal, characteristic, complemented
12#14583634C411yescharacteristic, complemented
13#14583632C412yescomplemented
14#14583627C411yescharacteristic, complemented
15#14583621C412yescomplemented
16#14583619C411yescharacteristic, complemented
17#14583598—22no—
18#14583595—21no—
19#14583570C411yescharacteristic, complemented
20#14583558—21no—
21#14583449C2211yescharacteristic
22#14583445C2212yes—
23#14583433—21no—
24#14583427—22no—
25C4×#10621898—21no—
26#14583367C2212yes—
27C2×C4×Dic86C2211yescharacteristic
28C2×#13063290—21no—
29#14583028—22no—
30#14583026—21no—
31#14583023—21no—
32#14582922C2212yes—
33C2×#13063253C2212yes—
34C2×#13063253C2212yes—
35C2×#13063252C2211yescharacteristic
36C2×#13063252C2211yescharacteristic
37C2×#13063251C2212yes—
38C2×#13063251C2212yes—
39C4×#10621877C2211yescharacteristic
40M16×Dic43C2212yes—
41C4⋊C4×Dic43—21no—
42C4×Dic43⋊C4C2212yes—
43#14582750—22no—
44C42×Dic43C2212yes—
45C42×Dic43C2211yescharacteristic
46#14582658C2211yescharacteristic
47#14582658C2211yescharacteristic
48C4×#41×C43C2211yescharacteristic
49C43×#423C2211yescharacteristic
50C2×#104×C43C2212yes—
51C4×C4⋊C4×C43C2211yescharacteristic
52C43×#339C2212yes—
53C2×#10621898—21no—
54C2×#10621898C2312yes—
55C22×Dic86D411yescharacteristic
56C2×#10621877C2311yescharacteristic
57C2×#10621877C2311yescharacteristic
58#13063325C2×C411yescharacteristic
59#13063323C2×C412yes—
60#13063322C2×C411yescharacteristic
61#13063321C2×C412yes—
62#13063320—22no—
63#13063319—22no—
64#13063318—22no—
65#13063317—21no—
66#13063315—22no—
67#13063314C2×C412yes—
68#13063313—21no—
69#13063313C2×C412yes—
70#13063312C2×C412yes—
71#13063311—22no—
72#13063310—22no—
73#13063308—22no—
74#13063307—22no—
75#13063304—21no—
76#13063303—22no—
77#13063299—21no—
78#13063299—21no—
79#13063299—21no—
80#13063298—22no—
81#13063297—22no—
82#13063297—22no—
83C4×Dic86—21no—
84C4×Dic86C2×C411yescharacteristic
85C4×Dic86C2×C411yescharacteristic
86C4×Dic86C2×C412yes—
87C4×Dic86D411yescharacteristic
88C4×Dic86D412yes—
89C4×Dic86D411yescharacteristic
90#13063290—28no—
91#13063290C2×C412yes—
92#13063290C2×C412yes—
93C4×D172—21no—
94C4×D172—21no—
95C4×D172—21no—
96#13063287C2×C412yes—
97#13063287C2×C412yes—
98C4×C22⋊D43—22no—
99C4×C22⋊D43—22no—
100C4×C22⋊D43—22no—
101(C22⋊D43)⋊C4—22no—
102(C22⋊D43)⋊C4—22no—
103#13063284—21no—
104#13063282—22no—
105#13063282—22no—
106C2×C4⋊Dic43D411yescharacteristic
107C2×Dic43⋊C4—22no—
108C2×Dic43⋊C4D412yes—
109C2×C4×Dic43—21no—
110C2×C4×Dic43—22no—
111C2×C4×Dic43—21no—
112C2×C4×Dic43—22no—
113C2×C4×Dic43C2311yescharacteristic
114C2×C4×Dic43C2311yescharacteristic
115C2×C4×Dic43C2312yes—
116C42×D43—22no—
117Dic43⋊C8—22no—
118Dic43⋊C8—22no—
119#13063253—24no—
120#13063253—42no—
121#13063252—22no—
122#13063252—22no—
123#13063251—24no—
124#13063251—42no—
125#13063236—21no—
126#13063235—22no—
127C4×C43⋊C8—21no—
128C8×Dic43—22no—
129C43⋊#95—22no—
130C2×#41×C43C2311yescharacteristic
131C2×M16×C43C2312yes—
132C4×Q8×C43C2×C411yescharacteristic
133C4×Q8×C43C2×C411yescharacteristic
134C4×D4×C43—21no—
135C4×D4×C43—21no—
136C4×D4×C43C2×C411yescharacteristic
137C4×D4×C43C2×C411yescharacteristic
138#117×C43—21no—
139#117×C43C2311yescharacteristic
140C2×C4⋊C4×C43—21no—
141C2×C42×C43—21no—
142C2×C42×C43C2312yes—
143C2×C42×C43C2311yescharacteristic
144C4⋊C8×C43—21no—
145C4⋊C8×C43—21no—
146#104×C43—42no—
147#95×C43—21no—
148#41×C43—21no—
149#41×C43—21no—
150#41×C43—21no—
151#41×C43—21no—
152C2×Q8×C43C22×C411yescharacteristic
153C2×D4×C43—21no—
154C2×D4×C43C22×C411yescharacteristic
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—22no—
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2411yescharacteristic
162C2×C22⋊D43—22no—
163C2×C22⋊D43—22no—
164C2×C22⋊D43—22no—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43C2×D412yes—
168C22×Dic43C2×D412yes—
169#10621898—22no—
170#10621898—22no—
171#10621898—22no—
172#10621898—22no—
173#10621898—44no—
174C2×D172—21no—
175C2×D172—21no—
176C2×D172C22×C412yes—
177C2×C4×D43—22no—
178C2×C4×D43—22no—
179C2×C4×D43—22no—
180C2×Dic86—24no—
181C2×Dic86C22⋊C412yes—
182C2×Dic86C22⋊C411yescharacteristic
183C2×Dic86C22⋊C411yescharacteristic
184C2×Dic86C22×C412yes—
185M16×C43—22no—
186M16×C43—22no—
187C2×C8×C43—22no—
188C4⋊C4×C43—24no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43C22×C411yescharacteristic
192C4⋊C4×C43C22×C411yescharacteristic
193C22⋊C4×C43—21no—
194C22⋊C4×C43—21no—
195C22⋊C4×C43—21no—
196C42×C43—21no—
197C42×C43—21no—
198C42×C43—21no—
199C42×C43—22no—
200C42×C43—22no—
201C42×C43C22×C411yescharacteristic
202C42×C43C22×C411yescharacteristic
203C42×C43C2×D411yescharacteristic
204C42×C43C2×D411yescharacteristic
205C22⋊Dic43—22no—
206C22⋊Dic43—22no—
207(C2×D43)⋊C4—22no—
208(C2×D43)⋊C4—22no—
209(C2×D43)⋊C4—22no—
210(C2×D43)⋊C4—22no—
211(C2×D43)⋊C4—22no—
212(C2×D43)⋊C4—22no—
213C4⋊Dic43—21no—
214C4⋊Dic43—21no—
215C4⋊Dic43C22⋊C411yescharacteristic
216C4⋊Dic43C22⋊C411yescharacteristic
217C4⋊Dic43C22⋊C412yes—
218Dic43⋊C4—28no—
219Dic43⋊C4—22no—
220Dic43⋊C4—22no—
221Dic43⋊C4—22no—
222Dic43⋊C4—22no—
223Dic43⋊C4C22⋊C412yes—
224Dic43⋊C4C22⋊C412yes—
225Dic43⋊C4C22⋊C412yes—
226Dic43⋊C4C22⋊C412yes—
227C4×Dic43—28no—
228C4×Dic43—24no—
229C4×Dic43—21no—
230C4×Dic43—22no—
231C4×Dic43—22no—
232C4×Dic43—21no—
233C4×Dic43—21no—
234C4×Dic43—44no—
235C4×Dic43—42no—
236C4×Dic43C22×C412yes—
237C4×Dic43C22×C412yes—
238C4×Dic43C2×D412yes—
239C4×Dic43C2×D412yes—
240C4×Dic43#4112yescomplemented
241#10621877—21no—
242#10621877—21no—
243#10621877—21no—
244#10621877#4112yescomplemented
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C23×C43—21no—
248C23×C43C22×D411yescharacteristic
249C22×D43—22no—
250Q8×C43—21no—
251Q8×C43—21no—
252D4×C43—21no—
253D4×C43—21no—
254D4×C43—41no—
255D4×C43—41no—
256C2×C4×C43—22no—
257C2×C4×C43—24no—
258C2×C4×C43—21no—
259C2×C4×C43—21no—
260C2×C4×C43—21no—
261C2×C4×C43—41no—
262C2×C4×C43—42no—
263C2×C4×C43—42no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43—42no—
267C2×C4×C43—81no—
268C2×C4×C43C2×C22⋊C411yescharacteristic
269C2×C4×C43C2×C22⋊C411yescharacteristic
270C2×C4×C43C2×C22⋊C411yescharacteristic
271C2×C4×C43C2×C22⋊C411yescharacteristic
272C2×C4×C43C23×C411yescharacteristic
273C2×C4×C43C22×D411yescharacteristic
274C2×C4×C43C2×#4111yescharacteristic
275C2×C4×C43C2×#4111yescharacteristic
276C2×C4×C43H(5,𝔽2)11yescharacteristic
277C2×C4×C432−1+411yescharacteristic
278C22⋊D43—42no—
279C22⋊D43—42no—
280C22⋊D43—44no—
281C22⋊D43—82no—
282C2×Dic43—22no—
283C2×Dic43—22no—
284C2×Dic43—22no—
285C2×Dic43—24no—
286C2×Dic43—22no—
287C2×Dic43—22no—
288C2×Dic43—42no—
289C2×Dic43—41no—
290C2×Dic43—41no—
291C2×Dic43C2×C22⋊C412yes—
292C2×Dic43C2×C22⋊C412yes—
293C2×Dic43C2×C22⋊C412yes—
294C2×Dic43C2×C22⋊C412yes—
295D172—22no—
296D172—22no—
297D172—42no—
298D172—81no—
299C4×D43—42no—
300C4×D43—42no—
301C4×D43—44no—
302C4×D43—82no—
303Dic86—22no—
304Dic86—24no—
305Dic86—22no—
306Dic86—22no—
307Dic86#10414yescomplemented
308C8×C43—42no—
309C43⋊C8—22no—
310C43⋊C8—41no—
311#22550—431nomaximal, Sylow
312C22×C43—21no—
313C22×C43—21no—
314C22×C43—41no—
315C22×C43—41no—
316C22×C43—41no—
317C22×C43C22×C22⋊C411yescharacteristic
318C22×C43#54811yescharacteristic
319C22×C43#55011yescharacteristic
320C2×D43—42no—
321C2×D43—42no—
322C2×D43—42no—
323C4×C43—21no—
324C4×C43—21no—
325C4×C43—21no—
326C4×C43—44no—
327C4×C43—41no—
328C4×C43—41no—
329C4×C43—41no—
330C4×C43C2×#10412yes—
331C4×C43C4×#4111yescharacteristic
332C4×C43#52011yescharacteristic
333C4×C43#54811yescharacteristic
334C4×C43#55011yescharacteristic
335Dic43—24no—
336Dic43—22no—
337Dic43—22no—
338Dic43—22no—
339Dic43—42no—
340Dic43—42no—
341Dic43C2×#10414yes—
342#3480—431no—
343Q8×M16—431no—
344C42×Q8—431no—
345#1980—432no—
346#1980—431no—
347#1962—431no—
348#1962—432no—
349#1806—432no—
350#1806D4311yescharacteristic, complemented
351C4×#104—432no—
352C4×#104—431no—
353C2×C43—21no—
354C2×C43—21no—
355C2×C43—81no—
356C2×C43#234111yescharacteristic
357C2×C43C22×#10411yescharacteristic
358C2×C43#290111yescharacteristic
359D43—82no—
360#559—431no—
361#559—432no—
362#557—431no—
363#556—432no—
364#556—431no—
365#553—861no—
366#553—862no—
367#550—431no—
368#548—861no—
369#532—432no—
370#532—431no—
371#529—861no—
372#529—862no—
373C4×#41—432no—
374C4×#41—861no—
375C4×#41C2×D4311yescharacteristic
376C2×C4×Q8—431no—
377C2×C4×Q8—861no—
378#446—861no—
379#446—862no—
380C8×Q8—861no—
381#423—432no—
382#423C2×D4311yescharacteristic
383C2×#104—431no—
384C2×#104—431no—
385C2×#104—432no—
386C2×#104—432no—
387C2×#104—432no—
388C2×#104—432no—
389C2×#104C2×D4312yes—
390C4×M16—432no—
391C4×M16—431no—
392C4×C4⋊C4—432no—
393C4×C4⋊C4—862no—
394C4×C4⋊C4—861no—
395C4×C4⋊C4C2×D4311yescharacteristic
396C43—432no—
397C43—431no—
398#339—431no—
399#339—431no—
400#339C2×D4312yes—
401C43#2255011yescharacteristic, complemented, Sylow
402C2×#41—432no—
403C2×#41—861no—
404C2×#41C22×D4311yescharacteristic
405C22×Q8—431no—
406C2×M16—431no—
407C2×M16—431no—
408C2×M16C22×D4312yes—
409C4⋊Q8—432no—
410C4⋊Q8—431no—
411#127—432no—
412#127—431no—
413#126—862no—
414#126—862no—
415#126—862no—
416#125—861no—
417#125—862no—
418#124—432no—
419#124—432no—
420#124—432no—
421#124—861no—
422#124—862no—
423#123—862no—
424#123—862no—
425#123—862no—
426C22⋊Q8—862no—
427C22⋊Q8—861no—
428#121—862no—
429#121—861no—
430#121—862no—
431#121—862no—
432#121—861no—
433#121—861no—
434C4×Q8—431no—
435C4×Q8—431no—
436C4×Q8—432no—
437C4×Q8—431no—
438C4×Q8—432no—
439C4×Q8—431no—
440C4×Q8—432no—
441C4×Q8—432no—
442C4×Q8—861no—
443C4×Q8—868no—
444C4×Q8C4×D4311yescharacteristic
445C4×Q8C4×D4311yescharacteristic
446C4×D4—21no—
447C4×D4—21no—
448C4×D4—432no—
449C4×D4—432no—
450C4×D4—861no—
451C4×D4—862no—
452C4×D4—862no—
453C4×D4—862no—
454C4×D4—862no—
455C4×D4—862no—
456C4×D4—861no—
457C4×D4—861no—
458C4×D4C4×D4311yescharacteristic
459C4×D4C4×D4311yescharacteristic
460#117—21no—
461#117—862no—
462#117—862no—
463#117—861no—
464#117C22×D4311yescharacteristic
465C2×C4⋊C4—21no—
466C2×C4⋊C4—432no—
467C2×C4⋊C4—431no—
468C2×C4⋊C4—862no—
469C2×C42—21no—
470C2×C42—432no—
471C2×C42—431no—
472C2×C42—431no—
473C2×C42—862no—
474C2×C42—862no—
475C2×C42—861no—
476C2×C42—862no—
477C2×C42—861no—
478C2×C42C22×D4312yes—
479C2×C42C22×D4311yescharacteristic
480C4⋊C8—21no—
481C4⋊C8—21no—
482C4⋊C8—862no—
483C4⋊C8—862no—
484#104—42no—
485#104—864no—
486#104—864no—
487#104—862no—
488#104—862no—
489#104—1722no—
490#104—1722no—
491#97—862no—
492#97—861no—
493C4×C8—862no—
494C4×C8—861no—
495#95—21no—
496#95—862no—
497#41—21no—
498#41—21no—
499#41—21no—
500#41—21no—
501#41—862no—
502#41—862no—
503#41—862no—
504#41—862no—
505#41—1724no—
506C2×Q8—431no—
507C2×Q8—432no—
508C2×Q8—431no—
509C2×Q8—432no—
510C2×Q8—864no—
511C2×Q8C2×C4×D4311yescharacteristic
512C2×D4—21no—
513C2×D4—432no—
514C2×D4—862no—
515C2×D4—862no—
516C2×D4—862no—
517C2×D4—861no—
518C2×D4—861no—
519C2×D4C2×C4×D4311yescharacteristic
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—432no—
525C22×C4—432no—
526C22×C4—862no—
527C22×C4—862no—
528C22×C4—861no—
529C22×C4—861no—
530C22×C4—862no—
531C22×C4D4×D4311yescharacteristic
532C22×C4D4×D4311yescharacteristic
533C22×C4C23×D4311yescharacteristic
534M16—22no—
535M16—22no—
536M16—432no—
537M16—861no—
538M16—861no—
539M16—861no—
540C2×C8—22no—
541C2×C8—861no—
542C2×C8—861no—
543C4⋊C4—24no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—432no—
547C4⋊C4—431no—
548C4⋊C4—432no—
549C4⋊C4—431no—
550C4⋊C4—432no—
551C4⋊C4—432no—
552C4⋊C4—432no—
553C4⋊C4—862no—
554C4⋊C4—862no—
555C4⋊C4—862no—
556C4⋊C4—862no—
557C4⋊C4—868no—
558C4⋊C4—861no—
559C4⋊C4—861no—
560C4⋊C4C2×C4×D4311yescharacteristic
561C4⋊C4C2×C4×D4311yescharacteristic
562C22⋊C4—21no—
563C22⋊C4—21no—
564C22⋊C4—21no—
565C22⋊C4—862no—
566C22⋊C4—862no—
567C22⋊C4—862no—
568C22⋊C4—862no—
569C22⋊C4—862no—
570C22⋊C4—862no—
571C22⋊C4—862no—
572C22⋊C4—862no—
573C42—21no—
574C42—21no—
575C42—21no—
576C42—22no—
577C42—22no—
578C42—432no—
579C42—432no—
580C42—432no—
581C42—432no—
582C42—432no—
583C42—862no—
584C42—862no—
585C42—864no—
586C42—868no—
587C42—861no—
588C42—861no—
589C42—861no—
590C42—1722no—
591C42—1724no—
592C42C2×C4×D4311yescharacteristic
593C42C2×C4×D4311yescharacteristic
594C42D4×D4311yescharacteristic
595C42D4×D4311yescharacteristic
596C23—21no—
597C23—862no—
598C23C2×D4×D4311yescharacteristic
599Q8—21no—
600Q8—21no—
601Q8—434no—
602Q8—864no—
603Q8—862no—
604Q8—862no—
605Q8—862no—
606D4—21no—
607D4—21no—
608D4—41no—
609D4—41no—
610D4—862no—
611D4—862no—
612D4—3441no—
613D4—3442no—
614D4—1724no—
615D4—1722no—
616D4—1722no—
617D4—1722no—
618C2×C4—22no—
619C2×C4—24no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—41no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—42no—
629C2×C4—81no—
630C2×C4—432no—
631C2×C4—432no—
632C2×C4—432no—
633C2×C4—432no—
634C2×C4—864no—
635C2×C4—862no—
636C2×C4—862no—
637C2×C4—862no—
638C2×C4—862no—
639C2×C4—862no—
640C2×C4—3442no—
641C2×C4—1724no—
642C2×C4—1722no—
643C2×C4—1721no—
644C2×C4—1721no—
645C2×C4—1722no—
646C2×C4—1722no—
647C2×C4C22⋊C4×D4311yescharacteristic
648C2×C4C22⋊C4×D4311yescharacteristic
649C2×C4C22⋊C4×D4311yescharacteristic
650C2×C4C22⋊C4×D4311yescharacteristic
651C2×C4C22×C4×D4311yescharacteristic
652C2×C4C2×D4×D4311yescharacteristic
653C2×C4#41×D4311yescharacteristic
654C2×C4#41×D4311yescharacteristic
655C2×C4#1306337011yescharacteristic
656C2×C4#1306337311yescharacteristic
657C8—42no—
658C8—862no—
659C8—1721no—
660C22—21no—
661C22—21no—
662C22—41no—
663C22—41no—
664C22—41no—
665C22—1722no—
666C22—1722no—
667C22—1722no—
668C22C2×C22⋊C4×D4311yescharacteristic
669C22#1458355911yescharacteristic
670C22#1458356711yescharacteristic
671C4—21no—
672C4—21no—
673C4—21no—
674C4—44no—
675C4—41no—
676C4—41no—
677C4—41no—
678C4—434no—
679C4—864no—
680C4—862no—
681C4—862no—
682C4—862no—
683C4—1722no—
684C4—1722no—
685C4#104×D4312yes—
686C4#1458336711yescharacteristic
687C4#1458338011yescharacteristic
688C4#1458355911yescharacteristic
689C4#1458356711yescharacteristic
690C2—21no—
691C2—21no—
692C2—81no—
693C2—3442no—
694C2#1913743211yescharacteristic
695C2C2×#104×D4311yescharacteristic
696C2#1914314111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1806C2
socleC22×C43C22×C22⋊C4
prime radical#19148188C2
cosocleC22×C4×C43C24
hypercenter#1806D43
hypocenterC43#22550
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1806

Complements

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

NH ≅ G/Ntype
2. #19143546C2semidirect
3. C4×#13063290C2semidirect
4. #19135513C2semidirect
5. #19135512C2semidirect
6. #19135422C2semidirect
7. #19135421C2semidirect
8. #19134614C2semidirect
9. C4×#13063252C2semidirect
10. #19134399C2semidirect
11. C43×#1806C2semidirect
12. #14583634C4semidirect
13. #14583632C4semidirect
14. #14583627C4semidirect
15. #14583621C4semidirect
16. #14583619C4semidirect
19. #14583570C4semidirect
240. C4×Dic43#41semidirect
244. #10621877#41semidirect
307. Dic86#104semidirect
350. #1806D43semidirect
401. C43#22550semidirect

Maximal subgroups

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

subgroupindex
#191481882
#191435462
C4×#130632902
#191355132
#191355122
#191354222
#191354212
#191346142
C4×#130632522
#191343992
C43×#18062
#2255043