Finite Group Databasebeta

← #25105189

Subgroups — #25105189

Order 11008.

1062 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×#14583292C211yesmaximal, characteristic
2C2×#14583001C211yesmaximal, characteristic
3C2×C4×#10621885C211yesmaximal, characteristic, complemented
4C2×C4×#10621884C211yesmaximal, characteristic
5#19137311C211yesmaximal, characteristic, complemented
6#19137302C211yesmaximal, characteristic
7#19135473C211yesmaximal, characteristic
8#19135463C211yesmaximal, characteristic, complemented
9#19135457C211yesmaximal, characteristic, complemented
10#19135447C211yesmaximal, characteristic
11#19135403C211yesmaximal, characteristic
12#19135395C211yesmaximal, characteristic, complemented
13#19134760C211yesmaximal, characteristic, complemented
14#19134283C211yesmaximal, characteristic, complemented
15C2×C43×#441C211yesmaximal, characteristic, complemented
16C22×#10621885C2211yescharacteristic
17C22×#10621873C2211yescharacteristic
18C22×#10621884C2211yescharacteristic
19C2×#13063323C2211yescharacteristic
20C2×#13063314C2211yescharacteristic
21C2×C4×Dic86C2211yescharacteristic
22C2×C4×D172C2211yescharacteristic
23#14583292C418yescomplemented
24#14583001—24no—
25C4×#10621885—24no—
26C4×#10621884—24no—
27C2×#13063259C2211yescharacteristic
28C2×#13063258C2211yescharacteristic
29C2×#13063256C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063249C2211yescharacteristic
33C2×#13063248C2211yescharacteristic
34C2×#13063247C2211yescharacteristic
35C2×#13063245C2211yescharacteristic
36C2×#13063235C2211yescharacteristic
37C2×#13063235C2211yescharacteristic
38C2×C4×C43⋊C8C2211yescharacteristic
39C2×C8×Dic43C2211yescharacteristic
40C2×C8×Dic43C2211yescharacteristic
41#14582806C2211yescharacteristic
42#14582806C2211yescharacteristic
43#14582804C2211yescharacteristic
44#14582800C2211yescharacteristic
45#14582790—22no—
46#14582783—22no—
47#14582780—22no—
48#14582770—22no—
49#14582768C2211yescharacteristic
50#14582764C2211yescharacteristic
51#14582745C2211yescharacteristic
52C22×Q16×C43C2211yescharacteristic
53C2×C4×Q8×C43C2211yescharacteristic
54C2×C4×Q8×C43C2211yescharacteristic
55C43×#441—24no—
56C2×#106×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C2×#97×C43C2211yescharacteristic
60C22×Dic86C2311yescharacteristic
61C22×D172C2311yescharacteristic
62C22×C4×D43—21no—
63C2×#10621885—22no—
64C2×#10621885—22no—
65C2×#10621885C2×C414yescomplemented
66C2×#10621873—22no—
67C2×#10621873—22no—
68C2×#10621873C2×C414yes—
69C2×#10621884—22no—
70C2×#10621884—22no—
71C2×#10621884C2×C414yes—
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74#13063323—22no—
75#13063323C2×C414yescomplemented
76#13063314—22no—
77#13063314C2×C414yes—
78C4×Dic86—22no—
79C4×Dic86—22no—
80C4×D172—22no—
81C4×D172—22no—
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×Dic43⋊C4—22no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—22no—
87C2×(C2×D43)⋊C4—22no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—22no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43C2311yescharacteristic
92C2×C4×Dic43C2311yescharacteristic
93#13063259—22no—
94#13063258—22no—
95#13063256—22no—
96#13063250—22no—
97#13063249—22no—
98#13063249—22no—
99#13063248—22no—
100#13063247—22no—
101#13063245—22no—
102#13063235—22no—
103#13063235C2×C414yescomplemented
104C4×C43⋊C8D414yes—
105C8×Dic43—22no—
106C8×Dic43—22no—
107C43⋊#95—22no—
108C43⋊#95—22no—
109C43⋊#95—22no—
110C43⋊#95—22no—
111C43⋊#95D412yes—
112C43⋊#95D412yes—
113C22×Q8×C43C2311yescharacteristic
114C22×Q8×C43C2311yescharacteristic
115C2×Q16×C43—22no—
116C2×Q16×C43—22no—
117C2×Q16×C43C2×C414yescomplemented
118C22×C8×C43C2311yescharacteristic
119C22×C8×C43C2311yescharacteristic
120C4×Q8×C43—22no—
121C4×Q8×C43—22no—
122C4×Q8×C43—22no—
123C4×Q8×C43—22no—
124C2×C4⋊C4×C43—21no—
125C2×C4⋊C4×C43—21no—
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C42×C43—21no—
129C2×C42×C43—21no—
130C2×C42×C43C2311yescharacteristic
131#106×C43—22no—
132#103×C43—22no—
133#103×C43—22no—
134#97×C43D414yes—
135C23×D43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43—21no—
139C2×Q8×C43—21no—
140C2×Q8×C43—21no—
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43C22×C412yes—
147C2×Q8×C43C22×C412yes—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2411yescharacteristic
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43C2×D412yes—
159C22×Dic43C2×D412yes—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172—21no—
164C2×D172—21no—
165C2×D172C22×C412yes—
166C2×C4×D43—42no—
167C2×C4×D43—82no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—21no—
172C2×Dic86—21no—
173C2×Dic86C22×C412yes—
174Q16×C43—28no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43C22×C412yes—
178C2×C8×C43C2×D412yes—
179C2×C8×C43C2×D412yes—
180C2×C8×C43#4112yes—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—42no—
186C4⋊C4×C43—42no—
187C42×C43—42no—
188C42×C43—42no—
189C42×C43C2×D412yes—
190C42×C43C2×D412yes—
191#10621885—28no—
192#10621884—28no—
193(C2×D43)⋊C4—28no—
194(C2×D43)⋊C4—42no—
195(C2×D43)⋊C4—82no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200Dic43⋊C4—28no—
201Dic43⋊C4—42no—
202Dic43⋊C4—82no—
203C4×Dic43—21no—
204C4×Dic43—21no—
205C4×Dic43—42no—
206C4×Dic43C22×C412yes—
207C4×Dic43#4112yes—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8C22×C412yes—
211C2×C43⋊C8C2×D412yes—
212C2×C43⋊C8C2×D412yes—
213C2×C43⋊C8#4112yes—
214#10621873—28no—
215C23×C43C22×D411yescharacteristic
216C22×D43—22no—
217C22×D43—41no—
218C22×D43—41no—
219C22×D43—42no—
220C22×D43—42no—
221Q8×C43—22no—
222Q8×C43—22no—
223Q8×C43—22no—
224Q8×C43—22no—
225Q8×C43—41no—
226Q8×C43—41no—
227Q8×C43—41no—
228Q8×C43—41no—
229C2×C4×C43—22no—
230C2×C4×C43—22no—
231C2×C4×C43—22no—
232C2×C4×C43—22no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—42no—
240C2×C4×C43—42no—
241C2×C4×C43#12712yes—
242C2×C4×C43#12712yes—
243C2×C4×C43C23×C411yescharacteristic
244C2×C4×C43C22×D411yescharacteristic
245C2×C4×C43C22×D411yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×Dic43—22no—
250C2×Dic43—22no—
251C2×Dic43—22no—
252C2×Dic43—22no—
253C2×Dic43—22no—
254C2×Dic43—22no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—42no—
260C2×Dic43—42no—
261C2×Dic43C4×D414yes—
262D172—22no—
263D172—22no—
264D172—41no—
265D172—41no—
266C4×D43—84no—
267Dic86—22no—
268Dic86—22no—
269Dic86—41no—
270Dic86—41no—
271C8×C43—22no—
272C8×C43C4×D414yes—
273C43⋊C8—22no—
274C43⋊C8C4×D414yes—
275#21703—431nomaximal, Sylow
276C22×C43C2×C4×D411yescharacteristic
277C22×C43C2×#12711yescharacteristic
278C22×C43#53211yescharacteristic
279C22×C43#57712yes—
280C22×C43#57812yes—
281C2×D43—42no—
282C2×D43—44no—
283C2×D43—81no—
284C2×D43—81no—
285C2×D43—82no—
286C4×C43—22no—
287C4×C43—22no—
288C4×C43—42no—
289C4×C43—42no—
290C4×C43—81no—
291C4×C43—81no—
292C4×C43C2×C4×D411yescharacteristic
293C4×C43C2×C4×D411yescharacteristic
294C4×C43#53211yescharacteristic
295C4×C43#53211yescharacteristic
296Dic43—24no—
297Dic43—42no—
298Dic43—42no—
299Dic43—81no—
300Dic43—81no—
301C2×#497—431no—
302C2×#441D4311yescharacteristic, complemented
303C2×#440—431no—
304C2×C4×Q16—431no—
305C2×C4×SD16—431no—
306#2327—431no—
307#2326—431no—
308#1973—431no—
309#1971—431no—
310#1969—431no—
311#1968—431no—
312#1958—431no—
313#1956—431no—
314#1847—431no—
315#1726—431no—
316C2×C43C4×#12711yescharacteristic
317C2×C43#294712yes—
318C2×C43#315411yescharacteristic
319C2×C43#315611yescharacteristic
320C2×C43#317812yes—
321D43—82no—
322C22×Q16—431no—
323C22×Q16C2×D4311yescharacteristic
324C22×SD16—431no—
325C22×SD16—431no—
326C2×C4⋊Q8—431no—
327C2×#124—431no—
328C2×C4×Q8—431no—
329C2×C4×Q8C2×D4311yescharacteristic
330C2×C4×Q8C2×D4311yescharacteristic
331C2×C4×D4—431no—
332#497—438no—
333#441—24no—
334#440—864no—
335C4×Q16—864no—
336C4×SD16—864no—
337C2×#107—431no—
338C2×#107—431no—
339C2×#106—431no—
340C2×#106C2×D4311yescharacteristic
341C2×#103—431no—
342C2×#103—431no—
343C2×#103—431no—
344C2×#103—431no—
345C2×#103C2×D4311yescharacteristic
346C2×#103C2×D4311yescharacteristic
347C2×#102—431no—
348C2×#102—431no—
349C2×#97—431no—
350C2×#97—431no—
351C2×#97C2×D4311yescharacteristic
352C2×C4×C8—431no—
353C2×C4×C8—431no—
354C2×C4×C8—431no—
355#391—431no—
356#391—431no—
357#391—431no—
358#390—431no—
359#388—862no—
360#387—862no—
361#387—862no—
362#385—862no—
363#384—431no—
364#382—431no—
365#376—431no—
366C43#2170311yescharacteristic, complemented, Sylow
367C22×Q8—431no—
368C22×Q8C22×D4311yescharacteristic
369C22×Q8C22×D4311yescharacteristic
370C22×D4—431no—
371C23×C4—861no—
372C2×Q16—22no—
373C2×Q16—22no—
374C2×Q16—434no—
375C2×Q16—862no—
376C2×Q16—862no—
377C2×Q16C4×D4314yescomplemented
378C2×SD16—434no—
379C2×SD16—434no—
380C2×SD16—862no—
381C2×SD16—862no—
382C2×SD16—862no—
383C2×SD16—862no—
384C22×C8—431no—
385C22×C8—431no—
386C22×C8C22×D4311yescharacteristic
387C22×C8C22×D4311yescharacteristic
388C4⋊Q8—434no—
389C4⋊Q8—862no—
390#124—434no—
391#124—862no—
392C4×Q8—22no—
393C4×Q8—22no—
394C4×Q8—22no—
395C4×Q8—22no—
396C4×Q8—862no—
397C4×Q8—862no—
398C4×D4—862no—
399C4×D4—862no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—431no—
403C2×C4⋊C4—431no—
404C2×C4⋊C4—862no—
405C2×C4⋊C4—862no—
406C2×C4⋊C4—861no—
407C2×C4⋊C4C22×D4311yescharacteristic
408C2×C4⋊C4C22×D4311yescharacteristic
409C2×C22⋊C4—862no—
410C2×C22⋊C4—862no—
411C2×C22⋊C4—861no—
412C2×C42—21no—
413C2×C42—21no—
414C2×C42—431no—
415C2×C42—431no—
416C2×C42—861no—
417C2×C42C22×D4311yescharacteristic
418#107—862no—
419#107—862no—
420#106—22no—
421#106—862no—
422#103—22no—
423#103—22no—
424#103—862no—
425#103—862no—
426#103—862no—
427#103—862no—
428#102—862no—
429#102—862no—
430#97—434no—
431#97—862no—
432#97C22⋊D4314yes—
433C4×C8—434no—
434C4×C8—862no—
435C4×C8—862no—
436#95—432no—
437#95—432no—
438#95—862no—
439#95—862no—
440#95—862no—
441#95—862no—
442C24—861no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—432no—
454C2×Q8—861no—
455C2×Q8—861no—
456C2×Q8—861no—
457C2×Q8—861no—
458C2×Q8—861no—
459C2×Q8C2×C4×D4312yes—
460C2×Q8C2×C4×D4312yes—
461C2×D4—432no—
462C2×D4—861no—
463C2×D4—861no—
464C2×D4—861no—
465C2×D4—861no—
466C2×D4—861no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—432no—
472C22×C4—432no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4—861no—
476C22×C4—3442no—
477C22×C4—1722no—
478C22×C4D4×D4311yescharacteristic
479C22×C4D4×D4311yescharacteristic
480C22×C4C23×D4311yescharacteristic
481Q16—28no—
482Q16—868no—
483SD16—868no—
484SD16—868no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—432no—
488C2×C8—432no—
489C2×C8—432no—
490C2×C8—432no—
491C2×C8—861no—
492C2×C8—861no—
493C2×C8C2×C4×D4312yes—
494C2×C8#1062189812yes—
495C2×C8C2×C22⋊D4312yes—
496C2×C8C2×C22⋊D4312yes—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—42no—
502C4⋊C4—42no—
503C4⋊C4—868no—
504C4⋊C4—861no—
505C4⋊C4—861no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C4⋊C4—3442no—
509C4⋊C4—1722no—
510C22⋊C4—868no—
511C22⋊C4—3442no—
512C22⋊C4—1722no—
513C42—42no—
514C42—42no—
515C42—432no—
516C42—432no—
517C42—861no—
518C42—861no—
519C42—1722no—
520C42D4×D4312yes—
521C42C2×C22⋊D4312yes—
522C23—862no—
523C23—1721no—
524C23—1721no—
525C23—1722no—
526C23—1722no—
527C23C2×D4×D4311yescharacteristic
528Q8—22no—
529Q8—22no—
530Q8—22no—
531Q8—22no—
532Q8—41no—
533Q8—41no—
534Q8—41no—
535Q8—41no—
536Q8—862no—
537Q8—862no—
538Q8—1721no—
539Q8—1721no—
540D4—862no—
541D4—862no—
542D4—1721no—
543D4—1721no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—434no—
557C2×C4—862no—
558C2×C4—862no—
559C2×C4—862no—
560C2×C4—862no—
561C2×C4—862no—
562C2×C4—862no—
563C2×C4—3444no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—1722no—
567C2×C4—1722no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4#1306332112yes—
571C2×C4#1306332112yes—
572C2×C4C22×C4×D4311yescharacteristic
573C2×C4C2×D4×D4311yescharacteristic
574C2×C4C22×C22⋊D4311yescharacteristic
575C2×C4#41×D4311yescharacteristic
576C2×C4#41×D4311yescharacteristic
577C2×C4C2×#1062189811yescharacteristic
578C8—22no—
579C8—434no—
580C8—862no—
581C8C4×C22⋊D4314yes—
582C22—3442no—
583C22—3441no—
584C22—3441no—
585C22—1724no—
586C22—1722no—
587C22C4×D4×D4311yescharacteristic
588C22C2×#1306332111yescharacteristic
589C22#1458344611yescharacteristic
590C22#1458370812yes—
591C22#1458371512yes—
592C4—22no—
593C4—22no—
594C4—42no—
595C4—42no—
596C4—81no—
597C4—81no—
598C4—864no—
599C4—3441no—
600C4—3441no—
601C4—1722no—
602C4—1722no—
603C4C4×D4×D4311yescharacteristic
604C4C2×C4×C22⋊D4311yescharacteristic
605C4#1458344511yescharacteristic
606C4#1458344611yescharacteristic
607C2—3442no—
608C2C4×#1306332111yescharacteristic
609C2#1914343712yes—
610C2#1914507411yescharacteristic
611C2#1914508811yescharacteristic
612C2#1914526912yes—
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#441C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenterC2×#441D43
hypocenterC43#21703
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
3. C2×C4×#10621885C2semidirect
5. #19137311C2semidirect
8. #19135463C2semidirect
9. #19135457C2semidirect
12. #19135395C2semidirect
13. #19134760C2semidirect
14. #19134283C2semidirect
15. C2×C43×#441C2semidirect
23. #14583292C4semidirect
65. C2×#10621885C2×C4semidirect
75. #13063323C2×C4semidirect
103. #13063235C2×C4semidirect
117. C2×Q16×C43C2×C4semidirect
302. C2×#441D43semidirect
366. C43#21703semidirect
377. C2×Q16C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145832922
C2×#145830012
C2×C4×#106218852
C2×C4×#106218842
#191373112
#191373022
#191354732
#191354632
#191354572
#191354472
#191354032
#191353952
#191347602
#191342832
C2×C43×#4412
#2170343