Finite Group Databasebeta

← #25004390

Subgroups — #25004390

Order 11008.

820 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582917C211yesmaximal, characteristic
2#19143112C211yesmaximal, characteristic
3C2×#14582872C211yesmaximal, characteristic
4C2×#14582669C211yesmaximal, characteristic, complemented
5#19134305C211yesmaximal, characteristic, complemented
6#19134304C211yesmaximal, characteristic, complemented
7C43×#1740C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10C22×#10621877C2211yescharacteristic
11C2×#13063284C2211yescharacteristic
12#14582917—22no—
13#14582917—22no—
14C2×#13063253—22no—
15#14582907C412yescomplemented
16#14582903C412yescomplemented
17#14582898—22no—
18#14582893—22no—
19#14582872—22no—
20#14582872—22no—
21C2×#13063239—22no—
22#14582669—22no—
23#14582659—22no—
24#14582658—22no—
25C2×#117×C43C2211yescharacteristic
26C2×#117×C43C2211yescharacteristic
27C2×#117×C43C2211yescharacteristic
28C43×#342—22no—
29C2×#10621898—21no—
30C2×#10621898—21no—
31C2×#10621898—21no—
32C2×#10621898—21no—
33C2×#10621898—21no—
34C2×#10621898—21no—
35C2×#10621898—21no—
36C2×#10621898—21no—
37C2×#10621898—21no—
38C2×#10621898—21no—
39C2×#10621898D412yes—
40C2×#10621898D412yes—
41C22×Dic86C2×C411yescharacteristic
42C22×D172C2×C411yescharacteristic
43C22×C22⋊D43—21no—
44C22×C4×D43—21no—
45C2×#10621877—21no—
46C2×#10621877—21no—
47C2×#10621877—21no—
48C2×#10621877—21no—
49C2×#10621877—21no—
50C2×#10621877—21no—
51C2×#10621877—21no—
52C2×#10621877—21no—
53C2×#10621877—21no—
54C2×#10621877—21no—
55C2×#10621877C2×C412yes—
56C2×#10621877D412yes—
57C22×C43⋊C8—21no—
58C22×C43⋊C8—21no—
59#13063284—21no—
60#13063284—21no—
61#13063284—21no—
62#13063284D412yes—
63C2×C4⋊Dic43—21no—
64C2×C22⋊Dic43—21no—
65C2×C4×Dic43—21no—
66#13063253—28no—
67#13063248—24no—
68#13063245—24no—
69#13063239—28no—
70C23×C4×C43C2311yescharacteristic
71#117×C43—21no—
72#117×C43—21no—
73#117×C43—21no—
74#117×C43—21no—
75#117×C43—21no—
76#117×C43—21no—
77#117×C43—21no—
78#117×C43—21no—
79#117×C43—21no—
80#117×C43—21no—
81#117×C43C2×C412yes—
82#117×C43D412yes—
83C2×C4⋊C4×C43—21no—
84C2×C4⋊C4×C43—21no—
85C2×C4⋊C4×C43—21no—
86C2×C22⋊C4×C43—21no—
87C2×C22⋊C4×C43—21no—
88C2×C22⋊C4×C43D412yes—
89C2×C42×C43—21no—
90C2×C42×C43—21no—
91C2×C42×C43—21no—
92C24×C43C2×D411yescharacteristic
93C23×D43—21no—
94C22×C4×C43—22no—
95C22×C4×C43—41no—
96C22×C4×C43—41no—
97C22×C4×C43C22×C411yescharacteristic
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43C2×D411yescharacteristic
100C22×C4×C43C2×D411yescharacteristic
101C22×C4×C43C2×D411yescharacteristic
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43#4111yescharacteristic
104C22×C4×C43#4111yescharacteristic
105C22×C4×C43#4111yescharacteristic
106C22×C4×C43#4111yescharacteristic
107C22×C4×C43#4111yescharacteristic
108C22×C4×C43#4111yescharacteristic
109C22×C4×C43#4111yescharacteristic
110C22×C4×C43#4111yescharacteristic
111C2×C22⋊D43—22no—
112C2×C22⋊D43—22no—
113C2×C22⋊D43—41no—
114C2×C22⋊D43—41no—
115C2×C22⋊D43—41no—
116C2×C22⋊D43—41no—
117C22×Dic43—21no—
118C22×Dic43—41no—
119#10621898—22no—
120#10621898—22no—
121#10621898—22no—
122#10621898—22no—
123#10621898—22no—
124#10621898—22no—
125#10621898—22no—
126#10621898—22no—
127#10621898—41no—
128#10621898—41no—
129#10621898—41no—
130#10621898—41no—
131#10621898—41no—
132#10621898—41no—
133#10621898—41no—
134#10621898—41no—
135C2×D172—21no—
136C2×D172—21no—
137C2×D172—21no—
138C2×D172—21no—
139C2×D172—21no—
140C2×D172C22⋊C412yes—
141C2×C4×D43—22no—
142C2×C4×D43—22no—
143C2×C4×D43—41no—
144C2×C4×D43—41no—
145C2×C4×D43—41no—
146C2×C4×D43—41no—
147C2×Dic86—21no—
148C2×Dic86—21no—
149C2×Dic86—21no—
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86C22⋊C412yes—
153C4⋊C4×C43—22no—
154C4⋊C4×C43—22no—
155C4⋊C4×C43—41no—
156C4⋊C4×C43—41no—
157C4⋊C4×C43—41no—
158C4⋊C4×C43—41no—
159C22⋊C4×C43—22no—
160C22⋊C4×C43—22no—
161C22⋊C4×C43—22no—
162C22⋊C4×C43—22no—
163C22⋊C4×C43—41no—
164C22⋊C4×C43—41no—
165C42×C43—22no—
166C42×C43—22no—
167C42×C43—41no—
168C42×C43—41no—
169C42×C43—41no—
170C42×C43—41no—
171C22⋊Dic43—22no—
172C22⋊Dic43—41no—
173C4⋊Dic43—22no—
174C4⋊Dic43—41no—
175C4×Dic43—22no—
176C4×Dic43—41no—
177#10621877—22no—
178#10621877—22no—
179#10621877—22no—
180#10621877—22no—
181#10621877—41no—
182#10621877—41no—
183#10621877—41no—
184#10621877—41no—
185C2×C43⋊C8—22no—
186C2×C43⋊C8—22no—
187C2×C43⋊C8—41no—
188C2×C43⋊C8—41no—
189C2×C43⋊C8—41no—
190C2×C43⋊C8—41no—
191C23×C43—81no—
192C23×C43C4×D411yescharacteristic
193C23×C43#12011yescharacteristic
194C23×C43#12111yescharacteristic
195C23×C43#12111yescharacteristic
196C23×C43#12111yescharacteristic
197C23×C43#12311yescharacteristic
198C23×C43#12411yescharacteristic
199C22×D43—22no—
200C22×D43—41no—
201C22×D43—41no—
202C22×D43—82no—
203C2×C4×C43—42no—
204C2×C4×C43—42no—
205C2×C4×C43—42no—
206C2×C4×C43—82no—
207C2×C4×C43—82no—
208C2×C4×C43—82no—
209C2×C4×C43C2×C22⋊C411yescharacteristic
210C2×C4×C43#11711yescharacteristic
211C2×C4×C43#11711yescharacteristic
212C2×C4×C43C4×D411yescharacteristic
213C2×C4×C43C4×D411yescharacteristic
214C2×C4×C43C4×D411yescharacteristic
215C2×C4×C43#12011yescharacteristic
216C2×C4×C43#12111yescharacteristic
217C2×C4×C43#12111yescharacteristic
218C2×C4×C43#12111yescharacteristic
219C2×C4×C43#12111yescharacteristic
220C2×C4×C43#12111yescharacteristic
221C2×C4×C43#12311yescharacteristic
222C2×C4×C43#12311yescharacteristic
223C2×C4×C43#12311yescharacteristic
224C2×C4×C43#12311yescharacteristic
225C2×C4×C43#12311yescharacteristic
226C2×C4×C43#12311yescharacteristic
227C2×C4×C43#12311yescharacteristic
228C2×C4×C43#12311yescharacteristic
229C2×C4×C43#12311yescharacteristic
230C2×C4×C43#12411yescharacteristic
231C2×C4×C43#12411yescharacteristic
232C2×C4×C43#12411yescharacteristic
233C2×C4×C43#12611yescharacteristic
234C2×C4×C43#12611yescharacteristic
235C2×C4×C43#12611yescharacteristic
236C2×C4×C43#12611yescharacteristic
237C22⋊D43—42no—
238C22⋊D43—42no—
239C22⋊D43—42no—
240C22⋊D43—42no—
241C2×Dic43—22no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—42no—
245C2×Dic43—82no—
246D172—22no—
247D172—22no—
248D172—41no—
249D172—41no—
250C4×D43—42no—
251C4×D43—42no—
252C4×D43—42no—
253C4×D43—42no—
254Dic86—22no—
255Dic86—22no—
256Dic86—41no—
257Dic86—41no—
258C43⋊C8—42no—
259C43⋊C8—42no—
260#11186—431nomaximal, Sylow
261C22×C43—41no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43—41no—
265C22×C43—41no—
266C22×C43—41no—
267C22×C43—41no—
268C22×C43#38611yescharacteristic
269C22×C43#38811yescharacteristic
270C22×C43#38811yescharacteristic
271C22×C43#39411yescharacteristic
272C22×C43#39411yescharacteristic
273C22×C43#39411yescharacteristic
274C22×C43#39711yescharacteristic
275C2×D43—42no—
276C2×D43—82no—
277C2×D43—82no—
278C2×D43—82no—
279C4×C43—82no—
280C4×C43—82no—
281C4×C43—82no—
282C4×C43#38111yescharacteristic
283C4×C43#38611yescharacteristic
284C4×C43#38811yescharacteristic
285C4×C43#38811yescharacteristic
286C4×C43#39411yescharacteristic
287C4×C43#39711yescharacteristic
288C4×C43#39711yescharacteristic
289C4×C43#39711yescharacteristic
290Dic43—42no—
291Dic43—82no—
292C2×#421—431no—
293#2896—431no—
294C2×#410—431no—
295C2×#344—431no—
296#1740D4311yescharacteristic, complemented
297#1733—431no—
298#1733—431no—
299C2×C43—21no—
300C2×C43—21no—
301C2×C43—21no—
302C2×C43—21no—
303C2×C43—21no—
304C2×C43—21no—
305C2×C43—21no—
306C2×C43#144011yescharacteristic
307D43—82no—
308C22×#41—431no—
309C22×M16—431no—
310C22×M16—431no—
311C2×#117—431no—
312C2×#117C2×D4311yescharacteristic
313C2×#117C2×D4311yescharacteristic
314C2×#117C2×D4311yescharacteristic
315#421—862no—
316#421—862no—
317C2×#104—862no—
318#419—432no—
319#418—432no—
320#417—862no—
321#416—862no—
322#410—862no—
323#410—862no—
324C2×#99—862no—
325#344—862no—
326#342—22no—
327#339—862no—
328#339—862no—
329C43#1118611yescharacteristic, complemented, Sylow
330C2×#41—432no—
331C2×#41—432no—
332C2×#41—861no—
333C2×#41—861no—
334C2×#41—861no—
335C2×#41—861no—
336C2×#41—861no—
337C2×#41—861no—
338C2×#41—861no—
339C2×#41—861no—
340C2×#41—861no—
341C2×#41—861no—
342C22×Q8—431no—
343C22×D4—431no—
344C22×D4—861no—
345C23×C4—861no—
346C23×C4C22×D4311yescharacteristic
347C2×M16—432no—
348C2×M16—432no—
349C2×M16—861no—
350C2×M16—861no—
351C2×M16—861no—
352C2×M16—861no—
353C2×M16—861no—
354C2×M16—861no—
355C2×M16—861no—
356C2×M16—861no—
357C2×M16—861no—
358C2×M16—861no—
359C22×C8—861no—
360C22×C8—861no—
361#117—21no—
362#117—21no—
363#117—21no—
364#117—21no—
365#117—21no—
366#117—21no—
367#117—21no—
368#117—21no—
369#117—21no—
370#117—21no—
371#117—432no—
372#117—861no—
373#117—861no—
374#117—861no—
375#117C4×D4312yes—
376#117D17212yes—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—861no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—861no—
384C2×C22⋊C4C22⋊D4312yes—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—861no—
389#104—868no—
390#103—864no—
391#102—864no—
392#99—868no—
393C24—861no—
394C24C2×C22⋊D4311yescharacteristic
395#41—862no—
396#41—862no—
397#41—862no—
398#41—862no—
399#41—862no—
400#41—862no—
401#41—862no—
402#41—862no—
403#41—1721no—
404#41—1721no—
405#41—1721no—
406#41—1721no—
407#41—1721no—
408#41—1721no—
409#41—1721no—
410#41—1721no—
411C2×Q8—432no—
412C2×Q8—861no—
413C2×Q8—861no—
414C2×Q8—861no—
415C2×Q8—861no—
416C2×Q8—861no—
417C2×D4—432no—
418C2×D4—862no—
419C2×D4—862no—
420C2×D4—861no—
421C2×D4—861no—
422C2×D4—861no—
423C2×D4—861no—
424C2×D4—861no—
425C2×D4—1721no—
426C2×D4—1721no—
427C2×D4—1721no—
428C2×D4—1721no—
429C22×C4—22no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—861no—
433C22×C4—862no—
434C22×C4—862no—
435C22×C4—1721no—
436C22×C4—1721no—
437C22×C4—1721no—
438C22×C4—1721no—
439C22×C4—1721no—
440C22×C4C2×C4×D4311yescharacteristic
441C22×C4C2×D17211yescharacteristic
442C22×C4#1062189811yescharacteristic
443C22×C4#1062189811yescharacteristic
444C22×C4#1062189811yescharacteristic
445C22×C4#1062189811yescharacteristic
446C22×C4D4×D4311yescharacteristic
447C22×C4D4×D4311yescharacteristic
448C22×C4D4×D4311yescharacteristic
449C22×C4D4×D4311yescharacteristic
450C22×C4#1062190011yescharacteristic
451C22×C4#1062190011yescharacteristic
452C22×C4#1062190211yescharacteristic
453C22×C4#1062190211yescharacteristic
454M16—862no—
455M16—862no—
456M16—862no—
457M16—862no—
458M16—1721no—
459M16—1721no—
460M16—1721no—
461M16—1721no—
462C2×C8—862no—
463C2×C8—862no—
464C2×C8—1721no—
465C2×C8—1721no—
466C2×C8—1721no—
467C2×C8—1721no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4—41no—
474C4⋊C4—862no—
475C4⋊C4—1721no—
476C22⋊C4—22no—
477C22⋊C4—22no—
478C22⋊C4—22no—
479C22⋊C4—22no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—862no—
483C22⋊C4—1721no—
484C42—22no—
485C42—22no—
486C42—41no—
487C42—41no—
488C42—41no—
489C42—41no—
490C42—862no—
491C42—1721no—
492C23—81no—
493C23—862no—
494C23—3442no—
495C23—1721no—
496C23—1721no—
497C23C4×C22⋊D4311yescharacteristic
498C23#1306329311yescharacteristic
499C23#1306329611yescharacteristic
500C23#1306329711yescharacteristic
501C23#1306329911yescharacteristic
502C23#1306330811yescharacteristic
503C23#1306331411yescharacteristic
504Q8—862no—
505Q8—862no—
506Q8—1721no—
507Q8—1721no—
508D4—862no—
509D4—862no—
510D4—1722no—
511D4—1722no—
512D4—1722no—
513D4—1722no—
514D4—1721no—
515D4—1721no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—82no—
520C2×C4—82no—
521C2×C4—82no—
522C2×C4—862no—
523C2×C4—3442no—
524C2×C4—1722no—
525C2×C4—1721no—
526C2×C4—1721no—
527C2×C4—1722no—
528C2×C4—1722no—
529C2×C4—1722no—
530C2×C4—1722no—
531C2×C4C22⋊C4×D4311yescharacteristic
532C2×C4#1306328211yescharacteristic
533C2×C4#1306328311yescharacteristic
534C2×C4(C22⋊D43)⋊C411yescharacteristic
535C2×C4#1306328711yescharacteristic
536C2×C4C4×D17211yescharacteristic
537C2×C4#1306329511yescharacteristic
538C2×C4#1306329811yescharacteristic
539C2×C4#1306329811yescharacteristic
540C2×C4#1306329811yescharacteristic
541C2×C4#1306330011yescharacteristic
542C2×C4#1306330011yescharacteristic
543C2×C4#1306330711yescharacteristic
544C2×C4#1306330711yescharacteristic
545C2×C4#1306330711yescharacteristic
546C2×C4#1306330911yescharacteristic
547C2×C4#1306331011yescharacteristic
548C2×C4#1306331011yescharacteristic
549C2×C4#1306331011yescharacteristic
550C2×C4#1306331011yescharacteristic
551C2×C4#1306331011yescharacteristic
552C2×C4#1306331111yescharacteristic
553C2×C4#1306331111yescharacteristic
554C2×C4#1306331311yescharacteristic
555C2×C4#1306331911yescharacteristic
556C2×C4#1306332011yescharacteristic
557C2×C4#1306332011yescharacteristic
558C2×C4#1306332011yescharacteristic
559C8—1722no—
560C8—1722no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—3442no—
569C22—3442no—
570C22—3442no—
571C22—1722no—
572C22#1458277511yescharacteristic
573C22#1458278911yescharacteristic
574C22#1458279011yescharacteristic
575C22#1458281411yescharacteristic
576C22#1458281511yescharacteristic
577C22#1458281611yescharacteristic
578C22#1458282511yescharacteristic
579C4—82no—
580C4—82no—
581C4—82no—
582C4—3442no—
583C4—1722no—
584C4#1458276111yescharacteristic
585C4#1458277711yescharacteristic
586C4#1458278811yescharacteristic
587C4#1458279111yescharacteristic
588C4#1458281711yescharacteristic
589C4#1458282611yescharacteristic
590C4#1458282811yescharacteristic
591C4#1458282811yescharacteristic
592C2—21no—
593C2—21no—
594C2—21no—
595C2—21no—
596C2—21no—
597C2—21no—
598C2—21no—
599C2—3442no—
600C2#1913284311yescharacteristic
subgroupG/H
centerC4#14582817
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1740C2
socleC2×C43#1440
prime radicalC22×#10621898C22
cosocleC23×C4×C43C23
hypercenter#1740D43
hypocenterC43#11186
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C23×C4 ◁ #1740

Complements

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

NH ≅ G/Ntype
4. C2×#14582669C2semidirect
5. #19134305C2semidirect
6. #19134304C2semidirect
7. C43×#1740C2semidirect
15. #14582907C4semidirect
16. #14582903C4semidirect
296. #1740D43semidirect
329. C43#11186semidirect

Maximal subgroups

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

subgroupindex
C2×#145829172
#191431122
C2×#145828722
C2×#145826692
#191343052
#191343042
C43×#17402
#1118643