Finite Group Databasebeta

← #25003787

Subgroups — #25003787

Order 11008.

882 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582872C211yesmaximal, characteristic
2#19143039C211yesmaximal, characteristic
3C2×#14582865C211yesmaximal, characteristic
4C2×#14582670C211yesmaximal, characteristic, complemented
5C2×#14582669C211yesmaximal, characteristic, complemented
6#19134291C211yesmaximal, characteristic, complemented
7C2×C43×#424C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10C22×#10621877C2211yescharacteristic
11C2×#13063284C2211yescharacteristic
12#14582872—22no—
13#14582872—22no—
14C2×#13063239C414yes—
15#14582867—22no—
16#14582865—22no—
17#14582865—22no—
18#14582865—22no—
19#14582862—22no—
20C2×(C2×D43)⋊C8—22no—
21#14582670—22no—
22#14582669—22no—
23#14582653—22no—
24C22×M16×C43C2211yescharacteristic
25C23×C8×C43C2211yescharacteristic
26C2×#117×C43C2211yescharacteristic
27C43×#424—22no—
28C43×#424—22no—
29C2×C4⋊C8×C43—22no—
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×#10621898—21no—
40C2×#10621898—21no—
41C2×#10621898—21no—
42C22×Dic86Q811yescharacteristic
43C22×D172Q811yescharacteristic
44C22×C22⋊D43C2×C412yes—
45C22×C4×D43D412yes—
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×#10621877—21no—
56C2×#10621877—21no—
57C2×#10621877D412yes—
58C22×C43⋊C8—21no—
59C22×C43⋊C8D412yes—
60#13063284—21no—
61#13063284—21no—
62#13063284—21no—
63#13063284—21no—
64C2×C4⋊Dic43—21no—
65C2×C22⋊Dic43C2×C412yes—
66C2×C4×Dic43—21no—
67#13063239—28no—
68(C2×D43)⋊C8—28no—
69(C2×D43)⋊C8—28no—
70C23×C4×C43C2311yescharacteristic
71C2×M16×C43—21no—
72C2×M16×C43—21no—
73C2×M16×C43—21no—
74C2×M16×C43—21no—
75C2×M16×C43—21no—
76C2×M16×C43—21no—
77C22×C8×C43—21no—
78C22×C8×C43—21no—
79C22×C8×C43—21no—
80C22×C8×C43—21no—
81C22×C8×C43—21no—
82C22×C8×C43—21no—
83C22×C8×C43D412yes—
84C22×C8×C43D412yes—
85#117×C43—21no—
86#117×C43—21no—
87#117×C43D412yes—
88#117×C43D412yes—
89C2×C4⋊C4×C43—21no—
90C2×C22⋊C4×C43C2×C412yes—
91C2×C42×C43—21no—
92C4⋊C8×C43—28no—
93C24×C43C22×C411yescharacteristic
94C23×D43C4⋊C412yes—
95C22×C4×C43—22no—
96C22×C4×C43C2×D411yescharacteristic
97C22×C4×C43C2×D411yescharacteristic
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43C2×D411yescharacteristic
100C22×C4×C43C2×D411yescharacteristic
101C22×C4×C43C2×D411yescharacteristic
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43C2×Q811yescharacteristic
104C22×C4×C43#4111yescharacteristic
105C22×C4×C43#4111yescharacteristic
106C22×C4×C43#4111yescharacteristic
107C22×C4×C43#4111yescharacteristic
108C22×C4×C43#4111yescharacteristic
109C22×C4×C43#4111yescharacteristic
110C2×C22⋊D43—22no—
111C2×C22⋊D43—22no—
112C2×C22⋊D43—22no—
113C2×C22⋊D43—22no—
114C2×C22⋊D43—22no—
115C2×C22⋊D43—22no—
116C22×Dic43—22no—
117C22×Dic43C4⋊C412yes—
118#10621898—41no—
119#10621898—41no—
120#10621898—41no—
121#10621898—41no—
122#10621898—41no—
123#10621898—41no—
124#10621898—41no—
125#10621898—41no—
126#10621898—41no—
127#10621898—41no—
128#10621898—41no—
129#10621898—41no—
130#10621898—41no—
131#10621898—41no—
132#10621898—41no—
133#10621898—41no—
134C2×D172—21no—
135C2×D172—21no—
136C2×D172—21no—
137C2×D172—21no—
138C2×D172—21no—
139C2×D172—21no—
140C2×C4×D43—22no—
141C2×C4×D43—22no—
142C2×C4×D43—22no—
143C2×C4×D43—22no—
144C2×C4×D43—22no—
145C2×C4×D43—22no—
146C2×Dic86—21no—
147C2×Dic86—21no—
148C2×Dic86—21no—
149C2×Dic86—21no—
150C2×Dic86—21no—
151C2×Dic86—21no—
152M16×C43—41no—
153M16×C43—41no—
154M16×C43—41no—
155M16×C43—41no—
156C2×C8×C43—22no—
157C2×C8×C43—22no—
158C2×C8×C43—22no—
159C2×C8×C43—22no—
160C2×C8×C43—22no—
161C2×C8×C43—22no—
162C2×C8×C43—41no—
163C2×C8×C43—41no—
164C2×C8×C43—41no—
165C2×C8×C43—41no—
166C4⋊C4×C43—22no—
167C4⋊C4×C43—22no—
168C22⋊C4×C43—22no—
169C22⋊C4×C43C22⋊C414yes—
170C42×C43—22no—
171C42×C43—22no—
172C22⋊Dic43—22no—
173C22⋊Dic43—22no—
174C4⋊Dic43—41no—
175C4⋊Dic43—41no—
176C4×Dic43—41no—
177C4×Dic43—41no—
178#10621877—22no—
179#10621877—22no—
180#10621877—41no—
181#10621877—41no—
182#10621877—41no—
183#10621877—41no—
184#10621877—41no—
185#10621877—41no—
186C2×C43⋊C8—22no—
187C2×C43⋊C8—22no—
188C2×C43⋊C8—22no—
189C2×C43⋊C8—22no—
190C2×C43⋊C8—41no—
191C2×C43⋊C8—41no—
192C23×C43—42no—
193C23×C43C2×C22⋊C411yescharacteristic
194C23×C43C2×C4⋊C411yescharacteristic
195C23×C43#11711yescharacteristic
196C23×C43C4×D411yescharacteristic
197C23×C43C4×D411yescharacteristic
198C23×C43C4×D411yescharacteristic
199C23×C43C4×D411yescharacteristic
200C22×D43—22no—
201C22×D43—22no—
202C22×D43—22no—
203C22×D43—44no—
204C2×C4×C43—24no—
205C2×C4×C43—44no—
206C2×C4×C43#12011yescharacteristic
207C2×C4×C43#12011yescharacteristic
208C2×C4×C43#12011yescharacteristic
209C2×C4×C43#12111yescharacteristic
210C2×C4×C43#12111yescharacteristic
211C2×C4×C43#12111yescharacteristic
212C2×C4×C43#12111yescharacteristic
213C2×C4×C43#12111yescharacteristic
214C2×C4×C43#12111yescharacteristic
215C2×C4×C43#12111yescharacteristic
216C2×C4×C43#12111yescharacteristic
217C2×C4×C43C22⋊Q811yescharacteristic
218C2×C4×C43C22⋊Q811yescharacteristic
219C2×C4×C43C22⋊Q811yescharacteristic
220C2×C4×C43C22⋊Q811yescharacteristic
221C2×C4×C43C22⋊Q811yescharacteristic
222C2×C4×C43C22⋊Q811yescharacteristic
223C2×C4×C43#12311yescharacteristic
224C2×C4×C43#12311yescharacteristic
225C2×C4×C43#12311yescharacteristic
226C2×C4×C43#12311yescharacteristic
227C2×C4×C43#12311yescharacteristic
228C2×C4×C43#12411yescharacteristic
229C2×C4×C43#12411yescharacteristic
230C2×C4×C43#12411yescharacteristic
231C2×C4×C43#12611yescharacteristic
232C2×C4×C43#12611yescharacteristic
233C2×C4×C43#12711yescharacteristic
234C22⋊D43—42no—
235C22⋊D43—42no—
236C22⋊D43—42no—
237C22⋊D43—42no—
238C2×Dic43—22no—
239C2×Dic43—22no—
240C2×Dic43—22no—
241C2×Dic43—44no—
242C2×Dic43—42no—
243D172—41no—
244D172—41no—
245D172—41no—
246D172—41no—
247C4×D43—42no—
248C4×D43—42no—
249C4×D43—42no—
250C4×D43—42no—
251Dic86—41no—
252Dic86—41no—
253Dic86—41no—
254Dic86—41no—
255C8×C43—42no—
256C8×C43—42no—
257C43⋊C8—42no—
258C43⋊C8—42no—
259#11088—431nomaximal, Sylow
260C22×C43—22no—
261C22×C43—22no—
262C22×C43—22no—
263C22×C43—41no—
264C22×C43—41no—
265C22×C43—41no—
266C22×C43—41no—
267C22×C43#38011yescharacteristic
268C22×C43#38511yescharacteristic
269C22×C43#38511yescharacteristic
270C22×C43#38611yescharacteristic
271C22×C43#38811yescharacteristic
272C22×C43#38811yescharacteristic
273C22×C43#39011yescharacteristic
274C2×D43—44no—
275C2×D43—44no—
276C2×D43—42no—
277C2×D43—82no—
278C4×C43—44no—
279C4×C43#39211yescharacteristic
280C4×C43#39311yescharacteristic
281C4×C43#39411yescharacteristic
282C4×C43#39411yescharacteristic
283C4×C43#39611yescharacteristic
284C4×C43#39611yescharacteristic
285C4×C43#39711yescharacteristic
286C4×C43#39911yescharacteristic
287Dic43—42no—
288Dic43—82no—
289C2×#424D4311yescharacteristic, complemented
290C2×#410—431no—
291#2879—431no—
292C2×#408—431no—
293C2×#344—431no—
294C2×#344—431no—
295#1729—431no—
296C2×C43—21no—
297C2×C43—21no—
298C2×C43—21no—
299C2×C43—21no—
300C2×C43—21no—
301C2×C43—21no—
302C2×C43#143911yescharacteristic
303C2×C43#186812yes—
304D43—82no—
305C22×#41—431no—
306C22×M16—431no—
307C22×M16—431no—
308C22×M16C2×D4311yescharacteristic
309C23×C8C2×D4311yescharacteristic
310C2×#117—431no—
311C2×#117C2×D4311yescharacteristic
312#424—22no—
313#424—22no—
314C2×C4⋊C8—22no—
315#410—862no—
316#410—862no—
317C2×#99—434no—
318#408—862no—
319#408—862no—
320#408—862no—
321#408—862no—
322#407—862no—
323C2×C22⋊C8—862no—
324#344—862no—
325#344—862no—
326#336—862no—
327C43#1108811yescharacteristic, complemented, Sylow
328C2×#41—861no—
329C2×#41—861no—
330C2×#41—861no—
331C2×#41—861no—
332C2×#41—861no—
333C2×#41—861no—
334C2×#41—861no—
335C2×#41—861no—
336C2×#41—861no—
337C2×#41—861no—
338C2×#41—861no—
339C2×#41—861no—
340C22×Q8—431no—
341C22×D4—432no—
342C22×D4—431no—
343C23×C4—432no—
344C23×C4C22×D4311yescharacteristic
345C2×M16—21no—
346C2×M16—21no—
347C2×M16—21no—
348C2×M16—21no—
349C2×M16—21no—
350C2×M16—21no—
351C2×M16—432no—
352C2×M16—861no—
353C2×M16—861no—
354C2×M16—861no—
355C2×M16—861no—
356C2×M16—861no—
357C2×M16—861no—
358C2×M16—861no—
359C2×M16—861no—
360C2×M16—861no—
361C2×M16—861no—
362C2×M16—861no—
363C22×C8—21no—
364C22×C8—21no—
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—21no—
368C22×C8—21no—
369C22×C8—432no—
370C22×C8—861no—
371C22×C8C22⋊D4312yes—
372C22×C8C22⋊D4312yes—
373#117—21no—
374#117—21no—
375#117—861no—
376#117—861no—
377#117—861no—
378#117—861no—
379#117D17212yes—
380#117C22⋊D4312yes—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—861no—
383C2×C22⋊C4—432no—
384C2×C22⋊C4C4×D4312yes—
385C2×C42—21no—
386C2×C42—861no—
387C4⋊C8—28no—
388#99—868no—
389C22⋊C8—868no—
390C22⋊C8—868no—
391C24—432no—
392C24C2×C4×D4311yescharacteristic
393#41—1721no—
394#41—1721no—
395#41—1721no—
396#41—1721no—
397#41—1721no—
398#41—1721no—
399#41—1721no—
400#41—1721no—
401#41—1721no—
402#41—1721no—
403#41—1721no—
404#41—1721no—
405#41—1721no—
406#41—1721no—
407#41—1721no—
408#41—1721no—
409C2×Q8—861no—
410C2×Q8—861no—
411C2×Q8—861no—
412C2×Q8—861no—
413C2×Q8—861no—
414C2×Q8—861no—
415C2×D4—862no—
416C2×D4—862no—
417C2×D4—862no—
418C2×D4—862no—
419C2×D4—862no—
420C2×D4—862no—
421C2×D4—861no—
422C2×D4—861no—
423C2×D4—861no—
424C2×D4—861no—
425C2×D4—861no—
426C2×D4—861no—
427C22×C4—22no—
428C22×C4—432no—
429C22×C4—862no—
430C22×C4—862no—
431C22×C4—862no—
432C22×C4—862no—
433C22×C4—862no—
434C22×C4—862no—
435C22×C4—862no—
436C22×C4C2×D17211yescharacteristic
437C22×C4#1062189811yescharacteristic
438C22×C4#1062189811yescharacteristic
439C22×C4D4×D4311yescharacteristic
440C22×C4D4×D4311yescharacteristic
441C22×C4D4×D4311yescharacteristic
442C22×C4#1062190011yescharacteristic
443C22×C4Q8×D4311yescharacteristic
444C22×C4#1062190211yescharacteristic
445C22×C4#1062190211yescharacteristic
446C22×C4#1062190211yescharacteristic
447C22×C4C2×C22⋊D4311yescharacteristic
448C22×C4C2×C22⋊D4311yescharacteristic
449C22×C4C2×C22⋊D4311yescharacteristic
450M16—41no—
451M16—41no—
452M16—41no—
453M16—41no—
454M16—862no—
455M16—862no—
456M16—1721no—
457M16—1721no—
458M16—1721no—
459M16—1721no—
460M16—1721no—
461M16—1721no—
462C2×C8—22no—
463C2×C8—22no—
464C2×C8—22no—
465C2×C8—22no—
466C2×C8—22no—
467C2×C8—22no—
468C2×C8—41no—
469C2×C8—41no—
470C2×C8—41no—
471C2×C8—41no—
472C2×C8—862no—
473C2×C8—862no—
474C2×C8—862no—
475C2×C8—862no—
476C2×C8—1721no—
477C2×C8—1721no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—1721no—
481C4⋊C4—1721no—
482C22⋊C4—22no—
483C22⋊C4—862no—
484C22⋊C4—862no—
485C22⋊C4(C2×D43)⋊C414yes—
486C42—22no—
487C42—22no—
488C42—1721no—
489C42—1721no—
490C23—42no—
491C23—862no—
492C23—862no—
493C23—862no—
494C23—1724no—
495C23C2×(C2×D43)⋊C411yescharacteristic
496C23C4⋊C4×D4311yescharacteristic
497C23#1306328311yescharacteristic
498C23C4×C22⋊D4311yescharacteristic
499C23C4×C22⋊D4311yescharacteristic
500C23#1306328711yescharacteristic
501C23#1306328711yescharacteristic
502Q8—1721no—
503Q8—1721no—
504Q8—1721no—
505Q8—1721no—
506D4—1722no—
507D4—1722no—
508D4—1722no—
509D4—1722no—
510D4—1721no—
511D4—1721no—
512D4—1721no—
513D4—1721no—
514C2×C4—24no—
515C2×C4—44no—
516C2×C4—862no—
517C2×C4—862no—
518C2×C4—862no—
519C2×C4—1724no—
520C2×C4—1722no—
521C2×C4—1722no—
522C2×C4—1722no—
523C2×C4—1722no—
524C2×C4—1722no—
525C2×C4#1306329311yescharacteristic
526C2×C4#1306329311yescharacteristic
527C2×C4#1306329411yescharacteristic
528C2×C4#1306329611yescharacteristic
529C2×C4#1306329711yescharacteristic
530C2×C4#1306329711yescharacteristic
531C2×C4#1306329911yescharacteristic
532C2×C4#1306329911yescharacteristic
533C2×C4#1306330011yescharacteristic
534C2×C4#1306330011yescharacteristic
535C2×C4#1306330011yescharacteristic
536C2×C4#1306330111yescharacteristic
537C2×C4#1306330111yescharacteristic
538C2×C4#1306330111yescharacteristic
539C2×C4#1306330311yescharacteristic
540C2×C4#1306330311yescharacteristic
541C2×C4#1306330511yescharacteristic
542C2×C4#1306330811yescharacteristic
543C2×C4#1306331011yescharacteristic
544C2×C4#1306331011yescharacteristic
545C2×C4#1306331011yescharacteristic
546C2×C4#1306331011yescharacteristic
547C2×C4#1306331411yescharacteristic
548C2×C4#1306331411yescharacteristic
549C2×C4#1306331411yescharacteristic
550C2×C4#1306332011yescharacteristic
551C2×C4#1306332011yescharacteristic
552C2×C4#1306332111yescharacteristic
553C8—42no—
554C8—42no—
555C8—1722no—
556C8—1722no—
557C22—22no—
558C22—22no—
559C22—22no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—3442no—
565C22—1724no—
566C22—1724no—
567C22—1722no—
568C22#1458275611yescharacteristic
569C22#1458277011yescharacteristic
570C22#1458277011yescharacteristic
571C22#1458277811yescharacteristic
572C22#1458278911yescharacteristic
573C22#1458278911yescharacteristic
574C22#1458280011yescharacteristic
575C4—44no—
576C4—3442no—
577C4—1722no—
578C4#1458280711yescharacteristic
579C4#1458281011yescharacteristic
580C4#1458281611yescharacteristic
581C4#1458281611yescharacteristic
582C4#1458282111yescharacteristic
583C4#1458282111yescharacteristic
584C4#1458282511yescharacteristic
585C4#1458283411yescharacteristic
586C2—21no—
587C2—21no—
588C2—21no—
589C2—21no—
590C2—21no—
591C2—21no—
592C2—3442no—
593C2#1913283711yescharacteristic
594C2#1913487912yes—
subgroupG/H
centerC2×C4#13063293
commutatorC24×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#424C2
socleC22×C43#385
prime radicalC22×#10621898C22
cosocleC23×C4×C43C23
hypercenterC2×#424D43
hypocenterC43#11088
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#424

Complements

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

NH ≅ G/Ntype
4. C2×#14582670C2semidirect
5. C2×#14582669C2semidirect
6. #19134291C2semidirect
7. C2×C43×#424C2semidirect
289. C2×#424D43semidirect
327. C43#11088semidirect

Maximal subgroups

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

subgroupindex
C2×#145828722
#191430392
C2×#145828652
C2×#145826702
C2×#145826692
#191342912
C2×C43×#4242
#1108843