Finite Group Databasebeta

← #25070231

Subgroups — #25070231

Order 11008.

1000 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144515C211yesmaximal, characteristic, complemented
2C2×#14583227C211yesmaximal, characteristic, complemented
3#19139088C211yesmaximal, characteristic, complemented
4#19133609C214yesmaximal, complemented
5#19133586C214yesmaximal, complemented
6#19133115C211yesmaximal, characteristic, complemented
7#19133086C211yesmaximal, characteristic, complemented
8#19132955C211yesmaximal, characteristic, complemented
9C43×#3536C211yesmaximal, characteristic
10C22×C4⋊Dic43C2211yescharacteristic
11#14583232—21no—
12#14583227—22no—
13#14583227C2214yes—
14#14583227C2212yes—
15#14583215—21no—
16#14583210C2212yes—
17#14582942—21no—
18C2×#13063256—21no—
19#14582900—21no—
20C2×#13063249—21no—
21#14582863C2211yescharacteristic
22C2×C22⋊(C43⋊C8)C2211yescharacteristic
23#14582824C2214yes—
24#14582802—21no—
25#14582779—22no—
26#14582764—21no—
27C4×C22⋊Dic43C2211yescharacteristic
28#14582636C2212yes—
29#14582636C2214yes—
30#14582633C2212yes—
31#14582623C2214yes—
32C43×#562—22no—
33C43×#554—21no—
34C43×#548—21no—
35C43×#547—21no—
36C43×#546—22no—
37C43×#546—21no—
38C43×#543C2212yes—
39C43×#542—21no—
40C43×#539—21no—
41C43×#538C2212yes—
42C43×#537—21no—
43C43×#537—21no—
44C43×#525C2211yescharacteristic
45C2×C22⋊Q8×C43C2211yescharacteristic
46C2×#121×C43C2211yescharacteristic
47C23×Dic43—21no—
48C2×#10621877—21no—
49C22×C43⋊C8—21no—
50C2×C4⋊Dic43—21no—
51C2×C4⋊Dic43—21no—
52C2×C4⋊Dic43—21no—
53C2×C4⋊Dic43—21no—
54C2×C4⋊Dic43—21no—
55C2×C4⋊Dic43C2312yes—
56C2×C22⋊Dic43—21no—
57C2×C22⋊Dic43—24no—
58C2×C4×Dic43—21no—
59#13063258—22no—
60#13063256—24no—
61#13063256—22no—
62#13063249—24no—
63#13063249—22no—
64#13063246—22no—
65C22⋊(C43⋊C8)—21no—
66C22⋊(C43⋊C8)—21no—
67C22⋊(C43⋊C8)C2312yes—
68C22⋊(C43⋊C8)C2312yes—
69C43⋊#95—24no—
70C43⋊#95C2312yes—
71C2×#41×C43—22no—
72C2×#41×C43—21no—
73C2×#41×C43D411yescharacteristic
74C22×Q8×C43D411yescharacteristic
75C22×D4×C43D411yescharacteristic
76C22×D4×C43D412yes—
77C23×C4×C43C2311yescharacteristic
78C4⋊Q8×C43—21no—
79#126×C43—22no—
80#125×C43—22no—
81#124×C43—21no—
82#124×C43—22no—
83#124×C43—22no—
84#123×C43—22no—
85#123×C43—22no—
86#123×C43—22no—
87#123×C43—21no—
88#123×C43—22no—
89C22⋊Q8×C43—21no—
90C22⋊Q8×C43—22no—
91C22⋊Q8×C43—22no—
92C22⋊Q8×C43—22no—
93C22⋊Q8×C43—21no—
94C22⋊Q8×C43—21no—
95C22⋊Q8×C43—22no—
96C22⋊Q8×C43—22no—
97C22⋊Q8×C43—22no—
98C22⋊Q8×C43D412yes—
99C22⋊Q8×C43D411yescharacteristic
100C22⋊Q8×C43C2312yes—
101C22⋊Q8×C43C2311yescharacteristic
102#121×C43—21no—
103#121×C43—22no—
104#121×C43—22no—
105#121×C43—22no—
106#121×C43—22no—
107#121×C43—22no—
108#121×C43—21no—
109#121×C43—21no—
110#121×C43—21no—
111#121×C43—21no—
112#121×C43D411yescharacteristic
113#121×C43C2311yescharacteristic
114#120×C43—21no—
115#120×C43—22no—
116C4×Q8×C43—21no—
117C4×D4×C43—22no—
118C4×D4×C43—21no—
119C4×D4×C43—21no—
120C4×D4×C43—21no—
121C4×D4×C43—22no—
122#117×C43D411yescharacteristic
123C2×C4⋊C4×C43—21no—
124C2×C4⋊C4×C43—21no—
125C2×C4⋊C4×C43D411yescharacteristic
126C2×C4⋊C4×C43D411yescharacteristic
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43—22no—
129C2×C22⋊C4×C43C2312yes—
130C24×C43C2×D411yescharacteristic
131C24×C43C2×D412yes—
132#41×C43—42no—
133#41×C43—84no—
134#41×C43—82no—
135C2×Q8×C43—22no—
136C2×Q8×C43—21no—
137C2×Q8×C43—42no—
138C2×Q8×C43C2×D411yescharacteristic
139C2×Q8×C43C2×D412yes—
140C2×D4×C43—22no—
141C2×D4×C43—22no—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—22no—
146C2×D4×C43—21no—
147C2×D4×C43—22no—
148C2×D4×C43—21no—
149C2×D4×C43—44no—
150C2×D4×C43—42no—
151C2×D4×C43C2×D411yescharacteristic
152C22×C4×C43—22no—
153C22×C4×C43—22no—
154C22×C4×C43—22no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—42no—
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2×D412yes—
165C22×C4×C43C2411yescharacteristic
166C22×Dic43—22no—
167C22×Dic43—22no—
168C22×Dic43—41no—
169C22×Dic43—41no—
170C22×Dic43—82no—
171C4⋊C4×C43—22no—
172C4⋊C4×C43—22no—
173C4⋊C4×C43—22no—
174C4⋊C4×C43—22no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—22no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—22no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43C2×D412yes—
183C4⋊C4×C43C2×D411yescharacteristic
184C4⋊C4×C43C2×D411yescharacteristic
185C22⋊C4×C43—22no—
186C22⋊C4×C43—22no—
187C22⋊C4×C43—22no—
188C22⋊C4×C43—22no—
189C22⋊C4×C43—22no—
190C22⋊C4×C43—21no—
191C22⋊C4×C43—22no—
192C22⋊C4×C43—22no—
193C22⋊C4×C43—21no—
194C22⋊C4×C43—22no—
195C22⋊C4×C43—21no—
196C22⋊C4×C43—21no—
197C22⋊C4×C43—22no—
198C22⋊C4×C43—21no—
199C42×C43—22no—
200C42×C43—21no—
201C22⋊Dic43—42no—
202C22⋊Dic43—84no—
203C4⋊Dic43—22no—
204C4⋊Dic43—22no—
205C4⋊Dic43—41no—
206C4⋊Dic43—41no—
207C4×Dic43—42no—
208#10621877—42no—
209C2×C43⋊C8—22no—
210C2×C43⋊C8—22no—
211C2×C43⋊C8—42no—
212C23×C43—22no—
213C23×C43—22no—
214C23×C43—22no—
215C23×C43—21no—
216C23×C43—24no—
217C23×C43—41no—
218C23×C43—42no—
219C23×C43—42no—
220C23×C43#12011yescharacteristic
221C23×C43#12011yescharacteristic
222C23×C43C22×D411yescharacteristic
223Q8×C43—42no—
224Q8×C43—41no—
225Q8×C43—42no—
226Q8×C43—82no—
227D4×C43—41no—
228D4×C43—42no—
229D4×C43—44no—
230D4×C43—42no—
231D4×C43—42no—
232D4×C43—81no—
233D4×C43—82no—
234D4×C43—81no—
235D4×C43—82no—
236D4×C43—82no—
237C2×C4×C43—22no—
238C2×C4×C43—22no—
239C2×C4×C43—22no—
240C2×C4×C43—21no—
241C2×C4×C43—22no—
242C2×C4×C43—21no—
243C2×C4×C43—22no—
244C2×C4×C43—21no—
245C2×C4×C43—22no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—42no—
250C2×C4×C43—42no—
251C2×C4×C43—42no—
252C2×C4×C43—81no—
253C2×C4×C43—82no—
254C2×C4×C43—82no—
255C2×C4×C43—82no—
256C2×C4×C43#12011yescharacteristic
257C2×C4×C43#12011yescharacteristic
258C2×C4×C43C22×D411yescharacteristic
259C2×C4×C43C22×D411yescharacteristic
260C2×Dic43—42no—
261C2×Dic43—42no—
262C2×Dic43—42no—
263C2×Dic43—42no—
264C2×Dic43—44no—
265C2×Dic43—82no—
266C2×Dic43—82no—
267C43⋊C8—42no—
268C43⋊C8—42no—
269#18266—431nomaximal, Sylow
270C22×C43—21no—
271C22×C43—21no—
272C22×C43—21no—
273C22×C43—21no—
274C22×C43—21no—
275C22×C43—21no—
276C22×C43—21no—
277C22×C43—44no—
278C22×C43—42no—
279C22×C43—41no—
280C22×C43—42no—
281C22×C43—41no—
282C22×C43—42no—
283C22×C43—41no—
284C22×C43—84no—
285C22×C43#45512yes—
286C22×C43C2×#12011yescharacteristic
287C22×C43#57712yes—
288C4×C43—21no—
289C4×C43—21no—
290C4×C43—21no—
291C4×C43—41no—
292C4×C43—42no—
293C4×C43—42no—
294C4×C43—41no—
295C4×C43—41no—
296C4×C43—42no—
297C4×C43#45812yes—
298Dic43—82no—
299Dic43—82no—
300#3536D4311yescharacteristic
301#3092—431no—
302C2×#483—431no—
303#2504—431no—
304#1612—434no—
305#1608—434no—
306#1508—431no—
307#1501—431no—
308#1471—431no—
309C2×C43—22no—
310C2×C43—22no—
311C2×C43—41no—
312C2×C43—81no—
313C2×C43—82no—
314C2×C43#301011yescharacteristic
315C2×C43C2×#45511yescharacteristic
316C2×C43C2×#45811yescharacteristic
317#562—22no—
318#554—21no—
319#548—21no—
320#547—21no—
321#546—22no—
322#546—21no—
323#543C2×D4312yes—
324#542—21no—
325#539—21no—
326#538C2×D4312yes—
327#537—21no—
328#537—21no—
329#525C2×D4311yescharacteristic
330C2×C22⋊Q8C2×D4311yescharacteristic
331C2×#121C2×D4311yescharacteristic
332C22×C4⋊C4—431no—
333#484—861no—
334#483—434no—
335#483—432no—
336#483—862no—
337#481—861no—
338#480—432no—
339#428—861no—
340C2×#106—861no—
341#417—861no—
342C2×#103—861no—
343#407—431no—
344C2×C22⋊C8—431no—
345#397—434no—
346#390—861no—
347#386—862no—
348#382—861no—
349C4×C22⋊C4—431no—
350#328—432no—
351#328—434no—
352#327—432no—
353#323—434no—
354C43#1826611yescharacteristic, complemented, Sylow
355C2×#41—22no—
356C2×#41—21no—
357C2×#41C22⋊D4311yescharacteristic
358C22×Q8C22⋊D4311yescharacteristic
359C22×D4C22⋊D4312yes—
360C22×D4C22⋊D4311yescharacteristic
361C23×C4—861no—
362C23×C4C22×D4311yescharacteristic
363C2×M16—861no—
364C22×C8—861no—
365C4⋊Q8—21no—
366#126—22no—
367#125—22no—
368#124—21no—
369#124—22no—
370#124—22no—
371#123—22no—
372#123—22no—
373#123—22no—
374#123—21no—
375#123—22no—
376C22⋊Q8—21no—
377C22⋊Q8—22no—
378C22⋊Q8—22no—
379C22⋊Q8—22no—
380C22⋊Q8—21no—
381C22⋊Q8—21no—
382C22⋊Q8—22no—
383C22⋊Q8—22no—
384C22⋊Q8—22no—
385C22⋊Q8C22⋊D4312yes—
386C22⋊Q8C22⋊D4311yescharacteristic
387C22⋊Q8C22×D4312yes—
388C22⋊Q8C22×D4311yescharacteristic
389#121—21no—
390#121—22no—
391#121—22no—
392#121—22no—
393#121—22no—
394#121—22no—
395#121—21no—
396#121—21no—
397#121—21no—
398#121—21no—
399#121C22⋊D4311yescharacteristic
400#121C22×D4311yescharacteristic
401#120—21no—
402#120—22no—
403C4×Q8—21no—
404C4×D4—22no—
405C4×D4—21no—
406C4×D4—21no—
407C4×D4—21no—
408C4×D4—22no—
409#117C22⋊D4311yescharacteristic
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—432no—
413C2×C4⋊C4—861no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4—861no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4C22⋊D4311yescharacteristic
419C2×C4⋊C4C22⋊D4311yescharacteristic
420C2×C22⋊C4—21no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—864no—
423C2×C22⋊C4—861no—
424C2×C22⋊C4C22×D4312yes—
425C2×C42—861no—
426#107—862no—
427#106—864no—
428#106—862no—
429#103—864no—
430#103—862no—
431#102—862no—
432C22⋊C8—432no—
433C22⋊C8—432no—
434C22⋊C8—861no—
435C22⋊C8—861no—
436#95—432no—
437#95—864no—
438C24C2×C22⋊D4311yescharacteristic
439C24C2×C22⋊D4312yes—
440#41—42no—
441#41—84no—
442#41—82no—
443C2×Q8—22no—
444C2×Q8—21no—
445C2×Q8—42no—
446C2×Q8C2×C22⋊D4311yescharacteristic
447C2×Q8C2×C22⋊D4312yes—
448C2×D4—21no—
449C2×D4—22no—
450C2×D4—21no—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—21no—
454C2×D4—22no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—42no—
458C2×D4—44no—
459C2×D4C2×C22⋊D4311yescharacteristic
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—42no—
467C22×C4—862no—
468C22×C4—862no—
469C22×C4—3442no—
470C22×C4—1721no—
471C22×C4—1721no—
472C22×C4C2×C22⋊D4311yescharacteristic
473C22×C4C2×C22⋊D4311yescharacteristic
474C22×C4C2×C22⋊D4311yescharacteristic
475C22×C4C2×C22⋊D4312yes—
476C22×C4C2×C22⋊D4311yescharacteristic
477C22×C4C2×C22⋊D4311yescharacteristic
478C22×C4C23×D4311yescharacteristic
479M16—1722no—
480C2×C8—862no—
481C2×C8—862no—
482C2×C8—1722no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—22no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—22no—
493C4⋊C4—21no—
494C4⋊C4—862no—
495C4⋊C4—862no—
496C4⋊C4—1721no—
497C4⋊C4—1721no—
498C4⋊C4C2×C22⋊D4312yes—
499C4⋊C4C2×C22⋊D4311yescharacteristic
500C4⋊C4C2×C22⋊D4311yescharacteristic
501C22⋊C4—22no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—22no—
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—22no—
510C22⋊C4—21no—
511C22⋊C4—21no—
512C22⋊C4—22no—
513C22⋊C4—22no—
514C22⋊C4—21no—
515C22⋊C4—3444no—
516C22⋊C4—1722no—
517C42—22no—
518C42—21no—
519C42—1722no—
520C23—22no—
521C23—22no—
522C23—22no—
523C23—21no—
524C23—24no—
525C23—41no—
526C23—42no—
527C23—42no—
528C23#1306329411yescharacteristic
529C23#1306329411yescharacteristic
530C23C22×C22⋊D4311yescharacteristic
531Q8—42no—
532Q8—41no—
533Q8—42no—
534Q8—82no—
535D4—41no—
536D4—44no—
537D4—42no—
538D4—42no—
539D4—42no—
540D4—81no—
541D4—82no—
542D4—81no—
543D4—82no—
544D4—82no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—21no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—21no—
553C2×C4—22no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—81no—
561C2×C4—82no—
562C2×C4—82no—
563C2×C4—82no—
564C2×C4—3442no—
565C2×C4—3442no—
566C2×C4—1722no—
567C2×C4—1722no—
568C2×C4—1722no—
569C2×C4—1722no—
570C2×C4—1724no—
571C2×C4#1306329411yescharacteristic
572C2×C4#1306329411yescharacteristic
573C2×C4C22×C22⋊D4311yescharacteristic
574C2×C4C22×C22⋊D4311yescharacteristic
575C8—1722no—
576C8—1722no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—44no—
585C22—41no—
586C22—42no—
587C22—41no—
588C22—42no—
589C22—41no—
590C22—42no—
591C22—84no—
592C22#1458307712yes—
593C22C2×#1306329411yescharacteristic
594C22#1458370712yes—
595C4—21no—
596C4—21no—
597C4—21no—
598C4—41no—
599C4—42no—
600C4—41no—
601C4—42no—
602C4—42no—
603C4—41no—
604C4—3442no—
605C4—3442no—
606C4#1458308912yes—
607C2—22no—
608C2—22no—
609C2—41no—
610C2—82no—
611C2—81no—
612C2#1914388111yescharacteristic
613C2C2×#1458307711yescharacteristic
614C2C2×#1458308911yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC43×#3536C2
socleC22×C43C2×#120
hypercenter#3536D43
hypocenterC43#18266
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3536

Complements

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

NH ≅ G/Ntype
1. #19144515C2semidirect
2. C2×#14583227C2semidirect
3. #19139088C2semidirect
4. #19133609C2semidirect
5. #19133586C2semidirect
6. #19133115C2semidirect
7. #19133086C2semidirect
8. #19132955C2semidirect
354. C43#18266semidirect

Maximal subgroups

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

subgroupindex
#191445152
C2×#145832272
#191390882
#191336092
#191335862
#191331152
#191330862
#191329552
C43×#35362
#1826643