Finite Group Databasebeta

← #24995583

Subgroups — #24995583

Order 11008.

668 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142894C211yesmaximal, characteristic
2C22⋊C8×Dic43C211yesmaximal, characteristic, complemented
3C2×#14582637C211yesmaximal, characteristic, complemented
4C2×#14582635C211yesmaximal, characteristic, complemented
5C2×#14582633C211yesmaximal, characteristic
6#19132821C211yesmaximal, characteristic, complemented
7C2×C43×#327C211yesmaximal, characteristic
8C2×#13063312C411yescharacteristic, complemented
9C2×#13063304C2211yescharacteristic
10C22×C4×Dic43C2211yescharacteristic
11C2×C22⋊(C43⋊C8)C2211yescharacteristic
12C2×C8×Dic43—21no—
13#14582804C411yescharacteristic, complemented
14#14582802C411yescharacteristic, complemented
15#14582793—21no—
16#14582793—21no—
17#14582779—21no—
18#14582779—21no—
19#14582764C411yescharacteristic, complemented
20C2×C43⋊#95—21no—
21C2×C43⋊#95—21no—
22C2×C43⋊#95C2211yescharacteristic
23#14582653—21no—
24#14582637—22no—
25#14582635—22no—
26#14582633—22no—
27C2×#121×C43C2211yescharacteristic
28C2×C22⋊C8×C43C2211yescharacteristic
29C2×#95×C43C2211yescharacteristic
30C43×#327—22no—
31C22×Dic86C2×C411yescharacteristic
32C23×Dic43—21no—
33C23×Dic43D411yescharacteristic
34C23×Dic43D411yescharacteristic
35C22×C43⋊C8—21no—
36#13063312—42no—
37#13063304—21no—
38#13063304—21no—
39#13063304—21no—
40#13063304—21no—
41C2×C4⋊Dic43C2×C411yescharacteristic
42C2×Dic43⋊C4—21no—
43C2×C22⋊Dic43—21no—
44C2×C22⋊Dic43—21no—
45C2×C22⋊Dic43—21no—
46C2×C22⋊Dic43—21no—
47C2×C22⋊Dic43—21no—
48C2×C4×Dic43—42no—
49C2×C4×Dic43C2×C411yescharacteristic
50C2×C4×Dic43C2×C411yescharacteristic
51C2×C4×Dic43D411yescharacteristic
52C2×C4×Dic43D411yescharacteristic
53C22⋊(C43⋊C8)—21no—
54C22⋊(C43⋊C8)D412yes—
55C8×Dic43—42no—
56C43⋊#95—24no—
57C43⋊#95—21no—
58C43⋊#95—21no—
59C43⋊#95—21no—
60C43⋊#95—21no—
61C43⋊#95—21no—
62C43⋊#95—21no—
63C43⋊#95—42no—
64C22×D4×C43—21no—
65C22×D4×C43C2×C411yescharacteristic
66C23×C4×C43—21no—
67C23×C4×C43C2311yescharacteristic
68C22×C8×C43—21no—
69#121×C43—21no—
70#121×C43—21no—
71#121×C43—21no—
72#121×C43—21no—
73C2×C4⋊C4×C43C2×C411yescharacteristic
74C2×C22⋊C4×C43—21no—
75C22⋊C8×C43—21no—
76C22⋊C8×C43D412yes—
77#95×C43—21no—
78#95×C43—21no—
79C24×C43—21no—
80C24×C43C2×D411yescharacteristic
81C2×D4×C43—21no—
82C2×D4×C43—21no—
83C2×D4×C43—41no—
84C2×D4×C43—41no—
85C2×D4×C43—41no—
86C2×D4×C43—41no—
87C2×D4×C43—41no—
88C2×D4×C43—41no—
89C2×D4×C43—41no—
90C2×D4×C43—41no—
91C22×C4×C43—22no—
92C22×C4×C43—21no—
93C22×C4×C43—41no—
94C22×C4×C43—41no—
95C22×C4×C43—41no—
96C22×C4×C43—41no—
97C22×C4×C43—41no—
98C22×C4×C43—41no—
99C22×C4×C43—41no—
100C22×C4×C43—41no—
101C22×C4×C43C22×C411yescharacteristic
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43C2×D411yescharacteristic
104C22×C4×C43C2×D411yescharacteristic
105C22×C4×C43#4111yescharacteristic
106C22×C4×C43#4111yescharacteristic
107C22×Dic43—22no—
108C22×Dic43—22no—
109C22×Dic43—22no—
110C22×Dic43—21no—
111C22×Dic43—21no—
112C22×Dic43—21no—
113C22×Dic43—21no—
114C22×Dic43—21no—
115C22×Dic43—21no—
116C22×Dic43—41no—
117C22×Dic43—41no—
118C22×Dic43—41no—
119C22×Dic43—41no—
120C22×Dic43—41no—
121C22×Dic43—41no—
122C22×Dic43—41no—
123C22×Dic43—41no—
124C22×Dic43C22⋊C411yescharacteristic
125C22×Dic43C22⋊C411yescharacteristic
126C22×Dic43C22⋊C411yescharacteristic
127C22×Dic43C22⋊C411yescharacteristic
128C2×Dic86—21no—
129C2×Dic86—21no—
130C2×Dic86—41no—
131C2×Dic86—41no—
132C2×C8×C43—22no—
133C2×C8×C43—41no—
134C2×C8×C43—41no—
135C4⋊C4×C43—21no—
136C4⋊C4×C43—21no—
137C22⋊C4×C43—41no—
138C22⋊C4×C43—41no—
139C22⋊Dic43—42no—
140C22⋊Dic43—42no—
141C22⋊Dic43—42no—
142C22⋊Dic43—42no—
143C22⋊Dic43—41no—
144C22⋊Dic43—41no—
145C4⋊Dic43—21no—
146C4⋊Dic43—21no—
147Dic43⋊C4—41no—
148Dic43⋊C4—41no—
149C4×Dic43—22no—
150C4×Dic43—22no—
151C4×Dic43—41no—
152C4×Dic43—41no—
153C2×C43⋊C8—22no—
154C2×C43⋊C8—41no—
155C2×C43⋊C8—41no—
156C23×C43—21no—
157C23×C43—21no—
158C23×C43—21no—
159C23×C43—21no—
160C23×C43—41no—
161C23×C43—41no—
162C23×C43—41no—
163C23×C43—41no—
164C23×C43—41no—
165C23×C43—41no—
166C23×C43—41no—
167C23×C43C2×C22⋊C411yescharacteristic
168C23×C43#12411yescharacteristic
169C23×C43#12711yescharacteristic
170C23×C43#13511yescharacteristic
171C23×C43#13511yescharacteristic
172C23×C43#13511yescharacteristic
173C23×C43#13511yescharacteristic
174D4×C43—81no—
175D4×C43—81no—
176D4×C43—81no—
177D4×C43—81no—
178D4×C43—81no—
179D4×C43—81no—
180C2×C4×C43—21no—
181C2×C4×C43—21no—
182C2×C4×C43—21no—
183C2×C4×C43—21no—
184C2×C4×C43—41no—
185C2×C4×C43—41no—
186C2×C4×C43—41no—
187C2×C4×C43—41no—
188C2×C4×C43—42no—
189C2×C4×C43—42no—
190C2×C4×C43—42no—
191C2×C4×C43—41no—
192C2×C4×C43—41no—
193C2×C4×C43—41no—
194C2×C4×C43—81no—
195C2×C4×C43—81no—
196C2×C4×C43—81no—
197C2×C4×C43—81no—
198C2×C4×C43C4×D411yescharacteristic
199C2×C4×C43C4×D411yescharacteristic
200C2×C4×C43#12111yescharacteristic
201C2×C4×C43#12111yescharacteristic
202C2×Dic43—21no—
203C2×Dic43—21no—
204C2×Dic43—21no—
205C2×Dic43—21no—
206C2×Dic43—21no—
207C2×Dic43—21no—
208C2×Dic43—21no—
209C2×Dic43—21no—
210C2×Dic43—21no—
211C2×Dic43—21no—
212C2×Dic43—42no—
213C2×Dic43—42no—
214C2×Dic43—42no—
215C2×Dic43—42no—
216C2×Dic43—42no—
217C2×Dic43—42no—
218C2×Dic43—42no—
219C2×Dic43—41no—
220C2×Dic43—41no—
221C2×Dic43—41no—
222C2×Dic43—41no—
223C2×Dic43—41no—
224C2×Dic43—41no—
225C2×Dic43—81no—
226C2×Dic43—81no—
227C2×Dic43—81no—
228C2×Dic43—81no—
229C2×Dic43#9912yes—
230C2×Dic43#10412yes—
231Dic86—81no—
232Dic86—81no—
233C8×C43—42no—
234C43⋊C8—42no—
235#9681—431nomaximal, Sylow
236C22×C43—21no—
237C22×C43—21no—
238C22×C43—21no—
239C22×C43—21no—
240C22×C43—21no—
241C22×C43—21no—
242C22×C43—21no—
243C22×C43—21no—
244C22×C43—21no—
245C22×C43—21no—
246C22×C43—21no—
247C22×C43—21no—
248C22×C43—81no—
249C22×C43—81no—
250C22×C43—81no—
251C22×C43—81no—
252C22×C43—81no—
253C22×C43—81no—
254C22×C43—81no—
255C22×C43#39011yescharacteristic
256C22×C43C2×#9911yescharacteristic
257C22×C43#41011yescharacteristic
258C22×C43#41611yescharacteristic
259C22×C43#41611yescharacteristic
260C22×C43C2×#10411yescharacteristic
261C22×C43#42111yescharacteristic
262C22×C43#48811yescharacteristic
263C22×C43#48811yescharacteristic
264C22×C43#49511yescharacteristic
265C22×C43#49511yescharacteristic
266C4×C43—21no—
267C4×C43—21no—
268C4×C43—21no—
269C4×C43—21no—
270C4×C43—82no—
271C4×C43—81no—
272Dic43—22no—
273Dic43—22no—
274Dic43—41no—
275Dic43—41no—
276Dic43—82no—
277Dic43—81no—
278Dic43—81no—
279#2850—431no—
280C4×C22⋊C8—431no—
281C2×#328—431no—
282C2×#328—431no—
283C2×#327—431no—
284C2×#327D4311yescharacteristic
285#1434—431no—
286C2×C43—21no—
287C2×C43—21no—
288C2×C43—21no—
289C2×C43—21no—
290C2×C43—161no—
291C2×C43#150011yescharacteristic
292C2×C43#150111yescharacteristic
293C2×C43#151611yescharacteristic
294C2×C43#152111yescharacteristic
295C2×C43#195811yescharacteristic
296C2×C43#196411yescharacteristic
297C2×C43#198011yescharacteristic
298C2×#124—431no—
299C2×C22⋊Q8—431no—
300C2×#121C2×D4311yescharacteristic
301C22×C42—431no—
302C2×C22⋊C8—431no—
303C2×C22⋊C8C2×D4311yescharacteristic
304C2×C4×C8—861no—
305#391—431no—
306#390—431no—
307#388—861no—
308#388—861no—
309#386—861no—
310#386—861no—
311#382—431no—
312C2×#95—431no—
313C2×#95—861no—
314C2×#95—861no—
315C2×#95C2×D4311yescharacteristic
316#336—861no—
317#328—862no—
318#328—862no—
319#327—22no—
320#327—862no—
321C43#968111yescharacteristic, complemented, Sylow
322C22×Q8—431no—
323C22×D4—21no—
324C22×D4C4×D4311yescharacteristic
325C23×C4—21no—
326C23×C4—431no—
327C23×C4—431no—
328C23×C4—861no—
329C23×C4C22×D4311yescharacteristic
330C22×C8—21no—
331C22×C8—861no—
332#124—1722no—
333C22⋊Q8—861no—
334C22⋊Q8—861no—
335C22⋊Q8—861no—
336C22⋊Q8—861no—
337#121—21no—
338#121—21no—
339#121—21no—
340#121—21no—
341C2×C4⋊C4—431no—
342C2×C4⋊C4—861no—
343C2×C4⋊C4C4×D4311yescharacteristic
344C2×C22⋊C4—21no—
345C2×C22⋊C4—861no—
346C2×C22⋊C4—861no—
347C2×C22⋊C4—861no—
348C2×C22⋊C4—861no—
349C2×C22⋊C4—861no—
350C2×C42—431no—
351C2×C42—431no—
352C2×C42—431no—
353C2×C42—431no—
354C2×C42—1722no—
355C22⋊C8—21no—
356C22⋊C8—432no—
357C22⋊C8—861no—
358C22⋊C8C22⋊D4312yes—
359C4×C8—1722no—
360#95—21no—
361#95—21no—
362#95—861no—
363#95—861no—
364#95—861no—
365#95—861no—
366#95—864no—
367#95—861no—
368#95—861no—
369#95—1722no—
370C24—21no—
371C24D4×D4311yescharacteristic
372C2×Q8—861no—
373C2×Q8—861no—
374C2×Q8—1721no—
375C2×Q8—1721no—
376C2×D4—21no—
377C2×D4—21no—
378C2×D4—41no—
379C2×D4—41no—
380C2×D4—41no—
381C2×D4—41no—
382C2×D4—41no—
383C2×D4—41no—
384C2×D4—41no—
385C2×D4—41no—
386C22×C4—22no—
387C22×C4—21no—
388C22×C4—41no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—41no—
393C22×C4—41no—
394C22×C4—41no—
395C22×C4—41no—
396C22×C4—431no—
397C22×C4—431no—
398C22×C4—431no—
399C22×C4—431no—
400C22×C4—862no—
401C22×C4—862no—
402C22×C4—861no—
403C22×C4—861no—
404C22×C4—861no—
405C22×C4—861no—
406C22×C4—862no—
407C22×C4—861no—
408C22×C4—861no—
409C22×C4—1721no—
410C22×C4—1721no—
411C22×C4—1721no—
412C22×C4—1721no—
413C22×C4—1721no—
414C22×C4—1721no—
415C22×C4—1721no—
416C22×C4—1721no—
417C22×C4C2×C4×D4311yescharacteristic
418C22×C4#1062189811yescharacteristic
419C22×C4D4×D4311yescharacteristic
420C22×C4D4×D4311yescharacteristic
421C22×C4#1062190011yescharacteristic
422C22×C4C2×C22⋊D4311yescharacteristic
423C2×C8—22no—
424C2×C8—41no—
425C2×C8—41no—
426C2×C8—862no—
427C2×C8—1721no—
428C2×C8—1721no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—861no—
432C4⋊C4—861no—
433C4⋊C4—1721no—
434C4⋊C4—1721no—
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—1722no—
438C22⋊C4—1722no—
439C22⋊C4—1722no—
440C22⋊C4—1722no—
441C22⋊C4—1721no—
442C22⋊C4—1721no—
443C42—862no—
444C42—862no—
445C42—1721no—
446C42—1721no—
447C23—21no—
448C23—21no—
449C23—21no—
450C23—21no—
451C23—41no—
452C23—41no—
453C23—41no—
454C23—41no—
455C23—41no—
456C23—41no—
457C23—41no—
458C23C22⋊C4×D4311yescharacteristic
459C23#1306331111yescharacteristic
460C23#1306332111yescharacteristic
461C23#1306334411yescharacteristic
462C23#1306334411yescharacteristic
463C23#1306334611yescharacteristic
464C23#1306334611yescharacteristic
465Q8—3441no—
466Q8—3441no—
467D4—81no—
468D4—81no—
469D4—81no—
470D4—81no—
471D4—81no—
472D4—81no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—81no—
488C2×C4—81no—
489C2×C4—81no—
490C2×C4—81no—
491C2×C4—432no—
492C2×C4—432no—
493C2×C4—861no—
494C2×C4—861no—
495C2×C4—861no—
496C2×C4—861no—
497C2×C4—861no—
498C2×C4—861no—
499C2×C4—861no—
500C2×C4—861no—
501C2×C4—861no—
502C2×C4—861no—
503C2×C4—3441no—
504C2×C4—3441no—
505C2×C4—3441no—
506C2×C4—3441no—
507C2×C4—1722no—
508C2×C4—1722no—
509C2×C4—1722no—
510C2×C4—1722no—
511C2×C4—1722no—
512C2×C4—1722no—
513C2×C4—1722no—
514C2×C4—1721no—
515C2×C4—1721no—
516C2×C4—1721no—
517C2×C4—1721no—
518C2×C4—1721no—
519C2×C4—1721no—
520C2×C4(C22⋊D43)⋊C411yescharacteristic
521C2×C4C4×C22⋊D4311yescharacteristic
522C2×C4#1306329711yescharacteristic
523C2×C4#1306329811yescharacteristic
524C8—42no—
525C8—1722no—
526C22—21no—
527C22—21no—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—21no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—21no—
538C22—81no—
539C22—81no—
540C22—81no—
541C22—81no—
542C22—81no—
543C22—81no—
544C22—81no—
545C22#1458279911yescharacteristic
546C22#99×D4311yescharacteristic
547C22#1458287111yescharacteristic
548C22#1458289211yescharacteristic
549C22#1458289211yescharacteristic
550C22#104×D4311yescharacteristic
551C22#1458291411yescharacteristic
552C22#1458325211yescharacteristic
553C22#1458325211yescharacteristic
554C22#1458328011yescharacteristic
555C22#1458328211yescharacteristic
556C4—21no—
557C4—21no—
558C4—21no—
559C4—21no—
560C4—82no—
561C4—81no—
562C4—862no—
563C4—862no—
564C4—3442no—
565C4—3441no—
566C4—3441no—
567C4—1721no—
568C4—1721no—
569C2—21no—
570C2—21no—
571C2—21no—
572C2—21no—
573C2—161no—
574C2#1913307811yescharacteristic
575C2#1913308311yescharacteristic
576C2#1913314811yescharacteristic
577C2#1913316911yescharacteristic
578C2#1913540511yescharacteristic
579C2#1913542911yescharacteristic
580C2#1913551211yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#327C2
socleC23×C43C2×C22⋊C4
prime radicalC2×#121×C43C22
cosocleC23×C4×C43C23
hypercenterC2×#327D43
hypocenterC43#9681
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. C22⋊C8×Dic43C2semidirect
3. C2×#14582637C2semidirect
4. C2×#14582635C2semidirect
6. #19132821C2semidirect
8. C2×#13063312C4semidirect
13. #14582804C4semidirect
14. #14582802C4semidirect
19. #14582764C4semidirect
321. C43#9681semidirect

Maximal subgroups

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

subgroupindex
#191428942
C22⋊C8×Dic432
C2×#145826372
C2×#145826352
C2×#145826332
#191328212
C2×C43×#3272
#968143