Finite Group Databasebeta

← #25066685

Subgroups — #25066685

Order 11008.

638 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144656C211yesmaximal, characteristic
2#19143704C211yesmaximal, characteristic, complemented
3#19143673C211yesmaximal, characteristic, complemented
4#19133472C211yesmaximal, characteristic, complemented
5#19133458C211yesmaximal, characteristic, complemented
6#19133437C211yesmaximal, characteristic, complemented
7#19133423C211yesmaximal, characteristic, complemented
8#19133418C211yesmaximal, characteristic, complemented
9#19133406C211yesmaximal, characteristic, complemented
10#19133394C211yesmaximal, characteristic, complemented
11#19133389C211yesmaximal, characteristic, complemented
12#19133027C211yesmaximal, characteristic, complemented
13#19132993C211yesmaximal, characteristic, complemented
14#19132895C211yesmaximal, characteristic, complemented
15C43×#1573C211yesmaximal, characteristic, complemented
16#14583449C2211yescharacteristic
17C4×#10621898C2211yescharacteristic
18#14583224C411yescharacteristic
19#14583224C411yescharacteristic
20#14583195C411yescharacteristic
21#14583190C411yescharacteristic
22#14583100C411yescharacteristic
23#14583095C411yescharacteristic
24#14583046C411yescharacteristic
25#14583046C411yescharacteristic
26#14583023C2211yescharacteristic
27#14583023C2211yescharacteristic
28C4×#10621873C2211yescharacteristic
29C4×#10621873C2211yescharacteristic
30C4×D344C2211yescharacteristic
31C4×D344C2211yescharacteristic
32#14582976C2211yescharacteristic
33#14582976C2211yescharacteristic
34#14582972—21no—
35#14582972—21no—
36#14582964C2211yescharacteristic
37#14582964C2211yescharacteristic
38#14582964C2211yescharacteristic
39#14582964C2211yescharacteristic
40C8×C22⋊D43—21no—
41C8×C22⋊D43—21no—
42#14582952C2211yescharacteristic
43#14582952C2211yescharacteristic
44#14582951—21no—
45C4⋊C8×D43—21no—
46#14582864—21no—
47#14582864—21no—
48#14582629C2211yescharacteristic
49#14582629C2211yescharacteristic
50#14582626C2211yescharacteristic
51#14582626C2211yescharacteristic
52#14582626C2211yescharacteristic
53#14582626C2211yescharacteristic
54#14582626C2211yescharacteristic
55#14582626C2211yescharacteristic
56#14582621C2211yescharacteristic
57#14582621C2211yescharacteristic
58#14582620C2211yescharacteristic
59C8×C43⋊C8C2211yescharacteristic
60C43×#432C2211yescharacteristic
61C43×#431C2211yescharacteristic
62C2×C4⋊C8×C43C2211yescharacteristic
63C43×#335C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#334C2211yescharacteristic
66C43×#334C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621898C2×C411yescharacteristic
69C2×#10621873C2×C411yescharacteristic
70C2×#10621873C2×C411yescharacteristic
71C2×D344C2×C411yescharacteristic
72C2×D344C2×C411yescharacteristic
73C2×#10621872—21no—
74C2×#10621872—21no—
75C2×C8×D43—21no—
76C2×C8×D43—21no—
77C2×C8×D43—21no—
78C2×C8×D43—21no—
79#13063325C2×C411yescharacteristic
80#13063322C2×C411yescharacteristic
81#13063313—21no—
82#13063299—21no—
83#13063299C2×C411yescharacteristic
84#13063299C2×C411yescharacteristic
85C4×Dic86C2×C411yescharacteristic
86C4×Dic86C2311yescharacteristic
87C4×D172—21no—
88C4×D172C2×C411yescharacteristic
89C4×D172C2311yescharacteristic
90C4×D172C2311yescharacteristic
91C4×D172C2311yescharacteristic
92C4×C22⋊D43—21no—
93C4×C22⋊D43—21no—
94#13063284C2×C411yescharacteristic
95#13063282—21no—
96C42×D43—21no—
97#13063259C2×C411yescharacteristic
98#13063259C2×C411yescharacteristic
99#13063257C2×C411yescharacteristic
100#13063257C2×C411yescharacteristic
101C4⋊(C43⋊C8)—21no—
102C4⋊(C43⋊C8)D411yescharacteristic
103C4⋊(C43⋊C8)D411yescharacteristic
104Dic43⋊C8—21no—
105Dic43⋊C8—21no—
106#13063250C2×C411yescharacteristic
107#13063250C2×C411yescharacteristic
108#13063247C2×C411yescharacteristic
109#13063247C2×C411yescharacteristic
110#13063247C2×C411yescharacteristic
111#13063247C2×C411yescharacteristic
112#13063247C2×C411yescharacteristic
113#13063247C2×C411yescharacteristic
114C22⋊(C43⋊C8)—21no—
115C22⋊(C43⋊C8)D411yescharacteristic
116C22⋊(C43⋊C8)D411yescharacteristic
117(C2×D43)⋊C8—21no—
118(C2×D43)⋊C8—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8—21no—
121(C2×D43)⋊C8—21no—
122(C2×D43)⋊C8—21no—
123C4×C43⋊C8C2311yescharacteristic
124C4×C43⋊C8C2311yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
126C4×C43⋊C8C2311yescharacteristic
127C8×Dic43—21no—
128C8×Dic43—21no—
129C22×C8×C43—21no—
130C2×C42×C43C2311yescharacteristic
131C4⋊C8×C43—21no—
132C4⋊C8×C43C2×C411yescharacteristic
133C4⋊C8×C43C2×C411yescharacteristic
134C4⋊C8×C43C2311yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C22⋊C8×C43—21no—
139C22⋊C8×C43C2×C411yescharacteristic
140C22⋊C8×C43C2×C411yescharacteristic
141#97×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C22×C4×C43C22×C411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43#4111yescharacteristic
147C2×C22⋊D43—21no—
148C2×C22⋊D43—21no—
149C2×C22⋊D43—21no—
150#10621898—22no—
151#10621898—22no—
152#10621898—81no—
153#10621898—81no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172C22×C411yescharacteristic
157C2×D172C22×C411yescharacteristic
158C2×D172C22×C411yescharacteristic
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43—21no—
162C2×C4×D43—21no—
163C2×C4×D43—21no—
164C2×Dic86—21no—
165C2×Dic86C22×C411yescharacteristic
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—81no—
171C2×C8×C43C22×C411yescharacteristic
172C2×C8×C43C22×C411yescharacteristic
173C2×C8×C43C22×C411yescharacteristic
174C2×C8×C43C22×C411yescharacteristic
175C42×C43C22×C411yescharacteristic
176C42×C43C2×D411yescharacteristic
177C42×C43#4111yescharacteristic
178C42×C43C2411yescharacteristic
179C22⋊Dic43—21no—
180(C2×D43)⋊C4—21no—
181(C2×D43)⋊C4—21no—
182(C2×D43)⋊C4—21no—
183(C2×D43)⋊C4—21no—
184(C2×D43)⋊C4—21no—
185(C2×D43)⋊C4—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43C22×C411yescharacteristic
188C4⋊Dic43C22×C411yescharacteristic
189C4⋊Dic43C22×C411yescharacteristic
190C4⋊Dic43C22×C411yescharacteristic
191Dic43⋊C4—21no—
192Dic43⋊C4—21no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8C2×D411yescharacteristic
199C2×C43⋊C8C2×D411yescharacteristic
200C2×C43⋊C8C2×D411yescharacteristic
201C2×C43⋊C8C2×D411yescharacteristic
202D344—22no—
203D344—22no—
204#10621873—22no—
205#10621873—22no—
206#10621872—81no—
207#10621872—81no—
208C8×D43—81no—
209C8×D43—81no—
210C8×D43—81no—
211C8×D43—81no—
212C23×C43C4×D411yescharacteristic
213C22×D43—21no—
214C22×D43—21no—
215C22×D43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—41no—
221C2×C4×C43C4×D411yescharacteristic
222C2×C4×C43C4×D411yescharacteristic
223C2×C4×C43C4×D411yescharacteristic
224C2×C4×C43C23×C411yescharacteristic
225C2×C4×C43C22×D411yescharacteristic
226C2×C4×C43C2×#4111yescharacteristic
227C22⋊D43—24no—
228C22⋊D43—81no—
229C22⋊D43—81no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235D172—21no—
236D172—21no—
237D172—21no—
238D172—21no—
239D172—21no—
240D172—81no—
241D172—81no—
242D172#13112yes—
243C4×D43—24no—
244C4×D43—41no—
245C4×D43—41no—
246C4×D43—41no—
247C4×D43—41no—
248C4×D43—41no—
249C4×D43—41no—
250C4×D43—81no—
251Dic86—21no—
252Dic86—81no—
253Dic86#13112yes—
254C8×C43—21no—
255C8×C43—21no—
256C8×C43—21no—
257C8×C43—21no—
258C8×C43—41no—
259C8×C43—41no—
260C8×C43—41no—
261C8×C43—41no—
262C43⋊C8—21no—
263C43⋊C8—21no—
264C43⋊C8—21no—
265C43⋊C8—21no—
266C43⋊C8—41no—
267C43⋊C8—41no—
268#17920—431nomaximal, Sylow
269C22×C43—21no—
270C22×C43—21no—
271C22×C43—21no—
272C22×C43C2×C4×D411yescharacteristic
273C2×D43—22no—
274C2×D43—41no—
275C2×D43—41no—
276C2×D43—41no—
277C2×D43—41no—
278C2×D43—41no—
279C2×D43—41no—
280C2×D43—41no—
281C2×D43—41no—
282C4×C43—21no—
283C4×C43—21no—
284C4×C43—21no—
285C4×C43—21no—
286C4×C43C2×#13111yescharacteristic
287C4×C43C2×#13111yescharacteristic
288C4×C43#57611yescharacteristic
289C4×C43#57711yescharacteristic
290Dic43—22no—
291Dic43—41no—
292Dic43—41no—
293Dic43—41no—
294Dic43—41no—
295#3106—431no—
296#2988—431no—
297#2981—431no—
298#1588—431no—
299#1586—431no—
300#1583—431no—
301#1581—431no—
302#1580—431no—
303SD16⋊C8—431no—
304C8×SD16—431no—
305C8×D8—431no—
306#1573D4311yescharacteristic, complemented
307#1488—431no—
308#1480—431no—
309#1454—431no—
310C2×C43—41no—
311C2×C43#292911yescharacteristic
312C2×C43#294611yescharacteristic
313C2×C43#295711yescharacteristic
314D43—42no—
315D43—81no—
316D43—81no—
317#532—431no—
318C4×#41—431no—
319#482—431no—
320#482—431no—
321#477—431no—
322#476—431no—
323#460—431no—
324#459—431no—
325#449—431no—
326#449—431no—
327C8×Q8—431no—
328C8×Q8—431no—
329C4×SD16—431no—
330C4×SD16—431no—
331C4×D8—431no—
332C4×D8—431no—
333#436—431no—
334#436—431no—
335#435—861no—
336#435—861no—
337C8×D4—431no—
338C8×D4—431no—
339C8×D4—431no—
340C8×D4—431no—
341C8×D4—861no—
342C8×D4—861no—
343#432C2×D4311yescharacteristic
344#431—431no—
345#431—431no—
346#431—861no—
347#431C2×D4311yescharacteristic
348C2×C4⋊C8—861no—
349C2×C4⋊C8C2×D4311yescharacteristic
350#408—861no—
351#408—861no—
352#335C2×D4311yescharacteristic
353#335C2×D4311yescharacteristic
354#334C2×D4311yescharacteristic
355#334C2×D4311yescharacteristic
356Q8⋊C8—431no—
357Q8⋊C8—431no—
358D4⋊C8—431no—
359D4⋊C8—431no—
360D4⋊C8—431no—
361D4⋊C8—431no—
362D4⋊C8—431no—
363D4⋊C8—431no—
364#322—431no—
365#322—431no—
366#322—431no—
367C82—431no—
368C43#1792011yescharacteristic, complemented, Sylow
369C2×#41—431no—
370C2×#41—861no—
371C2×SD16—431no—
372C2×SD16—431no—
373C2×D8—431no—
374C2×D8—431no—
375C2×M16—861no—
376C2×M16—861no—
377C22×C8—21no—
378C22×C8—861no—
379C22×C8—861no—
380C22×C8—861no—
381C22×C8—861no—
382C4⋊Q8—431no—
383#127—431no—
384#124—861no—
385#121—431no—
386#121—431no—
387#121—861no—
388C4×Q8—431no—
389C4×Q8—431no—
390C4×D4—431no—
391C4×D4—431no—
392C4×D4—431no—
393C4×D4—431no—
394C4×D4—861no—
395C4×D4—861no—
396C4×D4—861no—
397#117—431no—
398#117—861no—
399C2×C42—861no—
400C2×C42C22×D4311yescharacteristic
401#107—431no—
402#107—431no—
403#106—431no—
404#106—431no—
405C4⋊C8—21no—
406C4⋊C8—431no—
407C4⋊C8—431no—
408C4⋊C8—861no—
409C4⋊C8—861no—
410C4⋊C8—861no—
411C4⋊C8C4×D4311yescharacteristic
412C4⋊C8C4×D4311yescharacteristic
413C4⋊C8C22×D4311yescharacteristic
414C4⋊C8C22×D4311yescharacteristic
415C4⋊C8C22×D4311yescharacteristic
416C4⋊C8C22×D4311yescharacteristic
417#103—431no—
418#103—431no—
419#102—431no—
420#102—431no—
421#102—431no—
422#102—431no—
423#102—431no—
424#102—431no—
425C22⋊C8—21no—
426C22⋊C8—431no—
427C22⋊C8—431no—
428C22⋊C8—861no—
429C22⋊C8—861no—
430C22⋊C8—861no—
431C22⋊C8—861no—
432C22⋊C8—861no—
433C22⋊C8—861no—
434C22⋊C8—861no—
435C22⋊C8C4×D4311yescharacteristic
436C22⋊C8C4×D4311yescharacteristic
437#97—21no—
438C4×C8—431no—
439C4×C8—431no—
440C4×C8—431no—
441C4×C8—431no—
442C4×C8—861no—
443C4×C8—861no—
444C4×C8C22×D4311yescharacteristic
445C4×C8C22×D4311yescharacteristic
446#41—862no—
447#41—862no—
448#41—3441no—
449#41—3441no—
450C2×Q8—431no—
451C2×Q8—861no—
452C2×D4—431no—
453C2×D4—431no—
454C2×D4—431no—
455C2×D4—861no—
456C2×D4—861no—
457C2×D4—861no—
458C2×D4—861no—
459C2×D4—861no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4C2×C4×D4311yescharacteristic
466C22×C4D4×D4311yescharacteristic
467C22×C4#1062190211yescharacteristic
468SD16—862no—
469SD16—862no—
470D8—862no—
471D8—862no—
472M16—3441no—
473M16—3441no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—81no—
479C2×C8—431no—
480C2×C8—431no—
481C2×C8—431no—
482C2×C8—431no—
483C2×C8—861no—
484C2×C8—861no—
485C2×C8—3441no—
486C2×C8—3441no—
487C2×C8—3441no—
488C2×C8—3441no—
489C2×C8C2×C4×D4311yescharacteristic
490C2×C8C2×C4×D4311yescharacteristic
491C2×C8C2×C4×D4311yescharacteristic
492C2×C8C2×C4×D4311yescharacteristic
493C4⋊C4—431no—
494C4⋊C4—431no—
495C4⋊C4—431no—
496C4⋊C4—431no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C22⋊C4—861no—
501C22⋊C4—861no—
502C22⋊C4—861no—
503C22⋊C4—861no—
504C22⋊C4—861no—
505C22⋊C4—861no—
506C22⋊C4—861no—
507C42—861no—
508C42—861no—
509C42—861no—
510C42C2×C4×D4311yescharacteristic
511C42D4×D4311yescharacteristic
512C42#1062190211yescharacteristic
513C42C23×D4311yescharacteristic
514C23—861no—
515C23—861no—
516C23—861no—
517C23#1306328711yescharacteristic
518Q8—432no—
519Q8—861no—
520Q8—3441no—
521D4—432no—
522D4—864no—
523D4—861no—
524D4—861no—
525D4—861no—
526D4—861no—
527D4—861no—
528D4—3441no—
529D4—3441no—
530D4—3441no—
531D4—3441no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—864no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—861no—
541C2×C4—861no—
542C2×C4—861no—
543C2×C4—3441no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4—1721no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4#1306328711yescharacteristic
551C2×C4#1306328711yescharacteristic
552C2×C4#1306328711yescharacteristic
553C2×C4C22×C4×D4311yescharacteristic
554C2×C4C2×D4×D4311yescharacteristic
555C2×C4C2×#1062190211yescharacteristic
556C8—21no—
557C8—21no—
558C8—21no—
559C8—21no—
560C8—41no—
561C8—41no—
562C8—41no—
563C8—41no—
564C8—861no—
565C8—861no—
566C8—861no—
567C8—861no—
568C8—1721no—
569C8—1721no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—862no—
574C22—1721no—
575C22—1721no—
576C22—1721no—
577C22—1721no—
578C22—1721no—
579C22—1721no—
580C22—1721no—
581C22—1721no—
582C22C2×#1306328711yescharacteristic
583C4—21no—
584C4—21no—
585C4—21no—
586C4—21no—
587C4—862no—
588C4—1721no—
589C4—1721no—
590C4—1721no—
591C4—1721no—
592C4#131×D4311yescharacteristic
593C4#131×D4311yescharacteristic
594C4#1458370311yescharacteristic
595C4#1458370811yescharacteristic
596C2—41no—
597C2—3441no—
598C2—3441no—
599C2—1722no—
600C2#1914328811yescharacteristic
601C2#1914342511yescharacteristic
602C2#1914351111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1573C2
socleC22×C43C2×C4×D4
prime radical#19144656C2
cosocleC42×C43C24
hypercenter#1573D43
hypocenterC43#17920
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1573

Complements

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

NH ≅ G/Ntype
2. #19143704C2semidirect
3. #19143673C2semidirect
4. #19133472C2semidirect
5. #19133458C2semidirect
6. #19133437C2semidirect
7. #19133423C2semidirect
8. #19133418C2semidirect
9. #19133406C2semidirect
10. #19133394C2semidirect
11. #19133389C2semidirect
12. #19133027C2semidirect
13. #19132993C2semidirect
14. #19132895C2semidirect
15. C43×#1573C2semidirect
306. #1573D43semidirect
368. C43#17920semidirect

Maximal subgroups

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

subgroupindex
#191446562
#191437042
#191436732
#191334722
#191334582
#191334372
#191334232
#191334182
#191334062
#191333942
#191333892
#191330272
#191329932
#191328952
C43×#15732
#1792043