Finite Group Databasebeta

← #25066693

Subgroups — #25066693

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#19144649C211yesmaximal, characteristic
2#19143704C211yesmaximal, characteristic, complemented
3#19143671C211yesmaximal, characteristic, complemented
4#19133476C211yesmaximal, characteristic, complemented
5#19133462C211yesmaximal, characteristic, complemented
6#19133441C211yesmaximal, characteristic, complemented
7#19133427C211yesmaximal, characteristic, complemented
8#19133416C211yesmaximal, characteristic, complemented
9#19133404C211yesmaximal, characteristic, complemented
10#19133398C211yesmaximal, characteristic, complemented
11#19133387C211yesmaximal, characteristic, complemented
12#19133378C211yesmaximal, characteristic, complemented
13#19133030C211yesmaximal, characteristic, complemented
14#19132895C211yesmaximal, characteristic, complemented
15C43×#1480C211yesmaximal, characteristic, complemented
16C4×#10621898C2211yescharacteristic
17#14583220C411yescharacteristic
18#14583220C411yescharacteristic
19#14583191C411yescharacteristic
20#14583186C411yescharacteristic
21#14583096C411yescharacteristic
22#14583091C411yescharacteristic
23#14583042C411yescharacteristic
24#14583042C411yescharacteristic
25#14583023C2211yescharacteristic
26#14583023C2211yescharacteristic
27C4×#10621883C2211yescharacteristic
28C4×#10621883C2211yescharacteristic
29C4×#10621882C2211yescharacteristic
30C4×#10621882C2211yescharacteristic
31#14582977C2211yescharacteristic
32#14582977C2211yescharacteristic
33#14582971—21no—
34#14582971—21no—
35D4×C43⋊C8C2211yescharacteristic
36D4×C43⋊C8C2211yescharacteristic
37#14582964C2211yescharacteristic
38#14582964C2211yescharacteristic
39C8×C22⋊D43—21no—
40C8×C22⋊D43—21no—
41#14582956C2211yescharacteristic
42#14582952C2211yescharacteristic
43#14582952C2211yescharacteristic
44#14582951—21no—
45C4⋊C8×D43—21no—
46#14582866—21no—
47#14582866—21no—
48#14582651C2211yescharacteristic
49#14582651C2211yescharacteristic
50#14582649C2211yescharacteristic
51#14582649C2211yescharacteristic
52#14582631C2211yescharacteristic
53#14582631C2211yescharacteristic
54#14582628C2211yescharacteristic
55#14582628C2211yescharacteristic
56#14582621C2211yescharacteristic
57#14582621C2211yescharacteristic
58#14582620C2211yescharacteristic
59C8×C43⋊C8C2211yescharacteristic
60C43×#532C2211yescharacteristic
61C43×#431C2211yescharacteristic
62C2×C4⋊C8×C43C2211yescharacteristic
63C43×D4⋊C8C2211yescharacteristic
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×D4⋊C8C2211yescharacteristic
67C2×#10621898C2×C411yescharacteristic
68C2×#10621883C2×C411yescharacteristic
69C2×#10621883C2×C411yescharacteristic
70C2×#10621882C2×C411yescharacteristic
71C2×#10621882C2×C411yescharacteristic
72C2×#10621877—21no—
73C2×#10621877—21no—
74C22×C43⋊C8—21no—
75C22×C43⋊C8—21no—
76C2×C8×D43—21no—
77C2×C8×D43—21no—
78C4×Dic86C2×C411yescharacteristic
79C4×Dic86C2311yescharacteristic
80C4×D172C2×C411yescharacteristic
81C4×D172C2311yescharacteristic
82C4×C22⋊D43—21no—
83C4×C22⋊D43—21no—
84#13063284C2×C411yescharacteristic
85#13063282—21no—
86C42×D43—21no—
87#13063258C2×C411yescharacteristic
88#13063258C2×C411yescharacteristic
89#13063256C2×C411yescharacteristic
90#13063256C2×C411yescharacteristic
91C4⋊(C43⋊C8)C2×C411yescharacteristic
92C4⋊(C43⋊C8)C2×C411yescharacteristic
93C4⋊(C43⋊C8)D411yescharacteristic
94C4⋊(C43⋊C8)D411yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97Dic43⋊C8—21no—
98Dic43⋊C8—21no—
99#13063248C2×C411yescharacteristic
100#13063248C2×C411yescharacteristic
101#13063246C2×C411yescharacteristic
102#13063246C2×C411yescharacteristic
103#13063246C2×C411yescharacteristic
104#13063246C2×C411yescharacteristic
105#13063245C2×C411yescharacteristic
106#13063245C2×C411yescharacteristic
107C22⋊(C43⋊C8)—21no—
108C22⋊(C43⋊C8)—21no—
109C22⋊(C43⋊C8)—21no—
110C22⋊(C43⋊C8)—21no—
111C22⋊(C43⋊C8)—21no—
112C22⋊(C43⋊C8)C2×C411yescharacteristic
113C22⋊(C43⋊C8)C2×C411yescharacteristic
114C22⋊(C43⋊C8)D411yescharacteristic
115C22⋊(C43⋊C8)D411yescharacteristic
116(C2×D43)⋊C8—21no—
117(C2×D43)⋊C8—21no—
118#13063236—21no—
119C4×C43⋊C8C2311yescharacteristic
120C4×C43⋊C8C2311yescharacteristic
121C4×C43⋊C8C2311yescharacteristic
122C4×C43⋊C8C2311yescharacteristic
123C8×Dic43—21no—
124C8×Dic43—21no—
125C2×#41×C43—21no—
126C22×C8×C43—21no—
127C4⋊Q8×C43C2×C411yescharacteristic
128#127×C43C2×C411yescharacteristic
129#124×C43—21no—
130#121×C43—21no—
131#121×C43C2×C411yescharacteristic
132#121×C43C2×C411yescharacteristic
133C4×D4×C43—21no—
134C4×D4×C43C2311yescharacteristic
135C4×D4×C43C2311yescharacteristic
136C2×C42×C43C2311yescharacteristic
137C4⋊C8×C43—21no—
138C4⋊C8×C43—21no—
139C4⋊C8×C43C2311yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141C22⋊C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144#41×C43—81no—
145#41×C43—81no—
146C2×Q8×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43C22×C411yescharacteristic
152C2×D4×C43C22×C411yescharacteristic
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43C22×C411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43#4111yescharacteristic
158C2×C22⋊D43—21no—
159#10621898—22no—
160#10621898—22no—
161C2×D172C22×C411yescharacteristic
162C2×C4×D43—21no—
163C2×C4×D43—21no—
164C2×C4×D43—21no—
165C2×Dic86C22×C411yescharacteristic
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—81no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43C22×C411yescharacteristic
173C4⋊C4×C43C22×C411yescharacteristic
174C22⋊C4×C43—21no—
175C22⋊C4×C43—21no—
176C22⋊C4×C43—21no—
177C22⋊C4×C43—21no—
178C42×C43C22×C411yescharacteristic
179C42×C43C2×D411yescharacteristic
180C42×C43#4111yescharacteristic
181C42×C43C2411yescharacteristic
182C22⋊Dic43—21no—
183#10621883—22no—
184#10621883—22no—
185#10621882—22no—
186#10621882—22no—
187(C2×D43)⋊C4—21no—
188(C2×D43)⋊C4—21no—
189C4⋊Dic43C22×C411yescharacteristic
190C4⋊Dic43C22×C411yescharacteristic
191Dic43⋊C4—21no—
192Dic43⋊C4—21no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196#10621877—81no—
197#10621877—81no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—81no—
201C2×C43⋊C8—81no—
202C2×C43⋊C8C22×C411yescharacteristic
203C2×C43⋊C8C22×C411yescharacteristic
204C2×C43⋊C8C22×C411yescharacteristic
205C2×C43⋊C8C22×C411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207C2×C43⋊C8C2×D411yescharacteristic
208C2×C43⋊C8C2×D411yescharacteristic
209C2×C43⋊C8C2×D411yescharacteristic
210C8×D43—81no—
211C8×D43—81no—
212C23×C43—21no—
213C23×C43—21no—
214C23×C43C4×D411yescharacteristic
215C22×D43—21no—
216Q8×C43—81no—
217D4×C43—21no—
218D4×C43—21no—
219D4×C43—21no—
220D4×C43—21no—
221D4×C43—81no—
222D4×C43—81no—
223D4×C43—81no—
224D4×C43—81no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43C4×D411yescharacteristic
237C2×C4×C43C4×D411yescharacteristic
238C2×C4×C43C4×D411yescharacteristic
239C2×C4×C43C23×C411yescharacteristic
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C22⋊D43—24no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246D172—21no—
247D172#13112yes—
248C4×D43—24no—
249C4×D43—41no—
250C4×D43—41no—
251C4×D43—81no—
252Dic86—21no—
253Dic86#13112yes—
254C8×C43—41no—
255C8×C43—41no—
256C8×C43—41no—
257C8×C43—41no—
258C43⋊C8—21no—
259C43⋊C8—21no—
260C43⋊C8—21no—
261C43⋊C8—21no—
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×C43—41no—
273C22×C43—41no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43—41no—
278C22×C43C2×C4×D411yescharacteristic
279C2×D43—22no—
280C2×D43—41no—
281C2×D43—41no—
282C4×C43—21no—
283C4×C43—21no—
284C4×C43—21no—
285C4×C43—21no—
286C4×C43—41no—
287C4×C43—41no—
288C4×C43C2×#13111yescharacteristic
289C4×C43C2×#13111yescharacteristic
290C4×C43#57611yescharacteristic
291C4×C43#57711yescharacteristic
292Dic43—22no—
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#1573—431no—
307#1488—431no—
308#1480D4311yescharacteristic, complemented
309#1454—431no—
310C2×C43—41no—
311C2×C43—81no—
312C2×C43—81no—
313C2×C43#292911yescharacteristic
314C2×C43#294611yescharacteristic
315C2×C43#295711yescharacteristic
316D43—42no—
317#532C2×D4311yescharacteristic
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#432—431no—
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#335—431no—
353#335—431no—
354#334—431no—
355#334—431no—
356Q8⋊C8—431no—
357Q8⋊C8—431no—
358D4⋊C8—431no—
359D4⋊C8—431no—
360D4⋊C8C2×D4311yescharacteristic
361D4⋊C8C2×D4311yescharacteristic
362D4⋊C8C2×D4311yescharacteristic
363D4⋊C8C2×D4311yescharacteristic
364#322—431no—
365#322—431no—
366#322—431no—
367C82—431no—
368C43#1792011yescharacteristic, complemented, Sylow
369C2×#41—21no—
370C2×#41—431no—
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⋊Q8C4×D4311yescharacteristic
383#127C4×D4311yescharacteristic
384#124—21no—
385#121—21no—
386#121C4×D4311yescharacteristic
387#121C4×D4311yescharacteristic
388C4×Q8—431no—
389C4×Q8—431no—
390C4×D4—21no—
391C4×D4—431no—
392C4×D4—431no—
393C4×D4—861no—
394C4×D4—861no—
395C4×D4C22×D4311yescharacteristic
396C4×D4C22×D4311yescharacteristic
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—21no—
407C4⋊C8—431no—
408C4⋊C8—431no—
409C4⋊C8—431no—
410C4⋊C8—431no—
411C4⋊C8—431no—
412C4⋊C8—431no—
413C4⋊C8—861no—
414C4⋊C8—861no—
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—431no—
429C22⋊C8—431no—
430C22⋊C8—861no—
431C22⋊C8—861no—
432C22⋊C8—861no—
433C22⋊C8—861no—
434C22⋊C8—861no—
435C22⋊C8—861no—
436C22⋊C8—861no—
437#97—861no—
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—81no—
447#41—81no—
448#41—862no—
449#41—862no—
450C2×Q8—21no—
451C2×Q8—431no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—431no—
457C2×D4—861no—
458C2×D4C2×C4×D4311yescharacteristic
459C2×D4C2×C4×D4311yescharacteristic
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4C2×C4×D4311yescharacteristic
466C22×C4D4×D4311yescharacteristic
467C22×C4#1062190011yescharacteristic
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—431no—
484C2×C8—431no—
485C2×C8—431no—
486C2×C8—431no—
487C2×C8—861no—
488C2×C8—861no—
489C2×C8—3441no—
490C2×C8—3441no—
491C2×C8—3441no—
492C2×C8—3441no—
493C4⋊C4—21no—
494C4⋊C4—431no—
495C4⋊C4—431no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4C2×C4×D4311yescharacteristic
499C4⋊C4C2×C4×D4311yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—861no—
505C22⋊C4—861no—
506C22⋊C4—861no—
507C42—861no—
508C42—861no—
509C42—861no—
510C42C2×C4×D4311yescharacteristic
511C42D4×D4311yescharacteristic
512C42#1062190011yescharacteristic
513C42C23×D4311yescharacteristic
514C23—21no—
515C23—21no—
516C23—861no—
517C23(C22⋊D43)⋊C411yescharacteristic
518Q8—81no—
519Q8—432no—
520Q8—861no—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—21no—
525D4—81no—
526D4—81no—
527D4—81no—
528D4—81no—
529D4—432no—
530D4—864no—
531D4—861no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—864no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—861no—
547C2×C4—3441no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4(C22⋊D43)⋊C411yescharacteristic
551C2×C4(C22⋊D43)⋊C411yescharacteristic
552C2×C4(C22⋊D43)⋊C411yescharacteristic
553C2×C4C22×C4×D4311yescharacteristic
554C2×C4C2×D4×D4311yescharacteristic
555C2×C4C2×#1062190011yescharacteristic
556C8—41no—
557C8—41no—
558C8—41no—
559C8—41no—
560C8—861no—
561C8—861no—
562C8—861no—
563C8—861no—
564C8—861no—
565C8—861no—
566C8—861no—
567C8—861no—
568C8—1721no—
569C8—1721no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—862no—
580C22—1721no—
581C22—1721no—
582C22C2×(C22⋊D43)⋊C411yescharacteristic
583C4—21no—
584C4—21no—
585C4—21no—
586C4—21no—
587C4—41no—
588C4—41no—
589C4—862no—
590C4—1721no—
591C4—1721no—
592C4#131×D4311yescharacteristic
593C4#131×D4311yescharacteristic
594C4#1458370011yescharacteristic
595C4#1458370511yescharacteristic
596C2—41no—
597C2—81no—
598C2—81no—
599C2—1722no—
600C2#1914329211yescharacteristic
601C2#1914342111yescharacteristic
602C2#1914350811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1480C2
socleC22×C43C2×C4×D4
prime radical#19144649C2
cosocleC42×C43C24
hypercenter#1480D43
hypocenterC43#17920
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1480

Complements

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

NH ≅ G/Ntype
2. #19143704C2semidirect
3. #19143671C2semidirect
4. #19133476C2semidirect
5. #19133462C2semidirect
6. #19133441C2semidirect
7. #19133427C2semidirect
8. #19133416C2semidirect
9. #19133404C2semidirect
10. #19133398C2semidirect
11. #19133387C2semidirect
12. #19133378C2semidirect
13. #19133030C2semidirect
14. #19132895C2semidirect
15. C43×#1480C2semidirect
308. #1480D43semidirect
368. C43#17920semidirect

Maximal subgroups

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

subgroupindex
#191446492
#191437042
#191436712
#191334762
#191334622
#191334412
#191334272
#191334162
#191334042
#191333982
#191333872
#191333782
#191330302
#191328952
C43×#14802
#1792043