Finite Group Databasebeta

← #25067989

Subgroups — #25067989

Order 11008.

566 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144635C211yesmaximal, characteristic
2#19143696C211yesmaximal, characteristic
3#19143685C211yesmaximal, characteristic
4#19133503C211yesmaximal, characteristic, complemented
5#19133491C211yesmaximal, characteristic, complemented
6#19133465C211yesmaximal, characteristic, complemented
7#19133465C211yesmaximal, characteristic, complemented
8#19133444C211yesmaximal, characteristic, complemented
9#19133444C211yesmaximal, characteristic, complemented
10#19133413C211yesmaximal, characteristic, complemented
11#19133401C211yesmaximal, characteristic, complemented
12#19133067C211yesmaximal, characteristic
13#19132989C211yesmaximal, characteristic
14#19132895C211yesmaximal, characteristic
15C43×#1572C211yesmaximal, characteristic
16#14583456C2211yescharacteristic
17C2×C4×Dic86C2211yescharacteristic
18#14583235C411yescharacteristic
19#14583235C411yescharacteristic
20#14583195C411yescharacteristic
21#14583195C411yescharacteristic
22#14583110C411yescharacteristic
23#14583110C411yescharacteristic
24#14583057C411yescharacteristic
25#14583057C411yescharacteristic
26#14583029—21no—
27#14583027—21no—
28#14583027—21no—
29#14583026C2211yescharacteristic
30#14583026C2211yescharacteristic
31#14583026C2211yescharacteristic
32#14583026C2211yescharacteristic
33C8×Dic86—21no—
34#14583023C2211yescharacteristic
35#14583023C2211yescharacteristic
36#14583023C2211yescharacteristic
37#14583023C2211yescharacteristic
38C4×Dic172C2211yescharacteristic
39C4×Dic172C2211yescharacteristic
40C4×Dic172C2211yescharacteristic
41C4×Dic172C2211yescharacteristic
42#14582957—21no—
43#14582957—21no—
44#14582953—21no—
45#14582952C2211yescharacteristic
46#14582952C2211yescharacteristic
47#14582949—21no—
48#14582629C2211yescharacteristic
49#14582629C2211yescharacteristic
50#14582629C2211yescharacteristic
51#14582629C2211yescharacteristic
52#14582629C2211yescharacteristic
53#14582629C2211yescharacteristic
54#14582629C2211yescharacteristic
55#14582629C2211yescharacteristic
56#14582621C2211yescharacteristic
57#14582621C2211yescharacteristic
58#14582620C2211yescharacteristic
59C8×C43⋊C8C2211yescharacteristic
60C43×#432C2211yescharacteristic
61C43×#431C2211yescharacteristic
62C43×#431C2211yescharacteristic
63C43×#335C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#334C2211yescharacteristic
66C43×#334C2211yescharacteristic
67C22×Dic86C2×C411yescharacteristic
68C2×Dic172C2×C411yescharacteristic
69C2×Dic172C2×C411yescharacteristic
70C2×Dic172C2×C411yescharacteristic
71C2×Dic172C2×C411yescharacteristic
72#13063325C2×C411yescharacteristic
73#13063325C2×C411yescharacteristic
74#13063317—21no—
75#13063304—21no—
76#13063304C2×C411yescharacteristic
77#13063304C2×C411yescharacteristic
78C4×Dic86—21no—
79C4×Dic86—21no—
80C4×Dic86—21no—
81C4×Dic86C2×C411yescharacteristic
82C4×Dic86C2×C411yescharacteristic
83C4×Dic86C2311yescharacteristic
84C4×Dic86C2311yescharacteristic
85C4×Dic86C2311yescharacteristic
86C4×Dic86C2311yescharacteristic
87#13063284—21no—
88C2×C4⋊Dic43C2×C411yescharacteristic
89C2×Dic43⋊C4—21no—
90C2×C4×Dic43—21no—
91#13063259C2×C411yescharacteristic
92#13063259C2×C411yescharacteristic
93#13063259C2×C411yescharacteristic
94#13063259C2×C411yescharacteristic
95C4⋊(C43⋊C8)—21no—
96C4⋊(C43⋊C8)D411yescharacteristic
97C4⋊(C43⋊C8)D411yescharacteristic
98Dic43⋊C8—21no—
99Dic43⋊C8—21no—
100Dic43⋊C8—21no—
101Dic43⋊C8—21no—
102Dic43⋊C8—21no—
103Dic43⋊C8—21no—
104Dic43⋊C8—21no—
105Dic43⋊C8—21no—
106#13063250C2×C411yescharacteristic
107#13063250C2×C411yescharacteristic
108#13063250C2×C411yescharacteristic
109#13063250C2×C411yescharacteristic
110#13063250C2×C411yescharacteristic
111#13063250C2×C411yescharacteristic
112#13063250C2×C411yescharacteristic
113#13063250C2×C411yescharacteristic
114C22⋊(C43⋊C8)—21no—
115C22⋊(C43⋊C8)D411yescharacteristic
116C22⋊(C43⋊C8)D411yescharacteristic
117#13063235—21no—
118#13063235—21no—
119#13063235—21no—
120#13063235—21no—
121C4×C43⋊C8C2311yescharacteristic
122C4×C43⋊C8C2311yescharacteristic
123C4×C43⋊C8C2311yescharacteristic
124C4×C43⋊C8C2311yescharacteristic
125C8×Dic43—21no—
126C8×Dic43—21no—
127C8×Dic43—21no—
128C8×Dic43—21no—
129C2×C42×C43C2311yescharacteristic
130C4⋊C8×C43C2×C411yescharacteristic
131C4⋊C8×C43C2×C411yescharacteristic
132C4⋊C8×C43C2311yescharacteristic
133C4⋊C8×C43C2311yescharacteristic
134C4⋊C8×C43C2311yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136C22⋊C8×C43—21no—
137C22⋊C8×C43—21no—
138C22⋊C8×C43C2×C411yescharacteristic
139C22⋊C8×C43C2×C411yescharacteristic
140#97×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C22×C4×C43C22×C411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43#4111yescharacteristic
147C22×Dic43—21no—
148C22×Dic43—21no—
149C2×Dic86—22no—
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86—41no—
153C2×Dic86C22×C411yescharacteristic
154C2×Dic86C22×C411yescharacteristic
155C2×Dic86C22×C411yescharacteristic
156C2×Dic86C22×C411yescharacteristic
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43C22×C411yescharacteristic
162C2×C8×C43C22×C411yescharacteristic
163C2×C8×C43C22×C411yescharacteristic
164C2×C8×C43C22×C411yescharacteristic
165C42×C43C22×C411yescharacteristic
166C42×C43C2×D411yescharacteristic
167C42×C43#4111yescharacteristic
168C42×C43C2411yescharacteristic
169C22⋊Dic43—21no—
170C22⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43C22×C411yescharacteristic
176C4⋊Dic43C22×C411yescharacteristic
177C4⋊Dic43C22×C411yescharacteristic
178C4⋊Dic43C22×C411yescharacteristic
179Dic43⋊C4—21no—
180Dic43⋊C4—21no—
181Dic43⋊C4—21no—
182Dic43⋊C4—21no—
183Dic43⋊C4—21no—
184Dic43⋊C4—21no—
185Dic43⋊C4—21no—
186Dic43⋊C4—21no—
187C4×Dic43—21no—
188C4×Dic43—21no—
189C4×Dic43—21no—
190C4×Dic43—21no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8C2×D411yescharacteristic
196C2×C43⋊C8C2×D411yescharacteristic
197C2×C43⋊C8C2×D411yescharacteristic
198C2×C43⋊C8C2×D411yescharacteristic
199Dic172—22no—
200Dic172—22no—
201Dic172—41no—
202Dic172—41no—
203C23×C43C4×D411yescharacteristic
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—41no—
209C2×C4×C43C4×D411yescharacteristic
210C2×C4×C43C4×D411yescharacteristic
211C2×C4×C43C4×D411yescharacteristic
212C2×C4×C43C23×C411yescharacteristic
213C2×C4×C43C22×D411yescharacteristic
214C2×C4×C43C2×#4111yescharacteristic
215C2×Dic43—21no—
216C2×Dic43—21no—
217C2×Dic43—21no—
218C2×Dic43—21no—
219C2×Dic43—21no—
220C2×Dic43—21no—
221C2×Dic43—21no—
222C2×Dic43—21no—
223C2×Dic43—42no—
224C2×Dic43—42no—
225Dic86—21no—
226Dic86—21no—
227Dic86—21no—
228Dic86—21no—
229Dic86—21no—
230Dic86—21no—
231Dic86—21no—
232Dic86—42no—
233Dic86—42no—
234Dic86#13112yes—
235C8×C43—21no—
236C8×C43—21no—
237C8×C43—21no—
238C8×C43—21no—
239C8×C43—41no—
240C8×C43—41no—
241C8×C43—41no—
242C8×C43—41no—
243C43⋊C8—21no—
244C43⋊C8—21no—
245C43⋊C8—21no—
246C43⋊C8—21no—
247C43⋊C8—41no—
248C43⋊C8—41no—
249#18032—431nomaximal, Sylow
250C22×C43—21no—
251C22×C43—21no—
252C22×C43—21no—
253C22×C43C2×C4×D411yescharacteristic
254C4×C43—21no—
255C4×C43—21no—
256C4×C43—21no—
257C4×C43—21no—
258C4×C43C2×#13111yescharacteristic
259C4×C43#56811yescharacteristic
260C4×C43#57811yescharacteristic
261C4×C43#57811yescharacteristic
262Dic43—22no—
263Dic43—41no—
264Dic43—41no—
265Dic43—41no—
266Dic43—41no—
267Dic43—41no—
268Dic43—41no—
269Dic43—41no—
270#3104—431no—
271#2986—431no—
272#2984—431no—
273#1593—431no—
274#1591—431no—
275#1587—431no—
276#1587—431no—
277#1584—431no—
278#1584—431no—
279#1579—431no—
280C8×Q16—431no—
281#1572D4311yescharacteristic
282#1497—431no—
283#1479—431no—
284#1454—431no—
285C2×C43—41no—
286C2×C43#293311yescharacteristic
287C2×C43#295011yescharacteristic
288C2×C43#295511yescharacteristic
289#533—431no—
290C2×C4×Q8—431no—
291#484—431no—
292#484—431no—
293#477—431no—
294#477—431no—
295#462—431no—
296#462—431no—
297#451—431no—
298#451—431no—
299#446—431no—
300#446—431no—
301#446—431no—
302#446—431no—
303#446—861no—
304#446—861no—
305#446—861no—
306C8×Q8—431no—
307C8×Q8—431no—
308C8×Q8—431no—
309C8×Q8—431no—
310C8×Q8—861no—
311C4×Q16—431no—
312C4×Q16—431no—
313C4×Q16—431no—
314C4×Q16—431no—
315#433—861no—
316#433—861no—
317#432—861no—
318#432C2×D4311yescharacteristic
319#431—431no—
320#431—431no—
321#431—861no—
322#431C2×D4311yescharacteristic
323#431C2×D4311yescharacteristic
324#335C2×D4311yescharacteristic
325#335C2×D4311yescharacteristic
326#334C2×D4311yescharacteristic
327#334C2×D4311yescharacteristic
328Q8⋊C8—431no—
329Q8⋊C8—431no—
330Q8⋊C8—431no—
331Q8⋊C8—431no—
332Q8⋊C8—431no—
333Q8⋊C8—431no—
334Q8⋊C8—431no—
335Q8⋊C8—431no—
336#322—431no—
337#322—431no—
338#322—431no—
339C82—431no—
340C43#1803211yescharacteristic, complemented, Sylow
341C22×Q8—431no—
342C2×Q16—431no—
343C2×Q16—431no—
344C2×Q16—431no—
345C2×Q16—431no—
346C4⋊Q8—431no—
347C4⋊Q8—431no—
348#125—861no—
349C22⋊Q8—431no—
350C22⋊Q8—431no—
351C22⋊Q8—861no—
352C4×Q8—431no—
353C4×Q8—431no—
354C4×Q8—431no—
355C4×Q8—431no—
356C4×Q8—431no—
357C4×Q8—431no—
358C4×Q8—861no—
359C4×Q8—861no—
360C4×Q8—861no—
361#117—861no—
362C2×C4⋊C4—431no—
363C2×C4⋊C4—861no—
364C2×C42—861no—
365C2×C42C22×D4311yescharacteristic
366#107—431no—
367#107—431no—
368#107—431no—
369#107—431no—
370C4⋊C8—431no—
371C4⋊C8—431no—
372C4⋊C8—861no—
373C4⋊C8—861no—
374C4⋊C8—861no—
375C4⋊C8—861no—
376C4⋊C8—861no—
377C4⋊C8—861no—
378C4⋊C8—861no—
379C4⋊C8—861no—
380C4⋊C8—861no—
381C4⋊C8C4×D4311yescharacteristic
382C4⋊C8C4×D4311yescharacteristic
383C4⋊C8C22×D4311yescharacteristic
384C4⋊C8C22×D4311yescharacteristic
385C4⋊C8C22×D4311yescharacteristic
386C4⋊C8C22×D4311yescharacteristic
387#103—431no—
388#103—431no—
389#103—431no—
390#103—431no—
391#103—431no—
392#103—431no—
393#103—431no—
394#103—431no—
395C22⋊C8—21no—
396C22⋊C8—21no—
397C22⋊C8—431no—
398C22⋊C8—431no—
399C22⋊C8—861no—
400C22⋊C8C4×D4311yescharacteristic
401C22⋊C8C4×D4311yescharacteristic
402#97—21no—
403#97—861no—
404#97—861no—
405#97—861no—
406#97—861no—
407C4×C8—21no—
408C4×C8—431no—
409C4×C8—431no—
410C4×C8—431no—
411C4×C8—431no—
412C4×C8—861no—
413C4×C8—861no—
414C4×C8—861no—
415C4×C8—861no—
416C4×C8C22×D4311yescharacteristic
417C4×C8C22×D4311yescharacteristic
418C2×Q8—431no—
419C2×Q8—431no—
420C2×Q8—431no—
421C2×Q8—431no—
422C2×Q8—862no—
423C2×Q8—861no—
424C2×Q8—861no—
425C2×Q8—1721no—
426C22×C4—861no—
427C22×C4—861no—
428C22×C4C2×C4×D4311yescharacteristic
429C22×C4D4×D4311yescharacteristic
430C22×C4#1062190211yescharacteristic
431Q16—862no—
432Q16—862no—
433Q16—1721no—
434Q16—1721no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—431no—
440C2×C8—431no—
441C2×C8—431no—
442C2×C8—431no—
443C2×C8—861no—
444C2×C8—861no—
445C2×C8C2×C4×D4311yescharacteristic
446C2×C8C2×C4×D4311yescharacteristic
447C2×C8C2×C4×D4311yescharacteristic
448C2×C8C2×C4×D4311yescharacteristic
449C4⋊C4—431no—
450C4⋊C4—431no—
451C4⋊C4—431no—
452C4⋊C4—431no—
453C4⋊C4—861no—
454C4⋊C4—861no—
455C4⋊C4—861no—
456C4⋊C4—861no—
457C4⋊C4—861no—
458C4⋊C4—861no—
459C4⋊C4—861no—
460C4⋊C4—861no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C22⋊C4—861no—
466C22⋊C4—861no—
467C42—861no—
468C42—861no—
469C42—861no—
470C42—861no—
471C42—861no—
472C42—861no—
473C42C2×C4×D4311yescharacteristic
474C42D4×D4311yescharacteristic
475C42#1062190211yescharacteristic
476C42C23×D4311yescharacteristic
477C23#1306328711yescharacteristic
478Q8—432no—
479Q8—861no—
480Q8—861no—
481Q8—861no—
482Q8—861no—
483Q8—861no—
484Q8—861no—
485Q8—861no—
486Q8—1722no—
487Q8—1722no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—41no—
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—1722no—
502C2×C4—1722no—
503C2×C4#1306328711yescharacteristic
504C2×C4#1306328711yescharacteristic
505C2×C4#1306328711yescharacteristic
506C2×C4C22×C4×D4311yescharacteristic
507C2×C4C2×D4×D4311yescharacteristic
508C2×C4C2×#1062190211yescharacteristic
509C8—21no—
510C8—21no—
511C8—21no—
512C8—21no—
513C8—41no—
514C8—41no—
515C8—41no—
516C8—41no—
517C8—861no—
518C8—861no—
519C8—861no—
520C8—861no—
521C8—1721no—
522C8—1721no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22C2×#1306328711yescharacteristic
527C4—21no—
528C4—21no—
529C4—21no—
530C4—21no—
531C4—862no—
532C4—1721no—
533C4—1721no—
534C4—1721no—
535C4—1721no—
536C4—1721no—
537C4—1721no—
538C4—1721no—
539C4#131×D4311yescharacteristic
540C4#1458366411yescharacteristic
541C4#1458371311yescharacteristic
542C4#1458371311yescharacteristic
543C2—41no—
544C2#1914331911yescharacteristic
545C2#1914346211yescharacteristic
546C2#1914349711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1572C2
socleC22×C43C2×C4×D4
prime radicalC23×C43C4×D4
cosocleC42×C43C24
hypercenter#1572D43
hypocenterC43#18032
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1572

Complements

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

NH ≅ G/Ntype
4. #19133503C2semidirect
5. #19133491C2semidirect
6. #19133465C2semidirect
7. #19133465C2semidirect
8. #19133444C2semidirect
9. #19133444C2semidirect
10. #19133413C2semidirect
11. #19133401C2semidirect
340. C43#18032semidirect

Maximal subgroups

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

subgroupindex
#191446352
#191436962
#191436852
#191335032
#191334912
#191334652
#191334442
#191334132
#191334012
#191330672
#191329892
#191328952
C43×#15722
#1803243