Finite Group Databasebeta

← #25067997

Subgroups — #25067997

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#19144630C211yesmaximal, characteristic
2#19143697C211yesmaximal, characteristic
3#19143685C211yesmaximal, characteristic
4#19133501C211yesmaximal, characteristic, complemented
5#19133489C211yesmaximal, characteristic, complemented
6#19133469C211yesmaximal, characteristic, complemented
7#19133463C211yesmaximal, characteristic, complemented
8#19133448C211yesmaximal, characteristic, complemented
9#19133442C211yesmaximal, characteristic, complemented
10#19133411C211yesmaximal, characteristic, complemented
11#19133399C211yesmaximal, characteristic, complemented
12#19133376C211yesmaximal, characteristic
13#19132991C211yesmaximal, characteristic
14#19132895C211yesmaximal, characteristic
15C43×#1497C211yesmaximal, characteristic
16C2×C4×Dic86C2211yescharacteristic
17#14583232C411yescharacteristic
18#14583232C411yescharacteristic
19#14583191C411yescharacteristic
20#14583191C411yescharacteristic
21#14583106C411yescharacteristic
22#14583106C411yescharacteristic
23#14583054C411yescharacteristic
24#14583054C411yescharacteristic
25#14583030—21no—
26#14583030C2211yescharacteristic
27#14583030C2211yescharacteristic
28#14583027—21no—
29#14583027—21no—
30#14583026C2211yescharacteristic
31#14583026C2211yescharacteristic
32Q8×C43⋊C8—21no—
33Q8×C43⋊C8C2211yescharacteristic
34Q8×C43⋊C8C2211yescharacteristic
35#14583023C2211yescharacteristic
36#14583023C2211yescharacteristic
37C4×#10621885C2211yescharacteristic
38C4×#10621885C2211yescharacteristic
39C4×#10621885C2211yescharacteristic
40C4×#10621885C2211yescharacteristic
41#14582960—21no—
42#14582960—21no—
43#14582953—21no—
44#14582952C2211yescharacteristic
45#14582952C2211yescharacteristic
46#14582952C2211yescharacteristic
47#14582949—21no—
48#14582651C2211yescharacteristic
49#14582651C2211yescharacteristic
50#14582649C2211yescharacteristic
51#14582649C2211yescharacteristic
52#14582631C2211yescharacteristic
53#14582631C2211yescharacteristic
54#14582631C2211yescharacteristic
55#14582631C2211yescharacteristic
56#14582621C2211yescharacteristic
57#14582621C2211yescharacteristic
58#14582620C2211yescharacteristic
59C8×C43⋊C8C2211yescharacteristic
60C43×#533C2211yescharacteristic
61C43×#432C2211yescharacteristic
62C43×#431C2211yescharacteristic
63C43×Q8⋊C8C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×Q8⋊C8C2211yescharacteristic
66C43×Q8⋊C8C2211yescharacteristic
67C22×Dic86C2×C411yescharacteristic
68C2×#10621885C2×C411yescharacteristic
69C2×#10621885C2×C411yescharacteristic
70C2×#10621885C2×C411yescharacteristic
71C2×#10621885C2×C411yescharacteristic
72C4×Dic86—21no—
73C4×Dic86—21no—
74C4×Dic86C2×C411yescharacteristic
75C4×Dic86C2×C411yescharacteristic
76C4×Dic86C2311yescharacteristic
77C4×Dic86C2311yescharacteristic
78C2×C4⋊Dic43C2×C411yescharacteristic
79C2×Dic43⋊C4—21no—
80C2×C4×Dic43—21no—
81#13063258C2×C411yescharacteristic
82#13063258C2×C411yescharacteristic
83#13063258C2×C411yescharacteristic
84#13063258C2×C411yescharacteristic
85C4⋊(C43⋊C8)—21no—
86C4⋊(C43⋊C8)—21no—
87C4⋊(C43⋊C8)—21no—
88C4⋊(C43⋊C8)—21no—
89C4⋊(C43⋊C8)C2×C411yescharacteristic
90C4⋊(C43⋊C8)C2×C411yescharacteristic
91C4⋊(C43⋊C8)D411yescharacteristic
92C4⋊(C43⋊C8)D411yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95Dic43⋊C8—21no—
96Dic43⋊C8—21no—
97Dic43⋊C8—21no—
98Dic43⋊C8—21no—
99#13063249C2×C411yescharacteristic
100#13063249C2×C411yescharacteristic
101#13063249C2×C411yescharacteristic
102#13063249C2×C411yescharacteristic
103#13063248C2×C411yescharacteristic
104#13063248C2×C411yescharacteristic
105#13063248C2×C411yescharacteristic
106#13063248C2×C411yescharacteristic
107C22⋊(C43⋊C8)—21no—
108C22⋊(C43⋊C8)C2×C411yescharacteristic
109C22⋊(C43⋊C8)C2×C411yescharacteristic
110C22⋊(C43⋊C8)D411yescharacteristic
111C22⋊(C43⋊C8)D411yescharacteristic
112#13063236—21no—
113#13063236—21no—
114#13063235—21no—
115#13063235—21no—
116C4×C43⋊C8—21no—
117C4×C43⋊C8—21no—
118C4×C43⋊C8—21no—
119C4×C43⋊C8C2311yescharacteristic
120C4×C43⋊C8C2311yescharacteristic
121C4×C43⋊C8C2311yescharacteristic
122C4×C43⋊C8C2311yescharacteristic
123C8×Dic43—21no—
124C8×Dic43—21no—
125C4⋊Q8×C43C2×C411yescharacteristic
126C4⋊Q8×C43C2×C411yescharacteristic
127#125×C43—21no—
128C22⋊Q8×C43—21no—
129C22⋊Q8×C43C2×C411yescharacteristic
130C22⋊Q8×C43C2×C411yescharacteristic
131C4×Q8×C43—21no—
132C4×Q8×C43C2311yescharacteristic
133C4×Q8×C43C2311yescharacteristic
134#117×C43—21no—
135C2×C42×C43C2311yescharacteristic
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139C22⋊C8×C43—21no—
140C22⋊C8×C43—21no—
141#97×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43C22×C411yescharacteristic
146C2×Q8×C43C22×C411yescharacteristic
147C22×C4×C43C22×C411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43#4111yescharacteristic
150C22×Dic43—21no—
151C22×Dic43—21no—
152C2×Dic86—22no—
153C2×Dic86—21no—
154C2×Dic86—41no—
155C2×Dic86C22×C411yescharacteristic
156C2×Dic86C22×C411yescharacteristic
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43C22×C411yescharacteristic
169C4⋊C4×C43C22×C411yescharacteristic
170C22⋊C4×C43—21no—
171C22⋊C4×C43—21no—
172C42×C43—21no—
173C42×C43—21no—
174C42×C43C22×C411yescharacteristic
175C42×C43C2×D411yescharacteristic
176C42×C43#4111yescharacteristic
177C42×C43C2411yescharacteristic
178#10621885—22no—
179#10621885—22no—
180#10621885—41no—
181#10621885—41no—
182C4⋊Dic43—21no—
183C4⋊Dic43C22×C411yescharacteristic
184C4⋊Dic43C22×C411yescharacteristic
185Dic43⋊C4—21no—
186Dic43⋊C4—21no—
187Dic43⋊C4—21no—
188Dic43⋊C4—21no—
189C4×Dic43—21no—
190C4×Dic43—21no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8C22×C411yescharacteristic
196C2×C43⋊C8C22×C411yescharacteristic
197C2×C43⋊C8C22×C411yescharacteristic
198C2×C43⋊C8C22×C411yescharacteristic
199C2×C43⋊C8C2×D411yescharacteristic
200C2×C43⋊C8C2×D411yescharacteristic
201C2×C43⋊C8C2×D411yescharacteristic
202C2×C43⋊C8C2×D411yescharacteristic
203C23×C43C4×D411yescharacteristic
204Q8×C43—21no—
205Q8×C43—21no—
206Q8×C43—21no—
207Q8×C43—21no—
208Q8×C43—42no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—41no—
218C2×C4×C43C4×D411yescharacteristic
219C2×C4×C43C4×D411yescharacteristic
220C2×C4×C43C4×D411yescharacteristic
221C2×C4×C43C23×C411yescharacteristic
222C2×C4×C43C22×D411yescharacteristic
223C2×C4×C43C2×#4111yescharacteristic
224C2×Dic43—21no—
225C2×Dic43—21no—
226C2×Dic43—21no—
227C2×Dic43—21no—
228C2×Dic43—42no—
229C2×Dic43—42no—
230Dic86—21no—
231Dic86—21no—
232Dic86—21no—
233Dic86—42no—
234Dic86#13112yes—
235C8×C43—41no—
236C8×C43—41no—
237C8×C43—41no—
238C8×C43—41no—
239C43⋊C8—21no—
240C43⋊C8—21no—
241C43⋊C8—21no—
242C43⋊C8—21no—
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×C43—41no—
259C4×C43—41no—
260C4×C43—41no—
261C4×C43—41no—
262C4×C43C2×#13111yescharacteristic
263C4×C43#56811yescharacteristic
264C4×C43#57811yescharacteristic
265C4×C43#57811yescharacteristic
266Dic43—22no—
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#1572—431no—
282#1497D4311yescharacteristic
283#1479—431no—
284#1454—431no—
285C2×C43—41no—
286C2×C43#293311yescharacteristic
287C2×C43#295011yescharacteristic
288C2×C43#295511yescharacteristic
289#533C2×D4311yescharacteristic
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—431no—
322#431—861no—
323#431C2×D4311yescharacteristic
324#335—431no—
325#335—431no—
326#334—431no—
327#334—431no—
328Q8⋊C8—431no—
329Q8⋊C8—431no—
330Q8⋊C8—431no—
331Q8⋊C8—431no—
332Q8⋊C8C2×D4311yescharacteristic
333Q8⋊C8C2×D4311yescharacteristic
334Q8⋊C8C2×D4311yescharacteristic
335Q8⋊C8C2×D4311yescharacteristic
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⋊Q8C4×D4311yescharacteristic
347C4⋊Q8C4×D4311yescharacteristic
348#125—21no—
349C22⋊Q8—21no—
350C22⋊Q8C4×D4311yescharacteristic
351C22⋊Q8C4×D4311yescharacteristic
352C4×Q8—21no—
353C4×Q8—431no—
354C4×Q8—431no—
355C4×Q8—431no—
356C4×Q8—431no—
357C4×Q8—861no—
358C4×Q8—861no—
359C4×Q8C22×D4311yescharacteristic
360C4×Q8C22×D4311yescharacteristic
361#117—21no—
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—21no—
371C4⋊C8—431no—
372C4⋊C8—431no—
373C4⋊C8—431no—
374C4⋊C8—431no—
375C4⋊C8—431no—
376C4⋊C8—431no—
377C4⋊C8—861no—
378C4⋊C8—861no—
379C4⋊C8—861no—
380C4⋊C8—861no—
381C4⋊C8—861no—
382C4⋊C8—861no—
383C4⋊C8—861no—
384C4⋊C8—861no—
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—431no—
400C22⋊C8—431no—
401C22⋊C8—861no—
402#97—21no—
403#97—861no—
404#97—861no—
405#97—861no—
406#97—861no—
407C4×C8—431no—
408C4×C8—431no—
409C4×C8—431no—
410C4×C8—431no—
411C4×C8—861no—
412C4×C8—861no—
413C4×C8—861no—
414C4×C8—861no—
415C4×C8—861no—
416C4×C8C22×D4311yescharacteristic
417C4×C8C22×D4311yescharacteristic
418C2×Q8—21no—
419C2×Q8—431no—
420C2×Q8—431no—
421C2×Q8—862no—
422C2×Q8—861no—
423C2×Q8—1721no—
424C2×Q8C2×C4×D4311yescharacteristic
425C2×Q8C2×C4×D4311yescharacteristic
426C22×C4—861no—
427C22×C4—861no—
428C22×C4C2×C4×D4311yescharacteristic
429C22×C4D4×D4311yescharacteristic
430C22×C4#1062190011yescharacteristic
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—431no—
444C2×C8—431no—
445C2×C8—431no—
446C2×C8—431no—
447C2×C8—861no—
448C2×C8—861no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—431no—
457C4⋊C4—431no—
458C4⋊C4—861no—
459C4⋊C4—861no—
460C4⋊C4—861no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4C2×C4×D4311yescharacteristic
464C4⋊C4C2×C4×D4311yescharacteristic
465C22⋊C4—21no—
466C22⋊C4—21no—
467C42—21no—
468C42—21no—
469C42—861no—
470C42—861no—
471C42—861no—
472C42—861no—
473C42C2×C4×D4311yescharacteristic
474C42D4×D4311yescharacteristic
475C42#1062190011yescharacteristic
476C42C23×D4311yescharacteristic
477C23(C22⋊D43)⋊C411yescharacteristic
478Q8—21no—
479Q8—21no—
480Q8—21no—
481Q8—21no—
482Q8—42no—
483Q8—432no—
484Q8—861no—
485Q8—861no—
486Q8—861no—
487Q8—1722no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—41no—
497C2×C4—861no—
498C2×C4—861no—
499C2×C4—861no—
500C2×C4—861no—
501C2×C4—1722no—
502C2×C4—1722no—
503C2×C4(C22⋊D43)⋊C411yescharacteristic
504C2×C4(C22⋊D43)⋊C411yescharacteristic
505C2×C4(C22⋊D43)⋊C411yescharacteristic
506C2×C4C22×C4×D4311yescharacteristic
507C2×C4C2×D4×D4311yescharacteristic
508C2×C4C2×#1062190011yescharacteristic
509C8—41no—
510C8—41no—
511C8—41no—
512C8—41no—
513C8—861no—
514C8—861no—
515C8—861no—
516C8—861no—
517C8—861no—
518C8—861no—
519C8—861no—
520C8—861no—
521C8—1721no—
522C8—1721no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22C2×(C22⋊D43)⋊C411yescharacteristic
527C4—21no—
528C4—21no—
529C4—21no—
530C4—21no—
531C4—41no—
532C4—41no—
533C4—41no—
534C4—41no—
535C4—862no—
536C4—1721no—
537C4—1721no—
538C4—1721no—
539C4#131×D4311yescharacteristic
540C4#1458366411yescharacteristic
541C4#1458371511yescharacteristic
542C4#1458371511yescharacteristic
543C2—41no—
544C2#1914332511yescharacteristic
545C2#1914345911yescharacteristic
546C2#1914349411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1497C2
socleC22×C43C2×C4×D4
prime radicalC23×C43C4×D4
cosocleC42×C43C24
hypercenter#1497D43
hypocenterC43#18032
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1497

Complements

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

NH ≅ G/Ntype
4. #19133501C2semidirect
5. #19133489C2semidirect
6. #19133469C2semidirect
7. #19133463C2semidirect
8. #19133448C2semidirect
9. #19133442C2semidirect
10. #19133411C2semidirect
11. #19133399C2semidirect
340. C43#18032semidirect

Maximal subgroups

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

subgroupindex
#191446302
#191436972
#191436852
#191335012
#191334892
#191334692
#191334632
#191334482
#191334422
#191334112
#191333992
#191333762
#191329912
#191328952
C43×#14972
#1803243