Finite Group Databasebeta

← #25067736

Subgroups — #25067736

Order 11008.

592 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144667C211yesmaximal, characteristic
2#19143612C211yesmaximal, characteristic
3#19143538C211yesmaximal, characteristic, complemented
4#19133496C211yesmaximal, characteristic, complemented
5#19133484C211yesmaximal, characteristic, complemented
6#19133472C211yesmaximal, characteristic, complemented
7#19133465C211yesmaximal, characteristic, complemented
8#19133444C211yesmaximal, characteristic, complemented
9#19133437C211yesmaximal, characteristic, complemented
10#19133413C211yesmaximal, characteristic, complemented
11#19133401C211yesmaximal, characteristic, complemented
12#19133067C211yesmaximal, characteristic, complemented
13#19132980C211yesmaximal, characteristic
14#19132890C211yesmaximal, characteristic, complemented
15C43×#1573C211yesmaximal, characteristic, complemented
16#14583456C2211yescharacteristic
17C4×#10621898C2211yescharacteristic
18#14583241C411yescharacteristic
19#14583241C411yescharacteristic
20#14583185C411yescharacteristic
21#14583180C411yescharacteristic
22#14583110C411yescharacteristic
23#14583105C411yescharacteristic
24#14583063C411yescharacteristic
25#14583063C411yescharacteristic
26#14583028—21no—
27#14583028—21no—
28#14583026C2211yescharacteristic
29#14583026C2211yescharacteristic
30#14583023C2211yescharacteristic
31#14583023C2211yescharacteristic
32#14583023C2211yescharacteristic
33#14583023C2211yescharacteristic
34C4×Dic172C2211yescharacteristic
35C4×Dic172C2211yescharacteristic
36C4×#10621873C2211yescharacteristic
37C4×#10621873C2211yescharacteristic
38#14582976C2211yescharacteristic
39#14582976C2211yescharacteristic
40#14582974—21no—
41#14582974—21no—
42#14582954—21no—
43#14582952C2211yescharacteristic
44#14582925—21no—
45#14582854—21no—
46C4×#10621877C2211yescharacteristic
47#14582851—21no—
48#14582629C2211yescharacteristic
49#14582629C2211yescharacteristic
50#14582629C2211yescharacteristic
51#14582629C2211yescharacteristic
52#14582629C2211yescharacteristic
53#14582629C2211yescharacteristic
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×#10621898C2×C411yescharacteristic
68C2×Dic172C2×C411yescharacteristic
69C2×Dic172C2×C411yescharacteristic
70C2×#10621873C2×C411yescharacteristic
71C2×#10621873C2×C411yescharacteristic
72C2×#10621877D411yescharacteristic
73C2×#10621877D411yescharacteristic
74C2×#10621872—21no—
75C2×#10621872—21no—
76#13063325C2×C411yescharacteristic
77#13063325C2×C411yescharacteristic
78#13063317—21no—
79#13063304—21no—
80#13063304C2×C411yescharacteristic
81#13063304C2×C411yescharacteristic
82C4×Dic86—21no—
83C4×Dic86C2×C411yescharacteristic
84C4×Dic86C2311yescharacteristic
85C4×Dic86C2311yescharacteristic
86C4×Dic86C2311yescharacteristic
87C4×D172C2×C411yescharacteristic
88C4×D172C2311yescharacteristic
89C4×C22⋊D43—21no—
90C4×C22⋊D43—21no—
91#13063284—21no—
92#13063284C2×C411yescharacteristic
93#13063282—21no—
94C42×D43—21no—
95#13063259C2×C411yescharacteristic
96#13063259C2×C411yescharacteristic
97#13063257C2×C411yescharacteristic
98#13063257C2×C411yescharacteristic
99C4⋊(C43⋊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#13063247C2×C411yescharacteristic
113#13063247C2×C411yescharacteristic
114C22⋊(C43⋊C8)—21no—
115(C2×D43)⋊C8—21no—
116(C2×D43)⋊C8—21no—
117#13063236D411yescharacteristic
118#13063236D411yescharacteristic
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—
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—
148#10621898—22no—
149#10621898—41no—
150C2×D172C22×C411yescharacteristic
151C2×C4×D43—21no—
152C2×C4×D43—21no—
153C2×C4×D43—21no—
154C2×Dic86—21no—
155C2×Dic86C22×C411yescharacteristic
156C2×Dic86C22×C411yescharacteristic
157C2×Dic86C22×C411yescharacteristic
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—42no—
163C2×C8×C43C22×C411yescharacteristic
164C2×C8×C43C22×C411yescharacteristic
165C2×C8×C43C22×C411yescharacteristic
166C2×C8×C43C22×C411yescharacteristic
167C42×C43C22×C411yescharacteristic
168C42×C43C2×D411yescharacteristic
169C42×C43#4111yescharacteristic
170C42×C43C2411yescharacteristic
171C22⋊Dic43—21no—
172C22⋊Dic43—21no—
173C22⋊Dic43—21no—
174(C2×D43)⋊C4—21no—
175(C2×D43)⋊C4—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43C22×C411yescharacteristic
180C4⋊Dic43C22×C411yescharacteristic
181C4⋊Dic43C22×C411yescharacteristic
182C4⋊Dic43C22×C411yescharacteristic
183Dic43⋊C4—21no—
184Dic43⋊C4—21no—
185Dic43⋊C4—21no—
186Dic43⋊C4—21no—
187Dic43⋊C4—21no—
188Dic43⋊C4—21no—
189C4×Dic43—21no—
190C4×Dic43—21no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194#10621877—22no—
195#10621877—41no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8C2×D411yescharacteristic
199C2×C43⋊C8C2×D411yescharacteristic
200C2×C43⋊C8C2×D411yescharacteristic
201C2×C43⋊C8C2×D411yescharacteristic
202Dic172—22no—
203Dic172—22no—
204#10621873—41no—
205#10621873—41no—
206#10621872—42no—
207#10621872—42no—
208C23×C43C4×D411yescharacteristic
209C22×D43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—41no—
215C2×C4×C43C4×D411yescharacteristic
216C2×C4×C43C4×D411yescharacteristic
217C2×C4×C43C4×D411yescharacteristic
218C2×C4×C43C23×C411yescharacteristic
219C2×C4×C43C22×D411yescharacteristic
220C2×C4×C43C2×#4111yescharacteristic
221C22⋊D43—42no—
222C2×Dic43—21no—
223C2×Dic43—21no—
224C2×Dic43—21no—
225C2×Dic43—21no—
226C2×Dic43—21no—
227C2×Dic43—21no—
228C2×Dic43—21no—
229D172—21no—
230D172—21no—
231C4×D43—42no—
232C4×D43—41no—
233C4×D43—41no—
234C4×D43—81no—
235Dic86—21no—
236Dic86—21no—
237Dic86—21no—
238Dic86—21no—
239Dic86—21no—
240Dic86—81no—
241Dic86#13112yes—
242C8×C43—21no—
243C8×C43—21no—
244C8×C43—21no—
245C8×C43—21no—
246C8×C43—41no—
247C8×C43—41no—
248C8×C43—41no—
249C8×C43—41no—
250C43⋊C8—21no—
251C43⋊C8—21no—
252C43⋊C8—21no—
253C43⋊C8—41no—
254C43⋊C8—41no—
255C43⋊C8#13712yes—
256#18013—431nomaximal, Sylow
257C22×C43—21no—
258C22×C43—21no—
259C22×C43—21no—
260C22×C43C2×C4×D411yescharacteristic
261C2×D43—41no—
262C2×D43—41no—
263C2×D43—41no—
264C4×C43—21no—
265C4×C43—21no—
266C4×C43—21no—
267C4×C43—21no—
268C4×C43C2×#13111yescharacteristic
269C4×C43#56811yescharacteristic
270C4×C43C2×#13711yescharacteristic
271C4×C43#57511yescharacteristic
272Dic43—22no—
273Dic43—41no—
274Dic43—41no—
275Dic43—41no—
276Dic43—41no—
277Dic43—41no—
278Dic43—41no—
279#3107—431no—
280#2971—431no—
281#2962—431no—
282#1592—431no—
283#1590—431no—
284#1588—431no—
285#1587—431no—
286#1584—431no—
287#1583—431no—
288#1579—431no—
289C8×Q16—431no—
290#1573D4311yescharacteristic, complemented
291#1497—431no—
292#1477—431no—
293#1453—431no—
294C2×C43—41no—
295C2×C43#293311yescharacteristic
296C2×C43C4×#13711yescharacteristic
297C2×C43#295711yescharacteristic
298D43—81no—
299#533—431no—
300C4×#41—431no—
301#485—431no—
302#485—431no—
303#475—431no—
304#474—431no—
305#462—431no—
306#461—431no—
307#452—431no—
308#452—431no—
309#446—431no—
310#446—431no—
311#446—861no—
312#446—861no—
313C8×Q8—431no—
314C8×Q8—431no—
315C8×Q8—431no—
316C8×Q8—431no—
317C4×Q16—431no—
318C4×Q16—431no—
319C4×SD16—431no—
320C4×SD16—431no—
321#436—431no—
322#436—431no—
323#436—861no—
324#436—861no—
325#432—861no—
326#432C2×D4311yescharacteristic
327#431—431no—
328#431C2×D4311yescharacteristic
329#424—861no—
330C2×C4⋊C8C2×D4311yescharacteristic
331#405—861no—
332C4×M16—431no—
333C4×M16—861no—
334#335C2×D4311yescharacteristic
335#335C2×D4311yescharacteristic
336#334C2×D4311yescharacteristic
337#334C2×D4311yescharacteristic
338Q8⋊C8—431no—
339Q8⋊C8—431no—
340Q8⋊C8—431no—
341Q8⋊C8—431no—
342Q8⋊C8—431no—
343Q8⋊C8—431no—
344D4⋊C8—431no—
345D4⋊C8—431no—
346#322—431no—
347#322—431no—
348#322—431no—
349C82—431no—
350C43#1801311yescharacteristic, complemented, Sylow
351C2×#41—431no—
352C2×Q16—431no—
353C2×Q16—431no—
354C2×SD16—431no—
355C2×SD16—431no—
356C2×M16—431no—
357C2×M16—431no—
358C2×M16—861no—
359C2×M16—861no—
360C22×C8—21no—
361C4⋊Q8—431no—
362C4⋊Q8—431no—
363#125—861no—
364C22⋊Q8—431no—
365C22⋊Q8—431no—
366C22⋊Q8—861no—
367C4×Q8—431no—
368C4×Q8—431no—
369C4×Q8—431no—
370C4×Q8—431no—
371C4×Q8—861no—
372C4×D4—431no—
373C4×D4—431no—
374C4×D4—861no—
375C4×D4—861no—
376#117—431no—
377#117—861no—
378#117—861no—
379C2×C42—861no—
380C2×C42C22×D4311yescharacteristic
381#107—431no—
382#107—431no—
383#106—431no—
384#106—431no—
385C4⋊C8—21no—
386C4⋊C8—861no—
387C4⋊C8—861no—
388C4⋊C8—861no—
389C4⋊C8—861no—
390C4⋊C8—861no—
391C4⋊C8—861no—
392C4⋊C8—861no—
393C4⋊C8C4×D4311yescharacteristic
394C4⋊C8C4×D4311yescharacteristic
395C4⋊C8C22×D4311yescharacteristic
396C4⋊C8C22×D4311yescharacteristic
397C4⋊C8C22×D4311yescharacteristic
398C4⋊C8C22×D4311yescharacteristic
399#103—431no—
400#103—431no—
401#103—431no—
402#103—431no—
403#103—431no—
404#103—431no—
405#102—431no—
406#102—431no—
407C22⋊C8—21no—
408C22⋊C8—861no—
409C22⋊C8—861no—
410C22⋊C8—861no—
411C22⋊C8C4×D4311yescharacteristic
412C22⋊C8C4×D4311yescharacteristic
413#97—21no—
414#97—431no—
415#97—431no—
416#97—861no—
417#97—861no—
418C4×C8—431no—
419C4×C8—431no—
420C4×C8—431no—
421C4×C8—431no—
422C4×C8—861no—
423C4×C8—861no—
424C4×C8—861no—
425C4×C8—861no—
426C4×C8C22×D4311yescharacteristic
427C4×C8C22×D4311yescharacteristic
428#41—862no—
429#41—1721no—
430C2×Q8—431no—
431C2×Q8—431no—
432C2×Q8—431no—
433C2×Q8—861no—
434C2×D4—431no—
435C2×D4—861no—
436C22×C4—861no—
437C22×C4—861no—
438C22×C4—861no—
439C22×C4C2×C4×D4311yescharacteristic
440C22×C4D4×D4311yescharacteristic
441C22×C4#1062190211yescharacteristic
442Q16—862no—
443Q16—862no—
444SD16—1721no—
445SD16—1721no—
446M16—862no—
447M16—1722no—
448M16—1722no—
449M16—1721no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—42no—
455C2×C8—431no—
456C2×C8—431no—
457C2×C8—431no—
458C2×C8—431no—
459C2×C8—861no—
460C2×C8—861no—
461C2×C8C2×C4×D4311yescharacteristic
462C2×C8C2×C4×D4311yescharacteristic
463C2×C8C2×C4×D4311yescharacteristic
464C2×C8C2×C4×D4311yescharacteristic
465C4⋊C4—431no—
466C4⋊C4—431no—
467C4⋊C4—431no—
468C4⋊C4—431no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C22⋊C4—861no—
479C22⋊C4—861no—
480C22⋊C4—861no—
481C22⋊C4—861no—
482C22⋊C4—861no—
483C42—861no—
484C42—861no—
485C42—861no—
486C42—861no—
487C42—861no—
488C42C2×C4×D4311yescharacteristic
489C42D4×D4311yescharacteristic
490C42#1062190211yescharacteristic
491C42C23×D4311yescharacteristic
492C23—861no—
493C23#1306328711yescharacteristic
494Q8—432no—
495Q8—861no—
496Q8—861no—
497Q8—861no—
498Q8—861no—
499Q8—861no—
500Q8—3441no—
501D4—861no—
502D4—861no—
503D4—1722no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—861no—
510C2×C4—861no—
511C2×C4—861no—
512C2×C4—861no—
513C2×C4—861no—
514C2×C4—861no—
515C2×C4—861no—
516C2×C4—3441no—
517C2×C4—1722no—
518C2×C4—1721no—
519C2×C4—1721no—
520C2×C4#1306328711yescharacteristic
521C2×C4#1306328711yescharacteristic
522C2×C4#1306328711yescharacteristic
523C2×C4C22×C4×D4311yescharacteristic
524C2×C4C2×D4×D4311yescharacteristic
525C2×C4C2×#1062190211yescharacteristic
526C8—21no—
527C8—21no—
528C8—21no—
529C8—21no—
530C8—41no—
531C8—41no—
532C8—41no—
533C8—41no—
534C8—432no—
535C8—861no—
536C8—861no—
537C8—861no—
538C8—1721no—
539C8—1721no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—1721no—
544C22—1721no—
545C22—1721no—
546C22C2×#1306328711yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—862no—
552C4—1721no—
553C4—1721no—
554C4—1721no—
555C4—1721no—
556C4—1721no—
557C4—1721no—
558C4#131×D4311yescharacteristic
559C4#1458366411yescharacteristic
560C4#137×D4311yescharacteristic
561C4#1458369511yescharacteristic
562C2—41no—
563C2—3441no—
564C2#1914331911yescharacteristic
565C2#1914341311yescharacteristic
566C2#1914351111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1573C2
socleC22×C43C2×C4×D4
prime radicalC2×#10621898C2×C4
cosocleC42×C43C24
hypercenter#1573D43
hypocenterC43#18013
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
3. #19143538C2semidirect
4. #19133496C2semidirect
5. #19133484C2semidirect
6. #19133472C2semidirect
7. #19133465C2semidirect
8. #19133444C2semidirect
9. #19133437C2semidirect
10. #19133413C2semidirect
11. #19133401C2semidirect
12. #19133067C2semidirect
14. #19132890C2semidirect
15. C43×#1573C2semidirect
290. #1573D43semidirect
350. C43#18013semidirect

Maximal subgroups

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

subgroupindex
#191446672
#191436122
#191435382
#191334962
#191334842
#191334722
#191334652
#191334442
#191334372
#191334132
#191334012
#191330672
#191329802
#191328902
C43×#15732
#1801343