Finite Group Databasebeta

← #25067071

Subgroups — #25067071

Order 11008.

558 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144632C211yesmaximal, characteristic
2#19143686C211yesmaximal, characteristic
3#19143677C211yesmaximal, characteristic
4#19133504C211yesmaximal, characteristic, complemented
5#19133503C211yesmaximal, characteristic, complemented
6#19133489C211yesmaximal, characteristic, complemented
7#19133489C211yesmaximal, characteristic, complemented
8#19133468C211yesmaximal, characteristic, complemented
9#19133445C211yesmaximal, characteristic, complemented
10#19133443C211yesmaximal, characteristic, complemented
11#19133372C211yesmaximal, characteristic
12#19133040C211yesmaximal, characteristic
13#19133014C211yesmaximal, characteristic
14#19132893C211yesmaximal, characteristic
15C43×#1587C211yesmaximal, characteristic, complemented
16#14583453C2211yescharacteristic
17C4×Q8×D43C2211yescharacteristic
18#14583236C411yescharacteristic
19#14583233C411yescharacteristic
20#14583193C411yescharacteristic
21#14583192C411yescharacteristic
22#14583108C411yescharacteristic
23#14583107C411yescharacteristic
24#14583056C411yescharacteristic
25#14583053C411yescharacteristic
26#14583030C2211yescharacteristic
27#14583030C2211yescharacteristic
28#14583029—21no—
29#14583029C2211yescharacteristic
30#14583028—21no—
31#14583028—21no—
32#14583027—21no—
33#14583026C2211yescharacteristic
34#14583026C2211yescharacteristic
35C8×Dic86C2211yescharacteristic
36C4×Dic172C2211yescharacteristic
37C4×#10621885C2211yescharacteristic
38C4×#10621885C2211yescharacteristic
39#14582959—21no—
40#14582958—21no—
41#14582955—21no—
42#14582955C2211yescharacteristic
43#14582954—21no—
44#14582951C2211yescharacteristic
45#14582950C2211yescharacteristic
46#14582950C2211yescharacteristic
47C4×#10621872C2211yescharacteristic
48#14582651C2211yescharacteristic
49#14582651C2211yescharacteristic
50#14582650C2211yescharacteristic
51#14582631C2211yescharacteristic
52#14582631C2211yescharacteristic
53Q8⋊(C43⋊C8)C2211yescharacteristic
54Q8⋊(C43⋊C8)C2211yescharacteristic
55#14582629C2211yescharacteristic
56#14582629C2211yescharacteristic
57#14582620C2211yescharacteristic
58#14582620C2211yescharacteristic
59C8×C43⋊C8C2211yescharacteristic
60C43×#446C2211yescharacteristic
61C8×Q8×C43C2211yescharacteristic
62C4×Q16×C43C2211yescharacteristic
63C43×#334C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×Q8⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C2×Q8×D43C2×C411yescharacteristic
68C2×Dic172C2×C411yescharacteristic
69C2×#10621885C2×C411yescharacteristic
70C2×#10621885C2×C411yescharacteristic
71C2×#10621872—21no—
72#13063324C2×C411yescharacteristic
73#13063323C2×C411yescharacteristic
74#13063315—21no—
75#13063305C2×C411yescharacteristic
76#13063303—21no—
77#13063301C2×C411yescharacteristic
78Q8×Dic43C2×C411yescharacteristic
79C4×Dic86—21no—
80C4×Dic86—21no—
81C4×Dic86C2311yescharacteristic
82C4×Dic86C2311yescharacteristic
83#13063290—21no—
84#13063290C2×C411yescharacteristic
85#13063282—21no—
86C4⋊C4×D43—21no—
87C4⋊C4×D43C2×C411yescharacteristic
88C42×D43—21no—
89C42×D43C2311yescharacteristic
90#13063259C2×C411yescharacteristic
91#13063258C2×C411yescharacteristic
92#13063258C2×C411yescharacteristic
93C4⋊(C43⋊C8)—21no—
94C4⋊(C43⋊C8)—21no—
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97Dic43⋊C8—21no—
98Dic43⋊C8—21no—
99Dic43⋊C8—21no—
100Dic43⋊C8—21no—
101Dic43⋊C8C2×C411yescharacteristic
102Dic43⋊C8C2×C411yescharacteristic
103Dic43⋊C8D411yescharacteristic
104Dic43⋊C8D411yescharacteristic
105#13063250C2×C411yescharacteristic
106#13063250C2×C411yescharacteristic
107#13063249C2×C411yescharacteristic
108#13063249C2×C411yescharacteristic
109#13063248C2×C411yescharacteristic
110#13063248C2×C411yescharacteristic
111(C2×D43)⋊C8—21no—
112(C2×D43)⋊C8—21no—
113(C2×D43)⋊C8C2×C411yescharacteristic
114(C2×D43)⋊C8C2×C411yescharacteristic
115(C2×D43)⋊C8D411yescharacteristic
116(C2×D43)⋊C8D411yescharacteristic
117#13063236—21no—
118#13063236—21no—
119#13063235—21no—
120#13063235—21no—
121#13063235—21no—
122#13063235—21no—
123#13063235—21no—
124C4×C43⋊C8C2311yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
126C4×C43⋊C8C2311yescharacteristic
127C8×Dic43—21no—
128C8×Dic43—21no—
129C2×Q16×C43C2×C411yescharacteristic
130C4×Q8×C43C2311yescharacteristic
131C4×Q8×C43C2311yescharacteristic
132#107×C43C2×C411yescharacteristic
133C4⋊C8×C43—21no—
134C4⋊C8×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137#103×C43C2×C411yescharacteristic
138#103×C43C2×C411yescharacteristic
139#97×C43—21no—
140C4×C8×C43—21no—
141C4×C8×C43C2311yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43C22×C411yescharacteristic
145C2×Q8×C43C22×C411yescharacteristic
146Q8×D43—41no—
147Q8×D43—41no—
148C2×C4×D43—21no—
149C2×C4×D43—21no—
150C2×C4×D43C22×C411yescharacteristic
151C2×C4×D43C2×D411yescharacteristic
152C2×C4×D43#4111yescharacteristic
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86C22×C411yescharacteristic
156C2×Dic86C22×C411yescharacteristic
157Q16×C43—41no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43C22×C411yescharacteristic
162C2×C8×C43C22×C411yescharacteristic
163C2×C8×C43C2×D411yescharacteristic
164C2×C8×C43C2×D411yescharacteristic
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43C22×C411yescharacteristic
168C4⋊C4×C43C22×C411yescharacteristic
169C42×C43—21no—
170C42×C43—21no—
171C42×C43C2411yescharacteristic
172#10621885—41no—
173#10621885—41no—
174(C2×D43)⋊C4—21no—
175(C2×D43)⋊C4—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43C22×C411yescharacteristic
179C4⋊Dic43C22×C411yescharacteristic
180Dic43⋊C4—21no—
181Dic43⋊C4—21no—
182Dic43⋊C4—21no—
183Dic43⋊C4—21no—
184Dic43⋊C4—21no—
185Dic43⋊C4—21no—
186Dic43⋊C4—21no—
187Dic43⋊C4—21no—
188C4×Dic43—21no—
189C4×Dic43—21no—
190C4×Dic43—21no—
191C4×Dic43—21no—
192C4×Dic43C22×C411yescharacteristic
193C4×Dic43C2×D411yescharacteristic
194C4×Dic43#4111yescharacteristic
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8C22×C411yescharacteristic
199C2×C43⋊C8C22×C411yescharacteristic
200C2×C43⋊C8C2×D411yescharacteristic
201C2×C43⋊C8C2×D411yescharacteristic
202Dic172—41no—
203#10621872—42no—
204C22×D43C4×D411yescharacteristic
205Q8×C43—21no—
206Q8×C43—21no—
207Q8×C43—21no—
208Q8×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43C23×C411yescharacteristic
214C2×C4×C43C22×D411yescharacteristic
215C2×C4×C43C2×#4111yescharacteristic
216C2×Dic43—21no—
217C2×Dic43—21no—
218C2×Dic43—21no—
219C2×Dic43—21no—
220C2×Dic43C4×D411yescharacteristic
221C2×Dic43C4×D411yescharacteristic
222C2×Dic43C4×D411yescharacteristic
223C4×D43—21no—
224C4×D43—21no—
225C4×D43—21no—
226C4×D43—21no—
227C4×D43—41no—
228C4×D43—42no—
229C4×D43—81no—
230Dic86—21no—
231Dic86—21no—
232Dic86—21no—
233Dic86—21no—
234Dic86—42no—
235Dic86—81no—
236C8×C43—22no—
237C8×C43—21no—
238C8×C43—21no—
239C8×C43—21no—
240C8×C43—21no—
241C8×C43—41no—
242C8×C43—41no—
243C43⋊C8—21no—
244C43⋊C8—21no—
245C43⋊C8—21no—
246C43⋊C8—21no—
247C43⋊C8—41no—
248C43⋊C8—41no—
249C43⋊C8—41no—
250#17953—431nomaximal, Sylow
251C22×C43C2×C4×D411yescharacteristic
252C2×D43—21no—
253C2×D43—21no—
254C2×D43—21no—
255C4×C43—21no—
256C4×C43—41no—
257C4×C43—41no—
258C4×C43—41no—
259C4×C43—41no—
260C4×C43#56811yescharacteristic
261C4×C43#56811yescharacteristic
262C4×C43#57811yescharacteristic
263C4×C43#57811yescharacteristic
264Dic43—21no—
265Dic43—21no—
266Dic43—21no—
267Dic43—41no—
268Dic43—41no—
269Dic43—41no—
270Dic43—41no—
271#3104—431no—
272#2985—431no—
273#2983—431no—
274#1593—431no—
275#1593—431no—
276#1591—431no—
277#1591—431no—
278#1587—431no—
279#1587D4311yescharacteristic, complemented
280#1584—431no—
281#1584—431no—
282#1572—431no—
283#1491—431no—
284#1485—431no—
285#1453—431no—
286C2×C43#293011yescharacteristic
287C2×C43#295011yescharacteristic
288C2×C43#295611yescharacteristic
289D43—41no—
290#533—431no—
291C2×C4×Q8—431no—
292#484—431no—
293#484—431no—
294#477—431no—
295#477—431no—
296#462—431no—
297#462—431no—
298#451—431no—
299#451—431no—
300#446—431no—
301#446—431no—
302#446—431no—
303#446—431no—
304#446—431no—
305#446—861no—
306#446—861no—
307#446—861no—
308#446—861no—
309#446C2×D4311yescharacteristic
310C8×Q8—431no—
311C8×Q8C2×D4311yescharacteristic
312C4×Q16—431no—
313C4×Q16—431no—
314C4×Q16—431no—
315C4×Q16C2×D4311yescharacteristic
316#433—861no—
317#433—861no—
318#432—431no—
319#432—861no—
320#432—861no—
321#431—431no—
322#431—431no—
323#431—431no—
324C4×M16—431no—
325#335—431no—
326#335—431no—
327#334—431no—
328#334C2×D4311yescharacteristic
329Q8⋊C8—431no—
330Q8⋊C8—431no—
331Q8⋊C8—431no—
332Q8⋊C8—431no—
333Q8⋊C8—431no—
334Q8⋊C8—431no—
335Q8⋊C8C2×D4311yescharacteristic
336Q8⋊C8C2×D4311yescharacteristic
337#322—431no—
338#322—431no—
339#322C2×D4311yescharacteristic
340C82—431no—
341C43#1795311yescharacteristic, complemented, Sylow
342C22×Q8—431no—
343C2×Q16—431no—
344C2×Q16—431no—
345C2×Q16—431no—
346C2×Q16C4×D4311yescharacteristic
347C2×M16—861no—
348C4⋊Q8—431no—
349C4⋊Q8—431no—
350#125—861no—
351C22⋊Q8—431no—
352C22⋊Q8—431no—
353C22⋊Q8—861no—
354C4×Q8—431no—
355C4×Q8—431no—
356C4×Q8—431no—
357C4×Q8—431no—
358C4×Q8—861no—
359C4×Q8—861no—
360C4×Q8—861no—
361C4×Q8C22×D4311yescharacteristic
362C4×Q8C22×D4311yescharacteristic
363#117—861no—
364C2×C4⋊C4—431no—
365C2×C4⋊C4—861no—
366C2×C42—431no—
367C2×C42—861no—
368#107—431no—
369#107—431no—
370#107—431no—
371#107C4×D4311yescharacteristic
372C4⋊C8—21no—
373C4⋊C8—21no—
374C4⋊C8—431no—
375C4⋊C8—431no—
376C4⋊C8—431no—
377C4⋊C8—431no—
378C4⋊C8—431no—
379C4⋊C8—431no—
380C4⋊C8—861no—
381C4⋊C8—861no—
382C4⋊C8—861no—
383C4⋊C8—861no—
384C4⋊C8—861no—
385C4⋊C8—861no—
386C4⋊C8C22×D4311yescharacteristic
387C4⋊C8C22×D4311yescharacteristic
388#103—431no—
389#103—431no—
390#103—431no—
391#103—431no—
392#103—431no—
393#103—431no—
394#103C4×D4311yescharacteristic
395#103C4×D4311yescharacteristic
396C22⋊C8—431no—
397C22⋊C8—431no—
398C22⋊C8—431no—
399C22⋊C8—431no—
400C22⋊C8—861no—
401C22⋊C8—861no—
402#97—21no—
403#97—861no—
404#97—861no—
405#97—861no—
406#97—861no—
407#97—861no—
408#97—861no—
409#97—861no—
410C4×C8—21no—
411C4×C8—431no—
412C4×C8—431no—
413C4×C8—431no—
414C4×C8—861no—
415C4×C8—861no—
416C4×C8C22×D4311yescharacteristic
417C4×C8C22×D4311yescharacteristic
418C4×C8C22×D4311yescharacteristic
419C2×Q8—431no—
420C2×Q8—431no—
421C2×Q8—861no—
422C2×Q8—861no—
423C2×Q8—1721no—
424C2×Q8—1721no—
425C2×Q8C2×C4×D4311yescharacteristic
426C2×Q8C2×C4×D4311yescharacteristic
427C22×C4—431no—
428C22×C4—431no—
429C22×C4—431no—
430C22×C4—861no—
431C22×C4—861no—
432Q16—41no—
433Q16—1721no—
434Q16—1721no—
435Q16—1721no—
436M16—1722no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—431no—
441C2×C8—431no—
442C2×C8—431no—
443C2×C8—431no—
444C2×C8—861no—
445C2×C8—861no—
446C2×C8—861no—
447C2×C8C2×C4×D4311yescharacteristic
448C2×C8C2×C4×D4311yescharacteristic
449C2×C8D4×D4311yescharacteristic
450C2×C8D4×D4311yescharacteristic
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—431no—
454C4⋊C4—431no—
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—
465C4⋊C4C2×C4×D4311yescharacteristic
466C4⋊C4C2×C4×D4311yescharacteristic
467C22⋊C4—861no—
468C22⋊C4—861no—
469C42—21no—
470C42—21no—
471C42—431no—
472C42—431no—
473C42—431no—
474C42—861no—
475C42—861no—
476C42—861no—
477C42—861no—
478C42C23×D4311yescharacteristic
479C23—431no—
480Q8—21no—
481Q8—21no—
482Q8—21no—
483Q8—21no—
484Q8—861no—
485Q8—861no—
486Q8—861no—
487Q8—861no—
488Q8—3441no—
489Q8—1722no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—431no—
495C2×C4—431no—
496C2×C4—431no—
497C2×C4—861no—
498C2×C4—861no—
499C2×C4—861no—
500C2×C4—861no—
501C2×C4—861no—
502C2×C4—861no—
503C2×C4—861no—
504C2×C4—861no—
505C2×C4—3441no—
506C2×C4—1721no—
507C2×C4—1722no—
508C2×C4C22×C4×D4311yescharacteristic
509C2×C4C2×D4×D4311yescharacteristic
510C2×C4#41×D4311yescharacteristic
511C8—22no—
512C8—21no—
513C8—21no—
514C8—21no—
515C8—21no—
516C8—41no—
517C8—41no—
518C8—861no—
519C8—861no—
520C8—861no—
521C8—861no—
522C8—1721no—
523C8—1721no—
524C8—1721no—
525C22—861no—
526C22—861no—
527C22—861no—
528C22C4×D4×D4311yescharacteristic
529C4—21no—
530C4—41no—
531C4—41no—
532C4—41no—
533C4—41no—
534C4—861no—
535C4—861no—
536C4—861no—
537C4—1721no—
538C4—1721no—
539C4—1721no—
540C4—1721no—
541C4#1458366411yescharacteristic
542C4#1458366511yescharacteristic
543C4#1458371511yescharacteristic
544C4#1458371511yescharacteristic
545C2—1721no—
546C2#1914329311yescharacteristic
547C2#1914346011yescharacteristic
548C2#1914350011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1587C2
socleC22×C43C2×C4×D4
prime radicalC22×D43C4×D4
cosocleC42×C43C24
hypercenter#1587D43
hypocenterC43#17953
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1587

Complements

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

NH ≅ G/Ntype
4. #19133504C2semidirect
5. #19133503C2semidirect
6. #19133489C2semidirect
7. #19133489C2semidirect
8. #19133468C2semidirect
9. #19133445C2semidirect
10. #19133443C2semidirect
15. C43×#1587C2semidirect
279. #1587D43semidirect
341. C43#17953semidirect

Maximal subgroups

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

subgroupindex
#191446322
#191436862
#191436772
#191335042
#191335032
#191334892
#191334682
#191334452
#191334432
#191333722
#191330402
#191330142
#191328932
C43×#15872
#1795343