Finite Group Databasebeta

← #25067526

Subgroups — #25067526

Order 11008.

602 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144632C211yesmaximal, characteristic
2Q8×#10621872C211yesmaximal, characteristic
3#19143537C211yesmaximal, characteristic
4#19133493C211yesmaximal, characteristic, complemented
5#19133489C211yesmaximal, characteristic, complemented
6#19133446C211yesmaximal, characteristic, complemented
7#19133445C211yesmaximal, characteristic, complemented
8#19133445C211yesmaximal, characteristic, complemented
9#19133444C211yesmaximal, characteristic, complemented
10#19133399C211yesmaximal, characteristic, complemented
11#19133368C211yesmaximal, characteristic
12#19133048C211yesmaximal, characteristic
13Q8⋊C8×D43C211yesmaximal, characteristic
14C8×#10621872C211yesmaximal, characteristic
15C8×Q16×C43C211yesmaximal, 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#14583029—21no—
28#14583029—21no—
29#14583029C2211yescharacteristic
30#14583029C2211yescharacteristic
31#14583028—21no—
32#14583026—21no—
33#14583026C2211yescharacteristic
34Q8×C43⋊C8C2211yescharacteristic
35#14583023C2211yescharacteristic
36C4×Dic172C2211yescharacteristic
37C4×#10621885C2211yescharacteristic
38C4×#10621885C2211yescharacteristic
39#14582950C2211yescharacteristic
40#14582924—21no—
41#14582921—21no—
42#14582921C2211yescharacteristic
43C4⋊C8×D43C2211yescharacteristic
44#14582853—21no—
45C4×#10621872—21no—
46C4×#10621872C2211yescharacteristic
47C4×C8×D43C2211yescharacteristic
48#14582652C2211yescharacteristic
49#14582651C2211yescharacteristic
50#14582651C2211yescharacteristic
51#14582631C2211yescharacteristic
52#14582631C2211yescharacteristic
53Q8⋊(C43⋊C8)C2211yescharacteristic
54Q8⋊(C43⋊C8)C2211yescharacteristic
55#14582629C2211yescharacteristic
56#14582629C2211yescharacteristic
57#14582621C2211yescharacteristic
58#14582620C2211yescharacteristic
59C8×C43⋊C8C2211yescharacteristic
60C8×Q8×C43C2211yescharacteristic
61C8×Q8×C43C2211yescharacteristic
62C4×Q16×C43C2211yescharacteristic
63C43×#335C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×Q8⋊C8C2211yescharacteristic
66C82×C43C2211yescharacteristic
67C2×Q8×D43C2×C411yescharacteristic
68C2×Dic172C2×C411yescharacteristic
69C2×#10621885C2×C411yescharacteristic
70C2×#10621885C2×C411yescharacteristic
71C2×#10621872—21no—
72C2×#10621872D411yescharacteristic
73C2×#10621872D411yescharacteristic
74C2×C8×D43—21no—
75C2×C8×D43—21no—
76#13063324C2×C411yescharacteristic
77#13063323C2×C411yescharacteristic
78#13063315—21no—
79#13063305C2×C411yescharacteristic
80#13063303—21no—
81#13063301C2×C411yescharacteristic
82Q8×Dic43C2×C411yescharacteristic
83C4×Dic86—21no—
84C4×Dic86—21no—
85C4×Dic86C2311yescharacteristic
86C4×Dic86C2311yescharacteristic
87#13063290—21no—
88#13063290C2×C411yescharacteristic
89#13063282—21no—
90C4⋊C4×D43—21no—
91C4⋊C4×D43C2×C411yescharacteristic
92C42×D43—21no—
93C42×D43C2311yescharacteristic
94#13063259C2×C411yescharacteristic
95#13063258C2×C411yescharacteristic
96#13063258C2×C411yescharacteristic
97C4⋊(C43⋊C8)—21no—
98C4⋊(C43⋊C8)—21no—
99C4⋊(C43⋊C8)C2311yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101Dic43⋊C8—21no—
102Dic43⋊C8—21no—
103Dic43⋊C8—21no—
104Dic43⋊C8—21no—
105Dic43⋊C8—21no—
106Dic43⋊C8—21no—
107Dic43⋊C8C2×C411yescharacteristic
108Dic43⋊C8C2×C411yescharacteristic
109#13063250C2×C411yescharacteristic
110#13063250C2×C411yescharacteristic
111#13063249C2×C411yescharacteristic
112#13063249C2×C411yescharacteristic
113#13063248C2×C411yescharacteristic
114#13063248C2×C411yescharacteristic
115(C2×D43)⋊C8C2×C411yescharacteristic
116(C2×D43)⋊C8C2×C411yescharacteristic
117#13063236—21no—
118#13063235—21no—
119#13063235—21no—
120#13063235—21no—
121#13063235D411yescharacteristic
122#13063235D411yescharacteristic
123C4×C43⋊C8—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
139C4×C8×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—22no—
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—22no—
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—22no—
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—22no—
204#10621872—42no—
205#10621872Q1614yescomplemented
206C8×D43—42no—
207C8×D43—42no—
208C22×D43C4×D411yescharacteristic
209Q8×C43—21no—
210Q8×C43—21no—
211Q8×C43—21no—
212Q8×C43#13112yes—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43C23×C411yescharacteristic
218C2×C4×C43C22×D411yescharacteristic
219C2×C4×C43C2×#4111yescharacteristic
220C2×Dic43—21no—
221C2×Dic43—21no—
222C2×Dic43—21no—
223C2×Dic43—21no—
224C2×Dic43C4×D411yescharacteristic
225C2×Dic43C4×D411yescharacteristic
226C2×Dic43C4×D411yescharacteristic
227C4×D43—21no—
228C4×D43—21no—
229C4×D43—41no—
230C4×D43—42no—
231C4×D43—81no—
232C4×D43C2×Q1612yes—
233C4×D43#13512yes—
234Dic86—21no—
235Dic86—21no—
236Dic86—21no—
237Dic86—21no—
238Dic86—42no—
239Dic86—81no—
240C8×C43—22no—
241C8×C43—21no—
242C8×C43—21no—
243C8×C43—21no—
244C8×C43—41no—
245C8×C43—41no—
246C8×C43C2×Q1612yes—
247C43⋊C8—21no—
248C43⋊C8—21no—
249C43⋊C8—21no—
250C43⋊C8—41no—
251C43⋊C8—41no—
252C43⋊C8—41no—
253C43⋊C8C2×Q1612yes—
254#17998—431nomaximal, Sylow
255C22×C43C2×C4×D411yescharacteristic
256C2×D43—21no—
257C2×D43—21no—
258C2×D43C4×Q1612yes—
259C4×C43—22no—
260C4×C43—21no—
261C4×C43—41no—
262C4×C43—41no—
263C4×C43—41no—
264C4×C43C2×#13111yescharacteristic
265C4×C43#56811yescharacteristic
266C4×C43C22×Q1611yescharacteristic
267C4×C43C2×#13511yescharacteristic
268Dic43—21no—
269Dic43—21no—
270Dic43—41no—
271Dic43—41no—
272Dic43—41no—
273Dic43—41no—
274Dic43C4×Q1612yes—
275#3104—431no—
276Q8×M16—431no—
277#2962—431no—
278#1591—431no—
279#1591—431no—
280#1584—431no—
281#1584—431no—
282#1584—431no—
283#1584—431no—
284C8×Q16—431no—
285C8×Q16D4311yescharacteristic, complemented
286#1571—431no—
287#1493—431no—
288C2×Q8⋊C8—431no—
289C8×M16—431no—
290C2×C43#293311yescharacteristic
291C2×C43C2×C4×Q1611yescharacteristic
292C2×C43#295611yescharacteristic
293D43—22no—
294#533—431no—
295C2×C4×Q8—431no—
296#484—431no—
297#484—431no—
298#477—431no—
299#477—431no—
300#462—431no—
301#462—431no—
302#451—431no—
303#451—431no—
304#446—431no—
305#446—431no—
306#446—431no—
307#446—431no—
308#446—861no—
309#446—861no—
310#446—861no—
311#446—861no—
312C8×Q8—431no—
313C8×Q8—431no—
314C8×Q8C2×D4311yescharacteristic
315C8×Q8C2×D4311yescharacteristic
316C4×Q16—431no—
317C4×Q16—431no—
318C4×Q16—431no—
319C4×Q16C2×D4311yescharacteristic
320#431—431no—
321#424—861no—
322#423—431no—
323#423—861no—
324C2×C4⋊C8—431no—
325#405—861no—
326C4×M16—431no—
327C4×M16—861no—
328C2×C4×C8—431no—
329#335—431no—
330#335—431no—
331#335—431no—
332#335C2×D4311yescharacteristic
333Q8⋊C8—431no—
334Q8⋊C8—431no—
335Q8⋊C8—431no—
336Q8⋊C8—431no—
337Q8⋊C8—431no—
338Q8⋊C8—431no—
339Q8⋊C8C2×D4311yescharacteristic
340Q8⋊C8C2×D4311yescharacteristic
341#322—431no—
342#322—431no—
343C82—431no—
344C82C2×D4311yescharacteristic
345C43#1799811yescharacteristic, complemented, Sylow
346C22×Q8—431no—
347C2×Q16—431no—
348C2×Q16—431no—
349C2×Q16—431no—
350C2×Q16C4×D4311yescharacteristic
351C2×M16—431no—
352C2×M16—431no—
353C2×M16—861no—
354C22×C8—861no—
355C22×C8—861no—
356C4⋊Q8—431no—
357C4⋊Q8—431no—
358#125—861no—
359C22⋊Q8—431no—
360C22⋊Q8—431no—
361C22⋊Q8—861no—
362C4×Q8—431no—
363C4×Q8—431no—
364C4×Q8—431no—
365C4×Q8—431no—
366C4×Q8—861no—
367C4×Q8—861no—
368C4×Q8—861no—
369C4×Q8C22×D4311yescharacteristic
370C4×Q8C22×D4311yescharacteristic
371#117—861no—
372C2×C4⋊C4—431no—
373C2×C4⋊C4—861no—
374C2×C42—431no—
375C2×C42—861no—
376#107—431no—
377#107—431no—
378#107—431no—
379#107C4×D4311yescharacteristic
380C4⋊C8—21no—
381C4⋊C8—21no—
382C4⋊C8—431no—
383C4⋊C8—431no—
384C4⋊C8—431no—
385C4⋊C8—431no—
386C4⋊C8—861no—
387C4⋊C8—861no—
388C4⋊C8—861no—
389C4⋊C8—861no—
390C4⋊C8—861no—
391C4⋊C8—861no—
392C4⋊C8—861no—
393C4⋊C8—861no—
394C4⋊C8C22×D4311yescharacteristic
395C4⋊C8C22×D4311yescharacteristic
396#103—431no—
397#103—431no—
398#103—431no—
399#103—431no—
400#103—431no—
401#103—431no—
402#103C4×D4311yescharacteristic
403#103C4×D4311yescharacteristic
404C22⋊C8—431no—
405C22⋊C8—431no—
406#97—431no—
407#97—431no—
408#97—861no—
409#97—861no—
410#97—861no—
411#97—861no—
412C4×C8—21no—
413C4×C8—21no—
414C4×C8—431no—
415C4×C8—431no—
416C4×C8—431no—
417C4×C8—861no—
418C4×C8—861no—
419C4×C8—861no—
420C4×C8C22×D4311yescharacteristic
421C4×C8C22×D4311yescharacteristic
422C4×C8C22×D4311yescharacteristic
423C2×Q8—431no—
424C2×Q8—431no—
425C2×Q8—861no—
426C2×Q8—861no—
427C2×Q8—862no—
428C2×Q8—1721no—
429C2×Q8C2×C4×D4311yescharacteristic
430C2×Q8C2×C4×D4311yescharacteristic
431C22×C4—431no—
432C22×C4—431no—
433C22×C4—431no—
434C22×C4—861no—
435C22×C4—861no—
436Q16—22no—
437Q16—862no—
438Q16—1721no—
439Q16—1721no—
440M16—434no—
441M16—862no—
442M16—1722no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—431no—
447C2×C8—431no—
448C2×C8—431no—
449C2×C8—431no—
450C2×C8—861no—
451C2×C8—861no—
452C2×C8—861no—
453C2×C8—1722no—
454C2×C8—1722no—
455C2×C8C2×C4×D4311yescharacteristic
456C2×C8C2×C4×D4311yescharacteristic
457C2×C8D4×D4311yescharacteristic
458C2×C8D4×D4311yescharacteristic
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—431no—
462C4⋊C4—431no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4C2×C4×D4311yescharacteristic
474C4⋊C4C2×C4×D4311yescharacteristic
475C22⋊C4—861no—
476C22⋊C4—861no—
477C42—21no—
478C42—21no—
479C42—431no—
480C42—431no—
481C42—431no—
482C42—861no—
483C42—861no—
484C42—861no—
485C42—861no—
486C42C23×D4311yescharacteristic
487C23—431no—
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—861no—
492Q8—861no—
493Q8—861no—
494Q8—861no—
495Q8—3441no—
496Q8—1722no—
497Q8#1306333112yes—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—431no—
503C2×C4—432no—
504C2×C4—432no—
505C2×C4—431no—
506C2×C4—431no—
507C2×C4—861no—
508C2×C4—861no—
509C2×C4—861no—
510C2×C4—861no—
511C2×C4—861no—
512C2×C4—861no—
513C2×C4—3441no—
514C2×C4—1721no—
515C2×C4—1722no—
516C2×C4C22×C4×D4311yescharacteristic
517C2×C4C2×D4×D4311yescharacteristic
518C2×C4#41×D4311yescharacteristic
519C8—22no—
520C8—21no—
521C8—21no—
522C8—21no—
523C8—41no—
524C8—41no—
525C8—432no—
526C8—861no—
527C8—861no—
528C8—861no—
529C8—1721no—
530C8—1721no—
531C8—1721no—
532C8Q16×D4312yes—
533C22—432no—
534C22—861no—
535C22—861no—
536C22C4×D4×D4311yescharacteristic
537C4—21no—
538C4—22no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—432no—
543C4—861no—
544C4—861no—
545C4—1721no—
546C4—1721no—
547C4—1721no—
548C4—1721no—
549C4C2×#1306333111yescharacteristic
550C4#1458366411yescharacteristic
551C4C2×Q16×D4311yescharacteristic
552C4#135×D4311yescharacteristic
553C2—862no—
554C2#1914331511yescharacteristic
555C2C4×Q16×D4311yescharacteristic
556C2#1914350011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC8×Q16×C43C2
socleC22×C43C2×C4×D4
prime radicalC22×D43C4×D4
cosocleC42×C43C24
hypercenterC8×Q16D43
hypocenterC43#17998
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×Q16

Complements

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

NH ≅ G/Ntype
4. #19133493C2semidirect
5. #19133489C2semidirect
6. #19133446C2semidirect
7. #19133445C2semidirect
8. #19133445C2semidirect
9. #19133444C2semidirect
10. #19133399C2semidirect
15. C8×Q16×C43C2semidirect
205. #10621872Q16semidirect
285. C8×Q16D43semidirect
345. C43#17998semidirect

Maximal subgroups

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

subgroupindex
#191446322
Q8×#106218722
#191435372
#191334932
#191334892
#191334462
#191334452
#191334442
#191333992
#191333682
#191330482
Q8⋊C8×D432
C8×#106218722
C8×Q16×C432
#1799843