Finite Group Databasebeta

← #25067784

Subgroups — #25067784

Order 11008.

600 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144675C211yesmaximal, characteristic
2#19143751C211yesmaximal, characteristic
3#19143684C211yesmaximal, characteristic, complemented
4#19133489C211yesmaximal, characteristic, complemented
5#19133482C211yesmaximal, characteristic, complemented
6#19133470C211yesmaximal, characteristic, complemented
7#19133469C211yesmaximal, characteristic, complemented
8#19133463C211yesmaximal, characteristic, complemented
9#19133455C211yesmaximal, characteristic, complemented
10#19133399C211yesmaximal, characteristic, complemented
11#19133392C211yesmaximal, characteristic, complemented
12#19133378C211yesmaximal, characteristic, complemented
13#19133056C211yesmaximal, characteristic
14#19132878C211yesmaximal, characteristic, complemented
15C2×C43×Q8⋊C8C211yesmaximal, characteristic, complemented
16#14583433C2211yescharacteristic
17#14583229C411yescharacteristic
18#14583212C411yescharacteristic
19#14583206C411yescharacteristic
20#14583206C411yescharacteristic
21#14583121C411yescharacteristic
22#14583121C411yescharacteristic
23#14583055C411yescharacteristic
24#14583038C411yescharacteristic
25#14583030—21no—
26#14583030—21no—
27#14583030C2211yescharacteristic
28#14583030C2211yescharacteristic
29#14583026C2211yescharacteristic
30Q8×C43⋊C8C2211yescharacteristic
31Q8×C43⋊C8C2211yescharacteristic
32#14583023C2211yescharacteristic
33C4×#10621885C2211yescharacteristic
34C4×#10621885C2211yescharacteristic
35C4×#10621884C2211yescharacteristic
36C4×#10621884C2211yescharacteristic
37#14582976C2211yescharacteristic
38#14582970—21no—
39#14582964C2211yescharacteristic
40C8×C22⋊D43—21no—
41#14582959—21no—
42#14582956—21no—
43#14582956C2211yescharacteristic
44#14582952—21no—
45#14582952C2211yescharacteristic
46#14582952C2211yescharacteristic
47#14582924—21no—
48#14582651C2211yescharacteristic
49#14582651C2211yescharacteristic
50#14582649C2211yescharacteristic
51#14582649C2211yescharacteristic
52#14582631C2211yescharacteristic
53#14582631C2211yescharacteristic
54#14582628C2211yescharacteristic
55#14582628C2211yescharacteristic
56#14582620C2211yescharacteristic
57#14582620C2211yescharacteristic
58C8×C43⋊C8C2211yescharacteristic
59C8×C43⋊C8C2211yescharacteristic
60C2×C4×Q8×C43C2211yescharacteristic
61C2×C4⋊C8×C43C2211yescharacteristic
62C2×C4×C8×C43C2211yescharacteristic
63C43×Q8⋊C8C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×Q8⋊C8C2211yescharacteristic
66C43×Q8⋊C8C2211yescharacteristic
67C2×#10621885C2×C411yescharacteristic
68C2×#10621885C2×C411yescharacteristic
69C2×#10621884C2×C411yescharacteristic
70C2×#10621884C2×C411yescharacteristic
71C2×#10621872—21no—
72C2×C8×D43—21no—
73#13063319—21no—
74#13063317C2×C411yescharacteristic
75#13063313C2×C411yescharacteristic
76#13063308—21no—
77#13063304C2×C411yescharacteristic
78#13063299C2×C411yescharacteristic
79C4×Dic86C2311yescharacteristic
80C4×D172C2311yescharacteristic
81C4×C22⋊D43—21no—
82#13063282—21no—
83#13063258C2×C411yescharacteristic
84#13063258C2×C411yescharacteristic
85#13063256C2×C411yescharacteristic
86#13063256C2×C411yescharacteristic
87C4⋊(C43⋊C8)—21no—
88C4⋊(C43⋊C8)—21no—
89C4⋊(C43⋊C8)—21no—
90C4⋊(C43⋊C8)—21no—
91C4⋊(C43⋊C8)C2×C411yescharacteristic
92C4⋊(C43⋊C8)C2×C411yescharacteristic
93C4⋊(C43⋊C8)D411yescharacteristic
94C4⋊(C43⋊C8)D411yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
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#13063245C2×C411yescharacteristic
106#13063245C2×C411yescharacteristic
107C22⋊(C43⋊C8)—21no—
108C22⋊(C43⋊C8)C2×C411yescharacteristic
109C22⋊(C43⋊C8)C2×C411yescharacteristic
110C22⋊(C43⋊C8)D411yescharacteristic
111C22⋊(C43⋊C8)D411yescharacteristic
112(C2×D43)⋊C8—21no—
113(C2×D43)⋊C8—21no—
114#13063236—21no—
115#13063236—21no—
116#13063236—21no—
117#13063235—21no—
118C4×C43⋊C8—21no—
119C4×C43⋊C8—21no—
120C4×C43⋊C8C2311yescharacteristic
121C4×C43⋊C8C2311yescharacteristic
122C4×C43⋊C8C2311yescharacteristic
123C4×C43⋊C8C2311yescharacteristic
124C8×Dic43—21no—
125C22×Q8×C43C2×C411yescharacteristic
126C22×C8×C43—21no—
127C22×C8×C43—21no—
128C4×Q8×C43—21no—
129C4×Q8×C43—21no—
130C4×Q8×C43C2×C411yescharacteristic
131C4×Q8×C43C2×C411yescharacteristic
132C4×Q8×C43C2311yescharacteristic
133C4×Q8×C43C2311yescharacteristic
134C2×C4⋊C4×C43—21no—
135C2×C4⋊C4×C43C2×C411yescharacteristic
136C2×C42×C43—21no—
137C2×C42×C43C2311yescharacteristic
138C4⋊C8×C43—21no—
139C4⋊C8×C43C2311yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—22no—
146C2×Q8×C43—41no—
147C2×Q8×C43C22×C411yescharacteristic
148C2×Q8×C43C22×C411yescharacteristic
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43C22×C411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43#4111yescharacteristic
154C2×C22⋊D43—21no—
155C2×D172C22×C411yescharacteristic
156C2×C4×D43—21no—
157C2×Dic86C22×C411yescharacteristic
158C2×C8×C43—24no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—81no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43C22×C411yescharacteristic
170C4⋊C4×C43C22×C411yescharacteristic
171C42×C43—21no—
172C42×C43—21no—
173C42×C43—21no—
174C42×C43—21no—
175C42×C43C22×C411yescharacteristic
176C42×C43C2×D411yescharacteristic
177C42×C43#4111yescharacteristic
178C42×C43C2411yescharacteristic
179C22⋊Dic43—21no—
180#10621885—22no—
181#10621885—41no—
182#10621884—22no—
183#10621884—41no—
184(C2×D43)⋊C4—21no—
185(C2×D43)⋊C4—21no—
186(C2×D43)⋊C4—21no—
187(C2×D43)⋊C4—21no—
188C4⋊Dic43C22×C411yescharacteristic
189C4⋊Dic43C22×C411yescharacteristic
190Dic43⋊C4—21no—
191Dic43⋊C4—21no—
192Dic43⋊C4—21no—
193Dic43⋊C4—21no—
194C4×Dic43—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8C22×C411yescharacteristic
198C2×C43⋊C8C22×C411yescharacteristic
199C2×C43⋊C8C22×C411yescharacteristic
200C2×C43⋊C8C22×C411yescharacteristic
201C2×C43⋊C8C2×D411yescharacteristic
202C2×C43⋊C8C2×D411yescharacteristic
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205#10621872—81no—
206C8×D43—81no—
207C23×C43C4×D411yescharacteristic
208C22×D43—21no—
209Q8×C43—21no—
210Q8×C43—21no—
211Q8×C43—21no—
212Q8×C43—42no—
213Q8×C43#13112yes—
214C2×C4×C43—21no—
215C2×C4×C43—22no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—42no—
224C2×C4×C43—42no—
225C2×C4×C43C4×D411yescharacteristic
226C2×C4×C43C4×D411yescharacteristic
227C2×C4×C43C4×D411yescharacteristic
228C2×C4×C43C23×C411yescharacteristic
229C2×C4×C43C22×D411yescharacteristic
230C2×C4×C43C2×#4111yescharacteristic
231C22⋊D43—42no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235D172—21no—
236D172—21no—
237C4×D43—41no—
238C4×D43—41no—
239Dic86—21no—
240Dic86—21no—
241C8×C43—22no—
242C8×C43—22no—
243C8×C43—41no—
244C8×C43—41no—
245C43⋊C8—21no—
246C43⋊C8—21no—
247C43⋊C8—21no—
248C43⋊C8—21no—
249C43⋊C8—21no—
250C43⋊C8—21no—
251C43⋊C8—21no—
252C43⋊C8—21no—
253C43⋊C8—41no—
254C43⋊C8—41no—
255#18017—431nomaximal, Sylow
256C22×C43—21no—
257C22×C43—21no—
258C22×C43#44312yes—
259C22×C43C2×C4×D411yescharacteristic
260C2×D43—41no—
261C2×D43—41no—
262C2×D43—41no—
263C4×C43—21no—
264C4×C43—22no—
265C4×C43—21no—
266C4×C43—21no—
267C4×C43—21no—
268C4×C43—41no—
269C4×C43—41no—
270C4×C43—41no—
271C4×C43C2×#13111yescharacteristic
272C4×C43#56811yescharacteristic
273C4×C43#57711yescharacteristic
274C4×C43#57811yescharacteristic
275Dic43—41no—
276Dic43—41no—
277Dic43—41no—
278#3108—431no—
279#2994—431no—
280#2984—431no—
281#1591—431no—
282#1590—431no—
283#1588—431no—
284#1587—431no—
285#1587—431no—
286#1585—431no—
287C8×Q16—431no—
288C8×SD16—431no—
289#1573—431no—
290#1494—431no—
291C2×Q8⋊C8D4311yescharacteristic, complemented
292#1450—431no—
293C2×C43—22no—
294C2×C43#293311yescharacteristic
295C2×C43#294711yescharacteristic
296C2×C43C2×#44311yescharacteristic
297D43—81no—
298#529—431no—
299C2×C4×Q8C2×D4311yescharacteristic
300#483—431no—
301#480—431no—
302#479—431no—
303#479—431no—
304#464—431no—
305#464—431no—
306#451—431no—
307#448—431no—
308#446—431no—
309#446—431no—
310#446—431no—
311#446—861no—
312#446—861no—
313C8×Q8—431no—
314C8×Q8—431no—
315C8×Q8—431no—
316C4×Q16—431no—
317C4×Q16—431no—
318C4×SD16—431no—
319C4×SD16—431no—
320#436—431no—
321#435—861no—
322C8×D4—431no—
323C8×D4—861no—
324#433—861no—
325#432—431no—
326#432—861no—
327#431—431no—
328#431—431no—
329#431—861no—
330#424—861no—
331C2×C4⋊C8C2×D4311yescharacteristic
332C2×C4×C8C2×D4311yescharacteristic
333#335—431no—
334#335—431no—
335#334—431no—
336#334—431no—
337Q8⋊C8—431no—
338Q8⋊C8—431no—
339Q8⋊C8C2×D4311yescharacteristic
340Q8⋊C8C2×D4311yescharacteristic
341Q8⋊C8C2×D4311yescharacteristic
342Q8⋊C8C2×D4311yescharacteristic
343D4⋊C8—431no—
344D4⋊C8—431no—
345#322—431no—
346#322—431no—
347C82—431no—
348C82—431no—
349C43#1801711yescharacteristic, complemented, Sylow
350C22×Q8C4×D4311yescharacteristic
351C2×Q16—431no—
352C2×Q16—431no—
353C2×SD16—431no—
354C2×SD16—431no—
355C2×M16—861no—
356C22×C8—21no—
357C22×C8—21no—
358C22×C8—861no—
359#126—861no—
360#125—431no—
361#124—431no—
362#123—861no—
363C22⋊Q8—431no—
364#121—431no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—431no—
368C4×Q8C4×D4311yescharacteristic
369C4×Q8C4×D4311yescharacteristic
370C4×Q8C22×D4311yescharacteristic
371C4×Q8C22×D4311yescharacteristic
372C4×D4—431no—
373C4×D4—861no—
374#117—861no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4C4×D4311yescharacteristic
377C2×C42—21no—
378C2×C42C22×D4311yescharacteristic
379#107—431no—
380#107—431no—
381#106—431no—
382#106—431no—
383C4⋊C8—21no—
384C4⋊C8—431no—
385C4⋊C8—431no—
386C4⋊C8—431no—
387C4⋊C8—431no—
388C4⋊C8—431no—
389C4⋊C8—431no—
390C4⋊C8—861no—
391C4⋊C8—861no—
392C4⋊C8—861no—
393C4⋊C8—861no—
394C4⋊C8—861no—
395C4⋊C8—861no—
396C4⋊C8C22×D4311yescharacteristic
397C4⋊C8C22×D4311yescharacteristic
398#103—431no—
399#103—431no—
400#103—431no—
401#103—431no—
402#103—431no—
403#103—431no—
404#102—431no—
405#102—431no—
406C22⋊C8—431no—
407C22⋊C8—431no—
408C22⋊C8—431no—
409C22⋊C8—431no—
410C22⋊C8—861no—
411C22⋊C8—861no—
412C22⋊C8—861no—
413#97—861no—
414#97—861no—
415#97—861no—
416#97—861no—
417C4×C8—21no—
418C4×C8—431no—
419C4×C8—431no—
420C4×C8—431no—
421C4×C8—431no—
422C4×C8—861no—
423C4×C8—861no—
424C4×C8—861no—
425C4×C8C22×D4311yescharacteristic
426C4×C8C22×D4311yescharacteristic
427C2×Q8—21no—
428C2×Q8—22no—
429C2×Q8—41no—
430C2×Q8—431no—
431C2×Q8C2×C4×D4311yescharacteristic
432C2×Q8C2×C4×D4311yescharacteristic
433C2×D4—431no—
434C2×D4—861no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—861no—
438C22×C4C2×C4×D4311yescharacteristic
439C22×C4D4×D4311yescharacteristic
440C22×C4#1062190011yescharacteristic
441Q16—862no—
442Q16—1721no—
443SD16—862no—
444SD16—1721no—
445M16—3441no—
446C2×C8—24no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—81no—
452C2×C8—431no—
453C2×C8—431no—
454C2×C8—431no—
455C2×C8—431no—
456C2×C8—431no—
457C2×C8—431no—
458C2×C8—431no—
459C2×C8—431no—
460C2×C8—861no—
461C2×C8—861no—
462C2×C8—3441no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—431no—
469C4⋊C4—431no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4C2×C4×D4311yescharacteristic
475C4⋊C4C2×C4×D4311yescharacteristic
476C22⋊C4—861no—
477C22⋊C4—861no—
478C22⋊C4—861no—
479C22⋊C4—861no—
480C22⋊C4—861no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—861no—
486C42C2×C4×D4311yescharacteristic
487C42D4×D4311yescharacteristic
488C42#1062190011yescharacteristic
489C42C23×D4311yescharacteristic
490C23—861no—
491C23(C22⋊D43)⋊C411yescharacteristic
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—42no—
496Q8—861no—
497Q8—861no—
498Q8#1306333112yes—
499D4—861no—
500D4—861no—
501D4—1722no—
502C2×C4—21no—
503C2×C4—22no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—861no—
514C2×C4—861no—
515C2×C4—861no—
516C2×C4—1721no—
517C2×C4—1721no—
518C2×C4(C22⋊D43)⋊C411yescharacteristic
519C2×C4(C22⋊D43)⋊C411yescharacteristic
520C2×C4(C22⋊D43)⋊C411yescharacteristic
521C2×C4C22×C4×D4311yescharacteristic
522C2×C4C2×D4×D4311yescharacteristic
523C2×C4C2×#1062190011yescharacteristic
524C8—22no—
525C8—22no—
526C8—41no—
527C8—41no—
528C8—861no—
529C8—861no—
530C8—861no—
531C8—861no—
532C8—861no—
533C8—861no—
534C8—861no—
535C8—861no—
536C8—1721no—
537C8—1721no—
538C22—21no—
539C22—21no—
540C22—1721no—
541C22—1721no—
542C22—1721no—
543C22#1458301312yes—
544C22C2×(C22⋊D43)⋊C411yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—22no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—1721no—
554C4—1721no—
555C4—1721no—
556C4C2×#1306333111yescharacteristic
557C4#1458366511yescharacteristic
558C4#1458370511yescharacteristic
559C4#1458371211yescharacteristic
560C2—22no—
561C2—3441no—
562C2#1914331611yescharacteristic
563C2#1914343211yescharacteristic
564C2C2×#1458301311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC2×C43×Q8⋊C8C2
socleC22×C43C2×C4×D4
prime radical#13063299C2×C4
cosocleC42×C43C24
hypercenterC2×Q8⋊C8D43
hypocenterC43#18017
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
3. #19143684C2semidirect
4. #19133489C2semidirect
5. #19133482C2semidirect
6. #19133470C2semidirect
7. #19133469C2semidirect
8. #19133463C2semidirect
9. #19133455C2semidirect
10. #19133399C2semidirect
11. #19133392C2semidirect
12. #19133378C2semidirect
14. #19132878C2semidirect
15. C2×C43×Q8⋊C8C2semidirect
291. C2×Q8⋊C8D43semidirect
349. C43#18017semidirect

Maximal subgroups

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

subgroupindex
#191446752
#191437512
#191436842
#191334892
#191334822
#191334702
#191334692
#191334632
#191334552
#191333992
#191333922
#191333782
#191330562
#191328782
C2×C43×Q8⋊C82
#1801743