Finite Group Databasebeta

← #25067717

Subgroups — #25067717

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#19144675C211yesmaximal, characteristic
2#19143593C211yesmaximal, characteristic
3Q8×#10621877C211yesmaximal, characteristic, complemented
4#19133501C211yesmaximal, characteristic, complemented
5#19133482C211yesmaximal, characteristic, complemented
6#19133463C211yesmaximal, characteristic, complemented
7#19133455C211yesmaximal, characteristic, complemented
8#19133448C211yesmaximal, characteristic, complemented
9#19133435C211yesmaximal, characteristic, complemented
10#19133410C211yesmaximal, characteristic, complemented
11#19133399C211yesmaximal, characteristic, complemented
12#19133383C211yesmaximal, characteristic, complemented
13#19133061C211yesmaximal, characteristic
14#19132890C211yesmaximal, characteristic, complemented
15C43×#1479C211yesmaximal, 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#14582974—21no—
39#14582973—21no—
40#14582964C2211yescharacteristic
41#14582958—21no—
42#14582952C2211yescharacteristic
43#14582923—21no—
44#14582923C2211yescharacteristic
45#14582853—21no—
46C4×#10621877—21no—
47C4×#10621877C2211yescharacteristic
48#14582651C2211yescharacteristic
49#14582651C2211yescharacteristic
50#14582649C2211yescharacteristic
51#14582649C2211yescharacteristic
52#14582631C2211yescharacteristic
53#14582631C2211yescharacteristic
54#14582628C2211yescharacteristic
55#14582628C2211yescharacteristic
56#14582621C2211yescharacteristic
57#14582621C2211yescharacteristic
58#14582620C2211yescharacteristic
59C8×C43⋊C8C2211yescharacteristic
60C2×C4×Q8×C43C2211yescharacteristic
61C43×#431C2211yescharacteristic
62C43×#431C2211yescharacteristic
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×#10621877—21no—
72C2×#10621877D411yescharacteristic
73C2×#10621877D411yescharacteristic
74C2×#10621872—21no—
75C2×C8×D43—21no—
76#13063319—21no—
77#13063317C2×C411yescharacteristic
78#13063313C2×C411yescharacteristic
79#13063308—21no—
80#13063304C2×C411yescharacteristic
81#13063299C2×C411yescharacteristic
82C4×Dic86C2311yescharacteristic
83C4×D172C2311yescharacteristic
84C4×C22⋊D43—21no—
85#13063282—21no—
86#13063258C2×C411yescharacteristic
87#13063258C2×C411yescharacteristic
88#13063256C2×C411yescharacteristic
89#13063256C2×C411yescharacteristic
90C4⋊(C43⋊C8)—21no—
91C4⋊(C43⋊C8)—21no—
92C4⋊(C43⋊C8)—21no—
93C4⋊(C43⋊C8)—21no—
94C4⋊(C43⋊C8)—21no—
95C4⋊(C43⋊C8)C2×C411yescharacteristic
96C4⋊(C43⋊C8)C2×C411yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99Dic43⋊C8—21no—
100Dic43⋊C8—21no—
101#13063249C2×C411yescharacteristic
102#13063249C2×C411yescharacteristic
103#13063249C2×C411yescharacteristic
104#13063249C2×C411yescharacteristic
105#13063248C2×C411yescharacteristic
106#13063248C2×C411yescharacteristic
107#13063245C2×C411yescharacteristic
108#13063245C2×C411yescharacteristic
109C22⋊(C43⋊C8)C2×C411yescharacteristic
110C22⋊(C43⋊C8)C2×C411yescharacteristic
111(C2×D43)⋊C8—21no—
112(C2×D43)⋊C8—21no—
113#13063236—21no—
114#13063236—21no—
115#13063236D411yescharacteristic
116#13063236D411yescharacteristic
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
126C4×Q8×C43—21no—
127C4×Q8×C43—21no—
128C4×Q8×C43C2×C411yescharacteristic
129C4×Q8×C43C2×C411yescharacteristic
130C4×Q8×C43C2311yescharacteristic
131C4×Q8×C43C2311yescharacteristic
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43C2×C411yescharacteristic
134C2×C42×C43—21no—
135C2×C42×C43C2311yescharacteristic
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139C22⋊C8×C43—21no—
140C22⋊C8×C43—21no—
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—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43C22×C411yescharacteristic
168C4⋊C4×C43C22×C411yescharacteristic
169C42×C43—21no—
170C42×C43—21no—
171C42×C43—21no—
172C42×C43—21no—
173C42×C43C22×C411yescharacteristic
174C42×C43C2×D411yescharacteristic
175C42×C43#4111yescharacteristic
176C42×C43C2411yescharacteristic
177C22⋊Dic43—21no—
178#10621885—22no—
179#10621885—41no—
180#10621884—22no—
181#10621884—41no—
182(C2×D43)⋊C4—21no—
183(C2×D43)⋊C4—21no—
184(C2×D43)⋊C4—21no—
185(C2×D43)⋊C4—21no—
186C4⋊Dic43C22×C411yescharacteristic
187C4⋊Dic43C22×C411yescharacteristic
188Dic43⋊C4—21no—
189Dic43⋊C4—21no—
190Dic43⋊C4—21no—
191Dic43⋊C4—21no—
192C4×Dic43—21no—
193#10621877—22no—
194#10621877—41no—
195#10621877—42no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8C22×C411yescharacteristic
199C2×C43⋊C8C22×C411yescharacteristic
200C2×C43⋊C8C22×C411yescharacteristic
201C2×C43⋊C8C22×C411yescharacteristic
202C2×C43⋊C8C2×D411yescharacteristic
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206#10621872—42no—
207C8×D43—42no—
208C23×C43C4×D411yescharacteristic
209C22×D43—21no—
210Q8×C43—21no—
211Q8×C43—21no—
212Q8×C43—21no—
213Q8×C43—42no—
214Q8×C43#13112yes—
215C2×C4×C43—21no—
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—41no—
224C2×C4×C43—42no—
225C2×C4×C43—81no—
226C2×C4×C43C4×D411yescharacteristic
227C2×C4×C43C4×D411yescharacteristic
228C2×C4×C43C4×D411yescharacteristic
229C2×C4×C43C23×C411yescharacteristic
230C2×C4×C43C22×D411yescharacteristic
231C2×C4×C43C2×#4111yescharacteristic
232C22⋊D43—81no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236D172—21no—
237D172—21no—
238C4×D43—41no—
239C4×D43—41no—
240Dic86—21no—
241Dic86—21no—
242C8×C43—41no—
243C8×C43—41no—
244C8×C43—41no—
245C8×C43—41no—
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—
255C43⋊C8#13712yes—
256#18012—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—22no—
266C4×C43—21no—
267C4×C43—21no—
268C4×C43—21no—
269C4×C43—41no—
270C4×C43—41no—
271C4×C43—41no—
272C4×C43C2×#13111yescharacteristic
273C4×C43#56811yescharacteristic
274C4×C43C2×#13711yescharacteristic
275C4×C43#57511yescharacteristic
276Dic43—41no—
277Dic43—41no—
278Dic43—41no—
279#3108—431no—
280#2969—431no—
281Q8×M16—431no—
282#1593—431no—
283#1590—431no—
284#1587—431no—
285#1585—431no—
286#1584—431no—
287#1583—431no—
288SD16⋊C8—431no—
289C8×Q16—431no—
290#1574—431no—
291#1495—431no—
292#1479D4311yescharacteristic, complemented
293#1453—431no—
294C2×C43—41no—
295C2×C43#293311yescharacteristic
296C2×C43C4×#13711yescharacteristic
297C2×C43#295711yescharacteristic
298D43—81no—
299#529—431no—
300C2×C4×Q8C2×D4311yescharacteristic
301#483—431no—
302#480—431no—
303#479—431no—
304#479—431no—
305#464—431no—
306#464—431no—
307#451—431no—
308#448—431no—
309#446—431no—
310#446—431no—
311#446—431no—
312#446—861no—
313#446—861no—
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—861no—
323#435—861no—
324C8×D4—431no—
325#433—861no—
326#431—431no—
327#431C2×D4311yescharacteristic
328#431C2×D4311yescharacteristic
329#423—431no—
330#423—861no—
331#405—861no—
332C4×M16—431no—
333C4×M16—861no—
334#335—431no—
335#335—431no—
336#334—431no—
337#334—431no—
338Q8⋊C8—431no—
339Q8⋊C8—431no—
340Q8⋊C8C2×D4311yescharacteristic
341Q8⋊C8C2×D4311yescharacteristic
342Q8⋊C8C2×D4311yescharacteristic
343Q8⋊C8C2×D4311yescharacteristic
344D4⋊C8—431no—
345D4⋊C8—431no—
346#322—431no—
347#322—431no—
348#322—431no—
349C82—431no—
350C43#1801211yescharacteristic, complemented, Sylow
351C22×Q8C4×D4311yescharacteristic
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—861no—
361#126—861no—
362#125—431no—
363#124—431no—
364#123—861no—
365C22⋊Q8—431no—
366#121—431no—
367C4×Q8—21no—
368C4×Q8—21no—
369C4×Q8—431no—
370C4×Q8C4×D4311yescharacteristic
371C4×Q8C4×D4311yescharacteristic
372C4×Q8C22×D4311yescharacteristic
373C4×Q8C22×D4311yescharacteristic
374C4×D4—431no—
375C4×D4—861no—
376#117—861no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4C4×D4311yescharacteristic
379C2×C42—21no—
380C2×C42C22×D4311yescharacteristic
381#107—431no—
382#107—431no—
383#106—431no—
384#106—431no—
385C4⋊C8—21no—
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⋊C8—861no—
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—21no—
409C22⋊C8—431no—
410C22⋊C8—431no—
411C22⋊C8—861no—
412C22⋊C8—861no—
413#97—431no—
414#97—431no—
415#97—861no—
416#97—861no—
417#97—861no—
418C4×C8—21no—
419C4×C8—431no—
420C4×C8—431no—
421C4×C8—431no—
422C4×C8—431no—
423C4×C8—861no—
424C4×C8—861no—
425C4×C8—861no—
426C4×C8C22×D4311yescharacteristic
427C4×C8C22×D4311yescharacteristic
428C2×Q8—21no—
429C2×Q8—22no—
430C2×Q8—41no—
431C2×Q8—431no—
432C2×Q8C2×C4×D4311yescharacteristic
433C2×Q8C2×C4×D4311yescharacteristic
434C2×D4—431no—
435C2×D4—861no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—861no—
439C22×C4C2×C4×D4311yescharacteristic
440C22×C4D4×D4311yescharacteristic
441C22×C4#1062190011yescharacteristic
442Q16—862no—
443Q16—1721no—
444SD16—862no—
445SD16—1721no—
446M16—862no—
447M16—1722no—
448M16—1721no—
449M16—1722no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—431no—
455C2×C8—431no—
456C2×C8—431no—
457C2×C8—431no—
458C2×C8—431no—
459C2×C8—431no—
460C2×C8—431no—
461C2×C8—431no—
462C2×C8—861no—
463C2×C8—861no—
464C2×C8—1722no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—431no—
471C4⋊C4—431no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4C2×C4×D4311yescharacteristic
477C4⋊C4C2×C4×D4311yescharacteristic
478C22⋊C4—861no—
479C22⋊C4—861no—
480C22⋊C4—861no—
481C22⋊C4—861no—
482C22⋊C4—861no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—861no—
488C42C2×C4×D4311yescharacteristic
489C42D4×D4311yescharacteristic
490C42#1062190011yescharacteristic
491C42C23×D4311yescharacteristic
492C23—861no—
493C23(C22⋊D43)⋊C411yescharacteristic
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—42no—
498Q8—861no—
499Q8—861no—
500Q8#1306333112yes—
501D4—861no—
502D4—861no—
503D4—3441no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—41no—
513C2×C4—42no—
514C2×C4—81no—
515C2×C4—861no—
516C2×C4—861no—
517C2×C4—861no—
518C2×C4—1721no—
519C2×C4—1721no—
520C2×C4(C22⋊D43)⋊C411yescharacteristic
521C2×C4(C22⋊D43)⋊C411yescharacteristic
522C2×C4(C22⋊D43)⋊C411yescharacteristic
523C2×C4C22×C4×D4311yescharacteristic
524C2×C4C2×D4×D4311yescharacteristic
525C2×C4C2×#1062190011yescharacteristic
526C8—41no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8—432no—
531C8—861no—
532C8—861no—
533C8—861no—
534C8—861no—
535C8—861no—
536C8—861no—
537C8—861no—
538C8—1721no—
539C8—1721no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—1721no—
544C22—1721no—
545C22—1721no—
546C22C2×(C22⋊D43)⋊C411yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—22no—
551C4—21no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—1721no—
556C4—1721no—
557C4—1721no—
558C4C2×#1306333111yescharacteristic
559C4#1458366511yescharacteristic
560C4#137×D4311yescharacteristic
561C4#1458369811yescharacteristic
562C2—41no—
563C2—3441no—
564C2#1914331611yescharacteristic
565C2#1914341011yescharacteristic
566C2#1914350811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1479C2
socleC22×C43C2×C4×D4
prime radical#13063299C2×C4
cosocleC42×C43C24
hypercenter#1479D43
hypocenterC43#18012
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
3. Q8×#10621877C2semidirect
4. #19133501C2semidirect
5. #19133482C2semidirect
6. #19133463C2semidirect
7. #19133455C2semidirect
8. #19133448C2semidirect
9. #19133435C2semidirect
10. #19133410C2semidirect
11. #19133399C2semidirect
12. #19133383C2semidirect
14. #19132890C2semidirect
15. C43×#1479C2semidirect
292. #1479D43semidirect
350. C43#18012semidirect

Maximal subgroups

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

subgroupindex
#191446752
#191435932
Q8×#106218772
#191335012
#191334822
#191334632
#191334552
#191334482
#191334352
#191334102
#191333992
#191333832
#191330612
#191328902
C43×#14792
#1801243