Finite Group Databasebeta

← #25067316

Subgroups — #25067316

Order 11008.

590 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145178C211yesmaximal, characteristic
2#19143526C211yesmaximal, characteristic
3#19143524C211yesmaximal, characteristic
4#19133448C211yesmaximal, characteristic, complemented
5#19133447C211yesmaximal, characteristic, complemented
6#19133446C211yesmaximal, characteristic, complemented
7#19133445C211yesmaximal, characteristic, complemented
8#19133444C211yesmaximal, characteristic, complemented
9#19133443C211yesmaximal, characteristic, complemented
10#19133442C211yesmaximal, characteristic, complemented
11#19133352C211yesmaximal, characteristic
12#19133048C211yesmaximal, characteristic
13#19133048C211yesmaximal, characteristic
14#322×D43C211yesmaximal, characteristic
15C43×#1584C211yesmaximal, characteristic, complemented
16#14583453C2211yescharacteristic
17#14583453C2211yescharacteristic
18#14583303C411yescharacteristic
19#14583277C411yescharacteristic
20#14583248C411yescharacteristic
21#14583248C411yescharacteristic
22#14583141C411yescharacteristic
23#14583139C411yescharacteristic
24#14583139C411yescharacteristic
25#14583137C411yescharacteristic
26#14583030C2211yescharacteristic
27#14583029C2211yescharacteristic
28#14583028—21no—
29#14583027—21no—
30#14583026C2211yescharacteristic
31Q8×C43⋊C8C2211yescharacteristic
32C8×Dic86—21no—
33C8×Dic86C2211yescharacteristic
34#14583023—21no—
35#14583023C2211yescharacteristic
36C4×Dic172C2211yescharacteristic
37C4×#10621885C2211yescharacteristic
38C4×#10621885C2211yescharacteristic
39#14582924—21no—
40#14582924—21no—
41#14582921C2211yescharacteristic
42#14582921C2211yescharacteristic
43#14582856—21no—
44#14582853—21no—
45C4×C8×D43C2211yescharacteristic
46C4×C8×D43C2211yescharacteristic
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#14582621C2211yescharacteristic
59#14582620C2211yescharacteristic
60C43×#446C2211yescharacteristic
61C8×Q8×C43C2211yescharacteristic
62C4×Q16×C43C2211yescharacteristic
63C43×#335C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×Q8⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C2×Dic172C2×C411yescharacteristic
68C2×#10621885C2×C411yescharacteristic
69C2×#10621885C2×C411yescharacteristic
70C2×#10621872—21no—
71C2×#10621872—21no—
72C2×C8×D43—21no—
73C2×C8×D43C2×C411yescharacteristic
74C2×C8×D43C2×C411yescharacteristic
75C2×C8×D43D411yescharacteristic
76C2×C8×D43D411yescharacteristic
77#13063324C2×C411yescharacteristic
78#13063324C2×C411yescharacteristic
79#13063323C2×C411yescharacteristic
80#13063323C2×C411yescharacteristic
81#13063315—21no—
82#13063315—21no—
83#13063305C2×C411yescharacteristic
84#13063305C2×C411yescharacteristic
85#13063303—21no—
86#13063303—21no—
87#13063301C2×C411yescharacteristic
88#13063301C2×C411yescharacteristic
89C4×Dic86—21no—
90C4×Dic86—21no—
91C4×Dic86C2311yescharacteristic
92C4×Dic86C2311yescharacteristic
93#13063282—21no—
94#13063282—21no—
95C42×D43C2311yescharacteristic
96#13063259C2×C411yescharacteristic
97#13063258C2×C411yescharacteristic
98#13063258C2×C411yescharacteristic
99C4⋊(C43⋊C8)—21no—
100C4⋊(C43⋊C8)—21no—
101C4⋊(C43⋊C8)C2311yescharacteristic
102C4⋊(C43⋊C8)C2311yescharacteristic
103Dic43⋊C8—21no—
104Dic43⋊C8—21no—
105Dic43⋊C8—21no—
106Dic43⋊C8—21no—
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109#13063250C2×C411yescharacteristic
110#13063250C2×C411yescharacteristic
111#13063249C2×C411yescharacteristic
112#13063249C2×C411yescharacteristic
113#13063248C2×C411yescharacteristic
114#13063248C2×C411yescharacteristic
115#13063236—21no—
116#13063235—21no—
117#13063235—21no—
118C4×C43⋊C8—21no—
119C4×C43⋊C8C2311yescharacteristic
120C4×C43⋊C8C2311yescharacteristic
121C4×C43⋊C8C2311yescharacteristic
122C8×Dic43—21no—
123C8×Dic43—21no—
124C8×Dic43—21no—
125C8×Dic43C2×C411yescharacteristic
126C8×Dic43C2×C411yescharacteristic
127C8×Dic43D411yescharacteristic
128C8×Dic43D411yescharacteristic
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
146C2×C4×D43C22×C411yescharacteristic
147C2×C4×D43C2×D411yescharacteristic
148C2×C4×D43#4111yescharacteristic
149C2×Dic86—21no—
150C2×Dic86—21no—
151C2×Dic86C22×C411yescharacteristic
152C2×Dic86C22×C411yescharacteristic
153Q16×C43—41no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43C22×C411yescharacteristic
158C2×C8×C43C22×C411yescharacteristic
159C2×C8×C43C2×D411yescharacteristic
160C2×C8×C43C2×D411yescharacteristic
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43C22×C411yescharacteristic
164C4⋊C4×C43C22×C411yescharacteristic
165C42×C43—21no—
166C42×C43—21no—
167C42×C43C2411yescharacteristic
168#10621885—41no—
169#10621885—41no—
170(C2×D43)⋊C4—21no—
171(C2×D43)⋊C4—21no—
172(C2×D43)⋊C4—21no—
173(C2×D43)⋊C4—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43C22×C411yescharacteristic
177C4⋊Dic43C22×C411yescharacteristic
178Dic43⋊C4—21no—
179Dic43⋊C4—21no—
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×Dic43C22×C411yescharacteristic
191C4×Dic43C2×D411yescharacteristic
192C4×Dic43#4111yescharacteristic
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8C22×C411yescharacteristic
197C2×C43⋊C8C22×C411yescharacteristic
198C2×C43⋊C8C2×D411yescharacteristic
199C2×C43⋊C8C2×D411yescharacteristic
200Dic172—41no—
201#10621872—42no—
202#10621872—42no—
203C8×D43—22no—
204C8×D43—41no—
205C8×D43—41no—
206C8×D43—42no—
207C8×D43Q1614yescomplemented
208C22×D43C4×D411yescharacteristic
209Q8×C43—21no—
210Q8×C43—21no—
211Q8×C43—21no—
212Q8×C43—21no—
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—22no—
230C4×D43C2×Q1612yes—
231C4×D43#13512yes—
232Dic86—21no—
233Dic86—21no—
234Dic86—21no—
235Dic86—21no—
236Dic86—42no—
237Dic86—42no—
238C8×C43—21no—
239C8×C43—21no—
240C8×C43—21no—
241C8×C43—41no—
242C8×C43—41no—
243C8×C43—41no—
244C8×C43C2×Q1612yes—
245C43⋊C8—21no—
246C43⋊C8—21no—
247C43⋊C8—21no—
248C43⋊C8—41no—
249C43⋊C8—41no—
250C43⋊C8—41no—
251C43⋊C8C2×Q1612yes—
252#17977—431nomaximal, Sylow
253C22×C43C2×C4×D411yescharacteristic
254C2×D43—21no—
255C2×D43—21no—
256C2×D43C4×Q1612yes—
257C4×C43—21no—
258C4×C43—41no—
259C4×C43—41no—
260C4×C43—41no—
261C4×C43—41no—
262C4×C43#56811yescharacteristic
263C4×C43#56811yescharacteristic
264C4×C43C22×Q1611yescharacteristic
265C4×C43C2×#13511yescharacteristic
266Dic43—21no—
267Dic43—41no—
268Dic43—41no—
269Dic43—41no—
270Dic43—41no—
271Dic43C4×Q1612yes—
272Dic43#44412yes—
273#3170—431no—
274#2960—431no—
275#2960—431no—
276#1584—431no—
277#1584—431no—
278#1584—431no—
279#1584—431no—
280#1584—431no—
281#1584—431no—
282#1584—431no—
283#1584D4311yescharacteristic, complemented
284#1567—431no—
285#1493—431no—
286#1493—431no—
287C2×#322—431no—
288C2×C43#293211yescharacteristic
289C2×C43C2×C4×Q1611yescharacteristic
290C2×C43C2×#44411yescharacteristic
291D43—22no—
292#533—431no—
293#533—431no—
294#500—431no—
295#494—431no—
296#487—431no—
297#487—431no—
298#467—431no—
299#467—431no—
300#467—431no—
301#467—431no—
302#446—431no—
303#446—431no—
304#446—431no—
305#446—861no—
306#446—861no—
307#446C2×D4311yescharacteristic
308C8×Q8—431no—
309C8×Q8—431no—
310C8×Q8—431no—
311C8×Q8—861no—
312C8×Q8—861no—
313C8×Q8C2×D4311yescharacteristic
314C4×Q16—431no—
315C4×Q16—431no—
316C4×Q16—431no—
317C4×Q16C2×D4311yescharacteristic
318#424—861no—
319#424—861no—
320#423—431no—
321#423—431no—
322#405—861no—
323#405—861no—
324C2×C4×C8—431no—
325C2×C4×C8—431no—
326C2×C4×C8—431no—
327#335—431no—
328#335—431no—
329#335—431no—
330#335C2×D4311yescharacteristic
331Q8⋊C8—431no—
332Q8⋊C8—431no—
333Q8⋊C8—431no—
334Q8⋊C8—431no—
335Q8⋊C8—431no—
336Q8⋊C8—431no—
337Q8⋊C8C2×D4311yescharacteristic
338Q8⋊C8C2×D4311yescharacteristic
339#322—431no—
340#322—431no—
341#322—431no—
342#322C2×D4311yescharacteristic
343C43#1797711yescharacteristic, complemented, Sylow
344C2×Q16—431no—
345C2×Q16—431no—
346C2×Q16—431no—
347C2×Q16C4×D4311yescharacteristic
348C2×M16—861no—
349C2×M16—861no—
350C22×C8—431no—
351C22×C8—431no—
352C22×C8—431no—
353C22×C8—431no—
354C22×C8—861no—
355C4⋊Q8—431no—
356C4⋊Q8—431no—
357C4⋊Q8—431no—
358C4⋊Q8—431no—
359#125—861no—
360#125—861no—
361C22⋊Q8—431no—
362C22⋊Q8—431no—
363C22⋊Q8—431no—
364C22⋊Q8—431no—
365C22⋊Q8—861no—
366C22⋊Q8—861no—
367C4×Q8—431no—
368C4×Q8—431no—
369C4×Q8—861no—
370C4×Q8—861no—
371C4×Q8C22×D4311yescharacteristic
372C4×Q8C22×D4311yescharacteristic
373#117—861no—
374#117—861no—
375C2×C42—431no—
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—861no—
385C4⋊C8—861no—
386C4⋊C8—861no—
387C4⋊C8—861no—
388C4⋊C8—861no—
389C4⋊C8—861no—
390C4⋊C8—861no—
391C4⋊C8—861no—
392C4⋊C8C22×D4311yescharacteristic
393C4⋊C8C22×D4311yescharacteristic
394#103—431no—
395#103—431no—
396#103—431no—
397#103—431no—
398#103—431no—
399#103—431no—
400#103C4×D4311yescharacteristic
401#103C4×D4311yescharacteristic
402#97—21no—
403#97—861no—
404#97—861no—
405#97—861no—
406C4×C8—21no—
407C4×C8—431no—
408C4×C8—431no—
409C4×C8—431no—
410C4×C8—431no—
411C4×C8—431no—
412C4×C8—431no—
413C4×C8—431no—
414C4×C8—861no—
415C4×C8—861no—
416C4×C8—861no—
417C4×C8—861no—
418C4×C8C22×D4311yescharacteristic
419C4×C8C22×D4311yescharacteristic
420C4×C8C22×D4311yescharacteristic
421C2×Q8—431no—
422C2×Q8—431no—
423C2×Q8—861no—
424C2×Q8—861no—
425C2×Q8C2×C4×D4311yescharacteristic
426C2×Q8C2×C4×D4311yescharacteristic
427C22×C4—431no—
428C22×C4—431no—
429C22×C4—431no—
430Q16—41no—
431Q16—1721no—
432Q16—1721no—
433Q16—1721no—
434M16—1722no—
435M16—1722no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—431no—
440C2×C8—434no—
441C2×C8—431no—
442C2×C8—431no—
443C2×C8—431no—
444C2×C8—862no—
445C2×C8—861no—
446C2×C8—861no—
447C2×C8—861no—
448C2×C8—1721no—
449C2×C8—1721no—
450C2×C8—1722no—
451C2×C8C2×C4×D4311yescharacteristic
452C2×C8C2×C4×D4311yescharacteristic
453C2×C8D4×D4311yescharacteristic
454C2×C8D4×D4311yescharacteristic
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—431no—
458C4⋊C4—431no—
459C4⋊C4—861no—
460C4⋊C4—861no—
461C4⋊C4—861no—
462C4⋊C4—861no—
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⋊C4C2×C4×D4311yescharacteristic
472C4⋊C4C2×C4×D4311yescharacteristic
473C22⋊C4—861no—
474C22⋊C4—861no—
475C22⋊C4—861no—
476C22⋊C4—861no—
477C42—21no—
478C42—21no—
479C42—431no—
480C42—431no—
481C42—431no—
482C42—861no—
483C42—861no—
484C42C23×D4311yescharacteristic
485C23—431no—
486Q8—21no—
487Q8—21no—
488Q8—21no—
489Q8—21no—
490Q8—861no—
491Q8—861no—
492Q8—861no—
493Q8—861no—
494Q8—1722no—
495Q8—1722no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—431no—
501C2×C4—431no—
502C2×C4—432no—
503C2×C4—432no—
504C2×C4—431no—
505C2×C4—862no—
506C2×C4—861no—
507C2×C4—861no—
508C2×C4—861no—
509C2×C4—861no—
510C2×C4—861no—
511C2×C4—861no—
512C2×C4C22×C4×D4311yescharacteristic
513C2×C4C2×D4×D4311yescharacteristic
514C2×C4#41×D4311yescharacteristic
515C8—21no—
516C8—21no—
517C8—21no—
518C8—41no—
519C8—41no—
520C8—41no—
521C8—432no—
522C8—861no—
523C8—861no—
524C8—861no—
525C8—1721no—
526C8—1721no—
527C8—1721no—
528C8Q16×D4312yes—
529C22—432no—
530C22—861no—
531C22—861no—
532C22C4×D4×D4311yescharacteristic
533C4—21no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—41no—
538C4—432no—
539C4—432no—
540C4—861no—
541C4—1721no—
542C4—1721no—
543C4—1721no—
544C4—1721no—
545C4#1458366411yescharacteristic
546C4#1458366511yescharacteristic
547C4C2×Q16×D4311yescharacteristic
548C4#135×D4311yescharacteristic
549C2—862no—
550C2#1914330911yescharacteristic
551C2C4×Q16×D4311yescharacteristic
552C2#444×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1584C2
socleC22×C43C2×C4×D4
prime radicalC22×D43C4×D4
cosocleC42×C43C24
hypercenter#1584D43
hypocenterC43#17977
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1584

Complements

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

NH ≅ G/Ntype
4. #19133448C2semidirect
5. #19133447C2semidirect
6. #19133446C2semidirect
7. #19133445C2semidirect
8. #19133444C2semidirect
9. #19133443C2semidirect
10. #19133442C2semidirect
15. C43×#1584C2semidirect
207. C8×D43Q16semidirect
283. #1584D43semidirect
343. C43#17977semidirect

Maximal subgroups

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

subgroupindex
#191451782
#191435262
#191435242
#191334482
#191334472
#191334462
#191334452
#191334442
#191334432
#191334422
#191333522
#191330482
#322×D432
C43×#15842
#1797743