Finite Group Databasebeta

← #25084425

Subgroups — #25084425

Order 11008.

712 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145181C211yesmaximal, characteristic, complemented
2#19145181C211yesmaximal, characteristic, complemented
3#19145154C211yesmaximal, characteristic
4#19145154C211yesmaximal, characteristic
5#19145109C211yesmaximal, characteristic, complemented
6#19144918C211yesmaximal, characteristic
7#19134272C211yesmaximal, characteristic, complemented
8#19134266C211yesmaximal, characteristic, complemented
9#19134255C211yesmaximal, characteristic, complemented
10#19134248C211yesmaximal, characteristic, complemented
11#19134241C211yesmaximal, characteristic, complemented
12#19134241C211yesmaximal, characteristic, complemented
13#19134228C211yesmaximal, characteristic, complemented
14#19134217C211yesmaximal, characteristic, complemented
15C2×C43×#322C211yesmaximal, characteristic, complemented
16#14583456C2211yescharacteristic
17#14583456C2211yescharacteristic
18#14583456C2211yescharacteristic
19#14583449C2211yescharacteristic
20#14583304C2211yescharacteristic
21#14583304C2211yescharacteristic
22#14583304C2211yescharacteristic
23#14583304C2211yescharacteristic
24#14583301—22no—
25#14583297C2211yescharacteristic
26#14583297C2211yescharacteristic
27#14583297C2211yescharacteristic
28#14583297C2211yescharacteristic
29#14583279C2211yescharacteristic
30#14583279C2211yescharacteristic
31#14583272C2211yescharacteristic
32#14583272C2211yescharacteristic
33#14583254—22no—
34#14583250C2211yescharacteristic
35#14583250C2211yescharacteristic
36#14583250C2211yescharacteristic
37#14583250C2211yescharacteristic
38#14583250C2211yescharacteristic
39#14583250C2211yescharacteristic
40#14583250C2211yescharacteristic
41#14583250C2211yescharacteristic
42#14583246C2211yescharacteristic
43#14583246C2211yescharacteristic
44#14583246C2211yescharacteristic
45#14583246C2211yescharacteristic
46#14583140—22no—
47#14583140—22no—
48#14583128—22no—
49#14583128—22no—
50C4×Dic172—22no—
51C4×Dic172—22no—
52C4×#10621873—22no—
53C4×#10621873—22no—
54#14582937—22no—
55#14582896—22no—
56C2×C4×C8×C43C2211yescharacteristic
57C2×C4×C8×C43C2211yescharacteristic
58C2×C4×C8×C43C2211yescharacteristic
59C43×#322C2211yescharacteristic
60C43×#322C2211yescharacteristic
61C43×#322C2211yescharacteristic
62C43×#322C2211yescharacteristic
63C2×#10621898—21no—
64C2×Dic172—22no—
65C2×Dic172—22no—
66C2×#10621873—22no—
67C2×#10621873—22no—
68#13063325C2311yescharacteristic
69#13063325C2311yescharacteristic
70#13063325C2311yescharacteristic
71#13063325C2311yescharacteristic
72#13063325C2311yescharacteristic
73#13063325C2311yescharacteristic
74#13063325C2311yescharacteristic
75#13063322C2311yescharacteristic
76#13063317—21no—
77#13063317—21no—
78#13063317—21no—
79#13063313—21no—
80#13063304—21no—
81#13063304—21no—
82#13063304—21no—
83#13063304—21no—
84#13063304—21no—
85#13063304—21no—
86#13063299—21no—
87#13063299—21no—
88C4×Dic86—21no—
89C4×Dic86—21no—
90C4×Dic86—21no—
91C4×Dic86—21no—
92C4×Dic86—21no—
93C4×Dic86—21no—
94C4×D172—21no—
95C4×D172—21no—
96#13063284—21no—
97#13063284—21no—
98#13063284—21no—
99#13063259—22no—
100#13063259—22no—
101#13063259—22no—
102#13063259—22no—
103#13063257—22no—
104#13063257—22no—
105#13063257—22no—
106#13063257—22no—
107#13063250—22no—
108#13063250—22no—
109#13063250—22no—
110#13063250—22no—
111#13063250—22no—
112#13063250—22no—
113#13063250—22no—
114#13063250—22no—
115#13063247—22no—
116#13063247—22no—
117#13063247—22no—
118#13063247—22no—
119C22×C8×C43D412yes—
120C22×C8×C43D412yes—
121C22×C8×C43D412yes—
122C2×C42×C43C2311yescharacteristic
123C4×C8×C43D412yes—
124C4×C8×C43D412yes—
125C4×C8×C43D412yes—
126C4×C8×C43C2311yescharacteristic
127C4×C8×C43C2311yescharacteristic
128C4×C8×C43C2311yescharacteristic
129C4×C8×C43C2311yescharacteristic
130C4×C8×C43C2311yescharacteristic
131C4×C8×C43C2311yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C2×C22⋊D43—41no—
136#10621898—44no—
137C2×D172—21no—
138C2×D172—21no—
139C2×D172—21no—
140C2×C4×D43—41no—
141C2×Dic86—21no—
142C2×Dic86—21no—
143C2×Dic86—21no—
144C2×Dic86—21no—
145C2×Dic86—21no—
146C2×Dic86—21no—
147C2×Dic86—21no—
148C2×C8×C43—24no—
149C2×C8×C43—24no—
150C2×C8×C43—42no—
151C2×C8×C43C2×D412yes—
152C2×C8×C43C2×D412yes—
153C2×C8×C43C2×D412yes—
154C2×C8×C43C2×D412yes—
155C2×C8×C43C2×D412yes—
156C2×C8×C43C2×D412yes—
157C42×C43C2×D411yescharacteristic
158C42×C43C2×D411yescharacteristic
159C42×C43C2×D411yescharacteristic
160C42×C43C2411yescharacteristic
161C22⋊Dic43—41no—
162C22⋊Dic43—41no—
163C22⋊Dic43—41no—
164(C2×D43)⋊C4—41no—
165(C2×D43)⋊C4—41no—
166C4⋊Dic43—21no—
167C4⋊Dic43—21no—
168C4⋊Dic43—21no—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180Dic43⋊C4—41no—
181Dic43⋊C4—41no—
182Dic43⋊C4—41no—
183Dic43⋊C4—41no—
184Dic43⋊C4—41no—
185Dic43⋊C4—41no—
186C4×Dic43—41no—
187C4×Dic43—41no—
188C4×Dic43—41no—
189Dic172—44no—
190Dic172—44no—
191#10621873—44no—
192#10621873—44no—
193C23×C43#12711yescharacteristic
194C22×D43—41no—
195C2×C4×C43—22no—
196C2×C4×C43—22no—
197C2×C4×C43#12711yescharacteristic
198C2×C4×C43#12711yescharacteristic
199C2×C4×C43#12711yescharacteristic
200C2×C4×C43#13714yes—
201C2×C4×C43C22×D411yescharacteristic
202C2×C4×C43C22×D411yescharacteristic
203C2×C4×C43C22×D411yescharacteristic
204C22⋊D43—82no—
205C2×Dic43—41no—
206C2×Dic43—41no—
207C2×Dic43—41no—
208C2×Dic43—41no—
209C2×Dic43—41no—
210C2×Dic43—41no—
211C2×Dic43—41no—
212D172—42no—
213D172—42no—
214D172—42no—
215C4×D43—82no—
216Dic86—42no—
217Dic86—42no—
218Dic86—42no—
219Dic86—42no—
220Dic86—42no—
221Dic86—42no—
222Dic86—42no—
223C8×C43—22no—
224C8×C43—22no—
225C8×C43—22no—
226C8×C43—22no—
227C8×C43—22no—
228C8×C43#13514yes—
229#19620—431nomaximal, Sylow
230C22×C43—21no—
231C22×C43—21no—
232C22×C43#49712yes—
233C22×C43C2×#12711yescharacteristic
234C2×D43—81no—
235C2×D43—81no—
236C2×D43—81no—
237C4×C43—21no—
238C4×C43—21no—
239C4×C43#49712yes—
240C4×C43C2×#13512yes—
241C4×C43C2×#13712yes—
242C4×C43#57512yes—
243Dic43—81no—
244Dic43—81no—
245Dic43—81no—
246Dic43—81no—
247Dic43—81no—
248Dic43—81no—
249Dic43—81no—
250#3170—431no—
251#3170—431no—
252#3167—431no—
253#3167—431no—
254#3160—431no—
255#3131—431no—
256#1723—431no—
257#1722—431no—
258#1720—431no—
259#1719—431no—
260#1718—431no—
261#1718—431no—
262#1716—431no—
263#1714—431no—
264C2×#322D4311yescharacteristic, complemented
265C2×C43—22no—
266C2×C43#314711yescharacteristic
267C2×C43C2×#49711yescharacteristic
268C2×C43#315011yescharacteristic
269D43—161no—
270#533—431no—
271#533—431no—
272#533—431no—
273#532—431no—
274#500—431no—
275#500—431no—
276#500—431no—
277#500—431no—
278#499—862no—
279#498—431no—
280#498—431no—
281#498—431no—
282#498—431no—
283#494—431no—
284#494—431no—
285#492—431no—
286#492—431no—
287#488—862no—
288#487—431no—
289#487—431no—
290#487—431no—
291#487—431no—
292#487—431no—
293#487—431no—
294#487—431no—
295#487—431no—
296#486—431no—
297#486—431no—
298#486—431no—
299#486—431no—
300#467—862no—
301#467—862no—
302#465—862no—
303#465—862no—
304C4×Q16—862no—
305C4×Q16—862no—
306C4×SD16—862no—
307C4×SD16—862no—
308#427—862no—
309#416—862no—
310C2×C4×C8C2×D4311yescharacteristic
311C2×C4×C8C2×D4311yescharacteristic
312C2×C4×C8C2×D4311yescharacteristic
313#322C2×D4311yescharacteristic
314#322C2×D4311yescharacteristic
315#322C2×D4311yescharacteristic
316#322C2×D4311yescharacteristic
317C43#1962011yescharacteristic, complemented, Sylow
318C2×#41—861no—
319C2×Q16—862no—
320C2×Q16—862no—
321C2×SD16—862no—
322C2×SD16—862no—
323C22×C8D17212yes—
324C22×C8D17212yes—
325C22×C8D17212yes—
326C4⋊Q8—431no—
327C4⋊Q8—431no—
328C4⋊Q8—431no—
329C4⋊Q8—431no—
330C4⋊Q8—431no—
331C4⋊Q8—431no—
332C4⋊Q8—431no—
333#127—431no—
334#125—861no—
335#125—861no—
336#125—861no—
337#124—861no—
338C22⋊Q8—861no—
339C22⋊Q8—861no—
340C22⋊Q8—861no—
341C22⋊Q8—861no—
342C22⋊Q8—861no—
343C22⋊Q8—861no—
344#121—861no—
345#121—861no—
346C4×Q8—861no—
347C4×Q8—861no—
348C4×Q8—861no—
349C4×Q8—861no—
350C4×Q8—861no—
351C4×Q8—861no—
352C4×D4—861no—
353C4×D4—861no—
354#117—861no—
355#117—861no—
356#117—861no—
357C2×C42C22×D4311yescharacteristic
358#107—862no—
359#107—862no—
360#107—862no—
361#107—862no—
362#106—862no—
363#106—862no—
364#106—862no—
365#106—862no—
366#103—862no—
367#103—862no—
368#103—862no—
369#103—862no—
370#103—862no—
371#103—862no—
372#103—862no—
373#103—862no—
374#102—862no—
375#102—862no—
376#102—862no—
377#102—862no—
378C4×C8D17212yes—
379C4×C8D17212yes—
380C4×C8D17212yes—
381C4×C8C22×D4311yescharacteristic
382C4×C8C22×D4311yescharacteristic
383C4×C8C22×D4311yescharacteristic
384C4×C8C22×D4311yescharacteristic
385C4×C8C22×D4311yescharacteristic
386C4×C8C22×D4311yescharacteristic
387#41—1724no—
388C2×Q8—861no—
389C2×Q8—861no—
390C2×Q8—861no—
391C2×Q8—861no—
392C2×Q8—861no—
393C2×Q8—861no—
394C2×Q8—861no—
395C2×D4—861no—
396C2×D4—861no—
397C2×D4—861no—
398C2×D4—1721no—
399C22×C4—1721no—
400C22×C4C2×D17211yescharacteristic
401C22×C4C2×D17211yescharacteristic
402C22×C4C2×D17211yescharacteristic
403Q16—1724no—
404Q16—1724no—
405SD16—1724no—
406SD16—1724no—
407C2×C8—24no—
408C2×C8—24no—
409C2×C8—42no—
410C2×C8C2×D17212yes—
411C2×C8C2×D17212yes—
412C2×C8C2×D17212yes—
413C2×C8C2×D17212yes—
414C2×C8C2×D17212yes—
415C2×C8C2×D17212yes—
416C4⋊C4—861no—
417C4⋊C4—861no—
418C4⋊C4—861no—
419C4⋊C4—861no—
420C4⋊C4—861no—
421C4⋊C4—861no—
422C4⋊C4—861no—
423C4⋊C4—861no—
424C4⋊C4—861no—
425C4⋊C4—861no—
426C4⋊C4—861no—
427C4⋊C4—861no—
428C4⋊C4—861no—
429C4⋊C4—861no—
430C4⋊C4—1721no—
431C4⋊C4—1721no—
432C4⋊C4—1721no—
433C4⋊C4—1721no—
434C4⋊C4—1721no—
435C4⋊C4—1721no—
436C22⋊C4—1721no—
437C22⋊C4—1721no—
438C22⋊C4—1721no—
439C22⋊C4—1721no—
440C22⋊C4—1721no—
441C42—1721no—
442C42—1721no—
443C42—1721no—
444C42C2×D17211yescharacteristic
445C42C2×D17211yescharacteristic
446C42C2×D17211yescharacteristic
447C42C23×D4311yescharacteristic
448C23—1721no—
449C23#1306332211yescharacteristic
450Q8—1722no—
451Q8—1722no—
452Q8—1722no—
453Q8—1722no—
454Q8—1722no—
455Q8—1722no—
456Q8—1722no—
457D4—3442no—
458D4—1722no—
459D4—1722no—
460D4—1722no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—3442no—
464C2×C4—1721no—
465C2×C4—1721no—
466C2×C4—1721no—
467C2×C4—1721no—
468C2×C4—1721no—
469C2×C4—1721no—
470C2×C4—1721no—
471C2×C4#1306332211yescharacteristic
472C2×C4#1306332211yescharacteristic
473C2×C4#1306332211yescharacteristic
474C2×C4#1306335814yes—
475C2×C4C22×D17211yescharacteristic
476C2×C4C22×D17211yescharacteristic
477C2×C4C22×D17211yescharacteristic
478C8—22no—
479C8—22no—
480C8—22no—
481C8—22no—
482C8—22no—
483C8#1306334714yes—
484C22—21no—
485C22—21no—
486C22—3441no—
487C22—3441no—
488C22—3441no—
489C22#1458329312yes—
490C22C2×#1306332211yescharacteristic
491C4—21no—
492C4—21no—
493C4—3441no—
494C4—3441no—
495C4—3441no—
496C4—3441no—
497C4—3441no—
498C4—3441no—
499C4—3441no—
500C4#1458329312yes—
501C4C2×#1306334712yes—
502C4C2×#1306335812yes—
503C4#1458369912yes—
504C2—22no—
505C2—6881no—
506C2#1914502311yescharacteristic
507C2C2×#1458329311yescharacteristic
508C2#1914504111yescharacteristic
subgroupG/H
centerC2×C4#13063322
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC2×C43×#322C2
socleC22×C43C2×#127
prime radical#14583449C22
hypercenterC2×#322D43
hypocenterC43#19620
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×#322

Complements

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

NH ≅ G/Ntype
1. #19145181C2semidirect
2. #19145181C2semidirect
5. #19145109C2semidirect
7. #19134272C2semidirect
8. #19134266C2semidirect
9. #19134255C2semidirect
10. #19134248C2semidirect
11. #19134241C2semidirect
12. #19134241C2semidirect
13. #19134228C2semidirect
14. #19134217C2semidirect
15. C2×C43×#322C2semidirect
264. C2×#322D43semidirect
317. C43#19620semidirect

Maximal subgroups

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

subgroupindex
#191451812
#191451542
#191451092
#191449182
#191342722
#191342662
#191342552
#191342482
#191342412
#191342282
#191342172
C2×C43×#3222
#1962043