Finite Group Databasebeta

← #25138072

Subgroups — #25138072

Order 11008.

674 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#19144404C211yesmaximal, characteristic
2C4×#13063356C211yesmaximal, characteristic
3#19143260C211yesmaximal, characteristic
4#19136036C212yesmaximal
5#19135895C212yesmaximal
6#19135585C211yesmaximal, characteristic, complemented
7#19135378C212yesmaximal, complemented
8#19135371C211yesmaximal, characteristic, complemented
9#19135247C212yesmaximal, complemented
10#19134591C211yesmaximal, characteristic, complemented
11C2×C43×#477C211yesmaximal, characteristic, complemented
12C2×#13063356C2211yescharacteristic
13C4×#10621898C2211yescharacteristic
14#14583191—21no—
15#14583186—21no—
16#14583181—21no—
17#14583176—21no—
18#14583004—21no—
19#14582997—21no—
20C4×#10621885—21no—
21C4×#10621884—21no—
22#14582959—22no—
23#14582955—21no—
24#14582951—21no—
25C2×#13063261C2212yes—
26#14582939C2212yes—
27#14582939C2211yescharacteristic
28#14582923C2211yescharacteristic
29#14582923C2211yescharacteristic
30#14582908C2211yescharacteristic
31#14582898C2211yescharacteristic
32#14582898C2212yes—
33C2×#13063244C2212yes—
34#14582865C2212yes—
35#14582854C2212yes—
36C4×#10621877C2211yescharacteristic
37#14582668C2212yes—
38#14582668C2212yes—
39#14582668C2212yes—
40#14582664C2212yes—
41C2×C4⋊Q8×C43C2211yescharacteristic
42C2×C4×Q8×C43C2211yescharacteristic
43C43×#477—21no—
44C43×#477—21no—
45C43×#477—22no—
46C2×#107×C43C2212yes—
47C2×C4⋊C8×C43C2211yescharacteristic
48C2×#103×C43C2212yes—
49C2×#10621898C2311yescharacteristic
50#13063356—22no—
51#13063356—22no—
52C2×#10621885—21no—
53C2×#10621884—21no—
54C2×#10621877C2311yescharacteristic
55C2×#10621877C2312yes—
56C2×#10621877C2312yes—
57C2×#10621877C2311yescharacteristic
58C4×Dic86D411yescharacteristic
59C4×Dic86D411yescharacteristic
60C4×D172D411yescharacteristic
61C4×D172D411yescharacteristic
62C4×C22⋊D43—21no—
63C4×C22⋊D43—21no—
64#13063284C2311yescharacteristic
65#13063282—21no—
66C42×D43—21no—
67#13063261—24no—
68#13063258—22no—
69#13063258—21no—
70#13063256—22no—
71#13063256—21no—
72C4⋊(C43⋊C8)—21no—
73C4⋊(C43⋊C8)—21no—
74C4⋊(C43⋊C8)—21no—
75C4⋊(C43⋊C8)—21no—
76#13063249—21no—
77#13063249—21no—
78#13063248—22no—
79#13063248—21no—
80#13063245—22no—
81#13063245—21no—
82#13063244—24no—
83(C2×D43)⋊C8—22no—
84(C2×D43)⋊C8—22no—
85#13063236—21no—
86#13063235—22no—
87C4×C43⋊C8—21no—
88C8×Dic43—22no—
89C22×Q8×C43—21no—
90C22×Q8×C43C2311yescharacteristic
91C22×C8×C43C2312yes—
92C4⋊Q8×C43—21no—
93C4⋊Q8×C43—21no—
94C4⋊Q8×C43—21no—
95C4⋊Q8×C43—21no—
96C4×Q8×C43—21no—
97C4×Q8×C43—21no—
98C4×Q8×C43—21no—
99C4×Q8×C43—21no—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43C2311yescharacteristic
103C2×C4⋊C4×C43C2312yes—
104C2×C42×C43—21no—
105C2×C42×C43C2311yescharacteristic
106#107×C43—22no—
107#107×C43—22no—
108C4⋊C8×C43D411yescharacteristic
109C4⋊C8×C43D411yescharacteristic
110C4⋊C8×C43D412yes—
111#103×C43—22no—
112#103×C43—22no—
113C2×Q8×C43—21no—
114C2×Q8×C43—21no—
115C2×Q8×C43—21no—
116C2×Q8×C43—21no—
117C2×Q8×C43—21no—
118C2×Q8×C43—41no—
119C2×Q8×C43—41no—
120C2×Q8×C43—82no—
121C2×Q8×C43#4112yes—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—22no—
125C22×C4×C43#4111yescharacteristic
126C22×C4×C43#4111yescharacteristic
127C22×C4×C43C2411yescharacteristic
128C2×C22⋊D43—21no—
129#10621898—21no—
130#10621898—21no—
131#10621898—21no—
132#10621898—21no—
133C2×D172C2×D411yescharacteristic
134C2×C4×D43—21no—
135C2×C4×D43—21no—
136C2×C4×D43—21no—
137C2×Dic86C2×D411yescharacteristic
138C2×C8×C43—22no—
139C2×C8×C43—22no—
140C2×C8×C43C2×D412yes—
141C2×C8×C43C2×D412yes—
142C4⋊C4×C43—22no—
143C4⋊C4×C43—21no—
144C4⋊C4×C43—21no—
145C4⋊C4×C43—22no—
146C4⋊C4×C43—41no—
147C4⋊C4×C43—41no—
148C4⋊C4×C43—41no—
149C4⋊C4×C43—41no—
150C42×C43—41no—
151C42×C43—41no—
152C42×C43C2×D411yescharacteristic
153C42×C43C2×D411yescharacteristic
154C42×C43C2×D411yescharacteristic
155C42×C43C2×D411yescharacteristic
156C22⋊Dic43—21no—
157#10621885—24no—
158#10621884—24no—
159(C2×D43)⋊C4—21no—
160(C2×D43)⋊C4—21no—
161C4⋊Dic43C2×D411yescharacteristic
162C4⋊Dic43C2×D411yescharacteristic
163Dic43⋊C4—21no—
164Dic43⋊C4—21no—
165C4×Dic43—21no—
166C4×Dic43—21no—
167C4×Dic43—21no—
168#10621877—21no—
169#10621877—22no—
170#10621877—22no—
171#10621877—22no—
172#10621877—21no—
173#10621877—21no—
174#10621877—22no—
175#10621877#4112yes—
176C2×C43⋊C8—21no—
177C2×C43⋊C8—22no—
178C2×C43⋊C8—21no—
179C2×C43⋊C8—22no—
180C23×C43C2×#4111yescharacteristic
181C22×D43—21no—
182Q8×C43—22no—
183Q8×C43—22no—
184Q8×C43—41no—
185Q8×C43—41no—
186Q8×C43—82no—
187Q8×C43—82no—
188C2×C4×C43—22no—
189C2×C4×C43—22no—
190C2×C4×C43—41no—
191C2×C4×C43—41no—
192C2×C4×C43—41no—
193C2×C4×C43—41no—
194C2×C4×C43—42no—
195C2×C4×C43—81no—
196C2×C4×C43—82no—
197C2×C4×C43#12111yescharacteristic
198C2×C4×C43#12111yescharacteristic
199C2×C4×C43#12111yescharacteristic
200C2×C4×C43#12111yescharacteristic
201C2×C4×C43C22×D411yescharacteristic
202C2×C4×C43C22×D411yescharacteristic
203C2×C4×C43C2×#4111yescharacteristic
204C2×C4×C43C2×#4111yescharacteristic
205C2×C4×C432−1+411yescharacteristic
206C2×C4×C432−1+411yescharacteristic
207C22⋊D43—41no—
208C22⋊D43—41no—
209C2×Dic43—21no—
210C2×Dic43—21no—
211C2×Dic43—21no—
212D172—21no—
213D172—21no—
214C4×D43—41no—
215C4×D43—41no—
216C4×D43—42no—
217C4×D43—81no—
218Dic86—21no—
219Dic86—21no—
220C8×C43—22no—
221C8×C43—22no—
222C43⋊C8—22no—
223C43⋊C8—42no—
224C43⋊C8—41no—
225C43⋊C8—42no—
226#24722—431nomaximal, Sylow
227C22×C43—21no—
228C22×C43—21no—
229C22×C43C2×#12111yescharacteristic
230C22×C43#55211yescharacteristic
231C22×C43#55611yescharacteristic
232C2×D43—41no—
233C2×D43—41no—
234C2×D43—41no—
235C4×C43—21no—
236C4×C43—21no—
237C4×C43—21no—
238C4×C43—42no—
239C4×C43—81no—
240C4×C43—82no—
241C4×C43#47312yes—
242C4×C43#52511yescharacteristic
243C4×C43#53611yescharacteristic
244C4×C43#54711yescharacteristic
245C4×C43#54811yescharacteristic
246Dic43—41no—
247Dic43—41no—
248Dic43—41no—
249#3079—431no—
250C2×#477D4311yescharacteristic, complemented
251C4×#137—431no—
252#2925—431no—
253#2078—432no—
254#2052—432no—
255#1997—431no—
256#1952—432no—
257#1950—431no—
258#1930—432no—
259#1801—431no—
260C2×C43—21no—
261C2×C43—21no—
262C2×C43#241511yescharacteristic
263C2×C43C2×#47311yescharacteristic
264C2×C43#306811yescharacteristic
265D43—81no—
266C2×#137—431no—
267C2×C4⋊Q8C2×D4311yescharacteristic
268C4×#41—431no—
269C2×C4×Q8C2×D4311yescharacteristic
270#477—21no—
271#477—21no—
272#477—22no—
273#477—861no—
274#476—861no—
275#475—861no—
276#474—861no—
277#441—861no—
278#440—861no—
279C4×Q16—861no—
280C4×SD16—861no—
281#433—862no—
282#432—861no—
283#431—861no—
284C2×#108—432no—
285#428—432no—
286#428—431no—
287C2×#107C2×D4312yes—
288#423—431no—
289#423—431no—
290C2×C4⋊C8C2×D4311yescharacteristic
291#419—431no—
292#417—432no—
293#417—431no—
294C2×#103C2×D4312yes—
295C2×#101—432no—
296#408—432no—
297#405—432no—
298C4×M16—431no—
299#343—432no—
300#343—432no—
301#343—432no—
302#341—432no—
303C43#2472211yescharacteristic, complemented, Sylow
304C2×#41—431no—
305C22×Q8—21no—
306C22×Q8C22×D4311yescharacteristic
307#137—862no—
308#137—862no—
309C2×Q16—861no—
310C2×SD16—861no—
311C2×M16—431no—
312C2×M16—431no—
313C2×M16—432no—
314C2×M16—432no—
315C22×C8C22×D4312yes—
316C4⋊Q8—21no—
317C4⋊Q8—21no—
318C4⋊Q8—21no—
319C4⋊Q8—21no—
320C4×Q8—21no—
321C4×Q8—21no—
322C4×Q8—21no—
323C4×Q8—21no—
324C4×Q8—431no—
325C4×Q8—431no—
326C4×D4—431no—
327C4×D4—431no—
328C4×D4—861no—
329C4×D4—861no—
330#117—431no—
331#117—861no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4C22×D4311yescharacteristic
335C2×C4⋊C4C22×D4312yes—
336C2×C42—21no—
337C2×C42—861no—
338C2×C42C22×D4311yescharacteristic
339#108—864no—
340#107—22no—
341#107—22no—
342#107—861no—
343#107—862no—
344#106—861no—
345#106—862no—
346C4⋊C8—861no—
347C4⋊C8—861no—
348C4⋊C8—861no—
349C4⋊C8—861no—
350C4⋊C8C22⋊D4311yescharacteristic
351C4⋊C8C22⋊D4311yescharacteristic
352C4⋊C8C22⋊D4312yes—
353#103—22no—
354#103—22no—
355#103—861no—
356#103—862no—
357#103—861no—
358#103—861no—
359#102—861no—
360#102—862no—
361#101—864no—
362C22⋊C8—862no—
363C22⋊C8—862no—
364#97—862no—
365#97—861no—
366C4×C8—862no—
367C4×C8—861no—
368#41—861no—
369#41—861no—
370#41—861no—
371#41—861no—
372C2×Q8—21no—
373C2×Q8—21no—
374C2×Q8—21no—
375C2×Q8—21no—
376C2×Q8—21no—
377C2×Q8—41no—
378C2×Q8—41no—
379C2×Q8—82no—
380C2×Q8—431no—
381C2×Q8#1062190212yes—
382C2×D4—431no—
383C2×D4—861no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—861no—
388C22×C4—861no—
389C22×C4—861no—
390C22×C4#1062190011yescharacteristic
391C22×C4#1062190011yescharacteristic
392C22×C4C23×D4311yescharacteristic
393Q16—864no—
394SD16—864no—
395M16—432no—
396M16—861no—
397M16—862no—
398M16—862no—
399M16—862no—
400M16—861no—
401M16—862no—
402M16—861no—
403C2×C8—22no—
404C2×C8—22no—
405C2×C8—861no—
406C2×C8—861no—
407C2×C8—862no—
408C2×C8—862no—
409C2×C8C2×C22⋊D4312yes—
410C2×C8C2×C22⋊D4312yes—
411C4⋊C4—21no—
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—21no—
415C4⋊C4—41no—
416C4⋊C4—41no—
417C4⋊C4—41no—
418C4⋊C4—41no—
419C4⋊C4—431no—
420C4⋊C4—431no—
421C4⋊C4—861no—
422C4⋊C4—861no—
423C22⋊C4—861no—
424C22⋊C4—861no—
425C22⋊C4—861no—
426C42—41no—
427C42—41no—
428C42—861no—
429C42—861no—
430C42—861no—
431C42D4×D4311yescharacteristic
432C42D4×D4311yescharacteristic
433C42C2×C22⋊D4311yescharacteristic
434C42C2×C22⋊D4311yescharacteristic
435C23—861no—
436C23C2×#1062190011yescharacteristic
437Q8—22no—
438Q8—22no—
439Q8—41no—
440Q8—41no—
441Q8—82no—
442Q8—82no—
443Q8—861no—
444Q8—861no—
445D4—861no—
446D4—861no—
447D4—1721no—
448D4—1721no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—82no—
457C2×C4—81no—
458C2×C4—861no—
459C2×C4—861no—
460C2×C4—861no—
461C2×C4—3441no—
462C2×C4—1721no—
463C2×C4—1722no—
464C2×C4—1721no—
465C2×C4#1306329611yescharacteristic
466C2×C4#1306329611yescharacteristic
467C2×C4#1306329611yescharacteristic
468C2×C4#1306329611yescharacteristic
469C2×C4C2×D4×D4311yescharacteristic
470C2×C4C22×C22⋊D4311yescharacteristic
471C2×C4#41×D4311yescharacteristic
472C2×C4C2×#1062190211yescharacteristic
473C2×C4#1306337211yescharacteristic
474C2×C4#1306337311yescharacteristic
475C8—22no—
476C8—22no—
477C8—862no—
478C8—1722no—
479C8—1722no—
480C8—1721no—
481C22—21no—
482C22—21no—
483C22—1721no—
484C22—1721no—
485C22—1721no—
486C22C2×#1306329611yescharacteristic
487C22#1458359111yescharacteristic
488C22#1458362011yescharacteristic
489C4—21no—
490C4—21no—
491C4—21no—
492C4—42no—
493C4—82no—
494C4—81no—
495C4—1721no—
496C4—1721no—
497C4—1721no—
498C4#1458317112yes—
499C4#1458341211yescharacteristic
500C4#1458347211yescharacteristic
501C4#1458354811yescharacteristic
502C4#1458356011yescharacteristic
503C2—21no—
504C2—21no—
505C2—3441no—
506C2#1913802011yescharacteristic
507C2C2×#1458317111yescharacteristic
508C2#1914431911yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#477C2
socleC22×C43C2×#121
prime radicalC2×#10621898C23
hypercenterC2×#477D43
hypocenterC43#24722
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
6. #19135585C2semidirect
7. #19135378C2semidirect
8. #19135371C2semidirect
9. #19135247C2semidirect
10. #19134591C2semidirect
11. C2×C43×#477C2semidirect
250. C2×#477D43semidirect
303. C43#24722semidirect

Maximal subgroups

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

subgroupindex
#191444042
C4×#130633562
#191432602
#191360362
#191358952
#191355852
#191353782
#191353712
#191352472
#191345912
C2×C43×#4772
#2472243