Finite Group Databasebeta

← #25081993

Subgroups — #25081993

Order 11008.

674 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145520C211yesmaximal, characteristic, complemented
2#19144050C211yesmaximal, characteristic
3#19143706C211yesmaximal, characteristic, complemented
4#19134023C212yesmaximal, complemented
5#19134016C212yesmaximal, complemented
6#19133945C212yesmaximal, complemented
7#19133938C212yesmaximal, complemented
8#19133367C211yesmaximal, characteristic, complemented
9#19133273C211yesmaximal, characteristic, complemented
10C2×#14582645C211yesmaximal, characteristic, complemented
11C43×#3079C211yesmaximal, characteristic, complemented
12C2×#13063345—21no—
13#14583449C2211yescharacteristic
14#14583273C2212yes—
15#14583249C2212yes—
16#14583121—21no—
17#14583114—21no—
18#14583109C2211yescharacteristic
19#14583104C2211yescharacteristic
20#14583101—21no—
21#14583101—21no—
22#14583099C2211yescharacteristic
23#14583094C2211yescharacteristic
24#14583038—22no—
25Q8×C43⋊C8C2212yes—
26D4×C43⋊C8—22no—
27D4×C43⋊C8C2212yes—
28#14582952—21no—
29#14582952C2211yescharacteristic
30C2×C4⋊(C43⋊C8)—21no—
31C2×C4⋊(C43⋊C8)C2211yescharacteristic
32C2×C4⋊(C43⋊C8)C2211yescharacteristic
33#14582893—21no—
34#14582649C2212yes—
35#14582649C2212yes—
36#14582646C2212yes—
37#14582645C2212yes—
38#14582645C2212yes—
39#14582642C2212yes—
40C2×C4⋊Q8×C43C2211yescharacteristic
41C4×#41×C43C2211yescharacteristic
42C43×#477—21no—
43C43×#476—21no—
44C43×#475C2212yes—
45C43×#474C2212yes—
46C43×#428—21no—
47C43×#423C2211yescharacteristic
48C43×#417—21no—
49C2×#10621898—21no—
50#13063345—44no—
51C2×#10621885—21no—
52C2×#10621883—21no—
53C2×#10621884—21no—
54C2×#10621884—22no—
55C2×#10621884—22no—
56C2×#10621882—21no—
57C22×C43⋊C8—21no—
58C22×C43⋊C8—21no—
59C22×C43⋊C8—22no—
60#13063325C2311yescharacteristic
61#13063322C2311yescharacteristic
62#13063313—21no—
63#13063299—21no—
64#13063299—21no—
65C4×D172—21no—
66C4×D172—21no—
67C4⋊(C43⋊C8)—21no—
68C4⋊(C43⋊C8)—21no—
69C4⋊(C43⋊C8)—22no—
70C4⋊(C43⋊C8)D411yescharacteristic
71C4⋊(C43⋊C8)D411yescharacteristic
72C4⋊(C43⋊C8)C2311yescharacteristic
73C4⋊(C43⋊C8)C2311yescharacteristic
74C4⋊(C43⋊C8)C2312yes—
75#13063249—22no—
76#13063249—22no—
77#13063248—21no—
78#13063248—21no—
79#13063245—21no—
80#13063245—21no—
81C22⋊(C43⋊C8)—22no—
82C22⋊(C43⋊C8)D412yes—
83C4×C43⋊C8—22no—
84C4×C43⋊C8C2312yes—
85C2×#41×C43D411yescharacteristic
86C22×Q8×C43—21no—
87C2×M16×C43—21no—
88C4⋊Q8×C43—21no—
89C4⋊Q8×C43—21no—
90C4⋊Q8×C43—21no—
91C4⋊Q8×C43C2312yes—
92C4×Q8×C43D411yescharacteristic
93C4×Q8×C43C2311yescharacteristic
94C4×D4×C43—21no—
95C4×D4×C43—21no—
96C4×D4×C43D411yescharacteristic
97C4×D4×C43C2311yescharacteristic
98#117×C43—21no—
99#117×C43D411yescharacteristic
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43—21no—
102C2×C42×C43—21no—
103C2×C42×C43C2311yescharacteristic
104#107×C43—22no—
105#106×C43—22no—
106C4⋊C8×C43—21no—
107C4⋊C8×C43C2312yes—
108#103×C43—22no—
109#102×C43—22no—
110#41×C43—22no—
111#41×C43SD1614yescomplemented
112C2×Q8×C43—22no—
113C2×Q8×C43—41no—
114C2×Q8×C43—81no—
115C2×Q8×C43—81no—
116C2×Q8×C43C2×D411yescharacteristic
117C2×D4×C43—21no—
118C2×D4×C43C2×D411yescharacteristic
119C22×C4×C43—21no—
120C22×C4×C43—21no—
121C22×C4×C43—21no—
122C22×C4×C43—41no—
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43#4111yescharacteristic
126C2×C22⋊D43—41no—
127#10621898—42no—
128#10621898—42no—
129C2×D172—21no—
130C2×D172—21no—
131C2×D172—21no—
132C2×C4×D43—41no—
133C2×Dic86—21no—
134M16×C43—42no—
135C2×C8×C43—22no—
136C4⋊C4×C43—21no—
137C4⋊C4×C43—21no—
138C4⋊C4×C43—22no—
139C4⋊C4×C43—22no—
140C4⋊C4×C43—41no—
141C4⋊C4×C43—41no—
142C4⋊C4×C43C2×D411yescharacteristic
143C4⋊C4×C43C2×D411yescharacteristic
144C22⋊C4×C43—21no—
145C22⋊C4×C43—21no—
146C22⋊C4×C43—21no—
147C42×C43—21no—
148C42×C43—21no—
149C42×C43—21no—
150C42×C43C2×D411yescharacteristic
151C42×C43C2×D411yescharacteristic
152C42×C43#4111yescharacteristic
153C42×C43C2411yescharacteristic
154#10621885—42no—
155#10621884—42no—
156#10621884—82no—
157#10621884—82no—
158#10621883—42no—
159#10621882—42no—
160(C2×D43)⋊C4—41no—
161(C2×D43)⋊C4—41no—
162C4⋊Dic43—21no—
163C4⋊Dic43—21no—
164C2×C43⋊C8—22no—
165C2×C43⋊C8—21no—
166C2×C43⋊C8—21no—
167C2×C43⋊C8—42no—
168C2×C43⋊C8—82no—
169C2×C43⋊C8—81no—
170C2×C43⋊C8C2×D412yes—
171C2×C43⋊C8C2×D412yes—
172C23×C43—21no—
173C23×C43#12111yescharacteristic
174C22×D43—41no—
175Q8×C43—21no—
176Q8×C43—42no—
177Q8×C43—42no—
178Q8×C43—82no—
179Q8×C43C2×SD1612yes—
180D4×C43—24no—
181D4×C43—21no—
182D4×C43C2×SD1612yes—
183C2×C4×C43—21no—
184C2×C4×C43—21no—
185C2×C4×C43—21no—
186C2×C4×C43—24no—
187C2×C4×C43—21no—
188C2×C4×C43—21no—
189C2×C4×C43—41no—
190C2×C4×C43—41no—
191C2×C4×C43—41no—
192C2×C4×C43—42no—
193C2×C4×C43—81no—
194C2×C4×C43—82no—
195C2×C4×C43#12111yescharacteristic
196C2×C4×C43#12111yescharacteristic
197C2×C4×C43#12111yescharacteristic
198C2×C4×C43C2×SD1612yes—
199C2×C4×C43#13512yes—
200C2×C4×C43C22×D411yescharacteristic
201C2×C4×C43C22×D411yescharacteristic
202C2×C4×C43C2×#4111yescharacteristic
203C22⋊D43—82no—
204C2×Dic43—41no—
205D172—41no—
206D172—41no—
207D172—41no—
208D172—41no—
209D172—81no—
210C4×D43—82no—
211Dic86—41no—
212Dic86—41no—
213C8×C43—42no—
214C43⋊C8—22no—
215C43⋊C8—22no—
216C43⋊C8—41no—
217C43⋊C8—41no—
218C43⋊C8—42no—
219#19408—431nomaximal, Sylow
220C22×C43—21no—
221C22×C43—21no—
222C22×C43—22no—
223C22×C43—41no—
224C22×C43—41no—
225C22×C43#46512yes—
226C22×C43C2×#12111yescharacteristic
227C2×D43—81no—
228C2×D43—81no—
229C2×D43—81no—
230C4×C43—21no—
231C4×C43—22no—
232C4×C43—21no—
233C4×C43—21no—
234C4×C43—41no—
235C4×C43—41no—
236C4×C43—82no—
237C4×C43#46512yes—
238C4×C43C22×SD1611yescharacteristic
239C4×C43C2×#13511yescharacteristic
240C4×C43#57611yescharacteristic
241C4×C43#57711yescharacteristic
242Dic43—81no—
243#3206—431no—
244#3079D4311yescharacteristic, complemented
245#3035—431no—
246#2988—431no—
247#1680—432no—
248#1679—432no—
249#1666—432no—
250#1665—432no—
251#1570—431no—
252#1547—431no—
253C2×#332—431no—
254C2×C43—22no—
255C2×C43—42no—
256C2×C43#304511yescharacteristic
257C2×C43C2×#46511yescharacteristic
258C2×C43#306911yescharacteristic
259D43—161no—
260C2×#135—861no—
261#532—431no—
262C2×C4⋊Q8C2×D4311yescharacteristic
263C4×#41C2×D4311yescharacteristic
264#492—432no—
265#487—432no—
266#477—21no—
267#476—21no—
268#475C2×D4312yes—
269#474C2×D4312yes—
270#464—861no—
271#463—861no—
272#462—431no—
273#461—431no—
274#461—861no—
275#461—861no—
276#460—431no—
277#459—431no—
278#448—862no—
279C8×Q8—432no—
280C8×D4—432no—
281C8×D4—862no—
282#431—431no—
283#431—861no—
284#428—21no—
285#423C2×D4311yescharacteristic
286C2×C4⋊C8—431no—
287C2×C4⋊C8—431no—
288C2×C4⋊C8—861no—
289#417—21no—
290#416—861no—
291#334—432no—
292#334—432no—
293#332—432no—
294#332—432no—
295#332—432no—
296#331—432no—
297C43#1940811yescharacteristic, complemented, Sylow
298C2×#41—861no—
299C2×#41C22⋊D4311yescharacteristic
300C22×Q8—21no—
301#135—1724no—
302C2×Q16—861no—
303C2×SD16—862no—
304C2×SD16—862no—
305C2×SD16—861no—
306C2×SD16—861no—
307C2×D8—861no—
308C2×M16—21no—
309C22×C8—862no—
310C22×C8—861no—
311C22×C8—861no—
312C4⋊Q8—21no—
313C4⋊Q8—21no—
314C4⋊Q8—21no—
315C4⋊Q8—431no—
316C4⋊Q8C22×D4312yes—
317#127—431no—
318#124—861no—
319#121—861no—
320#121—861no—
321C4×Q8C22⋊D4311yescharacteristic
322C4×Q8C22×D4311yescharacteristic
323C4×D4—21no—
324C4×D4—21no—
325C4×D4—861no—
326C4×D4—861no—
327C4×D4C22⋊D4311yescharacteristic
328C4×D4C22×D4311yescharacteristic
329#117—21no—
330#117C22⋊D4311yescharacteristic
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C42—21no—
334C2×C42C22×D4311yescharacteristic
335#107—22no—
336#106—22no—
337C4⋊C8—21no—
338C4⋊C8—431no—
339C4⋊C8—431no—
340C4⋊C8—432no—
341C4⋊C8—431no—
342C4⋊C8—431no—
343C4⋊C8—862no—
344C4⋊C8—861no—
345C4⋊C8—861no—
346C4⋊C8C22×D4312yes—
347#103—22no—
348#103—862no—
349#103—862no—
350#103—861no—
351#103—861no—
352#102—22no—
353#102—861no—
354#102—861no—
355C22⋊C8—432no—
356C22⋊C8—862no—
357C4×C8—432no—
358C4×C8—862no—
359#41—22no—
360#41—1722no—
361#41—1722no—
362#41#1062188414yescomplemented
363C2×Q8—22no—
364C2×Q8—41no—
365C2×Q8—81no—
366C2×Q8—81no—
367C2×Q8—861no—
368C2×Q8C2×C22⋊D4311yescharacteristic
369C2×D4—21no—
370C2×D4—861no—
371C2×D4—861no—
372C2×D4—861no—
373C2×D4—1721no—
374C2×D4C2×C22⋊D4311yescharacteristic
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—41no—
379C22×C4—1721no—
380C22×C4D4×D4311yescharacteristic
381C22×C4#1062190011yescharacteristic
382C22×C4C2×C22⋊D4311yescharacteristic
383Q16—1722no—
384SD16—3442no—
385SD16—3442no—
386SD16—1722no—
387SD16—1722no—
388D8—1722no—
389M16—42no—
390C2×C8—22no—
391C2×C8—432no—
392C2×C8—432no—
393C2×C8—862no—
394C2×C8—861no—
395C2×C8—861no—
396C2×C8—3442no—
397C2×C8—3441no—
398C2×C8—1722no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—22no—
402C4⋊C4—22no—
403C4⋊C4—41no—
404C4⋊C4—41no—
405C4⋊C4—861no—
406C4⋊C4—861no—
407C4⋊C4C2×C22⋊D4311yescharacteristic
408C4⋊C4C2×C22⋊D4311yescharacteristic
409C22⋊C4—21no—
410C22⋊C4—21no—
411C22⋊C4—21no—
412C22⋊C4—1721no—
413C22⋊C4—1721no—
414C42—21no—
415C42—21no—
416C42—21no—
417C42D4×D4311yescharacteristic
418C42#1062190011yescharacteristic
419C42C2×C22⋊D4311yescharacteristic
420C42C23×D4311yescharacteristic
421C23—21no—
422C23—1721no—
423C23#1306329711yescharacteristic
424Q8—21no—
425Q8—42no—
426Q8—42no—
427Q8—82no—
428Q8—1721no—
429Q8—1721no—
430Q8C2×#1062188412yes—
431D4—24no—
432D4—21no—
433D4—3441no—
434D4—3442no—
435D4—1721no—
436D4—1721no—
437D4—1721no—
438D4—1721no—
439D4C2×#1062188412yes—
440C2×C4—21no—
441C2×C4—24no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—42no—
450C2×C4—81no—
451C2×C4—82no—
452C2×C4—3442no—
453C2×C4—1721no—
454C2×C4#1306329711yescharacteristic
455C2×C4#1306329711yescharacteristic
456C2×C4#1306329711yescharacteristic
457C2×C4C2×#1062188412yes—
458C2×C4#1306334512yes—
459C2×C4C2×D4×D4311yescharacteristic
460C2×C4C22×C22⋊D4311yescharacteristic
461C2×C4C2×#1062190011yescharacteristic
462C8—42no—
463C8—862no—
464C8—862no—
465C8—1721no—
466C8—1721no—
467C8—1722no—
468C22—21no—
469C22—21no—
470C22—22no—
471C22—41no—
472C22—41no—
473C22—3441no—
474C22—3441no—
475C22—3441no—
476C22#1458313012yes—
477C22C2×#1306329711yescharacteristic
478C4—21no—
479C4—21no—
480C4—21no—
481C4—22no—
482C4—41no—
483C4—41no—
484C4—82no—
485C4—3441no—
486C4#1458313012yes—
487C4C22×#1062188411yescharacteristic
488C4C2×#1306334511yescharacteristic
489C4#1458370311yescharacteristic
490C4#1458370911yescharacteristic
491C2—22no—
492C2—42no—
493C2—6881no—
494C2#1914413811yescharacteristic
495C2C2×#1458313011yescharacteristic
496C2#1914432911yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3079C2
socleC22×C43C2×#121
prime radical#19144050C2
hypercenter#3079D43
hypocenterC43#19408
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3079

Complements

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

NH ≅ G/Ntype
1. #19145520C2semidirect
3. #19143706C2semidirect
4. #19134023C2semidirect
5. #19134016C2semidirect
6. #19133945C2semidirect
7. #19133938C2semidirect
8. #19133367C2semidirect
9. #19133273C2semidirect
10. C2×#14582645C2semidirect
11. C43×#3079C2semidirect
111. #41×C43SD16semidirect
244. #3079D43semidirect
297. C43#19408semidirect
362. #41#10621884semidirect

Maximal subgroups

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

subgroupindex
#191455202
#191440502
#191437062
#191340232
#191340162
#191339452
#191339382
#191333672
#191332732
C2×#145826452
C43×#30792
#1940843